Modelling pollution-generating technologies in performance benchmarking: Recent developments, limits and future prospects in the non-parametric framework
Externalities or spillovers arise in the presence of market failures where some actions of a group of agents generate social costs (or social benefits) that accrue to external parties not involved in the market transaction (McConnell and Brue, 2007). The case of pollution-generating activities is particularly relevant in this context. The question of the internalisation of the social costs arising from pollution has become an important area of interest for economists. In the presence of environmental regulations aimed at the internalisation of pollution costs by firms, some resources within firms might be diverted to mitigate pollution and, hence, best-practice comparisons (i.e. performance benchmarking) that do not account for this would inevitably lead to spurious results (Kopp, 1981). Besides, integrating environmental aspects into productive efficiency can provide policy-makers with helpful information on production systems that can lead to improving the design of new policies. Within this framework, Pittman (1983) used the index number theory of Caves et al. (1982) to develop a new productivity comparison methodology that incorporated undesirable outputs’2 control behaviour. However, this methodology was based on a translog transformation function which required information on prices for undesirable outputs. Pollution being a non-marketed good, computing Pittman’s productivity indices may be challenging. By contrast, the development of activity analysis enables efficiency evaluation based on quantity information only.
Two paradigms have been developed, one involving parametric models (econometric models which require the specification of a functional form) and one using mathematical programming methods (such as Data Envelopment Analysis – DEA). In this chapter we focus on the latter, since such methods offer a large range of possibilities due to their flexibility and the less restrictive assumptions inherent in them. In the literature using such mathematical programming methods, the implicit positive correlation between pollution and desirable outputs has been formalised in different ways.
i-) A first approach treats pollution as a free disposable input (Dyckhoff and Allen, 2001; Hailu and Veeman, 2001b; Yang and Pollitt, 2009).3 The main argument behind this approach is that emissions of environmentally detrimental products can be viewed as the use of the environment’s capacity that is necessary for their disposal (Paul et al., 2002; Considine and Larson, 2006). Thus, according to the advocates of this approach, considering these emissions as inputs is likely to be a good way of accounting for the consumption of natural resources. Some other scholars (Baumol et al., 1988; Barbera and McConnell, 1990; Cropper and Oates, 1992; Tahvonen and Kuuluvainen, 1993) believe in a positive relationship between good and bad outputs for a reason clearly expressed in Mahlberg and Sahoo (2011) as: “undesirable outputs incur costs for a firm because it requires the diversion of productive inputs from the production of desirable (good) outputs for abatement purposes in compliance with the environmental regulations”. However, as argued by Førsund (2009), this idea is more convincing at a macro level where “a single relation with residuals as inputs may be regarded as a reduced form of a larger system”. From another perspective, Haynes et al. (1993) stated that undesirable outputs can be viewed as “unavoidable” residuals, which are subsets of pollution-generating inputs, and thus can be treated as inputs. The idea of considering undesirable outputs as additional inputs has, however, been seriously challenged as it deflects from the physical laws (Färe and Grosskopf, 2003) and the materials balance principles (Ayres and Kneese, 1969; Ayres, 1995). Rigorously speaking, undesirable outputs are not inputs, and treating them as additional inputs will not reflect the true production process (Seiford and Zhu, 2002). As summarised by Scheel (2001), when pollution is treated as an input “one abstracts from the underlying input-output structure which is usually defined by the nature of the production process. Instead, the only information needed is whether the data have to be minimized or maximized . . .” Moreover, by assuming free disposability of undesirable outputs, such modelling includes situations where “finite amount of input can produce an infinite amount of bad output, thus violating the law of mass conservation” (Podinovski and Kuosmanen, 2011). Considering bads as inputs is then physically unacceptable because of the violation of the boundedness of output sets. All these criticisms make the model that treats bad outputs as extra inputs unrealistic and thus to be avoided. Based on this situation, we do not discuss this case further in the chapter.
