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Modelling environmental inefficiency under a quota system

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Abstract

This paper introduces the methodology necessary to evaluate inefficiency of regulated decision making units that operate under quotas through data envelopment analysis, accounting for both quotas restrictions and negative environmental externalities of production. Three technical inefficiency measures are proposed: inefficiency in the production of marketed output, environmental inefficiency, and inefficiency with quotas. It is then shown how to aggregate these measures in order to obtain indicators of overall performance. The new approach is illustrated through a numerical example that uses real data available for the European Union dairy sector. The results show that considerable differences in inefficiencies could be found when quotas restrictions are accounted for in the model than in the model without quota imposition, indicating that not accounting explicitly for quotas when measuring performance in regulated sectors may lead to a not accurate estimation of firms’ technical inefficiency.

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Notes

  1. Despite the recent removal of the quota system from the EU dairy sector, as soon as 2016 a new policy to regulate this market with an objective similar to quotas—to reduce the quantity of milk available on the market was introduced. This policy is called ‘milk production reduction scheme’ (European Commission 2016).

  2. The quantities of quotas were divided among producers in each EU member country. The quota transfers and exchanges were allowed with trading rules differing across member countries leading to a large heterogeneity in the implementation of quotas between countries (Ang and Oude Lansink 2016). If the quantities of milk exceeded the quota at country level, the levy needed to be paid by the member country responsible for producing the surplus.

  3. The review of different approaches to modeling environmental efficiency in the agriculture sector is made by Oude Lansink and Wall (2014).

  4. The literature on modeling efficiency of dairy farms without taking into account environmental factors is more extensive including the studies by Mbaga et al. (2003), Alvarez and del Corral (2010), Emvalomatis et al. (2011) or Sauer and Latacz-Lohmann (2015).

  5. Ayres and Kneese (1969) proposed these two same groups when introducing the materials balance to economists.

  6. Bad outputs are introduced as “inputs” in sub-technology T2, something that was criticized in the previous literature on environmental efficiency measurement, as we pointed out in this section. However, Murty and Russell (2018) have recently defended the by-production approach, indicating that there are a lower bound and an upper bound on emission generation for given amounts of emission-generating inputs. The existence of an upper and lower boundary for emissions complicates the modeling of an emission-generating technology, particularly in the study of its disposability and the implied monotonicity properties. Fortunately, as they treat emissions as undesirable by-products, efficiency requires minimization of the production of emissions, conditional on input quantities. Therefore, the attention can be restricted to the study of the properties of the lower bounds on emission generation, which is what is really estimated by the specification of T2.

  7. The reason why we select this particular orientation is twofold. First, from a methodological point of view, it seems natural to resort to the same orientation as used by Murty et al. (2012) since our approach is, in part, an extension of that model. Second, from an empirical point of view, it makes sense to investigate the direct effect of the quota on the inefficiency measure through an output-oriented framework since quota limits the output production and affects it directly.

  8. In model (3) we could substitute \( \theta_{j} \le 1 \) by \( \theta_{j} \) free in the presence of quotas in order to avoid the possibility of infeasibilities when the assessed DMU exceeds the quota constraints. However, if we use that modified model to evaluate a unit that satisfies the quotas, then it is not possible to assure that \( \theta_{j} \le 1 \) for all \( j \) at optimum, which allows to apply the Pareto dominance notion. In this sense, the model that we propose in this paper may be seen as more natural for dealing with this type of context since we do not need to adapt it for units satisfying the quotas and for units exceeding them.

  9. We assume that data observed from the DMUs, inputs and outputs, are affected by the quota restrictions because it is reasonable to think that farms have accounted for quotas in their production plans before producing. Consequently, quotas affect the input mix and thereby influence the pollutant inputs and, implicitly, the bad outputs. However, in our mathematical approach, the constraint associated with the quota appears exclusively in the model related to the standard technology (T1) since good outputs, which are in this case the type of outputs that are regulated, are the only part of the model for measuring standard technical efficiency. Note that, in fact, following Murty et al. (2012), good outputs are not a part of the model associated with the environmental technology T2.

  10. Brännlund et al. (1995) is related to our approach. Brännlund et al. (1995) analyzed the impact of environmental regulation in the Swedish pulp and paper industry on firms’ profit. On one hand, a common feature of Brännlund et al. (1995) and our approach is the way in which regulation is introduced in the model: an upper bound for good outputs. On the other hand, there are two main differences between our model and Brännlund et al. (1995). Firstly, Brännlund et al. (1995) focused on profit inefficiency while our approach focuses on technical inefficiency. In particular, we selected the directional distance function (DDF) for measuring environmental technical inefficiency and defined a suitable DDF to work in the context of by-production (Murty et al., 2012). Secondly, Brännlund et al. (1995) introduced the bad outputs in their model as inputs in one step without distinguishing between non-pollution causing inputs and pollution-generating inputs. In our approach, which is based on the recent by-production model (Murty et al., 2012), the bad outputs are exclusively introduced in sub-technology T2, distinguishing between the two mentioned types of inputs.

