This is the final version. Available from the American Economic Association via the DOI in this recordWe study optimal tax policies in a life- cycle economy with permanent ability differences and risky human capital investments that have both an unobservable component, learning effort, and an observable component, schooling. The optimal policies balance redistribution across agents, insurance against human capital shocks, and incentives to learn and work. In the optimum, (i ) high- ability agents face risky consumption while low- ability agents are insured; (ii ) the optimal schooling subsidy is substantial but less than 100 percent; (iii ) if utility is separable in labor and learning effort, the inverse labor wedge follows a random walk; ...