Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis

22MARGINAL RATE OF TRANSFORMATION AND RATE OF SUBSTITUTION

22.1 INTRODUCTION

This chapter¹ discusses the use of DEA environmental assessment to measure the marginal rate of transformation (MRT) and rate of substitution (RSU) among production factors, in particular between desirable and undesirable outputs. In the methodological concern, this chapter is an extension of Chapter 9 which discusses the quantitative approach on MRT within a conventional framework of DEA. In discussing the new approach for measuring MRT and RSU, it is necessary for us to describe that both estimates depend upon the magnitude and sign of dual variables, or multipliers, obtained from the proposed formulations. A problem associated with the estimation of MRT and RSU is that the two measures often become unstable, so often being inconsistent with economic and/or business reality, because DEA does not assume any functional form among the three production factors (X, G and B). The non‐parametric feature makes the DEA‐based MRT and RSU measurement very difficult because it often produces large or small multipliers. As a result, DEA does not attain a high level of estimation accuracy and thus has limited practicality. Consequently, almost no previous studies have explored the measurement of MRT and RSU, only paying attention to efficiency measurement. Exceptions can be found in Cooper et al. (2000)² and Asmild et al. (2006)³.

To overcome such a research difficulty, the proposed measurement of MRT and RSU pays attention ...