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Testing a Parametric Model Against a Nonparametric Alternative with Identification Through Instrumental Variables
Author(s) -
Horowitz Joel L.
Publication year - 2006
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/j.1468-0262.2006.00670.x
Subject(s) - nonparametric statistics , instrumental variable , mathematics , parametric statistics , econometrics , null hypothesis , statistical hypothesis testing , statistics , inference , moment (physics) , semiparametric regression , monte carlo method , parametric model , computer science , artificial intelligence , physics , classical mechanics
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.