Hernck and Squires Measuring fishing fleet productivity 



91 



Table 3 



Implicit aggregate output and input price and total-factor- 

 productivity chain indices. 



Note: Implicit price indices formed by Fisher's weak factor- 

 reversal relationship. See text for details. Total-factor pro- 

 ductivity, calculated as Tornqvist bilaterial chain indices, ad- 

 justed for variations in biomass and capacity utilization (using 

 ton-days-absent). 



A 

 / \ 

 \ 



Total Factor / 

 Productivity 



\ Aggregate 



\ Input Price 



\ 



Figure 1 



Total-factor productivity and implicit price indices. 



defined it, should be greater than full economic-capa- 

 city output. Thus, the engineering capacity-utilization 

 rates should be biased downward, and the correspond- 

 ing productivity growth rates will inherit this bias. The 

 preferred capacity-utilization correction, consistent with 

 economic theory, should adjust the capital stock by its 

 time in use to provide a flow measiu-e of capital services. 



Productivity measures adjusted for 

 biological abundance 



The total-factor productivity growth rates presented 

 in column (5) of Table 1 are based on the actual flow 

 of capital services and the growth of the yellowfin 

 biomass in the CYRA (Table 2, column [5]). Compar- 

 ing columns (3) and (5) of Table 1 indicates that the in- 

 crease in the CYRA yellowfin biomass during most of 

 the period acts to partially offset gains in total-factor 

 productivity otherwise attributable to technical pro- 

 gress. The resource and capacity utilization adjusted 

 total-factor productivity growth rates from Table 1 , col- 

 umn (5) are used to compute the index of total factor 

 productivity for the U.S. tropical tuna fleet shown in 

 Table 3 and in Figure l.^" 



Implicit output and input price indices 



Fleet economic performance depends upon the real 

 prices of outputs and inputs in addition to total-factor 



"These period-to-period changes in total-factor productivity, i.e., pro- 

 ductivity growth, were computed following footnote 6. Next, the 

 exponent is taken of each value in column (5) of Table 1, giving 

 TFP,i^. The Tornqvist bilateral-chain index is then formed 

 following Equation (4), to give the first column of Table 3. Note 

 that the value 1.000 for 1981 is the exponent of zero, where zero 

 refers to the zero change for the first period. 



productivity. Corresponding to the aggregate output 

 and input quantity indices are implicit aggregate out- 

 put and input prices. These are calculated by a rela- 

 tionship due to Fisher (1922), which states that the pro- 

 duct of the price index times the quantity index equals 

 the expenditure ratio between the two time-periods. 

 The implicit price index for an output (or input) can be 

 interpreted as the ratio of the price level in period / -i- 1 

 to the price level t. Fisher's relationship for the price 

 (PI) and quantity (QI) indices for aggregate output i' 

 can be written as: 



P/(P,,P,,i,F,,F,,,)Q/(P,,P,,,,y,, }',,,) 



= I,p„,,F,„,/I,p„y„. (6) 



Given either a price index or quantity index, the other 

 function can be defined implicitly by Equation (6). 



Implicit Tornqvist bilateral-aggregate output-price 

 and input-price chain indices for the U.S. tropical tuna 

 purse-seine fleet, along with the resource-abundance 

 adjusted total-factor productivity index, are presented 

 in Table 3 and in Figure 1. Increases in total-factor pro- 

 ductivity or output prices, or both, improve the fleet's 

 economic performance, while increases in input prices 

 worsen the fleet's economic performance. 



Taken together, the changes in total-factor produc- 

 tivity, aggregate input-price, and aggregate output- 

 price indices shown in Figure 1 and Table 3 indicate 

 that the 1981-85 period was highly unstable with re- 

 gard to the fleet's economic performance. Herrick and 

 Koplin (1986, 1987) point out that this was a time of 

 massive restructuring in the U.S. tuna industry, dur- 

 ing which the U.S. fleet began a significant shift of its 

 operations from the eastern to the western Pacific 



