Quarterly National Accounts Manual

Quarterly National Accounts ManualConcepts, Data Sources, and Compilation

By Adriaan M. Bloem, Robert J. Dippelsman, and Nils Ø. Mæhle

INTERNATIONAL MONETARY FUND

Washington DC

2001

©2001 International Monetary Fund

Library of Congress Cataloging-in-Publication data

Bloem, Adriaan M.

Manual for quarterly national accounts : concepts, data sources, and compilation /

by Adriaan M. Bloem, Robert J. Dippelsman, and Nils Ø. Mæhle. -- Washington, D.C. :

International Monetary Fund, 2001.

p. : ill. ; cm.

Includes bibliographical references.

ISBN 1-58906-031-8

1. National income – Accounting – Handbooks, manuals, etc. I. Dippelsman, Robert

J. II. Mæhle, Nils Øyvind. III. International Monetary Fund.

HC79.I5 B46 2001

Price: US$40.00

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Internet: http://www.imf.org

Although this manual has benefitted from comments from IMFcolleagues, it represents the views of the authors and not necessarilythose of the IMF.

Table of contents

Foreword x

Preface xi

I Introduction 1

II Strategic Issues in Quarterly National Accounts 14

III Sources for GDP and its Components 31

IV Sources For Other Components of the 1993 SNA 64

V Editing and Reconciliation 74

VI Benchmarking 82

VII Mechanical Projections 119

VIII Seasonal Adjustment and Estimation of Trend-Cycles 125

IX Price and Volume Measures: Specific QNA-ANA Issues 147

X Work-in-Progress 174

XI Revision Policy and the Compilation and Release Schedule 186

Bibliography 192

Index 203

iii

iv

Table of contents

Foreword x

Preface xi

Acknowledgments xii

I Introduction 1A. Introduction 1B. Purposes of Quarterly National Accounts 1C. Quarterly National Accounts as Time Series 3D. Seasonally Adjusted Data and Trend-Cycle Estimates 4E. Conceptual Links between Quarterly and Annual Accounts 5F. Transparency in Quarterly National Accounting 7G. Flash Estimates 8H. An Outline of the Manual 9Box 1.1. Seasonal Adjustment: Unadjusted Data, Seasonally Adjusted Data,

Trend-Cycle Estimates—What Do Users Want? 6Example 1.1. Monitoring Business Cycles—Quarterly GDP Data (Seasonally Adjusted)

versus Annual GDP Data 2

Annex 1.1. Identification of Turning Points 11Example 1.A1.1. Identification of Turning Points 12

II Strategic Issues in Quarterly National Accounts 14A. Introduction 14B. Statistical Issues 14

1. The Link between Quarterly and Annual National Accounts 142. Coverage of QNA 16

a. General issues 16b. Measurement of GDP and its components 17c. Quarterly GDP by the supply and use approach 18

3. Compilation Level 194. Assessing Source Data and the Compilation System 20

a. Assessing individual source data 20b. Assessing the overall compilation system 22

5. Statistical Processing 236. Relationship between QNA and Source Data Statistics 24

C. Dissemination 25D. Managerial Issues 26

1. General 262. Timing of the Compilation Process 26

a. Structuring the compilation process 26

Contents

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b. Planning workloads 26c. Methods of speeding compilation 27

3. Organizing Staff 274. Organizing Data Supply 285. Managing Data Compilation Systems 28

Box 2.1. Main Steps to Establish and Maintain Quarterly National Accounts 15Box 2.2. Review: Assessment of Indicators and Compilation Methods 20Box 2.3. Elements of a QNA Processing System Built on Database Software 29

III Sources for GDP and its Components 31A. General Issues 31

1. Introduction 312. Data Sources 313. Issues with Surveys 324. Issues with Administrative Byproduct Data 345. Sources in the Absence of Surveys or Administrative Data 34

B. GDP by Industry 351. General Issues 352. Sources for Industries 36

a. Current price data on outputs and/or inputs 36b. Data on quantities of output and/or inputs 38c. Labor input measures 39d. Indirect indicators 40e. Price indicators 41f. Industrial production indices 42

3. Adjustment Items 42C. GDP by Type of Expenditure 43

1. General Issues 432. Sources 43

a. Household final consumption expenditure 43(i) Value indicators 43(ii) Volume indicators 44(iii) Price indicators 45

b. Government final consumption expenditure 45(i) Value indicators 45(ii) Volume indicators 46(iii) Price indicators 46

c. Final consumption expenditure by nonprofit institutions serving households 47(i) Value indicators 47(ii) Volume indicators 47(iii) Price indicators 47

d. Gross fixed capital formation 47(i) General value indicators 47(ii) Specific value, volume, and price indicators 48

e. Changes in inventories 53(i) Introduction 53(ii) Value indicators 54(iii) Volume indicators 54(iv) Price indicators 55

f. Exports and imports of goods and services 55(i) Value indicators 55(ii) Volume indicators 55(iii) Price indicators 55

CONTENTS

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D. GDP by Income Category 561. General Issues 562. Value Indicators 57

a. Compensation of employees 57b. Operating surplus/mixed income 57c. Taxes and subsidies on products, production, and imports 58

3. Volume and Price Indicators 59Box 3.1. Data for the Production Approach 35Box 3.2. Overview of Value and Volume Indicators Commonly Used for Quarterly

GDP by Industry 37

Annex 3.1. Estimation of Changes in Inventories 60Example 3.A.1. Calculation of Changes in Inventories 62

IV Sources For Other Components of the 1993 SNA 64A. General Issues 64B. Main Aggregates for the Total Economy 64C. Accounts for the Total Economy 65

1. Production Account 652. Income Accounts 66

a. Generation of income account 66b. Allocation of primary income account 66c. Secondary distribution of income account 67d. Use of disposable income account 67

3. Capital Account 674. Financial Accounts 675. Balance Sheets 68

D. Institutional Sector Accounts 681. General Government 692. Financial Corporations 723. Households 724. Nonfinancial Corporations 725. Nonprofit Institutions Serving Households 736. Rest of the World 73

Box 4.1. Main Aggregates for the Total Economy 65Box 4.2. The Sequence of Institutional Sector Transactions Accounts 70

V Editing and Reconciliation 74A. Introduction 74B. Causes of Data Problems 75C. How To Identify Data Problems 76

1. Eyeball Testing 762. Analytical Testing 76

a. Logical 76b. Plausibility 77

D. Reconciliation 78E. Editing as Part of the Compilation Process 80

VI Benchmarking 82A. Introduction 82B. A Basic Technique for Distribution and Extrapolation with an Indicator 84

1. Pro Rata Distribution and the Step Problem 842. Basic Extrapolation with an Indicator 85

C. The Proportional Denton Method 87

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1. Introduction 872. The Basic Version of the Proportional Denton Method 873. Enhancements to the Proportional Denton Method for Extrapolation 90

D. Particular Issues 931. Fixed Coefficient Assumptions 932. Within-Year Cyclical Variations in Coefficients 943. Benchmarking and Compilation Procedures 964. Balancing Items and Accounting Identities 965. More Benchmarking Options 976. Benchmarking and Revisions 977. Other Comments 97

Chart 6.1. Pro Rata Distribution and the Step Problem. 86Chart 6.2. Solution to the Step Problem: The Proportional Denton Method. 89Chart 6.3. Revisions to the Benchmarked QNA Estimates Resulting from Annual Benchmarks

for a New Year 92Chart 6.4. Extrapolation Using Forecast BI Ratios 95Example 6.1. Pro Rata Distribution and Basic Extrapolation 85Example 6.2. The Proportional Denton Method 88Example 6.3. Revisions to the Benchmarked QNA Estimates Resulting from Annual Benchmarks

for a New Year 91Example 6.4. Extrapolation Using Forecast BI Ratios 94

Annex 6.1. Alternative Benchmarking Methods 98A. Introduction 98B. The Denton Family of Benchmarking Methods 99

1. Standard Versions of the Denton Family 992. Further Expansions of the Proportional Denton Method 100

C. The Bassie Method 101D. The Ginsburgh-Nasse Method 103E. Arima-Model-Based Methods 105F. General Least-Squares Regression Models 106G. The Chow-Lin Method 107Example 6.A1.1. The Bassie Method and the Step Problem 102

Annex 6.2. Extrapolation Base and the Forward Step Problem 109A. Introduction 109B. Alternative Extrapolation Bases 109C. The Forward Step Problem 113D. Annual Rate of Change in the Derived Forward Series 114E. Extrapolation Base and Robustness Toward Errors in the Indicator 115F. Extrapolation Base and Seasonality 116Chart 6.A2.1. Alternative Extrapolation Bases and the Forward Step Problem 112Example 6.A2.1. Extrapolation Bases and the Forward Step Problem 110Example 6.A2.2. Extrapolation Base and Robustness Toward Errors in the Indicator 113

Annex 6.3. First-Order Conditions for the Proportional Denton Benchmarking Formula 117

VII Mechanical Projections 119A. Introduction 119B. Trend Projections Based on Annual Data 120

1. The Lisman and Sandee Quarterly Distribution Formula 1202. Least-Squares Distribution 121

C. Projection Based on Monthly or Quarterly Data 121Example 7.1. Quarterly Distribution of Annual Data Without a Related Series 122Example 7.2. Quarterly Distribution of Annual Data with a Superimposed Seasonal Pattern 124

CONTENTS

viii

VIII Seasonal Adjustment and Estimation of Trend-Cycles 125A. Introduction 125B. The Main Principles of Seasonal Adjustment 126C. Basic Features of the X-11 Family of Seasonal Adjustment Programs 129

1. Main Aspects of the Core X-11 Moving Average Seasonal Adjustment Filters 1302. Preadjustments 1323. Estimation of Other Parts of the Seasonal Component Remaining Trading-Day

and Other Calendar-Related Effects 1324. Seasonal Adjustment Diagnostics 133

D. Issues in Seasonality 1341. Changes in Seasonal Patterns, Revisions, and the Wagging Tail Problem 1352. Minimum Length of the Time Series for Seasonal Adjustment 1423. Critical Issues in Seasonal Adjustment of QNA 142

a. Compilation levels and seasonal adjustment of balancing items and aggregates 142b. Seasonal adjustment and the relationship among price, volume, and value 143c. Seasonal adjustment and supply and use and other accounting identities 144d. Seasonal adjustment and consistency with annual accounts 144

4. Status and Presentation of Seasonally Adjusted and Trend-Cycle QNA Estimates 144Box 8.1. Main Elements of the X-12-ARIMA Seasonal Adjustment Program 130Box 8.2. X-11/X-11-ARIMA/X-12-ARIMA Tests for Existence of Seasonality 134Box 8.3. X-11-ARIMA/X-12-ARIMA M- and Q-Test Statistics 136Box 8.4. Annualizing, or Compounding, Growth Rates 146Example 8.1. Seasonal Adjustment, Trend-Cycle Component, Seasonal Component,

and Irregular Component. Multiplicative Seasonal Model 128Example 8.2. Moving Seasonality 138Example 8.3. Changes in Seasonal Patterns, Revisions of the Seasonally Adjusted Series,

and the Wagging Tail Problem. Revisions to the Seasonally Adjusted Estimates by Adding New Observations 139

Example 8.4. Changes in Seasonal Patterns, Revisions, and the Wagging Tail Problem. Revisions to Trend-Cycle Estimates 140

Example 8.5. Changes in Seasonal Patterns, Revisions, and the Wagging Tail Problem. Concurrent Adjustment Versus Use of One-Year-Ahead Forecast of Seasonal Factors 141

Example 8.6. Presentation of Seasonally Adjusted Series and the Corresponding Trend-Cycle Component 146

IX Price and Volume Measures: Specific QNA-ANA Issues 147A. Introduction 147B. Aggregating Price and Volume Measures Over Time 148C. Choice of Price Weights for QNA Volume Measures 150

1. Laspeyres-Type Volume Measures 1502. Fisher-Type Volume Indices 152

D. Chain-Linking in the QNA 1531. General 1532. Frequency of Chain-Linking in the QNA 1553. Choice of Index Number Formulas for Annually Chain-Linked QNA Data 1574. Techniques for Annual Chain-Linking of Quarterly Data 1585. Chain-Linked Measures and Nonadditivity 1596. Chain-Linking, Benchmarking, Seasonal Adjustment, and Compilation Procedures

Requiring Additivity 1637. Presentation of Chain-Linked Measures 163

Chart 9.1 Chain-Linking of QNA Data 162Example 9.1. Weighted and Unweighted Annual Averages of Prices (or Price Indices)

When Sales and Price Patterns Through the Year are Uneven 149

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Example 9.2. Basic Chain-Linking of Annual Data. The 1993 SNA Example 155Example 9.3. Frequency of Chain-Linking and the Problem of “Drift” in the case of

Price and Quantity Oscillation 156Example 9.4.a. Quarterly Data and Annual Chain-Linking. Annual Overlap 159Example 9.4.b. Quarterly Data and Annual Chain-Linking. One-Quarter Overlap 160Example 9.4.c. Quarterly Data and Annual Chain-Linking. The Over-the-Year Technique 161Example 9.5.a. Chain-Linking and Nonadditivity 164Example 9.5.b. Choice of Reference Period and Size of the Chain Discrepancy 166

Annex 9.1. Aggregation over Time and Consistency Between Annual and Quarterly Estimates 167A. Introduction 167B. Relationship Between Quarterly and Annual Deflators 167C. Annual Average Prices as Price Base 168

Annex 9.2. Annual Chain-Linking of Quarterly Laspeyres Volume Measures: A Formal Presentation of the Annual and On-Quarter Overlap Techniques 170A. The Annual Overlap Technique 170B. The One-Quarter Overlap Technique 172Example 9.A2.1. Quarterly Data and Annual Chain-Linking 173

X Work-in-Progress 174A. Introduction 174B. Why Should Work-in-Progress Be Treated as Output? 175C. Measurement of Work-in-Progress 176

1. Economic Concepts 1762. Business Accounting Treatment of Work-in-Progress 1763. Measurement in a National Accounts Context 177

D. Special Issues for Agriculture 182Example 10.1. Ex Post Estimation of Work-in-Progress with (a) Total Value of Project

(b) Quarterly Costs 178Example 10.2. Ex Ante Estimation of Work-in-Progress with (a) Quarterly Costs

(b) Markup Ratio 180Example 10.3. Estimation of Work-in-Progress with (a) Estimate of Output Quantities

(b) Cost Profile 181

Annex 10.1 Recording Work-in-Progress in the 1993 SNA Sequence of Accounts 184Box 10.A.1 Effects of Work-in-Progress on Main Aggregates in the 1993 SNA

Sequence of Accounts and Balance Sheets 185

XI Revision Policy and the Compilation and Release Schedule 186A. Introduction 186B. User Requirements and Resource Constraints 187C. Waves of Source Data and Related Revision Cycles 187D. The Compilation and Release Schedule 188E. Other Aspects of Revision Policy 190Box 11.1. Compilation and Revision Schedule, An Illustration 190Box 11.2. Presentation of Revisions, An Illustration 191

Bibliography 192

Index 203

x

Foreword

The recent financial crises taught us a number of important lessons. We were reminded that, for adjustmentprograms to be sustainable, there must be careful attention to institution-building, the social dimensions ofstructural change, and a country’s political and cultural traditions. We have worked closely with otherinternational organizations to develop standards and codes for sound monetary and fiscal policies, bankingsupervision, and economic data. Work in all of these areas helps to promote financial stability, and it helpscountries take advantage of the enormous potential of private capital markets. In this context, it is important todevelop instruments to improve the ability to detect sources of vulnerability and to propose timely correctivemeasures. One focus of the IMF’s work in this area is on increasing the availability of key data.

The IMF has undertaken a range of activities in this regard. Significant among these is the development of twodata initiatives, namely, the Special Data Dissemination Standard and the General Data Dissemination System.For both these initiatives it is important that international guidelines be available to help countries develop inter-nationally comparable statistics. In several areas where international guidelines have been lacking or have becomeoutdated, the IMF has undertaken to fill the gaps. One such area concerns quarterly national accounts, and I amvery pleased to introduce the Quarterly National Accounts Manual, which has been drafted to help countriesestablish or strengthen quarterly national accounts that meet international standards. This manual takes its placealongside the other manuals prepared or being prepared in the IMF’s Statistics Department, including the Balanceof Payments Manual, the Government Finance Statistics Manual, and the Monetary and Financial StatisticsManual. Like these other manuals, this manual is fully consistent with the System of National Accounts 1993.

This manual is a direct result of technical assistance in support of the Special Data Dissemination Standard. It drawsheavily from course material prepared for national accounts seminars for countries considering subscription to thisStandard. The Manual has benefited from comments from country experts during these seminars and during anexpert group meeting in June 2000, in which country experts and experts from other international organizationsparticipated. I would like to thank all experts for their participation in the gestation process of this manual.

Quarterly national accounts data play a vital role in the development and monitoring of sound economic andfinancial programs. At this time, only a minority of Fund member countries have the benefit of a well-establishedsystem of quarterly national accounts, although their number is rapidly increasing. I hope that this trend continuesand would like to commend the Manual to compilers as an important instrument in this work.

Horst KöhlerManaging DirectorInternational Monetary Fund

xi

Preface

This Quarterly National Accounts Manual was developed from materials prepared for seminars in Thailand(1997 and 1998) and Jordan (2000). Like the seminars, the Manual is aimed particularly at compilers whoalready have a knowledge of national accounting concepts and methods in an annual context and are in theprocess of introducing or improving a quarterly national accounts (QNA) system. As well, we believe it will beof interest to national accounts compilers generally and to sophisticated QNA users. QNA are an increasinglyimportant specialty within national accounting. More and more countries are recognizing QNA as an essentialtool for the management and analysis of the economy. The Manual aims to complement the System of NationalAccounts 1993 (1993 SNA), which has only limited discussion of QNA, while retaining full consistency with thatdocument.

Some general guidelines that emerge from this manual are the following:• QNA should be built on a foundation of timely and accurate quarterly source data that directly cover a high

proportion of the totals. Econometric methods and indirect behavioral relationships are not a substitute for datacollection.

• QNA should be made consistent with their annual equivalents, partly for the convenience of users and partly—and more fundamentally—because the benchmarking process incorporates the information content of theannual data into the quarterly estimates.

• Revisions are needed to allow timely release of data and to allow incorporation of new data. Possible incon-venience of revisions can best be dealt with by openness about the process.

• QNA data should be presented as consistent time series.• The potential scope of QNA is the whole of the 1993 SNA sequence of accounts. Although gross domestic

product (GDP) and its components—the usual starting point—are important, other parts of the nationalaccounts system are also useful and achievable.

• Seasonally adjusted data, trend data, and unadjusted data all provide useful perspectives, but the unadjusteddata should be the foundation of national accounts compilation.

Within these guidelines, the sources, methods, and scope of each country’s QNA system will differ according tocircumstances such as user preferences, availability of source data, and economic conditions. Accordingly, ourobjective is not to give fixed answers but to indicate the range of alternatives and to supply general principles thatcan be applied to develop a QNA system suitable for each country’s circumstances.

We hope that the Manual will find its way to a broad readership and will support the introduction, improvement,and wise use of QNA in many countries.

Carol S. CarsonDirectorStatistics DepartmentInternational Monetary Fund

xii

Acknowledgments

The authors are grateful for comments from IMF colleagues, particularly from Carol S. Carson, Paul Armknecht,Paul Cotterell, Jemma Dridi, Segismundo Fassler, Cor Gorter, John Joisce, Sarmad Khawaja, Manik Shrestha,and Kim Zieschang. The authors are also grateful for comments from the participants in a workshop held in July,2000 to discuss the draft manual, namely, Mr. Roberto Barcellan (Eurostat), Mr. Raúl García Belgrano (ECLAC),Ms. Marietha Gouws (South Africa), Mr. Peter Harper (Australia), Ms. Barbro Hexeberg (World Bank),Ms. Olga Ivanova (World Bank), Mr. Ronald Janssen (The Netherlands), Mr. Paul McCarthy (OECD), Mr. DaveMcDowell (Canada), Ms. Chellam Palanyandy (Malaysia), Mr. Robert Parker (USA), Mr. Eugene Seskin (USA),Mr. Jan van Tongeren (UN), and Mr. Agustín Velázquez (Venezuela). Useful comments were also receivedthrough the IMF’s website. The authors retain full responsibility for any remaining omissions and errors.

I Introduction

A. Introduction

1.1. Quarterly national accounts (QNA) constitute asystem of integrated quarterly time series coordinatedthrough an accounting framework. QNA adopt thesame principles, definitions, and structure as theannual national accounts (ANA). In principle, QNAcover the entire sequence of accounts and balancesheets in the System of National Accounts 1993 (1993SNA); in practice, the constraints of data availability,time, and resources mean that QNA are usually lesscomplete than ANA. The coverage of the QNA systemin a country usually evolves. In the initial stage ofimplementation, only estimates of gross domesticproduct (GDP) with a split by industry and/or type ofexpenditure may be derived. Gross national income(GNI), savings, and consolidated accounts for thenation can follow fairly soon. Extensions can be madeas the use of the system becomes more established,resources become available, and users become moresophisticated; additional breakdowns of GDP, institu-tional sector accounts and balance sheets, and supply-use reconciliation may be added.1

1.2. This manual is written for both beginning andadvanced compilers. In addition, it may be of interestto sophisticated data users. Most of the Manualaddresses issues, concepts, and techniques that applyto the whole system of national accounts. The discus-sion of indicators in Chapter III focuses on compo-nents of GDP. Although this reflects the interest offirst-stage compilers, it should not be taken to meanthat QNA should stop there. As shown in Chapter IV,

GNI and savings for the total economy can be readilyderived in most cases, and further extensions are alsofeasible. In particular, the quarterly expenditure andincome components of GDP, in conjunction withbalance of payments data, provide all items for the fullsequence of consolidated accounts for the totaleconomy. Several countries have expanded their QNAsystems to cover selected institutional sector accounts.A number of countries are currently aspiring to expandtheir QNA systems to include a more complete set ofinstitutional sector accounts and balance sheets.

1.3. This manual is intended for readers who have ageneral knowledge of national accounts method-ology. The Manual aims at full consistency with the1993 SNA, and duplication of material presented inthe latter is avoided as much as possible. Thus, forgeneral national accounts issues, readers are referredto the 1993 SNA.

1.4. This introductory chapter discusses the mainpurposes of QNA and the position of QNA betweenANA and short-term indicators. This chapter also dis-cusses some important aspects of QNA, such as theirrelation to ANA, their time-series character, the use-fulness of seasonally adjusted QNA data, and theimportance of transparency.

B. Purposes of Quarterly NationalAccounts

1.5. The main purpose of QNA is to provide a pictureof current economic developments that is more timelythan that provided by the ANA and more comprehen-sive than that provided by individual short-term indi-cators. To meet this purpose, QNA should be timely,coherent, accurate, comprehensive, and reasonablydetailed. If QNA fulfill these criteria, they are able toserve as a framework for assessing, analyzing, and monitoring current economic developments.

1

1 Another extension could be the development of monthly nationalaccounts. This would be particularly useful in a situation of high infla-tion. To justify the extra resources needed, such an extension shouldprovide a system of monthly data and not be limited to one singleGDP number. A single GDP number offers little added value beyondthe underlying indicators. Also, higher volatility in monthly data maymake it more difficult to pick up underlying trends. Monthly nationalaccounts compilation raises no new methodological issues comparedwith QNA.

Furthermore, by providing time series of quarterly dataon macroeconomic aggregates in a coherent account-ing framework, QNA allow analysis of the dynamicrelationships between these aggregates (particularly,leads and lags). Thus, QNA provide the basic data forbusiness cycle analysis and for economic modelingpurposes. Also, QNA have a particular role to play foraccounting under high inflation and where annualsource data are based on varying fiscal years. In addi-tion, as with the annual accounts, QNA provide a coor-dinating conceptual framework for design andcollection of economic source statistics and a frame-work for identifying major gaps in the range of avail-able short-term statistics.

1.6. QNA can be seen as positioned between ANAand specific short-term indicators in many of thesepurposes. QNA are commonly compiled by combin-ing ANA data with short-term source statistics andANA estimates, thus providing a combination that ismore timely than that of the ANA and that hasincreased information content and quality comparedwith short-term source statistics.

1.7. QNA are usually available within three monthsafter a quarter. ANA, on the other hand, are producedwith a considerable time lag. The initial ANA(accounts based on annual data as opposed to firstestimates on the basis of the sum of the four quarters)are often only available six months or more after theend of the year. Thus, ANA do not provide timelyinformation about the current economic situation,which hampers monitoring the business cycle and thetiming of economic policy aimed at affecting thebusiness cycle. The strength of the ANA is to provideinformation about economic structure and long-termtrends, not to provide data needed for monitoring thebusiness cycle.

1.8. Lack of timeliness is also a major disadvantagefor the use of ANA for constructing forecasts, whichare best based on up-to-date information on the cur-rent economic situation. Furthermore, quarterly datamore adequately reflect the dynamic relationshipsbetween economic variables, leads and lags in partic-ular, and they provide four times as many observa-tions, which is very helpful when using mathematicaltechniques such as regression analysis.

1.9. ANA are less suitable than QNA for businesscycle analyses because annual data mask short-termeconomic developments. In-year economic develop-ments are not shown in the ANA. In addition, develop-

ments that started in one year and end in the next maynot show up in the ANA (see Example 1.12).

1.10. ANA are also less useful at times of high infla-tion, when QNA are virtually indispensable, for tworeasons. First, in these circumstances one of the basicaxioms of the ANA is violated, namely, the assump-tion of price homogeneity over time. Although thisbasic axiom never fully applies (unless there are noprice changes), in times of low inflation it does notnegate the usefulness of the ANA. However, in thesituation of high inflation, summing of current price

I INTRODUCTION

2

2The use of QNA data exemplified in the example is best made withseasonally adjusted data or trend estimates.

Example 1.1. Monitoring Business Cycles—Quarterly GDP Data (Seasonally Adjusted) versus Annual GDP Data

The chart shows quarterly and annual constant price GDP for an imaginaryeconomy and illustrates how annual data may mask the cyclical movements.In this example, the QNA data show that the economy was growing during1998 and that the upturn from the preceding slump started around the firstquarter of 1998. In contrast, the ANA data show that the economy con-tracted in 1998 compared with 1997. The growth during 1998 first shows upin the ANA when the annual estimates for 1999 become available.

The situation is further aggravated by the usual time lag of the ANA, with thefirst annual estimates for 1999 not available until 2000.While the QNA willshow the upturn in the first quarter of 1998 in 1998, the ANA will not showthat upturn until 2000.By that time, the economy in this example has just gonethrough a second downturn.Thus,an upturn in economic activity would alreadyhave changed into a downturn while the ANA would still show positive growth.

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20001999199819971996

Seasonally adjusted quarterly GDP(left-hand scale)

Annual GDP(right-hand scale)

data over a year becomes meaningless because theprices vary so much within the year. QNA are muchless affected by this situation (although underextreme circumstances the accounting period shouldeven be shorter). Second, the problem of holdinggains is much less severe for QNA than for ANA andcan more easily be eliminated because changes invaluation are less in a shorter accounting period.

1.11. QNA are less timely than individual short-term indicators, but they provide a more comprehen-sive picture of current economic developmentsorganized in an integrated framework for analyzingthe data. Short-term indicators, such as price indices,labor market indicators, industrial productionindices, and turnover data for retail trade are oftenavailable on a monthly basis shortly after the refer-ence period. These short-term indicators provideinvaluable information on specific aspects of currenteconomic developments. However, for want of inte-gration into a consistent analytical framework suchas the national accounts, these indicators do not pro-vide a coherent, comprehensive, and consistent pic-ture of the different aspects of the current economicsituation. This hampers tracing the causes of currentproblems and identifying potential future develop-ments. For instance, for a country facing decreasingdomestic output growth, in addition to identifyingaffected industries (as a detailed production indexwould allow), it would be helpful to identify causes,such as decreasing domestic demand or fallingexports, and to further trace deeper causes, such asincome, saving, and investment patterns affectingdemand categories.

1.12. A critique of QNA is that quarterly GDP is nota good business cycle indicator because GDPincludes activities such as government and agricul-ture that do not necessarily respond to changes in thebusiness cycle. For this reason, it is argued that a lesscomprehensive measure, such as a volume index formanufacturing industries, is preferable as a businesscycle indicator. This critique seems pertinent only ifthe QNA were to be restricted to GDP as a singleindicator. However, the QNA should not be regardedas only a vehicle for compiling summary aggregatessuch as GDP; it also provides an integrated frame-work for analyzing economic statistics, thus allowingexamination and analyses of developments andbehavior. Furthermore, breaking down GDP into spe-cific economic activities would allow a view of eco-nomic activities that are deemed more relevant forbusiness cycle analyses.

C. Quarterly National Accounts asTime Series

1.13. It is important for QNA to have a time-seriescharacter. A time series is defined here as a series ofdata obtained through measurement of the same con-cept over time that allows different periods to becompared. Thus, to form a time series, the data haveto be comparable over time. Most important, thisimplies that the data have to be consistent over timewith respect to concepts and measurement. Amongother things, this requires that the time periods haveto be identical (e.g., months, quarters). Cumulativedata (that is, data that cover, for instance, Januarythrough March, January through June, Januarythrough September, and so on), as commonly used informerly centrally planned economies, do not consti-tute time series. Series of measures of changes fromthe same period of the previous year (for instance, thegrowth between the third quarter of the previous yearand of the current year) also do not constitute timeseries, because they do not allow for the comparisonof different time periods. The same applies to period-to-period changes (for instance, the growth betweenthe second and the third quarter of a year), althoughperiod-to-period changes can be linked together toform a proper time series (in the format of an indexseries).

1.14. Having QNA data in a time-series format isessential for business cycle analysis, for identifyingturning points, for trend-cycle analyses, for studyingthe dynamic relationships between economic vari-ables (in particular, leads and lags), and for forecast-ing. For these purposes it is also important that thetime series are sufficiently long. In a situation whereQNA have only recently been started, it is recom-mended to extend the series backward. As a rule ofthumb, for purposes of regression analyses and sea-sonal adjustment, the time series should cover at leastfive years. A QNA series that is restricted to the quar-ters of the preceding year and the current year, evenif it fulfills the criteria in paragraph 1.13, cannot beconsidered a time series, because such a presentationwould not allow comparisons with previous years.This requirement for a time-series character for theQNA has important implications for the design ofQNA compilation techniques, as will be evident inlater chapters.

1.15. The importance of presenting monthly andquarterly data as time series for the purposes ofanalyzing trends and turning points in the data is

Quarterly National Accounts as Time Series

3

illustrated in Annex 1.1. The numerical exampleprovided there shows that in measures of changefrom the same period of the previous year, turningpoints in the data show up with a systematic delay,which in most circumstances can be substantial.The average delay can be shown to be around half ayear in discrete data and around three-quarters of ayear in cumulative data. Thus, as shown in theexample, rates of change from the same period inthe previous year can, for example, indicate that aneconomy is still in recession when it has actuallybeen recovering for some time.

D. Seasonally Adjusted Data and Trend-Cycle Estimates

1.16. Seasonal adjustment3 means using analyticaltechniques to break down a series into its seasonal,trend-cycle, and irregular components. The purposeis to identify these components and to allow, for cer-tain uses, a view of the series where some of thesecomponents have been removed. In seasonallyadjusted data, the effects of recurrent within-a-yearpatterns—the seasonal pattern—are removed, and intrend-cycle estimates the impact of irregular eventsare adjusted for as well. Seasonal patterns may becaused by economic behavior or recurrent exogenousfactors such as weather patterns, holidays, religiousevents, and calendar effects such as variations in thenumber and type of trading days and paydays.Although it is feasible to focus seasonal adjustmenton any of such factors in isolation or in sequence (forinstance, calendar effects only or first), all seasonalpatterns should be taken into account simultaneously,for reasons that are explained in Chapter VIII.

1.17. Opinions differ among both users and compil-ers on the appropriateness of statistical offices pro-ducing seasonally adjusted and trend-cycle estimates.These differences are caused both by differences inopinion over the usefulness of seasonally adjusteddata as such for various uses of the data, and by dif-ferences in opinion over whether seasonal adjustmentand trend-cycle estimation should be undertaken byusers or by compilers of official statistics.Consequently, country practices in this respect differ.Some statistical offices do not publish any seasonallyadjusted data or trend-cycle estimates at all, consid-ering it to be outside the responsibility of producers

of official statistics and part of users’ analysis of thedata. Others focus mainly on seasonally adjusteddata/trend-cycle estimates and may not even compileor publish unadjusted QNA estimates, but rathercompile seasonally adjusted QNA estimates directlyfrom seasonally adjusted source data. Most publishseasonally adjusted and trend-cycle data at least forthe main aggregates, and this practice is stronglyencouraged.

1.18. A basic premise of this manual is to compileQNA from unadjusted source data and apply seasonaladjustment/trend-cycle estimation on the resultingestimates. The discussions on sources and methods inthis manual, and in particular the discussions concern-ing benchmarking, are all based on this premise. Thispremise is derived from the need to serve differentusers’needs as well as from practical compilation con-siderations. As illustrated in Box 1.1, unadjusted data,seasonally adjusted data, and trend-cycle estimates areuseful for different purposes. The unadjusted data tellwhat actually happened in each period, while the sea-sonally adjusted data and the trend-cycle estimates tellwhat the underlying movements in the series are. Thus,users should have access to all three sets of data.Obviously, while QNA estimates based on unadjusteddata allow seasonal adjustment, deriving unadjustedQNA estimates from seasonally adjusted estimates isnot possible. Thus, if QNA compilation is based onadjusted data, providing unadjusted QNA estimatesnecessitates a separate compilation process, using aseparate set of (unadjusted) data.

1.19. Seasonally adjusted data and trend-cycle esti-mates are indispensable for identification of changesin the business cycle and turning points in particular.Identifying turning points in the business cycle is animportant purpose of QNA that can be significantlyimpeded if seasonal patterns and one-time events inthe data are not separated out. One alternative to sea-sonal adjustment is to use growth rates from the cor-responding quarter of the previous year rather thanfrom the previous quarter. This is not an adequatesolution, as explained in paragraph 1.15 above (seeAnnex 1.1 for further explanation of this issue).Furthermore, growth rates from the correspondingquarter do not fully exclude seasonal elements (forinstance, Easter may fall in the first or in the secondquarter, and the number and type of working days ina quarter differ from year to year).

1.20. Unadjusted data and other components of theseries are needed for other purposes, including various

I INTRODUCTION

4

3Well-established techniques are available for seasonal adjustment,such as the Census X11/X12 method; these will be discussed inChapter VIII.

aspects of monitoring current economic develop-ments. For short-term forecasting of highly seasonalseries, all components may be needed, particularly theseasonal component. Economic policy formulationmay also require information on all components of theseries, while for analysis of the effects of particularevents, identification of the irregular component maybe most important. Unadjusted data are also requiredfor purposes such as econometric modeling, where theinformation contained in the seasonal component ofthe series may play a particular role in determining thedynamic relationship among the variables.4 A furtherargument for requiring that unadjusted data always beprovided is that for the most recent data in the series,seasonally adjusted and trend-cycle estimates are sub-ject to additional revisions compared with the unad-justed series (the “wagging tail” problem—seeChapter VIII.)

1.21. Some users may prefer the unadjusted databecause they regard seasonally adjusted data as arti-ficial and arbitrary, or they may want to seasonallyadjust the data themselves by applying their own sea-sonal adjustment preferences. Seasonally adjusteddata represent one answer of several to the hypothet-ical question “What would the data have been if noseasonal factors affected them?” In that respect, sea-sonally adjusted data are obviously artificial.However, most economic analysts find the answer tothis hypothetical question indispensable for businesscycle analysis. Still, various aspects of seasonaladjustment remain controversial,5 partly reflectingthe many subjective and somewhat arbitrary choicesinvolved in seasonal adjustment, including the choiceof method (e.g., X11/X12 versus TRAMO-SEATS,BV4, SABLE, STAMP) and model (additive or mul-tiplicative), the treatment of outliers, and the choiceof filter lengths. For these and other reasons it hasbeen argued that statistical offices “should producethe raw data and the users can then use their own soft-ware for treating seasonal data in the way they wantand in which their analysis calls for.”6 However,while sophisticated users can and sometimes maywant to seasonally adjust the data themselves, thepublic at large require that the data be adjusted forthem. In addition, the statistical office may have par-ticular information about special events impacting onthe series and thus have advantages in carrying outseasonal adjustment.

1.22. Compilation considerations also support thebasic premise of statistical offices compiling season-ally adjusted data and trend-cycle estimates based onunadjusted QNA estimates. When compiling QNAestimates, seasonally adjusted versions of the esti-mates may assist in detecting abnormalities in the dataand allow better checks on plausibility of data (in par-ticular, growth rates.) Thus, it may be easier to iden-tify errors or discrepancies and their causes withadjusted data than with unadjusted data. On the otherhand, the adjustments may obscure discrepancies andabnormalities in the unadjusted data that do not relateto seasonality. Also, it is more difficult to interpret dis-crepancies in the adjusted data because it is uncertainto what extent the discrepancies were already implicitin the unadjusted data. Finally, practice has shownthat seasonally adjusting the data at the detailed levelneeded for compiling QNA estimates can leave resid-ual seasonality in the aggregates.

1.23. Although seasonal adjustment removes theidentifiable regular repeated influences on the series,it does not and should not remove the impact of irreg-ular events. Consequently, if the impact of irregularevents is strong, seasonally adjusted series may notrepresent a smooth and easily interpretable series. Tofurther highlight the underlying trend-cycle, moststandard seasonal adjustment packages also calculatea smoothed trend-cycle series running through theseasonally adjusted data (representing an estimate ofthe combined long-term trend and the business cyclemovements in the series). Several countries includethese estimates in their publications, and this practiceis strongly encouraged.

E. Conceptual Links betweenQuarterly and Annual Accounts

1.24. To avoid confusion about interpreting economicdevelopments, it is imperative that the QNA7 are con-sistent with the ANA. Differences in growth ratesbetween QNA and ANA would perplex users and causeuncertainty about the actual situation. Concerning thelevel of the data, this means that the sums of the esti-mates for the four quarters of the year should be equalto the annual estimates. In a situation where the ANA orANA components are built up from the QNA, this ismore or less self-evident. However, more commonly,the ANA are based on different sources than the quar-terly estimates, and if that is the case, differences could

Conceptual Links between Quarterly and Annual Accounts

5

4See, for instance, Bell and Hillmer (1984), pp. 291-320.5See, for instance, Chapter 5 of Alterman, Diewert, and Feenestra(1999) for a discussion of many of these controversial issues.6Hyllenberg (1998), pp. 167-168. 7That is, the non-seasonally adjusted QNA.

develop. To avoid this, the QNA data should be alignedwith the annual data; the process to achieve this isknown as “benchmarking.” One advantage of bench-marking is that incorporating the usually more accurateannual information into the quarterly estimatesincreases the accuracy of the quarterly time series.Benchmarking also ensures an optimal use of the quar-terly and annual source data in a time-series context.

1.25. Benchmarking deals with the problem of com-bining a time series of high-frequency data (e.g., quar-terly data) with less frequent but more accurate data(e.g., annual or less frequent data). Benchmarkingissues arise both in QNA and ANA compilations. Forthe ANA, benchmarking arises when the estimates areanchored to more comprehensive and detailed surveysand censuses that are performed only every few years.The same basic principle applies to quarterly andannual benchmarking; however, as apparent from thetechnical discussion in Chapter VI, quarterly bench-marking is technically more complicated.

1.26. Benchmarking has two main aspects, which inthe QNA context are commonly looked upon as twodifferent topics; these are (a) quarterization8 of annualdata to construct time series of historical QNA esti-mates (“back series”) and to revise preliminary QNAestimates to align them to new annual data when theybecome available, and (b) extrapolation to update theseries by linking in the quarterly source data (the indi-cators) for the most current period (“forward series”).

1.27. The general objective9 of benchmarking is topreserve as much as possible the short-term move-ments in the source data under the restrictions

I INTRODUCTION

6

Box 1.1. Seasonal Adjustment: Unadjusted Data, Seasonally Adjusted Data,Trend-Cycle Estimates—What Do Users Want?

Components that are:

Main use of the data Of interest Not of interest

Business cycle analysis Trend-cycle and irregular component Unadjusted data

Turning point detection Trend-cycle and irregular component Unadjusted data

Short-term and medium-term forecasts The original unadjusted series and all its components (trend-cycle, irregular,seasonal factors, preadjustment factors, etc.)

Short-term forecasts of stable but highly seasonal The seasonal factors plus the trend-cycle items such as electricity consumption component

Long-term forecasts Annual data and possibly the trend-cycle Unadjusted monthly and quarterly data,component of monthly and quarterly data seasonally adjusted data and the irregular

components

Analysis of the effect of particular events, such as The irregular component and any a strike preadjustment factors

To determine what actually happened (e.g., The original unadjusted series Seasonally adjusted data and trend-cycle data how many people were unemployed in November)

Policy formulations The original unadjusted series and all components (trend-cycle, irregular,seasonal factors, preadjustment factors, etc.)

Macroeconomic model building Could be unadjusted, adjusted, trend-cycle,or all components, depending on the main purpose of the model

Estimation of behavioral relationships Could be unadjusted, adjusted, trend-cycle,and all components, depending on the main use of the estimated relationships

Data editing and reconciliation by statistical compilers Original unadjusted series, seasonally adjusted data, irregular component, and trend-cycle component

8Quarterization is defined here as generation of quarterly data for pastperiods from annual data and quarterly indicators; it encompasses thetechniques of interpolation for stock data and temporal distribution forflow data. For more on this, see Chapter VI.9The only exceptions to this general objective concern the rare caseswhere (a) the relationship between the indicator and the target variablefollows a known short-term pattern or (b) knowledge about the under-lying error mechanism indicates that the source data for some quartersare weaker than for others and thus should be adjusted more.

provided by the annual data and, at the same time,for forward series, ensure that the sum of the fourquarters of the current year is as close as possible tothe unknown future annual data. It is important topreserve as much as possible the short-term move-ments in the source data because the short-termmovements in the series are the central interest ofQNA , about which the indicator provides the onlyavailable explicit information. Optimally preserv-ing the short-term movements in the data is one ofthe basic premises of this manual. Therefore, thecore problem of benchmarking in a quarterly con-text is how to align a quarterly time series to annualdata while maintaining the quarterly pattern andwithout creating a discontinuity in the growth ratefrom the last quarter of one year to the first quarterof the next year. This problem is known as the “stepproblem.” To solve the step problem, several math-ematical techniques have been developed. ChapterVI presents one technique, the proportional Dentontechnique with enhancements, that by logical con-sequence is optimal10 under the general bench-marking objective stated above. The othertechniques proposed in the literature are reviewedin Annex 6.1.

1.28. To be consistent, QNA and ANA should usethe same concepts. As mentioned, this manualseeks full consistency with the 1993 SNA and aimsto avoid any unnecessary duplication.Nevertheless, some conceptual issues have astronger emphasis and more substantial conse-quences in QNA than in ANA, which necessitatessome further discussion. The most important con-ceptual issue in this respect is time of recording,particularly in two cases, namely, (a) long produc-tion cycles, and (b) low-frequency payments. Longproduction cycles, or production cycles that arelonger than one accounting period, mainly concernconstruction, manufacturing of durable goods, andagriculture and forestry. The problems involved canbe very substantial for QNA compilation and arediscussed in Chapter X. Low-frequency paymentsare payments made on an annual basis or in infre-quent installments over the year. Examples of suchpayments are dividends, end-of-year bonuses,vacation bonuses, and taxes on the use of fixedassets and other taxes on production. These issuesare discussed in Chapter IV.

F. Transparency in Quarterly National Accounting

1.29. Transparency11 concerning QNA is a funda-mental requirement of users, and is particularly perti-nent in dealing with revisions. To achievetransparency, it is important to provide users withdocumentation regarding the source data used and theway they are adjusted. As well, documentationshould be provided on the compilation process. Thiswill enable users to make their own judgments on theaccuracy and the reliability of the QNA and will pre-empt possible criticism of arbitrary data manipula-tion. In addition, it is important to inform the publicat large about release dates so as to prevent accusa-tions of manipulative timing of releases. To avoidmisperceptions, it is advisable to take a proactiveapproach to educate users.

1.30. Revisions are undertaken to provide users withdata that are as timely and accurate as possible.Resource constraints and respondent burden, in com-bination with user needs, cause tension betweentimeliness of published data, on the one hand, andreliability, accuracy, and comprehensiveness on theother hand. To balance these factors, preliminary dataare compiled that later are revised when more andbetter source data become available. Revisions pro-vide the possibility to incorporate new and moreaccurate information into the estimates, and thus toimprove the accuracy of the estimates, without intro-ducing breaks in the time series.

1.31. Although revisions sometimes may be per-ceived as reflecting negatively on the trustworthinessof official statistics, delaying the implementation ofrevisions may cause later revisions to be greater ifsuccessive revisions are in the same direction(because they are cumulative). In fact, experience hasshown that more sophisticated users understand thatletting large revisions through is a sign of integrity.Not incorporating known revisions actually reducesthe trustworthiness of data because the data do notreflect the best available information, and the publicmay know this or find out (for instance, the publicmay wonder why a revision in the monthly produc-tion index is not reflected in the QNA). In a time-series-oriented compilation system, suppression ofrevised information can also be cumbersome andcostly and can cause estimation errors.

Transparency in Quarterly National Accounting

7

10The enhancements developed in Chapter VI also provide for supe-rior solutions in the case of the two exceptions to this objective pre-sented in footnote 9.

11Which can be described with terms such as openness, candor, andso on.

1.32. To minimize the number of revisions neededwithout suppressing information, it is advisable tocoordinate statistical activities. The revision scheduleshould be largely driven by arrival of source data, andcoordinating their arrival would help reduce thenumber of revisions needed.

1.33. To face any concerns users may have aboutrevisions, it is important to have both an establishedand transparent publication policy and a revisionpolicy in place. In addition, users need to be edu-cated about the causes of revisions and the policiesfor dealing with them. Countries have adopted dif-ferent approaches to revisions in response to theirown circumstances. However, some important ele-ments that constitute best practice are (a) candid andeasily available documentation of sources andmethods, (b) easily available documentation of thesize and causes of revisions, and (c) release andrevision dates that are well known and publishedthrough an advance release calendar. These prac-tices are all required or encouraged by the IMF’sSpecial Data Dissemination Standard (SDDS) andthe General Data Dissemination System (GDDS). Inaddition, electronic release of the complete timeseries, not only the data for the most recent periods,will make it easier for users to update their data-bases. These issues will be further discussed inChapter XI.

1.34. To avoid unwanted perceptions, it is advisableto take a proactive approach to educate users.Educating users, while valuable for most statisticalareas, is particularly important for QNA because oftheir policy relevance and technical complexity. Thisintroductory chapter has emphasized the usefulnessof QNA, but also has pointed out inherent weak-nesses. Compilers must be candid about these issueswith the public and pursue transparency of sourcesand methods for compiling their QNA. For instance,experience has shown that a proactive approach canhelp reduce complaints about revisions. Althoughbeginning compilers may well face more difficultiesin this respect than well-established ones, the valu-able experience gained by the latter should be a stim-ulus to move to a proactive approach as soon ascircumstances permit. Also, compilers are oftenahead of users in terms of sophistication of analysisand potential uses of the data. Compilers should edu-cate users about the analytical possibilities and otherbenefits of the QNA data. Enhanced contact withusers may also help compilers detect weaknesses inthe estimates or their presentation. In addition, users

sometimes have their own economic information thatcould be helpful to compilers.

1.35. Users should be informed about the meaningof the data and their limits, and inappropriate usesshould be discouraged. Given the likelihood of futurerevisions, users should be cautioned against overem-phasizing the most recent release. To achieve a pru-dent appraisal of developments, users should beadvised to consider the trend in the data over severalquarters rather than the latest quarter. As well, ifQNA data are presented in an annualized format,either as compounded growth rates or as levels mul-tiplied by four, it is important to explain that this pre-sentation magnifies the irregularity and uncertaintyof QNA data (for further explanation, see ChapterVIII). Similarly, using growth rates with more thanone digit behind the decimal point gives the impres-sion that the data are significantly more precise thanthey generally are.

1.36. Several approaches can be taken to educateusers. Seminars could be conducted for specific audi-ences, such as specialized journalists, interested parlia-mentarians, users within the central bank, orgovernment agencies such as the ministry of finance orthe department of commerce. Direct inquiries by usersare good occasions for compilers to explain specificissues. For the general public, the occasion of newreleases, which often brings the QNA to public atten-tion, can be used to highlight points of interest. In par-ticular, attention should be given to revisions and theircauses. Also, in presenting the data, care should betaken to exemplify proper use, as indicated above. Thebest way to go about this is to provide press releases tai-lored to the style of the media, ready to print.

G. Flash Estimates

1.37. In some countries, the term “flash estimates” isused for a first release of QNA data fairly shortly afterthe reference period. The terminology is designed toemphasize that shortcuts have been taken and that, con-sequently, the data are particularly subject to revision.The shortcuts usually include use of data for only oneor two months of the quarter for some or all compo-nents, with the missing month(s) estimated by extrapo-lation using mechanical methods such as thosediscussed in Chapter VII. Another common shortcut isuse of data with less complete response rates than thedata used for subsequent QNA estimates. Because theuse of shortcut sources and methods is a general feature

I INTRODUCTION

8

of QNA compilation, flash estimates only differ fromsubsequent QNA estimates in that they use a higherproportion of such methods. Consequently, flash esti-mates do not raise additional conceptual issues,although the practical concerns about informing usersof their limitations and assessing the record of revisionsfor QNA are even more crucial. The flash estimatesmay be more limited in coverage of the 1993 SNA vari-ables (for instance, they may cover variables from theproduction account only) or be published in a moreaggregated form. Publication of less detail is a recogni-tion that the statistical noise is greater in disaggregateddata and will emphasize the limitations of the estimatesto users. Preferably, the level of compilation would bethe same as for subsequent estimates, because a differ-ent level of compilation requiring use of different meth-ods may cause unnecessary revisions.

1.38. In some cases, flash estimates may be used todescribe data derived from aggregated econometricmodels that use factors such as behavioral relation-ships, leading indicators, or other indicators that donot have a close measurement relationship to thevariable. These techniques are not a substitute for sta-tistical measurement and are outside the scope ofQNA compilation. As they require different skillsfrom those used in statistical compilation, they arebest undertaken by other agencies.

H. An Outline of the Manual

1.39. The outline of this manual can be summa-rized as follows. The Manual discusses strategic andorganizational matters (Chapter II), the source datathat are the foundation of QNA (Chapters III-V),mathematical techniques that are applied to data(Chapters VI-VIII), and, finally, a number of spe-cific issues (Chapters IX-XI).

1.40. Chapters II-V are intended to be of particularinterest to those setting up a new system. In addition,these chapters will be useful to those reviewing exist-ing systems. In Chapter II, strategies for a QNA sys-tem and the management of QNA compilation arediscussed, with the warning that data are the founda-tion of QNA and mathematical techniques are not asubstitute. The chapter introduces the benchmark-indicator framework used throughout the Manual tounderstand QNA compilation and its relationship toANA. It emphasizes the nature of QNA data as timeseries and the necessity of closely linking QNA andANA using benchmarking techniques.

1.41. The commonly used sources and the issues thatarise concerning them are outlined in Chapters III(GDP and its components, according to the produc-tion, expenditure, and income approaches) and IV(institutional accounts). The Manual recommendsthat even when GDP can only be estimated from asingle approach, other splits of GDP should be pro-duced with one category as a residual. Chapter IVpoints out that completion of some of the institutionalaccounts is usually feasible and always desirable.

1.42. Chapter V advises on good practices for han-dling data through checking and reconciliation.

1.43. Chapters VI-VII deal with benchmarking andprojection techniques. The Manual warns againstmethods that introduce a step problem and presentsan optimal benchmarking technique to solve the stepproblem under the general benchmarking objectivepresented in Section C above. The technique pre-sented should be applied even in a newly establishedQNA system, and an understanding of the basicaspects of the technique and its compilation implica-tions is fundamental for QNA compilers. However,the detailed discussions of the mathematics behind it,enhancements, and possible alternatives providedtoward the end of the chapter and in the annexes areconsidered optional and are intended for moreadvanced readers.

1.44. Basic principles of seasonal adjustment arecovered in Chapter VIII. The chapter is intended par-ticularly for those starting a new system as well asthose with existing systems that do not yet have sea-sonally adjusted data.

1.45. Chapter IX deals with issues in price and vol-ume measurement. The problem of aggregation overtime is relevant to all compilers, while the issuesassociated with annual chaining pertain to moreadvanced systems.12

An Outline of the Manual

9

12The term volume is used for measures that exclude the effects ofchanges in prices of the components that make up the item. The exclu-sion of the effect of price changes means that changes in a time-seriesof volume measures are driven by quantity and quality changes.Volume can be contrasted with quantity, which is limited to data thatcan be expressed in physical units. Accordingly, quantity measures donot take into account quality change and are not applicable forunquantifiable items or aggregates of different items. Volume can alsobe contrasted with estimates in real terms which refer (in precisenational accounts terminology) to measures of the purchasing powerof an item, that is, in reference to prices of other items. In commonusage, “real” is often used for purchasing power as well as volumemeasures. While constant price estimates are a common form of vol-ume measure, the term also includes fixed-base and chain-linked vol-ume indices.

1.46. Work in progress is dealt with in Chapter X.The issues are relevant to all national accounts com-pilers, but the degree of sophistication of methodsused will depend on the stage of QNA compilation.

1.47. Chapter XI discusses revision policy and thecompilation cycle. Although policies need to differaccording to the circumstances of each country, atransparent policy is required in all cases.

I INTRODUCTION

10

Annex 1.1. Identification of Turning Points


11

1.A1.1. This annex provides a numerical exampleillustrating the importance of presenting monthly andquarterly economic information as time series and thederived rates of change in the time series on a period-to-period basis, for the purposes of analyzing trendsand turning points in the data, as emphasized inChapters I and VIII. In the absence of seasonallyadjusted time series and trend-cycle estimates, it iscommon practice to present changes from the sameperiod in the previous year, instead of period-to-periodchanges. As shown in the numerical example, rates ofchange from the same period of the previous year canbe inadequate in identifying the current trend in eco-nomic activity—indicating, for example, that an econ-omy is still in recession when it has actually beenrecovering for some time. If changes from the sameperiod of the previous year are used, turning points inthe data show up with some delay, which in some cir-cumstances can be substantial. The average delay canbe shown to be around half a year in discrete data andaround three-quarters of a year in cumulative data.

1.A1.2. In addition to delaying identification of turningpoints, changes from the same period of the previousyear do not fully exclude all seasonal elements (e.g.,Easter may fall in the first or second quarter, or thenumber of working days of a quarter may differ fromyear to year.) Moreover, in addition to any irregularevents affecting the current period, these year-to-yearrates of change will reflect any irregular events affect-ing the data for the same period of the previous year.

1.A1.3. Consequently, year-to-year rates of changeare not suitable for business cycle analysis, and ana-lyzing the economy on the basis of these rates ofchange can have an adverse impact on the soundnessof macroeconomic policy.

1.A1.4. If the changes from the same period in theprevious year are based on cumulative data (e.g., datathat cover January, January through March, Januarythrough June, and so on), which has been the tradi-tion in some countries, the delays in determining theturning points are even longer.

1.A1.5. The numerical example presented inExample 1.A1.1 is based on a time series of hypo-thetical data, starting in the first quarter of 1996, thatcan be viewed as representing tons of steel producedin each quarter, or, alternatively, quarterly GDP atconstant prices. It contains three turning points. Thefirst turning point occurs in quarter 1 of 1998, thesecond occurs in quarter 1 of 1999, and the third inquarter 4 of 1999.

1.A1.6. From the discrete quarterly data presented inthe first column of Example 1.A1.1, these three turn-ing points are easily seen as the series (a) turns fromdecreasing to increasing in quarter 1 of 1998, (b)turns from increasing to decreasing in quarter 1 of1999, and (c) turns from decreasing to increasing inquarter 4 of 1999.

1.A1.7. Similarly, from the quarter-to-quarter rates ofchange presented in the third column of Example1.A1.1, the first turning point is indicated by thechange in quarterly rates of change from a negativerate in quarter 1 of 1996 to a positive rate in quarter 2of 1998, the second turning point by the change froma positive to a negative rate of change between quarter1 and quarter 2 of 1999, and the third turning point bythe change from a negative to a positive rate of changebetween quarter 4 of 1999 and quarter 1 of 2000.

1.A1.8. When using changes from the same period ofthe previous year (e.g., the change from quarter 1 of1996 to quarter 1 of 1997) instead of quarter-to-quarterchanges, the delays in identifying the turning pointscan be substantial. In the example, the changes fromthe same quarter of the previous year are presented inthe fourth column and show the third turning point ashaving taken place in quarter 3 of 1999—that is, threequarters after it actually occurred.

1.A1.9. If the changes from the same quarter in theprevious year are based on cumulative data, asshown in the final column, the analysis gives theimpression that the turning point took place even onequarter later.

I INTRODUCTION

12

I INTRODUCTION

Example 1.A1.1. Identification of Turning Points

Tons of Steel Produced

Bold type indicates turning points.Rates of Change

———————————————————————————————Changes from the Changes from the Same Quarter of Same Quarter of the Previous Year the Previous Year

Quarter Discrete Data Cumulative Data Quarter-to-Quarter (Discrete Data) (Cumulative Data)

q1 1996 1,537.9 1,537.9q2 1996 1,530.2 3,068.1 –0.5%q3 1996 1,522.6 4,590.7 –0.5%q4 1996 1,515.0 6,105.8 –0.5%q1 1997 1,507.5 1,507.5 –0.5% –2.0% –2.0% q2 1997 1,500.0 3,007.5 –0.5% –2.0% –2.0% q3 1997 1,470.0 4,477.5 –2.0% –3.5% –2.5% q4 1997 1,440.0 5,917.5 –2.0% –5.0% –3.1% q1 1998 1,350.0 1,350.0 –6.3% –10.4% –10.4% q2 1998 1,395.0 2,745.0 3.3% –7.0% –8.7% q3 1998 1,425.0 4,170.0 2.2% –3.1% –6.9% q4 1998 1,575.0 5,745.0 10.5% 9.4% –2.9% q1 1999 1,605.0 1,605.0 1.9% 18.9% 18.9% q2 1999 1,590.0 3,195.0 –0.9% 14.0% 16.4% q3 1999 1,575.0 4,770.0 –0.9% 10.5% 14.4% q4 1999 1,500.0 6,270.0 –4.8% –4.8% 9.1% q1 2000 1,500.0 1,500.0 0.0% –6.5% –6.5%q2 2000 1,515.0 3,015.0 1.0% –4.7% –5.6% q3 2000 1,530.0 4,545.0 1.0% –2.9% –4.7% q4 2000 1,545.0 6,090.0 1.0% 3.0% –2.9%


13

Example 1.A1.1. (continued)

1,300

1,350

1,400

1,450

1,500

1,550

1,600

20001999199819971996

Discrete quarterly data

Quarter to quarter rates of change

Changes from the same period in the previous year

Changes from the same period in the previous year, cumulative data

–15

–10

–5

0

5

10

15

20

20001999199819971996

14

II Strategic Issues in Quarterly National Accounts

A. Introduction

2.1. Strategic statistical and managerial issues have tobe dealt with to facilitate a smooth and efficient opera-tion of quarterly national accounts (QNA). These issuesarise when QNA are being set up, and it could be use-ful to revisit them from time to time once the QNA arefully operational. The most important statistical issuesto be considered are the relationship of the QNA to theannual national accounts (ANA), coverage of the QNA,assessment of quarterly source data, and statisticalcompilation processes. Important managerial aspectsconcern the release cycle, the timing of the compilationprocess, and organizing the staff involved in the compi-lation. In this chapter, both statistical and managerialissues are examined from a strategic perspective, with-out much detail (statistical issues will be discussed inmore detail in later chapters).

2.2. When considering these strategic issues, it isessential to have a broad understanding of the overallprocess. The main steps in establishing and maintain-ing QNA are summarized in Box 2.1. In this box, tworelated phases are distinguished, namely, an establish-ing phase and an operational phase. In the establishingphase, the compilation approach is decided, sourcedata are selected and assessed, compilation processesare developed and assessed, and the whole compila-tion system is used to establish time series of QNAdata on past years (“back series”). An important firststep in this phase is to consult with potential users tosee what kind of use they could make of QNA data.Obviously, consulting users should not be restricted tothe first phase, because user wishes will probablyevolve as the QNA develop.

2.3. In the operational phase, the compilation system isused to compile estimates for the current quarters; theseestimates are subsequently revised when new quarterlyand annual information becomes available. The sources,statistical techniques, and compilation system used for

establishing the back series in the establishing phase andfor updating the series in the operational phase shouldbe identical. In contrast, managing the work on QNAmay differ between the preparatory and the operationalphase, and the alternatives countries have developed arediscussed in this chapter.

B. Statistical Issues

1. The Link between Quarterly and AnnualNational Accounts2.4. It is generally agreed that QNA estimates shouldbe kept consistent with ANA estimates (that is, the non-seasonally adjusted QNA estimates). Reasons for thiswere discussed in Chapter I and include aspects ofquality and transparency. Ideally, the QNA should bebased on the same data sources and methods as theANA and compiled using the same system. However,in practice, this ideal is generally not achievable. Toachieve both timeliness and accuracy within resourceconstraints, it is common to collect detailed and com-prehensive source statistics only annually or less fre-quently, and to compile a more limited set of short-termindicators on a monthly and quarterly basis usingsmaller sample surveys. For the same reasons, it iscommon to compile a detailed and more comprehen-sive system of national accounts only annually, and tocompile a simplified and aggregated set of QNA esti-mates immediately after each quarter based on lesscomprehensive source data.

2.5. A QNA compilation system may be separatefrom the ANA compilation system or integrated withit. Separate systems are commonly found in countrieswith a comprehensive and detailed ANA system,including a supply and use (SU) table. Applying anSU framework implies an extensive cross-sectionalreconciliation that these countries do not find feasibleon a quarterly basis, at least not on the same level ofdetail. This implies that some of the transformation to

which the annual source data are subjected cannot beperformed quarterly. As a result, the QNA sourceshave to be benchmarked to ANA estimates derivedfrom the transformation that takes place in the ANAcompilation process. Integrated ANA-QNA systemsare typically found in countries not using an SUframework for their ANA, which makes it easier touse the same system for QNA as for ANA. In an inte-

grated system, the data storage and calculation func-tions for both ANA and QNA are carried out withinthe same processing system, although the level ofdetail may differ. In this situation, QNA sources maybe benchmarked to annual source data,1 rather than to

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Box 2.1. Main Steps to Establish and Maintain Quarterly National Accounts

To Establish QNA

1. Consult potential users• Concerning possible uses• Concerning required coverage, detail, and so on

2. Take inventory • Of annual compilation methods• Of available quarterly and annual source data

3. Design compilation methods and procedures• Consider relationship to sources and methods used in the annual accounts• Decide coverage of QNA, including which parts of the 1993 SNA are to be implemented • Determine compilation level• Choose integrated or separate ANA-QNA compilation system• Make compilation schedule, including timeliness of first estimates and revision policy

4. Review the quality of source data and compilation procedures• Study correlation between annual and quarterly source data• Study revisions to main aggregates based on historic data (historic simulation of the compilation system)

� Revisions to the quarterly compilation system5. Generate time series of QNA data for past years (“back series”)

• Benchmark the time series of quarterly source data to the time series of annual data (using methods such as the enhanced proportional Denton method)� To be done for a sufficiently long time series� To be done at the most detailed compilation level

6. Perform real-time test runs and update the quarterly time-series with estimates for the quarters of the current year(year y)• Link monthly and quarterly source data for the current quarters with estimates for the back series

� Extrapolation with indicators—Benchmark the time series of quarterly source data to the time series of annual data (using methods such as the enhanced proportional Denton method)

• Fill information gaps 7. First release

To Maintain QNA

8. Revise the quarterly estimates for the current year when new quarterly data become available• Link monthly and quarterly source data for the current quarters with estimates for the back series

� Extrapolation with indicators—Benchmark the time series of quarterly source data to the time9. Revise the quarterly estimates when new annual data become available

• Revise the quarterly estimates for year y (and preceding years) to incorporate new benchmark data without introducing steps in the series� Benchmark the time series of quarterly source data to the new series of annual data� To be done at the most detailed compilation level

10. Update the quarterly time series with estimates for the next current year (year y+1)• Compile quarterly estimates for year y+1 by linking monthly and quarterly source data for the quarters of year y+1 with the

revised and benchmarked QNA estimates for year 1 to year y� Extrapolation with indicators—Benchmark the time series of quarterly source data to the time series of annual data� To be done at the most detailed compilation level.

1These may have been pre-benchmarked to more comprehensive anddetailed surveys and censuses that are performed only every few years.

ANA estimates. A variant is the situation in which aperfect one-to-one correspondence exists between theannual levels and annual movements in the quarterlydata and the corresponding annual data; in such cases,the annual data may even be derived from the QNAdata. However, this situation occurs for only a fewcomponents.

2.6. The choice between these alternative compila-tion styles depends on circumstances in each country.One factor is whether the annual data are subject to adetailed reconciliation process that cannot be appliedeach quarter. Another factor is whether the existingannual system has a time-series dimension or a year-by-year style of calculation, as the time-series focusis a requirement for QNA. A third factor is whetherrevisions of annual data sources tend to arrive at thesame time of year or spread throughout the year,because in a separate ANA-QNA system, revisedannual source data cannot be taken into account in theQNA until after the ANA are revised. It is importantthat QNA system designers think about these issuesexplicitly and do not choose one style without con-sidering the alternatives.

2.7. Consequently, QNA are commonly compiledby benchmarking the quarterly source data toannual source data or to ANA estimates derivedfrom a separate ANA system. In the benchmarkingprocedure, the quarterly source data serve only todetermine the short-term movements in the series,while the annual data determine the overall leveland long-term movements in the series (see ChapterVI for a detailed discussion of benchmarking).Thus, the quarterly source data are used as indica-tors to• split ANA estimates into quarters for years for

which ANA estimates are available; and• update the QNA series by using the short-term

movements in the QNA source data to generateQNA estimates for the most current period that areconsistent with the QNA estimates for years forwhich ANA are available.

As shown in Chapter VI, the level and movements inthe final QNA estimates will depend on thefollowing:• the movements, but not the level, of the short-term

indicators;• the level of the ANA estimates for the current year;

and• the level of the ANA estimates for several preced-

ing and following years.

2. Coverage of QNA

a. General issues

2.8. When establishing QNA, one of the first choicesthat has to be made is which parts of the 1993 SNAshould be implemented initially. The choice willdepend on availability of quarterly source data, theANA system in place, available capacity, and userrequirements. As mentioned in the introduction to thischapter, an important first step is to consult with poten-tial users to see what kind of use they could make ofQNA data. This implies assessing what kind of detail,coverage, and so on users would find desirable.Because potential users may not be aware of the possi-ble benefits of QNA, statistical leadership is needed inthis phase, and statisticians may have to set the stage byanticipating future needs.

2.9. When establishing QNA, ANA are usually alreadyin place, along with supporting source data. Also, coun-tries considering establishing QNA usually have somemonthly or quarterly source data available. The next stepin designing QNA is to take an inventory of availablesource data to decide which parts of the ANA can beimplemented on a quarterly basis. The initial design ofQNA should be based on the ANA as much as possible,although it is usually simpler and more aggregated.

2.10. In the initial stage of implementation, only esti-mates of GDP with corresponding components fromthe production or expenditure side as well as GNI andsavings may be derived. Over time, it may be useful torevisit the extent of coverage of the QNA in view ofchanges in the availability of source data and changesin the coverage of the ANA. As the QNA become moreestablished and as problems and gaps are identified,users needs for additional data may guide future exten-sion. Experience has shown that once QNA are well-established, users become more sophisticated and maypromote providing increased resources to extend theQNA to include supply-use reconciliation, institu-tional sector accounts, and balance sheets.

2.11. Extending the QNA beyond basic compilationof GDP has several advantages. It provides users witha more comprehensive picture of the various aspectsof the current economic developments organized inan integrated framework for analyzing the data. Also,the extended accounting framework enables cross-checking of the data.

2.12. Because, as argued above, QNA should beanchored on ANA, the coverage of the QNA should

II STRATEGIC ISSUES IN QUARTERLY NATIONAL ACCOUNTS

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be consistent with the coverage of the ANA, whichmeans that it should either be the same as the ANA orconstitute a subset of the ANA. For instance, if theANA covers only compilation of GDP estimates,with components from the production and the expen-diture sides, the initial coverage of the QNA will haveto be restricted to compilation of GDP from the samesides or at least one of them.

2.13. Obviously, establishing QNA requires thathuman resources and equipment should be available.If no extra capacity is forthcoming and it is not pos-sible to realize efficiency gains, reprioritizing will beneeded with ANA or other statistical tasks. If thecapacity needed for the development of the QNA hasto be found from the resources currently used for theANA, this may imply cutting back on developments;for instance, this may imply that the 1993 SNA can-not be fully implemented as rapidly as otherwisewould have been possible. In a more dire scenario,generating capacity for the development of QNA maynecessitate cutting back on the existing ANA pro-gram; the alternative of decreasing accuracy shouldbe avoided. Rather, capacity should be generated bydiscontinuing marginal activities or by discontinuingparts of the ANA that have not been in demand. It isimportant to consult users on the choices to be madein such a situation.

2.14. The introduction of a QNA system is similarfor both developing and developed countries. Theneed for the type of information provided throughQNA may be as urgent in developing as in developedcountries, although more efforts may be needed toconvince users of the importance of QNA data andinform them about the limitations of QNA data.Countries now starting QNA have the advantage thatsoftware supporting the implementation of therequired techniques (such as benchmarking) is nowwidely available.

b. Measurement of GDP and its components

2.15. Measurement of GDP constitutes a core part ofalmost all national accounts systems, and a break-down of GDP into its components is usually one ofthe first QNA results available. Traditionally, a dis-tinction is made among three approaches2 to GDPmeasurement, namely, (a) the production approach,(b) the expenditure approach, and the (c) the income

approach. This distinction is somewhat artificialbecause these three approaches often use the samesource data. For instance, government output andgovernment consumption estimates are often basedon the same source data; the estimates of fixed capi-tal formation for the expenditure approach are partlybased on output estimates of construction and pro-duction of machinery, which are also used in the pro-duction approach; and the wages and salariesestimates used in the income approach are oftenderived from the same statistics that provide the dataon industry output and value added that are used inthe production approach. However, the variousapproaches also use specific source data and allow adistinct perspective on development and level ofGDP. Although, as argued, these approaches are notfully independent, applying various approaches facil-itates cross-checking of data. Therefore, this manualrecommends that countries should aspire to estimateGDP from at least two of the three sides. Because oftheir relative strength, it would be particularly usefulto apply both the production and the expenditureapproach.

2.16. Another important reason to apply at least theproduction and expenditure approaches is that theyprovide different breakdowns of GDP. To the extentthat demand is driving short-term changes in theeconomy, the expenditure split provides particularlyuseful data for business cycle and macroeconomicpolicy analysis and for forecasting. The industrycomposition of growth provides a useful but lessimportant supplementary perspective.

2.17. The production approach is the most widelyused in the QNA for measuring GDP, probablybecause of a traditional focus in many countries onshort-term statistics on manufacturing industries asmajor indicators. The production approach involvescalculating output, intermediate consumption, andvalue added at current prices as well as in volumeterms by industry. However, the available sourcedata are usually restricted to either output or inter-mediate consumption, and the situation in whichboth types of source data are available is relativelyrare. In most countries, output data are reasonablywell covered for manufacturing industries, but thecoverage of construction and services is usually lesscomprehensive. Components missing from output,intermediate consumption, and value added are esti-mated using ratios that reflect fixed input-output(IO) coefficients. Single-indicator-based estimateswill be biased to the extent that the ratios vary with

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2A distinction is made between a compilation approach (which leads toa GDP total) and production of splits (in which a GDP total is derivedfrom one approach, but some components of another approach arederived, so the remaining item can be derived as a residual).

factors such as seasonal effects, capacity utilization,change in composition, technological change, andproductivity trends.

2.18. The expenditure approach for measuring GDP isless common than the production approach amongQNA-compiling countries. This is because of problemsin availability, timing, valuation, and coverage inexpenditure source data. The expenditure side usuallyhas two strong pillars of quarterly data, namely, foreigntrade and government consumption; the other cate-gories are often less well covered. The major compo-nents of external transactions are usually available fromthe balance of payments and through merchandisetrade statistics that often have a strong basis in compre-hensive data collection for customs purposes. Data ongovernment consumption can usually be derived fromgovernment administrative data. Other expenditurecomponents (namely, household final consumption,parts of fixed capital formation, and changes in inven-tories) are usually covered less well. Directly observeddata on fixed capital formation and changes in invento-ries may in many cases be lacking.

2.19. If expenditure data are incomplete, it may stillbe possible to derive a useful split of GDP by type ofexpenditure. For example, if total GDP is derived bythe production approach and the available source dataallow some of the key expenditure components to beestimated, the missing items may be derived as aresidual. This situation can arise because data onchanges in inventories are incomplete or inadequate.Although not an independent check of the GDP esti-mates, use of incomplete expenditure data in this wayprovides benefits for analysis in addition to plausibil-ity checks of GDP.

2.20. The expenditure split is, in some ways, the mostpractical to measure in constant price or volume termsbecause there is a relatively clear concept of price andvaluation for each demand category. In contrast, theprice and volume dimensions of value added are morecomplex because value added cannot be directlyobserved, and the income approach is not suited forprice and volume measures. As mentioned, the expen-diture split also provides particularly useful data forbusiness cycle and macroeconomic policy analysis andfor forecasting. Also, this split is most useful for policyreasons because, over the short-term, demand can bemore easily influenced than supply.

2.21. The income approach is the least commonlyused of the three approaches but is potentially useful

as an alternative measure of GDP. The incomeapproach avoids some of the problems the productionand expenditure approaches may have, such as thereliance on fixed IO ratios in production data; how-ever, it lacks a constant price dimension. Also, itrequires that businesses have quarterly data on prof-its and some expenses. The income approach mayhave a sound underpinning in wage statistics or inadministrative data on wages (for instance, for socialsecurity purposes), but quarterly observations ofoperating surplus/mixed income are often unavail-able, particularly for unincorporated enterprises.

2.22. Even if income data are incomplete, it may stillbe possible to derive an income split of GDP where oneof the categories (usually gross operating surplus) isderived residually. The distribution of income fromGDP provides a useful alternative perspective on eco-nomic development. For a country interested in issuessuch as profitability and wage bargaining, this could bean important economic statistic. It also shows the linkbetween business accounting and the national accounts,particularly if a bridge table from profits to operatingsurplus/mixed income is provided.

2.23. The weaknesses of the various methods forcompiling GDP can be mitigated by combining severalof them. Production and expenditure data can be com-bined using the commodity flow method. This methodis based on the fundamental national accounting iden-tity shown in the goods and services account and SUtables, namely, that total supply (by product) mustequal total use. The commodity flow method can beapplied on different levels, for instance, for groups ofcommodities or for individual commodities. The moredetailed the level at which the method is applied, themore accurate the result (detailed information requiresfewer assumptions on origin and use). This method isparticularly strong if applied in an SU3 framework,even one of limited dimensions (see next section).Production and income data can be checked if both areclassified by industry, which is particularly meaningfulif the value added data for industries can be brokendown into compensation of employees, operating sur-plus, and mixed income (for a discussion on reconcili-ation issues, see Chapter V).

c. Quarterly GDP by the supply and use approach

2.24. Several countries have developed quarterly SUtables as the basis for their quarterly compilation of


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3Input-output tables may also be used. For simplicity, we will refer tothis whole area as supply and use (SU).

the GDP-related part of the national accounts.Compilation of SU tables is basically a common-sense method of compiling the GDP-related part ofthe overall national accounts system. For each indi-vidual product—at a more or less detailed level—SUtables show the sources of supply (production andimports) and the uses (intermediate consumption,households and nonprofit institutions serving house-holds final consumption, government final consump-tion, and gross capital formation and exports). Ifsupply and use for each individual product is bal-anced, the aggregated goods and services accountsfor the total economy will also be balanced.

2.25. Application of an SU framework may seemdaunting in a quarterly context, but it has proved fea-sible.4 In particular, if SU tables are used as a compi-lation tool without being published, less rigor may beapplied in balancing conflicting data and removingdiscrepancies. For instance, it may not be necessaryto remove minor discrepancies that remain aftermajor imbalances have been solved, as is usuallydone if SU tables are to be published.

2.26. SU tables provide an instrument to makemaximum use of whatever information is available.SU tables are particularly suitable for filling gapsand reconciliation of data. With problems of datagaps caused by unrecorded economic activities anderrors in the reported data, it is particularly desir-able to use the SU framework to organize and coor-dinate the compilation work. The SU framework is,therefore, suitable for good data systems as wellwhere the data sources are limited in coverage or areof poor quality.

2.27. The SU framework also allows the generationof more detailed data; for instance, retail sales maybe available only for broad product groups, but thereconciliation with detailed production and externaltrade data can enable the production of detailed dataon household consumption. Such detailed data canbe useful to some users and can also help improvethe quality of deflation. Making calculations at amore detailed level reduces the dependence on thefixed weights used in Laspeyres price indices,resulting in aggregate implicit deflators that arecloser approximates to the preferred Paasche defla-tors. The SU framework also provides the ideal basisfor making separate volume measures for output and

intermediate consumption, and thus for value added,using the double indicator method.

2.28. A few advanced countries compile both currentand constant price SU tables. SU tables at currentprices alone are more common. However, many of theassumptions about relationships are more likely tohold in constant price data. Having both current andconstant price tables also makes it possible to separateprice and volume aspects and to balance price, volume,and value (current price) data simultaneously.

2.29. The production of components of a quarterlySU system is broadly the same as for the equivalentcomponents in the other approaches, as already dis-cussed. However, there is an extra element of overallbalancing and reconciliation. In effect, the use of theother approaches often involves elements of the SUapproach. For example, the production approachoften involves using fixed ratios on partial data, andcommodity balances are often used to derive esti-mates. Each of these is a typical element of the SUapproach. Using them is like using the SU approachfor particular industries or products, but without thebenefits of using the overall accounting frameworkfor checking the aggregates. For all these reasons,countries that have a developed system of annual SUtables should consider using them systematically as abasis for QNA estimation.

3. Compilation Level

2.30. QNA are almost always compiled at a lesserlevel of detail than the annual estimates. Of course,it is not easy to draw the line on the level of detailrequired, but it should maintain separate data foritems that are large, of interest to data users, orbehave in atypical ways. Less detail does not alwaysmean making the compilation process simpler,faster, and less resource demanding, because some-times a more detailed level of compilation makes iteasier to eliminate differences between indicators.For instance, when balancing supply and use ofvehicles, having more details about different typesof vehicles (such as trucks and passenger cars)makes balancing of supply and use easier (the use oftrucks is mostly for fixed capital formation, whileuse of passenger cars can be both for fixed capitalformation and for household consumption). Also, inautomated compilation processes, more detail neednot make much of a difference in compilation speedand resource needs. Finally, as mentioned above,making the calculations at a more detailed levelreduces the dependence on fixed IO assumptions or

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4For instance, these methods are being used in the QNA context inDenmark, France, the Netherlands, and Norway.

the fixed weights used in Laspeyres price indices,resulting in improved estimates.

4. Assessing Source Data and the CompilationSystem

2.31. Before commencing publication of QNA esti-mates, it is important to review the quality of bothsource data and the proposed compilation procedures.Because of the general demand for long time series,this review should go back as many years as feasible.The main purpose of the review is to identify weak-nesses in the quarterly compilation system and possi-bilities for improvements to minimize future revisionsof the main aggregates. It is important to establishwhether source statistics properly indicate the direc-tion and overall size of the changes and whether theyenable catching turning points. The review also givesan indication of the quality of the estimates and thedegree of revisions that can be expected in the future.Because of resource constraints and lack of suffi-ciently accurate and detailed source statistics, weak-nesses will remain and revisions are inevitable; forsome series, the revisions may be large. Thus, uponrelease of the first quarterly estimates, it is vital thatthe users are well informed of the accuracy and thereliability of the estimates and the degree of revisionsthat can be expected in the future.

2.32. In the national accounts context, the term“accuracy” is used to mean “closeness to the truth,”while “reliability” is used to mean “degree of revi-sions the series is subject to.” Because QNA areanchored to the ANA, the accuracy of the ANA sets aceiling on the accuracy of the QNA; the reliability ofthe QNA is also thus determined because the extent ofrevisions depends on the closeness of the initial QNAestimates to the ANA estimates and the extent of revi-sions to the ANA estimates (for a more comprehen-sive discussion of revisions, see Chapter XI).

2.33. It is essential that decisions about sources andmethods be well documented. The documentation isuseful for compilers when problems arise or whenthere is staff turnover or absence. It also provides thebasis for documentation for users, who often wish toknow more about the data.

2.34. Assessing the source data and the compilationsystem involves conducting the following threetracking exercises:

(a) To assess the ability of the quarterly sourcedata for individual series to track the annualestimates.

(b) To assess preliminary quarterly source data forthe individual series to track the final quarterlysource data.

(c) To assess the ability of the overall compilationsystem to track the annual estimates for majoraggregates.

The overall tracking exercise will also, on an ex antebasis, provide a measure of the reliability of the QNAin the sense discussed in paragraph 2.31. Assessingthe source data and the compilation system should beseen as a continuous process that should also be con-ducted regularly in the operational phase (in the oper-ational phase this concerns ex post revision studies).The main aspects of assessing the source data and thecompilation system are summarized in Box 2.2.

a. Assessing individual source data

2.35. Source data should be assessed for accuracy,reliability, and timeliness. Such an assessment isimportant for several reasons. First, it will revealwhether a specific series of source data is suitable forQNA purposes; second, where more than one datasource is available for a particular variable, it will aid


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Box 2.2. Review:Assessment of Indicatorsand Compilation Methods

1. Relationship to the sources and methods used in theannual estimates

• Are the same sources available quarterly?• Are other sources/indicators available quarterly?• Are several alternative sources/indicators available

for the same item?2. Compilation level

• As detailed as possible?• At the level of the main aggregates?

3. Coverage• What parts of the ANA can be covered?

4. Assessment of sources and methods • Accuracy in predicting annual changes • Systematic bias or noise• Individual and aggregated tracking exercises• Definitions of source data

� Coverage� Units� Classifications

• Reliability (revision of indicators)� Systematic bias� Noise

• Timeliness� Reliability of preliminary estimates� Amount of gap filling and guess estimation

5. Do the annual sources and methods need to be changed?

in choosing among them; third, when source data areconflicting, it will facilitate a choice on where toadjust; fourth, it will help to identify areas for improve-ment; and fifth, it will facilitate informing users aboutthe quality of the estimates and expected future revi-sions to the individual series. Of course, in many cases,there will be little or no choice about the source to beused—in particular, in the short term. However, it isstill necessary to assess indicators that could possiblybe used. These assessments should be discussed withthe data providers, who may be able to give additionalbackground information. (In addition, nationalaccountants are sometimes able to identify problemsthat the data collectors had not discerned.)

2.36. The main criterion for the accuracy of quar-terly source data is to what extent they are successfulin indicating annual movements. This follows fromthe need to keep QNA consistent with ANA and theassumed higher quality of the annual source data. Theaccuracy of the short-term source statistics as indica-tors for the annual movements depends on definitionsand specification of the variables and on issues suchas coverage, units, and classifications.

2.37. The ability of the quarterly source data to trackthe annual estimates should be assessed by comparingthe growth rates in the annual sum of the quarterlysource data with growth rates in the correspondingANA estimates (this is the first of the three trackingexercises listed in paragraph 2.34). Large differences inthe rates of change indicate inconsistencies betweenthe quarterly and annual source data for that series andpotential weaknesses in the quality of either the quar-terly or the annual source data. Large differences in theannual rates of change in the quarterly and annualsource data for the back series also indicate that largerevisions can be expected in the future as additionalsource data become available. Mathematical tech-niques can be used to more formally study the correla-tion between annual and quarterly data and to identifyand remove any systematic errors (that is, bias) in thequarterly source data’s long-term movements. Use ofmathematical techniques to identify and adjust forbiases is discussed in Chapter VI.

2.38. Specific problems may arise if annual reportingis on a fiscal year basis rather than a calendar yearbasis. In this respect, the main problem is that inannual statistics, respondents with a nonstandardreporting year (that is, a reporting year that differsfrom the rest of the industry) are usually included inthe statistics for the year that has the largest overlap,

which will then create a mismatch with the sum of thequarters. A solution to this problem with the annualdata could be found if the annual source statisticswould use the information from the quarterly sourcestatistics to allocate the data of an individual respon-dent to the standard accounting period using thebenchmarking technique presented in Chapter VI.

2.39. The reliability of the quarterly source data hasimportant implications for how early sufficiently reli-able initial QNA estimates can be prepared. Often thefirst estimates will have to be based on published orunpublished preliminary versions of source data thatare still open to revisions. One important reason forsuch revisions to the source data is that early responserates are lower, and estimates may change as responseincreases. These changes may follow a consistent pat-tern, which implies a “bias,” or the changes may beirregular, which implies “noise.” A bias in early esti-mates of an indicator may be caused by selectivity inthe response. The reliability of the quarterly sourcedata can be assessed by comparing period-to-periodrates of change in the preliminary versions with thecorresponding rates of change in the final versions ofthe series. Obviously, this can only be done if the pre-liminary versions of the data have been retained in thedatabases rather then being continually overwritten.

2.40. The timeliness of the quarterly source data alsohas important implications for how early sufficientlyreliable initial QNA estimates can be prepared. Oftenthe first estimates will have to be based on an incom-plete set of source data. For some series, data for onlytwo months of the last quarter may be available,while data for other series may be missing altogether.To fill these source data gaps, provisional estimateswill have to be made based on simple trend extrapo-lation or on alternative indicators that are more timelybut less accurate. For each individual variable, theimpact of these provisional estimates on the reliabil-ity of the first estimates can be assessed by construct-ing provisional estimates for the past years as if onewere in the past and comparing the period-to-periodrate change in those estimates with correspondingrates of change in the final quarterly source data forthat variable. This and the assessment of the reliabil-ity of the quarterly source data described in para-graph 2.39 represent the second of the three trackingexercises listed in paragraph 2.34.

