On the Normalization of Structural Equations: Properties of Direction Estimators

In the general structural equation model only the direction of the vector of coefficients of the endogenous variables is determined.The traditional normalization rule defines the coefficients that are of interest but should not be embodied in the estimation procedure: we show that the properties of the traditionally defined ordinary least squares and two stage least squares estimators are distorted by their dependence on the normalization rule.Symmetrically normalized analogues of these estimators are defined and are shown to have essentially similar properties to those of the limited information maximum likelihood estimator.