Examining the Nonlinear Effects of Urban Population Polycentricity on Carbon Emissions Efficiency Using a Gradient Boosting Decision Tree Model: Evidence from 295 Chinese Cities

Transforming urban spatial structures to promote green and low-carbon development is an effective strategy. Although prior studies have examined the impact of urban polycentricity on carbon emissions and economic development, research on its role in the synergistic relationship between these factors regarding carbon emission efficiency is limited. Furthermore, existing literature often overlooks nonlinear effects and interactions with other urban variables. This paper analyzed data from 295 Chinese cities in 2020, calculating urban population polycentricity, population dispersion indices, and carbon emission efficiency. Utilizing local spatial autocorrelation tools, we reveal interactions among urban population polycentricity, dispersion, carbon emissions, and carbon emission efficiency. We then employ a gradient boosting decision tree model (GBDT) to explore nonlinear and synergistic effects of polycentric urbanization. Key findings include: 1) polycentric urbanization in Chinese cities exhibits significant spatial differentiation characteristics. The Polycentricity index is relatively high in economically developed eastern coastal regions with an overall low level, carbon emissions are concentrated in industrialized north-central cities and some Yangtze River Delta hubs, and carbon emission efficiency is the highest in the Yangtze River Delta while relatively low in Northeast China; there are significant spatially heterogeneous interaction characteristics among population polycentricity, population dispersion, carbon emissions, and carbon emission efficiency. 2) Urban population polycentricity contributes 9.42% to total carbon emissions and 6.24% to carbon emission efficiency. 3) The polycentricity index has a nonlinear impact on carbon emissions and carbon emission efficiency: no significant effect when below 0.50 or above 0.55, increased carbon emissions in 0.50–0.53, and reduced carbon emissions with improved efficiency in 0.53–0.55. 4) The polycentricity index has an interaction effect with other variables; specifically, when the polycentricity index is between 0.53 and 0.55, its interaction with urban gross domestic product (GDP), urban population, urban built-up area, green coverage rate in built-up areas, urban technological expenditure, and the proportion of the output value of the secondary industry will reduce carbon emissions and improve carbon emission efficiency. These findings enhance the understanding of urban spatial structures and carbon emissions, providing valuable insights for policymakers in developing green and low-carbon strategies.