The catch equation in (45) can be expressed in terms of nominal

effort and fishing power by substituting equation (44) into equation
(45) for Eit. The resulting reduced form catch equation is


 I i Xli x 2i (46)
 it = exp[A'(S)t] V Xlit (46)


where the term A'(S)it denotes the fact that the constant k in equation
(44) has been incorporated into the stochastic process A(S)it and the

reduced form parameters are ji = BiOi' j = 1, 2. To facilitate

further discussion, it is convenient to write equation (46) in an alter-
native form. By defining cit = In Cit, x = In Xi and so on, equation

(46) can be written in double log form as

 cit = A'(S)it + i + i li Xlit + 2ix2it (47)

 i = 1, ..., 5
 t = ..., 19


 The nature of the stochastic process A'(S)it can be analyzed in this
 form.

 Stochastic Approximation of Resource Stock Effects

 The expected presence of a stochastic process in the catch equation

 derives from the nature of the omitted resource stock variable.4 From

 the discussion contained in Chapter II, it is apparent that the change
 in the resource stock over time is proportional to the difference
 between catch and sustainable yield. An expression for the size of the


 4The discussion that follows implicitly assumes that the resource
 stock variable is uncorrelated with the included set of regressors.