Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness

Authors

Timothy B. Armstrong
Michal Kolesár

Document Type

Discussion Paper

Publication Date

12-1-2017

CFDP Number

2115R

CFDP Revision Date

December 1, 2018

CFDP Pages

63

Journal of Economic Literature (JEL) Code(s)

C14

Abstract

We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional mean of the outcome variable, we derive estimators and confidence intervals (CIs) that are optimal infinite samples when the regression errors are normal with known variance. In contrast to conventional CIs, our CIs use a larger critical value that explicitly takes into account the potential bias of the estimator. When the error distribution is unknown, feasible versions of our CIs are valid asymptotically, even when √n-inference is not possible due to lack of overlap, or low smoothness of the conditional mean. We also derive the minimum smoothness conditions on the conditional mean that are necessary for √n-inference. When the conditional mean is restricted to be Lipschitz with a large enough bound on the Lipschitz constant, the optimal estimator reduces to a matching estimator with the number of matches set to one. We illustrate our methods in an application to the National Supported Work Demonstration.

Comments

Supplement Materials, 8 pp

Recommended Citation

Armstrong, Timothy B. and Kolesár, Michal, "Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness" (2017). Cowles Foundation Discussion Papers. 162.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/162