1. POTENTIAL METHODS FOR ASSESSING CAPACITY AND CAPACITY UTILIZATION
There should be little doubt that if sufficient information were available, the economicbased measures of capacity and capacity utilization are appropriate for determining harvesting capacity in fisheries. Alternatively, the restricted frontier profit or cost function with economic and technical efficiency included could serve as the basis for obtaining the variable input and output levels consistent with the capital stock, resource levels, and the goals and objectives of fisheries management.
With a rigorous, theoretical, economicbased assessment, however, one must ask whether or not this would provide practical information for fisheries management. For example, how would managers implement a policy prescription suggesting the elimination of $3,000,000 in capital stock? Since managers and policy makers appear to be primarily concerned about physical capacity and overcapitalization (e.g., level of inputs relative to catch), measures of capacity should ideally convey information about catch, fishing mortality, costs, industry and fleet structure (e.g., number of large vs. small boats), employment, and profits. Such measures of capacity should also ideally convey information about net benefits to society.
From a practical perspective, the measurement and assessment of harvesting capacity could proceed along several lines of thought. The levels of capital, labor, energy, materials, other inputs, and catch could be determined in a dynamic setting which maximized net benefits to society subject to biological constraints and the underlying form of the technology. Such an approach would allow policy makers to compare optimal levels to actual levels and subsequently assess the necessary reductions. This is an appropriate approach, but one which would likely be severely limited by inadequate data, extreme uncertainty associated with resource conditions and the technology, and various goals and objectives of resource management. It also begs the questions of a steadystate solution vs. a bangbang solution, determination of the appropriate social rate of discount, the nature of industry structure in response to capacity reduction programs, and the possible need for a cautious approach which ensures no excess harvesting.
In Appendix XI, we explore various empirical approaches for assessing capacity and capacity utilization. The primary focus is on determining capacity and capacity utilization and identifying operating units which might be targeted for decommissioning. A secondary focus is to identify procedures which can be used to assess capacity and capacity utilization given the data typically available on fisheries. We considering the following procedures for determining capacity and capacity utilization in fisheries: (1) peaktopeak; (2) stochastic frontier; and (3) data envelopment analysis (DEA).
2. PEAKTOPEAK
Of the various approaches for assessing capacity and capacity utilization, the peaktopeak method is perhaps the easiest to use. Ballard and Roberts (1977) appear to be the first researchers to apply this approach to fisheries. The peaktopeak approach is a variant of the concept of economic capacity but provides information more closely resembling that of physical capacity. The approach focuses on outputs but certainly can be modified to reflect inputbased measures; alternatively, it is easy to calculate capacity and CU relative to outputs and solve back to assess an inputbased measure (i.e., level of inputs associated with each level of output, capacity, and capacity utilization).
The peaktopeak approach assumes an underlying production function. The simplest form is to start with a CobbDouglas (similar to shortrun Schaeffer model) specification of production:
U_{t }= a_{0} L_{t}^{a1 }K_{t}^{a2} F_{t}^{a3} T_{t}
where Y is catch, L is labor, K is capital, F is fuel, and T is a technology trend. If a_{1} + a_{2} + a_{3} sum to one, the technology displays constant returns to scale (i.e., doubling all input levels causes output to double). Given the functional form, a composite or aggregate input V_{t} can be defined:
V_{t }= L_{t }^{a1} K_{t }^{a2 }F_{t }^{a3}
To assess capacity utilization, output, Y, is divided by the composite or aggregate input, V, and set equal to a_{0} T_{t}.
The technology trend, T_{t}, must be estimated:
In this case, the level of technology in a particular time period, t, is determined by the average rate of change in productivity between peak years. The values of m and n correspond to the length of time from the previous and following peak years. The value of a_{0} is assumed to equal one.
For the purpose of using the peaktopeak method, we present the Dungeness crab example offered by Ballard an Roberts [Table 1]. The peaktopeak approach is particularly useful when data are extremely limited (e.g., the only data available are for catch and number of operating units). With the approach a technology trend, based on the ratio of output to input, is calculated which allows potential output to be estimated. The utilization rate is subsequently calculated as the ratio of observed to potential output.
Table 1. Catch, operating units, and capacity utilization in the Dungeness crab fishery, 19591973.
