High-value units of public service accessibility are concentrated in built-up areas, while low-value units are located at the urban fringe. Larger public services have more significant clustering effects than smaller ones. Recreational, medical, educational and financial facilities all have capitalisation effects on housing prices. Both the geographical detector model and the spatial association detector model could identify the drivers of housing prices, but the explanatory power of the latter is greater and could enhance the validity and reliability of the findings.
Spatial segregation and social exclusion, caused by rapidly growing global population pressures and the wealth gap, are driving unprecedented changes in social systems 
. Socioeconomic status inequities are growing both within and among societies 
and have become an indisputable reality in human settlements, especially in cities 
. The rate of new housing construction has lagged far behind population growth in urban centres, and the gap between high housing prices and low affordability has led to growing migration to the outskirts of many burgeoning cities 
. Housing costs have a significant impact on access to adequate and affordable housing, particularly for vulnerable groups 
. In the context of the Sustainable Development Goals, the provision of equitable housing and infrastructure in settlements is fundamental to social equity 
. Therefore, a redirection towards sustainability and well-being, which achieves the progressive realisation of the right to adequate housing, has been regarded as the most viable option for further development.
The spatial distribution, supply and demand of urban public service facilities are vital factors that affect the residents’ well-being 
. Public services, as non-competitive public goods provided by the government, could bring economic benefits. When such economic benefits persist, they will enter asset prices and be influenced by the real estate market. This capitalisation effect represents a significant increase in the value of nearby housing as a result of investment in public services. Public services, such as cultural services, healthcare, eldercare and public transportation, could serve as catalysts to stimulate surrounding real estate development 
. Public service facilities of superior quality in urban centres could stimulate residents’ willingness to buy houses and form a cluster of advantaged groups, thus attracting more public investment and providing better services 
. However, imbalanced urbanisation and fragmented local government structures may cause concentralised patterns and spatial differences in public service provision 
. These are capitalised to varying degrees, and thus affect housing price elasticities 
. In addition, as residents are willing to pay more for better access to high-quality public services, space for high housing prices is likely to cluster together, and this distribution may offset the expected incentive effects of some policies 
. For example, the simplistic educational policies pursuing equity, such as ‘nearby enrolment’ and ‘zero school choice’ policies 
, cannot achieve true equity, but rather reinforce the school district effect and aggravate inequities in neighbourhoods and educational opportunities 
. In general, the spatial effect of accessibility to public service facilities on housing prices is not yet recognised.
In addition, the causes of urban housing inequity could be explained by the dual mechanisms of the emerging housing market and the persisting socialist institution 
). Prior to the economic reform and opening-up in 1978, China’s urban housing system was a welfare system that relied on unified national construction and low rent distribution 
. This system had a strong constraint on urban spatial layout and social differentiation. After the economic reform and opening-up, China’s urban housing reform transformed access to housing from a socialist administrative allocation system to a more market-oriented housing development and consumption system 
. The abolition of welfare housing policy provision in 1998 was a paramount milestone in Chinese urban housing reform, which shaped a market-oriented urban housing provision system 
. Since then, the goal of housing commercialisation has provided Chinese urban households with the opportunity to choose their suitable houses and living environments 
. Individuals with higher political status, better socioeconomic conditions and the possession of organisational resources and power were more likely to have access to superior living conditions 
. The combined action of power and the market accelerates the division of urban housing space and gives way to the stratification process of housing space 
. Accordingly, this historical process not only reveals China’s economic transformation and massive urbanisation process, but also affects residents’ well-being.
Figure 1. The change of housing policy in China includes five stages: (a) 1978–1978: housing development was relatively slow, low-rent welfare housing allocation, (b) 1978–1988: exploration and experimentation in housing allocation, (c) 1988–1998: housing distribution reform was gradually carried out, (d) 1998–2016: monetisation of housing allocation and establishment of housing security system and (e) 2016–present: deepening housing system reform.
