Core Inflation Revisited: Forecast Accuracy across Horizons

Throughout 2023, inflation forecasting was the focus of our On the Economy blog posts. Our main interest lay in the predictive content of individual components of inflation for aggregate inflation. That is, we asked: Out of the goods or services in the proverbial basket today, whose price increases will be most useful in predicting the price increase of the whole basket, h months into the future? Answering this question helps clarify the motivation behind core measures, which either excludes only energy inflation (core excluding energy), or both energy and food inflation (core), due to the volatility in food and energy prices.

We tried to answer this question in a couple of different ways. In May 2023, we evaluated the signal-to-noise ratio of select consumer price index (CPI) and personal consumption expenditures (PCE) price index components in the context of predicting 12-months-ahead headline inflation—with “noise” referring to the volatility of a given component. In November 2023, we did a simple forecasting exercise, comparing the root mean squared errors (RMSEs) from using CPI components and core CPI measures to predict 12-months-ahead headline CPI inflation. We found that core measures of inflation were more accurate than using individual components, even those with the highest predictive content.

In this essay, we shift our perspective away from comparisons between core and its components. Instead, we focus on core and its “content horizon.” This concept, discussed in Jorg Breitung and Malte Knüppel’s 2021 article, asks how far into the future a particular forecast remains informative beyond just using the historical average. Based on a collection of forecasts from professional forecasters and a range of countries, they found that the content horizons were two to three quarters in the future for annualized quarterly GDP growth and three to four quarters in the future for year-over-year inflation. Beyond that you might as well just use the historical average.

In this post, we revisit their results with an emphasis on the content horizon of core inflation as a forecast of headline inflation. Specifically, we use monthly year-over-year core inflation to forecast year-over-year headline inflation. In contrast to our earlier work on CPI inflation, we use the inflation measure preferred by the Fed—headline inflation as measured by the PCE price index (represented by π). Hence, we use core PCE inflation to forecast headline PCE inflation. We then consider a constant 2% as the benchmark forecast, based on the Federal Reserve’s target of inflation averaging 2% over time. The idea is that the Fed enacts optimal policy to achieve that level of inflation.

We consider a collection of forecast horizons h for this exercise. These range from three to 24 months ahead in increments of three months. Let^{^}π_t^(c)caret pi subscript t superscript c and^{^}π_t^(2%)caret pi subscript t superscript 2% denote the respective time t forecasts. Their relative accuracy is evaluated using the difference of the squared forecast errors d_t,h= (π_t+h-^{^}π_t^(c))² - (π_t+h-^{^}π_t^(2%))².d subscript t comma h end subscript equals left parenthesis pi subscript t plus h end subscript minus caret pi subscript t superscript c right parenthesis squared minus left parenthesis pi subscript t plus h end subscript minus caret pi subscript t superscript 2% right parenthesis squared. If d_t,hd subscript t comma h end subscript is positive, this implies that the 2% forecast is more accurate for forecasting year-over-year headline PCE inflation h months into the future. If d_t,hd subscript t comma h end subscript is negative, this implies that core PCE inflation forecast is more accurate.

In the figure below we plot the cumulative sum of the differentials starting in January 2007 and proceeding through November 2023. There are eight such cumulative sums, each associated with a distinct forecast horizon. The lines are aligned with the date being forecasted, t+h, and not the forecast origins, t, which explains why the longer horizons are missing earlier in the sample. It’s worth emphasizing that at any given time, if the line is below zero, then, on average up to that point, core PCE inflation is a better predictor of headline inflation than just using the 2% target as a forecast. If the line is above zero, core PCE inflation is a worse predictor.

Cumulative Sum of Difference in Squared Forecast Errors: Core PCE Inflation vs. 2% Inflation Target

SOURCES: Bureau of Economic Analysis (retrieved via Haver Analytics) and authors’ calculations.

The plots give a clear story about the content horizon of the forecasts. The paths associated with the shorter horizons are almost uniformly lower than those for the longer horizons. In fact, at the 3- and 6-month horizons, the values are always negative, suggesting that core PCE inflation forecasts headline PCE inflation more accurately than just using the 2% target.

Prior to mid-2021, the results largely align with the conclusion in Breitung and Knüppel’s paper. For the shortest two (and perhaps three) horizons, there is predictive content of core PCE inflation beyond just using the benchmark inflation target of 2%. At longer horizons the advantage vanishes, and the two forecasts tend to be equally accurate.

The story shifts in the latter part of 2021, when inflation begins to accelerate. Here we see wild swings in forecast advantage. The shortest four horizons experience large gains in accuracy when using core PCE inflation relative to the 2% target. At the longest horizons, however, core PCE inflation’s advantage disappears and becomes a weakness as the values become firmly positive. Interestingly, at all horizons, the paths start to flatten in May 2023, which suggests that the two forecasts are providing comparably accurate forecasts.

Our results suggest that there are clear limitations to how far into the future we can forecast inflation. Forecasts using core inflation typically outperform the Fed’s inflation target at horizons less than a year—an observation that aligns with the results in Breitung and Knüppel’s paper. At longer horizons, it seems prudent to use the Fed’s 2% target as a forecast of inflation. This is logical since policymakers actively conduct monetary policy so that future inflation will reach its target.