Zipf's Law for Cities: On a New Testing Procedure

In this paper, we provide a new framework to assess the validity of Zipf 's Law for cities. Zipf 's Law states that, within a country, the distribution of city sizes follows a Pareto distribution with a Pareto index equal to 1. We adopt a two-step approach where we formally test if the distribution of city sizes is a Pareto distribution and then we estimate the Pareto index. Through Monte Carlo experiments, we investigate the nite sample performances of this testing procedure and we compare the small-sample properties of a new estimator (the minimum variance unbiased estimator) to those of commonly used estimators. The minimum variance unbiased estimator turns out to be more efficient and unbiased. We use this two-step approach to examine empirically the validity of Zipf 's Law on a sample of 115 countries. Zipf 's Law is not rejected in most countries (62 out of 115, or 53.9%).