Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT

Abstract

We propose inverse probability weighted estimators for the local average treatment effect (LATE) and the local average treatment effect for the treated (LATT) under instrumental variable assumptions with covariates. We show that these estimators are asymptotically normal and efficient. When the (binary) instrument satisfies one-sided noncompliance, we propose a Durbin–Wu–Hausman-type test of whether treatment assignment is unconfounded conditional on some observables. The test is based on the fact that under one-sided noncompliance LATT coincides with the average treatment effect for the treated (ATT). We conduct Monte Carlo simulations to demonstrate, among other things, that part of the theoretical efficiency gain afforded by unconfoundedness in estimating ATT survives pretesting. We illustrate the implementation of the test on data from training programs administered under the Job Training Partnership Act in the United States. This article has online supplementary material.

KEY WORDS:

• Instrumental variables
• Inverse probability weighted estimation
• Local average treatment effect
• Nonparametric estimation

ACKNOWLEDGMENTS

We thank Jason Abrevaya, Yu-Wei Hsieh, David Kaplan, Chung-Ming Kuan, Blaise Melly, Chris Taber, Ed Vytlacil, the editors, and three anonymous referees for useful comments. All errors are our responsibility.