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1994 Feature Article - "Real" Estimates in the National Accounts
TABLE 1. THE EXPENDITURE SIDE OF THE PRODUCTION ACCOUNT
For year 2 the same result is obtained using the ‘production approach’ to measure current price GDP (i.e. $640 million made up of $1,000 million of output less $360 million of intermediate usage). It is apparent that the income available from the production of the same volume of output has fallen because of the decline in the terms of trade which resulted from the rise in import prices. In the absence of a higher price for wheat on world markets, the only way in which the income from production can be maintained is for physical production to increase.
There is no single agreed way in which to measure the “terms of trade effect” on GDP, but the method adopted in the Australian national accounts is generally accepted as being a suitable way of calculating the adjustment. It also has the advantage of being simple to implement. (In practice, the various methods produce fairly similar results in most circumstances.) In the Australian national accounts, the adjustment has been calculated by revaluing exports of goods and services by the IPD of imports of goods and services to provide a measure of the purchasing power of exports over imports. This value has then been substituted for the actual constant price value of exports of goods and services on the expenditure side of the constant price domestic production account Real gross domestic income has been calculated by summing final expenditures, the changes in stocks and (adjusted) exports less imports.
In the simple example above, the constant price export estimates adjusted for the terms of trade effect would be $250 million, obtained as the current price value ($300 million) deflated by the imports IPD (120.0). The expenditure estimates adjusted for the terms of trade effect would be as follows:
TABLE 2. EXPENDITURE ESTIMATES ADJUSTED FOR THE TERMS OF TRADE
In this example, even though there has teen no change in constant price GDP(I) between year 1 and year 2, there has been a decline of 7.1 per cent in real gross domestic income.
Graph 1 below compares movements between the reference period and the same period of the previous year for trend estimates of real gross domestic income and constant price GDP(l) and highlights the effects of movements in the terms of trade. The fall in the terms of trade over 1985, 1986 and 1990 led to weaker growth in gross domestic income than in constant price GDP(l) and the recovery in the terms of trade in 1987 and 1988 resulted in stronger growth in gross domestic income than in constant price GDP(I).
GRAPH 1. REAL GROSS DOMESTIC INCOME AND GDP(I) AT AVERAGE 1989-90 PRICES, TREND
Change from same quarter of previous year
While real gross domestic income was the first estimate published by the ABS which extended beyond the traditional constant price values, further income estimates expressed in real terms have subsequently been released in ABS publications, namely real gross national product and real household disposable income. In addition, the ABS is working in other areas with the aim of further supplementing the range of traditional constant price estimates published in the Australian national accounts. One such area is chain volume indexes.
Chain volume indexes
As discussed previously, changes over time in Australia’s production, as measured by gross domestic product (GDP) in current price terms, reflect the interaction of changes in the physical volumes of the goods and services produced and changes in their prices. Constant price estimates of GDP are derived by expressing transactions in terms of the prices of a base year in order to eliminate the direct effects of price change and allow movements in the underlying volumes to be analysed. Although these constant price estimates are traditionally rebased every five years, for some aggregates this may not be sufficiently frequent. Chain volume indexes are frequently rebased estimates with the price weights always reflecting the price relativities relevant to the reference period. Thus such chain volume indexes provide better indicators of growth than the more conventional constant price estimates in situations where the price and volume relativities of major components change rapidly over time. This is currently occurring to varying degrees for aggregates with computer equipment as a substantial component. Computer equipment prices have been falling rapidly and usage has been growing at a faster rate than for most other goods. In these circumstances the traditional constant price estimates will be inaccurate indicators of growth. The solution is to construct chain indexes, i.e. the accumulation of quarterly or annual volume indexes, in which each successive volume index is derived using the price relativities pertaining at the time.
Laspeyres volume indexes
The constant price value of a good or service at time n is the product of the quantity at time n and the price in the base period. Aggregate constant price values are simply the sum of the constant price estimates of their components, i.e.
Total constant price value at time n =
where p0 is the price of a good or service in the base period and qn is the quantity at time n. In effect, the prices in the base period (p0) are the weights used to combine the quantities of each component. When the constant price values of an aggregate are compared over time, an inaccurate measure of growth will result if the weights have changed appreciably from the base period.
