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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28
(54)
E(vlz)=f(e(2), 2)
Thanks to the isomorphism here briefly touched upon, eo ipso
predictors are a most convenient tool for the analysis of cause-
effect relationships. Since behavioural relations are cause-effect
relationships, this last comment leads us to the second point,
namely:
(2) The rationale of making use of eo ipso predictors in
the specification of behavioural relations. The main argument
ts, of course, that unless a behavioural relation makes an eo
1pso predictor it cannot provide forecasts that are unbiased in
the sense of expected or average values. This point is brought
in relief by (47) and (50), and the reader will have no diffi-
culty to supply any number of similar illustrations.
(3) Eo ipso predictors in multipurpose model building.
Speaking broadly, the transition from deterministic to stochastic
models makes no trouble, in principle, if the model involves
just one relation of potential use for forecasting; all that is
needed is to design the relation so as to make an eo ipso pre-
dictor. It is quite another matter that the relation can be a
bad forecasting device because of specification errors, but in
this respect there is no difference between deterministic rela-
tions and eo ipso predictors. The trouble begins when the
model involves two or more predictive relations, inasmuch as
the corresponding eo ipso predictors may be incompatible. It
is important to note that the ensuing questions of compatibility
or noncompatibility belong to the pure probability theory; no
empirical or substance-matter considerations enter into these
matters. Such is the situation in (48)-(49), where the inference
from p to d and from d to p cannot be obtained by way of
two eo ipso predictors that form a pair of inverse functions.
This nonexistence theorem in probability theory was one of
the cornerstones when KARL Pearson laid the foundations of
correlation and regression analysis, but its implications for
causal analysis by regression methods remained obscure for
2] Wold - pag. 28