Economic versus physical input measures in the analysis of
1technical efficiency in fisheries
1123Sean Pascoe, Parastoo Hassaszahed, Jesper Anderson and Knud Korsbrekke
1. CEMARE, University of Portsmouth, UK; 2. SJFI, Denmark;
3. Institute for Marine Research, Norway.
The measurement of technical efficiency requires the estimation of an appropriate production frontier. This is based on a set of inputs that are assumed to influence the level of output. Deviations from this frontier production function are separated into random variation and inefficiency. However, mis-specification of the production function through the use of inappropriate input measures may result in a bias in the measures of inefficiency. In fisheries, production is generally assumed to be a function of stock size, fishing time and the level of physical inputs employed. Defining the appropriate levels of physical inputs, however, is not straightforward, and several alternative measures are available. While economic measures of capital are more intuitively appealing, physical measures are generally readily available and hence less costly to collect. In this study, technical efficiency is measured for three fleet segments operating in the North Sea using three different gear types. The effects of using different measures of capital in the production frontier on the efficiency estimates are examined.
Paper presented at the XII Conference of the European Association of Fisheries Economists,
Salerno, Italy, 18-20 April 2001.
1 The study was undertaken as part of two EU funded projects: "On the applicability of economic indicators to improve the understanding of the relationship between Fishing Effort and Mortality. Examples from the Flat- and Roundfish Fisheries of the North Sea" (DGXIV 98/027) and “Technical efficiency in EU fisheries: implications for monitoring and management through effort controls” (QLK5-CT1999-01295)
An understanding of the relationship between the quantity of inputs employed in fishing and the resultant catch is an essential pre-condition for effective management, especially where inputs are controlled. While most fisheries in the EU are managed though aggregate output controls, ensuring that the fleet catching capacity is in line with the harvest limits has become an important feature of the Structural Policy of the Common Fisheries Policy (CFP). In most EU countries, fleet reduction has been required through the Multi-Annual Guidance Programme in order to reducing the overall harvesting capacity of the fleet. However, variations in efficiency between boats can greatly affect the effectiveness of such policies, as removing inefficient vessels will have proportionally less of an impact on the overall harvesting capacity of the fleet (Pascoe and Coglan, 2000).
Measurement of efficiency in fisheries is important for several reasons, particularly when input controls are in place. As well as the obvious impact on the harvesting capacity, increases in efficiency over time could result in biased effort measures and hence affect stock assessments. Also, where effort controls are in place, changes in efficiency over time need to be measured in order to determine if the controls need to be adjusted.
The measurement of efficiency of individual firms requires some benchmark against which their performance can be assessed. A common approach has been to estimate a production frontier, which represents the relationship between the maximum potential output for a given set of inputs. The individual‟s output is compared to the frontier level of output given the level of inputs employed, and the resultant difference represents the level of inefficiency of the firm. The estimation of stochastic production frontiers allows also for the effects of random variation in output to be separated from inefficiency.
The econometric estimation of technical inefficiency has been applied extensively to a wide range of industries, although relatively few attempts to measure technical efficiency in fisheries have been undertaken (for examples, see Kirkley, Squires and Strand, 1995, 1998; Campbell and Hand, 1998; Coglan, Pascoe and Harris, 1999; Sharma and Leung, 1999; Squires and Kirkley, 1999; Grafton, Squires and Fox, 2000; Pascoe, Andersen and de Wilde, 2001). These studies have used a range of different input measures, although the most common input measures have involved some measures of capital, labour and stock size.
In many fisheries, detailed information on the level of capital and labour employed in fishing is limited, and any analysis of fisheries production and efficiency will need to be based on physical inputs. Further, the measurement of the economic inputs (capital and labour) are also subject to problems that may make their use in productivity analysis less than desirable. The
use of inappropriate measures of the input use may result in mis-specification problems in the model, consequently affecting the measures of efficiency.
In this paper, the effect of different input measures on efficiency estimates is examined through three different types of fisheries – Norwegian trawlers, Danish seiners and Danish
gillnetters. Problems in the estimation of the economic inputs are also examined. Implications for future studies of efficiency in fisheries are then drawn from the results of the analyses.
