Factors affecting technical efficiency in fisheries: stochastic production frontier versus data envelopment analysis approaches

Fisheries Research 73 (2005) 363–376

Factors affecting technical efficiency in fisheries: stochastic production frontier versus data envelopment analysis approaches Diana Tingley, Sean Pascoe ∗ , Louisa Coglan Centre for the Economics and Management of Aquatic Resources (CEMARE), University of Portsmouth, Boathouse No. 6, College Road, HM Naval Base, Portsmouth PO1 3LJ, UK Received 12 March 2004; received in revised form 11 January 2005; accepted 13 January 2005

Abstract Technical efficiency (TE) measures the relationship between a vessel’s inputs to the fishing process and its outputs, with full efficiency being achieved when outputs are maximised from a given set of inputs. Inputs can be fixed (e.g. the vessel, gear, engine, onboard equipment, etc.) or variable (e.g. time spent fishing, size of crew). Fixed inputs may also be intangible, such as skipper skill and quality differences between technologies. TE scores can be calculated using the econometric stochastic production frontier (SPF) or the non-stochastic, linear-programming data envelopment analysis (DEA) methodologies. This paper compares the results of both techniques for segments of the English Channel fisheries. The influence of factors most affecting technical efficiency is analysed using an SPF inefficiency model and tobit regression of DEA-derived scores. Such factors include vessel and skipper characteristics. It is argued that DEA can be used as an alternative to SPF techniques when there is difficulty in specifying the correct SPF model. There is general consistency between SPF and DEA analyses in regard to the factors affecting TE. © 2005 Elsevier B.V. All rights reserved. Keywords: Technical efficiency; Data envelopment analysis; Stochastic production frontiers; Tobit regression; Fisheries

1. Introduction Fisheries management in Europe is imposed through a series of input and output controls. The level of output ∗ Corresponding author. Present address: Department of Economics, Centre for the Economics and Management of Aquatic Resources (CEMARE), University of Portsmouth, Boathouse No. 6, HM Naval Base, College Road, Portsmouth PO1 3LJ, UK. Tel.: +44 23 92844242; fax: +44 23 92844614. E-mail address: [email protected] (S. Pascoe).

0165-7836/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fishres.2005.01.008

produced by each Member State’s fleet is, for most key species, constrained through the use of aggregate quotas imposed centrally by the Council of the European Union. The continual decline in key stocks subject to quota controls over the last two decades has resulted in the development of a complex licensing and decommissioning system in an attempt to balance the level of inputs employed with the available output. Total fleet capacity limits have been imposed on each EU Member State, defined in terms of total gross tonnage and engine power. These have been progressively reduced

364

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

over the last two decades under a series of multi-annual guidance programmes (MAGPs), part of the Structural Policy of the EUs Common Fisheries Policy. Although the last MAGP finished in 2002, limits on total tonnage and engine power remain. Limits on numbers of days that vessels can spend at sea have also been implemented to control fishing effort, and form the basis of the EUs current stock recovery programmes for cod and hake. An implicit assumption in the use of input controls is that vessels are relatively homogeneous in terms of efficiency and capacity utilisation. If such was the case, then a given reduction in fleet numbers would result in a proportional reduction in fishing effort and, consequently, fishing mortality. However, heterogeneity in efficiency and capacity utilisation has been demonstrated to be a feature of many European fisheries (see Vestergaard et al., 2003; Tingley et al., 2003; for recent examples of capacity utilisation; Pascoe et al., 2001, 2003; Herrero and Pascoe, 2003; for recent examples of efficiency). Given this heterogeneity, the choice of which vessel to remove has an impact on the efficacy of the management measure. Further, understanding the factors that affect the level of efficiency and capacity utilisation is important, as changes in these factors may reduce the benefit of any input control programme. Relatively few studies have attempted to determine the factors affecting efficiency in fisheries. Pascoe et al. (2001) found that boat characteristics (e.g. vintage of engine and hull, crew number, etc.) as well as management changes can directly affect the efficiency of individual fishing vessels. Similarly, Eggert (2001) found that boat age, size and base location (i.e. home port) have a significant impact on the level of technical efficiency. Pascoe and Coglan (2002) found that differences in boat characteristics explained around one third of the variation in technical efficiency of English Channel trawlers, and attributed the remainder to unmeasurable characteristics such as skipper skill and differences in technology that could not be quantified. Other studies have also suggested that much of the difference in efficiency between vessels may be due to differences in skipper skill (e.g. see Squires and Kirkley, 1999). The previous studies of efficiency were limited in that information on skipper characteristics and onboard technology was generally not available. As a result, these factors were assumed to explain much of the unaccounted variation in efficiency, but were not directly

quantified. In this study, the contribution of skipper characteristics and technology to efficiency is explicitly examined. Further, the effects of different estimation techniques on the derived relationships (and efficiency scores) is also examined. Technical efficiency (TE) of vessels undertaking a range of fishing activities in the English Channel is estimated using two contrasting methodologies. The stochastic production function (SPF) approach is an econometrically based method of estimating a quantitative measure of TE. Efficiency scores are also estimated using data envelopment analysis (DEA), a linear programming-based method. Whilst the distribution of SPF and DEA efficiency scores have been compared in other studies (e.g. Sharma et al., 1997), a comparison of the information implicitly contained in these scores (i.e. the factors affecting efficiency) has generally not been undertaken. In this paper, the results of the two approaches applied to three different fleet types operating in the English Channel are compared, and consistencies and inconsistencies identified. Tobit regression was used to estimate at the impact of boat and skipper characteristics on the DEA-derived scores. Similarly, an inefficiency model was incorporated into the SPF analysis to estimate the contribution of these factors to the econometrically derived TE scores. Implications of the results for management are also discussed.

