Technological externalities and environmental policy How to simulate manure management regulation within a DEA framework Isabelle Piot-Lepetit
[email protected]
Published as: Piot-Lepetit I. (2014), Technological externalities and environmental policy: How to simulate manure management regulation within a DEA framework. Annals of Operations Research, Special Issue: Advances in Data Envelopment Analysis, 214, 1, 31–48.
Abstract
The directional distance function defined in a DEA type non-parametric framework provides a highly flexible framework for modelling producer behaviour in the presence of polluting emissions and environmental regulations. This article presents different models describing more or less restrictive "command and control" type policy measures as an economic one concerning nitrogen pollution of agricultural origin. These measures regard the management of the mandatory constraint on the spreading of organic manure and the investment in manure treatment facilities. The study also simulates the use of an economic instrument by enforcing the individual manure constraint at an aggregated level. Using individual and aggregated DEA models, this paper provides insights into the impact of individual and collective management of environmental policy instruments.
Keywords
Directional Distance Function, Data Envelopment Analysis, Nitrate Pollution, Environmental Regulation, European Nitrates Directive.
Economic literature generally distinguishes between two types of externalities: technological and pecuniary externalities. The fundamental difference between these externalities is that technological externalities modify the functional relationship between the quantities of resources used as inputs and the quantity or quality of the physical output. Pecuniary externalities only influence the financial situation of an affected individual. They do not involve any change in the efficiency of the production process when regarded as a transformation of inputs into physical outputs (Baumol and Oates, 1988). Environmental externalities are considered as technological externalities. These externalities occur whenever the production or consumption decision of one agent in the economy, such as a firm or a household, affects the welfare of another agent in an unintended way, and when, additionally, the affected party does not receive any compensation from the agent producing the externality. In the case of environmental externalities, the generation of a polluting output affects society as a whole, whereas it is the result of a private decision made by an economic agent. Environmental pollution therefore takes on the character of a public good in the sense that the consumption of a polluted environment does not reduce the consumption of pollution by another economic agent. In other words, the marginal cost of providing the public good is zero. In a competitive market, where private producers price their products equal to marginal costs, the supply of public goods would hence result in zero returns to the private producer. This implies that a purely competitive market fails to achieve an optimal supply of public goods (Randall, 1972). With no prices to provide the proper incentives for reducing polluting activities, the inevitable result is excessive demand on the assimilative capacity of the environment (Baumol and Oates, 1988). As there are no private rights for public goods, it is the responsibility of the government to guarantee the provision of these goods. Furthermore, the occurrence of negative externalities due to agricultural activities indicates the misallocation of resources. In the presence of a "public bad", the ordinary price system of a competitive economy is unable to provide an efficient outcome. In such a situation, the right to use the environment needs to be limited by law. Government intervention in private decisions implies the reallocation of a certain proportion of the bundle of property rights to society. One important issue is how to dispose of polluting wastes in the least costly way to society. The problem lies in finding a set of incentives that induce behaviour consistent with the social optimum of society. To internalize the social costs of pollution, the solution provided by the economist is to place an appropriate price or tax on polluting activities. Rather than doing this, 2
policy-makers have often opted for the more traditional "command and control" instruments involving explicit limitations on allowable levels of emissions and the use of specified abatement techniques. Pricing measures for environmental regulation are rare (Baumol and Oates, 1988). To examine the effects of different environmental policies, models representing the behaviour of economic agents can be used to determine the sought-after social optimum. Of the models that can be used to study producer behaviour, we have chosen the analysis framework proposed by the Data Envelopment Analysis or DEA (Charnes et al., 1978; Färe et al., 1985). The DEA approach requires no assumptions about efficiency or functional form while supporting multiple inputs and outputs. A linear programming framework is used to construct a best-practice frontier over a data set according to an evaluation criterion. We have chosen the directional distance function, recently introduced into the literature (Chung et al., 1997) as the evaluation criterion. Based on Luenberger's (1992) previous work, this function provides a representation of the production technology and measures the distance of each observation at the frontier in a direction specified by a vector known as the "direction vector". It is a generalization of Shephard’s distance function (Chambers et al., 1996). As noticed by Chavas and Cox (1999), it allows for the rescaling of inputs and outputs in a more flexible way than in Shephard's distance