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

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 non-compliance, 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 non-compliance 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 effciency gain afforded by unconfoundedness in estimating ATT survives pre-testing. We illustrate the practical implementation of the test on data from training programs administered under the Job Training Partnership Act.