Finite‐Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness
研究了在无混淆假设下，利用非参数光滑性或形状约束，构造平均处理效应的有限样本最优估计量和置信区间，并在误差分布未知时给出渐近有效的可行版本。
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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msqrt> <a:mi>n</a:mi> </a:msqrt> </a:math>‐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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msqrt> <c:mi>n</c:mi> </c:msqrt> </c:math>‐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.