Econometrica: May 1974, Volume 42, Issue 3

Three Stage Least Squares and Some Extensions where the Structural Disturbance Covariance Matrix May Be Singular

https://doi.org/0012-9682(197405)42:3<547:TSLSAS>2.0.CO;2-T
p. 547-558

R. H. Court

This paper looks at some aspects of the three stage least squares approach to estimating simultaneous econometric models. Three stage least squares is derived along the lines of best linear unbiased estimators in classical regression, whereby it is indicated that the usual assumption of non-singularity of the disturbance covariance matrix is unnecessary. Consistency of the estimator is shown as is the irrelevance of exactly identified equations to the estimation of other equations in a model when three stage least squares is used. Also included are an easily computed test for the validity of all specified overidentifying restrictions, and a method of efficiently estimating the reduced form using only the information contained in structural equations that are thought to be well specified.

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