I develop and estimate a structural equilibrium model of the college market. Students, having heterogeneous abilities and preferences, make application decisions subject to uncertainty and application costs. Colleges, observing noisy measures of student ability, choose tuition and admissions policies to compete for better students. Tuition, applications, admissions, and enrollment are joint equilibrium outcomes. I estimate the model using the NLSY97 via a three-step procedure to deal with potential multiple equilibria. I use the model to examine the extent to which college enrollment can be increased by expanding college supply and to assess the importance of various measures of student ability.

We model household choice of schools under the Boston mechanism (BM) and develop a new method, applicable to a broad class of mechanisms, to fully solve the choice problem even if it is infeasible via the traditional method. We estimate the joint distribution of household preferences and sophistication types, using administrative data from Barcelona. Counterfactual policy analyses show that a change from BM in Barcelona to the deferred-acceptance mechanism would decrease average welfare by €1,020, while a change to the top-trading-cycles mechanism would increase average welfare by €460.