Economic versus physical input measures in the analysis of
technical efficiency in fisheries1
Sean Pascoe1, Parastoo Hassaszahed1, Jesper Anderson2 and Knud Korsbrekke3
1. CEMARE, University of Portsmouth, UK; 2. SJFI, Denmark;
3. Institute for Marine Research, Norway.
Abstract
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 Flatand 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)
Introduction
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
1
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:
ln q j  f (ln x)  v j  u j
(1)
where qj is the output produced by firm j, x is a vector of factor inputs, vj is the stochastic
error term and uj is the estimate of the technical inefficiency of firm j. Both vj and uj are
assumed to be independently and identically distributed (iid) with variance  v2 and  u2
respectively.
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
2
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, v j  u j , represents deviations away from the frontier that
are due to either random variation (vj) or inefficiency. The term ui,t represents technical
inefficiency. When ui,t = 0, the i-th firm at time t lies on the stochastic frontier, and hence can
be considered technically efficient at time t. If ui,t > 0, the production lies below the frontier
and hence the firm is inefficient. The measure of technical efficiency of the firm when
working with logged variables is given by
TEi,t  e
ui ,t
(2)
where TEi,t is the relative technical efficiency of the firm i in period t.
In order to separate the stochastic and inefficiency effects in the model, a distributional
assumption has to be made for uj (Bauer, 1990). A range of distributional assumptions have
been proposed: an exponential distribution such that uj ~ exp() (Meeusen and van der
Broeck, 1977); a normal distribution truncated at zero (i.e. uj ~ |N(j , u2)|) (Aigner, Lovell
and Schmidt, 1977); a half-normal distribution truncated at zero i.e. uj ~ |N(0, u2)| (Jondrow
et al., 1982) a two-parameter Gamma/normal distribution (Greene 1990), the density function
given by f (u ) 
 u 
um
exp
  for m>-1 (Kumbhaker and Lovell, 2000); and a
(m  1) um1
 u 
3
truncated normal distribution around a deterministic mean (i.e. uit ~ |N(mit,u2)|), where mit is a
function 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 valuebased 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.
Capital value
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
4
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.
Labour
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
5
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
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
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.
6
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.
Danish data
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.
7
Table 1. Correlation between output (real revenue) and potential inputs for Danish Seiners
Output
Output (real value)
Gross Tonnage (GT)
Horsepower (HP)
Length
Hull and engine capital
Total Capital - accounts
Capital - constant
Days
Fuel cost
Crew size
1.00
0.83
0.64
0.79
0.80
0.83
0.84
0.34
0.75
0.62
Physical fixed inputs
GT
HP
1.00
0.71
0.86
0.87
0.86
0.85
0.17
0.71
0.56
1.00
0.74
0.78
0.73
0.74
0.13
0.74
0.51
Length
1.00
0.88
0.84
0.85
0.18
0.70
0.57
Capital value
Hull and
Total
engine
accounts
1.00
0.91
0.92
0.17
0.76
0.60
1.00
0.99
0.36
0.80
0.53
Total
(constant)
1.00
0.35
0.78
0.53
Variable inputs
Days
Fuel cost
1.00
0.40
-0.07
1.00
0.58
Crew size
1.00
Table 2. Correlation between output (real revenue) and potential inputs for Danish Gillnetters
Output
Output (real value)
Gross Tonnage (GT)
Horsepower (HP)
Length
Hull and engine capital
Total Capital - accounts
Capital - constant
Days
Fuel cost
Crew size
1.00
0.68
0.73
0.79
0.75
0.82
0.82
0.65
0.87
0.84
Physical fixed inputs
GT
HP
1.00
0.90
0.93
0.79
0.84
0.85
0.50
0.81
0.65
1.00
0.86
0.84
0.83
0.83
0.44
0.82
0.66
Length
1.00
0.82
0.88
0.88
0.60
0.84
0.81
8
Capital value
Hull and
Total
engine
accounts
1.00
0.92
0.90
0.40
0.77
0.68
1.00
0.99
0.54
0.84
0.77
Total
(constant)
1.00
0.55
0.85
0.76
Variable inputs
Days
Fuel cost
1.00
0.59
0.60
1.00
0.71
Crew size
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).
Norwegian data
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
Real revenue
Horsepower (HP)
Book value
Constant value
Fuel costs
Days
Real revenue
HP
1.00
0.88
0.70
0.71
0.79
0.41
1.00
0.83
0.84
0.82
0.31
Capital value
Book value
Constant
value
1.00
0.98
0.66
0.15
1.00
0.64
0.17
Variable inputs
Fuel costs
Days
1.00
0.43
1.00
Model specification
The production frontier model for vessels operating in the three fisheries was specified as a
translog production function2. 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 CobbDouglas specification, as seen in the results section.
9
ln Vi ,t   0   D ln Di ,t   S ln S t   C ln Ci ,t 
 D , D (ln Di ,t ) 2   S , S (ln S t ) 2   C ,C (ln Ci ,t ) 2 
 D , S ln Di ,t ln S t   D ,C ln Di ,t ln Ci ,t   C , S ln Ci ,t ln S t 
(3)
v i ,t  u i , t
where Vi,t is the output index of fisher i (expressed in terms of value of landings deflated using
a Fisher price index) in time t, Di,t are the measure of capital utilisation (e.g. number of days
fished by fisher i in time t), St is the composite stock index in time t, and Ci,t is the level of the
capital employed by fisher i in time t (expressed in either value terms or as a function of the
physical characteristics of the vessel), vi,t is the random variation and ui,t is the level of
inefficiency of fisher i in year t.
