106 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
vel 
ideal conditions are concerned, then, there seems little or no 
reason for preferring one limited-information estimator to 
another. 
4.3. Small Sample Properties 
The situation is not very different at the present time when 
one considers small sample properties. To date, relatively little 
is known about these and work has proceeded largely by means 
of Monte Carlo experiments. Moreover, all such experiments 
and such analytic work as is available have been exclusively 
concerned with the case in which lagged endogenous variables 
do not appear (or at least are not used as predetermined instru- 
ments) and the analytic work has dealt only with those members 
of the k-class with non-stochastic &. In the present context, 
the former limitation is a severe one. Nevertheless, it seems 
worth briefly discussing what is known about small sample 
properties in such cases as the situation when lagged endogen- 
ous variables are present is probably no more hopeful. 
The principal point that has emerged on small sample pro- 
perties of limited-information estimators is that the sampling 
variances involved are infinite in some cases. Such a 
conclusion is borne out both from the analytic work that 
has been accomplished to date and by the results of the Monte 
Carlo experiments that have been performed (%). It seems 
idle to hope that this circumstance does not occur when lagged 
endogenous variables are present in the model. 
In practice, this unhappy circumstance has a number of 
consequences. First, it is clearly the case that relatively little 
reliance can be placed on judgments of goodness of fit derived 
from consideration of asymptotic standard errors. Such asvmp- 
(?°) See BASMANN [4], [5], BERGSTROM [6], NaGAR [22], and SARGAN 
[28] for the analysis. JOHNSTON [I5, pp. 275-295] summarizes most of 
the Monte Carlo experiments: see also OUANDT [2:5]. [26] 
[6] Fisher - pag. 22