“Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness,” Tim Armstrong, Yale
MACMILLAN-CSAP WORKSHOP ON QUANTITATIVE RESEARCH METHODS
Abstract: 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.
Tim Armstrong earned his B.A. in economics-mathematics from Reed College and received his Ph.D. in economics from Stanford University. His research is in econometrics with applications in empirical microeconomics. He is currently an assistant professor in the Economics Department at Yale.
This workshop series is being sponsored by the ISPS Center for the Study of American Politics and The Whitney and Betty MacMillan Center for International and Area Studies at Yale with support from the Edward J. and Dorothy Clarke Kempf Fund.