Testing a Parametric Model Against a Nonparametric Alternative with Identification Through Instrumental Variables

Joel L. Horowitz

Econometrica, 2006, vol. 74, issue 2, 521-538

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-super- - 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. Copyright The Econometric Society 2006.

Date: 2006
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