IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/10907.html
   My bibliography  Save this paper

Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions

Author

Listed:
  • Fack, Gabrielle
  • Grenet, Julien
  • He, YingHua

Abstract

We propose novel approaches and tests for estimating student preferences with data from centralized matching mechanisms, like the Gale-Shapley Deferred Acceptance, when students are strictly ranked by, e.g., test scores. Without requiring truth-telling to be the unique equilibrium, we show that the matching is (asymptotically) stable, or justi?ed-envy-free, implying that every student is matched with her favorite school/college among those she is quali?ed for ex post. Having illustrated the approaches in simulations, we apply them to school choice data from Paris and demonstrate evidence supporting stability but not truth-telling. We discuss when each approach is more appropriate in real-life settings

Suggested Citation

  • Fack, Gabrielle & Grenet, Julien & He, YingHua, 2015. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions," CEPR Discussion Papers 10907, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:10907
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP10907
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Justine S. Hastings & Christopher A. Neilson & Seth D. Zimmerman, 2013. "Are Some Degrees Worth More than Others? Evidence from college admission cutoffs in Chile," NBER Working Papers 19241, National Bureau of Economic Research, Inc.
    2. Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2010. "Constrained School Choice: An Experimental Study," American Economic Review, American Economic Association, vol. 100(4), pages 1860-1874, September.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Antonio Romero-Medina, 1998. "Implementation of stable solutions in a restricted matching market," Review of Economic Design, Springer;Society for Economic Design, vol. 3(2), pages 137-147.
    5. Frankel, David M. & Volij, Oscar, 2011. "Measuring school segregation," Journal of Economic Theory, Elsevier, vol. 146(1), pages 1-38, January.
    6. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    7. Gabrielle Fack & Julien Grenet & Yinghua He, 2019. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions," American Economic Review, American Economic Association, vol. 109(4), pages 1486-1529, April.
    8. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    9. Yinghua He & Antonio Miralles & Marek Pycia & Jianye Yan, 2018. "A Pseudo-Market Approach to Allocation with Priorities," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 272-314, August.
    10. Atila Abdulkadiro?lu & Yeon-Koo Che & Yosuke Yasuda, 2015. "Expanding "Choice" in School Choice," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 1-42, February.
    11. Simon Burgess & Ellen Greaves & Anna Vignoles & Deborah Wilson, 2015. "What Parents Want: School Preferences and School Choice," Economic Journal, Royal Economic Society, vol. 125(587), pages 1262-1289, September.
    12. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    13. Parag A. Pathak, 2011. "The Mechanism Design Approach to Student Assignment," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 513-536, September.
    14. Caterina Calsamiglia & Chao Fu & Maia Güell, 2014. "Structural Estimation of a Model of School Choices: the Boston Mechanism vs. Its Alternatives," Working Papers 2014-21, FEDEA.
    15. Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2014. "Inference for functions of partially identified parameters in moment inequality models," CeMMAP working papers CWP05/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Parag A. Pathak & Tayfun Sönmez, 2013. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," American Economic Review, American Economic Association, vol. 103(1), pages 80-106, February.
    17. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    18. Ergin, Haluk & Sonmez, Tayfun, 2006. "Games of school choice under the Boston mechanism," Journal of Public Economics, Elsevier, vol. 90(1-2), pages 215-237, January.
    19. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    20. Kojima, Fuhito, 2012. "School choice: Impossibilities for affirmative action," Games and Economic Behavior, Elsevier, vol. 75(2), pages 685-693.
    21. Reynolds Farley, 1977. "Residential segregation in urbanized areas of the United States in 1970: An analysis of social class and racial differences," Demography, Springer;Population Association of America (PAA), vol. 14(4), pages 497-518, November.
    22. Akyol, Pelin & Krishna, Kala, 2017. "Preferences, selection, and value added: A structural approach," European Economic Review, Elsevier, vol. 91(C), pages 89-117.
    23. Avinatan Hassidim & Assaf Romm & Ran I. Shorrer, 2016. ""Strategic" Behavior in a Strategy-Proof Environment," Working Paper 413411, Harvard University OpenScholar.
