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Feature Article  Revisions to Quarterly Economic Growth Rates 19841993
Revisions can, however, prove useful indicators to the possibility of inaccurate source data or inefficient compilation methodologies. If it can be established that:
then it is selfevident that such estimates are inaccurate. Failure to account for known deficiencies of this type in the initial estimates would also constitute inefficiency in the estimation process. It may be deduced that initial estimates of a given data item are both inaccurate and inefficient if it can be shown conclusively that revisions may be reduced by employing additional (contemporaneous) information or alternative methods of compilation. In such cases, it is incumbent upon the ABS to investigate and eliminate any systematic distortions arising from the estimation process. Users may sometimes classify statistics as unreliable even though they are compiled efficiently and accurately (within the limitations of the available data sources). One example might be statistics subject to frequent revisions whose magnitudes are large relative to the underlying movement in the statistics. In this case, the unreliability is shown by revisions which have the potential to substantially alter the magnitude or even the direction of economic change indicated by the initial statistics. In general, such problems may only be addressed by extending the current statistical collections. Finally, it is important to note that the ABS is constantly reviewing and developing its compilation procedures. Users are therefore advised to treat the results presented in this article as a benchmark against which future revisions may be compared  and not as a guide to the likely characteristics of future revisions. SOURCES OF REVISIONS Revisions are a natural consequence of the statistical process, arising from the progressive incorporation of more uptodate information as it becomes available. For example, the initial estimates for the quarterly national accounts are based upon the survey responses received and processed to that time. Late responses, and the resultant amended adjustments for nonresponse, will lead to revisions when they are subsequently included in the estimates. For many data items, the quarterly survey data provide only partial indicators of the economic aggregate which is to be measured. Superior (but less timely) estimates are often available from annual (or less frequent) collections. The process of adjusting the quarterly indicators so that they are consistent with the more accurate annual estimates is known as benchmarking. Benchmarking typically leads to revisions over an extended period of time  often several years. Before the annual benchmarks become available, the quarterly estimates are compiled by extrapolating the benchmarked data of earlier years, generally using quarterly indicator series that are known to have a good relationship with the underlying aggregate being measured. These extrapolations will be revised successively as the quarterly indicator data are revised and again once new benchmarks become available. Often the first benchmark data to become available are also preliminary estimates, and therefore subject to revision over successive quarters or years. Moreover, the mathematical method by which the quarterly estimates are adjusted to the benchmarks can itself lead to characteristic patterns of revisions  sometimes restricted to the current year, but usually impacting upon the estimates for adjacent years. Seasonally adjusted estimates will usually experience some degree of revision over several years, due to the prolonged period required to finalise the estimation of seasonal adjustment factors. In the past, constant price estimates have been subject to substantial revisions approximately every five years due to the updating of the base year for which these estimates are calculated. This has generally led to substantial upward revisions to the levels of those estimates, but somewhat less predictable revisions to growth estimates.(See Endnote 1) From time to time, the availability of a major new data source or development of a superior estimation method may allow the reassessment of previous estimates for an existing time series of data or the introduction of a totally new data item. For example, in the mid1980s, the national accounts underwent considerable revisions stemming from the incorporation of some major conceptual and other large oneoff improvements:
