-10-
where
-1
D = (r- )' I
and W represents the block diagonal matrix such that the ith block
of W is
Wi = plim (X'X)-Ix'(Yi Xi).
The importance of obtaining the restricted reduced form parameters
and their estimated variances will become clear when the varying para-
meter recursive model is set forth. The other measures developed are
traditionally estimated and reported in most studies. The method
adopted by Schmidt for obtaining E is particularly attractive due to
its ease of implementation. This method,however,is based on the original
Goldberger, et al. approach which is a Taylor series approximation
based on large sample theory (Dhrymes).
To incorporate a first order Markov process as a parameter variation
scheme, the recursive structural model may be written as2
Vec(YT) = ZTAT + Vec(nT) ATVec(UT) (21)
which introduces the structure of expression (4) to the system in
(17). The matrix AT is a block diagonal matrix whose ith block would
th
be AiT and would correspond to UiT, the partition of UT for the i
equation. Again, the full model may be expressed
Vec(YT) = ZTAT + VT (22)