SIMPLE CAPACITY INDICATORS FOR PEAK-TO-PEAK AND DATA ENVELOPMENT ANALYSES OF FISHING CAPACITY - A PRELIMINARY ASSESSMENT - Timothy C.T. Hsu^[147]

Abstract: It is generally recognized that there is an imbalance between the resources and fishing capacity in major world fisheries. Improved management and monitoring of fishing capacity will contribute to sustainable, conservation-based fisheries. To facilitate the consistent measurement and assessment of fishing capacity worldwide, some simple and practical methods must be devised so that they can be readily applied by most countries without undue investment of human and financial resources. The FAO Technical Working Group on the Management of Fishing Capacity recommended the use of peak-to-peak analysis and Data Envelopment Analysis (DEA) as the most practical alternatives for measuring capacity. This paper presents some preliminary work on the application of both peak-to-peak and DEA methodologies using simple capacity indicators to a number of important fisheries in Canada. The indicators selected are: the number of species licences, the number of registered fishers, the number of registered fishing vessels, gross registered tonnage, and annual landings by species. All of these are readily available across fisheries and fleet sectors. Based on the preliminary results, it appears that, while more complex physical or economic data are required for better understanding of fishing capacity, with careful interpretation a coordinated use of simple indicators could serve as a minimum requirement for estimating actual and desired capacity level and trends in capacity utilization over time.

1. INTRODUCTION

Fishery resources provide a major source of protein and incomes in many regions of the world. Over the past decades, the world fishery resources have been subject to intense stress due to the rapid growth of global population and economic activities. Aside from natural or human-induced adverse environmental changes, the steady build-up of the world fishing fleets and continuous increase in fishing intensity has contributed to the depletion of some high-value resources. It is generally recognized that there is an imbalance between the resources and fishing capacity in major world fisheries. The 1995 FAO Code of Conduct for Responsible Fisheries calls for improved management and monitoring of fishing capacity that will contribute to sustainable, conservation-based fisheries. To facilitate the consistent measurement and assessment of fishing capacity worldwide, some simple and practical methods must be devised so that they can be readily applied by most countries without undue investment of human and financial resources. The FAO Technical Working Group on the Management of Fishing Capacity recommended the use of peak-to-peak analysis and Data Envelopment Analysis (DEA) as the most practical alternatives for measuring capacity. The Working Group also called for worked examples and case studies to evaluate the peak-to-peak and DEA methodologies for measurement.

This paper presents some preliminary work on the application of both peak-to-peak analysis and DEA using simple capacity indicators. First, a brief discussion is given to some commonly used simple capacity indicators. This is followed by an assessment of the availability of basic technical/biological data in the existing data systems that can be used as capacity indicators. The indicators selected are: the number of species licences, the number of registered fishers, the number of registered fishing vessels, gross registered tonnage (GRT), and annual landings by species, all of which are readily available across fisheries and fleet sectors. Next, preliminary results are presented and discussed on the application of both methodologies using the above mentioned simple capacity indicators to a number of important fisheries in Canada. The paper concludes with a brief discussion of some data and methodological issues with respect to the measurement of fishing capacity as a result of this preliminary investigation. Tables and charts are included in a statistical annex.

It should be noted that the intent of this paper is of an exploratory nature with a view to contributing to an international effort to develop a practical and effective monitoring system for fishing capacity worldwide. As such, the preliminary findings and conclusions presented in this paper do not represent the official endorsement of any set of methods or capacity indicators without further research and validation. It is also important to recognize that such a monitoring system once tested and implemented would provide a useful indication of fishing capacity relative to the level of fishery resources regardless of the capacity/fisheries management regimes in place. On the other hand, what the monitoring system provides would be a set of indicators that can not replace the more comprehensive information and more rigorous analysis required for appropriate actions by the government or industry according to the conservation, economic and social objectives on hand.

2. SIMPLE CAPACITY INDICATORS

In economic terms, a conventional definition of capacity is the output level at which the short-run average total cost of production is minimum. Other economic capacity measures can be defined in terms of break-even point or profit maximization. Economic capacity is usually less than physical capacity which is the maximum output that can be physically produced under a given set of resource and technology constraints. For application in fisheries, both capacity measures require complex economic, biological and technical data that are not always available and can be quite computation intensive. To achieve the purpose of consistent measurement and assessment of fishing capacity worldwide, it is desirable that some simple and practical measures be developed so that they can be readily applied by most countries without undue investment of human and financial resources.

The Technical Working Group recommended that the definition of fishing capacity be formulated in units of catch as it is consistent with economic production theory and makes more sense to the fishing industry (FAO, 1998). For fisheries management purposes, this output measure sometimes needs to be translated into input terms, e.g. the number of vessels and number of participants. Therefore, capacity indicators can be either output or input oriented. In output terms, the most commonly used simple indicators are annual landings and landed values by species. In input terms, simple indicators can be defined in volumetric measures such as gross or net registered tonnes, cubic numbers and hold capacity, or in number of operating units/participants such as the number of vessels, licences and fishers.

Under normal resource conditions, annual vessel landings present a good capacity indicator as it usually reflects a rational business decision under a given set of economic, biological and technological realities at the time. In an overexploited fishery beyond a certain long-term production limit such as maximum sustainable yield, the usefulness of annual vessel landings as a capacity indicator is very limited as it reflects rather an act of economic survival under a stressed resource than normal economic activities. The same can be said of annual vessel landed value, but it also gives an additional dimension of income earned by fishers. In a highly volatile market, however, annual vessel landed values usually exhibit a great fluctuation over time even under normal resource conditions and thus can hardly bear any indication of capacity utilization.

Gross or net registered tonnes are volumetric measures in units of 100 cubic feet of total space or cargo space respectively onboard a vessel. Cubic number is the product of three outer dimensions of a vessel, i.e. length, width and depth. As such, these measures are more an indicator for carrying capacity than fishing capacity. Nonetheless, larger vessels usually catch more fish and thus possess greater fishing capacity. There is also hold capacity which actually measures the fish holding/carrying capacity. Again, one can expect larger vessels with greater fishing capacity. But it is well known that hold capacity is rarely fully utilized during fishing trips and thus cannot be taken as the maximum amount of fish that can be caught per trip (Smith and Hanna, 1990).

