The Settlement of the United States, 1800 to 2000: The Long Transition Towards Gibrat's Law

Gibrat's law, the orthogonality of growth to initial levels, is considered a stylized fact of local population growth. But throughout U.S. history, local population growth has significantly deviated from orthogonality. In earlier periods smaller counties strongly converged whereas larger counties moderately diverged. Over time, due to changes in the age composition of locations and net congestion, convergence dissipated and divergence weakened. Gibrat's law gradually emerged without fully attaining it. A simple one-sector model, with entry of new locations, a growth friction, and decreasing net congestion closely matches these and many other observed relationships. Our findings suggest that orthogonal growth is a consequence of reaching a steady state population distribution, rather than an explanation of that distribution.

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