-3-
specification may reduce the effects of these factors (Cooley and
Prescott, 1973). Additionally, Cooley and Prescott (1976) have re-
marked that constant parameter formulations are inconsistent with
theoretical specifications in the sense that the dynamics of economic
behavior do not suggest constant-parameter behavioral equations.
The type of varying parameter structure adopted allows one or
more coefficients to follow a first order Markov process.1 Specifi-
cally, the tth observation for the model may be written
yt = xtat + Ct t = 1, 2, ..., T (1)
t t- + Pt (2)
where xt is a lxk vector of observations on the independent variables,
and at is a kxl vector of coefficients at time t. The stochastic
assmuptions for the model are
E(et) = E(pt) = E(Esst) = 0 (3a)
E(2S) 2 (3b)
s : st%
E(st) stQ (3c)
where Q is a kxk covariance matrix assumed known and 6st denotes the
Kronecker delta. The specification of Q is not as difficult as might
seem. In the constant parameter case Q is identically equal to a null
matrix. Otherwise, the variances and covariances may be specified in
a manner similar to that used in mixed estimation (Cooper). That is,
qii represents the variance of the varying parameter process of Bi