2. Estimation of efficiency Farrell (1957) developed a conceptual model involving the contraction of inputs to an efficient frontier that laid the foundations for the development of both the parametric (SPF) and non-parametric (DEA) estimation of efficiency. The efficient frontier can be considered in terms of either the maximum output for a given set of inputs (an output orientation), or the minimum set of inputs required to produce a given set of output (an input orientation). These both relate to the assumption of profit maximisation, the former approach representing the maximisation of revenue for a given level of costs, while the latter approach minimises the costs for a given level of revenue.1

1 Neither approach necessarily ensures profit maximisation, as different combinations of inputs and outputs could further increase prof-

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

The study of efficiency in fisheries, as in many other industries, has largely adopted an output oriented (or primal) approach, on the assumption that fishers aim to maximise their revenue each trip. Given such an assumption, the level of efficiency of a particular firm is characterised by the relationship between observed production and some ideal or potential level of production (Greene, 1993). The measurement of firm specific technical efficiency is based upon deviations of observed output from the best production or efficient production frontier. If a firm’s actual production point lies on the frontier it is perfectly efficient. If it lies below the frontier then it is technically inefficient, with the ratio of actual to potential production defining the level of efficiency of the individual firm. Two methodologies are commonly used to describe the efficient production frontier and therefore estimate efficiency scores: stochastic production frontier (SPF) analysis and data envelopment analysis (DEA). These involve a parametric and non-parametric approach respectively to the estimation of the frontier and the level of efficiency. 2.1. Stochastic production frontier and inefficiency model

(1)

where yj is the output produced by firm j, x a vector of factor inputs, vj the stochastic error term and uj is the estimate of the technical inefficiency of firm j (where TEj = e−uj ). The stochastic error term is assumed to by normally distributed (N[0, σv ]), while the inefficiency term has a distribution truncated at zero. Several alternative assumptions about this distribution can be examined, as will be discussed below. There are several potential function forms of the production frontier, the most common being the translog production function, given by
ln yj = β0 + βi ln xj,i i

+

1

2

i

βi,k ln xj,i ln xj,k − uj + vj

The Cobb–Douglas production function is a special case of the translog production function, where all βi,k = 0.In order to separate the stochastic and inefficiency effects in the model (i.e. vj and uj from the combined error term, vj − uj ) , a distributional assumption has to be made for uj . Several different distributional assumptions have been proposed, the most common being a normal distribution truncated at zero,   for example, uj ≈ N(µj , σu2 ) (Aigner et al., 1977) and a half-normal  distribution truncated at zero, i.e. uj ≈ N(0, σu2 ) (Jondrow et al., 1982). A further approach is to define the inefficiency as a function of the firm specific factors such that u = zδ + w

(3)

where z is the vector of firm-specific variables which may influence the firms efficiency, δ the associated matrix of coefficients and w is a matrix of random error terms (N[0, σw ]). The parameters of the inefficiency model are estimated in a one-step procedure (Battese and Coelli, 1995) along with the parameters of the production frontier. 2.2. Data envelopment analysis

A general SPF model can be given by ln yj = f (ln x) + vj − uj

365

(2)

k

its. However, if we consider that either outputs or inputs are constrained (such as under individual quotas or days at sea restrictions, respectively), then the models do approximate profit maximisation.

DEA is a non-parametric, linear-programming approach to the estimation of TE. The technique does not require any pre-described structural relationship between the inputs and resultant outputs, as is the case with SPF analysis, so allowing greater flexibility in the frontier estimation. It can also accommodate multiple outputs into the analysis. A disadvantage of the technique, however, is that it does not account for random variation in the output, and so attributes any apparent shortfall in output to technical inefficiency (i.e. the estimated efficiency score is effectively vj − uj following the same terminology as for the SPF model, where the true values of both vj and uj are unknown). Random error can, and typically will, push out the frontier as well as lead to misinterpreting error for inefficiency at the individual boat level.2 2 For example, if v > u , the frontier is effectively pushed out j j by vj − uj , resulting in a downward bias in the estimated efficiency scores of other vessels. Thus, an inefficient vessel might be determined to be fully efficient (on the frontier) due to random error, while an efficient vessel may be determined to be inefficient (e.g. if vj < 0, uj = 0). This error is further compounded by the frontier

366

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

The DEA model is formulated as a linear programming (LP) model, where the value of θ for each vessel can be estimated from the set of available input and output data. Following F¨are et al. (1989, 1994), the DEA model of technically efficient output requires both variable and fixed inputs to be considered. The DEA model for this technically efficient measure of output is given as Max θ subject to

2.3. DEA versus SPF

max θ θy0,m ≤
subject to

that fishing would be subject to decreasing returns to scale (DRS),3 although imposing DRS may result in an infeasible solution when considering vessels on the frontier. Imposing non-increasing returns to scale overcomes this problem. The technically efficient level of output is defined TE = θy as θ multiplied by observed output (i.e. y0,m 0,m ). The level of TE is estimated as TE = 1/θ, which has a value 0 ≤ TE ≤ 1.




