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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

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