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Introduction

13.1 This chapter discusses the methods used to derive annual benchmarks and quarterly estimates for relevant aggregates in the gross domestic product account in current price and chain volume terms.

Current price estimates

13.2 The supply and use (S-U) tables provide annual benchmarks for the major current price aggregates included in the gross domestic product account for all years from 1994-95 (except for the latest financial year, for which S-U tables are not available). S-U tables were first compiled in respect of 1994-95. As explained in Chapter 12, three versions of the S-U tables are compiled in respect of each financial year. Consequently, the annual current price estimates are revised progressively for three years, as more complete information becomes available to construct the successive S-U tables for a particular financial year.

13.3 Initial quarterly current price estimates are benchmarked to the annual estimates from the supply-use tables using an 'optimal' benchmarking procedure which seeks to minimise amendments to the quarterly growth rates of the initial quarterly estimates while ensuring that the final quarterly estimates sum to their annual counterparts. The benchmarking procedure used was developed by Pierre Cholette of Statistics Canada. It is used to benchmark the quarterly flow data to the annual data. Let c_t and b_t respectively denote the unbenchmarked and benchmarked current price estimates for quarters t. The estimates of b_t minimise the sum of (c_t /b_t - c_t-1 /b_t-1 )² over a moving five year span subject to the bts summing to the annual current price estimate. The values of the b_ts in the central year are used, except at the ends of the series.

13.4 Estimates for the latest financial year are obtained by aggregation of the quarterly estimates, which are obtained in turn by extrapolation from the latest annual benchmark estimates using the most appropriate indicators. In some cases these are basically the same sources as those used in constructing the annual S-U tables (e.g. private gross fixed capital formation on new dwellings is mainly based on data for the value of work done from the Building Activity Survey). In other cases the indicators used are closely related to the aggregate being estimated (e.g. quarterly gross operating surplus of non-financial corporations is mainly based on data from the Company Profits Survey), while in a few cases the indicators used provide only a general indication of movements in the aggregate being estimated.

13.5 In conjunction with the implementation of the I-O approach in respect of 1994-95, some improvements to estimation methods were applied to the gross domestic product account estimates for earlier years. These improvements related mainly to compensation of employees (where refinements were implemented to the measure of wage and salary earners receiving pay in the reference period, which is obtained from the monthly Labour Force Survey), as well as to gross fixed capital formation on private dwellings and to other buildings and structures (where improved estimates were incorporated for various building services, such as those provided by architects, quantity surveyors and structural engineers).

13.6 The annual S-U tables also provided benchmark estimates for industry gross value added by ANZSIC Division from 1994-95. As these estimates were significantly different to the previous (i.e. SNA68-based) estimates for some industries, the new SNA93-based industry estimates were backcast to 1989-90. The changes due to differences between SNA68 and SNA93 were directly estimated by industry, but the changes resulting from benchmarking to balanced S-U tables were extrapolated using previously estimated movements prior to 1994-95.

Quarterly estimation methods

13.7 Four general methods are used to compile quarterly current price national accounts estimates for Australia:

• direct sources;

• indicators (pro rata);

• indicators (using 'benchmark'); and

• trend interpolation with or without specific annual forecasts.

Quarterly estimation methods - direct sources

13.8 The preferred method of compiling quarterly national accounts estimates is to use a high quality data source which provides data for the aggregate being measured according to the conceptual basis required for the national accounts. In such cases both the quarterly and annual estimates may be compiled from the same source, the annual estimates being obtained simply as the sum of the quarterly estimates. The new dwellings component of private gross fixed capital formation on dwellings is an example of where this method is applied.

