© 2004 by ICES/CIEM International Council for the Exploration of the Sea/Conseil International pour l'Exploration de la Mer
Determination of technical efficiency of fisheries by stochastic frontier models: a case on the Gulf of Cádiz (Spain)
Modelización Econométrica y Matemática de Pesquerías (MEMPES), Departamento de Economía General y Estadística, Facultad de Ciencias Empresariales, Universidad de Huelva Plaza de la Merced, 11, Huelva, 21071, Spain
*Correspondence to D. Castilla Espino: tel: +34 959017868; fax: +34 959017828. e-mail: david.castilla{at}dehie.uhu.es.
We give a broad review of a variety of econometric procedures to estimate technical efficiency and compare the results of several of them based on an application to the purse-seine fishery operating in the Gulf of Cádiz in 1998 and 1999. As these approaches provide different technical efficiency estimates, they might have different policy implications. Two conclusions are obtained: firstly, the higher the useful life of vessels is, the smaller the technical efficiency is; and secondly, the present total allowable catch regime based only on vessels larger than 12 m is unsuitable for this fishery.
Keywords: comparison, deterministic frontier, Gulf of Cádiz, management measures, purse-seine fishing, stochastic frontiers, technical efficiency
Received 15 May 2003; accepted 17 February 2004.
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1 Introduction |
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 Top 1 Introduction 2 Methods3 Results4 DiscussionReferences |
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Technical efficiency is defined (Kumbhakar and Lovell, 2000) as the ability of a decision-making unit (DMU) to obtain the maximum output from a set of inputs (output orientation) or to produce an output using the lowest possible amount of inputs (input orientation). Technical efficiency, its measurement, and the factors determining it are of crucial importance in production theory. Technical efficiency of a DMU and the degree of use of variable inputs determine the output and capacity utilization. Determining those factors affecting it allows stakeholders to take measures to limit or improve it.
In the fisheries context, there is a growing interest in the measurement of technical efficiency of different fishing fleets. This interest is twofold: to establish the underlying factors (Kirkley et al., 1998; Sharma and Leung, 1998), and to assess the effects of management measures on technical efficiency and potential catch. Fishery managers may reduce technical efficiency by constraining the use of certain inputs (Kirkley et al., 1995; Pascoe et al., 2001a), or alternatively, they may improve it by expanding these inputs or by taking measures that properly define the property rights of the fishery.
Any assumption on the economic behaviour of fishermen (e.g. minimizing costs) leads to the concept of economic efficiency (also sensitive to management measures; Grafton et al., 2000), which is composed of technical and allocative efficiency (Farrell, 1957). Allocative efficiency is defined as the ability to optimize allocation of outputs or inputs depending on the orientation. Measuring economic efficiency requires availability of economic data.
From the end of the 1970s onwards, several techniques have been developed for efficiency analysis, based on the comparison of the output (input) of a group of DMUs. Methods to measure efficiency can be classified into two groups: non-parametric models, exemplified by Data Envelopment Analysis (DEA); and parametric models, incorporating Deterministic Frontier Analysis (DFA) and Stochastic Frontier Analysis (SFA).
Apart from measuring efficiency, applications using DEA have been recommended by FAO (1998) from the late-1990s onwards to measure also fishing capacity (Kirkley and Squires, 1999; Pascoe et al., 2001b; Kirkley et al., 2002; Reid et al., 2003; Vestergaard et al., 2003). Although several studies compare results obtained with parametric and non-parametric techniques as well as with some of their variants (Van den Broek et al., 1980; Hjalmarsson et al., 1996; Reinhard et al., 2000; Huang and Wang, 2002), comparative studies for fisheries are so far lacking. Our objective is to compare results obtained using DFA and different SFA variants for the purse-seine fleet operating in the Gulf of Cádiz, a fleet characterized by a large overcapacity during the years considered. Ultimately, these techniques might be used as a tool in assessing fishing effort within this fleet.
1.1 Description of the fishery
The purse-seine fleet in the Gulf of Cádiz (from the Strait of Gibraltar to Cape San Vicente) targets middle- and small-sized pelagic, schooling species, including anchovy (Engraulis encrasicholus), sardine (Sardina pilchardus), mackerel (Scomber spp.), and horse mackerel (Trachurus trachurus). The stocks targeted by this fleet are managed at different levels.
