Student Portfolios and the College Admissions Problem ∗

We develop the first Bayesian model of decentralized college admissions, with heterogeneous students, costly portfolio applications, and uncertainty about student calibers. Students face a nontrivial portfolio choice, and colleges choose admissions standards that act like market-clearing prices. We solve for the two college model equilibrium, deriving a “law of demand”. The lesser college impacts its rival through student portfolio reallocation. Notably, it might impose higher standards, and weaker students sometimes apply more aggressively. We show that the weaker college counters affirmative action at its rival with a discriminatory admissions policy. Earlier versions were called “The College Admissions Problem with Uncertainty” and “A Supply and Demand Model of the College Admissions Problem”. Greg and Lones are grateful for the financial support of the National Science Foundation. We have benefited from seminars at BU, UCLA, Georgetown, HBS, the 2006 Two-Sided Matching Conference (Bonn), 2006 SED (Vancouver), 2006 Latin American Econometric Society Meetings (Mexico City), and 2007 American Econometric Society Meetings (New Orleans), Iowa State, Harvard/MIT, the 2009 Atlanta NBER Conference, and Concordia. Parag Pathak and Philipp Kircher provided useful discussions of our paper. We are also grateful to John Bound and Brad Hershbein for providing us with student college applications data. Arizona State University, Department of Economics, Tempe, AZ 85287-3806. Harvard University, Department of Economics, Cambridge, MA 02138. University of Michigan, Economics Department, Ann Arbor, MI 48109-1220.