A Transformation for General Variance Covariance Structures in a Two-Way Error Component Model

Abstract

This note examines general variance-covariance structures for the specific effects and the overall error term in a two-way error component (EC) model. So far panel data literature has considered these general structures in a one-way model and followed the approach of a Cholesky-type transformation that brings the model back to a 'classical' one-way EC setting. In this note, we first show that in a two-way context 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 two solutions which use 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 and this is illustrated by taking some interesting special cases and showing how the spectral decomposition can be derived using our results.