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On the Estimated Variances of RegressionCoefficients in Misspecified Error ComponentsModels

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 errorcomponents, the covariance matrix of thedisturbances has three equivalent representations aslinear combinations of matrices. Furthermore, thisproperty is invariant with respect to powers, matrixaddition, and matrix multiplication. This result isapplied to the derivation and interpretation of theinconsistency of the estimated coefficient varianceswhen the error components structure is improperlyrestricted. This inconsistency is defined as thedifference between the asymptotic variance obtainedwhen the restricted model is correctly specified,and the asymptotic variance obtained when therestricted model is incorrectly specified; when someerror components are improperly omitted, and theremaining variance components are consistentlyestimated, it is always negative. In the case wherethe time component is improperly omitted from thetwo-way model, we show that the difference betweenthe true and estimated coefficient variances is oforder greater than N–1in probability.

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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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