Koen, Vincent, and Steven Phillips, “Price liberalization in Russia: The Early Record, International Monetary Fund Working Paper 92 (Washington: International Monetary Fund, 1992).
Koen, Vincent, and Steven Phillips, “Price Liberalization in Russia: Behavior of Prices, Household Incomes and Consumption in the First Year,” Occasional Paper No. 104 (Washington: International Monetary Fund, June 1993).
Moulton, Brent, “Basic Components of the CPI: Estimation of Price Changes,” in U.S. Bureau of Labor Statistics, Monthly Labor Review (Washington: U.S. Bureau of Labor Statistics, December 1993).
Szulc, Bohdan, “Linking Price Index Numbers,” in W.E. Diewert and C. Montmarquette, eds., Price Level Measurement: Proceedings of a Conference Sponsored by Statistics Canada (Ottawa: Statistics Canada, 1983), pp. 537–562.
The authors would like to thank V. Koen, D. Citrin, and M. Dieckman of the Fund’s European II Department; R. Dippelsman and P. Cotterell of the Fund’s 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.
See, among others, the two papers by Vincent Koen and Steven Phillips on price liberalization in Russia: IMF Working Paper 92, 1992, and IMF Occasional Paper 104, June 1993.
It should be noted that the problem with the Producer Price Index formula that is the subject of this paper also exists, in some instances, for the Consumer Price Index (CPI). Correction of this problem with the CPI should therefore be undertaken wherever it is encountered with countries of the FSU. However, 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)).
This fact is not necessarily well known outside the Fund, however. The recent OECD publication entitled Short-term Economic Indicators for Central and Eastern Europe: Sources and Definitions incorrectly attributed a Laspeyres methodology to the Estonian PPI.
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 in which the weights remain constant from period to period—hence the term “generalized Sauerbeck.”
Szulc points out that the Sauerbeck is consistent with the assumption of very strong substitution effects. From equation (9), it may be seen that this is also true of the generalized Sauerbeck/WAPR index. The correlation between percentage changes in ρ and q from the same time period for the same item is clearly -1.
it may be argued that, for the WAPR, the correlation between r and y becomes a function of the correlations between r in the current period and its reciprocal from previous periods back to the base. If the short-term relatives are positively serially correlated, the correlation between r in the current period and the product of its past values would be positive. By implication, the correlation of current period r with the reciprocal of the product of its past values would be negative. The correlation between r and y will therefore be negative for the WAPR formula when the short-term relatives are positively serially correlated, and the WAPR will display downward drift in comparison with the Laspeyres. If the same reasoning is used, it may be argued that negative serial correlation in r will induce upward drift.
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. Some republics, such as Lithuania and Georgia, do not publish a PPI. Others, such as Uzbekistan and Tajikistan, do not publish both one- and twelve-month indexes. In Belarus, the statistical office corrected calculation of the index for aggregation of regional data to the national level, but problems remain in the effective index formula used by some of the regions. The one- and twelve-month indexes are therefore consistent at the national level and drift is not evident in the most recently revised data. However, inconsistencies leading to drift at lower levels of geographical aggregation remain but cannot be measured because the necessary data are not published.
The drift is equal to [(1)+100] / [(2)+100].
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.
The monthly drift is equal to the (1/12)th power of the annual drift.
For example, the base period, 0 in wi0, is in general not the same as the t-12 period for the price relative, Pit/Pit-12, as would be required by the Laspeyres formula.