DESCRIPTION OF ANALYSIS UNDERTAKEN The statistical investigation reported in this article examines ten years of economic data from the Domestic Production Account  published in Australian National Accounts: National Income, Expenditure and Product (ABS cat. no. 5206.0). Initial estimates of quarteronquarter growth over the period from the March quarter 1984 to the December quarter 1993 are compared with the corresponding ‘revised’ estimates published three years later. The focus is on the growth rates derived from seasonally adjusted estimates of the key income and expenditure aggregates, as well as the headline estimates of GDP. The decision to analyse revisions to quarterly growth rates is motivated by the prominence given to those estimates at the time of release. In addition, by focusing upon growth rates it is possible to partly abstract from the effects of irregular or oneoff revisions to levels arising, for example, from the introduction of major conceptual changes or the rebasing of constant price estimates. As the analysis focuses upon revisions measured over a fixed interval of three years (rather than revisions between the initial estimates and estimates based on the current state of the data), the statistics may subsequently be compared, on a consistent basis, with corresponding statistics for different time periods. Tables A.1 and A.2 in the Statistical Appendix report a range of descriptive statistics which are designed to characterise the reliability properties of the initial growth estimates for 27 key economic aggregates, as measured by revisions. Table A.1 reports descriptive statistics for revisions to quarterly growth rates in seasonally adjusted current price estimates, while Table A.2 reports the corresponding statistics for seasonally adjusted constant price estimates. In both tables, the statistics which summarise the behaviour of the data over ten years (or 40 quarterly observations for most data items) are contrasted with the statistics calculated from the last five years (20 quarters) of the sample. It is important to appreciate the overlapping nature of these statistics, and to recognise that significant differences between these two measures are indicative of an even more marked difference between the characteristics of the first and second halves of the sample period. Note that a number of major conceptual changes to the accounts (listed in the previous section) were concentrated in the first half of the decade. While the descriptive statistics are explained in greater detail in the Statistical Appendix, it is worth reviewing the key measures which appear in the following commentary on the results:
The quarterly growth rates analysed in this study are all derived from seasonally adjusted data. Revisions arising from the seasonal adjustment process will thus contribute to the overall extent of revisions observed. These changes can sometimes significantly raise the magnitude of revisions but would not be expected to have a major impact upon measures of bias. In the case of constant price data, it will frequently be the case that initial growth estimates will be compared with revised estimates having a different base year. The identification of revisions due to rebasing is not an objective of this study, but it is useful to recognise that such revisions may contribute to apparent anomalies in the revisions to current and constant price growth estimates for individual data items. MAIN FINDINGS TABLE 1: REVISIONS TO QUARTERLY GROWTH RATES IN GROSS DOMESTIC PRODUCT  SUMMARY
Gross domestic product (at current and constant prices) (see Table 1 and Tables A1 and A2 in the Statistical Appendix) Initial estimates of quarterly growth in constant price GDP were subjected to roughly equal numbers of upward and downward revisions  whether measured by the expenditure, income or production approach. Mean and median revisions tended to be positive, suggesting a small negative bias in the initial estimates of growth. However, these biases did not prove to be statistically significant. Revisions to the expenditurebased (GDP(E)) measure of growth, at constant prices, were found to be larger than for the alternative GDP measures. In 50% of cases, the magnitude of revisions exceeded 0.75 percentage points, while in about 25% of cases, the initial estimates of GDP(E) gave an erroneous indication of the direction of growth. (Note: Sign reversal statistics are not shown in the tables.) Over the decade 1984 to 1993, growth estimates based upon the constant price incomebased (GDP(I)) measure generally experienced much smaller relative revisions than the GDP(E) estimates and showed no evidence of systematic bias. In current price terms, though, initial estimates of GDP(I) were found to underestimate the revised rate of growth by an average of 0.19 percentage points per quarter during the latter half of the sample period (i.e. 1989 to 1993). Over the last five years of the sample period, the relative bias of the productionbased (GDP(P)) measure of growth exceeded the relative bias in the real GDP(E) and GDP(I) measures. That is, initial growth estimates derived from GDP(P) tended to be more conservative. (See Endnote 3) Since GDP(A) is derived as the arithmetic mean of the three measures of GDP at constant prices, it may be expected to exhibit less volatile quarterly movements and smaller revisions. This is confirmed by the analysis. While GDP(A) must, by definition, inherit a share of any biases present in its component measures, no evidence of significant bias was detected. While no significant bias was detected in the initial growth estimates of GDP(E) and GDP(I), several component aggregates nonetheless displayed significant bias over the period 19841993. As a general observation, initial estimates of growth in the public sector tended to be inflated (requiring subsequent downward revision), while initial estimates for the private sector tended to be conservative (requiring upward revision). On the expenditure