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The College Admissions Problem Under Uncertainty


  • Hector Chade

    () (Arizona State University)

  • Greg Lewis
  • Lones Smith


We consider a college admissions problem with uncertainty. We realistically assume that (i) students' college application choices are nontrivial because applications are costly, (ii) college rankings of students are noisy and thus uncertain at the time of application, and (iii) matching between colleges and students takes place in a decentralized setting. 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 show that the optimal student application portfolio need not be monotone in types, and we construct a robust example to show that this can lead to a failure of assortative matching in equilibrium. More importantly, we prove that a unique equilibrium with assortive matching exists provided application costs are small and the lower-ranked college has sufficiently high capacity. We also provide equilibrium comparative static results with respect to college capacities and application costs. We apply the model to the question of race-based admissions policies

Suggested Citation

  • Hector Chade & Greg Lewis & Lones Smith, 2006. "The College Admissions Problem Under Uncertainty," 2006 Meeting Papers 125, Society for Economic Dynamics.
  • Handle: RePEc:red:sed006:125

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    References listed on IDEAS

    1. Kenneth Burdett & Shouyong Shi & Randall Wright, 2001. "Pricing and Matching with Frictions," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 1060-1085, October.
    2. Chade, Hector, 2006. "Matching with noise and the acceptance curse," Journal of Economic Theory, Elsevier, vol. 129(1), pages 81-113, July.
    3. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    4. Axel Anderson & Lones Smith, 2006. "Assortative Matching and Reputation," Cowles Foundation Discussion Papers 1553, Cowles Foundation for Research in Economics, Yale University.
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    More about this item


    matching; directed search; noise;

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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