Digital–Physical Integration and Carbon Productivity: An Empirical Assessment from China

The integration of digital technologies with the physical economy has emerged as a crucial driver of sustainable and high-quality development. Drawing on a patent co-classification framework, this study constructs a provincial-level indicator of digital–real integration in China to evaluate its influence on carbon productivity and the underlying mechanisms. The empirical findings show that digital–real integration exerts a clear and statistically significant positive impact on carbon productivity. Moreover, the improvement in carbon productivity occurs mainly through three channels: green technological innovation, adjustments in industrial structure toward upgrading, and enhancements in resource allocation efficiency. Industrial upgrading is reflected in the gradual shift toward more advanced and low-carbon industrial configurations, whereas the allocation channel captures the coordinated optimization of traditional and emerging production factors. Regarding the nonlinearity, a threshold pattern is identified between digital–real integration and carbon productivity, shaped by the degree of biased technological progress. When the technological bias remains low, the productivity gains are modest; once the bias surpasses a certain critical level, the positive effect of integration intensifies substantially. The magnitude of this threshold effect also varies by bias type, with capital-biased technological progress producing the strongest influence. Overall, the results provide theoretical and policy implications for advancing digital–real integration and supporting a green and low-carbon transition.