Robert Kirchner Statistics DepartmentDeutsche Bundesbank

Thoughts on the presentation of growth rates

OECD SCHORT-TERM ECONOMIC STATISTICS EXPERT GROUP MEETING26 – 27 June 2003, Paris

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Outline

1. Introduction

2. Definition

3. Actual change from previous period

4. Actual change from previous year

5. Change in seasonally-adjusted data

6. Change in trend data

7. Annualised growth rates

8. Summary

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1. Introduction

Growth rates are typically used to describe the development of variables. For this reason, growth rates are often a central feature of press releases, analyses and newspaper reports concerning economic activities (such as movements in prices or output). In this context, it is not always entirely clear what type of growth rate is appropriate for answering the question to be addressed. This relationship is discussed below.

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2. Definition

Growth rates express the change in values of a time series between two different periods of time. For example, the percentage change of a time series value Xt from Xt-d is expressed as Xt / Xt-d * 100 - 100.

Depending on the question to be answered using growth rates, it is advisable to use various intervals d between the original values or to relate the growth rates to the seasonally-adjusted results.

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Conclusion In press releases, database presentations and so on, attention should be paid to the relationship between the type of question to be addressed and the type of growth rate.

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3. Actual change from previous Period

If, for example, the idea is to present the actual change of a monthly variable from the value of the previous month, the percentage growth rate based on the original values is Xt / Xt-1 * 100 - 100. The Federal Statistical Office in Germany uses this formula to show, for instance, short-term consumer price movements. The general public is also interested in the actual monthly change in unemployment (expressed as an absolute change Xt – Xt-1).

7IW/S31S17#E

Change from previous period

1999 2000 2001 2002 2003

Thousands

Unemployment in Germany *

* Definition of the Federal Labour Office’s statistics.

400+

300+

200+

100+

0

100–

200–

4800

4600

4400

4200

4000

3800

3600

8

JA/S

31S18#E

JanFeb

March

Ap

rilM

ayJune

JulyA

ugS

epO

ctN

ovD

ec

1999

2000

2001

2002

2003

Unem

plo

yment in G

ermany *

Chang

e from

previo

us perio

d in tho

usands

*D

efinition of the Federal Lab

our Office’s statistics.

400+

400+

350+

350+

300+

300+

250+

250+

200+

200+

150+

150+

100+

100+

50+

50+

00

50–

50–

100–

100–

150–

150–

200–

200–

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When analysing cyclical developments, however, such changes have no informative value if they primarily reflect seasonal and/or calendar-induced influences. For example, unemployment in Germany goes up every winter, one of the reasons being that when the weather is colder there are fewer employment prospects in outdoor occupations. Therefore, temporary increases in unemployment by themselves do not reveal anything about cyclical movements.

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Conclusion Monthly change, quarterly change or other change in the space of less than a year and based on original series subject to seasonal changes, should only be used to present actual developments and not to describe cyclical movements.

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4. Actual change from previous year

The presentation of current economic statistics is frequently accompanied by a comparison of the present situation with that of the previous year (in the case of monthly time series, usually with the percentage year-on-year change Xt / Xt-12 * 100 - 100). Examples of this practice can be found in Italy (industrial output, retail sales) as well as in Korea.

12IU/S03S05#E

year 1 year 2

January

June

January

June

are in accordance withthe following time series...

-0.5-1.4

-2.3-3.2

-4.1-5.0

-2.5

0.0

2.5

5.0

7.5

10.0The following changes fromprevious year...

Meaningfulness of changes fromprevious year

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In cyclical analyses, too, this measure is frequently used. Assuming that the conditions responsible for the seasonal variation this year and last year are equal, the year-on-year rate is free from seasonal influences. Nevertheless, it should be borne in mind that year-on-year change depends on movements over the last twelve months and not solely on the most recent developments, which is what cyclical analyses actually seek to measure.

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Even more, the year-on-year difference may be influenced by calendar effects. For example, if a given month has one more working day than the same month in the previous year, German industrial production will be 3% higher on average. It would be wrong to interpret this growth as a result of a cyclical movement.

15IZ/S31S20#E

Based

onunad

justed d

ata

Based

on working d

ayad

justed d

ata

19981999

20002001

20022003

Change from

previous year in %

Outp

ut in industry

*

*M

anufacturing sector not allocated to m

ain grouping energy p

lus mining and

quarrying, excep

t energy prod

ucing materials.

20+

20+

15+

15+

10+

10+

5+

5+

00

5–

5–

10–

10–

16

Year-on-year comparisons also have less informative value for cyclical observations if the year-on-year change is either particularly high or unusually low as a result of special factors which occurred in the last year (base effect).

