## 2 Literature Review  
Total factor productivity (TFP) is considered a source of economic growth. Sustainable economic growth depends on endogenous technological progress [20; 21; 22]. The main methods to measure total factor productivity include Solow residual, stochastic frontier analysis and data envelopment analysis (DEA). Among them, Solow residual method is developed based on the work of [PERSON] [23]. Generally speaking, the Solow residual method is a \"black box\". Therefore, at present, scholars mainly use stochastic frontier analysis and DEA to measure total factor productivity. Stochastic frontier analysis is a parametric method based on econometric regression analysis, which requires a deep understanding of specific economic operations. DEA is a non-parametric method, the weight does not need to be calculated and method is more objective and comprehensive. Therefore, DEA is the most common method used by scholars to measure total factor productivity. The actual production process is bound to be accompanied by pollutants, which will harm the ecological environment. Therefore, incorporating undesirable out into the framework of TFP analysis is important in order to better coordinate the relationships between energy, the environment, and economic growth. The TFP index that considers undesirable outputs usually refers to green total factor productivity (GTFP). Regarding GTFP measurement, based on the pioneering work of [PERSON] et al. [24], many researchers have employed the directional distance function (DDF), which can consider undesirable outputs to calculate the Malmquist-Luenberger (ML) productivity index. For example, [PERSON] and [PERSON] [25] measured the GTFP of twenty-eight of China's two-digit manufacturing sectors during the 11 th FYP (2006-2010). [PERSON] et al. [16] measured the green total factor productivity growth of China's 36 industrial sectors from 2000 to 2014. However, most of these studies were mostly limited to radial and oriented methods, and cannot effectively overcome the measurement bias caused by radial or oriented selection. Therefore, [PERSON] and [PERSON] [26] established a more general slack based measure (SBM) directional distance function, following the non-radial and non-oriented basis proposed by [PERSON] [27], which is highly favored by scholars. For example, [PERSON] et al. [28] evaluated the industrial \"green\" productivity growth rates of China's 30 provinces. Based on the panel data of OECD countries' industrial sectors, [PERSON] et al. [29] analyzed the stringency of environmental regulation policies and measured the green productivity growth using an extended SBM-DDF approach. [PERSON] et al. [30] used the super-SBM model to calculate China's agricultural green total factor productivity based on carbon emissions. In view of the fact that the ML index, usually calculated with the adjacent frontier, may have no feasible solution or the index is not transitive, [PERSON] [31] constructed a global production possibility set and presented the global Malmquist-Luenberger (GML) productivity index. Since then, several scholars have evaluated GTFP with the GML index. For example, [PERSON] and [PERSON] [32] measured green total factor productivity in 273 cities of China in 2003-2013. [PERSON] et al. [33] adopted the Luenberger indicator to estimate the GPP of China's 36 industrial sub-sectors over 2001-2013. [PERSON] et al. [8] combined the SBM model with the GML index to analyze the GTFP of China's mining and quarrying industry for the period of 1991-2014. [PERSON] and [PERSON] [34] used a GML index based on SBM directional distance function to evaluate provincial GTFP in China. The current GTFP research is primarily based on calculations and analyses of the regional economy. A few studies have focused on the GTFP of the industrial sector. As the industrial output data of China's manufacturing sub-sectors have not been released since 2012, most studies could only measure green total factor productivity of the industrial sectors before 2013.