Is Gibrat’s ‘Economic Inequality’ Lognormal?

Published in Empirical Economics, 2020

In 2016, Jinhui Bai invited me to give a talk at Washington State University, and after my talk I had a conversation with Sherzod Akhundjanov, who was a Ph.D. student. He was interested in power laws, and we corresponded occasionally. In 2017 he asked me if I had projects where I needed a collaborator. When I was writing my Econometrica paper with Brendan, which we started in 2016, as part of the literature review I read Gibrat (1931) Les Inégalités Économiques and thought it would be cool to redo a modern statistical analysis because Gibrat made a big deal about the lognormal distribution and criticized Pareto. In particular, in the conclusion (p. 258), Gibrat triumphantly states (English translation by me)

La distribution des revenus, et toutes les autres sont ramenées par la loi de l’effet proportionnel à la loi célèbre de Laplace et la courbe qui les représente devient une courbe en cloche. Il suffit de considérer non les variations absolues, mais les variations relatives. Les répartitions économiques ne semblent plus singulières comme l’avait fait croire un moment la loi de Pareto. Leur explication est simple et générale.

(The distribution of revenues, and all others are brought about by applying the law of proportional effect to the celebrated law of Laplace and the bell curve. It suffices to consider not absolute variations, but relative ones. The size distributions in economics no longer appear singular as we have been at a moment made to believe the law of Pareto. The explanation is simple and general.)

It turns out that Gibrat was made to believe the lognormal distribution due to “eyeballing”, which is not necessarily suitable for weighting individual observations properly.

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