Board of Governors of the Federal Reserve System

Figure 1. Density plot

The black line in this Figure displays a hypothetical baseline cross-sectional distribution of subcomponent price changes that is consistent with the annualized two percent inflation target for Total PCE inflation, that is, the mean (hollow diamond) is equal to a 0.165 monthly percent change. The x-axis spans the range -1 to 1.5 percent. The y-axis spans the range from 0 to 4. This distribution has no skewness and is hence symmetric such that the median (hollow circle) is equal to the mean. The thick dark red line displays a second hypothetical distribution that corresponds to a doubling of the baseline monthly inflation rate (diamond with cross in middle) which is driven entirely by a higher median (circle with cross in middle) as the entire distribution shifts to the right. This distribution therefore remains symmetric and so the mean is equal to the median. The dashed dark green line displays a third hypothetical distribution that also corresponds to a doubling of the baseline monthly inflation rate (square) but this time it is driven partly by a higher median (triangle) and partly by more weight in the right tail of the distribution or right skewness which is reflected by the mean being above the median.

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Figure 2. Inflation Filter

The hollow circles in this figure plot -- for each month from January 1995 through February 2020 -- the total PCE monthly inflation rate in that month (y-axis) against our measure of asymmetry or skewness (x-axis). The y-axis spans the range -1 to 1 percent. The x-axis spans the range from 0 to 1. This measure of skewness simply compares the mean to the median of the cross-sectional distribution of price changes in a given month across all subcomponents of the total PCE price index, using the lowest level of disaggregation (more than 200 components). Specifically, the x-axis plots the percentile of this cross-sectional distribution of subcomponent price changes in a given month at which the mean falls. By definition, the median (vertical black line) always falls at the 50th percentile of the distribution. If the mean falls below the median (to the left of the center of the x-axis) the distribution is skewed to the left, while if the mean falls above the median (to the right of the center of the x-axis) the distribution is skewed to the right. The horizontal red line marks the monthly inflation rate consistent with two percent at an annual rate. The gray solid line plots the fitted line from a local polynomial regression of y against x using the pre-pandemic data. The dotted black lines denote the corresponding two standard deviation prediction interval. The blue circles mark the observations from March 2020 through May 2023, with darker shading being more recent. The observations since June 2023 are shown by the colors and shapes described in the legend of the chart.

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Figure 3. Inflation Deviation

The solid black line in this figure plots the 1-month percent change in the total PCE price index in a given month minus the fitted value in that month (i.e the position of the gray regression line in Figure 2 in that month based on the asymmetry of the price change distribution in that month). The dashed gray lines plot the same information using either the upper or lower confidence band instead of the fitted line from Figure 2. The horizontal blue line denotes zero. The x-axis spans the range from March 2020 through September 2024. The y-axis spans the range -0.6 to 0.8 percent per month.

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Figure 4. Inflation Tracker

The solid blue line in this figure plots the 12-month average of the monthly fitted inflation deviations from Figure 3. The dashed blue lines present the same information for the upper and lower confidence bands. The monthly fitted deviations are computed as the 1-month percent change in the total PCE price index in a given month minus the predicted value from the fitted value in that month (i.e the position of the gray regression line in Figure 2 in that month based on the asymmetry of the price change distribution in that month). The x-axis spans the range from February 2021 through September 2024. The y-axis spans the range -0.4 to 0.6 percent per month.

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Figure 5. Inflation Tracker and Other Measures

The thick solid black line in this figure plots the 12-month average of the monthly prediction errors from Figure 4. The monthly predictions errors are computed as the 1-month percent change in the total PCE price index in a given month minus the fitted value in that month (i.e the position of the gray regression line in Figure 2 in that month based on the asymmetry of the price change distribution in that month). The dashed blue line is the 12-month average of total PCE inflation in a given month minus its average value from January 1995 through February 2020. The thin solid red line plots the same information for core PCE inflation. The x-axis spans the range form February 2021 through September 2024. The y-axis spans the range from -0.5 to 5.5 percent per month (annualized).

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Figure 6. Diffusion Index

This Figure plots the monthly total PCE inflation rate (y-axis) against the weighted share of subcomponents that underlie the total PCE price index -- using the lowest level of disaggregation -- that have price increases above a three percent annualized rate in that month. Each circle corresponds to one month from January 1995 through February 2020. The y-axis spans the range -1.2 to 1 percent. The x-axis spans the range 0 to 1.

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Figure 7. Scale-free Diffusion Index

The thick solid red line in this Figure graphs the 12-month moving average of the weighted share of price changes above the mean in each month using the fitted relationship from the pre-COVID period, conditional on the rate of inflation observed in that month. The dashed red lines graph the corresponding two standard deviation prediction interval. The thin solid black line graphs the 12-month moving average of the actual weighted share of price changes above the mean in each month conditional on the rate of inflation observed in that month. The x-axis spans the range from February 2021 through September 2024. The y-axis spans the range from 0 to 1.

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