Matteo Luciani and Riccardo Trezzi. The inflation objective of the FOMC is set in terms of the rate of change of the price index for total personal consumption expenditures PCE. However, total PCE price inflation is highly volatile, even on a year-to-year basis. Consequently, economists and policymakers have suggested alternative procedures for reweighting the index's components so as to reduce the variance of the measured inflation, to better distinguish transitory from persistent movements, and, ultimately to better anticipate future developments in inflation.
The literature has used the generic term "core" inflation to refer to these alternative measures. The most commonly used indicators of core inflation are exclusion indexes and central-tendency statistical measures, where the former are computed by removing a pre-specified list of components from the overall index and the latter are constructed by deleting a fixed proportion of extreme price changes.
The goal of this note is to provide an assessment of two of the most commonly used indicators of core inflation: the PCE price index excluding food and energy an exclusion index , and the Dallas Fed trimmed mean PCE price index a central-tendency statistical measure. In particular, we consider their relative performance in terms of three arguably desirable properties of a core measure: its ability to be less volatile than total inflation while having the same average rate over longer periods of time, its power to predict future inflation, and its ability to avoid undergoing large revisions across data vintages.
Starting in , this exclusion index was routinely included in the CPI Detailed Report ; subsequently, a similar exclusion measure was computed for the price index for personal consumption expenditures in the national accounts. The rationale behind an exclusion index is quite simple, and involves excluding a fixed list of items that are judged to be relatively more volatile and more subject to idiosyncratic shocks on average.
Like an exclusion index, a trimmed-mean index is based on the idea that large movements in prices for a subset of items can induce high volatility in total inflation. However, a trimmed-mean index differs from an exclusion index in that the price changes that are omitted can differ in each period the index is computed that is, they are not confined to a fixed list of items that is specified in advance.
The statistical motivation for the trimmed-mean measure is that a suitably chosen trimmed mean will provide a robust estimator of the location of a fat-tailed distribution, while a weighted mean typically will not.
Hence, to the extent that the empirical distribution of individual consumer price changes tends to exhibit fat tails, a trimmed-mean inflation measure might be viewed as preferable to an exclusion measure on purely statistical grounds.
The particular application of the trimmed-mean approach to PCE price inflation that we consider in this note was suggested by Dolmas , published regularly by the Dallas Fed since August Metric I: mean and volatility of the series Figure 1 provides a visual representation of the issue that exclusion indexes and central-tendency statistical measures try to address. For each month in the sample, the gray areas show the distribution of the monthly percent changes of the PCE price index components used by the Dallas Fed to construct the trimmed mean PCE price index.
The blue, red, and green lines show the one-month percent changes of the total PCE price index, the PCE excluding food and energy index, and the trimmed mean index, respectively. There are three main takeaways from Figure 1. First, in each month there is a wide distribution of price changes Panel A of Figure 1 ; it is precisely this dispersion that makes it difficult for policymakers and others to interpret high-frequency inflation readings.
Second, the index excluding food and energy and the trimmed-mean measure are both considerably less volatile than the total PCE price index. Finally, although the trimmed mean is able to smooth across idiosyncratic episodes more effectively than the index excluding food and energy for example, during the episode shown in Panel B of Figure 1 , both indexes tend to lie within the inner 25 percent range of the distribution of individual price changes.
Accessible version. Note: The gray areas show the inner range of monthly price changes for the percentiles specified in the figure's lower-left legend generated by subcomponents of the overall PCE price index. The dotted blue line plots monthly changes in the total PCE price index; the red line plots the monthly change in the PCE price index excluding food and energy, and the thick green line shows the monthly percent change of the trimmed-mean PCE price index.
Table 1 provides summary statistics for the annualized monthly percent change in the total PCE price index and the two core measures over various subsamples. For a policymaking body such as the FOMC, which specifies its longer-term price objective in terms of total PCE inflation, it is useful if a core price index has an average rate of change that matches the mean rate of total inflation over a sufficiently long period of time.
As is evident from line 1 of the table, from to the average change in the trimmed-mean measure is identical to the average change in the total PCE price index. Note: The table shows descriptive statistics for monthly percent changes at an annual rate for three measures of PCE price inflation. To summarize, despite their methodological differences, both indexes appear capable of reducing the variance of total inflation while capturing the location of the overall distribution of price changes.
The trimmed mean PCE index is able to smooth across large idiosyncratic episodes better than the index excluding food and energy; however the fact that the trimmed-mean inflation measure has run consistently higher than total PCE price inflation since the mids suggests that its current level should be interpreted carefully.
Metric II: relative forecasting performance A key purpose of a measure of core inflation is to provide an indication of the future direction of total inflation. Hence, we investigate the relative forecasting performance of the index excluding food and energy and the trimmed mean index.
The forecasting exercise is run in real time, meaning that we construct our forecasts using the actual vintages of data that were available at each point in time. The first forecast we produce is for inflation over the 24 months from June to June , using data available as of June Next, we produce a forecast for July using the data available as of July We then repeat the same procedure until June , thereby yielding a total of forecasts.
The target is the annualized month-ahead percent change in the total PCE price index computed using the latest available data meaning the data published by the BEA on July 31, Figure 2 summarizes the results of this exercise. Starting with the RMSEs computed over rolling windows top panel , the index excluding food and energy and the trimmed mean each yield better forecasts than total PCE price inflation itself, although the improvement is minimal in recent years. In addition, until very recently the index excluding food and energy performs slightly better than the trimmed-mean measure.
For the forecasting models that use core inflation measures computed over alternative horizons bottom panel , both core measures perform better than total inflation, but none of them clearly dominates the other.
Note: The top panel shows the 5-years rolling window root mean squared error of the month change of total dotted blue line , exFE red line , and TM thick green line in predicting the month change of total PCE inflation.
Each point in the first panel represents the RMSE for the 5-year window ending at that date. The bottom panel shows the root mean squared error when different number of months is used in constructing the core measure's inflation rate i. For example, the point corresponding to the number "6" on the x-axis represents the RMSE of the month total inflation has been predicted using the 6-month changes.
Summing up, the results of the forecasting exercise show that the two measures of core inflation predict future inflation significantly better than total PCE price inflation itself. While the CPI focuses on out-of-pocket expenditures, the PCE also includes items we buy through indirect arrangements.
Health insurance is a good example. The difference here is not an exhibit of CPI weakness, but instead the result of different focus. The CPI, on the other hand, is aimed at capturing the impact of prices themselves on consumers; long-term expenditures are not affected overnight by inflation, and sometimes not at all, as with a car loan. In other words, if we want to study price changes for the purposes of anticipating short-term swings in consumer spending, the CPI is preferable. If, on the other hand, our purpose is to track longer-term trends in the economy, the PCE serves us better.
Third, and perhaps most important: there are differences in the demographics they base their surveys on. The CPI is based on a survey of consumers in urban areas. It is said to represent consumer expenditures and prices among percent of the U. The PCE, on the other hand, is universal in its application, making it the preferable index. This gives the CPI an accuracy edge over the PCE edge, especially insofar as consumer-experienced inflation is concerned.
So, back to the question — and please without the two-word standard economist answer: which of the two indexes is preferable? If our concern is fiscal and monetary policy and how they can affect consumer behavior, the CPI is preferable. If our purpose is more long term and more academic in nature, we go with the PCE. Despite the shortages of the CPI in terms of capturing expenses on certain types of items, it gives us a better idea of how consumers perceive inflation and therefore a better idea of how they may respond in the near future.
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