Abstract
Salmon aquaculture generates good output (i.e., salmon) and bad output (e.g., pollution). A joint production function approach is applied to model both outputs simultaneously. Two environmental production technologies are specified, namely, regulated and unregulated technologies. Two production functions with different mapping rules are applied. Pollution abatement costs are estimated based on a series of data from the Norwegian salmon aquaculture industry. Results indicate that pollution abatement costs vary among observations and models. On average, pollution abatement cost is estimated to be about 3.5% in terms of total farmed salmon production, and 6.5% in terms of total revenue of farmed salmon. (JEL D24, Q22)
I. Introduction
Salmon aquaculture is known for providing highly valuable products to the growing seafood market, creating employment and income opportunities as well as foreign earnings (Tidwell and Alan 2001; Garcia and Grainger 2005). However, salmon aquaculture is currently under scrutiny and criticism because it appears to generate negative economic and environmental impacts (e.g., Naylor et al. 2000; Pauly et al. 2002). Pollution is one of the environmental concerns associated with salmon aquaculture. Pollutants from salmon aquaculture consist of uneaten feed, feces, and other organic matter from salmon farms. They are directly discharged into the marine environment because there are no solid and effective barriers between open net-cage production systems and the surrounding environment. Pollution may potentially create negative impacts on sediments and water columns, on benthic communities, and on some fishery resources (e.g., Milewski 2001; Levings et al. 2002; Brooks and Mahnken 2003; Naylor, Eagle, and Smith 2003). For instance, pollution in the form of nitrogen and phosphorus may increase the risk of eutrophication, and alter species composition and phytoplankton density in the water column (Statistics Norway 2006). Pollution in the form of organic matter may change sediment chemistry, resulting in changes in sediment flora and fauna in affected areas (e.g., Mazzola et al. 2000; McGhie et al. 2000; Pohle, Frost, and Findlay 2001). Some impacts are measurable near-field changes in sediments and water variables that are sensitive to organic matter and nutrient additions, while some are far-field effects, which are difficult to observe and measure, such as eutrophication and effects on food webs (Hargrave 2003). There is an extensive literature that documents these ecological and environmental impacts, especially in Europe, North America, and Chile, where most farmed salmon are produced (e.g., Tlusty et al. 2000; Pohle, Frost, and Findlay 2001; Levings et al. 2002; Brooks et al. 2003; Naylor, Eagle, and Smith 2003). These negative impacts may be considered small at a large scale, but they can be very significant locally, especially in areas where salmon farms are concentrated.
In the case of the Norwegian salmon aquaculture industry, pollution from fish farms together with discharge from households, industry, and agriculture have posed a potentially serious risk in the coastal waters and fjords (Statistics Norway 2006). Figure 1 shows that nitrogen and phosphorus from aquaculture have increased rapidly over the last two decades, and their contributions to the overall nitrogen and phosphorus production have become larger over time. Today, Norwegian aquaculture is the largest source of phosphorus, and the second largest source of nitrogen in the coastal areas of the country (Statistics Norway 2006). Although pollution has not increased at the same rate as the rapid growth of aquaculture production, it is still increasing.
Nitrogen And Phosphorus From The Norwegian Salmon Aquaculture Industry And Other Sources Into The Marine Environment
Data source: Statistics Norway 2006.
While the impacts of pollution on the environment and natural resources have been widely acknowledged, the economic analysis of pollution is limited and needs to be studied further. Therefore, in this paper, we estimate the environmental costs associated with pollution from the salmon aquaculture sector. According to the polluterpays principle, salmon producers should bear the environmental costs of pollution. In other words, salmon producers should pay for the cost of removing the pollution, or provide compensation to those who have been affected by the pollution. Hence, estimating environmental costs is the first and essential step to establish public damage abatement and compensation programs or formulate economic-based environmental policies.
In general, environmental cost can be measured in two ways. First, it can be determined by estimating the cost of the direct damage to others that can be attributed to pollution from a given economic activity. Second, it can be estimated by calculating the pollution abatement or prevention costs imposed on polluters by improving their production practice and/or investing in abatement activities. In most cases, the environmental costs estimated from these two approaches differ. This is because they are estimated from two dimensions and administered by different environmental policies. The first method, however, is more difficult to execute than the second approach, due to complex ecological and economic consequences. Therefore, in this paper, we estimate pollution abatement cost by applying a joint production approach. These pollution abatement costs can be assumed to be proxies for environmental costs associated with salmon aquaculture.
