SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC. 41] 
ings, the Ith subvector of a given vector x will be denoted 
as x'. Similarly, the submatrix of a given matrix M which 
occurs in the Ith row and Jth column ..f submatrices of that 
matrix will be denoted br MT 
5-1) 
We shall always assume the diagonal blocks, M" to be square 
If when written in this way, the matrix M has the propert, 
that MY =o for all I=1, ..., N and J>I, the matrix will be 
called block-triangular. If MV =o for all I=1, ..., N anc 
J#I1, the matrix will be called block-diagonal (*). 
Now consider the system (2.1). Suppose that there exists a 
partition of that system (with N>1) such that: 
(BR.1) A is block-triangular; 
(BR. ’ V(o) is block-diagonal; 
(BR., Y(3)=0 for all 8>o. 
(Note that these are generalizations of (R.1)- (R.3)). In this 
case, it is easy to show that the current endogenous variables 
of any given sector are uncorrelated in probability with the 
current disturbances of any higher-numbered sector. Such 
variables may thus be consistently treated as predetermined 
instruments in the estimation of the equations of such higher 
numbered sectors. 
To establish the proposition in question, observe that (2.2)- 
fa * "wer hold (3). By (BR.3), (2.5) holds also, so that: 
W(o)= DV(o0' 
‘> 
(8) Block-triangularity and block-diagonality are the respective canonica. 
forms of decomposabilitv and complete decomposability. 
37\ Continuine to assume that DR is stable 
Fisher - pag.