Testing a parametric function against a non-parametric alternative in IV and GMM settings

Abstract

This paper develops a specification test for functional form for models identified by a conditional moment restriction, including IV and GMM settings. The framework is one where the moment restriction is specified as a function of data, a finite-dimensional parameter vector and a non-parametric function (an infinite-dimensional parameter vector). The null hypothesis is that the moment restriction does not depend on the non-parametric function. The test is relatively easy to implement and its asymptotic distribution is known. The test performs well in simulation experiments.