-7-


the filter adjusts this weighting according to equation (11) which

contains an expression for the (inverse of the) forecast variance. That

is, if the system indicates "large" forecast errors due to lack of

resolution, then the forecast errors are weighted less because K is

"smaller". However, if the forecast variance is (in some sense) small

while the forecast error is large, then the updated parameter vector

will depend much less on its previous value, i.e., the last observation

will be weighted heavily.


 The Varying Parameter Recursive Model


 The extension of single-equation varying parameter techniques to

simultaneous equation systems has been presented in several studies

(Mariano and Schleicher, Narasimham et al., Mahajan and Mahajan), how-

ever, none of these studies showed the effect of a varying parameter

structure on the evolution of the restricted reduced form. Further,

it is not immediately clear whether the structure should be updated

with predictions being formed from the restricted reduced form, or

whether knowledge of the structure should be used to specify a re-

stricted reduced form that can be updated directly. In view of the

fact that combinations of restricted and unrestricted reduced forms

(Maasoumi, Sant,1978) may provide desirable properties, this latter

approach will be developed as well.

 The recursive simultaneous system represents a useful vehicle for

 development of the multiequation varying parameter model because the

 structural equations may be consistently estimated via immediate