Spatial Patterns and Granger Causality Between Carbon Balance Capacity and Urban–Rural Integration in China

Carbon balance capacity (CBC) and urban–rural integration (URI) represent two interconnected systems involving ecological sustainability and socioeconomic development. Understanding their interactions is essential for advancing low-carbon development, yet the spatial heterogeneity and directional relationships between these systems remain insufficiently explored. Using panel data for 30 Chinese provinces from 2005 to 2024, this study measures CBC by assessing the relative capacity of regional carbon absorption to balance carbon emissions and constructs URI as a composite index based on a five-dimensional indicator system covering population, economy, space, society, and ecology. Exploratory spatial data analysis (ESDA) and the Dumitrescu–Hurlin panel Granger causality test are then applied to examine the spatiotemporal dynamics and directional relationships between CBC and URI. The results show that carbon emissions exhibit an increasingly pronounced “high East–low West” pattern, whereas carbon absorption maintains a relatively stable “high West–low East” distribution. Accordingly, CBC shows a contraction of high-value regions and increasing concentration of carbon balance advantages in ecologically endowed provinces. Meanwhile, URI has improved continuously, with spatial, ecological, and social dimensions becoming increasingly important, while economic integration remains relatively limited. Granger causality analysis reveals substantial heterogeneity in CBC–URI interactions, with decoupling as the dominant pattern, while some regions exhibit development-related pressures or ecological constraints during urban–rural transformation. Positive interaction pathways, where urban–rural integration contributes to improvements in carbon balance capacity, are identified only in a limited number of regions, indicating diverse evolutionary pathways between urban–rural transformation and carbon balance capacity. This study further develops a typological framework and identifies differentiated development pathways toward more coordinated CBC–URI interactions, providing empirical evidence and policy insights for place-based low-carbon urban–rural transformation.