Economists who have worked with former Soviet Union (FSU) price data have noted the striking difference between the cumulative price increase derived by chaining the reported monthly producer price index (PPI)1 and the reported change of this index over 12 months.2
The purpose of this paper is to show that, in the context of the price fluctuations characterizing most transition economies, a chain index derived from the month-to-month price change of the PPI dramatically overstates the rate of price inflation in most cases. The analysis is based in part on a seminal paper by Szulc,3 who studied the problem of drift for a wide class of index formulas, and in part on observations made by the IMF’s technical assistance missions on price statistics of detailed price movements in the FSU countries. Greatest during the year 1992, the drift declines with slower rates of inflation (and possibly with changing patterns of price increases) but remains important for countries in which monthly inflation continues to run at nearly 10 percent.4
Consequently, the current version of the PPI should not be used as a deflator of the value of production to obtain a volume indicator. Indices of industrial production so derived would largely underestimate the growth (or overestimate the decline) in output. As the bias under discussion is measured in relation to the Laspeyres standard, the overestimation of price change would be effectively eliminated if the basis for calculation of the PPI were changed to a Laspeyres formula.
The paper also provides an explanation for the difference between the chained monthly index and the t/t – 12 version of the PPI and guidance on which of these indices should be used.
Koen, Vincent, and Steven Phillips, “Price Liberalization in Russia: The Early Record,” IMF Working Paper No. 92/92 (Washington: International Monetary Fund, November 1992).
Koen, Vincent, and Steven Phillips, “Price Liberalization in Russia: Behavior of Prices, Household Incomes and Consumption in the First Year,” IMF Occasional Paper No. 104 (Washington: International Monetary Fund, June 1993).
Moulton, Brent R., “Basic Components of the CPI: Estimation of Price Changes,” in Monthly Labor Review, by U.S. Bureau of Labor Statistics (Washington: U.S. Bureau of Labor Statistics, December 1993), pp. 13–24.
Szulc, Bohdan J., “Linking Price Index Numbers,” in Price Level Measurement: Proceedings of a Conference Sponsored by Statistics Canada, ed. by W.E. Diewert and C. Montmarquette (Ottawa: Minister of Supply and Services Canada, 1983), pp. 537–66.
François I. Lequiller and Kimberly D. Zieschang are both Economists in the Real Economy Division of the Statistics Department. The authors would like to thank Vincent Koen, Daniel Citrin, and Melanie Dieckman of the European II Department; Robert Dippelsman and Paul Cotterell of the Statistics Department; and Ralph Turvey, London School of Economics, for their useful discussion and comment.
The PPI is often referred to as the Wholesale Price Index (WPI) or, in Russian, as optoviy. This nomenclature is misleading as the observed prices are, in fact, producer prices (ex-factory gate) and not wholesale prices.
The problem with the producer price index formula that is the subject of this paper would also exist with any other price index, including the consumer price index (CPI), if this index was using the same nonstandard formula. Correction of this problem should therefore be undertaken wherever it is encountered. Fortunately, most of the FSU countries have introduced a new CPI using standard Laspeyres formulas with the assistance of the IMF’s Statistics Department. In fact, the problem may not be limited to transition economies. An interesting instance of similar linking problems seems to have occurred at low levels of aggregation in the U.S. CPI, although with less serious consequences (see Moulton (1993)).
Szulc refers to a chain of unweighted averages of price relatives for adjacent pairs of time periods as “the Sauerbeck formula.” The formula used in FSU countries is a chain of weighted averages of price relatives in which the weights remain constant from period to period—hence the term “generalized Sauerbeck.”
The opposite holds true when the same tendency of relative price change persists during the entire period, from the base time, 0, to the target time, t. Szulc’s demonstration on the Sauerbeck index is applicable to the generalized Sauerbeck index.
The example uses the Sauerbeck formula and thus equally weights the price relatives in constructing each chain link.
The data needed to calculate drift are not available in all republics of the former Soviet Union.
December 1992 registers the highest yearly drift. The year 1992 began with a large price shock in January, making it the most inflationary annual period in these countries in recent years.
For example, the base period, 0 in wi0, is in general not the same as the t – 12 period for the price relative, pi, t/i, t-12, as would be required by the Laspeyres formula.