Recently there has been a surge in econometric work focusing on estimating average treatment effects under various sets of assumptions. One sirand of this literature has developed methods for estimating average treatment effects for a binary treatment under assumptions variously described as exogeneity. unconfoundedness. or selection on observables. The implication of these assumptions is that systematic (for example, average or distributional) differences in outcomes between treated and control units with the same values for the covariates are attributable to the treatment. Recent analysis has considered estimation and inference for average treatment effects under weaker assumptions than typical of the eariier literature by avoiding distributional and functional-form assump- tions. Various methods of semiparametric estimation have been proposed, including estimating the unknown regression functions, matching, meth- ods using the propensity score such as weighting and blocking, and combinations of these approaches. In this paper I review the state of this literature and discuss some of its unanswered questions, focusing in particular on the practical implementation of these methods, the plausi- bility of this exogeneity assumption in economic applications, the relative performance of the various semiparametric estimators when the key assumptions (unconfoundedness and overlap) are satisfied, alternative estimands such as quantile treatment effects, and alternate methods such as Bayesian inference.
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