Green innovation in family businesses is a significant yet underexplored area of research, particularly with regard to the influence of dynamic succession characteristics on intergenerational inheritance and its impact on innovation. This study, integrating the social-emotional wealth theory (SEW) and the agency theory, examines 505 Chinese listed family firms spanning from 2011 to 2020. Employing the Difference-in-Differences (DID) method, we investigate how intergenerational inheritance affects green innovation investment over time. Our findings reveal that initially, intergenerational transmission tends to inhibit green innovation investment in family businesses; however, this effect diminishes as the intergenerational process unfolds, indicative of the maturation of the second generation. Notably, we observe that a higher education level among second-generation heirs weakens the inhibitory effect of intergenerational inheritance on green innovation investment. This study addresses a gap in green innovation research by considering intergenerational transmission dynamics in family businesses, thus enhancing our understanding of innovation behaviors within this context. By synthesizing SEW and agency theory, this research offers novel insights into the varying impacts of intergenerational inheritance on firm innovation, shedding light on approaches to reconcile the willingness-ability paradox in family business innovation and promoting effective governance of succession processes.

Some cities in China are facing challenges due to population loss while also attempting to address energy conservation and emissions reduction. Although urban shrinkage can relieve pressure from energy consumption demands, such as water, electricity and gas, does it improve urban energy efficiency? This study attempts to answer this question. Based on Point of Interest (POI) big data and Global Human Settlement Layer (GHSL) raster data, this study identifies urban shrinkage from the coupling perspective of administrative and economic boundaries. It also examines the impact of urban shrinkage on energy efficiency. The results suggest that Chinese counties’ overall energy efficiency is experiencing a four-stage “decline-rise-decline-rise” trend, and the urban shrinkage of Chinese counties exists in three major areas: the Northeast, the Southwest, and the Centre. Compared to non-shrinking cities, urban shrinkage has a significant negative impact on improving energy efficiency. This impact exhibits significant heterogeneity. Specifically, compared with mature resource cities and cities in Western China, regenerative cities, non-resource cities and cities in Central China have less impact on energy efficiency. In addition, urban shrinkage may impede energy efficiency improvement by hindering industrial structure transformation and upgrading, energy-saving technology innovation, and financial development. Clarifying the relationship between urban shrinkage and energy efficiency is helpful for shrinking cities to change their development strategies, which is critical for sustainable development.