88 



Fishery Bulletin 



1990 



Failure to capture this additional source of variation 

 creates a potential bias in the true productivity resid- 

 ual, A /A, which varies with the rate of capacity 

 utilization. 



Methods of capacity utilization adjustment 



When the firm is in temporary or short-run equilibrium 

 rather than long-run equilibrium, the productivity 

 residual formula can be adjusted for variations in CU 

 in two different ways. The first relaxes the assump- 

 tion that service flows are proportional to stocks by ad- 

 justing the stock of a quasi-fixed input to reflect its flow 

 of services^ (Berndt and Fuss 1986). Thus, rather than 

 specifying capital as a stock (e.g., the number of vessels 

 in the fleet), capital is measured by its flow of services 

 or total time of utilization (e.g., as fleet vessel-days 

 fished). Such a flow adjustment corresponds to an 

 economic notion of CU, because we assume that a pro- 

 ducer's decision to increase or decrease running and 

 fishing time is the outcome of an economic optimiza- 

 tion process. 



The second approach to adjusting the productivity 

 residual for CU variations uses engineering notions of 

 the proportion of available productive capacity that is 

 actually being utilized. Let capacity output Y* repre- 

 sent the maximum possible output level corresponding 

 to "normal" input usage, existing technology, and the 

 stocks of quasi-fixed inputs. A measure of capacity 

 utilization is then obtained by the identity: CU= YIY*, 

 where Y is the observed output level. 



Data and empirical issues 



Tornqvist output indices for the U.S. ti'opical tuna 

 purse-seine fleet were constructed using annual deliv- 

 eries of skipjack and yellowfin tuna by the fleet to U.S. 

 canneries and the corresponding dollar values of these 

 deliveries. Weighted exvessel implicit prices for skip- 

 jack and yellowfin tuna were calculated by dividing the 

 total dollar value of cannery receipts for each species 

 by the total volume of cannery receipts. Revenue and 

 cannery receipts data were obtained from the South- 

 west Region, National Marine Fisheries Service 

 (NMFS). Dollar values were deflated by the GNP 

 implicit price index. 



To construct the input indices, four major categories 

 of factors used in owning and operating a tropical tuna 



•An alternative approach to accounting for variations in economic 

 capacity utilization adjusts the cost or income shares rather than 

 the flows of capital services. Berndt and Fuss (1986) and Hulten 

 (1986) develop this approach, and Squires and Herrick (1988) pro- 

 vide a fisheries application. This approach is well suited when ac- 

 curate and detailed data on running and fishing time are unavailable. 



purse seiner wei'e identified: labor, capital, fuel, and 

 other intermediate inputs (transshipment services, 

 repairs, gear, insurance, helicopter services, travel, and 

 other). Constant-dollar unit prices for these inputs were 

 estimated based on purse-seine expenditure data 

 reported by the U.S. International Trade Commission 

 (ITC 1986). 



The labor index incorporates the flow of lal)or ser- 

 vices derived by multiplying estimated total days ab- 

 sent (at sea or absent from port) per vessel per year 

 by 19 crew members, which is the assumed average 

 crew size in each year of the period. The unit price of 

 labor, cost per crew-day-absent, was estimated by 

 dividing the sum of the ITC's reported annual crew- 

 related expenditures per vessel by a measure of annual 

 crew-days-absent per vessel. 



Three different capital indices were constructed for 

 the total-factor productivity analysis of the U.S. 

 tropical tuna fleet. The first two capital indices both 

 assumed that firms were in long-run equilibrium and 

 that the flow of capital services was proportional to the 

 capital stock. The first capital index specified capital 

 as the annual number of vessels in the fleet. The sec- 

 ond capital index captured the effect of different vessel 

 sizes (where size is a measure of the vessel's hold or 

 carrying capacity) upon catch rates by measuring 

 capital as the annual carryitig capacity of the fleet. 



The third capital index not only captured the effects 

 of different-sized vessels, but also accounted for actual 

 changes in the flow of services from this size-differen- 

 tiated capital stock. In this third case, the flow of 

 capital services was measured in annual ton-days- 

 absent, an aggregation of each vessel's cai-rying capa- 

 city multiplied by the number of days it spent at sea 

 during the year. Measures of annual ton-days-absent 

 were derived from purse-seine-tleet activity data com- 

 piled by NMFS. The cost share for capital used in 

 construction of all the capital indices was its market 

 rental price, the sum of the annual interest expense and 

 reported annual depreciation per vessel from the ITC 

 sample. 



The fuel index was constnicted by dividing the annu- 

 al fuel expenditure per vessel (from the ITC sample) 

 by average fuel prices provided by the American Tuna 

 Boat Association. Fuel consumption per vessel was 

 then multiplied by the number of vessels in the fleet 

 resulting in the aggregate annual fuel consumption. 



The index of other intermediate inputs was derived 

 by deflating the fleet's nominal expenditure on this 

 category of inputs by the producer price index for in- 

 dustrial commodities. This approach represents the 

 collective use of these inputs in real terms. The nominal 

 expenditure for this category of inputs divided by the 

 corresponding deflated ex])enditure was used as a 

 proxy for the unit price of other intermediate inputs. 



