Long-Term Firm Growth Derived from Non-Gibrat’s Property and Gibrat’s Law

With the Orbis database provided by Bureau van Dijk, we analyzed the dependence of firms’ operating revenues, total assets, and number of employees (firm-size variables) on firm age in Japan and France from 2010 to 2013. As a result, we confirmed that the geometric mean value of the firm-size variables obeys a power-law growth for its first 10 years and subsequently follows exponential growth. Using numerical simulations, these long-term properties of firm-size growth were derived from short-term growth law and properties that were observed in two successive years. First, early power-law growth under a size threshold comes from the extended non-Gibrat’s property. Second, subsequent exponential growth over the threshold is derived from Gibrat’s law.