function. Furthermore, the directional distance function easily represents the jointness of production between the intended output and polluting emissions (Färe and Grosskopf, 2004). Using modelling based on the directional distance function defined from a DEA type nonparametric structure, it is possible to directly obtain a measurement of production and environmental performance and to assess the variations caused by a change in environmental policy. It is also possible to explicitly model different measures of "command and control" type policies. Two policy instruments are modelled at an individual level: the mandatory constraint on spreading of 170kg/ha of organic manure and the investment in a manure treatment facility. Based on previous works on the relationship between firm-specific efficiency indices and industry efficiency (Li and Ng, 1995; Brännlund et al., 1998; Färe and Zelenyuk, 2003; Kuosmanen et al., 2006), aggregate DEA models are developed to provide insights on a collective management of previous "command and control" policy as well as an economic measure by imposing the constraint on organic manure at an aggregated level. This extension explicitly models several policy measures applicable at the level of a group of farms located in a geographical area. 3
The article is organized as follows. Section 1 provides a summary of the analysis framework as it is usually presented in the literature. It describes how the production technology can be represented using a production frontier and the extension required to take nitrogen pollution into account. Section 2 presents the directional distance function used to assess the production and environmental performance of the producers. Section 3 proposes an extension to this framework to model more restrictive policy applicable to areas with a high concentration of livestock farms necessitating search for off-farm spreading land, exchange of spreading rights, or treatment of manure. Section 4 provides an empirical illustration of this framework. Finally, section 5 concludes. 1. Modelling production technology with polluting goods 1.1. Representation of production technology Production is the process of transforming inputs into outputs. The fundamental reality which firms must contend with in this process is technological feasibility. The state of technology determines and restricts what is possible in combining inputs to produce outputs. There are several ways that can be used to represent this constraint. The most general way is to conceive of the firm as possessing a production possibility set T where:
(1) T ( x, y, b) N M S : ( x, y, b) is a feasible production plan
A production plan is a vector of both inputs and outputs. Let x RN denote the input vector, and y RM the output vector. The standard approach in environmental economics literature characterizes pollution as a public "bad" that results from waste discharges associated with the production of a private good. Let b RS denote the bad output vector or pollution emissions. Pollution results from waste emissions b in the production process of y. In this formulation, pollution emissions are treated simply as a by-product of the production activity. As we will focus in our presentation on the output side effect by studying how substitutions between goods and bads might be implemented, we will use the output set that is a subset of production possibility set T that specifies all the output vectors (y,b) which can be produced from a given input vector x.
(2) P( x) ( y, b) M S : ( x, y, b) T
x N
The production technology P(x) is assumed to satisfy certain axioms to be a valid model of production as the possibility of inaction, no free production, null-jointness of bad and good
4
outputs, input free disposability, output weak disposability, good output free disposability, closeness, compactness and convexity (Shephard, 1970; Färe and Grosskopf, 2004). 1.2. Construction of production technology In terms of empirical implementation, the production technology can be constructed based on a linear programming framework. We use the nonparametric approach known as Data Envelopment Analysis or DEA. . Let a set of observations of inputs and outputs ( xk , y k , bk ) RN M S , k=1,…,K where xk ( x1,k , x2,k ,...., x N ,k ) is an observed input vector used in the production of good outputs y k ( y1,k , y 2,k ,...., y M ,k ) and bad outputs bk (b1,k , b2,k ,...., bS ,k ) . A production set depending
on the assumptions of the production technology and on the set of observations can be constructed for each k' as: K
K
P( xk ' ) ( yk ' , bk ' ) : z kk ' ym,k ym,k ' , m 1,..., M ; z kk 'bs , k bs ,k ' , s 1,..., S ; k 1
(3)
k 1
K
z k 1
k' k n,k
x
xn,k ' , n 1,..., N ; z kk ' 0, k 1,..., K
with the vector z k ' ( z1k ' , z2k ' ,...., zKk ' ) K denoting the intensity levels at which each of the K firms might be conducted. This vector enables the modeller to increase or decrease individual observed activities, so as to construct unobserved or virtual but nonetheless feasible activities. It provides weight for the construction of the linear segments of the piecewise linear boundary of the production possibility set. This model satisfies the axioms assumed for the validity of the technology P(x) (Färe et al., 1994). The weak disposability of bad outputs is modelled by the equalities, and strong disposability of good outputs and inputs is represented by inequalities in their respective constraints. The technology in (3) exhibits constant returns to scale. This assumption can be relaxed by imposing restrictions on the intensity variables. This can be done by using the following restriction
K
z 1 as in Färe and Grosskopf (2003) if a uniform abatement factor across
k' k 1 k
