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Is Gibrat’s “Economic Inequality” lognormal?

Author

Listed:
  • Sherzod B. Akhundjanov

    (Utah State University)

  • Alexis Akira Toda

    (University of California San Diego)

Abstract

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.

Suggested Citation

  • Sherzod B. Akhundjanov & Alexis Akira Toda, 2020. "Is Gibrat’s “Economic Inequality” lognormal?," Empirical Economics, Springer, vol. 59(5), pages 2071-2091, November.
    • Handle: RePEc:spr:empeco:v:59:y:2020:i:5:d:10.1007_s00181-019-01719-z
    DOI: 10.1007/s00181-019-01719-z
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    References listed on IDEAS

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    More about this item

    Keywords

    Economic history; Fat tails; Law of proportional effect; Lognormal distribution; Pareto distribution;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • N01 - Economic History - - General - - - Development of the Discipline: Historiographical; Sources and Methods
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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