22 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA 
a factor less than unity and the square of another such factor. 
There is clearly a reasonable sense in which one may be pre- 
pared to take such terms as negligible at least when compared 
with the non-zero elements of the first term in the expansion 
for W(1) which involve only the diagonal elements of A to 
the first power. If one is willing to do this, then one is saying 
that the use of endogenous variables lagged one period as 
instruments in higher-numbered sectors involves only negligible 
inconsistency at least as compared with the use of the same 
variables as instruments in their own or lower-numbered 
sectors. 
There may be considerable difficulties in accepting such a 
judgment, however. In the first place, it is well to be aware 
that there are two different statements involved. It is one 
thing to say that the effects in question are negligible compared 
to others and quite another to say that they are negligible in 
a more absolute sense. If one accepts the stability assumption, 
then there certainly is a value of 6 beyond which further terms 
in the expansion of W(1) are negligible on any given standard. 
These may not be all terms after the first, however: we shall 
discuss the case in which there are non-negligible terms after 
the first below. 
Second (a minor point but one worth observing) even our 
conclusion about relative importance need not hold although 
other assumptions are granted. While it is true that as 0 be- 
comes large the right-hand side of (5.25) approaches zero, such 
approach need not be monotonic. To put it another way, every 
element of the matrix involved is a sum of terms. Each such 
term involves a diagonal element of A to the 8 and a diagonal 
element of H to the 6 - 1. If all such diagonal elements are 
less than unity in absolute value, then the absolute value of 
each separate term approaches zero monotonically as 6 in- 
creases; this need not be true of the sum of those terms, how- 
ever, and it is easy to construct counter-examples. Neverthe- 
less, there is a sense in which it seems appropriate to assume 
61 Fisher - pag. 38