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

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  • Bernard Salanié

    ()
    (Columbia University - Department of Economics)

  • Alfred Galichon

    ()
    (Ecole Polytechnique - Department of Economics)

Abstract

We investigate a matching game 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 of two terms. The first term is simply the average surplus due to the observable characteristics; and the second one can be interpreted as a generalized entropy function that reflects the impact of the 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. Moreover, we show that if transfers are observed, then the pre-transfer utilities of both partners are also identified. We conclude by discussing some empirical approaches suggested by these results for the study of marriage markets, hedonic prices, and the market for CEOs.

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Bibliographic Info

Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 1011-03.

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Date of creation: 2011
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Handle: RePEc:clu:wpaper:1011-03

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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. 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.
  3. Nicolas Jacquemet & Jean-Marc Robin, 2011. "Marriage with Labor Supply," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00639313, HAL.
  4. Shimer, R. & Smith, L., 1997. "Assortative Matching and Search," Working papers 97-2b, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. 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.
  6. Xavier Gabaix & Augustin Landier, 2006. "Why Has CEO Pay Increased So Much?," 2006 Meeting Papers 518, Society for Economic Dynamics.
  7. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-offs: Revealed Preferences over Competiting Characteristics," Working Papers hal-00473173, HAL.
  8. 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.
  9. 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.
  10. 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.
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Cited by:
  1. Nicolas Jacquemet & Jean-Marc Robin, 2013. "Assortative matching and search with labour supply and home production," CeMMAP working papers CWP07/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Arnaud Dupuy & Alfred Galichon, 2012. "Personality Traits and the Marriage Market," Working Papers 2012/41, Maastricht School of Management.

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