@article{403bd09a5950416ba3544eb23453daa6,
title = "Matching in closed-form: equilibrium, identification, and comparative statics",
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.",
keywords = "Assignment, Marriage, Matching",
author = "Raicho Bojilov and Alfred Galichon",
note = "Funding Information: Date: January 12, 2016. A preliminary version of this paper containing the main results was first presented in September 2012 under the title “Closed-Form Formulas for Multivariate Matching”. We would like to thank Nicholas Yannelis, the Editor, and two anonymous referees, as well as Arnaud Dupuy, Bernard Salani{\'e} and seminar participants at CREST and the 2013 Search and Matching Conference in Paris for helpful comments. Galichon{\textquoteright}s research has received funding from the European Research Council under the European Union{\textquoteright}s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreements no 313699, and from FiME, Laboratoire de Finance des March{\'e}s de l{\textquoteright}Energie. Bojilov{\textquoteright}s work is supported by a grant of the French National Research Agency (ANR), “Investissements d{\textquoteright}Avenir” (ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047). Publisher Copyright: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",
year = "2016",
month = apr,
day = "1",
doi = "10.1007/s00199-016-0961-8",
language = "English (US)",
volume = "61",
pages = "587--609",
journal = "Economic Theory",
issn = "0938-2259",
publisher = "Springer New York",
number = "4",
}