This chapter was concerned with the case of non-stochastic explanatory variables. It examines the properties of the predictor resulting from the Two-Stage Aitken (TSA) estimator. The TSA estimator and predictor are asymptotically best linear unbiased (BLU) and invariant with respect to the choice of the constraint item (CI). The Aitken Estimator (IA) estimator have the same asymptotic properties as the TSA estimator, but for finite samples we will show that the IA estimator Beta isinvariant with respect to the choice of the CI. The chapter shows that the IA and maximum likelihood estimators are equivalent and have noted that they are asymptotically BLU and invariant with respect to the choice of the CI. One would expect the IA estimator to outperform the TSA estimator for finite samples but the Kmenta-Gilbert Monte Carlo studies show that this is not always the case.