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

Timothy B. Armstrong, Michal Kolesár

Research output: Contribution to journalArticlepeer-review

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 (Formula presented.) -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 (Formula presented.) -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.

Original languageEnglish (US)
Pages (from-to)1141-1177
Number of pages37
JournalEconometrica
Volume89
Issue number3
DOIs
StatePublished - May 2021

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

Keywords

  • finite-sample inference
  • honest inference
  • overlap
  • Treatment effects
  • unconfoundedness

Fingerprint Dive into the research topics of 'Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness'. Together they form a unique fingerprint.

Cite this