Optimal Student Loans and Graduate Tax under Moral Hazard and Adverse Selection

We characterize the set of second-best optimal "menus" of student-loan contracts in a simple economy with risky labour-market outcomes, adverse selection, moral hazard and risk aversion. The model combines student loans with an elementary optimal income-tax problem. The second-best optima provide incomplete insurance because of moral hazard; they typically involve cross-subsidies between students. Generically, optimal loan repayments cannot be decomposed as the sum of an income tax, depending only on earnings, and a loan repayment, depending only on education. Therefore, optimal loan repayments must be income-contingent, or the income tax must comprise a graduate tax. The interaction of adverse selection and moral-hazard, i.e., self-selection constraints and effort incentives, determines an equal treatment property; the expected utilities of different types of students are equalized at the interim stage, conditional on the event of academic success (i.e., graduation). But individuals are ex ante unequal because of differing probabilities of success, and ex post unequal, because the income tax trades off incentives and insurance (redistribution).