When boat size (gross tonnage) and engine power (horsepower) were used, the functional
form of the model was
ln Vi ,t   0   D ln Di ,t   S ln S t   G ln GTi   H ln HPi 
 D , D (ln Di ,t ) 2   S , S (ln S t ) 2   G ,G (ln GTi ) 2   H , H (ln HPi ) 2 
 D , S ln Di ,t ln S t   D ,G ln Di ,t ln GTi   D , H ln Di ,t ln HPi 
(4)
 G , S ln GTi ln S t   G , H ln GTi ln HPt   H , S ln HPi ln S t 
v i ,t  u i ,t
where GTi and HPi are the gross tonnage and horsepower of boat i respectively. For the
Norwegian trawlers, information was only available on horsepower.
When fuel was used as the key input, the model was specified as
ln Vi ,t   0   F ln Fi ,t   S ln St   F , F (ln Fi ,t ) 2   F ,S ln Fi ,t ln St  vi ,t  ui ,t
(5)
where Fi,t is the cost of fuel used by fisher i in time t. Fuel use is assumed to encompase both
features relating to the size of the vessel (e.g. boat size and engine power) as well as capital
utilisation (e.g. days fished).
Value was used as the dependent variable rather than quantity as there was not sufficient
information on the catch composition of the Norwegian vessels to construct a quantity based
measure. As a consequence, the resultant efficiency measures include a mix of both technical
as well as allocative efficiency (i.e. how well the fishers both catch fish and catch the most
valuable combination of fish). As the ability of fishers to target individual species is limited, it
10
is most likely that allocative efficiency does not vary significantly between fishers such that
the efficiency measures largely reflect differences in technical efficiency.
Inefficiency was modelled as a 'random effect' (Coelli, Rao and Battese 1998). This involves
imposing a range of different distributional assumptions on the inefficiency term, and
determining which assumption is most appropriate through econometric testing of the results.
Insufficient information for the Norwegian fleet was available to estimate efficiency as a
function of boat characteristics, while the short time series for the Danish fleet and relatively
small sample size would have made an inefficiency model fairly unreliable.
The key distributional assumptions tested was a normal distribution truncated at zero (i.e. uj ~
|N(i , u2)|) (Aigner, Lovell and Schmidt, 1977) and a half-normal distribution truncated at
zero i.e. uj ~ |N(0, u2)| (Jondrow et al. 1982). The model was also tested for time variant
technical efficiency. The approach adopted, proposed by Battese and Coelli (1992), assumes
that
u j ,t  u j e  (t T )
(6)
where uj are assumed to be iid truncations at zero of the normal distribution N(j, 2). If >0,
the inefficiency term, uj,t, is always decreasing with time, whereas <0 implies that uj,t is
always increasing with time. One of the main problems of this model is that technical
efficiencies are forced to be a monotonous function of time.
Results
As noted above, several variants of the production frontier were estimated using different
input measures for each fleet segment. These involved a measure of physical inputs (gross
tonnage and horsepower for the Danish boats and only horsepower for the Norwegian
trawlers); a measure of capital value (taken as the measure of total capital in the first year of
the data held constant over the period of the data); and the use of fuel costs. Days fished was
used as the measure of capital utilisation for the first two instances, whereas fuel cost was
assumed to represent both fixed inputs (i.e. boat size and engine power) as well as variable
inputs (i.e. days fished). All models also included a measure of stock size.
The models were estimated using FRONTIER 4.1 (Coelli, 1996). As well as providing
estimates of the coefficients of the production function (not presented in this paper), the
output from the analyses included estimates of ,  and , the latter representing the
proportion of variation in the residuals (i.e.  j ,t  v j ,t  u j ,t ) explained by inefficiency, such
that    u2 /  u2   v2 .
11
Tests on the structural form
A number of tests were conducted on the structural form of the model by incorporating
restrictions on parameters. This was to determine the most appropriate functional form of the
model and inefficiency distribution, in order that the most appropriate measures of efficiency
were produced for comparison. The restrictions were tested using the likelihood ratio (LR)
test, where the test statistic is given by LR  2ln L( H o )  ln L( H 1 ), where ln[L(H0)] and
ln[L(H1)] are the values of the likelihood function under the null and alternative hypothesis
respectively. This has a 2 distribution, with the degrees of freedom given by the number of
restrictions imposed.
The key tests were on the functional form of the production function (i.e. translog vs CobbDouglas), the existence of time varying efficiency and the appropriate distribution of
inefficiency (half normal vs trunctated normal). A further standard test is the test for the
existence of a frontier. This is equivalent to testing that =0 (i.e. that inefficiency effects do
not exist). As the alternative hypothesis is that >0 (since 01), a one-sided test is required
and the standard 2 values are not appropriate. Kodde and Palm (1986) developed a series of
critical values based on a mixture of 2 distributions that are appropriate for testing this
restriction. The results of these tests are presented in Tables 4-7 below.
Table 4. Tests of Translog vs Cobb-Douglas production function
Log-likelihood value
Cobb-Douglas
Translog
Likelihood
Ratio test
χ2
Degrees
of
freedom
Probabilty
(%)
Accept/
reject
Norwegian Trawlers

