Exploring the nonlinear effect of population shrinkage on carbon emission intensity in Chinese counties using an interpretable XGBoost model

Understanding how population shrinkage affects carbon emission intensity aids sustainable regional development and carbon reduction. This study investigates this influence across 1218 Chinese counties using an interpretable Extreme Gradient Boosting (XGBoost) model, with a focus on regional heterogeneity by analyzing Eastern, Central, Western, and Northeastern China separately. The main findings are: 1) Counties with more significant population shrinkage and higher carbon emission intensity are concentrated in northern and northeastern China, whereas southern counties tend to be less affected on both fronts; 2) Globally, the nonlinear relationship between population shrinkage and carbon emission intensity follows a “V-shaped” pattern, with carbon emission intensity decreasing as shrinkage intensifies from 0 to approximately −0.007, and then rising again when shrinkage exceeds −0.016. Locally, the nature of this nonlinear relationship varies across regions; 3) Population shrinkage interacts nonlinearly with key variables such as government expenditure per capita GDP, land transaction area, Normalized Difference Vegetation Index, and number of patents per 10000 people to influence carbon emission intensity, with distinct threshold effects observed. For example, carbon emission intensity peaks at moderate levels of government expenditure per capita GDP (0.10–0.15) during mild shrinkage (−0.005–0), but this interaction weakens as shrinkage intensifies. Notably, these interaction patterns vary considerably across regions in both strength and direction. The results identify clear thresholds, helping policymakers design targeted interventions based on the specific socioeconomic contexts of counties with different levels of population shrinkage.