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The Effect of Nuisance Parameters on Size and Power; LM Tests in Logit Models

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Author Info
N.E. Savin
Allan H. Wuertz () (Department of Economics, University of Aarhus, Denmark)

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Abstract

In econometrics, most null hypotheses are composite, dividing the parameters into parameters of interest and nuisance parameters. Typically, a composite hypothesis can be tested using two or more testing procedures. Competing testing procedures are commonly compared using size-corrected powers. What is often overlooked is that the size-corrected critical value of a test can be sensitive to the set of admissible values of the nuisance parameters, and hence its size-corrected power. As a result, different choices for the admissible set can produce different conclusions about which test is best. This fact complicates the interpretation of Monte Carlo power studies because in many cases there is no natural definition of the set of admissible values. We find this fact to be crucial when choosing a Lagrange Multiplier test in the case of a logit model. A theoretical explanation for this effect is developed using large parameter asymptotics.

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Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 1997-17.

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Handle: RePEc:aah:aarhec:1997-17

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Related research
Keywords: Composite hypotheses; finite sample power; Hessian information matrix; Lagrange multiplier test; logit model; nuisance parameter; outer product information matrix.;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models

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  1. Davidson, Russel & MacKinnon, James G., 1983. "Small sample properties of alternative forms of the Lagrange Multiplier test," Economics Letters, Elsevier, vol. 12(3-4), pages 269-275. [Downloadable!] (restricted)
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  2. Dufour, J.M., 1995. "Some Impossibility Theorems in Econometrics with Applications to Instrumental Variables, Dynamic Models and Cointegration," Cahiers de recherche 9539, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  3. Russell Davidson & James G. MacKinnon, 1985. "Testing Linear and Loglinear Regressions against Box-Cox Alternatives," Canadian Journal of Economics, Canadian Economics Association, vol. 18(3), pages 499-517, August. [Downloadable!] (restricted)
  4. Campbell, Bryan & Dufour, Jean-Marie, 1997. "Exact Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 151-73, February.
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  5. Davidson, Russell & MacKinnon, James G, 1992. "A New Form of the Information Matrix Test," Econometrica, Econometric Society, vol. 60(1), pages 145-57, January. [Downloadable!] (restricted)
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  6. Russell Davidson & James G. MacKinnon, 1982. "Convenient Specification Tests for Logit and Probit Models," Working Papers 514, Queen's University, Department of Economics. [Downloadable!]
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  7. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May. [Downloadable!] (restricted)
  8. 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)
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  9. Godfrey, Leslie G & McAleer, Michael & McKenzie, Colin R, 1988. "Variable Addition and LaGrange Multiplier Tests for Linear and Logarithmic Regression Models," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 492-503, August. [Downloadable!] (restricted)
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  1. Henrik Christoffersen & Martin Paldam, . "Markets and Municipalities. A Study of the Behaviour of the Danish Municipalities," Economics Working Papers 1998-3, School of Economics and Management, University of Aarhus. [Downloadable!]
  2. Torben M. Andersen & Steinar Holden, . "Business Cycles and Fiscal Policy in an Open Economy," Economics Working Papers 1998-5, School of Economics and Management, University of Aarhus. [Downloadable!]
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  3. Martin Paldam, . "Soft Criteria in Danish Development Aid. An Essay on Post-Materialist Values in Practice," Economics Working Papers 1998-4, School of Economics and Management, University of Aarhus. [Downloadable!]
  4. Philipp J.H. Schroeder, . "The Fiscal Constraint to Restructuring of Firms in Transition Economies," Economics Working Papers 1998-2, School of Economics and Management, University of Aarhus. [Downloadable!]
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