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Matching in Closed-Form: Equilibrium, Identification, and Comparative Statics

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  • Raicho Bojilov
  • Alfred Galichon

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 (J Polit Econ 114:172-201, 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 closed-form 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 Bojilov & Alfred Galichon, 2021. "Matching in Closed-Form: Equilibrium, Identification, and Comparative Statics," Papers 2102.04295, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:2102.04295
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    References listed on IDEAS

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    1. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
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    6. 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.
    7. 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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    Cited by:

    1. Jaerim Choi, 2021. "Two-sided heterogeneity, endogenous sharing, and international matching markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 473-509, September.
    2. Salanié, Bernard & Chiappori, Pierre-André, 2021. "Mating Markets," CEPR Discussion Papers 16041, C.E.P.R. Discussion Papers.
      • Pierre-André Chiappori & Bernard Salanié, 2021. "Mating Markets," Working Papers 2021-016, Human Capital and Economic Opportunity Working Group.
    3. Alfred Galichon & Bernard Salani'e, 2021. "Structural Estimation of Matching Markets with Transferable Utility," Papers 2109.07932, arXiv.org.

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