The Effect of Nuisance Parameters on the Power of LM Tests in Logit and Probit Models

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The Effect of Nuisance Parameters on the Power of LM Tests in Logit and Probit Models

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N.E. Savin (Univ. of Iowa)
Allan Wurtz (Univ of Iowa)

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Allan H. Würtz

Abstract

In econometrics, most null hypotheses are composite, dividing the parameters into parameters of interest and nuisance parameters. The domain of the nuisance parameters can influence the size-corrected critical value and hence the power of a test. We show that the domain of the nuisance parameters determines which version of the LM test to use in logit and probit models. In these models there are two commonly used ways to construct the LM test: it can be based on the Hessian matrix or the outer product (OP) matrix of the score vectors. For the OP based LM test, the domain of the nuisance parameters strongly influences the size-corrected critical value whereas the same is not true for the Hessian based LM test. A theoretical explanation is developed using large nuisance parameter asymptotics. For empirically relevant domains, the experimental evidence shows that the Hessian based LM test has better finite sample power than the OP based LM test.

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Paper provided by EconWPA in its series Econometrics with number 9606002.

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Length: 28 pages
Date of creation: 17 Jun 1996
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Handle: RePEc:wpa:wuwpem:9606002

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Paper
- Savin, N.E. & Wurtz, A., 1996. "The Effect of Nuisance Parameters on the Power of LM Tests in Logit and Probit Models," Working Papers 96-05, University of Iowa, Department of Economics.

Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

References listed on IDEAS
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Russell Davidson & James G. MacKinnon, 1982. "Convenient Specification Tests for Logit and Probit Models," Working Papers 514, Queen's University, Department of Economics. [Downloadable!]
Other versions:
- Davidson, Russell & MacKinnon, James G., 1984. "Convenient specification tests for logit and probit models," Journal of Econometrics, Elsevier, vol. 25(3), pages 241-262, July. [Downloadable!] (restricted)
Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-15, November. [Downloadable!] (restricted)
Other versions:
- Dagenais, M.G. & Dufour, J.M., 1987. "Invariance, Nonlinear Models and Asymptotic Tests," Cahiers de recherche 8738, Universite de Montreal, Departement de sciences economiques.

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

DUFOUR, Jean-Marie & TORRÈS, Olivier, 2000. "Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes," Cahiers de recherche 2000-12, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
Other versions:
- Dufour, J.M. & Torres, O., 2000. "Markovian Progresses, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes," Cahiers de recherche 2000-12, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Jean-Marie Dufour & Olivier Torrès, 2000. "Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes," CIRANO Working Papers 2000s-17, CIRANO. [Downloadable!]
- Dufour, Jean-Marie & Torres, Olivier, 2000. "Markovian processes, two-sided autoregressions and finite-sample inference for stationary and nonstationary autoregressive processes," Journal of Econometrics, Elsevier, vol. 99(2), pages 255-289, December. [Downloadable!] (restricted)

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