ii-) A second group of approaches extends models such as the frontier eco-efficiency models based on Korhonen and Luptacik (2004) and Lauwers (2009), which construct a production system where only undesirable outputs are used as inputs to produce the good output (Mahlberg et al., 2011). This approach is not discussed here since it is based on an incomplete production process. Another approach known as the LCA+DEA approach associates Life Cycle Assessment (LCA) and DEA (Iribarren et al., 2010).4 We also ignore this model here because its objective is not the minimisation of undesirable outputs, but rather the potential reduction of these outputs in the case where all production units are technically efficient. The model fails to capture all the input’s substitution possibilities that could help optimise the environmental performance. Another range of approaches relies on data transformation so that undesirable outputs can be equivalently treated as good outputs (Lovell et al., 1995; Sahoo et al., 2011). However, Färe and Grosskopf (2004a) showed that the results obtained from such data transformation are inconsistent. This is intuitive since the transformation distorts the real production process. Moreover, the model implies that undesirable outputs can be reduced without any cost, which is not realistic (Du et al., 2014). Hence, we also do not consider this approach in this chapter.
iii-) A third approach considers pollution as outputs by assuming the weak disposability of these bad outputs and the null-jointness of both production types (good outputs and bad outputs) (Färe et al., 1986; Färe and Grosskopf, 2009; Färe et al., 2012). The weak disposability concept describes a situation where outputs are intimately linked and their amounts cannot be changed independently. In the case where bad outputs are present, it implies that reducing the levels of these outputs necessarily requires reducing the quantities of intended outputs in a proportional way. The null-jointness property accounts for situations where if zero levels of good outputs are produced then zero levels of bad outputs are generated. This approach relying on weak disposability and null-jointness is commonly used in the literature. However, as argued by Coelli et al. (2007) and Hoang and Coelli (2011), the weak disposability assumption (WDA) violates the first law of thermodynamics.5 It can be demonstrated that under certain conditions, such as the presence of end-of-pipe technologies to abate pollution, the WDA and the null-jointness assumption can become compatible with the materials balance principles (Hampf and Rødseth, 2014). Yet, in many situations end-of-pipe equipment is technologically unavailable or economically unaffordable (Rødseth and Romstad, 2013). In addition, making the WDA conform to the materials balance principles, does not mean that the approach is correct. We provide a thorough discussion of the limits of the WDA in the third section.
iv-) With respect to the limits associated with the WDA, an approach based on the materials balance principles was introduced into production theory by Lauwers et al. (1999) and later furthered by Lauwers and Van Huylenbroeck (2003); Coelli et al. (2005). Relying on the mass/energy balance equation – which is simply an accounting identity that links in an equivalent way the quantity of materials that goes into a production process to the amount of outputs including residual ones – enables the estimation of an iso-environmental line in the same vein as iso-cost lines. However, as explained by Ebert and Welsch (2007), it essentially focuses on materials inputs and ignores any interaction that might exist between these materials inputs and non-materials ones. The method will thus identify decision making units (DMUs)6 that use few materials inputs as environmentally efficient, despite their reliance on non-materials inputs. In addition, recently Hoang and Rao (2010) underlined the problem of “the lack of universally accepted weights for various material inputs”. Taking the example of eutrophication and gas pollution in agriculture, the authors discussed the difficulties in aggregating these two impacts in the case of the materials balance. They then proposed an extension based on the use of the cumulative exergy7 balance (see also Hoang and Alauddin (2011)). However, the “premises and conclusions are still being strongly debated” (Dewulf et al., 2008), and the notion of exergy is complicated due to technical and theoretical limitations (Maes and Van Passel, 2014). Along the same lines, Hampf and Rødseth (2014) offered a new approach named the weak G-disposability, which relies on the first two laws of thermodynamics8 to model a pollution-generating technology without resorting to any transformation of the non-materials inputs. This approach combines the mass/energy identity equation and the G-disposability developed in Chung (1996) around the directional distance function (DDF) (see Färe and Grosskopf (2000) for a discussion of the theory and application of the DDF). We discuss this recent development in this chapter.
