Measuring ecological efficiency with data envelopment analysis (DEA)

Abstract

The measurement of ecological efficiency provides some important information for the companies’ environmental management. Ecological efficiency is usually measured by comparing environmental performance indicators. Data envelopment analysis (DEA) shows a high potential to support such comparisons, as no explicit weights are needed to aggregate the indicators. In general, DEA assumes that inputs and outputs are ‘goods’, but from an ecological perspective also ‘bads’ have to be considered. In the literature, ‘bads’ are treated in different and sometimes arbitrarily chosen ways. This article aims at the systematic derivation of ecologically extended DEA models. Starting from the assumptions of DEA in production theory and activity analysis, a generalisation of basic DEA models is derived by incorporating a multi-dimensional value function f. Extended preference structures can be considered by different specifications of f, e.g. specifications for ecologically motivated applications of DEA.

Introduction

`Organizations of all kinds are increasingly concerned to achieve and demonstrate sound environmental performance by controlling the impact of their activities, products or services on the environment [...].' (see introduction to ISO 14000). This quotation reflects the fact that environmental protection has become a ‘trendy’ topic. One reason for this development is that companies want to realise the idea of ‘sustainable development’. But more importantly, there are increasingly more benefits to be gained due to for example growing concern from the stakeholders, expanding environmental legislation, and cost savings.

An important instrument within the companies’ environmental management is the measurement of ecological efficiency (also: environmental performance measurement). Greatly varying definitions of ‘ecological efficiency’ are given in the literature, depending on the application context and subjective influences. The best-known definition is the one of the world business council for sustainable development (WBCSD): `Eco-efficiency is reached by the delivery of competitively-priced goods and services that satisfy human needs and bring quality of life, while progressively reducing environmental impacts and resource intensity throughout the life cycle, to a level at least in line with the earth’s estimated carrying capacity' (DeSimone and Popoff, 1997, p. 47). In order to measure ecological efficiency, it is necessary to operationalise such ‘global’ definitions in terms of environmental performance indicators (EPIs) and to draw a comparison of these indicators. ISO 14031 differentiates between operational performance indicators, management performance indicators, and environmental condition indicators. Ecological efficiency is usually measured by operational performance indicators which are based on material and energy balances. EPIs can be used for either target-performance comparisons, comparisons over time, internal or external eco-benchmarking. It should be noted that the measurement of ecological efficiency may include some typical ‘economic’ indicators.

There are several problems regarding comparisons of EPIs. The data base usually contains numerous, but non-standardised EPIs. Furthermore, even if companies have reliable and standardised environmental data, they might not publish it. Therefore, usually just a small number of companies are included in the comparison of EPIs. These deficits may be overcome in future by e.g. initiatives of the European Union regarding the standardisation and publicity of environmental data. As a technical problem, the literature does not address methods to support the comparison of EPIs. The difficulty is that weights are needed to aggregate the data into indicators and to aggregate those indicators into top-indicators, where the data and the indicators are extensive, complex, and measured on different scales. The derivation of weight coefficients (revealing prices, some measure of equivalence, trade-offs, or functional relationships) turns out to be very difficult. This is due to subjective and political influences and to lack of knowledge on the impacts of consuming natural resources and of emitting pollutants into nature.

Data envelopment analysis (DEA) is a well-established methodology for the assessment of performance of a homogeneous set of decision making units (DMUs), e.g. economies, bank branches, schools or hospitals, which are described by their input and output quantities. DEA shows a high potential regarding the aggregation problem mentioned before, as DEA does not require explicit weights. The main problem when using DEA in the ecological context is the fundamental assumption that for a DMU, to achieve efficiency, ceteris paribus larger quantities of outputs and smaller quantities of inputs are preferable. In only a small number of articles the underlying assumption, ‘all objects are goods’, is modified in order to consider undesirable outputs. Undesirable outputs are prominent in the ecological context (waste or emissions), but may also appear e.g. in health care (complications of medical operations) and business applications (tax payments). Most of the applications of and theoretical papers on DEA-models in the ecological context presented so far show some deficits, especially arbitrary approaches regarding the treatment of such ‘bads’. Up to now, the ecological extension of DEA does not have a theoretical foundation. Such a foundation would, amongst other things, reveal the ‘mirror’ case of desirable input, e.g. the destruction of waste in a waste-burning power plant or its transformation in a recycling plant.

To improve the state-of-the-art, this paper aims at a systematic approach to derive models for measuring ecological efficiency with DEA. A certain degree of generalisation allows to open DEA to objects other than ‘goods’, or to put it another way, for more complex preference structures. In order to generalise DEA, it is necessary to start from the axioms and foundations of DEA in production theory and activity analysis, as well as to consider other methods and findings, e.g. from decision theory and vector maximum theory.

The paper is organised as follows. Section 2 outlines the state-of-the-art of the ecological extension of DEA. Especially, an ecologically extended additive model is presented in detail and compared to alternative approaches. In Section 3, a systematic approach for deriving ecological DEA-models is developed. The main idea of this approach is to generalise a DEA-model by allowing for a more complex preference structure of the inputs and outputs by integrating a multi-dimensional value function f. For illustration, we present the generalisation of the additive model by Charnes et al. (1985) and two different specifications of f. The rest of the section discusses the theoretical and practical relevance of the approach presented. In Section 4 we summarise the findings of the paper and point out some ideas for future research.