and crew size. If we did this the following 

 equation would result: 



(3) C = cuE - b,E'^ + cL + dT + e 

 Where: 



C = Total landings 

 E = Fishing effort 

 L = Labor employed or crew size 

 T = Technological change expressed 

 as T = 1 in period 1, T = 2 in 

 period 2, T = 3 in period 3, etc. 



If the coefficients of "L" and "T" are statisti- 

 cally significant (as given by their f-values), 

 it means that the measure of fishing effort used, 

 "E," did not adequately include the effect of 

 these variables on catch. Consequently, the use 

 of equation (2) alone would produce biased 

 estimators of the coefficients "a" and "ft" of 

 "E" and "E-," respectively. In this case we 

 can either correct the measure of fishing effort 

 used (which is the first procedure indicated in 

 Figure 1) or we can isolate the effect of other 

 variables on catch using a multiple regression 

 equation that would include these variables 

 (which is equivalent to the second approach 

 indicated in Figure 3). 



If the second approach is used, technological 

 innovation and crew size must be kept at a fixed 

 level in equation (3). Usually this would be at 

 the current levels. After this is done we can 

 obtain the true value of fishing effort by maxi- 

 mizing catch in equation (3). Keeping the effect 

 of "T" and "L" on catch at some constant level 

 K, equation (3) would become 



C 



ttiE - b,E'^ + K 



or 



(4) (C - A') = a,E - bxE-^ 



Which is the model as developed by Schaefer 

 (1957) after the effect of technological change 

 and crew size is removed. The optimal level 

 of fishing effort, at constant vessel capacity 

 and crew size, that will maximize catch is 

 given by equating zero to the first derivative 

 of equation (4) as follows: 



d{C-K) 

 de 



a, -2 6, E = 



or 



(5) Optimal fishing effort = E* = 



0| 



2 6, 



STATISTICAL RESULTS 



Using the data presented in Table 1, several 

 regressions were made to test for the adequacy 

 of the measures of fishing effort available to us. 

 In Table 1, total landings is defined as the catch 

 by the fishermen in thousands of pounds. The 

 unit used for fishing effort is the number of 

 trips made times the average vessel capacity. 

 Data on fishing effort was compiled by the 

 Instituto del Mar del Peru, and it is supposed 

 to be adjusted for the effect of closed seasons, 

 strikes, and for some changes in gear efficiency. 

 Other variables included in the analysis are the 

 number of fishermen employed in the industry, 

 the size of the bird population (which is supposed 

 to be an important element in fishing mortality), 

 and veda (closed) seasons. 



As has been recognized by Gulland (1968) 

 and by Schaefer (1967), because of the rapid 

 growth of the Peruvian fishery, it has not 

 remained in steady state equilibrium in every 

 year. Under these circumstances, the use of a 

 relationship of catch to effort will produce too 

 high an estimate of steady state abundance 

 and catch for a given fishing effort. One way to 

 correct this situation is to use the "Gulland 

 Method" (Gulland, 1961) in which the total 

 landings are related to the average effort exist- 

 ing during the life span of a fish in the fishery, 

 which is approximately two years. This method 

 has been used in this paper. 



Schaefer (1970) used the same data presented 

 in Table 1 to estimate the maximum sustainable 

 yield of the stock and the optimum level of fishing 

 effort. I have added observations for the year 

 1968-1969. The regression equivalent to the 

 one used by Schaefer in 1970 is as follows: 



(6) C = 0.7769 £ - 0.1706 fi"-^ 

 (8.6) (-3.8) 



Coefficient of Determination {R-) = 0.84 

 Durbin-Watson Statistic (D-W) = 0.7 

 Standard Error of Estimate (SEE) = 813 

 Figures in parentheses are f-values. 



Equation (6) is useful for findingthe maximum 

 sustainable yield of the fi.shery. The estimated 

 MSY is given at 8.8 million metric tons. This 

 value is very close to the value of 8.5 million 

 metric tons obtained by Schaefer (1970). By 

 observing the data of total landings in Table 1 

 we cannot appreciate the danger of overfishing 



61 



