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Cupid's Invisible Hand: Social Surplus and Identification in Matching Models

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  • Salanié, Bernard
  • Galichon, Alfred

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), 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

  • Salanié, Bernard & Galichon, Alfred, 2021. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," CEPR Discussion Papers 16228, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:16228
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    1. is not listed on IDEAS
    2. Pęski, Marcin, 2017. "Large roommate problem with non-transferable random utility," Journal of Economic Theory, Elsevier, vol. 168(C), pages 432-471.
    3. 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.
    4. 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.
    5. Arnaud Dupuy & Alfred Galichon, 2012. "Personality traits and the marriage market," SciencePo Working papers hal-01070393, HAL.
    6. 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.
    7. 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.
    8. Yu Hao & Hiroyuki Kasahara, 2024. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models with 2-period Finite Dependence," Papers 2405.12467, arXiv.org.
    9. 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.
    10. 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.
    11. Esben Scrivers Andersen, 2024. "Note on solving one-to-one matching models with linear transferable utility," Papers 2409.05518, arXiv.org, revised Jul 2025.
    12. 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.
    13. Pierre-Andr'e Chiappori & Robert McCann & Brendan Pass, 2016. "Multidimensional matching," Papers 1604.05771, arXiv.org.
    14. 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.
    15. Yagan Hazard & Toru Kitagawa, 2025. "Who With Whom? Learning Optimal Matching Policies," Papers 2507.13567, arXiv.org.
    16. Arnaud Dupuy & Alfred Galichon, 2012. "Personality traits and the marriage market," Sciences Po Economics Publications (main) hal-01070393, HAL.
    17. Cheremukhin, Anton & Restrepo-Echavarria, Paulina & Tutino, Antonella, 2020. "Targeted search in matching markets," Journal of Economic Theory, Elsevier, vol. 185(C).

    More about this item

    Keywords

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    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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