Econometrica: Oct, 1969, Volume 37, Issue 4

The Consistency and Efficiency of Generalized Least Squares in Simultaneous Equation Systems with Autocorrelated Errors

https://doi.org/0012-9682(196910)37:4<651:TCAEOG>2.0.CO;2-3
p. 651-659

M. R. Wickens

Several existing single equation estimators, designed for the case where the structural disturbances are generated by a first order autoregressive process, are generalized for situations where the autoregressive process is of higher order than one. These generalized estimators are shown to be consistent, both when the parameters of the generating process are known and unknown; and their asymptotic relative efficiencies are compared. Three full information estimators are also examined. They are shown to be consistent with asymptotic efficiencies ranked like their single equation counterparts. Among the results derived are the consistency of 2SLS and 3SLS in this situation and the overall relative efficiencies of the "Theil-Fisher" type estimators compared with the 2SLS-3SLS and "Madansky" type estimators.