The classical method of least-squares estimation of the coefficients α in the (matrix) equation y = Zα + e yields estimators α̂ = Ay = + Ae. This method, however, employs only one of a class of transformation matrices, A, which yield this result; namely, the special case where A = (Z′Z)-1Z′. As is well known, the consistency of the estimators, α̂, requires that all of the variables whose sample values are represented as elements of the matrix Z be asymptotically uncorrelated with the error terms, e. In recent years some rather elaborate methods of obtaining consistent and otherwise optimal estimators of the coefficients α have been developed. In this paper we present a straightforward generalization of classical linear estimation which leads to estimates of α which possess optimal properties equivalent to those of existing limited-information single-equation estimators, and which is pedagogically simpler and less expensive to apply.3
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