LAUSR

It is important to investigate the sustainability nexus using composite ecological efficiency (eco-efficiency) indicators from quantitative and computational modeling perspectives. To provide a more comprehensive measure of eco-efficiency, this paper develops three data envelopment analysis (DEA) models incorporating metafrontier and undesirable outputs into a slacks-based measure (SBM), an epsilon-based measure (EBM), and minimum distance to weak efficient frontier (MinDW), respectively, named Meta-U-SBM, Meta-U-EBM, and Meta-U-MinDW. We show theoretically: if a decision-making unit (DMU) is being Meta-U-SBM-efficient, it is also being Meta-U-EBM-efficient and Meta-U-MinDW-efficient, and vice versa. For each DMU, its score measured by Meta-U-MinDW is the highest, while its score measured by Meta-U-SBM is the lowest. Using the proposed models, we make a first empirical attempt at measuring the eco-efficiency of the Key Environmental Protection prefecture-level cities in China from 2003 to 2015. The results show that: (1) the eco-efficiency of eastern cities performs the best, followed by central cities and western cities. Cities not listed as resource-based (RB) outperform RB cities; (2) eastern cities are closer to metafrontier than central and western cities; and (3) efficiency change and technological progress dominate the basic trend of the eco-efficiency growth. Results derived from the proposed methodologies can help managers and policymakers in the city to assess sustainability development quantitatively and comprehensively, they can also provide implications for the environmental management of sustainability development at city level. Policy implementations are presented based on the empirical results.