In order to allow comparisons to be made between countries of measures of growth in national accounts estimates, it is practical to express the series with respect to a common reference year. The move from expressing the constant price series with respect to an original base year, to a reference year common across all countries, requires the series to be re-referenced. This generates differences between re-referenced components and aggregates and other estimates derived through accounting relationships, such as GDP.
There are two common cases where the problem arises with respect to World Bank economic data.
First, when a series of revised country estimates in constant prices ‘is supplied’ to the country management unit in the World Bank, which do not extend back to the start of the time series at present maintained in the database, a discontinuity where the new series meets the old one will exist. This is typically the case when a country re-bases its national accounts, and submits new constant price figures for recent years.
Second, it is preferable to move from the original base year of country economic series, to a common reference year for the purposes of comparison across countries. Countries compile constant price estimates according to their own selected base years. The Bank’s task is to convert the constant price series to a comparable basis in constant price terms using a standard/common reference year.
As the reason for compiling constant price estimates is to enable estimates of real growth to be made, it is logical that in determining the process of re-referencing the original series to a new year, growth rates be preserved. However, this leads to loss of additivity, as it can be trivially shown that both growth rates and additivity cannot be preserved except under exceptional circumstances.
It is important to make a clear distinction between the fundamental nature of the re-basing process which is carried out by the statistical producer at country level, and the superficial re-referencing process which is carried out in the Bank (and can easily be done by anyone).
Country re-basing of national accounts at constant prices
Changes over time in the values of flows of goods and services can be directly factored into two components: one reflects changes in the prices of goods and services and the other reflects changes in their volumes.
Value ( v ) at the level of a single product is equal to the price ( p ) per unit of quantity multiplied by the number of quantity units ( q ); so
v = p . q
The time series reflecting real change in a macro-economic variable for a country, is often shown as a series of values expressed in the prices of a common base year. In the course of time, the pattern of relative prices of the base period becomes less relevant to the economic situations of later periods, to the point where it becomes unacceptable to continue using the base year prices to derive volume changes from one later period to the next. It is then necessary to update the base year period, and express the years near this new base year in the prices of the new base year.
This process of re-basing a country’s national accounts requires a detailed re-compiling of the country’s national accounts constant price estimates, using relevant price indices to deflate current price values to generate volume estimates. These price indices will reflect the updated structure of the economy and the relative prices reigning in the new base year. Aggregates are compiled by summing the components, as using Paasche style price indices to measure price change and so compile estimates of volume change by stripping the effect of inflation from value change, will result in volume measures of the Laspeyres type. For a common base year, aggregates of volume measures based upon the Laspeyres index will be the sum of the components at constant prices. This additivity property is not a universal rule, but stems from the mathematical form of the indices used in the deflation process, and that components have been expressed in the prices of a common base year.
Re-referencing - First case - Taking on new constant price estimates for a recent period
Assuming that the country has re-based their national accounts for the latest years, in order to provide long-run time series of volume growth, it is necessary to link the new series to the series on the old base-year to provide a common reference year over time so that volume changes are measured consistently over the whole time-span.
For a single index taken in isolation, re-scaling is a simple arithmetic operation. A link year is chosen where the estimates exist for the old and new base year prices. The link factor is calculated as the ratio of the new to old values for this link year. The old series estimates prior to the link year are then multiplied by this link factor to place the complete series on a consistent basis. This ensures that for the link year and before, the growth rates of the original series are preserved.
The problem faced in the country is to decide how to handle the apparent breakdown of accounting relationships for years prior to the period surrounding the new base year. If each series is re-referenced using the factor from a common year to splice the two parts of the series together, then the individual series values will no longer sum to the linked total. This is demonstrated below, omitting the 1985 values at 1990 prices as typical of the form of data presented from the country national accounts.
It should be emphasized at this point that by its very nature, re-scaling must cause any existing accounting relationships which hold at constant prices to break down. But this is not a penalty, as any existing additivity property is there only because of the special nature of the Laspeyres-style index underlying the constant price series construction. Additivity is not an important property of constant price series, and it can be argued that all such series compiled to allow estimates of growth to be derived, should be expressed only in index form. This would prevent false expectations of additivity on the user’s part. The question of how the apparent breakdown of additivity in the early periods is discussed in the new System of National Accounts (SNA93). Clear guidance is given and some countries already follow this practice:
16.58 When base year values are extrapolated by chain volume indices there are effectively three ways of dealing with the ensuing non-additivity. The first is simply to publish the non-additive "constant price" data as they stand without any adjustment. This method is transparent and indicates to users the extent of the problem. Users may, or may not choose to eliminate the discrepancies for analytical purposes, choosing whatever method they consider most appropriate for their purposes. Some countries prefer to publish unadjusted non-additive data for these reasons. The second possibility is to distribute the discrepancies over the components at each level of aggregation. This procedure is not without its cost as the volume movements for the components are distorted as a result. For certain types of analysis such distortion could be a serious disadvantage. On balance, it would seem preferable to let users decide whether or not to eliminate the discrepancies so that users mainly interested in volume changes for particular components are not disadvantaged. A third possibility would be to eliminate the discrepancies by building up the values of the aggregates as the sum of the values of the components at each level of aggregation. This procedure cannot be recommended in general. Not only would it introduce distortions into the volume movements of the aggregates but it would also make the results for the aggregates depend quite arbitrarily on the level of disaggregation distinguished within the accounts. By distorting the volume movements for the aggregates this method would appear to defeat the whole objective of trying to obtain improved volume measures at an aggregate level through chaining.
16.59 Similar considerations have to be taken into account when time series of fixed base Laspeyres volume indices and their accompanying constant price series have to be rebased. As noted above, assuming the re-basing is not carried backwards, the linked data for series prior to the new base year will not be additive. For reasons just given, the transparent procedure is simply to publish the non-additive data without adjustment leaving it to users to decide whether, or how to deal with the resulting discrepancies.
Re-referencing - Second case - Re-referencing constant price estimates to a common reference year for comparison purposes in the World Bank
Constant price series in Bank databases are re-referenced so that each series of every country is expressed with respect to a common reference year. This is a simple process, and requires that each original estimate is multiplied by the ratio of the new reference year estimate in current prices to the estimate in constant prices on the original base. All estimates are linked in the same way; aggregates are not derived as component sums. This preserves growth rates, as described above, while additivity is lost and simple accounting relation ships are no longer satisfied.
Thus, the re-referenced constant price value of GDP is no longer the sum of the referenced value of consumption, gross domestic investment and export less imports, but simply the re-referenced version of the estimate at the original base year prices of the country. One way to encourage users to think of constant price series purely as a means to measure growth (and not expect additivity), is to store and publish the series in index form only. |
RSS