Methodological Advances in Gibrat's and Zipfs 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 modeling features, they express similar fundamental characteristics in an equilibrium situation. Zipf’s law is formalized 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 papers analyze both the laws looking at the validity of these regularities, very few empirical investigations assess the implication of a law to the other (i.e. deviations from Zipf’s Law result in a deviation of Gibrat’s Law). Moreover, due to the heterogeneity of the data sources, comparative analysis between countries are difficult to run. The present chapter aims at building the basis for further research in this field but it wants also be a sort of warning signal to avoid common mistakes. Specifically, we put 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 clues about 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 one, then the variance is dependent on city size.