414 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA 
may be more willing to assume no correlation between con- 
temporaneous disturbances in two different aggregate sectors 
than between disturbances in any two single equations. A si- 
milar 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 pre- 
determined in higher-numbered sectors will be small (*0). 
Nevertheless, the assumption of no correlation between con- 
temporaneous disturbances from different sectors, the assump- 
tion of no serial correlation in the disturbances, and the as- 
sumption 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 endo- 
genous variables as instruments in higher-numbered sectors 
leads to non-negligible inconsistencies. We shall show, how- 
ever, 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 va- 
riables, assuming that A is known to be at least nearly block- 
triangular. 
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 equa- 
tions 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