high. When weighted by value, these differences 

 disappear. 



On the basis of these statistical tests, we 

 conclude that the best specification of the pro- 

 duction function for the New England ground- 

 fish fleet is shown in Problem 4, where total 

 value is the measure of output and days absent 

 is the measure of fishing time. Good descriptions 

 of the capital variable are given by gross 

 registered tonnage, horsepower, vessel age, and 

 construction materials. The contribution of 

 labor is measurable and important. 



The Tuna Seine Fleet 



In fisheries such as the tropical tuna fishery, 

 the species are, in the jargon of the economist, 

 "joint products." That is, the fishermen take as 

 much of both species (yellowfin and skipjack) 

 as they can in an effort to fill their holds as 

 quickly as possible. They are essentially indis- 

 criminate between tunas in that they do not 

 appear to pass up any that they sight solely 

 because it is the less desirable species, although 

 such behavior was noted up to about 1950 

 (Shimada and Schaefer, 1956). 



According to lATTC records, the probability 

 of a successful set on yellowfin is higher than 

 on skipjack. This leads one to hypothesize 

 that a ton of skipjack represents in some way 

 more input than a ton of yellowfin because it 

 takes more work to catch skipjack. There are at 

 least two techniques that might be used in this 

 fishery to determine a weighting system for 

 output. One technique (which is not used here) 

 is canonical regression which was developed by 

 Hotelling and described by Tintner (1952). In 

 a sense, it is a search technique that "weights" 

 the dependent and independent variables in 

 such a way that the sum of the squares of the 

 unexplained variance of all the variables is 

 minimized. The second technique-^ is to .sys- 

 tematically try different weights (whose sum 

 is one) for the dependent variable and run a 

 series of regressions using a common set of 

 independent variables. The regression that 

 maximizes the coefficient of determination would 

 have the weights, which are, in a sense, best. 



' Suggested by Henri Theil during a discussion of 

 this problem with the author. 



The following regression was run in an at- 

 tempt to arrive at the best weighting system 

 for output: 



(4) Q = /(D, T, CAPAC, CRT, ND, PR, 



CR,AGE,HP) 



where Q = (aY + |3S + SB) and (a + /J + 6 ) = 1 



and Y is tons of yellowfin landed, 



S is tons of skipjack landed, 

 B is tons of bluefin landed, 

 D is days at sea of each vessel, 

 T is the number of trips of each vessel, 

 CAPAC is the capacity of each vessel, 

 GRT is the gross registered tonnage, 

 ND is a dummy for new design, 

 PR is 1 for Puerto Rico home port, 



zero otherwise, 

 CR is the crew size, 

 AGE is the age of the vessel, 

 HP is the horsepower of each vessel. 



The results of this experiment are shown in 

 Table 2, where the left hand column shows the 

 different weights applied to each species. The 

 column headings are for each year's observations 

 and for pooled observations. Tests using the 

 H statistic show that the observations are not 

 random. Weights of .3 for yellovdin, .4 for 

 skipjack, and .3 for bluefin are best. This fits our 

 a priori expectation that a vessel exhibited 

 more productivity when it caught a ton of 

 skipjack than a ton of yellowfin. The statistical 

 results indicate that a vessel does one-third 

 more work to catch a ton of skipjack than a 

 ton of yellowfin. 



The above experiment presents one approach 

 to the determination of output in a fishery. 

 Three alternative specifications of output in 

 the tuna fishery were used in estimating the 

 production function. These specifications were 

 as follows: total value, total pounds, and 

 weighted total pounds using the weights 

 determined above. 



Selected results of the regi'ession experiments 

 run are shown in Table 3 and in Appendix 

 Table 2. The various specifications of the 

 dependent variable could be explained with 

 varying degrees of precision. As expected, 

 weighted total pounds had the highest coef- 

 ficient of determination, followed by total 

 pounds, total value, skipjack and yellowfin, in 

 that order. The actual difference between co- 



49 



