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Matching in Closed-Form: Equilibrium, identification, and comparative statics

Author

Listed:
  • Raicho Bolijov

    (Department of Economics, Ecole Polytechnique)

  • Alfred Galichon

    (Département d'économie)

Abstract

This paper provides closed-form formulas for a multidimensional two-sided matching problem with transferable utility and heterogeneity in tastes. When the matching surplus is quadratic, the marginal distributions of the characteristics are normal, and when the heterogeneity in tastes is of the continuous logit type, as in Choo and Siow (2006), we show that the optimal matching distribution is also jointly normal and can be computed in closed form from the model primitives. Conversely, the quadratic surplus function can be identified from the optimal matching distribution, also in closed-form. The analytical formulas make it computationally easy to solve problems with even a very large number of matches and allow for quantitative predictions about the evolution of the solution as the technology and the characteristics of the matching populations change.

Suggested Citation

  • Raicho Bolijov & Alfred Galichon, 2014. "Matching in Closed-Form: Equilibrium, identification, and comparative statics," Sciences Po publications info:hdl:2441/34a8d5vcod9, Sciences Po.
  • Handle: RePEc:spo:wpmain:info:hdl:2441/34a8d5vcod96oo2cch2e7gs4v6
    as

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    File URL: http://spire.sciencespo.fr/hdl:/2441/34a8d5vcod96oo2cch2e7gs4v6/resources/matching-in-closed-form.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
    3. Arnaud Dupuy & Alfred Galichon, 2014. "Personality Traits and the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 122(6), pages 1271-1319.
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    13. 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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    More about this item

    Keywords

    Matching; Marriage; Assignment;

    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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