Labor migration can help absorb asymmetric shocks within a currency union. However, if workers are heterogeneous in both their productivity and geographic mobility, this may thwart the mitigating effect of integrated labor markets. We document a higher mobility among more educated Europeans, and develop a dynamic spatial equilibrium model in which workers differ in skill and in their preference for migration. We calibrate this model to European data, and find that migration improves outcomes following a negative shock to a country's productivity or demand primarily for high skilled workers, who are relatively more mobile. Although high skilled outmigration harms low skilled workers, mobility in Europe is too low to leave an overall negative effect of open borders on the low skilled, who benefit from integrated labor markets, albeit to a lower degree.

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