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

Timothy Armstrong and Michal Koles'r
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Michal Koles'r: Princeton University

No 2115R, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 square root 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 square root 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.

Keywords: Semiparametric estimation; Relative efficiency; Matching estimators; Treatment effects (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Pages: 71 pages
Date: 2017-12, Revised 2018-12
Note: Includes Supplimental Material
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: Finite‐Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness (2021)
Working Paper: Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness (2021)
Working Paper: Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness (2017)
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