SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 166 
of observations. Their procedure amounts to replacing predeter 
mined variables by a certain number of their principal components 
The specification of that number remains an arbitrarv choice 
2. I like the idea of the JaNUs quotient. Its application requires 
that the forecasts are generated by some kind of probabilistic mo- 
del, e.g., a regression model. It is therefore not applicable when 
there is no such model, e.g., when we wish to determine the accu 
racy of entrepreneurial investment forecasts derived from an invest 
ment survev. 
3. As to your bi-expectational procedure, I would like to sug 
gest that you subtract the reduced-form disturbances, not only from 
your right-hand dependent variables, but also from your left-hand 
dependent variable . Doing so, one finds that there is no disturb- 
ance left in the equation at all, because all random parts are re- 
moved. 
Wolbp 
The comments by Professors FISHER and THEIL reflect that 
simultaneous equations as an area of research cover a wide range 
of theoretical and applied problems. The discussion is mainly orient- 
ed towards the general foundations of the approach. Specifically 
the following aspects are referred to : 
1) The rationale of the approach from the point of view of economic 
theory, probability theory, statistics, and the theory of knowledge. 
Hereunder, much of the discussion is concerned with : 
a) Predictive aspects of simultaneous equation svstems: 
b) Causal aspects of the systems. 
2) The statistical estimation of the parameters of simultaneous equa 
Hons 
(21 Wold - pag. 55