The U-shaped Law of High-growth Firms

This paper investigates firm growth dynamics by using the theory of stochastic processes and data on corporate tax records covering almost all firms in Japan. We show that the growth path of high-growth firms (HGFs) is characterized by a single large jump rather than a gradual increase. Specifically, before the jump occurs, the growth path of a HGF is similar to that of non-HGFs, but then it experiences a rapid increase in size. This growth pattern with a jump is typical (i.e., most likely) for HGFs. To provide further empirical evidence, we consider the ratio of the growth rate in the first period to the entire growth rate over two periods. The histogram of this ratio exhibits a U-shaped curve for HGFs, indicating that high growth over the two periods is explained by high growth either in the first or second period (but not both). This U-shaped curve is consistent with the idea that a single large jump determines the growth path of HGFs.