With the unemployment rate in the United States currently below estimates of its natural rate we examine if the relationship between inflation and unemployment is nonlinear. Using aggregate data we are unable to reject a linear relationship. However, using metropolitan-level data we find the slope of the Phillips curve is roughly twice as large when unemployment is low compared to when it is high. Nevertheless the simple nonlinear Phillips curves used here suggest a core CPI inflation rate that is only slightly different than the linear version over the next couple of years.

This paper examines a number of alternative PCE price inflation measures including overall PCE inflation, PCE inflation excluding food and energy, trimmed mean PCE inflation, component-smoothed inflation, variance-weighted inflation, inflation with weights based on disaggregated regressions, and survey measures of inflation expectations. When averaging across a handful of specifications based on the primary uses of a core inflation measure three conclusions arise: 1. Inflation rates for nearly all the measures best track ex-post trend inflation or predict future overall inflation when they are averaged over a considerable number of months. Overall PCE price inflation should be averaged over 18 months or longer. A shorter averaging period is appropriate for core measures, often on the order of 12 months. 2. Even after appropriately averaging each index, core inflation indexes generally perform better than overall inflation. 3. Exclusion indexes, such as PCE excluding food and energy, perform slightly worse than many other possible core inflation measures; trimmed mean PCE, or a variance-weighted index, may be better choice for a summary inflation measure.

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