On the Normalization of Structural Equations: Properties of Direct Estimators.

In a single structural equation, only the direction of the vector of coefficients of the endogenous variables is determined. Estimators for that direction can be defined directly, but are also induced by classical estimators that embody the traditional normalization rule. Exact distribution results show that the properties of estimators that depend on the usual normalization rule--which gives special emphasis to a particular direction--are distorted by that dependence, while those of the direct estimators are not. Thus, the traditional normalization rule may serve to define the parameters of interest, but should not be embodied in the estimation procedure. Copyright 1990 by The Econometric Society.