Production functions and frontiers in fisheries
A production function defines the relationship between the level of inputs and the resultant level of outputs. It is estimated from observed outputs and input usage and indicates the average level of outputs for a given level of inputs (Schmidt, 1986). A number of studies have estimated the relative contribution of the factors of production through estimating production functions at either the individual boat level or total fishery level. These include Cobb-Douglas production functions (Hannesson, 1983), CES production functions (Campbell and Lindner, 1990), and translog production functions (Squires, 1987; Pascoe and Robinson, 1998).
An implicit assumption of production functions is that there are no differences in efficiency in the use of the inputs between firms. In contrast, the production frontier indicates the maximum potential output for a given set of inputs. From the production frontier, it is possible to measure the relative efficiency of certain groups or set of practices from the relationship between observed production and some ideal or potential production (Greene, 1993).
A general stochastic production frontier model can be given by:
where q is the output produced by firm j, x is a vector of factor inputs, v is the stochastic jj
error term and u is the estimate of the technical inefficiency of firm j. Both v and u are jjj
22assumed to be independently and identically distributed (iid) with variance and ??vu
The deterministic part of the frontier (i.e. f(ln x)) represents the effects of changes in input
levels on the level of output. In all of the previous studies of efficiency, the key inputs used have included a measure of capital, capital utilisation, and stock, while some studies have also included a measure of labour utilisation in the production function (e.g. Kirkley, Squires and Strand, 1995, 1998; Sharma and Leung, 1999). This is broadly in keeping with traditional
economic production theory, where output is assumed to be a function of land (i.e. stock), labour and capital.
The level of capital employed in the fishery has been measured in terms of the monetary investment level (e.g. Kirkley, Squires and Strand, 1995, 1998) or in terms of physical inputs such as boat size and engine power (e.g. Coglan, Pascoe and Harris, 1999). Pascoe, Andersen and de Wilde (2001) estimated capital inputs in monetary terms based on the combination of boat size and engine power, with a differing relationship for small and large boats. Capital utilisation has been incorporated into the analyses in terms of either days fished or fuel use.
The use of economic measures of capital rather than physical inputs has been preferred in the literature as they are assumed to capture the full range of inputs employed (e.g. onboard technology, differences in materials used in the boat construction etc). In contrast, physical measures, such as boat size and engine power, only capture some of the inputs employed, with potential differences in the use of inputs not included in the production function potentially affecting the relative measures of efficiency. That is, the measure of inefficiency reflects differences in the level of inputs used as well as differences in the use of these inputs by the skipper.
The stochastic part of the frontier, , represents deviations away from the frontier that v？ujj
are due to either random variation (v) or inefficiency. The term u represents technical ji,t
inefficiency. When u = 0, the i-th firm at time t lies on the stochastic frontier, and hence can i,t
be considered technically efficient at time t. If u > 0, the production lies below the frontier i,t
and hence the firm is inefficient. The measure of technical efficiency of the firm when working with logged variables is given by
where TE is the relative technical efficiency of the firm i in period t. i,t
In order to separate the stochastic and inefficiency effects in the model, a distributional assumption has to be made for u (Bauer, 1990). A range of distributional assumptions have j
been proposed: an exponential distribution such that u ~ exp(?) (Meeusen and van der Broeck, j
21977); a normal distribution truncated at zero (i.e. u ~ |N(?, ?)|) (Aigner, Lovell and jj u
2Schmidt, 1977); a half-normal distribution truncated at zero i.e. u ~ |N(0, ?)| (Jondrow et al., ju
1982) a two-parameter Gamma/normal distribution (Greene 1990), the density function given
m：?uu，？by for m>-1 (Kumbhaker and Lovell, 2000); and a truncated ()expfu，?m？1?！？?(1)m?u?u
2normal distribution around a deterministic mean (i.e. u~ |N(m,?)|), where m is a function it ituit
of particular characteristics of the firm (Battese and Coelli, 1995).
