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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28
2.3. Recursive Systems in Economy-wide Models
Are the assumptions of the recursive model just discussed
likely to be valid for an economy-wide econometric model? In
general, the answer appears to be in the negative.
In the first place, the argument for the triangularity of A
that causation takes place sequentially in time (which, inciden-
tally, would imply diagonality) is not conclusive if the data
are collected as averages over a much longer period than the
causal interval involved. It may be true that simultaneous
structures are but approximations to underlying recursive ones
with very short time lags; this does not make the matrices in-
volved triangular, however, whatever it implies about appro-
priate estimators (19).
Even if triangularity of the A matrix is satisfied in an
economy-wide model, however, the other conditions discussed
are unlikely to be fulfilled. Even the best specified econometric
models inevitably omit variables the effects of which then enter
the disturbance terms. If the model is well specified, these
effects will not be large and systematic, rather they will be
small and random. Even so, the omitted variables appearing
in the disturbances cannot all generally be expected to be dif-
ferent ones for different equations. Indeed, one expects there
to be some events which act as shocks on many or all the equa-
tions in an economy-wide model. Such action may indeed be
of different magnitudes for different equations, but it is surely
extremely restrictive to assume zero correlation among the
(1) StroTz [30] considers a model in which the variables are observed
at discrete intervals longer than a short causal period which is allowed to
approach zero — a problem not quite the same as that considered in the
text. He argues that the usual estimators are not approached in the limit
by the maximum likelihood estimator of his model. The status of the
argument is presently in some doubt as Gorman [11] has suggested that
« natural » assumptions on the continuity of the stochastic process generat-
ing the disturbances do lead to the usual estimators in the limiting case
nf simultaneitv.
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Fisher - pag. 10
