Is Gibrat’s “Economic Inequality” lognormal?

  • Sherzod B. AkhundjanovEmail author
  • Alexis Akira Toda


In the seminal book “Les Inégalités Économiques,” Gibrat (Les Inégalités Économiques, 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 Inégalités Économiques, 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.


Economic history Fat tails Law of proportional effect Lognormal distribution Pareto distribution 

JEL Classification

D31 L11 N01 R12 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied EconomicsUtah State UniversityLoganUSA
  2. 2.Department of EconomicsUniversity of California San DiegoLa JollaUSA

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