There are no a priori reasons for choosing one distributional form over the other, and all have advantages and disadvantages (Coelli, Rao and Battese, 1998). Most of the above studies of fisheries have tended to adopt the Battese and Coelli (1995) approach, where inefficiency is explicitly modelled as a function of the characteristics of the vessels. However, the objective of these studies has been to examine the effects of particular factors on the efficiency of fishing vessels, rather than just to measure the distribution of efficiency.
Difficulties in the use of economic and physical inputs
As noted above, most studies of production and efficiency in fisheries have used some value-based measure of capital (e.g. investment). In addition, some studies have included labour and fuel use in the production function. While these measures have theoretical advantages, including conformity with general economic production theory, the measurement of the inputs is subject to considerable problems. In addition, economic information is generally not routinely collected, and sample surveys of fisheries are, in many countries, limited in their scope and their time series. As a result, information on the measures is generally only available for a small subset of the fleet. Economic measures of capital are also subject to measurement errors. In many cases, estimates of capital values are accountancy based rather than economic based.
In contrast, physical input measures are generally more robust (in terms of measurement), and are often more readily available. However, as noted above, these measures do not include all inputs employed in fishing. In particular, information on onboard technology, which presumably is included in the estimate of capital value, is generally not readily available nor easy to incorporate into a production function. The key difficulties with particular input measures (both economic and physical) are briefly outlined below.
Estimates of capital values of fishing vessels are generally derived from economic surveys of fisheries. These differ in their approach to the measurement and depreciation of capital. In theory, the capital value should represent the productive capacity of the investment, such that the use of more productive capital inputs are associated with higher capital values. Consequently, capital value should provide a good indicator of the total level of capital inputs employed in the fishery.
In practise, the valuation of the capital inputs used in fishing is not related to their productive use. In many cases, capital value is estimated on the basis of the level of key physical inputs
employed rather than all inputs. For example, the capital measures used by Pascoe, Andersen and de Wilde (2001) were derived from the gross registered tonnage and engine power of the vessel based on the valuation method proposed by Davidse et al (1993). Similar approaches to
the estimation of capital value are employed in most economic analyses of European fisheries (see Concerted Action, 2000), as obtaining information on all capital inputs employed in fishing is generally impractical. While these measures may be appropriate for providing an indication of trends in capital input use, they are not necessarily ideal for productivity and efficiency analyses.
In many studies, the capital value of the vessels have been estimated on the basis of book values, where the (estimated) replacement values are depreciated by a given depreciation rate. In many economic reports (e.g. Concerted Action, 2000; Danish Institute of Agricultural and Fisheries Economics, 1998), capital value is depreciated at a common rate for all activities. Pascoe, Robinson and Coglan (1996) demonstrated that economic depreciation (i.e. the actual loss in value of the vessels over time) was related to the level of repairs and maintenance, and hence may vary between boats within a fleet segment and between fleet segments.
While the vintage of the boat may result in differences in efficiency (i.e. due to new technologies incorporated into the more recent vessel design and construction), there is generally no reason to presume that a boat would become less efficient as it aged provided it underwent regular maintenance. Hence, the depreciated capital values derived in many economic surveys have little relationship to the productive capacity of the vessel.
A number of econometric models of fisheries production function and frontiers include crew numbers as a variable input (e.g. Squires, 1987; Kirkley, Squires and Strand, 1995, 1998), on the basis that bigger crews result in greater output levels. While this may be true for some fisheries, particularly those involving pole and lines, the relevance of crew as an input into the production process in all fisheries is questionable.
For most fisheries, crew numbers are more a consequence rather than cause of production. Vessels that expect to have large catches need large crews to handle the catch once caught. For trawl vessels, some minimum number of crew are required to operate the boat and winch equipment for any production to occur. Adding crew above this minimum is not likely to result in additional production from the vessel. However, it could be argued that more crew enable the catch to be removed and processed more quickly, allowing more trawls to take place over a given period of time (e.g. a day or trip).
