US city size distribution revisited: Theory and empirical evidence

We develop a urban economic model in which agents locate in cities of different size so as to maximize the net output of the whole system of cities in a country. From this model two new city size distributions are exactly derived. We call these functions “threshold double Pareto Generalized Beta of the second kind” and “double mixture Pareto Generalized Beta of the second kind”. In order to test empirically the theory, we analyze the US urban system and consider three types of data (incorporated places from 1900 to 2000, all places in 2000 and 2010 and City Cluster Algorithm nuclei in 1991 and 2000). The results are encouraging because the new distributions clearly outperform the lognormal and the double Pareto lognormal for all data samples. We consider a number of different tests and statistical criteria and the results are robust to all of them. Thus, the new distributions describe accurately the US city size distribution and, therefore, support the validity of the theoretical model.