At the European level, the Common Fisheries Policy (CFP) applies, focusing on management by annual total allowable catches (TAC). This conservation policy aimed at protecting fish resources is complemented by a fleet structure policy, a market policy, and an external policy concerned with agreements with countries outside the European Union (EU). The fleet structure policy mainly consists of the EU aid and Multi-Annual Guidance Programmes (MAGP). Under the MAGP, each member state has to analyse the evolution of its fleet during the forthcoming four years and to establish aims for a reduction of fishing effort. The CFP effort control is restricted to vessels exceeding 12 m according to the third MAGP1 (Council Decision 97/413/EC).
At the national level, the part of the TAC allocated to Spain each year (quota) is managed by the Spanish authorities by implementing management measures directed towards bioeconomic sustainability of the resources, within the limitations set by the approved MAGP. According to the regulations, purse-seiners have to measure at least 20 GRT (Gross Registered Tonnage). The mesh size (under wet and used conditions) should measure at least 14 mm and size of the nets is restricted to a maximum of 450 m long and 80 m high. A limited number of authorized vessels is allowed to participate on a permanent basis in the fishery (census). However, temporary licences may be issued to other vessels by the responsible governmental organization.
The purse-seine fleet usually operating from ports in the Gulf of Cádiz (mainly Barbate, Punta Umbría, and Isla Cristina) can be divided into two groups. The first group comprises vessels of quite different sizes that can only fish with a purse-seine and are included in the purse-seine census. Vessels from Barbate are relatively large and could fish also in Moroccan waters outside the EU Economic Exclusive Zone (EEZ) during the period of the investigation (the agreement between Morocco and the EU was terminated on 30 November 1999). Vessels from Punta Umbría and Isla Cristina only operate in the Gulf of Cádiz.
The second group consists of multi-gear vessels using mostly trawls and/or artisanal fishing gears, but which may be given a temporary purse-seine license. These vessels participated in the mackerel fishery during most purse-seine trips during the period.
1.2 Data
To obtain balanced panel data, daily catches (mainly sardine and, to a lesser extent, anchovy) from trips undertaken by 14 census vessels fishing in EU waters only were aggregated by week during the summer seasons of 1998 and 1999 (July/August: weeks 27–34). The sample thus consists of 112 observations annually (14 vessels; 8 weeks). On average, landings of the sampled vessels represented around 60% of total landings (Table 1), the difference between the two years being caused by the fraction of vessels receiving a temporal licence or fishing elsewhere. Moreover, some vessels did not participate throughout the two summer seasons for some reason or another. Data for 1997 were not available and data for 2002 were excluded, because 80% of the fleet had been substituted by newly built vessels.
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Table 2provides descriptive technical statistics of the sampled vessels in the two years. Key variables considered were fishing days and number of crew as variable inputs, and GRT as fixed input.
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2 Methods |
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Top1 Introduction2 Methods3 Results4 DiscussionReferences |
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2.1 Fish capture function
The maximum attainable catch of a vessel (i) during a certain period (hit) is a function of two productive inputs, fishing effort (Eit) and exploited stock (St):
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| (1) |
it represents an error term. While exploited stock has a straightforward interpretation (higher stock densities lead to higher yields), fishing effort has a more difficult interpretation. Fishing effort is generally thought (Beverton and Holt, 1957) to be a function of fishing power (Wit) and activity (Tit), so that we may write
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| (2) |
To estimate Equation (2), cross-section, time-series, or panel data may be used (Hannesson, 1983, Campbell, 1991). For cross-section data, we would have to formulate some hypothesis on the distribution of the stock in the fishery, because this variable is unobservable. Stock is usually assumed to be the same for all vessels within the period considered. Although this hypothesis seems plausible, it may be completely erroneous as well (Clark, 1982). For time-series data, information about the evolution of the stock must be available, or at least techniques that can statistically treat this input. Panel data allow estimating stock as a fixed effect that may be different for each period but is the same for all vessels within each period.
Another problem faced is choosing an appropriate functional form to represent fishing effort. The first-best option is to consider a translog flexible functional form, because it represents a second-order approximation of any arbitrarily chosen function as well as being theoretically possible (Berndt and Christensen, 1973):
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| (3) |
ij=ji). Consequently, different restrictions on the translog function can be tested to establish the most appropriate final form for the fish capture function (García et al., 2001).
2.2 Efficiency analysis
Farrell (1957) proposed an empirical method to compute economic efficiency by means of the comparison of the output in the production frontier of a DMU and its effective output. Although the further description relates to output, a similar reasoning applies to input. The production frontier, or the maximum potential output of a completely efficient DMU, cannot be observed directly and a wide range of techniques has been developed to overcome this problem, the foremost techniques being DEA, DFA, and SFA.
