The Consumer Price Index (CPI), calculated by the Bureau of Labor Statistics, and the Personal Consumption Expenditures index (PCE), calculated by the Bureau of Economic Analysis, are the two most common measures of inflation. From December 2022 to January 2023, the CPI indicated that the year-to-year inflation fell by 0.1% from 6.5% to 6.4%; while the PCE rose by 0.1% from 5.3% to 5.4% over the same period. Of course, this muddles the inflation picture but leads us to inquire into the differences between the two measures. There are several differences, but here’s a big one. 

Any inflation measure starts with a bundle of goods and services that presumably reflects some average of actual consumption. Inflation is when it’s more expensive to purchase that bundle of goods. Suppose our typical household consumes 50 apples and 50 oranges a month, and the initial price of both apples and oranges is $1. A household can buy the bundle for $100. Let’s say next month apple prices rise to $2 while orange prices rise to $1.50. The dollar cost of the original market basket is $175 so the basket’s price has risen by 75%. 

However, economists have long noted this ignores the reality of consumers mitigating the price hikes by substituting into relatively less expensive goods and out of the relatively more expensive goods. While both fruits rise in dollar price, the costs of oranges in terms of apples decreases. The 75% price increase does not include substituting into oranges. Suppose in the second month consumers adjust, consuming 35 apples and 65 oranges. That basket’s price increased from $100 to $167.50—reflecting a 67.5% price increase.  

So which method is “right?” Most economists think neither is definitive. If the first month’s basket overestimates price rises, then the second month’s  basket underestimates them. About 100 years ago, Yale economist Irving Fisher argued an “ideal” measure would use a geometric average of the change in the price of the two bundles, which is the convention most economists accept. (In this measure the fruit bundle’s price rose by 71.2%) 

The PCE more closely approximates the Fisher ideal since the bundle of goods and services is updated quarterly; while the CPI bundle of goods and services is updated every 2 years. This is one reason the Fed “prefers” the PCE to the CPI. We will see if the recent divergence repeats in the next data release.