Is Gibrat’s “Economic Inequality” lognormal?

Abstract

In the seminal book “Les Inegalites Economiques,” Gibrat (Les Inegalites Economiques, Librairie du Recueil Sirey, Paris, 2013) proposed the law of proportional effect and claimed that a variety of empirical size distributions—such as income, wealth, firm size, and city size—obey the lognormal distribution. Gibrat’s law went on to become a stylized result stimulating a voluminous subsequent research that has contributed to our understanding of stochastic growth processes and a statistical regularity of the size distribution. However, many of the motivating examples used by Gibrat in his original work were subject to various data issues, and Gibrat’s reasoning of lognormal fit was based solely on graphical analysis. In this paper, we revisit the original 24 data sets considered by Gibrat (Les Inegalites Economiques, Librairie du Recueil Sirey, Paris, 2013) and show that in the majority of cases, the Pareto-type distribution actually provides a better fit to the data than lognormal. We show that Gibrat’s erroneous conclusion is partly due to data binning, truncation, and failure to weight data points properly.