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Large Matching Markets as Two‐Sided Demand Systems

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  • Konrad Menzel

Abstract

This paper studies two‐sided matching markets with non‐transferable utility when the number of market participants grows large. We consider a model in which each agent has a random preference ordering over individual potential matching partners, and agents' types are only partially observed by the econometrician. We show that in a large market, the inclusive value is a sufficient statistic for an agent's endogenous choice set with respect to the probability of being matched to a spouse of a given observable type. Furthermore, while the number of pairwise stable matchings for a typical realization of random utilities grows at a fast rate as the number of market participants increases, the inclusive values resulting from any stable matching converge to a unique deterministic limit. We can therefore characterize the limiting distribution of the matching market as the unique solution to a fixed‐point condition on the inclusive values. Finally we analyze identification and estimation of payoff parameters from the asymptotic distribution of observable characteristics at the level of pairs resulting from a stable matching.

Suggested Citation

  • Konrad Menzel, 2015. "Large Matching Markets as Two‐Sided Demand Systems," Econometrica, Econometric Society, vol. 83(3), pages 897-941, May.
    • Handle: RePEc:wly:emetrp:v:83:y:2015:i:3:p:897-941
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    Cited by:

    1. Anna NAZSZODI & Francisco MENDONCA, 2023. "A new method for identifying the role of marital preferences at shaping marriage patterns," JODE - Journal of Demographic Economics, Cambridge University Press, vol. 89(1), pages 1-27, March.
    2. Yash Kanoria & Seungki Min & Pengyu Qian, 2020. "The Competition for Partners in Matching Markets," Papers 2006.14653, arXiv.org, revised Jan 2023.
    3. Bryan S. Graham & Guido W. Imbens & Geert Ridder, 2020. "Identification and Efficiency Bounds for the Average Match Function Under Conditionally Exogenous Matching," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 303-316, April.
    4. Shuyang Sheng & Xiaoting Sun, 2023. "Social Interactions with Endogenous Group Formation," Papers 2306.01544, arXiv.org.
    5. Pęski, Marcin, 2017. "Large roommate problem with non-transferable random utility," Journal of Economic Theory, Elsevier, vol. 168(C), pages 432-471.
    6. Liang Chen & Eugene Choo & Alfred Galichon & Simon Weber, 2023. "Existence of a Competitive Equilibrium with Substitutes, with Applications to Matching and Discrete Choice Models," Papers 2309.11416, arXiv.org.
    7. Jaerim Choi, 2021. "Two-sided heterogeneity, endogenous sharing, and international matching markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 473-509, September.
    8. Ismael Mourifié, 2019. "A marriage matching function with flexible spillover and substitution patterns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 421-461, March.
    9. Suhas Vijaykumar, 2021. "Stability and Efficiency of Random Serial Dictatorship," Papers 2110.07024, arXiv.org.
    10. Jacob Schwartz, 2018. "Schooling Choice, Labour Market Matching, and Wages," Papers 1803.09020, arXiv.org, revised Aug 2019.
    11. Dagsvik, John K. & Strøm, Steinar & Locatelli, Marilena, 2021. "Marginal compensated effects in discrete labor supply models," Journal of choice modelling, Elsevier, vol. 41(C).
    12. Bryan S. Graham & Guido Imbens & Geert Ridder, 2016. "Identification and efficiency bounds for the average match function under conditionally exogenous matching," CeMMAP working papers 10/16, Institute for Fiscal Studies.
    13. Gutierrez, Federico H., 2020. "A simple solution to the problem of independence of irrelevant alternatives in Choo and Siow marriage market model," Economics Letters, Elsevier, vol. 186(C).
    14. Han, Xuehui & Zhang, Tao & Dagsvik, John K. & Cheng, Yuan, 2023. "A cross-sectional exploration of labor supply, gender, and household wealth in urban China," Journal of choice modelling, Elsevier, vol. 48(C).
    15. Thierry Magnac, 2018. "Quels étudiants pour quelles universités ? Analyses empiriques de mécanismes d’allocation centralisée," Revue économique, Presses de Sciences-Po, vol. 69(5), pages 683-708.
    16. 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.
    17. Sonia Jaffe & Simon Weber, 2019. "The effect of meeting rates on matching outcomes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 363-378, March.
    18. John K. Dagsvik & Zhiyang Jia, 2018. "Aggregate behavior in matching markets with flexible contracts and non-transferable representations of preferences," Discussion Papers 875, Statistics Norway, Research Department.
    19. 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.
    20. Itai Ashlagi & Mark Braverman & Geng Zhao, 2023. "Welfare Distribution in Two-sided Random Matching Markets," Papers 2302.08599, arXiv.org.
    21. repec:hal:spmain:info:hdl:2441/13gl57r1jn8ns9de5346ma76lr is not listed on IDEAS
    22. repec:spo:wpmain:info:hdl:2441/13gl57r1jn8ns9de5346ma76lr is not listed on IDEAS
    23. Leung, Michael P., 2019. "A weak law for moments of pairwise stable networks," Journal of Econometrics, Elsevier, vol. 210(2), pages 310-326.
    24. Alfred Galichon & Simon Weber, 2024. "Matching under Imperfectly Transferable Utility," Papers 2403.05222, arXiv.org, revised Oct 2024.
    25. Itai Ashlagi & Mark Braverman & Yash Kanoria & Peng Shi, 2020. "Clearing Matching Markets Efficiently: Informative Signals and Match Recommendations," Management Science, INFORMS, vol. 66(5), pages 2163-2193, May.

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