Quarterly National AccountsQuarterly National Accounts

Workshop on National Accounts Workshop on National Accounts for Asian for Asian Member States of the Organization of Islamic Member States of the Organization of Islamic

ConferenceConference

Ankara, 1-2 December 2008Ankara, 1-2 December 2008

UN Statistics DivisionUN Statistics Division

Objectives of presentationObjectives of presentation

• Background on QNABackground on QNA

• General principles for QNAGeneral principles for QNA

• Coverage, sources and methods for Coverage, sources and methods for QNA estimationQNA estimation

• BenchmarkingBenchmarking

• Seasonality and seasonal adjustment Seasonality and seasonal adjustment of QNAof QNA

Importance of QNAImportance of QNA

““The importance of quarterly accounts The importance of quarterly accounts derives essentially from the consideration derives essentially from the consideration that they are the only coherent set of that they are the only coherent set of indicators, available with a short time-lag, indicators, available with a short time-lag, able to provide a short-term overall picture of able to provide a short-term overall picture of both non-financial and financial economic both non-financial and financial economic activity” (ESA 1995, § 12.02)activity” (ESA 1995, § 12.02)

QNA provides a picture of current economic QNA provides a picture of current economic developments that is more timely than that developments that is more timely than that provided by ANA, and more comprehensive provided by ANA, and more comprehensive and coherent than that provided by individual and coherent than that provided by individual short-term indicatorsshort-term indicators

Specific Purposes of QNASpecific Purposes of QNA

Framework for business cycle Framework for business cycle analysis - analysis - ANA are less suitable than QNA for business ANA are less suitable than QNA for business cycle analyses because annual data mask short-term cycle analyses because annual data mask short-term economic developmentseconomic developments

Early indicator economic developmentEarly indicator economic development

Early estimates annual accountsEarly estimates annual accounts

ForecastingForecasting

SPECIAL IMPORTANCE FOR:SPECIAL IMPORTANCE FOR: Accounting under high inflationAccounting under high inflation

General principles related to QNAGeneral principles related to QNA

To avoid confusion about interpreting economic developments, To avoid confusion about interpreting economic developments, it is imperative that the QNA are consistent with the ANA it is imperative that the QNA are consistent with the ANA

Differences in growth rates and levels between QNA and ANA Differences in growth rates and levels between QNA and ANA would perplex users and cause uncertainty about the actual would perplex users and cause uncertainty about the actual situationsituation

Transparency of QNA is a fundamental requirement of users, Transparency of QNA is a fundamental requirement of users, and is particularly pertinent in dealing with revisions and is particularly pertinent in dealing with revisions

To achieve transparency, it is important to provide users with To achieve transparency, it is important to provide users with documentation regarding the source data used, the way they documentation regarding the source data used, the way they are adjusted and compilation processesare adjusted and compilation processes

This will enable users to make their own judgments on the This will enable users to make their own judgments on the accuracy and the reliability of the QNA and will pre-empt accuracy and the reliability of the QNA and will pre-empt possible criticisms of data manipulationpossible criticisms of data manipulation

General principles related to QNAGeneral principles related to QNA

In addition, it is important to inform the public at In addition, it is important to inform the public at large about release dates so as to prevent large about release dates so as to prevent accusations of manipulative timing of releasesaccusations of manipulative timing of releases

Revisions in QNA can be due to a number of Revisions in QNA can be due to a number of factors, both technical (seasonal adjustment, factors, both technical (seasonal adjustment, benchmarking etc.) and linked to data sourcesbenchmarking etc.) and linked to data sources

There is often a trade-off between timeliness and There is often a trade-off between timeliness and accuracy of published data: the request by users accuracy of published data: the request by users of prompt information can generate increased of prompt information can generate increased revisions later onrevisions later on

Revisions provide the possibility to incorporate Revisions provide the possibility to incorporate new and more accurate information into the new and more accurate information into the estimates, and thus to improve their accuracyestimates, and thus to improve their accuracy

Data sources for QNA estimatesData sources for QNA estimates

Ideally, ANA should be derived as the sum (or Ideally, ANA should be derived as the sum (or average for stock variable ) of the corresponding average for stock variable ) of the corresponding quarterly dataquarterly data

Sources for ANA are generally different, more Sources for ANA are generally different, more exhaustive, reliable and comprehensive than the exhaustive, reliable and comprehensive than the corresponding ones for QNAcorresponding ones for QNA

