-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