The College Admissions Problem with Uncertainty ∗

We consider the classic college admissions problem. Unlike Gale and Shapley (1962), we realistically assume that (i) students’ college application choices are nontrivial because applications are costly, and (ii) college rankings of students are noisy and thus uncertain at the time of application. We analyze a general equilibrium model where two ranked colleges set admissions standards for student quality signals, and students, knowing their types, decide where to apply to. We describe conditions that guarantee assortative matching in this context — namely, better students apply to better sets of schools, and better schools impose higher standards. We find that the latter may be undermined by disparate college capacities, but otherwise obtains for low enough application costs. We also show how student application costs introduce negative externalities of the worse-ranked colleges upon the better ones. Lones is grateful for the financial support of the National Science Foundation. Email: [email protected] Email: [email protected] (Michigan PhD student) Email: [email protected]; web: www.umich.edu/∼lones.