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

We study the US city size distribution using the Census places data, without size restriction, for the period (1900-2010). Also, we use the recently introduced 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 widely outperform any of the previously used density functions for each type of data. We also develop a theory which generates 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.