Pierre-André Chiappori and Bernard Salanié
Journal of Economic Literature 2016, 54(3), 832–861
Abstract: Many questions in economics can be fruitfully analyzed in the framework of matching models. Until recently, empirical work has lagged far behind theory in this area. This review reports on recent developments that have considerably expanded the range of matching models that can be taken to the data. A leading theme is that in such two-sided markets, knowing the observable characteristics of partners alone is not enough to credibly identify the relevant parameters. A combination of richer data and robust, theory-driven restrictions is required. We illustrate this on leading applications.
Here is the opening paragraph:
"In October 2012, the Nobel prize was attributed to Al Roth and Lloyd Shapley
for their work on matching. Both the seminal Gale and Shapley (1962) paper and most of Roth’s work were concerned with allocation mechanisms when prices or other transfers cannot be used—what we will call nontransferable utility (NTU) in this survey. Gale and Shapley used college admissions, marriage, and roommate assignments as examples; Roth’s fundamental work in market design has led to major improvements in the National Resident Matching Program (Roth and Peranson 1999) and to the creation of a mechanism for kidney exchange (Roth, Sönmez, and Ünver 2004). While these are important economic applications, matching problems are much more pervasive. Market and nonmarket mechanisms such as auctions match agents with goods and buyers with sellers; agents match to each other in production teams, and production tasks are matched with workers; and in international trade, countries are matched with goods or varieties. Yet while the basic theory of matching was in place forty years ago, only recently has there been an explosion of empirical work in this area. Several developments have concurred to bring it to the attention of applied researchers."