A commonly used index for measuring volume growth is the Laspeyres volume index. A Laspeyres volume index may be defined as a weighted average of quantity relatives, the weights being the prices of the goods and services in the earlier of the two periods being compared. A Laspeyres volume index comparing values at times t and n takes the form:
In general, it is best to calculate a volume index spanning a number of periods by chaining together volume indexes calculated over consecutive time periods. A chain Laspeyres volume index connecting periods 0 and n takes the following form:
Paasche volume index
Closely related to the Laspeyres index is the Paasche index, which can be thought of as the mirror image of its Laspeyres counterpart. A Paasche volume index may be defined as a weighted average of quantity relatives, the weights being the prices of the goods and services in the later of the two periods being compared. A Paasche index comparing values at times t and n takes the following form:
A chain Paasche volume index is obtained by adding 1 to each of the price subscripts in the formula for the chain Laspeyres index to produce the following formula:
Fisher Ideal volume indexes
The 1993 System of National Accounts (SNA) states that the best volume index in most circumstances is a chain Fisher Ideal index, which is derived as the geometric mean of a chain Laspeyres index and a chain Paasche index. Such indexes have a number of desirable properties, including the fact that they satisfy the ‘time reversal’ test. This means that if all the price and quantity changes that occur between period 0 and t are subsequently reversed between and n, the chain Fisher index linking 0 to n through t returns to unity. Neither the chain Laspeyres nor chain Paasche indexes share this property and so they are more susceptible to ‘drift’ (due to fluctuations in price and volume relativities) than the Fisher index. Nevertheless, the revised SNA states that a chain Laspeyres index is likely to provide a reasonable alternative to a chain Fisher index.
Comparison of alternative volume indexes
The table below presents three volume indexes of imports of goods - an aggregate which has a significant computer equipment component. The first two are indexes of the constant price estimate at average 1984-85 prices and 1989-90 prices, respectively, and the third is a chain Laspeyres index. All three have been re-referenced to 1984-85 = 100.0. (It has not been possible to update the series beyond 1991-92 because constant price estimates on a 1984-85 base have not been compiled beyond 1991-92.)
TABLE 3. VOLUME INDEXES OF IMPORTS OF GOODS(a)
Consider the growth rate between the two years 1984-85 and 1989-90. According to the 1984-85 base year estimates, the volume of imports grew by 43.8 per cent, but according to the 1989-90 base year estimates, the volume of imports grew by only 35.8 per cent. Without the methodological improvements introduced with the 1989-90 based estimates, the latter growth rate would have been even lower. However, ignoring the methodological improvements and viewing the matter conceptually, it can be said that neither is more correct than the other. In the first case 1984-85 price relativities are used, while in the second case 1989-90 price relativities are used. The standard percentage change formula can be expressed as follows:
Percentage change between 1984-85 and 1989-90 = ( (Value in 1989-90 / Value in 1984-85) -1) x 100When the percentage change is calculated at average 1984-85 prices the quotient in the brackets is a Laspeyres volume index, but when the percent-age change is calculated at average 1989-90 prices the quotient is a Paasche volume index. A better indicator of the growth between the two years is obtained by computing the geometric mean of the two, to give a direct Fisher Ideal index, which indicates growth of 39.7 per cent. In this way both the 1984-85 and 1989-90 price relativities are treated symmetrically. Alternatively, we can refer to the Laspeyres chain index which indicates very similar growth of 40.4 per cent. It can be seen from the table that the chain Laspeyres index calculated for imports of goods generally follows an intermediate path between the 1984-85 and 1989-90 based constant price estimates, and provides a superior indicator of the growth in volume because it takes account of the changing price relativities.
ABS plans to produce chain indexes
The development of systems to produce chain volume indexes for publication is underway at the ABS. Experimental Fisher and Laspeyres type chain indexes will be derived from annually rebased constant price estimates for selected series, including imports and private capital expenditure on equipment. These aggregates have been chosen because they are the components most affected by the ‘computer equipment price problem’. It is intended to publish such estimates in addition to the existing five-yearly rebased constant price estimates rather than as a replacement for them. Any improvement in estimates of growth yielded by these estimates is at the expense of the additivity between components and aggregates which is a feature of unlinked constant price estimates.
A variety of real measures may be derived from one particular flow or stock estimate, reflecting the different perspectives of a number of transactors or the choice of factors such as the base period. In some instances, such as analysing estimates within an accounting framework, additivity may be essential and constant price estimates will be more useful than volume indexes. In other cases the focus may be on growth in components and aggregates individually and therefore chain volume indexes may prove more useful. Similarly, there will be situations where real measures, reflecting changes in purchasing power, are more relevant than constant price estimates which reflect changes in volumes of activity. Neither real nor constant price estimates are unique measures and users need to consider their characteristics in deciding on the appropriate real indicator for their application.
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