Zipf's law for cities: An empirical examintion

Abstract

We use data for metro areas in the United States, from the US Census for 1900-1990, to test the validity of Zipf's Law for cities. Previous investigations are restricted to regressions of log size against log rank. In contrast, we use a nonparametric procedure to estimate Gibrat's Law for city growth processes as time-varying geometric Brownian motion and to calculate local Zipf exponents from the mean and variance of city growth rates. Despite variation in growth rates as a function of city size, Gibrat's Law does hold. The local Zipf exponents are broadly consistent with Zipf's Law. Deviations from Zipf's Law are easily explained by deviations from Gibrat's Law. © 2002 Elsevier Science B.V. All rights reserved.