Reexamining the Estimation of Simultaneous Equations Systems

This paper generalises a classical theorem on the minimisation of the ratio of two quadratic forms so as to permit the denominator to be nonnegative definite, provides a modified formula for the minimum variance ratio estimation including the limited information maximum likelihood, and collaterally shows that the use of the principal components of some predetermined variables in the first stage of two stage least squares is afraid of leading to biased estimators.