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 pro- 
perties 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 un- 
correlated 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 contempo- 
raneous disturbances from different sectors may be highly cor- 
related, and despite the fact that every disturbance may be 
highly auto-correlated, a given disturbance will not be cor- 
related with a lagged disturbance from another sector unless. 
the economy-wide implicit disturbances are themselves auto- 
correlated. To put it another way, the presence of economy- 
wide implicit disturbances and the presence of substantial serial 
correlation do not prevent us from taking V(6) as block-dia- 
gonal 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