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Conclusion Year-on-year rates of change based on original series subject to calendar changes should only be used to present actual developments and not to describe cyclical developments. Where necessary, special effects contained in the base period should be pointed out when presenting year-on-year rates of change.

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5. Change in seasonally-adjusted and calendar-adjusted data

Common use is made of percentage changes based on seasonally-adjusted and calendar-adjusted data to describe economic developments. These rates are intended to describe new phenomena which do not occur in the same season each year with almost the same intensity or which are not attributable to calendar regularities. Besides cyclical movements, these rates also include “irregular” influences, such as reactions to fiscal policy measures, the placing of large orders, the effects of strikes, unusual weather conditions, purely random disruptions or even errors when estimating seasonally adjusted results.

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Where such irregular effects contribute in relevant measure to changes in values from one month to the next, particular account of them should be taken when interpreting such movements. If these influences balance out over several months, it is advisable to summarise the values of several months in order to clarify underlying cyclical movements (such as percentage changes based on two or three months’ worth of values: (Xt + Xt-1) / (Xt-2 + Xt-3)* 100 - 100 or (Xt + Xt-1 + Xt-2 ) / ( Xt-3 + Xt-4 + Xt-5)* 100 - 100).Examples of this procedure can be found in Germany (press releases on the output index or the index of new industrial orders) and France.

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Conclusion Percentage changes based on seasonally-adjusted and calendar-adjusted values serve to describe new phenomena and are used as an tool for analysing current economic developments.

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6. Percentage changes of trend data

Percentage changes based on the trend cycle component of a time series (estimated with sophisticated mathematical methods or simply with a 12-term moving average) are designed to make the cyclical change clearer. However, since the trend cycle values at the current end of the series are usually estimated by extrapolating the underlying trend of the recent past, it often takes months until the interesting economic turning points are shown. Not least on account of such difficulties, many statistical offices deliberately refrain from publishing current trend growth rates (exception: Federal Statistical Office in Germany).

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Trend versus seasonally adjusted data– Orders received by the manufacturing sector from abroad –

1992 1993

1985 = 100, log scale

December 1994

PC/S31S05#E

October 1993

October 1993

May 1993

May 1993

February 1993 April 1993June 1993

December 1994

Seasonally adjusted figures ...

Trend (BV4)

... smoothed with a three-period moving average

ASA II (ifo)BV4 (StBA)Census

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Conclusion Percentage changes based on the trend cycle component of a time series illustrate past economic developments; they are, however, unsuited to describing current economic movements.

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7. Annualised growth rates

Annualised rates help to answer the question of which annual percentage change would occur if the development established during the year were to continue unchanged. Technically, the annualised percentage change extrapolated from the monthly change is (Xt / Xt-1)12 * 100 - 100.

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Annualised growth rates should not be calculated on the basis of seasonally-influenced or calendar-influenced original series. For example, if for German construction output the climate-induced change in results from a normal warm autumn to a typically cold winter were annualised, this would imply that spring would be significantly colder than winter and summer then colder than spring, which would be nonsense.

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Annualised growth rates are therefore generally calculated on the basis of seasonally-adjusted and calendar-adjusted values. However, since they also reflect one-off irregularities, care should also be taken when annualising the figures. If, for example, the seasonally-adjusted data are influenced by a one-off strike, when annualising the data it would be wrong to assume that additional strikes would occur in subsequent months.

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IU/S

31S19#E

19981999

20002001

20022003

Change from

previous p

eriod

Annualised

changefrom

previous p

eriod

Annual change (b

ased on yearly sum

s)

Seasonally ad

justed, change in %

Gro

ss value add

ed in the co

nstruction secto

rat 1995 p

rices

20+

20+

15+

15+

10+

10+

5+

5+

00

5–

5–

10–

10–

15–

15–

20–

20–

28

In addition, current trend data are not suited to calculating annualised growth rates since they derive from the condition of the current trend estimate which is explained under item 4 and states that the past trend will continue unchanged until the end of the series – at the most interesting turning points in the cycle, this is wrong.

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For these reasons, annualised growth rates are not often used. One exception to this rule can be found in the context of the presentation of seasonally adjusted figures for the national accounts in the USA.

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Conclusion Particular caution should be exercised when annualising changes that occur within the space of a year. The shorter the base period for the extrapolation is, the more uncertain the results are (annualised monthly changes are more problematic than annualised six-month changes). The data should only be annualised on the basis of seasonally-adjusted and calendar-adjusted time series which only contain minor irregularities. If special effects result in problems when annualising, the limited informative value of these annual growth rates would have to be indicated separately.

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8. SummaryConclusion In press releases, database presentations and so on, attention should be paid to the relationship between the type of question to be addressed and the type of growth rate.