Firm Growth and Laplace Distribution: The importance of large jumps

Author Name ARATA Yoshiyuki (Fellow, RIETI)
Creation Date/NO. June 2014 14-E-033
Research Project Issues Faced by Japan's Economy and Economic Policy Part III: Heterogeneity among economic agents
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Revised: March 2017
Revised: June 2018
Revised: November 2018


Recent empirical studies have shown that firm growth rate distribution is not Gaussian but closely follows a Laplace distribution. This robust feature of the growth rate distribution challenges existing models based on Gibrat's model because it predicts a Gaussian distribution. First, we analyze more than 100,000 Japanese firms and empirically show that the Laplace shape can be observed for the Japanese firms. Then, by using the theory of stochastic processes, we theoretically show that the absence of jumps causes the discrepancy between Gibrat's model and the Laplace shape. In particular, based on the Laplace shape and the law of proportionate effect, we show that the firm growth process is a jump process. In other words, firm growth cannot be explained by the consequence of many small shocks but is determined by a few large jumps. The widely observed Laplace distribution reflects this jump property of firm growth dynamics.

Published: Arata, Yoshiyuki, 2019. "Firm growth and Laplace distribution: The importance of large jumps," Journal of Economic Dynamics and Control, Vol. 103, pp. 63-82