We consider testing for correct specification of a nonparametric instrumental variable regression. First we study the notion of correct specification, misspecification and overidentification in this ill-posed inverse problem setting. Second we study a test statistic based on the empirical minimum distance criterion corresponding to the conditional moment restriction evaluated with a Tikhonov Regularized estimator of the functional parameter. The test statistic admits an asymptotic normal distribution under the null hypothesis, and the test is consistent under global alternatives. A bootstrap procedure is available to get simulation based critical values. Finally, we explore the finite sample behavior with Monte Carlo experiments, and provide an empirical illustration for an estimated Engel curve.

Keywords : Specification Test, Nonparametric Regression, Instrumental Variables, Minimum Distance, Tikhonov Regularization, Ill-posed Inverse Problems, Generalized Method of Moments, Bootstrap, Engel Curve.

JEL : C13, C14, C15, D12.

MSC 2000 : 62G08, 62G20.