Frequently asked questions about trimmed mean inflation measures.
- What is a “trimmed mean estimator”?
A trimmed-mean is a mean that eliminates the tails of the sample distribution so as to reduce their influence on the estimator.
- What is the advantage of a trimmed-mean estimate of inflation?
When estimating the inflation rate, it’s standard to sample a large number of prices, record price changes, and weight the items by their significance. This is precisely what the Consumer Price Index, produced monthly by the Bureau of Labor Statistics, does. For some distributions, notably “fat-tailed” distributions, the sample mean is a very inefficient estimator of the true population mean that you wish to see. In these cases, a trimmed-mean estimator provides a vastly superior estimate of the population.
- What accounts for the fat-tails of price-change distributions?
The short answer is that this is an unresolved question. In very early work (1994) Bryan and Cecchetti posited that these fat tails may be an artifact of menu costs to the price setting decisions of firms. In later work, we suggest a purely statistical explanation. Fat tails can be produced simply by mixing together price data with widely different variances.
- Is the trimmed-mean estimator “core” inflation?
In the usual sense of the term, the answer is no. The trimmed-mean estimate is not a core inflation measure. “Core” inflation was introduced by Robert Gordon (1975) as the Consumer Price Index less food and energy goods. Certainly, the trimmed-mean approach and the “ex-food and energy” approach are methodological cousins. Both exclude some part of the weighted inflation statistic from consideration. However, there is a very important distinction between the two approaches. By systematically removing some components of the inflation statistic, you have produced a new inflation statistic, different in construction and concept from the original. From a statistical perspective, these two price statistics will not share the same trend. This is not true of the trimmed-mean estimators. In this case, the weighted mean and the trimmed-mean are trying to estimate the same thing, and if done correctly, they will have identical trends.
- What is “asymmetric” trimming?
Asymmetric trimming is when you remove one tail of the price-change distribution more than you do the other side. You do this when the population distribution in question is asymmetric–that is, the tails are fatter on one side of the distribution than on the other. You must asymmetrically trim the estimator in order to avoid bias to your estimator. Remember, the object of trimmed-mean estimators is not to produce a different inflation statistic from the weighted mean, but a more efficient one.
- Why are some price change distributions asymmetric?
Some (cite) have indicated that the asymmetry found in some price change distributions may be evidence of a “zero nominal bound” or some other imperfection in the price adjustments of firms. But we have documented asymmetric price change distributions for many countries in our research. To our knowledge, the first use of an asymmetric trimmed-mean inflation estimator was produced by Roger (1996) for the Reserve Bank of New Zealand. Bryan and Cecchetti encountered an extreme case of asymmetry in the price change distribution in work done for the Bank of Brazil (2000). The PCE price index in the United States if also known to have persistent asymmetry.
- Should the trimmed-mean estimator be the target of a central bank?
There is no reason for a central bank to change its inflation target to a trimmed-mean estimator. Remember, the weighted mean and the trimmed-mean estimator are two estimators of the same object. However, we strongly believe that the trimmed-mean estimator should be the short-term lens through which to monitor recent developments on inflation. The relative efficiency of the trimmed-mean estimator is far superior to the weighted mean estimator reported by the data agencies.