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

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.

45 pages, plus supplemental materials (11 pages)

References in corpus (5)

• Piecewise linear regularized solution paths
• Semiparametric efficiency in GMM models with auxiliary data
• Optimal inference in a class of regression models
• Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness
• Sensitivity Analysis using Approximate Moment Condition Models

Cited by in corpus (9)

• Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness
• Overlap in Observational Studies with High-Dimensional Covariates
• Finite Sample Analysis of Minimax Offline Reinforcement Learning: Completeness, Fast Rates and First-Order Efficiency
• Nonparametric identification is not enough, but randomized controlled trials are
• Bias-Aware Inference in Regularized Regression Models
• Incremental causal effects
• Matching Estimators with Few Treated and Many Control Observations
• Causal Inference in Longitudinal Data under Unknown Interference
• $\beta$-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap