Random Division and the Size Distribution of Business Firms

The positively skewed distribution of firm sizes, with a large number of relatively small firms coexisting alongside fewer larger firms, is an enduring empirical fact in market economies. Typically, when data points conform to a Gaussian distribution, they are supposed to be the result of multiple random factors and not worthy of further investigation. A skewed distribution, on the other hand, calls out for a theory. In 1931, French economist Robert Gibrat applied Jacobus Kapteyn’s 1903 work on skew distributions in biology to explain the observed distribution of firm sizes. He speculated that the distribution was lognormal and generated in the steady state by a process of stochastic proportional growth [1]. Gibrat’s explanation is the dominant one in the economics literature, having set the direction for subsequent research on the distribution of firm sizes, as well as on the distribution of city sizes. Simon [2], in a variation of the model based on Yule’s [3] analysis of the distribution of species across genera, shows that a positively skewed distribution with a Pareto upper tail arises if the stochastic proportional growth process allows for the random addition of new firms. Another variation of the model that shows a Pareto upper tail in the steady state postulates a lower reflective barrier preventing the stochastically growing entity from becoming too small [4]. Stochastic proportional growth models are susceptible, however, to several criticisms. Criticism can be made regarding the realism of the Gibrat model assumption that the growth rate of a firm is independent of its size. And on a more fundamental level, it can be argued that the steady-state construct is not appropriate for economic