In practice, crew numbers are highly correlated with boat size (i.e. bigger boats have more crew), and hence the contribution of crew to the production process is often captured in the
boat size measure (either capital value or physical measure). Further, in most fisheries information on the number of crew employed is generally collected annually, while actual crew use could vary from month to month (e.g. based on expected variation in catch levels due to seasonal factors). In such a case, the addition of a constant measure of crew does not capture the labour input, and as the effects are largely captured in the boat size variable, does not contribute substantially to the production function.
Fuel use has been used in some studies to represent the capital utilisation rate (e.g. Squires, 1987). A feature of fuel use is that it also captures some of the boat characteristics, so can be used as a measure of both physical and variable inputs (e.g. larger boats with larger engines use more fuel per day). This has both advantages and disadvantages. Including both fuel use and boat size measures may result in substantial multicollinearity problems. While this may not be problematic for efficiency estimation, the corresponding elasticity estimates would be unreliable. If the correlation between fuel use and boat size is substantially high, then the problem of multicollinearity may become excessive and the models unable to solve.
In contrast, using a measure of fuel use to represent both fixed and variable inputs involves the implicit assumption of perfect substitution between the inputs. That is, if a given level of fuel use results in a given output, then this could be achieved by either a small boat fishing for a long period or a large boat fishing for a short period.
In practice, information on the quantity of fuel used is rarely collected in economic surveys. Instead, information on fuel costs is more generally collected. While this is highly correlated to fuel use, variations in fuel price between areas may result in the measure of fuel costs being inconsistent between vessels. As a result, differences in prices may be interpreted as differences in input usage and, consequently, inefficiency.
Physical measures of fixed inputs generally include measures of boat size (e.g. GRT, length, width, etc) and engine power (in kW or horsepower). These have been used as proxy measures of the level of capital invested in the fishery (e.g. Pascoe and Robinson, 1998; Coglan, Pascoe and Harris, 1998). Physical measures of capital utilisation generally involves some measure of time fished, such as days, hours or trips.
A key advantage of the measures is that they are generally readily available for a large proportion of the fleet. Most countries record the physical characteristics of the vessels in boat registers, while many countries required fishers to complete logbooks of their fishing activity. As a result, the proportion of the fleet that is able to be studied is generally substantially larger than that for which economic data are available.
The key disadvantages of the measures are that they generally do not encompass all inputs. Information on differences in onboard technologies, for example, is often not available. These differences will be captured in the inefficiency component of the model. Hence, part of the apparent inefficiency will be measurement error in the deterministic component of the production frontier.
Effects of different input measures on technical efficiency
From the above, it is apparent that all potential input measures are subject to some problems. While there are potential benefits in using economic measures of capital and capital utilisation, obtaining appropriate measures is difficult and time consuming, especially if a regular economic survey program is not undertaken. In contrast, physical data, while potentially less accurate, has the advantage that is it readily available. The effect of using different input data on efficiency estimates was examined for a number of different fleet segments operating in the North Sea. Economic and physical input data were obtained for the Danish seine and gillnet fleet as well as the Norwegian trawler fleet.
The Danish economic analysis of technical efficiency is based on a data set that is drawn from the Danish Institute of Agricultural and Fisheries Economics' (SJFI) account database for the years 1995-98 inclusive. This database forms the basis of the Danish Account Statistics for Fishery, which covers all types of commercial fisheries in Denmark. For the purposes of this study, only netters and seiners that fished for consumption species in the North Sea and/or Skagerrak were included. Further, only boats that fished for at least 3 of the 4 years were included in the analysis. This resulted in observations for 26 netters and 13 seiners being usable for the analysis. Measures of the biomass of key species were obtained from the International Bottom Trawl Survey (IBTS), and a stock index (expressed in „value‟ terms) was derived based on revenue shares of each species.
A range of different input measures – both economic and physical – were available (Tables 1
and 2). All economic input values were inflated to 1998 values using the retail price index. A range of different capital value measures were available, including estimates of the value of the engine and hull and the total depreciated value of all capital inputs (including electronics and fishing gear). As there is no a priori reason to assume that efficiency would decrease as
boats aged, a constant measure of capital (based on the 1995 value for each boat) was also derived. While this value still contains an element of depreciation, this reflects the vintage of the vessel. Hence, the constant capital value is a composite measure of the level and vintage of capital employed.
