Introduction to the Symposium on the Econometrics of Matching

Abstract

The papers in this symposium address issues in the econometrics of matching. In this literature, interest typically focuses on nonparametric estimation of a relation Yi f(Di,Xi), where Yi is an outcome variable for individual i,Di is a dichotomous indicator of having received a treatment at some point in the past, and Xi is a set of other characteristics. However, unlike the case of general nonparametric regression, the interest in this case is in a nonparametric estimate of the average effect of Di on Yi, E(YiDi 1) E(YiDi 0), taken over the Xi distribution as well as over the conditional distribution of Yi, recognizing that the effect of the treatment can vary arbitrarily with Xi. This effect is estimated by comparing the values of Yi for a group of individuals having Di 1 with those drawn from a comparison group of individuals having Di 0. The two groups are nonparametrically matched on common values of Xi. For consistent estimation of the effect, matching methods require at a minimum that there be no unobservable differences between the two groups after conditioning on Xi (the “conditional independence” or “se lection on observables” assumption). Thus the issues considered in the large literature on endogenous treatment effects and selection bias (“selection on unobservables”) are ruled out. However, compared to least squares estimation of the relationship, with its attendant assumptions of linearity and additivity that can only awkwardly be relaxed in full, matching provides a method by which no functional form restrictions on the relation between Yi, Di, and Xi need be made. The ten papers in the symposium fall into distinct groups. Two overview papers, one by Imbens and the other by Heckman and Navarro-Lozano, provide, respectively, a review of the literature on matching and a comparison of matching with control function and instrumental variable methods (the latter two methods allow selection on unobservables). Two theoretical papers, by Angrist and Hahn and by Hahn, address efficiency issues in choice of matching