-12-


 Alternatively the time varying structural model can be viewed

as a convenient vehicle by which some appropriate structural specifi-

cations are employed to produce restrictions on both the parameter

space and the parameter evolution process. The reduced form model

implied by (22) is

 YT = XTT + T (27)

 S* -th *
such that 11T+l/T = 11T and *iT represents the i column of ET where

 E('T T) = 1rT T( + RT (28)

The matrix.,RT represents a remainder term which is not required by

the Kalman filter algorithm. Once (27) and (28) are given at time

T additional information about the reduced form parameters is required

in order to update expression (27) directly. Specifically the variance-

covariance of the parameter nT and its evolutionary covariance must be

determined. This first measure is derived by noting that

 Var(nT) = DW TTW D = :T (29)

Lastly the time update for the reduced form parameters' covariance

follows directly as


 ET+l/T = T + DWQ W (30)

 Expressions (27)-(30) permit updating the restricted reduced

 form directly. As additional sample observations are included it is

 expected that the restricted reduced form derived from the updated

 structure will diverge (26) from the directly updated reduced form.

 The rate of this divergence will be conditioned by numerous factors