This paper studies the cyclical dynamics of skill mismatch and quantifies its impact on labor productivity. We build a tractable directed search model, in which workers differ in skills along multiple dimensions and sort into jobs with heterogeneous skill requirements. Skill mismatch arises because of information frictions and is prolonged by search frictions. Estimated to the United States, the model replicates salient business cycle properties of mismatch. Job transitions in and out of bottom job rungs, combined with career mobility, are key to account for the empirical fit. The model provides a novel narrative for the scarring effect of unemployment.