Best Linear Estimation and Two-Stage Least Squares

Charles Beach and David Prescott

Working Paper from Economics Department, Queen's University

Abstract: This paper attempts to extend and implement the theory of best linear estimation to a simultaneous equation framework. The approach involves defining a general minimum mean square error estimator for the regression coefficients of a single equation in a simultaneous equation model. Such an estimator, however, requires prior knowledge of the regression coefficients and an error covariance matrix. Then consistent estimates of these unknown parameters are substituted to yield a feasible or approximate best linear estimator. Where these estimates are based on simple two-stage least squares, the feasible minimum mean square estimator is simply a shortening of the 2SLS vector of regression coefficients, and the former is consistent and asymptotically equivalent to the "true" minimum mean square error estimator being approximated as well as to the 2SLS estimates.

Pages: 24
Date: 1974
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Persistent link: https://EconPapers.repec.org/RePEc:qed:wpaper:154

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