all firms applies for scaling down good and bad outputs. Otherwise, if different abatement factors are expected for each observed activity, the approach developed in Kuosmanen (2005) should be used. This approach involves a partition of the intensity vector of firm k' in two parts as z k ' k ' k ' . The second component k ' represents the part of firm's output that is abated by scaling down its activity while the first component k ' represents the part of firm's output that remains active. This decomposition allows for individual abatement factors with a 5
technology that is still linearly designed. The output of firm k' are weighted by the non disposed part k ' , wheras the inputs are weighted by the sum of the disposed and non disposed weight components (for further details, see Kuosmanen, 2005, Färe and Grosskopf, 2009; Kuosmanen and Podinovski, 2009). 1.3. Production technology with an environmental standard In response to the joint production of bad outputs that are not marketable, public authorities use standards that serve as targets for environmental quality. They are introduced in order to restrict the production of bad outputs. The effect of an environmental regulation defined as a standard is to restrict the production possibility set to a proper subset that is considered as less polluting. Environmental standards do not affect the shape of the production frontier but prevent firms from using a portion of the feasible production plans. The restriction stated by the standard introduced by the European environmental regulation concerning water pollution is only applicable to one component of the polluting emission. Up to a certain level, organic manure can be applied to fields for fertilization purposes. Furthermore, fertilizers are often added as well, especially to secure nitrate availability for the crops. The nutrients contained in manure and fertilizers are to some extent removed when the crops are harvested. However, only surplus nutrients pose potential environmental problems. When the maximum level of nutrients needed for fertilizing purposes is reached, the surplus from spreading runs off on the land and contaminates surface and ground waters (OECD, 2003). The level of nitrogen surplus is derived from the nutrient balance of the farm, which can be stated as follows for the farm k': (4) bNsurpl,k ' bNorg,k ' bN min, k ' bNdep,k ' bN exp, k ' where bNorg,k ' is the level of organic manure, bN min,k ' the level of mineral fertilizers, bNdep,k ' the atmospheric nitrogen deposition and, bN exp,k ' the level of nitrogen that is taken up by the crops on the land (OECD, 2001). In this specific case, the quantitative standard resulting from the European Nitrates directive only applies to one component of the nutrient balance, bNorg,k ' , and not to bNsurpl,k ' . It may be expressed as follows: (5) bNorg,k ' 170 xland,k ' where xland,k ' is the total area of the farm that can be used for disposal of organic manure. The production set defined in (3) is modified in the following way:
6
(6)
P170 ( xk ' ) ( yk ' , bk ' ) P( xk ' ), bNsurpl,k ' bNorg ,k ' bN min, k ' bNdep,k ' bN exp, k ' , bNorg ,k ' 170 xland,k '
2. Efficiency measurement with polluting goods 2.1. Definition of the directional distance function One common assumption about the economic behavior of the firm is that the firm chooses an output vector that maximizes revenue at given output prices for a given input vector. This optimization assumption implies that all firms operate on the frontier of the production set. When we allow for the existence of inefficient production as an empirical fact, the technology frontier is constructed on the basis of all the producers' production possibilities, and measures their degree of efficiency in relation to that frontier. The performance of the firm is measured as a possible divergence between actual and optimal performance. Constructing an efficient frontier and measuring the extent of efficiency are the two major topics of efficiency measurement. When the output production set is defined as in the previous sub-section, the firm's technology can be represented by the mean of an output distance function. The output distance function gives the distance between each observed output and the maximum output that can be achieved from any vector of inputs. In the multi-input multi-output framework, Shephard’s (1970) distance functions have been generalized in a number of ways. Among them, Luenberger's shortage function (Luenberger, 1995) allows the rescaling of inputs and outputs in any particular direction. It provides a generalization to Shephard's distance functions (Chambers et al., 1996). The Shortage function is similar to the directional distance function, which we shall now present (Färe and Grosskopf, 2004). Let g R M S with g 0 . The output directional distance function with reference g can be defined by: (7) Do ( x, y, b; g ) sup : ( y, b) g P( x) The dimension of the g vector is the same as that of the output vector, but the domain is not constrained by non-negativity. To find Do ( x, y, b; g ) , we add g to (y,b), until we find the largest such that ( y, b) g belongs to P(x). Thus, the directional output distance function characterizes technology by measuring a radial expansion of outputs in the direction of the g vector. We have: (8) Do ( x, y, b; g ) 0 if and only if ( x, y, b) P( x) 7
