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Two-Sided Matching Without Transfers: A Unifying Empirical Framework

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  • Ederer, Tim

Abstract

This paper provides a unifying framework of one-to-one and many-to-one matching without transfers and investigates how data on realized matches can be leveraged to identify preferences of participating agents. I find that, under parsimonious assumptions on preferences, one can only identify the joint surplus function both in the one-to-one and many-to-one case. While this negative identification result was already established for the one-to-one case, I reconcile this finding with the recent literature showing that preferences are separately identified when having data on many-to-one matchings. I find that these positive identification results are mostly driven by restrictions imposed on preferences rather than the additional identification power made available through the many-to-one structure of the data. I then show that by imposing similar restrictions on preferences, one can recover identification of preferences both in the one-to-one and many-to-one case. Finally, I show that the additional data brought by many-to-one matchings can alternatively be used to estimate more precisely the distribution of un-observed preference heterogeneity.

Suggested Citation

  • Ederer, Tim, 2022. "Two-Sided Matching Without Transfers: A Unifying Empirical Framework," TSE Working Papers 22-1340, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:127031
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    References listed on IDEAS

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    1. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    2. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    3. Atila Abdulkadiroğlu & Nikhil Agarwal & Parag A. Pathak, 2017. "The Welfare Effects of Coordinated Assignment: Evidence from the New York City High School Match," American Economic Review, American Economic Association, vol. 107(12), pages 3635-3689, December.
    4. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    5. YingHua He & Shruti Sinha & Xiaoting Sun, 2021. "Identification and Estimation in Many-to-one Two-sided Matching without Transfers," Papers 2104.02009, arXiv.org, revised Jul 2023.
    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. 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.
    8. Eduardo M. Azevedo & Jacob D. Leshno, 2016. "A Supply and Demand Framework for Two-Sided Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1235-1268.
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