The number of licences, vessels and fishers measure the number of operating units/participants in fisheries. These are probably the most commonly available data that can be used as proxies to fishing capacity. However, careful interpretation is required in their applications. Fishing capacity implications would be quite different between removal of a licence attached to a large vessel and removal of a licence attached to a small vessel. For example, the 1993 Northern Cod Adjustment and Recovery Programme (NCARP) retired 876 groundfish licences that accounted for five percent of groundfish licences but less than 1 percent of the groundfish value because over 90 percent of the licences retired were associated with vessels under 35 feet (Gardner Pinfold, 1994). The same can be said of using the number of vessels as capacity indicator. The number of fishers, on the other hand, is more an indicator for labour capacity/social dependence on fisheries than fishing capacity.

Despite the shortcomings cited of the above simple indicators, it is thought that, through coordinated use of both input and output indicators, some reasonable estimates of fishing capacity may be achievable. In other words, capacity can be defined as either the potential output given certain inputs or the optimal input given certain outputs.

3. ASSESSMENT OF EXISTING DATABASES

The Canada Department of Fisheries and Oceans (DFO) maintains harvesting and licensing data for both Atlantic and Pacific fisheries. In the early 1990s, the harvesting sector employed about 35 000 vessels, over 90 percent of which are under 65 feet. The harvesting data comprises fish catches/landings and fishing efforts by species. Because of the sheer number of landings made by small vessels, individual vessel landings data are often incomplete for these small vessels and only aggregates are available on a geographic basis. This is especially true for the Atlantic fisheries prior to 1993. For the same reason, it is difficult to link species licences with individual vessel landings for the small vessel sector. It is also impossible to link fish landings with individual fishers.

In terms of vessel characteristics, overall length is required universally for registration of fishing vessels in Canada. Cubic numbers are used for some fisheries. Information on GRT and hold capacity is not mandatory. GRT usually accompanies length information as both are commonly used vessel characteristics, but often incomplete for small vessels. However, there is generally a high correlation between GRT and overall length and, with adequate data, it is possible to estimate missing GRT based on available length information.

Given the above data constraints, only aggregate data from the existing databases are used for the preliminary analysis: annual total landings and landed values by species, total GRT, the number of species licences issued, the number of registered vessels and the number of registered fishers. The study period is chosen to begin with 1984, as more compatible and comprehensive Quebec harvesting and licensing data only became available in 1984 when DFO resumed management responsibilities for marine fisheries from the Province of Quebec.

Eight fisheries are selected for the preliminary analysis: Atlantic coast - inshore (vessels under 100 feet) groundfish, herring, scallop, lobster, shrimp, queen crab, total inshore fishery; Pacific coast - total salmon fishery. The Atlantic inshore groundfishery provided a major source of incomes to many fishers and their communities prior to the extensive fisheries closures since 1992 and has been the target for licence retirement programmes under NCARP, TAGS (The Atlantic Groundfish Strategy) and CFAR (Canadian Fisheries Adjustment and Restructuring). Atlantic herring supports the most important pelagic fishery off Canada's east coast while scallop, lobster, shrimp and queen crab have always supported the lucrative shellfish industry and maintained the viability of the Atlantic fisheries after the collapse of the groundfishery. Pacific salmon has long been the staple fishery on Canada's west coast, and has been the subject of major restructuring and adjustment programmes such as PSRS (Pacific Salmon Revitalization Strategy) and CFAR since it hit the lowest harvest level in 1995-1996. Finally, the total Atlantic inshore fishery (groundfish, pelagic and shellfish) is selected not only because of its social and economic importance to the region but also with a view to providing some initial indication of multiple-species effect on the level of desired capacity.

4. PEAK-TO-PEAK ANALYSIS

Peak-to-peak analysis is a univariate time series model to assess the capacity utilization over time. Given a time series of output-to-input ratios, the outstanding peaks during the period represent relatively full capacity utilization (or capacity production) under normal operating and economic conditions. These peaks also reflect changes in technology over time. The capacity output-to-input ratios in the intervening years between the peak years can be estimated by mathematical interpolation/extrapolation. The capacity utilization is then defined as the actual output-to-input ratio divided by the capacity output-to-input ratio. Detailed description of the peak-to -peak analysis can be found in Ballard and Roberts (1977), and Kirkley and Squires (1999).

Let U_t represent the output that can be produced in the current period t and V_t the input or a composite index of inputs in time t, the following relationship can be established:

where A is a constant and T_t is an adjusting technology trend. The above equation measures the short-run capacity or potential productivity under constant returns to scale (i.e. a proportionate increase in inputs results in the same proportionate increase in output).

The potential productivity is then estimated by identifying the peak years as having relatively full-capacity production and, for the intervening years, through linear interpolation between the peak years.

where m and n correspond to the length of time from the previous and following peak years.

Over the longer run, however, the above productivity measure given by equation (1) also reflects the changing economic conditions and the corresponding business decision made on the optimal production level. Thus it is desirable to separate the effects of technological and economic factors, if possible, so that a better indication of the economic capacity can be obtained. If the technology trend can be reasonably estimated, a normalized potential activity measure is given by rewriting equation (1) as

where X_t (=T_tV_t) is the technology-adjusted input index. It can be seen that At is no longer a constant and may encompass the effects of long-term economic trend and cycles. In its estimation of capacity utilization in non-manufacturing industries, Statistics Canada (1993) uses the Hodrick-Prescott filter (1980) to estimate the effect of long-term economic trend and cycles by minimizing

where N is the total number of periods, Y_t (=U_t/X_t) is the original series and G_t is the smoothed trend/cyclic series, g_t and b are adjustable weighting factors, and m is the tolerance limit for the smoothing process. As b approaches infinity, a linear trend line is produced. The trend/cyclic series generated can be further adjusted to take into account additional information available from actual capacity surveys or other economic indicators. Prior to 1992, capacity utilization rates were calculated using the simple straight-line peak-period approach.

