Journal of Economic Literature (JEL) Code(s)
We consider estimation and inference on average treatment eﬀects under unconfoundedness conditional on the realizations of the treatment variable and covariates. We derive ﬁnite-sample optimal estimators and conﬁdence intervals (CIs) under the assumption of normal errors when the conditional mean of the outcome variable is constrained only by nonparametric smoothness and/or shape restrictions. When the conditional mean is restricted to be Lipschitz with a large enough bound on the Lipschitz constant, we show that the optimal estimator reduces to a matching estimator with the number of matches set to one. In contrast to conventional CIs, our CIs use a larger critical value that explicitly takes into account the potential bias of the estimator. It is needed for correct coverage in ﬁnite samples and, in certain cases, asymptotically. We give conditions under which root-n inference is impossible, and we provide versions of our CIs that are feasible and asymptotically valid with unknown error distribution, including in this non-regular case. We apply our results in a numerical illustration and in an application to the National Supported Work Demonstration.
Armstrong, Timothy B. and Kolesár, Michal, "Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness" (2017). Cowles Foundation Discussion Papers. 163.