2.41. The assessment of possible source data willdetermine what source data are suitable for QNA pur-poses and, from there, which parts of the 1993 SNA

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can be implemented. Sometimes the assessment willlead to the conclusion that biases and noise are toosubstantial for a particular set of data to be used tocompile QNA data. This can imply that the QNAcompilers have no other choice than to not use thesedata, but it would be important to discuss with thecompilers of the source data whether improvementscan be made (see below). While the decision not touse a certain data set might mean that the system can-not be fully implemented, this is likely to be prefer-able to the use of data that can result in misleadingresults.

2.42. Sometimes, a choice has to be made amongvarious sources for the same variable. Although inmost cases QNA compilers face a lack of source datarather than an abundance, the situation may occur inwhich several indicators are available for one partic-ular variable. If alternative indicators are available forthe same variable, it is important to have some knowl-edge of their accuracy and reliability to choosebetween them. Note that the lesser quality data maystill be useful as a check on the preferred series.

2.43. Often, QNA compilers need to adjust thesource data in the QNA compilation process. If dataon supply and use are confronted through SU tablesor in a commodity flow equation, it is likely thatinconsistencies will emerge. In such cases, knowl-edge about the accuracy and reliability of the datawill provide guidance on how much leeway there isfor adjusting the data.

2.44. Assessment of the source data may also helpidentify areas that need improvement, both for theQNA and the ANA. Necessary improvements mayconcern coverage, definitions, units, and so on.Obviously, it will be easier for QNA compilers torequest improvement of statistics collected by thesame agency, but even data from other agencies maybe improved. Agencies collecting data for their ownuse that do not fit well into the QNA compilationmight prefer adapting their questionnaires to allowuse in the QNA context rather than having theirrespondents exposed to a new survey.

2.45. In setting priorities for improvements, the rel-ative importance of an indicator should be one of theconsiderations. For many components, the basicdata are so poor that refinement of methods wouldbe of doubtful benefit. There are also likely to becomponents of little economic significance thathave poor data. National accountants need to be

careful about expending too much effort on numer-ous, trivial items at the expense of large, importantitems. Of course, the fact that an item is small can-not be an excuse for deliberately choosing a poormethod when a better one is available, and the meth-ods adopted for even the smallest components needto be defensible to inquisitive users. Also, it shouldbe noted that small items may have a substantialeffect on growth estimates (changes in inventoriesare an example of this).

2.46. In some cases, the development of QNAmethods also leads to improvements in the ANA.The process of review often brings to light outdatedor unrealistic assumptions in annual estimation, aswell as faulty annual compilation practices. In afew cases, the quarterly data may be superior and somay be used to replace the annual data. Oneinstance is annual deflators that are best built upfrom quarterly data as the ratio between the annualsum of quarterly current and constant price data(see Chapter IX, Section B), instead of constructedas a simple annual average of monthly price datafor the year. Similarly, data on inventories andwork-in-progress are best built up from short-termdata. QNA can also contribute to an improved allo-cation of fiscal year data to calendar years in caseswhere the two do not coincide.

b. Assessing the overall compilation system

2.47. Before QNA estimates are published, an aggre-gate tracking exercise should be undertaken to assessthe overall consistency of the quarterly and annualsource data and compilation systems with respect toannual rates of change for major aggregates (this isthe third of the three tracking exercises listed in para-graph 2.34). Errors in the individual series may go inopposite directions and, thus, may not give a goodindication of the degree of future revisions of themain aggregates that can be expected. To undertakean aggregate tracking exercise, the entire compilationprocess needs to be simulated on historic data to pro-duce time series of unbenchmarked estimates for themajor aggregates. That is, the proposed QNA compi-lation system should be used to produce estimates ofQNA aggregates for the past years as if one were inthe past and were producing the first preliminary sumof four quarter estimates for those years without laterannual benchmarks. If feasible, it is preferable to per-form the aggregate tracking exercise based on theincomplete set of source data that would actuallyhave been available when the first sum of four quar-ter estimates would have been produced.


22

2.48. Later, in the operational phase, the aggregatetracking exercise should be repeated by comparingthe various releases of annual data from the QNAsystem with the eventual ANA data. As emphasizedin Chapter XI, best practice also involves periodi-cally conducting and publishing studies of long-term trends in the revision patterns. Summaries ofthese studies may accompany the regular quarterlyrelease of data to remind users that data are subjectto revisions.

2.49. It is advisable to also perform test runs in realtime before going public with the QNA. Only experi-ence from such test runs can sufficiently ensure therobustness of a QNA system and its ability to copewith unexpected problems. Although user demandsand other compelling reasons may provide a push forgoing public as soon as possible, in the establishmentphase, QNA compilers should endeavor to schedulesufficient time to run one or two real-time test runs.

2.50. The tracking exercise on the aggregate levelcan be used to remove weaknesses in the systemoverall. For instance, the exercise may indicate thatestimates from the production approach are morerobust than the estimates from the expenditureapproach, which would provide guidance to adjust-ments in the course of the compilation process.

5. Statistical Processing

2.51. Statistical processing encompasses the assem-bly of data, benchmarking, deflation, seasonal adjust-ment, aggregation, and other calculations. Indesigning a processing system, it is useful to antici-pate the differences and links between the prepara-tory and operational phases of QNA compilation sothat different needs can be satisfied using the sameprocessing system. In general, the processes for com-piling data in the preparatory and operational phaseswill be the same. However, the operational phase hassome extra complexities that may not be evident inthe preparatory phase.

2.52. In the QNA preparatory phase, the objective isto compile data on past years (back series).Compilation of QNA data for a single quarter or yearis of little value. The back series of historical dataprovide greater perspective on economic develop-ments, and for that reason should go as far back asfeasible. Long back series also allow compilers set-ting up a new system to check the data, gain experi-ence in the behavior of the series, and supportseasonal adjustment.

2.53. In the operational phase, the objective is toupdate the time series with data for the current quar-ters as well as revising the data for past years. Theoperational phase differs from the preparatory phasein several respects. These differences arise because,in the preparatory phase, compilation was done afterthe fact with existing ANA totals as benchmarks,which would not be available for the most recentquarters. Other differences are that in the operationalphase, the data will be less complete for the mostrecent quarters, data source revisions will be anissue, and the timing of data supply in a propersequence becomes much more important. Only run-ning the quarterly compilation system in real timewill reveal all the implications. A trial run of a quar-ter or two before the official release (as recom-mended above) will allow these problems to beidentified and resolved without delays the publicmay notice.

2.54. For the operational phase, the forward orextrapolation part of the series presents its own diffi-culties because there will be no annual benchmarksfor that part of the series. The challenge is to extendthe series beyond the end of the last benchmark,tracking the likely future ANA estimates so thatfuture revisions are minimized while preserving theshort-term movements in the quarterly source data (tothe extent possible).

2.55. Finally, during the operational phase, there arecontinuing cycles of revisions to quarterly indicators,revisions to annual benchmarks, and the receipt ofannual benchmarks for the most recent years. Thisnew information needs to be incorporated in the QNAestimates as it becomes available.

2.56. The calculations applied to the data arediverse and depend on the characteristics of theseries. Some data will be received in a form readyto use without adjustment, but more commonlythere will be the straightforward manipulationsfamiliar in annual compilation—addition, subtrac-tion, multiplication (whether called scaling, gross-ing up, or quantity revaluation), and division (e.g.,deflation). However, the mathematical techniquesused to produce QNA estimates by combining aquarterly indicator and an annual benchmark seriesare more complex. Inevitably, the movements inany two nonidentical quarterly and annual serieswill differ. The challenge is to align the QNA esti-mate to the ANA estimate while preserving thetime-series properties of the data. This process—

Statistical Issues

23

called benchmarking—is not an easy matterbecause simple methods such as pro rata distribu-tion of the annual total introduce a discontinuity inthe series between years—the “step problem.”Benchmarking improves the quarterly data by tak-ing into account the superior annual information.

2.57. The proportional Denton benchmarkingtechnique with enhancements as presented in thismanual, is recommended as an integrated way ofdealing with these tasks for both the back and for-ward parts of the series. It gives results superior tothose methods that treat the back data in thepreparatory phase, the extrapolation phase, and thearrival of new benchmarks separately. In practice,the Denton technique can be readily automated sothat it is not time-consuming. It is worthwhile to setup the system correctly because using alternativemethods with step problems can undermine thetime-series properties that are the key focus ofQNA. The importance of good benchmarkingmethods increases as quarterly indicators showmore divergence in movements from annual data.The Denton method with enhancements is pre-sented in Chapter VI, along with some discussionof its implications and the alternatives.

2.58. It should be emphasized that in the case ofincorporation of revised or new benchmarks, thecalculations should be based on the original quar-terly indicator, not on the preliminary QNA esti-mates that have already been adjusted. Otherwise,the compilation process risks deteriorating into anunorganized data hashing, in which the compilerslose track of the original data, the effects of bench-marking, and the effects of other adjustments.

2.59. To avoid introducing distortions in theseries, incorporation of new annual data for oneyear will generally require previously publishedquarterly data for the past several years to berevised. This is a basic feature of all acceptablebenchmarking methods. As explained in paragraph6.30 and as illustrated in Example 6.3, in additionto the QNA estimates for the year for which newannual data are to be incorporated, the quarterlydata for one or several preceding and followingyears may have to be revised. In principle, previ-ously published QNA estimates for all precedingand following years may have to be adjusted tomaximally preserve the short-term movements inthe indicator if the errors in the indicator are large.However, in practice, with most benchmarking

methods, the impact of new annual data will grad-ually diminish until it no longer has any impact onsufficiently distant past years. With the recom-mended proportional Denton benchmarking tech-nique, the impact on data for proceeding years willnormally become insignificant after three to fouryears. One of the advantages of the Denton tech-nique is that it allows for revisions to as many pre-ceding years as desired.

6. Relationship between QNA and Source DataStatistics

2.60. As a consequence of benchmarking and cal-culations in the QNA compilation process, theQNA data may differ from the source statistics.Subjecting data to a balancing process in a com-modity flow or SU framework will also generatedifferences with the source data. Users may findthese differences puzzling and awkward, andefforts should be made to work the differences backinto the source data. Certain limitations may apply;for instance, the implicit deflator of household con-sumption in the QNA may differ from the consumerprice index (CPI), owing to differences in coverageand differences caused by the use of different indexformulas. However, if the variables in the QNA arebasically identical to those in the source statistics,consistency should be pursued. Owing to consis-tency requirements, this consistency should besought through adjustments in the source statistics.For instance, output and value added data from aproduction index should tally with the correspond-ing data from the QNA. At the very minimum,causes for differences should be explored, and theyshould be documented in a way that facilitatesaccess by users.

2.61. Initially, working the differences resultingfrom the QNA compilation process back into thesource statistics may not be popular with the com-pilers of these statistics, if only because this wouldentail a revision process that they may not be accus-tomed to. However, compilers of source statisticsmay come to accept that adjusting their statistics tothe QNA is beneficial to the consistency of the sta-tistical system and to the quality of their own sta-tistics. One important effect of adjustment may bean increased awareness among the compilers ofsource statistics of the need to ensure consistencybetween data from high-frequency statistics(monthly and quarterly data) and annual data; thesecompilers may also be encouraged to apply bench-marking procedures. Discussions with the compil-


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ers of source statistics about the differences willmost likely increase their involvement in the waytheir data are used in the QNA compilation process.For instance, they may develop an interest in par-ticipating in the deliberations during the balancingprocess, for which they could provide valuableinput. Obviously, the adjustment process of theQNA source statistics will be easier to establish if asimilar process is in place for the ANA. If this is notthe case, starting a QNA system is a good opportu-nity to initiate an adjustment process for the ANAsource statistics as well.

C. Dissemination

2.62. Dissemination of QNA has much in commonwith dissemination of other statistics, and generalguidance can be found in the IMF’s SDDS andGDDS. These standards center on integrity, andimportant themes include avoiding nonstatisticalinterference with the data, simultaneous release to allusers, general accessibility of the data, and trans-parency. These issues are mentioned in Chapter I andelaborated on in Chapter XI.

2.63. This section focuses on some QNA-specificdissemination issues, especially concerning releaseand presentation. With regard to release, owing tothe nature of QNA and their importance for decisionmaking, the predominant condition is that therelease should be fast. Rather than spending time onpreparing and printing a glossy and comprehensivepublication, the emphasis should be on releasing theQNA data as soon as they are available or, if arelease calendar is in place, on the scheduled releasedate.

2.64. Thus, the first release may be a rather limitedone, focusing on the most important data. Forinstance, the focus could be on GDP growth in cur-rent and constant prices—both seasonally adjustedand nonadjusted—as well as on trend estimates. As afurther extension, it could include breakdowns ofexpenditure categories and industries. Also, it isimportant to mention the most important revisionsconcerning earlier releases (see Chapter XI for moreon this subject).

2.65. The quickest ways to release these data arethrough a press release and the Internet. The pressrelease text should be short (as a rule, not longerthan one typed page) and ready for use without

rewriting. These conditions promote acceptance bythe media and also prevent misrepresentation byhasty or less knowledgeable media staff. Mediaoften mention the source of press releases, whichmay generate the perception that the publishedarticle reflects the view of the statistical agency.Thus, it is important to prepare press releases in away that prevents tinkering with the text by themedia. Try to have a catchy heading; if the pressrelease does not have one, the media will make oneup that might be more creative than statisticianswould like. Also, because the media shorten arti-cles by simply removing text at the end, the mostimportant news should be first. Furthermore, it isadvisable to support the press release with a smalltable containing the most important data. For easyrecognition by the general public, it makes sense tostandardize such a table and to consult with mediastaff about its content. Consulting with the mediaabout press releases is good advice in general.Publication through the Internet should be simulta-neous with the press release, and to promote speedit could simply have the same text. Preparation ofthe releases should start as early as possible andneed not wait until all the publishable data areready; usually an impression of the important newscan be developed on the basis of the data thatbecome available in the last phases of the compila-tion process.

2.66. Many countries also publish a more com-prehensive quarterly statistical publication dedi-cated to the QNA. These publications provide amore thorough analysis of the data, supported bycharts depicting the economic developments invarious ways. Pie charts depicting contributions toGDP growth from demand categories or fromindustries are often used; such charts are usuallybased on seasonally adjusted constant price data.Column diagrams showing the composition ofGDP and the changes in this composition are alsooften published.

2.67. The extent to which statisticians comment onthe data differs among countries. In some countries,statistical offices basically provide only the datawith technical explanation as needed; in other coun-tries, statistical organizations see it as their task tointerpret economic developments. Either way, keepclose to the facts to avoid giving the impression thatthe statistical agency wishes to influence publicopinion by taking a position on economic and polit-ical issues.

Dissemination

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D. Managerial Issues

1. General

2.68. Management of QNA differs from that of ANAbecause of the greater intensity of work and tightnessof deadlines. Also, compilation of QNA is more cre-ative because more assumptions need to be used andmore use is made of indirect indicators, with less“bean counting.” This implies a need for staff with asolid economic background. As well, because of themore intensive use of mathematical techniques, somestaff with a background in mathematical statistics areneeded.

2.69. As mentioned before, QNA can only startwhen sufficient quarterly source data are available.These source data are more efficiently managed inthe compilation of QNA when they are available inelectronic databases.

2.70. There is no single best way of organizing QNAcompilation. Each country develops its systemaccording to its own experience and circumstances.The objective of this chapter is to raise some issuesfor consideration rather than to give recommenda-tions or answers.

2.71. The pattern of workload peaks is quite differ-ent for QNA than for ANA. A statistical office thatproduces only annual estimates is accustomed to aproduction cycle spread over a year. The annual esti-mation may often have some clustering of taskstoward the end of the cycle, and there may be tightdeadlines to be met. In a quarterly compilation sys-tem, the workload is typically relatively low at thebeginning of each quarter because data on the previ-ous quarter are not yet available and compilation ofthe preceding quarter should be finalized.

2.72. For both ANA and QNA compilation, datafrom a wide range of sources are brought together.Data are sometimes collected by national accountantsthemselves; more typically, data come from otherparts of the same organization or from other organi-zations. The sequencing and timing of QNA compi-lation are complex because it needs to be built aroundthe arrival of the results from numerous collectionsand suppliers.

2.73. An important organizational issue to be dealtwith at an early stage concerns the release cycle—the timing of the first release of the data on a quar-ter and of subsequent revisions. In a QNA system

that is linked closely to the ANA, as promulgated inthis manual, the release cycle will also depend onthe release cycle of the ANA. As mentioned inChapter I, it is best practice to publish first resultswithin the next quarter. After the first release, revi-sions are usually needed, depending on, amongother things, the arrival of new or revised sourcematerial and, eventually, the arrival of annual data.The release cycle derives directly from the revisionpolicy, which is discussed in Chapter XI.

2. Timing of the Compilation Process

a. Structuring the compilation process

2.74. Sequential and “big bang” processing are alter-native ways to structure the compilation process. Thesequential approach involves processing in stages(data entry, basic checks, aggregation at lower levels,deflation, seasonal adjustment, overall aggregation).In contrast, with the big bang approach, the data areentered and the whole system is run simultaneously;the results are then viewed in detail in the context ofthe aggregate trends. This may be done iteratively sev-eral times as new data arrive and adjustments aremade. In practice, there may be some blending of thesetwo approaches. Some of the considerations to betaken into account in designing the processing systemare whether the source data arrive within a short periodof time or over several weeks, how much checking ofsource data is necessary, and the nature of the com-puter system being used. The big bang approach lendsitself to SU methods because it emphasizes interrela-tionships between different data.

b. Planning workloads

2.75. Because the point of QNA is timeliness,deadlines are necessarily short and tight. Thismeans that QNA compilers are subject to pressure.QNA compilation is also particularly vulnerable toproblems like delays in major data inputs or bugs incomputing systems.

2.76. To deal with timing problems, a quarterlywork schedule should be drawn up. The scheduleshould take into account the agreed-upon releaseschedule, the expected time of arrival of each of therequired data sources, the period required to carryout each process, and the flow of data from onestage to the next. In this way, it is possible to predictwhen the results will be ready for publication. It willalso help in identifying the sequence of tasks andcalculating the effects of delays. The work scheduleshould identify the following:


26

• the data inputs and when they are expected toarrive;

• the tasks of the national accounts compilers,including how long each task is expected to takeand the order in which they are carried out; and

• the delineation of responsibility for each task.

2.77. The work schedule should account for unfore-seen delays. As discussed in Chapter XI and asrequired by the SDDS, release dates should be prean-nounced. However, unforeseen problems occur andfailure to release the estimates as announced may cre-ate suspicion of manipulation for political reasons.When compilers first start compiling QNA, there is agreater potential for unforeseen problems. Therefore,countries might initially provide for a longer compi-lation period and greater margin for delay and gradu-ally increase timeliness as they gain QNAcompilation experience.

c. Methods of speeding compilation

2.78. Because source data are often released onlyafter the end of the quarter and QNA are producedquickly, compilation is necessarily concentrated in ashort period. This situation makes accelerating jobsparticularly important. Compilation can be speededup in a number of ways.

2.79. First, it is important to reduce peaks in pro-cessing workloads. One way to reduce the burdenduring the peak processing period is to do as muchwork as possible in advance. For example, monthlydata for the first one or two months of the quartercan be processed early. Similarly, it may be possi-ble to implement revisions made to data for earlierquarters before compilation for the new quarterbegins. Some problems in data can be foreseen anddealt with in advance. For example, if a series willbe rebased or its coverage changed, it may be pos-sible to set up a program that splices together theold and new series before the data become avail-able.

2.80. Second, QNA often achieve earlier releaseby improving the arrangements for the supply ofsource data. Data suppliers may be able to providepreliminary data. Data may be supplied by fastermethods, such as by e-mail, on a shared database,on diskettes, or on printouts rather than in a morepolished publication that takes longer to produce.Also, data should be supplied in the most efficientformat, with the data in the required order andexcluding irrelevant data.

2.81. Third, printing of statistical publications canbe slow. Timeliness is more important for QNA, so itmay be necessary to develop dissemination proce-dures as discussed in Section C of this chapter.

2.82. The practice runs recommended above willalso help to identify general problems that wouldcause delays and undermine punctuality.

3. Organizing Staff

2.83. The topic of organizing staff needs to be consid-ered according to circumstances in each country.Concerns include the agency involved in compilingQNA, the unit compiling QNA, the number of staffinvolved, the organization of this staff, and the place ofthe QNA unit (if there is one) in the compiling agency.The most common situation is for all national accountsdata, including QNA, to be compiled in the nationalstatistical office, often by the same part of that institu-tion. In some countries, compilation of quarterlyaccounts is done in the central bank. In some cases,QNA estimates are done by yet another organization,such as a research institute. Unless there are particularproblems with staff and other resources, it is generallyundesirable to have different organizations involvedbecause of the potential problems of inconsistent dataand methods as well as the loss of synergies betweenthe annual and quarterly systems.

2.84. All too often, the national accounts compilerswill have little say in the total number of staff,although they may be able to determine the allocationof staff between quarterly and other activities.Obviously, a small staff means a much more basicquality of estimation and a lower level of detail andtimeliness.

2.85. The organization of national accounting divi-sions varies. In a small organization, there may be nodivision. In a larger organization, units can be dividedin one or more of the following ways:• detailed sources/integrating data and working on

aggregates;• quarterly data/annual data;• industries/expenditure components/income com-

ponents;• current price data/constant price data; • orientation on process/orientation on product; and• development and analyses/operational work.

2.86. Some of the considerations regarding allocationof staff are balancing peaks and troughs in workloads,linking common subject matters and techniques, and

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having teams that are easy to manage (too large makescommunication harder, too small means fewer skillsand more vulnerability to absences and departures).When related issues are dealt with by different teams,there is a risk of duplication or conflicting opinionsabout methods.

2.87. An important organizational choice to be madeis whether there should be a unit focused specificallyon QNA or whether QNA or annual national accountsshould be compiled within the same unit by the samestaff. The pattern of workload peaks is quite different,so peaks in the annual compilation may not crowd outactivities in QNA (and vice versa). An advantage ofcombining both functions is that harmonizationbetween QNA and ANA is more likely if the samestaff are working on both.

2.88. When setting up a new QNA system, it is oftendesirable to identify a separate QNA team.Otherwise, the developmental work may be ham-pered if staff are continually being called to other,more urgent, tasks. The development of a new systemrequires a high level of conceptual ability, so the staffshould have a good knowledge of the 1993 SNA andthe annual compilation system. Some staff with goodbackground knowledge on monthly and quarterlysurveys may complement the knowledge of ANAcompilers.

4. Organizing Data Supply

2.89. National accounts are unique in their use ofmany data sources from different agencies. Becausethe timing of QNA is typically more crucial than thetiming of ANA, coordination with data suppliers isone of the important tasks of the QNA compiler. Thisissue is discussed in Section D.2.c. of this chapter inthe context of speeding compilation.

2.90. National accountants need to be in close contactwith their suppliers so that both sides understand theother’s needs and problems. The timing, content, andformats of data supply can be arranged. Data sourcescan have changes in base year, coverage, definitions,procedures, and classifications that need to be identi-fied in advance so that there is no unpleasant surpriseduring data compilation. Data suppliers can also begood sources of information on what is happening inthe economy, shortcomings of the data, and how todeal with problems such as breaks in the series.

2.91. Data suppliers are not always aware of howtheir data are used. It is the responsibility of national

accountants to provide them with this informationthrough meetings or discussions. In some countries,national accountants run seminars or courses for datasuppliers.

5. Managing Data Compilation Systems

2.92. For QNA data, the time-series dimension is thedominant feature of the data. Thus, any computersystem for compiling QNA estimates must be time-series oriented. Box 2.3 sets out the main elements ofa compilation system built on time-series-orienteddatabase software. Most elements are also relevantfor spreadsheet-based systems.

2.93. National accounts data processing systems aredeveloped to meet the situations of each country. Asnoted in paragraph 2.5, some countries have separateQNA and ANA systems while others use the samesystem. Some countries base their national accountsprocessing system on spreadsheets such as Lotus orExcel. For large-scale systems, a processing systembased on a general database package is preferable.The structure of a database package is built on dataseries and algorithms to manipulate them. In contrast,the structure of a spreadsheet is based on individualcells linked by formulas. The large volumes of datainvolved in national accounts compilation favor theuse of databases. Databases are more efficient in han-dling large volumes of data and are also more suitablefor handling data transfer to and from seasonaladjustment and benchmarking packages. In spread-sheets containing massive amounts of numbers, mak-ing errors is easy and tracing them difficult. Transferof data between spreadsheets is clumsy, and it is hardto keep track of different versions of data.Spreadsheets also make it difficult to change compi-lation methods and to ensure that changes are cor-rectly put through.

2.94. Accordingly, as a general guideline, spread-sheets are useful in small-scale tasks like develop-ment work, pre-editing, and summary measures. Asthe system moves from development to operations, itis desirable to shift to a compilation system built ondatabase software and use it for the large-scale tasksof data storage, calculations, seasonal adjustment,and benchmarking. A database system should allowfor receiving and downloading data in spreadsheetformat, which will facilitate transition from aspreadsheet-based QNA system and assist in dataexchange with suppliers and users. With good inter-faces, it is also possible to have mixed systems thatuse spreadsheets for some functions, such as data


28

supply or editing charts, while using a database forothers, such as large-scale storage and calculation.

2.95. The core of a national accounting processingsystem built on database software is generally ageneral-purpose, commercially available databasepackage. A custom-made interface to the databasemay be needed to ease data exchange between thedatabase and other software packages; smaller tailor-made compilation modules may also be needed.Access, Oracle, Sysbase, and dBase are relationaldatabase packages specialized for cross-sectionaloperations. In contrast Fame, Dbank, and Aremos arespecialized for time-series operations. None of thedatabase packages currently available is optimal forboth types of operations. Time-series databases treatall data objects (data arrays or data vectors) as timeseries and are particularly suitable when the timedimension is the dominant feature of the data, such asfor QNA. Relational databases are more suitablewhen the time dimension is not the most importantfeature of the data. Compilation of SU tables and edit-ing and aggregation of microdata are examples ofoperations best undertaken with relational databases.

2.96. A well-thought-out naming structure for theseries is essential for the functionality of a compila-tion system built on time-series-oriented databasesoftware. The naming structure determines how thedata are organized and thus how to navigate withinthe database. The structure should be easy to under-stand, follow the classification system, show the typeof data (frequency, value/price index), and show thestage of processing. Other aspects of a well-designedsystem include well-documented programs and easyoperation of the system. The programs should be doc-umented by descriptive files and by comments andnotes within the programs themselves. Finally, thesystem should be able to be run by national accountscompilers, rather than by computer specialists with-out any national accounts expertise.

2.97. In a spreadsheet-based system, or in spread-sheet components of a system otherwise built ondatabase software, some good practices to be fol-lowed include these:• Separate sheets should be used for data entry and

subsequent stages of processing. Each figureshould be entered only once and subsequentlyalways referenced by links so that all consequentialchanges are made in the event of revisions.

• Documentation of sources, processes, assump-tions, and adjustments to assist later compilers

should be included in spreadsheets as text or notes.Data should have headings that describe the seriesand its units.

• Standardized formats should be used for all parts ofthe system (e.g., basic sheets for input, deflation,checking, aggregation; time series as either rows orcolumns, not both; several years of data should bevisible on the screen; choose millions or billions,not both). The formats should be designed for com-patibility with input formats required by seasonaladjustment and benchmark tasks that need to bedone outside the spreadsheet.

• Multiple layers of worksheets should be used toshow stages separately while allowing links torelated stages.

• Color and font options should be used to separateinputs, outputs, data that have a different referencebase (to facilitate later changing of the base), and editchecks.

• Spreadsheets should be dated (e.g., printedcopies can be dated by using the Excel function“=today()”). Backups of previous versionsshould be stored. One option would be to store

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Box 2.3. Elements of a QNA Processing SystemBuilt on Database Software

The core of a well-designed computer system for compiling QNA esti-mates should contain the following main elements:

• Databases for data input� A set of databases for storage of monthly quarterly and annual

source data� A database for storage of ANA estimates� A set of databases for storage of annual source data

• Compilation routines� Benchmarking of time series of indicators to time series of

annual data—quarterization and extrapolation� Deflation/reflation� Source data assessment procedures—tracking on a detailed

level, editing� Compilation system assessment procedures—simulations on

historical data/tracking on an aggregated level� Reconciliation/comparison of GDP estimates from the production,

expenditure, and income sides� Seasonal adjustment (link to X-11-Arima and/or X-12-Arima)

• Databases for storage of compiled QNA data� Database(s) for official published data � Archived copies of previous quarters—published data, to facilitate

studies of revisions� Working databases for unpublished estimates� Storage of alternative versions of data (i.e., both before and after

adjustments/revisions) to facilitate verifiability and checking• Routines for tabulation of the data to construct publication tables and

for transferring data to diskettes and external databases

all the spreadsheets from a quarter in a singlefolder to separate them from other quarters with-out having to rename each file. As well, the prac-tice of automatic overwriting of previousversions means that a mistake may be hard toundo. Within each quarterly run, it may be saferto rename files each time they are changed (e.g.,“Manufacturing Aug22-B” for the second time itwas saved on August 22; after completion, thelast version could be archived and the othersdeleted).

• Files and worksheets should have meaningfulnames (e.g., not “Sheet1” and “Sheet 2” but “CPIData Entry” and “CPI Rereferencing”).

• Formulas should be double-checked to see thatthey do what was intended and have not been unin-tentionally affected by other changes.

• The chart facility of the spreadsheet packageshould be used frequently.

• Row and column headings should always be visible(in Excel, applying the “split” command followedby the “freeze panes” option achieves this result).


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31

III Sources for GDP and its Components

A. General Issues

1. Introduction

3.1. This chapter deals with the process of identifi-cation and assessment of quarterly data sources.Because circumstances differ, it is not possible tocreate a standard set of sources that can be appliedin all countries. Rather, the approach taken in thischapter is to describe the alternatives that are usedin quarterly national accounts (QNA) compilationin various countries and some of the considerationsthat need to be taken into account in choosingamong them.

3.2. In general, the same principles for designingsources and methods apply to both annual nationalaccounts (ANA) and QNA. Accordingly, this chapterdoes not seek to provide a general introduction tonational accounts sources and methods. Rather, itdeals with issues that are specific to or are of height-ened importance in a QNA context.

3.3. This section deals with general issues that applyto more than one component of GDP compilation.The remaining sections of this chapter cover the com-ponents of each of the production, expenditure, andincome splits of GDP. Even if expenditure or incomedata are incomplete, it may still be possible to derivea useful split of GDP by type of expenditure orincome, as noted in Chapter II. For the productionapproach, the presentation in this chapter is by typeof indicator, because there are common issues in datasources that cut across a wide range of industries. Incontrast, a presentation arranged by output, interme-diate consumption, and value added would not showthe links between the compilation of these items, anda presentation by industry would be repetitivebecause some issues apply across many industries.The other approaches are discussed by component—expenditure by household consumption, governmentconsumption, and so on; income by compensation of

employees, operating surplus, and so on. Some indi-cators are used in more than one approach; for exam-ple, the same construction indicators are used for theconstruction industry in the production approach andfor capital formation in the expenditure approach. Inthese cases, specific issues for such indicators are dis-cussed under the heading of expenditure.

2. Data Sources

3.4. The basic principle in selecting and developingQNA sources is to obtain indicators that best reflectthe items being measured. In some cases, source dataare available in a form ready for use in the ANA orQNA with little or no adjustment. In other cases, thesource data will differ from the ideal in some way, sothat the source data will need to be adjusted. Theseadjustments may typically be established for one or afew main benchmark years for which additionalsources such as the results of more comprehensiveand detailed surveys or censuses may be available. Inthese cases, the annual and quarterly time series areanchored to these main benchmark years and the reg-ular source data are used as indicators to update thebenchmark estimates (extrapolation or, equivalently,forward carrying of the benchmark adjustments). Asthe ANA provide the benchmarks for QNA theyshould be the starting point in selecting and develop-ing QNA sources. In some cases, the same sourcesthat are used annually or for the main benchmarkyears may also be available on a quarterly basis, mostcommonly foreign trade, central government, andfinancial sector data. More commonly, QNA datasources are more limited in detail and coverage thanthose available for the ANA because of issues of dataavailability, collection cost, and timeliness. For eachcomponent, the available source that best captures themovements in the target variable both in the past andin the future constitutes the best indicator.

3.5. The use of an indicator implies an assumptionthat it is representative of the target variable. The best

strategy is to make such assumptions explicit andreview them regularly. When assumptions are notmade explicit, there is a greater risk that they are notbeing carefully evaluated. As well, the economic con-ditions that underlie an assumption may be initiallyrealistic, but later change, so the assumptions need tobe reviewed from time to time.

3.6. The suitability of an indicator can be assessedqualitatively by looking at the differences from the tar-get variable in coverage, definitions, and so on. Thereare a range of possibilities for the closeness of the indi-cator and the target variable. After the ANA datasources themselves, the most desirable indicators dif-fer only slightly from those used in the ANA, forexample, by being based on a sound sample but withless detailed data. Less satisfactory are indicators thatcover only a part of the total, such as the major prod-ucts or largest establishments in an industry. Even lesssatisfactory as indicators are those that measure some-thing related to the process or population of the targetvariable, but less directly, such as labor inputs as anindicator of service industry outputs. Least acceptableare indicators that apply past trends or measure some-thing that is connected to the target variable only by abehavioral relationship or statistical correlation. Suchindicators should be avoided because the underlyingrelationships can be expected to be less stable than isthe case for an indicator with a direct intrinsic rela-tionship to the target variable.

3.7. The indicator and the assumptions behind its usecan also be assessed quantitatively by comparing thegrowth rates in the annual sum of the quarterly indi-cator with growth rates in the corresponding ANAestimate. Equivalently, the ratio of the ANA estimateto the sum of the quarterly indicator shows the rela-tionship between the two series as a single figure,which in this manual is called the benchmark-indicator ratio. (The process of indicator assessmentis described in depth in Chapter II.)

3.8. A stable benchmark-indicator ratio shows thatthe indicator represents the movements in the targetvariable well. Changes in the ratio may point to prob-lems and help identify ways to improve the indicatorin the future. The benchmark-indicator ratio does nothave to equal one, as differences between the levelsof the annual estimate and the quarterly indicator caneasily be solved by multiplication. For example, aquarterly indicator in the form of an index can read-ily be converted to a money value. This lack of con-cern about levels is an important difference in focus

between QNA and ANA compilation: while estab-lishing correct levels is essential in ANA compila-tion, levels in QNA can be derived from the ANA.The essential task in QNA is to obtain the datasources that provide the best indication of quarterlymovements.

3.9. Even with careful selection of the most suit-able indicators and improvements to data sources,benchmark-indicator ratios will vary over time,because indicators are not fully representative ofthe target variable. Chapter VI deals with the math-ematical processes used to make a QNA estimatethat follows the movements of the indicator asclosely as possible while being fully consistentwith the levels and growth rates of the annual esti-mates. Use of fixed ratio adjustments is anotherway of using an indicator in conjunction with abenchmark. However, the adjustment of indicatorsto the levels of the annual data should be donethrough the benchmarking process, not using fixedratios, because benchmarking takes into accountchanges in the ratios as smooth changes and soavoids step problems. (This issue is discussed inmore detail in Section D.1 of Chapter VI.)

3.10. Two or more indicators may be available forthe same item. In some cases, the indicators mayrepresent different parts of the item. For example,clothing may have separate indicators for men’s,women’s, and children’s clothing. In these cases,the best solution is to split the annual data into eachcomponent and benchmark each indicator andcomponent separately. If that is not possible, thecomponents should be added or weighted togetherto form a single indicator before benchmarking.Alternatively, if the various indicators do notrepresent different parts of an item but rather arealternative indicators, the one that is most represen-tative in terms of concept and past annual move-ments should be adopted. If they are equallysuitable, the indicators could be added or weightedtogether to produce a single indicator.

3. Issues with Surveys

3.11. A common problem for surveys is the delay inthe inclusion of new businesses and deletion of non-operating businesses in survey frames and estimationprocedures. This problem is more serious for QNAthan for ANA because of the more limited collectiontime for the quarterly source data and because theinformation needed to update the survey frames maybe more limited on a quarterly basis. The continuing

III SOURCES FOR GDP AND ITS COMPONENTS

32

process of births and deaths of establishments andenterprises occurs in all industries but particularly inthose with a large number of small-scale, short-livedestablishments, such as retailing and consumer ser-vices. Births and deaths of establishments and enter-prises are an important factor in changes in the overalltrends. In fact, growth often occurs largely throughincreases in the number of businesses rather thanthrough growth in the output of existing businesses.Moreover, new businesses are particularly likely tohave higher rates of growth and high levels of capitalformation (particularly in the start-up quarter), as wellas being more likely to be established during eco-nomic upturns. Closed businesses are included in thescope of surveys but may be misclassified as nonre-sponse. Because of these factors, quarterly businesssurveys should be designed to reflect changes in thepopulation of businesses or they will tend to under-state growth for a booming economy and understatedeclines for an economy in recession.

3.12. For the survey results to reflect changes in thepopulation of businesses, the following considera-tions need to be taken into account when designingbusiness surveys:• The business register that provides the population

frame1 for the survey needs to be updated on a con-tinuous basis to ensure complete coverage of theentire population of businesses in the frame.

• New businesses should be incorporated in the sur-vey as soon as they start, either by drawing supple-mentary samples of new businesses or redrawingthe sample for the whole population.

• Deceased businesses need to be separated fromnonresponding businesses in the original sample.The contribution of deceased businesses to theirindustry should be recorded as nil; for nonrespond-ing businesses, values should be estimated.

• For each industry, the original sample and the sup-plementary samples should be stratified by size,location, age, and other dimensions of businessesthat may explain major variations in the level andgrowth rates of the target variable for each businessfor which corresponding population-wide informa-tion is available in the frame. Different stratifica-tion principles may have to be used for new andcontinuing businesses in cases where the availablepopulation-wide information differs for the twosubgroups.

• The estimation procedure should be level oriented,not index oriented, because the introduction of newbusinesses and products is more difficult in an indexframework. In contrast to an index formulation, alevel formulation of the estimation procedure allowsdifferent grossing-up factors to be used for differentparts of the sample. Levels can be easily convertedto indices for presentation purposes.

3.13. If new businesses cannot be incorporated in thesurvey as soon as they start or there is a large infor-mal economy, household labor force surveys mayprovide information that can be used to adjust incom-plete coverage of business surveys. To be useful forthis purpose, household surveys should include ques-tions about the kind of work done and the number ofhours worked by each resident of the household, aswell as information that allows the place of employ-ment to be identified from the business register, ifpossible. The survey should include each positionheld by those with more than one job. Business sur-veys would need corresponding questions about thenumber of employees and the number of hoursworked. The comparison of labor force and businesssurvey results would give adjustment factors forundercoverage in business surveys. The adjustments,or grossing-up procedures, should be conducted at adetailed industry level with stratification by dimen-sions that explain variations in the ratio between thetarget variable and the grossing-up factor. If used toderive measures of business survey undercoverage inthis way, monthly or quarterly labor force surveyscan be an important data source for QNA.

3.14. Infrequent changes in survey frames or otherchanges in survey methodology can lead to distor-tions in the time-series qualities of the QNA.Movements in the indicator will be misleading ifcaused by changes in survey methods or coverage,rather than actual changes. In these cases, it is essen-tial to separate the causes of movements in the data.If an overlapping period is available for both the oldand new survey bases, it would be possible to sepa-rate the effect of frame and method changes from thequarterly change. In the case of changes in the frame,the adjustment should be allocated over all the peri-ods since the frame was last updated. For otherchanges in methods, the old and new series would belinked by a factor to take into account the effect of thechange. If it were not possible to have an overlappingperiod, adjustments could be based on indicators notaffected by the change, sometimes including thehousehold labor surveys mentioned in the previous

General Issues

33

1The sources of information available to update the business registerdepend on the legal and economic conditions in each country. Sourcesinclude business licenses, taxation registers, business bank accounts,and telephone directories.

paragraph, or derived from any other available infor-mation comparing the old and new survey bases.

4. Issues with Administrative Byproduct Data

3.15. Administrative byproduct data tend to be usedmore in QNA than in ANA. These data are derivedfrom information gathered in the process of govern-ment taxation or regulation, rather than from a surveydesigned for statistical purposes. For example, taxa-tion and control of foreign trade, taxation of payrollsand collection of social security contributions, andregulation of particular activities such as transport orland transfer all generate information that can be use-ful for QNA purposes. As these systems weredesigned with other objectives than obtaining statis-tics, there may be limitations from a nationalaccounts perspective in matters such as coverage,units, data definitions, period covered, and level ofdetail. For these reasons, direct statistical collectionsmay be preferred for annual data. On the other hand,if the administrative information has already beencollected, the costs and response burden associatedwith a survey can be avoided. As well, governmentsoften ensure high or even universal compliance on atimely basis. However, timing problems from differ-ences in periods covered can become be a problemwith administrative data and can be more severe inQNA, as any timing difference is relatively larger ina quarterly context. For example, a biweekly systemcould have six two-week periods in some quartersand seven two-week periods in others.

3.16. An important type of administrative data forQNA is from value added tax (VAT) systems (alsocalled “goods and services tax” in some countries).VAT systems collect monthly or quarterly data onsales and purchases as part of the tax collectionprocess. The data may also be suitable for statisticalpurposes and are being used in an increasing num-ber of countries. VAT systems have the benefit ofoffering comprehensive or, at least, very wide cov-erage. Since the VAT system would collect informa-tion in any case, the extra cost and burdens ofstatistical collections can be avoided. However, VATsystems are not always designed with statisticalobjectives in mind, so there may be problems withregard to national accounts requirements on issuessuch as timeliness, timing, tax exemptions, industryclassifications, units, the effects of rebates or back-dated assessments, and limited product detail.2

Because VAT is usually collected from legal entities

rather than establishments, VAT data from multi-industry enterprises lacks industry detail. VAT datafor the single industry enterprises could be supple-mented by a survey of multi-industry enterprises. Ifsuch a survey is not possible, data by industry ofenterprise could be used as an indicator of data byindustry of establishment. There may also need tobe extensive communication with the tax collectionauthorities to understand the data, to produce tabu-lations in a form suitable for national accounts com-pilation, and to make adjustments to tax forms andprocedures to better meet statistical objectives.Other product tax systems may also provide data onthe underlying flows of taxable products, such asalcohol and petroleum.

5. Sources in the Absence of Surveys orAdministrative Data

3.17. If no statistical collections or administrativedata are available, industry associations, industryexperts, or leading enterprises in a particular industrymay be able to assist with finding or making quarterlyindicators.

3.18. If no quarterly indicator is available, there isstill a need to fill gaps to ensure a comprehensivetotal. Ideally, these gaps will be few in number, rep-resent a small proportion of the total, and be closedlater as other data sources become available. Amongthe alternatives for such items are use of:• a somewhat related item as an indicator;• totals of a wide range of other items as an indicator;• the overall economy as an indicator; or• mathematical methods based on distribution of

annual data and extrapolation of past annualtrends.

3.19. In choosing among alternatives, past patternsin the annual data for that variable can be used as aguide. If a series is volatile and related to the eco-nomic cycle, growth rates of the rest of the economycould be a suitable indicator. If the annual series doesnot relate to fluctuations in the rest of the economy, agrowth rate based on past trends may be suitable.Extrapolation on the basis of past trends is generallynot desirable, as it tends to hide the actual data oncurrent trends. If there really is no suitable indicator,a simple method that is transparent may be moreappropriate than something that is time-consumingand complicated but not necessarily any better.Mathematical techniques for generating syntheticdata in the absence of indicators are discussed inChapter VII.


34

2Some product details may be available if different tax rates are applied.

B. GDP by Industry

1. General Issues3.20. The production approach is the most commonapproach to measuring quarterly GDP. To some extent,this may reflect the availability of data before the intro-duction of QNA. In addition, the production approachshows the industry composition of growth, which pro-vides a useful perspective on economic performance.The production approach is also particularly suitablefor deriving productivity measures because industriesfor which output volumes are poorly measured can beexcluded for this type of analytical use.

3.21. The general principles of deflation and choice ofdouble and single indicator methods are the same forQNA and ANA. The production approach involves cal-culating output, intermediate consumption, and valueadded at current prices as well as in volume terms byindustry. Because of definitional relationships, if twoout of output, intermediate consumption, and valueadded are available, the third can be derived residually.Similarly, if two out of values, prices, and volumes areavailable, the third can be derived. (See Box 3.1.)

3.22. Observed data on both output and intermediateconsumption at current prices may be available quar-terly in some cases; in these cases, the double indicatormethod for value added can be used. For example, insome countries, government-owned enterprises inindustries such as oil, transport, or telecommunicationsmay be economically significant and able to supplydata directly. Commodity flow methods may be used togenerate information on some specialized inputs, forexample, pesticides and fertilizers for agriculture. In asystem of quarterly supply and use tables, the requireddata can be generated on the basis of available data, pasttables, and national accounting identities.

3.23. However, the data required for the productionapproach are commonly incomplete on a quarterlybasis. Because compiling the production accounts atcurrent prices and in volume terms requires detailedaccounting information on both output and currentexpenses, the required data may not be available quar-

terly or may not be collected with the speed needed fortimely QNA compilation. Then the missing data mustbe estimated by using another series as an indicator.Most commonly, output data are available, while dataon intermediate consumption are not. In other cases,data on total intermediate consumption, component(s)of intermediate consumption, labor inputs, or capitalinputs may be available as indicators. The quality of theestimate depends on the assumption of a stable rela-tionship between the indicator and the target variable.

3.24. Relationships between inputs and outputs (input-output or IO coefficients) may change as a result oftechnological changes, differences in the seasonal pat-terns of outputs and inputs, or variations in capacity uti-lization caused by changes in the business cycle. Theimpact of technological changes may not be significantin the short term and can be handled through the bench-marking process if they happen gradually over a longerperiod. As discussed in Section D of Chapter VI, it ispreferable to use benchmarking rather than fixed ratios.The reliance on fixed coefficients is particularly unsat-isfactory for calculations at current prices because ofthe additional factor of changes in relative prices.

3.25. It is recommended that output, intermediate con-sumption, and value added—at current prices, in vol-ume terms, and the corresponding deflators—alwaysbe derived and published in a complete presentation. Insome countries, value added is derived directly, withoutexplicitly calculating output and intermediate con-sumption. This practice is undesirable for several rea-sons. It is not consistent with the 1993 SNA presentationof the production account or with supply and use tables.It reduces the analytical usefulness of the data. Also,because value added is not able to be directly observedor deflated, it encourages the use of inappropriate cal-culation or deflation methods when better options areavailable. It does not facilitate comparison of quarterlyestimates with subsequent annual output data or help inpinpointing weaknesses. As an example, compiling thefull production account by industry makes explicit theassumptions about IO ratios that might otherwise beimplicit or ignored. An assumption of fixed IO ratios atboth current and constant prices might be highlighted in

GDP by Industry

35

Box 3.1. Data for the Production Approach

Current price values Prices/price index Volumes/constant price values

Output � � �

Intermediate consumption � � �

Value added (usually derived indirectly) (usually derived indirectly) (usually derived indirectly)


36

implausible implicit price deflator movements, ordeflating value added by an output price index3 mightresult in unacceptable changes in IO ratios.

3.26. If data on intermediate consumption are notavailable, the preferred method is first to obtain an esti-mate of intermediate consumption at constant pricesusing constant price output as an indicator. Thismethod uses an assumption of a stable IO ratio modi-fied by annual trends in the ratio that are incorporatedthrough the benchmarking process. Intermediate con-sumption at current prices can then be derived byreflating the constant price estimate by price indicesthat reflect the product composition of intermediateinputs. In the likely event that there is not a specificproducer price index (PPI) for inputs, industry-specificintermediate consumption price deflators can be con-structed by weighting together relevant price indexcomponents from, for example, the consumer priceindex (CPI), PPI, and foreign trade price indicesaccording to the composition of inputs. A use table4 fora recent year would provide weights to derive industry-specific intermediate consumption deflators (or refla-tors). A more detailed level of reflation is preferable asit allows the effect of changes in the composition ofoutput to be captured in the estimates.

3.27. Output and value added should be estimated atbasic prices according to the 1993 SNA, although pro-ducers’ prices are an acceptable alternative. A num-ber of countries that follow the 1953 SNA or 1968SNA use factor cost valuation.5 Measurement of valueadded at basic prices is preferred in the 1993 SNA and

is increasingly common in practice. To derive GDPfrom value added at basic prices, customs duties,VAT, and other taxes on products are added and sub-sidies on products are subtracted. This measure isconsistent with the expenditure-based estimate ofGDP, while separating the processes of productionand taxation of products in the generation of GDP.6

2. Sources for Industries

3.28. Commonly used types of source data for theproduction approach on a quarterly basis include cur-rent price data from accounting and administrativesystems, quantity indicators, labor and other inputmeasures, and price indices. Most commonly, defla-tion will be used to derive a volume measure, that is,a current price value is divided by a correspondingprice index. Due to problems that are discussedbelow, deflation is usually preferable to direct mea-sures of volumes. In other cases, there may be vol-ume and price indicators only or current price valueand volume indicators only. Box 3.2 provides anoverview of the value and volume indicators mostcommonly used for the production approach.7

a. Current price data on outputs and/or inputs

3.29. Current price data can be obtained from account-ing systems through surveys or as administrativebyproducts. Accounting data are particularly suited forthe collection of aggregates. Compared with volumemeasures, these data have the advantages of being com-prehensive and cutting the costs associated with col-lecting detailed data, which reduces respondent burden.In contrast, quantities of different products need to becollected separately for each product, and there arepotential serious problems if new products are omitted.

3.30. The sources of accounting aggregates may bedirect surveys, published accounts, or administrativesystems for regulation or taxation.

3.31. For goods-producing industries, the values ofsales together with opening and closing values ofinventories of finished goods and work-in-progress8

are required to derive an output indicator. The simplestindicators cover only total sales of goods manufac-tured by the enterprise. A more sophisticated systemmay collect separate data by product group and/or

6Note that the effects of nonproduct taxes and subsidies on productionare reflected in basic prices along with other production costs.7The Organisation for Economic Co-Operation and Development(1996) provides information about sources in its member countries.8Output = sales + changes in inventories of finished goods and work-in-progress (excluding any revaluation effects).

3Unlike the other single indicator methods, deflation of value added byoutput price indices assumes that prices of inputs, outputs, and valueadded are all moving in the same proportions. Relative prices can oftenbe quite volatile because of factors such as changes in exchange rates,wage rates, profitability, and commodity prices. It is almost always pos-sible and better to• deflate output at current prices by the output deflator; then• estimate intermediate consumption at constant prices by using output

as an indicator (assumes a stable input-output ratio, although this willbe modified by annual trends by the benchmarking process); then

• derive value added as the difference between the estimates of out-put and intermediate consumption, all at constant prices.

This method requires no additional data; rather, it uses more realisticassumptions.4A use table shows use by industry of each product. When a use table isnot available, an industry-by-industry input-output table may be con-sidered as a less satisfactory substitute. An industry-by-industry input-output table shows the use by industry of the output of each industry,and it is less useful in this context because it is more difficult to relatethe price data (as they typically refer to products) and because productprices tend to be more homogeneous than industry prices.5The factor price concept has virtually been dropped in the 1993 SNAbecause factor cost does not correspond to observable prices in con-trast to basic, producers’, and purchasers’prices and is actually a mea-sure of income, not production.

establishment. (In establishment-level data for multi-establishment enterprises, shipments of goods and pro-vision of services to other establishments in theenterprise need to be recorded.) Other revenue, such assales of goods not produced by the factory, repairs, orrental services, might also be collected in total or sep-arately. Data on inventories used in calculations shouldhave the effects of valuation changes excluded.

3.32. Value data for construction projects are col-lected in some countries. If only the total value of aproject is available, it is necessary to allocate it overthe life of the project and exclude holding gains (seeChapter X). Otherwise, data are collected on value ofwork done during the quarter. Collecting this kind ofdata avoids the difficulties of making assumptionsabout the allocation of a total value for a whole pro-ject to particular quarters. However, the feasibility islimited by the availability of data, as constructionenterprises are often small scale and work done maybe hard to separate into quarters. Progress payments

for work done may be an acceptable approximation ifinterviews suggest that they approximate the value ofwork put in place. (Construction indicators are dis-cussed further in Section C.2 of this chapter.)

3.33. Sales data are commonly used as quarterly indi-cators for the output of wholesale and retail trade. Salesdata could be obtained from a business survey or as anadministrative byproduct of a tax on sales. Output atcurrent prices is defined as the trader’s margin, that is,sales less the replacement cost of goods sold.

3.34. Output at current prices of other business andconsumer services can be measured by turnover orsales. In some countries, there are surveys of sales ofservices such as restaurants, hotels, clubs, hairdressers,theaters, and repairers.

3.35. Government agencies are an important source ofquarterly accounting data for activities that they oper-ate, regulate, or tax. Publicly owned corporations are

GDP by Industry

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Box 3.2. Overview of Value and Volume Indicators Commonly Used for Quarterly GDP by Industry

Current price data Data on quantities on outputs and/or inputs of outputs and/or inputs Labor input measures Other indicators

Agriculture, forestry, X X Population (subsistence) fishing, hunting

Mining X X X Industrial Production Index (may bederived from range including output, quantities, and input)

Manufacturing, utilities X X X Industrial Production Index (may be derived from range including output, quantities, and input)

Construction X X Supply of building materials

Wholesale and retail trade X Supply of goods handled

Restaurants and hotels X X X

Transport, storage, X X Volume of goods transported and communications

Financial intermediation X X Value of loans/ deposits

Real estate, business services X X

Ownership of dwellings X Stock of dwellings (capital input)

Public administration X X Xand defense

Education, health, X X Xother services

Net taxes on products X Constant price value of relevant (including import duties,VAT) products (equivalent to applying

base year tax rates)

important in some activities, for example, transport,post, and telecommunications. General governmentdominates the service industries of public administra-tion, defense, and community services. Governmentregulation of activities such as banking, insurance, andhealth may give rise to quarterly value data. Sales infor-mation concerning products subject to a specific tax—gambling, for example—may be obtained fromgovernments. In some of these cases, it may be possibleto use the same methods used for the annual estimates;in others, a less detailed version may be acceptable.

3.36. VAT systems can supply helpful data that can beused for the production approach. In addition to thegeneral issues discussed in Section A of this chapter,VAT systems have the problem that they do not takechanges in inventories into account because the datacover sales (not output) and purchases (not intermedi-ate consumption). Also, purchases of goods and ser-vices that are deductible for VAT usually include bothcapital formation and intermediate consumption. Fornational accounts indicators, it is highly desirable toseparate these two components. Otherwise, the pur-chases data would not be usable as an indicator ofintermediate consumption because fixed capital for-mation is usually large, lumpy, or both.

b. Data on quantities of output and/or inputs

3.37. Data on quantities of output are available formany products. Quantities are easy to define for thegoods-producing industries, for example, metric tonsof wheat and coal, kiloliters of beer, and numbers ofcars. Less tangible quantities can be measured for otherindustries, for example, kilowatts of electricity, floorarea of construction, and ton-kilometers of freight.

3.38. The concepts of quantity measures and volumemeasures should be distinguished. Quantity data areexpressed in terms of physical units. Volume data areexpressed in terms of constant price values or volumeindices; these data differ from the quantity databecause quality changes are accounted for and becausethe measures can be meaningfully aggregated.Quantity data can be converted to constant price valuesby multiplying them by base year prices and makingadjustments (if any) for quality change.

3.39. In some cases, businesses can supply quantitydata more readily than they can supply financialinformation on a quarterly basis. The businesses maynot compile quarterly accounts, or they may takelonger to complete than simply collecting numbersthat do not require processing or valuation. Quantity

indicators can be multiplied by price indices or aver-age prices for the quarter to obtain current price indi-cators. Such estimates avoid the inventory valuationissues that arise for current price values that havebeen derived from data that include inventories mea-sured at historic cost.

3.40. The limitations of quantity data are significant,and quantity data should be avoided if products areheterogeneous or subject to quality change. The rangeof products in an economy is enormous, so the list ofproducts is limited to the major ones and is usually farfrom comprehensive. Products are not the same asindustries, so secondary production should be includedwith the industry of actual production, not with theindustry to which they are primary. The usefulness ofquantity data is limited by the homogeneity of theproducts. For basic commodities, such as wheat andbase metals, there is often relatively little variation inquality over time, particularly if data are broken downby grades of quality, so quantity indicators may besuitable. However, many products vary considerably inquality—that is, they are heterogeneous. For suchgoods, deflated current price data should be used. Thissituation applies to a large number of manufacturedgoods and to some agricultural and mining products.The more narrowly such products are defined, themore the estimates will be able to reflect the actual vol-ume of output. For example, if cars are treated as a sin-gle product, changes in the mix of output toward largercars or cars with more accessories or better quality willnot affect the number of cars but should be treated asan increase in the volume of output. There are manyproducts for which quantities are poor indicators or forwhich output is not readily quantifiable, such as cloth-ing, medicines, and specialized equipment. One wayof dealing with the problems of heterogeneity of prod-ucts is to collect extra detail, although it may not bepractical owing to greater collection costs, respondentburden, and delay in tabulation.

3.41. Quantity indicators are usually developed on acase-by-case approach for each industry, rather thanas a unified system. The following are some exam-ples of quantity indicators:• Agriculture: quantities are usually closely moni-

tored, heavily regulated, or subsidized by Ministriesof Agriculture. Quantity data for agricultural prod-ucts may be obtained from some point along the dis-tribution chain if the number of farms is large andthe distributors few. However, differences betweenquantity of products at the farm and quantity ofproducts at the distribution site can be caused by


38

wastage, timing differences, double counting,grower-consumed products, informal sales, andother factors. Conceptual issues associated with thetiming of agricultural production are dealt with inChapter X.

• Construction: floor area built, preferably dividedby type of building. (Indicators for construction arediscussed further under gross fixed capital forma-tion on construction in the expenditure approach inSection C of this chapter.)

• Hotels and restaurants: numbers of bed-nights;numbers of meals. Numbers of foreign touristsmay be an acceptable indicator in countries whereexpenditures by foreign tourists are a high propor-tion of the total.

• Transport: numbers of passengers or passenger-kilometers; metric tons of freight or ton-kilometers;numbers of licensed taxis and hire cars. To theextent that prices, and therefore the volume of ser-vice, reflect distance, data with a kilometer dimen-sion are better indicators. For example, metricton-kilometers would be a better indicator of thevolume of freight than a measure of metric tons thatdid not take into account differences in distancescarried. (Ideally, if there were both fixed anddistance-related elements to the price, the twowould be weighted together.)

• Services to transport: numbers of ships handled inports; numbers of aircraft and passengers handledat an airport; numbers of days for which cars arehired; weight or volume of goods stored or refrig-erated; numbers of cars parked in pay parking;numbers of journeys on toll roads.

• Communications: numbers of letters, parcels, orlocal telephone calls; minutes of long-distance orinternational telephone calls; numbers of telephonelines. In view of technological change in the area ofcommunications, it is important to include newproducts, such as electronic data lines, internetconnections, and mobile phones.

• Ownership of dwellings: numbers of dwellings,preferably broken down by location, size, and typeof dwelling and with adjustments for newdwellings and alterations and quality change.(Sources and methods are covered later in moredetail in the discussion of indicators for householdconsumption of rent.)

• Other business services: numbers of wills, courtcases, and divorces for lawyers; numbers of regis-tered land transfers for real estate agents; numbersof deaths for undertakers; stock market turnover forstock market dealers.

• Public administration services: numbers of pen-

sions processed, licenses issued, and court casesprocessed. Because these indicators are partial anddo not reflect quality well, they are used to only alimited extent.

• Other services: numbers of tickets sold by theatersand other forms of entertainment; numbers of vehi-cle repairs.

3.42. The potential range of sources is very wide.Unlike industrial production indices, these indicatorsare not usually part of a comprehensive system ofindicators. As a result, there are typically many gaps,and data often need to be obtained from differentagencies. Some potential indicators may be unpub-lished but could be obtained by making a request tothe relevant agency.

c. Labor input measures

3.43. Labor input measures are sometimes used asindicators of the volume of output of service indus-tries. The assumption behind the use of this method isthat employment is directly related to output andvalue added in volume terms. Labor is a major inputto the service industries, and compensation ofemployees plus mixed income typically constitutevery high proportions of value added. As well, com-prehensive monthly or quarterly data on employmentby industry are available in many countries, fromspecific surveys or as a byproduct of a payroll orsocial security tax system.

3.44. Number of hours worked is preferable to num-ber of employees as an indicator of labor input.Output is affected by changes in standard weeklyworking hours, the proportions of part-time employ-ees, and hours of overtime. Hours worked takes intoaccount these effects, but numbers employed doesnot. However, hours worked is still an imperfect mea-sure of labor input. Ideally, labor input measureswould take into account different types of labor (e.g.,disaggregating by occupation or skill level) weightedby their different rates of remuneration. The totalvalue of wages and salaries divided by a fixed speci-fications wage and salary index would give an indi-cator that also takes into account such compositionaleffects, but it would need to be supplemented by ameasure for self-employed labor. It is preferable thatactual hours worked be covered, rather than paidhours which include sick leave, vacations, and publicholidays but exclude unpaid work. The labor inputmeasure should include working proprietors and theself-employed as well as employees.

GDP by Industry

39

3.45. Labor input would seldom be preferred as avolume measure because the relationship of labor tooutput is variable. Because of the delays and costsassociated with hiring and firing, labor tends to beless responsive to output than some other inputs. Therelationship between labor input and output alsochanges as a result of changes in capital intensity andtotal factor productivity.

3.46. In the case of the nonmarket activities of gen-eral government and nonprofit institutions servinghouseholds, current price output is measured on thebasis of the cost of inputs. It is preferable that theoutput volume measure take into account the ser-vices provided by the government or nonprofit insti-tution, if measurable. It is common, however, to useinput indicators if suitable volume measures are notavailable.

3.47. As with other sources, calculations at a greaterlevel of detail will usually improve the estimates. Forexample, cleaning and litigating may both be in thebusiness services industry category, but the outputper hour worked of a cleaning business is much lessthan that of a law firm. Accordingly, an indicator thatseparates the two activities will better reflect changesin output.

d. Indirect indicators

3.48. Where direct measures are not available, adiverse range of indirect indicators may be consid-ered. It is sometimes possible to identify a down-stream or upstream activity that can be used as abasis to generate indicators. For example, the supplyof building materials can be used as an indicator ofconstruction activity. Construction is often difficultto measure because of the large number of small-scale and ephemeral contractors, own-account work,and work done without permits. The supply of build-ing materials, on the other hand, can often beobtained from a relatively small number of manufac-turers and quarries (with adjustments for exports andimports, if applicable). To the extent that there is astable relationship between building material inputsand output, this is a suitable indicator that can beobtained with relatively little cost or compilationtime. The quality of the assumption deteriorates ifthere are changes in any of the mix of types of build-ing, techniques of building, productivity, and inven-tories of building materials. If changes in thesefactors are known to be occurring, it may be desir-able to explore more complex methods (e.g., a cal-culation that takes into account the different

products used by different types of construction orcollection of data on inventories).

3.49. An indicator for the wholesale and/or retailindustries could be obtained from the supply ofgoods that are distributed by these industries.Although it would be conceptually preferable toobtain data on sales and purchases directly from theenterprises, data on the supply of goods handled areoften better or easier to collect9 because manywholesalers and retailers are small scale. (Data onsales of goods to consumers are discussed later inthis chapter in the context of GDP by expenditurecategory.) Similarly, if the types of commoditieshandled by wholesalers are known, the value of sup-ply of those commodities can be used as an indicatorfor wholesale output. The wholesaling activity ofspecialist importers can be measured by the volumeof imports. As the estimation procedures rely on anassumption of fixed markups (i.e., the margin as apercentage of the price), the method will give betterresults if calculated at a greater level of productdetail to take into account the combined effect ofchanges in the product mix with varying markups ofdifferent products.

3.50. If data on road freight transport activities areinadequate, it may be possible to derive an indicatorbased on the supply of goods that are usually trans-ported, or at least the major components. Indicatorsfor other supporting industries may also be derivedfrom the output of the industries served, such as ser-vices to agriculture, mining, and transport.

3.51. Population is sometimes used as an indicatorin areas where nothing more specific is available,such as subsistence agriculture, housing, and someconsumer services. The indicators should beadjusted for long-term trends; for example, popula-tion could be used to represent dwelling services, butadjustments should be used to account for trends inquality of dwellings and persons per household.Adjustments for divergence in long-term trendsbetween the population indicator and the annual esti-mates can be incorporated through the benchmark-ing process.

3.52. All of the methods discussed in this sectionassume ratios based on the benchmark data. Such


40

9The supply of goods is derived from output less exports plus imports(plus any other adjustments for any other known use in intermediateconsumption, inventories, or capital formation, or tax or distributionmargins).

ratios are more likely to be stable in constant priceterms, so it is generally better to make the assumptionin constant price terms and then reflate to currentprices. Also, in all of these cases, if the benchmarkdata are more detailed, the quarterly estimates willtend to be better if the calculations are done at adetailed level.

e. Price indicators

3.53. If a current price value is available for anitem, a volume measure can be obtained by deflat-ing with a price index. Alternatively, if a volumemeasure is available, a current price measure can beobtained by reflating (or inflating) with a priceindex. Often appropriate deflators will already beavailable in the form of published price indices, butsometimes deflators will need to be derived by thenational accounts compiler by recombining compo-nents of other indices or obtaining supplementaryprice information.

3.54. For manufacturing output, relevant detailedcomponents of the producer price index (PPI) areusually available. PPI measures prices at the factorygate (usually at basic values, sometimes at pro-ducer’s prices) and is, therefore, most suitable fordeflating data at basic values, such as output. In anincreasing number of countries, PPIs are extended tocover a wider range of industries beyond manufac-turing, possibly including agriculture, mining, con-struction, and services. For consumer services,particular components of the consumer price index(CPI) could be used. A wholesale price index (WPI)measures prices including transport and distributionmargins (and sometimes product taxes) and also cov-ers imports. As a result, WPIs are less suitable fordeflating output measures than is PPI, but WPI maybe more suitable for deflating intermediate con-sumption that has passed through the distributionsystem and includes inputs.

3.55. In some cases, national accountants may be ableto develop specific-purpose price indices to fill in gaps.For example, if there are a small number of airports orrail operators, it may be possible to obtain a selectionof their charges directly (e.g., from their rate sheets ifthese show actual transaction prices). When a productis largely exported, average unit values may be used.Professional associations, such as those of lawyers orarchitects, may have information on fees. Ministries ofagriculture and other government bodies that regulateor monitor agricultural activities are often sources ofprice data for agricultural products. The data are usu-

ally expressed in terms of average prices. It is neces-sary to exclude transport and distribution costs toderive “farm gate” prices.

3.56. Where no direct data are available, prices ofone or more similar or closely related products orindustries that have a tendency to move in the sameway may be suitable. Suitable comparable productsor industries should have somewhat related coststructures or demand. For example, CPIs for domes-tically produced components are more likely to berepresentative for unmeasured domestic productsthan the total CPI, which includes imports and so is more affected by exchange rate movements.Similarly, CPI service items are more likely to be rep-resentative of unmeasured services than the total CPIto the extent that services tend to have similar, labor-dominated cost structures.

3.57. It may be necessary to produce output deflatorsor reflators based on input costs, for example,weighting together wage indices or information onwage rates with the prices of major intermediateinputs. Because this technique does not account foroperating surplus, it is unsatisfactory to the extentthat profitability varies. However, to the extent thatprofitability and productivity are taken into accountin annual data, the benchmarking process will incor-porate the annual variations.

3.58. Wholesaling and retailing present special diffi-culties in identifying the price dimension. The diffi-culty arises because they are industries thatpredominantly produce margins; the service compo-nents are combined with the prices of the goods, andthe quality aspects are difficult to measure. The pre-ferred solution is to avoid deflating the margindirectly by deriving independent volume and valuemeasures. A volume indicator of the margin servicecan be made from the volume of goods bought or soldusing an assumption of a stable volume of the distri-bution service per unit of goods, that is, no qualitychange in the service. The suitability of the assump-tion is improved by compiling at a greater level ofdetail, as markups differ among products andbetween outlet types. The price indices of the goodsshould not be used as a proxy deflator or reflator ofmargins because margins have different cost struc-tures and can vary differently than goods prices.

3.59. Like output of wholesaling and retailing, theoutput of financial intermediation services indirectlymeasured (FISIM) is a margin and so is not readily

GDP by Industry

41

observable. The recommended approach for QNAestimation is to use the deflated values of loans anddeposits as volume indicators for the service pro-vided in conjunction with the annual benchmarks.The value of loans and deposits should be deflated bya price index measuring the general price level (e.g.,the CPI). The method would ideally be applied at adisaggregated level, with a detailed breakdown oftypes of assets and types of liabilities, because theinterest margin varies among different types of assetsand liabilities, reflecting the fact that the value of ser-vice provided varies for different categories. Notethat interest margins for financial services can bequite volatile. Interest margin changes are priceeffects and do not affect the volume of loans, so theywill be correctly shown as a price effect with thismethod. A less satisfactory alternative would bedirect deflation of the value of FISIM by a generalprice index or by financial service input prices.However, these deflators do not measure the price ofFISIM and ignore interest margin changes. As aresult, changes in financial institutions’ profitabilitywould be wrongly shown as a volume change.

3.60. In cases where independent current price andvolume measures for output are obtained, the corre-sponding implicit price deflator should be checkedfor plausibility.

3.61. Intermediate consumption usually has no spe-cific aggregated deflators, so it is necessary to buildthem from components of other price indices for therelevant products. Note that even when a fixed coef-ficient method has been used to derive volume mea-sures for an industry, it is desirable to reflateintermediate consumption and output separately andundesirable to use the fixed coefficient method at cur-rent prices.

f. Industrial production indices

3.62. An industrial production index (IPI) is typi-cally already available in countries that compileQNA. It is usually at least quarterly and sometimesmonthly. IPIs can use any of the methods used forindustry volume indicators, namely deflated values,quantity measures, or selected inputs. In some cases,the IPI may use a mix of methods, such as quantitiesfor homogeneous goods and deflation for others.

3.63. It is preferable to compile QNA estimates fromthe IPI source data or from IPI components at a dis-aggregated level, rather than from the total IPI. Themore detailed compilation allows differences in cov-

erage and concepts between the IPI and QNA to beresolved. Benchmarking, structural assumptions, andreflation tend to be better when carried out at agreater level of detail. The national accounts measureof output requires weights to reflect output at basicprices or producers’ prices, while the IPI may useother weights or valuations. The IPI may have gaps incoverage that may need supplementary sources, forexample, particular industries, goods that are not eas-ily quantified, repair service revenue, newspaperadvertising revenue, hiring revenue, and secondaryoutput. The base years may also differ. Published IPIsare sometimes adjusted for variations in the numberof working days, rendering them unsuitable as QNAindicators. For compilation of non-seasonallyadjusted QNA, the data should reflect the actualactivity in each quarter, without adjustments forworking days or other calendar and seasonal effects.

3.64. If different methods are used in the IPI and QNA,it will prevent confusion if the QNA sources and meth-ods documentation clearly states the differences. Thesedifferences should be explained (e.g., weights, cover-age, valuation) and quantified, if possible.

3.Adjustment Items

3.65. To derive GDP at market prices, total valueadded of industries at basic prices needs to have nettaxes on products added and unallocated FISIMdeducted.

3.66. Net taxes on products consists of import duties,value added taxes, and other taxes less subsidies onproducts. Data on net taxes on products at currentprices are normally available from governmentfinance statistics and present few problems. In a fewcountries, some components, such as state and localproduct taxes, may need to be estimated. Such esti-mates can be based on data on the supply of the taxedproducts.

3.67. Net taxes or subsidies in volume terms can bedefined as the base year rate of tax (or subsidy)applied to the current volume of the good or service.Technically, this is equivalent to the base year valueof taxes (or subsidies) extrapolated by the volume ofthe taxed (or subsidized) goods and services. To theextent that tax (or subsidy) rates differ, it is desirableto do the calculations at a more detailed level to takeinto account the differing rates.

3.68. The QNA treatment of FISIM should follow theANA treatment. Under the preferred 1993 SNA treat-


42

ment, FISIM should be allocated to users (viz., inter-mediate consumption by industries, final consumptionexpenditure, exports) and so would not be an adjust-ment item to total GDP. In the 1968 SNA, FISIM wastreated as the intermediate consumption of a nominalindustry rather than allocated across users. With the1968 SNA treatment, it is necessary to deduct unallo-cated FISIM in aggregate from value added by indus-try in order to derive GDP. The same indicators that areused to derive and deflate output of financial servicesshould be used for the adjustment. The 1993 SNA alsopermits the use of the 1968 SNA treatment.

C. GDP by Type of Expenditure

1. General Issues

3.69. GDP by type of expenditure shows the finaldemand for goods and services and so is particularlyuseful for economic analysis. One benefit for compi-lation of the expenditure approach is that prices arereadily observable; also, this approach does not relyas much on fixed ratios as the quarterly productionestimates. Nevertheless, the expenditure approach isless common than the production approach amongQNA compiling countries because of problems ofavailability, timing, valuation, and coverage ofexpenditure source data, as detailed in the following: • Government and international trade are typically

well covered by quarterly data, but the timing ofrecording of data is often inconsistent with thenational accounts requirements. Government dataare usually recorded on a cash basis, althoughaccrual adjustments are sometimes made for par-ticular, identifiable items and accrual accounting isbecoming more common in government accounts.Merchandise trade data are recorded when the mer-chandise passes through the customs frontier,although adjustments may already have been madefor some timing problems in balance of paymentsstatistics. Inconsistencies in the timing of transac-tions may lead to discrepancies and errors. Timingdifferences are a much more important issue inquarterly data than in annual data: with the sametiming differences affecting the annual and quar-terly series, the relative impact of an error is fourtimes more significant.

• Expenditure estimates are more strongly influencedby coverage problems in the business register. Thisinfluence arises because of the high proportion ofretailing and consumer services output that goes tohousehold consumption and the high proportion ofbuilding output that goes to capital formation. These

activities often have high proportions of smaller,shorter-lived, less formal businesses. The sameactivities are included in GDP by industry, but onlyto the extent of their value added.

• Changes in inventories have serious valuationproblems. These problems also occur in productionand income approach estimates, although they maybe partly avoided by use of quantities of output inthe production estimates.

3.70. If the available expenditure data have seriousgaps, the expenditure approach cannot be used.However, it may still be possible to derive a usefulsplit of GDP by type of expenditure. The sum of theavailable expenditure components can be derived sothat the total of the missing components can then bederived as the residual from total GDP from the pro-duction approach. For example, many countriesderive changes in inventories in this way. Althoughnot an independent check on the production esti-mates, use of incomplete expenditure data in this wayis helpful to data analysts.

2. Sources

a. Household final consumption expenditure

(i) Value indicators

3.71. Household final consumption is usually thelargest component of GDP by expenditure. The mainsources of data on household consumption are sur-veys of retailers and service providers, value addedtax (VAT) systems, and household surveys. Also, dataon the production and foreign trade in consumerproducts can be used to derive estimates by commod-ity flow methods.

3.72. Business surveys of retailers and providers ofother consumer services are a common data source forhousehold consumption at current prices. Many typesof retailers and almost all services are fairly specialized,but supermarkets and department stores sell a widerange of goods, so that collecting product breakdownsfor these stores is desirable. A detailed breakdown byproduct improves the quality of the deflation and pro-vides extra information to users. If product mixes arestable, satisfactory quarterly data by product can beestimated by using total sales of a retail industry as anindicator for the benchmark values of sales by product.

3.73. A VAT or sales tax system may be able to providedata on sales by type of enterprise. Such a tax systemmay also divide sales into different product categoriesif different tax rates are applied. It is necessary to

GDP by Type of Expenditure

43

identify which sales are indicators of household con-sumption, for example, sales by retailers and consumerservices. The systems used to collect other taxes, suchas taxes on alcohol or tobacco, may also be a potentialsource of information.

3.74. Some countries conduct continuous householdexpenditure surveys. If the results are processed on atimely basis by quarter, they could be useful indica-tors for QNA. Data collected from households havedifferent benefits and shortcomings compared withbusiness data. Reporting quality and omissions ofsmall or sensitive items may be a problem in house-hold surveys, depending on the behavior of respon-dents. For example, expenditure on socially sensitiveitems such as alcohol and tobacco is often under-stated, requiring adjustments to be made on the basisof other information.10 As well, there are often prob-lems with purchases of consumer durables as a resultof recall and infrequency of purchases. On the otherhand, household surveys ensure good coverage ofpurchases from informal, small-scale retailers andservice providers. These are difficult to cover in busi-ness surveys, but the purchaser has no reason tounderstate this expenditure, which is no more diffi-cult to report than any other expenditure. Householdsurveys may be favored in developing and transitioneconomies because they cover purchases from theinformal activities. In countries with small informalsectors, business surveys may be preferred because ofissues such as collection cost, delay, and reportingquality of quarterly household expenditure data. ForQNA estimation, a level bias in household surveys isnot a problem as long as the bias is stable so that itgives a correct indication of movement. In general, acombination and reconciliation of data from severalsources will give the best results.

3.75. In addition to broad sources such as retail sales,VAT systems, and household surveys, there are a rangeof specific indicators for components of householdconsumption. The sources of specific indicatorsinclude specialized statistical surveys, major supply-ing enterprises, and regulators. Where there are a smallnumber of large suppliers of a particular item but nocurrently published data, the information can some-times be collected specifically for QNA. Examplescould include sales to residences of electricity and gas,as well as some components of transport, communica-tion, and gambling.

3.76. Household consumption expenditure estimatesthat are based on indicators from the retailers and ser-vice providers will need adjustments for expenditureby residents when abroad and expenditure by nonres-idents while in the country. Both of these can beobtained from balance of payments statistics, if avail-able on a quarterly basis (and, if not, by using themethods discussed in the IMF’s Balance of PaymentsCompilation Guide).

3.77. Commodity flow methods can be used in caseswhere there are good data on the supply of products.Total supply to the domestic market at purchasers’prices for a product can be derived as• domestic output at basic prices,• plus changes in inventories,• less exports,• plus imports,• plus taxes on products,• less subsidies on products, and• plus trade and transport margins.

3.78. To obtain household consumption as a resid-ual, other uses (i.e., intermediate consumption, gov-ernment consumption, fixed capital formation, andchanges in inventories) should be deducted from totaldomestic supply. This method often relies on ratios tofill in gaps, for example, taxes and margins may becalculated as a proportion of the underlying flows. Asexplained in Chapter VI, variation in the annual ratiosis taken into account through the benchmarkingprocess. In some cases, particular components are nil.The commodity flow method can be particularly use-ful for goods because goods are often supplied by arelatively small number of producers and importers,and data on the supply of the goods are easier to col-lect than data on sales at the retail level. Where a sig-nificant part of retailing is informal, surveys ofretailers are likely to have incomplete coverage, sothe commodity flow method could provide more suit-able indicators than a survey of retailers.

(ii) Volume indicators

3.79. Data on consumption of dwelling services canbe estimated by extrapolation on the basis of the num-ber of dwellings. If construction data do not allowestimates of the net increase in the number ofdwellings, population could be used as a proxy(preferably adjusted for any trends in the averagenumber of persons per dwelling). Because of differ-ences in the average rent per dwelling, the quality ofthe estimation would be improved by doing separatecalculations by location and for different dwelling


44

10For example, from tax data if smuggling and tax evasion are notmajor problems.

types (e.g., house/apartment; number of bedrooms). Itwould also be desirable to put in an adjustment factorto account for any shortcomings in this method (e.g.,for long-term changes in the size and quality ofdwellings). These factors should be accounted forannually so that their effects can be incorporated inthe QNA by the benchmarking process. Because thestock of dwellings is large and changes slowly,acceptable estimates can be derived for dwelling ser-vices, even in the absence of quarterly volume indica-tors. The methods used should be consistent withthose used in the production estimates.

3.80. Indicators for some services, such as insur-ance, education, and health, may be obtained as abyproduct of government regulation. In addition,motor vehicle regulation may provide indicators forthe volume of vehicle purchases. The components tobe included are household purchases of cars andother light vehicles, both new and secondhand, frombusinesses and governments.

3.81. Administrative byproduct data may help fillother gaps. For example, taxis, financial intermedia-tion, insurance, health, and gambling are often regu-lated. As a result, indicators may be published orpotentially available on request to the regulatoryauthorities. Other administrative data can be used asindirect indicators. For example, numbers ofdivorces and wills in probate are a potential indica-tor for legal services; numbers of deaths for funeralservices; total numbers of vehicles and numbers ofroad accidents for vehicle repairs. In each case, adirect survey would usually be better but may not bejustifiable on a quarterly basis because of the datacollection cost and the relative unimportance of theactivity. (Value may also sometimes be availablefrom these sources.)

3.82. Consumption from subsistence production offood can be quite important in expenditure estimatesfor developing countries. The methods should beconsistent with those used in the production esti-mates. In some cases, estimates of agricultural outputinclude subsistence agriculture, so that the consump-tion can be identified separately or derived by thecommodity flow method. In the absence of quarterlysurveys of subsistence production, population trendsmay be an acceptable indicator.

(iii) Price indicators

3.83. CPI components usually provide appropriatedeflators for household consumption expenditure.

The coverage of household consumption expendi-ture is typically fairly close to that of the CPI.

3.84. Deflation should be carried out at a detailedlevel to ensure that each component is deflated bythe price index that most closely matches its actualcomposition and to minimize the impact of usingdeflators constructed using the Laspeyres formulaand not the preferred Paasche formula. For example,it would be better to deflate each type of food sepa-rately to account for different price movements. It isseldom justifiable to use the total CPI in deflation.National accountants should work closely withprice statisticians to have consistent classificationsand coverage of all required components.

3.85. There may be gaps where a component ofexpenditure is not covered by a matching CPIitem. An example is insurance, which is measuredas a margin in the national accounts and which CPIcompilers may exclude or measure as total premi-ums. A possible alternative as a deflator is a priceindicator based on input costs (e.g., a weightedindex of wages, taxes, and intermediate consump-tion components such as office-related items,together with an adjustment for profitability, ifavailable). In other cases, it may be necessary totake the most closely related CPI item or group ofitems.

3.86. For expenditure by residents abroad, theCPIs of the main destination countries adjusted forexchange rate movements could be used as defla-tors. If available, it would be preferable to obtainspecific indices for the most relevant components,for example, hotels, transport, meals, or any par-ticularly important categories of goods, rather thanthe total CPI. Expenditure of nonresidents could bedeflated by the domestic CPI items that relate tothe major components of tourist expenditures, thatis, hotels, transport, meals, and so on.

b. Government final consumption expenditure


3.87. Government accounting data are often avail-able on a monthly or quarterly basis. These could beprepared on the basis of the various internationalhandbooks or country-specific accounting systems.The most important need for QNA is to have expen-ditures classified by economic type, in particular,consumption of goods and services, capital forma-tion of goods and services, other expenditures, and


45

data on offsetting sales. Even if not published, thedata may be available on request. Governmentaccounts usually have the advantage of beingreported on the same basis as the annual data so thatthe quarterly data are consistent.

3.88. Data for the central government are generallyreadily available. In some cases, lack of data ordelays may require estimation for state, provincial,or local government. In the absence of comprehen-sive data, consideration can be given to alternativeindicators that relate to the actual level of activity inthe quarter, such as the following: • a sample collection for local governments; • wages paid by the governments concerned (prefer-

ably excluding those involved in own-account cap-ital formation such as road building);

• expenditure data not classified by economic type; • central government payments where these are the

major source of funds; or, • where actual data are not yet available, govern-

ment budget estimates. Before forecasts are used,the track record should be checked to see whetherthey are reliable.

3.89. Government accounts are traditionally pre-pared on a cash basis. Government cash paymentscan be large and lumpy, and their timing can bedetermined by political or administrative concerns.Differences between the cash basis used and theaccrual basis required by the 1993 SNA could causeerrors and discrepancies in the estimates. These tim-ing errors are the same in both QNA and ANA, butthe impact in QNA is relatively larger since theyhave a magnitude only about 25 percent of the cor-responding ANA estimates. A particular instance ofa distortion caused by cash recording is where gov-ernment employees are paid every two weeks.While some quarters will have six paydays, otherswill have seven, causing fluctuations in the quar-terly data that would not be a serious issue in annualdata. To the extent that such timing problems can beidentified, adjustments that are supported by evi-dence can be used to get closer to an accrual basis.Information may be available for some large indi-vidual transactions, such as the payday effect orlarge purchases of weapons.11 Accrual accountinghas already been introduced by some governments,and the 2001 IMF Manual on Government FinanceStatistics recommends accrual accounting.

3.90. The links to the production estimates for gen-eral government should be noted. If inconsistentmethods or data are used, errors in the residual itemor discrepancies will occur. The scope of governmentconsumption and general government output differ inthat government consumption is equal to: (a) general government nonmarket output; (b) less own-account capital formation included in

output; (c) less any sales and fees recovered, i.e., govern-

ment output paid for by others; (d) plus purchases that government provides free to

households without processing.

Although the same indicators can often be used forboth production and expenditure, the factors causingdifferences between them need to be taken intoaccount, especially if they are changing proportionsof the total.


3.91. In a few cases, it may be possible to obtainquantity measures for output of government services.For example, numbers of students at governmentschools, numbers of operations or bed-nights forpatients in public hospitals, and numbers of benefitrecipients served by a government social assistanceoffice may be available. However, these indicatorsfail to take into account important quality aspects.Further, there are many other activities of govern-ment where output is difficult to quantify, such asresearch and policymaking.

