The deviation characteristics and influencing factors of urban scaling laws in China: industrial and sectoral perspective

When facing the complex and enormous system of cities, it is imperative to interpret urban development phenomena in a scientifically rigorous manner. Urban scaling laws describe the logarithmic relationship between the population size of a city and various systemic indicators, providing insights into the reasons behind urban population distribution patterns and scaling characteristics. While research related to urban scaling laws has garnered increasing attention, current studies often focus on revealing the relationships between urban size and economic, social, and infrastructural indicators, neglecting investigations into the relationships between population size and industrial sector indicators. Therefore, this study approaches the topic from the perspective of industries and sectors, employing methods such as ordinary least squares regression and comparative analysis to identify the deviation characteristics of urban scaling laws in China. Additionally, the XGBoost + Shap value modeling method is utilized to discern the factors influencing these deviations. The study findings indicate that from 1988 to 2019, China’s secondary industry scaling index exhibited superlinear growth, while the tertiary industry scaling index demonstrated linear growth, with significant differences observed across various industries. The range of deviation in China’s industry scaling index is relatively large. Among the variables considered, the growth rate of gross domestic product (GDP) exerts the strongest influence on the industry scaling index, followed by urbanization growth rate and urbanization rate. Factors such as population density, per capita national income, and the proportion of secondary industry to GDP also impact industry scaling indices. The research reveals disparities in urban development and suggests responses through urban policy interventions, thereby providing a basis for urban planning and policy formulation.