Ballard and Roberts (1977) and Ballard and Blomo (1978) applied the peak-to-peak analysis to a number of Pacific fisheries in the United States In Canada, a DFO working group on capacity measurement estimated capacity utilization in the Atlantic processing sector between 1971 and 1989 (DFO 1990). The capacity utilization rates were calculated using Statistics Canada's simple base-year approach calibrated by some benchmark DFO capacity surveys. In this paper, the peak-to-peak analysis incorporating the Hodrick-Prescott filter is used. The productivity index is measured by the annual catch divided by technology-adjusted number of licences for the selected fisheries under study. A set of technology coefficients weighted by distributions of fixed and mobile-gear licences over time are calculated for each of the selected fisheries based on the trend of relative technology coefficients reported by Fitzpatrick (1996).

5. DATA ENVELOPMENT ANALYSIS (DEA)

There is a wealth of literatures on DEA as a powerful tool for non-parametric frontier modelling and efficiency measurement (e.g. Afriat, 1972; Färe, Grosskopf and Kokkelenberg, 1989; Coelli, 1995; Coelli and Perelman, 1996a, 1996b). In essence, DEA is a mathematical programming technique that can be used to find frontier production, minimum cost or maximum profit involving multiple inputs and outputs. As in all the mathematical programming problems, an objective function is defined for maximization or minimization subject to a set of constraint functions. The unique feature of DEA, however, lies in its underlying assumption about the shape of the frontier function. The frontier function is assumed to be a non-decreasing and concave function. In other words, DEA models the rising limb of a production function where the marginal product is constant or the effect of diminishing marginal product prevails. Other than the property of non-decreasing and concavity, the production frontier assumes no specific functional form and is derived completely in terms of the given data sets of inputs and outputs.

In this paper, three types of DEA applications are studied: output maximization, input minimization and profit maximization. Output maximization involves, for each given pair of inputs and outputs, finding an optimal set of inputs that maximize the outputs. The resultant inputs and outputs are expressed as a linear combination of all inputs and outputs respectively in the data space. The present study comprises a single output and up to two inputs. The following maximization scheme can be formulated:

where the z's are weighting factors; u's are outputs and ; x's are inputs and ; i=1,2,...,K number of data points and n=1,2,...,N number of inputs.

The above scheme estimates the production function under constant returns to scale (CRS). For variable returns to scale (VRS), an additional constraint is imposed, i.e. .

Input minimization provides another perspective of the frontier function by determining the most efficient set of inputs for the fixed outputs. The resultant production function comprises the fixed outputs and the corresponding most efficient set of inputs again as a linear combination of all inputs in the data space. The minimization scheme is formulated as follows:

where again z's are weighting factors; u's are outputs and; x's are inputs, , and; i=1,2,...,K number of data points and n=1,2,...,N number of inputs.

As both output maximization and input minimization model the same frontier function, the resulting function from one approach would simply be the extension of the resulting function from the other approach. In the case of single-output and single-input, the frontier function under CRS is expected to be a straight line with a positive slope which equals to the productivity of the most efficient period. For the frontier function under VRS, a non-decreasing curve with diminishing slope is expected which should also contain the point corresponding to the most efficient period.

The above optimization schemes estimate frontier production functions in terms of technical efficiency. Profit maximization adds an economic dimension to DEA. It not only estimates the frontier production based on minimum cost along the frontier but also provides information on economic capacity in terms of break-even point and maximum profit given the price-cost structure. Profit maximization follows the following optimization scheme:

where again z's are weighting factors; u's are outputs and ; x's are inputs, , and; is the output price and c's are unit input costs; i=1,2,...,K number of data points and n=1,2,...,N number of inputs.

Both output maximization and input minimization are used to estimate frontier functions for the selected Canadian fisheries. Annual harvest by species is the single output while the number of species licences is the main input studied. Multiple inputs including the number of registered fishers and fishing vessels are used for the total Atlantic inshore fishery. GRT is also tested for the Atlantic inshore ground fishery. Profit maximization requires costs and earnings information, which is not universally available for the Canadian fisheries under study. As such, the example of world fisheries used in a global bio-economic model by Garcia and Newton (1994) is adopted for profit maximization as well as output maximization and input minimization. Again, all the inputs are adjusted with their respective technology coefficients to reflect advances in fishing technology over time.

6. PRELIMINARY MODEL APPLICATIONS TO SELECTED FISHERIES

The following sections present the preliminary results of application of both peak-to-peak analysis and DEA to Atlantic inshore (vessels under 100 feet) ground fishery, Atlantic inshore fishery (DEA only); Pacific salmon fishery; and world capture fisheries (DEA only). Although preliminary analyses were also carried out for herring, scallop, lobster, shrimp and queen crab fisheries on the Atlantic coast, the results are not presented due to space constraint of the paper. Annual landings and landed value by species are taken as the output variable. The number of species licences is the main input variable used in most Canadian fisheries except the total Atlantic inshore fishery where the number of registered fishers and fishing vessels are used as multiple inputs. GRT is also tested for the Atlantic inshore ground fishery while both GRT and the number of decked vessels are assessed separately for world capture fisheries. All input variables other than fishers are adjusted for technological advances over time using the technology coefficients given in Table 1. Landed values are expressed in constant 1986 dollars and the technology coefficients used are also 1986 based. It should be noted that all the Canadian fisheries investigated are managed through various types of input or output control. As such, the model results would likely be conservative.

Table 1. Technology Coefficients for Selected Fisheries

* Based on the trend of relative technology coefficients reported by Fitzpatrick (1996), it was assumed that the technical efficiency of mobile gear doubled between 1980 and 1995 while that of fixed gear increased by 50 percent for the same period. These coefficients are then weighed by distributions of fixed and mobile-gear licences over time for each of the selected Canadian fisheries. ** Based on Garcia and Newton (1994). Technology coefficients are simple arithmetic averages of Fitzpatrick's relative technology coefficients over time.