The distance function completely characterizes the technology. Thus, the properties imposed on the underlying production technology have the corresponding statement in terms of the properties of the distance function. These properties are translation, homogeneity, monotonicity in input and output vectors, concavity and continuity (Färe and Grosskopf, 2004). 2.2. Efficiency measurement with a directional distance function The directional output distance function can be used as an efficiency measurement. We can say that an observation is efficient in the g direction if: (9) Do ( x, y, b; g ) 0 If an output vector belongs to the frontier of the production possibility set, then the directional distance function takes the value of zero when evaluated in the g direction. When the g vector is given, we can get an efficiency measurement, which is invariant with the change in the unit of measurement, by calculating the directional output distance function. The problem is the choice of the g vector. As the economic impact of bads is different from that of goods, we can state a direction for the directional distance function that credits producers for an increase in the production of goods and a decrease in the generation of bads for a given level of inputs. Thus, in our case, we use g ( y,b) for measuring a firm's performance when polluting outputs are produced jointly with good outputs. The directional output distance function with g ( y,b) can be rewritten as: (10) Do ( x, y, b; g ) max : ((1 ) y, (1 )b) P( x) When good outputs are expanded, bad outputs are contracted by the same proportion as denoted by the same parameter . 2.3. Efficiency measurement with a standard restriction on manure The regulatory constraint faced by farms is quantitative in nature, i.e. organic manure is restricted in quantity and is described in equation (5) and introduced in the production set through the technology representation described in (6). Thus, it is possible to measure the efficiency of individual farms by using the following linear program. For the farm k' (k'=1,…,K), we have: Mod-P170: k' D0170 ( xk ' , yk ' , bk ' ; yk ' ,bk ' ) max 170
8
s.t. K
z k 1 K
z k 1
k' k
k' y mk (1 170 ) y mk '
k' b (1 170 )bsk '
k' k sk
K
z k 1 K
(11)
z k 1
k' k Nsurpl, k
b
m 1,..., M s 1,..., S 1
k' bNsurpl
x xnk '
k' k nk
n 1,..., N
z kk ' 0 k 1,..., K k' k' bNsurpl bNorg bN min, k ' bNdep,k ' bN exp, k ' k' bNorg 170 xland k '
where bs (s=1,…,S-1) are all other bad outputs resulting from the production of animals (phosphorus, heavy metals, etc.). These are not directly considered by the specific constraint on manure from the Nitrates directive. However, they can be expected to be reduced. In the model, all the variables with a lower index k' are observed data while the variables with an upper index k' are variable, i.e. they are optimized by the linear programming model. Thus, k' the variable bNsurpl is optimised, while the variable bNsurpl,k ' is drawn from the data set.
This model is run for each farm in the sample and provides an individual optimal value for the k' k' k' efficiency measurement 170 , the nitrogen surplus bNsurpl , the organic manure bNorg and the
intensity vector zk', (k'=1,…,K). 3. Modelling alternative environmental policy on manure reduction The objective of this section is to develop alternative models that can simulate the impact on farmers' efficiency of various environmental policy constraints on manure. Due to the intensity of production in some European regions, the standard cannot be complied with by the farms located in these regions. The number of animals produced each year means that the level of spreading greatly exceeds the standard. In these regions, stringent regulations have been brought in by their government. The framework presented herein focuses on French farms located in areas with a high concentration of livestock farms, and in particular, of pig farms as in Brittany. Of the set of restrictive measures defined by the French government and applicable to these farms, the obligation to search for off-farm spreading land and the requirement to treat manure are now mandatory.
9
3.1. Search for off-farm spreading lands If we consider the search for off-farm spreading land at the individual level, the production technology defined in (3) can be rewritten as follows:
(12)
Poff
farm
k' k' ( xk ' ) ( yk ' , bk ' ) P( xk ' ), bNsurpl bNorg bN min, k ' bNdep,k ' bN exp, k ' ,
k' off farm, k ' bNorg 170 ( xland,k ' xland )
off farm, k ' where xland is the level of off-farm lands that is necessary for organic manure spreading
purposes. In this specific case, the optimal level of organic manure produced on-farm depends on the spreading land disposability of the farm k' and on the possibility of finding off-farm off farm, k ' spreading land. Thus, the optimal value for xland is expected to be constrained by land
availability. In France, the exchange of spreading areas is mandatory only in regions like Brittany where the production of pigs is so intensive that it is impossible to comply with the mandatory standard brought in by the Nitrates Directive. The land availability is delimited by the geographical area that can be exchanged by farmers within the region of concern. Thus, it implies a collective management of the mandatory restriction on manure that can be modelled by the following production technology set:
(13)
K K Pcoll ( xk ' ) Poff k ' 1 k'
K
farm ( xk ' ),
K
k' 170 xland, k ' bNorg k ' 1
k ' 1
K
x k ' 1
k' land
K
x k ' 1
off farm, k ' land
xland,k ' k '1 K
This model allows for the collective management of spreading land by a group of farmers located in a given geographical area. In this framework, all producers are able to continue their activity in compliance with the European regulation. Exchanges of spreading land are possible. With the aim of improving the productive and environmental efficiency of each farm in the group, this collective model provides an ideal allocation of spreading land among the farms in the sample in the direction specified by the European environmental regulation. Regarding the linear programming model, it is necessary to build only one model containing all individual output sets and constraints shared by all farmers. Individual efficiency measurements are optimised by using a common objective function wich is: 10
coll
(14) Do ( x, y, b; y,b) max where
K
k '1
k' coll
k' coll is the efficiency measurement of farm k'.
