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The green total factor productivity (GTFP) has become an important index of balancing the energy consumptions, economic development, and environmental protections. This study extends the slacks-based directional distance function (SDDF) of Fare and Grosskopf into the framework of the Malmquist-Luenberger productivity index to estimate the slack-based GTFP.This SDDF can allow decision-making units to explore the optimal direction and measure a more precise productivity index. For the empirical study, we employ the new model to measure the slack-based GTFP for Chinese 30 provinces over the period of 2005-2017. Furthermore, we investigate the effect of the regional differences on the GTFP and the convergence of the Chinese GTFP with β-converge and σ-convergence. Our results show that there is a rapid improvement in the GTFP in China, which is attributed to the technical change. However, there exists a significant difference in GTFP for three regions of China. The eastern region performs significantly better than the others. Finally, we find there is a strong convergence in China, and the eastern region has a faster convergence than the other regions.

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