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Quarterly National Accounts. Workshop on National Accounts for Asian Member States of the Organization of Islamic Conference Ankara, 1-2 December 2008 UN Statistics Division. Objectives of presentation. Background on QNA General principles for QNA

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quarterly national accounts

Quarterly National Accounts

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

Ankara, 1-2 December 2008

UN Statistics Division

objectives of presentation
Objectives of presentation
  • Background on QNA
  • General principles for QNA
  • Coverage, sources and methods for QNA estimation
  • Benchmarking
  • Seasonality and seasonal adjustment of QNA
importance of qna
Importance of QNA

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

  • QNA provides a picture of current economic developments that is more timely than that provided by ANA, and more comprehensive and coherent than that provided by individual short-term indicators
specific purposes of qna
Specific Purposes of QNA
  • Framework for business cycle analysis - ANA are less suitable than QNA for business cycle analyses because annual data mask short-term economic developments
  • Early indicator economic development
  • Early estimates annual accounts
  • Forecasting
      • Accounting under high inflation
general principles related to qna
General principles related to QNA
  • To avoid confusion about interpreting economic developments, it is imperative that the QNA are consistent with the ANA
  • Differences in growth rates and levels between QNA and ANA would perplex users and cause uncertainty about the actual situation
  • Transparency of QNA is a fundamental requirement of users, and is particularly pertinent in dealing with revisions
  • To achieve transparency, it is important to provide users with documentation regarding the source data used, the way they are adjusted and compilation processes
  • This will enable users to make their own judgments on the accuracy and the reliability of the QNA and will pre-empt possible criticisms of data manipulation
general principles related to qna1
General principles related to QNA
  • In addition, it is important to inform the public at large about release dates so as to prevent accusations of manipulative timing of releases
  • Revisions in QNA can be due to a number of factors, both technical (seasonal adjustment, benchmarking etc.) and linked to data sources
  • There is often a trade-off between timeliness and accuracy of published data: the request by users of prompt information can generate increased revisions later on
  • Revisions provide the possibility to incorporate new and more accurate information into the estimates, and thus to improve their accuracy
data sources for qna estimates
Data sources for QNA estimates
  • Ideally, ANA should be derived as the sum (or average for stock variable ) of the corresponding quarterly data
  • Sources for ANA are generally different, more exhaustive, reliable and comprehensive than the corresponding ones for QNA
  • In many cases, data are collected only at the lower (annual) frequency, and at the higher frequency (quarterly or monthly) only ‘indicators’ or proxies are available, if any
  • This situation implies that ANA play a leading role and serve as a reference benchmark for QNA, and QNA generally ‘follow’ annual estimates
data sources for qna estimates1
Data sources for QNA estimates
  • In some cases, the same sources for ANA are also available on a quarterly basis, most commonly foreign trade, central government, and financial sector data
  • More commonly, QNA data sources are more limited in detail and coverage than those available for the ANA because of issues of data availability, collection cost, and timeliness
  • For each component, the available source that best captures the movements (rates of growth) in the target variable both in the past and in the future constitutes the best indicator.
data sources for the production approach
Data sources for the production approach
  • The production approach is the most common approach to measuring quarterly GDP
  • The production approach involves calculating output, intermediate consumption and value added at current prices as well as in volume terms by industry
  • Because of definitional relationships, if two out of output, intermediate consumption, and value added are available, the third can be derived residually. Similarly, if two out of values, prices, and volumes are available, the third can be derived
methods for qna estimation
Methods for QNA estimation
  • Methods for compiling QNA may differ quite considerably from those used for ANA.

Two major approaches:

    • Direct approach - based on the availability at quarterly intervals, of the similar sources as used to compile the ANA.
    • Indirect approach - based on time disaggregation of the ANA data in accordance with mathematical or statistical methods using reference indicators which permits the extrapolation of the current year.
  • Choice between these approaches depends, among other things, on the information available at quarterly level.
indirect estimation methods
Indirect estimation methods
  • We distinguish between methods that do not make use of any information (purely mathematical methods), and methods that use related time series as indicators for the unknown quarterly series

