Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Sep, 1990, Volume 58, Issue 5

On the Normalization of Structural Equations: Properties of Direction Estimators<1181:OTNOSE>2.0.CO;2-S
p. 1181-1194

Grant H. Hillier

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.

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