How factor digitalization shapes urban carbon TFP: mechanisms, thresholds, and spillovers in Chinese cities

Digitalization and decarbonization are reshaping urban production, yet the relationship between factor-level digitalization and cities' carbon total factor productivity (CTFP) remains underexplored, particularly concerning its mechanisms, boundary conditions, and spatial reach. This study develops a Digitalization Index of Urban Elements (DIUE), encompassing labor, capital, and energy, to examine its association with CTFP in 213 Chinese cities from 2011 to 2023. CTFP is measured using an undesirable-output slacks-based measure, and the empirical analysis employs a two-step system GMM with Windmeijer correction, mediation analysis, spatial-lag models, and dynamic panel threshold tests. Robustness checks utilize an alternative productivity index and a difference-in-differences design based on early smart-city pilots. Three key findings emerge. First, factor-level digitalization is positively associated with urban CTFP; a one-standard-deviation increase in DIUE corresponds to a 1.5-1.7% increase in CTFP, which accumulates to approximately 4% in the long run. Second, this relationship is primarily mediated by green innovation, accounting for approximately 47% of the mediated effect, while industrial upgrading and agglomeration provide additional support, accounting for about 24% and 6%, respectively. Third, the benefits of digitalization exhibit both spatial spillovers and conditional effects: the indirect spillover effect constitutes roughly one-third of the direct effect, and positive gains are more pronounced in contexts with lower labor and capital misallocation and stronger local low-carbon commitment. By integrating a transparent and replicable measure of factor digitalization with evidence on its underlying mechanisms, spatial spillovers, and activation thresholds, this study clarifies the conditions under which digitalization can be effectively translated into enhanced carbon productivity. The policy implication is that cities should complement digital investment with measures to reduce factor misallocation, strengthen low-carbon commitment, and foster innovation.