College educated workers are known to migrate more between US cities than the low skilled. This may be due to differences in returns to migration, or differences in constraints. The relative contribution of constraints has important implications for welfare. I model migration as a frictional cross-city job matching process. Within this framework, the constraints hypothesis yields testable predictions on the cross-city elasticity of local wages and unemployment with respect to housing costs. I verify these empirically, and provide further descriptive evidence from observed migration data that casts doubt on the importance of returns. Finally, my results reveal important aspects of the interaction between housing and labour markets.