A production process, such as salmon aquaculture, produces desirable or “good” outputs (salmon), while simultaneously generating undesirable or “bad” outputs (e.g., pollution). Bad outputs are the byproducts of good outputs (i.e., good outputs cannot be produced without producing some bad outputs). Generally, good outputs are marketable, while bad outputs are not traded in the market. In conventional production theory, the productivity and efficiency of a firm or an industry are generally measured based on good outputs. However, joint production approaches have been recognized and developed to incorporate bad outputs along with good outputs for measuring efficiency and productivity (e.g., Färe et al. 1989, 2005; Chung, Färe, and Grosskopf 1997; Chambers, Chung, and Faare 1998; Faare, Grosskopf, and Pasurka 2007). The joint production approaches have several advantages compared to conventional production approaches. First, the approaches do not require information on pollution abatement technology and its associated costs. The cost of pollution abatement is captured by the reduction in good output production. Second, they avoid the difficulties associated with directly measuring changes in the production process through survey efforts. Also, the production technology automatically captures the synergies among the abatement processes of two or more pollutants (Pasurka 2001).
Joint production models, especially the directional distance output function model, have gained growing interest and become the favorite kind of model for this kind of analysis because of their flexibility of mapping rules and clear connection to traditional production functions (e.g., Chung, Faare, and Grosskopf 1997; Chambers, Chung, and Faare 1998; Pasurka 2001; Faare et al. 2005; Verdanyan and Noh 2006; Faare, Grosskopf, and Pasurka 2007). The directional distance output function model has been used to estimate shadow prices (e.g., Färe, Grosskopf, and Weber 2006), productivities (e.g., Chung, Färe, and Grosskopf 1997), and pollution abatement costs (e.g., Pasurka 2001; Verdanyan, and Noh 2006; Färe, Grosskopf, and Pasurka 2007). Also, joint production models can be used to test the economic effects ofdifferent environmental policies on different sectors (e.g., Brannlund, Färe, and Grosskopf 1995; Martinez-Cordero and Leung 2004). For instance, if the government sets a pollution level as the pollution reduction target, we can use joint production models to test how much production, revenue, or profit producers have to give up in order to meet the target.
In this study, production technology that results in the joint production of good and bad outputs is specified based on the assumptions of strong and weak disposability for bad outputs. If dumping bad outputs is not regulated, dumping is costless to the firm, in other words, bad outputs can be “freely” disposed of without any cost; hence, this can be modeled as strong disposability of bad outputs. On the other hand, if dumping of bad outputs is regulated, dumping becomes costly to the polluter. It implies that environmental regulations force producers to engage in pollution abatement activities (Färe et al. 1989). Thus, abating pollution becomes a costly activity, and producers have to internalize pollution abatement costs into their production process. This can be modeled as weak disposability of bad outputs.
We assume that salmon aquaculture operates under certain forms of regulatory constraints. This means that salmon producers, especially those in Norway, have engaged in pollution abatement activity. This assumption is appropriate because, in fact, there are some regulatory frameworks, both proposed and implemented, for the Norwegian salmon aquaculture industry. For instance, Norway has implemented a number of regulations such as limitations on production level, farm size, and fish density, and feed quota (Hjelt 2000; Maroni 2000). Feed is the key factor that contributes to pollution. Feed formulation and feeding technology have been greatly improved over the years. For example, the feed conversion ratio, a measure of the efficiency of converting feed into increased body weight of farmed fish, has been greatly reduced from around 4.0 in the 1980s to about 1.2 at present (Asche, Guttormsen, and Tveteras 1999; Bjorndal, Tveteras, and Asche 2002; Tveretas 2002). Moreover, feeding technology has improved from hand feeding to automatic feeders (Bjorndal et al. 2002).
II. Theoretical Framework
Let us assume a production process that employs a vector of inputs x ∈ Rn+ to yield a set of good outputs denoted by a vector y ∈ Rm+, and bad outputs denoted by a vector z ∈ Rj+. The technology (T) for the production process is represented by
[1]The technology illustrates all technically feasible relationships between inputs and outputs. For a given input vector x, the output set P(x) represents all feasible output vectors (y,z), that is,
[2]The production possibility set P(x) illustrates the trade-offs between good and bad outputs along the production possibility frontier. Since both good and bad outputs are included, the production possibility set P(x) is also an environmental output set (Färe et al. 2005; Färe, Grosskopf, and Pasurka 2007). The environmental production possibility set P(x) has the following properties:
P(x) is convex and compact, P(x) ∈ Rn+ and satisfies the condition of no free lunch. That is, P(0) = (0,0).
