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

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  • Joel L. Horowitz

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 thehypothesis that g belongs to a finite-dimensional parametric family against a nonparametricalternative. The test does not require nonparametric estimation of g and is not subject to the illposed inverse problem of nonparametric instrumental variables estimation. Under mildconditions, the test is consistent against any alternative model and has asymptotic poweradvantages over existing tests. Moreover, it has power arbitrarily close to 1 uniformly over aclass of alternatives whose distance from the null hypothesis is O(n-1/2), where n is the samplesize.

Suggested Citation

  • Joel L. Horowitz, 2004. "Testing a parametric model against a nonparametric alternative with identification through instrumental variables," CeMMAP working papers 14/04, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:14/04
    DOI: 10.1920/wp.cem.2004.1404
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    References listed on IDEAS

    as
    1. Peter Hall & Joel L. Horowitz, 2003. "Nonparametric methods for inference in the presence of instrumental variables," CeMMAP working papers CWP02/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Guerre, Emmanuel & Lavergne, Pascal, 2002. "Optimal Minimax Rates For Nonparametric Specification Testing In Regression Models," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1139-1171, October.
    3. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    4. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
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