Power-Law and Log-Normal Distributions in Temporal Changes of Firm-Size Variables

In this paper the author shows that signed temporal changes of firm size variables follow the power-law for large changes; while, for middle changes a log-normal distribution is found. In the analyses, the author employed three databases: highincome data, high-sales data and positive-profits data of Japanese firms. It is particularly worth noting that the growth rate distributions in temporal changes of the firm size data have no wide tail, unlike the distributions observed in assets and sales of firms, the number of employees and personal income data. An Extended-Gibrat's Law was also found in the growth rate distributions of temporal changes of firm size variables, which induces both the power-law and the log-normal distributions in the temporal changes of firm size under the Detailed Balance.