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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA 
By (BR.1), however, D=(I- A)-! is block-triangular, while 
V(o) is block diagonal by (BR.2). It follows that their product 
is block triangular with the same partitioning. Thus: 
(5.3) W(0o)" =o for all I, J=1, …, N and J>I, 
but this is equivalent to the proposition in question. 
As in the special case of recursive systems, assumption 
(BR.3) can be replaced by a somewhat different assumption: 
(BR.3*) B is block-triangular with the same partitioning 
as A, as is V(6) for all 6>>0. Further, either all B" or all 
V(0) (6>0) are zero (I=1, ..., N). 
To see that this suffices, observe that in this case every 
term in (2.4) will be block-triangular. 
Note, however, that whereas (BR.1)-(BR.3) patently suffice 
to give W(1)=0 and thus to show that lagged endogenous 
variables are uncorrelated with current disturbances, this is 
not the case when (BR.3) is replaced by (BR.3*). As in the 
similar case for recursive systems, what is implied by (BR.1), 
(BR.2), and (BR.3*) in this regard is that W(1) is also block- 
triangular with zero matrices on the principal diagonal so that 
lagged endogenous variables are uncorrelated with the current 
disturbances of the same or higher-numbered blocks, but not 
necessarily with those of Jower-numbered ones. 
If A and B are both block-triangular with the same parti- 
tioning, then the matrix DB is also block-triangular and the 
system of difference equations given by (2.2) is decomposable. 
In this case, what occurs in higher-numbered sectors never 
influences what occurs in lower-numbered ones, so that there is 
in any case no point in using current or lagged endogenous 
variables as instruments in lower-numbered sectors. This is 
an unlikely circumstance to encounter in an economy-wide 
model in any essential way, but it may occur for partitionings 
which split off a small group of equations from the rest of the 
61 Fisher - pag. 28