72

PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -

200

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 relations
 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 variables
 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 biexpectational
 framework (B,)—(B,), for he specifies the -demand relation
 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 current
 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 pitfall
 about least squares: If a theoretical relation is an eo ipso predictor,
 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