Year 
Catch 
Operating 
Capacity 
Catch Rate 

Units 
Rate 
Possible 
Observed 

1959 
36.95 
87.30 
100.0 
423.2 
423.2 
1960 
36.16 
92.30 
90.3 
434.0 
391.7 
1961 
32.70 
90.55 
81.2 
444.8 
361.1 
1962 
23.36 
88.01 
58.3 
455.6 
265.5 
1963 
24.86 
87.49 
60.9 
466.4 
284.2 
1964 
23.04 
90.82 
53.2 
477.2 
253.7 
1965 
28.91 
100.36 
59.0 
488.0 
288.1 
1966 
39.72 
93.91 
84.8 
498.8 
422.9 
1967 
42.44 
91.70 
90.8 
509.6 
462.8 
1968 
49.97 
96.03 
100.0 
520.4 
520.4 
1969 
48.06 
122.44 
73.5 
533.6 
392.5 
1970 
58.51 
130.08 
82.2 
546.9 
449.8 
1971 
41.61 
157.43 
47.2 
560.2 
264.3 
1972 
28.25 
179.52 
27.4 
573.4 
157.3 
1973 
14.37 
171.45 
14.3 
586.7 
83.8 
While the peaktopeak approach has considerable merit as one possible method for examining harvesting capacity, it is also quite limited. For one thing, it completely ignores the biological characteristics of fish (e.g., the concept of maximum sustainable yield). It also fails to directly link back to input utilization which is the main focal point of harvesting capacity.
There are some possible approaches for mitigating the limitations of the peaktopeak approach. A sustainable yield function could be estimated (e.g., ). The maximum sustainable yield could be estimated and compared to observed harvest levels over time to estimate capacity and capacity utilization. Alternatively, fishery independent data could be used to estimate maximum yields. The level of effort corresponding to the maximum sustainable yield could subsequently be calculated or estimated; the estimated or calculated level of effort would be the level of effort associated with harvesting capacity.
The need to modify the peaktopeak approach really becomes a question of what information management desires. If management desires information on actual capacity and capacity utilization in the strict economic sense (i.e., what is the potential harvest given the size of the fleet and the potential utilization of inputs in the absence of resource constraints), the peaktopeak approach provides relatively useful information.
3. FRONTIER APPROACH
An alternative to the peaktopeak approach is the frontier approach. With the frontier approach, the maximum output possible given input levels is estimated. The frontier may be estimated at the firm level or for the fleet. The more aggregation, the less precision one obtains.
There are two basic options for consideration: (1) nonparametric frontier, and (2) stochastic frontier.^{16} Since both approaches provide similar information and programs are readily available to estimate the stochastic frontier, we focus additional attention on using the stochastic frontier to assess harvesting capacity. With some modification, we may estimate the frontier and assess the relationship between maximum output and input levels. We adopt the modification developed by Battese and Coelli (1993) in which a term for inefficiency is expressed as a function of variables which might influence inefficiency.
In simple terms, the stochastic frontier approach amounts to specifying the relationship between output and input levels and using two error terms. One error term is the traditional normal error term in which the mean is zero and the variance is constant. The other error term represents technical inefficiency and may be expressed as a halfnormal, truncated normal, exponential, or twoparameter gamma distribution. Technical efficiency is subsequently estimated. Letting U be the technical inefficiency error term, technical efficiency is estimated as the ratio of the expected value of the predicted frontier output conditional on the value of u to the expected value of the predicted frontier output conditional on the value of u being 0.0:
where E is the expectations operator, Y^{*} is the predicted frontier output, U is the error term for inefficiency, and X is the vector of inputs used to produce Y.
Using the Dungeness crab data, a frontier function specified as a transcendental is estimated:
All parameters except that for year were statistically significant at the five percent level of significance and a likelihood ratio test of the existence of a frontier was also significant.
The predicted frontier values were higher than the observed values [Table 2]. The onestage routine of Battese and Coelli (1993) permit a determination of the number of operating units at which inefficiency is zero. Solving for the number of operating units yielded an estimate of 89.31 operating units. Operating units in excess of 89.31 causes severe deviations from the frontier output. Relative to the number of operating units in the Dungeness crab fishery between 1959 and 1973, the fleet was clearly overcapitalized in 1965 and from 1969 through 1973. Production was found to be relatively inefficient for all years except 1959, 1967, and 1968. Between 1969 and 1973, technical efficiency declined by 61.4 percent. The period coincided with a large expansion in the number of operating units78.54 percent.