3.92. In the absence of suitable output volume indi-cators, an indicator based on labor inputs may beused, such as number of employees or hours worked.Because government consumption is a labor-intensiveservice, this is a more acceptable assumption than itwould be for other expenditure components. In addi-tion to the limitations of labor input measures formeasuring production, measuring consumption ismore difficult because of work contracted out to theprivate sector, capital work on own account, and theoffsetting effect of charges for some services.Structural changes in the proportions of staff engagedin capital work, the proportions of output recoveredthrough charges, or the proportion of work outsourcedcould be significant on a quarterly basis.


3.93. Although current price measures for governmentare clearly defined as being based on costs, the priceand volume dimensions are less clearly defined and


46

11These issues also occur for government gross fixed capital forma-tion derived from cash-based sources.

have several alternatives. Prices are usually not directlyobservable. One option is to derive independent valueand volume measures so that the price dimension isobtained indirectly. Alternatively, a deflator could beobtained as a weighted average of input costs. Theusual input costs are wage indices or pay scales of civilservants and military staff, combined with relevantcomponents of price indices reflecting typical inputcosts such as rents, electricity, stationery, and repairs.

3.94. Methods based on input costs have the short-coming that they do not account for productivitychanges. Of course, these measurement problems arethe same for annual and quarterly estimates. For thequarterly national accounts compiler, the simplestsolution is usually to adopt the annual method andallow the benchmarking techniques to incorporateany adjustment factors.

c. Final consumption expenditure by nonprofit insti-tutions serving households


3.95. Much of the discussion on measurement of gov-ernment consumption also applies to nonprofit institu-tions serving households (NPISHs). Like generalgovernment, their output and consumption of nonmar-ket services at current prices is measured at cost.However, quarterly accounting data are less availablethan for general government. However, data for somelarger institutions may be published or available onrequest. Governments may be a good source of statis-tical indicators if they monitor, regulate, or providetransfers to charities, private schools, and similar insti-tutions. Otherwise, since they are mainly involved inservices, wages and salaries paid may be an acceptablesubstitute. Balance of payments data on transfers tonongovernment institutions may be an important indi-cator in countries where foreign aid is a major sourceof funding for NPISHs.


3.96. Labor input measures may be suitable indicators.If data are unavailable and the NPISH sector has beenshown to be economically stable in annual data, pasttrends may be an acceptable volume indicator. Themethod for the expenditure estimates should be consis-tent with that for the equivalent production estimates.


3.97. The methods are analogous to those used forgeneral government consumption, where output atcurrent prices is also defined as the sum of costs. A

weighted average of input costs may be used for con-sumption by nonprofit institutions serving house-holds so that the deflator corresponds with thecomposition of the current price value measured frominput costs. Items could include wages, rents, repairs,stationery, and electricity.

d. Gross fixed capital formation

(i) General value indicators

3.98. Annual and quarterly surveys of capital expen-diture by businesses are the conceptually preferredsources of capital formation data. However, capitalformation surveys are particularly expensive and dif-ficult to conduct on a quarterly basis for the follow-ing reasons. First, such surveys are very sensitive tocoverage problems in the business register becausenew enterprises, which may not yet even be in opera-tion, are particularly likely to have higher rates ofcapital formation than established businesses.Second, the potential population is almost everyenterprise in the economy, and there will be a largenumber of enterprises having little or no capital for-mation in any particular quarter. As a consequence,the sample frame needs frequent updating and thesamples have to be relatively large. Product splits arealso more difficult to obtain than from the supplyside. Another problem is that the 1993 SNA includeswork done on contract as capital formation of thefinal purchaser at the time it is done, while onlyprogress payments will be known to the purchaser. Ifpossible, it would be desirable to compare data fromthe alternative indicators for construction and equip-ment noted in this section.

3.99. Where a VAT system requires capital and inter-mediate purchases to be split, a useful indicator ofcapital formation can be obtained. However, VATlacks a product split and excludes capital work onown account. VAT returns in some countries do notseparate capital and intermediate purchases. (Thelumpiness of capital purchases may assist in identify-ing enterprises undertaking capital formation duringthe period and provide the basis for generating a splitat the level of individual enterprise.)

3.100. The largest components of gross fixed capi-tal formation are construction and equipment. Inaddition, capital formation includes cultivatedassets (such as livestock and orchards) and intangi-ble assets (such as mineral exploration; computersoftware; and entertainment, literary, and artisticoriginals; but not research and development). Costs


47

associated with the purchase of fixed and otherassets are also included, such as transfer costs(including real estate agents’ commissions, legalcosts, and taxes on real estate purchases), architects’fees, and installation costs. In addition to purchases,own-account production of capital can be importantin some cases, including construction, computersoftware, and legal work, and can be hard to includeother than directly in surveys.

(ii) Specific value, volume, and price indicators

Construction

Value indicators

3.101. Gross fixed capital formation on constructionassets includes the nonmaintenance parts of the out-put of the construction industry, own-account con-struction of other industries, and associated expensessuch as architectural services and real estate agents’commissions.

3.102. Estimates of capital formation on construc-tion raises a number of special measurement issuesand problems, such as the following:• Large numbers of small businesses. Construction is

typically carried out by numerous enterprises thatare often small and informal. Data collection andobtaining sufficient coverage from constructionbusinesses can, therefore, be particularly difficult.

• Long projects. The length of construction projectsgives rise to issues of holding gains and allocationof the output to quarters (as will be discussed inChapter X).

• Subcontracting. Work is often arranged by aprime contractor with a number of specializedsubcontractors which means that several enter-prises may be involved in the same project, giv-ing rise to the possibility of double counting oromissions.

• Speculative construction. Where the work isundertaken by a developer with no final buyer, theprice is not known at the time after the work isdone. In addition, land costs are included in theprice, and holding gains and operating surplus aremixed together.

3.103. These problems apply to the correspondingestimates for construction industry by the produc-tion approach as well. They also apply to annualdata, but quarterly data are more sensitive to theslowness or high cost of data collection and moresubject to difficulty allocating the value of long-term projects to quarters.

3.104. Gross fixed capital formation of constructioncan be measured in various ways, corresponding todifferent stages in the building process, include thefollowing:• supply of building materials,• issue of government permits for particular projects,• data reported by construction businesses,• data reported by construction-purchasing busi-

nesses, and• data reported by households engaged in own-

account construction.

3.105. In many countries, construction requires per-mits from local or regional governments, and thepermit system can be used as a source for estimatesof construction in the national accounts. The permitsystem may cover only larger projects or urbanareas, while in other cases it may cover all exceptminor construction work. Permits usually show thetype of construction, value, size, proposed startingand ending dates, and the name and address of theowner and/or builder. If the data are in volume termsonly (e.g., numbers of dwellings, number of squaremeters) or the value data are of poor quality, then anaverage price per unit is also necessary to derive cur-rent price values for national accounts purposes.Data in this form need to be allocated to periods (seeExample 10.2 in Chapter X), usually with informa-tion from builders, approval authorities, or engineersin order to obtain average construction times foreach building type. It is also necessary to makeadjustments, to the extent practical, for realizationratios (i.e., to account for projects that do not goahead), biases in builders’ estimation of their costs,the effect of holding gains included in prices, and theproportion of projects that are carried out without apermit. Government decisions and newspapers maybe used to identify large-scale work that otherwisemay be missed.

3.106. In some countries, the approval process isused to identify construction projects, and thisprocess then provides the frame for a separate survey.Direct information about the project, such as thevalue of work done each quarter and changes fromthe original proposal in the cost or size orstarting/ending dates, can be collected in such a sur-vey. Using survey information prevents the need formaking the kind of assumptions that have to be madewhen permit data are used directly. The surveymethod is conceptually much closer to statisticalrequirements, but it is more expensive and time-consuming to perform. The usefulness of the survey


48

is also limited by the degree of sophistication ofbuilders’ accounting records about the value of workdone in the period. In practice, the value of work donemay have to be represented by progress payments.

3.107. Architectural and approval costs are a part ofcapital formation on construction and need to beadded to the values that represent construction out-put. These items are related to construction activity,so construction indicators could be used as indirectindicators if more direct data are not available.However, as some of these expenses precede con-struction work, their timing is different. As a conse-quence, the timing pattern built into constructionestimates may have to be adjusted.

3.108. Real estate transfer costs consist of itemssuch as lawyers’ fees, real estate agents’ commis-sions, land title transfer taxes, loan application feesand other set-up costs for finance, and inspectionfees. These costs relate both to new construction andto purchases of land and existing dwellings. If theseland dealings are registered with a governmentagency, it may be possible to obtain a quarterly indi-cator from this source. Data on financing of land andbuilding purchases is a poorer indicator; an evenworse indicator is the value of new construction. Forreal estate transfer expenses, numbers of transfersmay be used as a volume indicator. To take intoaccount compositional changes, it would be better toclassify by type of property (e.g., houses, apartments,shops, complexes) and other variables that may affectthe cost (e.g., by state or province if charges are dif-ferent). In some cases, it may be necessary to derivea current price measure from the volume measure,which would require information about transfer taxrates, real estate commission rates, lawyers’ fees, andso on.

3.109. Speculative construction raises special issuesregarding valuation and timing. With speculativeconstruction, the work is undertaken by the builderbefore a purchaser is identified. Under the 1993 SNA,speculative construction is regarded as inventories ofwork-in-progress. (In contrast, the 1968 SNA treatedit as capital formation at the time the work was done.)Whatever the conceptual considerations, the avail-ability of data tends to determine the treatment ofspeculative construction. For example, data based onsupply of building materials only suit the 1968 SNAtreatment because they would not allow speculativeconstruction to be identified separately. Surveys ofbuilders or building permits could be designed to

meet either treatment, although extra informationwould need to be collected to separate speculativeconstruction. Surveys of construction purchasers aremore suited to the 1993 SNA treatment. Note that thenet effect on GDP of the different treatments shouldbe nil, since they cause offsetting differences in grossfixed capital formation and changes in inventories. If,contrary to the 1993 SNA recommendations, it isdecided to include unsold speculative constructionwork in gross fixed capital formation, there is a valu-ation issue in that the estimated price may differ fromthe realized price. If unsold speculative constructionwork is shown as changes in inventories, there needsto be a valuation adjustment to make the withdrawalfrom inventories consistent with the gross fixed cap-ital formation. This topic is discussed further inChapter X.

3.110. Construction in rural areas in developingcountries is often carried out by households on theirown account and made with their own labor, outsidethe scope of official permits. A household survey mayprovide information on the numbers of householdsinvolved and the cost of materials. These resultswould need to be adjusted to an estimated marketprice by taking the equivalent market prices (if sucha market exists) or a shadow price based on costs(including labor). Usually, these indicators wouldonly be available for a benchmark period and not ona quarterly basis. The building material approachcaptures some of this activity to the extent that a sig-nificant proportion of materials is produced by facto-ries, although some materials may be made by thehousehold. In the absence of other data, the size ofthe rural population could be used as a quarterly indi-cator for this type of construction.

3.111. It is desirable to obtain data on gross fixedcapital formation of construction by type of asset,both for economic analysis and for improving defla-tion. Data by the industry and institutional sector ofthe purchaser are also useful for analysts. The esti-mates based on building materials give little or nobreakdown, while other estimation methods can givemore. In some cases, the general government sectordata could be obtained from the government financestatistics, allowing the nongovernment component tobe derived as a residual. Because residuals magnifythe effects of errors, implausible values of the residu-als may point to data problems.

3.112. Gross fixed capital formation of construc-tion and construction industry output will often be


49

estimated from the same data sources. The estimates,however, will differ because of different treatment ofthe following:• repair work (part of output, but not fixed capital

formation);• secondary activity (secondary capital construction

by establishments outside the construction industryis part of capital formation, while constructionestablishments may have secondary activity innonconstruction goods and services);

• speculative construction work (output of the indus-try when the work is put in place; in the 1993 SNA,it is included in inventories when produced and infixed capital formation when sold); and

• associated expenses, such as nonconstructiongoods included in a structure; architectural, legal,and approval fees (which are not part of construc-tion output, but are fixed capital formation); or theeffect of any product taxes and subsidies.

Volume indicators

3.113. Building permit systems may provide volumeindicators such as floor area. To the extent that thecomposition of the variable is stable, quality changesper unit will not distort the estimates, so calculationin more detail is beneficial.

3.114. The supply of building materials is often themost readily available construction volume indicator.While builders are often small and dispersed, build-ing materials are often produced by a relatively smallnumber of large factories and quarries. Data onexports and imports of building materials are alsogenerally available and may be important for somekinds of building materials in some countries.Therefore, measures of the total supply of buildingmaterials or selected major building materials to thedomestic market can be obtained as output plusimports less exports. Preferably, trade, tax, and trans-port markups would be taken into account, to theextent that they have changed or that differentialmarkups affected the weights of different compo-nents. A lag factor may be included to take intoaccount the time it takes for materials to get from thefactory (local production) and customs frontier(imports) until they are incorporated in constructionwork.

3.115. The advantages of the building materialsmethod are the ready availability of data and thedata’s inclusion of informal and unapproved work.(Use of materials is one of the few ways that informalconstruction leaves a statistical trace.) The limitation

of this indicator is that it assumes a stable relation-ship between building materials and output. Theassumptions may not be stable because differentkinds of construction work use different materialsand have different materials-to-output ratios.Preferably, this method would only be used quarterly,so the benchmarking process would capture changesin these relationships as shown in the annual data.There may also be variations in the lags between pro-duction and use. As well, the building materialsmethod does not provide details that may be of inter-est, for instance, by type of building, industry of pur-chase or use, or institutional sector.

Price indicators

3.116. Because each construction project differs,compiling a price of construction presents specialdifficulties. Three alternative methods that are used toderive construction price indices are• model specifications,• hedonic techniques, and• input costs.

3.117. One method of obtaining output prices is tocollect or derive hypothetical prices for constructionoutput. House builders may have standard models ofhouses that are offered. Although options and individ-ual circumstances mean that the model is not imple-mented in every case, it can still form the basis of thebuilder’s pricing, and it would be relatively easy toobtain quotations from the builder for the standardmodel on a consistent basis. However, standard mod-els are usually only found for dwellings, where a massmarket exists, but not for other types of construction.Another approach to model specification is to divideconstruction into a number of particular tasks, forexample, painting a certain area of wall, laying a cer-tain height and type of brick, cost per hour of electricalwork, and so on. A weighted total of each of thesecomponents could be used to represent overall pricesfor a particular type of construction. A possible short-coming is that the most difficult jobs might be omitted,such as the prime contractor’s organizational work andunique, large-scale engineering tasks. Construction isusually highly cyclical, with margins cut or increasedin line with conditions. Because the prices are hypo-thetical, the statistician needs to be careful if list pricesare being reduced by discounts or bargaining during arecession or if more is charged during a busy period tocover overtime costs.

3.118. In recent years, some countries have exploredthe use of hedonic techniques to measure prices of


50

one-off goods. In addition to collecting the prices ofa range of buildings, these countries also collect dataon characteristics of the building that affect the price(such as floor area, height, fittings, materials, andlocation). A regression model is then developed toidentify the effect of each characteristic on the price.This allows the prices of the different kinds of build-ings to be converted to a standard basis and, hence,allows a price index to be derived. This methodrequires a great deal of work in data collection andanalysis of data. A limitation is that characteristicsmay be too numerous or abstract to be quantified, sothe model would only explain a limited part of theprice variation. Also, the coefficients of the modelmay not be stable over time.

3.119. Input cost measures are based on the prices ofconstruction materials and labor. These shouldinclude building materials (from a producer orwholesale price index12) and wages (preferablyspecifically for occupations employed in construc-tion). An adjustment could also be made for changesin markups to account for builders’ operating surplusand mixed income, if indicators were available,because these represent a major part of the price andcould be quite variable. Data on intermediate con-sumption by product supplied to the constructionindustry would be required for a benchmark period.Use tables could present these data or they could beobtained directly from surveys of construction enter-prises. Otherwise, it would be necessary to seekexpert advice or a sample of bills of quantities forbuilding projects. Data on employment in construc-tion by type of employee (occupation groups) wouldalso be useful for weighting the labor cost part of theindex. Because of different input structures, it wouldbe desirable to compile separate indices for differenttypes of building and construction (i.e., houses, apart-ments, offices, shops, etc.)

3.120. Generally, it is desirable to avoid using inputcosts to represent output prices, because input costsignore changes in productivity and profitability.However, the input cost method avoids the difficultiesof obtaining an output price index for heterogeneousproducts. Many types of construction are one-off, andeven where the same model is used in different places,

differences in soil type, slope, or options mean that itis not possible to find exactly comparable observa-tions. Finding actual buildings that are representativeand consistently priced is close to impossible.

3.121. In practice, countries may often use a mix ofdifferent pricing measures for the different types ofconstruction.

3.122. In situations where independent volume andvalue indicators are available, it is beneficial to derivean implicit price per unit to check that the result isplausible. Erratic results may mean that one of theindicators is unsuitable (e.g., the implicit deflatormay fluctuate because of quality changes that werenot taken into account in floor area data used as avolume indicator).

Equipment

Value indicators

3.123. The four sources for measuring equipment,reflecting the stages along the distribution process,are the following:• survey data on supply of capital goods,• survey data reported by the purchasing businesses,• VAT data on purchases of capital goods (if identi-

fied separately from intermediate goods), and• registration data from governments.

3.124. Derivation of the supply of capital goods is anapplication of the commodity flow method. The supplyof capital goods is measured, most simply, as the valueof domestically produced capital goods plus importedcapital goods, less exported capital goods. Changes intax rates and margins should be taken into account, ifpossible, because they are subject to change.Deductions should also be made for capital goods thatwere used for intermediate consumption (e.g., parts forrepairs), final consumption (e.g., computers, cars, andfurniture that are used for nonbusiness purposes), orinventories, and for net sales of capital goods (e.g.,company cars sold secondhand to households).

3.125. Data from the supply side provide totals andsplits by asset type, but not estimates by industry orinstitutional sector of use, which are of analyticalinterest. Like construction, government finance datacould be used to obtain government capital formationof equipment, and then a private total could be calcu-lated as a residual.

3.126. Transactions in secondhand goods presentsome additional issues. Some sources may only


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12Wholesale price indexes (WPIs) would generally be more suitablethan producer price indexes (PPIs), because they include taxes,imports, and distribution costs. If a WPI is not available to deflateitems that include margins, taxes, and imports, a PPI could be used asa substitute, preferably with adjustments for changes in import prices,tax rates, and other markups (if available).

provide data on new products. Data on some second-hand components—such as government asset sales,goods sold or purchased internationally, or vehi-cles—may be available. Data in some cases may notneed to be collected if the transactions are small, sta-ble, or occur within a single component.

Volume indicators

3.127. Capital goods tend to be heterogeneous, soquantities are unavailable or meaningless. A possibleexception is transport equipment, where governmentregistration systems sometimes provide numbers.These systems usually cover motor vehicles, aircraft,and seacraft. From these systems, it is often possible toobtain indicators of capital formation in these assets.Ideally, the registration authorities would be able tosupply information on numbers and values and distin-guish among types of owner (corporations, govern-ment, nonprofit institutions serving households—allcapital; household purchases are more complicated inthat they can be capital, consumption, or a mix), andbetween new and secondhand acquisitions.

Price indicators

3.128. Data derived from a survey of equipmentpurchases are at purchasers’ prices. The most appro-priate price indicators are the capital goods compo-nents of a WPI, because wholesale prices wouldtake into account trade, transport, and tax marginsand would generally include both imported andlocally produced goods. If data on wholesale pricesare not available, components of the PPI and importprice index could be weighted and used as a proxy.However, PPIs are designed to deflate output ratherthan capital formation and, thus, exclude the mar-gins. It would be desirable to make adjustments iftrade, transport, and tax margins were known to beunstable. The most likely instance is taxes, whereinformation on tax rates to adjust producer pricesfor taxes would generally be available. Similarly,import price indices are typically measured at thepoint of arrival in the country rather than the pointof final purchase and, thus, exclude domestic trade,transport, and tax margins.

3.129. If the equipment data had been derived fromthe supply side, the current values for domestically-produced goods would have been reported at basic orproducers’ prices. If so, the best method would be todevelop volume indicators by deflating the supplyvalues of domestically-produced equipment by therelevant PPI component. As the value and price mea-sures would be consistent, it would be expected to be

a superior volume indicator to one derived from valueand price measures that were based at inconsistentpricing points.

3.130. Imports are a major component of capital for-mation in many countries. Import unit values wouldbe expected to be poor indicators of prices. If noimport price index is available for some or all types ofequipment, a solution may be to take advantage of theproducer price or export price indices of the mainequipment-supplying countries. These should beobtained at a detailed level so that the components canbe weighted to reflect the composition of importedequipment in the importing country. The data shouldalso be adjusted for exchange rate movements andlagged to account for shipping times, if the lag is sub-stantial. It would also be desirable to take into accountchanges in shipping costs if an indicator were avail-able. It is possible in practice that the effect ofexchange rate changes is lagged or smoothed by for-ward exchange cover and by squeezing or expansionof margins. Because of changes in exchange rates andinternational specialization in types of equipment,prices of imported and domestically produced equip-ment may move in quite different ways.

Other fixed capital formation and acquisitions less disposals

of valuables

3.131. Computer software was included separately infixed capital formation for the first time in the 1993SNA. As with other capital items, the estimates couldbe made on the supply side (manufacture plus softwaredevelopers plus imports less exports) or the demandside. Supply data may be easier to collect because ofthe relatively smaller number of businesses involved;demand data are complicated by the fact that almost allbusinesses are potentially involved in using software.However, the data on the supply side have thelimitation—as do the data for motor vehicles—that asubstantial proportion of computer software is forhousehold consumption. Another issue is that somesoftware can be developed in-house. If important, dataon own-account software expenditure should be col-lected in surveys. A further issue is that some softwareis sold in conjunction with hardware, possibly raisingquestions of double counting. Price indices are alsoproblematic; possible alternatives are cost-based mea-sures, hedonic techniques, or the relevant indices ofsoftware-exporting countries.

3.132. Indicators for other components of grossfixed capital formation—such as mineral explo-ration, forests, orchards, livestock, and intangible


52

assets—are less commonly available. If significant, asurvey could be considered. For example, in coun-tries where mining or forestry is important, a specificsurvey on the topic would be justified. In some cases,administrative requirements for copyright registra-tion or mining exploration permits may give rise toinformation that could be used as an indicator. Evenin those cases, the timing of registration or permis-sion could differ substantially from the time of eco-nomic activity.

3.133. In the 1993 SNA, an additional category ofcapital formation is created for “valuables” such aspaintings and jewelry. These were previously largelyincluded in household consumption. They could berecorded from the point of production (e.g., factories)or import (customs data), from the point of sale (usu-ally retailers), or from purchasers (household expen-diture survey).

e. Changes in inventories

(i) Introduction

3.134. Inventories are defined as goods and someservices that were produced or imported but have notyet been used for consumption, fixed capital forma-tion, or export. This delay between supply and usebrings about valuation issues. Inventories appearexplicitly only in the expenditure estimates. Theymust, however, be taken into account in both the pro-duction estimates (both output and intermediate con-sumption) and income estimates (operating surplusand mixed income). The valuation issues also arise inthe other approaches, except where output or inputmeasures are expressed in quantity terms for produc-tion estimates.

3.135. Inventories consist of finished goods, work-in-progress, goods for resale, raw materials, andauxiliary materials.13 These components of invento-ries differ according to their stage and role in theproduction process. Finished goods are part ofoutput and are of the same form as their consumedequivalents. Work-in-progress is also part of output,but is harder to quantify than finished goods becausethe product is incomplete. Inventories of goods forresale, that is, goods held for the purpose of whole-saling and retailing are neither part of output norfuture intermediate consumption of the holder. Netincreases in inventories of goods for resale need to

be deducted from purchases of goods for resale toderive cost of goods sold and, hence, wholesale andretail margins, which are defined as the value ofgoods sold less the cost of goods sold. Raw materi-als are goods intended for intermediate consumptionby the holder. Auxiliary materials are also to be usedfor intermediate consumption but are not physicallypart of the final goods—office stationery, for exam-ple. Because auxiliary materials are typically minor,they are usually included as part of intermediate con-sumption at the time of purchase. The separation ofdifferent components is important because theyinclude different products, and, therefore, the priceindices to be used in deflation will also differ. Inpractice, attention can be confined to those compo-nents of inventories that are important; for instance,quarterly surveys could be limited to miners, manu-facturers, wholesalers, and retailers.

3.136. Although changes in inventories are a smallcomponent of GDP, they can swing substantiallyfrom strongly positive to strongly negative.Consequently, this small component can be a majorfactor in GDP movements. In the quarterly data, theaverage absolute quarterly contribution to growthcan be large, often being one of the major quarterlygrowth factors. Over the long term, the contributionof changes in inventories to GDP growth tends to besmall because some of the quarterly volatility willcancel itself out over the year. The importance ofinventories follows from its nature as a swing vari-able in the economy. It represents the differencebetween total demand (the sum of the other compo-nents of GDP expenditure) and total supply. Anincrease in inventories would represent supply thatwas not used during the period, while a reductionwould show the amount of demand that was metfrom previous supply. Without these data, the expen-diture estimates would show demand, not produc-tion. Data on changes in inventories are alsoimportant for analysis because the gap betweendemand and supply can be an indication of futuretrends. For example, a decrease in inventoriessuggests that demand exceeds supply, and output orimports will need to increase just to keep pace withthe existing level of demand.

3.137. Changes in inventories present particular dif-ficulties in terms of valuation. Businesses use severaldifferent varieties of historic cost, none of whichmatch national accounting valuation concepts.Measurement practice also varies, from completephysical stock-takes to samples and estimates. The


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13Called “stocks” in the 1968 SNA. In the 1993 SNA, the term “stocks”refers to balance sheet items in general and is used as a contrast to theterm “flows.”

valuation problems are sometimes ignored but aresignificant, as can be illustrated with some simple butconservative assumptions: if inventories are stable,the total holdings of inventories of inputs and outputsare equivalent to three months of output, and if valueadded is half of output, then 1 percent of price changein inventories will amount to a valuation effect of 2percent of quarterly value added. Thus, even quitelow rates of inflation can cause a significant over-statement of the level of value added, and this effectwill be concentrated in the major inventory-holdingindustries. Similarly, a small increase in the rate ofinflation will overstate the growth of GDP.

(ii) Value indicators

3.138. The 1993 SNA14 sets out the perpetual inven-tory method to produce estimates of changes ininventories. The method requires that data bereported transaction by transaction, with continu-ously updated replacement prices. While ensuringthat valuation is consistent throughout the system,this method requires so much respondent and com-pilation time that it is not implemented in practice,and simplified methods have to be used. Withadvances in accounting software and sophisticatedcomputing-based inventory monitoring, however,there is potential for improvements in the futurethrough compiling perpetual inventory model dataat the establishment level.

3.139. A number of issues arise concerning data oninventories. Some businesses may have computer-ized inventory controls; others have full physicalstock-takes at less frequent intervals with samplingor indicator methods for more frequent measures;and some small enterprises may not measure inven-tories on a quarterly basis at all. The values ofinventories may also be a particularly sensitivecommercial issue. Valuation effects can generallybe better calculated with higher frequency data.This is because higher frequency data reduce thepossibility of uneven price and volume movementswithin the period. As a consequence, the annualsum of the quarterly valuation adjustments may besuperior to annually calculated ones, unless there issome other compelling difference, such as differ-ences in coverage or detail. Similarly, if monthlydata are available, the calculation should generallybe done on a monthly basis for use in quarterly esti-mates. These factors all need to be assessed in lightof each country’s conditions.

3.140. Annex 3.1 shows how values of changes ininventories on a national accounts basis can bederived from business accounting data. The methodinvolves conversion from historic cost prices to con-stant prices, then reflation to current prices. Becausevaluation changes can occur within the period andinteract with changes in volume, better estimates canbe obtained by making calculations for shorter peri-ods. (Indeed, the perpetual inventory methodinvolves the same calculations effectively made forevery instant.) As a result, a quarterly estimate fromthe sum of monthly data will differ from and be bet-ter than one calculated from quarterly data. Similarly,the annual estimate would be better if made as a sumof the quarters than if made from annual data.

3.141. Some countries derive changes in inventoriesin GDP by expenditure as a residual. The residualmethod could be used quarterly even if the annualmeasures were obtained directly. This method is onlypossible if there is a complete measure of GDP fromthe production approach and estimates are availablefor all other expenditure categories. However,because inventories should also be included in esti-mates of output and intermediate consumption, themeasurement problems still need to be dealt with,even though quantity data that sidestep these valua-tion issues can sometimes be used. Derived as aresidual, changes in inventories would also includethe net effect of errors and omissions. In that light,compilers should review it carefully for signs of anyerrors that could be dealt with directly. As well, usersshould be advised to use caution in interpreting theestimate of changes of inventories, which should belabeled as being “changes in inventories plus neterrors and omissions” to emphasize the limitations.

3.142. One method that should not be used is toaccept changes in inventories at book values asreported by enterprises without adjustment. Businessaccounting practices typically use historic costs,which result in the inclusion of holding gains in thevalue of changes in inventories.

(iii) Volume indicators

3.143. Inventory data may be available in quantityterms for some products held by some enterprises.Because inventories include almost every type ofgoods (as well as a few kinds of services) and firmstypically use a range of products (especially theirinputs), this solution cannot be implemented com-prehensively. However, it may be available for someof the major components of inventories, such as


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14See 1993 SNA, Chapter XII Annex.

principal agricultural commodities, oil, or someminerals. (These goods have the most volatileprices, and inventory holdings are often large.) Withquantity data, valuation problems can be side-stepped by directly revaluing the change in thequantity over the period by the base year averageprices (constant price measures) and average pricesof the period (current price measures).15

(iv) Price indicators

3.144. Price indicators can be chosen according tothe composition of the inventories, making use ofCPIs, PPIs, trade prices, and average prices for spe-cific commodities. The opening and closing levels ofinventories (never the change in inventories) shouldalways be deflated. If inventories are usually valuedat historic cost, prices of several preceding periodsmay be relevant.

f. Exports and imports of goods and services


3.145. Countries that compile QNA data typicallyhave a well-developed system of trade and balance ofpayments statistics that produce quarterly data ontrade in merchandise and services. Merchandise dataare derived from customs records, surveys of tradingenterprises, or both. Services data are typicallyderived from specific surveys, administrative sys-tems, and international transaction reporting(exchange record) systems.


3.146. Quantity data on merchandise are usuallyobtained in a customs system. For homogeneous prod-ucts, they may be used to derive volume estimates.

3.147. Quarterly balance of payments data on ser-vices may have been derived using volume indica-tors, for example, international arrivals anddepartures for travel and air and ship movements forpassenger, freight, port, and airport services.Although the focus of balance of payments is towardvalue data, the derivation of volume measures fornational accounts purposes may be of special interestto balance of payments analysts because they providea perspective on whether price or volume forces are

driving changes in values. Specific volume indicatorsmay also be available. For example, for freight andpassenger services it may be possible to obtain vol-ume indicators, such as ton-kilometers or passenger-kilometers, from the carriers.


Merchandise

3.148. Customs and other trade data systems usuallycollect quantity information (e.g., metric tons, liters,numbers). These data are often processed to providevolume and unit value indices directly from the infor-mation already included on customs declarations.The unit values and volumes at the most detailedlevel of classification are combined to derive aggre-gate indices using weights from the value data.

3.149. Some countries have import and/or exportprice indices. These are collected from businesses inthe same way as wholesale and producer priceindices. Components of these indices can also beused to deflate the current price value data at the mostdetailed level to derive volume measures. If available,this will be the preferred method. The price indicatorsshould be consistent with any adjustments for trans-fer pricing in the value data.

3.150. A price index is a better way of dealing withheterogeneous products than is a unit value index.The price index approach of identifying productswith fixed specifications and transaction conditionsfor each product allows price effects to be isolated.However, a trade price index system has the disad-vantages of high cost and respondent burden. Also,the actual transaction prices that make up trade maybe affected by factors such as the mix of prices fromcontracts made at different times and the effects offoreign exchange hedging. These effects may not beeasy to capture in a price index.

3.151. Unit values are derived by dividing the valueof trade in a product by its quantity. Unit valueshave the advantage of being able to be derived frominformation collected by the customs system.However, the unit values, like the correspondingvolume measures, often cover quite diverse prod-ucts, even at the most detailed level of classification.For example, as discussed under capital formation,large-scale equipment, such as ships or heavymachinery, is often one-off in nature. Even for otherproducts, changes in composition within the prod-uct group can be important, for example, a particu-lar class of clothing can vary substantially in quality


55

15The result will be an estimate of the value of the physical change ininventories. At current prices, this is only an approximation of the1993 SNA concept, which also includes adjustments for all valuationchanges that occur between the time of production and the time offinal expenditure. The two concepts will be the same if price changesand transactions are spread evenly over the quarter.

of material, workmanship, and fashionableness. It isusually possible to identify the products affected byserious compositional changes by examining thevariances in the average unit values of the product.

3.152. There are several ways of dealing withheterogeneous products in unit value indices. Onepossibility is to supplement the customs data withspecific price surveys. Another possibility is to nar-row the specifications by also taking into accountthe partner country. A further option is to use unitvalues and volumes only for those products withunit values not subject to high variance. In caseswhere unit values are too variable, the unit values ofthe most closely related homogeneous productscould be used. The use of this price indicatorassumes that prices for related products move insimilar ways, which is often realistic—certainlymore realistic than assuming that volumes of relatedproducts move in similar ways. This method worksbest for the “not elsewhere classified” productswithin a group, as there are usually readily identifi-able related products with similar price behavior inthe same group.

3.153. In some cases, both unit value and priceindices may be unavailable or unsuitable. In thesecases, a solution may be to use price indices fromother countries. In the case of imports, the exportprice indices of the main supplying countries can beused. If export prices are not available for some sup-plying countries, a producer price index may be anacceptable substitute, although factory gate prices areless relevant than export prices. Preferably, theindices would be obtained at a fairly detailed level sothat different imported products could be deflatedseparately to reflect the actual composition of trade,rather than the fixed composition used in the indicesof the supplying country or countries. It would alsobe desirable to obtain price index data from several ofthe main supplying countries, to take into accountdifferent composition and price pressures. The priceindices should be adjusted for exchange rate move-ments between the currencies of the supplying coun-tries and the importing country. If the source of thetrade is remote, it may be desirable to allow a lag toaccount for shipping times (e.g., if shipping takes twomonths, the January export price represents theMarch import price).

3.154. Similarly, for exports, the import price indices ofthe customer countries could be used. Alternatively, formajor agricultural commodities, the world prices shown

in the IMF’s International Financial Statistics and otherpublications could be used.

3.155. Imports are deducted from total expenditureto derive GDP. In other words, the imported compo-nent of each type of final expenditure and intermedi-ate consumption is excluded from total expenditureto derive the expenditure on domestic output. It istherefore highly desirable that the deflation ofimports and the imported components in the corres-ponding other expenditure categories be as consistentas possible, so as not to create inconsistencies thatlead to errors in total GDP. For example, differentdeflation methods for imported capital equipment incapital formation and imports could generate differ-ences in data that would affect GDP.

Services

3.156. Overall price indices for international trade inservices are not usually available. However, price orvolume indicators are often available for many com-ponents of traded services. If the current price datahave been derived by balance of payments compilers,it is essential to find out the methods they have used,because the data may sometimes have been compiledfrom volume and price indicators. In other cases,other price indices may be relevant. Hotels and trans-port components of the consumer price index may berelevant to travel service exports, while hotels andtransport in the main destination countries may berelevant to travel service imports (adjusted forexchange rate movements). Price indices and implicitprice deflators from particular industries in GDP bythe production approach (exports) or from the sup-plying country (imports) may be useful. In the case ofFISIM, the deflated value of loans and deposits maybe used, as discussed under the production approach.

D. GDP by Income Category

1. General Issues

3.157. The income approach is built up from com-ponents of compensation of employees, operatingsurplus, mixed income, and taxes less subsidies onproducts, production, and imports. It is the leastcommonly used of the three approaches. Incomeestimates are particularly suitable for data by insti-tutional sector, while industry data are more diffi-cult to obtain. Income data provide a usefulperspective on the distribution of income from GDP,for example, looking at compensation of employeesand operating surplus as a proportion of value added


56

for the nonfinancial corporations sector. The incomeapproach requires that businesses have quarterlydata on, at least, profits, depreciation, and net inter-est paid, so the availability of data on businessincomes determines whether independent quarterlyincome estimates are developed. The data could beparticularly important in analyzing issues such asrates of return and profitability. The incomeapproach is potentially useful as an alternative mea-sure of GDP if the other approaches have seriousdata problems; for example, if IO ratios in produc-tion data are known to be changing rapidly with thebusiness cycle.

3.158. The drawbacks of the income approachshould also be noted. It does not support constantprice and volume estimation because not all of theincome components of GDP have a price dimension.In addition, the ability to produce data by industry ofestablishment on a quarterly basis is limited becausesome income components are only obtainable at theenterprise level.

3.159. Benchmark data for the income approachcan be compiled in two ways. The income estimatescan be compiled in the same way as value added inthe production approach—that is, from goods andservices produced less goods and services used—with the additional step of using expense data tosplit value added among compensation of employ-ees, net taxes on production, and the residual,namely, operating surplus/mixed income. As for theproduction approach, getting this information is notusually feasible in a quarterly context. Alternatively,income estimates can be built up from the primaryincome components. This method is viable in somecountries on a quarterly basis using profits, interest,and depreciation as indicators.

3.160. In the absence of an independent estimate ofGDP from the income side, an income split can usu-ally be derived with one category as a residual. Suchdata are as analytically useful as the full approach.Operating surplus/mixed income is always theresidual in countries that use this method, because itis the most difficult component to measure.

2.Value Indicators

a. Compensation of employees

3.161. Data on compensation of employees arereadily available in many countries. The major indi-cators are

• administrative byproducts from the collection ofsocial security or payroll taxes,

• business surveys of employment and wages andsalaries, and

• business or household surveys of numbers ofemployees in conjunction with business surveys ofaverage wages.

Where government regulates employment, clear def-initions of employment and data are usually readilyavailable. The data may refer to total compensation ofemployees paid or received, but an industry or insti-tutional sector split may also be available.

3.162. Often only wages and salaries are availablequarterly. Pension fund contributions and other socialcontributions paid by employers are also included inthe definition of compensation of employees. Datamay be available for programs run or highly regu-lated by government, but data are less likely to beavailable for private programs, where they wouldneed to be collected by survey or derived using wagesand salaries as an indicator. There is also a wide vari-ety of supplements and fringe benefits that vary fromcountry to country, such as annual bonuses, thirteenthmonth of salary, profit sharing, stock plans, conces-sional loans, discounts on purchases, commissions,redundancy payments, and remuneration in kind.Ideally, quarterly source data would also cover theseitems. If some items are not available, and especiallyif these items are small and/or stable, use of the avail-able items to indicate the unavailable ones will bequite acceptable (i.e., an implicit ratio adjustmentthrough benchmarking the quarterly data to annualdata that include these items). However, the larger ormore volatile they are, the stronger the case for col-lecting additional data to record them separately.

3.163. In quarterly estimates, there are potentiallyimportant questions of allocation over time that aremore significant than in annual data. The usualnational accounting concept requires that compensa-tion of employees be recorded on an accruals basis.For payments that are paid once a year but earnedduring the year, it would be desirable that they beallocated over the time they accrued, not just thequarter in which they are paid.

b. Operating surplus/mixed income

3.164. An indicator that approximates gross operat-ing surplus or mixed income can be derived byadding operating profits, net interest paid, and depre-ciation. These kinds of business accounting data can

GDP by Income Category

57

potentially be collected directly from businesses bysurveys.

3.165. Profits data should be collected with defini-tions as close as practical to national accounts con-cepts. “Operating profit” is closer to the nationalaccounts concept than some bottom-line profit mea-sures, to the extent that it excludes one-off items suchas capital gains, foreign exchange gains and losses,and insurance claims. It also excludes income fromthe operation of other enterprises, that is, profitsreceived as dividends from subsidiaries and othershare holdings. The 1993 SNA definitions of produc-tion and, therefore, operating surplus also exclude theeffect of provisions for bad debts, so these should beadded back. In a quarterly context, some adjustmentsmay need to be made implicitly through benchmark-ing an incomplete quarterly indicator to the morecomprehensive annual data. Business accountingmeasures of profits include the effect of pricechanges from inventories, which should be excludedin national accounts measures. (The adjustmentwould be the same as the corresponding adjustmentsmade to the production and expenditure estimates,that is, the inventory valuation adjustment discussedin Annex 3.1.)

3.166. Net interest paid and depreciation also needto be added back to profits to get closer to gross oper-ating surplus and mixed income. It would, therefore,be worth collecting data on these items at the sametime as profits, because the relationship of operatingsurplus to profits is likely to be much less stable thanthe relationship of operating surplus to profits plusnet interest and depreciation. Expense data fromdetailed annual or benchmark surveys would allowthe identification of other expenses that are not inter-mediate consumption, compensation of employees,or taxes on production. Similarly, detailed incomedata would allow the exclusion of any items that werenot from production. If these factors are small andstable, an implicit ratio adjustment through thebenchmarking process may be suitable. Otherwise,consideration may need to be given to collecting thedata quarterly.

3.167. Large enterprises often calculate theirincomes on a quarterly or even monthly basis, andpublicly listed companies are often required torelease quarterly or half-yearly information.Similarly, data may be available for governmententerprises and market producers within generalgovernment. Privately held corporations and unin-

corporated enterprises are typically less inclined tohave sophisticated monthly or quarterly accountingsystems. This is changing, however, with computer-ization of business accounts. Standard accountingsoftware packages can make quarterly and evenmonthly data available to even the smallest of busi-nesses. Once the basic transactions are recorded,these packages can generate data for any requiredperiod or level of detail at little extra cost. Manysmall enterprises do not have quarterly accounts,particularly in developing countries. In these cases,their operating surplus cannot be collected, but itmay be derived by estimating their output, interme-diate consumption, and compensation of employ-ees. The same indicators used for estimating valueadded under the production approach could be usedand estimates of their wages and net taxes on pro-duction deducted. In the case of ownership ofdwellings, the sources for estimating output andvalue added can be used with the addition of data onproperty taxes paid and compensation of employ-ees. To the extent that the same indicators are usedin the income and production approaches, theybecome less independent and more integrated.

c. Taxes and subsidies on products, production, andimports

3.168. Data on total taxes on imports, value addedtaxes, other taxes and subsidies on products, andother taxes and subsidies on production are usuallyavailable from a government finance statistics (GFS)system. Although GFS systems are generally amongthe most accurate and timely data sources, the datacan suffer from problems of time of recording andmay not provide any industry/institutional sectorsplit.16 Typically, GFS data have been compiled on acash basis, not on an accrual basis as required in thenational accounts. However, an accrual basis isbecoming more common and will be recommendedin the forthcoming Manual on Government FinanceStatistics. Knowledge of the tax payment regulationsmay provide a basis for adjusting cash-based data toan approximately accrual basis. In some cases, state,provincial, or local government data may not beavailable for the most recent quarters. If this is thecase, it would be necessary to make estimates. Forlarge components, the estimate should be based onactual data on trends in the tax base and changes intax rates, while simpler methods could be used onsmall items.


58

16An industry and/or sector split may sometimes be possible from theunderlying administrative data.

3. Volume and Price Indicators

3.169. The income approach is oriented to currentprice data only because prices of some income com-ponents are not observable. It is possible to measurelabor inputs in volume terms and make estimates of nettaxes on products at base year rates, but there is nomeaningful price or volume dimension to operatingsurplus/mixed income and other taxes on production.

3.170. A few countries derive GDP by the incomeapproach at constant prices by deflating by the

implicit price deflator for GDP from the productionor expenditure-based estimates. Only if the income-based GDP figure differs from the other approachwill this give a different GDP, and it will differ fromthe other approach by the same percentage as at cur-rent prices. This treatment is valid only for totalGDP and is not valid for splits by type of income.Deflating income components by a generalizedprice index, such as the CPI, is a measure of pur-chasing power (called “real” income in the 1993SNA) that should not be confused with volume mea-sures of product.

GDP by Income Category

59

Annex 3.1. Estimation of Changes in Inventories

60

3.A1.1. This annex discusses the calculation ofchanges in inventories from business accounting dataand gives a simple example. In most countries,accounting practice is to value withdrawals from inven-tories at historic cost, that is, the prices at the time ofacquisition or some notional approximation, rather thanthe prices at the time of withdrawal as required by the1993 SNA and economic concepts. In a few countries,most of which have had high inflation, accounting prin-ciples use a current replacement price concept approx-imating the one used by the 1993 SNA. If prices arechanging, the change in the book value of inventoriesbetween the beginning and end of the period will beaffected by valuation changes. Changes due to pricemovements do not contribute to GDP and should beexcluded from production, income, and expendituredata. The valuation effects are usually removed by aninventory valuation adjustment (IVA). The IVA shouldbe deducted/added to the book value of changes ininventories, operating surplus, and value added.17

3.A1.2. The inventory valuation practices of busi-nesses need to be understood before making calcula-tions. In historic cost measures, inventories as of theend of each quarter are valued at a mix of prices paidover several earlier periods. If data are at historic cost,the periods that prices relate to need to be known inorder to adjust from those prices to current prices.Historic cost has several variations, of which the mostcommon are FIFO (first in, first out), LIFO (last in, firstout), WAC (weighted average cost), and “specific cost.”Note that, other than specific cost, the valuation meth-ods do not necessarily reflect actual ages of products inthe inventory—they are simply valuation conventions.

3.A1.3. FIFO means that withdrawals are valued atthe earliest prices, and hence the stock of inventoriesis valued at relatively recent prices. In contrast, underLIFO, the withdrawals are at recent prices, but thestock of inventories is valued at old prices. Thus,

FIFO usually results in lower values of withdrawalsand higher values of inventories, and it usuallyrequires larger valuation adjustments to withdrawalsthan does LIFO. However, under FIFO, the valuationof stocks of inventories is more stable and recent, soinventory valuation calculations are more straightfor-ward. The specific cost valuation is the least abstractand is now feasible as a result of computer-basedinventory recording. Rather than using a hypotheticalvaluation rule, with specific cost valuation, each itemis valued individually at its actual price at the time ofits purchase or production. In many businesses, thiswill approximate FIFO to the extent that inventorymanagement practice is to turn goods over quickly.

3.A1.4. Sometimes, the historic cost principle ismodified to allow for declines in value (COMWILvaluation, i.e., “cost or market, whichever is less”). Ifprice declines are major, this may need to be takeninto account.

3.A1.5. The data required to derive value of physicalchange in inventories are the following:• Values of opening (beginning of period) and clos-

ing (end of period) stocks of inventories.Preferably, these would be classified by productgroups and/or industries and/or stages of process-ing (raw materials/work-in-progress and finishedgoods/goods for resale). If available, product datawould be preferable to industry data because theprice behavior would be more homogeneous.

• Price indices for relevant products.• Information on the product composition of

inventories.• Information on the valuation methods used by

enterprises.• Information on the age structure of inventories.

3.A.1.6. The steps involved in the calculation are thefollowing:• Create an inventory-specific book value deflator.

The deflator should reflect both the product com-position and the valuations used for the itemsincluded in the book values.

17Note that “holding gains” in the 1993 SNA sense arise from changes inprices during the period. If the source data are at historic cost, the inven-tory valuation adjustment (IVA) will cover holding gains from changesin prices between the time of initial valuation and the current period.

• Deflate the opening and closing book values toobtain constant price values.

• Obtain changes in inventories at constant prices asthe difference.

• Create reflators to convert from constant price tocurrent price values.

• Reflate constant price values of levels and changesin inventories to obtain current price values.

3.A1.7. The price indices would also need to reflectthe products included in inventories. These would notnecessarily be in the same proportions as in sales, pro-duction, or intermediate consumption. Data on inven-tories should be collected in detail, if possible. For aquarterly collection, this may not be viable, so moreaggregated data may have to be collected.

3.A1.8. The appropriate price index for raw materi-als would be input prices; for work-in-progress andfinished goods, it would be output prices. Goods forresale are the typical holdings of retailers and whole-salers, but manufacturers and others may also act aswholesalers. The appropriate price index wouldreflect these goods and could be different from theequivalent finished goods indices because goods forresale could include imports and different types ofgoods. More detailed information on the productcomposition of inventories could be obtained inannual or less frequent business surveys or in a sur-vey or interview program for a subsample of firms. Ina quarterly system, a range of producer, wholesale,import, and consumer prices may be combined infixed proportions. It would be desirable to assess thestability of the composition of inventories to seewhether the fixed proportions need to be changed.

3.A1.9. Note that two price indices usually need tobe derived for each period and component: first, aprice index to deflate historic cost data to constantprices, and second, a price index to reflate constantprice data to current prices. The two indices are dif-ferent because the historic cost prices of goods ininventories differ from current replacement prices.For the first price index—the historic cost deflator—a mix of historic prices is obtained. For instance, if

the producer price index relates to average prices ofthe month and if investigations have shown that theinventory is valued by FIFO principles at prices of theprevious three months—each month with an equalquantity and none from earlier months—the deflatorfor the book value on December 31 would be anequally weighted average of the October, November,and December price indices. (This treatment assumesthat the prices and transactions were spread evenlyover the period.) The most sophisticated inventoryvaluation adjustment calculations have proportionsfor weighting previous months’ prices that take intoaccount fluctuations in the level of inventories (e.g.,when inventory levels fall, the proportions of newerinventories rise).

3.A1.10. The second price index is for convertingfrom base period prices to current replacementprices. For example, for flow data for the fourth quar-ter, the index would be an average of October,November, and December prices. The required cur-rent price measure should reflect the average pricesof the whole quarter. Note that prices used for the endof the period would not be comparable to prices usedfor other transactions during the quarter.

3.A1.11. Even when balance sheets are not calcu-lated, it is necessary to obtain both the opening andclosing values in order to make valuation adjustmentsto inventory data in value terms. Direct data on thechanges in inventories are almost useless because val-uation effects occur on the whole value and so cannotbe calculated without data on the inventory levels.

3.A1.12. The quality of all these calculations wouldusually be improved by working at a more detailedlevel of product or industry dissection. This isbecause price movements are more likely to behomogeneous at a more detailed level. To the extentthat price movements are similar across differenttypes of goods, the results will not be affected somuch by aggregation or choice of index. Primarycommodity prices that are particularly volatile anddiffer from product to product are a higher priorityfor disaggregation.


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62

Example 3.A.1. Calculation of Changes in Inventories

InformationThe book values of inventories of coal for use as a raw material are as follows:

December 31, 2000 1,000.0 March 31, 2001 1,500.0

Both are valued at historic cost on a first-in, first-out valuation basis.The inventory holdings at both points represent three months of purchases.The coal was acquired evenly over the previous three months.

Price indices and constant price data use a reference base of 2000.The price index for coal is as follows:

2000 2001

January 94.5 106.5 February 95.5 107.5 March 96.5 108.5 April 97.5 109.5 May 98.5 110.5 June 99.5 111.5 July 100.5 112.5 August 101.5 113.5 September 102.5 114.5 October 103.5 115.5 November 104.5 116.5 December 105.5 117.5 Average 100.0 112.0

The price indices are based on average prices for the month.

Calculations (1) Derive an inventory-specific price index to deflate the book value of inventories.

Weight Dec. 31, 2000 Mar. 31, 2001

2-3 months 0.3333333 103.5 106.5 1-2 months 0.3333333 104.5 107.5 < 1 month 0.3333333 105.5 108.5 Total index 1.0000 104.5 107.5

The resulting index reflects the book valuation of the inventories, based on equal proportions of coal from each of the three previous months.

A more complex example would involve several price indices and differing proportions being assigned to each month (typically showing atapering off for earlier months). If the weights for each month are based on quantities or volumes, the indices can be combined in this way;but if the weights are based on values, the total value should be split into component months of purchase according to the proportions andeach month deflated by its price index.

(2) Deflate the opening and closing book values of inventories to obtain constant price values.

Dec. 31, 2000 Mar. 31, 2001

Book value of inventories 1,000.0 1,500.0 Deflators 104.5 107.5 Value of inventories at average 2000 prices 956.9 1,395.3 (Derived by dividing the book value by the book value deflator.)

(3) Derive the change in inventories at constant prices.The change in inventories from January through March 2001 at average prices of the year 2000 is 438.4 (=1,395.3 – 956.9)

(continued on next page)


63

Example 3.A.1. (continued)

(4) Derive price indices to reflate from constant price to current price values.

Index for flows, q1 2001 107.5 (average January 2001 through March 2001) Index for stocks, Dec. 31, 2000 106.0 (average December 2000 through January 2001) Index for stocks, Mar. 31, 2001 109.0 (average March 2001 through April 2001)

As the original price index data relate to the average for the month, an end-of-month value (required for balance sheet items) can be approx-imated, in the absence of better information, as the (geometric) mean of the two surrounding months.

(5) Reflate constant price values to obtain current price values.

Estimated change in inventories at average prices of January through March 2001 471.3 = 438.4 /1.075

Inventory valuation adjustment 28.7 = 500.0 – 471.3 (book value of inventory changes less estimated change in inventories at average prices of January through March 2001 where book value ofinventory changes are equal to 500.0 = 1500.0 – 1000.0)

Stock data at current pricesInventory value at current prices on December 31, 2000 1014.4 = 956.9 • 1.060 Inventory value at current prices on March 31, 2001 1,520.9 = 1,395.3 • 1.090 Total change in inventory current price values January through March 2001 506.6 = 1,520.9 – 1,014.4 “Holding gains” in the 1993 SNA sense 35.3 = 506.6 – 471.3

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IV Sources For Other Components of the 1993 SNA

A. General Issues

4.1. The 1993 SNA presents a comprehensive set ofrelated accounts that are of considerable analyticalinterest and were designed with a wide range of eco-nomic analyses in mind. The accounts can also helpcompilers identify inconsistencies and errors in thedata. Just as compilers are urged to extend theirannual data to a wider range of accounts, a quarterlynational accounts (QNA) system should seek to covermore than GDP and its components.

4.2. For the convenience of countries at the first stageof development of QNA, the previous chapter pre-sented sources organized around the three approachesto GDP measurement. The splits of GDP by expendi-ture and income components discussed in Chapter III,however, also provide the foundation for the widersequence of accounts. The expenditure approach toGDP provides components of the goods and services,income, and capital accounts. The income approach toGDP provides data used in the income accounts.

4.3. The general issues associated with the identifica-tion and evaluation of sources discussed in the intro-duction to Chapter III also apply to the other accounts.As with data used in estimating GDP components,quarterly indicators for other national account variablesoften have shortcomings and need to be benchmarked.

4.4. QNA potentially can include the whole sequenceof accounts, but coverage invariably is more limited.There are no recommendations on which accountsshould be given priority to be produced quarterly;rather, the choice will depend on user priorities, theavailability of indicators, and the stage of developmentof QNA in the country. The choice will also be influ-enced by the range of accounts published annually.Data for items beyond GDP and its components maynot be included in the initial stage of QNA develop-ment and may have lower priority and accuracy than

the quarterly GDP measures, but they should not beignored, especially in the plans for future improve-ments. Several countries produce some of the accountsin the 1993 SNA sequence quarterly. Although the cov-erage differs, the most common are the transactionaccounts for the total economy, general government,and financial corporations.

4.5. The sequence of accounts can be presented ingross or net terms, that is, with or without deductingconsumption of fixed capital. For simplicity, the fol-lowing discussion will refer to gross measures, butquarterly consumption of fixed capital can beobtained. Annual estimates of capital consumption thatfollow 1993 SNA concepts are usually derived by theperpetual inventory method (PIM); in the same way,quarterly estimates could be derived by enhancing the PIM calculations with a quarterly dimension.Alternatively, capital consumption is typically a rela-tively stable item because the stock of capital is largein relation to additions and retirements, so quarterlydistribution and extrapolation of annual data wouldusually give acceptable estimates.1

B. Main Aggregates for the TotalEconomy

4.6. The main aggregates for the total economyinclude important balancing items such as national anddisposable income, saving, and net lending/net borrow-ing. They can usually be compiled at an early stage inthe development of QNA because the data require-ments are quarterly splits of current price GDP by typeof expenditure and quarterly balance of payments.Splits of GDP by expenditure can be derived eitherdirectly or, if necessary, by treating one component as aresidual. In the usual pattern of statistical evolution,

1See Chapter VII for methods of distribution without use of indicatorsthat avoid step problems.

quarterly balance of payments data are already avail-able in a country setting up a new QNA system.National accounting systems usually work “down” the1993 SNA sequence of accounts—starting with GDPand subsequently deriving balancing items for incomeand capital accounts. It is also possible in a countrywhere financial data are better than production data tostart with the balance on the financial accounts and sub-sequently derive saving, income, and GDP by working“up” the sequence of accounts. An example of consoli-dated and simplified accounts is shown in Box 4.1.2

C. Accounts for the Total Economy

4.7. A further step in the development of a QNAwould be the development of the unconsolidatedaccounts for the economy as they appear in Annex V

to the 1993 SNA. The data required for this presenta-tion differ from the presentation of main aggregatesbecause income and transfer flows among residentsare also shown. This presentation makes the links tothe 1993 SNA formats and institutional sectoraccounts more obvious and facilitates observation ofsome relationships. The unconsolidated accountsrequire more data than the consolidated presentation,however, and thus tend to occur at a later stage in thedevelopment of QNA. Because many of the datasources for transactions among residents have aninstitutional sector perspective, compilation ofunconsolidated accounts for the total economy alsocontributes to some institutional sector data.

1. Production Account

4.8. The production account in gross terms showsoutput at basic prices plus net taxes on products asresources, and intermediate consumption as a use.GDP is the balancing item. The estimation of GDP atcurrent prices by the production approach provides

Accounts for the Total Economy

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Box 4.1. Main Aggregates for the Total Economy

Goods and Services Account in the 1993 SNA (consolidated)

GDP 1,854= Government consumption expenditures 368+ Households consumption expenditures 1,015+ NPISHs* consumption expenditures 16+ Acquisitions less disposals of nonfinancial assets 414+ Exports 540– Imports 499

Current and Capital Accounts in the 1993 SNA (consolidated)GDP 1,854 Source+ Net primary income received from abroad 29 BOP**= National income, gross 1,883+ Net current transfers received from abroad –28 BOP= Disposable income, gross 1,855– Final consumption expenditures 1,399

Government 368Households 1,015NPISHs 16

= Saving, gross 455+ Net capital transfers received from abroad –3 BOP– Gross capital formation (fixed, inventories, valuables) 414= Net lending (+)/Net borrowing (–) 38 BOP

Financial Account in 1993 SNANet acquisition of financial assets less net acquisition of liabilities 38 BOPErrors and omissions 0 BOP= Net lending (+)/Net borrowing (–) 38 BOP

*NPISHs = nonprofit institutions serving households**BOP = balance of paymentsMore detail of the financial account, including gross flows by type, may be available from the BOP.Numbers are from the example in the 1993 SNA. Figures in italics are derived.

2The presentation in Box 4.1 is derived from the 1993 SNA sequenceof accounts by consolidation, that is, removing flows between resi-dents that appear on both sides of the same account.

these items by industry. In addition to the presentationof the whole production account and a fuller presenta-tion of the production process, the explicit calculationof output and intermediate consumption is recom-mended as good compilation practice for reconcilingdata with other sources and manifesting the implica-tions of assumptions.

2. Income Accounts

4.9. The four income accounts shown in the 1993SNA are each discussed separately in this subsection.In addition to the specific issues for each account,there are some timing issues that are particularly seri-ous in QNA and that apply to more than one of theincome accounts.

4.10. Timing issues become particularly significantfor some quarterly income account items. Incomesmay be paid in lumps, rather than evenly through theyear. Examples of paying in lumps include dividends,interest, taxes, and employee bonuses. The basic prin-ciple on the timing of recording in the 1993 SNA is theuse of the time of accrual. In the case of distributivetransactions, the time of accrual is when the claimarose rather than when it was paid. This issue of tim-ing of recording also plays a role in the annual nationalaccounts (ANA), to the extent that some paymentsmay partly relate to another year, but the effect is morepronounced in the QNA.

4.11. In order to deal with timing issues, it is usefulto identify two categories of payments based on theirrelationship to previous periods:(a) Payments that have a purely ad hoc character

should be recorded in the period in which they areactually made. Dividends, for example, are usu-ally determined only after the books are closed ona fiscal year and may not even relate to the com-pany’s profits over that year.

(b) Payments that have a fixed relation to a particularperiod (e.g., accrued in a previous period oraccrued over a number of accounting periods)should be allocated to the periods in which theyaccrued. Examples are taxes on incomes and prod-ucts that may be collected in a subsequent periodand vacation bonuses that build up over the periodof a year and on which employees have a claim ifthey leave the employment before payment is due.To obtain accrual-based data, the options mayinclude surveys if businesses use accrual princi-ples, allocating data on payments back to the rele-vant periods, or estimating the accrual of incomefrom data on the underlying flow (e.g., income

taxes from wages and profits, possibly subject to alag). Once these issues are considered on a quar-terly basis, it may also be realized that the annualdata need to be adjusted to meet accrual principles.

4.12. The application of accrual principles to quar-terly data in such cases may present such seriouspractical and conceptual problems that it becomes anobstacle to completion of the data. In these cases, itmay be better to publish data on a cash basis whileclearly stating the problems than to publish nothingor publish something that has been subject to adjust-ments without a firm foundation.

a. Generation of income account

4.13. The generation of income account shows thederivation of operating surplus/mixed income asGDP less the sum of compensation of employees andtaxes less subsidies on production and on imports.This account shows the identity that underlies thecalculation of GDP by the income approach.Accordingly, the required data have already beencompiled if the income approach has been used or anincome split has been compiled with operatingsurplus/mixed income as a residual.

b. Allocation of primary income account

4.14. The allocation of primary income accountshows the derivation of national income. Primaryincomes include compensation of employees andproperty income (interest, dividends, etc.). The dis-tributive income transactions paid between residentscancel out for the whole economy. As a result, grossnational income (GNI) can be derived simply as GDPplus primary income receivable from the rest of theworld less primary income payable to the rest of theworld. The external primary income items can beobtained from the balance of payments and are usu-ally derived from surveys or banking records.

4.15. The allocation of primary income account inunconsolidated form, as recommended in the 1993SNA, requires estimates of property income paid byresidents to other residents. The interest and insur-ance components may be available as byproducts ofthe system of financial regulation or financial sectorsurveys. Alternatively, the flows may have to beestimated from the levels of the assets and liabilitiesand raised by a rate of return. Dividends could beestimated from a survey of businesses, from pub-lished statements of companies listed on the stockexchange, or from (lagged) estimates of operatingsurplus. Dividend behavior depends on national

IV SOURCES FOR OTHER COMPONENTS OF THE 1993 SNA

66

circumstances such as company law, business prac-tices, and tax law. The predictability of this behaviorcan be assessed from past annual patterns. Seasonalpatterns within the year may be unknown withoutextra information but present fewer serious problemsfor analysis (see Chapter VIII).

c. Secondary distribution of income account

4.16. The secondary distribution of income accountshows the derivation of disposable income fromnational income by taking into account redistributionof income through taxes, social security contributionsand benefits, and other transfers. Transfers paid bygovernments are usually available from governmentfinance statistics. Other items include non-life insur-ance premiums and claims, which may be availablefrom regulators or may be estimated based on dis-tributed annual values if they are accrued evenlythroughout the year. Note that these transactionswithin the country cancel out in total and so can beignored in a consolidated presentation. Internationalaid, social contributions and benefits to governmentsof other countries, and other current transfers to andfrom the rest of the world can be obtained from thebalance of payments.

d. Use of disposable income account

4.17. The use of disposable income account showsdisposable income as a resource. It shows household,nonprofit institutions serving households (NPISHs),and government consumption as uses, and saving asthe balancing item. Disposable income is obtainedfrom the secondary distribution of income account,while consumption is derived as part of the expendi-ture approach to measuring GDP.

3. Capital Account

4.18. The capital account shows how saving and cap-ital transfers are available to fund capital formationand capital consumption with net lending or borrow-ing as the balancing item. Saving is obtained from theuse of disposable income account, while capital for-mation is obtained as was shown under the expendi-ture approach to GDP. Capital transfers payable orreceivable by government, if needed for an unconsol-idated presentation, can be obtained from a system ofgovernment finance statistics. Capital transfersbetween residents and nonresidents can be obtainedfrom the balance of payments. Following the harmo-nization of statistical concepts between the 1993 SNAand the fifth edition of the Balance of PaymentsManual, net lending/borrowing is equivalent to thesum of the current and capital account balances in the

balance of payments. The elaboration of saving andlending is important in understanding the forcesbehind current account imbalances.

4. Financial Accounts

4.19. The financial accounts show changes causedby transactions in financial assets and liabilitiesclassified by type of instrument. Data on stocks offinancial assets or liabilities by counterpart sectorsare often readily available from the financial corpo-rations as a byproduct of regulation or monitoring ofthe financial sector. Data on transactions, however,are less readily available, so there may be problemsin splitting changes in stocks into transactions andother changes in volumes and values. Financial cor-porations tend to be relatively large and havesophisticated records, however, making collectionof data on transactions and other flows practical andfeasible. In contrast, the counterparts to the finan-cial corporations in these transactions are wide-spread and often small, making data collection lessfeasible.

4.20. Other sources may be available to check orcomplement data from the financial corporations.Data on government financial transactions can oftenbe obtained directly. The financial account of thebalance of payments records transactions with non-residents. It is important that consistent classifica-tions and valuations be used in all these sources. Ifall are consistently defined, the government andexternal transactions with the financial sector can bereconciled. Also, the transactions not involving thefinancial sector can be obtained to complete thetotals. The data will also support the simultaneousdevelopment of the accounts by institutional sector.

4.21. If transactions data are not available, the dif-ferences between opening and closing balancesheets may have to be used as a proxy. In additionto changes caused by transactions, however, thedifference between opening and closing valuesincludes revaluation and other changes in volumesof assets.

4.22. Information on financing through shares andother equities can be more difficult to obtain. Thisfinancing occurs outside the financial sector, andthus data are frequently less complete. For listedcompanies, data may be available from stock-exchange registers. In other cases, company regis-tration requirements include issue of equity. In stillother cases, surveys would be necessary.

Accounts for the Total Economy

67

4.23. The balancing item on the financial accountis net lending or borrowing. Net lending or borrow-ing is conceptually the same as in the capitalaccount. In practice, if the measure is derived inde-pendently, it could differ significantly because ofnet errors and omissions. In a country with well-developed financial statistics, the net errors andomissions may help point to problems in otheraccounts. Alternatively, net lending or borrowingderived from the financial account can be used toobtain a missing item in the capital account as aresidual (or vice versa).

4.24. In consolidated form, the financial account ofthe 1993 SNA presents the same information as thefinancial account of the balance of payments. Thetotal economy and balance of payments are the samebecause all the internal transactions net out.

5. Balance Sheets

4.25. The balance sheets show the opening and clos-ing values of assets and liabilities. The financial assetsand liabilities part of the balance sheets use similarsources as, and should be compatible with, the trans-actions data shown in the financial accounts. Theinternational investment position is the balance ofpayments equivalent of the national accounts balancesheets for the financial assets and liabilities, and thenet values for each type of instrument are the same.

4.26. Estimates for nonfinancial assets are derivedby methods similar to those used annually. Forinventories, the same source as for changes ininventories can provide either inventory levels or anestimate of the change in the levels since the previ-ous estimate of the level. For land, the basic volumeis fixed or changes only slowly. For fixed capital,these estimates tend to be based on calculationswith the perpetual inventory method. The sameissues arise as for estimates of consumption offixed capital. The calculations could be made quar-terly, or, alternatively, they could be made as inter-polations from the annual values. The stability ofcapital is typically strongest in volume terms, whileasset prices can be volatile. As a result, currentprice measures should preferably be derived fromthe volume measures for each component if thereare price indices available for each of the majorasset types (e.g., land, buildings, various categoriesof equipment).

4.27. The collection of balance sheet data is moresubject to problems in valuation than transaction

data. Because some stock data in business accountsare valued at historic costs rather than current values,adjustments may be needed. It is a good practice toobtain information on valuation methods at the sametime the value data are collected.

4.28. Balance sheet data are useful in measuringproductivity (using capital input) and analyzingspending and saving decisions (through wealtheffects). As a result, interest in these items on a quar-terly basis has been increasing among economists.

4.29. The difference between the opening andclosing values in the balance sheets is explained bytransactions, revaluations, and other changes. Thetransactions are shown in the capital account fornonfinancial assets and financial accounts forfinancial assets. The revaluations could be obtainedseparately or residually.

D. Institutional Sector Accounts

4.30. In addition to the sequence of accounts forthe total economy, a more advanced QNA systemmay consider the compilation of the 1993 SNAsequence of accounts by institutional sector. Theinstitutional sector accounts could be introducedsimultaneously or, more commonly, be graduallydeveloped in several stages. For example, central ortotal general government accounts may be intro-duced first because of availability of data and thedesirability of having the data in a nationalaccounting framework to allow them to be linked tothe rest of the economy. Households and other sec-tors could initially be combined and calculated as aresidual. For some institutional sectors, incomeaccounts may be developed before capital accountsbecause of lack of data on transactions in second-hand assets. Financial accounts may be easier toimplement than the nonfinancial accounts becausedata on transactions and stocks of financial assetsor liabilities by counterpart sectors often are avail-able readily from the financial corporations as abyproduct of regulation or monitoring of the finan-cial sector. Data compilers often find the usefulnessof institutional accounts is not appreciated untilafter the data become available, so statistical com-pilers should anticipate future uses.

4.31. In order to assist in understanding the followingdiscussion of the institutional sector accounts, Box4.2 shows the sequence (excluding balance sheets) in


68

matrix form, similar to Table 2.8 in the 1993 SNA. Thetabulation here emphasizes the interrelationshipsbetween sectors. It is intended for presentational pur-poses and should not be taken as a recommendedmain presentation of the data for a QNA publication;first, because it would be expected in practice thatsome accounts and sectors would be missing; and sec-ond, because the QNA usually emphasize time series,the main presentation should be time-series oriented.

4.32. A basic principle of compiling institutionalsector accounts is making use of counterpart infor-mation; that is, in any transaction involving two par-ties, information can be collected from the party fromwhich it can be most efficiently collected. Forinstance, interest paid by government to householdscan be obtained from one or a small number of gov-ernment agencies, rather than a large number ofhouseholds. Counterpart information is the equiva-lent of using commodity balances in the goods andservices and production accounts to fill gaps.Counterpart information becomes particularlyimportant in a quarterly context when there are morelikely to be gaps. One issue to be taken into accountis that data providers may not always be able to pro-vide data on the institutional classification of thecounterparts if they do not have sufficient informa-tion or motivation to do so.

4.33. If the production accounts are based on surveysof businesses and other units, the derivation of pro-duction by institutional sector is practical. All that isrequired is that the institutional sector of the unit beidentified in the relevant survey. Some of the lessdirect methods, however, may not provide any insti-tutional sector splits.

4.34. The income approach to GDP is a foundationfor the income accounts by institutional sector. Theavailability of GDP by income component and insti-tutional sector provides the primary income accountsto be completed by institutional sector. As a result,countries that use the income approach in the QNAsystem typically have better-developed quarterlyinstitutional sector accounts.

4.35. Estimates of capital formation by institutionalsector are practical if the data are collected from thepurchaser rather than the supplier of the capital.These estimates are an important component of thecapital accounts. The institutional sector capitalaccounts are more difficult to prepare than theaccounts for the total economy. For institutional sec-

tor data, it is necessary to cover the secondhand assets(including land), while for the total economy, trans-actions in existing assets largely cancel out (exceptfor transactions with nonresidents, which can beobtained from trade and balance of payments statis-tics, and sales of used vehicles from businesses andgovernments to households). The same considera-tions apply to the stocks of nonfinancial assets forbalance sheets. Similar to the stocks for the wholeeconomy, they are likely to be stable in aggregate,although transactions in secondhand assets may be amore significant issue. From the value of net lendingor borrowing obtained in the financial accounts, itmay be possible to derive a net estimate of acquisi-tion of secondhand assets as a residual (althoughlarge errors and omissions may make this unaccept-able, as they would all accumulate in this small item).

4.36. The financial accounts and the financial compo-nents of the balance sheets are usually among the morecomplete institutional sector data. Balance sheet ortransaction data are often already collected from finan-cial corporations. If the counterparts in each transac-tion, asset, or liability are classified by institutionalsectors, there is a strong basis for compiling the datafor all the sectors, not only the financial corporationsthemselves. In addition, balance of payments andinternational investment position data would showtransactions, assets, and liabilities between nonresi-dents and residents that are not financial corporations.One should also pay attention to financial transactionsand stocks of assets and liabilities not included infinancial sector and balance of payments data, such ashousehold equity in corporations and direct financialrelationships between nonfinancial corporations.

4.37. Net lending/borrowing is the balancing itemfor both the capital and financial accounts. If theaccounts are derived independently, they will act aschecks on each other. Alternatively, if only oneaccount is available, the balancing item can be usedas a starting point for compiling the other. Of course,although the relationship between the balancingitems on the two accounts is a conceptual identity, thebalancing item is a small residual of a number oflarge items and could turn out to be of poor quality ifthere are problems in any of the component series.

1. General Government

4.38. Quarterly data are often readily available forgeneral government or at least central government.The 1993 SNA presentation may involve some refor-matting or supply of more detailed data from the

Institutional Sector Accounts

69


70

Box

4.2

.T

he S

eque

nce

of I

nsti

tuti

onal

Sec

tor T

rans

acti

ons

Acc

ount

s

Use

sR

esou

rces

Non

-N

on-

Res

t of

fin

anci

alFi

nanc

ial

Gen

eral

Hou

se-

finan

cial

Fina

ncia

lG

ener

alH

ouse

-R

est

of

the

Tota

l co

rp-

corp

-go

vern

-ho

lds

corp

-co

rp-

gove

rn-

hold

sTo

tal

the

Wor

ldec

onom

yor

atio

nsor

atio

nsm

ent

+ N

PISH

s*Tr

ansa

ctio

nor

atio

nsor

atio

nsm

ent

+ N

PISH

s*ec

onom

yW

orld

I.P

rodu

ctio

n A

ccou

nt/E

xter

nal A

ccou

nt

of G

oods

and

Ser

vice

s

Out

put,

basic

pric

es1,

753

102

440

1,30

93,

604

1,88

389

929

252

703

Inte

rmed

iate

con

sum

ptio

n

1,72

185

473

188

606

Gro

ss v

alue

add

ed

Taxe

s le

ss s

ubsid

ies

on p

rodu

cts

133

1,85

4G

DP

Impo

rts

of g

oods

and

ser

vice

s49

9

540

Expo

rts

of g

oods

and

ser

vice

s

-41

Exte

rnal

bal

ance

of

good

s an

d se

rvic

es

II.1

.1G

ener

atio

n of

Inc

ome

Acc

ount

Val

ue a

dded

/ GD

P85

473

188

606

1,85

4

762

545

1514

062

Com

pens

atio

n of

em

ploy

ees

133

Taxe

s le

ss s

ubsid

ies

on p

rodu

cts

5851

32

2O

ther

tax

es le

ss s

ubsid

ies

on p

rodu

ctio

n

901

258

5546

542

Gro

ss o

pera

ting

sur

plus

/mix

ed in

com

e

II.1

.2A

lloca

tion

of P

rim

ary

Inco

me

Acc

ount

Ope

rati

ng s

urpl

us/m

ixed

inco

me

258

5546

542

901

–41

6C

ompe

nsat

ion

of e

mpl

oyee

s7

6676

62

Taxe

s le

ss s

ubsid

ies

on p

rodu

ctio

ns19

119

1

6339

113

516

742

47Pr

oper

ty in

com

e 86

141

3215

741

638

(inte

rest

s,di

vide

nds,

rent

s,w

ithdr

awal

s)

1,88

320

929

227

1,41

8B

alan

ce o

f pr

imar

y in

com

e/na

tion

al in

com

e


71

II.2

/3Se

cond

ary

Dis

trib

utio

n of

Inc

ome

Acc

ount

Bal

ance

of p

rim

ary

inco

me/

nati

onal

inco

me

209

2922

71,

418

1,88

3

121

224

1017

8C

urre

nt t

axes

on

inco

me

and

wea

lth21

321

3

322

322

Soci

al c

ontr

ibut

ions

1439

268

132

2

332

1329

289

1So

cial

ben

efits

332

332

1026

911

4613

973

Oth

er c

urre

nt t

rans

fers

1049

108

7324

039

1,85

518

532

388

1,25

0D

ispo

sabl

e in

com

e,ne

t

II.4

Use

of I

ncom

e A

ccou

nt

Dis

posa

ble

inco

me,

net

185

3238

81,

250

1,85

5

1,39

936

81,

031

Fina

l con

sum

ptio

n ex

pend

iture

s

1111

Adj

ustm

ent

for

the

chan

ge in

net

equ

ity11

11

of h

ouse

hold

s on

pen

sion

fund

s

4,56

185

2120

230

Savi

ng,G

ross

–42

Cur

rent

ext

erna

l bal

ance

III.1

Cap

ital

Acc

ount

Cha

nges

in a

sset

sC

hang

es in

liab

iliti

es a

nd n

et w

orth

Savi

ng,G

ross

185

2120

230

456

Cur

rent

ext

erna

l bal

ance

–42

376

250

937

80G

ross

fixe

d ca

pita

l for

mat

ion

2826

2C

hang

es in

inve

ntor

ies

102

35

Acq

uisit

ions

less

disp

osal

s of

val

uabl

es

–72

5A

cqui

sitio

ns le

ss d

ispos

als

of n

onpr

oduc

ed/n

onfin

anci

al a

sset

s

Cap

ital t

rans

fers

,rec

eiva

ble

336

2362

4

Cap

ital t

rans

fers

,pay

able

–16

–7–3

4–8

–65

–1

–39

39–6

95

–50

153

Net

lend

ing(

+)/N

et b

orro

win

g(–)

III.2

Fina

ncia

l Acc

ount

Net

lend

ing(

+)/ N

et b

orro

win

g(–)

–69

5–5

015

339

–39

4964

271

237

120

214

Net

acq

uisit

ion

of fi

nanc

ial a

sset

s

Net

incu

rren

ce o

f lia

bilit

ies

140

232

170

6160

388

*NPI

SHs

= no

npro

fit in

stitu

tions

ser

ving

hou

seho

lds

accounting system; however, government accountingsystems have traditionally not emphasized balancesheets, so that data may be limited to the transactionaccounts. In addition, issues of timing may be a prob-lem in countries where the government accounts are ona cash basis because timing issues are more significantin quarterly data. The Government Finance StatisticsManual is used as a basis for presentation of govern-ment data in many countries and provides data that canbe converted to 1993 SNA formats. With the revision ofthe Government Finance Statistics Manual, most con-ceptual differences with the 1993 SNA will beresolved, although the presentation will differ.

4.39. Quarterly government accounting data that donot follow national accounts principles may alreadybe available in some countries. Analysts may alreadyuse these data to meet many needs. It is worthwhile,however, to also produce the national accounts pre-sentation of government, as it adds value by facilitat-ing analysis of links between government and otherparts of the economy and requires relatively littleextra compilation cost.

4.40. In most countries, central government data canbe obtained relatively easily. As with governmentdata for measuring GDP discussed in Chapter 3,state/provincial and local data may be available onlylater or in less detail. Even if all data are available atthe same time, it may be desirable for analytical pur-poses to show the accounts for each level of govern-ment separately.

2. Financial Corporations

4.41. There is often a wide range of data obtained asa byproduct of regulation of the financial corpora-tions sector. As mentioned in the context of financialassets and liabilities, this sector is usually relativelygood in terms of the availability of administrativebyproduct data and ability to provide survey data. Asfor general government data, the 1993 SNA providesa presentation for quarterly financial data in an inter-nationally standard manner that is designed to sup-port general economic analysis.

3. Households

4.42. A few countries have continuous household sur-veys that collect revenue and expenditure that wouldprovide a basis for some of the accounts. As mentionedin Chapter III in the discussion of sources for householdconsumption, household surveys may suffer from levelbiases; for QNA purposes, however, the data are suit-able indicators of movement if the bias is consistent.

4.43. Alternatively, the specialized nature of manycomponents of household income and expendituremeans that many of the items of the accounts can becompleted from income, expenditure, and counter-part accounts. Households receive almost all com-pensation of employees, mixed income, and socialbenefits, with the only adjustments for payments toand from nonresidents that can be obtained from thebalance of payments. Households typically receivemost of the operating surplus of dwellings. Pensionsand annuities are also specific to households, anddata are often available from pension providers or arelikely to be relatively stable from quarter to quarter.Interest receivable and payable by households couldbe available separately from financial corporations,or it could be estimated from data on householddeposits and loans if those assets and liabilities areidentified separately by the financial corporations.The remaining major income component is divi-dends. The timing and data issues for dividends werediscussed in the context of accounts for the totaleconomy. Dividends received by households may beable to be estimated from lagged operating surplus ofcorporations and (in some cases) property incomedata from the balance of payments, if they show a sta-ble relationship with the corresponding householdincome items in annual data.

4.44. For the uses of income, a range of indicators isusually already available. Household final consump-tion is derived as part of the expenditure approach toGDP and relates entirely to the household sector.Social contributions are obtainable from governmentaccounts and are also specialized to households.Taxes have varying degrees of specificity to house-holds. Interest and insurance premiums payable byhouseholds can be obtained or estimated in similarways to the corresponding income items discussed inthe previous paragraph. A capital formation surveycovering businesses may be designed to producegross capital formation by institutional sector byidentifying the institutional sector of each business inthe survey. If all the above items were obtained, itwould be possible to derive income and capitalaccounts for households, and, hence, the analyticallyimportant household saving and net lending balanc-ing items.

4. Nonfinancial Corporations

4.45. A direct survey of corporations would providethe necessary data, but such surveys are seldomconducted on a quarterly basis. Data may be availablefor nonfinancial corporations as a result of the


72

lodgment of information under company legislation.Alternatively, companies listed on the stockexchange or foreign corporations may be required todisseminate quarterly or half-yearly data, and thesecompanies may constitute a significant or representa-tive proportion of the nonfinancial corporations sec-tor. It would be necessary to investigate from annualdata whether the other nonfinancial corporationsbehaved in the same way as the unobserved ones.

4.46. If such direct sources are unavailable, data fornonfinancial corporations may be obtained fromcounterpart transactions with the other sectors or as aresidual. Dividends play a large part in the incomeaccounts for nonfinancial corporations. Taxes anddividends are often not determined on a quarterlybasis; for example, dividends may be payable twice ayear, and profits tax four times a year on the basis ofthe previous year’s earnings.

5. Nonprofit Institutions Serving Households

4.47. NPISHs often receive little attention in ANAand are not always economically volatile enough tojustify high priority in quarterly data. NPISHs maybe quite significant in some countries, however. TheNPISH sector is defined more narrowly in the 1993SNA than the normal use of the term nonprofit maysuggest, as it is confined to institutions that do notcharge economically significant prices and may dif-fer from some sources of information about nonprofitinstitutions. For example, private schools, private

hospitals, and trade unions that charge fees that covera substantial proportion of costs are not included inthe NPISHs sector.

4.48. Government transfers or transfers from the restof the world may be major contributions to dispos-able incomes of NPISHs. When that is the case, suchindicators would be available from counterpartsthrough government accounts or the balance of pay-ments, respectively. A household expenditure surveycould provide data on donations and other revenuefrom households. If the NPISHs sector is economi-cally significant, as it is in some countries, surveys ofthe institutions themselves would be necessary.Although undesirable for analytical purposes, theNPISHs sector is sometimes combined with thehousehold sector in quarterly data.

6. Rest of the World

4.49. Balance of payments statistics provide all thedata required for the rest of the world accounts. As aresult of the harmonization of balance of paymentsand national accounts concepts, there is simply aneed for rearrangement of items to a different pre-sentation. Because the rest of the world accounts arefrom the perspective of the nonresidents, the signs arereversed compared to the balance of payments, whichare presented from the point of view of the countryitself. A terminological difference is that the balancesheets in the balance of payments are called “interna-tional investment position.”

A-head

73


74

V Editing and Reconciliation

A. Introduction

5.1. Editing and reconciliation are essential stages ofstatistical production and are among the tasks innational accounts compilation that require the greatestskill. While other chapters deal with the sources of dataand techniques, this chapter emphasizes reviewing andunderstanding the data. The process of reviewing andunderstanding data can be called “editing,” “check-ing,” or “data validation.” It should occur at allstages—before, during, and after—of the calculationof the estimates. “Reconciliation” or “confrontation”is a special kind of editing done after initial compila-tion, in which alternative data are checked in the con-text of national accounting relationships. Editing andreconciliation may involve fixing errors or adoptingalternative sources and methods; these tasks should,however, never be an excuse for manipulating datawithout evidence or adjusting data to fit forecasts or forpolitical reasons.

5.2. National accounts compilation is a complicatedprocess, bringing together a wide range and large vol-ume of data. The data cover different periods; comefrom varying sources; are of varying quality; and mayhave different units, concepts, and timing. Large vol-umes of data mean that mistakes are easy to make andhard to find. In addition, when a method or programhas worked well in the past, the production processhas gone smoothly, or the calculations are compli-cated, there is a natural tendency for busy compilersto accept the data without close scrutiny, resulting ina risk of errors.

5.3. Data suppliers are an integral part of nationalaccounts compilation, so editing should be supple-mented by continuing contact with suppliers to gainknowledge from them about problems they have iden-tified or suspect. In addition, the national accountscompilation process itself may shed new light throughvolume measures, seasonally adjusted and trend-cycle

data, analysis of revision patterns, and reconciliationwith related data sources. Thus, communication needsto be in both directions.

5.4. Many of the reconciliation and editing issues inquarterly national accounts (QNA) are the same as inannual national accounts (ANA). However, theseissues are particularly important in the compilation ofQNA. Deadlines for QNA are usually much tighterthan for ANA, work is more rushed, and a higher pro-portion of source data may be preliminary or unpub-lished. As a result, errors are more likely to occur.There is typically less detailed information in QNA.The tight deadlines applying to quarterly compilationimpose a severe limit on the amount of investigationdone for the latest quarter. In the time available, itmay be necessary to limit checks to known problemareas, the most recent periods, and some major ratios.In the time between the end of one quarterly compi-lation cycle and the beginning of the next, however,there may be opportunities to undertake furtherinvestigation.

