SEMAINE D'ETUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC. 407
totic standard errors are obviously inappropriate when directly
taken as approximations to an infinite sample variance and may
or may not be reliable when used to derive approximations to
the probability that an estimate diverges from the true parameter
by more than a given amount. In general, the latter
approximation is probably better for small divergences than
for large ones as the normal approximation to the small sample
distribution is almost certainly worst in the tails (¥).
Second, as already indicated, the absence of this property
in ordinary least squares makes the latter estimator rather more
attractive than would be the case if limited-information estimators
always had finite variance. Certainly, there is a certain
amount of justification for using ordinary least squares as an
approximation while building the model provided that assumptions
(R.1)-(R.3) are not too badly violated (which we have
argued cannot be assumed in economy-wide models). Further,
QUANDT has recently suggested combining ordinary least squares
and limited-information estimators to take advantage of the
fact that the latter are consistent while the former has a finite
variance (%).
Furthermore, the infinite small sample variance of limitedinformation
estimators casts doubt on the convergence in some
cases of the expansions used by NAGAR to demonstrate the
unbiasedness of his suggested estimator to order 1/T, where T
is the sample size (¥). When such expansions do converge,
such unbiasedness is about the only known sample property
in which one limited-information estimator is demonstrably
superior to the others. As it happens, however, NAGAR’s demonstration
assumes that there are no lagged endogenous variables
in the model so that, even aside from the convergence
problem iust mentioned, his results are not applicable in the
present . ~
(77) See BASMANN [5]. Sarg:
for the probabilities just described
(3) QUANDT [25].
(2%) NAGAR [22]. See SarG'
derives approximate expressions
Fisher - pag. 2:
