Methodological Advances in Gibrat's and Zipf's Laws: A Comparative Empirical Study on the Evolution of Urban Systems

The regional economics and geography literature has in recent years shown interesting conceptual and methodological contributions on the validity of Gibrat's law and Zipf's law. Despite distinct modelling features, they express similar fundamental characteristics in an equilibrium situation. Zipf's law is formalised in a static form, while its associated dynamic process is articulated by Gibrat's law. Thus, it seems that both Zipf's law and Gibrat's law share a common root. Unfortunately, although several studies analyse both the laws looking at the validity of these regularities, very few empirical investigations assess the implication of one law from the other one (i.e. deviations from Zipf's law result in a deviation from Gibrat's law). Moreover, due to heterogeneity in data sources, comparative analyses between countries are difficult to perform. The present chapter aims at building the basis for further innovative research in this field, while it also aims to provide some caveats in empirical research. Specifically, we pay particular attention to the role of the mean and the variance of city population as key indicators for assessing the (non-)validity of the so-called generalised Gibrat's law. Our empirical experiments are based on illustrative case studies on the dynamics of the urban population of five countries with entirely mutually contrasting spatial-economic characteristics: Botswana, Germany, Hungary, Japan and Luxembourg. We provide evidence on the following results: if (i) the mean is independent of city size (first necessary condition of Gibrat's law) and (ii) the coefficient of the rank-size rule/Zipf's law is different from 1, then the variance is dependent on city size.