Matching models have become increasingly popular in several areas of economics, and in particular in the economic analysis of the marriage market. Models based on frictionless matching, with or without transferable utility, have several distinctive advantages. First, they provide a general equilibrium representation of the market; as such, they emphasize the impact of the total distribution of potential spouses on aggregate marital patterns. Second, they allow deriving the intrahousehold allocation of resources as an endogenous phenomenon, which is either constrained or exactly determined by equilibrium conditions. As such, they constitute a useful complement to 'collective' models of household behavior, which describe efficient household behavior conditional on some (exogenously given) allocation rule. Third, they provide a tractable tool for analyzing several dynamic issues, such as divorce or the impact of premarital investments on marital prospects (including marriage probability, the distribution of potential spouses and the resulting allocation of resources). Fourth, advances have recently been made regarding their empirical implementation; we now have robust methods for identifying the structural determinants of such models from observed matching patterns. Finally, the basic concepts can be applied to a variety of different economic contexts, such as labor, industrial organization and others.

The class will first present the basic concepts; a particular emphasis will be put on models based on transferable utility and their mathematical interpretation in terms of linear programming/optimal transportation problems a la Monge-Kantorovitch. A series of theoretical applications will then be discussed, involving ex ante investments, multidimensional matching, matching with imperfectly transferable utility and others aspects. Finally, the empirical implementation of matching models will be discussed.