-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