52


relationships discussed are necessarily aggregate in nature. Such

aggregation unfortunately limits the resulting empirical models in many

undesirable ways.

 Catch Equation Specification and Estimation


 In order to specify state catch equations, the form of the catch

equation for an arbitrary region is first developed in a deterministic

fashion. After developing the typical region's catch equation, the

corss-sectional specification is presented. Commensurate with this

discussion is the stochastic specification of the catch equation. The

presentation concludes with the choice of the appropriate estimator.

 A general expression for a fishery catch equation is given by

 C = f(E, S) (41)


where C refers to catch, E is effective fishing effort and S denotes the

resource stock size. Since stock size is seldom observable, the catch

equation stated in (41) is often modified for empirical analysis to

 C = f*(E) (42)

 In equation (42) aggregate catch is expressed as a function of only

 effective fishing effort. The f (E) function is used to denote the fact

 that the influence of the resource stock is not considered explicitly as

 in equation (41) but rather indirectly. The equilibrium yield models

 presented in the previous chapter are one such class of models.1


 1Consider the Schaefer formula as an example. Equation (41) cor-
 responds to C = KEP in the Schaefer model. In this context P is elimi-
 nated through algebraic manipulation to derive the Schaefer type
 equilibrium yield function C = AE BE2. Here, AE BE2 corresponds to
 f*(E) in equation (42) above.