Returns to Scale and Damages to Scale with Strong Complementary Slackness Conditions in DEA Assessment: Japanese Corporate Effort on Environment Protection

This study proposes a use of Data Envelopment Analysis (DEA) for environmental assessment. All organizations in private and public sectors produce not only desirable (good) but also undesirable (bad) outputs as a result of their economic activities. The proposed use of DEA determines the level of unified (operational and environmental) efficiency of all the organizations. A contribution of this study is that it explores how to measure not only RTS (Returns to Scale) on desirable outputs but also a new concept regarding “DTS: Damages to Scale” (corresponding to RTS for undesirable outputs). This study discusses how to measure RTS under natural disposability and DTS under managerial disposability by DEA. The measurement of RTS and DTS is formulated by incorporating “Strong Complementary Slackness Conditions (SCSCs)”. As a result, this study can handle an occurrence of multiple reference sets and multiple projections in the RTS/DTS measurement. The incorporation of SCSCs makes it possible both to restrict DEA multipliers in a specific range without any prior information and to identify all possible efficient organizations as a reference set. Using the unique capabilities of SCSCs, this study discusses the use of DEA environmental assessment by exploring how to classify the type of RTS/DTS with SCSCs. Such analytical capabilities are essential, but not previously explored in DEA environmental assessment for energy industries. As an illustrative example, this study applies the proposed approach for the performance evaluation of Japanese manufacturing industries. This study finds that these firms need to introduce technology innovation to reduce an amount of greenhouse gases and wastes. The empirical result confirms the importance of measuring RTS/DTS in DEA environmental assessment.