7. ATLANTIC INSHORE GROUNDFISH

The Atlantic inshore groundfish landings registered 427 000 tonnes in 1984 and had declined ever since. Before the closure of the most important northern cod fishery in 1992 and subsequent closures of other major groundfish stocks Atlantic wide, the inshore groundfish landings plunged to 321 000 tonnes in 1991. Because of the extensive fisheries closures since 1992, the study period is therefore confined to 1984-1991. During this period, however, the number of groundfish licences had not decreased due to a number of factors including relatively good prices for groundfish since 1986, industry's expectation of early recovery of the declining resources and lack of alternative economic opportunities in many coastal communities. Consequently, there existed an imbalance between the resource and fishing capacity. This gap has been further widened over time because of the continuous improvement in fishing technology (FRCC, 1997). As described earlier, the number of licences is thus adjusted with the technology coefficient over time to reflect increased fishing capacity due to technological advances. The landings and landed values versus actual and technology-adjusted number of licences between 1984 and 1991 are shown in Figures 1a and 1b respectively. The total number of groundfish licences is used as a proxy to inshore licences. The inclusion of offshore licences is not expected to cause significant bias to the analysis as offshore licences only accounts for approximately one percent of total groundfish licences.

Figure 1. Inshore Atlantic Groundfishery, 1984-1991 - landings and licences

Figure 1. Inshore Atlantic Groundfishery, 1984-1991 - landed values (1986 US$) and licences

7.1 Peak-to-peak analysis

The peak-to-peak analysis incorporating the Hodrick-Prescott filter (Equations 3 and 4) is performed on both annual landings per adjusted unit of licence and annual landed value per adjusted unit of licence and the results are shown in Figures 2a and 2b. In terms of landings, the capacity utilization rate throughout 1984-1991 was quite high (averaging over 95 percent during 1984-1990 and 72 percent in 1991) despite declining landings (Figure 2a). This implies that fishers consciously lower their catches to achieve minimum average total cost. However, it is well known that the Atlantic fishing industry in general and the groundfish industry in particular are price takers who would catch all the fish available to them if a constant TAC could be maintained. In the presence of declining resources/TAC and non-decreasing fishing capacity, one would expect corresponding decrease in capacity utilization. As such, it is thought that a constant capacity productivity based on the maximum productivity observed in 1984, i.e. 27.3 t/licence, as shown in Figure 3a would be more appropriate. The revised capacity utilization rates now follow a downward from the relatively full-capacity production in 1984 to only 60 percent in 1991. As for capacity utilization in terms of landed values, a smoothed curve (Figure 2b) or a straight line (Figure 3b) all result in a similar pattern of capacity utilization. The utilization rate reached its maximum in 1987 when the record landed value of US$370.9 million was registered and tapered towards both ends of the time span around 50-60 percent. It is quite clear that such a utilization pattern merely reflects the fluctuation in market prices and bears no indication of actual capacity utilization. It also confirms that landed value is not a very useful capacity indicator unless a steady price prevails over time.

Figure 2. Potential Capacities and Capacity Utilization (based on Hodrick-Prescott filter) - Inshore Atlantic Groundfish - landings/licence

Figure 2. Potential Capacities and Capacity Utilization (based on Hodrick-Prescott filter) - Inshore Atlantic Groundfish - landed value/licence

Figure 3. Potential Capacities and Capacity Utilization (based on Constant Capacity Productivity) - Inshore Atlantic Groundfish - landings/licence

Figure 3. Potential Capacities and Capacity Utilization (based on Constant Capacity Productivity) - Inshore Atlantic Groundfish - landed value/licence

7.2 DEA

The DEA results are presented in Figures 4a and 4b for annual landings and annual landed values as the output respectively. Output-based (OB) maximization (Equation 5) and input-based (IB) minimization (Equation 6) are both performed under the scenarios of constant returns to scale (CRS) and variable returns to scale (VRS). The results are combined and displayed in one graph. From Figure 4a, it can be seen that the CRS estimates form a straight line as expected with a positive slope of 27.3 t/licence which in effect is the 1984 productivity, the maximum productivity observed during the 1984-1991 period. The VRS estimates, on the other hand, exhibit a rather peculiar pattern. Instead of a non-decreasing function, it follows a downward trend with increasing licences. This can be explained by the fact of declining catches in the presence of increasing fishing capacity as approximated by the adjusted number of licences (Figure 1a). Keeping in mind that DEA only models the rising limb of a production function, in the present case only the maximum point should be kept and the remaining points on the falling limb can be disregarded. As expected, the maximum point in terms of the 1984 catches and adjusted number of licences, i.e. 427 352 tonnes and 15 627 licences, is contained in both CRS and VRS functions. The CRS function suggests that with the 1991 catch level at 321 156 tonnes it can only support 11 744 licences while the 1991 level of 19 695 licences have the capacity to harvest 538 587 tonnes of groundfish if the resource is not a constraint. Both estimates imply a 1991 capacity utilization around 60 percent (=11 744/19 695=321 156/538 587). The VRS seems to indicate that with the capacity of 15 627 licences the potential harvest limit is reached at 427 352 tonnes, any increase in capacity beyond this point would result in decreasing catches. It appears that the CRS estimates give an indication of instant catchability at maximum efficiency while the VRS estimates provide information on long-term potential yields. In this context, the 1991 level of 19 695 licences certainly is not desirable as it would result in catches way beyond the apparent long-term potential harvest limit of 427 352 tonnes.

Figure 4a. - Potential Harvest vs licences

Figure 4b. - Potential Revenue (1986US$) vs licences - Inshore Atlantic Groundfish

The CRS and VRS functions presented in Figure 4b based on landed values can be examined in the same vein. In summary, the estimated level of capacity for the 1991 revenue of US$225.7 million would be 10 060 licences, the instant earning potential for the 1991 capacity at maximum efficiency would be US$441.8 million and the long-term maximum sustainable revenue would be US$370.9 million with a fishing capacity of 16 531 licences. Again, DEA results based on landed values do not seem to provide meaningful information on a realistic relation between potential production and capacity due to the influence of fluctuating prices, and annual landed values thus cannot be considered as a good capacity indicator. As such, all the subsequent discussions will focus on the use of annual landings as the primary output indicator.

Two additional observations can be drawn from the above model results. First, when comparing the results between the peak-to-peak analysis with a constant capacity productivity and the DEA CRS approach, it can be seen that both methods yield exactly the same results. Second, by multiplying the estimated 1991 capacity utilization rate of 58.8 percent to the 1991 actual number of licences, i.e. 17 200, results in a lower level of capacity at 10,136 which compares favourably to the estimated level of 10 435 core groundfish licences for TAGS (Auditor General, 1997). This gives some assurance that both peak-to-peak analysis and DEA can indeed provide some reasonable first-cut estimates of actual and desired level of capacity.

