A new framework for US city size distribution: Empirical evidence and theory

We study US city size distribution using places data from the Census, without size restrictions, for the period 1900-2010, and the recently constructed US City Clustering Algorithm (CCA) data for 1991 and 2000. We compare the lognormal, two distributions named after Ioannides and Skouras (2013) and the double Pareto lognormal with two newly introduced distributions. The empirical results are overwhelming: one of the new distributions greatly outperforms any of the previously-used density functions for both types of data. We also develop a theory compatible with the new distributions based on the standard geometric Brownian motion for the population in the short term. We propose some extensions of the theory in order to deal with the long term empirical features.