SEMAINE D ETUDE SUR LE ROLE DE L'ANALYSE ECONOMETRIQUE ETC. 405
Indeed, when one looks only at the properties of limited-
information estimators under ideal conditions, there are rela-
tively few grounds for choice among them. In the next sub-
section we shall consider the little which is known of their small
sample properties, here we merely observe that they all have
essentially the same large sample properties. It can be argued
that limited-information maximum likelihood has the desirable
property of treating all included endogenous variables in an
equation symmetrically; indeed, CHow has shown that it is a
natural generalization of ordinary least squares in the absence
of a theoretically given normalization rule (?).
On the other hand, such an argument seems rather weak
since normalization rules are in fact generally present in prac-
tice, each equation of the model being naturally associated with
that particular endogenous variable which is determined by the
decision-makers whose behavior is represented by the equa-
tion. The normalization rules are in a real sense part of the
specification of the model, and the model is not completely
specified unless every endogenous variable appears (at least
implicitly) in exactly one equation in normalized form. For
example, it is not enough to have price equating supply and
demand, equations should also be present which explain price
quotations by sellers and buyers and which describe the equi
librating process. (For most purposes, of course, such addi
tional equation can remain in the back of the model builders’
mind, although the rules for choosing instrumental variables
given below may sometimes require that they be made explicit.)
Thus, symmetry may be positively undesirable in a well-
specified model where one feels relatively certain as to appro-
priate normalization, although it may be desirable if one wishes
to remain agnostic as to appropriate normalization. So far
as arguments of this type or from large sample properties under
=,
*.-
Fisher - pag. 2.
