Firm Dynamics and the Granular Hypothesis

Abstract

Building on the standard firm dynamics setup of Hopenhayn (1992), we develop a quan- titative theory of aggregate fluctuations arising from idiosyncratic shocks to firm level productivity. This allows us to generalize the theoretical results in Gabaix (2011) to ac- count for persistent micro-level shocks, optimal size decisions as well as endogenous firm entry and exit. We then use our model to provide a quantitative evaluation of Gabaix’s “granular hypothesis” and find that it yields aggregate fluctuations of the same order of magnitude as a standard representative-firm real business cycle model. A calibration of our model to the US economy with a large number of firms leads to sizable aggregate fluctuations: the standard deviation of aggregate TFP (respectively output) is 0.8% (re- spectively 1.7%). We use this calibration to explore firms’ comovement over the business cycle. The model predicts that the differential growth between large and small firms is pro-cyclical as it is in the data