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A Generalized Classical Method of Linear Estimation of Coefficients in a Structural Equation

R. L. Basmann
Econometrica
Vol. 25, No. 1 (Jan., 1957), pp. 77-83
Published by: The Econometric Society
DOI: 10.2307/1907743
Stable URL: http://www.jstor.org/stable/1907743
Page Count: 7
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A Generalized Classical Method of Linear Estimation of Coefficients in a Structural Equation
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Abstract

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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