Econometrica: Jul 1980, Volume 48, Issue 5

Sufficient Linear Structures: Econometric Applications<1083:SLSEA>2.0.CO;2-Z
p. 1083-1098

Alain Monfort, Christian Gourieroux

This paper is concerned with linear models. In this context it gives a necessary and sufficient condition for equality of two generalized least squares estimators of any subset of the parameters. The result is applied to many kinds of problems: the Frisch-Waugh problem, equality of OLS and GLS estimators, equality of the single equation GLS and the overall GLS estimators in seemingly unrelated regressions, equality of partial and overall 3SLS, lineartransformation of a linear model, superfluous observations, and mixed estimation.

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