L08 - Benchmarking Techniques (ENG)

1Quarterly National Accounts CourseJoint Vienna InstituteAugust 5 - 16, 2013

L-8: Benchmarking Techniques

Reproductions of this material or any parts of it should refer to the IMF Statistics Department as the source

Lecture Outline

Benchmarking Principles in QNABenchmarking Principles in QNAThe Denton PFD method

Enhanced formula for extrapolation

Benchmarking and revisions

JVI/QNA/L8 : 2IMF Statistics Department

2IntroductionQuarterly compilation involves:Q y p

Establishing a set of quarterly national accounts for periods the annual estimates are available

Construction of historical quarterly accountsUpdating a set of quarterly national accounts -derivation of quarterly estimates for most current periods with no annual estimatescurrent periods with no annual estimates


Discrepancy Between QNA and ANA

Discrepancies occur due to:Discrepancies occur due to:Independent collection of quarterly and annual data sources for the same phenomena

Quarterly data based on (smaller) sample surveys using simplified questionnairesAnnual data based on censuses/larger sample surveys using more comprehensive questionnairesAnnual data based on data from audited business accounts


3Discrepancy Between QNA and ANA

Discrepancies occur due to:Discrepancies occur due to:More information, and more detailed information, available annuallyQuarterly estimates based on:

Fixed input output coefficientsTrend extrapolationsTrend extrapolationsGuesstimates


Discrepancy Between QNA and ANA

Discrepancies occur due to:Discrepancies occur due to:Compilation procedures for annual and quarterly national accounts estimates may differ

Annual accounts more detailedAnnual accounts more completeUse of supply and use tables as compilation tool for Use o supp y a d use tab es as co p at o too othe annual accountsUse of simplified methods in the quarterly accounts


4Discrepancy Between QNA and ANADiscrepancies removed byp y

Benchmarking the quarterly data to the ANA estimates

So thatTime series of quarterly and annual data for the same phenomena are consistentAccuracy and quality of the quarterly data areAccuracy and quality of the quarterly data are increasedQuarterly data could be used to forecast annual data


Benchmarking: Basic ApproachesManual reconciliation and revision of independent annual and quarterly data sources, and annual and quarterly estimatesMechanical methods

Pro-rata distribution breaks in series (the step problem)Time series method no breaks in seriesTime series method no breaks in series


5Pro Rata Distribution and Step Problem

Distribution presentation Xq is the level of theDistribution presentation Xq, is the level of the QNA estimate for quarter q of year

Iq, is the level of the indicator in quarter q of year

q q

qq I

IAX

,, .

q y A is the level of the

ANA estimate for year

q qI ,


Pro Rata Distribution and Step Problem

Benchmark-to-indicator Xq is the level of theBenchmark to indicator ratio presentation

Xq, is the level of the QNA estimate for quarter q of year

Iq, is the level of the indicator in quarter q of year

qqq I

AIX

,, . q y

A is the level of the ANA estimate for year

q qI ,


6Pro Rata Distribution and Step Problem

Both equations are algebraically equivalent

Only the presentation differs


Extrapolation with an IndicatorFor the quarters of the current year or even the q ymost recent year, independent ANA data are not available.QNA estimates for these periods should be consistent with the QNA estimates for previous periods that are benchmarked to the annual data.M t i th t l i di t i d tMovements in the quarterly indicator is used to extrapolate/update the QNA estimates (benchmarked to the ANA) to derive the QNA estimates for quarters with no ANA estimates.


7Extrapolation with an Indicator

Extrapolation presentation Xq is the level of theExtrapolation presentation Xq, is the level of the QNA estimate for quarter q of year

Iq, is the level of the indicator in quarter

IIXX qq

,4

1,,41, .

indicator in quarter q of year

,4


Extrapolation with an Indicator

Benchmark-to-indicator Xq is the level of theBenchmark to indicator presentation

Xq, is the level of the QNA estimate for quarter q of year

Iq, is the level of the indicator in quarter

IXIX qq

,4

,41,1, .

indicator in quarter q of year

,4


8Pro Rata Distribution: Step Problem

98 0

100.0

102.0

104.0

106.0

108.0 -------------------------Back Series-------------------------

980

1000

1020

1040

1060

1080-------Forward series-----

96.0

98.0

1997 1998 1999960

980

Indicator (left hand scale)QNA estimates derived using pro rata distribution (right hand scale)