Strong disposability of good outputs and of inputs: If (y,z) ∈ P(x), then for y′≤y, (y′,z) ∈ P(x), and for x′≥x, (y′,z) ∈ P(x) ⊆ p(x′).
Null-jointness: If (y,z) ∈ P(x) and z = 0, then y = 0.
Weak disposability in good and bad outputs: If (y,z) ∈ P(x), and 0≤λ≤1, then (λy,λz) ∈ P(x).
The first and second properties are standard assumptions in production theory (Shephard 1970). The first assumption implies that inactivity results in no outputs (i.e., no free lunch), and finite inputs produce finite outputs. The second assumption is strong disposability for good outputs and inputs implying that y′ can be produced as long as y′ ≤ y given an input vector x. It is also called free disposability (Färe et al. 1989, 2005; Färe, Grosskopf, and Pasurka 2007). The third assumption is null-jointness between good and bad outputs, implying that if no bad outputs are produced, then good outputs will not be produced as well. The fourth assumption is weak disposability of outputs, implying that both good and bad outputs can be reduced proportionally. The third and fourth assumptions are of special interests to this study.
Ifdumping ofbad outputs is unregulated, dumping is costless to the polluter, and firms can divert all inputs into good production while jointly producing bad outputs for given inputs. In other words, in the absence ofenvironmental regulations, producers can freely dispose of bad outputs without bearing cost. This can be modeled as strong disposability of good and bad outputs. On the other hand, if dumping of bad outputs is regulated, dumping becomes costly to the firm, as it should, in other words, producers have to engage in abatement activities to reduce bad outputs. For a given level of inputs, this can only be done by diverting some inputs away from producing good outputs and into reduction of bad outputs. If the targeted level of bad outputs is very low, large amount ofinputs will be required to be put into the abatement ofbad outputs, and therefore, a small amount ofinputs will be available for the production of good outputs. This can be modeled as jointly weak disposability ofgood and bad outputs.
The environmental output set is illustrated in Figure 2. The production possibility frontier P(x) is constructed from observations of inputs and outputs. The points A and B represent the combinations of good and bad outputs given a set of input (x). Since nonparametric linear programming methods are used to measure production efficiency, the production possibility frontier P(x) is piecewise linear. The environmental output set is bounded by the piecewise linear segments OABCO. If bad output is assumed to be as strongly disposable as good output, it means that the maximum feasible amount of good outputs (e.g., OA or AB) at a given level of inputs (x) can be produced with any level of production of bad outputs equal to or less than OC, including zero (thus violating the null-jointness assumption).
Environmental Output Sets
Based on these assumptions about inputs and outputs, a joint production approach is developed to model both good and bad outputs in different mapping rules. It is assumed that producers attempt to maximize good outputs and minimize bad outputs if there is an environmental regulation implemented. We specify two production models with different mapping rules for outputs, known as (1) environmental production function (EPF); and (2) directional distance output function (DDOF). These two models serve as the functional representation of environmental production technology. EPF is constructed for solely maximizing good output and keeping bad outputs constant in a directional vector (e.g., Färe, Grosskopf, and Pasurka 2007). DDOF is used for expanding good outputs and contracting bad outputs in a directional vector (e.g., Chung, Färe, and Grosskopf 1997; Picazo-Tadeo, Reig-Martinez, and Hernandez-Sancho 2005; Färe et al. 2005; Färe, Grosskopf, and Pasurka 2007). Both models are additive, and their expansion and/or contraction take place in a directional vector. In fact, EPF is a special case of DDOF.
Environmental Production Function
Like traditional production functions, given the vectors of inputs and bad outputs (x,z), an environmental production possibility frontier is defined as F(x,z) and constructed based on observations. We assume that F(x,z) is the bounded line segments OABCO in graph S1 of Figure 2. The maximum amount ofgood outputs can be produced based on the production possibility frontier F(x,z). Given a set of inputs and bad outputs (x0,z0), the maximum feasible production of good outputs is defined as F(x0,z0). Because good outputs can be freely disposed, y is feasible if y≤F(x,z). Then, the environmental production set is defined as P(x)= {(y,z) : y≤F(x,z)}. Hence, an environmental production function is “a complete characterization of the single output environmental technology” (Färe, Grosskopf, and Pasurka 2007).
