SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 172 
regression is chosen for the estimation of a specified theoretical re- 
lationship, the choice of estimation method will not make this rela- 
tionship an eo ipso predictor). I take the opportunity to emphasize 
the truth of a related negative statement: If least squares regression 
is not a consistent estimate of a specified theoretical relationship 
then this relationship is not an eo ipso predictor. 
Coming to the last paragraph of Professor FISHER’s comments, 
[ am afraid it reveals rather deepgoing differences between our views. 
As regards the dangers of overfitting, they are certainly a real heada- 
che (see e.g. the comments by H. THEIL, Ref. 33, section 6 D), and 
the trouble does not become less real because it is « quite a common 
one in dealing with large econometric models. » (2) 
As to the approach of instrumental variables, this is a surrogate 
of an ad hoc nature, inasmuch as the instrumental! variables are not 
specified a priori in the model. It remains to be seen whether the 
results of the approach are as a rule good enough to pass the test ot 
confronting the ensuing forecasts with actual evidence by way of 
predictive tests. Hoping for the best, I have no desire to disen- 
courage; all I want to say is that this is one of the open questions 
in the present stage of development. 
In reply to the first point made by Professor THEIL, I am con- 
fident that KLOEK-MENNES’ adaptation of the principal components 
approach goes a long way to overcome the difficulty of overfitting 
and related headaches in the statistical estimation of interdependent 
systems. The approach has the nature of a shortcut, however, and 
obviously it runs the risk that in sieving forth the principal com- 
ponents of the predetermined variables z, it may throw away one 
or more z's that contribute relatively little to the total variability 
of the predetermined varnables. and vet are highly important as 
(?) Professor L. KLEIN in the paper (a) referred to in footnote (') strongly 
emphasizes how troublesome the current techniques for parameter estima- 
tion of multi-relation models are in the present stage of development. To 
quote from the Monaco discussion of Professor Klein's paper, the results 
he reports from the estimation of a 12 relation model give clear evidence 
of overfitting, inasmuch as most of his OLS (ordinary least squares) and 
TSLS (two stage least sauares: estimates coincide up ta the third figure 
‘21 Wold - pag. s0