The methods available for deriving both output- and input-based measures of capacity and capacity utilization largely depend upon the level of existing data. (See Appendix A for a discussion of preferred methods for estimating capacity, given different levels of data.) If data are extremely limited or unavailable, surveys and rapid appraisal techniques can be used to derive measures of capacity and capacity utilization. If detailed costs and earnings information are available, it may be possible to estimate various economic, either static or dynamic, concepts of capacity and capacity utilization using a wide array of mathematical or statistical methods. The most typical situation, however, is one in which data are known only on: physical input levels, vessel characteristics, and output levels. Even in this case, it may be possible to use a wide range of mathematical or statistical techniques to estimate capacity and capacity utilization.
Rapid appraisal (RA) is a participatory research technique developed to obtain data when formal data collection procedures were not practical. The technique often has been used in developing countries where records or information were not available, and the most expeditious method to obtain data was to rely upon the recall of participants in the fishery. The technique places particular emphasis on the collection of local knowledge and combining it with knowledge from outside.
RA is to a large extent an informal method of data collection that has characteristics of both the formal survey and the extraction of information through the use of expert knowledge. The technique is exploratory and highly interactive. It generally involves rapid and progressive learning, with information analyzed and revised in the field to allow further clarification or re-estimation.
The technique largely involves informal interviews conducted with key participants in the fishery. Key participants include fishers, fisher representatives and others who have input into the production process (e.g. head fisher or person in village responsible for managing the fishery). The technique is consequently relatively labour-intensive, because a wide range of participants need to be questioned in the field.
For the purpose of capacity measurement, questions can be asked about both current and past catch levels, as well as activity levels and potential activity levels. Where quantitative estimates are not possible, relative estimates can be derived through the use of drawings and diagrams. For example, ten dots may represent current catch while 12 dots represent best-ever catch. Average catch composition can be illustrated through use of a pie chart with the participants, with each segment representing their perception of species composition. Questions also can be asked about how much fishing activity may increase, why the activity is at its current level, and potential constraints that would impose limits on fishing activity.
The information is compiled in the field and quantified as much as possible. The information is supplemented with other quantitative information available (e.g. quantity of sales on a central market can be used as a benchmark). Participants are re-interviewed, and the compiled information is presented for cross-checking and validation purposes. This process may need to be repeated several times. Such repetition allows fine-tuning of estimates to provide values that are believable to the participants in the fishery.
The technique is likely to enable, at the very least, qualitative estimates of capacity and capacity utilization. Depending on the level of knowledge in the fishery, it may be possible to also derive more precise estimates of capacity and capacity utilization, and on a per-species basis.
Surveys can be undertaken to collect subjective but quantitative estimates of capacity. Such surveys are often conducted to assess capacity output in other industries. For example, in the United States, surveys are employed by the Federal Reserve and the United States Census Bureau to estimate capacity and capacity utilization in a number of industries to supplement more directly quantified estimates.
Like RA, this is particularly useful if data are limited or non-existent. Participants can be surveyed to determine their current catch and activity (e.g. days fished) as well as provide subjective estimates of their potential activity and corresponding potential catch. A survey may require less labour than a RA, but it also provides less possibility for feedback and clarification of the analysis with the industry.
Several separate surveys may be required to estimate capacity and potential overcapacity, each directed at different groups in the industry. Individual participants (i.e. fishers) can be asked to estimate their catch, effort and potential effort. From this, an estimate of potential catch (i.e. output capacity) of each individual can be derived (assuming a linear relationship between potential effort and potential catch). In some cases, it may be possible to derive estimates of catch by species. The more disaggregated the data request, the greater the potential for errors to compound, particularly if most of the information provided by the interviewee is being recalled from memory. Ideally, if detailed information is to be collected on a species basis, then some form of logbook programme should be established and fishers record their catches as they occur.
