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another case I am thinking of is when we use current GNP as an 
endogenous explanatory variable y; but are aware that the statistical 
assessment of GNP is not quite adequate in the explanatory context 
of the model; it may then be meaningful to use the expectation y} 
as explanatory variable, in the hope that it gives a better proxy to 
the nonobserved explanatory variable than the observed value of 
GNP. Another potential application that comes to mind is that 
if y, is individual consumer income, y;* might serve as a proxy for 
permanent income in the sense of M. FRIEDMAN’s well known theory. 
In specifying the subject matter content of his models J. F. MUTH 
makes use of causal notions, and the expectational variables enter 
both as causal factors and as effect variables, His use of causal 
notions makes for a general affinity with my own work, which to 
à large extent has been concerned with the much debated questions 
that arise if we wish to provide a causal interpretation for the rela- 
tions and individual parameters of interdependent systems. When 
an interdependent system (A) is respecified by way of (B,), this 
transition makes for a clearcut interpretation of the expectational 
variables y, * as causal factors, and from ;(B,) we see that the va- 
riables y * will also play the part of effect variables. It will be noted 
that J. F. MUTH’s model is not quite in accordance with the bi- 
expectational framework (B,)—(B,), for he specifies the -demand re- 
lation as deterministic by not including an error term, and in the 
customary manner of cobweb models he treats the demand relation 
as causally reversible by taking current demand to determine cur- 
rent price. It would seem however that MuTH’s line of argument 
only requires some slight qualification to be in accordance with the 
bi-expectational form (B,)—(B,) of interdependent systems. 
Professor FISHER’s comment on J2 is certainly to the point, and 
it brings in relief that the simple proxy J2 cor primarily refers to 
‘he case of stationary deviations from the theoretical model. 
I appreciate very much that Professor FISHER emphasizes a pit- 
fall about least squares: If a theoretical relation is an eo ipso pre- 
dictor, it can be consistently estimated by least squares regression, 
but it does not follow that the reverse is true (that is, if least squares 
[2] Wold - pag. 58