Testing a parametric model against a nonparametric alternative with identification through instrumental variables
Joel L. Horowitz ()
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Joel L. Horowitz: Institute for Fiscal Studies and Northwestern University
No CWP14/04, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies
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 illposed inverse problem of nonparametric instrumental variables estimation. Under mild conditions, the test is consistent against any alternative model and has asymptotic power advantages over existing tests. Moreover, it has power 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.
Date: 2004-09-14
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