A Consistent Nonparametric Bootstrap Test of Exogeneity

We propose a way of testing exogeneity of an explanatory variable without any parametric assumptions in the presence of a conditional "instrumental variable". A testable implication is derived that if an explanatory variable is exogenous, the conditional distribution of the outcome given explanatory variables is independent of the instrumental variable. We propose a consistent nonparametric bootstrap test to implement this testable implication. We show that our bootstrap test can be asymptotically justi…ed in the sense that it produces asymptotically correct size under the null of exogeneity, and it has unit power asymptotically. Our nonparametric test can be applied to a case in which the outcome is generated by an additively non-separable structural relation, which has not been studied in the literature.