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Testing a Parametric Model Against a Nonparametric Alternative with Identification Through Instrumental Variables
Joel L. Horowitz
Abstract
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 the hypothesis that g belongs to a finite-dimensional parametric family against a nonparametric alternative. The test does not require nonparametric estimation of g and is not subject to the ill-posed inverse problem of nonparametric instrumental variables estimation. Under mild conditions, the test is consistent against any alternative model. In large samples, its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is O(n−1/2), where n is the sample size. In Monte Carlo simulations, the finite-sample power of the new test exceeds that of existing tests.
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