Testing Unconfoundedness Assumption Using Auxiliary Variables

In this paper, we propose an alternative test procedure for testing the conditional independence assumption which is an important identication condition commonly imposed in the literature of program analysis and policy evaluation. We transform the conditional independence test to a nonparametric conditional moment test using an auxiliary variable which is independent of the treatment assignment variable conditional on potential outcomes and observable covariates. The proposed test statistic is shown to have a limiting normal distribution under null hypotheses of conditional independence. Furthermore, the suggested method is shown to be valid under time series framework and thus the corresponding test statistic and its limiting distribution are also established. Monte Carlo simulations are conducted to examine the finite sample performances of the proposed test statistics. Finally, the proposed test method is applied to test the conditional independence in real examples: the 401(k) participation program and return to college education.