404 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - .& 
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 limited- 
information method in which such instruments are to be ap- 
plied. 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 distinc- 
tion 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