Theoretical arguments and previous country-level evidence indicate that immigrants are more fluid than natives in responding to changing labor shortages across countries, skill-groups or industries. The diversity across EU member states enables us to test this hypothesis across various institutional, economic and policy contexts. Drawing on the EU LFS and EU SILC datasets we study the relationship between residual wage premia as a measure of labor shortages in different skill-industry-country cells and the shares of migrants and natives working in these cells. We find that immigrants' responsiveness to labor market shortages exceeds that of natives in the EU15, in particular in member states with higher unemployment rates, higher levels of (recent) immigration, and more open immigration and integration policies; but also those with barriers to citizenship acquisition or family reunification. Whereas higher welfare expenditures seem to exert a lock-in effect, a comparison across different types of welfare states indicates that institutional complementarities neutralize that effect.