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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2.
variable y,, occurs as causal (explanatory) variable it must
be replaced by its expected value y,, as given by the reduced
form. Or to paraphraze in terms of MARSHALL elasticities, if
all variables y, z; in (18) are logarithmic, and y i,t 1S current
demand and y, current price, then a,; is the elasticity of
demand with respect not to observed price y, but to expected
price y 7.
It will be noted that the expected value yj, of a current
endogenous variable is in (58) introduced as a purely stochastic
concept. It is an entirely different issue whether this expected
value can be given a subject-matter interpretation as an expectation
in the psychological sense. Thus if y; is observed
market price, and the consumers’ anticipations of market price
could be assessed, say y;;, for example by interviews on a
sampling basis, the definition (58) involves no implicit conjec-‘ure
as to whether y;, and y;; will be approximately equal.
The parameters of a BEID-system are numerically the same
as for the corresponding ID-system. Hence the problem of
parameter estimation is precisely the same for BEID- as for
[D-systems. Among the estimation techniques developed for
[D-systems, specific reference is made to H. THEIL’s two-stage
method of least squares, Ref. 33, which conforms operationally
to an extension to BEID-systems. Briefly stated, the procedure
is to estimate the reduced form by least squares regression,
substitute the resulting estimates for the left-hand members into
the right-hand members of the primary form, and then estimate
the primary form by least squares regression.
In the following illustration we shall consider three types
of model, all with the same patterns of nonzero coefficients A
and B in (18), but in general with different numerical values
for the nonzero coefficients.
(x) ID-systems, or RFUE- (reduced form uni-expectational)
systems. This is an arbitrary system of type (18).
(2) PFUE- (primary form uni-expectational) systems.
This model is obtained from (18) by respecifying the nonzero
2] Wold - pag. 32
