Cross sectional evolution of the US city size distribution

We report nonparametrically estimated stochastic transition kernels for the evolution of the distribution of US metropolitan area populations, for the period 1900 to 1990. These suggest a fair amount of uniformity in the patterns of mobility during the study period. The distribution of city sizes is predominantly character-sed by persistence. Additional kernel estimates do not reveal any stark differences in intra-region mobility patterns. We characterise the nature of intra-size distribution dynamics by means of measures that do not require discretisation of the city size distribution. We employ these measures to study the degree of mobility within the US city size distribution and, separately, within regional and urban subsystems. We find that different regions show different degrees of intra-distribution mobility. Second-tier cities show more mobility than top-tier cities.