General Variance Covariance Structures in Two-Way Random Effects Models

Applied Mathematics, 2013, 4, 614-623

10 Pages Posted: 19 Nov 2014

See all articles by Carlos de Porres

Carlos de Porres

University of Geneva, Department of Economics

Jaya Krishnakumar

University of Geneva

Date Written: February 28, 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.

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

Suggested Citation

de Porres, Carlos and Krishnakumar, Jaya, General Variance Covariance Structures in Two-Way Random Effects Models (February 28, 2013). Applied Mathematics, 2013, 4, 614-623, Available at SSRN: https://ssrn.com/abstract=2526847

Carlos De Porres

University of Geneva, Department of Economics ( email )

102 Bd Carl Vogt
Geneva 4, 1211
Switzerland

Jaya Krishnakumar (Contact Author)

University of Geneva ( email )

40 Bd. du Pont d'Arve
Genève 4, CH - 1211
Switzerland

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