The non-parametric DEA does not require a specification of the production process and only certain formal properties need to be defined that verify the points of the production set. These properties are related to returns to scale, availability of inputs and outputs, or convexity. Data are enveloped by a frontier under these properties and efficiency can be obtained by comparing the actual values of the outputs with the envelope (production frontier). This technique uses linear programming methods to determine the frontier and inefficiency (Cooper et al., 2000). Although the method is in essence non-stochastic, recent developments try to account for stochastic effects also (Sengupta, 1987; Land et al., 1993; Olesen and Petersen, 1995).
The parametric DFA and SFA techniques require specification of the technological characteristics of the production process. In DFA, any deviation from the frontier output of a DMU is assumed to be caused by inefficiency, whereas in SFA, random effects are also taken into account. As in DEA, efficiency is derived from the comparison of actual output values with the production frontier using econometric techniques (Kumbhakar and Lovell, 2000).
In contrast to DFA and SFA, DEA does not need a specification of the production process technology, is easily adapted to a multiproduct technology, and allows imposing theoretical restrictions. Although difficulties arise with DFA and SFA when multi-output technologies are considered, they can still be applied using distance functions. Moreover, they allow testing linear restrictions. Only SFA accounts for exogenous or stochastic effects, which are especially important in natural resource and environmental economics. As a consequence, SFA leads to higher efficiency estimates than DEA and DFA (Hjalmarsson et al., 1996; Reinhard et al., 2000).
We focus here on the comparison between DFA and several SFA variants to estimate technical efficiency using production and technological data. The deviations (it in Equation (1)) from the catch frontier [f(Eit,St)] are represented in DFA by an asymmetric one-sided error, and in SFA by an asymmetric two-sided error composed of a two-sided random (
it) and a one-sided error term (uit
0):
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| (4) |
it is usually assumed to be normally distributed, with zero mean and constant variance. There are no a priori reasons to prefer a specific distribution on the inefficiency error uit, although a truncated (half-normal) or strongly asymmetric (exponential) model may be preferred from an econometric point of view (Greene, 1990). These distributions were assumed here.
If cross-section data are used, t is eliminated from Equation (3). In contrast, if panel data are used, t remains in. In DFA, the deterministic frontier for cross-section data may be estimated by Corrected Ordinary Least Squares (COLS). First, a classical regression model is estimated by Ordinary Least Squares (OLS). At a second stage, OLS intercept and residuals are corrected using the maximum residual estimated. Therefore, the catches of all vessels lie under the estimated frontier and all new residuals (technical inefficiency) are smaller or equal to zero (Winsten, 1957). Once technical inefficiency is estimated, technical efficiency (TE) can be computed using Equation (5).
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| (5) |
The estimation procedure for the stochastic frontier in SFA depends on the kind of data used. Cross-section data and panel data models may be estimated by a maximum likelihood (ML) procedure. In the case of panel data, it is possible to consider time-invariant or time-variant technical efficiency, or to incorporate technological change. Panel data models may also be estimated by Least Squares with Dummy Variables or fixed-effects model (LSDV; Cornwell et al., 1990).
When using the ML procedure, the estimation is based on the mean or the mode of the conditional distribution of the inefficiency error for each DMU (JLMS; Jondrow et al., 1982) and technical efficiency can be computed using Equation (5). Another option is to consider the expected value of (5) directly (BC; Battese and Coelli, 1988).
In the case of the fixed-effects model for panel data, technical inefficiency can be computed by subtracting the maximum intercept from all intercepts estimated in the model for each DMU and technical efficiency would result from Equation (5).
Four technical efficiency models were estimated:
- Model 1: DFA for cross-section data estimated by COLS.
- Model 2: SFA for cross-section data estimated by ML, assuming a half-normal distribution for the inefficiency error term. Inefficiency terms were estimated by JLMS and BC.
- Model 3: Fixed-effects model for panel data estimated by LSDV.
- Model 4: SFA for panel data estimated by ML, assuming a half-normal distribution for the inefficiency error term. Inefficiency terms were estimated by BC.
- Model 2: SFA for cross-section data estimated by ML, assuming a half-normal distribution for the inefficiency error term. Inefficiency terms were estimated by JLMS and BC.
