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Price growth at the tails

When policymakers discuss the inflation rate, they’re referring to a measure of the “central tendency” of a distribution of price changes. There are many many many (many) prices in a developed economy. Here in the U.S., for example, we have maybe 20 types of sugar-coated flake-shaped cereal whose prices can change from one month to the next. So, to make the inflation rate meaningful, we must condense this distribution of prices to a measure of, as statisticians would call it, “central tendency.” However, reasonable people can differ on the proper measure because the distribution of price changes has long “tails.”

In short, the tail of a distribution is the part that’s farther away from the average. For example, we see evidence of the tail of the distribution of prices every morning when we pick up a coffee and a newspaper and drive into work: The prices of the first two items, like most other prices, change very slowly; but the price of gasoline fluctuates wildly from day to day. Certain categories—namely, food and energy—have larger swings than most other goods, so some prefer a price measure that looks at all goods except food and energy. This measure is called the “core” CPI. However, food and energy are not the only highly variable goods.

The top graph shows the ratio of mean CPI inflation to median CPI inflation.* The CPI measures inflation by choosing a basket of goods that are prominent among the average consumer’s purchases. Within this basket, the distribution of price changes is usually approximately symmetric, which we see because the ratio of the mean to median is usually about 1. (Actually, it’s slightly less, at about 0.9.) The interesting exception is during the Great Recession period, when commodity prices fell sharply, bringing a strong negative skewness for the first time since the mid-1980s. We can see this by looking at the bottom graph, which plots the ratio of mean core CPI to median CPI. Notice there is no negative spike in this measure of skewness. The Great Recession and its aftermath, however, show large changes in the “third moment.” In this period when the economy seemed to be in tremendous flux, the headline, average CPI moved little. However, the skewness—and the tails of the price distribution—changed quite a bit.

* This is not totally precise, because the change in headline CPI is not exactly the mean change in prices nor is median CPI exactly the median of the change distribution.

How to create these graphs: Top graph: Search for and select “median consumer price index” and “consumer price index for all urban consumers,” selecting “All items” and “Seasonally adjusted.” Chose “Percentage change” for the units in both. In the formula field, apply b/a. Bottom graph: Do the same, but instead of adding the “All items” consumer price index for all urban consumers, select “All Items Less Food and Energy.”

Suggested by David Wiczer.

View on FRED, series used in this post: CPIAUCSL, CPILFESL, MEDCPIM157SFRBCLE

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