2. Accessibility and Capitalisation Effect of Public Service Facilities on Housing Prices
Housing prices are an external feature of the housing economy and are related to the indispensable public service facilities in urban space resources. High-priced clusters with higher public service accessibility are found in the central urban areas, whereas low-priced clusters with lower accessibility are concentrated in the urban fringes 
. The distribution of transportation hubs 
, educational facilities 
, green spaces 
and leisure facilities 
has a capitalisation effect on housing prices, even in different social systems and backgrounds. It has been proven that the spatial distribution pattern of housing prices is affected by the diverse functions of multiple public service facilities 
, and a bivariate enhancement effect emerges when any two of these interact 
. The spatial convenience of the high coverage rate of public service facilities may conflict with the housing price enhancement effect of a single facility in a region 
. However, most previous studies have aimed to examine the impact of single type of public service on housing prices.
The impact of the quality of various public service facilities on housing prices has been explored to capture capitalisation 
. The same type but different grades of public service facilities have different capitalisation effects on housing prices 
. For instance, Wen et al. proved that adding one kindergarten within 1 km of the community increased housing prices by 0.3%, and the distance between housing and high schools or universities within 1 km increased housing prices by 2.737% or 0.904% in Hangzhou, China 
. Thus, the research on housing prices could benefit from an integrated framework that considers the comprehensive capitalisation effect of the grade of various public service facilities as well as the surrounding environment on housing prices.
3. The Hedonic Price Model Is Rooted in Public Services Being Capitalised into Housing Prices
The hedonic price model allows for the investigation of the impact of micro-factors on housing prices, revealing that almost all types of public goods are capitalised into housing prices to varying degrees 
. Location, housing and environmental attributes all affect housing prices in the hedonic price model 
. Relevant studies in China 
, the United States 
, Britain 
and other countries have confirmed that there is a significant spatial dependence of housing prices. As a result, location attributes such as accessibility to public service facilities and the nearest-neighbour distance to metro and bus stations, as one of the factors influencing housing prices, are widely utilised to explain spatial variation in housing prices 
. Although low-income groups could obtain employment opportunities through public transportation 
, the incremental effect of housing prices around metro and bus stations will increase the economic burden of low-income groups 
. In addition, marginal prices of key housing attributes (e.g., building height) vary over space 
, and models containing spatially correlated variables are more applicable to most areas 
. Buyers refer to the surrounding environmental attributes (e.g., rivers/lakes, parks and air quality) in the actual purchase process 
. On the one hand, accessibility could increase housing prices through access to opportunities and services 
. On the other hand, environmental changes caused by accessibility could increase air pollution and lead to lower housing prices 
. However, the combined effects of accessibility and environmental health risks on housing prices have not been well-examined in the literature, especially in auto-oriented urban environments.
4. Measurement of the Capitalisation Effect of Different Levels in Public Service Facilities
Most previous studies have implicitly assumed that valuations are under uniform capitalisation conditions. However, the extent of capitalisation may vary in light of differences in land use and geographical location 
. Likewise, Cheshire and Sheppard have demonstrated that the capitalisation of school quality is significantly discounted, especially in areas with new construction 
. The supply level and supply quantity of urban public goods such as educational facilities, landscapes and hospitals are insufficient and spatially uneven relative to people’s growing demand 
. Consequently, the implied prices of public service facilities are spatially heterogeneous 
. Nevertheless, the traditional hedonic price model, which ignores the effect of spatial heterogeneity, is far from sufficient to reveal real-world phenomena and could be somewhat misleading.
Although the spatial lag model and spatial error model make up for the lack of a spatial dependence effect in the ordinary least squares model in the traditional hedonic price model and improve the fitting degree 
, they ignore the spatial variation and non-stationarity caused by the differences in spatial location characteristics 
. The geographical detector model has been utilised in a range of studies to detect driving factors 
. It could reflect the similarity of the same region and the differences between different regions 
. Its main advantage is that it has fewer assumptions than other methods, such as regression 
, which overcomes the limitations of traditional statistical methods in dealing with variables 
. In addition, it could detect the interaction between two variables without considering the collinearity of multiple independent variables 
. Therefore, it is widely adopted in the study of natural and human influence mechanisms. However, the geographical detector model does not explicitly consider the spatial characteristics of the data and is also affected by factor discretisation 
. The spatial association detector model is an improved spatial data association method, which takes into account the spatial characteristics of data and the information loss caused by discretisation. It allows better measurement of associations between spatial data distribution and reflects the relationship between the accessibility of public service facilities and housing prices.