Given that all estimators for the above equation system possesses only

asymptotic properties, it is appropriate to use a relative efficiency
criterion in small samples as a basis for choosing the "best" estimator

for the system of catch equations given in equation (53).
 Drawing on the results of Monte Carlo studies conducted by Kmenta

and Gilbert (1968), a four stage Aitken's estimator (FSAE) was chosen as

the appropriate estimator. The formation of this estimator proceeds in

two basic steps. Given that the disturbances in each equation in the
system are known to follow a first order autoregressive process, the

first step involves the application of the two stage Aitken's estimator

to equation (53) to generate a sequence of estimated residuals for each

state catch equation. These residuals correspond to those given in

equation (54). The use of this four stage estimator is the reason that
the residuals estimated using equation (54) were used in the order
parameter identification. The estimation of the autoregressive parame-
ters is accomplished by

 N U N
 p. it- / Z i = 1, N (56)
 t=2 T 1 t=l T

 where U is the estimated residual for the ith state and tth time
 it
 period defi-ned in equation (54).

 The second step in deriving the FSAE involves a second application

 of the Atiken's two stage estimator. Before this estimator is applied,
 however, the data is transformed by


 i = 1 p. C i = 1, ..., N (57a)
 111 i1