Abstract
This article provides a generalization of the materials balance-based production model introduced by Coelli et al. (2007). Based on this, some new environmental efficiency (EE) measures are presented. The Coelli et al. (2007) EE measure and its extension by Rødseth (2016) produce biased efficiency estimates if the material flow coefficients (MFCs) are heterogeneous across decision-making units and non-discretionary. Furthermore, the Coelli et al. (2007) measure fails to reward emission reductions by emission control. To overcome these shortcomings, this paper proposes production models which allow for heterogeneous MFCs reflecting differences of external environmental factors or non-controllable heterogeneities in inputs and outputs, and which properly take into account emission abatement activities. Based on this, EE measures are provided and decomposed into (i) a part reflecting emission control efficiency (ECE), (ii) a part measuring material input efficiency (MIE), and (iii) a part reflecting the efficient allocation between material and non-material inputs (environmental allocative efficiency, EAE). The approach is illustrated by an empirical application to arable farming in Austria utilizing data from 90 farms for the year 2011. Soil erosion is considered an undesirable output and land a material input. The average EE, ECE, MIE, and EAE are 0.53, 0.96, 0.69, and 0.79, respectively. The results indicate that actual output can be potentially achieved with 47% less soil loss. Most of the potential to improve EE is due to differences in MIE and EAE. Removing inefficiencies in the implementation of existing, subsidized erosion controls allows soil loss to be reduced by 4%.
Highlights
Multiple approaches to incorporate environmental perspectives into productivity and efficiency analysis exist: (i) Färe et al (1986, 1989) were the first to introduceJournal of Productivity Analysis popularity.1All these approaches have been criticized for various reasons
The relationship between the new EE measures in Eqs. (25.1)–(25.3) with the EE measures of Coelli et al (2007) and Rødseth (2016) are explored in proposition 3: Proposition 3: If the material flow coefficients (MFCs) are homogeneous across all decision-making unit (DMU), Eq (18) and Eq (21) collapse into Eq (7) and Eq (8), respectively. It follows from this result and Proposition 1 and 2 that the new EE measures, EE1, EE2, and EE3 are generalizations of the Coelli et al (2007) measure and coincide with the Coelli et al (2007) measure if the MFCs are homogeneous across all DMUs, none of the producers control emissions and the MFCs of the desirable outputs are zero
The materials-balance based productive efficiency models and EE measures introduced by Coelli et al (2007) and Rødseth (2016, 2017) produce biased efficiency estimates if the MFCs are non-discretionary and heterogeneous across DMUs
Summary
Multiple approaches to incorporate environmental perspectives into productivity and efficiency analysis exist (see Dakpo et al 2016 for a survey of the literature): (i) Färe et al (1986, 1989) were the first to introduceJournal of Productivity Analysis popularity (see e.g., Dakpo et al 2017; Ait Sidhoum et al 2020).1All these approaches have been criticized for various reasons (see, e.g., Färe and Grosskopf 2004; Førsund 2009; Dakpo et al 2016; Førsund 2018; Hampf 2018). The most widely applied approaches, for example, (i) and (ii), are criticized for not complying with physical laws (i.e., the materials balance principle, law of mass conservation, or first law of thermodynamics) and for allowing for physically impossible production possibilities (Färe and Grosskopf 2003; Coelli et al 2007; Førsund 2009; Hoang and Coelli 2011; Podinovski and Kuosmanen 2011; Rødseth 2017). To overcome this problem, Coelli et al (2007) and Rødseth (2017) introduced production models that insure consistency with the materials balance principle.. Residuals (i.e., pollutants or bad outputs), inputs and good outputs are linked by material flow coefficients (MFCs) such that the amount of materials tied up in the inputs must equal the amount of the flow of materials embedded in intended outputs plus residuals
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