3.2. Enforcement of the manure constraint at a more aggregated level This section is devoted to the development of a model where the manure constraint is no more set at an individual level, but rather at an aggregated one. The level of emissions is restricted to be no greater that the total emissions allowed under the individual system. This model simulates an optimal allocation of spreading rights among farmers. There is a possibility for trading constraints on manure spreading. This can be written in the following way: K K (15) Ptrade ( xk ' ) Psurpl ( xk ' ), k '1 k'
K
K
k '1
k '1
k' 170 xland,k ' , bNorg
K k' x xland,k ' land k '1 k '1 K
k' k' with Psurpl ( xk ' ) ( yk ' , bk ' ) P( xk ' ), bNsurpl bNorg bN min, k ' bNdep,k ' bN exp, k '
It is like a tradable permit system. Based on Environmental Economics literature (Montgomery, 1972; Baumol and Oates, 1988), it is expected to provide under certain assumptions the prescribed environmental quality at the least cost. 3.3. Investment in a manure treatment system by an individual producer The objective is now to model the standard applicable to manure when producers decide to reduce the potential impact of their production activity on the environment by investing in a manure treatment system. While these technologies offer the potential to reduce the environmental impacts of pig production, the additional costs of installing some of these systems have to be taken into account when considering the changes in producers' behavior induced by the implementation of mandatory environmental regulations. A large share of the costs associated with the adoption of these new technological systems is the capital investment cost, and there is no immediate reward to offset it, except when some form of financial support is granted to farmers. Let assume that each producer can invest in a specific treatment system. This involves an investment cost Cok ' . There is also a further cost to consider, which is linked to the running costs associated with the treatment system. This cost depends on the level of manure treated
11
treat, k ' k' by each farm. Let Ctreat denote the cost of treatment of bNorg units of organic manure
produced by the farm k', we have: k' treat,k ' (16) Ctreat ck ' bNorg
where ck ' is the unit cost associated with the specific treatment investment chosen by the producer k'. Thus, it is possible to measure the efficiency of individual farms by using the following production technology. Ptreat ( xk ' ) Psurpl ( xk ' ),
K
K
k 1
k 1
k' , z kk 'Co, k Cok ' zkk 'Ctreat,k Ctreat no treat, k ' Norg , k '
b
(17)
C
k' treat
170 xland, k '
treat, k ' ctreat, k ' bNorg ,k '
k' no treat, k ' treat, k ' bNorg bNorg bNorg ,k ' ,k '
no treat,k ' treat,k ' where bNorg is the amount of organic manure that is treated, bNorg is the amount of organic
manure that is not treated due to the producer 's budgetary constraints, the cost of manure treatment and its availability of land for spreading. 3.4. Sharing the cost of investing in a manure treatment system As the cost of investing in new manure treatment technologies can discourage producers from adopting these systems, a collective investment by a group of farmers can be encouraged to reduce the weight of the capital investment borne by each farm. The following production technology allows for this type of cost sharing. K K (18) Pinvest ( xk ' ) Pinv ( xk ' ), k '1 k '1
and Pinv ( xk ' ) Ptreat ( xk ' ),
K
c k '1
K
z k 1
k' k o,k
c
k' o
cok '
Co
where Co the capital investment in the treatment system, and cok ' the capital investment cost borne by the producer k'. As defined by (17) and (18), the above models implicitly assume that non-treated organic manure produced by a farm is spread on its own land. However, it is possible to represent a situation where a group of producers collectively invests in a treatment system and searches for off-farm spreading areas by developing a model based on models (13) or (15) and (18). 12
4. Empirical illustration 4.1. Data To illustrate previous models, a sample of livestock farms has been drawn from the Farm Accountancy Data Network (FADN) data set. These 90 farms are specialized in pig farming activities in France in 2001. The FADN data set provides annual information on quantities, both in physical and monetary terms, relating to marketable outputs and inputs. To obtain data on the impact of these farms on the environment, levels of organic manure and nitrogen surplus have been calculated. The evaluation of organic manure produced by farm is based on the number and type of animals on farm to which coefficients provided by the Corpen1 can be applied to convert animals into kilograms of organic manure. To derive the level of nitrogen surplus from the nutrient balance of a farm as defined in (4), an evaluation of the amount of nitrogen uptaken by harvested crops and by livestock sold and of nitrogen deposition was done by using Corpen’s coefficients. These calculations are presented in table 1. All farms in the sample have a positive nitrogen surplus with a mean of 285kg/ha and an average level of organic manure of 357kg/ha. They all have a negative impact on the environment. Among the 90 farms, only 30% of them comply with the mandatory limit introduced by the European directive Nitrates in 19912, i.e., a level of organic manure spread per hectare less than or equal to 170kg/ha as defined in (5). The average level of the undesirable output for these farms is of 112kg/ha and the average level of organic manure is of 129kg/ha. Concerning the rest of the sample, the average level of organic surplus is largely above the mandatory limit by 285kg/ha.