5.5. The highest priority in editing is usually to iden-tify and remove errors before publication; however,there are other benefits. Editing helps national accoun-tants understand the data and the economy better. Italso helps national accountants anticipate queries fromusers, because unusual movements will already havebeen identified; explanations for the expected queriescan thus be given immediately. Successful editingenhances both the quality of the data and the confi-dence of users in the compilation procedures.

5.6. Editing procedures usually rely on relationshipswithin data to identify problems and questions. Onlyrarely will looking at a single number help point toanomalies. The foundation of editing is to compareobservations of the same variable in different periodsor to compare one variable with other variables that areexpected to have some linkage.

5.7. Editing and reconciliation may result in changesin the estimates. It is important that such changes arejustified and documented. For example, sometimesmistakes are identified and the correct figure can beused instead. In other instances, a method may havebecome unsuitable because the assumptions behind ithave become obsolete, or the source data may haveproblems in reporting or coverage. A distinction needsto be made, however, between editing and unacceptablemanipulation of data. An unexpected change in a seriesshould lead to checking that there is no error or prob-lem with the data source. Editing may suggest that analternative source or method is justified; however, datashould not be changed just because they are unex-pected, as this may lead to charges of manipulation andmay undermine the reputation of compilers if itbecomes known. Further, in reality, many unexpecteddevelopments occur, and the purpose of QNA is toshow actual developments in the economy, particularlywhen they are unexpected. In line with principles ofintegrity and transparency, QNA estimates should beable to be explained by reference to source data, pub-licly available compilation methods, and adjustmentsdocumented with the supporting evidence.

B. Causes of Data Problems

5.8. There is a range of causes for failure of data to fitexpected relationships. When there is a data problem,it is first necessary to confirm that the input data areconsistent with those supplied by the data collectors. Ifthe QNA are compiled by computer, as is the usualcase, it is necessary to confirm that the computer pro-gram is doing what was intended. This check will showwhether any anomalies were due to mistakes made inthe national accounts compilation system itself. In theinterest of good relationships with data suppliers, thepossibility of an error in the compilation system shouldbe excluded before pursuing other avenues of inquiry.Causes of data failing to fit expected relationshipsinclude the following:(a) Errors in data entry by national accounts compilers.

These include mistyping of numbers, putting num-bers in the wrong place, and using old data thatshould have been updated.

(b) Errors in national accounts compilation systems.At a basic level, these include wrong formulas,which are particularly likely when changes aremade to programs, especially in spreadsheets. Inaddition, the assumptions and indicators maybecome inappropriate as conditions change; forexample, use of a generalized deflator or direct

deflation of value added may give acceptableresults when there is little relative price change butmay become quite misleading under different eco-nomic circumstances. Adjustments are requiredwhen data sources do not fully meet nationalaccounts requirements and are particularly prone tobecoming outdated by economic changes.Examples are adjustments for timing, valuation,and geographic/size/product coverage.

(c) Errors in data recording by respondents. Reportingquality is often a problem, but it can be improved bygood questionnaire design, helpful completioninstructions, and availability of assistance in com-pleting forms. Timing problems can be particularlyimportant in QNA. Timing problems occur whentransactions are not recorded at the time required bythe 1993 SNA. The 1993 SNA standard is based onaccrual principles and change of ownership; how-ever, many data sources do not meet these require-ments. Government data are often recorded on acash basis. International trade data are typicallyrecorded at the time the goods cross the customsfrontier or when the customs authorities process theform. Administrative byproduct data (e.g., valueadded or payroll tax data) may cover periods that donot coincide with a quarter because the agency ismore interested in tax collection than statisticalobjectives. Businesses may also use differentaccounting periods that do not exactly match thethree-month period used in the QNA, such asweeks, four-week periods, or nonstandard quarters.These problems are also found in annual data but aremore significant in QNA because a timing error ofthe same size is relatively larger in quarterly data.

(d) Errors and problems in source collection systems.Problems can occur in classification, data entry, esti-mation of missing items or returns, sample design,tabulation, treatment of late response, incompletebusiness registers, and omitted components.Estimation of nonreporting units is a particularlyimportant issue for QNA because of the higher pro-portion of missing data owing to earlier deadlines.Early estimates are often based on incompleteresponse, complemented by estimation processes forthe missing respondents. Treatments of outliers mayalso differ. A systematic difference between earlyand late estimates suggests that the estimation for themissing components is biased. Large but nonsys-tematic errors suggest that it would be desirable toput more effort into early follow-up. Nationalaccounts compilers need to be sympathetic to theconstraints of resources and respondent cooperationfaced by their data collection colleagues.

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(e) Changes in the structure of economy. In manyinstances, it is possible to confirm that there hasbeen a surprising but valid change in the seriesowing to a known cause, such as a large individualtransaction or a business closure. This informationhelps the national accountant understand the dataand deal with queries from users. Some changes inthe structure of the economy have the effect of mak-ing assumptions used in the national accounts com-pilation obsolete and so may require changes inmethods. For example, the representativeness of anindicator that does not fully match the required cov-erage may deteriorate.

(f) Inexplicable reasons. There is also likely to be aresidue of cases where the movement is surprising,and neither an error nor an actual cause can befound. It is still better to know about such cases, sothat a query from a user is not a surprise and in casean explanation subsequently comes to light.

5.9. The causes of some data problems are obvious,while in other cases investigation is needed to iden-tify the cause. Some can be easily resolved, whileothers involving data collection will take longer toimplement; examples of the latter may include prob-lems that require changes in survey coverage or ques-tionnaire design, design of new imputation methodsfor nonresponse, or revised procedures for incorpora-tion of new businesses in surveys. Even where it isnot possible to fix or explain data immediately, it isimportant that the issues be identified for later inves-tigation and resolution.

C. How To Identify Data Problems

5.10. In this chapter, various ways of identifying dataproblems are presented. The terminology and classifi-cation were developed for this chapter because there islittle or no literature about its subject and no standardterminology.

1. Eyeball Testing

5.11. “Eyeball testing”—that is, just looking at thenumbers as they will be published, without any addi-tional calculations, tabulations, or charts—is the mostbasic kind of editing. Even with this limited presenta-tion of data, a number of potential problems will beapparent to the careful eye:• Different orders of magnitude, different numbers of

digits.• Numbers that change too much—excessive growth

or decline.

• Numbers that do not change at all—no change atall may suggest that numbers have been copied intothe wrong period.

• Numbers that change too little—a much slowergrowth than other items may point to a problem.

5.12. Eyeball testing does not use a computer or othertools to pinpoint problems, so it depends solely on theeditor’s ability. As a result, many data problems willnot be apparent and may be missed. Despite these lim-itations, such a basic examination can be implementedquickly and is much better than no editing at all.Someone who was not involved in the original calcula-tions is more likely to notice potential problems.

5.13. A slightly more sophisticated check is to presentthe numbers as charts. Charts of data can be generatedreadily with spreadsheet and other packages. Unusualmovements and inconsistencies stand out in charts to amuch greater extent than they do in tables.

2. Analytical Testing

5.14. A more advanced form of editing uses addi-tional calculations or charts to assist in checking data.It is a more sophisticated and time-consuming formof editing but will usually reveal more problems thaneyeball testing alone.

a. Logical

5.15. Logical edits are those in which exact relation-ships must hold, based on mathematical identities ordefinitions, such as in the following examples:• Total is equal to the sum of components (e.g., GDP

= Household final consumption + Government finalconsumption + Gross fixed capital formation +Changes in inventories + Acquisitions less disposalof valuables [if applicable] + Exports of goods andservices – Imports of goods and services;Manufacturing = Food + Textiles + Clothing, etc.).

• Commodity balances, which are checks of the rela-tionship between supply and use when they have beenderived independently. They can best be done as a partof a comprehensive supply and use framework inwhich balancing and interrelationships between com-ponents are dealt with simultaneously. Even without acomprehensive supply and use framework, however,balancing supply and uses of particular products is auseful way to find errors or inconsistencies betweendata from different data sources. (If the supply and usedata are complete, this is a logical edit.)

• Year is equal to the sum of the quarters (in originaldata; not necessarily true in seasonally adjusted ortrend-cycle data).

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• Definitions of specific terms (e.g., Implicit pricedeflator = Current price value/Constant price value;Value added = Output – Intermediate consumption).

5.16. Rounding errors may sometimes disturb theserelationships slightly, but they should be relativelyminor and not used as an all-purpose excuse for accep-tance of inconsistency.

b. Plausibility

5.17. Edits of plausibility rely on expectations of howseries should move in relation to past values of thesame series and to other series. In contrast to logicaledits, there is not an exact requirement that the datamust satisfy; rather, data can be seen as being in a spec-trum that goes from expected values, to less expectedbut still believable values, to unusual values, and on tounbelievable values. This assessment requires anunderstanding of what is a realistic change; that is, thenational accountant must have a good grasp of eco-nomic developments as well as an understanding of thestatistical processes.

5.18. It is important to assess QNA indicators for theirability to track movements in the corresponding annualseries. As explained in Chapters II and VI, the annualbenchmark-indicator (BI) ratio shows the relationshipbetween the two series. A stable annual BI ratio showsthat the indicator is representative. Alternatively, atrend increase or decrease in the BI ratio points to biasin the movements of the indicator series. Volatilechanges in the annual BI ratio point to problems thatare less easily diagnosed and solved.

5.19. The following are some other editing calculationsthat can be made to assess the plausibility of data:• Percentage changes (e.g., for quarterly estimates,

compared with one quarter or four quarters earlier)can be calculated. These can help identify caseswhere rates of growth or decline are excessive, orwhere one component is moving in a different wayfrom a related series. It may be feasible to developthresholds to identify unusual changes on the basisof past behavior. As well as being useful in editing,percentage change tables are a useful supplementaryway of presenting data.

• Contributions to growth,1 which show the factorsbehind growth in aggregates (rather than just

growth of series in their own right), can becalculated.

• Commodity balances can be made. (These are alreadydiscussed under logical edits. If the supply and usedata are incomplete, this is more a test of plausibility.)

• Ratios of various kinds can be calculated (particu-larly where series have independent sources):� Implicit price deflators—that is, the ratio of cur-

rent price values to constant price values, are akind of price index. � At a detailed level, if the value and volume mea-

sures have been obtained independently, a pecu-liar implicit price deflator movement willindicate incompatible trends.

� At an aggregated level, it is useful to calculatethe corresponding Laspeyres price indices.Comparison between the Laspeyres priceindices and implicit price deflators points to theeffect of compositional changes on the implicitprice deflators. No extra data are required to cal-culate the Laspeyres price indices, and they areof analytical interest in their own right.

� Productivity measures show the relationshipbetween inputs and output/value added and,hence, may point to problems in input or outputdata. The most common and simple measure islabor productivity, that is, output or value added atconstant prices per employee or hour worked. Forexample, the output, value added, and employ-ment series may not look unreasonable individu-ally, but they could be moving in incompatibleways. In this case, the productivity measure willhighlight the inconsistency in the trends by theimplausible movement. Some countries publishlabor or total factor productivity estimates; again,these are of analytical interest.

� Ratios between other closely related series (e.g.,construction in gross fixed capital formation andconstruction output in production estimates; valueadded and output for the same industry; compo-nents to total ratios, such as manufacturing/total;inventories/sales).

� Other ratios between series. Less stable ratios willoccur for series that are linked by behavioral rela-tionships, for example, consumption and saving toincome, current account deficit to saving.However, changes in these ratios can point to dataproblems and also help national accounts compil-ers advise data users.

• Implicitly derived series should be examined closely,as they may highlight data problems, for example,intermediate consumption when value added hasbeen derived with an output indicator.

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1Calculated as (xt–xt– 1) /At– 1 where x is the component series and Ais an aggregate. For example, if household consumption has increasedby 5 since the previous period, and GDP was 1000 in the previousperiod, the change in household consumption makes a contribution toGDP growth of 0.5 percentage point.

• Revisions (since the previous publication or severalpublications earlier) should be examined. Newlyintroduced mistakes will show up as revisions.Consistent patterns of revisions (i.e., consistentlyupward or downward) suggest a biased indicator.Large, erratic revisions may indicate a problem withearly data that can be investigated. The incorporationof annual benchmarks into quarterly estimates willcause revisions and could reflect problems in thesources or methods for either annual or quarterlydata. To calculate and track down the causes of revi-sions, it is necessary to archive data from previousreleases, by keeping printouts and copies of com-puter files or by saving earlier data in the computingsystem under separate identifiers.

5.20. It is not a coincidence that many of these toolsfor plausibility editing are also of interest to users ofthe statistics. Both editors and analysts are perform-ing similar tasks of looking at how the data are mov-ing and why.

5.21. Analytical editing can be done with charts ortables. Usually, the interest in this case is in big changesrather than precise relationships. Charts are particularlysuitable in this task because they can be read by glanc-ing, especially to identify outliers. Line charts and barcharts are alternative presentations that give differentemphases. Charts may sometimes take more time to setup than tables but are worth it because of their useful-ness. Tables allow errors to be traced more easilybecause an exact number is known, so they might beused to investigate a problem detected by a chart.Choices between charts and tables are often influencedby the capacities of the computer processing systembeing used. Different formats each have their own uses,so it is desirable to have a range of presentations.

5.22. In general, editing and reconciliation are bestdone at both detailed and aggregate levels. In aggregateform, problems can be hidden by large values of data orby errors in offsetting directions canceling each otherout. With more specific identification of the affectedcomponents, it is possible to focus on the cause of theproblem. Some problems are only apparent at a detailedlevel, because they get swamped at a higher level ofaggregation. In other cases, the level of “noise” or irreg-ular movements in the series is high at a micro level, soproblems may become more obvious at a higher level,as the noise in the series becomes relatively smaller.

5.23. Problems are sometimes more apparent in con-stant-price or seasonally adjusted data. These presen-

tations remove some sources of volatility and henceisolate remaining fluctuations. For example, an unad-justed series may have a strong seasonal pattern, withquarter-to-quarter changes so large that trends andirregularities are hidden.

5.24. Discrepancies and residual items should receiveparticular attention because they are not deriveddirectly, and problems in certain components are oftenhighlighted by the balancing item.

D. Reconciliation

5.25. When there are two or more independent mea-sures of an item, inconsistencies inevitably will arise.The inconsistencies could be between two measuresof GDP estimated by different approaches or, in adetailed system, between the supply and use of a par-ticular product. Reconciliation is the process of deal-ing with these inconsistencies. This section discussesdifferent options for reconciliation and the consider-ations that need to be taken into account in choosingamong them. Reconciliation issues arise in bothannual and quarterly estimates. The approach to ANAreconciliation will typically be the starting point forQNA, although some different approaches mayemerge because of the quarterly emphasis on speedand time-series maintenance. In addition, the QNAdata will be strongly influenced by the reconciliationcarried out in the annual data because the annual bal-ances (or imbalances) will be passed to QNA throughthe benchmarking process. The options available arereconciliation by detailed investigation, reconcilia-tion by mathematical methods, or publication of dis-crepancies in varying ways.

5.26. One important type of reconciliation is theprocess of balancing data at a detailed level within afull supply and use (or input-output) table frameworkor through commodity balances for key products.Supply and use tables provide a coherent framework toidentify inconsistencies at the detailed product level.Supply and use balancing is at its most useful wheninvestigations are used to identify the cause of discrep-ancies. Even if supply and use data are not available ina comprehensive framework, a partial version in theform of commodity balances for particular productscan provide some of the benefits of supply and usetables for reconciliation. A few countries use a supplyand use framework on a quarterly basis, typically at aless detailed level than annually and as a compilationtool that is not intended for publication.


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5.27. Another type of reconciliation occurs when thereare independent estimates of GDP by two or moreapproaches but without the details of a supply and useframework.2 In such cases, discrepancies becomeapparent only when the data are aggregated, makingwell-based reconciliation difficult or impossiblebecause the aggregate discrepancies provide no indica-tions of which components are causing the discrepan-cies. Investigations may still prove useful, however, aspatterns in the discrepancies may point to specific prob-lems (e.g., reversed fluctuations point to timing prob-lems, persistent differences of a similar size point to abias in a major source, and procyclical differences maypoint to problems in measuring new businesses).

5.28. Some countries have a mix of methods in whichsupply and use balancing occurs on an annual or lessfrequent basis, while independent estimates are madequarterly. In these cases, the quarterly discrepancieswill cancel out within the quarters of balanced yearsand generally tend to be smaller because of the bench-marking process.

5.29. A number of countries do not have an apparentproblem of reconciliation because they do not have sup-ply and use tables; they have only one approach to mea-suring GDP; or they have two or more approaches, butonly one is derived independently, with one componentin the other(s) derived as a residual. Besides the analyt-ical interest of having different approaches, however,discrepancies can be useful pointers to data problemsthat would otherwise be undiagnosed.

5.30. For both supply-use and independent measuresof GDP, investigation and resolution of the problems isthe ideal method of reconciliation. The processes ofconfrontation and reconciliation at a detailed level canidentify many issues and are highly regarded bynational accounts compilers. The extent of adjustmentthat can be made should depend on the expertise of thestatistical compilers. Adjustment should not be madelightly but should be based on evidence and be welldocumented. There is potential for concern if unin-formed guesses are made or adjustments are made witha view to meeting some political objective (or that accu-sations could be made that politically-motivated manip-ulation has occurred). Adjustments should bemonitored to see if they later need to be reversed.

5.31. For cases in which there is insufficient time,expertise, or information for investigation to achieve

complete reconciliation, there are a number of alterna-tives for treating the discrepancies. There is no interna-tional consensus, however, and treatments mustaccount for national circumstances.

5.32. One technique to remove discrepancies is theallocation of discrepancies to a single category by con-vention. The discrepancy is, then, no longer apparent.Usually the chosen category is large (such as house-hold consumption) or poorly measured (such aschanges in inventories). In effect, the estimates are nolonger independent, and one source is forced to equalthe other. As a consequence, the information content ofthe chosen component is reduced or even lost. Andalthough the discrepancy is hidden in this way, it is notsolved. At least, the component should be properlylabeled, for example as “changes in inventories plus neterrors and omissions.”

5.33. A related option for removing the remainingdiscrepancies is to allocate them by mathematical ormechanical techniques across a number of cate-gories. The chosen categories could be a selectedgroup or all categories. Methods may involve simpleor iterative prorating; for example, the RAS methodis an iterative prorating method used for supply anduse tables and other multidimensional reconciliationsituations. The selection of which categories toadjust by prorating and which categories to leaveunchanged should be based on explicit assessmentsof which estimates were better. Like allocation to asingle category, the problem with allocation acrossseveral categories is that the process removes someof the information content of the original data. As aresult, balance may be achieved at the expense ofdamaging the time-series quality of the individualcomponents. If an error that belongs in one compo-nent is distributed across a number of components,all the components will be less accurate. If the dis-crepancies are trivial, this may not be of concern.But if they are significant, these techniques merelyhide the problem rather than solving it. It is a disser-vice to users to leave them unaware of the actualextent of uncertainty. Minimizing problems in datasources can also undermine the attempts of nationalaccountants to highlight those problems and reducethe chance of bringing about improvements.Because of the greater significance of timing prob-lems in source data and the reduced time for investi-gation of the causes of inconsistencies, thelimitations of reconciliation are more serious inQNA than in ANA. As a result, some countries thathave balanced ANA allow imbalances in QNA.

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2These issues are dealt with in Bloem et. al. (1997).

5.34. The alternative to reconciliation by investigation,allocation to a single component, or mathematicalremoval is to present the remaining discrepanciesopenly. Within that alternative, one presentation is topublish more than one measure of GDP or supply anduse of a product. Alternatively, a single measure can beidentified as preferred on the basis of a qualitativeassessment of data sources or mathematical testing ofthe properties of the alternative measures (or a mixtureof them). Explicit statistical discrepancy items wouldthen be needed (in aggregate for independent measuresof GDP; at the product level for supply and use), so thatthe sum of the items equals the preferred total.

5.35. The main concerns about showing explicit dis-crepancies are that they may cause confusion amongusers and criticism or embarrassment to the compilers.To the extent that the discrepancies represent problemsthat have identifiable causes and can be solved, the crit-icism is justified and investigations should have beencarried out to make appropriate adjustments. To theextent that the discrepancies are trivial, mechanicaltechniques would be justified to remove them. In theremaining cases where the differences are significantand the causes unknown, however, it is better to admitthe limitations of the data because the uncertainty isgenuine. The ultimate objective must be to solve theproblem, and being transparent to users about short-comings is more likely to help bring about the requiredchanges in data collection or compilation resources.While it is understandable that some compilers mightbe inclined to “sweep problems under the carpet,” in thelonger term, being open will avoid even more serious—and valid—criticism about secretiveness and coveringup important problems.

5.36. The objective of soundly based reconciliation isthe same in both ANA and QNA. Similarly, the optionsand considerations to be taken into account in choosingbetween them apply in both situations. There are, how-ever, some procedural and practical differences.Procedurally, QNA reconciliation problems are likelyto be most severe for the most recent quarters, becausefor earlier quarters the same issues would already havebeen identified in the ANA. Benchmarking brings thebenefits of annual reconciliation to QNA, so that addi-tional quarterly reconciliation may be a lower priority.There are also practical considerations, because there isless opportunity to investigate discrepancies duringquarterly compilation.

5.37. Benchmarking means that QNA will benefitindirectly from the reconciliation carried out on the

annual data, so that discrepancies may be smaller andreconciliation less urgent. If the ANA are already bal-anced and the QNA are benchmarked, the need forseparate reconciliation is reduced. For the balancedyears, discrepancies within quarters will cancel outover the whole year and tend to be small. For quartersoutside the annually reconciled period, the discrep-ancies will tend to be smaller close to the benchmarkyears. For the most recent quarters that have noannual benchmark, if the indicators correctly tracktheir benchmarks, previously identified causes ofinconsistencies will already have resulted in adjust-ments that are carried forward. Accordingly, theQNA discrepancies will tend to be limited to thosecaused by noise, divergence between benchmarksand indicators, or data problems that have emergedsince the last benchmark. Of course, if the annualdata contain unreconciled inconsistencies, they willalso be carried forward to the QNA, which will be atleast as imbalanced as their ANA equivalents. Theimplications of benchmarking for reconciliation arediscussed further in Chapter VI.

5.38. QNA are typically compiled with less time,information, and detail than ANA. The reduced timeand information tend to restrict the capacity to inves-tigate problems that have emerged in the most recentquarters. Timing errors and statistical noise may bedifficult to resolve by investigation. These issues aremore significant in QNA because they tend to cancelout over a whole year. In terms of user interests,analysis of QNA tends to strongly emphasize thetime-series aspects of QNA data rather than structuralrelationships. Also, in a quarterly supply and use sys-tem, the tables are compilation tools and are not gen-erally published in their own right, so that time-seriesconsistency is given more weight then structural bal-ance. Therefore, there is likely to be less investigationand more acceptance of unresolved discrepancies ina QNA system than an ANA system.

E. Editing as Part of the CompilationProcess

5.39. Editing can occur at all stages of dataprocessing:(a) before receipt by the national accounts compilers,(b) during data input (i.e., the data as supplied to the

national accounts compilers),(c) during data output (i.e., the data as planned to be

published), and(d) during intermediate stages:


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(i) before and after benchmarking,(ii) before and after deflation,(iii) before and after reconciliation, and(iv) before and after seasonal adjustment.

5.40. Good editing practices should be applied by allcompilers of statistical data. Those who collect the dataneed to monitor the results and anticipate queries fortheir own purposes. In some countries, the nationalaccounts compilers have contributed toward educatingthe data collection staff through the perspective thatcomes from seeing macroeconomic links, from under-taking deflation and seasonal adjustment, and frommaintaining consistent time series. In addition,national accounts compilers may have meetings orstandardized data supply forms to allow the data col-lectors to notify them of major movements in the data,known economic developments, response rates, stan-dard errors, changes to questionnaires, and otherchanges in methods. Good procedures or structures forinteraction between data collection staff and nationalaccounts compilers help maintain effective coopera-tion and avoid conflicts.

5.41. Editing at each stage through the compilationprocess is desirable. Each stage of processing andadjustment can introduce new errors or hide earlierones. Earlier identification of problems and errors isgenerally preferable.

5.42. Original estimates, adjustments, and reasonsshould be documented along with supporting evidence.As a good practice, when national accounts data arechanged during the editing process, the source data,original estimates, and adjusted estimates should bestored. Although only the adjusted data will be pub-lished, it is important to be able to document how thesource data were amended and the cause of the prob-lem. Documentation is necessary so that the reasonsmay be understood and verified later. While it is tempt-ing to put off documentation work, memories are not agood substitute, because people move on to other jobs,forget, are on leave at a crucial time, or have conflict-ing recollections. Documentation is a defense againstaccusations of manipulation. As later data becomeavailable, patterns may be more apparent from a con-sistent series of original data, or alternative adjustmentsmay be developed. Later information may lead to theconclusion that some adjustments were ill-advised andshould be revised. Documentation could be on paperfiles or, better still, on the computer system if it allowsdifferent versions of a series to be saved and associatedmetadata to be linked to a series.

5.43. The ability of the national accounts compiler tomake adjustments is limited if consistency with someor all published source data is a constraint. In somecountries, particular data are regarded as binding forQNA compilation because of their relatively high qual-ity or need for consistency. While some sources maynot be published, making overt inconsistency not anissue, the basic criterion for adjustments should betheir justifiableness. In some countries, data that areknown to be particularly poor are identified as beingsubject to adjustments (e.g., consistency between theproduction and expenditure estimates being achievedby adjustments to changes in inventories because thatcomponent is known to be of poor quality).

5.44. Deciding how much editing work to do dependson staffing, deadlines, and knowledge of the kinds ofproblems that typically arise. In the abstract, more edit-ing is always better. In practice, the extra work and timerequired to establish editing systems and then checkthe data mean that edits must be limited to the typesthat are most likely to be useful.

5.45. Computers have greatly increased the capacityfor editing. At the first stage of computerizing thenational accounts, the tasks from clerical systems areoften transferred directly to computers withoutchanges. However, this does not fully use the capacityof computers to do additional tasks. The next stage inthe evolution of processing is to use the strengths of thecomputer to implement new tasks, especially editing.Calculations for editing (such as percentage changesand ratios) that would be time consuming in a clericalsystem involve very little cost in a computerized systemand so are much more feasible. At the same time, com-puterized systems may need more checking because thedata processing itself involves less human observation.

5.46. The compilation schedule needs to allow timefor editing and subsequent investigation and revision ofdata. If time is only allocated to carry out basic dataentry and calculation tasks, it will not be possible tomake any changes before the publication deadline.

5.47. More complicated estimation methods for par-ticular components are at more risk of mistakes.Similarly, the need for editing is stronger when data ormethods are weak because the risk of inappropriateresults is greater. Because numbers in a computer areall treated as numbers regardless of their origin, it isimportant for the compiler to bear in mind the linkbetween the quality of data input and the quality of dataoutput: “garbage in, garbage out.”

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VI Benchmarking

A. Introduction

6.1. Benchmarking deals with the problem of com-bining a series of high-frequency data (e.g., quarterlydata) with a series of less frequent data (e.g., annualdata) for a certain variable into a consistent time series.The problem arises when the two series show incon-sistent movements and the less frequent data are con-sidered the more reliable of the two. The purpose ofbenchmarking is to combine the relative strengths ofthe low- and high-frequency data. While benchmark-ing issues also arise in annual data (e.g., when a surveyis only conducted every few years), this chapter dealswith benchmarking to derive quarterly nationalaccounts (QNA) estimates that are consistent withannual national accounts (ANA) estimates, where theannual data1 provide the benchmarks.2 Quarterly datasources often differ from those used in the correspond-ing annual estimates, and the typical result is thatannual and quarterly data sources show inconsistentannual movements. In a few cases, the quarterly datamay be superior and so may be used to replace theannual data.3 More typically, the annual data providethe most reliable information on the overall level andlong-term movements in the series, while the quarterlysource data provide the only available explicit4 infor-mation about the short-term movements in the series,so that there is a need to combine the information con-tent of both the annual and quarterly sources.

6.2. Benchmarking has two main aspects, which inthe QNA context are commonly looked upon as twodifferent topics; these are (a) quarterization5 ofannual data to construct time series of historical QNAestimates (“back series”) and revise preliminaryQNA estimates to align them to new annual datawhen they become available, and (b) extrapolation toupdate the series from movements in the indicator forthe most current period (“forward series”). In thischapter, these two aspects of benchmarking are inte-grated into one common benchmark-to-indicator(BI) ratio framework for converting individualindicator series into estimates of individual QNAvariables.

6.3. To understand the relationship between the cor-responding annual and quarterly data, it is useful toobserve the ratio of the annual benchmark to the sumof the four quarters of the indicator (the annual BIratio). Movements in the observed annual BI ratioshow inconsistencies between the long-term move-ments in the indicator and in the annual data.6 As aresult, movements in the annual BI ratio can helpidentify the need for improvements in the annual andquarterly data sources. The technical discussion inthis chapter treats the annual benchmarks as bindingand, correspondingly, the inconsistencies as causedby errors7 in the indicator and not by errors in theannual data. Benchmarking techniques that treat thebenchmarks as nonbinding are briefly described inAnnex 6.1.

1That is, the annual source data, or ANA estimates based on a separateANA compilation system.2A trivial case of benchmarking occurs in the rare case in whichannual data are available for only one year. In this case, consistencycan be achieved simply by multiplying the indicator series by a singleadjustment factor.3One instance is annual deflators that are best built up from quarterlydata as the ratio between the annual sums of the quarterly current andconstant price data, as discussed in Chapter IX Section B. Anothercase is that of nonstandard accounting years having a significant effecton the annual data.4The annual data contain implicit information on aspects of the short-term movements in the series.

5Quarterization refers to generation of quarterly data for the backseries from annual data and quarterly indicators, and encompassestwo special cases, namely:(a) Interpolation—that is, drawing a line between two points—which

in the QNA mainly applies to stock data (except in the rare case ofperiodic quarterly benchmarks).

(b) Temporal distribution, that is, distributing annual flow data overquarters.

6See Section B.4 of Chapter II for a further discussion of this issue.7The errors can be systematic (“bias”) or irregular (“noise”).

6.4. The general objective of benchmarking is• to preserve as much as possible the short-term

movements in the source data under the restrictionsprovided by the annual data and, at the same time,

• to ensure, for forward series, that the sum of thefour quarters of the current year is as close as pos-sible to the unknown future annual data.

It is important to preserve as much as possible theshort-term movements in the source data because theshort-term movements in the series are the centralinterest of QNA, about which the indicator providesthe only available explicit information.

6.5. In two exceptional cases, the objective shouldnot be to maximally preserve the short-term move-ments in the source data: (a) if the BI ratio is knownto follow a short-term pattern, for example, is subjectto seasonal variations; and (b) if a priori knowledgeabout the underlying error mechanism indicates thatthe source data for some quarters are weaker thanothers and thus should be adjusted more than others.

6.6. As a warning of potential pitfalls, this chapterstarts off in Section B by explaining the unacceptablediscontinuities between years—the “step problem”—caused by distributing annual totals in proportion to thequarterly distribution (pro rata distribution) of the indi-cator. The same problem arises if preliminary quarterlyestimates are aligned to the annual accounts by distrib-uting the differences between the annual sums of thequarterly estimates and independent annual estimatesfor the same variable evenly, or pro rata, among the fourquarters of each year. Techniques that introduce breaksin the time series seriously hamper the usefulness ofQNA by distorting the view of developments and pos-sible turning points. They also thwart forecasting andconstitute a serious impediment for seasonal adjust-ment and trend analysis. In addition to explaining thestep problem, section B introduces the BI ratio frame-work that integrates quarterization and extrapolationinto one framework.

6.7. Subsequently, the chapter presents a BI ratio-based benchmarking technique that avoids the stepproblem (the “proportional Denton” technique withextensions).8 The proportional Denton techniquegenerates a series of quarterly estimates as propor-tional to the indicator. as possible subject to the

restrictions provided by the annual data. The chaptergoes on to propose an enhancement to the Dentontechnique to better deal with the most recent periods.Other enhancements to the Denton are also men-tioned and some other practical issues are considered.

6.8. Given the general objective stated above it fol-lows that, for the back series, the proportional Dentonis by logical consequence9 optimal, if • maximal preservation of the short-term move-

ments in the indicator is specified as keeping thequarterly estimates as proportional to the indicatoras possible; and

• the benchmarks are binding. Under the same conditions, it also follows that for theforward series, the enhanced version provides the bestway of adjusting for systematic bias and still maxi-mally preserving the short-term movements in thesource data. In addition, compared with the alterna-tives discussed in Annex 6.1, the enhanced propor-tional Denton technique is relatively simple, robust,and well suited for large-scale applications.

6.9. The technical discussion in this chapter alsoapplies to estimates based on periodically “fixed”ratios in the absence of direct indicators for somevariables that also result in a step problem. As men-tioned in Chapter III, these cases include cases inwhich (a) estimates for output are derived from datafor intermediate consumption, or, estimates for inter-mediate consumption are derived from data for out-put; (b) estimates for output are derived from otherrelated indicators such as inputs of labor or particularraw materials; and (c) ratios are used to gross up forunits not covered by a sample survey (e.g., establish-ments below a certain threshold). In all these cases,the compilation procedure can be expressed in abenchmark-to-(related) indicator form, and annual,or less frequent, variations in the ratios result in stepproblems. The proportional Denton technique canalso be used to avoid this step problem and, for thereasons stated above, would generally provide opti-mal results, except in the case of potential seasonaland cyclical variations in the ratios. This issue is dis-cussed in more detail in Section D.1, which also pro-vides a further enhancement to the proportionalDenton that allows for incorporation of a prioriknown seasonal variations in the BI ratio.10

Introduction

83

9Because the proportional Denton is a mathematical formulation ofthe stated objective.10Further enhancements, which allow for incorporating a priori knowl-edge that the source data for some quarters are weaker than others, andthus should be adjusted more than others, are also feasible.

8Some of the alternative techniques that have been proposed are dis-cussed in Annex 6.1, which explains the advantages of the propor-tional Denton technique over these alternatives.

6.10. In the BI ratio benchmarking framework, onlythe short-term movements—not the format and overalllevel11—of the indicator are important, as long as theyconstitute continuous time series.12 The quarterly indi-cator may be in the form of index numbers (value, vol-ume, or price) with a reference period that may differfrom the base period13 in the QNA; be expressed inphysical units; be expressed in monetary terms; or bederived as the product of a price index and a volumeindicator expressed in physical units. In the BI frame-work, the indicator only serves to determine the short-term movements in the estimates, while the annualdata determine the overall level and long-term move-ments. As will be shown, the level and movements inthe final QNA estimates will depend on the following:• The movements, but not the level, in the short-term

indicator.• The level of the annual data—the annual BI ratio—

for the current year.• The level of the annual data—the annual BI

ratios—for several preceding and following years.Thus, it is not of any concern that the BI ratio is notequal to one,14 and the examples in this chapter aredesigned to highlight this basic point.

6.11. While the Denton technique and its enhance-ments are technically complicated, it is important toemphasize that shortcuts generally will not be satis-factory unless the indicator shows almost the sametrend as the benchmark. The weaker the indicator is,the more important it is to use proper benchmarkingtechniques. While there are some difficult concep-tual issues that need to be understood before settingup a new system, the practical operation of bench-marking is typically automated15 and is not prob-lematic or time-consuming. Benchmarking shouldbe an integral part of the compilation process andconducted at the most detailed compilation level. Itrepresents the QNA compilation technique forconverting individual indicators into estimates ofindividual QNA variables.

B. A Basic Technique for Distribution and Extrapolation with an Indicator

6.12. The aim of this section is to illustrate the stepproblem created by pro rata distribution and relatepro rata distribution to the basic extrapolation withan indicator technique. Viewing the ratio of thederived benchmarked QNA estimates to the indica-tor (the quarterly BI ratio) implied by the pro ratadistribution method shows that this method intro-duces unacceptable discontinuities into the timeseries. Also, viewing the quarterly BI ratios impliedby the pro rata distribution method together with thequarterly BI ratios implied by the basic extrapola-tion with an indicator technique shows how distrib-ution and extrapolation with indicators can be putinto the same BI framework. Because of the stepproblem, the pro rata distribution technique is notacceptable.

1. Pro Rata Distribution and the Step Problem

6.13. In the context of this chapter, distributionrefers to the allocation of an annual total of a flowseries to its four quarters. A pro rata distribution splitsthe annual total according to the proportions indi-cated by the four quarterly observations. A numericalexample is shown in Example 6.1 and Chart 6.1.

6.14. In mathematical terms, pro rata distributioncan be formalized as follows:

Distribution presentation (6.1.a)

or

Benchmark-to-indicatorratio presentation (6.1.b)

whereXq,β is the level of the QNA estimate for quarter q of

year β;Iq,β is the level of the indicator in quarter q of year

β; andAβ is the level of the annual data for year β.

6.15. The two equations are algebraically equivalent,but the presentation differs in that equation (6.1.a)emphasizes the distribution of the annual benchmark(Aβ) in proportion to each quarter’s proportion of the

q qqq

X IA

I, ,

,β β

β

β= ⋅

∑

qq

qq

X AI

I,

,

,β β

β

β= ⋅

∑

VI BENCHMARKING

84

11The overall level of the indicators is crucial for some of the alterna-tive methods discussed in Annex 6.1. 12See definition in paragraph 1.13.13For traditional fixed-base constant price data, see Chapter IX.14In the simple case of a constant annual BI ratio, any level differencebetween the annual sum of the indicator and the annual data can beremoved by simply multiplying the indicator series by the BI ratio.15Software for benchmarking using the Denton technique is used inseveral countries. Countries introducing QNA or improving theirbenchmarking techniques, may find it worthwhile to obtain existingsoftware for direct use or adaptation to their own processing systems.For example, at the time of writing, Eurostat and Statistics Canadahave software that implement the basic version of the Denton tech-nique; however, availability may change.

annual total of the indicator16 (Iq,β /ΣqI4,β), whileequation (6.1.b) emphasizes the raising of each quar-terly value of the indicator (Iq,β ) by the annual BIratio (Aβ /ΣqIq,β).

6.16. The step problem arises because of disconti-nuities between years. If an indicator is not growingas fast as the annual data that constitute the bench-mark, as in Example 6.1, then the growth rate in theQNA estimates needs to be higher than in the indica-tor. With pro rata distribution, the entire increase inthe quarterly growth rates is put into a single quarter,while other quarterly growth rates are left unchanged.The significance of the step problem depends on thesize of variations in the annual BI ratio.

2. Basic Extrapolation with an Indicator

6.17. Extrapolation with an indicator refers to using themovements in the indicator to update the QNA time series

with estimates for quarters for which no annual data areyet available (the forward series). A numerical example isshown in Example 6.1 and Chart 6.1 (for 1999).

6.18. In mathematical terms, extrapolation with anindicator can be formalized as follows, when movingfrom the last quarter of the last benchmark year:

Moving presentation (6.2.a)

orBI ratio presentation

(6.2.b)

6.19. Again, note that equations (6.2.a) and (6.2.b)are algebraically equivalent, but the presentationdiffers in that equation (6.2.a) emphasizes that thelast quarter of the last benchmark year (X4,β ) isextrapolated by the movements in the indicator fromthat period to the current quarters (Iq,β +1/I4, β), whileequation (6.2.b) shows that this is the same as

4 1 4 14

4, ,

,

,β β

β

β+ += ⋅

X IX

I

4 1 44 1

4, ,

,

,β β

β

β+

+= ⋅

X XI

I

A Basic Technique for Distribution and Extrapolation with an Indicator

85

Example 6.1. Pro Rata Distribution and Basic Extrapolation

Indicator Derived QNA EstimatesPeriod-to- Period-to-

The Period Annual Annual PeriodIndicator Rate of Data BI ratio Distributed Data Rate of

(1) Change (2) (3) (1) • (3) = (4) Change

q1 1998 98.2 98.2 • 9.950 = 977.1q2 1998 100.8 2.6% 100.8 • 9.950 = 1,003.0 2.6%q3 1998 102.2 1.4% 102.2 • 9.950 = 1,016.9 1.4%q4 1998 100.8 –1.4% 100.8 • 9.950 = 1,003.0 –1.4%Sum 402.0 4000.0 9.950 4,000.0q1 1999 99.0 –1.8% 99.0 • 10.280 = 1,017.7 1.5%q2 1999 101.6 2.6% 101.6 • 10.280 = 1,044.5 2.6%q3 1999 102.7 1.1% 102.7 • 10.280 = 1,055.8 1.1%q4 1999 101.5 –1.2% 101.5 • 10.280 = 1,043.4 –1.2%Sum 404.8 0.7% 4161.4 10.280 4,161.4 4.0%q1 2000 100.5 –1.0% 100.5 • 10.280 = 1,033.2 –1.0%q2 2000 103.0 2.5% 103.0 • 10.280 = 1,058.9 2.5%q3 2000 103.5 0.5% 103.5 • 10.280 = 1,064.0 0.5%q4 2000 101.5 –1.9% 101.5 • 10.280 = 1,043.4 –1.9%Sum 408.5 0.9% ? ? 4,199.4 0.9%Pro Rata DistributionThe annual BI ratio for 1998 of 9.950 is calculated by dividing the annual output value (4000) by the annual sum of the indicator (402.0).This ratio is then usedto derive the QNA estimates for the individual quarters of 1998. For example, the QNA estimate for q1 1998 is 977.1, that is, 98.2 times 9.950.

The Step ProblemObserve that quarterly movements are unchanged for all quarters except for q1 1999, where a decline of 1.8% has been replaced by an increase of 1.5%. (Inthis series, the first quarter is always relatively low because of seasonal factors.) This discontinuity is caused by suddenly changing from one BI ratio to anoth-er, that is, creating a step problem.The break is highlighted in the charts, with the indicator and adjusted series going in different directions.

ExtrapolationThe 2000 indicator data are linked to the benchmarked data for 1999 by carrying forward the BI ratio for the last quarter of 1999. In this case, where the BIratio was kept constant through 1999, this is the same as carrying forward the annual BI ratio of 10.280. For instance, the preliminary QNA estimate for thesecond quarter of 2000 (1058.9) is derived as 103.0 times 10.280. Observe that quarterly movements are unchanged for all quarters.

(These results are illustrated in Chart 6.1.)

16The formula, as well as all subsequent formulas, applies also to flowseries where the indicator is expressed as index numbers.

VI BENCHMARKING

86

Chart 6.1. Pro Rata Distribution and the Step ProblemThe Indicator and the Derived Benchmarked QNA Estimates

In this example, the step problem shows up as an increase in the derived series from q4 1998 to q1 1999 that is not matched by the move-ments in the source data.The quarterized data erroneously show a quarter-to-quarter rate of change for the first quarter of 1999 of 1.5%while the corresponding rate of change in source data is –1.8% (in this series, the first quarter is always relatively low because of seasonalfactors).

Benchmark-to-Indicator Ratio

It is easier to recognize the step problem from charts of the BI ratio, where it shows up as abrupt upward or downward steps in the BI ratiosbetween q4 of one year and q1 of the next year. In this example, the step problem shows up as a large upward jump in the BI ratio from q41998 to q1 1999.

1998 1999 2000

Indicator (left-hand scale)

QNA estimates derived using pro rata distribution (right-hand scale)

Back Series Forward Series

(The corresponding data are given in Example 6.1)

96

98

100

102

104

106

108

960

980

1,000

1,020

1,040

1,060

1,080

9.8

9.9

10.0

10.1

10.2

10.3

10.4

10.5

1998 1999 2000

scaling up or down the indicator (Iq,β +1) by the BIratio for the last quarter of the last benchmark year(X4,β/I4,β).

6.20. Also, note that if the quarterly estimates for thelast benchmark year X4,β were derived using the prorata technique in equation (6.1), for all quarters, theimplied quarterly BI ratios are identical and equal tothe annual BI ratio. That is, it follows from equation(6.1) that

(X4,β/I4,β) = (Xq,β/Iq,β) = (Aβ/ΣqIq,β).17

6.21. Thus, as shown in equations (6.1) and (6.2),distribution refers to constructing the back seriesby using the BI ratio for the current year as adjust-ment factors to scale up or down the QNA sourcedata, while extrapolation refers to constructing theforward series by carrying that BI ratio forward.

C. The Proportional Denton Method

1. Introduction

6.22. The basic distribution technique shown inthe previous section introduced a step in the series,and thus distorted quarterly patterns, by making alladjustments to quarterly growth rates to the firstquarter. This step was caused by suddenly chang-ing from one BI ratio to another. To avoid this dis-tortion, the (implicit) quarterly BI ratios shouldchange smoothly from one quarter to the next,while averaging to the annual BI ratios.18

Consequently, all quarterly growth rates will beadjusted by gradually changing, but relativelysimilar, amounts.

2. The Basic Version of the Proportional DentonMethod

6.23. The basic version of the proportional Dentonbenchmarking technique keeps the benchmarkedseries as proportional to the indicator as possible byminimizing (in a least-squares sense) the differencein relative adjustment to neighboring quarters sub-ject to the constraints provided by the annualbenchmarks. A numerical illustration of its opera-tion is shown in Example 6.2 and Chart 6.2.

6.24. Mathematically, the basic version of the pro-portional Denton technique can be expressed as19

(6.3)

under the restriction that, for flow series,20

.

That is, the sum21of the quarters should be equal tothe annual data for each benchmark year,22

wheret is time (e.g., t = 4y – 3 is the first quarter of year y,

and t = 4y is the fourth quarter of year y);Xt is the derived QNA estimate for quarter t;It is the level of the indicator for quarter t;Ay is the annual data for year y; β is the last year for which an annual benchmark is

available; andT is the last quarter for which quarterly source data

are available.

X A ytt

T

y=∑ = ∈ { }

2

1, ..... β

min –

,... ,...

..., ,......

–

–1 4

1

12

2

1 4

X X X

t

t

t

tt

T

T

XI

XI

t T

β

β

( ) =

∈ ( ){ }

∑

The Proportional Denton Method

87

17Thus, in this case, it does not matter which period is being moved.Moving from (a) the fourth quarter of the last benchmark year, (b)the average of the last benchmark year, or (c) the same quarter ofthe last benchmark year in proportion to the movements in the indi-cator from the corresponding periods gives the same results.Formally, it follows from equation (6.1) that

18In the standard case of binding annual benchmarks.

qq

qq

q

q

qq

X XI

I

XI

I

AI

I

, ,,

,

,,

,

,

,

β ββ

β

ββ

β

ββ

β

++

+

+

= ⋅

= ⋅

= ⋅

∑

1 41

4

1

1

19This presentation deviates from Denton’s original proposal by omit-ting the requirement that the value for the first period be predeter-mined. As pointed out by Cholette (1984), requiring that the values forthe first period be predetermined implies minimizing the first correc-tion and can in some circumstances cause distortions to the bench-marked series. Also, Denton’s original proposal dealt only withestimating the back series. 20For the less common case of stock series, the equivalent constraint isthat the value of the stock at the end of the final quarter of the year isequal to the stock at the end of the year. For index number series, the con-straint can be formulated as requiring the annual average of the quartersto be equal to the annual index or the sum of the quarters to be equal tofour times the annual index. The two expressions are equivalent.21Applies also to flow series in which the indicator is expressed asindex numbers; the annual total of the indicator should still beexpressed as the sum of the quarterly data.22The annual benchmarks may be omitted for some years to allow for casesin which independent annual source data are not available for all years.

6.25. The proportional Denton technique implicitlyconstructs from the annual observed BI ratios a timeseries of quarterly benchmarked QNA estimates-to-indicator (quarterly BI) ratios that is as smooth aspossible and, in the case of flow series:• For the back series, (y � {1,...β}) averages23 to the

annual BI ratios for each year y.• For the forward series, (y � {β + 1.....}) are kept

constant and equal to the ratio for the last quarter ofthe last benchmark year.

We will use this interpretation of the proportionalDenton method to develop an enhanced version in thenext section.

6.26. The proportional Denton technique, as pre-sented in equation (6.3), requires that the indicatorcontain positive values only. For series that containzeroes but not negative values, this problem can becircumvented by simply replacing the zeroes withvalues infinitesimally close to zero. For series thatcan take both negative and positive values, and arederived as differences between two non-negativeseries, such as changes in inventories, the problemcan be avoided by applying the proportional Dentonmethod to the opening and closing inventory levelsrather than to the change. Alternatively, the problemcan be circumvented by temporarily turning the indi-cator into a series containing only positive values byadding a sufficiently large constant to all periods,benchmarking the resulting indicator using equation(6.3), and subsequently deducting the constant fromthe resulting estimates.

6.27. For the back series, the proportional Dentonmethod results in QNA quarter-to-quarter growthrates that differ from those in the indicator (e.g., see

VI BENCHMARKING

88

Example 6.2. The Proportional Denton MethodSame data as in Example 6.1.

Indicator EstimatedThe Period-to-Period Annual Annual BI Derived QNA Quarterly Period-to-Period

Indicator Rate of Change Data Ratios Estimates BI ratios Rate of Change

q1 1998 98.2 969.8 9.876q2 1998 100.8 2.6% 998.4 9.905 3.0%q3 1998 102.2 1.4% 1,018.3 9.964 2.0%q4 1998 100.8 –1.4% 1,013.4 10.054 –0.5%Sum 402.0 4000.0 9.950 4,000.0q1 1999 99.0 –1.8% 1,007.2 10.174 –0.6%q2 1999 101.6 2.6% 1,042.9 10.264 3.5%q3 1999 102.7 1.1% 1,060.3 10.325 1.7%q4 1999 101.5 –1.2% 1,051.0 10.355 –0.9%Sum 404.8 0.7% 4161.4 10.280 4,161.4 4.0%q1 2000 100.5 –1.0% 1,040.6 10.355 –1.0%q2 2000 103.0 2.5% 1,066.5 10.355 2.5%q3 2000 103.5 0.5% 1,071.7 10.355 0.5%q4 2000 101.5 –1.9% 1,051.0 10.355 –1.9%Sum 408.5 0.9% ? ? 4,229.8 1.6%BI Ratios• For the back series (1998–1999):

In contrast to the pro rata distribution method in which the estimated quarterly BI ratio jumped abruptly from 9.950 to 10.280, the proportional Dentonmethod produces a smooth series of quarterly BI ratios in which:� The quarterly estimates sum to 4000, that is, the weighted average BI ratio for 1998 is 9.950.� The quarterly estimates sum to 4161.4, that is, the weighted average for 1999 is equal to 1.0280.� The estimated quarterly BI ratio is increasing through 1998 and 1999 to match the increase in the observed annual BI ratio.The increase is smallest at

the beginning of 1998 and at the end of 1999.• For the forward series (2000), the estimates are obtained by carrying forward the quarterly BI ratio (10.355) for the last quarter of 1999 (the last benchmark year).

Rates of Change• For the back series, the quarterly percentage changes in 1998 and 1999 are adjusted upwards for all quarters to match the higher rate of change in the annual data.• For the forward series, the quarterly percentage changes in 1999 are identical to those of the indicator; but note that the rate of change from 1999 to 2000

in the derived QNA series (1.6%) is higher than the annual rate of change in the indicator (0.9%).The next section provides an extension of the methodthat can be use to ensure that annual rate of change in the derived QNA series equals the annual rate of change in the indicator, if that is desired.


23annual weighted average

where the weights are

q y q y q yq

w I I, , ,==∑

1

4

X

Iw A Iq y

q yq y y q y

qq

,

,, ,⋅ =

==∑∑

1

4

1

4

Example 6.2). In extreme cases, the method may evenintroduce new turning points in the derived series orchange the timing of turning points; however, thesechanges are a necessary and desirable result of incor-porating the information contained in the annual data.

6.28. For the forward series, the proportional Dentonmethod results in quarter-to-quarter growth rates thatare identical to those in the indicator but also in an

annual growth rate for the first year of the forwardseries that differs from the corresponding growth rateof the source data (see Example 6.2). This differencein the annual growth rate is caused by the way theindicator is linked in. By carrying forward the quar-terly BI ratio for the last quarter of the last benchmarkyear, the proportional Denton method implicitly“forecasts” the next annual BI ratio as different fromthe last observed annual BI ratio, and equal to the


89

Chart 6.2. Solution to the Step Problem:The Proportional Denton MethodThe Indicator and the Derived Benchmarked QNA Estimates

Benchmark-to-Indicator Ratios

960

980

1000

1020

1040

1060

1080

96

98

100

102

104

106

108

1998 1999 2000


QNA estimates derived using pro rata distribution (right-hand scale)

1998–99 distributed 2000 extrapolated using Proportional Denton (right-hand scale)



1998 1999 20009.8

9.9

10.0

10.1

10.2

10.3

10.4

10.5

Annual step change

1998–99 distributed 2000 extrapolated using Proportional Denton

quarterly BI ratio for the last quarter of the lastbenchmark year. As explained in Annex 6.2, the pro-portional Denton method will result in the following:• It will partly adjust for any systematic bias in the

indicator’s annual rate of change if the bias is suf-ficiently large relative to any amount of noise, andthus, on average, lead to smaller revisions in theQNA estimates.

• It will create a wagging tail effect with, on average,larger revisions if the amount of noise is suffi-ciently large relative to any systematic bias in theannual growth rate of the indicator.

The next section presents an enhancement to thebasic proportional Denton that better incorporatesinformation on bias versus noise in the indicator’smovements.

6.29. For the forward series, the basic proportionalDenton method implies moving from the fourthquarter of the last benchmark year (see equation(6.2.a)). As shown in Annex 6.2, other possible start-ing points may cause a forward step problem, if usedtogether with benchmarking methods for the backseries that avoid the step problem associated withpro rata distribution: • Using growth rates from four quarters earlier.

Effectively, the estimated quarterly BI ratio is fore-cast as the same as four quarters earlier. Thismethod maintains the percentage change in theindicator over the previous four quarters but it doesnot maintain the quarterly growth rates, disregardsthe information in past trends in the annual BI ratio,and introduces potential sever steps between theback series and the forward series.

• Using growth rates from the last annual average.Effectively, the estimated quarterly BI ratio is fore-cast as the same as the last annual BI ratio. Thismethod results in annual growth rates that equalthose in the indicator; however, it also disregardsthe information in past trends in the annual BI ratioand introduces an unintended step between theback series and the forward series.

6.30. When the annual data later become available,the extrapolated QNA data would need to be re-esti-mated. As a result of the benchmarking process, newdata for one year will also lead to changes in the quar-terly movements for the preceding year(s). Thiseffect occurs because the adjustment for the errors inthe indicator is distributed smoothly over severalquarters, not just within the same year. For example,as illustrated in Example 6.3 and Chart 6.3, if the

1999 annual data subsequently showed that thedownward error in the indicator for 1998 for Example6.2 was reversed, then• the 1999 QNA estimates would be revised down;• the estimates in the second half of 1998 would be

revised down (to smoothly adjust to the 1999 val-ues); and

• the estimates in the first half of 1998 would need tobe revised up (to make sure that the sum of the fourquarters was still consistent with the 1998 annualtotal).

While these effects may be complex, it should beemphasized that they are an inevitable and desiredimplication of incorporating the information pro-vided by the annual data concerning the errors in thelong-term movements of the quarterly indicator.

3. Enhancements to the Proportional DentonMethod for Extrapolation

6.31. It is possible to improve the estimates for themost recent quarters (the forward series) and reducethe size of later revisions by incorporating informa-tion on past systematic movements in the annual BIratio. It is important to improve the estimates forthese quarters, because they are typically of the keen-est interest to users. Carrying forward the quarterlyBI ratio from the last quarter of the last year is animplicit forecast of the annual BI ratio, but a betterforecast can usually be made. Accordingly, the basicDenton technique can be enhanced by adding a fore-cast of the next annual BI ratio, as follows: • If the annual growth rate of the indicator is system-

atically biased compared to the annual data,24 then,on average, the best forecast of the next year’s BIratio is the previous year’s value multiplied by theaverage relative change in the BI ratio.

• If the annual growth rate of the indicator is unbi-ased compared to the annual data (i.e., the annualBI follows a random walk process), then, on aver-age, the best forecast of the next year’s BI ratio isthe previous annual value.

VI BENCHMARKING

90

24The indicator’s annual growth rate is systematically biased if theratio between (a) the ratio of annual of change in the indicator and (b)the ratio of annual change in the annual data on average is signifi-cantly different from one or, equivalently, that the ratio of annualchange in the annual BI ratio on average is significantly different fromone, as seen from the following expression:

A A

I I

A I

A I

BI

BIy y

q yq

q yq

y q yq

y q yq

y

y

–

, , –

,

– , ––

1

1

4

11

41

4

1 11

41

= =

=

=∑ ∑

∑

∑<=> =

• If the annual BI is fluctuating symmetricallyaround its mean, on average, the best forecast ofthe next year’s BI ratio is the long-term average BIvalue.

• If the movements in the annual BI ratio are follow-ing a stable, predictable time-series model (i.e., anARIMA25 or ARMA26 model) then, on average, the

best forecast of the next year’s BI ratio may beobtained from that model.

• If the fluctuations in the annual BI ratio are corre-lated with the business cycle27 (e.g., as manifestedin the indicator), then, on average, the best forecastof the next year’s BI ratio may be obtained bymodeling that correlation.


91

Example 6.3. Revisions to the Benchmarked QNA Estimates Resulting from AnnualBenchmarks for a New Year

This example is an extension of Example 6.2 and illustrates the impact on the back series of incorporating annual data for a new year, and sub-sequent revisions to the annual data for that year.

Assume that preliminary annual data for 2000 become available and the estimate is equal to 4,100.0 (annual data A). Later on, the preliminaryestimate for 2000 is revised upwards to 4,210.0 (annual data B). Using the equation presented in (6.3) to distribute the annual data over thequarters in proportion to the indicator will give the following sequence of revised QNA estimates:

Indicator Revised QNA Estimates Quarterized BI RatiosPeriod-to Derived Derived

Period Annual Annual Annual Annual in inThe rate of Data BI Ratio Data BI Ratio Example With With Example With With

Date Indicator Change 2000A 2000A 2000B 2000B 6.2 2000A 2000B 6.2 2000A 2000B

q1 1998 98.2 969.8 968.1 969.5 9.876 9.858 9.873q2 1998 100.3 2.6% 998.4 997.4 998.3 9.905 9.895 9.903q3 1998 102.2 1.4% 1,018.3 1,018.7 1,018.4 9.964 9.967 9.965q4 1998 100.8 –1.4% 1,013.4 1,015.9 1,013.8 10.054 10.078 10.058Sum 402.0 4,000.0 9.950 4,000.0 9.950q1 1999 99.0 –1.8% 1,007.2 1,012.3 1,008.0 10.174 10.225 10.182q2 1999 101.6 2.6% 1,042.9 1,047.2 1,043.5 10.264 10.307 10.271q3 1999 102.7 1.1% 1,060.3 1,059.9 1,060.3 10.325 10.321 10.324q4 1999 101.5 –1.2% 1,051.0 1,042.0 1,049.6 10.355 10.266 10.341Sum 404.8 0.7% 4,161.4 10.280 4,161.4 10.280q1 2000 100.5 –1.0% 1,040.6 1,019.5 1,037.4 10.355 10.144 10.323q2 2000 103.0 2.5% 1,066.5 1,035.4 1,061.8 10.355 10.052 10.308q3 2000 103.5 0.5% 1,071.7 1,034.1 1,065.9 10.355 9.991 10.299q4 2000 101.5 –1.9% 1,051.0 1,011.0 1,044.9 10.355 9.961 10.294Sum 408.5 0.9% 4,100.0 10.037 4,210.0 10.306 4,229.8 4,100.0 4,210.0

As can be seen, incorporating the annual data for 2000 results in (a) revisions to both the 1999 and the 1998 QNA estimates, and (b) the estimates for oneyear depend on the difference in the annual movements of the indicator and the annual data for the previous years, the current year, and the following years.

In case A, with an annual estimate for 2000 of 4100.0, the following can be observed:• The annual BI ratio increases from 9.950 in 1998 to 10.280 in 1999 and then drops to 10.037 in 2000. Correspondingly, the derived quarterly BI ratio

increases gradually from q1 1998 through q3 1999 and then decreases through 2000.• Compared with the estimates obtained in Example 6.2, incorporating the 2000 annual estimate resulted in the following revisions to the path of the quar-

terly BI ratio through 1998 and 1999:� To smooth the transition to the decreasing BI ratios through 2000, which are caused by the drop in the annual BI ratio from 1999 to 2000, the BI ratios

for q3 and q4 of 1999 have been revised downwards.� The revisions downward of the BI ratios for q3 and q4 of 1999 is matched by an upward revision to the BI ratios for q1 and q2 of 1999 to ensure that

the weighted average of the quarterly BI ratios for 1999 is equal to the annual BI ratio for 1999.� To smooth the transition to the new BI ratios for 1999, the BI ratios for q3 and q4 of 1998 have been revised upward; consequently, the BI ratios for q1

and q2 of 1998 have been revised downwards.• As a consequence a turning point in the new time series of quarterly BI ratios has been introduced between the third and the fourth quarter of 1999, in

contrast to the old BI ratio time series, which increased during the whole of 1999.

In case B, with an annual estimate for 2000 of 4210.0, the following can be observed:• The annual BI ratio for 1999 of 10.306 is slightly higher than the 1999 ratio of 10.280, but:

� The ratio is lower than the initial q4 1999 BI ratio of 10.325 that was carried forward in Example 6.2 to obtain the initial quarterly estimates for 2000.� Correspondingly, the initial annual estimate for 2000 obtained in Example 6.2 was higher than the new annual estimate for 2000.

• Consequently, compared with the initial estimates from Example 6.2, the BI ratios have been revised downwards from q3 1999 onwards.• In spite of the fact that the annual BI ratio is increasing, the quarterized BI ratio is decreasing during 2000.This is caused by the steep increase in the quar-

terly BI ratio during 1999 that was caused by the steep increase in the annual BI ratio from 1998 to 2000.


27Lags in incorporating deaths and births of businesses in quarterlysample frames may typically generate such correlations.

25Autoregressive integrated moving average time-series models.26Autoregressive moving average time-series models.

Note that only the annual BI ratio and not the annualbenchmark value has to be forecast, and the BI ratiois typically easier to forecast than the annual bench-mark value itself.

6.32. To produce a series of estimated quarterly BIratios taking into account the forecast, the same prin-ciples of least-square minimization used in the

Denton formula can also be used with a series ofannual BI ratios that include the forecast. Since thebenchmark values are not available, the annual con-straint is that the weighted average of estimated quar-terly BI ratios is the same as the correspondingobserved or forecast annual BI ratios and that period-to-period change in the time series of quarterly BIratios is minimized.

VI BENCHMARKING

92

Chart 6.3. Revisions to the Benchmarked QNA Estimates Resulting from Annual Benchmarksfor a New Year


960

980

1000

1020

1040

1060

1080

96

98

100

102

104

106

108

1998 1999 2000


With 2000A (right-hand scale) With 2000B

(right-hand scale)



1998–99 distributed 2000 extrapolated using Proportional Denton (right-hand scale)

1998 1999 2000

With 2000A

With 2000B


9.8

9.9

10.0

10.1

10.2

10.3

10.4

10.5

6.33. In mathematical terms:

(6.4.a)

under the restriction that

(a)

and

(b)

Where ,

and whereQBIt is the estimated quarterly BI ratio (Xt /It) for

period t;ABIy is the observed annual BI ratio (At/Σq

Iq,y)for year y � {1,...β}; and

ÂBIy is the forecast annual BI ratio for year y � {β + 1.....}.

6.34. Once a series of quarterly BI ratios is derived,the QNA estimate can be obtained by multiplying theindicator by the estimated BI ratio.

Xt = QBIt • It (6.4.b)

6.35. The following shortcut version of the enhancedDenton extrapolation method gives similar results forless volatile series. In a computerized system, theshortcut is unnecessary, but it is easier to follow in anexample (see Example 6.4 and Chart 6.4). Thismethod can be expressed mathematically as

(a) QBI2,β = QBI2,β + 1/4 • η (6.5)

QBI3,β = QBI3,β + 1/4 • ηQBI4,β = QBI4,β – 1/2 • η

(b) QBI1,β + 1 = QBI4,β – ηQBIq,β + 1 = QBIq – 1,β + 1 – η

where η = 1/3(QBI4,β – ÂBIβ + 1) (a fixed parameter for

adjustments that ensuresthat the estimated quar-terly BI ratios average tothe correct annual BIratios);

QBIq,β is the original BI ratio estimated for quarter qof the last benchmark year;

QBIq,β is the adjusted BI ratio estimated for quarterq of the last benchmark year;

QBIq,β + 1 is the forecast BI ratio for quarter q of the fol-lowing year; and

ÂBIβ + 1 is the forecast average annual BI ratio for thefollowing year.

6.36. While national accountants are usually reluc-tant to make forecasts, all possible methods are basedon either explicit or implicit forecasts, and implicitforecasts are more likely to be wrong because theyare not scrutinized. Of course, it is often the case thatthe evidence is inconclusive, so the best forecast issimply to repeat the last observed annual BI ratio.

D. Particular Issues

1. Fixed Coefficient Assumptions

6.37. In national accounts compilation, potential stepproblems may arise in cases that may not always bethought of as a benchmark-indicator relationship. Oneimportant example is the frequent use of assumptionsof fixed coefficients relating inputs (total or part ofintermediate consumption or inputs of labor and/orcapital) to output (“IO ratios”). Fixed IO ratios can beseen as a kind of a benchmark-indicator relationship,where the available series is the indicator for the miss-ing one and the IO ratio (or its inverse) is the BI ratio.If IO ratios are changing from year to year but are keptconstant within each year, a step problem is created.Accordingly, the Denton technique can be used togenerate smooth time series of quarterly IO ratiosbased on annual (or less frequent) IO coefficients.Furthermore, systematic trends can be identified toforecast IO ratios for the most recent quarters.

2. Within-Year Cyclical Variations in Coefficients

6.38. Another issue associated with fixed coefficientsis that coefficients that are assumed to be fixed may infact be subject to cyclical variations within the year. IOratios may vary cyclically owing to inputs that do not

w I I tt t tt y

y

= ∈ ( ){ }=∑4 3

4

1 4–

,...for β

QBI w ABI

t y

tt y

y

t y⋅ =

∈ ( ){ } ∈ +{ }=

+∑4 3

4

4 1

4 1

––

ˆ

...... , ,.... .for Tβ β

QBI w ABI

t y

tt y

y

t y⋅ =

∈ ( ){ } ∈ { }=∑4 3

4

1 4 1

–

,... , ,... .for β β

min –

,... ,....

...., ,.......–

1 4

12

2

1 4

QBI QBI QBIt t

t

T

T

QBI QBI

t T

β

β

( ) =[ ]

∈ ( ){ }

∑

Particular Issues

93

vary proportionately with output, typically fixed costssuch as labor, capital, or overhead such as heating andcooling. Similarly, the ratio between income flows(e.g., dividends) and their related indicators (e.g., prof-its) may vary cyclically. In some cases, these variationsmay be according to a seasonal pattern and be known.28

It should be noted that omitted seasonal variations areonly a problem in the original non-seasonally adjusteddata, as the variations are removed in seasonal adjust-ment and do not restrict the ability to pick trends andturning points in the economy. However, misguidedattempts to correct the problem in the original datacould distort the underlying trends.

6.39. To incorporate a seasonal pattern on the targetQNA variable, without introducing steps in the series,one of the following two procedures can be used:

(a) BI ratio-based procedureAugment the benchmarking procedure as out-lined in equation (6.4) by incorporating the a pri-ori assumed seasonal variations in the estimatedquarterly BI ratios as follows:

(6.6)

under the same restrictions as in equation (6.4), whereSFt is a time series with a priori assumed seasonal factors.

min –

,... ,....

...., ,.......

–

–1 4

1

12

2

1 4

QBI QBI QBI

QBI

SF

QBI

SF

t

T

t

t

t

tt

T

β

β

( ) =

∈ ( ){ }

∑

T

VI BENCHMARKING

94

28Cyclical variations in assumed fixed coefficients may also occurbecause of variations in the business cycle. These variations cause seriouserrors because they may distort trends and turning points in the economy.They can only be solved by direct measurement of the target variables.

Example 6.4. Extrapolation Using Forecast BI RatiosSame data as Examples 6.1 and 6.3

Original estimates Quarter to quarter rates of changefrom Example 6.2 Original

QNA Extrapolation using EstimatesAnnual estimates forecast BI ratios from Based on

Annual BI BI for Forecast Original Example forecastDate Indicator data ratios ratios 1997–1998 BI ratio Estimate indicator 6.2 BI ratios

q1 1998 98.2 9.876 969.8q2 1998 100.8 9.905 998.4 2.60% 3.00% 3.00%q3 1998 102.2 9.964 1,018.3 1.40% 2.00% 2.00%q4 1998 100.8 10.054 1,013.4 –1.40% –0.50% –0.50%Sum 402.0 4,000.0 9.950 4,000.0q1 1999 99.0 10.174 1,007.2 –1.80% –0.60% –0.60%q2 1999 101.6 10.264 1,042.9 10.253 1,041.7 2.60% 3.50% 3.40%q3 1999 102.7 10.325 1,060.3 10.314 1,059.2 1.10% 1.70% 1.70%q4 1999 101.5 10.355 1,051 10.376 1,053.2 –1.20% –0.90% –0.20%Sum 404.8 4,161.4 10.280 4,161.4 10.280 4,161.4 0.70% 4.00% 4.00%q1 2000 100.5 10.355 1,040.6 10.42 1,047.2 –1.00% –1.00% –0.60%q2 2000 103 10.355 1,066.5 10.464 1,077.8 2.50% 2.50% 2.90%q3 2000 103.5 10.355 1,071.7 10.508 1,087.5 0.50% 0.50% 0.90%q4 2000 101.5 10.355 1,051 10.551 1,071 –1.90% –1.90% –1.50%Sum 408.5 10.355 4,229.8 10.486 4,283.5 0.90% 1.60% 2.90%

This example assumes that, based on a study of movements in the annual BI ratios for a number of years, it is established that the indicator on average under-states the annual rate of growth by 2.0%.

The forecast annual and adjusted quarterly BI ratios are derived as follows:

The annual BI ratio for 2000 is forecast to rise to 10.486, (i.e., 10.280 • 1.02).

The adjustment factor (η) is derived as –0.044, (i.e., 1/3 • (10.355 – 10.486).

q2 1999: 10.253 = 10.264 + 1/4 • (–0.044)q3 1999: 10.314 = 10.325 + 1/4 • (–0.044)q4 1999: 10.376 = 10.355 – 1/2 • (–0.044)

q1 2000: 10.420 = 10.376 – (–0.044) q2 2000: 10.464 = 10.420 – (–0.044)q3 2000: 10.508 = 10.464 – (–0.044)q4 2000: 10.551 = 10.508 – (–0.044)

Note that for the sum of the quarters, the annual BI ratios are as measured (1999) or forecast (2000), and the estimated quarterly BI ratios move in a smoothway to achieve those annual results, minimizing the proportional changes to the quarterly indicators.


(b) Seasonal adjustment-based procedure(i) Use a standard seasonal adjustment package

to seasonally adjust the indirect indicator.(ii) Multiply the seasonally adjusted indicator

by the known seasonal coefficients.(iii) Benchmark the resulting series to the corre-

sponding annual data.

6.40. The following inappropriate procedure issometimes used to incorporate a seasonal pattern

when the indicator and the target variable have dif-ferent and known seasonal patterns:(a) distribute the annual data for one year in propor-

tion to the assumed seasonal pattern of the series,and

(b) use the movements from the same period in theprevious year in the indicator to update the series.

6.41. This procedure preserves the superimposedseasonal patterns when used for one year only. When

Particular Issues

95

Chart 6.4. Extrapolation Using Forecast BI Ratios


960

980

1000

1020

1040

1060

1080

96

98

100

102

104

106

108

1998 1999 2000


1998–99 distributed 2000 extrapolated using Proportional Denton(right-hand scale)

Extrapolating using forcasted BI ratios(right-hand scale)



1998 1999 2000

Extrapolating using forcasted BI ratios


9.8

10.0

10.2

10.4

10.6

the QNA estimates are benchmarked, however, thisprocedure will introduce breaks in the series that canremove or distort trends in the series and introducemore severe errors than those that it aims to prevent(see Annex 6.2 for an illustration).

3. Benchmarking and Compilation Procedures

6.42. Benchmarking should be an integral part of thecompilation process and should be conducted at themost detailed compilation level. In practice, this mayimply benchmarking different series in stages, wheredata for some series, which have already been bench-marked, are used to estimate other series, followed bya second or third round of benchmarking. The actualarrangements will vary depending on the particulari-ties of each case.

6.43. As an illustration, annual data may be availablefor all products, but quarterly data are available onlyfor the main products. If it is decided to use the sumof the quarterly data as an indicator for the otherproducts, the ideal procedure would be first to bench-mark each of the products for which quarterly dataare available to the annual data for that product, andthen to benchmark the quarterly sum of the bench-marked estimates for the main products to the total.Of course, if all products were moving in similarways, this would give similar results to directlybenchmarking the quarterly total to the annual total.

6.44. In other cases, a second or third round ofbenchmarking may be avoided and compilation pro-cedure simplified. For instance, a current price indi-cator can be constructed as the product of a quantityindicator and a price indicator without first bench-marking the quantity and price indicators to any cor-responding annual benchmarks. Similarly, a constantprice indicator can be constructed as a current priceindicator divided by a price indicator without firstbenchmarking the current price indicator. Also, ifoutput at constant prices is used as an indicator forintermediate consumption, the (unbenchmarked)constant price output indicator can be benchmarkedto the annual intermediate consumption data directly.It can be shown that the result is identical to firstbenchmarking the output indicator to annual outputdata, and then benchmarking the resulting bench-marked output estimates to the annual intermediateconsumption data.

6.45. To derive quarterly constant price data bydeflating current price data, the correct procedure

would be first to benchmark the quarterly currentprice indicator and then to deflate the benchmarkedquarterly current price data. If the same price indicesare used in the annual and quarterly accounts, thesum of the four quarters of constant price data shouldbe taken as the annual estimate, and a second roundof benchmarking is unnecessary. As explained inChapter IX Section B, annual deflators constructed asunweighted averages of monthly or quarterly pricedata can introduce an aggregation over time error inthe annual deflators and subsequently in the annualconstant price data that can be significant if there isquarterly volatility. Moreover, if, in those cases, quar-terly constant price data are derived by benchmarkinga quarterly constant price indicator derived by deflat-ing the current price indicator to the annual constantprice data, the aggregation over time error will bepassed on to the implicit quarterly deflator, whichwill differ from the original price indices. Thus, inthose cases, annual constant price data should in prin-ciple be derived as the sum of quarterly or evenmonthly deflated data if possible. If quarterly volatil-ity is insignificant, however, annual constant priceestimates can be derived by deflating directly andthen benchmarking the quarterly constant price esti-mates to the annual constant price estimates.

4. Balancing Items and Accounting Identities

6.46. The benchmarking methods discussed in thischapter treat each time series as an independent vari-able and thus do not take into account any accountingrelationship between related time series. Consequently,the benchmarked quarterly time series will not auto-matically form a consistent set of accounts. For exam-ple, quarterly GDP from the production side may differfrom quarterly GDP from the expenditure side, eventhough the annual data are consistent. The annualsum of these discrepancies, however, will cancel outfor years where the annual benchmark data arebalanced.29 While multivariate benchmarking methodsexist that take the relationship between the time seriesas an additional constraint, they are too complex anddemanding to be used in QNA.

6.47. In practice, the discrepancies in the accountscan be minimized by benchmarking the differentparts of the accounts at the most detailed level andbuilding aggregates from the benchmarked compo-nents. If the remaining discrepancies between, for

VI BENCHMARKING

96

29The within-year discrepancies will in most cases be relativelyinsignificant for the back series.

instance, GDP from the production and expenditureside are sufficiently small,30 it may be defensible todistribute them proportionally over the correspond-ing components on one or both sides. In other cases,it may be best to leave them as explicit statistical dis-crepancies, unless the series causing these discrepan-cies can be identified. Large remaining discrepanciesindicate that there are large inconsistencies betweenthe short-term movements for some of the series.

5. More Benchmarking Options

6.48. The basic version of the proportional Dentontechnique presented in equation (6.3) can beexpanded by allowing for alternative benchmarkoptions, as in the following examples:• The annual benchmarks may be omitted for some

years to allow for cases where independent annualsource data are not available for all years.

• Sub-annual benchmarks may be specified byrequiring that

� the values of the derived series are equal tosome predetermined values in certain benchmarkquarters; or� the half-yearly sums of the derived quarterlyestimates are equal to half-yearly benchmarkdata for some periods.

• Benchmarks may be treated as nonbinding.• Quarters that are known to be systematically more

error prone than others may be adjusted relativelymore than others.

The formulas for the two latter extensions are pro-vided in Section B.2 of Annex 6.1.

6. Benchmarking and Revisions

6.49. To avoid introducing distortions in the series,incorporation of new annual data for one year will gen-erally require revision of previously published quar-terly data for several years. This is a basic feature of allacceptable benchmarking methods. As explained inparagraph 6.30, and as illustrated in Example 6.3, inaddition to the QNA estimates for the year for whichnew annual data are to be incorporated, the quarterlydata for one or several preceding and following years,may have to be revised. In principle, previously pub-

lished QNA estimates for all preceding and followingyears may have to be adjusted to maximally preservethe short-term movements in the indicator, if the errorsin the indicator are large. In practice, however, withmost benchmarking methods, the impact of newannual data will gradually be diminishing and zero forsufficiently distant periods.

6.50. One of the advantages of the Denton methodcompared with several of the alternative methodsdiscussed in Annex 6.1, is that it allows for revi-sions to as many preceding years as desired. Ifdesired, revisions to some previously publishedQNA estimates can be avoided by specifying thoseestimates as “quarterly benchmark restrictions.”This option freezes the values for those periods,and thus can be used to reduce the number of yearsthat have to be revised each time new annual databecome available. To avoid introducing significantdistortions to the benchmarked series, however, atleast two to three years preceding (and following)years should be allowed to be revised each timenew annual data become available. In general, theimpact on more distant years will be negligible.

7. Other Comments

6.51. Sophisticated benchmarking techniques useadvanced concepts. In practice, however, they requirelittle time or concern in routine quarterly compilation.In the initial establishment phase, the issues need to beunderstood and the processes automated as an integralpart of the QNA production system. Thereafter, thetechniques will improve the data and reduce futurerevisions without demanding time and attention of theQNA compiler. It is good practice to check the newbenchmarks as they arrive each year in order toreplace the previous BI ratio forecasts and make newannual BI forecasts. A useful tool for doing so is atable of observed annual BI ratios over the past severalyears. It will be usual for the BI ratio forecasts to havebeen wrong to varying degrees, but the importantquestion is whether the error reveals a pattern thatwould allow better forecasts to be made in the future.In addition, changes in the annual BI ratio point toissues concerning the indicator that will be of rele-vance to the data suppliers.

Particular Issues

97

30That is, so that the impact on the growth rates are negligible.

Annex 6.1. Alternative Benchmarking Methods

98

A. Introduction

6.A1.1. There are two main approaches to bench-marking of time series: a purely numerical approachand a statistical modeling approach. The numericaldiffers from the statistical modeling approach bynot specifying a statistical time-series model thatthe series is assumed to follow. The numericalapproach encompasses the family of least-squaresminimization methods proposed by Denton (1971)and others,1 the Bassie method,2 and the methodproposed by Ginsburgh (1973). The modelingapproach encompasses ARIMA3 model-basedmethods proposed by Hillmer and Trabelsi (1987),State Space models proposed by Durbin andQuenneville (1997), and a set of regression modelsproposed by various Statistics Canada staff.4 Inaddition, Chow and Lin (1971) have proposed amultivariable general least-squares regressionapproach for interpolation, distribution, and extrap-olation of time series. While not a benchmarkingmethod in a strict sense, the Chow-Lin method isrelated to the statistical approach, particularly toStatistics Canada’s regression models.

6.A1.2. The aim of this annex is to provide a briefreview, in the context of compiling quarterlynational accounts (QNA), of the most familiar ofthese methods and to compare them with the pre-ferred proportional Denton technique with enhance-ments. The annex is not intended to provide anextensive survey of all alternative benchmarkingmethods proposed.

6.A1.3. The enhanced proportional Denton tech-nique provides many advantages over the alterna-tives. It is, as explained in paragraph 6.7, by logicalconsequence optimal if the general benchmarkingobjective of maximal preservation of the short-term

movements in the indicator is specified as keepingthe quarterly estimates as proportional to the indica-tor as possible and the benchmarks are binding. Inaddition, compared with the alternatives, theenhanced proportional Denton technique is rela-tively simple, robust, and well suited for large-scaleapplications. Moreover, the implied benchmark-indicator (BI) ratio framework provides a generaland integrated framework for converting indicatorseries into QNA estimates through interpolation,distribution, and extrapolation with an indicatorthat, in contrast to additive methods, is not sensitiveto the overall level of the indicators and does nottend to smooth away some of the quarter-to-quarterrates of change in the data. The BI framework alsoencompasses the basic extrapolation with an indica-tor technique used in most countries.

6.A1.4. In contrast, the potential advantage of thevarious statistical modeling methods over theenhanced proportional Denton technique is that theyexplicitly take into account any supplementaryinformation about the underlying error mechanismand other aspects of the stochastic properties of theseries. Usually, however, this supplementary infor-mation is not available in the QNA context.Moreover, some of the statistical modeling methodsrender the danger of over-adjusting the series byinterpreting true irregular movements that do not fitthe regular patterns of the statistical model as errors,and thus removing them. In addition, the enhance-ment to the proportional Denton provided in SectionD of Chapter VI allows for taking into account sup-plementary information about seasonal and othershort-term variations in the BI ratio. Furtherenhancements that allow for incorporating any sup-plementary information that the source data forsome quarters are weaker than others, and thusshould be adjusted more than others, are provided inSection B.2 of this annex, together with a nonbind-ing version of the proportional Denton.

6.A1.5. Also, for the forward series, the enhance-ments to the proportional Denton method developed

1Helfand, Monsour, and Trager (1977), and Skjæveland (1985).2Bassie (1958).3Autoregressive integrated moving average.4Laniel, and Fyfe (1990), and Cholette and Dagum (1994).

in Section C.3 of Chapter VI provide more and bet-ter options for incorporating various forms of infor-mation on past systematic bias in the indicator’smovements. The various statistical modeling meth-ods typically are expressed as additive relationshipsbetween the levels of the series, not the movements,that substantially limit the possibilities for alterna-tive formulation of the existence of any bias in theindicator. The enhancements to the proportionalDenton method developed in Chapter VI expresssystematic bias in terms of systematic behavior ofthe relative difference in the annual growth rate ofthe indicator and the annual series or, equivalently,in the annual BI ratio. This provides for a moreflexible framework for adjusting for bias in theindicator.

B. The Denton Family of Benchmarking Methods

1. Standard Versions of the Denton Family

6.A1.6. The Denton family of least-squares-basedbenchmarking methods is based on the principle ofmovement preservation. Several least-squares-based methods can be distinguished, depending onhow the principle of movement preservation is madeoperationally. The principle of movement preserva-tion can be expressed as requiring that (1) the quar-ter-to-quarter growth in the adjusted quarterly seriesand the original quarterly series should be as similaras possible or (2) the adjustment to neighboringquarters should be as similar as possible. Withineach of these two broad groups, further alternativescan be specified. The quarter-to-quarter growth canbe specified as absolute growth or as rate of growth,and the absolute or the relative difference of thesetwo expressions of quarter-to-quarter growth can beminimized. Similarly, the difference in absolute orrelative adjustment of neighboring quarters can beminimized.

6.A1.7. The proportional Denton method (formulaD4 below) is preferred over the other versions ofthe Denton method for the following three mainreasons:• It is substantially easier to implement.• It results in most practical circumstances in

approximately the same estimates for the backseries as formula D2, D3, and D5 below.

• Through the BI ratio formulation used in ChapterVI, it provides a simple and elegant frameworkfor extrapolation using the enhanced propor-tional Denton method, which fully takes into

account the existence of any systematic bias orlack thereof in the year-to-year rate of change inthe indicator.

• Through the BI ratio formulation used in ChapterVI, it provides a simple and elegant frameworkfor extrapolation, which supports the understand-ing of the enhanced proportional Denton method;the Denton method fully takes into account theexistence of any systematic bias or lack thereof inthe year-to-year rate of change in the indicator.

6.A1.8. In mathematical terms, the following are themain versions5 of the proposed least-squares bench-marking methods:6

MinD1: (6.A1.1)

Min D2: (6.A1.2)

Min D3: (6.A1.3)

Min D4:7 (6.A1.4)min –..., ,....

–

–1 4

1

1

2

2X X X

t

t

t

tt

T

T

X

I

X

Iβ( ) =

∑

min –..., ,....

– –1 4 1 1

2

2X X X

t

t

t

tt

T

T

X

X

I

Iβ( )

=∑

min

min

min

..., ,....

–

–

..., ,....– –

..., ,....–

1 4

1 4

1 4

1

1

1

1

1

2

2

1 1

2

2

1

X X X

t t

t tt

T

X X X

t t

t tt

T

X X Xt t

T

T

T

X X

I I

X I

X I

X X

β

β

β

( )

( )

( )

(

=

=

∑

∑<=>

<=>

n

n

n

)) ( )[ ]=

∑ – –1 1

2

2

n I It tt

T

min – –

min – –

..., ,....

..., ,....

1 4

1 4

1 1

1 1

2

2

2

2

X X X t

T

X X X t

T

T

T

X X I I

X I X I

t t t t

t t t t

β

β

( )−

<=>( )

−

−( ) −( )[ ]∑

−( ) −( )[ ]∑

=

=


99

5The abbreviations D1, D2, D3, and D4, were introduced bySjöberg (1982), as part of a classification of the alternative least-squares-based methods proposed by, or inspired by, Denton (1971).D1 and D4 were proposed by Denton; D2 and D3 by Helfand,Monsour, and Trager (1977); and D5 by Skjæveland (1985).6This presentation deviates from the original presentation by thevarious authors by omitting their additional requirement that thevalue for the first period is predetermined. Also, Denton’s originalproposal only dealt with the back series.7This is the basic version of the proportional Denton.