Table 2. Estimated Frontier Output Conditional on Effort, Dungeness Crab
Year 
Operating Units 
Observed Output 
Capacity Output 
Capacity Utilization 
1959 
87.30 
36.95 
37.72 
97.9 
1969 
92.30 
36.16 
45.03 
80.3 
1961 
90.55 
32.70 
42.66 
76.7 
1962 
88.01 
23.36 
39.10 
59.7 
1963 
87.49 
24.86 
38.46 
64.6 
1964 
90.82 
23.04 
43.44 
53.0 
1965 
100.36 
28.91 
56.52 
51.2 
1966 
93.91 
39.72 
48.15 
82.5 
1967 
91.70 
42.44 
45.12 
94.1 
1968 
96.03 
49.97 
51.39 
97.2 
1969 
122.44 
48.06 
72.58 
66.2 
1970 
130.08 
58.51 
72.01 
81.3 
1971 
157.43 
41.61 
51.90 
80.2 
1972 
179.52 
28.25 
30.82 
91.7 
1973 
171.45 
14.37 
38.28 
37.5 
In the case of assessing capacity and capacity utilization in fisheries, the DEA approach of Fare et al. (1994) or Forsund (1995) may be utilized. By appropriately specifying a DEA problem, the ith input utilization rate and plant capacity utilization rates may be determined. Given the utilization rate of capital (the capital contained in the vessel and gear), the capacity of capital could easily be estimated subject to maximum technical, scale, allocative, and/or economic efficiency.
The determination of capacity and capacity utilization may be done at the individual firm level or relative to fleet performance. Relative to fisheries and the needs of resource managers, the preferred solution should probably be relative to individual vessel level production. By rearranging observations in terms of maximum efficiency, the number and characteristics of operating units could be determined by simply adding output of each DMU until the total equaled a specified TAC.
As an example of how the DEA approach might be used to determine capacity and capacity output and the number and type of operating units which should be decommissioned, consider the MidAtlantic sea scallop, Placopecten magellanicus, fishery. We have detailed data on a per trip basis, which includes information on days at sea, crew size, fuel used, ice, length of trip, output, vessel characteristics, supplies used, and materials. While we could solve for all variables, we only consider resource abundance, output, days at sea, and crew size. We also only consider the levels of inputs and output which maximize technical efficiency; a similar solution could be obtained for maximum profit or revenue or minimum cost. We specify our problem and solution relative to an outputbased measure of efficiency (i.e., we measure efficiency relative to the output set taking input quantities as given); this appears to be consistent with the intent of the Expert Consultancy group to determine maximum production capability given a fleet. An inputbased measure could also be developed; an inputoriented measure indicates the potential reductions in input levels which would yield the same level of output.
We have a panel data set for ten vessels operating between 1987 and 1990; one vessel left the fishery in 1988. The vessels are relatively homogeneous in characteristics and operations. The data set is inadequate for assessing capacity and capacity utilization for the actual fleet; we only use the data set to illustrate a possible approach for assessing capacity and CU. We obtain 581 estimates of technical efficiency and subsequently the frontier or maximum output. We restrict our analysis, however, to 1990.
In 1990, the nine vessels operating in the fleet landed 1,308,520 pounds of scallop meats [Table 3]. The overall average efficiency was 0.573. In contrast, maximum output or the output with nine vessels operating efficiently was estimated to equal 2,301,910 between 1987 and 1990; the capacity output for the one vessel which exited the fishery in 1988 was excluded from the analysis. CU was estimated to equal 0.568. That is, the capacity output was estimated to equal 2.30 million pounds while CU in 1990 equaled 0.568.
We find that the fishery has considerable excess capital utilization in the shortrun. With simply efforts by captains and crew to be more efficient, catch could have been increased from 1.31 million pounds to 1.52 million pounds. With reorganization of trips or simply increasing the number of trips per year and being more efficient, total output could be 2.70 million pounds per year. Relative to the potential frontier output given the same number of days and trips or with respect to reorganizing or restructuring fishing activities, the fleet could harvest considerably more than the observed 1.31 million pounds. In essence, the fleet had considerable excess capacity. If, for example, the first three boats with minimum efficiency were eliminated from the fleet and the remaining vessels became more efficient or took more trips, the same overall catch could easily be maintained.
Table 3. Outputbased technical efficiency and potential output
Boat 
Efficiency 
Total Catch 
Frontier Catch 
Reorganized For Frontier Catch 
5 
0.56 
129.4 
162.3 
297.9 
9 
0.58 
138.7 
168.3 
332.9 
3 
0.59 
117.7 
141.5 
267.6 
6 
0.60 
137.5 
120.3 
314.5 
10 
0.64 
152.8 
177.5 
308.1 
4 
0.67 
171.5 
211.2 
313.2 
1 
0.69 
163.3 
199.9 
309.9 
8 
0.72 
137.0 
154.3 
264.0 
7 
0.73 
160.6 
183.7 
291.2 