There are parametric and nonparametric methods of specifying production models. The parametric method specifies a mathematical equation for a production model, for example, a quadratic function for a directional distance function (e.g., Färe et al. 2005; Vardanyan and Noh 2006). The nonparametric method uses the data envelopment analysis (DEA) technique to measure the efficiency performance of producers. DEA uses linear programming techniques that first identify the theoretically best producers based on observed data (e.g., inputs and outputs). Then, a production possibility frontier is constructed as a piecewise linear envelope of all observed outputs and inputs. The producers on the frontier are assumed to operate efficiently. Producers who are not on the frontier are regarded as inefficient. The production level due to inefficiency is calculated by comparing the performance ofeach producer to the best producer. Nonparametric methods have advantages over parametric methods because they can incorporate several inputs and outputs without generating different estimates. They can be performed with limited data sets, and they also avoid the biases brought about by different parametric models. Also, they require only quantitative data on inputs and outputs; no specific price data are needed (Färe et al. 1989; Färe, Grosskopf, and Pasurka 2003). Therefore, in this study, a nonparametric method is adopted.
Assuming there is a sample of k = 1,...,K producers employing a vector of inputs xnk, n = 1,...,N to obtain a vector ofgood output ykm, m = 1,...,M, and a vector of bad outputs zjk, j = 1,...,J, the environmental production function on the production technology T is then defined by
[3]Let g denote a directional vector, g = (gy) for good outputs, where gy ∈ Rm+, and gm ≠ 0. EPF on the production technology T is defined by
[4]The objective function of EPF is to maximize good output by increasing quantity θ in the directional vector gy, given inputs and bad outputs. When bad outputs are unregulated, the objective function for observation k′ is written as
[5.1]subject to
[5.1a]
[5.1b]
[5.1c]
[5.1d]where xn,ym,zj,αk,θ ≥ 0, and αk are the intensity variables. They are weights assigned to each observation when constructing the production frontier. Since αk is nonnegative, variable returns to scale are imposed, and the summation of αk is assumed to be 1.
When bad outputs are regulated, the objective function for observation k′ is written as
[5.2]subject to
[5.2a]
[5:2b]
[5.2c]
[5.2d]where xn,ym,zj,αk,θ ≥ 0 are defined as above. The right-hand side of the constraints of linear programming problems represents the actual amounts of inputs or outputs employed or produced, while the left-hand side of the constraints represents the amount of inputs or outputs used or produced by the most efficient or best producers. It should be noted that the signs of the constraints for bad outputs in two equations are different. In the third constraint equation above (equations [5.1c] and [5.2c]), the equality sign means that bad outputs are weakly disposable under a regulated technology, in other words, the observed amount ofbad outputs equals the amount of bad outputs produced by the most efficient producers. On the other hand, the inequality sign means that bad outputs are strongly disposable under an unregulated technology, in other words, the observed amount of bad outputs equals or is less than the amount of bad outputs produced by the most efficient producers.
Directional Distance Output Function
A DDOF has the quality that it can allow the expansion of good outputs and contraction of bad outputs at the same time. Let g denote a directional vector, g = (gy − gz), for good and bad outputs, where gy = Rm+, gz = Rj+, and gm+j ≠ 0. DDOF on the production technology T is then defined by
[6]where β is the maximum attainable expansion of good outputs along the +gy direction, and largest feasible contraction of bad outputs along the −gz direction vector. Applying the same principles for strong and weak disposability for bad outputs as in EPF, the objective function of DDOF under unregulated technology is
[7.1]subject to
[7.1a]
[7.1b]
[7.1c]
[7.1d]The objective function under regulated technology is
[7.2]subject to
[7.2a]
[7.2b]
[7.2c]
[7.2d]where, xn,ym,zj,αk,θ ≥ 0, the input and output constraints are defined as in the case of EPF.
