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Robust Wald Tests in SUR Systems with Adding Up Restrictions: An Algebraic Approach to Proofs of Invariance

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Author Info
Surajit Ray (University of Iowa)
B. Ravikumar (University of Iowa)
N. Eugene Savin (University of Iowa)

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Abstract

In this paper, we examine the robust Wald test statistic for SUR systems with adding up restrictions where the same explanatory variables are present in all equations and where heteroskedasticity and/or autocorrelation of unknown forms may be present. For this case, the coefficients are usually estimated by least squares, equation by equation. For testing the typical hypotheses of interest, we show that the robust Wald statistic, i.e., the statistic based on the heteroskedasticity and autocorrelation consistent covariance matrix estimator, is invariant to the equation deleted. Our proof of invariance is algebraic and does not rely on parametric assumptions or on the knowledge of the covariance matrix of disturbances. Furthermore, the adding-up restrictions we consider are of a general form: the weighted sum of the dependent variables adds up to one of the explanatory variables, not necessarily a constant. We illustrate our results using the Capital Asset Pricing Model.

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Publisher Info
Paper provided by EconWPA in its series Econometrics with number 9802002.

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Length: 22 pages
Date of creation: 09 Feb 1998
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Handle: RePEc:wpa:wuwpem:9802002

Note: Type of Document - Postscript; pages: 22 ; figures: included
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Related research
Keywords: SUR System; Adding up; Wald test; Heteroskedasticity; Autocorrelation;

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General

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. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May. [Downloadable!] (restricted)
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  2. Berndt, Ernst R & Savin, N Eugene, 1975. "Estimation and Hypothesis Testing in Singular Equation Systems with Autoregressive Disturbances," Econometrica, Econometric Society, vol. 43(5-6), pages 937-57, Sept.-Nov. [Downloadable!] (restricted)
  3. Ravi Jagnnathan & Ellen R. McGrattan, 1995. "The CAPM debate," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 2-17. [Downloadable!]
  4. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May. [Downloadable!] (restricted)
  5. Barten, A. P., 1969. "Maximum likelihood estimation of a complete system of demand equations," European Economic Review, Elsevier, vol. 1(1), pages 7-73. [Downloadable!] (restricted)
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Cited by:
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  1. Javed Iqbal & Robert Brooks & Don U.A. Galagedera, 2008. "Multivariate tests of asset pricing: Simulation evidence from an emerging market," Monash Econometrics and Business Statistics Working Papers 2/08, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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