SEMAINE D’ETUDE SUR LE ROLE DE L'ANALYSE ECONOMETRIQUE ETC.
41;
model. If it does not occur, then (BR.3) is generally neces-
sary for the block-triangularity of W(o). Indeed unless either
(BR.3) or the first statement of (BR.3*) holds, no W(0)" can
generally be expected to be zero if Bo.
To see this, observe that (2.4) implies that W(o) cannot
generally be expected to have any zero submatrices unless every
term in the sum which is not wholly zero has a zero submatrix
in the same place. This cannot happen unless every matrix
involved is either block-diagonal or block-triangular. Hence,
if V(8)=0o for all 8>>0, all such V(8) must at least be block-
triangular as must B (3%
5.3. Block-Recursive Assumbtions in Economv-wide Models
Unfortunately, while block-triangularity of A is not an un-
reasonable circumstance to expect to encounter in practice (*)
the assumptions on the disturbances involved in (BR.2) and
(BR.3) or (BR.3*) seem rather unrealistic in economy-wide
models for much the same reasons as did the parallel assump-
tions of the recursive model. Thus, it does not seem reasonable
to assume that the omitted effects which form the disturbances
in two different sectors have no common elements; nor, as
already discussed, does it seem plausible to assume either that
there is no serial correlation of disturbances or that the dynamic
system involved is decomposable.
Note, however, that these assumptions may be better ap
proximations than in the case of recursive systems. Thus one
(38) Of course, this does not show that (BR.3) or (BR.3*) is necessary,
since counter-examples may easily be produced in which different non-zero
terms in (2.4) just cancel out. The point is that this cannot be assumed
to occur in practice. To put it another way, since such cancellation cannot
be known to occur, it clearly occurs only on a set of measure zero in the
parameter space. Thus (BR.3) or (BR.3*) is necessary with probability 1.
(**) It is encountered in preliminary versions of the Brookings-SSRC
model. C. Hort and D. Stewarp have developed a computer program for
organizing a model in block-toaneular form
ar
Fisher - pag. 70
