Identification in One-to-One Matching Models with Nonparametric Unobservables

This paper considers a one-to-one matching model with transferable utilities, in two-sided markets. In the model, the agents have preferences over some observable agent characteristics (called types) on the other side of the market. There are other observed characteristics aggregated at the level of types that determine the systematic preferences over these types. These systematic preferences enter the agent utilities in the form of a linear index. Agents also have idiosyncratic taste shocks. This paper shows the identification of systematic preference parameters over types, without making any parametric assumptions on the distribution of the unobserved taste shocks. The matching model reduces to two separate discrete-choice problems linked together by market clearing conditions, satisfied in the presence of equilibrium transfers. However, transfers are endogenous and unobserved which makes the discrete-choice problem non-standard. This paper gives conditions under which transfers are simply functions of the linear indices. This insight along with variation across i.i.d. markets is used to reduce the matching model to a semiparametric multi-index model with an unknown link function. Identification is shown under appropriate exclusion restrictions on the regressors.