zj yj,m ∀m

j

zj xj,n ≤ x0,n ∀n

(4)

j




zj = 1, zj ≥ 0

j

where θ (≥1) is a scalar denoting the multiplier that describes by how much the output of the target boat (i.e. j = 0) can be expanded using inputs in a technically efficient configuration. Further, yj,m is the output m produced by boat j, xj,n is the amount of input n used by boat j, and zj are weighting factors such that technically efficient output is the weighted sum of the output of other vessels in the data set, including itself. The value of θ is estimated for each vessel separately, with the target vessel’s outputs and inputs being denoted by y0,m and x0,n , respectively. Inputs include both fixed and variable factors, which are constrained to their current levels. The shape of the frontier will differ depending on the scale assumptions that underlie the model. The  restriction zj = 1 imposes variable returns to scale. In contrast, excluding this constraintimplicitly  imposesconstant returns to scale, while zj > 1, zj < 1 and zj ≤ 1 imposes increasing, decreasing and nonincreasing returns to scale, respectively (F¨are et al., 1989). There are generally a priori reasons to assume being pushed out by ‘lucky’ but potentially inefficient vessels. Other vessels’ efficiency might be either under or overestimated both because of the shift in the frontier and where it is placed relative to the frontier. Random error in its own production, i.e. vj < 0 results in the efficiency being underestimated while vj < uj results in the efficiency being overestimated.

Several studies in other industries have compared the distributions of the efficiency scores estimated using the two techniques (e.g. Neff et al., 1993; Sharma et al., 1997), or confirming the trends in efficiency (e.g. Zaibetand and Dharmapala, 1999; Uri, 2001). However, relatively few comparative studies in fisheries have been undertaken (e.g. Coglan et al., 1998; Pascoe et al., 2003). The studies in both fisheries and other industries have generally found that the DEA efficiency scores are correlated with, but lower than, those estimated using SPF—a consequence of random error biasing the DEA scores downwards (see Footnote 2). In more recent studies of efficiency, attention has been focused on factors that affect efficiency rather than the level of efficiency per se (e.g. Pascoe et al., 2001; Pascoe and Coglan, 2002). This can be undertaken using a one-step process with SPF, where the inefficiency model incorporating variables believed to affect efficiency is estimated simultaneously with the production frontier (Battese and Coelli, 1995). With DEA, a twostage process is required. Efficiency scores are first estimated, and these are then regressed against the factors believed to affect efficiency. Given the limited range of the efficiency scores (i.e. 0–1), tobit regression analysis is more appropriate than ordinary least squares. In this paper, several factors are examined. These include measures relating to both technology and skill. Several different technologies are considered, including sonar and navigational aids. Skipper education, experience, family history and age characteristics are incorporated as proxies for ‘skipper skill’.

3 This assumption generally holds for most demersal fisheries (Pascoe and Robinson, 1998; Herrero and Pascoe, 2003).

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

3. Data The data set used in this analysis was derived from two main sources. The first source was logbook records of trip-level data for vessels fishing in the English Channel, provided by the UKs Department for Environment, Food and Rural Affairs (DEFRA). These data were used primarily to generate TE scores and included information on the value of catch landed, gear type, area fished and length of trip. Vessel characteristics such as size, engine power and vessel age were also available from the DEFRA database. Trip records were summarised by vessel at the annual level for the period available, 1993–1998. The second source of data was provided by a survey of skippers fishing a range of mobile and static gears in the English Channel area. Only skippers fishing fulltime were interviewed, with full-time being defined as activity in more than 4 months of a year and in at least three of the years being studied. The survey collected information on annual revenues and fishing activity in 1999 and 2000 thus allowing the original DEFRA data set to be updated to cover the period 1993–2000. TE estimation requires data on inputs and outputs to the production process. A limitation of the SPF approach is that it only considers a single output. As the vessels catch a range of species, some form of aggregation of output was necessary. For consistency, the same measure was used in the DEA analysis. Average annual real revenue per vessel was used as the output measure in the estimation of efficiency. Reliable information on catch quantities was not available from the 1999 to 2000 surveys, restricting the potential for using other aggregation methods (e.g. divisia index). The revenues were inflated/deflated to 1998 values using a Fisher price index. A different Fisher price index was estimated for each fleet segment representing the different combinations of species in the catch, thereby removing the effect of price changes in the output measure.

367

These data were also adjusted for changes in relative stock abundance following the method of Pascoe and Herrero (2004). Input data were available in the form of number of days fished per year, vessel engine power and overall length (Table 1). The fleet were divided into three categories according to main fishing activities: (1) mobile gears (otter trawl, beam trawl and scallop dredge), (2) pots (mostly targeting crustaceans) and (3) other static gear (nets and hand line). While many vessels are multi-purpose, often using several gears over the year, most of their activities are limited to within one of these three groups. The main objective of the skipper survey was to gather information about the level of a vessel’s fishing activity, operational details and onboard technology as well as the skipper’s characteristics. Additional information not available from the DEFRA logbooks, such as crew numbers, was also collected. The onboard electronic technology categories included data on whether vessels were using navigational aids (GPS, GPS plotter), echo sounder, sonar and autopilot. Skipper characteristics included information on age, length of fishing experience, family fishing history, formal and vocational education levels and training in boat handling skills. A number of additional variables were also generated from the available data. The total time the vessel fished over the period of the data was taken as a proxy for the level of activity in the fishery. This was designed to address the question: are more efficient skippers more active in the fishery? An interaction term (kW/OL) between the overall length (OL) of the vessel and its engine power (kW) was also developed for use in the inefficiency model. This was assumed to be an alternative proxy measure of boat size, as the ratio of engine power to length increases exponentially as boat size increases. This variable allows the relationship between boat size and efficiency to be investigated,

Table 1 Input and output data used to calculate TE scores (1993–2000)

Mobile Pots Net–line

No. of boats in sample

Total number of observations

Inputs Avg. annual days fished

Engine power (kW)

Overall length (m)

Outputs: adjusted average annual revenue (£)

18 26 24

117 95 87

171 116 120

217 72 113

14 8 10

144613 39101 53635

368

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

while avoiding having the same variables in both the production function and inefficiency model. The latter set of variables (i.e. length, engine power and the interaction terms) is used to estimate the contribution of these inputs to the level of production, whereas the variable in the inefficiency model addresses the question: do more efficient skippers also tend to operate larger vessels?

