c = Ct pCi i = 1, ..., N (57b)
 it it 1 i ,t- t =2, ..., T

 ^ .
 Xi = 1 p X all i, j (57c)

 ^
 Xit = it pixjitl all j (57d)
 jt =2, ..., T


where cit and xjit are defined as in equation (53a). In matrix form,

the transformed system can be written as


 C = X + U (58)

 *
where C is an NT x 1 vector of transformed logged catch values and X

is an NT x (N + K) matrix of transformed regressors in log form. The

effect of the transformation is to remove the autoregressive effects
 *I
from the NT x 1 disturbance vector, U Thus, EU U = I IT where


 11 h12 "' 1N

 S= 21 22 "' 2N (59)


 N1l RN2 NN


corresponds to the contemporaneous covariance matrix of the transformed

disturbances. To estimate t, ordinary least squares was applied to

equation (58) to yield


 ^* *^ (60)
 U = C X (60)


where B = (X* X*)- (X*' C*). Estimates of the ij were calculated by