Pollution Abatement Costs
When bad outputs are not regulated, their disposal is costless for producers but not to society, and all inputs are used for producing good outputs. When environmental regulations are imposed, disposing ofbad outputs (pollution) becomes a costly activity for producers because it takes away resources from producing good outputs to reduce/abate bad outputs. In other words, some of the inputs that are used to produce good outputs have to be diverted for cleaning/abating bad outputs. The reduction in the production of the bad outputs comes at a cost in the form of a reduction in the production of the good outputs. Hence, pollution abatement cost (PAC) is defined as the lost good outputs to producers related to pollution abatement activity. PAC can also be seen as the opportunity cost of the environmental regulations because it is measured by the difference of the forgone good outputs under unregulated and regulated technologies (Färe et al. 2005; Färe, Grosskopf, and Pasurka 2007). Therefore, PACs under two production functions are expressed as follows:
Environmental production function:
[8.1]Directional distance output function:
[8.2]It should be noted that these production models are usually used to measure the technical inefficiency of producers. Given input vectors, technical inefficiency measures are determined by the ratio of actual good outputs to maximum potential good outputs. If observed data points lie on the frontier, producers are defined as efficient, otherwise they are inefficient. The magnitude of technical inefficiency measures the distance between observed data points and the production possibility frontier.
Figure 3 illustrates an environmental production function and a directional distance output function. The dotted line OABCO represents the regulated technology, while the solid line OY2BCO represents the unregulated technology. Points A and B are on the frontier P(x) and are efficient. Point a, for instance, operates inside the frontier and it is therefore inefficient. Any point on or inside P(x) can be expanded and/or contracted in both (y,z). For instance, in the case of the EPF, keeping bad output unchanged, the producer operating at point a can expand its good output from a to a1 with the regulated technology or from a to a2 with the unregulated technology. Under the DDOF, the producer can increase its good output and decrease bad output by moving from a to b1 with the regulated technology or from a to b2 with the unregulated technology.
Illustration of Environmental Production and Directional Distance Output Functions
Thus, PACs can be determined by the difference between the maximum good output production associated with unregulated and regulated production technologies, or they can be determined on the loss of good output production related to technical inefficiency (Färe, Grosskopf, and Pasurka 2007). As can be seen in Figure 3, if the EPF is used, the lost output due to inefficiency is the distance between a and a1 under the regulated technology and between a and a2 under the unregulated technology; the PAC is the distance between a1 and a2. If the DDOF is used, the lost output due to inefficiency is the distance between a and b1 under the regulated technology and between a and b2 under the unregulated technology; the PAC is the vertical distance between b1 and b2, that is, the distance between Y1 and Y2. Since farmed salmon are sold in the market, the potential revenue losses are calculated using average yearly market prices and potential output production losses. Therefore, PACs also can be determined by the potential revenue losses.
Directional Vector
Before conducting the programming, we need to specify the directional vector g(gy) and g(gy,gz) for the EPF and DDOF models, respectively. We choose the directional vector g = gy − gz) = (1,0) for the EPF model, and g = gy − gz) = (1,−1) for the DDOF model. The reason for choosing the unity directional vectors (gy = 1 and gz = 1) is that they indicate the “shortest” distance when optimizing over the direction to reach the production frontier (Färe and Grosskopf 2000). In other words, the estimates from the two models give the maximum unit expansion in good output production and simultaneous unit contraction in bad output production. We test the effects of using different directional vectors for inputs and outputs on the pollution abatement costs in the sensitivity analysis.
Linear programming is used to solve the maximization problem for each functional form. The computer software General Algebraic Modeling System (GAMS) is used to execute the calculation. GAMS is a high-level modeling system for mathematical programming and optimization.1 The optimal solutions are achieved for unregulated and regulated production technologies for two production models based on explicitly differentiating the assumptions on the constraints regarding inputs and outputs, in particular, the constraints on bad outputs.
III. The Data
Since Norway has widely available ecological and economic data related to salmon aquaculture, we use the Norwegian salmon aquaculture industry as the case of an empirical application of the joint production models proposed herein. Norway is the pioneer in salmon aquaculture development and production. The country has been the number one farmed salmon producer in the world since the beginning ofsalmon farming. However, due to the lack of farm-level data, we consider salmon aquaculture as a whole and use the data collected at an aggregated industry level, on an annual basis.
