How can digital-real integration affect urban total factor energy efficiency? An approach based on dual machine learning modeling

As a key solution for reshaping factor utilization patterns and industrial chain structures, digital-real integration (DRI) opens up new opportunities for enhancing China’s Urban Total Factor Energy Efficiency (TFEE). This study measures the DRI through a patent co-classification network and examines its impact on urban TFEE using samples from 270 prefecture-level Chinese cities between 2007 and 2022. The results indicate that the DRI significantly improves urban TFEE, and the conclusion remains valid after multiple robustness tests. Further mechanism analysis identifies market potential, labor mobility, urban functional specialization, and deepening digital financial inclusion as the principal conduits through which DRI contributes to urban TFEE. Notably, digital inclusive finance accounts for the largest share of the mediating effect among these channels.Moreover, the heterogeneity analysis reveals that the positive effects are particularly pronounced in larger cities, economically dynamic regions, cities designated as key environmental protection areas, and cities with high energy consumption. While DRI generates positive local effects, its spatial spillover effect is negative, suggesting a potential siphon effect across regions. Overall, the study provides practical insights into how DRI can advance China’s green and low-carbon transition under the “dual carbon” goals.