Econometrica: Mar, 2006, Volume 74, Issue 2

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

https://doi.org/10.1111/j.1468-0262.2006.00670.x
p. 521-538

Joel L. Horowitz

This paper is concerned with inference about a function that is identified by a conditional moment restriction involving instrumental variables. The paper presents a test of the hypothesis that belongs to a finite‐dimensional parametric family against a nonparametric alternative. The test does not require nonparametric estimation of 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 (), where 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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