Uit = PiUit-I + e it (55)


The stochastic specification of U in equation (55)7 is then given by


 E(Uit) = ii (55a)


 E(UitUjt) = (55b)

 4ij t = s
 E(e ite) = { (55c)
 o t t s

 E(Uio Ujo) = ij /1 -Pi Pj (55d)

 1ii) 1
for i, j = 1, ..., N and Uio N(O, 2) and eit N(O, i).
 1 Pi
 As a result of the residual identification process, the system of
catch equations can be characterized as a system of seemingly unrelated
regression equations with cross equation parameter restrictions.
Furthermore, the disturbances exhibit first order autoregression. A
great deal of literature pertaining to the estimation of this type of
equation system is available. Most notable is the work done by Parks
(1967), Kmenta (1971), Kmenta and Gilbert (1968) and Zellner (1962).
The most important of these insofar as this study is concerned is the
work done by Kmenta and Gilbert on the small sample properties of alter-
native estimators for systems of equations similar in nature to the
catch equations above. As mentioned previously, data on the catch equa-
tion variables is limited, resulting in rather small sample sizes.


 The form of U is given by
 U1 = [ Uil ..., UiT, ..., UN1, ..., UNT '