150 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
en 
statistical estimation of multirelation models. Assumptions R 2-3 
at first sight look very stringent, and in section 2.3 Prof. FISHER 
argues that they are not likely to be valid for economy-wide econo- 
metric models. The first point I wish to make is that the narrow 
stringency of Assumptions R 2-3 is only apparent. They come in 
a better light if the relations of the systems are specified in terms 
of eo ipso predictors (an ea ipso predictor is the conditional expec- 
tation that constitutes the residual-free part of the relation). This 
type of assumption has the fundamental advantage that it corre- 
sponds directly to the operational use for which the relations are 
intended. Furthermore, R 2-3 become automatically satisfied as an 
implication, not as an assumption, and this implication in its turn 
implies that the relations can be consistently estimated by least 
squares regression, 
(#) The theory of eo ipso predictors has shed new light on the 
much-discussed question about the operational significance of the 
structural relations of ID-systems. With reference to my report to 
the Study Week for details of the argument, it can be shown that 
the clearcut cause-effect interpretation of the behavioural relations 
of CC-systems does extend to ID-systems, but only at the price of 
a respecification of the system. For example, if the ID-system 
involves a behavioural relation which specifies the elasticity of in- 
vestments with respect to profits as 0.4, the respecified assumption 
will be that 0.4 is the elasticity of savings with respect to expected 
profits. Actual profits and expected profits are different notions, 
conceptually and observationally; the actual profits are given by the 
statistical data, whereas the expected profits in the present context 
are given by the reduced form of the ID-system. The snag is that 
expected profits as derived from the reduced form stand in no ob- 
vious connection with expected profits in the sense of psychological 
anticipation. The respecification of the ID-system thus involves an 
element of arbitrariness. 
The point just mentioned has a bearing upon the doubts that 
Prof. FISHER expresses in section 2.3 about the matrix triangularity 
in Assumption R 1. When Prof. FISHER states that it is somewhat 
6] Fisher - pag. 66