Selection and monetary non-neutrality in time-dependent pricing models

Given the frequency of price changes, the real effects of a monetary shock are smaller if adjusting firms are disproportionately likely to be ones with prices set before the shock. This selection effect is important in a large class of sticky-price models with time-dependent price adjustment. We characterize conditions on the distribution of the duration of price spells associated with the real effects of monetary shocks, and provide a very general analytical characterization of the real effects of such shocks. We find that: 1) Selection is stronger and real effects are smaller if the hazard function of price adjustment is more strongly increasing; 2) Selection is weaker and real effects are larger if there is sectoral heterogeneity in price stickiness; 3) Selection is stronger and real effects are smaller if the durations of price spells are less variable. We also show that 4) If monetary shocks affect primarily the level of nominal aggregate demand, the mean and variance of price durations are sufficient statistics for the real effects of such shocks.