European Journal of Operational Research 250 (2016) 342–346 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor Short Communication Environmental eﬃciency measurement and the materials balance condition reconsidered Kenneth Løvold Rødseth ∗ Institute of Transport Economics, Department of Economics and Logistics, Gaustadalléen 21, NO-0349 Oslo, Norway article info Article history: Received 18 April 2014 Accepted 29 October 2015 Available online 10 November 2015 Keywords: OR in environment and climate change Environmental eﬃciency Data envelopment analysis Weak G-disposability abstract This note takes up a shortcoming of Coelli et al.’s (2007) popular environmental eﬃciency measure and its extension to economic-environmental trade-off analysis (see Van Meensel et al. (2010)), namely that they do not reward emission reductions by pollution control. A new environmental eﬃciency measure that over- comes this issue and - similar to Coelli et al.’s eﬃciency measure - is in line with the materials balance principle is proposed and further decomposed into “technical environmental eﬃciency” and “material and nonmaterial allocative environmental eﬃciencies”. The new eﬃciency measure collapses into Coelli et al.’s eﬃciency measure if none of the considered Decision Making Units control pollutants. A numerical example using Data Envelopment Analysis is provided to further explore the properties of the new eﬃciency measure. © 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved. 1. Introduction The productivity and eﬃciency analysis literature has become engaged with production processes in which undesirable outputs (pollutants) are jointly produced with desirable outputs. Conse- quently, the appropriate way to model undesirable outputs has been debated. Among the most popular approaches are to incorpo- rate pollutants as freely disposable inputs (Baumol & Oates, 1975; Pittman, 1981) or weakly disposable outputs (Färe, Grosskopf, Lovell, & Pasurka, 1989; Färe, Grosskopf, Noh, & Weber, 2005) in the pro- duction model. They have recently been criticized for not complying with the materials balance condition (e.g. Coelli, Lauwers, & Van Huylenbroeck, 2007; Rødseth, 2013; Rødseth & Romstad, 2014), a law of physics that explains the generation of pollution in many conventional production processes. Coelli et al. (2007) introduced a new environmental eﬃciency measure that ensures consistency with the materials balance condi- tion. Unlike the above-mentioned modeling approaches, Coelli et al. (2007) do not treat pollutants as inputs or outputs to be included in the production model, but utilize material ﬂow coeﬃcients to iden- tify the input mix that results in the minimal material inﬂow required to produce a certain bundle of desirable outputs. Their material in- ﬂow minimization problem is parallel to the well-known cost min- imization problem in economics, and Coelli et al.’s (2007) eﬃciency measure therefore corresponds to Farrell’s (1957) cost eﬃciency mea- ∗ Corresponding author. Tel.: +47 92234670. E-mail address: klr@toi.no sure. Economic-environmental trade-offs can further be assessed by comparing the material inﬂow minimization to cost minimization; see e.g. Van Meensel, Lauwers, Van Huylenbroeck, and Van Passel (2010). This note takes up an issue that was not satisfactory dealt with by Coelli et al. (2007), namely the role of pollution control in envi- ronmental eﬃciency measurement. More speciﬁcally, it shows that Coelli et al.’s eﬃciency measure may provide biased eﬃciency rank- ings in cases where pollution control is a common compliance strat- egy. The reason is that their approach only cares about reallocation (or minimization) of material inputs to minimize uncontrolled emis- sions, and neglects the fact that additional inputs can be used to con- trol pollutants. Pollution control, e.g. end-of-pipe abatement, is quite common in many of the industries which Coelli et al.’s model has been applied to – e.g. electricity (Welch & Barnum, 2009) and agricul- ture (Coelli et al., 2007) – although it has not been taken into account in these empirical analyses. Rødseth (2015) recently introduced the axioms “weak G- disposability” and “output essentiality” and showed that they al- low the speciﬁcation of a production model that includes pollutants and, at the same time, is consistent with the materials balance con- dition. Hampf and Rødseth (2015) showed how Rødseth’s theoreti- cal production model can be implemented using Data Envelopment Analysis (Charnes, Cooper, & Rhodes, 1978), abbreviated DEA. This approach makes up the foundation of the current note, which intro- duces a new environmental eﬃciency measure that rewards emis- sion reductions by pollution control. Coelli et al.’s (2007) environ- mental eﬃciency measure is a special case of the proposed eﬃciency measure. http://dx.doi.org/10.1016/j.ejor.2015.10.061 0377-2217/© 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.