The reliability of survey estimates will vary depending on the degree to which records of current and recent activity are readily available. If the information is based solely on memory (i.e. the fishers do not keep any records), the potential to overestimate (or underestimate) the average catch and potential effort is considerable. As a result, the estimate of capacity output is most likely to be unreliable or highly imprecise. Data collected by such a survey should be regarded as indicative rather than accurate. When fishers maintain good records, potential bias will decrease, and more comprehensive data construction and development are possible.
The reliability of survey estimates will depend also on the size and representativeness of the sample. Ensuring that a wide cross-section of fishers is surveyed will help improve reliability of the estimates. Reliability also will improve with increased sample size, although there is a trade-off between reliability and survey cost. Doubling the sample size will not double the reliability of the results but will smooth potential errors.
Additional information also can be collected from fishers at the same time as the minimum information requirements for capacity estimation. This may include more information on the fishing activity, the boat (e.g. size, engine power if mechanized) and the gear used. Full surveys of fishing activity, including costs and earnings, also can be undertaken. The level of data collected through the survey will depend on the ultimate use of these data, and the cost of acquiring it.
To estimate capacity from the survey information, an estimate of the total number of participants in the fishery is required (unless the survey includes all participants - a census of producers). This may involve a second survey of regional industry representatives (e.g. head fishers) or purchasers. Such a survey could be used to provide estimates of participation rates (i.e. number of boats or individuals) in the fisheries.
Surveys of experts (e.g. biologists, industry representatives) also can be undertaken to provide estimates of capacity output and utilization. This is potentially a more expedient method than collecting a sample from individual participants in the fishery and deriving estimates of capacity from the bottom up. However, if expert opinions vary, some subjective weighting needs to be applied to each opinion to derive a composite estimate, or more formal approaches need to be undertaken. One such formal approach is described under the section outlining methods for assessing target capacity (in Section 5).
The peak-to-peak approach assumes a direct relationship between the level of inputs and the level of output. An index of catch-per-unit input (e.g. catch per day or catch per boat) is derived from the data. An assumption is made that peak levels of catch-per-unit input equate to complete capacity utilization. The peaks are assumed to represent years that the fishery was achieving the maximum output in the short run, given harvesting technology and capital stock. Hence, lower catch rates are assumed to indicate underutilization of capacity. Further details on the method, including an example of its application, are presented in Appendix B.
The technique also allows for technological change over time, such that the difference in catch rates between two peak years is assumed to be the result of changes in technology. Capacity catch rates in the years between the peaks are estimated as a function of the estimated change in technology between the peaks, which is assumed to be a linear trend. (In recent years, however, researchers have developed quite sophisticated analytical methods to better determine trends in technical progress.) Capacity utilization is then estimated as the ratio of the observed catch rate to the derived capacity catch rate. Capacity output is estimated as the product of the level of inputs and the capacity catch rate.
An advantage of this technique is that it only requires information about one input and one output. Consequently, it represents the most widely applicable and least demanding of data in all mathematical methods for estimating capacity and capacity utilization (Kirkley and Squires 1999). A disadvantage of the technique, however, is that it does not allow for changes in the stock between years or any other structural changes affecting input-output relationships. Changes in catch rates are assumed to be a function of changes in technology only. A decline in stock size between two peak years would be interpreted as capacity underutilization.
Peak-to-peak analysis has been applied in fisheries by Ballard and Roberts (1977), Ballard and Blomo (1978), and Hsu (2003). Further information on the technique, including the mathematical specification of the approach, also is provided in Kirkley and Squires (1999).
Stochastic production frontiers indicate the maximum expected output for a given set of inputs. They are derived from production theory and are based on the assumption that output is a function of the level of inputs and the efficiency of the producer in using those inputs. Explicit representation of this relationship as a production frontier allows a detailed characterization of input and output relationships and returns that facilitates quantification of the diagrams and equations presented in Section 2.
