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

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  • Deschamps, Philippe J.

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.

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  • Deschamps, Philippe J., 1991. "On the Estimated Variances of Regression Coefficients in Misspecified Error Components Models," Econometric Theory, Cambridge University Press, vol. 7(3), pages 369-384, September.
  • Handle: RePEc:cup:etheor:v:7:y:1991:i:03:p:369-384_00
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    1. van de Klundert, Theo C N J & van der Ploeg, Frederick, 1987. "Wage Rigidity and Capital Mobility in an Optimizing Model of a Small Open Economy," CEPR Discussion Papers 168, C.E.P.R. Discussion Papers.
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    4. Greenwald, Bruce C., 1983. "A general analysis of bias in the estimated standard errors of least squares coefficients," Journal of Econometrics, Elsevier, vol. 22(3), pages 323-338, August.
    5. Nerlove, Marc, 1971. "A Note on Error Components Models," Econometrica, Econometric Society, vol. 39(2), pages 383-396, March.
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