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Invariance and the Wald Test

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  • Kemp, GCR

Abstract

Many models and hypotheses of interest in econometrics are invariant to certain types of data transformations such as measurement unit changes. Dagenais and Dufour (1991, 1992) and Dufour and Dagenais (1992) have shown that Wald test are not invariant in general to such data transformations. In this paper, I provide a simple set of sufficient conditions to ensure that a Wald test for a null hypothesis is invariant to such a data transformation. I then use this set of conditions to help account for certain features of the Monte Carlo results from Gregory and Veall (1986) on the properties of a variety of Wald tests for Sargan's COMFAC restriction (Sargan 1980) in the first-order autoregressive distributed-lag model.

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  • Kemp, GCR, 2000. "Invariance and the Wald Test," Economics Discussion Papers 2887, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:2887
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    References listed on IDEAS

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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. Gregory, Allan W. & Veall, Michael R., 1986. "Wald tests of common factor restrictions," Economics Letters, Elsevier, vol. 22(2-3), pages 203-208.
    3. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-1083, September.
    4. Dagenais, Marcel G. & Dufour, Jean-Marie, 1992. "On the lack of invariance of some asymptotic tests to rescaling," Economics Letters, Elsevier, vol. 38(3), pages 251-257, March.
    5. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-1468, November.
    6. Sargan, J D, 1980. "Some Tests of Dynamic Specification for a Single Equation," Econometrica, Econometric Society, vol. 48(4), pages 879-897, May.
    7. Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
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    1. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Axioms of invariance for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 891-902, November.
    2. Naorayex K Dastoor, 2008. "A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis," Economics Bulletin, AccessEcon, vol. 3(62), pages 1-10.
    3. repec:ebl:ecbull:v:3:y:2008:i:62:p:1-10 is not listed on IDEAS
    4. Peter Huber & Michael Pfaffermayr, 2010. "Testing for Conditional Convergence in Variance and Skewness: The Firm Size Distribution Revisited," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(5), pages 648-668, October.
    5. Naorayex Dastoor, 2009. "The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?," Working Papers 2009-25, University of Alberta, Department of Economics.

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