    24. He, Yinghua & Li, Sanxi & Yan, Jianye, 2015. "Evaluating assignment without transfers: A market perspective," Economics Letters, Elsevier, vol. 133(C), pages 40-44.
    25. Cristian Pop-Eleches & Miguel Urquiola, 2013. "Going to a Better School: Effects and Behavioral Responses," American Economic Review, American Economic Association, vol. 103(4), pages 1289-1324, June.
    26. Bugni, Federico A. & Canay, Ivan A. & Shi, Xiaoxia, 2015. "Specification tests for partially identified models defined by moment inequalities," Journal of Econometrics, Elsevier, vol. 185(1), pages 259-282.
    27. Moon, Hyungsik Roger & Schorfheide, Frank, 2009. "Estimation with overidentifying inequality moment conditions," Journal of Econometrics, Elsevier, vol. 153(2), pages 136-154, December.
    28. Monique De Haan & Pieter A. Gautier & Hessel Oosterbeek & Bas van der Klaauw, 2023. "The Performance of School Assignment Mechanisms in Practice," Journal of Political Economy, University of Chicago Press, vol. 131(2), pages 388-455.
    29. Peter Arcidiacono, 2005. "Affirmative Action in Higher Education: How Do Admission and Financial Aid Rules Affect Future Earnings?," Econometrica, Econometric Society, vol. 73(5), pages 1477-1524, September.
    30. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    31. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    32. Federico Echenique & M. Bumin Yenmez, 2015. "How to Control Controlled School Choice," American Economic Review, American Economic Association, vol. 105(8), pages 2679-2694, August.
    33. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    34. Chung-Piaw Teo & Jay Sethuraman & Wee-Peng Tan, 2001. "Gale-Shapley Stable Marriage Problem Revisited: Strategic Issues and Applications," Management Science, INFORMS, vol. 47(9), pages 1252-1267, September.
    35. Min Zhu, 2014. "College admissions in China: A mechanism design perspective," Post-Print halshs-00871352, HAL.
    36. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
    37. Nikhil Agarwal & Paulo Somaini, 2018. "Demand Analysis Using Strategic Reports: An Application to a School Choice Mechanism," Econometrica, Econometric Society, vol. 86(2), pages 391-444, March.
    38. Scott Duke Kominers & Tayfun Sönmez, 2012. "Designing for Diversity: Matching with Slot-Specific Priorities," Boston College Working Papers in Economics 806, Boston College Department of Economics.
    39. Zhu, Min, 2014. "College admissions in China: A mechanism design perspective," China Economic Review, Elsevier, vol. 30(C), pages 618-631.
    40. Carvalho, José-Raimundo & Magnac, Thierry & Xiong, Qizhou, 2014. "College Choice Allocation Mechanisms: Structural Estimates and Counterfactuals," TSE Working Papers 14-506, Toulouse School of Economics (TSE).
    41. Umut M. Dur & Scott Duke Kominers & Parag A. Pathak & Tayfun Sönmez, 2013. "The Demise of Walk Zones in Boston: Priorities vs. Precedence in School Choice," NBER Working Papers 18981, National Bureau of Economic Research, Inc.
    42. Eduardo M. Azevedo & Jacob D. Leshno, 2016. "A Supply and Demand Framework for Two-Sided Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1235-1268.
    43. Atila Abdulkadiroğlu & Nikhil Agarwal & Parag A. Pathak, 2015. "The Welfare Effects of Coordinated Assignment: Evidence from the NYC HS Match," NBER Working Papers 21046, National Bureau of Economic Research, Inc.
    44. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    45. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    46. repec:hal:pseose:halshs-00986984 is not listed on IDEAS
    47. Mora, Ricardo & Romero-Medina, Antonio, 2001. "Understanding preference formation in a matching market," UC3M Working papers. Economics we015919, Universidad Carlos III de Madrid. Departamento de Economía.
    48. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    49. He, Yinghua, 2012. "Gaming the Boston School Choice Mechanism in Beijing," TSE Working Papers 12-345, Toulouse School of Economics (TSE).
    50. Saygin, Perihan Ozge, 2016. "Gender differences in preferences for taking risk in college applications," Economics of Education Review, Elsevier, vol. 52(C), pages 120-133.
    51. Chen, Yan & Onur, Kesten, 2013. "From Boston to Chinese parallel to deferred acceptance: Theory and experiments on a family of school choice mechanisms," Discussion Papers, Research Unit: Market Behavior SP II 2013-205, WZB Berlin Social Science Center.
    52. Parag A. Pathak & Peng Shi, 2014. "Demand Modeling, Forecasting, and Counterfactuals, Part I," NBER Working Papers 19859, National Bureau of Economic Research, Inc.
    53. Atila Abdulkadiroğlu & Nikhil Agarwal & Parag A. Pathak, 2017. "The Welfare Effects of Coordinated Assignment: Evidence from the New York City High School Match," American Economic Review, American Economic Association, vol. 107(12), pages 3635-3689, December.
