Gibrat’s Law Does Not Imply Zipf’s Law

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