86 



Fishery Bulletin 88(1). 1990 



In the following section we introduce the methodol- 

 ogy used to analyze total factor productivity in fishing 

 fleets. The potential bias from failing to account for 

 variation in economic capacity utilization is investigated 

 in the third section. We discuss the data, empirical 

 issues, and the construction of index numbers for the 

 U.S. tropical tuna purse-seine fleet in the fourth sec- 

 tion, and then we develop the implicit price indices and 

 report and interpret results of the empirical analyses 

 in the fifth section. 



Total-factor productivity 



The standard procedure for estimating total-factor pro- 

 ductivity is derived from the economic theory of pro- 

 duction. In common-property natural resource indus- 

 tries, the production function expresses a stock-flow 

 relationship between the resource stock and the flow 

 of resource extraction or output from the production 

 activity in any given time-period. An important con- 

 sideration when measuring productivity growth in 

 fishing industries is defining the role of the common- 

 property resource stock in the production technology. 

 Rather than treating the common-property resource 

 as a conventional input (Scott 1954, Clark 1976, 

 Dasgupta and Heal 1979), it is more appropriately 

 specified as a constraint to the production technology. 

 The fish stock is a biological constraint on the produc- 

 tion technology because its abundance affects the pro- 

 duction environment within which fishing firms oper- 

 ate, but it is beyond the control of any individual firm. 

 That is, the use of conventional inputs such as capital, 

 labor, and energy is conditional upon expected 

 resource-abundance levels. Changes in resource abun- 

 dance shift the production technology. McFadden 

 (1978) develops this approach by treating environmen- 

 tal parameters (such as resource abundance) in a man- 

 ner similar to disembodied technical change; i.e., 

 technological progress due to more efficient use of ex- 

 isting inputs. Finally, resource abundance is a techno- 

 logical constraint because the total catch cannot exceed 

 the abundance available, and an increase (decrease) in 

 resource abundance allows an increase (decrease) in 

 catch for any given level of input usage and state of 

 technology.- 



^Gordon (19.54) similarly treated biological abundance as a techno- 

 logical constraint. Gordon (p. I'M')) states, "For each given level of 

 population, a larger fishing effort will result in larger landings. Each 

 population contour is, then, a production function for a given popula- 

 tion level." Moreover, as Gordon noted, this approach does not 

 preclude the impact that increases in catch typically have in reduc- 

 ing the resource stock. If resource abundance was in.stead another 

 factor of production, like labor or capital, then changes in resource 

 abundance would imply movements along the existing production 

 function rather than shifts up or down the production function. 



When the fish stock is treated as a technological con- 

 straint, the production function, F, relates the max- 

 imum flow of output in time t (such as tons of fish 

 extracted), Y{t), to the flow of iV-i-1 inputs, Xi{t), 

 X2{t ), . . . ,X^ + 1 , the state of technology represented 

 by A{t ),^ and abundance of the fish stock indexed by 

 Bit): 



Y{t) = F[Xi{f). X.it),. . .,X^.,,(t)', A(t), B(t)]. (1) 



Growth-accounting framework 



Total-factor productivity measures are derived from 

 equation (1) using the growth-accounting framework 

 and economic index numbers.'' This approach accounts 

 for the growth in output flow over time by partition- 

 ing this output growth among the growth in inputs, 

 technical progress, and changes in resource stock abun- 

 dance. Total-factor productivity is then measured as 

 the residual in the growth of output flow after account- 

 ing for all of the measurable sources of growth. 



Under the growth-accounting framework, a constant- 

 re turns-to-scale production function is as.sumed, so that 

 a proportional increase in inputs yields a proportional 

 increase in output flow for any given level of resource 

 stock abundance and state of technology. Movement 

 in time t is assumed to lead to improvements in the 

 state of technology, so that 6FI6A (t )>0 (Solow 1957). 

 Following conventional practice, we further assume a 

 particular form of technological change, Hick's-neutral 

 disembodied technical change.^ Moreover, 6F/6B{t)>0, 

 so that increases (decreases) in resource stock-size 

 allow an increase (decrease) in the flow rate of extrac- 

 tion for any given input bundle and state of technical 

 progress. We assume a Schaefer (1957)-tyf:)e produc- 

 tion technology, and further assume that changes in 

 resource stock-size are Hick's neutral, so that the 



^The state of technology refers to the current level of technology 

 or kind of producti<in process utilized. For e.xample, the current state 

 of technology in the U.S. tuna fleet is represented by purse seining 

 with some level of usage of vessel electronics. 



^For a discussion of some of the limitations to the growth-accounting 

 approach to measuring total-factor productivity, see Nelson (1981). 



''Technological change or progress refers to the changes in a pro- 

 duction process that come from the application of knowledge. These 

 changes in the production process can be realized in various ways: 

 through improved methoris of utilizing existing resources, such that 

 a higher catch-rate per unit of input ("effort") is obtained for a given 

 level of resource stock abundance, often referred to as disembodied 

 technological change; through changes in input quality, referred to 

 as embodied technological change; or through the introduction of 

 new processes and new inputs, which can be either (or both) disem- 

 bodied and embodied technological change. 



Hick's neutral technological change, whether disembodied or em- 

 bodied, means that the technological advance does not change the 

 proportions in which different inputs are u.sed. Thus, for example, 

 after technological change, capital, labor, energy, and any other in- 

 puts woul<l be combined in the same proportions as before. 



