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ancorrelated with lagged values of low-numbered disturbances. 
Further, either B or all V(6) (A >o) have zeros evervwhere 
on the principal diagonal. 
If (R.1), (R.2), and (R.3*) hold, every term in (2.4) will 
be triangular, so that W(o) will likewise be triangular as re- 
quired. Further, W(1) will also be triangular rather than zero 
and will have zeros on its principal diagonal, but this will be 
all that is needed, since if B is triangular no lagged endogenous 
variable appears in an equation of (2.1) explaining a lower- 
numbered current endogenous variable. 
Intuitively, the general necessity of no serial correlation for 
the consistency of least squares is that an element of y,_, is 
influenced by an element of «, ;. If that element of u,_, is 
itself correlated with a lower-numbered element of #,, then the 
corresponding element of y,_, cannot be assumed to be uncor- 
related with that element of u,. Even if V(8) is triangular for 
8>0 (or even diagonal) and B is not triangular, the dynamics 
of the system will carry serial correlation into relations between 
any current disturbance and any current endogenous variable. 
If both V(6) and B are triangular, however, such effects are 
only carried toward higher-numbered equations. 
That triangularity of both V(6) for all 6>>0 and B are 
generally necessary in the presence of serial correlation may be 
seen from the fact that since D is triangular, the terms in (2.4) 
will generally not otherwise be triangular and the fact that if B 
is not triangular, even triangularity of W(1) will not suffice. 
(The condition as to the principal diagonals can be easily seen 
to be required by considering a single-equation model). 
Of course, as is also the case for the assumption of the 
diagonality of V(0), even if such assumptions fail generally, 
similar weaker assumptions concerning certain off-diagonal ele- 
ments may hold and yield the consistency of ordinary least 
squares for certain equations. The indicated assumptions are 
necessary for such consistency in all equations, however. (Such 
weaker conditions are fairly readily obtained from the genera 
lization of the current discussion given in a later section’ 
Lo 
Fisher - pag. 
C,