HP
60.466
70.970
21.008
6
0.18
reject

capital
24.810
33.836
18.050
6
0.61
reject
 fuel
Danish Seiners
10.819
26.781
31.924
3
0.00
reject

GT and HP
33.158
-
-
-
-
accept

capital
34.188
39.113
9.851
6
13.10
accept
 fuel
Danish Gillnetters
28.429
29.466
2.074
3
55.73
accept

GT and HP
24.328
33.215
17.773
6
0.68
reject

capital
30.072
37.816
15.488
6
1.68
reject

fuel
21.909
25.402
6.985
3
7.24
accept
With the exception of the Danish Seiners, the translog production function was considered the
most appropriate functional form (Table 4). The small sample size and larger number (of
highly correlated) explanatory variables when using physical inputs resulted in an inability to
estimate the translog for the Danish Seiners using these variables. However, a Cobb-Douglas
12
production function could not be rejected for the seiners when using the other inputs, so it is
expected that this is the most appropriate functional form of the production function.
Time invariant efficiency (i.e. =0) was found to be consistently accepted for the trawlers and
gillnetters with all inputs, and rejected for all inputs for the seiners (Table 5). Given the length
of the time series, time varying efficiency was not expected. For the seiners, efficiency was
found to be increasing at an average rate of between 9 per cent (based on capital values) and
22 per cent a year (based on fuel costs). This latter figure appears unrealistic, and may be an
artefact of fuel price changes (i.e. if fuel prices fell, then the apparent resource use would have
decreased per unit of output).
Table 5. Tests of time invariant efficiency
Log-likelihood value
=0
0
Likelihood
Ratio test
χ2
Degrees
of
freedom
Probabilty
(%)
Accept/
reject
Norwegian Trawlers (TL)

HP
70.257
70.970
1.427
1
23.22
accept

capital
33.910
33.836
0.000
1
100.00
accept
 fuel
Danish Seiners (CD)
26.772
26.781
0.018
1
89.35
accept

GT and HP
31.031
33.158
4.254
1
3.92
reject
capital
31.846
34.188
4.683
1
3.05
reject
 fuel
Danish Gillnetters (TL)
24.521
28.429
7.816
1
0.52
reject

