SEMAINE D'ETUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC.
40.
easy to dispose of it. We shall then be free to turn our attention
to the class of estimators ordinarily used in these problems
the limited-information class.
It is customary in these discussions to pay lip-service to
full-information maximum likelihood as the optimal estimator
using all information available and then to dismiss it in practice
as too difficult of computation. While it is still true that
such computational difficulties are still prohibitive in practice
for even moderately large systems (1%), such dismissal no longer
suffices. This is the case because there are now two full
information estimators which are known to have the same
asymptotic distribution as full-information maximum likelihood
and which are not particularly difficult to compute. These
are the three-stage least squares estimator proposed by ZELLNER
and THEIL and the linearized maximum likelihood method of
ROTHENBERG and LEENDERS (!°). Since the known virtues of
full-information maximum likelihood are all asymptotic, com:
putational difficulty can no longer be considered a valid reasor
for not using some such method.
As it happens, however, there are more cogent reasons thar
computational difficulty for the abandonment of full-information
methods in practice. However desirable the properties of
full-information methods may be in principle when all assumptions
are met, such estimators suffer relatively heavily from
a lack of robustness in the presence of common practical difficulties.
Thus KLEIN and NAKAMURA have suggested that
full-information maximum likelihood is more sensitive to
multicollinearity than are limited-information estimators (%)
(18) The difficulties are being overcome, however. See EISENPRESS [7%]
(19) ZELLNER and THEIL [37]; ROTHENBERG and LEENDERS [26]. Ro-THENBERG
and LEENDERs give the proof that these estimators have the same
asymptotic distribution as full-information maximum likelihood. See also
SARGAN [27] and MapaNsky [20]. BrowN’s simultaneous least squares {6?]
[which is a member of the full-information class] is known to be consistent
but is not known to have the same asvmptotic distribution as the other
members.
(2°) KLEIN and NAKAMUR/
‘vi Fisher - pag.
1”,
