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