In many cases, data are collected only at the lower In many cases, data are collected only at the lower (annual) frequency, and at the higher frequency (annual) frequency, and at the higher frequency (quarterly or monthly) only ‘indicators’ or proxies are (quarterly or monthly) only ‘indicators’ or proxies are available, if anyavailable, if any

This situation implies that ANA play a leading role This situation implies that ANA play a leading role and serve as a reference and serve as a reference benchmarkbenchmark for QNA, and for QNA, and QNA generally ‘follow’ annual estimatesQNA generally ‘follow’ annual estimates

Data sources for QNA estimatesData sources for QNA estimates

In some cases, the same sources for ANA are In some cases, the same sources for ANA are also available on a quarterly basis, most also available on a quarterly basis, most commonly foreign trade, central government, commonly foreign trade, central government, and financial sector dataand financial sector data

More commonly, QNA data sources are more More commonly, QNA data sources are more limited in detail and coverage than those limited in detail and coverage than those available for the ANA because of issues of available for the ANA because of issues of data availability, collection cost, and data availability, collection cost, and timeliness timeliness

For each component, the available source For each component, the available source that best captures the movements (rates of that best captures the movements (rates of growth) in the target variable both in the past growth) in the target variable both in the past and in the future constitutes the best and in the future constitutes the best indicator.indicator.

Data sources for the production approachData sources for the production approach

The production approach is the most common The production approach is the most common approach to measuring quarterly GDPapproach to measuring quarterly GDP

The production approach involves calculating The production approach involves calculating output, intermediate consumption and value output, intermediate consumption and value added at current prices as well as in volume added at current prices as well as in volume terms by industryterms by industry

Because of definitional relationships, if two out of Because of definitional relationships, if two out of output, intermediate consumption, and value output, intermediate consumption, and value added are available, the third can be derived added are available, the third can be derived residually. Similarly, if two out of values, prices, residually. Similarly, if two out of values, prices, and volumes are available, the third can be and volumes are available, the third can be derivedderived

Indicators for GDP by industryIndicators for GDP by industryCat.Cat. ActivityActivity Data Sources/indicatorsData Sources/indicators

A+BA+B Agriculture, hunting, Agriculture, hunting, forestry and fishingforestry and fishing

Harvesting data; Quantity of meat produces Harvesting data; Quantity of meat produces and prices from abattoirs; Number of and prices from abattoirs; Number of animals slaughtered; Quantity of timbers animals slaughtered; Quantity of timbers felled; Fodder and consumption of felled; Fodder and consumption of fertilizers; Value and size of catches; fertilizers; Value and size of catches; Fishermen’s landingFishermen’s landing

C+D+C+D+EE

Industry, including Industry, including energyenergy

Industrial production index; Qualitative Industrial production index; Qualitative business surveys; Employment databusiness surveys; Employment data

FF ConstructionConstruction Employment data; Supply of building Employment data; Supply of building materialsmaterials

G+H+G+H+II

Wholesale and retail Wholesale and retail trade, repairs, hotels trade, repairs, hotels and restaurants, and restaurants, transport and transport and communicationscommunications

Turnover statistics; Volume of goods Turnover statistics; Volume of goods transported; Nights spent in hotels; Number transported; Nights spent in hotels; Number of passengers; Subscribers to TV servicesof passengers; Subscribers to TV services

J+KJ+K Financial, real estate, Financial, real estate, renting and business renting and business activitiesactivities

Value of loans/deposits; Interest rates Value of loans/deposits; Interest rates spreads; Expenditures of households on spreads; Expenditures of households on dwelling rents; dwelling rents;

Industry indicatorsIndustry indicators

L to PL to P Other service Other service activitiesactivities

Number of employees; Wages and salariesNumber of employees; Wages and salaries

Indicators for GDP by type of expenditureIndicators for GDP by type of expenditure

DescriptionDescription Main Indirect SourcesMain Indirect SourcesHousehold final Household final consumption expenditureconsumption expenditure

Sales or revenues statistics; Surveys of retailers Sales or revenues statistics; Surveys of retailers and service providers; VAT systems; Turnover and service providers; VAT systems; Turnover index; Household budget survey; Commodity flow index; Household budget survey; Commodity flow approach; Cars registration; Business consumer approach; Cars registration; Business consumer qualitative surveys; Employment/earnings in the qualitative surveys; Employment/earnings in the activities concerned; Population; Radio and TV activities concerned; Population; Radio and TV licences; Overnight stays; Traffic indicators; licences; Overnight stays; Traffic indicators; Changes in number of dwellings Changes in number of dwellings