In this analysis, salmon aquaculture operation needs four inputs (feed, smolt, labor, and capital) to produce one good output (salmon production) and two bad outputs (nitrogen and phosphorus). The quantities ofsalmon production and inputs are extracted from Statistics Norway and the Fisheries Directorate ofNorway (www.ssb.no),2 whereas the quantities of nitrogen and phosphorus were estimated by the Norwegian Institute for Water Research (NIVA) and compiled by Natural Resource and Environment, Norway (Statistics Norway 2006). Several methods are used to quantify nitrogen and phosphorus from aquaculture. The production parameters, such as production, feed used, nitrogen and phosphorus contents in feed and farmed salmon, treatment yield, wastewater volume, nitrogen and phosphorus concentration of samples, and number of sampling periods are used for these calculations, and the detailed information is presented by Borgvang and Selvik (2000). The data set ranges from 1986 to 2005 and is summarized in Table 1. Since both the EPF and DDOF are additive models, the measurement unit and magnitude of inputs and outputs may affect the results (Picazo-Tadeo, Reig-Martinez, and Hernandez-Sancho 2005; Färe, Grosskopf, and Pasurka 2007). To avoid these problems, we scale all inputs and outputs into fractions by dividing these by their respective maximum values in the samples of inputs and outputs. In other words, the values of all the inputs and outputs are normalized between 0 and 1.
Summary Statistics for Norwegian Salmon Aquaculture, 1986–2005
The lost good outputs associated with technical inefficiency are estimated for the EPF and DDOF models using the same data set. The PACs are simply the difference between the lost good outputs resulting from technical inefficiency for unregulated and regulated production technologies. By multiplying by the prices of good output, namely, the annual farmgate price, the losses of good outputs in terms of revenue are calculated. Hence, the pollution abatement costs are expressed in both lost production and revenue of the good output.
IV. Results and Discussions
Figure 4 shows the pollution abatement costs over time for the two production models. Over the years, PACs in terms of both production and revenue have shown a decreasing trend for both models. Especially in the last several years, the PACs are trivial. In this study, the technological production possibility frontier (PPF) is constructed from all the data sets for a period of 20 years, (i.e., series production processes). Pasurka (2001) indicates that the technology for any year is cumulative, meaning the producers use the production process in that year or any preceding year. Therefore, the technology based on time series data can be considered as improved technology. The PPF is constructed based on cumulative technologies. In other words, the individual observations in recent years are more closed to the boundary points of PPF for both unregulated and regulated frontiers. Also, it indicates that the PACs are measured based on improved production technology. That is why the PACs are virtually zero or at no measurable costs in recent years. Further, he points out that pollution abatement costs based on a time series data may be underestimated because technical change tends to reduce measured pollution abatement costs (Pasurka 2001). Although our models do not explicitly specify the technical changes of the industry, these technical changes have been taken place and been captured in the production process through input- and output-related variables such as the improvement of feed formulation and feeding technology, and husbandry management (Bjorndal, Tveteras, and Asche 2002).
Pollution Abatement Costs (PACs) for Two Production Models: Environmental Production Function (EPF) and Directional Distance Output Function (DDOF) (Scale of The Y Axis Differs on The Two Graphs)
However, the PACs show a wide variation depending on years (producers) and the production models applied. In some years, PACs increase unexpectedly. For instance, in 1989, 1994, and 2002, PACs were much higher than in their respective adjacent years. These sudden increases in PACs may be caused by different factors, such as investment in production, market conditions, regulatory changes, or biophysical shocks (e.g., disease outbreaks and accidents). Tveretas (1999) and Tveretas, and Heshmati (2002) indicated that these factors might result in technical changes from year to year. For instance, in 1989, Furunculosis, a bacterial disease, became endemic in Norway, hitting the salmon aquaculture industry hard, with 189 salmon farms and wild salmon populations in 18 rivers affected (Johnsen and Jensen 1994).
We averaged the 20-year PACs (Table 2). This will help us average out the variations in PACs observed. On average, pollution abatement costs expressed in terms of lost production and revenue are about 10.1 thousand tonnes and 472 million NOKs (1 US$ = 5.5 NOKs), respectively, over the 20 years. These comprise 3.5% and 6.5% of total farmed salmon production and revenue, respectively. The PACs estimated from the DDOF and EPF models are about 12.1 and 8.2 thousand tonnes, which corresponds to about 4.2%, and 2.9% of total salmon production, respectively. In terms of revenue, the costs are around 544 and 400 million NOKs, which works out to about 7.5% and 5.5% of total revenues, respectively. Out of a total of 20 observations, 8 in the DDOF model, and 10 in the EPF model do not incur pollution abatement costs.
