The Real Effects of Monetary Shocks in Sticky Price Models: A Sufficient Statistic Approach

Abstract

We prove that the ratio of kurtosis to the frequency of price changes is a sufficient statistic for the real effects of monetary shocks, measured by the cumulated output response following the shock. The sufficient statistic result holds in a large class of models which includes Taylor (1980); Calvo (1983); Reis (2006 ); Golosov and Lucas (2007 ); Nakamura and Steinsson (2010); Midrigan (2011); and Alvarez and Lippi (2014). Several models in this class are able to account for the positive excess kurtosis of the size distribution of price changes that appears in the data. We review empirical measures of kurtosis and frequency and conclude that a model that successfully matches the microevidence on kurtosis and frequency produces real effects that are about four times larger than in the Golosov-Lucas model, and about 30 percent below those of the Calvo model. We discuss the robustness of our results to changes in the setup, including small inflation and leptokurtic cost shocks. (JEL, E23, E31)

Market Structure and Monetary Non-neutrality

“…42 As per Figure 8D and 41 Alvarez, LeBehin, and Lippi (2016) prove that to a second order approximation, the real effects of small monetary shocks in monopolistically competitive menu cost models will be equal provided they match the same frequency, average absolute size, and kurtosis of price changes. Changing the elasticity of demand while recalibrating the model ensures that these statistics are the same.…”

Do Mortgage Subsidies Help or Hurt Borrowers?

“…Dávila (2015) analyzes optimal bankruptcy exceptions for unsecured debt. Other applications of this approach include the analysis of monetary policy (Alvarez, Le Bihan, and Lippi, 2016;Auclert, 2016), welfare effects of trade liberalization (Arkolakis, Costinot, and Rodríguez-Clare, 2012), and welfare analysis with behaviorally biased consumers (Chetty, Looney, and Kroft, 2009;Allcot and Taubinsky, 2015). Although I focus on the case of mortgages and housing, the techniques and insights developed here are suitable to analyze debt subsidies in other contexts where debt is used to finance capital expenditures, like corporate investment in fixed assets or college students' investment in human capital.…”

Investigating Nonneutrality in a State‐dependent Pricing Model With Firm‐level Productivity Shocks

“…In Section 7, we report how our model relates to the striking result in Alvarez et al. (). Section 8 concludes.…”

“…Alvarez et al. () prove a general result in the spirit of Midrigan: In a relatively large class of models with normal shocks, there is a simple relationship between the average kurtosis of price changes and the real response to a monetary policy shock. Karadi and Reiff () model firm‐level heterogeneity with shocks drawn from a mixture of normal process that nests those in Midrigan () and Golosov and Lucas ().…”