GT and HP
32.570
33.215
1.290
1
26
accept
capital
37.371
37.816
0.889
1
35
accept
25.144
25.402
0.516
1
 fuel
Note: TL - translog production function; CD - Cobb-Douglas production function
47
accept


In most instances, a half-normal distribution was found to be appropriate, the exception being
for the Norwegian trawlers when only horsepower was considered as a fixed input (Table 6).
As there is no a priori reason to assume either distribution, nothing substantial can be
concluded from these results. For consistency, a truncated normal distribution was imposed
for all input-variants of the model for the Norwegian trawlers.
The 'final' functional forms of the model and inefficiency distribution were tested for the
existence of a frontier. This is effectively a test that inefficiency is zero for all observations,
such that =0 (i.e. the proportion of total variation in the residuals due to inefficiency). In all
cases, the assumption that =0 was rejected, indicating that a frontier (rather than just a
production function), and inefficiency, existed.
13
Table 6. Tests of half-normal (=0) vs truncated normal (0) distribution
Log-likelihood value
=0
0
Likelihood
Ratio test
χ2
Degrees
of
freedom
Probabilty
(%)
Accept/
reject
HP
67.079
70.257
6.355
1
1.17
reject

capital
33.432
33.910
0.955
1
32.85
accept

fuel
26.586
26.772
0.372
1
54.17
accept
Norwegian Trawlers (TL) (=0)

Danish Seiners (CD) (0)

GT and HP
32.143
33.158
2.030
1
15.42
accept

capital
33.049
34.188
2.277
1
13.13
accept

fuel
27.184
28.429
2.490
1
11.46
accept
GT and HP
32.536
32.570
0.068
1
79.49
accept
capital
37.225
37.371
0.294
1
58.80
accept
24.693
25.144
0.901
1
 fuel
Note: TL - translog production function; CD - Cobb-Douglas production function
34.25
accept
Danish Gillnetters (TL) (=0)


Table 7. One sided test of the existence of a frontier
Log-likelihood value
=0
 0
Likelihood
Ratio test
Degrees
of
freedom
Critical
valuea
Accept/
reject
Norwegian Trawlers (TL) (=0)(0)
47.116
 HP
70.257
46.283
2
5.138
reject

capital
-22.478
33.910
112.775
2
5.138
reject

fuel
21.938
26.772
9.668
2
5.138
reject
Danish Seiners (CD) (0)(=0)

GT and HP
19.277
33.158
27.763
2
5.138
reject

capital
17.834
34.188
32.709
2
5.138
reject

fuel
16.653
28.429
23.553
2
5.138
reject
Danish Gillnetters (TL) (=0)( =0)
-22.174
 GT and HP
32.536
109.419
1
2.706
reject