7.3 GRT

GRT has been widely used in international communities as a capacity indicator. Even though overall length (LOA) or cubic meters are more commonly used management tool in Canada, it is nevertheless desirable to test the use of GRT as an alternative capacity indicator. Using more detailed Atlantic licensing data available for 1986-1991 at the DFO headquarters, a functional relationship is established between GRT and LOA. The missing GRT values are then estimated from the existing LOA information which is universally required on licences and vessel registration. Annual landings versus actual and technology-adjusted GRT from 1986 to 1991 are shown in Figure 5. It can be seen that, after adjustment for technological advances, GRT is on a rising trend between 1986 and 1991.

Figure 5. Inshore Atlantic Groundfishery, 1986-1991 - landings and total GRT

Both peak-to-peak analysis and DEA are performed and the results are given in Figures 6 and 7 respectively. Because of the shorter time series, the most efficient period falls in 1986 with the maximum productivity of 2.9 t/GRT. Both the peak-to-peak analysis with a constant capacity productivity and the DEA CRS approach yield the same 1991 capacity utilization rate of 60 percent. The CRS estimates suggest that, given the best fishing efficiency, the 1991 catch level of 321 156 tonnes can only support an effort level of 109 602 GRT. On the other hand, the 1991 level of 182 554 GRT possesses a potential harvest capacity of 534 921 tonnes. The VRS estimates appear to indicate that with an effort level of 149 971 GRT the long-term sustainable catch limit is reached at 420 308 tonnes.

Figure 6. Potential Capacities and Capacity Utilization (based on Constant Capacity Productivity) - Inshore Atlantic Groundfish landings/GRT

Figure 7. Potential Harvest vs GRT - Inshore Atlantic Groundfish

Since there exists a high correlation between GRT and LOA, it is expected that LOA could also serve as a potential capacity indicator. Annual landings versus actual and technology-adjusted GRT from 1986 to 1991 are presented in Figure 8. It can be seen that adjusted LOA follows the same rising trend as GRT during 1986-1991. The peak-to-peak analysis and DEA all yield similar results as GRT (Figures 9 and 10). The 1991 capacity utilization rate at maximum efficiency is estimated to be around 63 percent. It is interesting to note that both GRT-based and LOA-based CRS estimates give comparable 1991 capacity utilization rates around 60 percent, which is also indicated by the licence-based analysis.

Figure 8. Inshore Atlantic Groundfishery, 1986-1991 - landings and total LOA

Figure 9. Potential Capacities and Capacity Utilization (based on Constant Capacity Productivity) - Inshore Atlantic Groundfish landings/LOA

Figure 10. Potential Harvest vs LOA - Inshore Atlantic Groundfish

7.4 Pacific salmon

Pacific salmon consists of five major pacific salmon species off Canada's west coast, i.e. chinook, sockeye, coho, pink and chum, and to a minor extent the steelhead salmon. It is known that Pacific salmon runs exhibit noticeable cyclic patterns. A preliminary analysis of long-term total salmon landings revealed a pronounced four-year cycle with possible three and six-year cycles. To accommodate these possible cycles, a 12-year landing series from 1984 to 1995 is selected for the study. Total Pacific salmon landings versus actual and technology-adjusted number of licences between 1984 and 1995 are presented in Figure 11. The Pacific salmon landings fluctuate over this period reaching a record high of 107 564 tonnes in 1985 and plunging to a historical low of 48 550 tonnes in 1995 after which major conservation measures including area closures were introduced. The number of salmon licences remained relatively stable around 4 400 to 4 500. Taking into account technological advances, however, the 1986-based adjusted number of licences reveals a steady upward trend from 4 198 in 1984 to 5 551 in 1995.

Figure 11. Pacific Salmon Fishery, 1984-1995 - landings and licences

7.5 Peak-to-peak analysis

The results from the application of peak-to-peak analysis are shown in Figure 12. Given the fact that the Pacific salmon industry is also a price taker, a constant capacity productivity based on the maximum productivity in 1985, i.e. 24.8 t/licence is used. The resulting capacity utilization pattern follows the same trend as landings with 1995 experiencing the lowest utilization rate at 35 percent.

Figure 12. Potential Capacities and Capacity Utilization (based on Constant Capacity Productivity) - Pacific Salmon landings/licences

7.6 DEA

The DEA results as shown in Figure 13 are quite different from those related to the inshore Atlantic ground fishery with respect to the VRS estimates. The VRS estimates reveal a rather steep rising limb of the production function. Given the cyclic nature in the natural production of the Pacific salmon fishery, however, it is clear that this steep slope just reflects the catch levels other than the cyclic peaks in the presence of a steady number of licences. Further, from Figure 6, it can be seen that the peak catches appear to follow a declining trend over the study period. Therefore the only valid point on the VRS function is the maximum productivity point observed in 1985, i.e. a catch level of 107 564 tonnes with 4 342 licences technology-adjusted. This then can lead to the conclusion that the Pacific salmon fishery, like the Atlantic ground fishery, may have fished beyond its long-term potential harvest limit with the capacity level in the early 1990s. The CRS estimates, on the other hand, suggest that with the 1995 catch level at 48 550 tonnes it can only support 1 960 licences while the 1995 level of 5 551 licences have the harvest capacity of 137 514 tonnes without resource constraint. This translates into a 1995 capacity utilization rate of 35 percent. One can probably argue that, in view of the cyclic nature of the Pacific salmon fishery, it may be more appropriate to estimate the desired capacity level in terms of the long-term average harvest instead of the low point of the catch cycle. This is done by including the 1984-1995 average of salmon catches and technology-adjusted average number of licences in the DEA model run. The results suggest that with the average catch level of 79 177 tonnes it can only support 3 196 licences while the average level of 5 670 licences can potentially catch 140 481 tonnes of salmon. In fact, these figures can be obtained by simple arithmetic interpolation/extrapolation from the CRS line. The resulting utilization rate for the average salmon fleet is estimated to be 56 percent.

