Abstract
In this paper, we consider a heteroscedastic linear regression model with omitted variables. We derive the density function of the pre-test estimator consisting of the two-stage Aitken estimator (2SAE) and the ordinary least squares estimator (OLSE) after the pre-test for homoscedasticity. We also derive the first two moments based on the density function and show the sufficient condition for the pre-test estimator to dominate the 2SAE in terms of the MSE. Our numerical evaluations show that when this sufficient condition does not hold and when the magnitude of the specification error is large, the pre-test estimator can be dominated by the 2SAE, and further, the 2SAE can be dominated by the OLSE.
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