Average Pollution Abatement Costs Associated with the Two Production Models
Considering that salmon producers have achieved low or even negative profit margins recently due to low market prices (e.g., 2001-2004), these PAC estimates are probably quite large in absolute value terms (Sumaila, Volpe, and Liu 2007). Especially for those producers who have not internalized the PACs into their production processes, the profit margins may disappear when they do fully internalize them. These results, however, suggest that without environmental regulations, farmed salmon could be theoretically increased by 3.5% in terms of tonnes of salmon production and 6.5% in terms of gross revenues. Given current production technology and environmental regulations, these potential increases in production and revenue have been diverted for reducing pollution. If the target pollution level is lower than the current level, reduction in good output production is possible. In particular, salmon farms that are too closely clustered may have to be closed down partially or fully. This has already happened in the North Sea. A recent North Sea Agreement declares that the pollution level in the North Sea has to be reduced to the level in 1985 for all production sectors and households in all the countries bordering the North sea. In order to meet the target, Norwegian fish farming facilities have been prohibited in the North sea region since 1997 (Statistics Norway 2006).
In reality, these PACs have partially, if not fully, been internalized by the Norwegian producers into the production process as a result of stringent environmental regulations and technical innovations (Asche, Guttormsen, and Tveteras 1999; Bjorndal, Tveteras, and Asche 2002; Tveretas 2002). The trend of reduced PACs may also imply that the technical improvement of the industry is confirmed to some extent by the Norwegian salmon aquaculture industry. Moreover, it may be argued that using averaged PACs measured from time series data is inappropriate because the PACs in the last several years are insignificant. However, we do believe that not all individual farms operate with the same technical efficiency (or inefficiency) and are regulated under the same environmental policies. Thus, the results based on the Norwegian data can be used as a basis to understand similar industries in other jurisdictions and/or used by policy makers in other countries to formulate environmental regulation policies that have not been in place.
It is expected that the DDoF estimates higher pollution abatement cost than the EPF. This is because different mapping rules for bad outputs are applied in these two models. DDoF increases good output and decreases bad outputs in a directional vector; EPF only increases good output and keeps bad outputs unchanged. In the DDOF model, some inputs have to be diverted to reduce bad outputs, while all inputs are used to increase good outputs in the EPF model. But, both models are appropriate in the case of salmon aquaculture because some producers are compelled to reduce bad output, such as in Norway, while other producers, such as those in Chile, are not so compelled to a significant degree.
V. Sensitivity Analysis
As the mapping rules for directional vectors have impacts on the estimated pollution abatement costs (e.g., Vardanyan and Noh 2006), a variety of mapping rules are applied for the two directional models, EPF and DDOF. First, it is assumed that the directional vector for bad outputs remains constant at 1, and the directional vector for good output is assumed to gradually increase on a scale of 1 to 10. Results show that the estimated PACs fall with increasing directional vector for good output (Figure 5). This is to be expected because more inputs are diverted to producing good output. The magnitude of the decline gets smaller as the directional vector for good output gets bigger. This is the case in both models (Figure 5).
Estimated Pollution Abatement Cost For Various Mapping Rules (Scale of The Y Axis Differs on The Two Graphs)
Next, in the base case, we assume that input factors are not regulated. Within a production process, assuming inputs are all used to produce good output when bad outputs are unregulated, some inputs have to be allocated for pollution abatement activity when bad outputs are regulated. However, in some cases, inputs do change depending on the resource, state of the economy, and time. For instance, feed use has gradually reduced with the improvement of feed formulation and feeding technology. Thus, we test the effect on PAC under an assumption of reducing input uses and expanding good output. Here, we use the DDOF to illustrate these effects on PACs. Two scenarios are presented: Scenario 1, increasing good output while reducing inputs and bad outputs simultaneously g(−gx, +gy −gz) = (−1,1,−1); and Scenario 2, increasing good output while reducing inputs and keeping bad outputs constant g(−gx, +gy −gz) = (−1,1,0). The results are compared with the base scenario g(−gx, +gy −gz) = (0,1,−1).
