Hillier, G. (2006) Yet more on the exact properties of IV estimators. Econometric Theory, 22 (5), 913-931. (doi:10.1017/S0266466606060415).
Abstract
We revisit the exact properties of two-stage least squares and limited information maximum likelihood estimators in a structural equation/IV regression under Gaussian assumptions. Simple derivations based on conditioning serve both to de-mystify the apparently complicated formulae, and to isolate the key quantities that determine the properties of the estimators. Some recent results obtained under weak-instrument asymptotics are sharpened and clarified by the exact analysis
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