A long-term, regional-level analysis of Zipf's and Gibrat's laws in the United States

Abstract

We test the validity of Zipf's and Gibrat's laws for city size distributions at the regional level from 1900 to 2010 by considering US states. Zipf's law is satisfied for a majority of states, but for the United States as a whole it only held during the first half of the twentieth century. The null hypothesis of a power law is not rejected at the national level or for most states (the maximum number of rejections in one year is 13 states out of 48). There is evidence supporting a weak version of Gibrat's law in the long-term; mean growth is independent of initial population for most city sizes over the entire United States and in 27 states, while the variance of growth is size-dependent.