The intermittent Phillips curve: Finding a stable (but persistence-dependent) Phillips curve model specification

We make substantial progress on understanding the Phillips curve, yielding important monetary policy implications. Inflation responds differently to persistent versus moderately persistent (or transient) fluctuations in the unemployment gap. This persistence-dependent relationship aligns with business-cycle stages, and is consistent with existing theory. Previous work fails to model this dependence, thereby finding the numerous “inflation puzzles”—for example, missing inflation/disinflation—noted in the literature. Our specification eliminates these puzzles; for example, the Phillips curve has not weakened; inflation's post-2012 slow upward trudge was predictable. The model's coefficients are stable, and it provides accurate out-of-sample conditional recursive forecasts through the Great Recession and recovery.