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Identification and Estimation in Two-Sided Matching Markets

Author

Listed:
  • Nikhil Agarwal

    (Dept. of Economics, MIT)

  • William Diamond

    (Dept. of Economics, Harvard University)

Abstract

We study estimation and non-parametric identification of preferences in two-sided matching markets using data from a single market with many agents. We consider a model in which preferences of each side of the market are vertical, utility is non-transferable and the observed matches are pairwise stable. We show that preferences are not identified with data on one-to-one matches but are non-parametrically identified when data from many-to-one matches are observed. The additional empirical content in many-to-one matches is illustrated by comparing two simulated objective functions, one that does and the other that does not use information available in many-to-one matching. We also prove consistency of a method of moments estimator for a parametric model under a data generating process in which the size of the matching market increases, but data only on one market is observed. Since matches in a single market are interdependent, our proof of consistency cannot rely on observations of independent matches. Finally, we present Monte Carlo studies of a simulation based estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:cwl:cwldpp:1905
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d19/d1905.pdf
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    References listed on IDEAS

    as
    1. Clark Simon, 2006. "The Uniqueness of Stable Matchings," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-28, December.
    2. repec:hal:spmain:info:hdl:2441/1293p84sf58s482v2dpn0gsd67 is not listed on IDEAS
    3. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    4. 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.
    5. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    6. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-offs: Revealed Preferences over Competiting Characteristics," Working Papers hal-00473173, HAL.
    7. 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.
    8. Donald Boyd & Hamilton Lankford & Susanna Loeb & James Wyckoff, 2003. "Analyzing the Determinants of the Matching Public School Teachers to Jobs: Estimating Compensating Differentials in Imperfect Labor Markets," NBER Working Papers 9878, National Bureau of Economic Research, Inc.
    9. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    10. Muriel Niederle & Leeat Yariv, 2009. "Decentralized Matching with Aligned Preferences," NBER Working Papers 14840, National Bureau of Economic Research, Inc.
    11. 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.
    12. Gordon, Nora & Knight, Brian, 2009. "A spatial merger estimator with an application to school district consolidation," Journal of Public Economics, Elsevier, vol. 93(5-6), pages 752-765, June.
    13. Morten Sørensen, 2007. "How Smart Is Smart Money? A Two‐Sided Matching Model of Venture Capital," Journal of Finance, American Finance Association, vol. 62(6), pages 2725-2762, December.
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    Citations

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    Cited by:

    1. 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.
    2. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    3. Jacob Schwartz, 2018. "Schooling Choice, Labour Market Matching, and Wages," Papers 1803.09020, arXiv.org, revised Aug 2019.
    4. Aue, Robert & Bach, Maximilian & Heigle, Julia & Klein, Thilo & Pfeiffer, Friedhelm & Zapp, Kristina, 2020. "The implication of school admission rules for segregation and educational inequality: Research report," ZEW Expertises, ZEW - Leibniz Centre for European Economic Research, number 223254.
    5. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    6. Hu, Yingyao, 2017. "The econometrics of unobservables: Applications of measurement error models in empirical industrial organization and labor economics," Journal of Econometrics, Elsevier, vol. 200(2), pages 154-168.
    7. 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.
    8. Yingyao Hu, 2015. "Microeconomic models with latent variables: applications of measurement error models in empirical industrial organization and labor economics," CeMMAP working papers CWP03/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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    More about this item

    Keywords

    Two-sided matching; Identification; Estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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