Exploring the spatial variation of intra-urban housing prices based on inverse S-function fitting of 35 cities

Xiaojin Liang¹Tianqi Qiu^1*Bingbing Jin¹Jiehong Lin¹Shihan Guo²

• ¹Guangzhou Urban Planning & Design Survey Research Institute Co., Ltd, Guangzhou, China
• ²Chengdu University of Technology, Chengdu, China

Housing prices serve as a crucial indicator of macroeconomic stability and urban spatial vitality. However, existing studies on intra-urban housing prices predominantly focus on single-city empirical analyses or localized examinations of individual factors, often lacking holistic approaches and cross-city comparative perspectives. Given the widespread application of the inverse S-function and its suitability for characterizing the spatial distribution of housing prices, this study employs this function to model the spatial variation of housing prices across 35 major Chinese cities. Methodologically, we identify urban centers through kernel density estimation and apply circle-layer gradient analysis to establish price gradients. Building on this foundation, we fit the inverse S-function model and further develop two quantitative indices— stability and concentration — for in-depth analysis. The results reveal that all 35 cities exhibit significant spatial agglomeration of housing prices according to global Moran's I analysis. The inverse S-function achieves an average R² of 0.98 in fitting price decay, categorizing the curves into three types: standard inverse S-decay, fast-then-slow decay, and linear decay. The two indices further indicate that cities with higher levels of economic development (e.g., Beijing, Shanghai) exhibit stronger spatial aggregation and stability in housing prices. In contrast, cities in the western and northeastern regions (e.g., Xining, Hohhot) demonstrate a significantly faster rate of price decline from the urban center outward. This study provides a new quantitative method for research on the spatial distribution of intra-urban housing prices and offers a reference for urban planning and real estate regulation policies.