A function is statistically estimated that defines the output associated with the best practice use of the inputs, while also recognizing the stochastic nature of the data arising from mis- or un-measured determinants of production. The difference between actual output and the potential output is generally attributed to a combination of inefficiency and random error (i.e. the stochastic element in production). Methods have been developed to separate out the random component from the efficiency component, so that a more realistic assessment of potential output can be achieved. That is, large levels of output that may have occurred through chance rather than as a consequence of normal practice do not overly influence the estimates. As a result, derived measures of capacity output are consistent with the earlier definition that measures output under normal working conditions. Further details of the underlying theory and an example of its use are provided in Appendix C.
SPF methods have been used for the assessment of technical efficiency in a wide range of industries (including fishing). While derived from efficiency theory, these techniques can be readily modified to produce estimates of capacity utilization. This is achieved through incorporating only fixed inputs in the production function, such as boat numbers (in aggregated analyses) or engine power, boat size, or some measure of capital inputs when vessel level data are available. By excluding variable factors of production (e.g. days or hours fished), the frontier output for a given size (for example) of boat is essentially determined by the boats of that size that produced the greatest output, taking into account fluctuations in output levels that might be considered attributable to luck. Lower levels of output would indicate a combination of inefficient input use and capacity underutilization.
One advantage of the SPF technique over peak-to-peak analysis is that several inputs in the production process can be incorporated into the analysis. While it is possible to use the technique with a single input and output, it also allows recognition of other available information on the level of fishing inputs or other production determinants. Hence, all available input data can be used in the same analysis to produce a single measure of capacity utilization. This can include information on biomass stock (where available), so that the effects of stock changes can be directly incorporated into the analysis. As a result, low levels of output in some years resulting from low levels of the resource stock will not mistakenly be attributed to underutilization of capacity.
The technique can also be used to estimate changes in efficiency, versus those due to technological change, over time. While peak-to-peak analysis assumed that any change in the catch rate was due to changes in technology, the SPF method can separately identify such changes, as well as those associated with utilization. Independent identification of the impacts from resource stock fluctuations, however, requires incorporating information on stock levels into the analysis in order to distinguish the effects of changes in technology and stock abundance on catch rates. Alternatively, when data are available, the SPF can distinguish between embodied and disembodied technical change.
The technique can be applied to either aggregated (fleet level) data or to the individual fishing vessel level. The latter is the most desirable, although particular care must be taken to separate noise, efficiency and utilization fluctuations separately for estimation at this aggregation level. Capacity and capacity utilization estimated for individual vessels then can be aggregated to the fleet level, although this requires recognition of aggregation issues.
The technique does have some limitations, however. Like peak-to-peak, the standard technique can generally only be used to estimate capacity utilization for a single output. For multispecies fisheries, some form of aggregation, or more complex estimating methods and approximations, may be necessary. The resulting measures of capacity utilization and capacity output may then be difficult to interpret, particularly where fisheries management is undertaken on a species-by-species basis (e.g. using quotas).
Estimation of the frontier also requires one to specify a functional form for the production function. Many functional specifications of the underlying technology impose undesirable or potentially unrealistic restrictions on the underlying production technology (e.g. the Cobb-Douglas, which is a multiplicative function, imposes unitary elasticity of substitution between inputs). However, flexible functional forms, which minimize the number of restrictions imposed on the underlying technology, are widely available. The flexible forms permit parametric evaluation of different properties of the underlying technology, and thus the fact that SPF requires specification of the technology should not be viewed as a substantive limitation of the approach.
Estimation of efficiency and capacity utilization is a relatively complex statistical problem. Fortunately, special software has been developed that makes the econometric estimation of the measures quite straightforward. (See Sena, 1999.) However, there are a range of assumptions that need to be made regarding the specification of the model and distributional assumptions about the measure of capacity utilization, and, being a statistical process, the results may vary considerably from one model to another. Identifying the most appropriate model out of a range of alternative models requires substantial testing. Ideally, the analysis should be undertaken by someone with experience in econometrics who has an appreciation of the potential statistical problems that may occur.
