414 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA

may be more willing to assume no correlation between contemporaneous
 disturbances in two different aggregate sectors
than between disturbances in any two single equations. A similar
 assumption may be even more attractive when the
disturbances in question are from different time periods as will
be seen below. Thus also, the dynamic system may be thought
close to decomposability when broad sectors are in view and
feedbacks within sectors explicitly allowed. If such assumptions
are approximately satisfied, then the inconsistencies involved
in the use of current and lagged endogenous variables as predetermined
 in higher-numbered sectors will be small (*0).
Nevertheless, the assumption of no correlation between contemporaneous
 disturbances from different sectors, the assumption
 of no serial correlation in the disturbances, and the assumption
 of decomposability of the dynamic system all seem
rather strong ones to make. If none of these assumptions is in
fact even approximately made, then the use of current endogenous
 variables as instruments in higher-numbered sectors
leads to non-negligible inconsistencies. We shall show, however,
 that this need not be true of the use of lagged endogenous
variables in higher-numbered sectors under fairly plausible
assumptions as to the process generating the disturbances. We
thus turn to the question of the use of lagged endogenous variables,
 assuming that A is known to be at least nearly blocktriangular.


5.4. Reasonable Properties of the Disturbances

The problems which we have been discussing largely turn
on the presence of common omitted variables in different equations
 and on the serial correlation properties of the disturbances.
It seems appropriate to proceed by setting up an explicit model

((#) See Frsurr [8]. The theorems involved are generalizations of the:
Proximity Theorem for recursive systems.

‘61 Fisher - pag. 30