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α: calibrated so average coauthorship-adjusted count equals average raw count
We 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; and (iv) if the utility is not separable then the "no distortion at the top" result does not apply. The welfare gains from switching to the optimal tax system are about 1 percent in annual consumption equivalents.