General Variance Covariance Structures in Two-Way Random Effects Models

作     者：Carlos De Porres Jaya Krishnakumar 

作者机构：Department of Economics University of Geneva Geneva Switzerland 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2013年第4卷第4期

页      面：614-623页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Error Components Matrix Decompositions Panel Data Spectral Decompositions 

摘      要：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.