Estimation of Variances in the Grouped Heteroskedasticity Model

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Abstract
Error variances for weighted least squares estimation of the grouped heteroskedasticity model can be estimated using residuals from individual group regressions or one pooled regression. The latter is more troublesome but is usually considered more efficient because the common coefficient vector is imposed on the first stage. However, the variances are biased. Monte Carlo results show this to be an important consideration when heteroskedasticity is strong. Then residuals from separate regressions lead to more efficient weighted least squares estimates. Furthermore, efficiency gains from the pooled method, even when iterated, seldom if ever appear to be of large consequence.
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