Consistent Evidence on Duration Dependence of Price Changes

We develop an estimator and tests of a discrete time mixed proportional hazard (MPH) model of duration with unobserved heterogeneity. We allow for competing risks, observable characteristics, and censoring, and we use linear GMM, making estimation and inference straightforward. With repeated spell data, our estimator is consistent and robust to the unknown shape of the frailty distribution. We apply our estimator to the duration of price spells in weekly store data from IRI. We find substantial unobserved heterogeneity, accounting for a large fraction of the decrease in the Kaplan-Meier hazard with elapsed duration. Still, we show that the estimated baseline hazard rate is decreasing and a homogeneous firm model can accurately capture the response of the economy to a monetary policy shock even if there is significant strategic complementarity in pricing. Using competing risks and spell-specific observable characteristics, we separately estimate the model for regular and temporary price changes and find that the MPH structure describes regular price changes better than temporary ones.