Level of 

 landings 

 that would 

 have been 

 obtained in 

 period 2, if 

 vessels had 

 efficiency 

 of period ^, 



Effort 



(ton-trips) 



Fi^re 3. — Actual and adjusted catch effort curves. 



first one is that in the first approach the fishing 

 effort is adjusted for efficiency changes and 

 catch remained at the observed levels; in the 

 second approach the catch is adjusted for ef- 

 ficiency changes and the fishing effort remains 

 at the level observed. The second approach has 

 the advantage that it can be more easily handled 

 with statistical techniques. It should be noted 

 that curve A in Figure 3 gives the level of 

 landings that would have been obtained in past 

 periods if vessels at that time had the efficiency 

 of the current period. Actually, this curve has 

 not been observed; and the maximum of the 

 curve, although it indicates the optimal level 

 of fishing effort in terms of current efficiency, 

 will not give the maximum sustainable yield 

 of the stock. The maximum sustainable yield 

 will in fact be given by curve B, as it was 

 shown in Figure 1. 



Since curve A in Figure 3 is actually the 

 relationship of effort to catch keeping all other 

 variables (including efficiency) constant, the 

 multiple regression technique can be applied. 

 In fact, the statistical meaning of a partial 

 regression coefficient is that it measures the 

 effect of the independent variable on the de- 

 pendent one, keeping all other variables constant. 



The use of the regression analysis to obtain the 

 optimal fishing effort is presented below. 



The logistic model as presented by Schaefer 

 (1957) and reproduced in equation (1) is a 

 stochastic rather than an exact relationship: 



(2) C = aE - bE'^ + e 

 Where "e" is an error term. 



In this model, if the measure of effort used 

 were a proxy for all the several inputs utilized 

 when fishing and affecting catch, then the error 

 term "f" should be randomly distributed. That 

 is, no other input variable, when added to 

 equation (2), should be statistically significant 

 in explaining changes in the level of catch. In 

 fact, if no variables have been omitted in 

 equation (2) (all of these are represented in the 

 proxy fishing effort), then no sign of auto- 

 correlation of the error term should exist. If 

 this is the case, one could conclude that the 

 measure of fishing effort used is adequate and 

 that it can be reliably used to estimate both the 

 maximum sustainable yield and the optimum 

 level of effort. 



We can further test if the measure of fishing 

 effort is adequate by introducing into equation 

 (2) input variables such as technological change 



60 



