Many developing countries exhibit a puzzling pattern given their scarce human capital: unemployment rates increase with education. We develop and estimate a model where educated unemployment arises from heterogeneous workers participating in a frictional labour market with three sectors (public, private and self-employment). We estimate that public sector distortions explain around two-thirds of educated unemployment in urban Burkina Faso and one-quarter in Senegal. We then simulate three equally costly policies. In contrast with public job creation and subsidies to self-employment income, subsidies for private sector vacancy creation effectively reduce educated unemployment and improve aggregate workers' welfare.