Green development is an effective way to reconcile the main contradictions between resources, environment, and regional development. Green total factor productivity (GTFP) is an important index to measure green development; an undesirable output-oriented SBM-DEA model and GML model can be used to calculate GTFP. China's 30 provinces (municipalities and autonomous regions) are divided into three groups: eastern, central, and western. The common frontier function and group frontier function are established, respectively, to deeply explore the temporal and spatial evolution characteristics and center of gravity shift of inter-provincial green total factor productivity (GTFP) in China, and test the convergence under group frontier, to compare the convergence problems under different regions. This study aims to point out the differences in economic growth in different regions of China, foster regional coordination and orderly progress, promote China's green development process, and improve the high-quality economic development level. According to the results, the efficiency of green development is more reasonable under the frontier groups. The average TGR in the eastern region was 0.993, indicating that it reached 99.3% of the meta-frontier green development efficiency technology. The inter-provincial GTFP in China gradually increased, with an average value of 1.043, which means China's green development and ecological civilization construction have achieved remarkable results and the three regions showed significant differences. Judging from the shift path of the spatial center of gravity, the spatial distribution pattern of inter-provincial GTFP in China tends to be concentrated and stable as a whole. Moreover, σ convergence only exists in the western region, while absolute β convergence and conditional β convergence exist in eastern, central, and western regions, indicating that the GTFP of different regions will converge to their stable states over time. The results provide a basis for improving the efficiency of institutional allocation of environmental resources, implementing regional differentiated environmental regulation policies, and increasing the value creation of factor resources, which is of great significance for realizing the high-quality economic development in which resources, environment, and economy are coordinated in China.
Keywords: SBM-GML Index Model; cluster cutting-edge; convergence; gravity-standard deviational ellipse; green total factor productivity.