Zipf's law for cities in the regions and the country

Abstract

The salient rank–size rule for city sizes known as ‘Zipf’s law’ is not only satisfied for Germany's national urban hierarchy, but also in single German regions. To analyse this phenomenon, we build on the theory by Gabaix (1999Quarterly Journal of Economics, 94:739–767) that Zipf's law follows (under certain conditions) from a stochastic urban growth process. In particular, Gabaix shows that if urban growth in all regions follows Gibrat's law, we should observe the Zipfian rank-size rule among large cities both at the regional and national level. This theory has never been addressed empirically. Using non-parametric techniques and various definitions of a ‘region’, we find that Gibrat's law holds at the regional level. Consistently, we find that city size distributions at the national and regional levels tend to follow a Zipfian power law.