Min D5: (6.A1.5)

All versions are minimized under the same restric-tions, that for flow series,

.

That is, the sum of the quarters should be equal to theannual data for each benchmark year.

6.A1.9. The various versions of the Denton family ofleast-squares-based benchmarking methods have thefollowing characteristics:• The D1 formula minimizes the differences in the

absolute growth between the benchmarked seriesXt and the indicator series It. It can also be seen asminimizing the absolute difference of the absoluteadjustments of two neighboring quarters.

• The D2 formula minimizes the logarithm of the rela-tive differences in the growth rates of the two series.Formula D2 can also be looked upon as minimizingthe logarithm of the relative differences of the relativeadjustments of two neighboring quarters and as thelogarithm of the absolute differences in the period-to-period growth rates between the two series.

• The D3 formula minimizes the absolute differencesin the period-to-period growth rates between thetwo series.

• The D4 formula minimizes the absolute differences inthe relative adjustments of two neighboring quarters.

• The D5 formula minimizes the relative differencesin the growth rates of the two series. Formula D5can also be looked upon as minimizing the relativedifferences of the relative adjustments of twoneighboring quarters.

6.A1.10. While all five formulas can be used forbenchmarking, only the D1 formula and the D4 for-mula have linear first-order conditions for a mini-mum and thus are the easiest to implement inpractice. In practice, the D1 and D4 formulas are theonly ones currently in use.

6.A.1.11. The D4 formula—the proportional Dentonmethod—is generally preferred over the D1 formula

because it preserves seasonal and other short-termfluctuations in the series better when these fluctuationsare multiplicatively distributed around the trend of theseries. Multiplicatively distributed short-term fluctua-tions seem to be characteristic of most seasonal macro-economic series. By the same token, it seems mostreasonable to assume that the errors are generally mul-tiplicatively, and not additively, distributed, unlessanything to the contrary is explicitly known. The D1formula results in a smooth additive distribution of theerrors in the indicator, in contrast to the smooth multi-plicative distribution produced by the D4 formula.Consequently, as with all additive adjustment formula-tions, the D1 formula tends to smooth away some ofthe quarter-to-quarter rates of change in the indicatorseries. As a consequence, the D1 formula can seriouslydisturb that aspect of the short-term movements forseries that show strong short-term variations. This canoccur particularly if there is a substantial differencebetween the level of the indicator and the target vari-able. In addition, the D1 formula may in a fewinstances result in negative benchmarked values forsome quarters (even if all original quarterly andannual data are positive) if large negative adjustmentsare required for data with strong seasonal variations.

6.A1.12. The D2, D3, and D5 formulas are very sim-ilar. They are all formulated as an explicit preserva-tion of the period-to-period rate of change in theindicator series, which is the ideal objective formula-tion, according to several authors (e.g., Helfand,Monsour, and Trager 1977). Although the three for-mulas in most practical circumstances will giveapproximately the same estimates for the back series,the D2 formula seems slightly preferable over theother two. In contrast to D2, the D3 formula willadjust small rates of change relatively more thanlarge rates of change, which is not an appealing prop-erty. Compared to D5, the D2 formula treats large andsmall rates of change symmetrically and thus willresult in a smoother series of relative adjustments tothe growth rates.

2. Further Expansions of the Proportional DentonMethod

6.A1.13. The basic version of the proportionalDenton technique (D4) presented in the chaptercan be further expanded by allowing for alternativeor additional benchmark restrictions, such as thefollowing:• Adjusting relatively more quarters that are known

to be systematically more error prone than others.• Treating benchmarks as nonbinding.

X A yt y

y

y14 3

4

1= ∈ { }=∑

–

, ,... β

min –

min –

,... , ....

..., ,....

–

–

..., ,....– –

1 4

1 4

1

1

2

2

1 1

2

2

1

1

1 4

X X X

t t

t tt

T

X X X

t t

t tt

T

T

T

X X

I I

X I

X I

t T

β

β

β

( )

( )

( ){ }

=

=

∑

∑<=>

∈

VI BENCHMARKING

100

6.A1.14. The following augmented version of thebasic formula allows for specifying which quartersshould be adjusted more than the others:

(6.A1.6)

under the standard restriction that

That is, the sum of the quarters should be equal to theannual data for each benchmark year.

Where wqt

is a set of user-specified quarterly weights thatspecifies which quarters should be adjustedmore than the others.

6.A1.15. In equation (6.A1.6), only the relativevalue of the user-specified weights (wqt

) matters. Theabsolute differences in the relative adjustments of apair of neighboring quarters given a weight that ishigh relative to the weights for the others will besmaller than for pairs given a low weight.

6.A1.16. Further augmenting the basic formula asfollows, allows for treating the benchmarks as non-binding:

(6.A1.7)

Whereway is a set of user-specified annual weights that

specifies how binding the annual benchmarksshould be treated.

Again, only the relative value of the user-specifiedweights matters. Relatively high values of the annualweights specify that the benchmarks should betreated as relatively binding.

C. The Bassie Method

6.A1.17. Bassie (1958) was the first to devise amethod for constructing monthly and quarterlyseries whose short-term movements would closely

reflect those of a related series while maintainingconsistency with annual totals. The Bassie methodwas the only method described in detail inQuarterly National Accounts (OECD, 1979).However, using the Bassie method as presented inOECD (1979) can result in a step problem if datafor several years are adjusted simultaneously.

6.A1.18. The Bassie method is significantly lesssuited for QNA compilation than the proportionalDenton technique with enhancements for the follow-ing main reasons:• The proportional Denton method better preserves

the short-term movements in the indicator.• The additive version of the Bassie method, as with

most additive adjustment methods, tends to smooththe series and thus can seriously disturb the quar-ter-to-quarter rates of change in series that showstrong short-term variations.

• The multiplicative version of the Bassie methoddoes not yield an exact correction, requiring asmall amount of prorating at the end.

• The proportional Denton method allows for the fulltime series to be adjusted simultaneously, in con-trast to the Bassie method, which operates on onlytwo consecutive years.

• The Bassie method can result in a step problemif data for several years are adjusted simultane-ously and not stepwise.8

• The proportional Denton method with enhance-ments provides a general and integrated frameworkfor converting indicator series into QNA estimatesthrough interpolation, distribution, and extrapola-tion with an indicator. In contrast, the Bassiemethod does not support extrapolation; it onlyaddresses distribution of annual data.

• The Bassie method results in a more cumbersomecompilation process.

6.A1.19. The following is the standard presentationof the Bassie method, as found, among others, inOECD (1979). Two consecutive years are consid-ered. No discrepancies between the quarterly andannual data for the first year are assumed, and the(absolute or relative) difference for the second year isequal to K2.

6.A1.20. The Bassie method assumes that the cor-rection for any quarter is a function of time, Kq = f(t)and that f(t) = a + bt + ct2 + dt3. The method then stip-ulates the following four conditions: (i) The average correction in year 1 should be equal

to zero:

min – – – ...., , ....

–

– –1 4 2

1

1

2

1 4 3

42

1X X X

qt

Tt

t

t

t

ay

t

yt y

y

Tt y

wX

I

X

Iw

X

Aβ

β

( ) = = =

∑ ∑ ∑⋅ ⋅

X A ytt y

y

y=∑ = ∈ { }4 1

4

1–

, ,... . β

min –

,... ,....

...., ,.......

–

–1 4 2

1

1

2

1 4

X X Xq

t

Tt

t

t

tTt

wXI

XI

t T

β

β

( ) =∑ ⋅

∈

( ){ }


101

(ii) The average correction in year 2 should be equalto the annual error in year 2 (K2):

(iii)At the start of year 1, the correction should bezero, so as not to disturb the relationship betweenthe first quarter of year 1 and the fourth quarter ofyear 0: f(0) = 0.

(iv) At the end of year 2, the correction should be nei-ther increasing nor decreasing:

6.A1.21. These four conditions allow computingthe following fixed coefficients to distribute the

annual error in year 2 (K2) over the four quarters ofyear 2 and to adjust the quarterly pattern withinyear 1:

6.A1.22. The difference between the annual sumof the quarterly estimates and the direct annual esti-mate in year 2 (K2) can be expressed either in anadditive form or in a multiplicative form. The addi-tive form is as follows:

(6.A1.8)

leading to the following additive version of theBassie adjustment method:

Zq,1 = Xq,1 + 0.25 • bq • K2 (6.A1.9)

Zq,2 = Xq,2 + 0.25 • cq • K2

K A Xqq

2 2 21

4

==∑– ,

df

dt

20

( ) = .

f t dt K( ) .=∫ 21

2

f t dt( ) .=∫ 00

1

VI BENCHMARKING

102

Example 6.A1.1. The Bassie Method and the Step Problem

Adjustment Coefficients ImpliedOriginal Annual Rate of Adjustment Adjustment Adjusted Growth Adjustment

Date Estimates Estimates Error of Year 2 of Year 3 Estimates Rates Ratio

Year 1q1 1,000.0 –0.0981445 990.2 0.990q2 1,000.0 –0.1440297 985.6 –0.5% 0.986q3 1,000.0 –0.0083008 999.2 1.4% 0.999q4 1,000.0 0.25048828 1,025.1 2.6% 1.025Total year 1 4,000.0 4,000.0 0.00 0.0 4,000.0Year 2q1 1,000.0 0.57373047 –0.0981445 1,057.4 3.2% 1.057q2 1,000.0 0.90283203 –0.1440297 1,090.3 3.1% 1.090q3 1,000.0 1.17911122 –0.0083008 1,117.9 2.5% 1.118q4 1,000.0 1.34423822 0.25048828 1,134.4 1.5% 1.134Total year 2 4,000.0 4,400.0 0.10 4.0 0.0 4,400.0Year 3q1 1,000.0 0.57373047 1,000.0 –11.9% 1.000q2 1,000.0 0.90283203 1,000.0 0.0% 1.000q3 1,000.0 1.17911122 1,000.0 0.0% 1.000q4 1,000.0 1.34423822 1,000.0 0.0% 1.000Total year 3 4,000.0 4,000.0 0.00 4.0In the example, revised annual estimates for years 2 and 3 were made available at the same time. As seen, the first–round adjustment of the quarterly seriesto align the quarterly estimates to the annual estimate for year 2 results in an upward adjustment in the growth through year 1 and year 2 but no adjustmentsto year 3, leading to a break in the series between q4 of year 2 and q1 of year 3.

The break introduced by the first round of adjustments is not removed in the second round of adjustments to align the series to the annual estimate foryear 3. In the example, the error in year 3 is zero, and the Bassie method, applied as described above, results in no further adjustments of the data.

8This step problem can be reduced, but not removed entirely, by areformulation of the standard presentation of the method; however,use of the Bassie method is still not advisable.

To be used for year 1 To be used for year 2

b1 -0.098145 c1 0.573730 b2 -0.144030 c2 0.902832 b3 -0.008301 c3 1.179111b4 0.250488 c4 1.344238

Sum 0.0 4.0

whereq is used as a generic symbol for quarters; Zq,y is the level of the adjusted quarterly estimate

for quarter q in year 1 (y = 1) and 2 (y = 2);Xq,y is the level of the preliminary quarterly estimate

for quarter q in year y; andA2 is the level of the direct annual estimate for year 2.

6.A1.23. The multiplicative form is as follows:

(6.A1.10)

leading to the following multiplicative version of theBassie adjustment method:

Zq,1 = Xq,1 • (1 + bq • K2) (6.A1.11)

Zq,2 = Xq,2 • (1 + cq • K2)

The multiplicative version of the Bassie method doesnot yield an exact correction, and a small amount ofprorating is necessary at the end of the computation.

6.A1.24. The Bassie method only works as long asnot more than one year is adjusted each time and thequarterly estimates represent a continuous timeseries. In particular, it should be noted that (contraryto what is stated in Quarterly National Accounts(OECD 1979, page 30), when several years are to beadjusted, the process cannot be directly “continuedfor years 2 and 3, years 3 and 4, etc., applying thecorrection factors for the ‘first year’ to year 2 (whichhas already been corrected once) and the correctionfactors for ‘the second year’ for year 3, and 4, etc.”That is, the following generalized version of themultiplicative Bassie method does not work:

Zq,y = Xq,y • (1 + cq • Ky) • (1 + bq • Ky + 1) (6.A1.12)

6.A1.25. Example 6.A1.1, using the multiplicativeversion of the Bassie method, illustrates the working ofthe Bassie method as described in OECD (1979) andthe step problem inherent in this version of the methodwhen used for adjusting several years simultaneously.

6.A1.26. The break introduced by the use of the Bassiemethod, as applied above, is caused by the fact that thequarterly time series used in aligning the series to year3 is not continuous. The time series used consists of theoriginal data for year 3 and the data for year 2 aligned

or benchmarked to the annual data for year 2. This dis-continuity is carried over into the revised series.

D. The Ginsburgh-Nasse Method

6.A1.27. Ginsburgh proposed a three-step method fordistribution of annual data using a related quarterlyseries. He did not address the problem of extrapolation,or estimation of the forward series. By slightly refor-mulating the original presentation of the method alongthe lines suggested by Ginsburgh himself, however, thebasic version of the QNA “regression-based” compila-tion system,9 as originally formulated by Nasse (1973),for estimating both the back and the forward seriesemerges. In this section the following is shown:• The Ginsburgh-Nasse method is in essence identi-

cal to the additive Denton (D1) method with a prioradjustment of the indicator for any significant aver-age difference between the level of the indicatorand the target variable.

• For both the back and forward series, theGinsburgh-Nasse method and the D1 method withprior level adjustment result in identical estimates.

• The regression component of the Ginsburgh-Nassemethod constitutes an unnecessarily complicated andcumbersome way of prior adjusting the indicator forany significant average difference between the levelof the indicator and the target variable.

• The same prior level adjustment can be obtainedsimply by using the ratio between the annualbenchmark and the annual sum of the indicator forone year as an adjustment factor.

6.A1.28. Ginsburgh’s proposal was to generate thebenchmarked quarterly data by using the followingthree-step procedure:

(a) Estimate the “quarterly trend” of the annual dataAy and the annual sum of the indicator

using a the following least-squares distributionformula:


Z A t ytt y

y=∑ = ∈ ( ){ } ∈ { }4 3

4

1 4 1–

,... , ,.... ,β

β β

min –.....,

–1 4

12

2

4

Z Zt t

t

Z Zβ

β

( ) =[ ]∑

I Iy q yq= ∑ ,

K A Xqq

2 2 21

4

1=

=∑ , –


103

9As presented in for instance Dureau (1995).

where Zt = Ât and Ît, respectively. Denote theresulting quarterized series Âq,y and Îq,y.

(b) Use the standard ordinary-least-squares (OLS)technique to estimate the parameters of the fol-lowing annual linear regression equation:

Ay = f(Iy) = a + b • Iy + εy, (6.A1.13)

E(εy) = 0, y � {1,....β}

whereεy stands for the error term assumed to be ran-

dom with an expected value equal to zero; anda and b are fixed parameters to be estimated.

(c) Finally, derive the benchmarked data for the backseries as follows:

Xq,y = Âq,y + b • (Iq,y – Îq,y) (6.A1.14)

q � {1,...4}, y � {1,...β}

where b is the estimated value of the fixed para-meter b in equation (6.A1.13).

6.A1.29. As shown by Ginsburgh, the derivedbenchmarked series in equation (6.A1.14) can equiv-alently be derived by solving the following least-squares minimization problem:

(6.A1.15)

This equation reduces to the additive Denton (D1)formula in equation (6.A1.1) if b is close to 1.

6.A1.30. In equation (6.A1.15), the parameter bserves to adjust for the average difference between thelevel of indicator and the target variable and thus helpsmitigate one of the major weaknesses of the standardadditive Denton formula. The parameter a, in the lin-ear regression equation (6.A1.13), serves to adjust forany systematic difference (bias) in the average move-ments of the indicator and target variable. The para-meter a does not appear in equations (6.A1.14) or(6.A1.15), however, and thus in the end serves no rolein deriving the estimates for the back series.

6.A1.31. The basic set-up of the QNA “regression-based” compilation system proposed by Nasse is thefollowing:

(a) Use an estimated econometric relationship suchas in step (b) of the Ginsburgh method above to

derive preliminary (nonbenchmarked) QNA timeseries (X p

q,y) as

X pq,y = â/4 + b • Iq,y, y � {1,....β} (6.A1.16)

where â is the estimated value of the fixed para-meter a in equation (6.A1.13).

(b) Compute the difference between the annual sumsof the quarterly estimates derived by using equa-tion (6.A1.16) and the corresponding indepen-dent annual data as follows:

εy = Ay – ΣqX p

q,y ≠ 0 (6.A1.17)

The OLS estimation technique will ensure thatthe error term sums to zero over the estimationperiod (ΣyΣqεq,y = 0) but will not ensure that theannual sum of the error term is equal to zero.

(c) Generate a smooth continuous time series of errorterms for year 1 to β using the following least-squares minimization expression:

(6.A1.18)


(d) Finally, derive the benchmarked data for both theback and the forward series as follows:

For the back series,Xq,y = â/4 + b • Iq,y + εq,y (6.A1.19)

y � {1,....β}

For the forward series,Xq,y = â/4 + b • Iq,y + ε4,β (6.A1.20)

y � {β + 1,.....}

6.A1.32. By combining equations (6.A1.17),(6.A1.18), (6.A1.19), and (6.A1.20), it can be shownthat steps (b) to (d) above reduce to

(6.A1.21)

and thus become identical to the Ginsburgh methodin equation (6.A1.15), expanded slightly to alsoencompass the forward series. Again, observe that the

min – – ˆ –..., ,......

– –1 4 4

1 12

2

4

X X Xt t t t

t

y

y

X X b I Iβ( ) =

( ) ( )[ ]⋅∑

ε εt yt y

y

==∑4 3

4

–

min – ,

,....

...,–

1 41

2

2

4

1

ε ε

β

β

ε ε

β( ) =

[ ]∈ { }

∑ t tt

y

min – – ˆ –...,

– –1 4

1 1

2

2

4

X Xt t t t

t

X X b I Iβ

β

( ) =( ) ⋅ ( )[ ]∑

VI BENCHMARKING

104

parameter â does not appear in equation (6.A1.21)and thus in the end serves no role in deriving the esti-mates, even for the forward series.

6.A1.33. Equations (6.A1.15) and (6.A1.21) showthat the Ginsburgh-Nasse method does not repre-sent any real difference from the additive Denton(D1) method for the following two reasons. First,and most importantly, the regression approach doesnot provide any additional adjustment for the exis-tence of any bias in the indicator’s movementscompared with the basic additive Denton method,neither for the back series nor for the forwardseries. Second, regression analysis represents anunnecessarily complicated way of adjusting for anysignificant average difference between the level ofthe indicator and the target variable. This average-level-difference adjustment can be obtained muchmore easily by a simple rescaling of the originalindicator, using the ratio between the annual bench-mark and the annual sum of the indicator for oneyear as the adjustment factor. Thus, as shown, theGinsburgh-Nasse method in the end constitutes anunnecessarily complicated and cumbersome10 wayof obtaining for both the back and the forwardseries the same estimates that can be obtainedmuch easier by using the D1 method.

6.A1.34. As with most additive adjustment formula-tions, the Ginsburgh-Nasse and D1 methods tend tosmooth away some of the quarter-to-quarter rates ofchange in the indicator series. As a consequence, theycan seriously disturb that aspect of the short-termmovements for series that show strong short-termvariations.11 This can particularly occur if there is asubstantial difference between the level of the indica-tor and the target variable.

6.A1.35. The procedure set out in (a) to (d) abovehas also been criticized (Bournay and Laroque1979) as being inconsistent in terms of statisticalmodels. OLS regression assumes that the errors arenot autocorrelated. This is inconsistent with thesmooth distribution of the annual errors in equation(6.A1.18), which implies an assumption that the

errors are perfectly autocorrelated with a unit auto-correlation coefficient. This inconsistency may nothave any significant impact on the back series butmay imply that it is possible to obtain a better esti-mate for the forward series by incorporating anyknown information on the errors’ autocorrelationstructure.

6.A1.36. The procedure can also be criticized forbeing sensitive to spurious covariance between theseries. Formulating the econometric relationship as arelationship between the level of non-stationary timeseries renders the danger of primarily measuringapparent correlations caused by the strong trend usu-ally shown by economic time series.

6.A1.37. Compared with the enhanced version of theproportional Denton method, the Ginsburgh-Nasseand D1 methods have two additional distinct disad-vantages, namely:12

(a) They will only partly adjust for any systematicbias in the indicator’s annual movements if thebias is substantial relative to any amount ofnoise.

(b) They will, on average, lead to relatively largerrevisions (a wagging tail effect) if the amount ofnoise is substantial relative to any bias in the indi-cator’s annual movements.

6.A1.38. The potential wagging tail effect that theGinsburgh-Nasse and D1 methods suffer from isassociated with the inconsistent use of statisticalmodels mentioned above (paragraph 6.A1.35). Inparticular, estimating the forward series by carry-ing forward the estimated error term for the fourthquarter of the last benchmark year εq,β is inconsis-tent with the assumptions underlying the use ofOLS to estimate the parameters of equation(6.A1.13). To see this, assume for the sake of theargument that the statistical model in equation(6.A1.13) is correctly specified and thus that theannual error term εy is not autocorrelated and has azero mean. Then the best forecast for the nextannual discrepancy εβ + 1 would be zero and not4 • εβ + 1 as implied by equation (6.A1.20).


105

10In contrast to the D1 method, the regression approach also requiresvery long time series for all indicators.11Some of the countries using these additive methods partly cir-cumvent the problem by applying them only on seasonally adjustedsource data. However, other short-term variations in the data willstill be partly smoothed away, and, as explained in Chapter I, lossof the original non-seasonally adjusted estimates is a significantproblem in itself.

12The basic version of the proportional Denton also suffers fromthese weaknesses. A detailed discussion of these issues with respectto the D4 formula is provided in Annex 6.2. The discussion inAnnex 6.2 is also applicable to the D1 formula, with the only dif-ference being how the annual movements are expressed: as additivechanges in the case of the D1 formula and as relative changes(growth rates) in the case of the D4 formula.

E. Arima-Model-Based Methods

6.A1.39. The ARIMA-model-based method pro-posed by Hillmer and Trabelsi (1987) provides onemethod for taking into account any known infor-mation about the stochastic properties of the seriesbeing benchmarked. As for most of the statisticalmodeling methods, the method was proposed inthe context of improving survey estimates, wherethe survey design may provide identifiable infor-mation about parts of the stochastic properties ofthe series (the sampling part of the underlyingerror-generating mechanism). Clearly, incorporat-ing any such information, if available, in the esti-mation procedure may potentially improve theestimates. In the QNA context, however, this infor-mation about the stochastic properties of the seriesis usually non-existent. Furthermore, non-sam-pling errors in the surveys may often be moreimportant than sampling errors, and incorporatingonly partial information about the underlyingerror-generating mechanism may introduce sys-tematic errors.

6.A1.40. The main advantages of the enhanced pro-portional Denton method over the ARIMA-model-based methods in the QNA compilation context arethe following: • The enhanced proportional Denton method is

much simpler, more robust, and better suited forlarge-scale applications.

• The enhanced proportional Denton method avoidsthe danger associated with the ARIMA-model-based method of over-adjusting the series by inter-preting as errors, and thus removing, true irregularmovements that do not fit the regular patterns of thestatistical model.

• The enhanced proportional Denton method avoidsthe danger of substantially disturbed estimatesresulting from misspecification of the autocovari-ance structure of the quarterly and annual errorterms in the ARIMA-model-based method.

• The enhanced proportional Denton method allowsfor extrapolation taking into account fully the exis-tence of any systematic bias or lack thereof in theyear-to-year rate of change in the indicator. In con-trast, the proposed ARIMA-model-based methoddoes not accommodate any bias in the indicator’smovements.

6.A1.41. The core idea behind the Hillmer-Trabelsi ARIMA-model-based method is to assumethe following:

(a) That the quarterly time series is observed with anadditive error, Iq,y = θq,y + εq,y where θq,y representsthe true but unknown quarterly values of theseries and is assumed to follow an ARIMAmodel. The error term εq,y is assumed to have zeromean and to follow a known ARMA13 model.Assuming that the error term has zero meanimplies that the observed series is assumed to bean unbiased estimate of the true series.

(b) That the annual benchmarks also are observedwith an additive error with zero mean and knownautocovariance structure. That is, the annualbenchmarks follow the model: Ay = Σq

θq,y + ξywhere ξy represents the annual error term, and isassumed independent of εq,y and ηq,y.

Based on the assumed time-series models andassumed known autocovariance structures, Hillmerand Trabelsi obtain the quarterly benchmarkedseries using what the time-series literature refers toas “signal extraction.”

F. General Least-Squares Regression Models

6.A1.42. An alternative, and potentially better,method to take into account any known informationabout the stochastic properties of the underlyingerror-generating process is represented by the alter-native general-least-squares (GLS) regression mod-els proposed by various Statistics Canada staff.

6.A1.43. The advantages of the enhanced propor-tional Denton method over the GLS regressionmodel methods, in the QNA compilation context,are basically the same as the advantages over theARIMA-model-based method listed in paragraph6.A1.40 above.

6.A1.44. The following three models constitute thecore of Statistics Canada’s benchmarking program“Program Bench”:• The additive model (Cholette and Dagum 1994)

It = a + θt + εt, (6.A1.22a)E(εt) = 0, E(εt εt – k) ≠ 0

t & k � {1,...(4β),....T}, y � {1,...β}

(6.A1.22b)A w

E w E w w

y t yt y

y

y y t k

= +

( ) = ( ) ≠

=

−

∑θ ,

,

–4 3

4

0 0

VI BENCHMARKING

106

13Autoregressive moving average.

wherea is an unknown constant bias parameter to be

estimated;θt is the true but unknown quarterly values to be

estimated;εt is the quarterly error term associated with the

observed indicator and is assumed to have zeromean and a known autocovariance structure; and

wy is the annual error term associated with theobserved benchmarks and is assumed to havezero mean and a known autocovariance structure.The benchmarks will be binding if the variance ofthe annual error term is zero and non-binding ifthe variance is different from zero.

• The multiplicative model (Cholette 1994)It = a • θt • εt, (6.A1.23a)E(εt) = 0, E(εt εt – k) ≠ 0

(6.A1.23b)

• The mixed model (Laniel and Fyfe 1990)It = a • θt + εt, (6.A1.24a)E(εt) = 0, E(εt εt – k) ≠ 0

(6.A1.24b)

6.A1.45. Cholette and Dagum (1994) provide theGLS solution to equation (6.A1.22) when the autoco-variance structure of the annual and quarterly errorterms is known. Similarly, Mian and Laniel (1993)provides the Maximum Likelihood solution to equa-tion (6.A1.24) when the autocovariance structure ofthe annual and quarterly error terms is known.14

6.A1.46. The three GLS models are implemented inStatistics Canada’s benchmarking program, assum-ing that the errors follow the following autocovari-ance structures:E(εt) = 0, (6.A1.25a)E(εt εt – k) ≠ σεt σεt – 1 ρk

(6.A1.25b)

whereσεt is the standard deviation of the quarterly

errors, which may vary with time t, meaningthat the errors may be heteroscedastic;

ρk is a parameter indicating the degree of autocor-relation in the errors; and

σ 2wy is the variance of the annual errors, which may

vary with time y, meaning that the errors may beheteroscedastic.

and where the autocorrelations ρk corresponds tothose of a stationary and invertible ARMA processwhose parameter values are supplied by the users ofthe program. This is equivalent to assuming that thequarterly errors follow a time-series process givenby εt = �t • σεt where �t follows the selected ARMAprocess.

6.A1.47. The regression models in equation(6.A1.22) to (6.A1.25) can be used to approximatethe D1, D3, and D4 versions of the Denton methodabove by specifying the autocovariance structureappropriately. The additive regression model inequation (6.A1.22) approximates D1 if(a) the bias parameter is omitted; (b) the benchmarks are binding (zero variances); (c) the variances of the quarterly errors are constant;

and (d) the ARMA model specified approximates a ran-

dom walk process (that is εt = σεt • (εt – 1 + vt )where vt represents “white noise”).

Similarly, the additive regression model in equation(6.A1.22) approximates D4 if (a) the bias parameter is omitted; (b) the benchmarks are binding; (c) the coefficients of variation (CVs, σεt/–ε (where –ε

is the average error) of the quarterly errors areconstant; and

(d) the ARMA model specified approximates arandom walk process (that is εt = σεt • (εt – 1 + vt )where σεt is given by the constant CVs).

Finally, the multiplicative regression model in equa-tion (6.A1.24) approximates D3 if (a) the benchmarks are binding; (b) the coefficients of variation (CVs) of the quarterly

errors are constant; and (c) the ARMA model specified approximates a

random walk process (that is, εt = σεt • (εt – 1 + vt)).

A w

E w E w

y t yt y

y

y y wy

= +

( ) = ( ) =

=∑θ

σ

,

,

–4 3

4

2 20

A w

E w E w w

y t yt y

y

y y t k

= +

( ) = ( ) ≠

=

−

∑θ ,

,

–4 3

4

0 0

A w

E w E w w

y t yt y

y

y y t k

= +

( ) = ( ) ≠

=

−

∑θ ,

,

–4 3

4

0 0


107

14The solutions are the “best linear unbiased estimates” (BLUE) underthe given assumptions.

G. The Chow-Lin Method

6.A1.48. The Chow-Lin method for distribution andextrapolation of time series is basically a multiple-regression version of the additive GLS model inequation (6.A1.22) above with binding benchmarks.By relating several loosely related indicator series toone annual benchmark series, it does not represent abenchmarking method in a strict sense.

6.A1.49. The main advantages of the enhanced pro-portional Denton method over the Chow-Lin methodare the same as listed above with respect to the GLSregression and ARIMA-model methods. In addition,the Chow-Lin method differs from the above GLSregression methods in the following two fundamentalaspects that make it unsuitable for QNA purposes inmost circumstances:15

• Multiple regression is conceptually fundamen-tally different from benchmarking. The Chow-Lin

method gives the dangerous impression that quar-terly estimates of GDP and other nationalaccounts variables can be derived simply by esti-mating the annual correlation between the nationalaccounts variables and a limited set of someloosely related quarterly source data. In contrast,benchmarking is about combining quarterly andannual source data for the same phenomena. Atbest, estimating the correlation between, forexample, GDP and a set of available quarterlytime series is a modeling approach to obtain fore-casts or nowcasts of GDP, but it has nothing to do with compiling quarterly national accounts.Furthermore, as a modeling approach for fore-casting it is overly simplified and may result insub-optimal forecasts.

• The multiple-regression approach implicitly assumesthat the (net) seasonal pattern of the related series isthe same as that of the target aggregate, which is notvery likely.

VI BENCHMARKING

108

15The Chow-Lin multiple-regression method may have an applicationin filling minor gaps with synthetic data where no direct observationsare available.

Annex 6.2. Extrapolation Base and the Forward Step Problem

109

A. Introduction

6.A2.1. The basic version of the proportionalDenton method presented in Chapter VI uses the lastquarter of the last benchmark year as the extrapola-tion base.16 Arguments have been made for usingalternative extrapolation bases. It is sometimesargued that using the last quarter of the last bench-mark year as the extrapolation base may make theestimates vulnerable to errors in the source data forthat quarter, and thus, it may be better to use the lastannual average as the extrapolation base. Similarly, itis sometimes argued that to preserve the seasonal pat-tern of the series, the same quarter in the previousyear should be used as the extrapolation base or,alternatively, that a strong seasonal pattern in theseries may cause distortions to the estimates if theyare not based on moving from the same quarter of theprevious year.

6.A2.2. In this annex we will show that these argu-ments for using alternative extrapolation bases arenot correct and that the alternative extrapolationbases generally should not be used. In particular, wewill show that use of different extrapolation baseswill result in different estimates only if the impliedquarterly benchmark-indicator (BI) ratios for theback series differ from quarter to quarter and from theannual (BI) ratio; which they must do to avoid theback series step problem. In those circumstances:• The alternative extrapolation bases introduce a

step between the back and forward series that canseriously distort the seasonal pattern of the series.

• Using the last quarter of the last benchmark year asthe extrapolation base will result in the following:17

� It will partly adjust for any systematic bias in theindicator’s annual rate of change if the bias is suf-ficiently large relative to any amount of noise, and

thus, on average, lead to smaller revisions in thequarterly national accounts (QNA) estimates.

� It will create a wagging tail effect with, onaverage, larger revisions if the amount of noiseis sufficiently large relative to any systematicbias in the annual growth rate of the indicator.

The annex also demonstrates that using the lastquarter of the last benchmark year as the extrapolationbase does not make the estimates more vulnerable toerrors in the source data for that quarter. Numericalillustrations of these results are given in Examples6.A2.1 and 6.A2.2, and Chart 6.A2.1.

B. Alternative Extrapolation Bases

6.A2.3. In mathematical terms the use of the alternativeextrapolation bases can be formalized as follows:(a) Fourth quarter of the last benchmark year as the

extrapolation base:

(6.A2.1)

(b) Quarterly average of the last benchmark year asthe extrapolation base:

(6.A2.2)

(c) Same quarter of the last benchmark year as theextrapolation base:

(6.A2.3)X XI

I

IX

I

q y

q y qq y

q

q yq

q

, ,,

,

,,

,

,... , ,... .

= ⋅

= ⋅

∈ { } ∈ +{ }

ββ

β

β

β1 4 1

X AI

I

IA

I

q y

q yq y

qq

q yqq

,,

,

,,

,... , ,... .

= ⋅ ⋅⋅

= ⋅

∈ { } ∈ +{ }

∑

∑

14 1

4

1 4 1

ββ

β

β

β

X XI

II

X

I

q y

q yq y

q y, ,,

,,

,

,

,... , ,...

= ⋅

= ⋅

∈ { } ∈ +{ }

44

4

4

1 4 1

ββ

β

β

β


16 In contrast, the recommended enhanced version of the proportionalDenton presented in section C of Chapter VI does not use any specificextrapolation base. 2The enhanced version of the proportional Denton presented in sec-tion C of Chapter VI provides means for avoiding the potential wag-ging tail effect, and for fully adjusting for any systematic bias.

VI BENCHMARKING

110

Example 6.A2.1. Extrapolation Bases and the Forward Step Problem

Estimates for 2000

(a)Extrapolation

Estimates for of q4 1999Quarterized 1998–1999 BI Ratio

Annual BI BI from CarriedIndicator Annual Data Ratios Ratios 6.2. Estimates Forward

q1 1998 98.2 9.876 969.8q2 1998 100.8 9.905 998.4q3 1998 102.2 9.964 1,018.3q4 1998 100.8 10.054 1,013.4Sum 402.0 4,000.0 9.950 9.950 4,000.0q1 1999 99.0 10.174 1,007.2q2 1999 101.6 10.264 1,042.9q3 1999 102.7 10.325 1,060.3q4 1999 101.5 10.355 1,051.0Sum 404.8 4,161.4 10.280 4,161.4q1 2000 100.5 1,040.6 10.355q2 2000 103.0 1,066.5 10.355q3 2000 103.5 1,071.7 10.355q4 2000 101.5 1,051.0 10.355Sum 408.5 4,229.9 10.355

In this example, the following is worth observing:

First, during 1999 the quarterized BI ratio is increasing gradually (10.174, 10.264, 10.325, and 10.355), and consequently the quarter-to-quarter rate of changein the indicator differs from the quarter-to-quarter rates of change in the derived QNA estimates for 1999.

Second, the three different QNA estimates for 2000 can be derived by carrying forward the 1998 BI ratios as follows:(a) Extrapolating the fourth quarter of 1999:

q1,00=1040.6 = 100.5 • 10.355 q2,00=1066.5 = 103.0 • 10.355 q4,00=1051.0 = 101.5 • 10.355;(b) Extrapolating the quarterly average for 1999:

q1,00=1033.2 = 100.5 • 10.280 q2,00=1058.9 = 103.0 • 10.280 q4,00=1043.4 = 101.5 • 10.280; and(c) Extrapolating the same quarter in 1999:

q1,00=1022.5 = 100.5 • 10.174 q2,00=1057.2 = 103.0 • 10.264 q4,00=1051.0 = 101.5 • 10.355.

Third,(a) Extrapolating the fourth quarter of 1999:

preserves the quarter-to-quarter rate of changes in the indicator series;(b) Extrapolating the quarterly average for 1999:

results in a break between the fourth quarter of 1999 and the first quarter of 2000 (period-to-period rate of change of –1.7 and not –1.0% as shown inthe indicator); and

(c) Extrapolating the same quarter in 1999:results in an even more severe break between the fourth quarter of 1999 and the first quarter of 2000 (period-to-period rate of change of –2.7% andnot –1.0% as shown in the indicator).

In addition, the breaks between the fourth quarter of 1999 and the first quarter of 2000 introduced by using extrapolation bases (b) and (c) are introduced bya discontinuity in the time series of quarterized BI ratios.That is, when using extrapolation base (b) the BI ratio changes abruptly from 10.355 in the fourthquarter of 1999 to 10.28 in the first quarter of 2000, and when using extrapolation base (c) the BI ratio changes abruptly from 10.355 in the fourth quarter of1999 to 10.174 in the first quarter of 2000.

Fourth,(a) Extrapolating the fourth quarter of 1999:

results in an estimated annual rate of change in the QNA series from 1999 to 2000 of 1.6%, which differs from the rate of change from 1999 to 2000of 0.9% shown in the indicator series;

(b) Extrapolating the quarterly average for 1999:results in an estimated rate of change from 1999 to 2000, which is identical to the rate of change shown in the indicator series (0.9%); and

(c) Extrapolating the same quarter in 1999:results in an estimated annual rate of change from 1999 to 2000, which is identical to the rate of change shown in the indicator series (0.9%).

Fifth, if the difference of 3.0 percentage points between the rate of change from 1999 to 2000 in the ANA estimate and in the indicator is due to an averagedownward bias in the annual movements of the indicator of 3.0 percentage points, then the annual data for 2000 can be expected to show an annual rate ofchange from 1999 to 1999 of 4.0 percent.Thus, the estimate derived by using extrapolation base (a) will still be downward biased.

(These results are illustrated in Chart 6.A2.1.)


111

Estimates for 2000 Quarter-to-Quarter Rates of Change(c)

(b) (c) ExtrapolationExtrapolation of the Average Extrapolation of the Same of the

Quarter for 1999 Quarter in the Previous Year (b) Same QuarterBI Ratio BI ratios Based (a) Based on in theCarried Carried on the Based average Previous

Estimates Forward Estimates Forward Indicator q4 1999 1999 Year

2.6% 3.0%1.4% 2.0%

–1.4% –0.5%Identical for All Methods

–1.8% –0.6%2.6% 3.5%1.1% 1.7%

–1.2% –0.9%0.7% 4.0%

1,033.2 10.280 1,022.5 10.174 –1.0% –1.0% –1.7% –2.7%1,058.9 10.280 1,057.2 10.264 2.5% 2.5% 2.5% 3.4%1,064.0 10.280 1,068.6 10.325 0.5% 0.5% 0.5% 1.1%1,043.4 10.280 1,051.0 10.355 –1.9% –1.9% –1.9% –1.6%4,199.4 10.280 4,199.3 10.280 0.9% 1.6% 0.9% 0.9%

VI BENCHMARKING

112

Chart 6.A2.1.Alternative Extrapolation Bases and the Forward Step Problem

In this example, the step problem shows up as a decrease in the derived series from q4 1999 to q1 2000 that is not matched by the move-ments in the source data.The quarter-to-quarter rate of change for the first quarter of 1999 of –1.0% in source data is –1.0%. In contrast, thecorresponding rate of change in the estimates derived by extrapolating the average of 1999 is –1.7%, and the corresponding rate of change inthe estimates derived by extrapolating the same quarter of 1999 is –2.7%.

Benchmark-to-Indicator Ratio

It is easier to recognize the step problem from charts of the BI ratio, where it shows up as abrupt upward or downward steps in the BI ratiosbetween q4 of one year and q1 of the next year. In this example, the step problem shows up as a large upward jump in the BI ratio betweenq4 1999 and q1 2000.

960

980

1000

1020

1040

1060

1080

96

98

100

102

104

106

108

1998 1999 2000


1998–99 distributed 2000 extrapolated based on q4 1999 (Proportional Denton) (right-hand scale)

2000 Based on extrapolation of q4 1999 (right-hand scale)

2000 Based on extrapolation of the same quarter in the previous year (right-hand scale)


(The corresponding data are given in Example 6.A2.1)

1998 1999 20009.8

9.9

10.0

10.1

10.2

10.3

10.4

10.51998–99 distributed 2000 extrapolated based on q4 1999 (Proportional Denton)

2000 Based on extrapolation of q4 1999

2000 Based on extrapolation of the same quarter in the previous year

6.A2.4. The use of different extrapolation baseswill result in different estimates only if the impliedquarterly BI ratios for the back series differ fromquarter to quarter and from the annual BI ratio.That is, if

6.A2.5. In Section C of Chapter VI it is explainedthat to avoid the back series step problem, the impliedquarterly BI ratios (Xq,y /Iq,y) must differ from quarterto quarter and from the annual BI ratio. Thus, differ-ent extrapolation bases will give different estimateswhen the back series is derived using benchmarkingmethods that avoid the (back series) step problemassociated with pro rata distribution.

C. The Forward Step Problem

6.A2.6. The forward step problem associated withextrapolation bases (b) and (c) above is caused by adiscontinuity in the implied quarterly BI ratios. Tokeep the benchmarked series as proportional aspossible to the original quarterly source data, theproportional Denton method generates quarterly BIratios that for the last year covered by annual dataeither increase or decrease gradually. Consequently,the quarterly BI ratio for the last quarter of the lastbenchmark year may differ significantly from theannual BI ratio and even more from the quarterly BIratio for the first quarter of the last benchmark year.It follows that:• Extrapolation base (b) introduces an upward step if

a downward step if

• Extrapolation base (c) introduces an upward step if

a downward step if

6.A2.7 It also follows that the step introduced byusing the same quarter of the previous year as theextrapolation base (base iii) will always be moresevere than the step caused by using the annual aver-age as the extrapolation base (base ii).

D. Annual Rate of Change in the Derived ForwardSeries

6.A2.8. Using the last quarter of the last bench-mark year as the extrapolation base implies adjust-ing the source data for all subsequent quarters witha factor that systematically differs from the averageadjustment in the last benchmark year. This is thecause for the difference between the annual growthrate in the source data and the annual growth rate inthe estimates derived by using the basic version ofthe proportional Denton for the first year of the for-ward series.18 It follows that using extrapolationbase (a) will result in an annual rate of change forthe first year of the forward series that is • higher than the corresponding change in the source

data if

• lower than the corresponding change in the sourcedata if

6.A2.9. The relative difference between the annualchanges in the derived QNA estimates and thecorresponding changes in the indicator is equal tothe relative difference between the quarterly BIratio for the fourth quarter and the annual averageBI ratio of the last benchmark year. This can beshown mathematically as follows:

A I X Iqq

β β β β, , , .=∑

> ( )

1

4

4 4

A I X Iqq

β β β β, , , ,=∑

< ( )

1

4

4 4 or

X I X Ib b b b1 1 4 4, , , , .( ) < ( )

X I X Ib b b b1 1 4 4, , , , ,( ) > ( ) or

A I X Iqq

β β β β, , , .=∑

< ( )

1

4

4 4

A I X Iqq

β β β β, , , ,=∑

> ( )

1

4

4 4 or

X I X I A Iq q qq4 4, , , , , .β β β β β β( ) ≠ ( ) ≠ ( )∑


113

18In contrast, it can be shown that the corresponding annual growthrates obtained by using extrapolation base (b) or (c) will for base (b)be identical, and for base (c) approximately identical, to the annualgrowth rates in the source data. Note that this may not be a desirableproperty if there is significant bias in the indicator’s annual rate ofmovements.

The ratio of annual change in the derived estimates isequal to

The ratio of annual change in the indicator is equalto

The ratio between these two expressions is equal tothe relative difference between the annual changes inthe derived estimates and in the indicator, and can bewritten as

(6A2.4)

where we have used that

(from equation (6.A2.1)) and that

The last expression in equation (6A2.4) is the relativedifference between the BI ratio for the fourth quarter andthe annual average BI ratio of the last benchmark year.

6.A2.10. Using the last quarter of the last bench-mark year as the extrapolation base will result in thefollowing:19

• It will partly adjust for any systematic bias in theannual growth rate of the indicator if the bias is suffi-ciently large relative to any amount of noise and thus,in those circumstances, give on average relativelysmaller revisions in the derived QNA estimates.

• It will create a wagging tail effect with, on average,larger revisions in the derived QNA estimates if theamount of noise is sufficiently large relative to any sys-tematic bias in the annual growth rate of the indicator.

6.A2.11. To see this, consider the case in which theannual rate of change in the indicator is consistentlydownward biased and in which the amount of noise iszero. Then, by definition, the ratio between the annualrate of change in the annual national accounts (ANA)estimates and the annual rate of change in the indica-tor will be constant and larger than one:

where δ is a fixed bias parameter.

In that case, the annual BI ratio will be increasingwith a constant rate from year to year:

6.A2.12. Quarterizing a time series of annual BIratios that increases with a constant rate will resultin a time series of quarterly BI ratios that alsoincreases steadily from quarter to quarter. In partic-ular, the quarterized BI ratio will be increasingthrough the last benchmark year,20 and thus, in thiscase, the BI ratio for the fourth quarter will alwaysbe larger than the annual BI ratio for the last bench-mark year:

6.A2.13. Thus, as explained in paragraph 6.A2.8,in this case, using extrapolation base (a) will resultin an annual change in the estimated QNA variablethat is higher than the corresponding change in the

X I A Iqq

4 41

4

, , , .β β β β( ) >

=∑

A I A Iy q yq

y q yq

, , .=

− −=

∑ ∑

= ⋅

1

4

1 11

4

δ

A A Iy y q yq

– , ,11

4

( )

=

=∑ δ

X Aqq

, .β β==∑

1

4

XX

IIq y q y,

,

,,= ⋅4

4

β

β

X

X

I

I

X

II

A

I

I

X

I

A

I

q yq

qq

q yq

qq

q yq

q yq

qq

qq

,

,

,

,

,

,, ,

,

,

,,

=

=

=

=

= =

=

=

∑

∑

∑

∑

∑ ∑

∑

∑

=

⋅=

1

4

1

41

4

1

4

4

41

4

1

4

1

4

4

4

1

4

β β

β

β

ββ

β

β

β

β

I I yq yq

qq

, , .= =∑ ∑ = +( )

1

4

1

4

1β β

X Xq yq

qq

, , .= =∑ ∑

1

4

4

4

β

VI BENCHMARKING

114

20The increase will taper off toward the end of the series if the seriesis based on a first difference least-square expression such as equation(6. 4) in Chapter VI.

19Note that the enhanced version presented in Section C of Chapter VIprovides means for avoiding the potential wagging tail effect and forfully adjusting for any bias.

indicator, as desired. If the rate of change in theindicator is upward biased, then δ < 1 and the line ofarguments in paragraphs 6.A2.11 and 6A2.12applies in the opposite direction.

6.A2.14 The adjustment for bias in the annualgrowth rate of the indicator will be partial onlybecause, as can be shown, the BI ratio for the fourthquarter will, at the same time, be smaller than theproduct of the bias parameter and the last annual BIratio:

To fully correct for the bias in the indicator, the aver-age adjustment of the indicator for the current yearsshould have been equal to the product of the biasparameter and the last annual BI ratio. The enhancedversion of the proportional Denton presented inChapter VI provides means for fully adjusting for anypersistent bias.

6.A2.15. The potential wagging tail effect is causedby erratic variations around the fixed bias parameterin the year-to-year increase of the annual BI ratio. Asa consequence:• The BI ratio for the fourth quarter may some-

times be larger than the product of the bias para-meter and the last annual BI ratio, resulting in anannual change in the estimated QNA variable thatis higher than the expected change in the annualdata.

• The quarterized BI ratio may sometimes bedecreasing through the last benchmark year,resulting in an annual change in the estimatedQNA variable that is lower than in the indicatorand lower than the expected change in the annualdata.

The enhanced version of the proportional Dentonpresented in Chapter VI provides means for avoidingthis wagging tail effect.

E. Extrapolation Base and Robustness TowardErrors in the Indicator

6.A2.16. Using a single quarter as the extrapolationbase does not make the estimates particularly vul-nerable to errors in the source data for that quarter. Itis sometimes erroneously argued that using extrapo-lation base (b) gives more robust estimates thanusing extrapolation base (a). The idea behind thisview is that basing the estimates on just one quartermakes them more vulnerable to errors in the indica-tor. The difference between the estimates derived byusing extrapolation base (a) and (b), however, issolely caused by the movements in the quarterizedBI ratio during the last benchmark year, which againis mainly a function of the annual BI ratios for thatyear and the previous years. In particular, as shownin Example 6.A2.2 below, the BI ratio for the fourthquarter of the last benchmark year is almost totallyindependent of the indicator value for that quarter.

F. Extrapolation Base and Seasonality6.A2.17. It should be evident from the above that topreserve the seasonal pattern of the series, the samequarter in the previous year generally should not beused as the extrapolation base. As shown, it can intro-duce an unintended step problem if used together withbenchmarking methods that avoid the back series stepproblem by keeping the derived series as parallel aspossible to the source data. In contrast, extrapolationbase (a) transmits to the QNA estimate the indicator’sseasonal pattern as unchanged as possible, which iswhat is generally being sought.

6.A2.18. Use of the same quarter in the previousyear as the extrapolation base is only acceptable inthe following rare circumstance:• annual benchmarks are not available for more than

one year; • the indicator and the target variable have different

seasonal patterns; and• initial quarterly estimates are available, with a

proper seasonal pattern, for a base year.

X I A Iqq

4 41

4

, , , .β β β βδ( ) < ⋅

=∑


115

VI BENCHMARKING

116

Example 6.A2.2. Extrapolation Base and Robustness Toward Errors in the Indicator

Quarter–to–Quarter Rates of Change

Basedon the

Original Original Estimates Original EstimatesIndicator Estimates New Based Estimates Based Based

from Annual from Original Quarterized on the from on the on theExample Revised Annual BI Example Quarterized BI Revised Example Revised Revised

Date 6.2 Indicator Data Ratios 6.2. BI Ratios Ratios Indicator 6.2 Indicator Indicator

q1 1998 98.2 98.2 969.8 9.876 9.875 969.7q2 1998 100.8 100.8 998.4 9.905 9.904 998.4 3.0% 2.6% 3.0%q3 1998 102.2 102.2 1,018.3 9.964 9.964 1,018.4 2.0% 1.4% 2.0%q4 1998 100.8 100.8 1,013.4 10.054 10.055 1,013.6 –0.5% –1.4% –0.5%Sum 402.0 402.0 4,000.0 9.950 4,000.0 4,000.0q1 1999 99.0 99.0 1,007.2 10.174 10.176 1,007.5 –0.6% –1.8% –0.6%q2 1999 101.6 101.6 1,042.9 10.264 10.268 1,043.2 3.5% 2.6% 3.5%q3 1999 102.7 132.7 1,060.3 10.325 10.329 1,370.7 1.7% 30.6% 31.4%q4 1999 101.5 71.5 1,051.0 10.355 10.350 740.1 –0.9% –46.1% –46.0%Sum 404.8 404.8 4,161.4 10.280 4,161.4 4,161.4q1 2000 100.5 100.5 1,040.6 10.355 10.350 1,040.2 –1.0% 40.6% 40.6%q2 2000 103.0 103.0 1,066.5 10.355 10.350 1,066.1 2.5% 2.5% 2.5%q3 2000 103.5 103.5 1,071.7 10.355 10.350 1,071.2 0.5% 0.5% 0.5%q4 2000 101.5 101.5 1,051.0 10.355 10.350 1,050.5 –1.9% –1.9% –1.9%Sum 408.5 408.5 4,229.8 10.355 10.350 4,228.0 1.6% 0.9% 1.6%

In this example the following is worth observing:First, compared with Example 6.2 the values of the indicator for the third and fourth quarter of 1999 have been substantially changed, but the annual sum ofthe quarterly values of the indicator, and thus the annual BI ratio, for 1999 is not changed.The data for 2000 are also not changed.

Second, in spite of the big changes in the 1999 data, the quarterized BI ratio for the fourth quarter of 1999 is almost the same as in Example 6.2 (10.350 ver-sus 10.355).This demonstrates that the quarterized BI ratio for the fourth quarter of the last benchmark year is almost totally independent of the value of theindicator for that quarter and that it is mainly a function of the annual BI ratios.

Annex 6.3. First-Order Conditions for the ProportionalDenton Benchmarking Formula

117

6.A3.1. The first-order conditions for a minimum of the proportional Denton adjustment formula can be found withthe help of the following Lagrange-function:

(6.A3.1)

6.A3.2. Which has the following first order conditions:

δδ

λ

δδ

λ

δδ

λ

δδ

LX I

XI I

X

LX I I

XI

XI I

X

LX I I

XI

XI I

X

LXt

1 12 1

1 22 1

2 1 21

22 2

2 33 1

5 4 54

52 5

5 66 2

1 10

1 2 10

1 2 10

= ⋅⋅

⋅ + =

=⋅

⋅ + ⋅⋅

⋅ + =

=⋅

⋅ + ⋅⋅

⋅ + =

=

•

•

•

•

•

–

– –

– –

–– – , ( }

– – , ( }

–

––

––

–

1 2 10 4

1 2 10 4

1

11 2

11

11 2

11

1

I IX

IX

I IX t

LX I I

XI

XI I

X t

LX I

t tt

tt

t tt y

t t tt

tt

t tt

T T

⋅⋅ + ⋅

⋅⋅ + = ≤

=⋅

⋅ + ⋅⋅

⋅ = >

=

++

++

•

•

•

λ β

δδ

β

δδ

for

for

⋅⋅⋅ + ⋅

⋅⋅ + = =

=⋅

⋅ + ⋅ = >

++I

XI

XI I

X T

LX I I

XI

X t

TT

TT

T TT y

T T TT

TT

–

––

– , ( }

– , ( }

1 21

1

11 2

1 10 4

1 10 4

λ β

δδ

β

for

for

L X XX

I

X

IX A

t T y

yt

t

t

tt

y

y tt y

y

y1 41

1

2

2

4

4 3

4

2

1 4 1

... – – ,

, ... , , .... , , ... .

–

– –

( )

( ){ } { }

= +

∈ ∈

= =∑ ∑ λ

β β

Annex 6.3. First-Order Conditions for the Proportional Denton Benchmarking Formula

(6.A3.2)

6.A3.3. These first-order conditions, together with the benchmark restriction(s)

(in this case, ),

constitute a system of linear equations. In matrix notation, I • X = A, and for a two-year adjustment period withT=4β=8, matrix I and vector X and A are the following:

X Att y

y

y=∑ =4 3

4

–

VI BENCHMARKING

118

I

I I I

I I I I I

I I I I I

I I I I I

I I I I

=

−⋅

−⋅

−⋅

−⋅

−⋅

−⋅

−⋅

−⋅

−

1 10 0 0 0 0 0 1 0

1 2 10 0 0 0 0 1 0

01 2 1

0 0 0 0 1 0

0 01 2 1

0 0 0 1 0

0 0 01 2 1

12

1 2

1 2 22

1 2

2 3 32

3 4

3 4 42

4 5

4 5 52

|

|

|

|

55 6

5 6 62

6 7

6 7 72

7 8

7 8 82

0 0 0 1

0 0 0 01 2 1

0 0 1

0 0 0 0 01 2 1

0 1

0 0 0 0 0 01 1

0 1

1 1 1 1 0 0 0 0 0 0

0 0 0 0 1 1 1 1 0 0

⋅−⋅

−⋅

−⋅

−⋅

−⋅

I

I I I I I

I I I I I

I I I

|

|

|

|

– – – – – – – – – – –

|

|

=

=X

X

X

X

X

X

X

X

X

A

1

2

3

4

5

6

7

8

1

2

0

0

0

0

λλ

00

0

0

0

1

2

A

A

119

VII Mechanical Projections

A. Introduction

7.1. This chapter presents some relatively simpletechniques that can be used to fill information gapswith synthetic data using mechanical projectionsbased on past trends. Note that this is a fundamentallydifferent situation from the situation described in theprevious chapter in that indicators are not available,although there are some similarities in the mathemat-ics. Reliance on mechanical trend projection tech-niques is only justifiable if the gaps are few and minorbecause over-reliance on these techniques can easilyimpart a fictional character to the accounts and doesnot add any information about current trends.Furthermore, historic trends that are no longer relevantcould muffle current trends that would be visible fromother components calculated from actual direct or indi-rect indicators. Thus, as far as possible, quarterlynational account (QNA) estimates should be based ondirect observations of the relevant detailed accountingitem, and QNA compilers should constantly be on thelookout for possibilities to improve the coverage of theeconomy with relevant source data.

7.2. Although great caution should be used in applyingany of these techniques, there may be situations inwhich they are a last resort solution to covering gaps inthe coverage of the economy. Even in the situation ofwell-established QNA that are underpinned by anextensive set of short-term data, there may be someeconomic activities for which no timely direct or indi-rect indicators are available. When that is the case, wecan distinguish two situations: (a) no directly relevantshort-term source data are available at all, and (b) anindicator becomes available with a time lag that bars itsuse in the compilation of the QNA. Obviously, the lat-ter situation is more prominent for the first estimates ofa quarter than for second or third estimates.

7.3. Compilation of national accounts requires that thewhole economy be covered and thus all data gaps be

filled, explicitly or implicitly. If QNA data are compiledfrom both the production and the expenditure side(which is a key recommendation of this manual), theconfrontation of supply and demand can help in fillingsome gaps, and in fact this is recommended for esti-mating changes in inventories if no direct observationsare available. Using the balancing process as an esti-mation process, however, diminishes the power of theplausibility checks that are such a strong advantage ofthe commodity flow method. Thus, it is recommendedthat estimates be generated for all elements of the com-modity flow equation, even if some of the estimates areless than satisfactory. Obviously, the less satisfactoryestimates are the first choice for making adjustments ifthe balancing process requires these, but having an esti-mate in place will support a well-considered decision.

7.4. To ensure control over the estimates, it is prefer-able to fill the gaps explicitly. Omitting an item fromthe estimation process means that implicitly the item isassumed either to be zero or to move in line with otherparts of the aggregate of which the item is a part. Forinstance, compiling an output estimate based on themovements in the data for two months without makingan explicit estimate of what the third month may looklike is the same as forecasting the third month to beequal to an average of the two first months in the quar-ter. This may not be the most satisfactory way of fore-casting (or nowcasting) the missing month. Thus, thereis a need to produce an estimate to fill in the gap toensure a comprehensive total, even if such an estimateis less than satisfactory.

7.5. Deriving estimates using projections based onpast trends is particularly undesirable for current pricedata because, implicitly, current price data also dependon underlying price trends, which tend to be morevolatile than volume trends. Thus, if possible, extrapo-lation based on past trends should be based on volumedata combined with available price data. Relevantprice data are often available. The timeliness of price

statistics generally does not cause any problems, andif price data for the item are not collected, priceindices for similar or related products may provideacceptable proxies.

7.6. There are two main QNA uses of projectionsbased on past trends: one based on past trends inannual data and one based on past trends inmonthly and quarterly data. Projections based onpast trends in annual data are used to fill gaps incases where no relevant quarterly information isavailable. Extrapolation based on past trends inmonthly or quarterly data is used to mechanicallyextend indicator series that become available with atime lag that bars direct use.

B. Trend Projections Based on AnnualData

7.7. This section deals with the situation in whichno short-term data are available at all and presentstechniques that can be used to construct quarterlydata based on past trends in annual data. The twomain elements of constructing quarterly data basedon past trends in annual data are (a) to extend theseries of annual data to include forecasts or now-casts for the current periods and (b) to fit a quarterlyseries through the annual totals. Extending theseries with nowcasts can be achieved by using avail-able forecasts (e.g., crop forecasts, forecasts basedon econometrics models) or by simply assuming acontinuation of the current trend in the data (e.g.,expressed as a simple average of the growth in theseries for the past years).

7.8. Fitting a quarterly series through annual totalsshould ideally be based on some actual informationabout the seasonal pattern of the series and the timingof any turning points in the series. In cases where datagaps have to be filled by trend projections based onannual data, however, information on the actual tim-ing of possible turning points is normally not avail-able. Although generally unknown, the seasonalpattern of the series may in some cases be broadlyknown from other information.

7.9. In cases where no information is availableabout a series’ seasonal pattern, the only availableoption is to use the trend in the annual data to con-struct a quarterly series without any seasonal pat-tern that equals the annual totals. Such a seriesshould be as smooth as possible to ensure that its

impact on the period-to-period change in the aggre-gates is minimized.

7.10. A large number of disaggregation methods,with different degrees of sophistication, have beenproposed in the academic literature. In general, mostof these methods produce similar results. The maingoal in these circumstances is to select a method tofill the gaps that is simple and can be implementedeasily.

7.11. It is important to emphasize that quarterly dis-tribution without any related series produces purelysynthetic numbers that may not be indicative of thereal developments. In particular, such numbers do notcontain any information about the precise timing ofturning points. Because of this, quarterly distributeddata may also deviate substantially from estimates ofthe underlying trend in subannual data produced bystandard seasonal adjustment packages.

7.12. In cases where the seasonal pattern of theseries is broadly known, the distribution procedurecan be improved by superimposing this known sea-sonal pattern on the derived quarterly series.

7.13. In this chapter, we look at two methods to con-struct synthetic quarterly data based on past trends inannual data that are reasonably simple and give simi-lar results, as illustrated in Example 7.1. Both are usedby several countries. The first is a purely numericaldisaggregation technique proposed by Lisman andSandee, while the second is based on the least-squarestechniques discussed in Chapter VI.1 The latter can, aswill be shown, easily be extended to incorporate aknown seasonal pattern into the estimates.

1. The Lisman and Sandee Quarterly DistributionFormula

7.14. Lisman and Sandee (1964) proposed a purelynumerical technique for constructing synthetic quar-terly data based on past trends in annual data. Itworks as follows:

(i) Make a forecast of the annual data for the current year (Aβ+1) and for the next year (Aβ+2).

VII MECHANICAL PROJECTIONS

120

1Some of the alternatives to the two methods presented in this chap-ter include the autoregressive integrated moving average (ARIMA)model-based procedure proposed in Stram and Wei (1986) and Weiand Stram (1990); and the state space modeling procedure proposedin Al-Osh (1989). While generally producing similar results to thetwo presented in this chapter, these alternative methods are substan-tially more complicated.

Trend Projections Based on Annual Data

121

Example 7.1. Quarterly Distribution of Annual Data Without a Related Series

Date Annual Data Least-Squares Distribution Lisman & Sandee Distribution

1994 3,930.0

q1 1995 967.8 979.2

q2 1995 983.7 967.0

q3 1995 1,015.4 1,001.4

q4 1995 4,030.0 1,063.1 1,082.4

q1 1996 1,126.6 1,163.8

q2 1996 1,204.4 1,226.3

q3 1996 1,296.4 1,288.8

q4 1996 5,030.0 1,402.7 1,351.2

q1 1997 1,523.2 1,466.9

q2 1997 1,565.1 1,581.2

q3 1997 1,528.5 1,564.7

q4 1997 6,030.0 1,413.2 1,417.2

q1 1998 1,219.4 1,225.8

q2 1998 1,104.1 1,088.6

q3 1998 1,067.4 1,056.4

q4 1998 4,500.0 1,109.1 1,129.2

q1 1999 1,229.5 1,234.6

q2 1999 1,285.8 1,296.6

q3 1999 1,278.2 1,281.0

q4 1999 5,000.0 1,206.6 1,187.8

q1 2000 1,071.0 1,062.3

q2 2000 988.3 969.0

q3 2000 958.7 953.4

q4 2000 4,000.0 982.0 1,015.4

q1 2001 1,058.3 1,088.6

q2 2001 1,115.5 1,130.1

q3 2001 1,153.6 1,145.8

q4 2001 4,500.0 1,172.7 1,135.5

2002 4,500.0

As can be seen, the two alternative procedures for quarterly distribution of annual data without using a related series give very similar results.

1995 1997 19981996 2000 20011999950

1,050

1,150

1,250

1,350

1,450

1,550

1,650

3,800

4,200

4,600

5,000

5,400

5,800

6,200

6,600

Annual data (right-hand scale)Least-squares

distribution

Lisman and Sandee distribution


122

Example 7.2. Quarterly Distribution of Annual Data with a Superimposed Seasonal Pattern

Date Assumed Seasonal Pattern Annual Data Least-Squares Distribution

q1 1995 3,930.0 979.2

q1 1995 0.9 870.7

q2 1995 0.8 785.2

q3 1995 1.0 1,008.2

q4 1995 1.3 4,030.0 1,365.9

q1 1996 0.9 1,002.1

q2 1996 0.8 952.0

q3 1996 1.0 1,278.6

q4 1996 1.3 5,030.0 1,797.3

q1 1997 0.9 1,355.5

q2 1997 0.8 1,245.8

q3 1997 1.0 1,543.8

q4 1997 1.3 6,030.0 1,884.9

q1 1998 0.9 1,126.1

q2 1998 0.8 900.3

q3 1998 1.0 1,064.3

q4 1998 1.3 4,500.0 1,409.4

q1 1999 0.9 1,088.4

q2 1999 0.8 1,019.9

q3 1999 1.0 1,287.5

q4 1999 1.3 5,000.0 1,604.2

q1 2000 0.9 985.1

q2 2000 0.8 803.3

q3 2000 1.0 957.2

q4 2000 1.3 4,000.0 254.4

q1 2001 0.9 939.2

q2 2001 0.8 883.5

q3 2001 1.0 1,149.6

q4 2001 1.3 1,527.7

1995 1997 19981996 2000 20011999600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,400

3,200

4,000

4,800

5,600

6,400

7,200

8,000

Annual data(right-hand scale)

Least-squares distribution

(ii) Derive a smooth continuous quarterly time series from the annual data using the follow-ing disaggregation formula:

X1,y = 1/4(0.291 • Ay – 1 + 0.793 • Ay – 0.084 • Ay +1) (7.1)

X2,y = 1/4(–0.041 • Ay – 1 + 1.207 • Ay – 0.166 • Ay + 1)

X3,y = 1/4(– 0.166 • Ay – 1 + 1.207 • Ay – 0.041 • Ay + 1)

X4,y = 1/4(– 0.084 • Ay – 1 + 0.793 • Ay + 0.291 • Ay + 1)

whereXq,y is the derived quarterly estimate for quarter q in

year y,Ay is the annual estimate for year y, andβ is the last year for which annual data are

available.

7.15. The coefficients in the Lisman and Sandee dis-aggregation formula were derived by imposing a num-ber of restrictions; for example, when the annual datafor three consecutive years y – 1, y, and y + 1 are not ona straight line, they are assumed to lie on a sine curve.

2. Least-Squares Distribution

7.16. Boot, Feibes, and Lisman (1967) proposed aleast-squares-based technique for constructing syn-thetic quarterly data based on past trends in annualdata. It works as follows:

(i) make a forecast of the annual data for the current year (Aβ + 1).

(ii) Derive a smooth continuous quarterly time series from the annual data using a least-squares minimization technique, as follows:

(7.2)


(that is, the sum of the quarterized data should beequal to the observed annual data)

wheret is used as a generic symbol for time (t = q,y)

(e.g., t = 4y – 3 is equal to the first quarter ofyear y, and 4y the fourth quarter of year y);

Xt is the derived quarterly estimate for quarter t;Ay is the annual estimate for year y; andβ is the last year for which any annual observa-

tions are available.

7.17. This least-squares-based technique can beextended to incorporate a known seasonal pattern intothe estimates by replacing the least-squares expressionin step (ii) above with the following expression:2

(7.3)


(that is, the sum of the quarterized data should beequal to the observed annual data)

whereSFt is a time series with assumed seasonal factors.

Example 7.2 shows the results of using equation (7.3)to superimpose a seasonal pattern on the annual dataused in Example 7.1.

7.18. A small problem with the Boot-Feibes-Lismanmethod, as well as other methods of distribution thatuse least squares, is a tendency of the derived seriesto flatten out at endpoints3 (as can be seen fromExample 7.1). This problem can be alleviated by pro-jecting the annual series for two years in both direc-tions and distributing the extended series.

C. Projection Based on Monthly orQuarterly Data

7.19. This section presents some simple techniquesthat can be used to mechanically extend data seriesthat are not sufficiently timely to be used when thefirst QNA estimates for a particular quarter are com-piled. The monthly and quarterly source data com-monly become available with varying delays. Somequarterly and monthly source data may be available

X At yt y

y

==∑4 3

4

–

min – ,

,.... ,....

.....,

–

–1 4

1

1

2

2

4

1 4 1 1 1

X X

t

t

t

tt

y

y

X

SF

X

SF

t y

( ) =

∈ +( ){ } ∈ +( ){ }∑

β β

X At yt y

y

==∑4 3

4

–

min – ,

,.... ,....

.....,–

1 41

2

2

4

1 4 1 1 1

X Xt t

t

y

y

X X

t y

( ) =[ ]

∈ +( ){ } ∈ +( ){ }∑

β β

A-head

123

Projection Based on Monthly or Quarterly Data

2As proposed in for example Cholette (1998a).3This is not a problem for using least squares for benchmarking as dis-cussed in Chapter VI. In that case, the implied flattening out at theendpoints of the quarterly benchmark-indicator (BI) ratios helpsreduce the potential wagging tail problem discussed in Annex 6.2.


124

within the first month after the end of the referenceperiod (e.g., price statistics and industrial productionindices), while other data may only be available witha delay of more than three months. Thus, whenpreparing the first estimates, for some series only datafor two months of the last quarter may be available,while for other series data may be missing altogether.

7.20. If no related indicator is available to support anextrapolation, several options can be considered,depending on the strength of the underlying trend inthe series and the importance of seasonality in theseries. One generally applicable option would be touse ARIMA4 time-series modeling techniques, whichin many cases have proved to produce reasonableforecasts for one or two periods ahead. ARIMA mod-eling, however, is complicated and time-consuming,and requires sophisticated statistical knowledge.Also, ARIMA models are basically not able to fore-cast changes in the underlying trend in the series.Their good forecasting reputation stems mainly fromtheir ability to pick up repeated patterns of the series,such as seasonality.

7.21. Thus, if there is strong seasonal variation andtrend in the series, a substantially less demanding,and potentially better, solution would be the follow-ing three-step procedure:• First, use standard seasonal adjustment software

(e.g., X-11-ARIMA or X-12-ARIMA) to season-ally adjust the series and to estimate the trend com-ponent of the series. For this particular purpose,only a basic knowledge of seasonal adjustment isrequired, and knowledge of ARIMA modeling isnot necessary.

• Second, extend the trend component of the seriesbased on judgment, forecasts, or annual data, or byprojecting the current trend using the simple trendformula in equation (7.5) below.

• Third, multiply the trend forecast with the seasonaland irregular factors computed by the program.

7.22. In many cases, the following, much simpler,approaches may prove sufficient:• If there is no clear trend or seasonality in the move-

ments of the series (either in volume or price), onemay simply repeat the last observation or set thevalue for the missing period equal to a simple aver-age of, for example, the last two observations.

• With strong seasonal variation in the series but noclear underlying trend in the series’ movements,one may simply repeat the value of the variable inthe same period of the previous year or set thevalue for the missing observation equal to theaverage for the same period in several of the pre-vious years.

• If there is a clear trend in the series but no pro-nounced seasonal variation, the past trend may beprojected using a weighted average of the period-to-period rates of change for the last observations,for example, by using a weighted average for threelast observations as follows:

(7.4)

• With both a clear trend and strong seasonal vari-ation in the series, one simple option may be toextrapolate the value of the series in the sameperiod in the previous year, using a weightedaverage of the rates of change from the sameperiod in the previous year for the last observa-tions as an extrapolator, for example, by using aweighted average for three last observations asfollows:

(7.5)

In this formula, s is the periodicity of the series, XT isthe level of the last observation, and t is the numberof periods to be projected.

X XX

X

X

X

X

XT t T t sT

T s

T

T s

T

T s+ += ⋅ ⋅ + ⋅ + ⋅

–

–

–

– –

–

– –

3

6

2

6

1

61

1

2

2

X XX

X

X

X

X

XT t T tT

T

T

T

T

T+ += ⋅ ⋅ + ⋅ + ⋅

–

–

–

–

–

–1

1

1

2

2

3

3

6

2

6

1

6

Projection Based on Monthly or Quarterly Data

4Autoregressive integrated moving average.

125

VIII Seasonal Adjustment and Estimation of Trend-Cycles

A. Introduction

8.1. Seasonal adjustment serves to facilitate anunderstanding of the development of the economyover time, that is, the direction and magnitude ofchanges that have taken place. Such understandingcan be best pursued through the analyses of timeseries.1 One major reason for compiling high-fre-quency statistics such as GDP is to allow timely iden-tification of changes in the business cycle,particularly turning points. If observations of, say,quarterly non-seasonally adjusted GDP at constantprices are put together for consecutive quarters cov-ering several years to form a time series and aregraphed, however, it is often difficult to identify turn-ing points and the underlying direction of the data.The most obvious pattern in the data may be a recur-rent within-a-year pattern, commonly referred to asthe seasonal pattern.

8.2. Seasonal adjustment means using analyticaltechniques to break down a series into its compo-nents. The purpose is to identify the different compo-nents of the time series and thus provide a betterunderstanding of the behavior of the time series. Inseasonally adjusted data, the impact of the regularwithin-a-year seasonal pattern, the influences ofmoving holidays such as Easter and Ramadan, andthe number of working/trading days and the weekdaycomposition in each period (the trading-day effect,for short) are removed. By removing the repeatedimpact of these effects, seasonally adjusted datahighlight the underlying trends and short-run move-ments in the series.

8.3. In trend-cycle estimates, the impact of irregularevents in addition to seasonal variations is removed.

Adjusting a series for seasonal variations removes theidentifiable, regularly repeated influences on theseries but not the impact of any irregular events.Consequently, if the impact of irregular events isstrong, seasonally adjusted series may not represent asmooth, easily interpretable series. To further high-light the underlying trend-cycle, most standard sea-sonal adjustment packages provide a smoothed trendline running through the seasonally adjusted data(representing a combined estimate of the underlyinglong-term trend and the business-cycle movements inthe series).

8.4. An apparent solution to get around seasonal pat-terns would be to look at rates of change from thesame quarter of the previous year. This has the disad-vantage, however, that turning points are onlydetected with some delay.2 Furthermore, these ratesof change do not fully exclude all seasonal elements(e.g., Easter may fall in the first or second quarter,and the number of working days of a quarter may dif-fer between succeeding years). Moreover, these year-to-year rates of change will be biased owing tochanges in the seasonal pattern caused by institu-tional or behavioral changes. Finally, these year-to-year rates of change will reflect any irregular eventsaffecting the data for the same period of the previousyear in addition to any irregular events affecting thecurrent period. For these reasons, year-to-year ratesof change are inadequate for business-cycle analysis.

8.5. Therefore, more sophisticated procedures areneeded to remove seasonal patterns from the series.Various well-established techniques are available forthis purpose. The most commonly used technique isthe Census X-11/X-12 method. Other available sea-sonal adjustment methods include, among others,TRAMO-SEATS, BV4, SABLE, and STAMP.

1Paragraph 1.13 defined time series as a series of data obtainedthrough repeated measurement of the same concept over time thatallows different periods to be compared.

2The delay can be substantial, on average, two quarters. A numericalexample illustrating this point is provided in Annex 1.1.

8.6. A short presentation on the basic concept ofseasonal adjustment is given in Section B of thischapter, while the basic principles of the CensusX-11/X-12 method are outlined in section C. Thefinal section, Section D, addresses a series ofrelated general seasonal adjustment issues, such asrevisions to the seasonally adjusted data and thewagging tail problem, and the minimum length oftime series for seasonal adjustment. Section D alsoaddresses a set of critical issues on seasonal adjust-ment of quarterly national accounts (QNA), such aspreservation of accounting identities, seasonaladjustment of balancing items and aggregates, andthe relationship between annual data and season-ally adjusted quarterly data. Section D also dis-cusses the presentation and status of seasonallyadjusted and trend-cycle data.

B. The Main Principles of SeasonalAdjustment

8.7. For the purpose of seasonal adjustment, a timeseries is generally considered to be made up ofthree main components—the trend-cycle compo-nent, the seasonal component, and the irregularcomponent—each of which may be made up of sev-eral subcomponents:(a) The trend-cycle (Tt) component is the underlying

path or general direction reflected in the data, thatis, the combined long-term trend and the busi-ness-cycle movements in the data.

(b) The seasonal (Sct ) component includes seasonal

effects narrowly defined and calendar-related sys-tematic effects that are not stable in annual tim-ing, such as trading-day effects and movingholiday effects.(i) The seasonal effect narrowly defined (St) is an

effect that is reasonably stable3 in terms ofannual timing, direction, and magnitude.Possible causes for the effect are natural factors,administrative or legal measures, social/culturaltraditions, and calendar-related effects that arestable in annual timing (e.g., public holidayssuch as Christmas).

(ii) Calendar-related systematic effects on thetime series that are not stable in annual timingare caused by variations in the calendar fromyear to year. They include the following:� The trading-day effect (TDt), which is

the effect of variations from year to yearin the number working, or trading, daysand the weekday composition for a par-ticular month or quarter relative to thestandard for that particular month orquarter.4,5

� The effects of events that occur at regu-lar intervals but not at exactly the sametime each year, such as moving holidays(MHt), or paydays for large groups ofemployees, pension payments, and soon.

� Other calendar effects (OCt), such as leap-year and length-of-quarter effects.

� Both the seasonal effects narrowly definedand the other calendar-related effects rep-resent systematic, persistent, predictable,and identifiable effects.

(c) The irregular component (Ict ) captures effects that

are unpredictable unless additional information isavailable, in terms of timing, impact, and dura-tion. The irregular component (Ic

t ) includes thefollowing:(i) Irregular effects narrowly defined (It).(ii) Outlier6 effects (OUTt).(iii) Other irregular effects (OIt) (such as the

effects of unseasonable weather, naturaldisasters, strikes, and irregular salescampaigns).

The irregular effect narrowly defined is assumed tobehave as a stochastic variable that is symmetri-cally distributed around its expected value (0 for anadditive model and 1 for a multiplicative model).

VIII SEASONAL ADJUSTMENT AND ESTIMATION OF TREND-CYCLES

126

3It may be gradually changing over time (moving seasonality).

4The period-to-period variation in the standard, or average, numberand type of trading days for each particular month or quarter of theyear is part of the seasonal effect narrowly defined.5Trading-day effects are less important in quarterly data than inmonthly data but can still be a factor that makes a difference.6That is, an unusually large or small observation, caused by either toerrors in the data or special events, which may interfere with estimat-ing the seasonal factors.

8.8. The relationship between the original seriesand its trend-cycle, seasonal, and irregular compo-nents can be modeled as additive or multiplicative.7

That is, the time-series model can be expressed as

Additive Model

Xt = Sct + Tt + Ic

t (8.1.a)

or with some subcomponents specified

Xt = (St + TDt + MHt + OCt) + Tt + (It + OUTt + OIt) (8.1.b)

where

the seasonal component is Sc

t = (St + TDt + MHt + OCt)

the irregular component is Ic

t = (It + OUTt + OIt), and

the seasonally adjusted series is At = Tt + Ic

t = Tt + (It + OUTt + OIt ) ,

or as

Multiplicative Model

Xt = Sct + Tt + Ic

t (8.2.a)

or with some subcomponents specified Xt = (St

• TDt• MHt

• OCt) • Tt• (It

• OUTt• OIt) (8.2.b)

where

the seasonal component is Sct = (St

• TDt• MHt

• OCt),

the irregular component is Ict = (It

• OUTt• OIt), and

the seasonally adjusted series is At = Tt

• Ict = Tt

• (It• OUTt

• OIt).

8.9. The multiplicative model is generally taken as thedefault. The model assumes that the absolute size of thecomponents of the series are dependent on each otherand thus that the seasonal oscillation size increases and

decreases with the level of the series, a characteristic ofmost seasonal macroeconomic series. With the multi-plicative model, the seasonal and irregular componentswill be ratios centered around 1. In contrast, the addi-tive model assumes that the absolute size of the com-ponents of the series are independent of each other and,in particular, that the size of the seasonal oscillations isindependent of the level of the series.

8.10. Seasonal adjustment means using analyticaltechniques to break down a series into its components.The purpose is to identify the different components ofthe time series and thus to provide a better understand-ing of the behavior of the time series for modeling andforecasting purposes, and to remove the regular within-a-year seasonal pattern to highlight the underlyingtrends and short-run movements in the series. The pur-pose is not to smooth the series, which is the objectiveof trend and trend-cycle estimates. A seasonallyadjusted series consists of the trend-cycle plus the irreg-ular component and thus, as noted in the introduction,if the irregular component is strong, may not representa smooth easily interpretable series.

8.11. Example 8.1 presents the last four years of a timeseries and provides an illustration of what is meant byseasonal adjustment, the trend-cycle component, theseasonal component, and the irregular component.

8.12. Seasonal adjustment and trend-cycle estima-tion represent an analytical massaging of the originaldata. As such, the seasonally adjusted data and theestimated trend-cycle component complement theoriginal data, but, as explained in Section D ofChapter I, they can never replace the original data forthe following reasons:• Unadjusted data are useful in their own right. The

non-seasonally adjusted data show the actual eco-nomic events that have occurred, while the season-ally adjusted data and the trend-cycle estimaterepresent an analytical elaboration of the datadesigned to show the underlying movements thatmay be hidden by the seasonal variations.Compilation of seasonally adjusted data, exclu-sively, represents a loss of information.

• No unique solution exists on how to conduct sea-sonal adjustment.

• Seasonally adjusted data are subject to revisions asfuture data become available, even when the origi-nal data are not revised.

• When compiling QNA, balancing and reconcilingthe accounts are better done on the original unad-justed QNA estimates.

The Main Principles of Seasonal Adjustment

127

7Other main alternatives exist, in particular, X-12-ARIMA includes apseudo-additive model Xt = Tt • (Sc

t + Ict – 1) tailored to series whose

value is zero for some periods. Moreover, within each of the mainmodels, the relationship between some of the subcomponentsdepends on the exact estimation routine used. For instance, in themultiplicative model, some of the sub-components may beexpressed as additive to the irregular effect narrowly defined, e.g., as:Xt = St • Tt • (It + OUTt + OIt + TRt + MHt + OCt).


128

Example 8.1. Seasonal Adjustment,Trend-Cycle Component, Seasonal Component, andIrregular Component

Multiplicative Seasonal Model

Unadjusted Seasonally Adjusted Trend-CycleTime Series Series Component

(Xt) Seasonal Factors1 Irregular Component (Xt /St) (Tt)Index 1980 = 100 (St) (It) Index 1980 = 100 Index 1980 = 100

Date (1) (2) (3) (4) = (1)/(2) (5) = (4)/(3)q1 1996 138.5 0.990 1.005 139.8 139.2q2 1996 138.7 1.030 0.996 134.6 135.2q3 1996 133.6 1.024 1.003 130.5 130.1q4 1996 120.9 0.962 1.000 125.7 125.7q1 1997 120.9 0.981 0.993 123.2 124.2q2 1998 130.6 1.027 1.002 127.2 126.9q3 1997 134.4 1.033 1.005 130.1 129.4q4 1997 124.5 0.964 0.994 129.1 129.9q1 1998 127.7 0.975 1.001 131.0 130.8q2 1998 135.0 1.023 1.003 131.9 131.5q3 1998 135.6 1.037 0.993 130.7 131.6q4 1998 132.1 0.968 1.035 136.4 131.8q1 1999 127.6 0.971 0.998 131.5 131.7q2 1999 134.6 1.020 0.997 131.9 132.4q3 1999 142.1 1.041 1.015 136.5 134.4q4 1999 131.5 0.970 0.999 135.5 135.7q1 2000 132.1 0.969 1.000 136.3 136.3With a multiplicative seasonal model, the seasonal factors are ratios centered around 1 and are reasonably stable in terms of annual timing, direction, and mag-nitude. The irregulars2 are also centered around 1 but with erratic oscillations.

Observe the particularly strong irregular effect, or outlier, for q4 1998. Examples 8.3 and 8.4 show how an outlier like this causes trouble in early identifica-tion of changes in the trend-cycle.1The values of the estimated seasonal component, particularly from the multiplicative model, are often called “seasonal factors.”2The irregular component is often referred to as “the irregulars,” and the seasonal component is often referred to as “the seasonals.”

120

125

130

135

140

1996 1997 1998 1999 2000

1996 1997 1998 1999 2000

1996 1997 1998 1999 2000

1996 1997 1998 1999 2000

1996 1997 1998 1999 2000

1996 1997 1998 1999 2000

Unadjusted time series Seasonally adjusted seriesSeasonally adjusted series and trend-cycle component

Irregular component

120

125

130

135

140

120

125

130

135

140

120

125

130

135

140

0.95

1.00

1.05

0.95

1.00

1.05

Seasonally adjusted series

Trend cycle component

Trend component Seasonal factors

• While errors in the source data may be more easilydetected from seasonally adjusted data, it may beeasier to identify the source for the errors and correctthe errors working with the unadjusted data.

• Practice has shown that seasonally adjusting the dataat the detailed level needed for compiling QNA esti-mates can leave residual seasonality in the aggregates.

The original unadjusted QNA estimates, the seasonallyadjusted estimates, and the trend-cycle component allprovide useful information about the economy (see Box1.1), and, for the major national accounts aggregates, allthree sets of data should be presented to the users.

