Exact and Stochastic Linear Restrictions

Abstract

As a starting point, which was also the basis of the standard regression procedures described in the previous chapters, we take a T -dimensional sample of the variables y and X₁, . . ., X_K. If the classical linear regression model y = Xβ + ε with its assumptions is assumed to be a realistic picture of the underlying relationship, then the least-squares estimator b = (X′X)⁻¹X′y is optimal in the sense that it has smallest variability in the class of linear unbiased estimators for β.