4. Model specification and results 4.1. SPF A translog frontier production function was initially specified for each of the three groupings of fishing activity. Inputs and outputs used in the model were as shown in Table 1. Gear specific dummy variables

Table 2 Production frontier and inefficiency model results Mobile gear

Production frontier Constant ln days ln kW ln OL ln2 days ln2 kW ln2 OL ln day × ln kW ln day × ln OL ln kW × ln OL Beam dummy Dredge dummy Pelagic dummy Line dummy R2 Inefficiency model Intercept ln activity ln (crew/m OL) ln (boat vintage) Ln (kW/m OL) Navigational aid Sounder/sonar Auto-pilot ln (skipper age) ln (experience) Family history Formal education Vocational education Boat handling σ2 γ γ* Log likelihood r2 ∗ ∗∗ ∗∗∗

Significant at the 10% level. Significant at the 5% level. Significant at the 1% level.

Potters

Net–liners

Coefficient

t-ratio

Coefficient

t-ratio

Coefficient

t-ratio

12.13 2.21 −7.04 3.57 −0.06 0.09 −0.05 0.82 −1.68 1.20 −2.59 0.11 1.67

10.28*** 2.85*** −8.31*** 1.75* −0.76 0.42 −0.05 4.15*** −3.66*** 1.68* −7.07*** 0.52 5.84***

−0.76 2.48 2.03 −2.39 −0.23 0.69 3.75 −0.15 0.34 −3.15

−0.79 2.95*** 2.73*** −1.34 −3.17*** 4.12*** 3.20*** −0.72 0.57 −4.54***

−3.33 1.50 0.87 1.37

−3.55*** 10.83*** 2.23** 1.53

−0.25

−0.95

0.94

−0.07 1.49 −0.54 −1.33 −0.47 −0.01 −0.20 −1.95 0.72 1.16 −0.21 0.44 −1.29 0.36 0.06 0.63 0.38 10.308 0.79

0.63

−0.06 4.42*** −2.42** −3.30*** −2.10** −0.06 −0.83 −4.56*** 1.92* 3.60*** −3.56*** 1.69* −2.54** 1.51 4.83*** 7.18***

0.83

2.24 1.66 1.90 1.52 −1.79 −3.21 0.21 −0.31 1.41 −2.01 0.13 2.39 −0.20 1.97

2.13** 2.90*** 1.97* 2.31** −3.46*** −3.48*** 0.35 −0.56 2.09** −3.21*** 0.55 2.56** −0.20 2.19**

−0.03 1.62 −0.55 −0.16 0.63 −1.05 −0.43 0.11

−0.04 4.56*** −1.37 −0.57 1.76* −3.38*** −1.15 0.25

1.24 0.90 0.77 −70.103 0.07

4.23*** 19.79***

0.39 0.08 0.03 −75.33 0.76

4.69*** 4.01***

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

369

Table 3 Specification tests L(H0 )

L(H1 )

λa

Significance

Mobile gears βi,i = βi,i = · · · = βi,i j = 0 γ =0 δ1 = δ 2 = · · · = δ n = 0

−26.22 −29.56 −24.27

10.31 10.31 10.31

73.06 79.74 69.15

0.00 0.01b 0.00

Potters βi,i = βi,i = · · · = βi,i = 0 γ =0 δ1 = δ 2 = · · · = δ n = 0

−76.27 −88.68 −88.68

−70.10 −70.10 −70.10

12.33 37.16 37.16

0.05 0.01b 0.00

Net–line boats βi,i = βi,i = · · · =βI,i = 0 γ =0 δ1 = δ 2 = · · · = δ n = 0 δ7 = δ8 = · · · = δ14 0

−72.23 −93.88 −93.62 −75.33

−64.09 −72.23 −72.23 −72.23

16.29 43.29 42.76 6.20

0.18 0.01b 0.00 0.62

a b

λ = −2[ln{L(H0 )} − ln{L(H1 )}]. Based on the critical value determined by Kodde and Palm (1986).

were used in each function to test the effect of specific gear types on the model. The inefficiency component of the model included data on vessel characteristics, onboard electronic technology and skipper characteristics. The results of each model are shown in Table 2. For all three gear types, the level of inputs was the main determining factor affecting the level of output, explaining 94%, 63%, and 83% of the variation in output of the mobile gear boats, potters and netter–liners, respectively. As with all econometric analysis, results are highly dependent on specifying the correct functional form of the model. In all cases, the model was original specified as a translog production frontier. The hypothesis that the correct functional form of the model is Cobb–Douglas was imposed by removing the squared and cross product terms from the translog production function (i.e. H0 :βi,k = 0) and re-estimating the model. This was rejected at the 1% level of significance for the mobile gear vessels (Table 3). For the potters, the likelihood ratio test value (λ) was almost significant at the 5% level, and most of the cross product and squared terms were significant, so the translog functional form was kept. For the net–liners, a Cobb-Douglas functional form was accepted as the restrictions (βi,k = 0) could not be rejected (Table 3). The presence of inefficiency was also confirmed for all gear types using the one-sided generalised likeli-