Figure 13. Potential Harvest vs licences - Pacific Salmon

As in the case of Atlantic inshore ground fishery, the peak-to-peak analysis with a constant capacity productivity and the DEA CRS approach yield exactly the same results in capacity utilization. In terms of the actual number of licences, the estimated 1995 utilization rate of 35 percent suggest a capacity level of 1 541 licences which is approximately 150 less than that recommended under a low catch projection scenario by the B.C. Job Protection Commission (1998). If one assumes a more optimistic average harvest level of 79 177 tonnes, a less drastic capacity reduction would be needed and the estimated desired capacity in terms of actual licences would be 2 513.

7.7 Total atlantic inshore fishery

The total Atlantic inshore fishery (including groundfish, pelagic and shellfish) is selected to study the effect of multiple-species fishery on level of estimated capacity. Total Atlantic inshore landings versus registered fishers and actual and technology-adjusted number of registered fishing vessels between 1984 and 1991 are presented in Figure 14. Despite the continuous decline in groundfish landings, total inshore landings did not discern drastic changes during the 1984-1991 period. Total inshore landings peaked over 850 000 tonnes in the late 1980s and the 1991 landings fell to the 1984 level around 710 000 tonnes. The number of registered fishers and fishing vessels were also quite steady around 60 000 and 30 000 (technology-adjusted) respectively and also peaked in the late 1980s.

Figure 14. Atlantic Inshore Fisheries, 1984-1991 - landings, fishers and vessels

The DEA is performed on total Atlantic inshore landings with two inputs - registered fishers and fishing vessels. For the two-input case, a composite input index is used in the optimization scheme (Equations 5 and 6). It is a input distance function defined as the square root of the sum of squares of the input variables (Coelli and Perelman, 1996a). For presentation purposes, the resultant frontier estimates are transformed into two-dimensional functions as shown in Figure 15. The CRS estimates reveal that there are two most efficient periods in 1986 and 1990 respectively. The results also suggest that, given the best fishing efficiency, the 1991 catch level of 711 102 tonnes can only support 50 829 fishers and 27 066 vessels. On the other hand, the 1991 level of 58 872 fishers and 31 883 vessels possess a potential harvest capacity of 823 631 tonnes. The VRS estimates appear to indicate that with the capacity of 65 791 fishers and 32 197 vessels the long-term potential catch limit is reached at 880 572 tonnes.

Figure 15. Potential Harvest vs composite input - Atlantic Inshore Fisheries

Based on the CRS results, the estimated desired level of fishing vessels at the 1991 harvest level is 27 066 (technology-adjusted). This represents a 15 percent reduction from the 1991 level of 31 883. Comparing to the desired reduction of 40 percent in inshore groundfish licences, a 15 percent reduction in vessels for the total inshore fishery seem to indicate that over-capacity problem would appear to be less severe in a multiple-species fishery than a single-species fishery even though it is understood that not every inshore fisher and vessel is engaged in multiple-species operation and the ground fishery itself consists of many different species. Further, in terms of actual number of vessels, the 15 percent reduction translates into 23 610 vessels. This combined with the estimated desired level of 50 829 fishers suggest that, assuming a future production at the 1991 level of 711 102 tonnes, the current (1997) numbers of 43 837 fishers and 22 643 fishing vessels appear to be headed in the right direction towards more responsible and efficient fisheries.

7.8 World capture fisheries

Garcia and Newton (1994) presented a generalized bio-economic model to assess the global over-capacity problem in the world capture fisheries. The fisheries data used involve annual landings and technology-adjusted GRT for 1970, 1975, 1978 and 1980-1989 as shown in Figure 16a. In this paper, the same data is used to test the applicability of DEA for assessment of global fishing capacity. Further, the number of decked fishing vessels (FAO, 1991) is used in addition to GRT as an alternative capacity indicator, which is also technology-adjusted as shown in Figure 16b. It can be seen that both landings and fishing fleet have undergone considerable growth during 1970-1989.

Figure 16. World Fisheries, 1970-1989 - a) landings and total GRT;

Figure 16. World Fisheries, 1970-1989 - b) landings and vessels

The DEA results based on GRT as input are presented in Figure 17. The VRS frontier follows a rather flat curve which appears to resemble the top portion of the production function derived by Garcia and Newton. It also implies that the world capture fisheries may have reached its long-term production limit of 86.4 million tonnes with the 1989 capacity of 40.2 million GRT. The most efficient period appear to fall in 1970 with the maximum productivity of 6.4 t/GRT. Given this maximum efficiency, the CRS estimates indicates that the 1989 global harvest of 86.4 million tonnes can only maintain an effort level of 13.6 million GRT while the 1989 effort level of 40.2 million GRT can reap a potential harvest of 255.9 million tonnes without resource constraint. In terms of fishing vessels, the VRS estimates shown in Figure 18 exhibit a similar form of production function and point to a possible production limit corresponding to the 1989 global harvest of 86.4 million tonnes and 1 864 000 vessels (technology-adjusted). The CRS results suggest that, operating with maximum efficiency, only 588 000 vessels would be required to achieve the 1989 catch level and the 1989 level of 1 864 000 vessels can potentially reach a harvest level of 273.7 million tonnes. It is interesting to note that GRT-based and vessel-based CRS estimates arrive at comparable capacity utilization rates for 1989, i.e. 34 percent and 32 percent respectively.

Figure 17. Potential Harvest vs GRT - World Fisheries

Figure 18. Potential Harvest vs vessels - World Fisheries

The world fisheries data is further used to test the DEA profit maximization scheme (Equation 7). It turns out that both CRS and VRS models yield exactly identical results as compared to those from the input minimization approach. This is expected, as stated earlier, because the profit maximization approach estimates the frontier production based on minimum cost along the frontier. In addition, it also provides information on economic capacity in terms of break-even point and maximum profit given the price-cost structure. The average price and unit cost information is taken from Garcia and Newton: US$862/t and US$2 895/adjusted GRT. The maximum profit curve along the production frontier is shown in Figure 19. It can be seen that net economic loss would be expected beyond the break-even effort level of 21 million GRT, which is in line with the 19 million GRT estimated by Garcia and Newton. The maximum profit, however, appears to realize at the most efficient effort level of 9.3 million GRT.

