Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis

26PROPERTY OF TRANSLATION INVARIANCE TO HANDLE ZERO AND NEGATIVE VALUES

26.1 INTRODUCTION

Acknowledging the contribution of previous DEA studies, it is necessary for this chapter to discuss a difficulty on how to assess the performance of DMUs, whose production factors contain many zero and negative values in an observed data set. Such an occurrence of zero and negative values is widely observed in previous studies. For example, paying attention to energy, nuclear and renewable generations do not produce GHG emissions when they produce electricity. So, their uses contain zero in the amount of GHG emissions. Thus, in discussing a fuel mix issue for future electricity generation, we need to consider the possible usage of nuclear and renewable sources with zero in their GHG emissions. For example, see Chapter 19 that used only 10 industrial nations for DEA environmental assessment because that chapter encountered the problem of zero in data. As a result, the data set of Chapter 19 contained only industrial nations without zero in their production factors. Other industrial nations which contained zero in their data set were excluded from Chapter 19. That is a drawback of the DEA environmental assessment discussed in previous chapters in Section II. Such a difficulty due to zero and negative values in a data set will be overcome in this chapter.

To overcome the methodological issue, this chapter first discusses an important property of non‐radial models. The non‐radial measures discussed ...