the conditions of a truly recursive model, r is upper triangular and

, is diagonal (Goldberger).

 The recursive system may be conveniently written


(17)


Vec(Y) = ZA + Vec(n)


where


Y :X
m. m


and A =


B.

(r2




m(r


: B:2)




: B'.M )
 m


The notation Y. and X. indicates the endogenous and predetermined

variables designated as regressors in the ith equation. Estimation of

the structural parameters is given by


 A = (Z'Z)-1Z'Vec(Y)


with the variance of the estimated parameters in the ith equation

determined as


Var(Ai) = ii(Z 'Zi)


(18)


(19)


= yi


If we let T represent the block diagonal matrix whose ith block is

T. then the variance of the restricted reduced form parameter may be

written as (Schmidt)


Var(6) = DW'W'D' = ()


Y2 X2


(20)