SEMAINE D ETUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC. 
425 
to unity in absolute value). In such cases, one will not be wil 
ling to assume that the use of endogenous variables lagged one 
period as instruments in higher-numbered sectors leads to only 
negligible inconsistencies. Accordingly, we must generalize 
our discussion. 
Fortunately, this is easy to do. There clearly does exist a 
smallest 6*>o such that for all 6°>6* even the diagonal blocks 
of V(0*) are negligible on any given standard. Consider 
W(6*), the covariance matrix of the elements of #, and those 
of y,_,» with the columns corresponding to elements of w, and 
the rows to elements of Clearly, 
(5.26) 
Tr 
+ 
+ 
JV 
_ 
e= 0% 1 
; 0-6" 
DB) DV(e) 
PH" P DONO 
Since D is block-triangular and V(6*) block-diagonal by (5.19), 
the product, DV(6*), is also block-triangular. Considering 
W(6*)# for ]>1, it is apparent that the covariances of endo- 
genous variables lagged 6* periods and current disturbances 
from higher-numbered sectors are made up of only negligible 
terms. Not only is V(8) negligible by assumption for 6>>6% 
but also every such term involves at least one power of H, 
which, by assumption, is diagonal and has diagonal elements 
less than unity in absolute value. 
Note, however, that a similar statement is clearly false as 
regards the covariances of endogenous variables lagged 6* 
periods and current disturbances from the same or lower-num- 
bered sectors. Such covariances involve the non-zero diagonal 
blocks of V(0*) in an essential way. It follows that the order 
of inconsistency, so to speak, involved in using endogenous 
variables lagged a given number of periods as instruments is 
less if such variables are used in higher-numbered sectors than 
if they are used in the same or lower-numbered sectors. To put 
it another way, the minimum lag with which it is reasonably 
61 
Fisher - pag. +1