side of the accounts, the positive mean revision to Private sector Gross fixed capital expenditure (GFCE) tended to slightly dominate the negative mean revisions to Public sector GFCE and Government final consumption expenditure. On the income side (in current prices), the mean revisions to Wages, salaries and supplements and Indirect taxes less subsidies were positive, offsetting the negative mean revision to Gross operating surplus (especially the general government component of GOS). Expenditure Components (at current and constant prices) (see Tables A1 and A2 in the Statistical Appendix) Final consumption expenditure Initial estimates of quarterly growth in Private final consumption expenditure proved to be highly consistent with their corresponding revised estimates. In both current and constant price terms, the mean and median of revisions were measured at less than 0.1 percentage point. The relative magnitude measures were lower than for any other aggregate, and there is no evidence of systematic bias  despite quite significant benchmarking adjustments to the level of the estimates over the period. By contrast, the initial constant price growth estimates for Government final consumption expenditure were biased (relative bias = 71.6%) and unreliable (relative magnitude = 191%). In about 40% of cases, the direction of growth indicated by the initial estimates was subsequently reversed within three years. Gross capital formation While mean and median revisions to the aggregate Gross capital formation(GCF), measured in current prices, were comparatively small (relative bias = 1.6%) and exhibited no signs of systematic bias, it is notable that the two dominant components of GCF ( Private and Public gross fixed capital expenditure) both showed strong evidence of bias in initial estimates. However, the significant negative bias in the initial estimates of Private sector GFCE growth (understated by 1.41 percentage points) plus Change in stocks almost exactly offset the significant positive bias in the initial Public sector GFCE growth estimates (overstated by 1.94 percentage points on average). Similar biases are evident in the constant price component estimates for the period, although in this case the biases do not balance. The negative bias arising from Private sector GFCE plus Change in stocks exceeded the positive bias contributed by Public sector GFCE, resulting in a net negative bias in initial estimates of GCF growth of 0.58 percentage points. Private sector GFCE Twothirds of all revisions to initial constant price growth rates for Private sector gross fixed capital expenditure were positive. The mean revision was 1.33 percentage points, which is judged to be highly significant by the statistical criteria used in this study. While there is evidence that the magnitude of the bias decreased between the first and second halves of the sample period, the hypothesis of unbiasedness is still strongly rejected by the data for 1989 to 1993. Similar negative biases are evident in the initial current price estimates. In almost one quarter of cases, initial indications of the direction of growth in Private sector GFCE at constant prices were reversed by subsequent revisions. All four component aggregates contributed to the negative bias in initial estimates of Private sector GFCE, but the most significant source of bias was clearly the investment in Equipment component, with a mean revision of 1.82 percentage points in constant price terms. While it is difficult to identify systematic bias in the revisions to investment in Nondwelling construction, these revisions were, on average, much larger and more volatile than the revisions to Equipment  reporting high measures of relative bias and relative magnitude. Between 1984 and 1993, almost 50% of the initial estimates for Nondwelling construction indicated the incorrect direction of quarterly growth. Public sector GFCE Initial constant price estimates of growth in Public sector gross fixed capital expenditure were revised downwards, on average, by 1.92 percentage points per quarter. The relative magnitude measure of 109% indicates that the magnitude of revisions to growth frequently exceeded the mean absolute growth rate. From examination of the current price data, it can be concluded that both components of Public sector GFCE display a tendency for positive bias. Twothirds of revisions to GFCE by General government were negative, and the mean revision of 1.73 percentage points is statistically significant. The mean revision to growth in GFCE by Public enterprises was 2.26 percentage points. International trade The mean revisions to Exports and Imports of goods and services were small and display no significant bias. However, 50% of revisions to individual constant price estimates exceeded 1.7 percentage points in magnitude, leading to quite high measures of relative magnitude  especially for Exports between 1989 and 1993. While revisions to Imports were much smaller in the second half of the sample, they became more unidirectional  70% of revisions to constant price growth in Imports between 1989 and 1993 were negative. INCOME COMPONENTS (at current prices) Wages, salaries and supplements Revisions to Wages, salaries and supplements growth