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

Listed author(s):
  • N.E. Savin

    (Univ. of Iowa)

  • Allan Wurtz

    (Univ of Iowa)

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
Handle: RePEc:wpa:wuwpem:9606002
Note: Zipped using PKZIP v2.04, encoded using UUENCODE v5.15. Zipped file includes 1 file -- ui9605.wpa (PostScript 28 pages)
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  1. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-1615, November.
  2. 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.
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