Spatiotemporal evolution mechanism of urban investment-vitality-carbon efficiency

Chinese cities have experienced rapid urbanization driven by massive investment. This process has improved urban vitality, but it has also increased carbon pressure. Existing carbon efficiency indicators are useful for evaluating production performance, yet they provide limited insight into how investment is converted into vitality under carbon constraints. Using panel data from 85 cities in China's five major urban agglomerations from 2001 to 2020, this study constructs an investment–vitality–carbon efficiency(IVCE) framework. Six categories of investment are used as inputs, urban vitality is treated as the desirable output, and carbon emissions are treated as the undesirable output within the Super slack-based model. The results show a clear structural divergence. Urban vitality gradually converges across cities, while IVCE scores become increasingly polarized. Stage-based analysis identifies four periods of pathway reorganization, with the dominant carbon drivers changing as urbanization progresses. Causal forest estimation further shows that the carbon effect of investment is not fixed. It varies with each city's vitality endowment, so similar investment shocks can lead to different carbon outcomes. Nonlinear fitting shows that emission reduction thresholds are shaped by the combined configuration of built environment, economic, and social vitality, rather than by the linear increase of any single dimension. Cluster analysis further indicates that IVCE scores should not be interpreted as absolute measures of sustainable development quality. High IVCE may reflect low-input and low-vitality conditions in some peripheral cities, while low IVCE in core cities may partly result from their regional functions and structural carbon burdens. These findings support an efficiency-neutral interpretation of IVCE and provide a basis for differentiated low-carbon governance across urban agglomerations.