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Monte Carlo Inference on Two-Sided Matching Models

Author

Listed:
  • Taehoon Kim

    (Department of Economics, Harvard University, Cambridge, MA 02138, USA)

  • Jacob Schwartz

    (Department of Economics, University of Haifa, Haifa 3498838, Israel)

  • Kyungchul Song

    (Vancouver School of Economics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada)

  • Yoon-Jae Whang

    (Department of Economics, Seoul National University, Seoul 08826, Korea)

Abstract

This paper considers two-sided matching models with nontransferable utilities, with one side having homogeneous preferences over the other side. When one observes only one or several large matchings, despite the large number of agents involved, asymptotic inference is difficult because the observed matching involves the preferences of all the agents on both sides in a complex way, and creates a complicated form of cross-sectional dependence across observed matches. When we assume that the observed matching is a consequence of a stable matching mechanism with homogeneous preferences on one side, and the preferences are drawn from a parametric distribution conditional on observables, the large observed matching follows a parametric distribution. This paper shows in such a situation how the method of Monte Carlo inference can be a viable option. Being a finite sample inference method, it does not require independence or local dependence among the observations which are often used to obtain asymptotic validity. Results from a Monte Carlo simulation study are presented and discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jecnmx:v:7:y:2019:i:1:p:16-:d:217155
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    References listed on IDEAS

    as
    1. Alfred Galichon & Bernard Salanié, 2022. "Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models [An Empirical Model of the Medical Match]," Review of Economic Studies, Oxford University Press, vol. 89(5), pages 2600-2629.
    2. Konrad Menzel, 2015. "Large Matching Markets as Two‐Sided Demand Systems," Econometrica, Econometric Society, vol. 83(3), pages 897-941, May.
    3. 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.
    4. 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.
    5. Bryan S. Graham & Guido W. Imbens & Geert Ridder, 2014. "Complementarity and aggregate implications of assortative matching: A nonparametric analysis," Quantitative Economics, Econometric Society, vol. 5, pages 29-66, March.
    6. Jeremy T. Fox & Patrick Bajari, 2013. "Measuring the Efficiency of an FCC Spectrum Auction," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 100-146, February.
    7. Mark A. Satterthwaite & Hugo Sonnenschein, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Oxford University Press, vol. 48(4), pages 587-597.
    8. Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2017. "Inference for subvectors and other functions of partially identified parameters in moment inequality models," Quantitative Economics, Econometric Society, vol. 8(1), pages 1-38, March.
    9. Park, Minjung, 2013. "Understanding merger incentives and outcomes in the US mutual fund industry," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4368-4380.
    10. 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.
    11. 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.
    12. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    13. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0c7apsi is not listed on IDEAS
    14. 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.
    15. Jacob Schwartz, 2018. "Schooling Choice, Labour Market Matching, and Wages," Papers 1803.09020, arXiv.org, revised Aug 2019.
    16. Chen, Jiawei & Song, Kejun, 2013. "Two-sided matching in the loan market," International Journal of Industrial Organization, Elsevier, vol. 31(2), pages 145-152.
    17. 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.
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