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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
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    2. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, January.
    3. Clark Simon, 2006. "The Uniqueness of Stable Matchings," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-30, December.
    4. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-offs: Revealed Preferences over Competiting Characteristics," Working Papers hal-00473173, HAL.
    5. 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.
    6. 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.
    7. 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.
    8. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    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.
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    12. 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.
    13. 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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    Citations

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    Cited by:

    1. Thilo Klein & Robert Aue & Josue Ortega, 2020. "School choice with independent versus consolidated districts," Papers 2006.13209, arXiv.org, revised Jul 2024.
    2. 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.
    3. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    4. Jacob Schwartz, 2018. "Schooling Choice, Labour Market Matching, and Wages," Papers 1803.09020, arXiv.org, revised Aug 2019.
    5. 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.
    6. 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.
    7. 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, March.
    8. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    9. 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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