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correlation in the disturbances cannot be presumed absent, the
choice of instrumental variables is likely to be of considerably
greater importance than the choice of the particular limitedinformation
 method in which such instruments are to be applied.
 The latter choice is clearly worth discussing, however,
although the major portion of our discussion will be reserved
for the former one which will be taken up in the two following
sections.

4.2. Classification and Large Sample Properties under Ideal
Conditions

The limited-information estimators in common use are those
of THEIL’s k-class. Chief among these are two-stage least
squares, limited-information maximum likelihood, and an
estimator due to NAGAR (¥). Another class of estimators, the
h-class, has also been suggested by THEIL, and NAGAR has
recently proposed still a third class, the double k-class (2).
For our purposes such subdivisions will not be particularly
important. What will be important is the fundamental distinction
 between limited-information maximum likelihood and all
other proposed limited-information estimators. Alone among
suggested members of the k-, h-, and double X-classes, the
fundamental distinguishing parameter (k in this case) is
stochastic in limited-information maximum likelihood, being
determined as a root of a stochastic determinantal equation.
As we shall see below, this distinction aside from making
limited-information maximum likelihood somewhat cumbersome
to compute leads to a lack of robustness in that estimator in
the presence of multicollinearity. Such a lack is not shared
by the other estimators of the limited-information class.

(¥) THEIL [32, pp. 231-232]; NAGAR zz].
(3 THEIL [32. DD. 353-254]: NAGAR [23]

16] Fisher - pag. 20