Student Portfolios and the College Admissions Problem

Abstract

We develop a decentralized Bayesian model of college admissions with two ranked colleges, heterogeneous students and two realistic match frictions: students find it costly to apply to college, and college evaluations of their applications are uncertain. Students thus face a portfolio choice problem in their application decision, while colleges choose admissions standards that act like market-clearing prices. Enrollment at each college is affected by the standards at the other college through student portfolio reallocation. In equilibrium, student-college sorting may fail: weaker students sometimes apply more aggressively, and the weaker college might impose higher standards. Applying our framework, we analyze affirmative action, showing how it induces minority applicants to construct their application portfolios as if they were majority students of higher caliber. * Earlier versions were called "The College Admissions Problem with Uncertainty" and "A Supply and Demand Model of the College Admissions Problem". We would like to thank Philipp Kircher (Co-Editor) and three anonymous referees for their helpful comments and suggestions. Greg Lewis and Lones Smith are grateful for the financial support of the National Science Foundation. We have benefited from seminars at BU,

Sorting through Search and Matching Models in Economics

“…Modeling search frictions in this simultaneous way appears in some equilibrium search models of price dispersion such as Burdett and Judd (1983); directed search models with one or multiple applications and ex ante identical firms such as Burdett, Shi, and Wright (2001) and Albrecht, Gautier, and Vroman (2006); as well as search problems with multiple applications and heterogeneous options such as Chade, Lewis, and Smith (2014) for college admissions, and Kircher (2009) and Galenianos and Kircher (2009) …”

“…Gale and Shapley (1962) ignore the wealth of search and information frictions that afflict the sorting of students into colleges. Chade, Lewis, and Smith (2014) explore how students and colleges react to these frictions and what happens to sorting.…”

“…We will exploit a simple graphical analysis of the student's problem for given college thresholds in Chade, Lewis, and Smith (2014). Consider a student with respective admission chances 0 ≤ α 1 , α 2 ≤ 1 .…”

Directed Search: A Guided Tour

“…All that remains is to show  satisfies (46), but that follows directly from (47) and (48) because they normalize  = 1 and  = 0. In fact, the weight on  is the probability a seller gets at least 2 buyers, and the weight on  is probability he gets just 1.…”

Academia or the Private Sector? Sorting of Agents into Institutions and an Outside Sector

“…Condition (ii) of the definition states that if a university has not reached its capacity then no researcher would be strictly better off by moving to that university. 5 One can think of the equilibrium as a result of an assignment procedure such as the one presented in Gale and Shapley (1962).…”