hood ratio-test (H0 :γ = 0, Table 3).4 The test to determine whether inefficiency variables were jointly not significant (H0 :δi = 0, Table 3) was also applied. This hypothesis was rejected at the 1% level for all models, except it was found that skipper characteristics for the net–liners could be excluded without significant effect on the model. The contribution of vessel characteristics and onboard electronic technology to the model was also found to be jointly non-significant. However, some individual variables were significant and so were kept in the model. For the SPF analysis, the relative importance of inefficiency and random error in the catch component not explained by the inputs, can be estimated. From Table 2, γ * indicates the proportion of total variance in the combined error attributable to inefficiency. Inefficiency was found to represent 38% of the residual variation of mobile activities, 77% for potting and only 3% for net–liners (Table 2). From this, random error explains 62%, 23% and 97% of the non-input related variation in catch, respectively, for the three gear types.

4 The proportion of the combined error term can be derived from the estimated value of γ(= σu2 /(σu2 + σv2 )). The estimate of γ provided in the MLE results is only an approximation of the contribution of inefficiency to total variance as the true variance of ui is proportional but not exactly equal to σu2 (Coelli et al., 1998). The corrected relative contribution of inefficiency is given by γ * = γ/[γ + (1 − γ)π/(π − 2) (Coelli, 1995).

370

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

In each of the mobile and potter models, eight variables were found to have a significant impact (at the 5% level) on efficiency scores. Only two variables were significant in the net–liner model; skipper characteristics had already been removed from the inefficiency model as their exclusion was found to have no significant effect. The components within the SPF inefficiency model explained varying proportions of the actual inefficiency. An approximation of the goodness of fit measure, R2 , can be obtained from the square of the correlation coefficient (i.e. r2 ) between the observed and predicted efficiency scores given the characteristics of the vessel. For the mobile gear and netter–liners, the factors explained over three quarters of the variation in efficiency (Table 2). In contrast, these factors explained less than 10% of the variation in efficiency for the potters, suggesting non-measurable factors such as skipper or crew skill not directly related to training or experience are a dominant influence. 4.2. DEA To allow for a direct comparison of results, the DEA measures of efficiency were estimated using the same set of inputs derived from the same data set as used in the SPF analysis (i.e. average annual days fished, engine power and overall vessel length). Despite the method’s ability to handle multiple-output data, the same single composite output measure was used for direct comparison.5 Each of the three fishing activity categories were analysed separately. Similarly, separate DEA analyses were run for each year in the 1993–2000 period. As DEA is a non-parametric method, no econometric tests are available to gauge the appropriateness of the estimated frontier and efficiency scores. Tobit regression was used to determine which factors influence efficiency, using a log-linear form of the model. The results of the second-stage analysis are shown in Table 4. Individual variables that were found to be not significant were excluded and the models re-estimated, with 5 F¨ are et al. (1994) suggest that a more appropriate specification of the DEA model when using revenue as the output measure is to separate out revenue into quantity and prices, and to include the individual output quantities in the constraint set. The objective function of such a model is then revenue maximisation. As catch quantity data were not available for all time periods, this approach could not be adopted.

appropriate exclusion tests performed to ensure that the restricted model was econometrically valid. As with the SPF analysis, the square of the correlation coefficient (r2 ) between the observed and predicted efficiency scores was used as an indication of the goodness-of-fit of the tobit regression models. The variables in the model explained 85% of the variation in efficiency scores of the mobile fleet (Table 4), and 55% of the variation in the net–line efficiency scores. However, as with the SPF model, only a small proportion (6%) of the variation in potting efficiency was explained by the model. 4.3. Comparison of the results The SPF TE scores were consistently greater than DEA scores and had smaller variances (Table 5 and Fig. 1). On average, SPF scores were between 16% (mobile) and 30% (net/line) greater. This result is largely expected and consistent with other studies, as the DEA scores are affected by the random error. Individual annual vessel scores were significantly correlated for all segments.6 However, when these scores were averaged for each vessel over the whole period, a significant correlation was only found between SPF and DEA TE scores for potters. Average scores at both the individual vessel and fleet level (i.e. average of all vessels) were weighted by revenue to reduce the potential influence of relatively inactive periods and/or vessels on the vessel or fleet averages (this influence may have been positive or negative, with no a priori expectations either way). Vessel rankings, as opposed to actual scores, for the whole time period were also found to be significantly correlated for potters. When weighted average annual fleet scores were examined, a significant correlation over time was only present for the mobile gear fleet There was a general consistency between the results of the factors affecting efficiency scores derived using each method (Table 6). For mobile gear vessels, the 6 The mobile gear correlation analysis excluded pelagic trawl vessels. Data were only available for one vessel over the period of the study. Its fishing method is very different to that of the other mobile gears, and preliminary analyses indicated that its inclusion distorted the correlation results. The pelagic vessel was included in the regression analysis, but its influence was moderated through the use of a dummy variable.

