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Matching in Closed-Form Equilibrium Identification and Comparative Statics

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Document pages: 30 pages

Abstract: This paper provides closed-form formulas for a multidimensional two-sidedmatching problem with transferable utility and heterogeneity in tastes. Whenthe matching surplus is quadratic, the marginal distributions of thecharacteristics are normal, and when the heterogeneity in tastes is of thecontinuous logit type, as in Choo and Siow (J Polit Econ 114:172-201, 2006), weshow that the optimal matching distribution is also jointly normal and can becomputed in closed form from the model primitives. Conversely, the quadraticsurplus function can be identified from the optimal matching distribution, alsoin closed-form. The closed-form formulas make it computationally easy to solveproblems with even a very large number of matches and allow for quantitativepredictions about the evolution of the solution as the technology and thecharacteristics of the matching populations change.

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