A machine learning approach to income inequality from environmental and demographic transitions

China’s aging population and green economic transition jointly shape urban–rural​ income disparities in complex ways. This study examines their nonlinear interplay using a hybrid framework that combines traditional econometric models with machine learning techniques, based on panel data from 31 provinces during 2005–2023. Empirical evidence reveals that the green patent ratio (GPR) consistently narrows the income gap, stabilizing disparities when GPR exceeds 10%. Institutional green investment (Green) displays a threshold effect: inequality rises below 0.56% but declines beyond this point, with diminishing marginal returns around 1.5%, suggesting policy saturation. The elderly dependency ratio (old) also shows conditional effects, turning from inequality-reducing to inequality-widening as green investment increases, highlighting resource allocation tensions. Interaction effects, old $\times$ Green and old $\times$ GPR, suggest that effective green development mitigates inequality in aging regions. These findings underscore the importance of coordinated region-specific strategies that integrate demographic trends with green development to promote balanced regional growth in China’s economic transition.