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

371

Table 4 DEA/tobit regression results Mobile gear Coefficient Gear intercept shifters Beam dummy Dredge dummy Pelagic dummy Line dummy Efficiency model Intercept ln activity ln (crew/m OL) ln (boat vintage) ln (kW/m OL) Navigational aid Sounder/sonar Auto-pilot ln (skipper age) ln (experience) Family history Formal education Vocational education Boat handling quality

∗ ∗∗∗

Coefficient

Net–line t-ratio

Coefficient

0.77 1.40

4.95*** 7.88***

−5.45 1.18

−12.18*** 13.08*** 0.56

0.18

2.27**

8.54

1.87*

0.79

2.99***

1.48

12.26*** 0.76 −0.49

1.18 3.05*** −1.79*

−0.32 0.23 0.97

−3.61*** 7.19*** 11.35***

0.57

7.26***

Mean square error r2 ∗∗

Potters t-ratio

0.01 0.85

11.10***

t-ratio

3.39***

2.15**

0.39

−2.51 −0.51

0.56 0.06

−4.09***

−2.30**

0.05 0.55

Significant at the 10% level. Significant at the 5% level. Significant at the 1% level.

variables kW/OL, fishing experience and family history are consistently signed and significant between the inefficiency model and linear tobit regression. The significance and positive influence of the kW/OL variable suggests that more efficient skippers are likely to be found on the larger vessels. Fishing experience is negatively related to efficiency, however family history

is positively related. It is assumed that the family history variable encompasses a handing down of fishing ‘knowledge’ and ‘intuition’ between generations and this would seem to affect efficiency positively as opposed to simply having spent many years working at sea as represented by the fishing experience variable. There is a contradiction between models as to the influence of

Table 5 TE scores derived from SPF and DEA analyses (average, 1993–2000) SPF

Mobile Pots Net/line ∗

Correlation between SPF and DEA scoresa

DEA

TE

Var

TE

Var

Average annual vessel score

Average vessel score over entire period

Individual vessel ranking over entire period

Average annual fleet score

0.65 0.76 0.79

0.049 0.059 0.083

0.56 0.63 0.61

0.077 0.106 0.106

0.443* 0.596* 0.293*

0.461 0.533* 0.227

0.283 0.619* 0.050

0.982* 0.157 0.461

Significance at 5% level. Pearson correlation coefficients are presented, except for ‘Individual vessel ranking’ where a Spearman rank correlation coefficient is presented. a

372

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

Fig. 1. Average efficiency estimates (a) for each vessel over time and (b) averaged over the vessels for each year.

Table 6 Summary of effects on efficiency Mobile gear

Boat characteristics Activity Crew/OL Boat vintage kW/OL Technology Navigational aid Sounder/sonar Auto-pilot Skipper characteristics Age Fishing experience Family history Formal education Vocational education Boat handling

Potters

Net–line

SPF

DEA

SPF

DEA

↓ ↑ ↑ ↑

↑

↓

↑

↓ ↑

↑

↑

↑

SPF ↓

DEA

↑ ↑

↑

↑ ↓ ↑ ↑

↓ ↑ ↑ ↑

Key: ↑, ↓ significant increase or decrease (respectively) at the 5% level.

↓ ↑

↓

↓

↓

↓

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

an index of the level of fishing activity—the variable is significant in each model but with opposite signs (Table 6). A general consistency between results was also shown for potting vessels: kW/OL and navigational aids were significant and similarly signed in both models. The positive influence of both engine size and navigational aids seems reasonable, particularly the latter which are important in the potting activity in terms of locating gear. A further six variables were significant in the SPF inefficiency model and a further two in the DEA tobit regression analyses, however none of these were common to both models. No variables were significant and similarly signed in both the net–line models; only two were significant in the inefficiency model, whilst four were significant for the tobit regression form.

5. Discussion and conclusions The use of revenue as the output measure is not ideal, as revenue is a function of prices as well as quantity. Consequently, price changes that affect the output measure independent of input use may be interpreted as changes in technical efficiency. This is particularly a problem for DEA, as there is the likelihood that price changes affecting all operators would enter the random error component when using SPF. Further, assuming fishers seek to maximise profit, a change in relative prices may result in a change in their fishing strategy. As a result, the function is not truly a production function and the efficiency scores may represent a combination of allocative as well as technical efficiency. The potential biases introduced into the analysis from using revenue as the output measure are not likely to be large. Squires (1987) and Sharma and Leung (1999) note that fishers base their fishing strategies on expected prices, the level of technology and resource abundance. However, price expectations are not always accurate, information on the variation in abundance of the stock across the fishery is generally not available, and catch composition is governed largely by fishing gear that is not perfectly species selective. Changing gears types is time consuming and usually needs to be done on shore rather than at sea (as only one type of gear is usually taken to sea at any one time, especially for the larger vessels operating in the English Channel).

373

Hence, the ability of fishers to respond to changes in relative prices by varying their fishing activity is limited. Several recent studies (e.g. Holland and Sutinen, 2000) have suggested that fishing activity is largely influenced by habit, with only relatively minor changes in effort allocations in response to price in the short term. The influence of price changes has been further reduced through the derivation of real revenues using the Fisher price index. The method used to adjust the output measure to remove the effects of changes in stocks also has the added advantage of removing any residual effects of relative price changes not captured in the price index, as well as technical change (Pascoe and Herrero, 2004). Consequently, the potential bias arising from the use of revenues is considered to be relatively small. In terms of factors influencing efficiency, both approaches were reasonably consistent. While not entirely consistent, the sign on the activity variable was, on balance, negative. This suggests that it is the less efficient skippers employing the most activity. This is consistent with a goal of profit maximisation, as fishing “flat out” would not necessarily lead to higher profits, and may lead to lower profits if the marginal cost of a trip exceeded the resulting marginal revenue. Conversely, the proxy measure for boat size (kW/OL) had a generally positive impact on efficiency. Rather than implying that larger vessels are inherently more efficient that smaller vessels, this suggests that the more efficient skippers tend to operate on the larger vessels. This is consistent with the finding of Boncoeur et al. (2000), who demonstrated that larger vessels had a greater income potential to the skipper, even if other economic performance indicators (e.g. rate of return to capital) suggested that smaller vessels were more profitable. Technology had varying impact on efficiency depending on the main gear types employed. For the mobile gear vessels, only the auto-pilot was found to significantly increase efficiency, and this only for the SPF model. From the coefficient in the SPF inefficiency model, vessels using an auto-pilot were, on average, seven times (i.e. e1.95 )7 more efficient than an 7 The SPF model is an inefficiency model. Hence, a negative coefficient indicates a decrease in inefficiency, so therefore an increase in efficiency. The DEA tobit regression model is an efficiency model, so a positive coefficient indicates an increase in efficiency associated with the variable (and vice versa).

