Human capital divergence and the size distribution of cities: Is Gibrat’s law obsolete?

Abstract

This article studies how the changing geographic distribution of skilled workers in the US affects theoretical models that use Gibrat’s law to explain the size distribution of cities. In the empirical literature, a divergence hypothesis holds that college share increases faster in cities where college share is larger, and a growth hypothesis maintains that the rate of city population growth is also directly related to initial college share. Examining the divergence hypothesis, the classic test for Gibrat’s law is shown to be a test for $\beta$ -convergence. Testing shows that there has been absolute, not relative, divergence in human capital since the 1970s. However, the combination of even absolute divergence and the growth hypothesis is shown to violate the condition that a city’s population growth is independent of its size. Additional testing finds that the relation between college share and city growth is concave rather than monotonic. These results imply that stochastic growth models can survive the challenge posed by divergence in the distribution of human capital.