Econometrica: Jan 1984, Volume 52, Issue 1

On the Moments of Ordinary Least Squares and Instrumental Variables Estimators in a General Structural Equation

https://doi.org/0012-9682(198401)52:1<185:OTMOOL>2.0.CO;2-G
p. 185-202

G. H. Hillier, T. W. Kinal, V. K. Srivastava

Exact expressions are given for the first two moments of a linear combination of the elements of an instrumental variables estimator for the coefficients of the endogenous variables in a general structural equation. These results generalize previous exact results for equations containing just two or three endogenous variables. In addition, we provide bounds on the moments that can easily be estimated, and generalize some earlier qualitative results for these estimators.

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