Efficient Inflation Estimation

Abstract

This paper investigates the use of trimmed means as high-frequency estimators of inflation. The known characteristics of price change distributions, specifically the . observation that they generally exhibit high levels of kurtosis, imply that simple averages of price data are unlikely to produce efficient estimates of inflation. Trimmed means produce superior estimates of 'core inflation,' which we define as a long-run centered moving average of CPI and PPI inflation. We find that trimming 9% from each tail of the CPI price-change distribution, or 45% from the tails of the PPI price-change distribution, yields an efficient estimator of core inflation for these two series, although lesser trims also produce substantial efficiency gains. Historically, the optimal trimmed estimators are found to be nearly 23% more efficient (in terms of root-mean-square error) than the standard mean CPI, and 45% more efficient than the mean PPI. Moreover, the efficient estimators are robust to sample period and to the definition of the presumed underlying long-run trend in inflation.

Core Measures of Inflation as Predictors of Total Inflation

“…10 10 For a description of the Cleveland Fed's measures, see Bryan and Cecchetti (1994) and Bryan, Cecchetti, and Wiggins (1997) for a description. Note, though, that the Cleveland Fed calculates the price change for a component as a simple percentage change rather than as a log difference as in these two papers.…”

A First Assessment of Some Measures of Core Inflation for the Euro Area

“…Besides those particular circumstances, the traditional motivation for looking at limited-influence estimators such as trimmed means is the observed tendency for the distribution of individual price changes to exhibit significant skewness and kurtosis at any particular point in time. This fact has been documented for many countries, by, among others, Balke and Wynne (2000), Bryan et al (1997), Ball and Mankiw (1995) and Vining and Elwertowski (1976). The observed skewness in the cross-section distribution of price changes can be used to motivate a statistical and an economic argument for limited-influence estimators of core inflation.…”

“…At the twelve‐month horizon, kurtosis ranges from 17.9 to 5.3. As argued in Bryan et al (1997), in the presence of excess kurtosis trimmed mean estimators are superior estimators of the central tendency of the cross‐section distribution of price changes, and thus of core inflation. The second important point to note from Table 2 is that there is very little skewness on average, although contrary to what we see with kurtosis, there is some tendency for skewness to increase with the horizon over which inflation is measured.…”

“…Figure 3– which depicts RMSE and bias as a function of the trim – confirms what one might suspect from the results reported in Table 6, namely that the gains from trimming come with only a small amount of trim. Bryan et al (1997) use plots of the RMSE as a function of the trim to estimate the optimal trim. They find strong U‐shaped relationships between the RMSE and the amount of trim in US Consumer Price Index and Producer Price Index data for the period 1967 to 1997.…”

Is inflation targeting feasible in Poland?

“…Our analysis suggests that according to the MSE criterion, approximately 20 per cent of the CPI categories should be trimmed from each tail. This compares with Bryan et al (1997) who find the optimal trim to be 9 per cent from each tail of the US consumer price index, but 45 per cent to be the optimal trim from each tail of the producer price index.…”