The green total factor productivity and convergence in China

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Abstract
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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