Gibrat’s Law Does Not Imply Zipf’s Law

14 Pages Posted: 29 Nov 2010

See all articles by Spyros Skouras

Spyros Skouras

Athens University of Economics and Business - Department of International and European Economic Studies

Date Written: November 29, 2010

Abstract

This note contests a widely cited, used and derived ‘result’ according to which Gibrat’s law implies Zipf’s law. I show that this result is only true under strict, unrecognized and ad hoc additional conditions some of which are even inconsistent with the economic models that have been used to explain Zipf’s law. The widespread confusion regarding the relationship between Gibrat and Zipf laws derives from the mathematically subtle effect on dynamics of lower boundaries in Gibrat processes. In order to make my argument concrete, I illustrate in the context of a paper widely credited for explaining Zipf’s law.

Keywords: Zipf’s Law, Regulated Geometric Brownian Motion, Gibrat’s law

JEL Classification: R11, R12, R15

Suggested Citation

Skouras, Spyros, Gibrat’s Law Does Not Imply Zipf’s Law (November 29, 2010). Available at SSRN: https://ssrn.com/abstract=1717112 or http://dx.doi.org/10.2139/ssrn.1717112

Spyros Skouras (Contact Author)

Athens University of Economics and Business - Department of International and European Economic Studies ( email )

GR-10434 Athens
Greece

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