General government General government consumption expenditureconsumption expenditure

Data from government accounts; Wage and Data from government accounts; Wage and salaries statisticssalaries statistics

Gross fixed capital Gross fixed capital formationformation

Commodity flow approach; Value/volume of work Commodity flow approach; Value/volume of work done by capital goods producers; Index of done by capital goods producers; Index of construction output; Hours worked/number of construction output; Hours worked/number of employees; Capital outlays by purchasers of employees; Capital outlays by purchasers of capital goodscapital goods

Change in inventoriesChange in inventories Business surveys; Information from holders of Business surveys; Information from holders of stocks; Qualitative business surveysstocks; Qualitative business surveys

Exports and imports of Exports and imports of goods and servicesgoods and services

Customs (values and unit values) and BoP dataCustoms (values and unit values) and BoP data

Methods for QNA estimationMethods for QNA estimation

Methods for compiling QNA may differ quite Methods for compiling QNA may differ quite considerably from those used for ANA.considerably from those used for ANA.

Two major approaches:Two major approaches: • Direct approachDirect approach - - based on the availability at based on the availability at

quarterly intervals, of the similar sources as used to quarterly intervals, of the similar sources as used to compile the ANA. compile the ANA.

• Indirect approachIndirect approach - - based on time disaggregation of based on time disaggregation of the ANA data in accordance with mathematical or the ANA data in accordance with mathematical or statistical methods using reference indicators which statistical methods using reference indicators which permits the extrapolation of the current yearpermits the extrapolation of the current year. .

Choice between these approaches depends, Choice between these approaches depends, among other things, on the information among other things, on the information available at quarterly level.available at quarterly level.

Indirect estimation methodsIndirect estimation methods

We distinguish between methods that do not We distinguish between methods that do not make use of any information (purely make use of any information (purely mathematical methods), and methods that mathematical methods), and methods that use related time series as use related time series as indicatorsindicators for the for the unknown quarterly seriesunknown quarterly series

Purely mathematical methodsPurely mathematical methods

Simple extrapolationSimple extrapolation DentonDenton Regression methodsRegression methods

No indicators

Indicators

Simple extrapolationSimple extrapolation

1

1

1

1 , with ,

t

ttt

t

ttttt x

xxx

y

yyyxy

The extrapolation method is the easiest from a mathematical and conceptual viewpoint

The main hypothesis is that the indicator (xt) and the quarterly unknown series (yt) have the same time profile, so that they increase at the same rate:

Simple extrapolationSimple extrapolation

This hypothesis is quite strong as it implies that in all the This hypothesis is quite strong as it implies that in all the economic phases the behaviour of the two variables is the economic phases the behaviour of the two variables is the same and that there are no lags or leads.same and that there are no lags or leads.

However, if the conditions discussed are respected, the However, if the conditions discussed are respected, the following simple extrapolation formula can be usedfollowing simple extrapolation formula can be used

Then, the problem is represented by the choice of the initial conditions y0. The level of yt+1 depends on the initial conditions, whereas the growth rate of yt is totally independent. This implies that simple extrapolation is a good method for the estimation of growth rates, but not necessarily for the estimation of levels

1

10111

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on,substitutiby and,

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t

iitttt

ttt

xyxxyy

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Simple extrapolationSimple extrapolation

If a plausible value of If a plausible value of yy00 has been chosen, the values has been chosen, the values yy11, , yy22, , yy33, , yy44 can be considered as reasonable until the can be considered as reasonable until the availability of the annual estimates. It is then necessary availability of the annual estimates. It is then necessary to run an adjustment procedure to run an adjustment procedure (benchmarking)(benchmarking) to make to make the levels for the quarters consistent with the figures for the levels for the quarters consistent with the figures for the yearthe year

Following the above adjustment, the first quarter of the Following the above adjustment, the first quarter of the second year can be estimated starting from a consistent second year can be estimated starting from a consistent level. level.