8.13. Seasonal adjustment is normally done usingoff-the-shelf programs—most commonly worldwideby one of the programs in the X-11 family. Other pro-grams in common use include the TRAMO-SEATSpackage developed by Bank of Spain and promotedby Eurostat and the German BV4 program. The orig-inal X-11 program was developed in the 1960s by theU.S. Bureau of the Census. It has subsequently beenupdated and improved through the development ofX-11-ARIMA8 by Statistics Canada9 and X-12-ARIMA by the U.S. Bureau of the Census, whichwas released in the second half of the 1990s. The coreof X-11-ARIMA and X-12-ARIMA is the same basicfiltering procedure as in the original X-11.10

8.14. For particular series, substantial experience andexpertise may be required to determine whether theseasonal adjustment is done properly or to fine-tunethe seasonal adjustment. In particularly unstable serieswith a strong irregular component (e.g., outliers owingto strikes and other special events, breaks, or levelshifts), it may be difficult to seasonally adjust properly.

8.15. It is also important to emphasize, however, thatmany series are well-behaved and easy to seasonallyadjust, allowing seasonal adjustment programs to beused without specialized seasonal adjustment expertise.

The X-11 seasonal adjustment procedure has in practiceproved to be quite robust, and a large number of the sea-sonally adjusted series published by different agenciesaround the world are adjusted by running the programsin their default modes, often without special expertise.Thus, lack of experience in seasonal adjustment or lackof staff with particular expertise in seasonal adjustmentshould not preclude one from starting to compile andpublish seasonally adjusted estimates. When compilingseasonally adjusted estimates for the first time, however,keep in mind that the main focus of compilation and pre-sentation should be on the original unadjusted esti-mates. Over time, staff will gain experience andexpertise in seasonal adjustment.

8.16. It is generally recommended that the statisticianswho compile the statistics should also be responsible—either solely or together with seasonal adjustmentspecialists—for seasonally adjusting the statistics. Thisarrangement should give them greater insight into thedata, make their job more interesting, help them under-stand the nature of the data better, and lead to improvedquality of both the original unadjusted data and the sea-sonally adjusted data. However, it is advisable in addi-tion to set up a small central group of seasonaladjustment experts, because the in-depth seasonaladjustment expertise required to handle ill-behavedseries can only be acquired by hands-on experience withseasonal adjustment of many different types of series.

C. Basic Features of the X-11 Family ofSeasonal Adjustment Programs

8.17. The three programs in the X-11 family—X-11,X-11-ARIMA, and X-12-ARIMA— follow an itera-tive estimation procedure, the core of which is based ona series of moving averages.11 The programs compriseseven main parts in three main blocks of operations.First (part A), the series may optionally be “pread-justed” for outliers, level shifts in the series, the effectof known irregular events, and calendar-related effectsusing adjustment factors supplied by the user or esti-mated using built-in estimation procedures. In addition,the series may be extended by backcasts and forecastsso that less asymmetric filters can be used at the begin-ning and end of the series. Second (parts B, C, and D),the preadjusted series then goes through three rounds ofseasonal filtering and extreme value adjustments, the“B, C, and D iterations” in the X-11/X-12 jargon. Third

Basic Features of the X-11 Family of Seasonal Adjustment Programs

129

8Autoregressive integrated moving average time-series models.ARIMA modeling represents an optional feature in X-11-ARIMAand X-12-ARIMA to backcast and forecast the series so that lessasymmetric filters than in the original X-11 program can be used atthe beginning and end of the series (see paragraph. 8.37).9Initially released in 1980, with a major update in 1988, the X-11-ARIMA/88.10The X-12-ARIMA can be obtained by contacting the U.S. Bureauof the Census (as of the time of writing, X-12-ARIMA was availablefree and could be downloaded with complete documentation andsome discussion papers from http://www.census.gov/pub/ts/x12a/).X-11-ARIMA can be obtained by contacting Statistics Canada, andTRAMO-SEATS can be obtained by contacting Eurostat. The origi-nal X-11 program is integrated into several commercially availablesoftware packages (including among others SAS, AREMOS, andSTATSTICA).

11Also called “moving average filters” in the seasonal adjustmentterminology.

(parts E, F, and G), various diagnostics and quality con-trol statistics are computed, tabulated, and graphed.12

8.18. The second block—with the parts B, C, and Dseasonal filtering procedure—represents the central(X-11) core of the programs. The filtering procedure isbasically the same for all three programs. X-12-ARIMA, however, provides several new adjustmentoptions for the B, C, and D iterations that significantlyenhance this part of the program. The main enhance-ments made in X-12-ARIMA to the central X-11 partof the program include, among others, a pseudo-additive Xt = Tt • (Sc

t + Ict – 1) model tailored to series

whose value is zero for some periods; new centered sea-sonal and trend MA filters (see next section); improve-ments in how trading-day effects and other regressioneffects—including user-defined effects (a new capabil-ity)—are estimated from preliminary estimates of theirregular component (see Subsection 3 below).

8.19. In contrast, the first block, and to some extentthe last block (see Subsection 4), differ markedlyamong the three programs. The original X-11 providedno built-in estimation procedures for preadjustmentsof the original series besides trading-day adjustmentsbased on regression of tentative irregulars in parts Band C (see Subsection 1), but it provided for user-sup-plied permanent or temporary adjustment factors. X-11-ARIMA, in addition, provided for built-inprocedures for ARIMA-model-based backcasts andforecasts of the series. In contrast, X-12-ARIMA con-tains an extensive time-series modeling block, theRegARIMA part of the program, that allows the userto preadjust, as well as backcasts and forecasts of theseries by modeling the original series. The main com-ponents of X-12-ARIMA are shown in Box 8.1.

8.20. The RegARIMA block of the X-12-ARIMAallows the user to conduct regression analysis directlyon the original series, taking into account that the non-explained part of the series typically will be autocorre-lated, nonstationary, and heteroscedastic. This is doneby combining traditional regression techniques withARIMA modeling into what is labeled RegARIMAmodeling.13 The RegARIMA part of X-12-ARIMAallows the user to provide a set of user-defined

regressor variables. In addition, the program contains alarge set of predefined regressor variables to identify,for example, trading-day effects, Easter effects,14 leap-year effects, length-of-quarter effects, level shifts, pointoutliers, and ramps in the series. As a simpler alterna-tive to RegARIMA modeling, X-12-ARIMA hasretained the traditional X-11 approach of regressing thetentative irregulars on explanatory variables, addingregressors for point outliers and facilities for user-defined regressors to X-11’s trading-day and Eastereffects (see Subsection 3).

1. Main Aspects of the Core X-11 Moving AverageSeasonal Adjustment Filters

8.21. This subsection presents the main elements ofthe centered moving average filtering procedure in theX-12-ARIMA B, C, and D iterations for estimating thetrend-cycle component and the seasonal effects nar-rowly defined. The moving average filtering procedureimplicitly assumes that all effects except the seasonaleffects narrowly defined are approximately symmetri-cally distributed around their expected value (1 for amultiplicative and 0 for an additive model) and thuscan be fully eliminated by using the centered moving


130

Box 8.1. Main Elements of the X-12-ARIMASeasonal Adjustment Program

RegARIMA Models(Forecasts, Backcasts, Preadjustments)

Seasonal Adjustment(Enhanced X-11)

ModelingModel Comparison Diagnostics

Diagnostics(Revision history, Sliding spans, Spectra, M1-M11

and Q test statistics, etc.)

12Test statistics that users should consult regularly are also includedin parts A and D.13The standard seasonal ARIMA model is generalized to includeregression parameters with the part not explained by the regressionparameters following an ARIMA process, that is, Xt = β'Yt = Zt, whereXt is the series to be modeled, β a parameters vector, Yt a vector offixed regressors, and Zt a pure seasonal ARIMA model. 14The user can select from different Easter-effect models.

average filter instead of ending up polluting the esti-mated trend-cycle component and the seasonal effectsnarrowly defined. Ideally, all effects that are notapproximately symmetrically distributed around theexpected value of 1 or 0 should have been removed inthe preadjustment part (part A).

8.22. The centered moving average filtering proce-dure described below only provides estimates ofthe seasonal effects narrowly defined (St), not theother parts of the seasonal component (Sc

t ).Subsection 3 briefly discusses the procedures avail-able for estimating the not-captured impact oftrading-day effects and other calendar-related sys-tematic effects. It includes, namely, the traditionalX-11 approach of regressing the tentative irregularson explanatory trading-day and other calendar-related variables as part of the B and C iterations,and the X-12-ARIMA option of estimating theseeffects as part of the RegARIMA-based preadjust-ment of the series.

8.23. The main steps of the multiplicative version of thefiltering procedure for quarterly data in the B, C, and Diterations, assuming preadjusted data, are as follows:15

Stage 1. Initial Estimates

(a) Initial trend-cycle. The series is smoothed using aweighted 5-term (2 x 4)16 centered moving aver-age to produce a first estimate of the trend-cycle.T1

t = !/8Xt – 2 + !/4Xt – 1 + !/4Xt + !/4Xt + 1+ !/8Xt +2.

(b) Initial SI ratios. The “original”17 series isdivided by the smoothed series (T1

t ) to give aninitial estimate of the seasonal and irregularcomponent StI

1t.

(c) Initial preliminary seasonal factors. A time seriesof initial preliminary seasonal factors is then

derived as a weighted 5-term (3 x 3) centeredseasonal18 moving average19 of the initial SI ratios(StI

1t). This method implicitly assumes that It

behaves as a stochastic variable that is symmetri-cally distributed around its expected value (1 for amultiplicative model) and therefore can be elimi-nated by averaging.S1

t = !/9SIt – 8 + �/9SIt – 4 + #/9SIt + �/9SIt + 4 + !/9SIt + 8

(d) Initial seasonal factors. A time series of initialseasonal factors is then derived by normalizingthe initial preliminary seasonal factors.

This step is done to ensure that the annual averageof the seasonal factors is close to 1.

(e) Initial seasonal adjustment. An initial estimate ofthe seasonally adjusted series is then derived as A1

t = Xt/S1t = Tt • St • It /St = T1

t • It.

Stage 2. Revised Estimates

(a) Intermediate trend-cycle. A revised estimate ofthe trend-cycle (T 2

t ) is then derived by applying aHenderson moving average20 to the initial season-ally adjusted series (A1

t).

(b) Revised SI ratios, are then derived by dividing the“original” series by the intermediate trend-cycleestimate (T 2

t ).

(c) Revised preliminary seasonal factors are thenderived by applying a 3 x 5 centered seasonalmoving average21 to the revised SI ratios.

SS

S S S S St

t

t t t t t

11

21

11 1

11

211

81

41

41

41

8

=+ + + ++ +

ˆ

ˆ ˆ ˆ ˆ ˆ– –


131

15Adapted from Findley and others (1996), which presents the filtersassuming monthly data.16A 2 x 4 moving average

is a 2-term moving average

of a 4-term moving average.

17The series may be pre-adjusted, and, for the C and D iterations,extreme value adjusted (see below).

X X X X Xtx

t t t t1 4

2 2 21

4= + + +( )( )+– – .

X Xtx

tx1 41

1 4+( )+

X X Xtx

tx

tx2 4 1 41

1 412= +( )( )+

18A seasonal moving average is a moving average that is applied to eachquarter separately, that is, as moving averages of neighboring q1s, q2s, etc.19The 3 x 3 seasonal moving average filter is the default. In addition,users can select a 3 x 5 or 3 x 9 moving average filter (X-12-ARIMAalso contains an optional 3 x 15 seasonal moving average filter). Theuser-selected filter will then be used in both stage 1 and stage 2.20A Henderson moving average is a particular type of weighted movingaverage in which the weights are determined to produce the smoothestpossible trend-cycle estimate. In X-11 and X-11-ARIMA, for quarterlyseries, Henderson filters of length 5, and 7 quarters could be automati-cally chosen or user-determined. In X-12-ARIMA, the users can alsospecify Henderson filters of any odd-number length. 21The 3 x 5 seasonal moving average filter is the default. In the D iter-ation, X-11-ARIMA, and X-12-ARIMA automatically select fromamong the four seasonal moving average filters (3 x 3, 3 x 5, 3 x 9,and the average of all SI ratios for each calendar quarter (the stableseasonal average)), unless the user has specified that the programshould use a particular moving average filter.

(d) Revised seasonal factors.A revised time series of ini-tial seasonal factors is then derived by normalizingthe initial preliminary seasonal factors as in stage 1.

(e) Revised seasonal adjustment. A revised estimateof the seasonally adjusted series is then derived asA2

t = Xt /S2t = T 2

t • It.

(f) Tentative irregular. A tentative estimate of the irreg-ular component is then derived by de-trending therevised seasonally adjusted series: I 2

t = A2t /T 3

t .

Stage 3. Final Estimates (D iteration only)

(a) Final trend-cycle. A final estimate of the trend-cycle component (T 3

t ) is derived by applying aHenderson moving average to the revised andfinal seasonally adjusted series (A2

t ).

(b) Final irregular. A final estimate of the irregularcomponent is derived by de-trending the revisedand final seasonally adjusted series I 3

t = A2t /T 3

t .

8.24. The filtering procedure is made more robust by aseries of identifications and adjustments for extremevalues. First, for the B and D iterations, when estimat-ing the seasonal factors in steps (b) to (d) (stages 1 and2) based on analyses of implied irregulars, extreme SIratios are identified and temporarily replaced. For the Biteration, this is done in both stages 1 and 2, while forthe D iteration it is done only at stage 2. Second, afterthe B and C iterations and before the next round of fil-tering, based on analyses of the tentative irregular com-ponent (I 2

t ) derived in step (f) of stage 2, extreme valuesare identified and temporarily removed from the origi-nal (or preadjusted) series (that is, before the C and Diterations, respectively).

2. Preadjustments

8.25. The series may have to be preadjusted beforeentering the filtering procedure. For the seasonal mov-ing average in step (c) (stages 1 and 2) above to fullyisolate the seasonal factors narrowly defined, the seriesmay have to be preadjusted to temporarily remove thefollowing effects:• outliers;• level-shifts (including ramps);• some calendar-related effects, particularly moving

holidays, and leap-years;• unseasonable weather changes and natural disasters;

and• strikes and irregular sale campaigns.

The extreme value adjustments described in para-graph 8.24 will to some extent take care of the distor-tions caused by point outliers but generally not theother effects. Furthermore, because outliers and theother effects listed cannot be expected to behave as astochastic variable that is approximately symmetri-cally distributed around its expected value (1 for amultiplicative model), they will not be fully elimi-nated by the seasonal moving average filter used instep (c) (stages 1 and 2), and may end up polluting theestimated seasonal factors narrowly defined. For thatreason, the impact of these effects cannot be fullyidentified from the estimated irregular component.Preadjustment can be conducted in a multitude ofways. The user may adjust the data directly based onparticular knowledge about the data before feedingthem to the program, or, in the case of X-12-ARIMA,use the estimation procedures built into the program.

3. Estimation of Other Parts of the SeasonalComponent Remaining Trading-Day and OtherCalendar-Related Effects

8.26. The moving average filtering procedure inparagraph 8.23 provides estimates of the seasonaleffects narrowly defined (St), but not of the otherparts of the overall seasonal component (S c

t ).Variations in the number of working/trading days andthe weekday composition in each period, as well asthe timing of moving holidays and other events thatoccur at regular calendar-related intervals, can have asignificant impact on the series. Parts of these calen-dar effects will occur on average at the same time eachyear and affect the series in the same direction andwith the same magnitude. Thus, parts of these calen-dar effects will be included in the (estimated) seasonaleffects narrowly defined. Important parts of these sys-temic calendar effects will not be included in the sea-sonal effect narrowly defined, however, because (a)moving holidays and other regular calendar-relatedevents may not fall in the same quarter each year and(b) the number of trading days and the weekday com-position in each period varies from year to year.

8.27. Seasonally adjusted data should be adjusted forall seasonal variations, not only the seasonal effect nar-rowly defined. Leaving parts of the overall seasonalcomponent in the adjusted series can be misleading andseriously reduce the usefulness of the seasonallyadjusted data. Partly seasonally adjusted series, wherethe remaining identifiable calendar-related effects havenot been removed, can give false signals of what’s hap-pening in the economy. For instance, such series may


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indicate that the economy declined in a particular quar-ter when it actually increased. Both the seasonal effectsnarrowly defined and the other calendar-related effectsrepresent systematic, persistent, predictable, and iden-tifiable seasonal effects, and all should be removedwhen compiling seasonally adjusted data.

8.28. Separate procedures are needed to estimate theremaining impact of the calendar-related systematiceffects. X-11 and X-11-ARIMA contain built-inmodels for estimation of trading-day and Eastereffects based on ordinary least-square (OLS) regres-sion analysis of the tentative irregular component(I 2

t ). When requested, the program derives prelimi-nary estimates and adjustments for trading days andEaster effects at the end of the B iteration and finalestimates and adjustments for trading days andEaster22 effects at the end of the C iteration. X-12-ARIMA, in addition, provides an option for estimat-ing these effects and others directly from the originaldata as part of the RegARIMA block of the program.

8.29. X-12-ARIMA’s options for supplying user-defined regressors make it possible for users to con-struct custom-made moving holiday adjustmentprocedures. This option makes it easier to take intoaccount holidays particular to each country or region,or country-specific effects of common holidays.Typical examples of such regional specific effects areregional moving holidays such as Chinese new year23

and Ramadan, and the differences in timing andimpact of Easter. Regarding the latter, while in somecountries Easter is mainly a big shopping weekendcreating a peak in retail trade, in other countries mostshops are closed for more than a week creating a bigdrop in retail trade during the holiday combined witha peak in retail trade before the holiday. Also, Eastermay fall on different dates in different countries,depending on what calendar they follow.

8.30. Some countries publish as “non-seasonallyadjusted data” data that have been adjusted forsome seasonal effects, particularly the number ofworking days. It is recommended that this approachnot be adopted for two main reasons. First, data pre-sented as non-seasonally adjusted should be fullyunadjusted, showing what actually has happened,not partly adjusted for some seasonal effects.

Working/trading-day effects are part of the overallseasonal variation in the series, and adjustment forthese effects should be treated as an integral part ofthe seasonal adjustment process, not as a separateprocess. Partly adjusted data can be misleading andare of limited analytical usefulness. Second, work-ing-day adjustments made outside the seasonaladjustment context are often conducted in a ratherprimitive manner, using fixed coefficients based onthe ratio of the number of working days in themonth or quarter to the number of working days ina standard month or quarter. Moreover, it has beenshown that the simple proportional method over-states the effect of working days on the series andmay render it more difficult to seasonally adjust theseries. Parts of these calendar effects will be cap-tured as part of the seasonal effect narrowly defined,and X-11/X-12’s trading-days adjustment proce-dures are able to handle the remaining part of thesecalendar effects in a much more sophisticated andrealistic manner.

4. Seasonal Adjustment Diagnostics

8.31. X-11-ARIMA and, especially, X-12-ARIMAprovide a set of diagnostics to assess the outcome,both from the modeling and the seasonal adjustmentparts of the programs. These diagnostics range fromadvanced tests targeted for the expert attempting tofine-tune the treatment of complex series to simpletests that as a minimum should be looked at by allusers of the programs. While the programs some-times are used as a black box without the diagnostics,they should not (and need not be) used that way,because many tests can be readily understood.

8.32. Basic tests that as a minimum should belooked at include F-tests for existence of seasonal-ity and the M- and Q-test statistics introduced withX-11-ARIMA. Other useful tests include tests forresidual seasonality (shown in Box 8.2), existenceof trading-day effects, other calendar-relatedeffects, extreme values, and tests for fitting anARIMA model to the series. Box 8.2 shows theparts of the output from X-12-ARIMA for the illus-trative series in Example 8.1 regarding the F-testsfor existence of seasonality. Similarly, Box 8.3shows the M- and Q-test statistics for the sameillustrative series. Series for which the programcannot find any identifiable seasonality or that failthe M- and Q-test statistics should be left unad-justed. Unfortunately, in these cases, the programswill not abort with a message that the series cannot


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22Custom-making may be needed to account for country-specificfactors (see paragraph 8.29).23The Chinese new year represents a moving holiday effect inmonthly data but not in quarterly data, because it always occurswithin the same quarter.

be properly adjusted. Instead, they will produce“adjusted” data. The only way to detect that theseadjusted data should not be used is to look at thediagnostics.

8.33. X-12-ARIMA provides, in addition, a largeset of new diagnostic tools to further gauge the qual-ity of the seasonal adjustment and the appropriate-ness of the seasonal adjustment and modelingoptions chosen. These new diagnostic tools includefeatures such as sliding span and frequency spec-trum estimates, revision history24 simulations, andoptions for comparing direct and indirect seasonaladjustments of aggregates.25 Sliding spans can beused to evaluate the overall quality of the seasonaladjustment in competition with the Q statistics.They can also be used to assess the stability oftrading-day estimates, to assess the adequateness ofthe length of the filters chosen, and to decidebetween direct and indirect adjustment. Frequencyspectrum estimates from the irregular componentcan help identify residual seasonality narrowlydefined and residual trading-day effects in differentparts of the series. Revision history simulations canhelp decide between direct and indirect adjustment,selection of competing RegARIMA models, andidentification of optimal length of forecast exten-sion before filtering. The RegARIMA part of X-12-ARIMA also contains a large set of test statistics formodel selection and outlier detection.

D. Issues in Seasonality

8.34. This section addresses a series of general andmore QNA-specific issues related to seasonaladjustment. • Subsection 1 explains how changes in the seasonal

patterns cause revisions to the seasonally adjustedand trend-cycle estimates—the wagging tail prob-lem. The subsection explains why trend-cycle esti-mates at the end of the series are particularly proneto revisions and why turning points can be identifiedonly after a lag of several observations, because it islogically impossible to distinguish an outlier from achange in the trend-cycle based on one observation.

• Subsection 2 discusses the minimum length oftime-series data required for obtaining seasonallyadjusted estimates.


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24See Section D.1 of this chapter for a discussion of revisions to sea-sonally adjusted data, and the wagging tail effect.25See Section D.3.a of this chapter for a discussion of direct-versus-indirect seasonal adjustment of balancing items and aggregates.

Box 8.2. X-11/X-11-ARIMA/X-12-ARIMA Tests forExistence of Seasonality

The following is an edited copy of the relevant parts of X-12-ARIMA’smain output file with the basic F-tests for existence of seasonality. Thetest statistics values are for the full 21 years of the illustrative series, ofwhich the last four years of data were presented in Example 8.1.The D8.A and D 11 codes refer to the various “output tables” in the main out-put file from the different programs in the X-11 family, documenting thevarious steps in the A, B, C, D, E, F, and G parts of the program.

As a minimum,Table D 8.A should be checked to make sure that the pro-gram returns an IDENTIFIABLE SEASONALITY PRESENT and not anIDENTIFIABLE SEASONALITY NOT PRESENT statement. The seriesshould generally be left unadjusted if the F-tests indicate that identifiableseasonality is not present.

D8.A F-Tests for Seasonality

Test for the Presence of Seasonality Assuming Stability

Sum of Degrees Mean Squares of Freedom Square F-Value

Between quarters 809.1996 3 269.73319 43.946** Residual 497.1645 81 6.13783 Total 1306.3640 84

Seasonality present at the 0.1 percent level.

Nonparametric Test for the Presence of Seasonality AssumingStability

Kruskal-Wallis Degrees Probability Statistic of Freedom Level

53.2410 3 0.000%

Seasonality present at the 1 percent level.

Moving Seasonality Test

Sum of Degrees of MeanSquares Freedom Square F-Value

Between Years 85.8291 20 4.291454 1.857 Error 138.6635 60 2.311058

Moving seasonality present at the 5 percent level.

COMBINED TEST FOR THE PRESENCE OF IDENTIFIABLE SEASONALITYIDENTIFIABLE SEASONALITY PRESENT

D 11 Final Seasonally Adjusted Data

Test for the Presence of Residual Seasonality.No evidence of residual seasonality in the entire series at the 1 percentlevel. F = 0.03No evidence of residual seasonality in the last 3 years at the 1 percentlevel. F = 0.48No evidence of residual seasonality in the last 3 years at the 5 percentlevel.

• Subsection 3 addresses a series of issues relatedparticularly to seasonal adjustment and trend-cycle estimation of QNA data, such as preserva-tion of accounting identities, seasonal adjustmentof balancing items and aggregates, and the rela-tionship between annual data and seasonallyadjusted quarterly data.

• Finally, Subsection 4 discusses the status and pre-sentation of seasonally adjusted and trend-cycleQNA estimates.

1. Changes in Seasonal Patterns, Revisions, andthe Wagging Tail Problem

8.35. Seasonal effects may change over time. Theseasonal pattern may gradually evolve as economicbehavior, economic structures, and institutional andsocial arrangements change. The seasonal patternmay also change abruptly because of sudden institu-tional changes.

8.36. Seasonal filters estimated using centered movingaverages allow the seasonal pattern of the series tochange over time and allow for a gradual update of theseasonal pattern, as illustrated in Example 8.2. Thisresults in a more correct identification of the seasonaleffects influencing different parts of the series.

8.37. Centered moving average seasonal filters alsoimply, however, that the final seasonally adjusted val-ues depend on both past and future values of the series.Thus, to be able to seasonally adjust the earliest and lat-est observations of the series, either asymmetric filtershave to be used for the earliest and the latest observa-tions of the series or the series has to be extended by useof backcasts and forecasts based on the pattern of thetime series. While the original X-11 program usedasymmetric filters at the beginning and end of theseries, X-12-ARIMA and X-11-ARIMA use ARIMAmodeling techniques to extend the series so that lessasymmetric filters can be used at the beginning and end.

8.38. Consequently, new observations may result inchanges in the estimated seasonal pattern for the lat-est part of the series and subject seasonally adjusteddata to more frequent revisions than the original non-seasonally adjusted series. This is illustrated inExample 8.3 below. Estimates of the underlyingtrend-cycle component for the most recent parts ofthe time series in particular may be subject to rela-tively large revisions at the first updates,26 however,

theoretical and empirical studies indicate that thetrend-cycle converges much faster to its final valuethan the seasonally adjusted series. In contrast, theseasonally adjusted series may be subject to lowerrevisions at the first updates but not-negligible revi-sions even after one to two years. There are two mainreasons for slower convergence of the seasonal esti-mates. First, the seasonal moving average filters aresignificantly longer than the trend-cycle filters.27

Second, revisions to the estimated regression para-meters for calendar-related systematic effects mayaffect the complete time series. These revisions tothe seasonally adjusted and trend-cycle estimates,owing to new observations, are commonly referredto as the “wagging tail problem.”

8.39. Estimates of the underlying trend-cycle compo-nent for the most recent parts of the series should beinterpreted with care, because signals of a change in thetrend-cycle at the end of the series may be false. Thereare two main reasons why these signals may be false.First, outliers may cause significant revisions to thetrend-cycle end-point estimates. It is usually not possi-ble from a single observation to distinguish between anoutlier and a change in the underlying trend-cycle,unless a particular event from other sources generatingan outlier is known to have occurred. In general, severalobservations verifying the change in the trend-cycleindicated by the first observation are needed. Second,the moving average trend filters used at the end of theseries (asymmetric moving average filters with or with-out ARIMA extension of the series) implicitly assumethat the most recent basic trend of the series will persist.Consequently, when a turning point appears at the cur-rent end of the series, the estimated trend values at firstpresent a systematically distorted picture, continuing topoint in the direction of the former, now invalidated,trend. It is only after a lag of several observations thatthe change in the trend comes to light. While the trend-cycle component may be subject to large revisions atthe first updates, however, it typically converges rela-tively fast to its final value.28 An illustration of this canbe found by comparing the data presented in Example8.3 (seasonally adjusted estimates) with that inExample 8.4 (trend-cycle estimates).

Issues in Seasonality

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27For instance, the seasonal factors will be final after 2 years with thedefault 5-term (3 x 3) moving average seasonal filter (as long as anyadjustments for calendar effects and outliers are not revised). In con-trast, the trend-cycle estimates will be final after 2 quarters with the5-term Henderson moving average trend-cycle filter (as long as theunderlying seasonally adjusted series is not revised).32The trend-cycle estimates will be final after 2 quarters with a 5-termHenderson moving average filter and after 3 quarters with a 7-term fil-ter as long as the underlying seasonally adjusted series is not revised.26Illustrated in Example 8.4.


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Box 8.3. X-11-ARIMA/X-12-ARIMA M- and Q-Test Statistics

The first and third column below are from the F 3 table of X-12-ARIMA’s main output file with the M- and Q-test statistics.The test statistic values are for the full 21 years of the illustrative series, of which the last four years of data were presented in Example 8.1.The F 3 and F 2.B codes refer to the various“output tables” in the program’s main output file.

The Q-test statistic at the bottom is a weighted average of the M-test statistics.

F 3. Monitoring and Quality Assessment StatisticsAll the measures below are in the range from 0 to 3 with an acceptance region from 0 to 1.

Statistics Weight in Q Value

1. The relative contribution of the irregular component over a one-quarter span 13 M1 = 0.245 (from Table F 2.B).

2. The relative contribution of the irregular component to the stationary portion 13 M2 = 0.037of the variance (from Table F 2.F).

3. The amount of quarter-to-quarter change in the irregular component compared 10 M3 = 0.048 with the amount of quarter-to-quarter change in the trend-cycle (from Table F2.H).

4. The amount of auto-correlation in the irregular as described by the average 5 M4 = 0.875duration of run (Table F 2.D).

5. The number of quarters it takes the change in the trend-cycle to surpass the amount 11 M5 = 0.200 of change in the irregular (from Table F 2.E).

6. The amount of year-to-year change in the irregular compared with the amount 10 M6 = 0.972

of year-to-year change in the seasonal (from Table F 2.H).

7. The amount of moving seasonality present relative to the amount of stable 16 M7 = 0.378

seasonality (from Table F 2.I).

8. The size of the fluctuations in the seasonal component throughout the whole series. 7 M8 = 1.472

9. The average linear movement in the seasonal component throughout the whole series. 7 M9 = 0.240

10. Same as 8, calculated for recent years only. 4 M10= 1.935

11. Same as 9, calculated for recent years only. 4 M11= 1.935

ACCEPTED at the level 0.52 Check the three above measures that failed. Q (without M2) = 0.59 ACCEPTED.

1Based on Eurostat (1998).2Based on Statistics Canada’s seasonal adjustment course material.


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Motivation1 Diagnose and Remedy if Fails2

The seasonal and irregular components cannot be separated sufficiently if Series too irregular.Try to preadjust the series.the irregular variation is too high compared with the variation in the seasonalcomponent. M1 and M2 test this property by using two different trend removers.

If the quarter-to-quarter movement in the irregular is too important in the SI Irregular too strong compared to trend-cycle.Try to preadjust the series.component compared with the trend-cycle, the separation of these component can be of low quality.

Test of randomness of the irregular component. (Be careful, because the estimator Irregulars are autocorrelated.Try to change length of the trend filter and of the irregular is not white noise and the statistics can be misleading.) (different) preadjustment for trading-day effects.There may be residual

trading-day effects in the series.

Similar to M3. Irregular too strong compared to trend-cycle.Try to preadjust the series.

In one step of the X-11 filtering procedure, the irregular is separated from the Irregular too strong compared with seasonality.Try to change length of

seasonal by a 3x5 seasonal moving average. Sometimes, this can be too flexible seasonal MA filter.

(I/S ratio is very high) or too restrictive (I/S ratio is very low). If M6 fails, you can

try to use the 3x1 or the stable option to adjust for this problem.

Combined F-test to measure the stable seasonality and the moving seasonality Do not seasonally adjust the series. Indicates absence of Seasonality.

in the final SI ratios. Important test statistics for indicating whether seasonality

is identifiable by the program.

Measurement of the random fluctuations in the seasonal factors.A high value Change seasonal moving average filter. Seasonality may be moving too fast.

can indicate a high distortion in the estimate of the seasonal factors.

Because one is normally interested in the recent data, these statistics give insights Look at ARIMA extrapolation. Indicate that the seasonality may be moving too

into the quality of the recent estimates of the seasonal factors.Watch these statistics fast at the end of the series

carefully if you use forecasts of the seasonal factors and not concurrent adjustment.

8.40. Studies have shown that using ARIMA modelsto extend the series before filtering generally signifi-cantly reduces the size of these revisions comparedwith using asymmetric filters.29 These studies haveshown that, typically, revisions to the level of theseries as well as to the period-to-period rate of changeare reduced. Use of RegARIMA models, as offeredby X-12-ARIMA, may make the backcasts and fore-casts more robust and thus further reduces the size ofthese revisions compared with using pure ARIMAmodels. The reason for this is that RegARIMA mod-els allow trading-day effects and other effects cap-tured by the regressors to be taken into account in theforecasts in a consistent way. Availability of longertime series should result in a more precise identifica-tion of the regular pattern of the series (the seasonalpattern and the ARIMA model) and, in general, alsoreduce the size of the revisions.

8.41. Revisions to the seasonally adjusted data can becarried out as soon as new observations become avail-able—concurrent revisions—or at longer intervals. Thelatter requires use of the one-year-ahead forecastedseasonal factors offered by X-11, X-11-ARIMA, andX-12-ARIMA to compute seasonally adjusted esti-mates for more recent periods not covered by the last

revision. Use of one-year-ahead forecast of seasonalfactors was common in the early days of seasonaladjustment with X-11 but is less common today.Besides full concurrent revisions and use of forecasts ofseasonal factors, a third alternative is to use period-to-period rates of change from estimates based on concur-rent adjustments to update previously released data andonly revise data for past periods once a year.

8.42. From a purely theoretical point of view, andexcluding the effects of outliers and revisions to theoriginal unadjusted data, concurrent adjustment isalways preferable. New data contribute new informa-tion about changes in the seasonal pattern that prefer-ably should be incorporated into the estimates as earlyas possible. Consequently, use of one-year-aheadforecasts of seasonal factors results in loss of infor-mation and, as empirical studies30 have shown and asillustrated in Example 8.5, often in larger, albeit lessfrequent, revisions to the levels as well as the period-to-period rates of change in the seasonally adjusteddata. Theoretical studies31 support this finding.

8.43. The potential gains from concurrent adjust-ment can be significant but are not always. In general


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Example 8.2. Moving Seasonality

The chart presents the seasonal factors for the last 21 years of the time series presented in Example 8.1 and illustrates how the seasonal pattern has beenchanging gradually over time, as estimated by X-12-ARIMA.

0.90

0.94

0.98

1.02

1.06

1.10

1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 19992000

Seasonal Factors

30See among others Dagum and Morry (1984), Hout and others.(1986), Kenny and Durbin (1982), and McKenzie (1984).31See among others Dagum (1981 and 1982) and Wallis (1982).

29See among others Bobitt and Otto (1990), Dagum (1987), Dagumand Morry (1984), Hout et al. (1986).

A-head

139


Example 8.3. Changes in Seasonal Patterns, Revisions of the Seasonally Adjusted Series, and the Wagging TailProblemRevisions to the Seasonally Adjusted Estimates by Adding New Observations(Original unadjusted data in Example 8.1.)

120

125

130

135

140

1996 1997 1998 1999 2000

Data until q1 00 Data until q4 99 Data until q3 99 Data until q2 99 Data until q1 99 Data until q4 98 Data until q3 98Period-to- Period-to- Period-to- Period-to- Period-to- Period-to- Period-to-

Period Period Period Period Period Period Period Rate of Rate of Rate of Rate of Rate of Rate of Rate of

Date Index Change Index Change Index Change Index Change Index Change Index Change Index Change

q1 1996 139.8 139.9 139.8 139.7 139.7 139.2 139.3q2 1996 134.6 –3.7% 134.6 –3.7% 134.6 –3.7% 134.5 –3.7% 134.5 –3.7% 134.4 –3.4% 134.5 –3.5%q3 1996 130.5 –3.1% 130.5 –3.1% 130.6 –3.0% 130.9 –2.7% 131.0 –2.6% 131.4 –2.2% 130.8 –2.7%q4 1996 125.7 –3.7% 125.6 –3.7% 125.6 –3.8% 125.6 –4.1% 125.6 –4.1% 125.9 –4.2% 126.3 –3.5%q1 1997 123.2 –2.0% 123.3 –1.9% 123.2 –2.0% 123.1 –2.0% 123.0 –2.0% 122.2 –2.9% 122.5 –3.0%q2 1997 127.2 3.2% 127.3 3.2% 127.2 3.3% 126.8 3.1% 126.8 3.0% 126.7 3.7% 126.8 3.5%q3 1997 130.1 2.3% 130.0 2.2% 130.3 2.4% 131.0 3.3% 131.1 3.5% 131.7 3.9% 130.7 3.1%q4 1997 129.1 –0.7% 128.9 –0.8% 128.8 –1.1% 128.7 –1.7% 128.7 –1.8% 129.3 –1.8% 130.0 –0.5%q1 1998 131.0 1.4% 131.1 1.7% 130.8 1.6% 130.7 1.6% 130.7 1.5% 129.6 0.2% 130.0 0.0%q2 1998 131.9 0.7% 132.1 0.8% 132.1 0.9% 131.4 0.5% 131.2 0.4% 131.0 1.1% 131.1 0.8%q3 1998 130.7 –1.0% 130.5 –1.2% 131.0 –0.8% 132.0 0.5% 132.2 0.7% 132.8 1.3% 131.4 0.2%q4 1998 136.4 4.4% 136.1 4.3% 136.1 3.9% 135.9 3.0% 135.9 2.8% 136.9 3.0%q1 1999 131.5 –3.6% 131.7 –3.2% 131.3 –3.5% 131.2 –3.4% 131.2 –3.5%q2 1999 131.9 0.3% 132.2 0.4% 132.1 0.6% 131.0 –0.2%q3 1999 136.5 3.4% 136.2 3.0% 136.9 3.6%q4 1999 135.5 –0.7% 135.1 –0.8%q1 2000 136.3 0.6%

Note how the seasonally adjusted data (like the trend-cycle data presented in Example 8.4 but less so) for a particular period are revised as later data become available, even when theunadjusted data for that period were not revised. In this example, adding q1 2000 results in an upward adjustment of the growth from q2 1999 to q3 1999 in the seasonally adjusted seriesfrom an estimate of 3.0 percent to a revised estimate of 3.4 percent. Minor effects on the seasonally adjusted series of adding q1 2000 can be traced all the way back to 1993.


140

Example 8.4. Changes in Seasonal Patterns, Revisions and the Wagging Tail ProblemRevisions to Trend-Cycle Estimates(Original unadjusted data in Example 8.1, seasonally adjusted in Example 8.3.)

120

125

130

135

140

1996 1997 1998 1999 2000

Data until q1 00 Data until q4 99 Data until q3 99 Data until q2 99 Data until q1 99 Data until q4 98 Data until q3 98Period-to- Period-to- Period-to- Period-to- Period-to- Period-to- Period-to-

Period Period Period Period Period Period Period Rate of Rate of Rate of Rate of Rate of Rate of Rate of

Date Index Change Index Change Index Change Index Change Index Change Index Change Index Change

q1 1996 139.8 139.9 139.8 139.7 139.7 139.2 139.3q1 1996 139.2 139.2 139.1 139.0 139.0 138.7 138.9q2 1996 135.2 –2.9% 135.2 –2.9% 135.2 –2.8% 135.2 –2.7% 135.2 –2.7% 135.0 –2.7% 135.0 –2.8%q3 1996 130.1 –3.7% 130.1 –3.8% 130.2 –3.7% 130.3 –3.6% 130.4 –3.6% 130.4 –3.4% 130.4 –3.4%q4 1996 125.7 –3.4% 125.6 –3.5% 125.6 –3.5% 125.7 –3.6% 125.7 –3.6% 126.2 –3.2% 126.6 –2.9%q1 1997 124.2 –1.2% 124.2 –1.1% 124.1 –1.2% 123.9 –1.4% 123.9 –1.4% 124.7 –1.2% 125.2 –1.1%q2 1997 126.9 2.2% 126.9 2.2% 126.8 2.1% 126.3 1.9% 126.2 1.9% 126.6 1.5% 126.7 1.2%q3 1997 129.4 2.0% 129.2 1.8% 129.1 1.8% 128.5 1.8% 128.4 1.8% 128.7 1.7% 128.8 1.7%q4 1997 129.9 0.4% 129.7 0.4% 129.5 0.4% 129.3 0.6% 129.3 0.7% 129.4 0.5% 129.9 0.8%q1 1998 130.8 0.7% 130.9 0.9% 130.7 0.9% 130.4 0.8% 130.3 0.8% 129.7 0.3% 130.3 0.4%q2 1998 131.5 0.5% 131.6 0.5% 131.6 0.7% 131.4 0.8% 131.4 0.8% 130.8 0.9% 131.0 0.5%q3 1998 131.6 0.1% 131.4 –0.2% 131.6 0.0% 132.2 0.5% 132.4 0.8% 133.3 1.9% 131.2 0.2%q4 1998 131.8 0.2% 131.6 0.2% 131.5 –0.1% 132.3 0.1% 132.7 0.3% 136.4 2.3%q1 1999 131.7 –0.1% 131.8 0.2% 131.4 –0.1% 131.5 –0.6% 131.3 –1.1%q2 1999 132.4 0.5% 132.9 0.8% 132.7 1.0% 131.1 –0.3%q3 1999 134.4 1.5% 135.1 1.6% 136.6 2.9%q4 1999 135.7 1.0% 135.0 –0.1%q1 2000 136.3 0.4%

The chart and table demonstrate how the trend-cycle estimates for a particular period may be subject to relatively large revisions as data for new periods become available, even whenthe unadjusted data for that period were not revised. In this example, adding q1 2000 results in an upward adjustment of the change in the estimated trend-cycle component from q3 1999to q4 1999, from an initial estimate of –0.1 percent to a revised estimate of 1.0 percent.

Also, observe how the strong irregular effect that occurred in q4 1998—an upward turn that disappears in the later trend-cycle estimates—wrongly resulted in an initial estimated stronggrowth from mid-1998 and onward in the earlier trend-cycle estimates.

the potential gains depend on, among other things,the following factors:• The stability of the seasonal component. A high

degree of stability in the seasonal factors implies thatthe information gain from concurrent adjustment islimited and makes it easier to forecast the seasonalfactors. On the contrary, rapidly moving seasonalityimplies that the information gain can be significant.

• The size of the irregular component. A high irregularcomponent may reduce the gain from concurrentadjustment because there is a higher likelihood forthe signals from the new observations about changesin the seasonal pattern to be false, reflecting an irreg-ular effect and not a change in the seasonal pattern.

• The size of revisions to the original unadjusteddata. Large revisions to the unadjusted data may


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Example 8.5. Changes in Seasonal Patterns, Revisions, and the Wagging Tail ProblemConcurrent Adjustment Versus Use of One-Year-Ahead Forecast of Seasonal Factors(Original unadjusted data in Example 8.1, revisions of last seven quarters with concurrent seasonally adjusted data in Example 8.3.)

Concurrent Seasonal Period-to-Period Rate Based on Seasonal Factors Period-to-Period RateDate Adjustment of Change Forecast from q1 1999 of Change

q1 1996 139.8 139.7q2 1996 134.6 –3.7% 134.5 –3.7%q3 1996 130.5 –3.1% 131.0 –2.6%q4 1997 125.7 –3.7% 125.6 –4.1%q1 1997 123.2 –2.0% 123.0 –2.0%q2 1997 127.2 3.2% 126.8 3.0%q3 1997 130.1 2.3% 131.1 3.5%q4 1997 129.1 –0.7% 128.7 –1.8%q1 1998 131.0 1.4% 130.7 1.5%q2 1998 131.9 0.7% 131.2 0.4%q3 1998 130.7 –1.0% 132.2 0.7%q4 1998 136.4 4.4% 135.9 2.8%q1 1999 131.5 –3.6% 131.2 –3.5%q2 1999 131.9 0.3% 130.8 –0.3%q3 1999 136.5 3.4% 138.6 6.0%q4 1999 135.5 –0.7% 134.9 –2.7%q1 2000 136.3 0.6% 136.0 0.8%

The chart and table demonstrate the effect of current update (concurrent adjustment) versus use of one-year-ahead forecast seasonal factors.As can be seenby comparing with Example 8.3, use of one-year-ahead forecasts of the seasonal factors results in loss of information and larger, but less frequent, revisions. Inparticular, in this example, using one-year-ahead forecasts of the seasonal factors gave an initial estimated decline from q3 to q4 1999 in the seasonally adjust-ed series of –2.7 percent, which is substantially larger compared with the initial estimate of –0.8 percent with current update of the seasonal factors (seeExample 8.3).

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1996 1997 1998 1999 2000

Concurrent Seasonal Adjustment

Based on Seasonal Factors Forecast from q1 1999

reduce the gain from concurrent adjustmentbecause there is a higher likelihood for the sig-nals from the new observations about changes inthe seasonal pattern to be false.

2. Minimum Length of the Time Series forSeasonal Adjustment

8.44. Five years of data and relatively stable seasonal-ity are required in general as a minimum length toobtain properly seasonally adjusted estimates. Forseries that show particularly strong and stable seasonalmovements, it may be possible to obtain seasonallyadjusted estimates based on only three years of data.

8.45. A longer time series, however, is required toidentify more precisely the seasonal pattern and toadjust the series for calendar variations (i.e., trad-ing days and moving holidays), breaks in the series,outliers, and particular events that may haveaffected the series and may cause difficulties inproperly identifying the seasonal pattern of theseries.

8.46. For countries that are setting up a new QNA sys-tem, at least five years of retrospective calculations arerecommended to conduct seasonal adjustment.

8.47. If a country has gone through severe structuralchanges resulting in radical changes in the seasonalpatterns, it may not be possible to seasonally adjustits data until several years after the break in the series.In such cases, it may be necessary to seasonallyadjust the pre-break and post-break part of the seriesseparately.

3. Critical Issues in Seasonal Adjustment of QNA

8.48. When producing seasonally adjusted nationalaccount estimates, four critical issues must be decided:(a) Should balancing items and aggregates be sea-

sonally adjusted directly or derived residually,and should accounting and aggregation relation-ships be maintained?

(b) Should the relationship among current pricevalue, price indices, and volume estimates bemaintained, and, if so, which component shouldbe derived residually?

(c) Should supply and use and other accounting iden-tities be maintained, and, if so, what are the prac-tical implications?

(d) Should the relationship to the annual accounts bestrictly preserved?

a. Compilation levels and seasonal adjustment ofbalancing items and aggregates

8.49. Seasonally adjusted estimates for balancingitems and aggregates can be derived directly or indi-rectly from seasonally adjusted estimates for the dif-ferent components; generally the results will differ,sometimes significantly. For instance, a seasonallyadjusted estimate for value added in manufacturing atcurrent prices can be derived either by seasonallyadjusting value added directly or as the differencebetween seasonally adjusted estimates for output andintermediate consumption at current prices.Similarly, a seasonally adjusted estimate for GDP atcurrent prices can be derived either by seasonallyadjusting GDP directly or as the sum of seasonallyadjusted estimates for value added by activity (plustaxes on products). Alternatively, a seasonallyadjusted estimate for GDP can be derived as the sumof seasonally adjusted estimates for the expenditurecomponents.

8.50. Conceptually, neither the direct approach northe indirect approach is optimal. There are argumentsin favor of both approaches. It is convenient, and forsome uses crucial, that accounting and aggregationrelationships are preserved.32 Studies33 and practice,however, have shown that the quality of the seasonallyadjusted series, and especially estimates of the trend-cycle component, may be improved, sometimes sig-nificantly, by seasonally adjusting aggregates directlyor at least at a more aggregated level. Practice hasshown that seasonally adjusting the data at a detailedlevel can leave residual seasonality in the aggregates,may result in less smooth seasonally adjusted series,and may result in series more subject to revisions.Which compilation level for seasonal adjustment givesthe best results varies from case to case and depends onthe properties of the particular series.

8.51. For aggregates, the direct approach may givethe best results if the component series shows thesame seasonal pattern or if the trend-cycles of theseries are highly correlated. If the component seriesshows the same seasonal pattern, aggregation oftenreduces the impact of the irregular components of thecomponent series, which at the most detailed level(the level of the source data) may be too dominant for


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32However, for time series of chain-linked price indices and volumedata, these accounting relationships are already broken (see SectionD.4 of Chapter IX for a discussion of the non-additivity feature ofchain-linked measures).33See, among others, Dagum and Morry (1984).

proper seasonal adjustment. This effect may be par-ticularly important for small countries where irregu-lar events have a stronger impact on the data.Similarly, if the component series do not show thesame seasonal pattern but their trend-cycles arehighly correlated, aggregation reduces the impact ofboth the seasonal and irregular components of thecomponent series.

8.52. In other cases, the indirect approach may givethe best results. For instance, if the component seriesshow very different seasonal patterns and the trend-cycles of the series are uncorrelated, aggregation mayincrease the appearance of irregular movements in theaggregate. Similarly, aggregation may cause large,highly volatile nonseasonal component series to over-shadow seasonal component series, making it difficultor impossible to identify any seasonality that is presentin the aggregate series. Moreover, it may be easier toidentify breaks, outliers, calendar effects, the seasonaleffect narrowly defined, and so on in detailed serieswith low to moderate irregular components thandirectly from the aggregates, because at the detailedlevel these effects may display a simpler pattern.

8.53. For balancing items, there is reason to believethat the indirect approach more often gives betterresults. Because balancing items are derived as thedifference between two groups of component series,in the balancing item, the impact of the irregularcomponents of the component series is more likely tobe compounded. In contrast, because aggregates arederived by summation, opposite irregular movementsin the component series will cancel each other out.

8.54. Some seasonal adjustment programs,including the X-11-ARIMA and the X-12-ARIMA, offer the possibility of adjusting aggre-gates using the direct and indirect approachsimultaneously and comparing the results. Forinstance, the X-12-ARIMA, using the Compositeseries specifications command, adjusts aggregatessimultaneously using the direct and indirectapproach and provides users with a set of test sta-tistics to compare the results. These test statisticsare primarily the M and Q statistics presented inExample 8.4, measures of smoothness, and fre-quency spectrum estimates from the directly andindirectly estimated irregular component. In addi-tion, sliding span and revision history simulationtests for both the direct and the indirect estimatesare available to assess which approach results inestimates less subject to revisions.

8.55. In practice, the choice between direct and indi-rect seasonal adjustment should be based on the mainintended use of the estimates and the relativesmoothness and stability of the derived estimates. Forsome uses, preserved accounting and aggregationrelationships in the data may be crucial, and thesmoothness and stability of the derived estimates sec-ondary. For other uses, the time-series properties ofthe derived estimates may be crucial, while account-ing and aggregation relationships may be of noimportance. If the difference is insignificant, repre-senting a minor annoyance rather than adding anyuseful information, most compilers will opt for pre-serving accounting and aggregation relationshipsbetween published data.

8.56. Consequently, international practice varieswith respect to the choice between direct and indirectseasonal adjustment. Many countries obtain the sea-sonally adjusted QNA aggregates as the sum ofadjusted components, while some also adjust thetotals independently, with discrepancies between theseasonally adjusted total and the sum of the compo-nent series as a result. Finally, some countries onlypublish seasonally adjusted estimates for main aggre-gates and typically seasonally adjust these directly orderive them indirectly by adjusting rather aggregatedcomponent series.

b. Seasonal adjustment and the relationship amongprice, volume, and value

8.57. As for balancing items and aggregates, season-ally adjusted estimates for national accounts priceindices, volume measures, and current price data canbe derived either by seasonally adjusting the threeseries independently or by seasonally adjusting twoof them and deriving the third as a residual, if all threeshow seasonal variations.34 Again, because of nonlin-earities in the seasonal adjustment procedures, thealternative methods will give different results; how-ever, the differences may be minor. Preserving therelationship among the price indices, volume mea-sures, and the current price data is convenient forusers.35 Thus, it seems reasonable to seasonallyadjust two of them and derive a seasonally adjustedestimate for the third residually. Choosing whichseries to derive residually must be determined on acase-by-case basis, depending on which alternativeseems to produce the most reasonable result.

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34Experience has shown that the price data may not always show iden-tifiable seasonal variations.35Note that chain-linking preserves this relationship (V = P • Q).

c. Seasonal adjustment and supply and use and otheraccounting identities

8.58. Seasonal adjustment may cause additionalstatistical discrepancies in seasonally adjusted databetween supply and use, GDP estimated from alter-native sides, and between the different sides ofother accounting identities. These statistical dis-crepancies are caused by nonlinearities in the sea-sonal filters, as well as use of different filter length,use of different pre-adjustments, and differences inestimated calendar effects on the various sides ofthe accounting identity. The statistical discrepan-cies may be reduced by forcing the programs tochoose the same filter length and use the same pre-adjustment factors and calendar-effect factors forall series. This may, however, reduce the smooth-ness and stability of the individual seasonallyadjusted series.

d. Seasonal adjustment and consistency with annualaccounts8.59. Annual totals based on the seasonallyadjusted data will not automatically—and oftenshould not conceptually—be equal to the corre-sponding annual totals based on the original unad-justed data. The number of working days, theimpact of moving holidays, and other calendar-related effects vary from year to year. Similarly,moving seasonality implies that the impact of theseasonal effect narrowly defined will vary fromyear to year. Thus, conceptually, for series withsignificant calendar-related effects or moving sea-sonality effects, the annual totals of a seasonallyadjusted series should differ from the unadjustedseries.

8.60. For series without any significant calendar-related or moving seasonality effects, X-11/X-12will produce seasonally adjusted data that automat-ically add up to the corresponding unadjustedannual totals if the seasonal components are addi-tive (equation 8.1) but not if the seasonals are mul-tiplicative (equation 8.2). Multiplicative seasonalfactors require that a current-period weighted aver-age of the seasonal factors averages to 1 and for theseasonally adjusted data to automatically add up tothe corresponding unadjusted annual totals.However, the normalization of the seasonal factorsin step (d) of the filtering procedure in stages 1 and2 described in paragraph 8.23 only ensures that theunweighted, and not the weighted, annual averageof the seasonal factors averages 1. It follows that,

for series with multiplicative seasonal factors andno significant calendar-related or moving seasonal-ity effects, the difference between the annual totalsof the adjusted and unadjusted series will depend onthe amplitude of the seasonal variation narrowlydefined, the volatility of the seasonally adjustedseries, and the pace of the change in the underlyingtrend-cycle. The difference will be small, and ofteninsignificant, for series with moderate to low sea-sonal amplitudes and for series with little volatilityand trend-cycle change.

8.61. X-11-ARIMA and X-12-ARIMA provideoptions for forcing the annual totals from the season-ally adjusted data to be equal to the original totals.Seasonal adjustment experts, however, generallyrecommend not using the forcing option36 if theseries show significant37 trading-day, other calendar-related, or moving seasonality effects and trading-day or other calendar adjustments are performed. Insuch cases, consistency with the annual series wouldbe achieved at the expense of the quality of the sea-sonal adjustment and would be conceptually wrong.

4. Status and Presentation of Seasonally Adjustedand Trend-Cycle QNA Estimates

8.62. The status and presentation of seasonallyadjusted and trend-cycle QNA estimates vary. Somecountries publish seasonally adjusted estimates foronly a few main aggregates and present them as addi-tional (sometimes unofficial) analytical elaborationsof the official data. Other countries focus on the sea-sonally adjusted and trend-cycle estimates and pub-lish an almost complete set of seasonally adjustedand trend-cycle QNA estimates in a reconciledaccounting format. They may present the originalunadjusted data as supplementary information.

8.63. The mode of presentation also varies substan-tially. Seasonally adjusted and trend-cycle data can bepresented as charts; as tables with the actual data,either in money values or as index series; and as tableswith derived measures of quarter-to-quarter rates ofchange. The last may be presented as the actual rates ofchange or as annualized rates (see Box 8.4).


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36The X-12-ARIMA manual explicitly recommends against using theforcing option if trading-day adjustment is performed or if the sea-sonal pattern is changing rapidly.37Relative to the “adding-up error” introduced by the unweighted, andnot the weighted, annual average of the seasonal factors averaging to1 for multiplicative seasonal adjustment.

8.64. The rates of change are sometimes annualized tomake it easier for the layman to interpret the data. Mostusers have a feel for the size of annual growth rates butnot for monthly or quarterly rates. Annualizing growthrates, however, also means that the irregular effects arecompounded. Irrespectively of whether the actual orannualized quarterly rates of change are presented, it isimportant to indicate clearly what the data represent.

8.65. Growth rates representing different measuresof change can easily be confused unless it is clearlyindicated what the data represent. For instance, termslike “annual percentage change” or “annual rate ofgrowth” can mean (a) the rate of change from onequarter to the next annualized (at annual rate); (b) thechange from the same period of the previous year; (c)the change from one year to the next in annual data,or, equivalently, the change from the average of oneyear to the average of the next year; or (d) the changefrom the end of one year to the end of the next year.

8.66. Some countries also present the level of quar-terly current and constant price data at annualizedlevels by multiplying the actual data by four. Thisseems artificial, does not make the data easier tointerpret, and may be confusing because annual flowdata in monetary terms no longer can be derived asthe sum of the quarters. Users not familiar with thepractice of annualizing levels of current and constantprice data by multiplying the actual data by four mayconfuse annualized levels with forecast annual data.For these reasons, this practice is not recommended.

8.67. Finally, whether to present seasonallyadjusted data or estimates of the trend-cycle com-ponent is still the subject of debate between expertsin this area. In this manual, it is recommended topresent both, preferably in the form of graphsincorporated into the same chart, as illustrated inExample 8.6.

8.68. An integrated graphical presentation high-lights the overall development in the two seriesover time, including the uncertainties representedby the irregular component. In contrast, measuresof quarter-to-quarter rates of change (in particular,annualized rates) may result in an overemphasis onthe short-term movements in the latest and mostuncertain observations at the expense of the generaltrend in the series. The underlying data and derivedmeasures of quarter-to-quarter rates of change,however, should be provided as supplementaryinformation.

8.69. The presentation should highlight the lower reli-ability, particularly for the trend-cycle component, ofthe estimates for the latest observations as discussed inthis section. Means of highlighting the lower quality ofthe end-point estimates include (a) noting past revi-sions to these estimates; (b) suppressing estimates ofthe trend-cycle component for the latest observationsin graphical presentations, as in Example 8.6; and (c)showing estimates for the latest observations with atrumpet on graphical presentations and with an esti-mated confidence interval in tabular presentations.

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Example 8.6. Presentation of Seasonally Adjusted Series and the Corresponding Trend-Cycle Component (Based on data from Example 8.1.)

Presenting the seasonally adjusted series and estimates of the trend-cycle components in the same chart highlights the overall development in the two seriesover time, including the uncertainties represented by the irregular component. Suppressing in the chart the estimates of the trend-cycle component at the endof the series or showing the trend-cycle estimates at the end with a trumpet based on estimated confidence intervals further highlights the added uncertain-ties at the end of the series.

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Seasonally adjusted series

Trend-cycle component

Box 8.4. Annualizing, or Compounding, Growth Rates

Period-to-period rates of change in quarterly data can be annualized using the following compounding formula:arq,y = (1 + rq,y)

4 – 1, rq,y = (Xq,y /Xq–1,y – 1)where:arq,y Annualized quarter-to-quarter rate of change for quarter q of year y.rq,y Original quarter-to-quarter rate of change for quarter q of year y in time series Xq ,y .

The purpose of annualizing the rates of change is to present period-to-period rates of change for different period lengths on the same scaleand thus to make it easier for the layman to interpret the data. For instance, annualizing the rates of change may help to clarify that a 0.8 per-cent growth from one month to the next is equivalent to:

• 2.4 percent growth from one quarter to the next (2.4% = [(1 + 0.008)3 – 1] • 100), or • 10.0 percent growth from one year to the next (10.0% = [(1 + 0.024)4 – 1] • 100 =[(1 + 0.008)12 – 1] • 100).Most users have a feel for annual growth rates and immediately recognize that a 10.0 percent annual growth in, for example, constant pricehousehold consumption expenditures is a lot, while 0.8 percent from one month to the next appears meager.

Annualized quarterly growth rates do not indicate what the annual growth will be and are not intended to be simple forecasts of what theannual growth rate would be if this growth continues for four quarters.The quarterly growth rate has to be constant for eight quarters forthe annualized quarterly growth rate to be equal to the annual growth rate.

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IX Price and Volume Measures:Specific QNA-ANA Issues

A. Introduction

9.1. This chapter addresses a selected set of issuesfor constructing time series of price and volume mea-sures that are of specific importance for the quarterlynational accounts (QNA). In particular, it discussesthe relationship between price and volume measuresin the QNA and in the annual national accounts(ANA): namely, (1) how to aggregate price and vol-ume measures over time; (2) how to choose the baseperiod in the QNA; (3) the frequency of chain-link-ing; and (4) the techniques for annual chain-linkingof quarterly data. In addition, the chapter addresseshow to deal with nonadditivity and presentation ofchain-linked volume measures in the QNA.

9.2. The 1993 SNA does not contain specific recom-mendations for price and volume measures for theQNA or the relationship between price and volumemeasures in the QNA and the ANA. The basic princi-ples for quarterly price and volume measures in theQNA and the ANA are the same, including the 1993SNA recommendation of moving away from the tra-ditional constant-price measures1 to annually chain-linked measures, preferably using superlative indexnumber formulas such as the Fisher and Tornquistformulas. The issues listed above raise new problems,however, many of which have not satisfactorily beendealt with to date in the literature. Conventionalintertemporal index number theory has mainly beenconcerned with price and quantity comparisonsbetween separate pairs of points in time and not withprice and volume measures in a time-series context.In particular, conventional index number theory hasnot been concerned with price and quantity compar-isons between periods of time of different duration(e.g., years and quarters) and the relationship among

these price and volume measures for longer timeperiods, the corresponding measures for the subperi-ods, and the point-to-point measures.

9.3. QNA price and volume measures should be inthe form of time series and should be consistent withcorresponding ANA estimates. For QNA price andvolume measures to constitute a time series, theymust meet the following four requirements:(a) The data should reflect both the short- and long-

term movements in the series, particularly thetiming of any turning points.

(b) The data should allow different periods to becompared in a consistent manner. That is, basedon the underlying time series, the data shouldallow measures of change to be derived betweenany period (i.e., from the previous period, thesame period in the previous year, and a particularperiod several years earlier).

(c) The data should allow periods of different dura-tion to be compared in a consistent manner. Thatis, based on the underlying time series, the datashould allow measures of change to be derivedbetween any periods of any length (e.g., betweenthe average of the last two quarters and of the pre-vious two quarters or the same two quarters sev-eral years earlier, from the average of the previousyear and of a year several years earlier).

(d) The data should allow subperiods and periods tobe compared in a consistent manner (e.g., quar-ters with years).

9.4. Consistency between QNA and ANA price andvolume measures, in principle, requires either that theANA measures are derived from quarterly measuresor that consistency is forced on the QNA data usingbenchmarking techniques. This is true even if thebasic requirement that the QNA and ANA measuresare based on the same methods of compilation andpresentation (i.e., same index formula, base year(s),and reference period) is met. Strict consistency

1Constant price measures are fixed-base Laspeyres-type volume mea-sures (fixed-price weights) and the corresponding price deflators arePaasche price indices.

between QNA and direct ANA price and volumemeasures is generally not possible because quarterlyindices based on most index formulas, includingPaasche and Fisher, do not aggregate exactly to theircorresponding direct annual indices. For fixed-baseLaspeyres volume indices, or traditional constantprice estimates, consistency requires that the esti-mates are derived by explicitly or implicitly valuingthe quantities at the annual quantity-weighted aver-age of the prices charged in different time periods ofthe base year,2 effectively implying that the annualvolume data are derived from the quarterly data3 (seeSection B) and not directly. Finally, for annuallychain-linked Laspeyres volume indices, strict consis-tency can only be achieved by use of an annual link-ing technique that can result in a break4 in theestimates between the fourth quarter of one year andthe first quarter of the next year (see Section D).

9.5. Consistency between QNA and ANA price andvolume measures also requires that new methods,like chain-linking, are implemented simultaneouslyin both the QNA and ANA. Although the 1993 SNArecommends moving to chain-linked volume mea-sures, for countries currently compiling traditionalconstant price estimates, it would generally be unde-sirable to complicate the introduction of QNA by alsointroducing new techniques for constructing and pre-senting volume measures at the same time. It is rec-ommended for these countries to introduce chainingin a second phase, concurrent with the introduction ofchain-linking in the ANA. Thus, for countries cur-rently compiling traditional constant price estimates,only the discussion in Section B of aggregating priceand volume measures over time is of immediateimportance.

B. Aggregating Price and VolumeMeasures Over Time

9.6. Aggregation over time means deriving lessfrequent data (e.g., annual) from more frequentdata (e.g., quarterly). Incorrect aggregation ofprices, or price indices, over time to derive annualdeflators can introduce errors in independently

compiled annual estimates and thus can causeinconsistency between QNA and ANA estimates,even when they are derived from the same underly-ing data. When deriving annual constant price esti-mates by deflating annual current price data, acommon practice is to compute the annual pricedeflators as a simple unweighted average ofmonthly or quarterly price indices. This practicemay introduce substantial errors in the derivedannual constant price estimates, even when infla-tion is low. This may happen when• there are seasonal or other within-year variations in

prices or quantities, and• the within-year pattern of variation in either prices

or quantities is unstable.

9.7. Volume measures for aggregated periods oftime should conceptually be constructed fromperiod-total quantities for each individual homoge-nous product. The corresponding implicit pricemeasures would be quantity-weighted period-aver-age price measures. For example, annual volumemeasures for single homogenous products5 shouldbe constructed as sums of the quantities in each sub-period. The corresponding implicit annual averageprice, derived as the annual current price valuedivided by the annual quantity, would therefore be aquantity-weighted average of the prices in eachquarter. As shown in Example 9.1, the quantity-weighted average price will generally differ, some-times significantly, from the unweighted averageprice. Similarly, for groups of products, conceptu-ally, annual volume measures can be constructed asa weighted aggregate of the annual quantities foreach individual product. The corresponding implicitannual price deflator for the group would be aweighted aggregate of the quantity-weighted annualaverage prices for the individual products. Thisannual price deflator for the group based on thequantity-weighted annual average prices wouldgenerally differ, sometimes significantly, from theannual price deflators derived as a simpleunweighted average of monthly or quarterly priceindices often used in ANA systems—deflation bythe latter may introduce substantial errors in thederived annual constant price estimates.

IX PRICE AND VOLUME MEASURES: SPECIFIC QNA-ANA ISSUES

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2The corresponding explicit or implicit annual deflators should bederived as current-year quantity-weighted averages of monthly orquarterly fixed-based Paasche price indices.3This is particularly an issue under high inflation and for highlyvolatile items.4This can occur if there are strong changes in relative quantities andrelative prices.

5Homogenous products are identical in physical and economic termsto other items in that product group and over time. In contrast, whenthere are significant variations among items or over time in the phys-ical or economic characteristic of the product group, each versionshould be treated as a separate product (e.g., out-of-season fruit andvegetables such as old potatoes may be regarded as different productsthan in-season fruit and vegetables such as new potatoes).

9.8. Consequently, to obtain correct volume mea-sures for aggregated periods of time, deflatorsshould take into account variations in quantities aswell as prices within the period. For example,annual deflators could be derived implicitly fromannual volume measures derived from the sum ofquarterly volume estimates obtained using thefollowing two-step procedure:(a) Benchmark the quarterly current price data/

indicator(s) to the corresponding annual currentprice data.

(b) Construct quarterly constant price data by deflat-ing the benchmarked quarterly current price data.Equivalently, the annual volume measure couldbe obtained by deflating using an annual deflatorthat weights the quarterly price indices by theconstant price values of that item for each quarter.

Either way of calculation achieves annual defla-tors that are quantity-weighted average annualprice measures.6

9.9. A more difficult case occurs when the annualestimates are based on more detailed price and valueinformation than is available quarterly. In thosecases, if seasonal volatility is significant, it would bepossible to approximate the correct procedure usingweights derived from more aggregated, but closelyrelated, quarterly data.

9.10. The issue of price and quantity variations alsoapply within quarters. Accordingly, when monthlydata are available, quarterly data will better take into

Aggregating Price and Volume Measures Over Time

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Example 9.1. Weighted and Unweighted Annual Averages of Prices (or Price Indices) WhenSales and Price Patterns Through the Year are Uneven

Constant Price ValueCurrent Unit Value At Unweighted At Weighted

Price Unweighted Weighted Average Average 1999Quantity Price Value Average Price Average Price 1999 Prices Prices

(1) (2) (3) (4) (5) = (3)/(1) (6) = (4)•(1) (7) = (5)•(1)

q1 0 80 0 0 0q2 150 50 7,500 7,500 6,750q3 50 30 1,500 2,500 2,250q4 0 40 0 0 01999 200 9,000 50 45 10,000 9,000q1 0 40 0 0 0q2 180 50 9,000 9,000 8,100q3 20 30 600 1,000 900q4 0 40 0 0 02000 200 9,600 40 48 10,000 9,000

% Changefrom 1999 to 2000 0.00% 6.70% –20.00% 6.70% 0.00% 0.00%

Direct Deflation of Annual Current Price Data2000 at 1999 prices 9600/(40/50) = 9600/0.8 = 12,000% change from 1999 (12000/9000-1) • 100 = 33.3%This example highlights the case of an unweighted annual average of prices (or price indices) being misleading when sales and price patterns through the yearare uneven for a single homogenous product.The products sold in the different quarters are assumed to be identical in all economic aspects.

In the example, the annual quantities and the quarterly prices in quarters with nonzero sales are the same in both years, but the pattern of sales shifts towardthe second quarter in 1998.As a result, the total annual current price value increases by 6.7 percent.

If the annual deflator is based on a simple average of quarterly prices then the deflator appears to have dropped by 20 percent.As a result, the annual constantprice estimates will wrongly show an increase in volume of 33.3 percent.

Consistent with the quantity data, the annual sum of the quarterly constant price estimates for 1999 and 2000, derived by valuing the quantities using theirquantity-weighted average 1999 price, shows no increase in volumes (column 7).The change in annual current price value shows up as an increase in the implic-it annual deflator, which would be implicitly weighted by each quarter’s proportion of annual sales at constant prices.

Price indices typically use unweighted averages as the price base, which corresponds to valuing the quantities using their unweighted average price.As shownin column 6, this results in an annual sum of the quarterly constant price estimates in the base year (1999) that differs from the current price data, which itshould not.This difference, however, can easily be removed by a multiplicative adjustment of the complete constant price time series, leaving the period-to-period rate of change unchanged.The adjustment factor is the ratio between the annual current price data and sum of the quarterly constant price data in thebase year (9000/10000).

6The corresponding formulas are provided in Annex 9.1.

account variations within the period if they are builtup from the monthly data.

9.11. In many cases, variation in prices and quanti-ties within years and quarters will be so insignifi-cant that it will not substantially affect theestimates. Primary products and high-inflationcountries are cases where the variation can be par-ticularly significant. Of course, there are manycases in which there are no data to measure varia-tions within the period.

9.12. A related problem that can be observed inquarterly data is the annual sum of the quarterlyconstant price estimates in the base year differingfrom the annual sum of the current price data, whichshould not be the case. This difference can becaused by the use of unweighted annual averageprices as the price base when constructing monthlyand quarterly price indices. As shown in Annex 9.1,deflating quarterly data with deflators constructedwith unweighted average prices as the price basecorresponds to valuing the quantities using theirunweighted annual average price rather than theirweighted annual average price. This difference inthe base year between the annual sum of the quar-terly constant price estimates and the annual sum ofthe current price data can easily be removed by amultiplicative adjustment of the complete constantprice time series, leaving the period-to-period rateof change unchanged. The adjustment factor is theratio between the annual current price data and thesum of the initial quarterly constant price data basedon the unweighted annual average prices in the baseyear, which, for a single product, is identical to theratio of the weighted and unweighted average price.

9.13. Two different concepts and measures ofannual change in prices are illustrated in Example9.1, which both are valid measures of economicinterest. The first—showing a decline in prices of 20percent based on unweighted annual averageprices—corresponds to a measure of the averagechange in prices. The second—showing an increasein prices of 6.7 percent based on weighted annualaverage prices—corresponds to change in averageprices. As shown in Example 9.1, only the latter fitsin a value/volume/price measurement frameworkfor time periods, as required by the nationalaccounts, in contrast to the measurement frameworkfor points in time addressed in conventional indexnumber theory. In Example 9.1, the annual valuechange is 6.7 percent, and the correct annual volume

change is an undisputable 0.0 percent, because theannual sum of the quantities is unchanged and thequantities refer to a single homogenous product.

9.14. An apparent difficulty is that the changesshown by the weighted annual average price measurefail the fundamental index number axiom that themeasures should reflect only changes in prices andnot changes in quantities. Thus, the weighted annualaverage price measure appears to be invalid as a mea-sure of price change. The 6.7 increase in averageprices from 1997 to 1998 results from changes in thequantities transacted at each price and not fromincreases in the prices, and therefore does not satisfybasic index number tests such as the identity and pro-portionality tests. For that reason, it can be arguedthat Example 9.1 shows that, in principle, it is notpossible to factor changes in values for time periodsinto measures of price and quantity changes that areeach acceptable as index numbers in their own right.The basic index number tests and conventional indexnumber theory, however, are concerned with priceand quantity comparisons between separate pairs ofpoints in time rather than with price and quantitycomparisons between time periods and, conse-quently, not with measures of the change in averageprices from one period to another. To measure thechange in average prices, for a single homogenousproduct, each period’s average price should bedefined as the total value divided by the correspond-ing quantities within that period; that is, they shouldbe unit values. From Example 9.1, it is clear thatannual average prices for national accounting pur-poses cannot be realistically defined without refer-ence to the corresponding quantities and thereforeshould be calculated using a weighted average withquarterly/subannual quantities as weights.

C. Choice of Price Weights for QNAVolume Measures

1. Laspeyres-Type Volume Measures

9.15. The time-series requirements and the QNA-ANA consistency requirement imply that the quantity-weighted average prices of a whole year should beused as price weights for ANA and QNA Laspeyres-type volume measures.7 Use of the prices of one


150

7The term “Laspeyres-type” is used to cover the traditional constantprice measures, fixed-base Laspeyres volume indices, and chain-linked Laspeyres volume indices.

particular quarter, the prices of the correspondingquarter of the previous year, the prices of the corre-sponding quarter of a fixed “base year,” or the prices ofthe previous quarter are not appropriate for time seriesof Laspeyres-type volume measures in the nationalaccounts for the following reasons:• Consistency between directly derived ANA and

QNA Laspeyres-type volume measures requiresthat the same price weights are used in the ANAand the QNA, and that the same price weights areused for all quarters of the year.

• The prices of one particular quarter are not suitableas price weights for volume measures in the ANA,and thus in the QNA, because of seasonal fluctua-tions and other short-term volatilities in relativeprices. Use of weighted annual average pricesreduces these effects. Therefore, weighted annualaverage prices are more representative for the otherquarters of the year as well as for the year as awhole.

• The prices of the corresponding quarter of the previ-ous year or the corresponding quarter of a fixed“base year” are not suitable as price weights for vol-ume measures in the QNA because the derived vol-ume measures only allow the current quarter to becompared with the same quarter of the previous yearor years. Series of year-to-year changes do not con-stitute time series that allow different periods to becompared and cannot be linked together to formsuch time series. In particular, because they involveusing different prices for each quarter of the year,they do not allow different quarters within the sameyear to be compared. For the same reason, they donot allow the quarters within the same year to beaggregated and compared with their correspondingdirect annual estimates. Furthermore, as shown inAnnex 1.1, changes from the same period in the pre-vious year can introduce significant lags in identify-ing the current trend in economic activity.

• The prices of the previous quarter are not suitableas price weights for Laspeyres-type volume mea-sures for two reasons:

(a) The use of different price weights for eachquarter of the year does not allow the quarterswithin the same year to be aggregated andcompared with their corresponding directannual estimates.

(b) If the quarter-to-quarter changes are linkedtogether to form a time series, short-termvolatility in relative prices may cause the quar-terly chain-linked measures to show substantialdrift compared to corresponding direct mea-sures. This is illustrated in Example 9.3.

9.16. Quarterly Laspeyres-type volume measureswith two different base-period8 price weights may beused: (a) The annual average of a fixed-base year, resulting

in the traditional constant price measures, whichis equivalent to a fixed-based Laspeyres volumeindex.

(b) The annual average of the previous year, resultingin the annually chain-linked quarterly Laspeyresvolume index.

9.17. The traditional volume measures at the con-stant price of a fixed base year, the fixed-based quar-terly Laspeyres volume index, and the short-term linkin the annually chain-linked quarterly Laspeyres vol-ume index can be expressed in mathematical terms asthe following:• At the constant “average” prices of a fixed base year:

(9.1.a)

• The fixed-based quarterly Laspeyres:

(9.1.b)

• Short-term link in the annually chain-linked quar-terly Laspeyres:

(9.1.c)

whereCPq,y–

0 is the total value in quarter q of year ymeasured at the annual average pricesof year 0.

LQ0→(q,y) represents a Laspeyres volume indexmeasuring the volume change from theaverage of year 0 to quarter q in year ywith average of year 0 as base andreference period;9

LQ —(y–1)→(q,y) represents a Laspeyres volume index

measuring the volume change from theaverage of year y – 1 to quarter q in year

LQp q

p qy q y

i y i q yi

i y i yi– ,

, – , ,

, – , –1

1

1 1( )→( ) =

⋅⋅

∑∑

LQp q

p qq yi i q yi

i ii0

0

0 0→( ) =

⋅⋅

∑∑,

, , ,

, ,

CP p qq y i i q yi, , , ,0 0= ⋅∑

Choice of Price Weights for QNA Volume Measures

151

8The term “base period” is defined in paragraph 9.22 as meaning (1)the base of the price or quantity ratios being weighted together (e.g.,period 0 is the base for the quantity ratio), and (2) the pricing year (thebase year) for constant price data.9The term “Reference period” is defined in paragraph 9.22 as meaningthe period for which the index series is expressed as equal to 100.

y with the average of year y – 1 as baseand reference period;

pi,q,y is the price of item i in quarter q ofyear y;

–pi,y–1 is the quantity-weighted arithmeticaverage of the price of item i in thequarters of year y – 1;

–pi,0 is the quantity-weighted arithmeticaverage of the price of item i in thequarters of year 0

;

qi,q,y is the quantity of item i in quarter q ofyear y;

–qi,y–1 is the simple arithmetic average of thequantities of item i in the quarters of y – 1; and

–qi,0 is the simple arithmetic average of thequantities of item i in the quarters ofyear 0.

2. Fisher-Type Volume Indices

9.18. The Fisher volume index, being the geometricaverage of a Laspeyres and a Paasche volume index,uses price weights from two periods—the baseperiod and the current period. Quarterly Fisherindices with three different base-period weights maybe used: (a) The annual average of a fixed-base year, resulting

in the fixed-based quarterly Fisher index. (b) The annual average of the previous year, resulting

in the annually chain-linked quarterly Fisherindex.

(c) The average of the previous quarter, resulting inthe quarterly chain-linked quarterly Fisherindex.

9.19. The fixed-based quarterly Fisher volumeindex and the short-term links in the annually andquarterly chain-linked quarterly Fisher volumeindex can be expressed in mathematical terms as thefollowing:• Fixed-based quarterly Fisher:

(9.2.a)

• Short-term link in the annually chain-linked quar-terly Fisher:

(9.2.b)

• Short-term link in the quarterly chain-linked quar-terly Fisher:

(9.2.c)

wheret is a generic symbol for time, which is

more convenient to use for period-toperiod measures than the quarter q inyear y notation used for most formulasin this chapter;

FQA→(q,y) represents a Fisher volume index mea-suring the volume change from periodA to quarter q in year y with period A asbase and reference period;

LQA→(q,y) represents a Laspeyres volume indexmeasuring the volume change fromperiod A to quarter q in year y withperiod A as base and reference period;

PQA→(q,y) represents a Paasche volume indexmeasuring the volume change fromperiod A to quarter q in year y withperiod A as base and reference period;and

pi,A is the price of item i in period A.

Period A is equal to the average of year 0 for thefixed-based Fisher, to the average of the previousyear for the annually chain-linked Fisher, and to theprevious quarter for the quarterly chain-linkedFisher.

9.20. For the same reasons as for Laspeyres-typevolume measures, the following alternative periodsare not suitable as base periods for time series ofFisher-type volume indices: • One particular fixed quarter.• The corresponding quarter of the previous year. • The corresponding quarter of a fixed “base year.”

FQ LQ PQ

p q

p q

p q

p q

t t t t t

i t i ti

i t i ti

i t i ti

i t i ti

–

, – ,

, – , –

, ,

, , –

1 1 1 1

1

1 1 1

( )→ −( )→( ) −( )→( )= ⋅

≡⋅

⋅⋅

⋅⋅

∑∑

∑∑

FQ LQ PQ

P q

P q

p q

p q

y q y y q y y q y

i y i q yi

i y i yi

i q y i q yi

i q y i yi

– , – , – ,

, – , ,

, – , –

, , , ,

, , , –

1 1 1

1

1 1 1

( )→( ) ( )→( ) ( )→( )= ⋅

≡⋅⋅

⋅⋅⋅

∑∑

∑∑

FQ LQ PQ

p q

p q

p q

p q

q y q y q y

i i q yi

i ii

i q y i q yi

i q y ii

0 0 0

0

0 0 0

→( ) →( ) →( )= ⋅

≡⋅⋅

⋅⋅⋅

∑∑

∑∑

, , ,

, , ,

, ,

, , , ,

, , ,

pp q

qii q i qq

i qq,

, , , ,

, ,0

0 0

0

=⋅∑

∑


152

Choice of Price Weights for QNA Volume Measures

153

D. Chain-Linking in the QNA

1. General

9.21. The 1993 SNA recommends moving awayfrom the traditional fixed-base year constant priceestimates to chain-linked volume measures.Constant price estimates use the average prices of aparticular period,10 the base period, to weighttogether the corresponding quantities. Constantprice data have the advantage for the users of thecomponent series being additive, unlike alternativevolume measures. The pattern of relative prices inthe base year, however, is less representative of theeconomic conditions for periods farther away fromthe base year. Therefore, from time to time it is nec-essary to update the base period to adopt weights thatbetter reflect the current conditions (i.e., with respectto production technology and user preferences).Different base periods, and thus different sets ofprice weights, give different perspectives. When thebase period is changed, data for the distant pastshould not be recalculated (rebased). Instead, toform a consistent time series, data on the old baseshould be linked to data on the new base.11 Changeof base period and chain-linking can be done withdifferent frequencies; every 10 years, every 5 years,every year, or every quarter/month. The 1993 SNArecommends changing the base period, and thus con-ducting the chain-linking, annually.

9.22. The concepts of base, weight, and referenceperiod should be clearly distinguished. Index numberterminology is not well established internationally,which can lead to confusion. In particular, the term“base period” is sometimes used for different con-cepts. Similarly, the terms “base period,” “weightperiod,” and “reference period” are sometimes usedinterchangeably. In this manual, following 1993 SNAand the current dominant national accounts practice,the following terminology is used:• Base period for (1) the base of the price or quantity

ratios being weighted together (e.g., period 0 is thebase for the quantity ratio qi,t /qi,0), and (2) the pric-ing year (the base year) for the constant price data.

• Weight period for the period(s) from which theweights are taken. The weight period is equal to thebase period for a fixed-base Laspeyres index and tothe current period for a fixed-base Paasche index.Symmetric fixed-base index formulas like Fisherand Tornquist have two weight periods—the baseand the current period.

• Reference period for the period for which the indexseries is expressed as equal to 100. The referenceperiod can be changed by simply dividing the indexseries with its level in any period chosen as the newreference period.

9.23. Chain-linking means constructing long-runprice or volume measures by cumulating movementsin short-term indices with different base periods. Forexample, a period-to-period chain-linked index mea-suring the changes from period 0 to t (i.e., CI0→t) canbe constructed by multiplying a series of short-termindices measuring the change from one period to thenext as follows:

(9.3)

where I(t–1)→τ represents a price or volume index mea-suring the change from period t – 1 to t, with periodt – 1 as base and reference period.

9.24. The corresponding run, or time series, ofchain-linked index numbers where the links arechained together so as to express the full time serieson a fixed reference period is given by

(9.4.a)

9.25. Chain-linked indices do not have a particularbase or weight period. Each link (I(t – 1)→t) of thechain-linked index in equation (9.4.a) has a baseperiod and one or two weight periods, and the baseand weight period(s) are changing from link to link.By the same token, the full run of index numbers in

CI

CI I

CI I I

CI I I I

CI It

t

0 0

0 1 0 1

0 2 0 1 1 2

0 3 0 1 1 2 2 3

0 11

1→

→ →

→ → →

→ → → →

→ ( )→=

=== ⋅= ⋅ ⋅

=

∏

...

–τ ττ

CI I I I I I

I

t t t

t

0 0 1 1 2 2 3 3 4 1

11

→ → → → → ( )→

( )→=

= ⋅ ⋅ ⋅ ⋅

≡ ∏

........ –

–τ ττ

10The period length should be a year, as recommended in the previoussection.11This should be done for each series, aggregates as well as subcom-ponents of the aggregates, independently of any aggregation oraccounting relationship between the series. As a consequence, thechain-linked components will not aggregate to the correspondingaggregates. No attempts should be made to remove this “chain dis-crepancy,” because any such attempt implies distorting the move-ments in one or several of the series.

equation (9.4.a) derived by chaining each linktogether does not have a particular base period—ithas a fixed reference period.

9.26. The reference period can be chosen freely with-out altering the rates of change in the series. For thechain-linked index time series in equation (9.4.a),period 0 is referred to as the index’s reference periodand is conventionally expressed as equal to 100. Thereference period can be changed simply by dividing theindex series with its level in any period chosen as a newreference period. For instance, the reference period forthe run of index numbers in equation (9.4.a) can bechanged from period 0 to period 2 by dividing all ele-ments of the run by the constant CI0→2 as follows:

(9.4.b)

9.27. The chain-linked index series in equation (9.3)and equations (9.4.a) and (9.4.b) will constitute aperiod-to-period chain-linked Laspeyres volume indexseries if, for each link, the short-term indices (I(t–1)→t) areconstructed as Laspeyres volume indices with the previ-ous period as base and reference period. That is, if

(9.5.)

whereLQ(t–1)→t represents a Laspeyres volume index mea-

suring the volume change from period t – 1to t, with period t – 1 as base and referenceperiod;

pi,t – 1 is the price of item i in period t–1 (the “priceweights”);

qi,t is the quantity of item i in period t;wi,t – 1 is the base period “share weight,” that is, the

item’s share in the total value of period t –1;and

Vt – 1 is the total value at current prices in periodt– 1.

