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

Timothy Armstrong and Michal Koles\'ar

Papers from arXiv.org

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 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 $\sqrt{n}$-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 $\sqrt{n}$-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.

Date: 2017-12, Revised 2021-01
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (19)

Published in Econometrica, Volume 89, Issue 3, May 2021, pages 1141-1177

Downloads: (external link)
http://arxiv.org/pdf/1712.04594 Latest version (application/pdf)

Related works:
Working Paper: Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness (2018)
Working Paper: Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness (2017)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1712.04594

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().