The distribution of city sizes in Turkey: A failure of Zipf’s law due to concavity

Abstract

The linearity of the distribution of city sizes is often assumed in the existing literature. Although different functional forms were tried, almost all of them impose a certain functional shape. In this study, we investigate the urban hierarchy and Zipf’s law using data for 973 Turkish subprovincial cities in 2019. We contribute to the literature in several ways. We force no definite functional form to observe the natural shape and employ nonparametric and quadratic regressions. We incorporate formal procedures of spatial dependence in regression models. We demonstrate that the linear model overestimates the Pareto exponent for small cities and underestimates it for bigger cities. We show that city sizes are unevenly distributed in Turkey. The rank–size rule is not valid in Turkey, either above or below a certain city-size truncation level. Thus, the Pareto exponent estimated from the linear model is not a reliable indicator as quadratic regressions perform much better.