Figure 19. Potential Profit vs GRT - World Fisheries

8. SENSITIVITY ANALYSIS

The following sections present the preliminary findings from various DEA runs to assess the sensitivity of model results to vessel size, geographic area, gear type and study duration. The sensitivity analysis uses the data on Atlantic inshore groundfishery. Vessel size is classified into four LOA categories: < 35', 35' - 44.9', 45' - 64.9' and 65' - 99.9'. Geographic breakdown of area includes Gulf of St. Lawrence, east coast of Newfoundland and Scotia-Fundy region. Gear type consists of fixed gear and mobile gear. Two study periods are used to assess sensitivity to duration: 1984-1991 and 1986-1991.

8.1 LOA effect

The frequency distribution of inshore groundfish licences by LOA is given in Figure 20. It can be seen that over 99 percent of licences are attached to vessels less than 65 ft and approximately 70 percent accounted for by vessels under 35 ft.

Figure 20. Atlantic Inshore Groundfish Licences by LOA

The harvesting productivity increases almost exponentially with LOA and is the highest among the 65'-99.9' group with the productivity over 400 t/licence most of the time compared to approximately ten t/licence for the <35' group (Figure 21). With such a drastic difference in fishing productivity among fleet sectors, one would expect a noticeable discrepancy between the capacity estimates with and without LOA stratification. DEA was carried out for each of the fleet sectors and results summed and compared to those based on the total inshore fleet as shown in Table 2. It turns out that the differences are quite moderate within five percent and the estimate of desired capacity for 1991 based on the total inshore fleet is only overestimated by 1.6 percent. This could be attributed to the fact that larger and highly productive vessels only accounts for less than one percent of the total inshore fleet and consequently does not exert much influence in determining the capacity level of the total inshore fleet.

Figure 21. Harvesting Productivity by LOA Atlantic Inshore Groundfish

Table 2. Effect of LOA on Capacity Estimation - Licences (Tech. Adj.), Atlantic Inshore Groundfish

8.2 Area effect

The area distribution of groundfish licences is presented in Figure 22. During 1986-1991, east coast of Newfoundland leads with over 45 percent of licences, followed by Gulf (35 percent) and Scotia-Fundy (20 percent). On the other hand, Scotia-Fundy fleet exhibits the highest productivity around 40 t/licence while the productivities of the Gulf and E. Nfld. fleets are comparable in the 20 t/licence range (Figure 23). The comparison of capacity estimates with and without area stratification are given in Table 3. Again, the differences are within five percent. By examining Figures 22 and 23, it shows that although productivities are quite different between Scotia-Fundy and rest of the Atlantic regions, the area distributions of licences remain relatively unchanged over time and the productivity trends are similar between the regions. As a result, both grouping scenarios display similar productivity trend patterns. This explains the little differences between the two sets of capacity estimates.

Figure 22. Atlantic Inshore Groundfish Licences by Area

Figure 23. Harvesting Productivity by Area - Atlantic Inshore Groundfish

Table 3. Effect of Area on Capacity Estimation - Licences (Tech. Adj.), Atlantic Inshore Groundfish

8.3 Gear effect

The frequency distribution of groundfish licences by gear type is shown in Figure 24. The dominance of fixed gear licences is evident throughout 1986-1991 averaging over 85 percent. The number of mobile gear licences dropped from 15 percent to seven percent since 1988. The fixed gear sector has experienced declining productivity from 17-18 t/licence in 1986-87 to around 10 t/licence in 1991 (Figure 25). The mobile gear fleet conversely showed a significant increase in productivity from around 70 t/licence in 1986-87 to 122 t/licence in 1988 and then a gradual decline to 102 t/licence in 1991. This productivity trend in the mobile gear sector is different from the trend exhibited by the total inshore fleet, which is more in line with the fixed gear sector. Consequently, capacity estimates based on the total inshore fleet show a consistent overestimation averaging slightly over five percent compared to those with gear stratification as shown in Table 4.

Figure 24. Atlantic Inshore Groundfish Licences by Gear

Figure 25. Harvesting Productivity by Gear Atlantic Inshore Groundfish

Table 4. Effect of Gear on Capacity Estimation - Licences (Tech. Adj.), Atlantic Inshore Groundfish

8.4 Duration effect

The harvesting productivity trend for the total inshore groundfish fleet from 1984 to 1991 is displayed in Figure 26. It shows a decline from 27.3 t/licence in 1984 to 16.7 t/licence in 1991. When the entire 1984-1991 period is used for analysis, the maximum productivity in 1984 is the basis for estimating annual capacities in both peak-to-peak analysis and DEA CRS model. When the study period is confined to 1986-1991, the maximum productivity during this period occurred in 1986 at 26.4 t/licence. As a result, capacity estimates based on the 1986-1991 data are consistently overestimated by 3.6 percent compared to those obtained using 1984-1991 data as shown in Table 5.

Figure 26. Harvesting Productivity 1984-1991 - Atlantic Inshore Groundfish

Table 5. Effect of Duration on Capacity Estimation - Licences (Tech. Adj.) Atlantic Inshore Groundfish

9. CONCLUSIONS

Capacity measurement is not a precise science. It may bear different definitions to biologists, economists and resource managers while conducting businesses in their respective disciplines. Nevertheless, there is seldom contradiction in describing capacity trends in relative terms. This leads to the notion that a set of indicators could be developed to provide a consistent yet reasonable indication of capacity level over time regardless of capacity/fisheries management regimes in place. In Canada as well as most developed fishing nations, governments are moving away from an interventionist approach to one that promotes co-management/partnership with industry towards responsible and sustainable fisheries. A practical and effective capacity monitoring system would be useful in providing a preliminary indication of fishing capacity relative to the level of fishery resources. Based on this information, government and industry may decide on further information and research required which would lead to appropriate actions according to the conservation, economic and social objectives on hand.

Based on the preliminary results presented above, it appears that, while more complex physical or economic data are required for better understanding of fishing capacity, with careful interpretation a coordinated use of simple indicators could serve as a minimum requirement for estimating actual and desired capacity level and trends in capacity utilization over time. The following summarizes some methodological and data issues worth noting in the measurement of fishing capacity.

