Inclusive ecological efficiency analysis in China's Hainan Island: an extended meta-frontier DEA approach

China is advocating the ecological civilization for a sustainable society and resource-economic-environmental system due to its environmental and climate problems. As a special resource-economic-environmental system, island systems are facing severe challenges due to the vulnerable coordination ability between ecological environment and economic development. To measure the sustainable performance of island systems more directly and specifically, this paper extends the concept of ecological efficiency to inclusive ecological efficiency. For the first time, we analyze the inclusive eco-efficiency of Hainan Island, the second largest island in China, from 2008 to 2017. Due to the large technological heterogeneity among the diverse industries, this paper combines inclusive eco-efficiency with meta-frontier data envelopment analysis (DEA). And we propose a revised meta-frontier slack-based measure (SBM) model and meta-frontier non-radial directional distance function (NRDDF) model, which makes the technology gap rate (TGR) no larger than 1. The empirical results show that the average inclusive total factor energy efficiency (ITFEE) of the tertiary industry under the group-frontier is the largest while the average ITFEE of the primary industry is the highest under the meta-frontier. Moreover, the technology gap rate of the primary industry is the largest. Policy implementations are presented based on the empirical results.