Bootstrap-DEA malmquist index measurement of energy productivity change in chinese provinces

Global sustainable development depends on the ability of major economies to decouple economic growth from resource consumption. As the world’s largest energy consumer, China’s provincial energy productivity is critical to achieving its “dual carbon” targets and advancing global sustainability. This study applies an input-oriented variable-returns-to-scale bootstrap DEA-Malmquist framework to evaluate provincial energy productivity in China from 2007 to 2020. GDP is treated as the desirable output, CO2 emissions as the undesirable output, and population as a non-discretionary input. The results yield three main findings. (1) China’s aggregate energy total factor productivity (TFP) index is 0.978 over 2007–2008 to 2019–2020, indicating a mild overall decline of 2.2%. Efficiency change(EC) remains close to unity (EC = 1.001), whereas technological change(TC) declines to 0.978, suggesting that the overall decline is more closely associated with TC than with efficiency loss. (2) TC exhibits dual-biased characteristics at the national level, with OBTC = 1.023 and IBTC = 1.029, while the scale-related component remains weak (MATC = 0.933), which may have constrained productivity growth. (3) Substantial heterogeneity exists across provinces and regions, and bootstrap inference shows that only part of the observed TFP changes is statistically significant. Overall, China’s energy productivity evolution is better characterized by uneven regional differentiation than by broad-based improvement.