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On the Estimated Variances of Regression Coefficients in Misspecified Error Components Models

Published online by Cambridge University Press:  11 February 2009

Philippe J. Deschamps
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Abstract

In a regression model with an arbitrary number of error components, the covariance matrix of the disturbances has three equivalent representations as linear combinations of matrices. Furthermore, this property is invariant with respect to powers, matrix addition, and matrix multiplication. This result is applied to the derivation and interpretation of the inconsistency of the estimated coefficient variances when the error components structure is improperly restricted. This inconsistency is defined as the difference between the asymptotic variance obtained when the restricted model is correctly specified, and the asymptotic variance obtained when the restricted model is incorrectly specified; when some error components are improperly omitted, and the remaining variance components are consistently estimated, it is always negative. In the case where the time component is improperly omitted from the two-way model, we show that the difference between the true and estimated coefficient variances is of order greater than N–1 in probability.

Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 3 , September 1991 , pp. 369 - 384
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

1. Amemiya, T. The estimation of the variances in a variance components model. International Economic Review 12 (1971): 1–13.CrossRefGoogle Scholar
2. Balestra, P. Best quadratic unbiased estimators of the variance-covariance matrix in normal regression. Journal of Econometrics 1 (1973): 17–28.Google Scholar
3. Balestra, P. & Nerlove, M.. Pooling cross section and time series data in the estimation of a dynamic model: the demand for natural gas. Econometrica 34 (1966): 585–612.CrossRefGoogle Scholar
4. Deschamps, P. A note on isomorphic characterizations of the dispersion matrix in error components models. Linear Algebra and Its Applications 111 (1988): 147–150.CrossRefGoogle Scholar
5. Fuller, W.A. & Battese, G.E.. Transformations for estimation of linear models with nestederror structure. Journal of the American Statistical Association 68 (1973): 626–632.10.1080/01621459.1973.10481396CrossRefGoogle Scholar
6. Graybill, F.A. An Introduction to Linear Statistical Models, vol. I. New York: McGraw- Hill, 1961.Google Scholar
7. Greenwald, B.C. A general analysis of bias in the estimated standard errors of least squares coefficients. Journal of Econometrics 22 (1983): 323–338.Google Scholar
8. Nerlove, M. A note on error components models. Econometrica 39 (1971): 383–396.Google Scholar
9. Searle, S.R. & Henderson, H.V.. Dispersion matrices for variance components models. Journal of the American Statistical Association 74 (1979): 465–470.Google Scholar
10 Wallace, T.D. & Hussain, A.. The use of error components models in combining cross section with time series data. Econometrica 37 (1969): 55–72.CrossRefGoogle Scholar