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 2115, 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. 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.

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: 44 pages
Date: 2017-12
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Citations: View citations in EconPapers (2)

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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 (2018)
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