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Asymptotic Results for Generalized Wald Tests

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Author Info
Donald W.K. Andrews () (Cowles Foundation, Yale University)

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Abstract

This note 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.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 761R.

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Length: 14 pages
Date of creation: Sep 1985
Date of revision: Apr 1986
Publication status: Published in Econometric Theory (1987), 3: 348-358
Handle: RePEc:cwl:cwldpp:761r

Note: CFP 694.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Generalized inverse; Wald test; asymptotics; chi-square;

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References listed on IDEAS
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.:
  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, Yale University. [Downloadable!]
  2. Vuong, Quang H., 1986. "Generalized Inverses and Asymptotic Properties of Wald Tests," Working Papers 607, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  3. Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245. [Downloadable!] (restricted)
  4. Donald W.K. Andrews, 1985. "Random Cell Chi-Square Diagnostic Tests for Econometric Models: II. Theory," Cowles Foundation Discussion Papers 763R, Cowles Foundation, Yale University, revised Jun 1986. [Downloadable!]
Full references

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.)

  1. Albert Satorra & Heinz Neudecker, 1995. "Compact Matrix Expressions for Generalized Wald Tests of Equality of Moment Vectors," Economics Working Papers 127, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  2. Donald W.K. Andrews, 1986. "Power in Econometric Applications," Cowles Foundation Discussion Papers 800, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. Geert Dhaene & Olivier Scaillet, 2000. "Reversed Score and Likelihood Ratio Tests," Econometric Society World Congress 2000 Contributed Papers 1746, Econometric Society. [Downloadable!]
    Other versions:
  4. Donald W.K. Andrews & Ray C. Fair, 1987. "Inference in Econometric Models with Structural Change," Cowles Foundation Discussion Papers 832, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  5. Helmut LUETKEPOHL & Maike MUELLER, . "Testing for Multi-Step Causality in Time Series," Sonderforschungsbereich 373 1994-3, Humboldt Universitaet Berlin.
  6. Pascale VALERY (HEC-Montreal) & Jean-Marie Dufour (University of Montreal), 2004. "A simple estimation method and finite-sample inference for a stochastic volatility model," Econometric Society 2004 North American Summer Meetings 153, Econometric Society. [Downloadable!]
  7. Zaka Ratsimalahelo, 2003. "Rank Test Based On Matrix Perturbation Theory," Econometrics 0306008, EconWPA. [Downloadable!]
  8. Ramdan Dridi, 2000. "Simulated Asymptotic Least Squares Theory," STICERD - Econometrics Paper Series /2000/396, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  9. A. Hadi & M. Wells, 1990. "A note on generalized wald’s method," Metrika, Springer, vol. 37(1), pages 309-315, December. [Downloadable!] (restricted)
  10. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA. [Downloadable!]
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