The Macroeconomics of Sticky Prices with Generalized Hazard Functions

We give a thorough analytic characterization of a large class of sticky-price models where the firm's price setting behavior is described by a generalized hazard function. Such a function provides a tractable description of the firm's price setting behavior and allows for a vast variety of empirical hazards to be fitted. This setup is microfounded by random menu costs as in Caballero and Engel (1993) or, alternatively, by information frictions as in Woodford (2009). We establish two main results. First, we show how to identify all the primitives of the model, including the distribution of the fundamental adjustment costs and the implied generalized hazard function, using the distribution of price changes or the distribution of spell durations. Second, we derive a sufficient statistic for the aggregate effect of a monetary shock: given an arbitrary generalized hazard function, the cumulative impulse response to a once-and-for-all monetary shock is given by the ratio of the kurtosis of the steady-state distribution of price changes over the frequency of price adjustment times six. We prove that Calvo's model yields the upper bound and Golosov and Lucas' model the lower bound on this measure within the class of random menu cost models