Price setting frequency and the Phillips curve

We develop a New Keynesian (NK) model with endogenous price setting frequency. Whether a firm updates its price is a discrete choice: when expected benefits outweigh expected costs, prices are reset optimally. The model gives rise to a non-linear Phillips curve as prices are more flexible during demand-driven expansions and less so during demand-driven recessions. Monetary policy can have substantial real effects despite the model having a state-dependent pricing component. Our quantitative analysis shows that contrary to the standard NK model, the assumed price setting behavior: (i) is consistent with micro data on price setting frequency; (ii) generates a direct effect of the time-varying price setting frequency on inflation; (iii) creates time-variation in the Phillips curve slope that explains shifts in the Phillips curve associated with different historical episodes; (iv) explains inflation dynamics without relying on implausible high cost-push shocks and nominal rigidities inconsistent with micro data; (v) reconciles the NK model with observed inflation moments.