rates were generally small and rarely resulted in a change of sign. However, the initial estimates underestimated the revised rate of growth by an average of 0.29 percentage points per quarter between 1989 and 1993. Gross operating surplus The most significant instance of positive bias on the income side of the accounts  as on the expenditure side  was provided by the public sector component. The mean revision of 0.36 percentage points per quarter to the GOS of General government was found to be statistically significant  although much of this result may be attributed to large negative revisions to the first two years of data following the inclusion of this aggregate in the accounts in 1986. There is little evidence of systematic bias or unidirectional revisions among the revisions to other components of GOS, although quite high measures of relative magnitude were recorded. Indirect taxes less subsidies The net income component Indirect taxes less subsidies contributes about 12% to estimates of the level of GDP. Initial quarterly growth estimates were revised upwards, on average, by 0.38 percentage points. This result, combined with the negative bias in initial estimates of Wages, salaries and supplements, helps to explain the apparent bias in initial estimates of growth in the incomebased measure of GDP. While the quarterly movements in this component were much smaller in the second half of the sample period, the revisions were not  resulting in a considerable increase in the measure of relative magnitude. GROSS FARM PRODUCT (at current and constant prices) Early estimates of annual Gross farm product (GFP) typically rely upon mediumterm forecasts of crop yields and commodity prices, while reliable and timely quarterly indicators are scarce. Under these circumstances, it might reasonably be expected that initial estimates of quarterly growth in GFP would be subject to considerable revision. While the range of revisions is rather broad (6.09 to 11.52 percentage points for the constant price estimates) and the measures of mean, median and magnitude are comparatively high (especially for the current price data), the measures of relative bias and relative magnitude indicate that GFP estimates do not perform noticeably worse than most other initial estimates. The mean revision of 0.93 percentage points to constant price growth is statistically significant, but the median revision of 0.30 percentage points indicates a comparatively low relative bias of 10.3%. MONITORING AND ANALYSING REVISIONS  ISSUES AND OPTIONS The recent improvements in source data, which are described in the accompanying article, will contribute to a pattern of future revisions that is different from the pattern observed in the past and, notwithstanding other changes that are made in the compilation of the national accounts, should lead to a reduction in the extent of revisions. Over the next few years, the ABS proposes to substantially modify the compilation procedures for the national accounts. These innovations will impact upon the conceptual framework in which the accounts are compiled, the collection and reconciliation of source data and the methodologies employed to compute the published aggregates. Some of these modifications may lead to transient increases in the extent of revisions to the national accounts during implementation. In the longer term, however, the enhancement of the other aspects of statistical quality (especially accuracy and coherence) should more than compensate. Users of ABS economic statistics will be interested in the impact of future revisions upon a wide diversity of analyses and decisionmaking processes. It is important then to ensure that future monitoring procedures are not narrowly focused upon particular data items and particular types of revisions. Conversely, a complete treatment of all aspects of the revisions process may overwhelm users with a vast amount of (largely redundant) material. It may be assumed that the majority of users will continue to be interested in likely revisions to the initial estimates of growth in GDP (measured in seasonally adjusted constant prices). However, in addition:
The ABS also has much to learn from analyses of revisions. In addition to identifying less reliable estimates for individual data items, the ABS may initiate studies which will, for example:
In summary, no single style of analysis can display the patterns of revisions (and the ways in which those patterns may evolve over time) that are of interest to all users. The ABS is currently developing a suite of analytical techniques designed to monitor the impact of current developments and to address the concerns of major groups of users. Suggestions or feedback from the readers of this article are encouraged and welcomed. FURTHER INFORMATION The analyses reported in this article were conducted by Peter Rossiter, an Assistant Director of the Analytical Services Section, ABS. For further information about the analyses contact Peter on telephone (02) 6252 6024, facsimile (02) 6252 8015 or email peter.rossiter@abs.gov.au. ENDNOTES 1. For most series, rebasing tends to reduce growth rates in recent periods, although the extent varies from series to series. The ABS will shortly be replacing its constant price estimates with chain volume measures, and this will essentially remove rebasing as a source of revisions to growth rates. 