418 PONTIFICTAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA

Evidently, V(8) will be non-zero unless a number of other
assumptions are imposed. Consider, however, the question of
whether V(0) will be block-diagonal. Since all the A and A
matrices are diagonal, and since ¥ is itself block-diagonal by
(5.10), we have:

G17) Vie) =o'A A (80: I Ter... N:]=1

Thus the off-diagonal blocks of V(8) depend only on the properties
 of the economy-wide disturbances.
This result is perhaps worth emphasizing. When applied
to 8 =o, it merely states formally what we have said previously,
that contemporaneous disturbances from the equations of the
model which occur in different sectors cannot be assumed uncorrelated
 if there are common elements in each of them, that
is, implicit disturbance elements affecting both sectors. When
applied to 6>o0, however, the result is at least slightly less
obvious. Here it states that despite the fact that contemporaneous
 disturbances from different sectors may be highly correlated,
 and despite the fact that every disturbance may be
highly auto-correlated, a given disturbance will not be correlated
 with a lagged disturbance from another sector unless.
the economy-wide implicit disturbances are themselves autocorrelated.
 To put it another way, the presence of economywide
 implicit disturbances and the presence of substantial serial
correlation do not prevent us from taking V(6) as block-diagonal
 for 6>0 provided that the serial correlation is entirely
confined to the sector and equation implicit disturbances.
Is it then reasonable to assume that the serial correlation
is so confined? I think it is reasonable in the context of a
carefully constructed economy-wide model. We argued above
that any such model inevitably omits variables the effects of
which are not confined within sectors. Effects which are highly
auto-correlated, however, are effects which are relatively
systematic over time. In an inevitably aggregate and approxim-6]

 Fisher - pag. 34