High relocation costs in search-matching models: theory and application to spatial mismatch

We develop a standard search-matching model in which mobility costs are so high that it is too costly for workers to relocate when a change in their employment status occurs. We show that, in equilibrium, wages increase with distance to jobs and commuting costs because firms need to compensate the transportation cost difference between the employed and unemployed workers at each location in the city. We also show that the equilibrium land rent is negatively affected by the unemployment benefit because an increase in the latter induce firms to create less jobs, which, in turn, reduces the competition in the land market. We then use this model to provide a mechanism for the observed spatial mismatch between where black workers live and where jobs are. Because blacks and whites differ by their contact rate, we show that the former reside far away from jobs, have higher unemployment rates and lower wages. This is because the housing market amplifies the negative effects of the labor market by creating additional frictions.