Since the information set used for QNA is generally Since the information set used for QNA is generally different from the set used for ANA, even if the estimates different from the set used for ANA, even if the estimates for the year for the year t t start from a fully consistent set of start from a fully consistent set of estimates of the last quarter of year estimates of the last quarter of year t-1t-1, they are not , they are not necessarily correct in level and, when a new annual necessarily correct in level and, when a new annual value becomes available, an adjustment procedure is value becomes available, an adjustment procedure is neededneeded

BenchmarkingBenchmarking

Benchmarking is a mathematical Benchmarking is a mathematical procedure that makes the information procedure that makes the information coming from the high frequency series coming from the high frequency series (quarterly) coherent with the low (quarterly) coherent with the low frequency series (annual)frequency series (annual)

Objective is to derive a consistent time Objective is to derive a consistent time series that preserves the short-term series that preserves the short-term movements of the quarterly indicator movements of the quarterly indicator subject to constraint that quarterly sum subject to constraint that quarterly sum equals the annual benchmarks. equals the annual benchmarks.

BenchmarkingBenchmarking

Numerical approaches used for distribution Numerical approaches used for distribution and extrapolation with an indicator:and extrapolation with an indicator:

- pro-rata distribution- pro-rata distribution- Bassie method- Bassie method- - proportional Denton techniqueproportional Denton technique- others.- others.

Statistical modeling approach:Statistical modeling approach:

- ARIMA- ARIMA- - regressionregression models models

Pro-Rata Distribution MethodPro-Rata Distribution Method

Distributes the annual level data according Distributes the annual level data according to the distribution of the quarterly to the distribution of the quarterly indicator. indicator.

BBq q = A/ Σ I = A/ Σ Iq q is called the “BI ratio” or the “rebasing is called the “BI ratio” or the “rebasing

ratio”ratio” Introduces a discontinuity in the growth Introduces a discontinuity in the growth

rate from the last quarter of one year to the rate from the last quarter of one year to the first quarter of the next year - “first quarter of the next year - “step step problemproblem”. ”.

Iq

AIqXq *

Iq

IqAXq *

BenchmarkingBenchmarking

Pro-rata method and “step problem”Pro-rata method and “step problem”

BI ratio has to be stable from year to yearBI ratio has to be stable from year to year

If the BI ratios for adjacent years are very If the BI ratios for adjacent years are very different, a trend break will occur from Q4 different, a trend break will occur from Q4 to Q1 of the following year. This is known to Q1 of the following year. This is known as “as “step problemstep problem”.”.

Avoiding the step problemAvoiding the step problem By smoothing out the changes in the BI By smoothing out the changes in the BI

ratiosratios

• BI ratios are treated as quarterly time series BI ratios are treated as quarterly time series which is then smoothened.which is then smoothened.

• Apply the smoothened BI series to the indicator Apply the smoothened BI series to the indicator series to derive benchmarked series.series to derive benchmarked series.

The Bassie methodThe Bassie method

The method is as follows:The method is as follows: 1. Select a pair of two years for benchmarking.1. Select a pair of two years for benchmarking.

2. Apply the simple prorating method to the original quarter 2. Apply the simple prorating method to the original quarter data of the first year in the pair.data of the first year in the pair.

3. Apply the following formula for adjusting the prorated 3. Apply the following formula for adjusting the prorated data of the first year and the original data of the second data of the first year and the original data of the second year as follows:year as follows:

  

Find the difference between the annual value of the second Find the difference between the annual value of the second year and the sum of quarter data:year and the sum of quarter data:DD2 2 = A= A22 - - X Xq,2q,2

Find the new adjusted value of the quarters for year 1 and Find the new adjusted value of the quarters for year 1 and year 2year 2ZZq1 q1 = X= X q,1 q,1 + 0.25 x b + 0.25 x bqq x D x D22

ZZq,2 q,2 = X= X q,2 q,2 + 0.25 x c + 0.25 x cqq x D x D22

Subscript 1,2 refer to the first and second year. Subscript 1,2 refer to the first and second year.

The Bassie methodThe Bassie method

The value of b and c are as follows:The value of b and c are as follows:

To be used for the first year To be used for the second year

b1 -0.0981445 c1 0.57373047

b2 -0.1440297 c2 0.90283203

b3 -0.0083008 c3 1.17911122

b4 0.25048828 c4 1.34423822

Sum 0.0   4.0

Denton methodDenton method

Numerical approach Numerical approach

Least squares minimisation methodsLeast squares minimisation methods The additive Denton (The additive Denton (DD11) minimises the ) minimises the

absolute differences of the absolute absolute differences of the absolute adjustments of two neighbouring quartersadjustments of two neighbouring quarters

The proportional Denton (The proportional Denton (DD44) minimises the ) minimises the absolute differences of the relative absolute differences of the relative adjustments of two neighbouring quartersadjustments of two neighbouring quarters

DD44 is preferred over is preferred over DD11 as it preserves as it preserves seasonal fluctuations better.seasonal fluctuations better.

