The Macroeconomics of Sticky Prices with Generalized Hazard Functions

Abstract

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.

Measuring Price Selection in Microdata: It's Not There

“…This is inconsistent with standard menu cost models (Golosov and Lucas, 2007;Karadi and Reiff, 2019;Bonomo et al, 2019), where selection is generally strong. We argue that second-generation state-dependent price-setting models with random menu costs (Dotsey et al, 1999;Luo and Villar, 2017;Alvarez et al, 2020) or rational inattention (Woodford, 2009) with a linear and flat price-adjustment (hazard) function are broadly consistent with our evidence. Related literature Our work contributes to the strand of literature that imposes minimal structure to estimate the strength of price selection in microdata.…”

“…These results imply that price adjustment in macroeconomic models generally should feature a state-dependent adjustment through the gross extensive margin and weak selection, implying a sizable monetary non-neutrality. We characterize conditions which state-dependent pricing models with random menu cost (such as Dotsey et al, 1999;Luo and Villar, 2017;Alvarez et al, 2020) or rational inattention (Woodford, 2009) are consistent with our findings.…”

“…Our work is also related to the long strand of literature that uses observations about micro-level price behavior to infer the level of monetary non-neutrality in fully specified state-dependent price-setting models (Dotsey, King and Wolman, 1999;Golosov and Lucas, 2007;Gertler and Leahy, 2008;Midrigan, 2011;Alvarez, Bihan and Lippi, 2014;Alvarez, Lippi and Oskolkov, 2020). These papers predominantly use unconditional moments of price changes to calibrate their parameters and deliver predictions that are modeldependent.…”

The Analytic Theory of a Monetary Shock

“…Alternatively, this prediction can be used to test the model. Finally, we mention that this result also applies to the Kurtosis of price changes because we have argued elsewhere that the steady state kurtosis and frequency of price changes characterize the cumulative IRF to a small monetary shock, see Alvarez, Le Bihan, and Lippi (2016); Alvarez, Lippi, and Oskolkov (2020).…”

“…It has also elements of the model developed by Woodford (2009) and Costain and Nakov (2011), where firms can affect the probability of a price change. In Section 4.5 we sketch a model, first proposed by Caballero and Engel (1999) and fully analyzed in Alvarez, Lippi, and Oskolkov (2020), which is equivalent to model presented below but where menu cost are fully random, instead of just having a two point distribution as in the Calvo-plus model.…”