Econometrica: Jan 1964, Volume 32, Issue 1

Efficient Estimation of Simultaneous Equation Systems

https://doi.org/0012-9682(196401/04)32:1/2<57:EEOSES>2.0.CO;2-F
p. 57-76

C. T. Leenders, T. J. Rothenberg

The asymptotic covariance matrix of the full-information maximum-likelihood estimator is derived. The paper then compares the asymptotic efficiency of three estimators: full-information maximum likelihood, three-stage least squares, and linearized maximum likelihood. It is shown that all three are efficient if the covariance matrix of the contemporaneous structural disturbances is unknown. If, however, some elements of this covariance matrix are known a priori, then three-stage least squares is no longer efficient.
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