Denton methodDenton method

Mathematically, Mathematically,

D1D1

D4D4

Under constraint Under constraint

xQxx

Q

q Iq

Xq

Iq

Xq

, 4 ,1(

2

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xQxx

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IqXqqXq

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Denton (proportional) methodDenton (proportional) method

The basic version of the proportional Denton benchmarking The basic version of the proportional Denton benchmarking technique keeps the benchmarked series as proportional to technique keeps the benchmarked series as proportional to the indicator as possible by minimizing (in a least-squares the indicator as possible by minimizing (in a least-squares sense) the difference in relative adjustment to neighbouring sense) the difference in relative adjustment to neighbouring quarters subject to the constraints provided by the annual quarters subject to the constraints provided by the annual benchmarksbenchmarks

The proportional Denton technique The proportional Denton technique implicitly constructs implicitly constructs from from the annual observed BI ratios a time series of the annual observed BI ratios a time series of quarterly quarterly benchmarked QNA estimates-to-indicator benchmarked QNA estimates-to-indicator (quarterly BI) (quarterly BI) ratios that is as smooth as possibleratios that is as smooth as possible

All quarterly growth rates are adjusted by gradually All quarterly growth rates are adjusted by gradually changing but relatively similar amountschanging but relatively similar amounts

Indicators growths are maintained as far as possible Indicators growths are maintained as far as possible

The sum of adjusted quarterly series adds up to the annual The sum of adjusted quarterly series adds up to the annual benchmarked values.benchmarked values.

Denton (proportional) methodDenton (proportional) method

Seasonal adjustmentSeasonal adjustment

  

Economic activity may vary by season. Economic activity may vary by season. The comparison makes sense only if an activity of a The comparison makes sense only if an activity of a

given quarter is compared to that of the same quarter given quarter is compared to that of the same quarter in the previous year. in the previous year.

Seasonally adjusted data are needed if you want to Seasonally adjusted data are needed if you want to have a comparison with the preceding quarter. have a comparison with the preceding quarter.   Seasonally adjusted data and seasonally unadjusted Seasonally adjusted data and seasonally unadjusted data have their own usefulness. Raw data can be data have their own usefulness. Raw data can be decomposed into three components:decomposed into three components:1.   Trend1.   Trend2.   Seasonal variation2.   Seasonal variation3.   Irregular variation 3.   Irregular variation

The commonly used method X11, X11-ARIMA and X-12-The commonly used method X11, X11-ARIMA and X-12-ARIMA. Seasonally adjusted data will not automatically ARIMA. Seasonally adjusted data will not automatically satisfy the accounting identities in national accounts, satisfy the accounting identities in national accounts, which must exist in original data.  which must exist in original data.  

Quarterly National AccountsQuarterly National Accounts

References:References:1.1. Eurostat (1999), Eurostat (1999), Handbook on Quarterly National Handbook on Quarterly National

AccountsAccounts, Luxembourg: European Communities, , Luxembourg: European Communities, available at:available at: http://http://epp.eurostat.cec.eu.int/portal/page?_pageidepp.eurostat.cec.eu.int/portal/page?_pageid=1073,1135281,1073_1135295&_dad==1073,1135281,1073_1135295&_dad=portal&_schemaportal&_schema==PORTAL&p_product_codePORTAL&p_product_code=CA-22-99-781=CA-22-99-781

2.2. A. M. Bloem, R. J. Dippelsman, and N. O. Maehle A. M. Bloem, R. J. Dippelsman, and N. O. Maehle (2001), (2001), Quarterly National Accounts Manual - Quarterly National Accounts Manual - Concepts, Data Sources, and Compilation, Concepts, Data Sources, and Compilation, Washington DC: International Monetary Fund, Washington DC: International Monetary Fund, available at: available at: http://www.imf.org/external/pubs/ft/qna/2000/Tehttp://www.imf.org/external/pubs/ft/qna/2000/Textbook/index.htmxtbook/index.htm

Thank YouThank You