Pro Rata Distribution: Step Problem

Benchmark-to-indicator ratioBenchmark to indicator ratio

9.8

10.3

1997 1998 1999


9Golden rules of BenchmarkingA benchmarking procedure should satisfy two g p y

requirements at the same time:Preserve as much as possible the short-term movements in the quarterly source data under the restrictions provided by the annual dataEnsure, for the forward series, that the sum of the four quarters of the current year is as close

ibl t th k f t l d tas possible to the unknown future annual data


Benchmarking Methods That Avoid Steps

Time series method avoiding stepsTime series method avoiding stepsVarious, but same purposeKeeps the movements of the short-term benchmarked series as proportional as possible to those in the original series


10

Benchmarking Methods That Avoid Steps

Proportional Denton methodProportional Denton methodKeeps the movements in the benchmarked QNA series as proportional as possible to those in the quarterly indicator series using a least square technique to minimize the difference in relative adjustment to neighboring quarters subject to annual total constraint.


Optimal Benchmarking SolutionFor the back series, the method ,recommended in the IMF QNA manual is the Proportional First Differences (PFD) solution proposed by Denton (1971) which

Preserves the short-term movements in the indicators keeping the quarterly estimates as proportional to the indicator as possible (avoid the step problem)Considers the annual benchmarks as binding constraints


11

Denton PFD methodIn mathematical terms, the benchmarked ,series Xt is the solution of the following minimization problem:

NtforYX

YXN tt 4,...,2,1min

241


NTforAXtsYY

TTt

t

t tt

,...,2,1..2 1

Proportional Denton Method

Benchmarking without Step ProblemsBenchmarking without Step Problems

98.0

100.0

102.0

104.0

106.0

108.0

980

1000

1020

1040

1060

1080------------------ Back series ------------------------------- ----Forward series ----

96.01997 1998 1999

960

Indicator (left hand scale)QNA estimates derived using pro rata distribution (right hand scale)1997-98 distributed 1999 extrapolated using Proportional Denton (right hand scale)


12

Proportional Denton Method

Benchmark-to-Indicator Ratios

10.3

9.81997 1998 1999

1997-98 distributed 1999 extrapolated using Proportional Denton Annual step change


Improving extrapolation of QNA results

Using proportional Denton method implies thatUsing proportional Denton method implies that the B-I ratio for the fourth quarter of the last benchmarked year is used to prepare the forward QNA seriesThe B-I ratios for quarters with ANA data are usually different and change smoothly y g y

Depends on the movements in the annual B-I ratios


13

Improving extrapolation of QNA resultsFor the forward series, the Denton PFD ,method results in quarter-to-quarter rates of change that are identical to those in the indicator series. But

When there is a bias between the movements of the target variable and those of the indicator, extrapolations should be adjusted to better predict the next annual growth rate of the target variable

An adjustment (or enhancement) to the original Denton method is proposed in the IMFs QNA manual (chapter 6)


Improving extrapolation of QNA results

The B-I ratios for quarters with no ANA data canThe B I ratios for quarters with no ANA data can be improved by

Forecasting annual B-I ratios Deriving quarterly B-I ratios taking into account the forecasted annual B-I ratio


14

Denton PFD method with enhancement for extrapolation

The minimization problem changes into:

4 2

1

2 1

4min for 1, 2, , ,t tt t t

N s X X tI I

N s

p g

B-I forecast for year N+1

4 14

4 1 1

,

s.t.

for 1, 2,3, 4

, for 1,2, ,t Tt TN s

t Nt

t N t N

X A T N

X Aw sI I


Benchmarking and Revisions

When the ANA data becomes available:When the ANA data becomes available:The QNA data for that year are benchmarked to the ANA dataThe QNA data for the quarters of the subsequent years are revisedThe QNA data for earlier years are revised


15

Benchmarking and Revisions

When ANA data for previous years are revised:When ANA data for previous years are revised:The QNA data for those years are benchmarked to the revised ANA dataThe QNA data for the quarters of the subsequent years are revisedThe QNA data for earlier years are revised


Benchmarking and RevisionIncorporation of new annual data for one yearp ywill generate revisions of quarterly data for neighboring yearsThe Denton method is optimal because revisions for one year are distributed smoothlyover several quarters, not just within the same yearyearThe enhanced Denton method tries to improve the B-I forecast for the next year, and then reduce revisions to preliminary QNA data


L08 - Benchmarking Techniques (ENG)

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