374

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

equivalent vessel and skipper not using an auto-pilot, ceteris paribus. Navigational aids were found to be significant for both potters and the net–line vessels in the SPF model and potters in the DEA model. This is as expected as the effectiveness of these gears relies on the fisher finding them again. Navigational aids such as GPS enable the skipper to find the gear faster, allowing more gear to be worked per day, and fewer incidences of lost gear (and associated catch). Education and training was generally associated with lower levels of efficiency. Formal education in particular was generally negatively related to efficiency. From the SPF model results, potter skippers with formal education were roughly 10% (i.e. e−2.56 ) as efficient as their uneducated counterparts, ceteris paribus. However, this may be offset to some extent by their lower ages (correlation between education and skipper age = −0.36) and use of newer boats (correlation between education and vessel age = 0.2). This is at odds with most studies of efficiency that use formal education as a proxy for skill. As noted previously, education is generally assumed to be associated with increased efficiency as it broadens the producers’ minds and enables them to acquire and process relevant information (Ali et al., 1996). In the case of potting, where the stock is fairly immobile and sites can generally be revisited once found, there is reduced need to second guess where the shellfish may be. The significance of education in the SPF analysis, therefore, may be an artefact of the model, and is not supported in the DEA tobit analysis. In contrast, use of mobile gear requires an understanding of how the resource moves with changes in seasonal and climatic conditions, so requires greater skipper input. Vocational education and family history (where knowledge can be transferred from one generation to the next) were found to be significant in affecting the efficiency of the mobile gear in the SPF model. Both these factors as well as formal education had a significant positive impact on the efficiency of mobile gear boats in the DEA analysis. For the potters, skipper age was also generally found to be negatively correlated with efficiency. A possible explanation for this is that the younger skippers are more willing to change their fishing patterns in response to catch rates or prices, whereas older skippers may be more set in their ways. This is consistent with the arguments of Maurer (2001), that the incentives to

learn and develop decrease with age. However, an alternative hypothesis is that older skippers are physically less fit than younger skippers. Most of the potting boats were small, with often only one (or in many cases no) additional crew member. The skipper plays an integral role in raising the pots and sorting the catch. Older skippers may not be sufficiently fit to do this at the same rate as younger skippers, resulting in fewer pots being worked per day. This is less of a problem for trawlers and even the netter–liners, which tend to have larger crews, reducing the reliance on the physical strength of the skipper. From the results, while there exists the potential to reduce the gap in efficiency differential through training and technology, at least for the mobile gear vessels, there are still a number of factors that affect efficiency beyond those that can be readily quantified. It is likely that there is an individualistic element to skill that is independent of education, training or technology employed. This was evident for the potting fleet, where over 90% of the variation in efficiency was not due to the quantifiable factors. This may represent the unobserved ability suggested by Card and Lemieux (1996) but generally ignored in studies of labour skill. In most industries, some participants are naturally pre-disposed to certain skills and abilities that give them a productive edge. While training and technology may improve the productivity of those individuals that are not naturally skilled in fishing, there is likely to remain a large portion of efficiency differentials that cannot be explained though measurable inputs. This has two particular implications for fisheries management, particularly effort reduction through decommissioning. Firstly, the potential for fishers to increase effort through increasing their own efficiency (either through training or technology) appears to be limited, at least in the case study fishery examined. Secondly, the results of the study suggest that the skipper is removed and their subsequent activity may be as important than which vessel. An apparently efficient vessel may be removed under the decommissioning programme, but the skipper may move to another vessel previously considered as less efficient. If this occurs, the average efficiency of the remaining fleet may appear to increase as the more efficient skippers replace the less efficient skippers. This could be particularly problematic where much of the fleet is company owned, as the mobility of skippers between vessels would be

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

high. If the majority of vessels were owner-operated, there would exist additional transactions costs involved in purchasing the vessel. While the overall DEA TE scores may be affected by random error, the results demonstrated that both techniques are able to produce reasonable models of factors that affect efficiency. With only one exception, the analysis of the efficiency scores using the two methods (DEA and SPF) was consistent, at least in terms of direction of the effect. Based on the explanatory power of the models and the number, sign and consistency of significant variables between models, it can be concluded that the tobit regression of DEA-derived scores are generally as robust as those of the comparative SPF inefficiency model. Therefore, where SPF model specification is problematic, tobit regression of DEA-derived TE scores can be used as an alternative method to explain inefficiency.

Acknowledgements The study has been carried out with the financial support of the Commission of the European Communities Fifth Framework programme, QLK5-CT199901295, “Technical efficiency in EU fisheries: implications for monitoring and management through effort controls”. The data used in the study were compiled with the assistance of Ben Cattermoul. The authors would also like to acknowledge the valuable comments provided by the two anonymous reviewers.

