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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: http://cowles.yale.edu/sites/default/files/files/pub/d19/d1905.pdf
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    References listed on IDEAS

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    1. 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.
    2. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, May.
    3. Clark Simon, 2006. "The Uniqueness of Stable Matchings," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-28, December.
    4. 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.
    5. 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.
    6. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    7. Muriel Niederle & Leeat Yariv, 2009. "Decentralized Matching with Aligned Preferences," NBER Working Papers 14840, National Bureau of Economic Research, Inc.
    8. Jeremy T. Fox, 2008. "Estimating Matching Games with Transfers," NBER Working Papers 14382, National Bureau of Economic Research, Inc.
    9. 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.
    10. 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. Jeremy T. Fox, 2008. "Estimating Matching Games with Transfers," NBER Working Papers 14382, National Bureau of Economic Research, Inc.
    2. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    3. 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.
    4. Jacob Schwartz, 2018. "Schooling Choice, Labour Market Matching, and Wages," Papers 1803.09020, arXiv.org, revised Apr 2018.
    5. 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.

    More about this item

    Keywords

    Two-sided matching; Identification; Estimation;

    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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