General Variance Covariance Structures in Two-Way Random Effects Models

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.

Cite this paper

C. Porres and J. Krishnakumar, "General Variance Covariance Structures in Two-Way Random Effects Models,"*Applied Mathematics*, Vol. 4 No. 4, 2013, pp. 614-623. doi: 10.4236/am.2013.44086.

C. Porres and J. Krishnakumar, "General Variance Covariance Structures in Two-Way Random Effects Models,"

References

[1] J. R. Magnus and C. Muris, “Specification of Variance Matrices for Panel Data Models,” Econometric Theory, Vol. 26, No. 1, 2010, pp. 301-310. doi:10.1017/S0266466609090756

[2] J. M. B. Brou, E. Kouassi and K. O. Kymn, “Double Autocorrelation in Two Way Error Component Models,” Open Journal of Statistics, Vol. 1, No. 3, 2011, pp. 185-198. doi:10.4236/ojs.2011.13022

[3] M. Nerlove, “A Note on Error Components Models,” Econometrica, Vol. 39, No. 2, 1971, pp. 383-396. doi:10.2307/1913351

[4] P. Balestra, “A Note on the Exact Transformation Associated with the First-Order Moving Average Process,” Journal of Econometrics, Vol. 14, No. 3, 1980, pp. 381-394. doi:10.1016/0304-4076(80)90034-2

[5] B. H. Baltagi and Q. Li, “A Transformation That Will Circumvent the Problem of Autocorrelation in an Error Component Model,” Journal of Econometrics, Vol. 48, No. 3, 1991, pp. 385-393. doi:10.1016/0304-4076(91)90070-T

[6] V. Zinde-Walsh, “Some Exact Formulae for Autoregressive Moving Average Processes,” Econometric Theory, Vol. 4, No. 3, 1988, pp. 384-402. doi:10.1017/S0266466600013360

[7] 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

[8] J. W. Galbraith and V. Zinde-Walsh, “Transforming the Error-Components Model for Estimation with General ARMA Disturbances,” Journal of Econometrics, Vol. 66, No. 1-2, 1995, pp. 349-355. doi:10.1016/0304-4076(94)01621-6

[9] M. H. Pesaran, “Exact Maximum Likelihood Estimation of a Regression Equation with a First Order Moving Average Errors,” The Review of Economic Studies, Vol. 40, No. 124, 1973, pp. 529-538. doi:10.2307/2296586

[1] J. R. Magnus and C. Muris, “Specification of Variance Matrices for Panel Data Models,” Econometric Theory, Vol. 26, No. 1, 2010, pp. 301-310. doi:10.1017/S0266466609090756

[2] J. M. B. Brou, E. Kouassi and K. O. Kymn, “Double Autocorrelation in Two Way Error Component Models,” Open Journal of Statistics, Vol. 1, No. 3, 2011, pp. 185-198. doi:10.4236/ojs.2011.13022

[3] M. Nerlove, “A Note on Error Components Models,” Econometrica, Vol. 39, No. 2, 1971, pp. 383-396. doi:10.2307/1913351

[4] P. Balestra, “A Note on the Exact Transformation Associated with the First-Order Moving Average Process,” Journal of Econometrics, Vol. 14, No. 3, 1980, pp. 381-394. doi:10.1016/0304-4076(80)90034-2

[5] B. H. Baltagi and Q. Li, “A Transformation That Will Circumvent the Problem of Autocorrelation in an Error Component Model,” Journal of Econometrics, Vol. 48, No. 3, 1991, pp. 385-393. doi:10.1016/0304-4076(91)90070-T

[6] V. Zinde-Walsh, “Some Exact Formulae for Autoregressive Moving Average Processes,” Econometric Theory, Vol. 4, No. 3, 1988, pp. 384-402. doi:10.1017/S0266466600013360

[7] 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

[8] J. W. Galbraith and V. Zinde-Walsh, “Transforming the Error-Components Model for Estimation with General ARMA Disturbances,” Journal of Econometrics, Vol. 66, No. 1-2, 1995, pp. 349-355. doi:10.1016/0304-4076(94)01621-6

[9] M. H. Pesaran, “Exact Maximum Likelihood Estimation of a Regression Equation with a First Order Moving Average Errors,” The Review of Economic Studies, Vol. 40, No. 124, 1973, pp. 529-538. doi:10.2307/2296586