# What’s Up with the Gap between the Core PCE and the Core CPI?

As of August, there was a somewhat sizeable gap (0.5 percentage point) between the 12-month growth rate in the core PCE and the core CPI, which stood at 1.4 percent and 0.9 percent, respectively. Normally, this isn’t much of an issue. However, this time the direction of the gap is reversed relative to historical norms (with the core CPI currently trending below the core PCE), and measured inflation rates are hovering just above zero. A quick look into the differences between these two series may clear up this mystery.

The first and perhaps the most obvious difference between these two series is their scope. The Consumer Price index (CPI) measures the out-of-pocket expenses of the urban consumer. Meanwhile, the Personal Consumption Expenditures (PCE) price index takes a somewhat broader approach, not only attempting to measure spending by households, but also by nonprofit institutions serving households. This amounts to the inclusion a variety of nonmarket, imputed prices such as financial services furnished without payment, insurance premiums, and social assistance services. For example, the PCE price index accounts for government and employer-paid medical care services, where the CPI only incorporates out-of-pocket medical care expenses.

The Bureau of Economic Analysis (BEA) publishes a “market-based” PCE price index (and a corresponding market-based “core” PCE price index), which excludes all imputed nonmarket prices (except for housing rents). This series serves as a rough control for the differences in scope between the core CPI and the core PCE. After excluding nonmarket-based prices, the core PCE is up 1.1 percent, accounting for about 0.3 percentage point of the gap between the core PCE and core CPI.

The PCE and CPI are also distinguished by two other aspects of their construction. First, the CPI and PCE are calculated using different formulas. The CPI is calculated using a Laspeyres index, while the PCE uses a Fisher-ideal index. Without getting into the mathematics, use of the Laspeyres index makes the CPI a “fixed-weight” price index, with the relative importance (or weight) of each item in the consumer market basket being adjusted for expenditure changes only every two years. On the other hand, the PCE is continuously updated for expenditure changes. This, in effect, is like the CPI asking the question, “What does it cost to maintain this fixed basket of goods and services?” while the PCE asks, “What does it cost to maintain this given level of satisfaction?” Because the CPI updates the expenditure weightings only every few years, it doesn’t allow for substitution effects. For example, if the price of coffee suddenly doubles, people may start to drink more tea. Thus, the CPI may tend to overstate the aggregate price level during periods of volatile relative price swings.

The last difference between the two series is called the “weight” effect. Due to the differences in the scope of the measures and in the source data for some items, the PCE and CPI have different weights on similar items. The largest difference comes from the shelter (housing) components, which in the CPI carry a relative importance value of roughly 32 percent, while in the PCE it is a little less than half of that. Such a huge difference in weights means that housing prices exert much more of an influence over the trajectory of the CPI than that of the PCE, leading to differences in their growth rates over time.

In a crude attempt to account for weight and formula effects, I reweighted the items in the market-based core PCE using CPI expenditure weights. As you can see, the market-based core PCE (reweighted with CPI relative importance values) is trending right on top of the core CPI at the moment.

Another interesting question that arose during this exercise was whether or not those imputed nonmarket-based items were useful predictors of future core PCE inflation. That is, are these prices just noise or is there a signal of future inflation embedded in them that would make them worth paying attention to? To test this, I ran some simple forecasting models that tried to predict core PCE inflation 12, 24, and 36 months ahead using lags (or past values) of either the core PCE or the market-based core PCE. These regressions were estimated between January 1987 and August 2000, with the number of lags set to 12 for each regression using revised data. I then tested the forecast accuracy using a commonly used statistic called root-mean-squared-error (RMSE). Like in golf, a lower score is better; hence, a lower RMSE indicates better forecasting performance. I examined the accuracy of forecasts for the period September 2000 to December 2005.

The table below shows that including the nonmarket imputed prices doesn’t seem to help forecasting accuracy. In fact, they seem to impair it a bit: Lags of the market-based core PCE do a better job of forecasting future core PCE than do lags of the core PCE itself. This tentative evidence suggests that there isn’t much information in the nonmarket prices that are included in the core PCE.

With the release of September’s data, the 12-month trend in the core PCE slowed to 1.2 percent. Part of this slowing was due to a flat reading on the core PCE in September, the other part was due to downward revisions to past data. The 12-month growth rate in the market-based core PCE also slowed—from 1.1 percent in August to 0.9 percent in September. The gap between the core PCE and core CPI did narrow slightly upon revision (from 0.5 percentage point to 0.4 percentage point), but the core PCE is still hanging above the core CPI at the moment. However, after excluding nonmarket imputed prices, that gap shrinks to roughly 0.1 percentage point.

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