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

TL;DR

This paper develops finite-sample optimal estimators and confidence intervals for average treatment effects under unconfoundedness, accounting for bias and smoothness restrictions, with practical applications demonstrated.

Contribution

It introduces new estimators and confidence intervals that are optimal in finite samples under certain smoothness and error assumptions, extending inference validity.

Findings

Optimal estimators derived under normal errors with known variance.

Confidence intervals that explicitly account for estimator bias.

Feasible CIs valid asymptotically even without overlap or high smoothness.

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.