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Exit rates from unemployment and re‐employment wages decline over a period of unemployment, after controlling for worker observable characteristics. We study the role of unobserved heterogeneity in an economy with asymmetric information and directed search. We show that the unique equilibrium is separating and that skilled workers have more job opportunities and higher wages. The composition of the unemployed varies with the duration of unemployment, so average exit rates and wages fall with time. The separating equilibrium relies on performance‐related pay schemes and the ability of firms to commit to renting an input that is complementary to worker skills.