This paper is concerned with inference about a function g that is identified by a conditional moment restriction involving instrumental variables. The paper presents a test of thehypothesis that g belongs to a finite-dimensional parametric family against a nonparametricalternative. The test does not require nonparametric estimation of g and is not subject to the illposed inverse problem of nonparametric instrumental variables estimation. Under mildconditions, the test is consistent against any alternative model and has asymptotic poweradvantages over existing tests. Moreover, it has power arbitrarily close to 1 uniformly over aclass of alternatives whose distance from the null hypothesis is O(n-1/2), where n is the samplesize.
Centre for microdata methods and practice