    54. repec:cwl:cwldpp:1840rr is not listed on IDEAS
    55. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    56. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 147-165.
    57. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    58. Rees-Jones, Alex, 2018. "Suboptimal behavior in strategy-proof mechanisms: Evidence from the residency match," Games and Economic Behavior, Elsevier, vol. 108(C), pages 317-330.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:hal:cesptp:halshs-01215998 is not listed on IDEAS
    2. Abdulkadiroglu, Atila & Andersson, Tommy, 2022. "School Choice," Working Papers 2022:4, Lund University, Department of Economics.
    3. Caterina Calsamiglia & Chao Fu & Maia Güell, 2014. "Structural Estimation of a Model of School Choices: the Boston Mechanism vs. Its Alternatives," Working Papers 2014-21, FEDEA.
    4. Nikhil Agarwal & Paulo Somaini, 2018. "Demand Analysis Using Strategic Reports: An Application to a School Choice Mechanism," Econometrica, Econometric Society, vol. 86(2), pages 391-444, March.
    5. Carvalho, José-Raimundo & Magnac, Thierry & Xiong, Qizhou, 2016. "College Choice and the Selection of Mechanisms: A Structural Empirical Analysis," IWH Discussion Papers 3/2016, Halle Institute for Economic Research (IWH).
    6. YingHua He & Thierry Magnac, 2022. "Application Costs and Congestion in Matching Markets," The Economic Journal, Royal Economic Society, vol. 132(648), pages 2918-2950.
    7. Thierry Magnac, 2018. "Quels étudiants pour quelles universités ? Analyses empiriques de mécanismes d’allocation centralisée," Revue économique, Presses de Sciences-Po, vol. 69(5), pages 683-708.
    8. Eduardo Duque & Juan Pablo Torres-Martinez, 2022. "The Strong Effects of Weak Externalities on School Choice," Working Papers wp542, University of Chile, Department of Economics.
    9. Cantillon, Estelle & Chen, Li & Pereyra, Juan S., 2024. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off?," Games and Economic Behavior, Elsevier, vol. 148(C), pages 82-96.
    10. Hoyer, B. & Stroh-Maraun, N., 2020. "Matching strategies of heterogeneous agents under incomplete information in a university clearinghouse," Games and Economic Behavior, Elsevier, vol. 121(C), pages 453-481.
    11. Tong Wang & Congyi Zhou, 2020. "High school admission reform in China: a welfare analysis," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 215-269, December.
    12. He, Yinghua & Magnac, Thierry, 2018. "A Pigouvian Approach to Congestion in Matching Markets," IZA Discussion Papers 11967, Institute of Labor Economics (IZA).
    13. Klein, Thilo & Aue, Robert & Ortega, Josué, 2024. "School choice with independent versus consolidated districts," Games and Economic Behavior, Elsevier, vol. 147(C), pages 170-205.
    14. Hayri A. Arslan, 2021. "Preference estimation in centralized college admissions from reported lists," Empirical Economics, Springer, vol. 61(5), pages 2865-2911, November.
    15. Aue, Robert & Klein, Thilo & Ortega, Josué, 2020. "What Happens when Separate and Unequal School Districts Merge?," QBS Working Paper Series 2020/06, Queen's University Belfast, Queen's Business School.
    16. Estelle Cantillon & Li Chen & Juan Sebastian Pereyra Barreiro, 2022. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off ?," Working Papers ECARES 2022-39, ULB -- Universite Libre de Bruxelles.
    17. Atila Abdulkadiroğlu & Joshua D. Angrist & Yusuke Narita & Parag A. Pathak, 2017. "Research Design Meets Market Design: Using Centralized Assignment for Impact Evaluation," Econometrica, Econometric Society, vol. 85, pages 1373-1432, September.
    18. Hatfield, John William & Kojima, Fuhito & Narita, Yusuke, 2016. "Improving schools through school choice: A market design approach," Journal of Economic Theory, Elsevier, vol. 166(C), pages 186-211.
    19. Pathak, Parag A. & Shi, Peng, 2021. "How well do structural demand models work? Counterfactual predictions in school choice," Journal of Econometrics, Elsevier, vol. 222(1), pages 161-195.
    20. Hayri Alper Arslan & Yang Song & Tong Wang, 2024. "Preference submission timing and college admission outcomes: evidence from Turkey," Review of Economic Design, Springer;Society for Economic Design, vol. 28(1), pages 189-241, February.
    21. Li, Mengling, 2020. "Ties matter: Improving efficiency in course allocation by allowing ties," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 354-384.

    More about this item

    Keywords

    College admissions; Gale-shapley deferred acceptance mechanism; Stable matching; School choice; Student preferences;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cpr:ceprdp:10907. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://www.cepr.org .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.