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

Author

Listed:
  • Raicho Bolijov

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • Alfred Galichon

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

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," Working Papers hal-01169654, HAL.
    • Handle: RePEc:hal:wpaper:hal-01169654
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01169654
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    References listed on IDEAS

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    1. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 49-100.
    2. 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.
    3. Pierre-André Chiappori & Sonia Oreffice & Climent Quintana-Domeque, 2012. "Fatter Attraction: Anthropometric and Socioeconomic Matching on the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 120(4), pages 659-695.
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    6. Decker, Colin & Lieb, Elliott H. & McCann, Robert J. & Stephens, Benjamin K., 2013. "Unique equilibria and substitution effects in a stochastic model of the marriage market," Journal of Economic Theory, Elsevier, vol. 148(2), pages 778-792.
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    Keywords

    Matching; Marriage; Assignment;
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