37.225
121.992
1
2.706
reject
capital
-23.771
-19.484
24.693
88.354
1
2.706
reject
 fuel
Note: TL - translog production function; CD - Cobb-Douglas production function. a) Kodde and Palm (1986)
critical values at 5% for a one sided test.
Comparison of efficiency scores
The efficiency scores from each of the 'final' models are illustrated in Figure 1. From this, it
can be seen that the scores differed considerably depending on the inputs used in the analysis.
Further, the correlation between the scores is relatively low in some instances (e.g. between
fuel use and horsepower for the Norwegian trawlers, Table 8).
14
Figure 1. Comparison of estimated efficiency scores
hp
capital
46
43
40
37
34
31
28
25
22
19
16
13
10
7
4
fuel
1
TE score
(a) Norwegian trawlers
1.20
1.00
0.80
0.60
0.40
0.20
0.00
Observation (vessel)
(b) Danish Seiners
1.00
TE score
0.90
GT and HP
capital
fuel
0.80
0.70
0.60
0.50
1
2
3
4
5
6
7
8
9
10
11
12
13
(c) Danish Gillnetters
1.00
0.80
0.60
0.40
0.20
0.00
25
23
21
19
17
15
13
11
9
7
5
3
ENG
CAP
FUEL
1
TE score
Observation (vessel)
Observation (vessel)
Tests on the sample distributions of the scores indicate that in some instances, the use of some
inputs can result in consistently higher (or lower) values of the efficiency score. For example,
the use of capital as an input measure results in significantly lower estimates of technical
efficiency than the use of either fuel or horsepower for the Norwegian trawlers (Table 8). In
other cases, correlation between economic and physical measures of capital are both
correlated, and exhibit no significant difference in the efficiency scores when compared pair
wise (e.g. the Danish seiners and gillnetters).
15
Table 8. Correlation and pair wise t-test between efficiency scores
Correlation
Norwegian Trawlers
1) Capital and 2) Fuel
1) Capital and 2) HP
1) Fuel and 2) HP
Danish Seiners
1) Capital and 2) GT and HP
1) Capital and 2) fuel
1) Fuel and 2) GT and HP
Danish Gillnetters
1) GT and HP and 2) fuel
1) GT and HP and 2) capital
1) fuel and 2) capital
Mean 1
Mean 2
t-test
(1-2=0)
Pr(T<=t)
two-tail
Accept/
reject
(1)
(1)
0.535
0.546
0.263
0.487
0.487
0.724
0.724
0.734
0.734
-11.008
-12.503
-0.456
0.000
0.000
0.651
rejected
rejected
accepted
0.597
0.813
0.802
0.738
0.738
0.758
0.719
0.758
0.719
-1.356
-2.182
-3.983
0.182
0.034
0.000
accepted
rejected
rejected
0.475
0.616
0.595
0.693
0.693
0.625
0.625
0.683
0.683
-1.713
-0.294
1.696
0.099
0.771
0.102
rejected
accepted
accepted
From the above analysis, no single input measure appears to result in consistently higher or
lower results, with the relationships varying by fleet segment. A comparison of the values of
the maximum log-likelihood derived from each of the production frontier (i.e. the case where
≠0 in Table 7) suggests that the physical and economic measures of capital are generally
'better' measures in terms of explaining production than fuel use, and that both measures of
capital inputs (i.e. economic and physical measures) are relatively comparable (Figure 2).
Figure 2. Comparison of log likelihood values
Value of maximum log likelihood function
80
Physical measures
Capital value
Fuel use
70
60
50
40
30
20
10
0
Trawlers
Seiners
Gillnetters
The use of fuel as a measure of input use (replacing both the capital and capital utilisation
rate) also resulted in mixed results. The estimated efficiency scores were statistically different
to those derived from capital value for the trawlers and seiners, but not significantly different
to those of the gillnetters. Conversely, the measures were significantly different to those
16
derived from physical measures of capital for the gillnetters and seiners, but not for the
trawlers.
Discussion and conclusions
The results of the above analyses suggest that the efficiency measures are dependent on the
inputs used in the production function, and that different input measures can result in
significantly different efficiency measures. Further, the effect of the input measure on the
efficiency measurement is not consistent. That is, no single input measure produced
consistently better or worse results than any other.
The differences in the efficiency scores reflects the measurement errors involved in the
different input measure. In each case, the inputs used were proxy measures of the inputs
involved in the fishing process. These measures captured the effects of a different set of
inputs, but not all inputs, resulting in part of the TE scores reflecting the mis-specification of
the model through omission of relevant variables. Kumhbaker (2001) suggested that the
estimation of production frontiers was more reliable than production functions when
estimating production elasticities as any measurement errors or omitted variables are captured
by the inefficiency term, and hence the derived elasticities are not biased. However, when the
key interest is in the inefficiency term, such mis-specification will result in biased estimates of
efficiency.
These results have significant implications for the analysis of efficiency in fisheries. Firstly,
the measures of efficiency are not independent of the variables that make up the deterministic
part of the production frontier. This is counter to the general assumption underlying efficiency
estimates. Further, models of technical inefficiency in fisheries will also be affected by the
inputs used. Hence, apparent significant relationships between inefficiency and, say boat size,
in an inefficiency model may reflect mis-specification of the production function rather than a
true inefficiency relationship. Further analysis of the effects in input measures on inefficiency
models needs to be undertaken.
The 'good news' is that physical measures of capital inputs are no better or worse than
'economic' measures, such as capital values. While the latter offer potential advantages in that
they should represent more of the inputs employed in fishing, in practice the values are
estimates that might represent no more of the inputs than the physical measures alone.
Further, the composition of these inputs in the aggregate value measure is not apparent. In
contrast, the physical measures are generally more robust, and are also more readily available,
allowing efficiency analyses to be conducted on a larger scale.
17
From the above result, the interpretation of efficiency in fisheries needs to be undertaken with
caution, and with regard to the inputs used in the production function.
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