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)