Insert Table 1 about here The implementation of the five models defined in the theoretical part, implies the definition of a set of inputs and outputs entering these models. For this illustration, we have assumed the production of two desirable outputs which are total gross products resulting from the production of livestock and from the production of other outputs on the farm as crops or milk. As this work focuses on organic manure, we have considered the co-production of only one 1
http://www.ecologie.gouv.fr/-CORPEN-.html
2
As the FADN data set does not contain any information on the area used by each farm for the spreading of
organic manure, an approximation of this area has been defined by using the total area of each farm. This approximation under-evaluates the area really used by farmers when they spread a part of their organic manure on some off-farm areas.
13
undesirable output, the nitrogen surplus level. The production process is assumed to be done by four inputs that are land, livestock herd, labour and other expenses from which fertilizer purchases have been excluded. For the simulation of the investment in a manure treatment system, some variables have been calculated based on information provided by experts relating to average investment and treatment costs. These costs are estimated to 11.11 Euros/kg of organic manure under treatment for the investment in a manure treatment system and to 2.28 Euros/kg for the running costs. To provide some data that can be used in the empirical illustration, we have assumed that, first, farmers dispose of organic manure by spreading on land until the mandatory limit and, then, they use the manure treatment system to dispose of the rest of their organic manure. These figures are presented in table 2.
Insert Table 2 about here 4.2. Results Efficiency measurements obtained from the five models defined in this paper are presented in table 3. For an easier reading of the results, we have translated the efficiency measure. An efficient farm has a score of unity while an inefficient farm has a score above unity. This latter can increase its efficiency by increasing its production with the use of a similar level of inputs and in accordance with the mandatory limit from the European directive. For some models, farms have a score less than unity. This means that it is impossible for these farms to maintain their activity at the observed level due to the set of constraints introduced in the definition of the production technology. The five models have been run under two specific assumptions regarding returns to scale: constant and variable. For the latter, the specification provided in Kuosmanen (2005) was used. The efficiency score are lesser under variable returns to scale than those provided under constant returns to scale. This is not surprising. In the former case, the efficiency measurement is expected to get insights in potential improvements at the current scale of farms' activities. In the latter case, it also takes into account potential inefficiency linked to the scale of each farm's activity. Thus, efficiency gains can be reached either by improving the technical implementation of the current production technology or by moving from decreasing or increasing returns to scale to constant ones. As it provides more flexibility for potential adjustments and as the impact on farms' activities is lesser, we will focus on results provided under the assumption of constant returns to scale. 14
The first model (Mod-P170) defined in (11) looks at some improvements in the level of production together with a compliance with the mandatory limit of the European Nitrates directive. Results show that none of the farms from the sample are efficient when this model is implemented. All the scores are below unity, with an average of 0.3. Among the 90 farms, 13 of them receive a score of zero. They stop their productive activity. 56 farms reduce their productive activity by more than 50%. For 76% of the farms in the sample, it becomes impossible to maintain their activity. The other farms have to reduce their activity by 11% to 50%. Thus, imposing a strict fulfilment of the mandatory limit to 170kg/ha implies a drop in the number of farms that can maintain their activity and in the level of production that can be done. The second model (Mod-Pcoll) is defined in (13) and (14). In this modelling framework, farms can use land off-farm for spreading purpose to comply with the mandatory limit of the European directive at an individual level with a restriction on land availability. The total amount of land that is available is equal to the total observed amount of land. Farms are allowed to do exchanges of land. Results show an average efficient score of 0.524. Only one of the farms has a score of zero but 55 farms have to reduce their activity by more than 50%. Thus, 62% of the farms cannot maintain their productive activity. This is less than the 76% in Mod-P170 but this is still very high. However, 9 farms have a score between 0.84 and unity, 2 farms have a score of unity and 2 farms can increase their