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

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Document pages: 56 pages

Abstract: We consider estimation and inference on average treatment effects underunconfoundedness conditional on the realizations of the treatment variable andcovariates. Given nonparametric smoothness and or shape restrictions on theconditional mean of the outcome variable, we derive estimators and confidenceintervals (CIs) that are optimal in finite samples when the regression errorsare normal with known variance. In contrast to conventional CIs, our CIs use alarger critical value that explicitly takes into account the potential bias ofthe estimator. When the error distribution is unknown, feasible versions of ourCIs are valid asymptotically, even when $ sqrt{n}$-inference is not possibledue to lack of overlap, or low smoothness of the conditional mean. We alsoderive the minimum smoothness conditions on the conditional mean that arenecessary for $ sqrt{n}$-inference. When the conditional mean is restricted tobe Lipschitz with a large enough bound on the Lipschitz constant, the optimalestimator reduces to a matching estimator with the number of matches set toone. We illustrate our methods in an application to the National Supported WorkDemonstration.

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