Stability of Zipf's law and occult spatial dependence effects: A study on the OECD countries

Abstract

We investigate spatial dependence in Zipf's law for cities among the OECD countries. The aim is to identify an upper tail of the distribution that follows a power law (Pareto) but is perturbed by spatial autocorrelation, as indicated by a coefficient with a significant minor or major deviation from a distribution corresponding to a (non-spatial) Zipf law. For that purpose, we augment the usual Pareto model with a spatial weight matrix and apply SEM/SAR regressions. The results for the OECD countries are mixed. In particular, we investigate the rank-size distribution of cities by estimating local Moran-I coefficients (LISA) along the city ranks to locate the causes of spatial dependence. As an example, we demonstrate the approach for Belgium, a medium-sized OECD country.