Only limited attempts to estimate stochastic production frontiers for fisheries have been undertaken (Kirkley, Squires and Strand, 1995 and 1998; Coglan, Pascoe and Harris, 1999; Sharma and Leung, 1999; Squires and Kirkley, 1999). These have largely focused on the estimation of efficiency rather than capacity. Kirkley and Squires (1999) and Kirkley, Paul and Squires (2001) provide examples of these techniques applied to capacity estimation.
Data Envelopment Analysis (DEA) is a mathematical programming technique for estimating technical efficiency and capacity utilization. It is similar to SFP in that it estimates a frontier level of production and measures inefficiency and capacity utilization as deviations from the frontier. Unlike SPF, however, it does not require imposing any particular functional form of the production frontier on the data, and it is able to analyse both single and multiple outputs. Further details on the methodology and an example are presented in Appendix D.
The fact that species-specific measures can be derived allows aggregation of capacity measures across different fleet segments and fisheries for a given species. As a result, capacity estimates can be directly compared to the target capacity measures. Capacity utilization measures at the fleet level also provide additional guidance for managers as to where capacity management may be most required.
A drawback of the technique is that it does not take into account random variations in the data. As a result, an above normal catch (due to luck) would define the frontier and all capacity measures would be made relative to this level of output, which does not correspond to normal operating conditions. Consequently, measures of capacity utilization may be less than what would occur if favourable random elements were removed. Conversely, an unlucky vessel would be regarded as operating at well below capacity. This is less problematic, as it is expected that vessel output would be higher under normal conditions. These problems can be eliminated to some extent by averaging the data over a number of years, thus reducing the effects of random variations. In doing so, however, information on changes in capacity utilization over the period being examined is lost.
The data required for a DEA analysis are the same types of data required for SPF. With DEA, however, multiple output technologies may be examined more easily. There is no need to aggregate outputs, and species-specific capacity measures are possible. Like the SPF approach, multiple inputs can also be incorporated in the analysis if available. Moreover, since DEA is a linear-programming-based approach, it is possible to estimate capacity under a wide array of social, biological and economic constraints. For example, total allowable days at sea constraints can be imposed, although this also may be done within SPF by simulation methods. Similarly, where restrictions on gear are in place, their effects on capacity output can be assessed by removing the constraints. Cost and revenue information also can readily be included into the analysis to provide information on economic capacity utilization. (See, for example, Färe, Grosskopf and Kirkley, 2000)
In fisheries, the technique has been applied to the Malaysian purse seine fishery (Kirkley et al., 2003), United States Northwest Atlantic sea scallop fishery (Kirkley et al., 2001), Atlantic inshore groundfish fishery (Hsu, 2003), Pacific salmon fishery (Hsu, 2003), the Danish gillnet fleet (Vestergaard, Squires and Kirkley, 2003), English Channel multispecies multigear fisheries (Pascoe, Coglan and Mardle, 2000; Tingley, Pascoe and Mardle, 2003), the Scottish fleet (Tingley and Pascoe, 2003) and the total world capture fisheries (Hsu, 2003). Additional details on the mathematical specification of the technique are available in Färe, Grosskopf and Lovell (1994), Coelli, Rao and Battese (1998) and Kirkley and Squires (1999).
 Thompson et al.
(1986) and Tone (1999) offer a framework for consensus-making based on expert
opinion. Tone, in particular, offers a framework for deriving quantitative
estimates using expert opinion.|
 More recently, multi-output forms of stochastic production frontiers have been developed but remain highly complex. For a comprehensive summary, see Kumbhakar and Lovell (2000).
 The development of stochastic DEA models is currently a key area of research, but operational models are not currently available. Approaches have been developed to capture some of the random variability in data (e.g. chance constrained DEA). Details on some of the recent developments in this area are given in Cooper, Seiford and Tone (2000). Bootstrapping techniques have also been applied to estimate the effects of random variation on the estimates of efficiency and capacity, and methods have been developed to compensate for some of these effects (see Simar and Wilson, 2000).
 There is presently considerable research being conducted on stochastic data envelopment analysis. See, for example, Resti (2000), and Ruggiero (2000).