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Asymptotic Results for Generalized Wald Tests

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  • Andrews, Donald W. K.

Abstract

This paper presents conditions under which a quadratic form based on a g-inverted weighting matrix converges to a chi-square distribution as the sample size goes to infinity. Subject to fairly weak underlying conditions, a necessary and sufficient condition is given for this result. The result is of interest because it is needed to establish asymptotic significance levels and local power properties of generalized Wald tests (i.e., Wald tests with singular limiting covariance matrices). Included in this class of tests are Hausman specification tests and various goodness-of-fit tests, among others. The necessary and sufficient condition is relevant to procedures currently in the econometrics literature because it illustrates that some results stated in the literature only hold under more restrictive assumptions than those given.

Suggested Citation

  • Andrews, Donald W. K., 1987. "Asymptotic Results for Generalized Wald Tests," Econometric Theory, Cambridge University Press, vol. 3(3), pages 348-358, June.
    • Handle: RePEc:cup:etheor:v:3:y:1987:i:03:p:348-358_01
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    References listed on IDEAS

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    1. Donald W.K. Andrews, 1985. "Random Cell Chi-Square Diagnostic Tests for Econometric Models: I. Introduction and Applications," Cowles Foundation Discussion Papers 762, Cowles Foundation for Research in Economics, Yale University.
    2. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-759, May.
    3. Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
    4. Donald W.K. Andrews, 1985. "Random Cell Chi-Square Diagnostic Tests for Econometric Models: II. Theory," Cowles Foundation Discussion Papers 763R, Cowles Foundation for Research in Economics, Yale University, revised Jun 1986.
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