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

  • Bernard Salanié

    (Department of Economics (Columbia))

  • Alfred Galichon

    (Département d'économie)

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.

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Date of creation: Sep 2012
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Handle: RePEc:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0c7apsi
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  1. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-46, July-Aug..
  2. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
  3. Xavier Gabaix & Augustin Landier, 2006. "Why Has CEO Pay Increased So Much?," 2006 Meeting Papers 518, Society for Economic Dynamics.
  4. 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.
  5. 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.
  6. Gunter J. Hitsch & Ali Horta�su & Dan Ariely, 2010. "Matching and Sorting in Online Dating," American Economic Review, American Economic Association, vol. 100(1), pages 130-63, March.
  7. Galichon, Alfred & Salanié, Bernard, 2010. "Matching with Trade-offs: Revealed Preferences over Competing Characteristics," CEPR Discussion Papers 7858, C.E.P.R. Discussion Papers.
  8. Nicholas Jacquemet & Jean-Marc Robin, 2011. "Marriage with Labor Supply," 2011 Meeting Papers 446, Society for Economic Dynamics.
  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. Marko Tervio, 2008. "The Difference That CEOs Make: An Assignment Model Approach," American Economic Review, American Economic Association, vol. 98(3), pages 642-68, June.
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