Purely mathematical methods

Simple extrapolation


Regression methods

No indicators


simple extrapolation
Simple extrapolation
  • 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 extrapolation1
Simple extrapolation
  • This hypothesis is quite strong as it implies that in all the economic phases the behaviour of the two variables is the same and that there are no lags or leads.
  • However, if the conditions discussed are respected, the following 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
simple extrapolation2
Simple extrapolation
  • If a plausible value of y0 has been chosen, the values y1, y2, y3, y4 can be considered as reasonable until the availability of the annual estimates. It is then necessary to run an adjustment procedure (benchmarking) to make the levels for the quarters consistent with the figures for the year
  • Following the above adjustment, the first quarter of the second year can be estimated starting from a consistent level.
  • Since the information set used for QNA is generally different from the set used for ANA, even if the estimates for the year t start from a fully consistent set of estimates of the last quarter of year t-1, they are not necessarily correct in level and, when a new annual value becomes available, an adjustment procedure is needed
  • Benchmarking is a mathematical procedure that makes the information coming from the high frequency series (quarterly) coherent with the low frequency series (annual)
  • Objective is to derive a consistent time series that preserves the short-term movements of the quarterly indicator subject to constraint that quarterly sum equals the annual benchmarks.
  • Numerical approaches used for distribution and extrapolation with an indicator:

- pro-rata distribution

- Bassie method

- proportional Denton technique

- others.

  • Statistical modeling approach:


- regression models

pro rata distribution method
Pro-Rata Distribution Method
  • Distributes the annual level data according to the distribution of the quarterly indicator.
  • Bq = A/ Σ Iq is called the “BI ratio” or the “rebasing ratio”
  • Introduces a discontinuity in the growth rate from the last quarter of one year to the first quarter of the next year - “step problem”.
pro rata method and step problem
Pro-rata method and “step problem”
  • BI ratio has to be stable from year to year
  • If the BI ratios for adjacent years are very different, a trend break will occur from Q4 to Q1 of the following year. This is known as “step problem”.

Avoiding the step problem

  • By smoothing out the changes in the BI ratios
    • BI ratios are treated as quarterly time series which is then smoothened.
    • Apply the smoothened BI series to the indicator series to derive benchmarked series.
the bassie method
The Bassie method

The method is as follows:

1. Select a pair of two years for benchmarking.

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

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

Find the difference between the annual value of the second year and the sum of quarter data:D2 = A2 -  Xq,2

Find the new adjusted value of the quarters for year 1 and year 2Zq1 = X q,1 + 0.25 x bq x D2

Zq,2 = X q,2 + 0.25 x cq x D2Subscript 1,2 refer to the first and second year.

the bassie method1

To be used for the first year

To be used for the second year




















The Bassie method

The value of b and c are as follows:

denton method
Denton method
  • Numerical approach
  • Least squares minimisation methods
      • The additive Denton (D1) minimises the absolute differences of the absolute adjustments of two neighbouring quarters
      • The proportional Denton (D4) minimises the absolute differences of the relative adjustments of two neighbouring quarters
  • D4 is preferred over D1 as it preserves seasonal fluctuations better.
denton method1
Denton method
  • Mathematically,
  • D1
  • D4
  • Under constraint
denton proportional method
Denton (proportional) method
  • The basic version of the proportional Denton benchmarking technique keeps the benchmarked series as proportional to the indicator as possible by minimizing (in a least-squares sense) the difference in relative adjustment to neighbouring quarters subject to the constraints provided by the annual benchmarks
  • The proportional Denton technique implicitly constructs from the annual observed BI ratios a time series of quarterly benchmarked QNA estimates-to-indicator (quarterly BI) ratios that is as smooth as possible
  • All quarterly growth rates are adjusted by gradually changing but relatively similar amounts
  • Indicators growths are maintained as far as possible
  • The sum of adjusted quarterly series adds up to the annual benchmarked values.
seasonal adjustment
Seasonal adjustment
  • Economic activity may vary by season.
  • The comparison makes sense only if an activity of a given quarter is compared to that of the same quarter in the previous year.
  • Seasonally adjusted data are needed if you want to have a comparison with the preceding quarter. Seasonally adjusted data and seasonally unadjusted data have their own usefulness. Raw data can be decomposed into three components:1.   Trend2.   Seasonal variation3.   Irregular variation
  • The commonly used method X11, X11-ARIMA and X-12-ARIMA. Seasonally adjusted data will not automatically satisfy the accounting identities in national accounts, which must exist in original data.  
quarterly national accounts1
Quarterly National Accounts


  • Eurostat (1999), Handbook on Quarterly National Accounts, Luxembourg: European Communities, available at:http://epp.eurostat.cec.eu.int/portal/page?_pageid=1073,1135281,1073_1135295&_dad=portal&_schema=PORTAL&p_product_code=CA-22-99-781
  • A. M. Bloem, R. J. Dippelsman, and N. O. Maehle (2001), Quarterly National Accounts Manual - Concepts, Data Sources, and Compilation, Washington DC: International Monetary Fund, available at: http://www.imf.org/external/pubs/ft/qna/2000/Textbook/index.htm