Zipf’s law for cities: an empirical examination

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 calculate local Zipf exponents from the mean and variance of city growth rates. This also allows us to test for the validity of Gibrat's Law for city growth processes. Despite variation in growth rates as a function of city size, Gibrat's Law does hold. In addition 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.