v-) Finally, a more recent approach suggests modelling the firm’s production technology by using two sub-technologies: one generating the intended outputs and a second generating the unintended outputs (Førsund, 2008; Sueyoshi and Goto, 2010; Sueyoshi et al., 2010; Murty et al., 2012). Operational efficiency and environmental efficiency can then each be evaluated using the specific corresponding sub-frontier. Within this framework, Murty et al. (2012) proposed the by-production model which relies on the cost disposability assumption of the technology with respect to undesirable outputs (for more theory on this, see also Murty (2012)). Based on the idea of the unavoidability of residuals’ generation when using materials inputs (that is to say polluting inputs), the approach suggests that for given levels of these inputs there is an associated minimal amount of pollution, and the presence of inefficiency can yield more than this minimal amount. Another recent approach is provided by Sueyoshi and Goto (2012a, 2012b, 2012c) who developed the concepts of natural and managerial disposability to characterise a firm’s adaptation potential in the case of pollution mitigation. Natural disposability implies reducing pollution by simply decreasing the levels of (polluting) inputs, thus requiring no managerial effort. By contrast, managerial disposability implies managerial efforts in the form of the adoption of new technologies, such as high quality inputs or other innovative technology, that can mitigate pollution. These two recent and promising approaches are developed in this chapter.
Reviews of works on DEA and environmentally bad outputs can be found in Tyteca (1996), Zhou et al. (2008a), and Manello (2012). This literature focuses mainly on the classical approaches that consider residuals as inputs or as outputs under the WDA, or that use some data transformation functions. this chapter firstly provides an update of the existing reviews by outlining the major recent developments around the inclusion of undesirable outputs in production technology modelling, namely the weak G-disposability assumption, the by-production model and the natural and managerial disposability concepts. Secondly, we discuss the limits inherent in each methodology. In fact, most of the existing literature surveys focus on a simple description of the models without a clear insight into the drawbacks associated with each model. This chapter contributes to filling this gap by synthesising the problems of the commonly-used models and discussing the challenges associated with the recent developments. Thus, the original contribution of this chapter is that we provide in a single place a critical review of all models, not only the ones widely used and already criticised (such as the ones relying on the WDA), but also the recently advanced ones developed to circumvent the shortcomings of previous models, and we show how the different approaches are interrelated.
Table of contents :
1. Background: Greenhouse Gas Emissions and livestock farming
1.1. Climate change, agriculture and livestock impacts
1.2. Sustainable development and theory of externalities
1.3. GHG mitigation alternatives in livestock farming and policy options
2. Problem statement, research questions and objective of the PhD
3. Livestock databases and GHG computations for the empirical applications
4. Structure of the dissertation
Chapter 1. Modelling pollution-generating technologies in performance benchmarking: Recent developments, limits and future prospects in the non-parametric fram
2. Methodology for our literature review
3. The weak disposability assumption (WDA)
3.1. Definition and operationalization
3.2. Limits of the WDA
4. Recent developments in modelling pollution-generating technologies: materials balance approach and multiple frontier technologies
4.1. The weak-G disposability and the materials balance principles
4.2. By-production technologies
4.3. Non-radial efficiency measure under natural and managerial disposability
5. Challenges and future trends of research
Chapter 2. On modelling pollution-generating technologies: a new formulation of the by-production approach
2. The classic by-production modelling
3. A new model: extension of the by-production approach
3.1. Definition of the extension
3.2. Efficiency assessment under the new extended BP approach
4. A numerical application
Chapter 3. Greenhouse gas emissions and efficiency in French sheep meat farming: a comparison of pollution-generating technologies in non-parametric modelling
2. The modelling of pollution-generating technologies in the literature
2.1. Different models available that include bad outputs in the production technology
2.2. Eco-efficiency assessment and decomposition, and shadow price computation
2.3. Empirical studies of efficiency and pollution-generating technologies in agriculture: a review of the literature
3. Data and methodology
3.2. Models implemented to assess eco-efficiency
4.1. Eco-efficiency and its components
4.2. Trade-offs between operational efficiency and environmental efficiency
4.3. Shadow prices
Annex: Applications of efficiency calculation accounting for bad outputs in agriculture
Chapter 4. Investments and dynamic eco-efficiency under the by-production of undesirable output: a non-parametric framework
2. Dynamic efficiency measurement in the literature
3. Dynamic aspects in pollution-generating technologies
4. Dynamic vs. static eco-efficiency estimation
5. Empirical application
Annex: Dynamic and static eco-efficiency scores under different investment ratios
Chapter 5. General Discussion
2. Environmental impacts’ analysis frameworks in the literature
3. Synthesis of main findings
4. Limits of the work
5. Suggestions for future research