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

Econometrica · 2006 · Volume 74 · Issue 2

DOI: 10.1111/j.1468-0262.2006.00670.x

Abstract

This paper is concerned with inference about a functiongthat is identified by a conditional moment restriction involving instrumental variables. The paper presents a test of the hypothesis thatgbelongs to a finite-dimensional parametric family against a nonparametric alternative. The test does not require nonparametric estimation ofgand 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 isO(n−1/2), wherenis the sample size. In Monte Carlo simulations, the finite-sample power of the new test exceeds that of existing tests.

Keywords

Hypothesis test, instrumental variables, specification testing, consistent testing

Enable JavaScript for citation tools and additional paper interactions.