production by 16%. As for ModP170, the results provided by Mod-Pcoll are strong in terms of number of farms that can be maintained in activity and production that can be done with a reduction by 54% of the initial level. The third model (Mod-Ptrade) defined in (15) is similar to Mod-Pcoll. The only difference is that farms can comply with the mandatory limit of the European directive at the sample level and no more at the individual level. The total amount of land availability is still restricted to the observed amount of land in the sample. The average of efficiency score is now 0.532, that is slightly higher than with the previous model. No farm receives a score of 0 and 2 farms are efficient with a score of 1. Otherwise, results are similar to those provided by the model ModPcoll. Insert Table 3 about here The fourth model (Mod-Ptreat) is defined in (17). It considers an investment in an individual manure treatment system to comply with the European Nitrates directive. Results provide 15
efficient scores that are above unity with an average of 1.12. 20 farms in the sample are efficient. More than half of them did not comply with the mandatory limit of 170 kg/ha in the observed situation. Farms that were initially above the limit can increase their production by 13% and farms that were below the limit by 10%. The last model or Mod-Pinvest in (18) deals with a collective investment in a manure treatment system. In this case, the investment costs are spread over all farms in the sample. With this model, the average efficient score is of 1.167. This score is higher than those allowed by ModPtreat that deals with an individual investment. Farms can now increase their production by near 17% and still comply with the mandatory limit on the spreading of organic manure. 2 farms have a score below unity, of 0.935 and 0.965. They slightly have to decrease their production by 3% and 6%. 13 farms are efficient while the others can increase their production by 18.8% with a range from 1 to 66%.
Then, observed levels of nitrogen surplus and organic manure are compared to optimal levels provided by the five models. Results are provided in table 4. With Mod-P170, there is a strong reduction in the amount of nitrogen surplus from 286 to 99kg/ha allowing the level of organic manure to strictly comply with the mandatory limit of 170kg/ha. All farms in the sample spread 170 kg/ha of organic manure. The farms that were initially above the limit decrease their level of organic manure from 454 to 170kg/ha while farms that were initially below increase it from 112 to 170kg/ha. Considering Mod-Pcoll, there is an average reduction in the level of nitrogen surplus from 286 to 153kg/ha. This decrease corresponds to an increase of the nitrogen surplus for farms below the limit from 112 to 129kg/ha and to a decrease for farms above the limit from 360 to 163kg/ha. The level of organic manure spread on land comply with the mandatory limit of 170kg/ha. Farms below the limit spread a higher level of organic manure, i.e., 141kg/ha rather than 129kg/ha while farms above the limit spread a lower level of 187kg/ha rather than the initial level of 454kg/ha. The amount of organic manure spread by farms initially above the limit is higher than 170kg/ha. This means that these farms spread a part of the organic manure they produce outside their own area. Exchanges of land are done by farms within the sample. This point is illustrated below in table 5. Results provided by Mod-Ptrade are similar. However, the level of organic manure is reduced for all types of farms. Thus, with an enforcement of the constraint regarding organic manure spreading at an aggregate level, a lesser nitrogen surplus is produced. The implementation of the regulation seems to be more profitable for the environment. 16
With Mod-Ptreat and Mod-Pinvest, the results provided for organic manure are higher than the mandatory level. This means that the amount that is above the limit is disposed of with the use of a manure treatment system. However, the amounts of nitrogen surplus and organic manure are lower than those initially observed. More details are provided below in table 6.
Insert Table 4 about here
The following table considers the availability of land for spreading purpose and compares results from the observed data set with those provided by Mod-Pcoll and Mod-Ptrade. Land initially available on farm is on average of 52.5ha while the amount of land that would be necessary to comply with the European Nitrates directive is of 76.2ha. Thus, there is an average lack of 23.7ha. Farms that were initially above the limit are highly constrained. They need of an average amount of 37ha while farms below the limit do not spread organic manure on an average area of 7ha. The demand for land off-farm requested by Mod-Pcoll is worth at 26.5ha. Farms initially below the limit do not use land off-farm for spreading while farms above the limit request for an average of 38ha outside their own area. With Mod-Ptrade, results are similar. A lesser amount of hectares is provided by off-farm land availability.
