We propose a theory of skill mobility across cities. It predicts the well documented city size-wage premium: the wage distribution in large cities first-order stochastically dominates that in small cities. Yet, because this premium is reflected in higher house prices, this does not necessarily imply that this stochastic dominance relation also exists in the distribution of skills. Instead, we find there is second-order stochastic dominance in the skill distribution. The demand for skills is non-monotonic as our model predicts a 'Sinatra' as well as an 'Eminem' effect: both the very high and the very low skilled disproportionately sort into the biggest cities, while those with medium skill levels sort into small cities. The pattern of spatial sorting is explained by a technology with a varying elasticity of substitution that is decreasing in skill density. Using CPS data on wages and Census data on house prices, we find that this technology is consistent with the observed patterns of skills.
matching theory sorting general equilibrium population dynamics cities wage distribution