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The law of large numbers for large stable matchings

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  • Schwartz, Jacob
  • Song, Kyungchul

Abstract

In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In this paper, we consider a setting in which the researcher observes either all or a nontrivial fraction of outcomes from a stable matching. We establish a concentration inequality for empirical matching probabilities assuming strong correlation among the colleges’ preferences while allowing students’ preferences to be fully heterogeneous. Our concentration inequality yields laws of large numbers for the empirical matching probabilities and other statistics commonly used in empirical analyses of a large matching market. To illustrate the usefulness of our concentration inequality, we prove consistency for estimators of conditional matching probabilities and measures of positive assortative matching.

Suggested Citation

  • Schwartz, Jacob & Song, Kyungchul, 2024. "The law of large numbers for large stable matchings," Journal of Econometrics, Elsevier, vol. 241(1).
    • Handle: RePEc:eee:econom:v:241:y:2024:i:1:s0304407624000885
    DOI: 10.1016/j.jeconom.2024.105742
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    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. 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.
    4. Julien Combe & Olivier Tercieux & Camille Terrier, 2022. "The Design of Teacher Assignment: Theory and Evidence [House Allocation with Existing Tenants]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3154-3222.
    5. 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.
    6. Guerre, Emmanuel & Sabbah, Camille, 2012. "Uniform Bias Study And Bahadur Representation For Local Polynomial Estimators Of The Conditional Quantile Function," Econometric Theory, Cambridge University Press, vol. 28(1), pages 87-129, February.
    7. Aue, Robert & Klein, Thilo & Ortega, Josué, 2020. "What happens when separate and unequal school districts merge?," ZEW Discussion Papers 20-032, ZEW - Leibniz Centre for European Economic Research.
    8. Erdil, Aytek & Ergin, Haluk, 2017. "Two-sided matching with indifferences," Journal of Economic Theory, Elsevier, vol. 171(C), pages 268-292.
    9. 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.
    10. Rania Gihleb & Kevin Lang, 2020. "Educational Homogamy and Assortative Mating Have Not Increased," Research in Labor Economics, in: Change at Home, in the Labor Market, and On the Job, volume 48, pages 1-26, Emerald Group Publishing Limited.
    11. Pierre-André Chiappori & Bernard Salanié, 2016. "The Econometrics of Matching Models," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 832-861, September.
    12. 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.
    13. Caterina Calsamiglia & Chao Fu & Maia Güell, 2020. "Structural Estimation of a Model of School Choices: The Boston Mechanism versus Its Alternatives," Journal of Political Economy, University of Chicago Press, vol. 128(2), pages 642-680.
    14. YingHua He & Shruti Sinha & Xiaoting Sun, 2021. "Identification and Estimation in Many-to-one Two-sided Matching without Transfers," Papers 2104.02009, arXiv.org, revised Jul 2023.
    15. Yeon‐Koo Che & Jinwoo Kim & Fuhito Kojima, 2019. "Stable Matching in Large Economies," Econometrica, Econometric Society, vol. 87(1), pages 65-110, January.
    16. Del Boca, Daniela & Flinn, Christopher J., 2014. "Household behavior and the marriage market," Journal of Economic Theory, Elsevier, vol. 150(C), pages 515-550.
    17. Akyol, Pelin & Krishna, Kala, 2017. "Preferences, selection, and value added: A structural approach," European Economic Review, Elsevier, vol. 91(C), pages 89-117.
    18. Marcus Hagedorn & Tzuo Hann Law & Iourii Manovskii, 2017. "Identifying Equilibrium Models of Labor Market Sorting," Econometrica, Econometric Society, vol. 85, pages 29-65, January.
    19. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    20. 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.
    21. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    22. 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.
    23. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    24. Nikhil Agarwal & Paulo Somaini, 2020. "Revealed Preference Analysis of School Choice Models," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 471-501, August.
    25. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    26. 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.
    27. Atila Abdulkadiroğlu & Joshua Angrist & Parag Pathak, 2014. "The Elite Illusion: Achievement Effects at Boston and New York Exam Schools," Econometrica, Econometric Society, vol. 82(1), pages 137-196, January.
    28. Michael P. Leung, 2020. "Treatment and Spillover Effects Under Network Interference," The Review of Economics and Statistics, MIT Press, vol. 102(2), pages 368-380, May.
    29. Thilo Klein & Robert Aue & Josue Ortega, 2020. "School choice with independent versus consolidated districts," Papers 2006.13209, arXiv.org, revised Jul 2024.
    30. Taehoon Kim & Jacob Schwartz & Kyungchul Song & Yoon-Jae Whang, 2019. "Monte Carlo Inference on Two-Sided Matching Models," Econometrics, MDPI, vol. 7(1), pages 1-15, March.
    31. Nathan Canen & Jacob Schwartz & Kyungchul Song, 2020. "Estimating local interactions among many agents who observe their neighbors," Quantitative Economics, Econometric Society, vol. 11(3), pages 917-956, July.
    32. 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.
    33. Donald Boyd & Hamilton Lankford & Susanna Loeb & James Wyckoff, 2013. "Analyzing the Determinants of the Matching of Public School Teachers to Jobs: Disentangling the Preferences of Teachers and Employers," Journal of Labor Economics, University of Chicago Press, vol. 31(1), pages 83-117.
    34. Kosuke Imai & Gary King & Elizabeth A. Stuart, 2008. "Misunderstandings between experimentalists and observationalists about causal inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 481-502, April.
    35. 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.
    36. William Diamond & Nikhil Agarwal, 2017. "Latent indices in assortative matching models," Quantitative Economics, Econometric Society, vol. 8(3), pages 685-728, November.
    37. 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.
    38. Blum, Yosef & Roth, Alvin E. & Rothblum, Uriel G., 1997. "Vacancy Chains and Equilibration in Senior-Level Labor Markets," Journal of Economic Theory, Elsevier, vol. 76(2), pages 362-411, October.
    39. Logan, John Allen & Hoff, Peter D. & Newton, Michael A., 2008. "Two-Sided Estimation of Mate Preferences for Similarities in Age, Education, and Religion," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 559-569, June.
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    More about this item

    Keywords

    Two-sided matching; Concentration inequality; Stable matching; Law of large numbers; Correlated preferences;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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