Explaining Zipf's Law for US Cities

Abstract

I develop an explanation of Zipf's law that is consistent with the observed marked heterogeneity in the growth of US cities. The explanation is that heterogeneous growth results in heterogeneous size distributions across cities, with the heaviest tailed distributions being Zipf and dominating the cross-sectional mixture distribution's tail. I demonstrate in the context of a popular model that this explanation is consistent with observed growth heterogeneity and other key stylized facts about city size and growth. This explanation has significant policy implications for controlling size distributions and the size of the largest cities in a country.

Keywords: Zipf's law, regulated geometric brownian motion, Gibrat's law

JEL Classification: R11, R12, R15