Efficient estimation with grouped data

We investigate efficient estimation when sample is drawn from several heterogenous groups. GLS adjusting inter-group heteroskedasticity is often used in this circumstance. But, the error variances conditional on the regressors could be different within each group. Focusing on this two tier heteroskedasticity problem, we propose an estimator that is asymptotically identical to GLS when no conditional heteroskedasticity is present, and otherwise more efficient.