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

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 b-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. 本文研究了美国技术工人地理分布的变化如何影响使用吉布拉特定律 (Gibrat’s law) 解释城市规模分布的理论模型。在实证文献中，差异假说认为大学份额在大学份额较高的城市增长较快，而增长假说认为城市人口增长率也与大学初始份额直接相关。通过考察差异假说，吉布拉特定律的经典检验被证明是对b-收敛的检验。测试表明，自20世纪70年代以来，人力资本的差异是绝对的，而不是相对的。然而，甚至绝对差异和增长假说的结合也被证明违反了城市人口增长与其规模无关的条件。额外的测试发现大学份额和城市增长之间的关系是凹面的而不是划一的。这些结果表明，随机增长模型能够经受住人力资本分布差异带来的挑战。