90 



Fishery Bulletin 88(1). 1990 



Productivity measures adjusted for 

 capacity utilization 



The total-factor productivity growth rates presented 

 in cohimn (3) of Table 1 incorporate the third capital 

 index: the annual flow of capital services from the size- 

 differentiated capital stock, ton-days-absent. Since the 

 number of ton-days-absent directly reflects the degree 

 to which economic capacity is utilized, resulting mea- 

 sures of total-factor productivity growth are not sub- 

 ject to a capacity-utilization bias as are the growth rates 

 shown in columns (1) and (2) of Table 1. 



The effects of adjusting for CU are revealed in 

 Table 2 by comparing the rates of change in the fleet's 

 capital stock and the fleet's flow of capital services: 

 fleet carrying capacity and ton-days-absent reported 

 in columns (3) and (4), respectively. Between 1982 and 

 1983, fleet carrying capacity decreased 18%, while ton- 

 days-absent decreased 15%. This means that the re- 

 duced fleet was fishing more intensively, and that a 

 measure of productivity growth based on the stock of 

 capital or fleet carrying capacity, without correcting 

 for the degree of capacity utilization, will be biased up- 

 wards. Similarly, comparing growth in fleet carrying 

 capacity and ton-days-absent between 1983 and 1984 

 reveals a greater decline in the latter relative to the 

 former. Therefore, a smaller fleet capital stock is util- 

 ized (fished) proportionately less, and productivity 

 growth based simply on the capital stock (carrying 

 capacity) will be understated. 



Column (4) of Table 1 reports growth in total factor 

 productivity for the U.S. tropical tuna fleet, where 

 changes in fleet carrying capacity— changes in the stock 

 of capital— are corrected for variations in the rate of 



capacity-utilization. In this case, the capacity utiliza- 

 tion adjustment is based on vessel design or engineer- 

 ing characteristics which act to establish an upper limit 

 on fleet output in a physical sense. To estimate fleet 

 engineering capacity, we assumed that each vessel was 

 capable of making three fishing trips annually, filling 

 its hold on each trip. Thus, maximum fleet output in 

 each year is three times the fleet's carrying capacity. 

 The ratio of actual fleet output (the total quantity of 

 tuna delivered to canneries) to maximum potential fleet 

 output estimates the degree of capacity utilization. 



Changes in the rate of capacity utilization using the 

 engineering adjustment are shown in column (6) of 

 Table 2. These capacity-utilization rates were then used 

 to derive the engineering-adjusted total-factor produc- 

 tivity growth rates presented in Table 1, column (4). 

 Comparing the total-factor productivity growth rates 

 in columns (2) and (4) of Table 1 discloses the extent 

 of the bias introduced by failing to account for varia- 

 tions in the degree of capacity utilization. 



The capacity-utilization adjustment is made to ap- 

 proximate the actual flow of services from the quasi- 

 fixed factor, the capital stock. Therefore, one might 

 expect the total-factor productivity growth rates using 

 ton-days-absent (Table 1 , column [3]) to closely corre- 

 spond to those based on correcting for cajjacity utiliza- 

 tion using the engineering approach (Table 1, column 

 [4]). The fact that they do not points out that, in an 

 economic sense, capacity-utilization adjustments ex- 

 plicitly recognize that quasi-fixed factors are not always 

 utilized at the long-run equilibrium or full economic- 

 capacity-output level, the level of output which mini- 

 mizes the per-unit-cost of production. Under these cir- 

 cumstances, engineering-capacity output, as we have 



