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Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models
[An Empirical Model of the Medical Match]

Author

Listed:
  • Alfred Galichon
  • Bernard Salanié

Abstract

We investigate a model of one-to-one matching with transferable utility and general unobserved heterogeneity. Under a separability assumption that generalizes Choo and Siow (2006, Journal of Political Economy, 114, 175–201), we first show that the equilibrium matching maximizes a social gain function that trades off exploiting complementarities in observable characteristics and matching on unobserved characteristics. We use this result to derive simple closed-form formulae that identify the joint matching surplus and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. We provide efficient algorithms to compute the stable matching and to estimate parametric versions of the model. Finally, we revisit Choo and Siow’s empirical application to illustrate the potential of our more general approach.

Suggested Citation

  • 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.
  • Handle: RePEc:oup:restud:v:89:y:2022:i:5:p:2600-2629.
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    File URL: http://hdl.handle.net/10.1093/restud/rdab090
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    References listed on IDEAS

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    9. Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2012. "The Roommate Problem is More Stable than You Think," Working Papers hal-03588302, HAL.
    10. Pierre-André Chiappori & Robert McCann & Lars Nesheim, 2010. "Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 317-354, February.
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    12. 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.
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    17. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    18. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-Offs: Revealed Preferences over Competing Characteristics," Sciences Po publications info:hdl:2441/1293p84sf58, Sciences Po.
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    21. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
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    Citations

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    Cited by:

    1. Goussé, Marion & Jacquemet, Nicolas & Robin, Jean-Marc, 2017. "Household labour supply and the marriage market in the UK, 1991-2008," Labour Economics, Elsevier, vol. 46(C), pages 131-149.
    2. Jerez, Belén, 2017. "Competitive search equilibrium with multidimensional heterogeneity and two-sided ex-ante investments," Journal of Economic Theory, Elsevier, vol. 172(C), pages 202-219.
    3. Cheremukhin, Anton & Restrepo-Echavarria, Paulina & Tutino, Antonella, 2020. "Targeted search in matching markets," Journal of Economic Theory, Elsevier, vol. 185(C).
    4. 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.
    5. Aloysius Siow, 2015. "Testing Becker's Theory of Positive Assortative Matching," Journal of Labor Economics, University of Chicago Press, vol. 33(2), pages 409-441.
    6. repec:hal:spmain:info:hdl:2441/660vg58v5k8erajtn9uj2uue81 is not listed on IDEAS
    7. Pęski, Marcin, 2017. "Large roommate problem with non-transferable random utility," Journal of Economic Theory, Elsevier, vol. 168(C), pages 432-471.
    8. Arnaud Dupuy & Alfred Galichon, 2012. "Personality traits and the marriage market," SciencePo Working papers hal-01070393, HAL.
    9. Pierre-Andr'e Chiappori & Robert McCann & Brendan Pass, 2016. "Multidimensional matching," Papers 1604.05771, arXiv.org.
    10. Veronica Rappoport & Catherine Thomas & Bernard Salanie & Maria Guadalupe, 2013. "The Perfect Match: Assortative Matching in International Acquisitions," 2013 Meeting Papers 1000, Society for Economic Dynamics.
    11. 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.
    12. Seul-Ki Shin, 2014. "Preferences vs. Opportunities: Racial/Ethnic Intermarriage in the United States," PIER Working Paper Archive 14-040, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    13. Goussé, Marion & Jacquemet, Nicolas & Robin, Jean-Marc, 2017. "Household labour supply and the marriage market in the UK, 1991-2008," Labour Economics, Elsevier, vol. 46(C), pages 131-149.
    14. Arnaud Dupuy & Alfred Galichon, 2012. "Personality traits and the marriage market," SciencePo Working papers Main hal-01070393, HAL.

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    More about this item

    Keywords

    Matching; Marriage; Assignment; Hedonic prices;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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