Capacity only makes sense when defined in terms of both input and output. It can be defined as either the potential output given certain inputs or the optimal input given certain outputs. The number of licences, vessels, GRT etc. alone does not give any indication on the level of fishing capacity without the concurrent knowledge of current resource use and potential output in units of catch. The preliminary results appear to indicate that the number of species licences, vessels, fishers and GRT are potential input indicators which would yield reasonable estimates of capacity level. LOA is also an alternative indicator because of the high correlation between GRT and LOA. As for the output indicators suitable for capacity estimation, annual landings by species are recommended in lieu of landed values. Landed values are often influenced by highly fluctuating market conditions and cannot be used as a meaningful indicator of the resource level. Finally, it is clear that technology coefficients affect the level of estimated capacity. To ensure meaningful and comparable capacity estimates worldwide, there is also a need for consistent application of a standard methodology for measuring technology coefficients, which is currently lacking.

Both peak-to-peak analysis and DEA prove to be a practical tool that makes coordinated use of input and output indicators to derive estimates of fishing capacity. DEA, however, offers more flexibility in that it can deal with multiple inputs and outputs and address a variety of economic optimization problems. It is important to note that no model can reveal information beyond what is contained in the given data. In other words, maximum efficiency and capacity estimates from both methods are confined in the period under study and constrained by the details of the data. Also, the results presented in this paper are mainly based on the maximum technical or economic efficiencies. If other objectives, e.g. equitable access to resources, are of primary concern, they could be incorporated in the model formulation and would result in a different set of capacity estimates.

It appears that the peak-to-peak analysis and DEA CRS estimates give an indication of instant catchability at maximum efficiency while the DEA VRS estimates provide information on long-term potential yields. It is important to keep in mind that DEA only models the rising limb of a frontier production function with a constant slope or where the effect of diminishing marginal product prevails. As such, the results would be meaningless for overexploited fisheries beyond the long-term production limit, other than a mere indication of a troubled resource in the presence of a downward sloping. Because of the short time series involved and the various input/out control regimes in place, these estimates would likely be conservative and must be used with discretion.

The fisheries data presented in this paper all involve multiple species and stocks. If DEA is to be used to estimate a more meaningful biological production function, stock-specific analysis and a better input indicator such as fishing effort would be required. On the other hand, the model results also appear to indicate that the multiple-species analysis would result in a higher level of capacity utilization than that based on the single-species analysis. This is somewhat expected as multiple-species fisheries usually provide required diversification and complementary sources of raw material and incomes to make most use of the existing capacity.

The results of sensitivity analysis seem to suggest that a macro-level assessment of capacity using either method would generally suffice. More detailed analysis with data stratification would be required if there is strong evidence of heterogeneity in distributions of inputs or productivity trends. On the safe side, however, some broad data stratification would be desirable provided that such effort would not cause undue computational burden. Also, longer time series whenever available should always be used to obtain better estimates of fishing capacity.

10. REFERENCES

Afriat S.N. 1972. Efficiency estimation of production functions. International Economic Review, 13(3): pp. 568-598.

Auditor General of Canada. 1997. Chapter 15, Fisheries and Oceans Canada - rationalization and renewal: Atlantic groundfish. Report of the Auditor General of Canada, Ottawa.

Ballard K. & Blomo, V. 1978. Estimating the structure of capacity utilization in the fishing industry. Marine Fisheries Review, 40(8): pp. 29-34.

Ballard K. & Roberts, J. 1977. Empirical estimation of the capacity utilization rates of fishing vessels in 10 major Pacific coast fisheries. National Marine Fisheries Service, Washington D.C.

British Columbia Job Protection Commission. 1998. Fishing for money: challenges and opportunities in the BC salmon fishery. Final Report. Prepared by G.S. Gislason & Associates Ltd., Vancouver.

Coelli T.J. 1995. Recent developments in frontier modelling and efficiency measurement. Australian Journal of Agricultural Economics, 39(3): pp. 219-245.

Coelli T. & Perelman, S. 1996a. Efficiency measurement, multiple-output technologies and distance functions: with application to European railways. CREPP Working Paper 96/05, Université de Liège.

Coelli T. & Perelman, S. 1996b. A comparison of Parametric and non-parametric distance functions: with application to European railways. CREPP Working Paper 96/11, Université de Liège. FAO. 1995. Code of conduct for responsible fisheries. Rome, FAO.

DFO Economic and Commercial Directors Committee. 1990. Report of the working group on capacity measurement. Canada Department of Fisheries and Oceans, Ottawa.

Färe R., Grosskopf, S. & Kokkelenberg, E.C. 1989. Measuring plant capacity, utilization and technical change: a nonparametric approach. International Economic Review, 30(3): 655-666.

FRCC (Fisheries Resource Conservation Council). 1997. A report on gear technology in eastern Canada. Report of the Gear Technology Subcommittee FRCC.97.R.1, Ottawa.

Fitzpatrick, J. 1996. Technology and fisheries legislation. Pages 191-200 in Precautionary approach to fisheries, part 2, scientific papers. FAO Fisheries Technical Report 350/2, Rome, FAO.

FAO. 1991. Bulletin of fisheries statistics - Fishery Fleet Statistics, No. 30. Rome, FAO.

FAO. 1995. Code of conduct for responsible fisheries. Rome, FAO.

FAO. 1998. Report of FAO technical working group on the management of fishing capacity, 15-18 April 1998, La Jolla,. United States. Rome, FAO.

Garcia S. M. & Newton, C. 1994. Current situations, trends, and prospects in world capture fisheries. Paper presented at the Conference on Fisheries Management, 14-16 June, Seattle, United States.

Gardner Pinfold Consulting Economics Ltd., and Canning & Pitt Associates Inc. 1994. Final evaluation of the Northern Cod Adjustment and Recovery Programme. Canada Department of Fisheries and Oceans, Ottawa.

Kirkley, J.E. & Squire, D. 1999. Measuring Capacity and Capacity Utilization in Fisheries. In: Gréboval, D (Ed). Managing Fishing Capacity: Selected Papers on Underlying Concepts and Issues. FAO Fisheries Technical Paper No 386. pp. 75-200. Rome, FAO.

Smith C. L. & Hanna, S. 1990. Measuring fleet capacity and capacity utilization. Canadian Journal of Fisheries and Aquatic Sciences, 47: pp.2085-2091.

Wallace D., & Dion, R. 1993. Industry capacity utilization rates in Canada - new methodology. Statistics Canada Working Paper, Ottawa.