assumed to be white noise.5 Before proceeding to a more detailed

specification of the stochastic properties of equation (50), it is

necessary to consider the cross-sectional specification of the catch

equations.


Cross-Sectional Specification Considerations


 The main consideration which must be addressed in the cross-

sectional specification of the catch equations involves determining what

restrictions exist on the catch equation parameters across states. Both

the nature of the fishing process and the nature of the data must be

considered in determining these restrictions.

 Consider the equality or non-equality of the fishing power function

 coefficients. In general, the fishing process and input characteristics

 of vessels across states are very similar. Given this, it seems reason-

 able to assume that the fishing power coefficients are constant across

 states in the GMRFF. The fishing power function, incorporating this

 restriction is given by


 E = exp(k) X t = 1, ..., 19 (51)
 it lit 2it
 i = 1, ..., 5


 The consequences of such a restriction are not without complications,

 however. The assumption that aji = ajk for j = 1, 2 and all i, k

 requires that non-linear restrictions be placed on the reduced form

 parameters of equation (50). More explicitly, these restrictions take


 5A white noise process is defined as a sequence of independent
 identically distributed random variables with zero mean and constant
 variance.