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Under the concept of metafrontier, technology gap ratio is alternatively interpreted as potential energy efficiency. Combined with Malmquist index framework and Shephard energy distance function, we then develop a metafrontier Malmquist energy productivity index to analyze the total-factor energy productivity growth with four specific components: groupfrontier efficiency change index, groupfrontier technological change index, efficiency catch-up index and technological catch-up index. Methodologically, a newly developed two-step stochastic metafrontier analysis is applied to address the potentially biased estimation problems in the previous mixed approach. This analytical framework is used to evaluate the energy productivity growth of China’s 35 sub-industries in industrial sector from 2001 to 2015. The main empirical results show that: (1) In terms of cumulative metafrontier Malmquist energy productivity growth, China’s overall industry has witnessed a 25% growth and a U-shaped growing trend bottoming out in 2006; meanwhile, 19 sub-industries have suffered an energy productivity loss and the remaining 16 sub-industries have experienced an energy productivity gain. (2) From the technology heterogeneity perspective, light industry outperforms heavy industry in metafrontier Malmquist energy productivity growth, while the intra-group and inter-group energy productivity develops roughly in balance for overall industry. (3) The change of metafrontier Malmquist energy productivity is mainly driven by technological change components rather than efficiency change components. On average, groupfrontier technological change makes the biggest contribution to energy productivity growth, followed by technological catch-up, then efficiency catch-up, and groupfrontier efficiency change is last. (4) The metafrontier Malmquist energy productivity growth has shown a significant convergence in heavy industry and light industry, as well as overall industry

China’s Industrial Total-Factor Energy Productivity Growth at Sub-Industry Level: A Two-Step Stochastic Metafrontier Malmquist Index Approach