Racing to Zipf's Law: Race and Metro Population Size 1910-2010

Abstract

Residential segregation scholarship traditionally focuses on segregation within metro- politan areas. Concurrently, urban economists have identi?ed that cities and metro areas within a coherent, connected system of cities have population distributions that follow a power law. Further, subpopulations with equal mobility should also have pop- ulation distributions that follow a power law. Using this insight, we introduce a novel method for identifying whether or not racial segregation between metro areas is due to geographical patterns of immigration into coherent systems or due to constrained mobility. We demonstrate the potential of this method by measuring the coherence of the U.S. urban system from 1910-2010 for the white, Black, Asian, and Hispanic populations. Black residents were only distributed across cities in a coherent system after the Great Migration, while Asian and Hispanic residents reached coherence more quickly and stayed coherent more consistently. It appears the Black reverse migration to the south has unsettled their power law distribution. We also ?nd that the size of those networks di?er across populations, and these di?erences are not an artifact of the relative size of the di?erent populations. We conclude with more potential applications of the methodology.