  11. A negative value in the traditional output-oriented directional distance function reflects that the evaluated output bundle is not feasible, i.e. the inputs are not sufficient to produce the output. However, in our approach this interpretation changes and a negative value is associated with producing beyond the quota (see Fig. 1 below).

  12. The data for quotas and milk production is available for the periods 2004/2005, 2006/2007, 2009/2010 and 2012/2013, which corresponds to the years 2005, 2007, 2010 and 2013, respectively, for which the rest of variables is presented.

  13. For Poland and Slovenia the period 2005/2006 was the first year of the application of the quota system, Bulgaria and Romania entered EU in 2007 and their first period of quota data was 2007/2008, while Croatia became EU member in 2013 and its first period of quota data is 2013/2014. So there is no relevant data of quotas for these countries for some of the years of the period analyzed in this paper, hence these countries were excluded from our sample.

  14. The aggregated data concerns specialist dairy farms and cattle-dairying, rearing and fattening combined farms.

  15. Full time corresponds to 1800 annual working hours.

  16. The main environmental issues of dairy sector concern water and air pollution, with the latter being mainly from manure management and enteric fermentation (OECD 2004). Due to the absence of data for water pollution of dairy sector, we restrict our analysis to bad outputs related with greenhouse gas emissions.

  17. As it was mentioned before, our analysis focuses on the delivery quotas. Hence, the variable of milk production is equivalent to quantities of milk delivered to dairies and quota is equivalent to available quota for deliveries.

  18. Usually in the literature concerning agricultural efficiency, the production technology is modeled also including general production costs or purchased feed (see for example, Emvalomatis et al. 2011). However, such data was missing in the datasets used in this study, while in other datasets such data would not be comparable to the remaining variables in our sample.

  19. We apply this test using the data for all analyzed years together instead of performing it year by year to have a large enough sample size. In particular, Li (1996) shows in Monte Carlo simulations that the test performs well for moderate sample sizes. Also, Simar and Zelenyuk (2006) show through Monte Carlo simulations that the test is a reliable tool for moderate dimensions of the DEA model (as measured by the number of inputs and outputs) relative to the sample size. In particular, they concluded that the power of the test is fairly good for the DEA model of two or three inputs and one output for as many as 50 observations in each group. And, for example, for five inputs and one output for 20 observations in each group, they show that the power of the test is quite low. Given the maximum of five dimensions of the DEA model that we have (to estimate good outputs technology we have three inputs and two outputs) and 23 observations of countries in each year, the application of the test on a yearly basis would result in the low power of the test. Hence, we decide to apply the S-Z test for all years together, which results in a considerably larger sample size given the dimensions of the DEA model.

  20. We estimated frontiers separately for each year, which means that we are not able to interpret the results of inefficiency changes over time as improving or worsening with certainty. To interpret the results of inefficiency changes over time with more certainty we would need, for example, to compute inefficiency for all years together (hence, assuming that technology and frontier is not changing over time).

  21. The test (presented in Table 6 and then also in Table 8) was performed for values of inefficiencies for each DMU and not for average values of inefficiencies. The average values of inefficiencies were computed to give an additional glance on countries’ performance over the entire period analyzed.

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Acknowledgements

The authors are grateful to the National Science Centre in Poland (grant number 2016/23/B/HS4/03398) and the Spanish Ministry for Economy and Competitiveness (Ministerio de Economia, Industria y Competitividad), the State Research Agency (Agencia Estatal de Investigacion) and the European Regional Development Fund (Fondo Europeo de Desarrollo Regional) under grant MTM2016-79765-P (AEI/FEDER, UE) for providing financial support for this article. The calculations of adapted Li test were made at the Wroclaw Centre for Networking and Supercomputing (www.wcss.wroc.pl), Grant No. 286.

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  1. Center of Operations Research (CIO), Miguel Hernandez University of Elche (UMH), Avda. de la Universidad s/n, 03202, Elche, Alicante, Spain

    Juan Aparicio & Lidia Ortiz

  2. Institute of Applied Mathematics, Department of Logistics, Wrocław University of Economics, Wrocław, Poland

    Magdalena Kapelko

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Aparicio, J., Kapelko, M. & Ortiz, L. Modelling environmental inefficiency under a quota system. Oper Res Int J 21, 1097–1124 (2021). https://doi.org/10.1007/s12351-019-00487-z

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