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SPECIFICATION OF VARIANCE MATRICES FOR PANEL DATA MODELS

Published online by Cambridge University Press:  19 June 2009

Jan R. Magnus  and
Chris Muris
Jan R. Magnus*
Affiliation:
Tilburg University
Chris Muris
Affiliation:
Tilburg University
*
*Address correspondence to Jan R. Magnus, Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands; e-mail: magnus@uvt.nl.
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Abstract

Many regression models have two dimensions, say time (t = 1,…,T) and households (i = 1,…,N), as in panel data, error components, or spatial econometrics. In estimating such models we need to specify the structure of the error variance matrix Ω, which is of dimension T N × T N. If T N is large, then direct computation of the determinant and inverse of Ω is not practical. In this note we define structures of Ω that allow the computation of its determinant and inverse, only using matrices of orders T and N, and at the same time allowing for heteroskedasticity, for household- or station-specific autocorrelation, and for time-specific spatial correlation.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 26 , Issue 1 , February 2010 , pp. 301 - 310
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Anselin, L. (1988) Spatial Econometrics: Methods and Models. Kluwer.CrossRefGoogle Scholar
Anselin, L. & Bera, A.K. (1998) Spatial dependence in linear regression models with an introduction to spatial econometrics. In Ullah, A. & Giles, D.E.A. (eds.), Handbook of Applied Economic Statistics, pp. 237–289. Marcel Dekker.Google Scholar
Arellano, M. (2003) Panel Data Econometrics. Oxford University Press.CrossRefGoogle Scholar
Baltagi, B.H. (2001) Econometric Analysis of Panel Data. Wiley.Google Scholar
Baltagi, B.H. & Griffin, J.M. (1988) A generalized error component model with heteroskedastic disturbances. International Economic Review 39, 745–753.CrossRefGoogle Scholar
Baltagi, B.H. & Raj, B. (1992) A survey of recent theoretical developments in the econometrics of panel data. Empirical Economics 17, 85–109.CrossRefGoogle Scholar
Baltagi, B.H., Song, S.H., Jung, B.C., & Koh, W. (2007) Testing for serial correlation, spatial autocorrelation and random effects using panel data. Journal of Econometrics 140, 5–51.CrossRefGoogle Scholar
Baltagi, B.H., Song, S.H., & Koh, W. (2003) Testing panel data regression models with spatial error correlation. Journal of Econometrics 117, 123–150.CrossRefGoogle Scholar
Driscoll, J.C. & Kraay, A.C. (1998) Consistent covariance matrix estimation with spatially dependent panel data. Review of Economics and Statistics 80, 549–560.CrossRefGoogle Scholar
Kapoor, M., Kelejian, H.H., & Prucha, I.R. (2007) Panel data models with spatially correlated error components. Journal of Econometrics 140, 97–130.CrossRefGoogle Scholar
Li, Q. & Stengos, T. (1994) Adaptive estimation in the panel data error component model with heteroskedasticity of unknown form. International Economic Review 35, 981–1000.CrossRefGoogle Scholar
Magnus, J.R. (1982) Multivariate error component analysis of linear and nonlinear regression models by maximum likelihood. Journal of Econometrics 19, 239–285.CrossRefGoogle Scholar
Magnus, J.R. (1988) Linear Structures. Griffin's Statistical Monographs and Courses 42. Edward Arnold and Oxford University Press.Google Scholar
Magnus, J.R. & Neudecker, H. (1988) Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley. [Second edition, 1999.]Google Scholar
Searle, S.R. & Henderson, H.V. (1979) Dispersion matrices for variance components models. Journal of the American Statistical Association 74, 465–470.Google Scholar
Wansbeek, T. & Kapteyn, A. (1982) A class of decompositions of the variance-covariance matrix of a generalized error components model. Econometrica 50, 713–724.CrossRefGoogle Scholar