This paper examines how policies, aimed at increasing the supply of education in the economy, affect the matching between workers and firms, and the wages of various skill groups. We build an equilibrium model where workers endogenously invest in education, while firms direct their technology toward skill intensive production activities. Search frictions induce mismatch on both extensive (unemployment) and intensive (over-education) margins, with ensuing wage consequences. We estimate the model using NLSY and O*NET data, and propose an ex-ante evaluation of prominent educational policies. We find that higher education cost subsidies boost college attainment, produce substantial welfare gains in general equilibrium, but increase wage inequality. These changes are associated with a substantial upward shift in the distribution of job complexity, which leads to worse allocations for high-school graduates who end up under-educated in less productive firms, while highly-educated workers match with more productive firms and experience less over-education during their careers.