Table 1. Correlation between output (real revenue) and potential inputs for Danish Seiners
Physical fixed inputs Capital value Variable inputs
Output GT HP Length Hull and Total Total Days Fuel cost Crew size
engine accounts (constant)
Output (real value) 1.00 Gross Tonnage (GT) 0.83 1.00 Horsepower (HP) 0.64 0.71 1.00 Length 0.79 0.86 0.74 1.00 Hull and engine capital 0.80 0.87 0.78 0.88 1.00 Total Capital - accounts 0.83 0.86 0.73 0.84 0.91 1.00 Capital - constant 0.84 0.85 0.74 0.85 0.92 0.99 1.00 Days 0.34 0.17 0.13 0.18 0.17 0.36 0.35 1.00 Fuel cost 0.75 0.71 0.74 0.70 0.76 0.80 0.78 0.40 1.00 Crew size 0.62 0.56 0.51 0.57 0.60 0.53 0.53 -0.07 0.58 1.00
Table 2. Correlation between output (real revenue) and potential inputs for Danish Gillnetters
Physical fixed inputs Capital value Variable inputs
Output GT HP Length Hull and Total Total Days Fuel cost Crew size
engine accounts (constant)
Output (real value) 1.00 Gross Tonnage (GT) 0.68 1.00 Horsepower (HP) 0.73 0.90 1.00 Length 0.79 0.93 0.86 1.00 Hull and engine capital 0.75 0.79 0.84 0.82 1.00 Total Capital - accounts 0.82 0.84 0.83 0.88 0.92 1.00 Capital - constant 0.82 0.85 0.83 0.88 0.90 0.99 1.00 Days 0.65 0.50 0.44 0.60 0.40 0.54 0.55 1.00 Fuel cost 0.87 0.81 0.82 0.84 0.77 0.84 0.85 0.59 1.00 Crew size 0.84 0.65 0.66 0.81 0.68 0.77 0.76 0.60 0.71 1.00
Correlation between these measures and output (expressed as total value of landings inflated to 1998 values using a Fisher price index) suggest that most of the fixed inputs are highly correlated with each other and roughly equally correlated with the output measure. As would be expected, fuel costs are also highly correlated with both the output measure and the measures of the fixed inputs (both physical and economic).
The Norwegian data were provided by the Norwegian Institute for Marine Research, covering the years 1994-98 inclusive. Again, only boats that operated for at least 3 years were included in the analysis, resulting in 46 boats being used to estimate the average efficiency. All economic variables were inflated to 1998 values using the retail price index. A stock index was derived from the geometric mean of value per unit of effort (standardised using horsepower) of boats that fished in all five years. While stock data were available in individual species, information on revenue shares were not available to allow the construction of a divisia-type index.
Relatively fewer potential inputs were available for the Norwegian trawlers than for the Danish vessels (Table 3). As with the Danish vessels, the fixed inputs were highly correlated with each other and the output measure (real revenue). Fuel costs were again also highly correlated with both the output measure and the fixed inputs.
Table 3. Correlation between output (real revenue) and potential inputs for Norwegian trawlers
Capital value Variable inputs
Real revenue HP Book value Constant Fuel costs Days
Real revenue 1.00
Horsepower (HP) 0.88 1.00
Book value 0.70 0.83 1.00
Constant value 0.71 0.84 0.98 1.00
Fuel costs 0.79 0.82 0.66 0.64 1.00
Days 0.41 0.31 0.15 0.17 0.43 1.00
The production frontier model for vessels operating in the three fisheries was specified as a
2translog production function. Three forms of the model were used, depending on the inputs
used. When capital value and days fished (capital utilisation) were used, the model was given by
2 The appropriateness of the translog functional form of the model was tested against a Cobb-Douglas specification, as seen in the results section.