Spatial Sorting: Why New York, Los Angeles and Detroit attract the greatest minds as well as the unskilled

We document that the wage distribution in larger and more productive cities nearly everywhere first-order stochastically dominates that in less productive cities. This confirms earlier evidence on the city size–wage premium. Yet, because this premium reflects higher house prices, this does not necessarily imply that this stochastic dominance relation also exists in the distribution of skills. We propose a model that entails evidence quite to the contrary: instead of first-order, there is secondorder stochastic dominance in the skill distribution. We show that this is due to patterns of sorting across cities in a model with mobility. Our model predicts a “Sinatra” as well as an “Eminem” effect: both the very high and the very low skilled workers disproportionately locate in the biggest cities. Firms in larger cities have a comparative advantage in employing both high as well as low skill workers. Based on our theory, the pattern of spatial sorting can be explained by a simple technology with varying elasticity of substitution by skill. Using CPS data on wages and Census data on house prices, this technology with the elasticity of substitution decreasing in skill density is consistent with the observed patterns of skills. ∗ICREA-UPF Barcelona [email protected]. †Leeds School, University of Colorado, [email protected]. ‡Department of Economics, Universitat Pompeu Fabra, [email protected].