The settlement of the United States, 1800-2000: The long transition towards Gibrat's law

Gibrat's law, the orthogonality of growth with initial levels, has long been considered a stylized fact of local population growth. But throughout U.S. history, local population growth has significantly deviated from it. Across small locations, growth was strongly negatively correlated with initial population throughout the nineteenth and early twentieth centuries. This strong convergence gave way to moderate divergence beginning in the mid-twentieth century. Across intermediate and large locations, growth became moderately positively correlated with initial population starting in the late nineteenth century. This divergence eventually dissipated but never completely. A simple-one sector model combining the entry of new locations, a friction from population growth, and a decrease in the congestion arising from the supply of land closely matches these and a number of other evolving empirical relationships.