Testing a parametric model against a nonparametric alternative with identification through instrumental variables

Joel L Horowitz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

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-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.

Original languageEnglish (US)
Pages (from-to)521-538
Number of pages18
JournalEconometrica
Volume74
Issue number2
DOIs
StatePublished - Mar 1 2006

Keywords

  • Consistent testing
  • Hypothesis test
  • Instrumental variables
  • Specification testing

ASJC Scopus subject areas

  • Economics and Econometrics

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