Economic Theory

, Volume 61, Issue 4, pp 587–609 | Cite as

Matching in closed-form: equilibrium, identification, and comparative statics

  • Raicho Bojilov
  • Alfred GalichonEmail author
Research Article


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.


Matching Marriage Assignment 

JEL Classification

C78 D61 C13 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of EconomicsÉcole polytechniquePalaiseauFrance
  2. 2.Economics Department, Courant InstituteNew York UniversityNew YorkUSA
  3. 3.Economics DepartmentSciences Po.ParisFrance

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