A Nonparametric Test for Exogeneity

This paper presents a test for exogeneity of explanatory variables that minimizes the need for auxiliary assumptions that are not required by the definition of exogeneity. It concerns inference about a nonparametric function g that is identified by a conditional moment restriction involving instrumental variables. A test of the hypothesis that g is the mean of a random variable Y conditional on a covariate X is developed that is not subject to the ill-posed inverse problem of nonparametric instrumental variables estimation. The test is consistent whenever g differs from E(Y|X) on a set of non-zero probability. The usefulness of this new exogeneity test is displayed through Monte Carlo experiments and an application to estimation of nonparametric consumer expansion paths.