DEA may be run using any general software developed for mathematical programming like GAMS (Brooke et al., 1998) or any other specifically designed software like DEAP. DFA and SFA may be run by any econometric software with optimization routines like LIMDEP (Greene, 1998) or FRONTIER2
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3 Results |
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Top1 Introduction2 Methods3 Results4 DiscussionReferences |
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Some linear restrictions on the flexible translog functional form (Equation (3)) have been tested in the order given in Table 3. This test provides information about some properties of the fish capture function. Based on the critical values shown, assumptions of homogeneity (R1), global separability (R3), and unitary elasticity of trips (R4) were accepted, whereas the assumption of constant returns to scale (R2) was rejected. Thus, the definitive form of the technology is a Cobb–Douglas function for 1998 and 1999, which after appropriate transformations in Equation (3) reads:
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| (6) |
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Initially, other technical characteristics of vessels (gross tonnage, GT; vessel length, VL) have been considered as well. However, linear correlations between size variables were high (GRT vs. GT: 0.91; GRT vs. VL: 0.66; GT vs. VL: 0.75). As a consequence, including all variables in the models resulted in multicollinearity. GRT was used instead of GT because of a recent regauge in the fleet. In addition, GRT was more significant than length.
FD, CM, and vessel age or engine power were less mutually correlated and multicollinearity was not a problem. Also, their correlations with size variables were much lower. Engine power was the only variable that did not contribute significantly to the model, indicating that this is not a crucial factor for purse-seine vessels. However, this fishing gear is quite labour-intensive and CM was significant and therefore included in the models. FD best explained weekly catch. The associated factor was almost equal to one in all models, indicating unitary elasticity of this variable (Table 4). Presence of the ship owner among the crew, nominal fishing gear of each vessel, and construction material (wood or polyester) were also considered. However, none proved to be significant and they were therefore deleted from further analyses.
The differences in the means and variation coefficients of the estimates of technical efficiency among the models (Table 5) are discussed in the next section.
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4 Discussion |
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Top1 Introduction2 Methods3 Results4 DiscussionReferences |
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Different models result in different estimates of parameter values and of technical efficiency. For cross-section data, model 1 provides much lower estimates of inefficiencies than model 2, but vessels are sorted in the same way in relation to inefficiencies. These differences are caused by the consideration of stochastic influences in the capture function in model 2.
Model 2 shows that BC efficiency indicator has more dispersion than JLMS and its average efficiency is a little bit lower. Model 2 is nearly the same as model 1 except for the intercept, as expected because of the mutual consistency of the two estimators (Fried et al., 1993).
For panel data, the variable GRT is not significant in model 3 because it does not change among the observations of individual vessels and would be highly correlated with the dummy variables of the intercepts determining the fixed effects. However, the capture technology of the fleet appears to be quite well explained because the model fits well.
The efficiency indicators determined by BC in model 4 are quite different from the results of model 3. This is caused by the scale change when efficiencies are determined using model 3. However, model 4 sorts vessels in the same way as the other models and its dispersion is the lowest of all indicators.
The results indicate how the production process in this fishery should be interpreted. Fishing power is determined by taking into account vessel characteristics. In purse-seine vessels, GRT and number of crew are especially important. However, the different technical efficiency estimates provided by these models might have different policy implications because they imply different levels of fishing capacity and, consequently, capacity excess.
The regulation of anchovy and sardine fisheries by EU based on total allowable catch (TAC) for vessels >12 m appears inappropriate because there is a small negative correlation between vessel efficiency and length and because a large number of vessels measure less than 12 m.
We have observed that the higher the useful life (the year in which vessels are made subtracted from the year in which they are decommissioned) is, the smaller the technical efficiency is (Pearson correlation coefficient = –0.86). Therefore, efficient, and more profitable, vessels are renewed (57% of the sample) before the least technically efficient vessels because their highest profits are reinvested in their activity.
Additional model changes in models should be evaluated to take account of possible changes in technology and vessel characteristics. For the bottom-trawl fleet, multispecies production functions appear to be the most promising approach because it is difficult to determine only one target specie for each trip.
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Acknowledgements |
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We thank Niels Daan, Jan Willem de Wilde, MEMPES research group members, and an anonymous referee for helpful comments and suggestions. The study was partly funded by EU project number QLK5-CT1999-01295 "Technical efficiency in EU fisheries: implications for management through effort controls (TEMEC)".
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Footnotes |
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This limit is only used to control effort, though the catch information provided to the EU takes into account vessels measuring <12m (Council Regulation EEC no. 2847/93).
DEAP and FRONTIER are free software developed by Tim Coelli and available from www.uq.edu.au/economics/cepa/index.htm.
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