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

Author

Listed:
  • Surajit, R.

    (University of Iowa)

  • Ravikumar, B.

    (University of Iowa)

  • Savin, N.E.

    (University of Iowa)

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.

Suggested Citation

  • Surajit, R. & Ravikumar, B. & Savin, N.E., 1998. "Robust Wald Tests in SUR Systems with Adding Up Restrictions: An Algebraic Approach to Proofs of Invariance," Working Papers 98-01, University of Iowa, Department of Economics.
    • Handle: RePEc:uia:iowaec:98-01
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    Cited by:

    1. Javed Iqbal & Robert Brooks & Don Galagedera, 2010. "Multivariate tests of asset pricing: simulation evidence from an emerging market," Applied Financial Economics, Taylor & Francis Journals, vol. 20(5), pages 381-395.
    2. Iqbal, Javed & Brooks, Robert & Galagedera, Don UA, 2007. "Robust Tests of the Lower Partial Moment Asset Pricing Model in Emerging Markets," MPRA Paper 25349, University Library of Munich, Germany, revised May 2007.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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