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Relative Prices, Inflation and Core Inflation WP/OO/58 IMF Working Paper Relative Prices, Inflation and Core Inflation Scott Roger INTERNATIONAL MONETARY FUND © 2000 International Monetary Fund WP/00/58 IMF Working Paper Asia and Pacific Department Relative Prices, Inflation and Core Inflation Prepared by Scott Roger' Authorized for distribution by Kanitta Meesook March 2000 Abstract The views expressed in this Working Paper arc those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author( s) and are published to elicit corrunents and to further debate. Empirical evidence on the distribution of relative price changes almost invariably reveals high kurtosis and a tendency toward right-skewness. Simple mixed distribution models including volatile and infrequently adjusted prices can account for these and other common features, such as correlation between the mean and variance of relative prices. In such circumstances, robust measures of central tendency are likely to outperform the mean or standard measures of "core" inflation as indicators of generalized inflation. The analysis also supports the use of geometric averaging in CPI construction and the targeting of the geometric mean inflation rate rather than the Laspeyres mean. JEL Classification Numbers: C43, E31, E52 Keywords: Inflation, relative prices, central tendency Author's E-Mail Address: SROGER@IMFORG 'The views expressed in the paper are my own and do not necessarily reflect the views of the IMF. I would like to thank, without incriminating, Francisco Nadal De Simone for helpful comments on an earlier draft. - 2- Contents Page I. Introduction .......................................................................... .......... 3 II. Empirical Evidence on the Distribution of Relative Prices .......... ..................... 4 III. Models of the Distribution of Price Changes ............................................................ 7 A. A Model with "Volatile" Prices: Mixed Log-Normal Price Changes .................... 7 B. A Model ofInfrequently Adjusted Prices ...................................................... 12 IV. Implications for Core Inflation Measurement.. ........................................................ 14 A. The Choice of the Target Measure of Central Tendency ..................................... 14 B. Estimation of the Core Inflation Rate ................................................................. 18 V. Concluding Comments ........................................................................................... 24 References ........................ ............................................................................... 26 Figures 1. Kurtosis ofthe Mixed Log-Normal Distribution ................ ...................... 11 2. Skewness of the Mixed Log-Normal Distribution ................................................... 11 3. Bias of the Arithmetic Mean of the Mixed Log-Normal Distribution Relative to the Geometric Mean (Measured in Standard Deviations) ..................................... 12 4. Skewness of the Distribution of Log-Normal Price Changes Mixed with Infrequently Adjusted Prices.... .... ..... ..... ..... .... ......... ..................... ......... 15 5. Kurtosis of the Distribution of Log-Normal Price Changes Mixed with Infrequently Adjusted Prices........................................................................ .15 6. Bias of the Arithmetic Mean with respect to the Geometric Mean Inflation Rate ..... 16 7. Bias of the Median with respect to the Geometric Mean Inflation Rate ................... 16 8. Mean Percentile of the Mixed Log-Normal Distribution ......................................... 23 9. Efficiency of the Sample Mean Percentile Relative to the Sample Mean of the Mixed Log-Normal Distribution ......................................................................... 23 Appendices I. The Mixed Normal Distribution, Kurtosis and the Efficiency of the Median Relative to the Mean ............................................................................ 30 II. Evolution of the Estimation of Central Tendency... ................... .......... 37 - 3 - I. INTRODUCTION Central banks concerned with inflation performance almost invariably seek to distinguish between a generalized or persistent component of the measured aggregate rate of inflation­ driven by demand pressures and expectations-and supply-driven, essentially transitory inflation developments associated with movements in relative prices. The more generalized, persistent element - usually described as "core" or "underlying" inflation - is regarded as a legitimate monetary policy concern, while the influence of specific relative price developments are generally regarded as transient "distortions" that should be largely ignored in forward-looking policy setting, as well as in backward-looking assessment of policy performance. Typically, "distortions" to the aggregate inflation rate are attributed to one of two sources: (a) the influence of particularly "volatile" prices-such as petroleum or fresh food prices­ largely determined by supply factors; and (b) the effects of infrequent price adjustments, most often involving prices set directly by the public sector or, at least, heavily influenced by government regulation or infrequently adjusted excise taxes and levies. In either case, the relative price movements are seen as distorting the aggregate inflation rate insofar as they do not reflect persistent or generalized demand pressures in the economy. A review of empirical evidence indicates that, over the entire period in which price indices have been constructed and across many countries, regular features ofthe distribution of price changes have included chronic excess kurtosis, right-skewness (even in periods oflow or negative inflation), and positive correlation between the mean and variance of relative price movements. Simple statistical models of price movements are then used to examine the impact of volatile and infrequently adjusted prices on the aggregate price index. These models generate results consistent with the empirical evidence. A consequence of the high kurtosis associated with high volatility of some prices is that robust estimators-such as the median or trimmed mean measures-are likely to give a much more reliable indication of the general trend of inflation than the CPI mean. Such measures are also likely to be more reliable than measures of core inflation based on excluding or down-weighting prices of particular items. Chronic skewness in the distribution of price movements-associated with arithmetic measurement of price changes and with infrequent price changes-leads different measures of central tendency to differ from one another. A simple method is suggested for designing a robust measure of core inflation that is unbiased with respect to the target measure. The analysis also suggests that, instead of targeting a CPI inflation target with an adjustment for the bias of the Laspeyres mean with respect to a superlative index, it would be more appropriate to set the inflation target in terms of the geometric mean. This is in part because the bias of the Laspeyres mean is likely to be more strongly correlated with the variance of relative prices and, therefore, is also likely to be more variable. -4- II. EMPIRICAL EVIDENCE ON THE DISTRIBUTION OF RELATIVE PRICES Ever since the first systematic efforts to construct aggregate or composite price indices in the 1860s, it has been observed that the cross-sectional distribution of price movements has not conformed to the Gaussian or Normal distribution.' Instead, the distribution has typically been found to be markedly leptokurtic (i.e., "high-peaked" or "long-tailed") and more often positively than negatively skewed. Jevons (1863) found that, over the period from 1782 to 1861, the distribution of annual price relatives for commodity prices in the United Kingdom was not typically symmetric but right­ skewed.' Consequently, Jevons advocated the use of geometric rather than arithmetic averaging in construction of aggregate price indices, since the distribution of logarithmic price changes was closer to Normal. Edgeworth (1887) also drew attention to an apparently systematic tendency towards right-skewness in the distribution of price movements. In addition to citing Jevons' research, he referred to reports on prices in Massachusetts and Illinois in the 1880s, as well as to Laspeyres' price indices for Germany. Mitchell (1915) analyzed the distribution of pooled annual percentage changes in prices for over 200 goods making up the U. S. wholesale price index over the period from 1891 to 1913. Mitchell found that the distribution displayed high kurtosis and right-skewness. Fisher (1922, pp. 230-31,408-10) also noted the right-skewness of the distribution of U.S. commodity price changes between 1913 and 1918. Mills' (1927) extension of the analysis of U.S. wholesale prices to 1926 corroborated Mitchel!'s findings. Mills summarized his findings with the observations that: "(a) The distributions of price relatives are ... erratic ... although Type IV of Pearson's classification predominates; (b) The conditions which give rise to the Normal distribution are seldom realized in the distribution of price relatives ... even when generous allowance is made for errors of sampling; and (c) There is some improvement. .. when logarithms of price relatives are used in place of relatives in natural form .... " (p.368)4 2The term "Normal" is capitalized when
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