Econometrica: May 2021, Volume 89, Issue 3

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

https://doi.org/10.3982/ECTA16907
p. 1141-1177

Timothy B. Armstrong, Michal Kolesár

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 in finite 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 ‐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 ‐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.



Log In To View Full Content

Supplemental Material

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

This zip file contains replication files for the manuscript.

Read More View ZIP


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

These supplemental materials are organized as follows. Supplemental Appendix C gives additional empirical results. Supplemental Appendix D proves Lemma A.3, gives the derivation of the solution path in the proof of Theorem 2.2, completes the proof of Theorem 2.3, proves Lemma B.1 and Lemma B.2, gives conditions for asymptotic efficiency of the matching estimator with a single match, and finally verifies Assumption B.1 for the matching estimator.

Read More View PDF


Back