Long-term firm growth properties derived from short-term laws of sales and number of employees in Japan and France

Abstract

In Japan, we observed rapid power law growth in the first 10 years of the existence of firms and subsequent slow exponential growth on their ages not only in their sales but also in their number of employees. We also confirmed similar long-term properties in France. These observations were found by employing around one million bits of exhaustive financial data of firms in Japan and France from 2004 to 2013. Comparing the parameters, the power law and exponential growth indices of sales are larger than those of the number of employees. Such long-term growth is derived from non-Gibrat’s law in the middle-scale range and Gibrat’s law in the large-scale range. We observed both non-Gibrat’s law and Gibrat’s law, which denotes the dependence of the growth rate distributions on the initial values, for two successive years in the short-term. By introducing a stochastic model based on the short-term laws, we showed that non-Gibrat’s law and Gibrat’s law lead to power law growth and the subsequent exponential growth, respectively.