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.