9.28. Similarly, the chain-linked index series inequation (9.3) and equations (9.4.a) and (9.4.b) willconstitute a period-to-period chain-linked Fisher vol-ume index series if, for each link, the short-termindices (I(t – 1)→t) are constructed as Fisher volumeindices with the previous period as base and refer-ence period as in equation (9.2.c).

9.29. Any two index series with different base andreference periods can be linked to measure thechange from the first to the last year12 as follows:

CI0→t = I0→(t–h) • I(t–h)→t (9.6)

That is, each link may cover any number of periods.

9.30. For instance, if in equation (9.6) t = 10 and h= 5, the resulting linked index (CI0→10) constitutes a5-year chain-linked annual index measuring thechange from year 0 to year 10. Example 9.2 providesan illustration of the basic chain-linking techniquefor annual data with t = 15 and h = 10.

9.31. Growth rates and index numbers computed forseries that contain negatives or zeroes—such aschanges in inventories and crop harvest data—gener-ally are misleading and meaningless. For instance,consider a series for changes in inventories at constantprices that is –10 in period one and +20 in period two.The corresponding growth rate between these twoperiods is –300 percent (= ((20/–10) – 1) • 100), whichobviously is both misleading and meaningless.Similarly, for a series that is 1 in period one and 10 inperiod two, the corresponding growth rate from periodone to two would be 900 percent. Consequently, forsuch series, only measures of contribution to percent-age change in the aggregates they belong to can bemade (see Section D.7. for a discussion of measure ofcontribution to percentage change in index numbers).

2. Frequency of Chain-Linking in the QNA

9.32. The 1993 SNA recommends that chain-linking should not be done more frequently thanannually. This is mainly because short-term volatil-ity in relative prices (e.g., caused by samplingerrors and seasonal effects) can cause volume mea-sures that are chain-linked more frequently thanannually to show substantial drift—particularly so

I LQq

qw

p q

p q

p q

V

t t t ti t

i ti i t

i t i ti

i t i ti

i t i ti

t

– –,

, –, –

, – ,

, – , –

, – ,

–

1 11

1

1

1 1

1

1

( )→ ( )→= = ⋅

≡⋅

⋅≡

⋅

∑

∑∑

∑

CI CI CI I I

CI CI CI I

CI CI CI

CI CI CI I

CI CI CI It t

t

2 0 0 0 0 2 0 1 1 2

2 1 0 1 0 2 1 2

2 2 0 2 0 2

2 3 0 3 0 2 1 2

2 0 0 2 11

1

1

1

→ → → → →

→ → → →

→ → →

→ → → →

→ → → ( )→=

= == == == =

= =

∏

...

–τ ττ


154

12As long as they have one period in common, that is, there is at leastone overlapping period. For instance, in equation (9.6) with t = 10 andh = 5, year 5 represents the overlap. Similarly, in Example 9.2, year 10represents the overlap.

for nonsuperlative index formulas like Laspeyresand Paasche—as illustrated in Example 9.3.Similarly, short-term volatility in relative quantitiescan cause price measures that are chain-linkedmore frequently than annually to show substantialdrift. The purpose of chain-linking is to take intoaccount long-term trends in changes in relativeprices, not temporary short-term variations.

9.33. Superlative index formulas, such as the Fisherindex formula, are more robust against the driftproblem than the other index formulas—as illus-trated in Example 9.3. For this reason, a quarterlychain-linked Fisher index may be a feasible alterna-tive to annually chain-linked Fisher or Laspeyres

indices for quarterly data that show little or no short-term volatility. The quarterly chain-linked Fisherindex does not aggregate exactly to the correspond-ing direct annual Fisher index.13 For chain-linkedFisher indices, consistency between QNA and ANAprice and volume measures can only be achieved byderiving the ANA measures from the quarterly mea-sures or by forcing consistency on the data with thehelp of benchmarking techniques. There is no reasonto believe that for nonvolatile series the average of anannually chain-linked Fisher will be closer to adirect annual Fisher index than the average of a quar-terly chain-linked Fisher.

Chain-Linking in the QNA

155

Example 9.2. Basic Chain-Linking of Annual DataThe 1993 SNA ExampleThe example is an elaborated version of the illustration provided in the 1993 SNA.(1993 SNA Table 16.1, pages 386–387.)

Basic DataYear 0 Year 10 Year 15

p0 q0 v0 p10 q10 v10 p15 q15 v15

Item A 6 5 30 9 12 108 11 15 165Item B 4 8 32 10 11 110 14 11 154Total 62 218 319

Constant price DataBase Year 0 Base Year 10

Year 0 Year 10 Year 15 Year 0 Year 10 Year 15p0 • q0 p0 • q10 p0 • q15 p10 • q0 p10 • q10 p10 • q15

Item A 30 72 90 45 108 135Item B 32 44 44 80 110 110Total 62 116 134 125 218 245

Laspeyres Volume Indices for the Total

Fixed-Based Year 0 Year 10 Year 15Year 0 as base and reference 100 187.1 216.1Period-to-period rate of change 87.1% 15.5%Year 10 as base and reference 57.3 100 112.4Period-to-period rate of change 74.4% 12.4%

Re-referenced to year 0 (year 10 as base) 100 174.4 196.0Chain-Linked IndexYear 0 =100 100 187.1 210.3=

112.4 • 1.871Period-to-period rate of change 87.1% 12.4%Year 10 = 100 100/1.871 = 53.4 100 112.4Period-to-period rate of change 87.1% 12.4%

The Laspeyres fixed-base volume index for the total with year 0 as base and reference period was derived as 62/62 • 100 = 100, 116/62 • 100 = 187.1, 134/62 • 100 = 216.1

Similarly, the Laspeyres fixed-base volume index for the total year with 10 as base and reference period was derived as125/218 • 100 = 57.3, 218/218 • 100 = 100, 245/218 • 100 = 112.4

And the Laspeyres fixed-base volume index for the total with year 10 as base and year 0 as reference period was derived as57.3/57.3 • 100 = 100, 100/57.3 • 100 = 174.4, 112.4/57.3 • 100 = 196.0

13Neither does the annually-linked, nor the fixed-based, Fisher index.

9.34. For Laspeyres-type volume measures, consis-tency between QNA and ANA provides an addi-tional reason for not chain-linking more frequentlythan annually. Consistency between quarterly dataand corresponding direct annual indices requiresthat the same price weights are used in the ANA andthe QNA, and consequently that the QNA shouldfollow the same change of base year/chain-linkingpractice as in the ANA. Under those circumstances,the annual overlap linking technique presented inthe next section will ensure that the quarterly dataaggregate exactly to the corresponding direct index.

Moreover, under the same circumstances, any dif-ference between the average of the quarterly dataand the direct annual index caused by the preferredone-quarter overlap technique will be minimized.

9.35. Thus, in the QNA, chain-linked Laspeyres-type volume measures should be derived by compil-ing quarterly estimates at the average prices of theprevious year. These quarterly volume measures foreach year should then be linked to form long, consis-tent time series—the result constitutes an annuallychain-linked quarterly Laspeyres index. Alternative


156

Example 9.3. Frequency of Chain-Linking and the Problem of “Drift”1 in the Case of Price andQuantity Oscillation

Observation/Quarter Quarter 1 Quarter 2 Quarter 3 Quarter 4

Price item A (pA) 2 3 4 2Price item B (pB) 5 4 2 5Quantities item A (qA,t ) 50 40 60 50Quantities item B (qB,t ) 60 70 30 60Total value (Vt ) 400 400 300 400

Volume Indices q1 q2 q3 q4

Fixed-based Laspeyres (q1-based) 100.0 107.5 67.5 100.0Fixed-based Paasche (q1-based) 100.0 102.6 93.8 100.0Fixed-based Fisher (q1-based) 100.0 105.0 79.6 100.0Quarterly chain-linked Laspeyres 100.0 107.5 80.6 86.0Quarterly chain-linked Paasche 100.0 102.6 102.6 151.9Quarterly chain-linked Fisher 100.0 105.0 90.9 114.3

Fixed-Based Laspeyres Index:It➝ 2 = [2 • 40+5 • 70]/400] • 100 = 107.5It➝ 2 = [2 • 60+5 • 30]/400] • 100 = 67.5It➝ 4 = [2 • 50+5 • 60]/400] • 100 = 100.0

Fixed-Based Paasche Index:It➝ 2 = [400/(3 • 50+4 • 60] • 100 = 102.6It➝ 3 = [300/(4 • 50+2 • 60] • 100 = 93.8It➝ 4 = [400/(2 • 50+5 • 60] • 100 = 100.0

Quarterly Chain-Linked Laspeyres Index:It➝ 3 = It➝ 2 • [3 • 60+4 • 30]/400] = 80.6It➝ 4 = It➝ 3 • [4 • 50+2 • 60]/400] = 86.0

Quarterly Chain-Linked Paasche Index:It➝ 3 = It➝ 2 • [300/(4 • 40+2 • 70] = 102.6It➝ 2 = It➝ 3 • [400/(2 • 60+5 • 30] = 151.9

In this example, the prices and quantities in quarter 4 are the same as those in quarter 1, that is, the prices and quantities oscillate ratherthan move as a trend.The fixed-base indices correspondingly show identical values for q1 and q4, but the chain-linked indices show com-pletely different values.This problem can also occur in annual data if prices and quantities oscillate and may make annual chaining inap-propriate in some cases. It is more likely to occur in data for shorter periods, however, because seasonal and irregular effects causethose data to be more volatile.

Furthermore, observe that the differences between the q1 and q4 data for the quarterly chain-linked Laspeyres and the quarterly chain-linked Paasche indices are in opposite directions; and, correspondingly, that the quarterly chain-linked Fisher index drifts less.This is auniversal result.

1The example is based on Szultc (1983).

CL Ip q

p qtt i ii

i ii

t0 11

1

1 11, –

, – ,

, – , –= =

⋅⋅( )→= =∏ ∑

∑∏τ τττ τ

τ ττ

CL Ip q

p qtt i ii

i ii

t0 11

1

1 11, –

, – ,

, – , –= =

⋅⋅( )→= =∏ ∑

∑∏τ τττ τ

τ ττ

Ip q

p q

V

p qti t i ti

i t ii

t

i t ii0

0 0→ =

⋅⋅

≡⋅

∑∑ ∑

, ,

, , , ,

Ip q

p q

p q

Vti i ti

i ii

i i ti0

0

0 0

0

0→ =

⋅⋅

≡⋅∑

∑∑, ,

, ,

, ,

linking techniques for such series are discussed in thenext section.

3. Choice of Index Number Formulas for AnnuallyChain-Linked QNA Data

9.36. The 1993 SNA recommends compiling annu-ally chain-linked price and volume measures,preferably using superlative index number formu-las such as the Fisher and Tornquist formulas. Therationale for this recommendation is that indexnumber theory shows that annually chain-linkedFisher and Tornquist indices will most closelyapproximate the theoretically ideal index. Fisherand Tornquist indices will, in practice, yieldalmost the same results, and Fisher, being the geo-metric average of a Laspeyres and a Paasche index,will be within the upper and lower bounds pro-vided by those two index formulas. Most coun-tries14 that have implemented chain-linking in theirnational accounts, however, have adopted theannually chain-linked Laspeyres formula for vol-ume measures with the corresponding annuallychain-linked Paasche formula for price mea-sures,15 and the European Union’s statistical office(Eurostat) is requiring member states to provideannually chain-linked volume measures using theLaspeyres formula.16

9.37. Annual chain-linking of quarterly dataimplies that each link in the chain is constructedusing the chosen index number formula with theaverage of the previous year (y – 1) as base and ref-erence period. The resulting short-term quarterlyindices must subsequently be linked to form long,consistent time series expressed on a fixed refer-ence period. Alternative annual linking techniquesfor such series will be discussed in Section D.3.While the discussion in Section D.3 focuses onLaspeyres indices, the techniques illustrated and

the issues discussed are applicable to all annuallychain-linked index formulas. The Laspeyres,Paasche, and Fisher annually chain-linked quar-terly volume index formulas for each short-termlink in the chain are given as• Short-term link in annually chain-linked Laspeyres:

(9.7.a)

• Short-term link in annually chain-linked Paasche:

(9.7.b)

• Short-term link in annually chain-linked Fisher:

(9.7.c)

where

is the base period “share weight,” that is, the item’sshare in the total value in year y – 1; andpi,q,y–1 is the price of item i in quarter q of year

y – 1.

9.38. Countries have opted for the annually chain-linked Laspeyres formula instead of the annuallychain-linked Fisher formula for volume measuresmainly for the following reasons:• Experience and theoretical studies indicate that

annual chain-linking tends to reduce the indexnumber spread to the degree that the exact choiceof index number formula assumes less signifi-cance (see, for example, 1993 SNA, paragraph16.51).

• The annually chain-linked quarterly Fisher indexdoes not aggregate to the corresponding direct

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157

14The use of chain-linked measures for official national accounts datawas pioneered by the Netherlands (1985) and Norway (1990).Subsequently, a large number of countries have adopted, or are in theprocess of adopting, chain-linking for their official measures.Currently, only the United States has opted for a chain-linked Fisherindex formula instead of the chain-linked Laspeyres formula. TheUnited States adopted in 1996 an annually chain-linked quarterly“Fisher-like” formula using annual weights in both the Laspeyres andthe Paasche part of the index but changed to a standard quarterlychain-linked Fisher index in 1999.15Laspeyres volume measures require that the corresponding pricemeasures are based on the Paasche formula so that the product of thevolume and price indices is equal to the corresponding value index. 16European Commission Decision of November 30, 1998, clarifyingthe European System of Accounts 1995 principles for price and vol-ume measures, and Eurostat (1999) paragraph 3.186.

annual index;17 the annually chain-linkedLaspeyres index linked, using the annually overlaptechnique presented in Example 9.4.a, does.18

• Chain volume measures in monetary terms19 basedon the annually chain-linked Laspeyres formulawill be additive in the reference year and the sub-sequent year,20 while volume measures based onthe Fisher index will not.

• The Laspeyres formula is simpler to work with andto explain to users than the Fisher index. Forinstance, time series of annually chain-linkedLaspeyres indices easily can be converted intoseries of data valued at the constant average pricesof the previous year that are additive if correspond-ing current price data are made available. This fea-ture makes it easy for users to construct their ownaggregates from published data.

• The formulas for computing contribution to per-centage change are easier for data based on thechain-linked Laspeyres formula than for data basedon the Fisher index.

• The Fisher formula is not consistent in aggregationwithin each link; it is only approximately consis-tent in aggregation.

• The Laspeyres formula, in contrast, is additivewithin each link. This makes it easier to combinechain-linking with compilation analytical tools likesupply and use (SU) tables and input-output tablesthat require additivity of components.21

4. Techniques for Annual Chain-Linking ofQuarterly Data

9.39. Two alternative techniques for annual chain-linking of quarterly data are usually applied: annualoverlaps and one-quarter overlaps. In addition tothese two conventional chain-linking techniques, athird technique sometimes is used based on changes

from the same period in the previous year (the “over-the-year technique”). While, in many cases, all threetechniques give similar results, in situations withstrong changes in relative quantities and relativeprices, the over-the-year technique can result in dis-torted seasonal patterns in the linked series. Whilestandard price statistics compilation exclusively usesthe one-quarter overlap technique, the annual over-lap technique may be more practical for Laspeyres-type volume measures in the national accountsbecause it results in data that aggregate exactly to thecorresponding direct annual index. In contrast, theone-quarter overlap technique and the over-the-yeartechnique do not result in data that aggregate exactlyto the corresponding direct annual index. The one-quarter overlap provides the smoothest transitionbetween each link, however, in contrast to the annualoverlap technique that may introduce a step betweeneach link. Examples 9.4.a, 9.4.b, 9.4.c, and Chart 9.1provide an illustration of these three chain-linkingtechniques. (A formal presentation of the two firstmethods is given in Annex 9.2.)

9.40. The technique of using annual overlaps impliescompiling estimates for each quarter at the weightedannual average prices of the previous year, with subse-quent linking using the corresponding annual data toprovide linking factors to scale the quarterly dataupward or downward. The technique of one-quarteroverlaps requires compiling estimates for the overlapquarter at the weighted annual average prices of thecurrent year in addition to estimates at the averageprices of the previous year. The ratio between the esti-mates for the linking quarter at the average prices of thecurrent year and at the average prices of the previousyear then provides the linking factor to scale the quar-terly data up or down. The over-the-year techniquerequires compiling estimates for each quarter at theweighted annual average prices of the current year inaddition to estimates at the average prices of the previ-ous year. The year-on-year changes in these constantprice data are then used to extrapolate the quarterlyconstant price data of the chosen reference period.

9.41. To conclude, there are no established standardswith respect to techniques for annually chain-linkingof QNA data, but chain-linking using the one-quarteroverlap technique, combined with benchmarking toremove any resulting discrepancies between thequarterly and annual data, gives the best result. Inmany circumstances, however, the annual overlaptechnique may give similar results. The over-the-yeartechnique should be avoided.


158

17Neither does the quarterly-chain linked, nor the fixed-based, quar-terly Fisher index.18However, this may not be a decisive argument for two reasons. First,simulations indicate that, in practice, the difference between a directannual Fisher and the average of a quarterly Fisher may often not besignificant and may easily be removed using benchmarking tech-niques. Second, the preferred quarterly overlap technique presented inSection D.3., even when used for Laspeyres indices, also introducesdifferences between direct annual indices and the average of quarterlyindices.19See Section D.7. and particularly paragraph 9.48 for a discussion ofchain volume measures in monetary terms.20See Example 9.5.a for an illustration of this and Section D.5. for adiscussion of the nonadditivity property of most index number for-mulas besides the fixed-based Laspeyres formula.21The first two countries to adopt chain-linking for their officialnational accounts price and volume measures both did it within an SUcompilation framework.


159

Example 9.4.a. Quarterly Data and Annual Chain-LinkingAnnual OverlapLaspeyres Volume IndexAnnual sums and averages in bold.

Chain-Linked

At Constant Prices of: Index1997 1998 1999 1997=100

Quanti- Quanti- Total at Index Index Index q-qties ties Price Price current 1997 1998 1999 Rate of

Basic data A B A B prices Level =100 Level = 100 Level =100 Level Change

1997 251.0 236.0 7.0 6.0 3,173.00 3,173.00 100.00 100.00q1 67.4 57.6 6.1 8.0 871.94 817.40 103.04 103.04 3.0%q2 69.4 57.1 5.7 8.6 885.51 828.40 104.43 104.43 1.3%q3 71.5 56.5 5.3 9.4 910.05 839.50 105.83 105.83 1.3%q4 73.7 55.8 5.0 10.0 926.50 850.70 107.24 107.24 1.3%1998 282.0 227.0 5.5 9.0 3,594.00 3,336.00 105.14 3,594.00 100.00 105.14q1 76.0 55.4 4.5 10.7 934.78 916.60 102.01 107.26 0.0%q2 78.3 54.8 4.3 11.5 963.07 923.85 102.82 108.10 0.8%q3 80.6 54.2 3.8 11.7 940.42 931.10 103.63 108.95 0.8%q4 83.1 53.6 3.5 12.1 940.73 939.45 104.56 109.93 0.9%1999 318.0 218.0 4.0 11.5 3,779.00 3,711.00 103.26 3,779.00 100.00 108.56q1 85.5 53.2 3.4 12.5 955.70 953.80 100.96 109.60 –0.3%q2 88.2 52.7 3.1 13.0 961.70 958.85 101.49 110.18 0.5%q3 90.8 52.1 2.8 13.8 973.22 962.35 101.86 110.58 0.4%q4 93.5 52.0 2.7 14.7 1018.36 972.00 102.88 111.69 1.0%2000 358.0 210.0 3.0 13.5 3,908.97 3,847.00 101.80 110.51 –1.1%

Independently chain-linked annuals1997 3,173.0 100.001998 3,336.0 105.1 3,594.0 105.141999 3,711.0 103.3 3,779.0 108.562000 3,847.0 101.8 110.51

Step 1: Compile estimates for each quarter at the annual average prices of the previous year; the annual data being the sum of the four quarters.e.g.: q1 1998 7.0 • 67.4+6.0 • 57.6 = 817.00

q4 1998 7.0 • 73.7+6.0 • 55.8 = 850.701998 817.0 + 828.4 + 839.5 + 850.7 = 3336.00

Step 2: Convert the constant price estimates for each quarter into a volume index with the average of last year = 100.e.g.: q1 1998 [817.0/(3173.0/4)] • 100 = 103.00

q4 1998 [850.7/(3173.0/4)] • 100 = 107.201998 3336.0/3173.0 • 100 = 105.10

Step 3: Link the quarterly volume indices with shifting base and reference year using the annual indices as linking factors (using 1997 as the reference period for thechain-linked index).e.g.: q1 1999 102.01 • 1.051 = 107.26

q4 1999 104.56 • 1.051 = 109.93q1 2000 100.9 • 1.0326 • 1.051 = 109.60

Observe that the unweighted annual average of the derived chain-linked quarterly index series is equal to the independently derived chain-linked annual data.e.g.: 2000 [109.6+110.18+110.58+111.69]/4 = 110.51

Finally, observe that the change from,e.g., q4 1999 to q1 2000, in the chain-linked series based on annual overlap differs from the corresponding change in the chain-linked indexbased on a one-quarter overlap in the next example.

e.g.: q1 2000/q 4 1999 based on annual overlap –0.3%≠ q1 1999/q 4 1998 based on one quarter overlap (and 1999 prices) 0.5%

This is the step in the series introduced by the annual overlap technique.

5. Chain-Linked Measures and Nonadditivity

9.42. In contrast to constant price data, chain-linkedvolume measures are nonadditive. To preserve thecorrect volume changes, related series should belinked independently of any aggregation or account-ing relationships that exist between them; as a result,additivity is lost. Additivity is a specific version ofthe consistency in aggregation property for indexnumbers. Consistency in aggregation means that anaggregate can be constructed both directly by aggre-gating the detailed items and indirectly by aggregat-ing subaggregates using the same aggregationformula. Additivity, in particular, implies that at eachlevel of aggregation the volume index for an aggre-gate takes the form of a weighted arithmetic average

of the volume indices for its components with thebase-period values as weights (1993 SNA, paragraph6.55). That is the same as requiring that the aggregatebe equal to the sum of its components when the cur-rent price value of the aggregate and the componentsin some reference period are multiplied, or extrapo-lated, with the aggregate index and the componentindices, respectively, resulting in chain volume mea-sures expressed in monetary terms. It follows that, atthe most detailed level, additivity is the same asrequiring that the value obtained by extrapolating theaggregate is equal to the sum of the components val-ued at the reference period’s prices. Thus, the addi-tivity requirement effectively defines the fixed-baseLaspeyres index and standard constant price data.


160

Example 9.4.b. Quarterly Data and Annual Chain-LinkingOne-quarter overlap Annual sums and averages in bold.

At Constant Prices of: Chain-linked1997 1998 1999 index

1997=100Total at Index Index Index q-qcurrent 1997 q4 1998 q4 1999 Rate of

Basic data q1 q2 p1 p2 prices Level =100 LeveI = 100 Level = 100 Level Change

1997 251.0 236.0 7.0 6.0 3,173.00 3,173.00 100.00 100.00q1 67.4 57.6 817.40 103.04 103.04q2 69.4 57.1 828.40 104.43 104.43 1.3%q3 71.5 56.5 839.50 105.83 105.83 1.3%q4 73.7 55.8 850.70 107.24 907.55 100.00 107.24 1.3%1998 282.0 227.0 5.5 9.0 3,594.00 3,336.00 105.14 3,594.00 105.14q1 76.0 55.4 916.60 101.00 108.31 1.0%q2 78.3 54.8 923.85 101.80 109.17 0.8%q3 80.6 54.2 931.10 102.59 110.03 0.8%q4 83.1 53.6 939.45 103.51 948.80 100.00 111.01 0.9%1999 318.0 218.0 4.0 11.5 3,779.00 3,711.00 3,779.00 109.63q1 85.5 53.2 953.80 100.53 111.60 0.5%q2 88.2 52.7 958.85 101.06 112.19 0.5%q3 90.8 52.1 962.35 101.43 112.60 0.4%q4 93.5 52.0 972.00 102.45 113.73 1.0%2000 358.0 210.0 3.0 13.5 3,908.97 3,847.00 112.53Step 1: Compile estimates for each quarter at the annual average prices of the previous year; the annual data being the sum of the four quarters.Step 2: Compile estimates for the fourth quarter of each year at the annual average prices of the same year.

e.g.: q4 1998 5.5 • 73.7+9.0 • 55.8 = 907.55Step 3: Convert the constant price estimates for the quarters of the first year after the chosen reference year (1997)

into a volume index with the average of the reference year = 100e.g.: q1 1998 [817.4/(3173.0/4)] • 100 = 103.04

q4 1998 [850.7/(3173.0/4)] • 100 = 107.24Step 4: Convert the constant price estimates for each of the other quarters into a volume index with the fourth quarter of last year = 100

e.g.: q1 1999 [916.60/907.55] • 100 = 101.00q4 1999 [936.45/907.55] • 100 = 103.51

Step 5: Link together the quarterly volume indices with shifting base using the fourth quarter of each year as link.e.g.: q1 1999 101.00 • 1.0724 = 108.31

q4 1999 103.51 • 1.0724 = 111.01q1 2000 100.53 • 1.1101 = 111.60

The resulting linked series is referenced to average 1997 = 100.

Finally, observe that the unweighted annual average of the derived chain-linked quarterly index series differs from the independently derived chain-linked annu-als in example 9.4.a.

e.g.: 2000 [111.6+112.19+112.6+113.73 ]/4 = 112.53 ≠ 110.51


161

Example 9.4.c. Quarterly Data and Annual Chain-Linking The Over-the-Year TechniqueLaspeyres Volume Index(i) Pair of years at the same prices.

(ii) Chain-linking using changes from the same quarter in the previous year.

Annual sums and averages in bold.

Chain-LinkedAt Constant Prices of : Index

1997 1998 1999 1997=100Quanti- Quanti- Total at Index q-q-

ties ties Price Price Current 1997 q–4 q–4 Rate of Basic Data A B A B Prices Level = 100 Level = 1 Level = 1 Level Change

1997 251.0 236.0 7.0 6.0 3,173.00 3,173.00 100.00 100.00q1 67.4 57.6 817.40 103.04 889.10 103.04 1.3%q2 69.4 57.1 828.40 104.43 895.60 104.43 1.3%q3 71.5 56.5 839.50 105.83 901.75 105.83 1.3%q4 73.7 55.8 850.70 107.24 907.55 936.50 107.24 1.3%1998 282.0 227.0 5.5 9.0 3,594.00 3,336.00 105.14 3,594.00 105.14

0q1 76.0 55.4 916.60 1.0309 941.10 106.23 –0.9%q2 78.3 54.8 923.85 1.0315 943.40 107.73 1.4%q3 80.6 54.2 931.10 1.0325 945.70 109.28 1.4%q4 83.1 53.6 939.45 1.0451 948.80 111.01 1.6%1999 318.0 218.0 4.0 11.5 3,779.00 3,711.00 3,779.00 108.56

0q1 85.5 53.2 953.80 1.0135 107.67 –3.0%q2 88.2 52.7 958.85 1.0164 109.49 1.7%2q3 90.8 52.1 962.35 1.0176 111.20 1.6%q4 93.5 52.0 972.00 1.0245 113.73 2.3%2000 358.0 210.0 3.0 13.5 3,908.97 3,847.00 110.52

Step 1: Compile estimates for each quarter at the annual average prices of the previous year.e.g.: q1 1998 7.0 • 67.4+6.0 • 57.6 = 817.00

q4 1998 7.0 • 73.7+6.0 • 55.8 = 850.70Step 2: Compile estimates for each quarter at the annual average prices of the same year.

e.g.: q1 1998 5.5 • 67.4+9.0 • 57.6 = 889.10q4 1998 5.5 • 73.7+9.0 • 55.8 = 895.60

Step 3: Convert the constant price estimates for each quarter of the first year after the chosen reference year (1997) into a volume index with the average of the previous year = 100e.g.: q1 1998 [817.4/(3173.0/4)] • 100 = 103.04

q4 1998 [850.7/(3173.0/4)] • 100 = 107.24Step 4: For the other years, based on the constant price estimates derived in steps 1 and 2, calculate the volume change from the same quarter of the

proceeding year as the following:e.g.: q1 1999/q1 1998 916.60 / 889.10 = 1.0309

q4 1999/q4 1998 939.45 / 907.55 = 1.0451Step 5: Link the quarterly volume indices with shifting base and reference year using the changes from the same period of the previous year as linking

factors (extrapolators).e.g.: q1 1999 1.0309 • 103.04 = 106.23

q4 1999 1.0451 • 107.24 = 111.07q1 2000 1.0135 • 106.23 = 107.67

Observe that the unweighted annual average of the derived chain-linked quarterly index series is only approximately equal to the independently derived chain-linked annuals.

e.g.: 2000 [107.67+109.49+111.20+113.73]/4 = 110.52 ≠ 110.51Finally, observe that the rate of change from q4 in one year to q1 in the next year in the chain-linked series based on the over-the-year technique differs sub-stantially from the corresponding changes in chain-linked index based on a one-quarter overlap in the previous example.

e.g.: q1 1999/q 4 1998 based on the over-the-year technique (106.23/107.24–1) • 100 = –0.9%≠ q1 1999/q 4 1998 based on one-quarter overlap (and 1998 prices): (108.31/107.24–1) • 100 = 1.0%

q1 2000/q 4 1999 based on the over-the-year technique (107.67/111.01–1) • 100 = –3.0%≠ q1 2000/q 4 1999 based on one-quarter overlap (and 1999 prices): (111.60/111.01–1) • 100 = 0.5%

Observe also that the rate of change from q4 in one year to q1 in the next year in the chain-linked series based on the over-the-year technique differs sub-stantially from the corresponding changes in the constant price measures based on the average prices of the current year. That is, q1 1999/q 4 1998 based onaverage 1999 prices (953.8/936.50–1) • 100 = 0.5%

These differences between the q4-to-q1 rate of change in the chain-linked series based on the over-the-year technique and the corresponding rate of changebased on direct measurements are the steps in the series introduced by the technique. Notice also that, in this example, the break appears to increase over time,that is, the breaks are cumulative.The breaks will be cumulative if there is a trend-wise change in relative prices and relative quantities, as in this example.


162

Chart 9.1 Chain-Linking of QNA Data

102

104

106

108

110

112

114

116

118

120

122

1998 1999 2000

Fixed-base Laspeyres index. 1997=100

One-quarter overlap

Annual overlap

The over-the-year technique

Index Levels 1997=100

1998 1999 2000

Quarter-to-Quarter Rates of Change

–4%

–3%

–2%

–1%

0%

1%

2%

3%


One-quarter overlap

Annual overlap


0%

1%

2%

3%

4%

5%

6%

7%

8%

19991998 2000


One-quarter overlap

Annual overlap


Rates of Change From the Same Period of the Previous Year

All other indices in common use are nonadditive.22

Example 9.5.a. illustrates the difference betweenconstant price data and chain volume measures pre-sented in monetary terms and shows the loss of addi-tivity stemming from chain-linking.

6. Chain-Linking, Benchmarking, SeasonalAdjustment, and Compilation ProceduresRequiring Additivity

9.43. Benchmarking and seasonal adjustmentrequire long consistent time series with a fixed refer-ence period at a detailed level, while many standardnational accounts compilation methods require addi-tive data. Examples of national accounts compilationmethods requiring additive data include estimating

value added as the difference between output andintermediate consumption, commodity flow tech-niques, and use of SU tables as a integrating frame-work. Both requirements may appear inconsistentwith chain-linking, but they may not be.

9.44. In practice, the problem of nonadditivity can inmost cases be circumvented by using the followingmultistep procedure (or its permutations):

Step 1

At the most detailed compilation level, construct longtime series of non-seasonally adjusted traditionalconstant price data with a fixed-base year and corre-sponding Paasche price deflators using benchmark-ing, commodity flow, and other standard nationalaccounts compilation techniques. These constantprice data may be reconciled within an SU-tableframework, if desired.


163

22The reason for non-additivity is that different weights are used fordifferent annual periods, and therefore, will not yield the same resultsunless there have been no shifts in the weights.

Example 9.5.a. Chain-Linking and Nonadditivity

This example illustrates the difference between constant price data and chain volume measures presented in monetaryterms and shows the loss of additivity stemming from chain-linking.The basic data are the same as in Examples 9.4.a, b, and c.

Chain VolumeMeasures

for the TotalBasic Data Referenced to Chain

Quanti- Quanti- Chain- its Average Discre-ties ties Price Price At Constant 1997 Prices Linked Current price pancyA B A B Item A Item B Total Index Level in 1997 (10)=(1) (2) (3) (4) (5)=(1)•(3) (6)=(2)•(4) (7)=(6)+(6) (8) (9)=(8)•3173.0/4 (7)– (8)

1997 251.0 236.0 7.0 6.0 1,757.0 1,416.0 3,173.0 100.00 3,173.0 0.0q1 1998 67.4 57.6 471.8 345.6 817.4 103.04 817.4 0.0q2 1998 69.4 57.1 485.8 342.6 828.4 104.43 828.4 0.0q3 1998 71.5 56.5 500.5 339.0 839.5 105.83 839.5 0.0q4 1998 73.7 55.8 515.9 334.8 850.7 107.24 850.7 0.0

q1 1999 76.0 55.4 532.0 332.4 864.4 107.26 850.8 13.6q2 1999 78.3 54.8 548.1 328.8 876.9 108.10 857.5 19.4q3 1999 80.6 54.2 564.2 325.2 889.4 108.95 864.3 25.1q4 1999 83.1 53.6 581.7 321.6 903.3 109.93 872.0 31.3

q1 2000 85.5 53.2 598.5 319.2 917.7 109.60 869.4 48.3q2 2000 88.2 52.7 617.4 316.2 933.6 110.18 874.0 59.6q3 2000 90.8 52.1 635.6 312.6 948.2 110.58 877.2 71.0q4 2000 93.5 52.0 654.5 312.0 966.5 111.69 886.0 80.5

The chain-linked Laspeyres volume index in column 8 was derived in Example 9.4.a.

The chain discrepancies are zero for all quarters in 1998 because the 1998 link in the chain-linked Laspeyres index in column 8 is based on1997 weights.

Finally, observe that the chain discrepancies for 2000 are substantially larger than for 1999.This is a general result.The chain discrepanciesincrease the more distant the reference period is if the weight changes are trend-wise and not cyclical.

Step 2Aggregate these detailed constant price data using oneof the following two alternative procedures:

A. Annual chain-linked Laspeyres framework(i) For each year, revalue all detailed constant price

data to the constant average prices of the previ-ous year.

(ii) Add together these revalued data measured at theaverage prices of the previous year to construct thevarious aggregates and subaggregates at the con-stant average prices of the previous year.

(iii) Construct long time series with a fixed referenceyear by chain-linking the aggregates and subag-gregates at the constant average prices of the pre-vious year, using the annual overlap technique inExample 9.4.a or the one-quarter overlap tech-nique in Example 9.4.b (preferred).

B. All index formulasUse the price-quantity version of the relevant indexformula,23 and treat in the formula the detailed constantprice data as if they were quantities and the detailedprice deflators as if they were prices.

Aggregation procedures A and B in step 2 will givethe same results for annually chain-linked Laspeyresindices.

9.45. The multistep procedure outlined above alsocan be used for indirect seasonal adjustment of aggre-gates. In that case, to obtain the best seasonallyadjusted estimates, aggregation to an intermediatelevel before seasonally adjusting the various compo-nents may be required for the reasons given inChapter VIII, Section D.3.a, which discusses the prosand cons of direct versus indirect seasonal adjustmentof aggregates.

7. Presentation of Chain-Linked Measures

9.46. There are some important aspects to considerin presenting chain-linked measures in publications: • Whether to present measures of percentage change

or time series with a fixed reference period.• Whether to present time series as index numbers or

in monetary terms. • Terminology to avoid confusing chain-linked mea-

sures in monetary terms for constant price data(fixed-based measures).

• Choice of reference year and frequency of refer-ence year change—among others, as a means toreduce the inconvenience of nonadditivity associ-ated with chain-linked measures.

• Whether to present supplementary measures ofcontribution of components to percentage changein aggregates.

9.47. Chain-linked price and volume measuresmust, at the minimum, be made available as timeseries with a fixed reference period. The main rea-son is that data presented with a fixed referenceperiod allow different periods and periods of differ-ent duration to be compared and provide measuresof long-run changes. Thus, presentation of priceand volume measures should not be restricted topresenting only tables with period-to-period oryear-on-year percentage change nor tables witheach quarter presented as a percentage of a previousquarter. For users, tables with percentage changesderived from the time series may represent a usefulsupplement to the time series with a fixed referenceperiod and may be best suited for presentation ofheadline measures. Tables with such data cannotreplace the time-series data with a fixed referenceperiod, however, because such tables do not pro-vide the same user flexibility. Tables with eachquarter presented as a percentage of a previousquarter (e.g., the previous quarter or the same quar-ter in the previous year) should be avoided becausethey are less useful and can result in users confus-ing the original index with the derived changes.Restricting the presentation of price and volumemeasures to presenting changes only runs counterto the core idea behind chain-linking, which is toconstruct long-run measures of change by cumulat-ing a chain of short-term measures.

9.48. Chain-linked volume measures can be pre-sented either as index numbers or in monetary terms.The difference between the two presentations is inhow the reference period is expressed. As explained inparagraph 9.26, the reference period and level can bechosen freely without altering the rates of change inthe series. The index number presentation shows theseries with a fixed reference period that is set to 100,as shown in Examples 9.4.a, b, and c. The presentationis in line with usual index practice. It emphasizes thatvolume measures fundamentally are measures of rel-ative change and that the choice and form of the ref-erence point, and thus the level of the series, isarbitrary. It also highlights the differences of chain-linked measures from constant price estimates and


164

23For value added, the “double indicator” version of the formulasshould be used.

prevents users from treating components as additive.Alternatively, the time series of chain-linked volumemeasures can be presented in monetary terms by mul-tiplying the series by a constant to equal the constantprice value in a particular reference period, usually arecent year. While this presentation has the advantageof showing the relative importance of the series, theindication of relative importance can be highly sensi-tive to the choice of reference year and may thus bemisleading.24 Because relative prices are changingover time, different reference years may give very dif-ferent measures of relative importance. In addition,volume data expressed in monetary terms maywrongly suggest additivity to users who are not awareof the nature of chain-linked measures. On the otherhand, they make it easier for users to gauge the extentof nonadditivity. Both presentations show the sameunderlying growth rates and both are used in practice.

9.49. Annually chain-linked Laspeyres volume mea-sures in monetary terms are additive in the referenceperiod. The nonadditivity inconvenience of chainvolume measures in monetary terms may further bereduced by simultaneously doing the following:• Using the average of a year and not the level of a

particular quarter as reference period.• Choosing the last complete year as reference year.• Moving the reference year forward annually.This procedure may give chain volume measures pre-sented in monetary terms that are approximatelyadditive for the last two years of the series. As illus-trated in Example 9.5.a, the chain discrepancyincreases (unless the weight changes are cyclical ornoise) the more distant the reference year is. Thus, asillustrated in Example 9.5.b, moving the referenceyear forward can reduce the chain discrepancies sig-nificantly for the most recent section of the timeseries (at the expense of increased nonadditivity atthe beginning of the series). For most users, additiv-ity at the end of the series is more important thanadditivity at the beginning of the series.

9.50. To avoid chain discrepancies completely for thelast two years of the series, some countries haveadopted a practice of compiling and presenting data forthe quarters of the last two years as the weighted annualaverage prices of the first of these two years. That

second-to-last year of the series is also used as refer-ence year for the complete time series. Again the refer-ence year is moved forward annually. This approachhas the advantage of providing absolute additivity forthe last two years. The disadvantage, however, is that italso involves a series of back-and-forth changes in theprice weights for the last two years, with added revi-sions to the growth rates as a result.

9.51. Chain-linked volume measures presented inmonetary terms are not constant price measures andshould not be labeled as measures at “Constant xxxxPrices.” Constant prices means estimates based onfixed-price weights, and thus the term should not beused for anything other than true constant price databased on fixed-price weights. Instead, chain-volumemeasures presented in monetary terms can bereferred to as “chain-volume measures referenced totheir nominal level in xxxx.”

9.52. The inconvenience for users of chain-linkedmeasures being nonadditive can be reduced some-what by presenting measures of the components’con-tribution to percentage change in the aggregate.Contributions to percentage change measures areadditive and thus allow cross-sectional analysis suchas explaining the relative importance of GDP compo-nents to overall GDP volume growth. The exact for-mula for calculating contribution to percentagechange depends on the aggregation formula used inconstructing the aggregate series considered and thetime span the percentage change covers. The follow-ing provides a sample of the most common cases:

• Contribution to percentage change from period t–nto t in current and constant price data:

(9.9)

• Contribution to percentage change from period t–1to t in a period-to-period as well as in an annuallychain-linked25 Laspeyres index series:

(9.8)

Where wi, t–1 is the base period “share weight,” thatis, the item’s share in the total value of period t –1.

% –, – , – , , – , –∆ i t t i t i t i t i i tiw I I w I1 1 1 1100( )→ = ⋅ ⋅ ⋅( ) ∑

% –

, ..

, – , , – , –∆ i t n t i t i t n i t niX X X

n

( )→ = ⋅( )∈ { }

∑100

1 2


165

25The formula assumes that the series is linked using the one-quarteroverlap technique.

24For the same reason, measuring relative importance from constantprice data can be grossly misleading. For most purposes, it is better tomake comparisons of relative importance based on data at currentprices—these are the prices that are most relevant for the period forwhich the comparisons are done, and restating the aggregates relativeto prices for a different period detracts from the comparison.

For a period-to-period chain-linked Laspeyres indexseries, as equation (9.5), the share weights are

Correspondingly, for an annually chain-linkedLaspeyres index series the share weights are

where year y – 1 is the base year for each short-term link in the index as given by equation (9.7.a).

• Contribution to percentage change from period t–1to t in a period-to-period chain-linked Fisher vol-ume index series:

(9.9)

where PFt is the Fisher price index for the aggregate in

period t with period t – 1 as base and reference period.

9.53. The nonadditivity inconvenience of chain-link-ing often can be circumvented by simply noting thatchain Laspeyres volume measures are additive withineach link. For that reason, chain-linked Laspeyresvolume measures, for instance, can be combined withanalytical tools like constant price SU and IOtables/models that require additivity.26

%–

, –

, , – , , –

, , – , –

∆ i t

i t tF

i t i t i t

i t tF

i ti i t

p P p q q

p P p q1 1

1 1

1 1

100( )→ = ⋅+ ⋅

+ ⋅

( ) ( )( )∑

w p q p qi y i y i y i y i yi, – , – , – , – , – ,1 1 1 1 1= ⋅ ⋅∑

w p q p qi t i t i t i t i ti, – , – , , – , – .1 1 1 1= ⋅ ⋅∑


166

26In fact, the first countries to adopt annually chain-linked volumemeasures as their official national accounts volume measures used SUtables as their integrating GDP compilation framework.

Example 9.5.b. Choice of Reference Period and Size of the Chain Discrepancy

This example illustrates how moving the reference period forward may reduce the nonadditivity inconvenience of chain volumemeasures.The basic data are the same as in Examples 9.4 and 9.5.a.


for the TotalBasic Data Chain Referenced to Chain

Quanti- Quanti- Linked- its Average Discre-ties ties Price Price At Constant 1999 Prices Index Current price pancyA B A B Item A Item B Total 1999=100 Level in 1999 (10)=(1) (2) (3) (4) (5)=(1)•(3) (6)=(2)•(4) (7)=(5)+(6) (8) (9)=(8) •3394.2/4 (7)–(8)

q1 1998 67.4 57.6 269.6 662.4 932.0 94.92 896.8 35.2q2 1998 69.4 57.1 277.6 656.6 934.2 96.20 908.8 25.4q3 1998 71.5 56.5 286.0 649.7 935.7 97.49 921.0 14.8q4 1998 73.7 55.8 294.8 641.7 936.5 98.79 933.3 3.2q1 1999 76.0 55.4 304.0 637.1 941.1 98.80 933.4 7.7q2 1999 78.3 54.8 313.2 630.2 943.4 99.68 940.8 2.6q3 1999 80.6 54.2 322.4 623.3 945.7 100.36 948.2 –2.5q4 1999 83.1 53.6 332.4 616.4 948.8 101.26 956.7 –7.91999 318.0 218.0 4.0 11.5 1,272.0 2,507.0 3,779.0 100.00 3,779.0 0.0q1 2000 85.5 53.2 342.0 611.8 953.8 100.96 953.8 0.0q2 2000 88.2 52.7 352.8 606.0 958.8 101.49 958.8 0.0q3 2000 90.8 52.1 363.2 599.1 962.3 101.86 962.3 0.0q4 2000 93.5 52.0 374.0 598.0 972.0 102.88 972.0 0.0

First, the chain-linked index in column 8 is obtained by re-referencing the chain-linked index derived in Example 9.4.a, to average 1999=100.Theoriginal index series derived in Example 9.4.a was expressed with 1997=100. Changing the reference period to 1999 simply means dividing theoriginal index series by its average level in 1999 (102.5).e.g.: q1 1998 103.04 / 1.0856 = 94.92

q3 1998 105.83 / 1.0856 = 97.49q1 1999 107.26 / 1.0856 = 98.80q4 1999 109.93 / 1.0856 = 101.26q4 2000 111.69 / 1.0856 = 102.88

The chain discrepancies are zero for all quarters in 2000 because the 2000 link in the original chain-linked Laspeyres index derived in Example9.4.a is based on 1999 weights.

Finally, observe that the chain discrepancies for 1998 are substantially larger than for 1999. Again, we see that the chain discrepancies increase themore distant the reference period is.

Annex 9.1. Aggregation Over Time and Consistency Between Annual and Quarterly Estimates

167

A. Introduction

9A1.1. This annex provides a formal presentation ofthe following conclusions about annual and quarterlyLaspeyres-type volume measures with correspondingPaasche deflators reached in Section B of the chapterand illustrated in Example 9.1:(a) To ensure consistency between quarterly and

annual data, annual Paasche deflators should inprinciple be derived as current period weightedaverages of monthly or quarterly price deflators,where the weights represent constant price data.

(b) These annual deflators correspond to quantity-weighted period-average price measures and,equivalently to being derived as in conclusion (a),can be constructed directly from current periodquantity-weighted average annual prices.

(c) Quarterly Paasche price indices should be basedon the quantity-weighted average of each item’sprices in the quarters of the base year and not onunweighted averages as typically used in priceindex compilations, to ensure that in the base yearthe annual sum of the quarterly constant priceestimates is equal to the annual sum of the currentprice data.

(d) Deflating quarterly data with deflators con-structed with unweighted average prices as theprice base corresponds to valuing the quantitiesusing their unweighted annual average pricerather than their weighted annual average price.

(e) Valuing the quantities using their unweightedannual average price rather than heir weightedannual average price causes the annual sum of thequarterly constant price estimates in the base year todiffer from the annual sum of the current price data.

(f) The error in conclusion (e) can be removed by amultiplicative adjustment of the complete constantprice time series. The adjustment factor is the ratioof the annual current price data to the sum of the ini-tial quarterly constant price data based on theunweighted annual average prices in the base year,which, for a single product, is identical to the ratioof the weighted to the unweighted average price.

The two first conclusions are formally shown inSection B and the last four conclusions in Section Cof this annex.

B. Relationship Between Quarterly and AnnualDeflators

9.A1.2. Quarterly data at current prices, at the “aver-age” prices of the base year (year 0), and the corre-sponding (implicit) quarterly deflator with theaverage of year 0 as base and reference period can beexpressed mathematically as the following:• At current prices:

(9.A1.1)

• At the “average” prices of the base year:

(9.A1.2)

• Quarterly deflator (quarterly fixed-base Paascheindex):27

(9.A1.3)

wherepi,q,y is the price of item i in quarter q of year y;qi,q,y is the quantity of item i in quarter q of year y;

PPV

CP

p q

p q

q yq y

q y

i q y i q yi

i q yi

0

0

00

→( ) =

≡⋅

⋅∑∑

,,

,

, , , ,

, ,

CP p q

pp q

q

pq

q

q y i i q yi

ii q i qq

i qq

i qqi q

i qq

, , , ,

,, , , ,

, ,

, ,, ,

, ,

,0 0

00 0

0

00

0

= ⋅

=⋅

≡ ⋅

∑∑

∑

∑ ∑

V p qq y i q y i q yi, , , , ,= ⋅∑


27In the remainder of this annex, index numbers are presented with thefollowing syntax: Type of index (Reference period)➝ (Current period)(base period).Using the following codes for the elements of the syntax: LQ for aLaspeyres volume index, PP for a Paasche price index,

—y–1 for aver-

age year y–1, and (q,y) for quarter q of year y.

Vq,y is the total value at current prices in quarterq of year y;

–pi,0 is the quantity-weighted annual arithmeticaverage of the price of item i in each quarterof year 0; and

CPq,y–0 is the total value in quarter q of year y mea-

sured at the annual average prices of year 0.

The quarterly deflator can either be implicitly derivedas the current price value divided by the constantprice value (Vq,y /CPq,y –

0) or explicitly as a quarterlyfixed-base Paasche index with the weighted averageprices in year 0 (–pi,0) as the price base.

9.A1.3. Similarly, annual data at current prices, atthe “average” prices of the base year (year 0), andthe corresponding (implicit) annual deflator withthe average of year 0 as base and reference periodcan be expressed mathematically as the following:• At current prices:

(9.A1.4)

• At the “average” prices of the base year:

(9.A1.5)

• Annual deflator (annual fixed-base Paasche index):

(9.A1.6a)

where

vi,q,y is the value of item i at current prices in quar-ter q of year y; and

CPy–0 is the total annual value for year y measured

at the annual average prices of year 0.

9.A1.4. Equations (9.A1.1) to (9.A1.6a) show that toensure consistency between quarterly and annual

data, annual Paasche deflators should in principle becurrent period weighted averages of the quarterlyprice deflators (PP –

0→(q,y) –0 ), where the weights

(CPq,y–0 /ΣqCPq,y–

0) are based on current periodconstant price data, as stated in paragraph 9.A1.1conclusion (a) above. These current period weightedaverages of the quarterly price deflators can either beimplicitly derived as the annual sum of the quarterlycurrent price data divided by the annual sum of thequarterly constant price data, or explicitly as aweighted average of monthly or quarterly priceindices.

9.A1.5. The implicit annual deflator in equation(9.A1.6a) can, as stated in paragraph 9.A1.1 con-clusion (b), equivalently be constructed directlyfrom current period quantity-weighted averageannual prices as evident from the following:

(9.A1.6b)

where–pi,y is the quantity-weighted annual arithmetic aver-

age of the price of item i in each quarter of yeary; and

–qi,y is the total annual quantity of item i in year y.

C. Annual Average Prices as Price Base

9.A1.6. In the base year 0, the annual sum of the quar-terly constant price data is given by the following:

(9.A1.7a)

9.A1.7. It follows that the annual sum of thequarterly constant price data is equal to the annualsum of the current price data in the base year, if, foreach item, the base price is the quantity-weightedaverage of the item’s prices in each quarter of thebase year. That is, the base price is derived as –pi,0 = Σq pi,q,0 • qi,q,0 /Σq qi,q,0.This conclusion isevident from the following:

CP CP p qqq i i qiq0 0 0 00 0= = ⋅∑ ∑∑, , , ,

PPV

CP

p q

p q

p q

p q

pp q

qq q

y

q yq

q yq

i q y i q yiq

i i q yiq

i y i yi

i i yi

i yi q y i q yq

i q yqi y i q y

0

0 0

00

→ =

=⋅

⋅=

⋅⋅

=⋅

=

∑∑

∑∑∑∑

∑∑

∑∑

,

,

, , , ,

, , ,

, ,

, ,

,, , , ,

, ,, , ,,when

qq∑

PPV

CP

PPCP

CP

y

q yq

q yq

q yq

q y

q yq

0

0

00

0

0

0

→

( )→( )

=

= ⋅

∑∑

∑ ∑

,

,

,

,

,

CP CP

p q

y q yq

i i q yiq

0 0

0

=

= ⋅

∑∑∑

,

, , ,

V v

p q

y i q yiq

i q y i q yiq

=

≡ ⋅

∑∑∑∑

, ,

, , , ,


168


169

(9.A1.7b)

9.A1.8. It follows furthermore, as stated in para-graph 9.A1.1 conclusion (c), that the quarterly defla-tors should be constructed with quantity-weightedaverage prices as the price base—as in equation(9.A1.3)—to ensure that in the base year the annualsum of the quarterly constant price estimates is equalto the annual sum of the current price data. This con-clusion is evident from the following in combinationwith equation (9.A1.7b):

(9.A1.7c)

9.A1.9. Deflating quarterly data with deflators con-structed with unweighted average prices as the pricebase, corresponds, as stated in paragraph 9.A1.1 con-clusion (d), to valuing the quantities using theirunweighted annual average price. This result is evi-dent from the following:

(9.A1.8)

wherepi,0 = 1/4Σq pi,q,0 is the unweighted annual arith-

metic average of the price ofitem i in each quarter of year 0;andis a Paasche index (deflator)constructed with unweightedaverage prices as price base.

9.A1.10. As stated in paragraph 9.A1.1 conclusion(e) above, in the base year, the constant price dataderived in equation (9.A1.8), in contrast to the con-stant price data derived in equation (9.A1.7), do notsum to the annual sum of the current price data.However, as stated in paragraph 9.A1.1 conclusion(f), this error can be removed by a multiplicativeadjustment, using the following adjustment factor:

(9.A1.9a)

That is, the ratio of the annual current price data tothe sum of the initial quarterly constant price databased on the unweighted annual average prices in the base year. This factor, for a single product, is identical to the ratio of the weighted andunweighted average price:

(9.A1.9b)p q

p q

p q q

p

p

p

i i qq

i i qq

i i qq i qq

i

i

i

, , ,

, , ,

, , , , ,

,

,

,

ˆ ˆ

ˆ

0 0

0 0

0 0 0

0

0

0

⋅

⋅=

⋅

≡

∑∑

∑ ∑

CP

CP

p q

p q

p q

p q

V

CP

qq

qq

i i qiq

i i qiq

i q i qqi

i i qqi

qq

qq

,

,

, , ,

, , ,

, , , ,

, , ,

,

,

ˆ

ˆ

0

0

0 0

0 0

0 0

0 0

0

0

0

0

0

∑∑

∑∑∑∑∑∑∑∑

∑∑

=⋅

⋅

≡⋅

⋅≡

p q

p qi q y i q yi

i q i q yi

, , , ,

, , , ,ˆ

⋅⋅

∑∑ 0

CP Vp q

p q

p qp q

p q

p q

q y q yi q y i q yi

i q i q yi

i q y i q yii q y i q yi

i q i q yi

i i q yi

, ,, , , ,

, , , ,

, , , ,, , , ,

, , , ,

, , ,

ˆ

ˆ

ˆ

00

0

0

=⋅⋅

≡ ⋅⋅⋅

≡ ⋅

∑∑

∑ ∑∑

∑

CPV

PP

p qp q

p q

p q

qq

q

i q i qii q i qi

i qi

i qi

,,

,

, , , ,, , , ,

, ,

, ,

00

0 0

0 00 0

0 0

0 0

00

=

= ⋅⋅

⋅

≡ ⋅

→( )

∑ ∑∑

∑

CP p q

p q

qq

p q V

i i qqi

i q i qi

i qqi qqi

i q i qqi

0 0 0

0 0

00

0 0 0

0= ⋅( )=

⋅⋅

≡ ⋅ ≡

∑∑

∑∑ ∑∑

∑∑

, , ,

, , , ,

, ,, ,

, , , ,


Annex 9.2. Annual Chain-Linking of Quarterly Laspeyres Volume Measures:A Formal Presentation of the Annual and One-Quarter Overlap Techniques

170

A. The Annual Overlap Technique

9.A2.1. Quarterly estimates at the quantity-weightedaverage prices of the previous year (year y–1) aregiven as

(9.A2.1)

wherepi,q,y–1 is the price of item i in quarter q of year y–1;qi,q,y–1 is the quantity of item i in quarter q in year y;–qi,y–1 is the simple arithmetic average of the quan-

tities of item i in the quarters of year y–1; –pi,y–1 is the quantity weighted arithmetic average

of the price of item i in the quarters of yeary–1; and

CPq,y —y–1 is the total value in quarter q of year y mea-

sured at the average prices of year y – 1.

9.A2.2. The corresponding short-term quarterlyLaspeyres volume index and (implicit) Paaschedeflator series with the average of the previousyear as base and reference period are given as thefollowing:28

• Short-term quarterly Laspeyres volume index:

(9.A2.2)

• Short-term (implicit) quarterly Paasche deflator:

(9.A2.3)

wherewi,y–1 is the base-period weight, that is,

item i’s share of the total value inperiod y–1 at current prices;

Vq,y–1 is the total value at current prices inquarter q of year y;

LQ —(y–1)➝ (q,y) —

(y–1) is a Laspeyres volume index for quar-ter q of year y with average year y–1as base and reference period; and

PP —(y–1)➝ (q,y) —

(y–1) is a Paasche price index (deflator) forquarter q of year y with average yeary–1 as base and reference period.

PPV

CP

p q

p q

y q y yy

q y

q y

i q y i q yi

i y i q yi

− →( ) −=

=⋅⋅

∑∑

1 11

1

,

–

,

,

, , , ,

, – , ,

LQCP

V

p q

p q

p q

p q

p q

y q y y

yq y

q yq

i y i q yi

i y i q yiq

i y i q yi

i yi i q yq

i y i q

− →( ) −

−=

≡⋅

⋅

≡⋅

⋅

≡⋅

∑∑

∑∑∑

∑ ∑

1 1

1

14

14

1

1

1 1

1

1 1

1

14

,

,

, –

, – , ,

, – , , –

, – , ,

, – , , –

, – , ,,

, – , , –

, ,

, –

, – , –

, – , , –

, ,

, –, –

yi

i y i q yi

i q y

i yi

i y i y

i y i q y

i q y

i yi i y

p q

q

q

p q

p q

q

qw

∑∑

∑ ∑

∑

⋅

≡

⋅

⋅⋅

= ⋅

1 1

1

1 1

1 1

11

CP p q

pp q

q

q y y i y i q yi

i yi q y i q yq

i q yq

, , – , ,

, –, , – , , –

, , –

,−

= ⋅

=⋅

∑∑

∑

1 1

11 1

1

28In the remainder of this annex, index numbers are presented with thefollowing syntax: Type of index (Reference period)➝ (Current period)(base period).Using the following codes for the elements of the syntax: LQ for aLaspeyres volume index, CLQ for a chain-linked Laspeyres volumeindex, PP for a Paasche price index, CPP for a chain-linked PaaschePrice index,

—y –1 for average year y–1, and (q,y) for quarter q of year y.

Annex 9.2. Annual Chain-Linking of Quarterly Laspeyres Volume Measures

171

9.A2.3. Similarly, the short-term annual Laspeyresvolume index and Paasche deflator series with theaverage of the previous year as base and referenceperiod are given as the following:

• Short-term annual Laspeyres volume index:

(9.A2.4)

• Short-term annual Paasche deflator:

(9.A2.5)

9.A2.4. Thus, the long-term annually chain-linkedquarterly Laspeyres volume index and Paasche defla-tor can be constructed as the following:

• Long-term annually chain-linked quarterlyLaspeyres volume index:

For measuring the overall change from the averageof year 0 (the reference year) to quarter q of year 2:

(9.A2.6a)

For measuring overall change from the average ofyear 0 (the reference year) to quarter q of year Y:

(9.A2.6b)

• Long-term annually chain-linked quarterlyPaasche deflator:

For measuring the overall change from the averageof year 0 (the reference year) to quarter q of year 2:

(9.A2.7a)

For measuring overall change from the average ofyear 0 (the reference year) to quarter q of year Y:

(9.A2.7b)

9.A2.5. The corresponding monetary term chain-volume measure for quarter q of year Y with the aver-age of year 0 as reference base can be constructed asthe following:

(9.A2.8)MCQ CLQ p q

CLQ V

q Y i iiq Y

q Y

, , ,,

,

0 0

0

0 0

14 0

= ⋅ ⋅

= ⋅

( ) ( )

( ) ( )

→

→

∑

CPPp q

p qs

p q

p qq Y

i y i yi

i y i yiy

Yi q Y i q Yi

i Y i q Yi

0

11

1

1

( ) ( )=

→ =⋅

⋅⋅

⋅

⋅

∑∑

∏ ∑∑

,

, ,

, – ,

–, , , ,

, – , ,

CPPV

VCLQ

p q

p q

p q

p q

p q

p q

p q

q q

q

i q i qi

i ii

i ii

i ii

i i qi

i ii

i q i qi

0 2 0 2

2

0

2 2

0 0

0 1

0 0

1 2

1 1

2 2

( ) ( ) ( ) ( )→ →=

=⋅

⋅

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=⋅

∑∑

∑∑

∑∑

∑

, ,

,

, , , ,

, ,

, ,

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, , ,

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pp q

p q

p qi i qi

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, ,

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⋅

⋅∑∑∑

CLQq Y

i y i yi

i y i yiy

Yi Y i q Yi

i Y i Yi

p q

p q

p q

p q0

1

1 11

11

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,

, – ,

, – , –

–, – , ,

, – , –

CLQp q

p q

p q

p qq

i ii

i ii

i i qi

i ii0 2

0 1

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=⋅⋅

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∑∑

∑∑,

, ,

, ,

, , ,

, ,

PPp p

p q

p q

p q

y yy

i q y i q yiq

i y i q yiq

i y i yi

i y i yi

− → −

=⋅

⋅

≡⋅⋅

∑∑∑∑

∑∑

11 1

1

, , , ,

, – , ,

, ,

, – ,

LQCP

V

p q

p q

p q

p q

p q

y y

y

y

q yq

q yq

i y i q yiq

i y i q yiq

i y i q yqi

i y i q yqi

i y i q yi

− →

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⋅

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∑∑∑∑

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1

1 1

1

1 1

1

1 1

1

,

, –

, – , ,

, – , , –

, – , ,

, – , , –

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pp q

q

qw

q

qw

i y i q yi

i q yq

i q yqi i y

i y

i yi i y

, – , , –

, ,

, , –, –

,

, –, –

1 1

11

11

⋅

= ⋅

≡ ⋅

∑∑∑∑

∑


172

9.A2.6. The monetary term chain-volume measurein equation (9.A2.8) can alternatively be derived byrescaling the constant price levels directly using thecorresponding implicit annual Paasche deflator index(annually chain-linked). This follows from the fol-lowing elaboration of equation (9.A2.8), for simplic-ity only shown in a three-period context, andExample 9.A2.1 below:

(9.A2.9)

whereis the corresponding implicit annualPaasche deflator index with period 0as base and reference period.

B. The One-Quarter Overlap Technique

9.A2.7. The short-term Laspeyres volume indexseries in (9.A2.2) can be re-referenced to beexpressed with the fourth quarter of the previous yearas reference period as follows:

(9.A2.10)

whereis a Laspeyres volume index forquarter q of year y with averageyear y –1 as base period and thefourth quarter of the previousyear as reference period.

9.A2.8. Thus, the corresponding long-term chain-linked volume index measuring the overall changefrom the average of year 0 (the reference year) toquarter q of year 2 can be constructed as

(9.A2.11)

9.A2.9 And the long-term chain-linked volumeindex measuring the overall change from the averageof year 0 (the reference year) to quarter q of year Ycan be constructed as

(9.A2.12)

9.A2.10. The corresponding monetary term chainvolume measure with the average of year 0 as refer-ence base can be constructed as

(9.A2.13)

9.A2.11. The monetary term chain volume measurein (9.A2.13) can alternatively be derived by re-scal-ing the constant price levels directly using the corre-sponding implicit fourth quarter weighted annualPaasche deflator. This follows from the followingelaboration of equation (9.A2.13), which for simplic-ity is only shown in a three period context:

(9.A2.14)

whereis the corresponding implicit fourth-quarter-weighted annual Paaschedeflator index with period 0 as baseand reference period.

p q

p qi ii

i ii

, , ,

, , ,

1 4 1

0 4 1

⋅⋅

∑∑

MCQ CLQ p q

p qp q

p q

p q

p q

p q

p q

q q i ii

i ii

i ii

i ii

i i qi

i ii

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i i

, , , ,

, ,, , ,

, ,

, , ,

, , ,

, , ,

, , ,

2 0 2 0 0

0 00 4 1

0 0

1 2

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0 4 1

0 4 1

0= ⋅ ⋅

= ⋅ ⋅⋅

⋅⋅

⋅

⋅

≡⋅

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( ) ( )→ ∑

∑ ∑∑

∑∑

∑ii

i i qi

i i qi

i ii

i i qi

p q

p qp q

p q

∑ ∑

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≡ ⋅⋅⋅

, , ,

, , ,, , ,

, , ,

1 2

1 21 4 1

0 2

MCQ CLQ p q

CLQ V

q Y q Y i ii

q Y

, , , ,

,

0 0 0 0

0 01

4

= ⋅ ⋅

= ⋅( )→( )

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∑

CLQ

p q

p q

p q

p q y

p q

p q

q Y

i ii

i ii

i y i yi

i y iiy

Yi i q Yi

i i Yi

( ) ,

, , ,

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0

0 4 1

0 0

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1 42

11

1 4 11

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p q

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p qqi ii

i ii

i ii

i ii( ) ,

, , ,

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1 4 2

1 4 1→( ) =

⋅⋅

⋅⋅⋅

∑∑

∑∑

LQ y q y y4 1 1, – , –( )→( )( )

LQp q

p q

p q

p q

p q

p q

y q yi y i q yi

i y i q yi

i y i q yi

i y i q yi

i y i q yi

i y i yi

y4 11

1 1

1

1 1

1

1 4 1

1, – ,, – , ,

, – , , –

, – , ,

, – , , –

, – , ,

, – , , –

–( ) ( )→ ( )=

⋅

⋅

⋅

⋅

≡⋅

⋅

∑∑

∑∑

∑∑

p q

p qi ii

i ii

, ,

, ,

1 1

0 1

⋅⋅

∑∑

MCQ CLQ p q

p qp q

p q

p q

p q

p q

p qp

q i ii

i ii

i ii

i ii

i i qi

i ii

i ii

i ii

i

q, , ,

, ,, ,

, ,

, , ,

, ,

, ,

, ,,

,2 0 0

0 00 1

0 0

1 2

1 1

0 1

1 11

0 0 2= ⋅ ⋅

≡ ⋅ ⋅⋅

⋅⋅

⋅

⋅

≡⋅

⋅⋅ ⋅

( ) ( )→∑

∑ ∑∑

∑∑

∑∑

qq

p qp q

p q

i qi

i i qi

i ii

i ii

, ,

, , ,, ,

, ,

2

1 21 1

0 1

∑

∑ ∑∑

≡ ⋅⋅⋅

Annex 9.2. Annual Chain-Linking of Quarterly Laspeyres Volume Measures

173

Example 9.A2.1. Quarterly Data and Annual Chain-LinkingAn Alternative “Annual Price Scaling” Version of the Annual Overlap Technique

Annual sums and averages in bold.The basic data are the same as in Example 9.4.This example provides an alternative presentation of the annual overlap chain-linking technique presented in Example 9.4.The final results are the same, but the procedure of obtaining the linked time series differs.


for the Total inMonetary Terms

At 1997 Implicit Referenced to itsTotal at Constant Paasche At 1998 Implicit At 1999 Average CurrentCurrent Prices Deflator Constant Paasche Constant Price Level

Prices 1998 = 100 1997 = 100 Prices Deflator Prices in 1997

1997 3,173.00 3,173.00 100.00 3,173.00q1 1998 871.94 817.40 106.67 817.40q2 1998 885.51 828.40 106.89 828.40q3 1998 910.05 839.60 108.40 839.60q4 1998 926.50 850.70 108.91 850.701998 3,594.00 3,336.00 107.73 3,594.00 100.00 3,336.00q1 1999 934.78 916.60 101.98 850.80q2 1999 963.07 923.85 104.25 857.53q3 1999 940.42 931.10 101.00 864.26q4 1999 940.73 939.45 100.14 872.011999 3,779.00 3,711.00 101.83 3,779.00 3,444.60q1 2000 955.70 953.80 869.40q2 2000 961.70 958.85 874.00q3 2000 973.22 962.35 877.19q4 2000 1018.36 972.00 885.992000 3,908.97 3,847.00 3,777.78Step 1: As in Example 9.4, compile estimates for each quarter at the annual average prices of the previous year; the annual data being the sum of the four quarters.

Step2: Derive the corresponding annual implicit Paasche deflators with the previous year as base and reference period.1998 [3594.0/3336.0] • 100 = 107.731999 [3779.0/3711.0] • 100 = 101.83

Step 3: Scale down the quarterly constant price estimates to measures at previous year’s average prices, to the average price level of 1997.e.g.: q1 1999 916.60/ 1.0773 = 850.80

q4 1999 939.45/ 1.0773 = 872.01q1 2000 953.80/ (1.0773 • 1.0183) = 869.40

Observe that the resulting monetary termed chain-linked volume measures are identical to the ones derived in Example 9.5.a.

174

X Work-in-Progress

A. Introduction

10.1. Work-in-progress concerns production thatgoes beyond one period. Measurement of such pro-duction poses the problem that a single process has tobe split into separate periods. Because of the shorteraccounting period, these difficulties are relativelymore significant for quarterly national accounts(QNA) than for annual national accounts (ANA).

10.2. The general national accounting principle isthat production should be measured at the time ittakes place and be valued at the prices of that time.In most cases, this treatment presents no problems,because the production process is short and thus out-put can be measured from the value of the finishedproduct. When the production process transcends asingle accounting period, however, production needsto be shown in two or more periods. This productionresults in output of unfinished products, which iscalled work-in-progress in both business andnational accounting. As stated in the 1993 SNA, “itwould distort economic reality to treat output as if itwere all produced at the moment of time when theprocess of production happens to terminate” (para-graph 6.39). Also, where prices have changed duringthe production process, the price paid at the end willinclude holding gains (or possibly losses) that needto be excluded in order to have a correct measure ofproduction.

10.3. There are many activities in which productioncycles go outside a single period. Even with veryshort processes, there can be work-in-progress. Someactivities have quite long production cycles and sowork-in-progress is particularly important. Theseactivities include the following:• Agriculture, animal husbandry, forestry, and fish-

ing. In agriculture, crops may grow over severalseasons. Similarly, growing livestock, cultivatingtimber, cultivating fruit, viticulture, and fish

farming are all cases where production occursover more than one period before the final outputis marketed. Also, wool is usually collected onlyonce a year.

• Manufacturing. Ships, submarines, airplanes, andsome heavy equipment have long productioncycles.

• Construction. The production cycle is often quitelengthy, varying from a few months for a house tomany years in the case of a civil engineeringproject.

• Services. Examples in this category are movies,architectural services, and large sport events.

10.4. This chapter first explores the general reasonswhy work on unfinished products is considered out-put. Subsequently, the principles of measurement andsome practical solutions are discussed. Briefly, thesolution for measuring of work-in-progress is to useoutput measures based on quarterly input costs inconjunction with values or markups for the wholeprocess. Where such costs are not available, proxiessuch as fixed proportions can be used.1

10.5. Recording work-in-progress poses special dif-ficulties for agriculture and related industries becauseof the uncertainties intrinsic to the dependence of theproduction process on forces of nature and because ofthe volatility of prices. Also, because the concept ofwork-in-progress is not generally applied in theseindustries, its application in national accounts isexposed to criticism denouncing it as artificial.2 It hasbeen suggested that most of the problems involved inapplying work-in-progress concepts to agriculturecould be solved through the application of seasonal

1As well as its direct effect on measuring output, work-in-progressalso has consequential effects on income accounts, capital accounts,and balance sheets. These effects are discussed in the annex.2Although examples can be mentioned in which prices do reflect thevalue of work-in-progress. One such example is keeping sheep forwool, where the price of sheep reflects the harvestable amount ofwool (prices plunge immediately after harvesting).

adjustment, but it should be emphasized that record-ing work-in-progress and seasonal adjustments areunrelated issues and that recording work-in-progressaffects the unadjusted estimates. These issues are dis-cussed in Section D.

10.6. Inclusion of work-in-progress affects many com-ponents of the accounts, but in a consistent way, so thatit does not create discrepancies. In addition to the effecton output, there is an equal effect on operating sur-plus/mixed income and other income aggregates. Onthe expenditure side, output in the form of work onunfinished products is classified either as fixed capitalformation or as changes in inventories of work-in-progress. It is part of fixed capital formation if it con-sists of construction work done on contract and put inplace in stages or if it consists of capital goods pro-duced on own account by their eventual final user. In allother cases, including speculative construction (that is,without a contract and not for own final use) and mostagricultural production, work-in-progress is included inchanges in inventories. Financial transactions are unaf-fected, except in the case of construction work on con-tract, because resulting changes in estimates on savingare fully absorbed in the estimates on fixed capital for-mation or changes in inventories for the same institu-tional unit. In the case of production of a capital goodunder contract, however, the full effect on savings forthe producer will be carried over to the financialaccount in the form of payments received from install-ments and other accounts receivable accrued.

10.7. Proper recording of work-in-progress has theadded advantage of removing production-related hold-ing gains and losses from the estimates, which shouldalso be done in ANA. The potential danger of leavingholding gains and losses in the estimates can be large,especially if inflation is substantial. If productionprocesses do not exceed the accounting period for theANA, the holding gains and losses involved in work-in-progress risk being ignored in the compilation of theseaccounts. An important message to the compilers ofANA is that they should also remove holding gains andlosses from their estimates on subannual productionprocesses, not only to ensure consistency between ANAand QNA, but also to achieve correct ANA estimates.

B. Why Should Work-in-Progress BeTreated as Output?

10.8. Production is “an activity in which an enter-prise uses inputs to produce outputs” (1993 SNA

paragraph 6.6, italics added). Thus, production is aprocess that leads to a distinct product, but therecording of inputs and outputs in the accounts is notdetermined by the time that the finished productbecomes available for use. Paragraph 6.39 of the1993 SNA explains this further as follows:

For simplicity, the output of most goods orservices is usually recorded when their pro-duction is finished. However, when it takes along time to produce a unit of output, itbecomes necessary to recognize that outputis being produced continuously and torecord it as work-in-progress.

10.9. While it is useful to emphasize that productionis a process rather than the resulting product, the def-initions are circular to the extent that the recognitionand measurement of production depend on the mean-ing of output. In the 1993 SNA, output does not meanfinished products but can be any goods or servicesthat “can be sold on markets or at least be capable ofbeing provided by one unit to another ...” (1993 SNAparagraph 1.20). For instance, an unfinished con-struction project or a crop growing in the field bothhave the quality of having value that can, at leastpotentially, be provided to another unit, and, hence,output can be recognized and measured.

10.10. In the absence of recognition of work onunfinished products as output, inputs would appear indifferent periods from the corresponding output. As aresult, value added could be negative in some periodsand disproportionally large in other periods. Thus,the meaning of value added for the affected periodswould be open for debate.3

10.11. An objection is sometimes made that recordingwork on unfinished products as output brings intrans-parency to the accounts. That is, it involves unnecessarycomplexity and artificiality and distorts the view ofincome generation and saving, because output does notgenerate money inflows before it is sold. Two argu-ments counter this view. First, transactions in thenational accounts need not necessarily involve actualmoney flows; well-known examples are barter transac-tions and wages in kind. Second, one could also argue

Why Should Work-in-Progress Be Treated as Output?

175

3Note that negative value added can legitimately occur (where nomarketable product appears at the end—for instance, an internalresearch project that failed—or where the marketable product is smallin relation to inputs—for instance, the start-up phase of a business orother loss-making situations). However, it is not desirable that nega-tive value added appears simply because of failure to recognize that aproductive process was occurring.

that disregard of work-in-progress results in artificialitybecause outlays on production would show up withoutany apparent link to output.

10.12. It is sometimes suggested that recordingwork-in-progress is relevant on the level of individ-ual units, but for the total economy, or even specificindustries, aggregation would cancel out the effectsof not recording work-in-progress. This would onlyapply in the situation of very stable period-to-periodproduction processes, however, which is highlyunlikely to reflect real conditions, particularly in thecontext of QNA.

C. Measurement of Work-in-Progress

1. Economic Concepts

10.13. The starting point for the theoretical and prac-tical issues in measurement of production is economictheory. The general principle of valuation in econom-ics is use of the transaction price. In a very few cases,an incomplete project may be marketed, such as whenan unfinished building project or a farm with crops inthe field changes hands. It is far more common, how-ever, that products are not sold until finished, so trans-action prices are not available for the unfinishedproduct. It is, therefore, necessary to adopt a conven-tion to value the production in each period.

10.14. The usual principle to value an item whenthere is no transaction is the market-equivalentprice. The market equivalent is what buyers wouldbe prepared to pay if they wished to obtain theunfinished product or what suppliers would need tobe paid to produce it. This value is equivalent to thetotal input costs for each period plus a markup.Because there is no separate markup for each quar-ter, the markup must be the ratio of output to costsfor the whole production cycle. In other words, thenet operating surplus is estimated as earned over theproduction cycle in proportion to costs in eachperiod.

10.15. In the rest of this section, the application ofthe convention of valuing work-in-progress carriedout in a certain quarter as input costs plus a markupis discussed in a business and national accountingcontext. The section also discusses methods to usewhen data are incomplete and how to account forthe effects of changes in prices during the produc-tion period.

2. Business Accounting Treatment of Work-in-Progress

10.16. Business accountants face the same problem ofsplitting incomplete production cycles into accountingperiods. Estimation of the value of work put in place ispart of an accrual accounting system. Businesses seek-ing to measure their own performance need to value thework put in place to match output with expenses andavoid lumpiness in their accounts. In the absence ofobservable prices, business accounts must also dependon input costs, with or without some markup.

10.17. However, there are two areas of differencebetween business accounting practice and economicconcepts. First, business measures of income do notdistinguish between holding gains and production,whereas this difference is fundamental in economicanalysis. Second, because of the doctrine of prudencein business accounting, work may be valued at lessthan the expected price (i.e., without a markup orwith an underestimated markup), so that profits arenot counted fully or at all until they are realized. Thisdelay in recognition of profits causes lumpiness at thecompletion of the work, but time-series consistencyis less important to business accounting.

10.18. There are three alternative arrangements forwork on products with long production cycles:• own final use,• contract, and• speculative basis (i.e., the final client is not known).

10.19. For work for own final use, the producer is thefinal user; for example, an electricity company buildsits own generating plant or distribution network. Inthis situation, there is no transaction price, even oncompletion. Accordingly, output is measured by theenterprise itself, ideally at a market-equivalent priceor, more typically, on the basis of input costs, includ-ing capital costs and overhead. If measured fromcosts, the data are already recorded on an ongoingbasis by the producer, and there is no more difficultyin measuring production in each period than there isin measuring the total project.

10.20. For contract work, there are different possiblepayment arrangements. A price may be fixed inadvance or variable; or paid by installments or at theend of the job. Progress payments are installmentsthat relate to the amount of work done. To the extentthat progress payments closely match work done,they already measure output on an ongoing basis.

X WORK IN PROGRESS

176

However, if payments are infrequent, delayed, orhave a substantial bonus component at the end, theygive a misleading time series, and a cost-based mea-sure would provide a better measure of production.

10.21. For work done on a speculative basis, there areno ongoing receipts, and usually the final value of theproduct is unknown until after completion. This situa-tion is common in manufacturing and construction. Inaddition, many agricultural products resemble specu-lative manufacturing or construction in that there is nosale or identified buyer until after the product is com-pleted. In contrast to manufacturing and construction,however, estimates of work-in-progress are not nor-mally made by farmers in their own accounts.

10.22. Measures of work-in-progress are often avail-able, particularly from larger and more sophisticatedproducers. Such estimates have the advantage that thedata are transparent and estimation is done at adetailed level with specific information. However,such data are not automatically suitable. For exam-ple, progress payments or installments may notmatch work done because of long lags or becausethere is a large component of bonus for the comple-tion of the job. Or it may also be too costly to collectbusiness data quarterly, for example, if building workis done by many small operators who are reluctant tocomplete statistical questionnaires. Or the quarterlydata may be too lumpy if the profit is only included atthe time of sale. In these circumstances, it is neces-sary to derive estimates for national accounts by mak-ing adjustments to business estimates.

3. Measurement in a National Accounts Context

10.23. The 1993 SNA’s recommendations on the val-uation of incomplete products follow from the eco-nomic concepts discussed in Subsection 1 of thissection and are partly compatible with the businesspractices discussed in Subsection 2. The 1993 SNArecommends following the businesses’ own estimatesif they approximate production, mentioning progresspayments on a contract (paragraph 6.74) and capitalgoods for own final use (paragraph 6.85). When noacceptable quarterly output data are available frombusinesses, the 1993 SNA principle is to measure pro-duction of incomplete products from costs for eachperiod, raised by a markup that relates to the wholeproduction cycle. The 1993 SNA considers two situa-tions for markup data: whether an estimate of thevalue of the finished product is available (paragraph6.77) or not (paragraph 6.78).

10.24. Changes in prices during the productioncycle affect the measurement of production. Whenprices are changing, the eventual value at the time ofcompletion will differ from the sum of the value ofwork-in-progress carried out in the production quar-ters, because the prices of that kind of product havechanged between the time of production and thetime of completion. The difference represents hold-ing gains or losses. In order to measure production,price changes between the time of production andthe time of sale must be removed from sellingprices. These problems can be avoided by compilingconstant price estimates first (to put all the flows ona consistent basis) and subsequently deriving thecurrent price estimates on the basis of the constantprice estimates. (This deflate-then-reflate method isfound in related areas of inventory valuation andcapital stock measurement where valuation alsoincludes prices from different periods.)

10.25. The measure of input costs should be as com-plete as possible. The input costs should include com-pensation of employees, intermediate consumption,taxes on production, and costs of using land and cap-ital (rent, consumption of fixed capital, and interest).In cases where owners and unpaid family membersare an important source of labor, it is desirable toderive a value for these inputs as well. In practice, thedata on costs may be incomplete, and so the markupneeds to be adjusted accordingly. Obviously, parts ofthese input costs are part of value added (for instance,compensation of employees) and some are includedin operating surplus/mixed income (for instance rentand interest). This does not preclude them, however,from being costs of production that must be takeninto account when estimating output from the costside.

10.26. Allocation of output on the basis of costsdoes not always apply in full. From the rationale forwork-in-progress—namely, allocating output toperiods in which production is occurring—it logi-cally follows that no output should be allocated toperiods in which there is no ongoing productionprocess, even if there are ongoing costs. Thisapplies in particular to the cost of using land andcapital, which may not correspond to the actual pro-duction process. For instance, interest on a loanfinancing a piece of equipment accrues over theperiod of the loan, no matter whether the equipmentis used. An example of a situation in which this mayapply is agriculture, where production may stopcompletely during certain periods. Food-processing

Measurement of Work-in-Progress

177

industries that are dependent on harvests coming inare also an example. In these cases, it is important toclearly define the production periods (for instance,in Nordic climates the agricultural production peri-ods may include fall when land preparation takesplace, exclude winter when no activities take place,and commence again in spring with seeding, fertil-izing, etc.).

10.27. Example 10.1 brings together the measure-ment issues discussed so far. It covers an ex post sit-uation, that is, after the completion of the productwhen the final price is known. Data on input costsare also available. In the example, the final price andcost data are used to derive a markup ratio for thewhole project. The example shows the derivation ofoutput estimates and, from that, the calculation ofholding gains.4

10.28. From the example, it is important to note thatholding gains are excluded from production measures.Hence, the output is 5040 in the example, not 5800. Asubstantial rate of price increases is assumed, so theholding gains are quite large in the example. It shouldalso be noted that the cost/markup ratio is derived atconstant prices (i.e., 4000/3000) and not at transactionprices (i.e., 5800/3780), because the latter includeholding gains. It is also worth noting that the quarterlyestimates of output, by definition, follow the samequarterly pattern as the costs. It can be seen that therecognition of work-in-progress results in a less lumpyseries for output. It is not a substitute for seasonaladjustment or calculation of a trend-cycle series, how-ever, because the series will still be subject to any sea-sonality or irregularity in the cost series.

10.29. Having established the general principles ofmeasurement, we will now consider some of the per-mutations arising from different data situations. Thesituations covered include deriving the markup when

X WORK IN PROGRESS

178

Example 10.1. Ex Post Estimation of Work-in-Progress with(a) Total Value of Project(b) Quarterly Costs

Objectives of example:(a) To illustrate the allocation of a total on the basis of costs.(b) To illustrate the inclusion of holding gains in the total value.Consider a speculative construction project taking place between January and December 1999. It is completed and sold at the end of

December 1999 for 5800.The objective is to produce output estimates for each quarter and exclude holding gains from the output esti-

mates.A high rate of price increases is assumed in order to highlight the effect of holding gains.

Primary Data

q1 1999 q2 1999 q3 1999 q4 1999 q1 2000

Output/input price index (average 1998 = 100) 110.0 120.0 130.0 140.0 150.0Production costs at current prices:Intermediate consumption 160 340 530 300+ Compensation of employees 300 310 340 400+ User-costs for use of land and capital, etc. 200 250 300 350=Total production costs at current prices 660 900 1170 1050

To simplify the calculations, the same price index is used for inputs and outputs; in principle, separate price measures should beused.

Step 1. Derive value of the project at average 1998 prices

Deflator value at the end of q4 1999 1/2(q4 1999 +q1 2000) =145.0Value at average 1998 prices 5800/1.45=4000

The value of the project at average 1998 prices is estimated by deflating the sales value with a price deflator that reflects changes in pricesof similar projects from average 1998 to the end of q4 1999.The price index given measures the average price level in each period of simi-lar construction products relative to their average price in 1998.Assuming a smooth change in prices over time, the deflator value at theend of q4 1999 can be estimated as approximately (140+150)/2=145.

