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5.5. Implications for the Use of Lagged Endogenous Variables

Of course, assuming (5.19) to hold is not sufficient to yield
consistency when lagged endogenous variables are treated as
predetermined. We have already seen that unless V(6)=o,
the decomposability of the dynamic system must be assumed
in addition to (5.19) to secure such consistency. We argued
above, however, that such decomposability was rather unlikely
in an interconnected economy, although the fact that (5.19) is
likely to hold approximately makes it important to look for
near-decomposability and thus secure near-consistency (**).
Even if such near-decomposability of the dynamic system
does not occur, however, (5.19) has interesting consequences for
the treatment of lagged endogenous variables as predetermined.
To these we now turn.
Consider the expression for W(1) given in equation (2.6).
Writing out the first few terms of the sum, we obtain:

(5.20)  W(1)=DV(1)+ DBDV(2)+(DB/DV(3) … .

Since D is block-triangular and V(1) block-diagonal by (5.19),
the first term in this expansion is also block-triangular. Hence
even if the dynamic system is not decomposable, endogenous
variables lagged one period are approximately uncorrelated
in the probability limit with disturbances in higher-numbered
sectors (but not in the same or lower-numbered sectors), to
the extent that the right-hand terms in (5.20) other than the
first can be ignored.
In what sense is it legitimate, then, to assume that such
terms can in fact be ignored? Assume that the matrix DB is

(*) Near-decomposability of a dynamic system has a number of interesting
 consequences in addition to this. Se ANDo. FTSHER, and SrMoN [3]
especially Anpo and Frsuer 2]

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