2. Sign reversal may clearly result from either small or large revisions  depending upon whether the initial growth estimate is ‘close’ to zero. However, as this statistic is quoted only in instances where revisions have already been identified as large (in a relative sense), it may be assumed that the proportion of ‘insignificant’ sign reversals is generally low. 3. Generally the quality of the source data underlying the quarterly estimates of GDP(P) tends to be less than the quality of data underlying the other two measures of GDP. STATISTICAL APPENDIX Tables A.1 and A.2 contain descriptive statistics which characterise the revisions, after three years, to initial estimates of quarterly growth rates. The initial estimates were published between the March quarter 1984 and the December quarter 1993 (40 quarters). The statistics calculated from 20 quarters of data pertain to the initial estimates published between the March quarter 1989 and the December quarter 1993. Revised estimates were extracted from publications released between the March quarter 1987 and the December quarter 1996. The descriptive statistics include, for each economic aggregate:
Where the distribution of revisions is symmetric about the mean, the mean revision will be almost identical with the median revision. Divergence between these two measures will generally indicate that the estimate of the mean is being influenced by a small number of extreme cases. (The largest positive and largest negative revisions may prove informative in such instances.) Since the median is more robust to the presence of extreme outcomes, and is perhaps the more intuitive measure of the midpoint of the distribution, it is used in reference to the mean in the construction of the relative biasmeasure. The median revision indicates the predominant direction of change between the initial and later growth estimates. The relative biasindicates whether the median revision is itself large relative to the average quartertoquarter movement. In summarising the findings for individual data items, it is often convenient to make reference to ‘bias’ in the initial estimates. To avoid confusion, note that a ‘positive mean or median revision’ equates to ‘negative bias in the initial estimates’. It is important to distinguish between patterns of revisions which are purely random and those which exhibit systematic bias. An indication of whether or not revisions to an aggregate are systematically biased can be obtained by assuming unbiasedness and then considering the likelihood of observing the current estimate of the mean revision. If the magnitude of the observed mean appears improbably large, taking account of the distribution of all the revisions, then it is said to be statistically significant. Estimates of the mean which are judged by standard statistical criteria to be significantly greater than or less than zero are highlighted in the tables. (A significance level of 10% has been used.) The average magnitude of revisions is computed as the median of the distribution of the absolute values of all revisions. As above, the median is preferred to the mean because it is a more stable measure when the distribution is skewed. The measure of relative magnitude is defined as the ratio of the median absolute revisionto the mean absolute growth rate. An alternative, though much less stable, measure could be obtained by computing the ratio of each revision to its respective initial (or final) estimate (without respect to sign) and taking the mean or median of the resulting distribution. The usefulness of the chosen measure depends to some extent on the supposition that the magnitudes of individual revisions are approximately independent of the magnitudes of their respective initial (or final) estimates. Since this may not be true, additional information concerning the incidence of sign reversal due to revisions has been provided in the commentary. It seems intuitively desirable for initial estimates to undergo roughly equal proportions of positive and negative revisions. Where a major imbalance occurs, it is necessary to distinguish whether this is due to a small number of extraordinary revisions (affecting the whole time series of estimates) or systematic bias in the initial estimates. Such extraordinary revisions will generally also be reflected in the median bias and magnitude statistics. Serial correlation  which may be regarded as a minor systematic influence  may be detected in the time series of revisions to most aggregates, and is generally sufficient to explain small deviations from the ‘equal probability’ hypothesis. The largest negative and largest positive revisions define the range of revisions to each aggregate in each time period. It is important to note that they are, by definition, extreme outcomes  often attributable to unusual or onceonly circumstances. TABLE A.1: REVISIONS TO QUARTERLY GROWTH IN SEASONALLY ADJUSTED CURRENT PRICE DATA  DESCRIPTIVE STATISTICS
TABLE A.2: REVISIONS TO QUARTERLY GROWTH IN SEASONALLY ADJUSTED CONSTANT PRICE DATA  DESCRIPTIVE STATISTICS
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