A new class of limited-information estimators for simultaneous equations systems

The TSLS and LIML estimators are evaluated by means of a new class of limited-information estimators, the so-called Ω-class estimators. Under certain assumptions the Ω-class estimator is a maximun-likelihood estimator. These assumptions are superfluous, however, if we view the Ω-class as a class of minimun-distance estimators; all the members are shown to be consistent under general conditions. Besides the TSLS and the LIML estimators some other interesting members are introduced, and it is shown that, under certain conditions, the Ω-class estimators are weighted averages of different TSLS estimators. The use of TSLS in small samples is criticized; an alternative estimator is proposed.