Spatiotemporal dynamics and nonlinear drivers of urban eco-efficiency in China's old industrial bases using explainable machine learning

Against the backdrop of climate change and the accelerating green transition, urban eco-efficiency (UEE) has become an important indicator for assessing the coordination between economic development and environmental sustainability. However, existing studies have focused predominantly on national regions, urban agglomerations, and economically developed areas, while relatively limited attention has been paid to old industrial base cities characterized by strong industrial path dependence, structural transformation constraints, and pronounced regional heterogeneity. Moreover, conventional linear econometric approaches may fail to adequately capture the nonlinear, stage-dependent, and threshold effects underlying UEE dynamics. To address these gaps, this study employs panel data from 95 prefecture-level cities in China's old industrial base regions from 2009 to 2023, and adopts a super-efficiency Slack-Based Measure (SBM) model with undesirable outputs to evaluate urban eco-efficiency (UEE). Kernel density estimation, Theil index decomposition, standard deviational ellipse, and spatial autocorrelation analyses are integrated to investigate the spatiotemporal evolution patterns of UEE. The Stacking ensemble machine-learning method is introduced to identify the nonlinear effects of influencing factors. Furthermore, SHAP (Shapley Additive Explanations) interpretable analysis and the GAM model are adopted to reveal the contributions and threshold effects of key variables. During the study period, the overall urban eco-efficiency in China's old industrial bases exhibited a fluctuating upward trend, with continuously enhanced spatial agglomeration characteristics. Regional disparities gradually shifted from being dominated by interregional differences to intraregional differences, and the spatial centroid migrated from the northeast to the southwest. The driving mechanism analysis revealed that economic level served as the core driver, and all influencing factors displayed evident nonlinear threshold characteristics and significant regional heterogeneity. This study deepens the understanding of eco-efficiency evolution mechanisms from a nonlinear perspective and provides a scientific basis for the green transformation and differentiated governance of old industrial bases.