Choice of Estimator for the Catch Equations-


 As a prelude to the discussion regarding the estimation of the

catch equations, it is convenient to place the system of equations into

matrix form. This is accomplished by


 C = .XB + U (53)

where

 C = NT x 1 vector of logged catch variables;

 g = (k + N) x 1 vector of parameters to be estimated; and

 U = NT x 1 vector of disturbances with EU = 0, EUU = 1.


The NT x (k + N) matrix of regressors is of the form


 X = [D X] (53a)


with the NT x N matrix, D, composed of appropriately defined state dummy

variables and X corresponding to the NT x K matrix of logged values of

regressors given in equation (52). Specification of the distrubance

term is given in general form to emphasize the covariance matrix is

non-spherical. The precise form is conditioned by the exact form of the

autoregressive processes corresponding to each state's disturbance

vector.

 Estimation of the catch equation parameters must be done in two

 basic steps. The first step involves the identification and estimation

 of the autoregressive processes for each state generated by the unobserv-

 able resource stock. Once this is accomplished, the appropriate form of

 the covariance matrix of the disturbances can be ascertained and the

 appropriate estimator for the reduced form parameters derived.