Student loans with income-contingent repayment insure borrowers against income risk but can reduce their incentives to earn more. Using a change in Australia's income-contingent repayment schedule, I show that borrowers reduce their labor supply to lower their repayments. These responses are larger among borrowers with more hourly flexibility, a lower probability of repayment, and tighter liquidity constraints. I use these responses to estimate a dynamic model of labor supply with frictions that generate imperfect adjustment. My estimates imply that the labor supply responses to income-contingent repayment decrease the optimal amount of insurance but are too small to justify fixed repayment contracts. Moving from a fixed repayment contract to a constrained-optimal income-contingent loan increases welfare by the equivalent of a 1.3% increase in lifetime consumption at no additional fiscal cost.