Insert Table 5 about here Results provided in table 6 concern the investment in a manure treatment system to comply with the mandatory limit of the European Nitrates directive. Either in the case of an individual or a collective investment, the amount of organic manure spread on land is lower that the no treat maximum amount of land that can be used for spreading as defined by bNorg in the observed
situation. While farms below the limit have no need of a manure treatment system, they invest in it and increase the amount of organic manure they produce in the optimal solution provided by Mod-Ptreat. At the opposite, farms initially above the limit reduce the amount of organic manure they produce. With Mod-Pinvest, the investment in the manure treatment system is collective. The average amount of organic manure to be treated is the same as the level in the observed situation while the level of organic nitrogen spread is lower. Farms initially below the limit invest in the collective manure treatment system but they use it for an amount of organic manure lower
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than in Mod-Ptreat. At the opposite, farms initially above the limit can put under treatment a larger level of organic manure than with Mod-Ptreat (individual investment). Insert Table 6 about here 4.3. Discussion To dispose of the organic manure, producers have several possibilities. The first one is spreading both on-farm and off-farm by using land purging capacity. The second one considers the possibility to reduce the effluents at its sources by changing the animal’s diet and by improving the management of mineral fertilizers. The third possibility is the treatment of manure while the last one is the reduction in production. The five models developed in this paper give some insights on these possibilities. Mod-P170 in (11) considers the case of the spreading of organic manure on farm. In this case all the farms have to reduce their production and some of them have to stop it because the level of organic manure produced by these farms is too high to be spread only on their own land. Mod-Pcoll in (13) provides a solution where an exchange of land is done between farms in the sample to collectively manage the mandatory spreading constraint from the European Nitrates directive. Some farms also have to reduce or to stop their activity. When the mandatory constraint on organic manure is specified at an aggregated level and no more at the individual one as in Mod-Ptrade in (15), it implies a reduction in the level of nitrogen surplus produced. However, half of the farmers are in trouble regarding their productive activity. Mod-Ptreat in (17) and Mod-Pinvest in (18) focus on the third possibility that is the treatment of organic manure. In this case, all farms can maintain or increase their activity and simultaneously comply with the mandatory limit of 170kg/ha of organic manure to be spread on their own land. The collective investment gives higher possibilities for farms initially above the limit to increase their production. This empirical illustration shows how the treatment of organic manure can help farmers to solve their problem of disposability of one by-product of livestock production in accordance with the existing environmental regulation. However, this result has to be analyzed in connection with the demand in pig meat. The over-production of meat was a cause of a decrease in prices and of some crises in the pig sector. Solving the problem of disposability of organic manure in accordance with environment regulation and with an increase in production may be only a short-term solution to the larger problem of this productive sector. A longerterm analysis would have to be done in order to analyze the structure of this sector and the 18
way of evolvement through a more friendly-environmentally production process that would be competitive on livestock markets and meet the demand.
5. Conclusion This article proposes an extension of the representation of producer behaviour using the directional distance function. This approach measures the production and environmental performance of farms. The use of the non-parametric framework provided by the DEA approach also enables a simple representation of "command and control" type environmental measures and of one economic measure based on exchange of productive rights, defined within the context of regulations on nitrogen pollution of agricultural origin. The analysis is conducted not only at the individual farm level, but also at a more aggregated level, i.e., a group of producers with a strong geographical identity, such as an intensive production region. The analysis framework is particularly extended to enable the modelling of restrictive measures such as farm manure treatment and off-farm spreading requirements. This framework based on five models has been illustrated on a sample of livestock farms specialized in pig production that have a nitrogen surplus. Only 30% of these farms comply with the mandatory limit of the European Nitrates directive of 170kg/ha of organic manure spread on land. Results show how the investment in a manure treatment can solve the problem of disposability of organic manure by dropping from spreading a part of the organic manure produced. The work carried out demonstrates the considerable flexibility of the approach used to measure farm efficiency and to model different and more or less restrictive "command and control" type environmental policy measures and one economic instrument. The use of a profit maximization type objective function within the non-parametric DEA framework would enable the representation of other regulatory instruments of an economic nature, which are little used in practice, such as taxation, productive rights market or finally, payments introduced to encourage producers to leave the sector with a view to reducing environmental pressure in the sector. Moreover, the development of these models over observed data may be used not only to assess the effects of a change in environmental policy on producer behaviour, but also to examine whether the direction of this change brought about by the regulations, directs the production system towards an optimal situation from the point of view of both the profitability of the production activities, and society’s environmental expectations.
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