What is a “trimmed-mean estimator”?

A trimmed-mean estimator is a sample mean that eliminates some portion of the tails of the sample so as to reduce the influence of the tails 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?

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 suggested a purely statistical explanation. Fat-tails can be produced simply by mixing together price data with widely different variances.  

What is “Core” Inflation?

The term “core” inflation is in desperate need of a clear definition. Unfortunately, no commonly accepted definition exists. And “core” inflation is sometimes used synonymously with “underlying” or “trend” inflation, although the latter term would seem to suggest a historical trend line.

The most common definition of “core” inflation is inflation less food and energy goods (as in the Consumer Price Index less food and energy, or the Price Index for Personal Consumption Expenditures less food and energy). The intellectual basis for this idea originates with Gordon (1975) who argued that U.S. inflation in early 1970s was primarily the consequence of temporary disturbances in U.S. food and global energy supplies. These, in turn, prompted Central bankers to react too aggressively to the “hard core” inflation they actually faced.

Inflation less food and energy goods is now the nearly ubiquitous definition of core inflation. A characteristic of this inflation measure (and most other measures that have appropriated the name “core” inflation) is that they alter the weights of the inflation statistic to produce an alternative measure for central bankers to consider when formulating policy. That is, they are different concepts of inflation from the one defined by the Consumer Price Index or the Price Index for Personal Consumption Expenditures.

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.  This is now the conventional use of the term. 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.  By systematically removing some components of the inflation statistic, the “core” measure produces a new inflation statistic that is different in construction and concept from the original. These two price statistics are unlikely to share the same growth trend.  This is not true of the trimmed-mean estimators.  In this case, the weighted mean and the trimmed-mean are estimators of the same object, and if done correctly, they will have identical growth trends.

What is “asymmetric” trimming?

Asymmetric trimming is when you eliminate more of one tail of the price-change distribution than the other tail.  You do this when the population distribution in question is asymmetric–that is, the tails are persistently “fatter” on one side of the distribution than on the other side.  The object of trimmed-mean estimators is not to produce a different inflation statistic from the weighted mean, but a more efficient one.  You must asymmetrically trim the estimator to match that of the underlying distribution to avoid a bias to your estimator.

To our knowledge, the first use of an asymmetric trimmed-mean inflation estimator was 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 Federal Reserve Bank of Dallas has been producing an asymmetric trimmed-mean estimate of the PCE price index in the United States since 2005.  

Why are some price change distributions asymmetric?

It is often assumed that some form of downward rigidity causes prices to be more flexible when they rise and relatively rigid when they decline.  In an influential 1972 paper, Tobin argued that these downward rigidities were explained by social norms. Ball and Mankiw (1994) offered a more refined explanation whereby the cost of price adjustment, combined with a positive inflation rate, produces asymmetry in price changes. More recent attempts to explain the asymmetry in price changes include inattention by consumers, and search costs, but as of yet, no single explanation is widely accepted.

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. The weighted mean and the trimmed-mean estimator are two estimators of the same underlying object.  However, we strongly believe that the trimmed-mean estimator should be the short-term lens through which to monitor inflation developments.  The relative efficiency of the trimmed-mean estimator is far superior to the weighted mean estimator reported by the data agencies. 

What is the “Sticky-Price” CPI?

A common motivation for alternative “core” inflation measures is to identify, or isolate, that part of the inflation rate that is likely to persist into the future. Presumably, this is the component of inflation that policymakers care most about, because it is the part of inflation that they can best influence. The Sticky-Price CPI attempts to do this by considering only the components of the price index that tend to change price infrequently. The idea here is that if price-setters only change prices infrequently, these price adjustments are likely to be the more forward looking, or “persistent.”