Quarterly estimation methods - indicators (pro rata)

13.9 In many cases the quarterly data sources used to compile the national accounts are less reliable, less detailed and/or less appropriate than those used for compiling the annual national accounts benchmarks for particular aggregates. Consequently, indicator series are used to allocate (on a pro rata basis) annual estimates for such aggregates to the quarters of each financial year, and to extrapolate forward for the quarters of the latest incomplete year. The quality of estimates compiled using this method will depend on how closely the indicator series relates to the required national accounts aggregate. If the indicator series is very closely related to the national accounts aggregate that it is being used to estimate, this method will provide good quality quarterly estimates. However, if the correlation between the indicator series and the national accounts aggregate is volatile, this method would provide relatively poor quarterly national accounts estimates. A particular problem that arises when using the indicators (pro rata) method is that the September quarter estimates can be adversely affected by what is known as the 'step problem'. A significant step problem will arise if the relationship between the annualised indicator series and the annual benchmark estimates varies significantly between any two consecutive financial years. In effect, the difference in the annual relationship between the benchmark and the indicator series is largely reflected in just the September quarter. This problem is reduced by using the 'benchmark' procedure discussed in the paragraph 13.10. Given the obvious advantage of using the 'benchmark' procedure, the pro rata method is generally only used in a limited number of cases where the step problem is not significant.

Quarterly estimation methods - indicators (using 'benchmark')

13.10 This method of deriving quarterly estimates involves applying a mathematical technique that maintains the movements in the indicator series for all quarters as far as possible, but with the constraint that the sum of the quarterly estimates for each financial year must equal the corresponding annual benchmark estimate. In effect, instead of all the differences in the relationship between the annualised indicator series and the benchmark series being reflected in the September quarter, as would occur if the simple pro rata method was used, the differences are distributed across all quarters (see also paragraph 13.3 above).

Quarterly estimation methods - trend interpolation with or without specific annual forecasts

13.11 Where there are no quarterly direct data sources or indicator series available it is necessary to generate a quarterly time series by adopting the most appropriate allocation procedure. One possible method would be to divide the annual estimate by four, but this would result in steps each September quarter and no change in the other three quarters. The method used in the ASNA is to apply a linear interpolation method to calculate quarterly time series from annual series. The procedure involves forecasting annual estimates for two extra years, using a weighted average of the movements in year t-1 and year t. However, if information is available which provides a superior forecast for the annual estimates for those two years, such forecasts are used in preference to the standard projection produced by the interpolation procedure. A mathematical representation of the trend interpolation procedure is provided in Appendix 6. This method is particularly appropriate for series such as consumption of fixed capital, where only annual estimates are available and where it is reasonable to expect that movements in the quarterly series will be relatively smooth.


Chain volume estimates

13.12 The annual S-U tables are compiled in both current prices and in the prices of the previous year. The latter, which are compiled from 1995-96, are used to benchmark the quarterly chain volume estimates of the gross domestic product account in exactly the same way as their current price counterparts. Estimates for the latest financial year are obtained by aggregating the quarterly estimates which are derived by extrapolation from the latest annual benchmarks, in just the same way as the current price estimates.

13.13 While quarterly current price estimates are compiled for the income and expenditure 'views' of gross domestic product, the chain volume estimates are compiled for the expenditure and production views. In general, the chain volume expenditure estimates are derived by revaluing their counterpart current price estimates using price indexes. The major exception is exports of goods, for which most of the aggregate is derived by revaluing quantity data - see Chapter 18 for further details.

13.14 The production view of gross domestic product comprises an industry dissection of gross value added at basic prices and the item 'taxes less subsidies on products'. The preferred method for deriving volume estimates of valued added is by subtracting a volume estimate of intermediate input from a volume estimate of output. This method is employed in the annual S-U tables, but is employed for only one industry, agriculture, in deriving quarterly chain volume estimates. For all the other industries, output or input indicators are used to extrapolate and interpolate the annual benchmark estimates.

13.15 Most of the output and input indicators used in deriving the quarterly chain volume estimates of gross value added are available quarterly. In most cases, the source of these data differs from that used in compiling the annual S-U tables. The major exception is the construction industry, for which the quarterly data for value of work done from the Building Activity Survey, and data from the Engineering Construction Survey, are also used in compiling the annual S-U tables.

13.16 Linear trend interpolation/extrapolation of annual data (without annual forecasts) is only used for fishing; for insurance; and for the general government components of the cultural and recreational services industry and the personal and other services industry.