References Aigner, D., Lovell, C.A.K., Schmidt, P., 1977. Formulation and estimation of stochastic frontier production function models. J. Econom. 6, 21–37. Ali, F., Parikh, A., Shah, M.K., 1996. Measurement of economic efficiency using the behavioral and stochastic cost frontier approach. J. Policy Model. 18 (3), 271–287. Battese, G.E., Coelli, T.J., 1995. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Econ. 20, 325–332. Boncoeur, J.L., Coglan, Le Gallic, B., Pascoe, S., 2000. On the (ir)relevance of rates of return measures of economic performance to small boats. Fish. Res. 49 (2), 105–115. Card, D., Lemieux, T., 1996. Wage dispersion, returns to skill, and black-white wage differentials. J. Econom. 74, 319–361.

375

Coelli, T., 1995. Estimators and hypothesis tests for a stochastic frontier function: a monte carlo analysis. J. Product. Anal. 6, 247–268. Coelli, T.J., Rao, D.S.P., Battese, G.E., 1998. An Introduction to Efficiency and Productivity Analysis. Kluwer Academic Publishers, USA. Coglan, L., Pascoe, S., Mardle, S., 1998. DEA versus econometric analysis of efficiency of demersal trawlers in the English Channel. In: Eide, A., Vassdal, T. (Eds.), IIFET’98 Tromso Proceedings. Norwegian College of Fisheries Science, Tromso, pp. 334–343. Eggert, H., 2001. Essays on Fisheries Economics. Ekonomiska Studier Utgivna av Nationalekonomiska Institutionen Handelsh¨ogskolan vid G¨oteborgs Universitet 106, Sweden. F¨are, R., Grosskopf, S., Kokkelenberg, E.C., 1989. Measuring plant capacity, utilization and technical change: a non-parametric approach. Int. Econ. Rev. 30 (3.), 655–666. F¨are, R., Grosskopf, S., Lovell, C.A.K., 1994. Production Frontiers. Cambridge University Press, UK. Farrell, M.J., 1957. The measurement of productive efficiency. J. R. Stat. Soc. A. 120, 253–281. Greene, W.H., 1993. Frontier Production Functions, EC-93-20. Stern School of Business, New York University. Herrero, I., Pascoe, S., 2003. Value versus volume in the catch of the Spanish South-Atlantic Trawl Fishery. J. Agric. Econ. 54 (2), 325–341. Holland, D.S., Sutinen, J.G., 2000. Location choice in New England fisheries: old habits die hard. Land Econ. 76 (1), 133–149. Jondrow, J., Lovell, C.A.K., Materov, I.S., Schmidt, P., 1982. On the estimation of technical inefficiency in the stochastic frontier production function model. J. Econom. 19, 223–238. Kodde, D.A., Palm, F.C., 1986. Wald criteria for jointly testing equality and inequality restrictions. Econometrica 54 (5), 1243–1248. Maurer, T.J., 2001. Career-relevant learning and development, worker age, and beliefs about self-efficacy for development. J. Manage. 27 (2), 123–140. Neff, D.L., Garcia, P., Nelson, C.H., 1993. Technical efficiency: a comparison of production frontier methods. J. Agric. Econ. 44 (3), 479–489. Pascoe, S., Coglan, L., 2002. Contribution of unmeasurable factors to the efficiency of fishing vessels. Am. J. Agric. Econ. 84 (3), 45–57. Pascoe, S., Herrero, I., 2004. Estimation of a composite fish stock index using data envelopment analysis. Fish. Res. 69, 91–105. Pascoe, S., Robinson, C., 1998. Input controls, input substitution and profit maximisation. J. Agric. Econ. 49 (1), 16–33. Pascoe, S., Andersen, J.L., de Wilde, J.W., 2001. The impact of management regulation on the technical efficiency of vessels in the Dutch beam trawl fishery. Eur. Rev. Agric. Econ. 28 (2), 187–206. Pascoe, S., Tingley, D., Mardle, S., 2003. Single output measures of technical efficiency in EU fisheries. CEMARE Report 61. CEMARE, UK. Sharma, K.R., Leung, P., 1999. Technical efficiency of the longline fishery in Hawaii: an application of a stochastic production frontier. Mar. Res. Econ. 13, 259–274. Sharma, K.R., Leung, P., Zaleski, H.M., 1997. Productive efficiency of the swine industry in Hawaii: stochastic frontier

376

D. Tingley et al. / Fisheries Research 73 (2005) 363–376

vs. data envelopment analysis. J. Product. Anal. 8 (4), 447– 459. Squires, D., 1987. Fishing effort: its testing, specification, and internal structure in fisheries economics and management. J. Env. Econ. Manage. 14, 268–282. Squires, D., Kirkley, J., 1999. Skipper skill and panel data in fishing industries. Can. J. Fish. Aquat. Sci. 56 (11), 2011–2018. Tingley, D., Pascoe, S., Mardle, S., 2003. Estimating capacity utilisation in multi-purpose, multi-meti´er fisheries. Fish. Res. 63 (1), 121–134.

Uri, N.D., 2001. The effect of incentive regulation on productive efficiency in telecommunications. J. Policy Model. 23 (8), 825– 846. Vestergaard, N., Squires, D., Kirkley, J., 2003. Measuring capacity and capacity utilisation in fisheries: the case of the Danish gillnet fleet. Fish. Res. 60 (2–3), 357–368. Zaibetand, L., Dharmapala, P.S., 1999. Efficiency of governmentsupported horticulture: the case of Oman. Agric. Sys. 62 (3), 159–168.