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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. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    2. 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.
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    6. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    7. 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.
    8. 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.
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