4This example is designed to show concepts and may not be realisticfrom the point of view of data availability.

there are (a) other payment times; (b) quantities avail-able but not values; and (c) forecasts available insteadof actual prices for the final product. When markupsfor a particular period are not available, other sourcesof markups are considered. Where cost data are notavailable, the use of a cost profile is proposed.

10.30. In some cases, payment is not made at the com-pletion of the product. It may be made at the beginningof work or in several installments. An advance paymentreflects prices of the beginning of the period. If theprice is paid in installments, such as progress paymentsfor construction work, the payments are from severaldifferent periods and, hence, different price levels. Ineach case, by converting the payments to constantprices (using the price index of the time of payment),the measurement can be put on a consistent basis, andthe calculations can be made accordingly. (As dis-cussed earlier in this section, if progress paymentsclosely match production costs and timing, they shouldbe used directly to estimate output.)

10.31. In some cases, the data available on the finalproduct are in quantity terms, for instance, a housemeasured in square meters or a crop in tons. The prin-ciples of measurement are the same as in Example10.1, except that the constant price values are derivedby multiplying the volume measure by a price perunit in the base year. Current price values can bederived by multiplying the volume measure by aprice per unit in the current period. In the case ofsome crops, there are special problems in measuringprices in periods between harvests; these issues arediscussed in Section D of this chapter.

10.32. Forecasts may need to be used for incompletework if the value of the final product is not yet known.While national accountants do not normally use fore-casts, unfinished production may require forecasts, andsuch forecasts are often available. For example,builders often forecast a value of a project at the time ofseeking building approval. Also, in many countries theministry of agriculture (or another government agency)


179

Example 10.1 (continued)

Step 2. Derive costs at constant prices

q1 1999 q2 1999 q3 1999 q4 1999 Total

Production costs at 1998 prices 600 750 900 750 3000

In step 2, input estimates at constant prices are derived by deflating the current price values.

Step 3. Derive the output/cost ratioOutput to cost ratio at average 1998 prices—the markup ratio—(1.333) is derived as the value of the project (4000)/total costs (3000).The output/cost markup ratio is calculated for the project. It has to be derived at constant prices to exclude holding gains.

Step 4. Derive output at constant and current prices

q1 1999 q2 1999 q3 1999 q4 1999 Total

Output at average 1998 prices 800 1000 1200 1000 4000Output at current prices 880 1200 1560 1400 5040Quarterly output at 1998 prices is derived by raising the value of costs at 1998 prices by the output/cost ratio. Quarterly output at current prices is derivedby reflating the estimates of output at 1998 prices.Step 5. Derive value of the stock of work-in-progress at current prices

Value of work put in place Value at time ofcurrent prices Holding gains in subsequent quarters sale

q1 1999 q2 1999 q3 1999 q4 1999 Dec . 1999

q1 1999 880 40 80 80 80 1,160q2 1999 1,200 50 100 100 1,450q3 1999 1,560 60 120 1,740q4 1999 1,400 50 1,450Total 5,040 40 130 240 350 5,800

<---------------------------------760 ----------------------------------->

The derivation of holding gains is shown in this step. In this example, the output price index shows that the prices of similar construction projects increasedcontinuously during 1999.Thus, the prices are higher at the end of each quarter than in the beginning or middle of the quarter.As a result, the total cumulat-ed value of work put in place (5040) differs from the project sales value (5800), because prices have risen between the time of construction and time of sale;that is, the sales price includes both output and holding gains.

For example, the work put in place in q1 is worth 800 at 1998 prices, but 880 at average q1 prices (i.e., 800•1.1); 920 at the end of q1 (i.e., 800•(1.1+1.2)/2);1000 at the end of q2 (i.e., 800•(1.2+1.3)/2); 1080 at the end of q3 (i.e., 800•(1.3+1.4)/2); and 1160 at the end of q4 (i.e., 800•(1.4+1.5)/2).

makes crop forecasts based on an estimate of the outputof a certain crop. (These usually are in volume terms,but sometimes also in value terms.) These crop esti-mates are typically based on an estimate of the acreageunder cultivation combined with yield estimates.Estimates of acreage under cultivation could be basedon surveys or on aerial and satellite photography; yieldestimates could be based on average crop yields andrevised on the basis of expert views and trends. It maybe surmised that in many agricultural countries, thiskind of information is available. In some cases, it maybe necessary for the national accounts compilers tomake forecasts themselves. While forecast values differin being more uncertain and more subject to revision,the method for calculation of quarterly output is thesame as the ex post situation. Of course, when actualdata become available, the data should be revised andthe difference between the forecast and actual valueassessed for accuracy and signs of bias.

10.33. When there is no actual or forecast estimateof the finished value, the 1993 SNA recommendsestimation of output on the basis of costs plus anestimate of a markup from another source. The 1993SNA does not elaborate how this markup is to bederived; possible sources are studies on standardmargins used in a particular industry, a previousyear’s data, or comparable recently completed pro-jects. Example 10.2 demonstrates how such methodscould work in practice.

10.34. The concept and measurement of quarterlyproduction are the same in Examples 10.1 and 10.2.Only the source of the markup ratio is different; inExample 10.1, a markup ratio for the particular pro-ject is derived in steps 1 to 3; in Example 10.2, it istaken from previous data. The estimates made exante, as in Example 10.2, would need to be revisedwhen actual prices and volumes became available.5

The technique shown in Example 10.1 could then beused, so that the markup ratio assumed in advancecould be replaced by the actual one. If markup ratiosvary substantially from year to year, as is often thecase for agriculture, the revisions may be quite large.This danger looms large in situations in which outputdepends on exogenous factors, as is the case for agri-culture and related industries (for instance, if a locustplague necessitates an extraordinary use of pesticidesfor a certain crop). In such cases, a markup based ona forecast of the annual crop should be preferred tomarkups based on previous data.

10.35. Another common data situation is that quar-terly cost data are unavailable; in that case, a costprofile can be used instead. Actual data on inputcosts may not be available because of collectioncosts or because businesses do not keep separaterecords of costs for each project. An alternative in

X WORK IN PROGRESS

180

Example 10.2. Ex Ante Estimation of Work-in-Progress with(a) Quarterly Costs(b) Markup Ratio

Objective of example:To illustrate the calculation of work on the basis of costs and markup.

Primary Data

q1 1999 q2 1999 q3 1999 q4 1999

Output/input price index (average 1998 = 100) 110.0 120.0 .. ..Production costs at current prices 660 900 .. ..(wages and salaries, raw materials, etc.) .. ..

Industry standard average markup over costs,33.3% after excluding holding gains 1.333 (in ratio form)

Step 1. Derive output at current and constant prices

q1 1999 q2 1999 q3 1999 q4 1999

Production costs at average 1998 prices 600 750 .. ..Output at average 1998 prices 800 1,000 .. ..Output at current prices 880 1,200 .. ..

The data are the same as for the first two quarters in Example 10.1.Production costs at constant prices are derived by deflating the current price value (e.g., for 1999 q1, 660/110*100).Output at average 1998 prices is derived by multiplying the production costs at 1998 prices by the markup ratio (e.g., for 1999 q1, 600*1.333=800).Output at current prices is derived by reflating the constant price value (e.g., for 1999 q1, 800*110/100).

5In some cases, such as the production of movies, no actual marketprice is available at the end of the production process, and the valuehas to be derived through an estimate of discounted future receipts.

such situations is to make an estimate for each quar-ter’s share of total costs, that is, a cost profile. Itcould be based on statistical observations on inputintensities in recent periods or on expert views.Statistical observations could be obtained throughsmall-scale surveys, because cost patterns in indus-tries of concern are often fairly standard betweenunits and also fairly stable. For instance, in agricul-ture the cost pattern is strongly dependent on thegrowth phases of crops, and in construction the paceof production is strongly dictated by an inherentsequence of activities. If a production process isstrongly dictated by physical or biological factors,expert opinions may suffice to establish a cost pro-file. If stable, the same profile could be used for allperiods. If all of this is not available, a very simpleproduction profile, such as an equal distribution overtime, could be used as a default. The cost profileshould be calculated from the constant price data onproduction costs.

10.36. Use of a cost/production profile is shown inExample 10.3. A cost profile is derived from the data

in Example 10.1—the production cycle lasts fourquarters, with 20 percent in q1 (i.e., 600/3000), 25 per-cent in q2, 30 percent in q3, and 25 percent in q4. Bydefinition, the cost profile has the same pattern as theresulting production estimate at constant prices.

10.37. The cost profile method is often used for con-struction in conjunction with data on building per-mits. In cases where only volume indicators such assquare meters are available, the values are derived byaverage prices per unit obtained from a benchmarksurvey or expert assessment. If value data are avail-able, the value concept needs to be identified—cur-rent prices or forecast end-of-period prices. The costprofile should take into account the lags betweenapproval, commencement, and completion. It mayalso account for low work periods such as monsoonsand holiday/vacation periods. The expected valueshould be adjusted for projects that are approved butnot implemented. Also, it might be desirable to esti-mate work-in-progress on individual large projectson a case-by-case basis; compilers of source statisticsmight be best placed to do this.


181

Example 10.3. Estimation of Work-in-Progress with(a) Estimate of Output Quantities(b) Cost ProfileConsider a crop that takes four quarters to grow, from preparation of the cultivation area beginning in thefirst quarter of 1999 to harvesting in the fourth quarter of 1999.

Primary Dataq1 1999 q2 1999 q3 1999 q4 1999 q1 2000

Output price index (average 1998 = 100) 110.00 112.00 114.00 116.00 118.00Cost profile 0.20 0.25 0.30 0.25

Total estimated crop 1000 tonsAverage value per ton for similar crops in 1998 5.0

Step 1. Derive total output at constant pricesValue at average 1998 prices 1000*5.0=5000

Step 2. Derive quarterly output at current and constant pricesq1 1999 q2 1999 q3 1999 q4 1999 Total

Output at average 1998 prices 1,000 1,250 1,500 1,250 5,000Output at current prices 1,100 1,400 1,710 1,450 5,660First, the value of the crop at average 1998 prices is estimated by multiplying the physical data on the volume of the crop by the obtained data on average valueper ton in 1998, that is, 1000• 5 = 5000.

Second, output estimates at constant prices are derived by distributing the estimated value of the crop at average 1998 prices over the quarters in proportionto the assumed production intensity. For instance, the constant price estimate for q1 1999 is derived as 0.2• 5000 = 1000.

Third, output estimates at current prices are derived by inflating with the output price index. For instance, the estimate for q1 1999 is derived as 1000• 1.1 = 1100.

Note that the harvest value (at end-of-production prices) could be derived as 1000• 5• (1.16+1.18)/2=5850.The difference between the harvest value and theestimate of output at current prices is holding gains (5850–5660 = 190). (One of the difficulties surrounding the inclusion of agricultural work-in-progress isthat output differs from harvest value, which may seem counterintuitive to many users.)

D. Special Issues for Agriculture

10.38. The general principles of recording produc-tion on an ongoing basis also apply to agriculture.Usually, it would be feasible to use one of the meth-ods discussed in the previous section, typically a costprofile in conjunction with actual totals (for previousyears) or forecasts (for the current year).

10.39. However, the degree of uncertainty about theeventual output makes the treatment somewhat moreproblematic for agriculture and related industries,both for practical and conceptual reasons. This hascaused many countries not to apply the work-in-progress concepts in the case of agriculture. Whilesupporting the allocation of agricultural output tononharvest periods in principle, the 1993 SNA recog-nizes the specific problems involved. It states the fol-lowing in paragraph 6.100:

There may be circumstances in which theuncertainties attached to the estimation ofthe value of work-in-progress in advance ofthe harvest are so great that no useful analyt-ical or policy purpose is served by compilingsuch estimates.

10.40. Weather is obviously the major component ofuncertainty in agriculture. There are variations intemperature, rainfall, and sunlight, with droughts,hurricanes, and floods being the extremes. Also, insome cases, insect or other animal plagues may beimportant. The degree of uncertainty varies signifi-cantly among countries.

10.41. One aspect of uncertainty is that estimatesmade before the harvest need to be based on fore-casts. This is particularly the case in the QNA, wherethe emphasis on timeliness implies that the estimatesfor preharvest quarters will have to be made well inadvance of harvest time. If the value is uncertain,there are concerns about potentially large revisions inthe national accounts.

10.42. Another aspect of uncertainty concerns cat-astrophic events. The treatment of output losses inthe national accounts is quite different betweennormal events and catastrophes. For normal events,the losses are reflected in reduced output becauseonly the output that materialized is recorded. Forcatastrophes, output is measured as if nothing hap-pened and the losses are recorded on the otherchanges in volume of assets account. Recording a

crop that never materialized in output because itwas hit by a catastrophe is counterintuitive.

10.43. The 1993 SNA restricts catastrophic events tosingular events of a general nature, for example,major earthquakes, volcanic eruptions, tidal waves,exceptionally severe hurricanes, drought, and othernatural disasters (paragraph 12.36). Limitation of cat-astrophic events to singular events of a general naturemeans, among other things, that losses of cropsthrough frequent floods and droughts should not beregarded as catastrophic losses, no matter how devas-tating they are for crops under cultivation. The 1993SNA’s definition of catastrophic events leaves roomfor interpretation, however, which may hamper inter-national comparability.

10.44. A further aspect of uncertainty concerns theprices to assign production in nonharvest periods.This issue of price uncertainty arises in both ex postand, even more, ex ante data. There may be no or onlya very limited market for crops in the nonharvestperiods, so that the prices are more uncertain andhave to be extrapolated (ex ante) or interpolated (expost). The prices of crops6 in nonharvest periods maybe available but may be misleading to the extent thatthey also include storage and holding costs or the off-season scarcity of fresh produce. In such cases, theobserved prices would not be relevant for valuing theharvest. As a solution, some downward adjustmentbased on past years’ off-season patterns may bederived, or the observed prices could be replaced byinterpolation or extrapolation of harvest prices. Inaddition, prices of subsequent years’ crops may bequite unrelated, so estimation of the work-in-progress on the new harvest with prices of the oldmay be misleading. The supply-and-demand situa-tion often differs considerably among crops, so thatthe prices may be completely different. For instance,if an abundant crop is followed by a meager one, theprice of the second crop at harvest time may jumpcompared with the price of the first crop. Obviously,in such a case, the current price estimates need to berevised, but the price development of the first crop isnot valid for the revision of the quarterly estimates. Arelatively simple solution to this problem would be toderive new indices relevant for the production quar-ters of the new crop by an interpolation between theprice of the previous crop at harvest time and theprice of the present crop at harvest time.

X WORK IN PROGRESS

182

6If no local prices are available, world-market prices could be con-sidered; however, these prices may not be indicative for local supplyin a particular country.

10.45. Consideration of behavioral aspects is relevantto the inclusion of agricultural work-in-progress innational accounts estimates. If the economic agentsthemselves react to the uncertainty of prices and vol-umes by behaving as if the work-in-progress carried outwere not output (and thus not generating income), thenthe estimates will not help in understanding economicdevelopments. For instance, the imputations needed torecord subsistence farming may impede the usefulnessof QNA data for monetary policies.7

10.46. By measuring production before the produc-ers do, statisticians may be exposed to the accusationof counting the chickens before they hatch. Unlikemany other producers, farmers do not normallyrecord their own work-in-progress. One singularaspect of this would be the imputation of incomeflows before they are realized, and possibly even incases in which they are not realized. As a result, theconcerns about artificiality and complexity of meth-ods made in the Section B of this chapter are particu-larly strong in the case of agriculture. For that reason,in the case of agriculture, recording production sim-ply as the harvest value may be considered.8

10.47. Whether a harvest or work-in-progressapproach is used for agriculture, the resulting outputseries will often be lumpy. In the case of the harvestapproach, the output will often be concentrated in oneor two quarters while the others may have little or nooutput. In the case of the work-in-progress approach,discontinuities will occur between crop years, effec-tively because of the change in the output/cost markupratio. With either approach, the lumpiness is the validand necessary result of the production conceptadopted in conjunction with the intrinsic limitationsof presenting an annual process in a quarterly form. Itwould be feasible to smooth out the lumpiness in theseries by mathematical techniques, but, in the context

of non-seasonally adjusted data, this would not be jus-tified by the economic concept of production andwould just cover up the issue. Users, however, mayprefer the seasonally adjusted or trend-cycle series forsome purposes.

10.48. Because of their special features, quarterly dataon agricultural production need to be interpreted care-fully. The data are necessarily artificial when a yearlyor multiquarter process is split into quarters. The quar-ter-to-quarter movements are driven by the cost profileused rather than by new information on output.Because the cost profile is a seasonal pattern, it will beremoved by the seasonal adjustment process.9

10.49. Techniques of presentation of the data may helpusers deal with the difficulties associated with mea-surement of quarterly output from agriculture. In viewof the multiple uses of quarterly accounts, there may bealternative solutions to the conceptual and practicalproblems. In this respect, three recommendations canbe made. First, document the methodology carefully sousers are able to form their own opinions. Although thiswill not enhance the quality of the figures, it will at leastenable a view on whether they are suitable for particu-lar purposes. Second, to serve users who deem the allo-cations unsuitable or do not care for allocationsanyway, specify and quantify the allocations. Third,present the data with sufficient details to allow users toexclude the work in progress if they wish.

10.50. In conclusion, as a general principle, the 1993SNA states that agricultural work-in-progress should beincluded in output. As mentioned in paragraph 6.100 ofthat manual, however, the uncertainty and data issuesassociated with agricultural work-in-progress are oftenmore severe than in other cases, so the decision onwhether to include it needs to take into account the cir-cumstances and analytical benefits in each country.

Special Issues for Agriculture

183

9If there are zero-production periods, a nonmultiplicative method ofseasonal adjustment must be used. See Chapter VII for a discussionof seasonal adjustment techniques.

7In the revision process in preparation of the 1993 SNA, the case wasmade for presenting a version of the accounts excluding all nonmon-etary imputations. This case seems particularly relevant for imputa-tions relating to the allocating of output from agriculture tononharvest quarters.8An alternative treatment that has been proposed is to measure outputfor nonharvest quarters as equal to cost without any markup and forthe harvest quarter as equal to the difference between cumulated costsand harvest value. While this would have the advantage of avoidingthe need to revise the back series at the time the crop is harvested, itwould also imply that all operating surplus/mixed income would beallocated to the harvest quarter. The latter has no economic rationale(it is difficult to see why operating surplus/mixed income would begenerated only in the harvest quarter). Also, if output is lower thancosts, this method would imply recording positive output in prehar-vest quarters and negative output in the harvest quarter. Such an out-come seems artificial.

X WORK IN PROGRESS

Annex 10.1. Recording Work-in-Progress in the 1993 SNA Sequence of Accounts

184

10.A1.1. Although estimation of work-in-progressprimarily concerns output, in the context of a consis-tent system such as the national accounts we will alsohave to consider other transactions that relate to work-in-progress, as well as balances (such as value added).In this annex we will explain which other transactionsand balances are affected. A numerical illustration ofthe effects of work-in-progress on main aggregates inthe 1993 SNA’s sequence of accounts and balancesheets is provided in Example 10.A.1. The exampledemonstrates that significant effects can be foundthroughout the full sequence of accounts.

10.A1.2. In the general case, where work-in-progress is not sold until the product is finished, thetwo initial entries in the accounts are (a) output and(b) changes in inventories (increases) in the case ofagriculture, manufacturing, services, and specula-tive construction, and capital formation in the caseof own-account capital formation. After the productis finished and sold, two further transactions are (a)changes in inventories (decreases) and (b) changesin financial assets. In the case of production of acapital good under contract, four entries have to berecorded: (a) output for the producer, (b) fixed cap-ital formation for the user, (c) increase in financialassets for the producer, and (d) decrease in financialassets for the user.

10.A1.3. In the production account of the producer,besides output, the only entry that is affected bywork-in-progress is value added; the other entries—intermediate consumption, taxes and subsidies onproduction, and consumption of fixed capital—arenot. Because inputs are actually made, there is noconceptual problem in allocating them to relevantperiods. Value added is derived as a balance and,thus, estimates will result automatically once theproblem of measuring output is resolved.Consumption of fixed capital is not an issue in thiscontext because, per axiom, it is assumed to takeplace on a continuous basis (for a discussion of con-sumption of fixed capital in a QNA context, seeChapter IV). Taxes and subsidies on production arenot affected because these are to be recorded at thetime the output is sold, transferred, or used (see 1993SNA, paragraph 8.49).

10.A1.4. In the generation of income account of the producer, the effect on value added in the produc-tion account will be carried over to operatingsurplus/mixed income, because wages as such are notaffected by work-in-progress. Similarly, in the allo-cation of primary income account, the impact onoperating surplus/mixed income will directly carryover to the closing balance, primary income, becausenone of the transactions on this account are affectedby work-in-progress. The same applies to transac-tions on the secondary distribution of income accountin that, again, only the closing balance of thisaccount, disposable income, will be affected.

10.A1.5. On the use of income account of the producer,the changes in disposable income would be fullyabsorbed by savings because consumption is notaffected. The effect on saving for the producer would, inthe case of work undertaken on own-account, not carryover to the financial account because increased savingswould be absorbed by offsetting changes in inventoriesor capital formation on the capital account for the sameinstitutional unit. In the case of production of a capitalgood under contract, however, the full effect on savingsfor the producer will be carried over to the financialaccount in the form of payments received from install-ments and other accounts receivable accrued.

10.A1.6. The other changes in assets accounts can beaffected in two ways. First, because prices of the goodsin inventories change over time, the resulting holdinggains or losses have to be recorded on the revaluationaccount. second, if work-in-progress is lost because ofcatastrophic events, this has to be recorded on the otherchanges in volume of assets account.

10.A1.7. Finally, the balance sheets of the systemshow the stocks resulting from the changes on thecurrent and accumulation accounts. The output ofunfinished products is recorded as inventories ofwork-in-progress unless it is sold. At the time theproduct is finished, a reclassification has to be madefrom inventories of work-in-progress to inventoriesof finished goods, and at the time the product is even-tually sold, this sale will be reflected on the balancesheets through lower inventories, with a concomitanteffect on financial assets and liabilities.

Annex 10.1. Recording Work-in-Progress in the 1993 SNA Sequence of Accounts

185

Example 10.A.1 Effects of Work-in-Progress on Main Aggregates in the 1993 SNA Sequence ofAccounts and Balance Sheets

(Data in bold refer to treatment with work-in-progress)In this Example, the results obtained in Example 10.1 are presented in the format of 1993 SNA sequence of accounts.The accounts showhow, with work-in-progress recorded, each quarter would have had a positive value added; whereas, without work-in-progress recorded, thefirst three quarters would have had a negative value added and only the fourth would have had a positive value added.The accounts alsoshow that without recording work-in-progress, a holding gain (caused by inflation) would have been included in output and value added.Furthermore, the example demonstrates that the increased saving is fully absorbed by increased inventories, so that the financial transactions(in this example, loans) are unaffected. (This example concerns an economic activity for which no installment payments are made that wouldaffect the financial accounts.)

Current Accounts

Intermediate Consumption Output

q1 160 160 0 880q2 340 340 0 1,200q3 530 530 0 1,560q4 300 300 5,800 1,400The year 1,330 1,330 5,800 5,040

Value Added

q1 –160 720 q2 –340 860 q3 –530 1,030 q4 5,500 1,100 The year 4,470 3,710

Compensation of Employees

q1 300 300q2 310 310q3 340 340q4 400 400The year 1,350 1,350

Saving

q1 –460 420q2 –650 550q3 –870 690q4 5,100 700The year 3,120 2,360

Capital Transactions, Financial Transactions and Balance Sheets

Opening Transactions ClosingBalance Sheet Additions Withdrawals Holding Gains Balance Sheet

Nonfinancial Assets (Inventories)Quarterly Dataq1 0 0 0 880 0 0 0 40 0 920q2 0 920 0 1,200 0 0 0 130 0 2,250q3 0 2,250 0 1,560 0 0 0 240 0 4,050q4 0 4,050 5800 1,400 0 0 0 350 5,800 5,800

Annual Data 0 0 5800 5,040 0 0 0 760 5,800 5,800

Financial Liabilities (Loans)Quarterly Dataq1 0 0 460 460 0 0 0 0 460 460q2 460 460 650 650 0 0 0 0 1,110 1,110q3 1,110 1,110 870 870 0 0 0 0 1,980 1,980q4 1,980 1,980 700 700 0 0 0 0 2,680 2,680

Annual Data 0 0 2,680 2,680 0 0 0 0 2,680 2,680

Net worthq1 0 0 –460 420 0 0 0 40 –460 460q2 –460 460 –650 550 0 0 0 130 –1,110 1,140q3 –1,110 1,140 –870 690 0 0 0 240 –1,980 2,070q4 –1,980 2,070 5,100 700 0 0 0 350 3,120 3,120

Annual Data 0 0 3,120 2,360 0 0 0 760 3,120 3,120

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XI Revision Policy and the Compilation and Release Schedule

A. Introduction

11.1. Revisions are an essential part of good quar-terly national accounts (QNA) compilation practicebecause they provide users with data that are astimely and accurate as possible. Resource con-straints, in combination with user needs, cause ten-sion between the timeliness of published data on theone hand and reliability, accuracy, and comprehen-siveness on the other hand. To reduce this tension,typically, preliminary data are compiled that later arerevised when more and better source data becomeavailable. Good management of the process of revi-sions requires the existence of a well-established andtransparent revision policy.

11.2. It is important to emphasize that revisions areconducted for the benefit of users, namely, to provideusers with data that are as timely and accurate as pos-sible. Revisions provide the possibility to incorporatenew and more accurate information, and thus toimprove the accuracy of the estimates, without intro-ducing breaks in the time series. Although repeatedrevisions may be perceived as reflecting negatively onthe trustworthiness of official statistics, delaying theincorporation of new data in the published estimatesmay increase the magnitude of later revisions (in par-ticular, if these go in the same direction). Furthermore,not passing on known revisions reduces the actualtrustworthiness of data even more because the data donot reflect the best available information, and the pub-lic may know this or find this out (for instance, thepublic may wonder why a revision in the monthly pro-duction index is not reflected in the QNA). Moreover,series that are revised frequently are not necessarilyless accurate, even initially, than those subject to littleor no revision. The absence of revisions may indicatethat no better information became available to improvepoor first estimates. Finally, attempting to avoid revi-sions by producing accurate but very untimely, andthus less useful, data may result in not making the best

use of the information available. If the official QNAcompilers fail to serve users’ needs, other organiza-tions may compile their own estimates, resulting inconfusion from conflicting estimates to the point thatmany users may consider the official data irrelevant.Obviously, that will result in reduced prestige andrespect for the official QNA compilers.

11.3. Revisions to past data are not without potentialproblems and may draw criticism if not properly han-dled. Revisions to past data are inconvenient to usersbecause they entail revisions to their databases andapplications. More important, frequent revisions—particularly to data for the most recent periods–maycause users to feel uncertain about the current eco-nomic situation and thus uncertain about what policyactions should be taken. Some of this uncertaintymay be unavoidable and merely reveal the fact thatthe information base for the estimates for the mostrecent periods is limited and thus that the data shouldbe used with care. Some of the uncertainty, however,may be caused unnecessarily by the way the revisionsare carried out or presented. On the other hand, thetemptation to suppress needed revisions may lead todeserved criticism from users and severely reduce theusefulness and trustworthiness of the data.Unjustified differences between national accountsestimates and their source data may cause users todoubt the competence of the national accounts com-pilers with serious—and justified—criticism of thenational accounts data as a result.

11.4. To deal with the issues surrounding revisionsand to avoid unnecessary criticism, a well-designedand carefully managed revision policy is needed.Essential features of a well-designed revision policyare predictability and openness, advance notice ofcauses and effects, and explanation, as well as easyaccess to sufficiently long time series of revised data.This chapter elaborates on the elements that make fora well-established revision policy.

B. User Requirements and ResourceConstraints11.5. The trade-off between timeliness on the onehand and accuracy and reliability on the other iscaused by a conflict between different userrequirements in combination with limitations instatistical resources. National accounts data areused for multiple purposes that have partly con-flicting requirements. To allow corrective policyactions to be taken in time, policymakers and otherusers need a coherent, comprehensive, and reason-ably accurate picture of the current economic situ-ation that is as up-to-date as possible. For otherpurposes, such as time series and structural analy-sis of past events, users require long time series ofvery detailed annual, or quarterly, nationalaccounts data. Finally, users are interested in boththe period-to-period rates of change in the seriesand their levels. The resources available for statis-tical purposes, however, are limited. Collection ofsufficiently accurate and detailed source statisticsis time-consuming and expensive both for the sta-tistical office and for the respondents, and compi-lation of comprehensive, accurate, and detailednational accounts is in itself time-consuming andexpensive. Also, frequent collection of compre-hensive and detailed data may impose an unwar-ranted burden on respondents, who themselvesmay not even have such data on a timely and short-term basis.

11.6. As a result, only a limited set of monthly orquarterly source data typically is available on avery timely basis. More detailed and more compre-hensive monthly or quarterly source statistics typi-cally become available on a less timely basis, whilethe most detailed, comprehensive, and reliablesource data may be annual or less frequent data thatbecome available with varying delays long after thereference year. And to provide sufficiently reliablebenchmark data, many countries conduct periodic“benchmark censuses,” collecting very detailed andreliable annual data every 5 or 10 years. These areoften linked to periodic compilation of supply anduse tables. The monthly and quarterly data com-monly are based on smaller samples and less com-plete sample frames than the corresponding annualdata. Finally, the annual data may be based onaudited business accounts through comprehensivequestionnaires that facilitate a thorough checkingand editing of the reported data, while the quarterlydata may be collected using simpler questionnairesthat allow less extensive checking and editing.

C. Waves of Source Data and RelatedRevision Cycles11.7. As explained above, national accountants mayexperience three “waves” of statistical source datathat become available. Each of these waves may leadto revisions of earlier estimates and the incorporationof more details in the published accounts. In accor-dance, three revision cycles may be distinguished. Aquarterly revision cycle is determined by the evolu-tion of the short-term statistics as used in the QNA,and an annual revision cycle is caused by incorpora-tion of annual source data or annual national accounts(ANA) estimates based on a separate ANA compila-tion system into the QNA through benchmarking.Finally, a periodic major revision cycle originatesfrom incorporating data from periodic benchmarkcensuses, revised international guidelines, and otherchanges that cannot be incorporated on a continuousbasis because of resource constraints. Revisions may,of course, also be caused by compilation errors,which need to be corrected when found.

11.8. The evolution of short-term statistics used inthe QNA may cause revisions for two reasons: (a)corrections or changes in specific short-term sourcedata and (b) incorporation of additional, somewhatless timely, short-term data. Changes in short-termsource data can be caused by late responsesreceived after initial publication of source statisticsand by the use of prepublished data that are stillopen to change. To increase the timeliness of theQNA, the first estimates may have to be based on anincomplete set of short-term source data. Monthlyand quarterly source data commonly become avail-able with varying delays. Thus, when preparing thefirst estimates, only data for two months of the lastquarter may be available for some series, while datamay be missing altogether for other series. To fillthese source data gaps, provisional estimates mustbe made based on simple trend extrapolation or onalternative indicators that are more timely but lessreliable. During the course of the current year,these provisional estimates must be revised toincorporate more and better data as the less timelyshort-term source statistics become available.

11.9. Incorporation of more reliable annual data intothe quarterly estimates implies several revisions tothe QNA estimates over time for two reasons. First,the annual data themselves may be revised. Second,for technical reasons, the benchmarking procedurewill result in revisions to quarterly data for earlieryears in addition to the year(s) with new annual data.

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As explained in Chapter VI, these additional revi-sions to past estimates are needed to avoid introduc-ing breaks (the “step problem”) in the QNA timeseries between successive pairs of years.Benchmarking of QNA on more reliable annual datahas the advantage of conveying the accuracy and reli-ability of the annual data to the QNA and allows fora degree of comprehensiveness that the short-termsource data by themselves do not admit. Annualsource data may become available throughout theyear or clustered around a few times of the year. Theannual data can either be incorporated into the QNAestimates series by series—when the new annualsource data for a series become available—or simul-taneously for all series, depending among otherthings on the design of the ANA and QNA compila-tion systems (see also paragraph 11.19 below as wellas Chapter II, paragraphs 2.5 and 2.6).

11.10. Periodic major revisions may be needed to thecomplete quarterly and annual time series or to alarge part of the time series. Over time, periodicbenchmark censuses may be conducted, new types ofannual source data may become available, andimproved compilation methods may be developed,all indicating a need for level adjustments. In addi-tion, international guidelines are periodically revised.To introduce these improvements without creatingbreaks in the quarterly and annual time series, thecomplete time series—or a large part of the timeseries—must be revised at the same time. Ideally, thisshould be done on a continuous basis, series byseries; however, resource constraints often do notpermit such a frequent backcasting approach.Simplified ratio-based backcasting techniques mayhelp in dealing with this problem.

D. The Compilation and ReleaseSchedule

11.11. A crucial part of a well-established and trans-parent revision policy is devising an appropriate com-pilation and release schedule. When establishing acompilation and release schedule, it is important todecide (a) how timely the initial quarterly estimatesshould be; (b) how frequent new quarterly source datashould be incorporated; (3) how early and how frequentannual source data should be incorporated; and (4) howfrequent regular major revisions should be conducted.

11.12. Major elements in determining the compila-tion and release schedule are (a) timing of arrival of

major data sources, and the source data revision pol-icy; (b) timing of preparation of important economicpolitical documents; (c) attitudes toward the trade-offbetween timeliness and accuracy, as well as towardsize and frequency of revisions; (d) disseminationmodes; and, finally, (e) workloads and the design ofthe national accounts compilation system.

11.13. To minimize the number of revisions neededwithout suppressing information, it is advisable tocoordinate statistical activities. The revision scheduleis, or should be, largely driven by the arrival of sourcedata, and coordinating their arrival would substan-tially help reduce the number of revisions needed.Tying introduction of new concepts and methods, ornew international guidelines such as the 1993 SNA, tothe time of other planned revisions would also helpreduce the number of revisions. Although the timingof censuses and new surveys may not be at the dis-cretion of national accountants, they may have astrong say in this, and they are well advised to usetheir influence to achieve maximum consistency withtheir revision policy.

11.14. Account needs to be taken of the coordinationof QNA with related economic policy documents, suchas the general government budget and other importantdocuments related to the parliament’s or legislature’sbudget discussions. To provide timely inputs to thepreparation of these documents, the release of the esti-mates may have to be brought forward or, if this isdeemed impossible, delayed. Release of new estimatesshortly after the government budget has been pre-sented or in the midst of a budget debate may causeproblems (although this should not change the releaseschedule once it has been fixed).

11.15. The initial estimates for a quarter could beprepared and released too early. Improved timelinesscould require use of a higher proportion of incom-plete source data, resulting in unacceptable reductionin the accuracy of the estimates and larger revisions.The information content of estimates based on veryincomplete source data may be limited and, in somecases, more misleading than informative. In thosecases, the users would be better served by less timelyinitial estimates for a quarter.

11.16. Finally, the design of the national accountscompilation system has important implications forhow frequently it is possible and appropriate toincorporate new source data. Large and complicatedcompilation systems with detailed and extensive

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balancing and reconciliation procedures (e.g., basedon quarterly or annual compilation of integrated sup-ply and use tables and a complete set of integratedsectoral accounts) make it costly to incorporate newsource data very frequently.

11.17. Timeliness of release of the initial estimatesfor a quarter varies greatly from country to country,mainly reflecting different perspectives on the time-liness-accuracy-revision trade-off. The earliestreleases of QNA data in some countries come withinthe first month after the reference quarter. A morecommon release time for the initial estimates amongstatistically advanced countries is around two tothree months after the end of the quarter.1,2 To pro-vide very early annual estimates, some countriesrelease their initial estimates earlier after the end ofthe fourth quarter than for other quarters.Correspondingly, there is typically a shift of focusin the presentation from the estimates of the quar-ters to the estimates for the full year. While the mainfocus may be on the estimates for the full year, thefourth-quarter data need to be published in theirown right because failing to do so will cause userswho need integrated annual and quarterly data towrongly derive the fourth quarter as the differencebetween the annual total and the sum of the threepreviously published quarters. If the initial esti-mates for the fourth quarter are released earlier thanfor other quarters, it is preferable to highlight thelower quality of the fourth-quarter estimate, forexample, by noting its revisions in previous yearsand the specific shortcomings in the data used.

11.18. How frequently new quarterly source data areincorporated varies. Countries that release their initialestimates within the first month of the reference quar-ter typically release revised and more detailed esti-mates shortly thereafter. These early estimates areoften revised once or twice in the first quarter after thereference quarter. The estimates may be open to quar-terly revisions thereafter. A more common practice,followed by countries that are less timely in releasingtheir initial estimates, is to revise the estimates quar-terly linked to the preparation and release of the initialestimates for the following quarters. To reduce thenumber of revisions, it may be tempting to allow theestimates to be revised only once during the ongoing

year. However, temporarily suppressing informationmay result in larger revisions later. Suppression ofinformation may also sometimes be technically diffi-cult to implement and thus may result in compilationerrors. The common practice is to let all estimates beopen to revision during the ongoing year.

11.19. Annual source data can be incorporated intothe QNA estimates either series by series, when thenew annual source data for a series become available,or simultaneously for all series. The first approachhas the advantage of allowing new annual informa-tion to be incorporated in as timely a manner as pos-sible. Some countries compile their quarterly andannual estimates using basically the same time-series-oriented compilation system—typically with-out detailed and extensive balancing andreconciliation procedures—making this approach thenatural choice. Most countries use a separate systemfor compiling their annual estimates, however, whichmakes it natural to filter the annual source datathrough the annual accounting system before incor-porating the information into the QNA estimates. Inthose circumstances, to avoid inconsistenciesbetween quarterly and annual accounts, the secondapproach may be the natural choice. Some countriesuse a combination of the two approaches.

11.20. Countries with an independent ANA compila-tion process typically revise their annual estimatesfrom two to four times before the books are closeduntil a major revision is undertaken. These regularrevisions to the annual estimates are normally under-taken once a year, although a few countries conductthem more frequently. The timing within the year ofthese annual revisions varies widely. The emphasis istypically on providing accurate and detailed data forstructural analysis, with less emphasis on timeliness.They are nearly always more detailed than the QNAand may encompass a more complete set of the inte-grated economic accounts, including supply and usetables. All these features make backcasting ademanding task and thus restrict the frequency withwhich level adjustment originating from new datasources and new methods can be incorporated.

11.21. Box 11.1 gives an illustration of a possiblecompilation and release schedule followed by coun-tries with independent ANA compilation systems. Inthis example, the annual accounts are revised onlyonce, but in many countries the annual accounts arerevised several times before they are declared final.These subsequent revisions of the ANA should also

The Compilation and Release Schedule

189

1These issues are dealt with and international practices are comparedin Smith, Philip, (1993).2The Special Data Dissemination Standard (SDDS) specifies timeli-ness for the initial QNA estimates at three months after the end of thequarter.

be put through in the QNA so that the number of revi-sions of QNA eventually depends on the number ofrevisions of the ANA. If a major overhaul of the ANAsystem is performed later, it should also be putthrough in the QNA time series. It should be notedthat in the benchmarking procedures recommendedin this manual, revisions of past years will also neces-sitate revisions in the quarters of later years, includ-ing the quarters of the current year. Revisions to thequarters of the current year (in Box 11.1, data for q1through q3 of year y+1) would not be necessary if theannual data for the past years were incorporatedbefore release of the initial estimates for the firstquarter of the current year (in Box 11.1, 5 to 6 monthsinstead of 10 to 12 months after the end of year y).

E. Other Aspects of Revision Policy

11.22. In addition to developing a compilation andrelease schedule, the following are other importantelements of a well-established revision policy:

• A balance between timeliness and accuracy of theinitial estimates.

• Well known release dates published through anadvance release calendar, as prescribed by the IMF’sSpecial Data Dissemination Standard (SDDS) andGeneral Data Dissemination System (GDDS).

• Candid and easily available documentation ofsources and methods showing the main flows ofsource data leading to revisions.

• Provision of Available information on the accuracyof the estimates and the degree of potential futurerevisions (e.g., through records of past revisions).

• Provision of sufficiently long, consistent time series. • Provision of detailed data in an easily accessible

format (e.g., electronic).• Published tables showing the revisions to the data

with accompanying text explaining their causes.• Advance notice to users of the national accounts

data.

11.23. To inform users and avoid unmerited criti-cism, a well-established revision policy requires

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Box 11.1. Compilation and Revision Schedule, An Illustration

Current Estimates for a Year y• Initial estimate: 2 to 3 months after the end of the quarter• Revised estimate: 5 to 6 months after the end of the quarter• All estimates may be open to revisions during the current year

First Annual Round of Revisions:Annual Data for: Quarterly Accounts

10–12 year Preliminary annual estimates based on a Revised estimates for q1 – q3months y separate annual accounting system of year y + 1after the + Revised quarterly estimatesend of year “Final” annual estimates based on a for year y, and y – 1year y y – 1 separate annual accounting system + Slightly revised quarterly pattern

through year y – 2 to y – 4 to avoid steps between year y – 1 and y – 2

Subsequent Annual Rounds of Revisions:22–24 months after Incorporation of “final” annual estimates for year y and preliminary estimates for year y + 1 basedthe end of year y on a separate annual accounting system

32–36 months after the end Incorporation of “final” annual estimates for year y + 1, of year yand preliminary annual estimates for year y + 2

46–48 months after the end Incorporation of “final” annual estimates for year y + 2, of year yand preliminary annual estimates for year y + 3

The last two rounds of revisions are caused by technical properties of the recommended benchmarking methods (more rounds with minorrevisions may in some cases be needed).

The “final” annual estimates may be revised later as needed, if new data become available or improved methods are developed.

candid communication with users and easy access tothe revised time series on a sufficiently detailed level.

11.24. Users should be properly informed of the qual-ity of the estimates and the degree of revisions to expecton predetermined dates in the future. Properly inform-ing users of the quality of the estimates involves givingthem candid and easily available documentation ofsources and methods for the different versions of thequarterly estimates, clearly showing the main flows ofsource data leading to revisions. When releasingrevised estimates, best practice is to simultaneouslypublish articles summarizing the main revisions andtheir causes since the previous release. (See Box 11.2for an illustration.) Best practice also involves periodi-cally conducting and publishing studies of long-termtrends in the revision patterns. Summaries of thesestudies may accompany the regular quarterly release ofdata to remind users that data are subject to revisions.

11.25. It is particularly important to inform usersproperly of the quality of the estimates when releas-ing QNA estimates for the first time. For a good indi-cation of the degree of future revisions of the main

aggregates to expect, the complete compilationprocess should be simulated based on historic databefore releasing the new estimates. That is, the pro-posed QNA compilation system should be used toproduce QNA estimates for the past years as if onewere back in time and were producing the initial pre-liminary estimates for those years (see the discussionof the “tracking exercise” in Chapter II).

11.26. Finally, providing easy access to the revisedtime series on a sufficiently detailed level should sub-stantially ease the inconvenience for users of frequentrevisions. This involves electronic release of the com-plete, detailed time series, not only the aggregateddata for the most recent periods, which will make iteasier for users to keep track of the revisions andupdate their databases. It should be emphasized thatrelease of complete time series for all revised periodsis needed because users often use QNA data in atime-series format and need to be alerted to anychanges in data for past periods. Not providing themwith revised historic data will create breaks in thetime series they use, which will seriously hamper theserviceability of the data.

Dissemination of Revised Data and Communication with Users

191

Box 11.2. Presentation of Revisions, An Illustration1

Changes in This IssueData for the mining and manufacturing industries have been revised as a result of the incorporation of new annual census results for the pre-vious year.As a result, value added for most industries has been revised upward in the previous and current years.

Retail output and household consumption have been revised for the most recent two quarters following the processing of late questionnaires.The most recent quarter has been revised down slightly as a result.

Changes in the Next IssueRelease date: xxxxx.

The methodology for estimating financial services will be revised in line with new international standards.The conceptual issues and quantita-tive effects are discussed in a research paper available on request.

Summary Tables of RevisionsTable 1: Revisions to Domestic Production Account in Currency Units: Eight Most Recent Quarters Table 2: Revisions to Percentage Changes in Domestic Production Account: Eight Most Recent Quarters

1Based on actual country practices.

192

Bibliography

This bibliography lists material bearing on quarterlynational accounts that came to the authors’ notice aswell as country sources and method publicationsfound on the IMF Dissemination Standards BulletinBoard, http://dsbb.imf.org.

I. Introduction

Commission of the European Communities,International Monetary Fund, Organization forEconomic Cooperation and Development,United Nations, and World Bank, 1993, Systemof National Accounts 1993 (1993 SNA) (NewYork: United Nations).

Eurostat, 1999, Handbook on Quarterly NationalAccounts (Luxembourg: Office for OfficialPublications of the European Communities).

Giovannini, E., 1988, “A Methodology for anEarly Estimate of Quarterly NationalAccounts,” Economia Internazionale, Vol.41 (August–November), pp. 197–215.

Hyllenberg, S., 1998, “Comment,” Journal of Businessand Economic Statistics, Vol. 16 (April), pp.167–68.

International Monetary Fund, DisseminationStandards Bulletin Board. Available via theInternet: http://dsbb.imf.org

Lääkäri, E., 1994, “The Monthly GDP Indicator,”paper presented at INSEE-Eurostat QuarterlyNational Accounts Workshop, Paris, December.

Organization for Economic Cooperation andDevelopment, 1968, Quarterly NationalAccounts as Data for Economic Policy: A

Report on Progress in OECD Countries,prepared with the assistance of T.P. Hill (Paris).

————, 1979, Quarterly National Accounts: AReport on Sources and Methods in OECDCountries (Paris).

————, 1996, Quarterly National Accounts:Sources and Methods Used by OECD MemberCountries (Paris).

————, 1998, Quarterly National Accounts:Central and Eastern Europe (Paris).

————, 2000, System of National Accounts, 1993:Glossary (Paris).

Reed, G., 2000, “How the Preliminary Estimate ofGDP Is Produced,” Economic Trends, No. 556(March), pp. 53–61.

Salazar, E., R. Smith, M. Weale, and S. Wright,1994, “Indicators of Monthly NationalAccounts,” paper presented at INSEE-EurostatQuarterly National Accounts Workshop, Paris,December.

Yeend, C., and A. Pottier, 1996, “A MonthlyIndicator of GDP,” Economic Trends, No. 509(March), pp. 28–33.

II. Strategic Issues in QuarterlyNational Accounts

Cainelli, G., and C. Lupi, 1999, “The Choice of theAggregation Level in the Estimation of QuarterlyNational Accounts,” Review of Income andWealth, Series 45 (December), pp. 483–92.

Caplan, D., and S. Lambert, 1995, “Quarterly GDP– Process and Issues,” Economic Trends, No.504 (October), pp. 40–43.

Cope, I., 1995, “Quarterly National Accounts in theUnited Kingdom: Overview of UK Approach,”Economic Trends, No. 498 (April), pp. 22–25.

Janssen, R., and S. Algera, 1988, Methodology ofthe Dutch System of Quarterly Accounts,Occasional Paper No. NA-025 (Voorburg:Netherlands Central Bureau of Statistics).

Janssen, R., P. Oomens, and N. van Stokrom, 1994,“Data Flows in the Dutch Quarterly NationalAccounts,” paper presented at the INSEE-Eurostat Workshop on Quarterly NationalAccounts, Paris, December.

III. Sources for GDP and Its Components

General and Multicountry:

Daniel, D., 1996, “The Use of Quarterly CurrentPrice Output Data in National Accounts,”Economic Trends, No. 516 (October), pp. 16–23.

Eurostat, 1998a, Methodology of Industrial ShortTerm Indicators–Rules and Recommendations(Luxembourg: Office for Official Publicationsof the European Communities).

————, 1998b, Handbook on the Design andImplementation of Business Surveys(Luxembourg: Office for Official Publicationsof the European Communities).

Pike, R., and G. Reed, 2000, “Introducing theExperimental Monthly Index of Services,”Economic Trends, No. 565 (December), pp.51–63.

United Nations, 1986, “Handbook of NationalAccounting. Accounting for Production:Sources and Methods,” Studies in Methods,Series F, No. 39 (New York).

Country publications:

The following list of country publications is derivedfrom information on the SDDS websitehttp://dsbb.imf.org; the SDDS website also containssummary methodologies:• Argentina: Sistema de Cuentas Nacionales

Argentina Año Base 1993, Estimacionestrimestrales y anuales: años 1993–1997,Ministerio de Económia y Obras y ServiciosPúblicos, Spanish.

• Australia: Australian National Accounts:Concepts, Sources and Methods, ABS CatalogueNumber 5216.0, and Statistical ConceptsReference Library on CD-ROM, AustralianBureau of Statistics.

• Austria: Annex B of the regulation (EG) Nr.2223/96 of the European Council.

• Canada: Guide to the Income and ExpenditureAccounts, Catalogue No. 13-603E-F; A Guide tothe Financial Flow and National Balance SheetAccounts, Catalogue No. 13-585E-F; A UserGuide to the Canadian System of NationalAccounts, Catalogue No. 13-589E-F; and TheInput-Output Structure of the Canadian Economy,Catalogue No. 15-511, Statistics Canada.

• Chile: Cuentas Nacionales de Chile 1985–1992,Central Bank of Chile.

• Colombia: Metodología de Cuentas Nacionales,Departamento Administrativo Nacional deEstadísticas.

• Croatia: Quarterly Gross Domestic Product,Monthly Statistical Report, and StatisticalYearbook, Central Bureau of Statistics.

• Czech Republic: National Accounts for the CzechRepublic and Annual National Accounts of theCzech Republic 1997, Czech Statistical Office.

• Denmark: Konjunkturstatistik: Supplement,Statistics Danmark.

• Ecuador: Cuentas Nacionales Trimestrales delEcuador 1980.II-1991.I and Cuentas NacionalesTrimestrales del Ecuador 1965.I–1992.II, BancoCentral del Ecuador.

• El Salvador: El Salvador: Metodologia delProducto Interno Bruto Trimestral, CentralReserve Bank of El Salvador.

• Estonia: National Accounts of Estonia, StatisticalOffice of Estonia.

• Finland: Statistics Finland Statistical Studies, No. 62(1980), Uotila, Leppä, Katajala, Statistics Finland.

• France: INSEE. Méthodes n˚13: Comptesnationaux trimestriels, Institut National de laStatistique et des Etudes Economiques.

Bibliography

193

• Germany: Selected Working Documents onFederal Statistics in number 7 Survey of NationalProduct Calculations of the Federal StatisticalOffice, number 19 Housing Rentals, number 21Input-Output Tables as the Basis of NationalProduct Calculation, number 22 ConstructionInvestments, number 23 Production Approach,number 24 Equipment Investments, and number25 Subsidies, and the working paper PrivateConsumption, State Consumption, Net Exports,Federal Statistical Office.

• Hong Kong SAR, China: Gross Domestic Product1961 to 1999, Census and Statistics Department.

• Hungary: 1999 issue of National AccountsHungary, Hungarian Central Statistical Office.

• Iceland: Compiling Icelandic National Accounts,Documentation of Methods Applied, Output andExpenditure Approaches, National EconomicInstitute.

• India: 1999 edition of the annual NationalAccounts Statistics, Central StatisticalOrganisation.

• Indonesia: Pendapala Nasional Indonesia,Triwulanan, 1991–93, Badan Pusat Statistik.

• Ireland: National Income and Expenditure,Central Statistics Office.

• Israel: Current Briefings in Statistics (March ofeach year), Central Bureau of Statistics.

• Italy: Statistica in Breve (May 26, 1999 andAugust 4, 1999), Comunicato Stampa (June 30,1999), Note Rapide (April 30, 1999), IstitutoNazionale di Statistica.

• Japan, The System of National Accounts in Japan,Economic Planning Agency.

• Korea: Estimation Methods of National IncomeAccounts in Korea, Bank of Korea.

• Latvia: National Accounts of Latvia, CentralStatistical Bureau of Latvia.

• Lithuania: Lithuanian National Accounts,Statistics Lithuania.

• Malaysia: Quarterly National Product andExpenditure Account, xxx Quarter xxxx,Departments of Statistics, Malaysia.

• Mexico: Producto Interno Bruto Trimestral,Oferta y Demanda Global Trimestral a PreciosCorrientes, and Oferta y Utilización Trimestrala Precios Constantes de 1993, InstitutoNacional de Estadística, Geografía eInformática.

• Netherlands: Fast GDP-growth Estimates, DataFlows in QNA, The Methodology of the DutchSystem of Quarterly National Accounts, and AProvisional Time Series of 1977 – 1994 QuarterlyNational Accounts data linking up with the 1995–1999 ESA 1995 figures: method and results,Statistics Netherlands.

• Norway: Quarterly National Accounts1978–1998. Production, Uses and Employment,Statistics Norway.

• Peru: Cómo Leer la Nota Semanal, CentralReserve Bank of Peru.

• Philippines: Sources and Methods, NationalStatistical Coordination Board.

• Poland: Gross Domestic Product by Quarters forthe Year 1995–1998, Central Statistical Office.

• Singapore: Singapore National Accounts 1987and Singapore System of National Accounts,1995, Department of Statistics.

• Slovak Republic: Macroeconomic Indicators ofQuarterly National Accounts and Value Addedand CESTAT Statistical Bulletin, Statistical Officeof the Slovak Republic.

• Slovenia: National Accounts of the Republic ofSlovenia. Sources, Methods and Estimates,Statistical Office of the Republic of Slovenia.

• South Africa: Statistical Release P0441 of June1999, Statistics South Africa.

• Spain: Contabilidad Nacional Trimestral deEspaña. Metodología y serie Trimestral1970–1992, Instituto Nacional de Estadística.

• Switzerland: Die Quartalsschätzungen desBruttoinlandproduktes, Mitteilungsblatt fürKonjunkturfragen, Heft 1, State Secretariat forEconomic Affairs.

• Turkey: Gross National Product; Concepts,Methods and Sources, State Institute of Statistics.

• United Kingdom: Concepts, Sources and Methodsand The UK National Accounts, Office forNational Statistics.

• United States: “A Guide to the NIPA’s,” Survey ofCurrent Business, March 1998, Bureau ofEconomic Analysis.

IV. Sources for Other Components ofthe 1993 SNA

Jenkinson, G., 1997, “Quarterly IntegratedEconomic Accounts – the United KingdomApproach,” Economic Trends, No. 520 (March),pp. 60–65.

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V. Editing and Reconciliation

Arkhipoff, O., 1990, “Importance et diversité desproblèmes d’agrégation en comptabiliténational: esquise d’une théorie générale del’agrégation,” in La Comptabilité National Faceau Defi International, ed. by E. Archambaultand O. Arkhipoff (Paris: Economica).

Aspden, C., 1990, “Which Is the Best Short-TermMeasure of Gross Domestic Product?” inAustralian National Accounts: National Income,Expenditure and Product, Catalogue 5206.0(Canberra: Australian Bureau of Statistics).

Bloem A., F. Maitland-Smith, R. Dippelsman, and P.Armknecht, 1997, “Discrepancies betweenQuarterly GDP Estimates,” IMF Working Paper97/123 (Washington: International MonetaryFund).

Kim, C., G. Salou, and P. Rossiter, 1994, “BalancedAustralian National Accounts,” AustralianBureau of Statistics Working Papers inEconometrics No. 94/2 (Canberra: AustralianBureau of Statistics).

Snowdon, T, 1997, “Quarterly Alignment Adjustmentsin the UK National Accounts,” Economic Trends,No. 528 (November), pp. 23–27.

Stone, R., D.G. Champernowne, and J.E. Meade,1942, “The Precision of National IncomeEstimates,” Review of Economic Studies, Vol. 9,No. 2, pp. 111–25.

Stone, J.R.N., 1975, “Direct and Indirect Constraints inthe Adjustment of Observations,” in NationalAccounts Models and Analysis. To Odd Aukrust inHonor of His Sixtieth Birthday,Samfunnsøkonomiske Studier no. 26 (SocialEconomic Studies No. 26) (Oslo: StatisticsNorway).

VI. Benchmarking

Alba, E. de, 1979, “Temporal Dissaggregration ofTime Series: A Unified Approach,” inProceedings of the Business and EconomicStatistics Section, American StatisticalAssociation (Washington: American StatisticalAssociation), pp. 359–70.

Barcellan, R., 1994, “ECOTRIM: A Program forTemporal Disaggregation of Time Series,” paperpresented at INSEE-Eurostat Quarterly NationalAccounts Workshop, Paris, December.

Bassi, V.L., 1939, “Interpolation Formula for theAdjustment of Index Numbers,” in Proceedingsof the Annual Meeting of the AmericanStatistical Association (Washington: AmericanStatistical Association).

————, 1958, “Appendix A,” in EconomicForecasting, ed. by V.L. Bassi (New York:McGraw-Hill).

Bournay, J., and G. Laroque, 1979, “Réflexions surla methode d’élaboration des comptestrimestriels,” Annales de l’Insee, Vol. 36(October–December), pp. 3–30.

Chen, Z.-G., P.A. Cholette, and E.B. Dagum, 1997,“A Nonparametric Method for BenchmarkingSurvey Data via Signal Extraction,” Journal ofthe American Statistical Association, Vol. 92(December), pp. 1563–71.

Cholette, P.A., 1978, “A Comparison andAssessment of Various Adjustment Methods ofSub-Annual Series to Yearly Benchmarks,”Research Paper No. 78-03-001B (Ottawa:Statistics Canada).

————, 1984, “Adjusting Sub-Annual Series toYearly Benchmarks,” Survey Methodology, Vol.10 (December), pp. 35–49.

————, 1988a, “Concepts, Definitions andPrinciples of Benchmarking and Interpolationof Time Series,” Working Paper No. TSRA-87-014e (Ottawa: Statistics Canada).

————, 1988b, “Benchmarking System of Socio-Economic Time Series,” Working Paper No.TSRA-88-017e (Ottawa: Statistics Canada).

————, 1994, “Users’ Manual of ProgrammeBENCH to Benchmark, Interpolate, andCalendarize Time Series Data,” Working PaperNo. TSRA-90-008 (Ottawa: Statistics Canada).

————, and A. Baldwin, 1988, “Converting FiscalYear Data into Calendar Values,” Working PaperNo. TSRA-88-012e (Ottawa: Statistics Canada).

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VII. Mechanical Projections

Al-Osh, M., 1989, “A Dynamic Linear ModelApproach for Disaggregating Time SeriesData,” Journal of Forecasting, Vol. 8 (June),pp. 85–96.

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Wei, W.W.S., and D.O. Stram, 1990,“Disaggregation of Time Series Models,”Journal of Royal Statistical Society, Series B,Vol. 52, No. 3, pp. 453–67.

VIII. Seasonal Adjustment andEstimation of Trend-Cycles

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Australian Bureau of Statistics, 1987, A Guide toSmoothing Time Series—Estimation of “Trend,”Information Paper 1316.0 (Canberra: AustralianBureau of Statistics).

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Baxter, M., 1999, “Seasonal Adjustment of RPIY,”Economic Trends, No. 546 (May), pp. 35–38.

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Butter, F.A.G. den, and M.M.G. Fase, 1991,Seasonal Adjustment as a Practical Problem(Amsterdam; New York: North-Holland).

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IX. Price and Volume Measures:Specific QNA-ANA Issues

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Brueton, A., 1999, “The Development of Chain-Linked and Harmonised Estimates of GDP atConstant Prices,” Economic Trends, No. 552(November), pp. 39–45.

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————, 1993, “Alternative Measures of Change inReal Output and Prices, Quarterly Estimates for1959–92,” Survey of Current Business, Vol. 73(March), pp. 31–37.

X. Work-in-Progress

XI. Revision Policy and theCompilation and Release Schedule

Barklem, A.J., 2000, “Revision Analysis of InitialEstimates of Key Economic Indicators and GDPComponents,” Economic Trends, No. 556(March), pp. 31–52.

Di Fonzo, T., S. Pisani, and G. Savio, 1994,“Revisions to Italian Quarterly NationalAccounts Aggregates: Some Empirical Results,”paper presented at INSEE-Eurostat QuarterlyNational Accounts Workshop, Paris, December.

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203

Index

Accounts for the total economy. See Unconsolidatedaccounts

Accrual accounting. See Time of recordingAdjustment process, 2.61Administrative byproduct data, 3.15–3.16, 3.81Aggregate tracking exercise, 2.47–2.50Aggregation, defined, 9.6Agriculture, work-in-progress issues, 10.3, 10.5,

10.38–10.50Alternative extrapolation base. See Extrapolation basesANA. See Annual national accountsAnalytical testing

about, 5.14edits of plausibility, 5.17–5.24logical edits, 5.15–5.16

Annual national accounts (ANA)conceptual links between QNA, 1.24–1.28consistency with QNA, 1.24, 1.28editing and reconciliation, 5.1–5.7QNA and, 1.5–1.12Annual reporting, fiscal- versus calendar-year basis,

2.38Architectural and approval costs, 3.107ARIMA-model-based method, 6.A1.39–6.A1.41

Balance of Payments Manual, 4.18Balance sheets, 4.25–4.29Balancing items, 4.6Bassie method, 6.A1.17–6.A1.26Benchmarking. See also Denton family of

benchmarking methodsabout, 1.24–1.27, 1.43, 2.7, 2.56–2.59, 6.1–6.11additivity in, 9.43–9.45alternative methods, 6.A1.1–6.A1.5ARIMA-model-based method, 6.A1.39–6.A1.41back series, 6.2balancing items and accounting identities,

6.46–6.47basic extrapolation with an indicator, 6.17–6.21

basic technique for distribution andextrapolation with an indicator, 6.12–6.21

Bassie method, 6.A1.17–6.A1.26benchmark-to-indicator ratio framework, 1.40,

6.2BI ratio-based procedure, 6.39BI ratio forecasts, 6.51Chow-Lin method, 6.A1.48and compilation procedures, 6.42–6.45editing and reconciliation and, 5.36, 5.37extrapolation, 6.2extrapolation base and forward step problem,

6.A2.1–6.A2.18fiscal- versus calendar-year reporting and, 2.38fixed coefficient assumptions, 6.37–6.41forward series, 6.2, 6.28–6.29. See also

Proportional Denton technique withenhancements

general-least-squares regression models,6.A1.42–6.A1.47

Ginsburgh-Nasse method, 6.A1.27–6.A1.38IO ratios, 6.37, 6.38more options, 6.48other comments, 6.49–6.50particular issues, 6.37–6.51pro rata distribution and the step problem,

6.13–6.16quarterization, 6.2and revisions, 6.49–6.50seasonal adjustment-based procedure, 6.39sources and methods and, 1.18

Biases, 2.37, 2.39extrapolation base and, 6.A2.2,

6.A2.10–6.A2.11Boot-Feibes-Lisman distribution method, 7.16–7.18Business accounting treatment of work-in-progress,

10.16–10.22

Calendar-related effects, seasonal adjustment andtrend-cycle estimates, 8.7, 8.26–8.30

Calendar year, annual reporting based on, 2.38Capital accounts, 4.18, 4.35Catastrophic events affecting agricultural production,

10.42–10.43Chain-linking in the QNA

about, 9.21–9.31additivity in, 9.42, 9.43–9.45base period, 9.22, 9.25chain-linked measures and nonadditivity, 9.42choice of index number formulas for annual

data, 9.36–9.38Fisher index and, 9.22, 9.33, 9.37, 9.38frequency of, 9.32–9.35Laspeyres index and, 9.23–9.44Paasche index and, 9.22, 9.32, 9.36, 9.37,

9.A1.1, 9.A1.2–9.A1.4, 9.A2.2–9.A2.6,9.A2.11

presentation of chain-linked measures,9.46–9.53

reference period, 9.22, 9.26techniques for annual chain-linking of quarterly

data, 9.39–9.41weight period, 9.22, 9.25

Changes in inventoriesabout inventories, 3.134–3.137estimation of, 3.A1.1–3.A1.12perpetual inventory method, 3.138price indicators, 3.144valuation problems, 3.69value indicators, 3.138–3.142volume indicators, 3.143

Characteristics of series, calculations and, 2.56Chow-Lin method, 6.A1.48Commodity flow method, 2.23Compensation of employees, value indicators for,

3.161–3.163Compilation and release schedule, in revision policy,

11.11–11.21Compilation system, 2.5

assessing, 2.31–2.34, 2.47–2.50choice between, 2.6

Compiling QNAadditivity in, 9.43–9.45compilation cycle, 1.47editing as part of, 5.39–5.47from unadjusted source data, 1.17–1.22

Components of the 1993 SNA other than GDPaccounts for the total economy (unconsolidated

accounts), 4.7–4.29general issues, 4.1–4.5

institutional sector accounts, 4.30–4.49main aggregates for the total economy, 4.6

Comprehensive quarterly statistical publications, 2.66Computer software

database software, 2.92–2.97in fixed capital formation, 3.131for seasonal adjustment and trend-cycle

estimates, 8.13COMWIL valuation (cost or market, whichever is

less), 3.A1.4Confrontation of data. See Editing and reconciliationConstant price estimates. See Price and volume

measurement Construction industry

price indicators, 3.116–3.122value indicators, 3.32, 3.101–3.112volume indicators, 3.113–3.115work-in-progress activities, 10.3

Consumer price index (CPI), 3.54, 3.83–3.86Consumption of dwelling services data, 3.79Consumption of fixed capital, 4.5, 4.26, 10.25,

10.A1.3 Cost or market, whichever is less (COMWIL

valuation), 3.A1.4Coverage of QNA

about, 2.8–2.14GDP measurement, 2.15–2.23

supply and use approach to GDP, 2.24–2.29CPI. See Consumer price indexCustoms data, 3.148

Data, reviewing. See Tracking exercises, and Editingand reconciliation

Data problemscauses of, 5.8–5.9identifying, 5.10–5.24

Data sources, 1.41, 3.4–3.10. See also Source data andspecific sources

filling gaps in, 3.17–3.19Data suppliers, contact with, 5.3Data validation. See Editing and reconciliationDenton family of benchmarking methods, 6.22–6.36,

6.A1.6–6.A1.16. See also Proportional Dentonmethod; Proportional Denton technique withenhancements

Differences between QNA and source data statistics,causes for, 2.60–2.61

Disposable income account, 4.17Dissemination

revised data, 11.23–11.26Dissemination issues, 2.62–2.67

INDEX

204

Dividends, 4.46Documentation, source data, 1.29, 1.33

Editing and reconciliationabout, 5.1–5.7adjusted data, 5.23benchmarking and, 5.36, 5.37at both detailed and aggregate levels, 5.22causes of data problems, 5.8–5.9changes in estimates, 5.7concerns in showing explicit discrepancies, 5.35deadlines and, 5.4dealing with inconsistencies, 5.25–5.38discrepancies and residual items, 5.24documentation and, 5.7editing as part of compilation, 5.39–5.47errors and mistakes, 5.2, 5.4–5.9explicit discrepancies, 5.34–5.35identifying data problems, 5.10–5.24independent estimates of GDP and, 5.27making adjustments, 5.30other alternatives for treating discrepancies,

5.31–5.34procedural and practical differences in

reconciliation, 5.36reconciliation process, 5.25–5.38relationships within data and, 5.6statistical noise and, 5.37supply and use balancing, 5.26, 5.28, 5.30timing errors and, 5.37

Edits of plausibility, 5.17–5.24Educating and informing users, 1.34–1.36Equipment

price indicators, 3.128–3.130value indicators, 3.123–3.126volume indicators, 3.127

Equipment capacity, 2.13Errors and mistakes. See Editing and reconciliationEstablishing phase, 2.2, 2.52Expenditure approach to GDP measurement, 2.15,

2.16, 2.18–2.20Exports and imports of goods and services

merchandise price indicators, 3.148–3.155price indicators, 3.148–3.155service price indicators, 3.156value indicators, 3.145volume indicators, 3.146–3.147

Extended accounting framework, 2.11Extrapolation, 1.26, 6.2

with an indicator, 6.17–6.21basic technique for distribution and

extrapolation with an indicator, 6.12–6.21

Extrapolation basesabout, 6.A2.1–6.A2.5alternative extrapolation bases, 6.A2.3–6.A2.5annual rate of change in derived forward series,

6.A2.8–6.A2.15biases, 6.A2.2, 6.A2.10–6.A2.11forward step problem and, 6.A2.6–6.A2.7and robustness toward errors in indicator,

6.A2.16and seasonality, 6.A2.17–6.A2.18

Eyeball testing, 5.11–5.13

FIFO (first in, first out), 3.A1.2, 3.A1.3Final consumption expenditure by nonprofit

institutions serving householdsprice indicators, 3.97value indicators, 3.95volume indicators, 3.96

Financial accounts, 4.19–4.24, 4.36Financial intermediation services indirectly measured

(FISIM), 3.59, 3.65, 3.68Fiscal year, annual reporting based on, 2.38Fisher-type volume indices, 9.18–9.20FISIM. See Financial intermediation services

indirectly measuredFixed coefficients, 3.24Flash estimates, 1.37–1.38

GDP by income categoryemployee compensation, 3.161–3.163general issues, 3.157–3.160operating surplus/mixed income, 3.164–3.167taxes and subsidies on products, production, and

imports, 3.168value indicators, 3.161–3.168volume and price indicators, 3.169–3.170

GDP by industryadjustment items, 3.65–3.68current price data on outputs and/or inputs,

3.29–3.36data on quantities of output and/or inputs,

3.37–3.42general issues, 3.20–3.27indirect indicators, 3.48–3.52industrial production indices, 3.62–3.64labor input measures, 3.43–3.47price indicators, 3.53–3.61types of source data, 3.28

GDP by type of expenditurechanges in inventories, 3.69, 3.134–3.144,

3.A1.1–3.A1.12

Index

205

exports and imports of goods and services,3.145–3.156

final consumption expenditure by nonprofitinstitutions serving households, 3.95–3.97

general issues, 3.69–3.70government final consumption expenditure,

3.87–3.94gross fixed capital formation, 3.98–3.113household final consumption expenditure,

3.71–3.86GDP measurement, 2.15–2.23GDP sources

in absence of surveys or administrative data,3.17–3.19

administrative byproduct data issues, 3.15–3.16,3.81

data sources, 3.4–3.10general issues, 3.1–3.3survey issues, 3.11–3.14

General-least-squares regression models,6.A1.42–6.A1.47

GFS. See Government finance statistics systemGinsburgh-Nasse method, 6.A1.27–6.A1.38GNI (gross national income), 4.14Goods and services

current price data on outputs/inputs, 3.31exports and imports of, 3.145–3.156volume indicators, 3.79

Goods and services tax, 3.16. See also Value addedtax (VAT) systems

Government accounting systems, 4.38–4.40Government final consumption expenditure

price indicators, 3.93–3.94value indicators, 3.87–3.90volume indicators, 3.91–3.92

Government finance statistics (GFS) system, 3.168Government Finance Statistics Manual, 4.38Gross domestic product (GDP). See under GDPGross fixed capital formation

construction industry, 3.101–3.122equipment, 3.123–3.130general value indicators, 3.98–3.100other fixed capital formation and acquisition less

disposables of valuables, 3.131–3.133specific value indicators, 3.101–3.133

Gross national income (GNI), 4.14Gross operating surplus, indicators for 3.164–3.167

Holding gains and losses, work-in-progressconsiderations, 10.7, 10.17, 10.24

Household final consumption expenditureprice indicators, 3.83–3.86

value indicators, 3.71–3.78volume indicators, 3.79–3.82

Human resources capacity, 2.13

Improvements to QNA source data, 2.44–2.46Income accounts

about, 4.9–4.12allocation of primary income account, 4.14–4.15generation of, 4.13secondary distribution of income account, 4.16timing issues, 4.10–4.11use of disposable income account, 4.17

Income approach to GDP measurement, 2.15,2.21–2.22

Inconsistencies among data. See Editing andreconciliation

Indirect indicators, 3.48–3.52Industrial production indices (IPI), GDP by industry,

3.62–3.64Industry approach. See Production approach to GDP

measurementInputs/outputs. See also IO coefficients

current price data on outputs and/or inputs,3.29–3.36

data on quantities of output and/or inputs,3.37–3.42

labor input measures, 3.43–3.47Institutional sector accounts

about, 4.30–4.37financial corporations, 4.41general government, 4.38–4.40households, 4.42–4.44nonfinancial corporations, 4.47–4.48rest of the world, 4.49

Insurance premiums, 4.44Intangible assets, in fixed capital formation, 3.131Integrated compilation systems, 2.5Interest, 4.43, 4.44Intermediate consumption, deriving and presenting,

3.25, 3.26International investment position, 4.49Inventories, 3.134–3.135. See also Changes in

inventoriesInventory valuation adjustment (IVA), 3.A1.1IO coefficients, relationship between, 3.24IO ratios, benchmarking and, 6.37, 6.38IPI (industrial production indices), 3.62–3.64Irregular changes (statistical noise), 2.39

editing and reconciliation and, 5.37IVA (inventory valuation adjustment), 3.A1.1

INDEX

206

Labor input measures, 3.43–3.47, 3.96Laspeyres-type volume measures

about, 9.15–9.17, 9.A1.1aggregation over time and consistency between

annual and quarterly estimates,9.A1.1–9.A1.10

annual average prices as price base,9.A1.6–9.A1.10

relationship between quarterly and annualdeflators, 9.A1.2–9.A1.5

Least-squares-distribution technique, 7.16–7.18LIFO (last in, first out), 3.A1.2, 3.A1.3Lisman and Sandee quarterly distribution formula,

7.14–7.15Loans and deposits, price indicator, 3.59Logical edits, 5.15–5.16Long production cycles, 1.28Low-frequency payments, 1.28, 4.10, 4.11

Maintaining QNA. See Operational phaseManagerial issues

about, 2.68–2.73database software, 2.92–2.97managing data compilation systems, 2.92–2.97methods of speeding compilation, 2.78–2.81organizing data supply, 2.89–2.91organizing staff, 2.68, 2.83–2.88planning workloads, 2.75–2.77spreadsheet-based systems, 2.92–2.97structuring the compilation process, 2.74timing compilation process, 2.74–2.82

Manual on Government Finance Statistics, 3.168Mechanical trend projections

about, 7.1–7.6based on annual data, 7.7–7.18based on monthly or quarterly data, 7.19–7.22

Boot-Feibes-Lisman distribution method, 7.16–7.18least-squares-distribution technique, 7.16–7.18

Lisman and Sandee quarterly distribution formula,7.14–7.15

Merchandise, price indicators, 3.148–3.155Mixed income, indicators for, 3.164–3.167 Monthly GDP, Ch. I footnote 1

Net taxes, 3.66–3.671993 SNA. See System of National Accounts 1993Noise. See Irregular changes (statistical noise)Nonprofit institutions serving households (NPISHs),

3.95–3.97, 4.47–4.48

Operating surplus/mixed income, value indicator,3.164–3.167

Operational phase, 2.2, 2.53–2.55Output. See also IO coefficients

allocating work-in-progress output to periods,10.26

current price data on outputs and/or inputs,3.29–3.36

data on quantities of output and/or inputs,3.37–3.42

deriving and presenting, 3.25, 3.27estimating work-in-progress output based on

cost plus estimate of markup from othersource, 10.33

work-in-progress treated as output, 10.4,10.8–10.12

Pensions and annuities, 4.43Perpetual inventory method, 3.138Population, as indicator, 3.49PPI (producer price index), 3.54Presentation of data, 2.62, 2.66

revisions, 11.24Press releases, 2.65Price and volume measurement

about, 9.1–9.5aggregating over time, 9.6–9.14,

9.A1.1–9.A1.10annual overlap technique, 9.A2.1–9.A2.9.A2.6chain-linking, 9.21–9.53, 9.A2.1–9.A2.11choice of price weights for volume measures,

9.15–9.20, 9.A1.1–9.A1.10consistency between annual and quarterly

estimates, 9.A1.1–9.A1.10Fisher-type volume indices, 9.18–9.20four requirements to constitute time series, 9.3Laspeyres-type volume measures, 9.15–9.17one-quarter overlap technique,

9.A2.7–9.A2.9.A2.11Price indicators

changes in inventories, 3.144construction industry, 3.116–3.122equipment, 3.128–3.130exports and imports of goods and services,

3.148–3.155, 3.156final consumption expenditure by nonprofit

institutions serving households, 3.97GDP by income category, 3.169–3.170GDP by industry, 3.53–3.61government final consumption expenditure,

3.93–3.94

Index

207

household final consumption expenditure,3.83–3.86

merchandise, 3.148–3.155services, 3.156specific-purpose price indices, 3.55

Producer price index (PPI), 3.54Production account, 4.8. See also Work-in-progressProduction approach to GDP measurement, 2.15, 2.16,

2.17, 3.20–3.23, 3.28Proportional Denton method (D4 formula), 6.7–6.8,

6.22–6.36, 6.48, 6.50, 6.A1.7, 6.A1.11,6.A1.13–6.A1.16, 6.A3.1–6.A3.3

Proportional Denton technique with enhancements,1.27, 2.57, 2.59, 6.8, 6.31–6.36, 6.A1.2–6.A1.5,6.A1.18, 6.A1.40, 6.A1.43, 6.A1.49

Publication policy, 1.33

QNA. See Quarterly national accountsQuantity measures, 3.38–3.41Quarterization, 1.26Quarterly National Accounts Manual, 1.2–1.3,

1.39–1.47Quarterly national accounts (QNA)

about, 1.1–1.4ANA and, 1.5–1.12availability, 1.7business cycle analysis and, 1.7–1.9, 1.12, 1.14conceptual links between ANA, 1.24–1.28consistency with ANA, 1.24, 1.28critique of use for business cycle analysis, 1.12high inflation and, 1.10purposes of, 1.5–1.12short-term indicators and, 1.11as time series, 1.13–1.15transparency in, 1.29–1.36

Real estate transfer costs, 3.108Reconciliation. See Editing and reconciliationRegulation, information gathered in process of,

3.15–3.16, 3.80, 3.81Release cycle, 2.73Release of data, 2.62–2.67

revisions, 11.23–11.26Rest of the world, institutional sector accounts, 4.50Retail trade, sales data, 3.33, 3.34Revision policy

about, 1.33, 1.47, 11.1–11.4communication with users and, 11.23–11.25frequency of data incorporation in, 11.16,

11.18–11.20other important elements of, 11.22

providing revised time series, 11.26timeliness in, 11.14, 11.15, 11.17user requirements and resource constraints, 11.1,

11.5–11.6waves of source data and related revision cycles,

11.7–11.10Revisions of preliminary data, 1.30–1.33Road freight transport, indicators, 3.49

Seasonal adjustment and trend-cycle estimatesabout, 1.16, 1.44, 8.1–8.6additive model, 8.8, 8.9additivity in, 9.43–9.45business cycle changes and, 1.19BV4 program, 8.13calendar-related systematic effects, 8.7,

8.26–8.30differing opinions on, 1.17impact of irregular events and, 1.23irregular component, 8.7irregular effects narrowly defined, 8.7moving holidays, 8.2, 8.7, 8.26, 8.28, 8.29multiplicative model, 8.8, 8.9other calendar effects, 8.7other irregular effects, 8.7outlier effects, 8.7seasonal adjustment principles, 8.7–8.16seasonal component, 8.7software, 8.13status and presentation of estimates, 8.62–8.69trading-day effect, 8.2, 8.7, 8.26–8.30TRAMO-SEATS software, 8.13trend-cycle estimates, 8.3trend-cycle component, 8.7unadjusted data and, 1.18–1.22, 5.23X-11 family of programs, 8.13, 8.17–8.33

Seasonality issueschanges in seasonal patterns, 8.34–8.43compilation levels and adjustment of aggregates,

8.49–8.52, 8.54, 8.55, 8.56compilation levels and adjustment of balancing

items, 8.49, 8.53consistency with annual accounts, 8.59–8.61direct and indirect approach to estimates,

8.49–8.56extrapolation base and, 6.A2.17–6.A2.18four critical issues in, 8.48–8.61minimum length of time series for adjustment,

8.44–8.47relationship among price, volume, and value,

8.57revisions, 8.35–8.43

INDEX

208

seasonal filters, 8.36, 8.37status and presentation of estimates, 8.62–8.69supply and use and other accounting identities,

8.58wagging tail problem, 8.35–8.43

Separate compilation systems, 2.5Sequence of accounts, 4.4–4.5Services. See also Goods and services

price indicators, 3.156work-in-progress activities, 10.3

Setting up new QNA systems, 1.40Social contributions, 4.43, 4.44Source data. See also Data sources and specific

sourcesassessing, 2.31–2.47future extension of QNA and, 2.10inventory of, 2.9

Source statistics, discussions with compilers aboutdifferences, 2.61

Statistical issuesassessing compilation system, 2.31–2.34,

2.47–2.50assessing source data, 2.31–2.47compilation level, 2.30coverage of QNA, 2.8–2.29link between QNA and ANA, 2.4–2.7relationship between QNA and source data

statistics, 2.60–2.61statistical processing, 2.51–2.59

Statistical noise. See Irregular changesStep problem, 1.27, 1.43, 2.56, 6.9, 6.13–6.16

Bassie method and, 6.A1.17–6.A1.26forward and back step problems, 6.A2.1–6.A2.2,

6.A2.6–6.A2.7Strategies for QNA systems, 1.40, 2.1–2.3. See also

Dissemination issues; Managerial issues; Statisticalissues

Subsidies on products, production, and imports, valueindicator, 3.168

Subsistence production of food, volume indicator, 3.82Supply and use approach to GDP, 2.24–2.29Survey issues, 3.11–3.14

Taxation, information gathered in process of,3.15–3.16

Taxeshouseholds and, 4.43, 4.44nonfinancial corporations, 4.46on products, production, and imports as value

indicator, 3.168Time of recording, 1.28, 4.10, 4.11Time series, 1.13–1.15, 8.1

Timeliness of source data, 2.40Timing errors, editing and reconciliation and, 5.37Tracking exercises, 2.34

aggregate tracking exercise, 2.47–2.50Trade data, 3.148Transparency in quarterly national accounting,

1.29–1.36, 1.47Trend cycle estimates. See Seasonal adjustment and

trend-cycle estimatesTrustworthiness of data, revisions and, 1.31Turning points, identification of, 1.A1.1–1.A1.9

Unadjusted source data, 1.18, 1.20, 1.21Unconsolidated accounts (accounts for the total

economy)about, 4.7balance sheets, 4.25–4.29capital account, 4.18financial accounts, 4.19–4.24income accounts, 4.9–4.17production account, 4.8

Usersand revisions to data, 1.30–1.31, 11.1–11.3, 11.5consulting with, 2.2, 2.8, 2.13educating and informing, 1.34–1.36, 2.31, 2.33,

2.35, 2.48guiding future extension of QNA, 2.10-2.11opinions on, and need for, seasonally adjusted

and trend-cycle estimates, 1.17–1.21revisionpolicy communication, 11.22–11.24

transparency requirement of, 1.29–1.36

Valuables, in fixed capital formation, 3.131Value added, deriving and presenting, 3.25, 3.27Value added tax (VAT) systems, 3.16, 3.36, 3.71, 3.73,

3.99Value data, 3.32, 3.35, 3.36Value indicators

changes in inventories, 3.138–3.142construction industry, 3.32, 3.101–3.112equipment, 3.123–3.126exports and imports of goods and services,

3.145final consumption expenditure by nonprofit

institutions serving households, 3.95GDP by income category, 3.161–3.168government final consumption expenditure,

3.87–3.90gross fixed capital formation, 3.98–3.133household final consumption expenditure,

3.71–3.78

Index

209

Variables, multiple sources for same, 2.42VAT. See Value added tax systemsVolume indicators

changes in inventories, 3.143construction industry, 3.113–3.115equipment, 3.127exports and imports of goods and services,

3.146–3.147final consumption expenditure by nonprofit

institutions serving households, 3.96GDP by income category, 3.169–3.170government final consumption expenditure,

3.91–3.92household final consumption expenditure,

3.79–3.82Volume measures. See also Price and volume

measurementdistinguished from quantity measures, 3.38

WAC (weighted average cost), 3.A1.2Wagging tail problem, 1.20, 6.A1.37–6.A1.38, 6.A2.2,

6.A2.10–6.A2.11, 6.A2.15, 8.36–8.44, 8.39Weighted average cost, 3.A1.2Wholesale and/or retail industries, indicators, 3.49,

3.58Wholesale price index (WPI), 3.54Work-in-progress

about, 1.46, 10.1–10.7allocating output to periods, 10.26alternatives for products with long production

cycles, 10.18business accounting treatment of, 10.16–10.22contract work, 10.19cost/production profiles, 10.35–10.37delay in recognition of profits and, 10.17economic concepts in measurement,

10.13–10.15

effects on main aggregates, 10.A1.1–10.A1.7estimating output based on cost plus estimate of

markup from other source, 10.33example of ex post situation, 10.27–10.28examples of, 10.3forecasts and, 10.32holding gains and losses considerations, 10.7,

10.17, 10.24input costs, 10.25measurement, 10.13–10.37permutations arising from different data

situations, 10.29–10.32recording in 1993 SNA sequence of accounts,

10.A1.1–10.A1.7special issues for agriculture, 10.3, 10.5,

10.38–10.50speculative work, 10.20treated as output, 10.4, 10.8–10.12work for own final use, 10.19

WPI (wholesale price index), 3.54

X-11 family of seasonal adjustment programsbasic features, 8.17–8.20calendar-related effects, 8.26–8.30data adjusted for only some seasonal effects,

8.30estimation of other parts of seasonal component

in working/trading days, 8.26–8.30holiday adjustment procedures, 8.26, 8.28, 8.29moving average filtering procedure, 8.21–8.24,

8.26multiplicative version of filtering, 8.23preadjustments, 8.25seasonal adjustment diagnostics using,

8.31–8.33X-11-ARIMA, 8.13, 8.17, 8.54, 8.60, 8.61X-12-ARIMA, 8.13, 8.17, 8.54, 8.60, 8.61

INDEX

210

Quarterly National Accounts Manual

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