Figure 6 shows that PACs decline when inputs are reduced. This indicates that directly reducing inputs may be more resource efficient than directly reducing bad outputs, because pollution is reduced at source in the former case. This result may provide producers and policy makers a useful insight for formulating environmental regulations and developing abatement programs. As in the case of salmon aquaculture, it is difficult to mitigate pollution once it is discharged into the environment. This is because pollution is quickly dispersed into the open ocean, given current production technology—an open net-cage system. Since feed is the key input factor in contributing waste discharges, controlling feed input may be the most efficient means to regulate pollution discharges for salmon aquaculture. For instance, a feed quota program has been established in Norway since 1995. The aim of the program is to control production through controlling feed (Hjelt 2000).
Pollution Abatement Costs (PACs) Under Different Mapping Rules For Inputs And Outputs
VI. Conclusions
We develop a joint production function to model both good and bad outputs from the salmon aquaculture industry. This allows us to calculate PACs from a production process and from a private producer’s perspective. Two production models, EPF and DDOF, are applied. Good and bad outputs are treated in an asymmetrical way in the models. EPF only maximizes good outputs and keeps bad outputs constant. DDOF expands good outputs and contracts bad outputs simultaneously. The analyses are conducted based on the assumptions of strong and weak disposability of bad outputs. Consequently, unregulated and regulated production technologies are specified. The empirical analyses are carried out on the Norwegian salmon aquaculture industry. One good output (salmon), two bad outputs (nitrogen and phosphorus), and four inputs (feed, smolt, labor, and capital) are included in the analyses. The data are aggregated at the industry level, covering a period of 20 years from 1986 to 2005. We choose a nonparametric approach to solve the maximization problem that this analysis entails. PACs are calculated by determining the difference between the foregone good outputs using two technologies.
Although PAC is estimated based on a production process from a producer’s perspective, it can be viewed as the pollution damage costs on the environment and resource users. Further, the PACs can be used as the economic bases to establish public damage abatement and compensation programs or to formulate economicbased environmental policies. For example, the PACs can be used as reference points to set pollution taxes that can be imposed on producers. The producers who fail to implement environmental regulations in their production decision making should be penalized. The level of penalty can be set based on the estimates of PACs. To the best of our knowledge, this study is the first attempt to use a joint production function approach to estimate PACs for aquaculture, in general, and salmon aquaculture, in particular, although a joint production model has been applied earlier to estimate productivity and technical efficiency for shrimp farming in Mexico (Martinez-Cordero and Leung 2004).
It should be noted that this joint production approach provides a framework to measure pollution abatement costs through technical inefficiency across farms and years. This study explores these costs for different years due to data constraints at the farm levels. Ideally, cross-sectional panel data of salmon farms are more appropriate than using time series of data aggregated from all the salmon farms. However, in the case of salmon aquaculture, such crosssectional panel data were just simply not available when the study was conducted. Thus, potential future research will be to measure annual PAC using panel data sets. And it would be interesting to investigate how the PAC changes over time by comparing the annual PACs. Further, technical efficiency and pollution abatement costs greatly differ from year to year, with a generally declining trend in the Norwegian case studied herein. This paper has provided a framework and an analysis that promises to be of help to policy makers in determining appropriate environmental policy regarding sustainable salmon aquaculture.
Footnotes
The authors are, respectively, postdoctoral fellow, Department of Economics, Norwegian University of Science and Technology; and associate professor and director, Fisheries Centre, University of British Columbia. This paper is part of the first author’s Ph.D. dissertation conducted at the Fisheries Economic Research Unit, Fisheries Centre of the University of British Columbia. The authors would like to thank Dr. Carl Pasurka from the U.S. Environmental Protection Agency for helping with GAMS, and extremely useful comments in the earlier version of this manuscript. Thanks also go to Dr. Sumeet Gulati of the University of British Columbia for helpful comments and discussions. The authors are also indebted to John Rune Selvik from the Norwegian Institute for Water Research and Mr. Svein Erik Stave from Statistics Norway for providing the information on pollution and sharing the nitrogen and phosphorus data with us. We are also grateful to two anonymous reviewers for their truly helpful comments and suggestions on an earlier version of this manuscript. Canada’s Research Network in Aquaculture (AquaNet) is acknowledged for financial support to the first author. Rashid Sumaila thanks the Sea Around Us Project for their support. Any errors, opinions, or conclusions expressed are those of the authors alone and should not reflect the funding agencies.
↵1 See www.gams.com for more information.
↵2 See www.ssb.no for more information.
