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

Author

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  • Bernard Salanié

    (Department of Economics (Columbia))

  • Alfred Galichon

    (Département d'économie)

Abstract

We investigate a model of one-to-one matching with transferable utility when some of the characteristics of the players are unobservable to the analyst. We allow for a wide class of distributions of unobserved heterogeneity, subject only to a separability assumption that generalizes Choo and Siow (2006). We first show that the stable matching maximizes a social gain function that trades off the average surplus due to the observable characteristics and a generalized entropy term that reflects the impact of matching on unobserved characteristics. We use this result to derive simple closed-form formulæ that identify the joint surplus in every possible match and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. If transfers are observed, then the pre-transfer utilities of both partners are also identified. We also present a very fast algorithm that computes the optimal matching for any specification of the joint surplus. We conclude by discussing some empirical approaches suggested by these results.

Suggested Citation

  • Bernard Salanié & Alfred Galichon, 2012. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
  • Handle: RePEc:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0c7apsi
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    References listed on IDEAS

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    1. John William Hatfield & Scott Duke Kominers & Alexandru Nichifor & Michael Ostrovsky & Alexander Westkamp, 2013. "Stability and Competitive Equilibrium in Trading Networks," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 966-1005.
    2. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
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    4. Maristella Botticini & Aloysius Siow, 2006. "Are There Increasing Returns in Marriage Markets?," Boston University - Department of Economics - Working Papers Series WP2006-050, Boston University - Department of Economics.
    5. Nicolas Jacquemet & Jean-Marc Robin, 2011. "Marriage with Labor Supply," Post-Print halshs-00639313, HAL.
    6. Marko Tervio, 2008. "The Difference That CEOs Make: An Assignment Model Approach," American Economic Review, American Economic Association, vol. 98(3), pages 642-668, June.
    7. 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.
    8. 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.
    9. John William Hatfield & Scott Duke Kominers, 2012. "Matching in Networks with Bilateral Contracts," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 176-208, February.
    10. 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..
    11. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-Offs: Revealed Preferences over Competing Characteristics," Sciences Po publications info:hdl:2441/1293p84sf58, Sciences Po.
    12. 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.
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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. 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. 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.
    6. Cheremukhin, Anton & Restrepo-Echavarria, Paulina & Tutino, Antonella, 2020. "Targeted search in matching markets," Journal of Economic Theory, Elsevier, vol. 185(C).
    7. 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.
    8. Taehoon Kim & Jacob Schwartz & Kyungchul Song & Yoon-Jae Whang, 2019. "Monte Carlo Inference on Two-Sided Matching Models," Econometrics, MDPI, Open Access Journal, vol. 7(1), pages 1-15, March.
    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. Pierre-Andr'e Chiappori & Robert McCann & Brendan Pass, 2016. "Multidimensional matching," Papers 1604.05771, arXiv.org.

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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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