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Demand Analysis using Strategic Reports: An application to a school choice mechanism

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  • Nikhil Agarwal
  • Paulo Somaini

Abstract

Several school districts use assignment systems that give students an incentive to misrepresent their preferences. We find evidence consistent with strategic behavior in Cambridge. Such strategizing can complicate preference analysis. This paper develops empirical methods for studying random utility models in a new and large class of school choice mechanisms. We show that preferences are non-parametrically identified under either sufficient variation in choice environments or a preference shifter. We then develop a tractable estimation procedure and apply it to Cambridge. Estimates suggest that while 82% of students are assigned to their stated first choice, only 72% are assigned to their true first choice because students avoid ranking competitive schools. Assuming that students behave optimally, the Immediate Acceptance mechanism is preferred by the average student to the Deferred Acceptance mechanism by an equivalent of 0.08 miles. The estimated difference is smaller if beliefs are biased, and reversed if students report truthfully.

Suggested Citation

  • Nikhil Agarwal & Paulo Somaini, 2014. "Demand Analysis using Strategic Reports: An application to a school choice mechanism," NBER Working Papers 20775, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:20775
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    1. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
    2. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    3. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    4. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    5. 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.
    6. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    7. 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.
    8. Parag A. Pathak & Tayfun Sonmez, 2008. "Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism," American Economic Review, American Economic Association, vol. 98(4), pages 1636-1652, September.
    9. Calsamiglia, Caterina & Güell, Maia, 2014. "The Illusion of School Choice: Empirical Evidence from Barcelona," IZA Discussion Papers 8202, Institute for the Study of Labor (IZA).
    10. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    11. 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.
    12. Chen, Yan & Sonmez, Tayfun, 2006. "School choice: an experimental study," Journal of Economic Theory, Elsevier, vol. 127(1), pages 202-231, March.
    13. Caterina Calsamiglia & Chao Fu & Maia Güell, 2014. "Structural Estimation of a Model of School Choices: the Boston Mechanism vs. Its Alternatives," Working Papers 811, Barcelona Graduate School of Economics.
    14. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    15. Chiappori, Pierre-André & Gandhi, Amit & Salanié, Bernard & Salanié, François, 2012. "From Aggregate Betting Data to Individual Risk Preferences," TSE Working Papers 13-453, Toulouse School of Economics (TSE).
    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. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    18. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2011. "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered," American Economic Review, American Economic Association, vol. 101(1), pages 399-410, February.
    19. Gunter J. Hitsch & Ali Hortaçsu & Dan Ariely, 2010. "Matching and Sorting in Online Dating," American Economic Review, American Economic Association, vol. 100(1), pages 130-163, March.
    20. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
    21. 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.
    22. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    23. He, Yinghua, 2012. "Gaming the Boston School Choice Mechanism in Beijing," TSE Working Papers 12-345, Toulouse School of Economics (TSE).
    24. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    25. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2006. "Changing the Boston School Choice Mechanism," Boston College Working Papers in Economics 639, Boston College Department of Economics.
    26. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-270, March.
    27. Eugene Choo & Aloysius Siow, 2006. "Who Marries Whom and Why," Journal of Political Economy, University of Chicago Press, vol. 114(1), pages 175-201, February.
    28. Steven T. Berry & Philip A. Haile, 2009. "Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers," Cowles Foundation Discussion Papers 1718, Cowles Foundation for Research in Economics, Yale University, revised Mar 2010.
    29. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    30. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    31. Troyan, Peter, 2012. "Comparing school choice mechanisms by interim and ex-ante welfare," Games and Economic Behavior, Elsevier, vol. 75(2), pages 936-947.
    32. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    33. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    34. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
    35. Nikhil Agarwal & William Diamond, 2013. "Identification and Estimation in Two-Sided Matching Markets," Cowles Foundation Discussion Papers 1905, Cowles Foundation for Research in Economics, Yale University, revised Feb 2014.
    36. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    37. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    38. Beggs, S. & Cardell, S. & Hausman, J., 1981. "Assessing the potential demand for electric cars," Journal of Econometrics, Elsevier, vol. 17(1), pages 1-19, September.
    39. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
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    Cited by:

    1. Magnac, Thierry, 2018. "Quels étudiants pour quelles universités ? Analyses empiriques de mécanismes d'allocation centralisée," TSE Working Papers 18-899, Toulouse School of Economics (TSE).
    2. Eduardo M. Azevedo & Eric Budish, 2017. "Strategy-proofness in the Large," NBER Working Papers 23771, National Bureau of Economic Research, Inc.
    3. Antonio Miralles & Marek Pycia, 2017. "Large vs. Continuum Assignment Economies: Efficiency and Envy-Freeness," Working Papers 950, Barcelona Graduate School of Economics.
    4. de Haan, Monique & Gautier, Pieter A. & Oosterbeek, Hessel & van der Klaauw, Bas, 2015. "The performance of school assignment mechanisms in practice," CEPR Discussion Papers 10656, C.E.P.R. Discussion Papers.
    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. 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.
    7. Yusuki Narita, 2016. "(Non)Randomization: A Theory of Quasi-Experimental Evaluation of School Quality," Cowles Foundation Discussion Papers 2056R, Cowles Foundation for Research in Economics, Yale University, revised Aug 2017.
    8. Fack, Gabrielle & Grenet, Julien & He, Yinghua, 2015. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice," CEPR Discussion Papers 10907, C.E.P.R. Discussion Papers.
    9. Fack, Gabrielle & Grenet, Julien & He, Yinghua, 2015. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions," TSE Working Papers 15-607, Toulouse School of Economics (TSE), revised Sep 2017.
    10. repec:wly:emetrp:v:85:y:2017:i::p:1373-1432 is not listed on IDEAS
    11. Parag A. Pathak & Peng Shi, 2017. "How Well Do Structural Demand Models Work? Counterfactual Predictions in School Choice," NBER Working Papers 24017, National Bureau of Economic Research, Inc.
    12. 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.
    13. Bertoni, Marco & Gibbons, Stephen & Silva, Olmo, 2017. "School Choice during a Period of Radical School Reform: Evidence from the Academy Programme," IZA Discussion Papers 11162, Institute for the Study of Labor (IZA).
    14. Yusuki Narita, 2016. "(Non)Randomization: A Theory of Quasi-Experimental Evaluation of School Quality," Cowles Foundation Discussion Papers 2056, Cowles Foundation for Research in Economics, Yale University.
    15. 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.
    16. 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.
    17. Adam Kapor & Christopher A. Neilson & Seth D. Zimmerman, 2017. "Heterogeneous Beliefs and School Choice Mechanisms," Working Papers 612, Princeton University, Department of Economics, Industrial Relations Section..

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    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • I20 - Health, Education, and Welfare - - Education - - - General

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