application of ordinary least squares. Thus, questions associated with
the appropriate means to generate instrumental variables within a
varying parameter system are avoided. This section proceeds by first
briefly developing the general simultaneous equation model and the
recursive system in particular. This system is extended to admit vary-
ing parameters and use of the updating alogorithms.
Let the Txm matrix of m jointly dependent variables and the Txz
matrix of predetermined variables be written
Yr + XB = n (14)
where r and B are coefficient matrices of dimension mxm and zxm re-
spectively and n is a Txm matrix of structural disturbances. The
restricted reduced form of (14) is, of course,
Y = Xn + E, (15)
where
n = -Br and E = nr .
The traditional stochastic assumptions concerning (14) and (15) include
E(n) = E(z) = 0 (16a)
E(n'n) = D (16b)
E(g'g) = r" -1 -1 (16c)
The matrix D represents the structural covariances between the
disturbances of the m equations in the system. In order to satisfy