Due to the small sample size of each cross section (T = 19), many

of the standard time series identification techniques for determining

the autoregressive order parameter are unsatisfactory. This mainly

results from the fact that most statistical tests on the order parameter

are only asymptotically valid and utilize a variance measure that is

inversely proportional to the sample size. There are, however, several

techniques, such as Akaike's (1969) FPE criterion which do not suffer

from this limitation. Several alternative identification procedures

were used in the identification of the residual autoregressive process.

These procedures are outlined in Appendix E.

 The estimated residuals used in the identification process were

generated by applying a two stage Aitken's estimation procedure to

equation (52). More precisely, the NT x 1 vector of residual estimates

is given by


 0 = C (54)


where 3 = (X'(i1 aI)X)-" (X'(" a I)C) and E is the N x N matrix of

estimated contemporaneous covariances. The estimated residual vector

was then partioned into N, T x 1 vectors corresponding to the N cross-

sections. The results of the identification procedure indicated that

all sets of estimated residuals were characterized by first order

autoregression.

 Having determined the order of the autoregressive processes for

each state catch equation, a complete specification of the distrubances

for the system of catch equations can now be made. Denote the stochas-

tic process of the ith region by