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J. W. Galbraith and V. Zinde-Walsh, “The GLS Transformation Matrix and a Semi-Recursive Estimator for the Linear Regression Model with ARMA Errors,” Econometric Theory, Vol. 8, No. 1, 1992, pp. 95-111. doi:10.1017/S0266466600010756

has been cited by the following article:

• TITLE: General Variance Covariance Structures in Two-Way Random Effects Models

  AUTHORS: Carlos De Porres, Jaya Krishnakumar

  KEYWORDS: Error Components; Matrix Decompositions; Panel Data; Spectral Decompositions

  JOURNAL NAME: Applied Mathematics, Vol.4 No.4, April 26, 2013

  ABSTRACT: This paper examines general variance-covariance structures for the specific effects and the overall error term in a two-way random effects (RE) model. So far panel data literature has only considered these general structures in a one-way model and followed the approach of a Cholesky-type transformation to bring the model back to a “classical” one-way RE case. In this note, we first show that in a two-way setting it is impossible to find a Cholesky-type transformation when the error components have a general variance-covariance structure (which includes autocorrelation). Then we propose solutions for this general case using the spectral decomposition of the variance components and give a general transformation leading to a block-diagonal structure which can be easily handled. The results are obtained under some general conditions on the matrices involved which are satisfied by most commonly used structures. Thus our results provide a general framework for introducing new variance-covariance structures in a panel data model. We compare our results with [1] and [2] highlighting similarities and differences.