Size Distributions of Firms: A Stochastic Model

Summary Stochastic approaches to the size-distributions of firms are means to explain the resulting distributions in fairly dynamic and growing economies. The first works were presented in the late fifties by Hart & Prais, I. Adelman and Simon & Bonini. This paper discusses the approach of the latter in the light of more recent papers. Simon & Bonini state in their paper that we can expect the upper tail of the steady-state distributions of firms to follow a Pareto-distribution. The parameters of this distribution can be derived from regression analysis. This has been done for the largest firms in the United States, countries outside the United States, Europe, Scandinavia and Sweden. The analysis doesn't give reasons to reject the Paretodistribution as a description of the size-distributions of the largest firms within the five areas. The validity seems, however, limited to firms of extreme size. The number of these firms doesn't within any of the five area exceed 200. From one of the parameters of the distribution it is possible to derive the ratio between net growth attributable to firms passing a minimi-size and the net growth of all firms. This seems to be largest in the population of firms outside the United States and Europe (40-50%) and smallest in the United States and Sweden (about 30%). The study also shows that this ratio has a close connection with Gini's measure of concentration. Areas with low net contribution from new firms also have a high degree of concentration. The study has revealed a need for further work, in order to refine the method and give better possibilities for interpretation of the results. Among methods suitable for the future work are studies of transition-matrices and simulation.