Econometrica: Mar, 1973, Volume 41, Issue 2

Small Sample and Asymptotic Relations Between Maximum Likelihood and Three Stage Least Squares Estimators

https://doi.org/0012-9682(197303)41:2<357:SSAARB>2.0.CO;2-S
p. 357-364

Phoebus J. Dhrymes

This paper deals with similarities and differences in the equations defining the full information maximum likelihood and three stage least squares estimators. It shows that the two sets of equations are similar, the difference being that the two estimators "purge" the jointly dependent variables differently. Hence, even if three stage least squares is iterated, it will not give an estimator which is the same as the maximum likelihood one. On the other hand, it is quite apparently asymptotically equivalent to full information maximum likelihood. A number of other results are also obtained.