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Journal of Geographical Sciences >

2021 , Vol. 31 >Issue 12: 1757 - 1774

DOI: https://doi.org/10.1007/s11442-021-1921-1

Unraveling the multi-scalar residential segregation and socio-spatial differentiation in China: A comparative study based on Nanjing and Hangzhou

  • SONG Weixuan , 1 ,
  • HUANG Qinshi , 2, 3, * ,
  • GU Yue 1, 4 ,
  • HE Ge 3
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  • 1. Nanjing Institute of Geography and Limnology, Key Laboratory of Watershed Geographic Sciences, CAS, Nanjing 210008, China
  • 2. School of Civil Engineering and Architecture, Zhejiang University of Science and Technology, Hangzhou 310023, China
  • 3. School of Architecture and Urban Planning, Nanjing University, Nanjing 210093, China
  • 4. University of Chinese Academy of Sciences, Beijing 100049, China
* Huang Qinshi (1990‒), Lecturer and PhD Candidate, E-mail:

Song Weixuan (1981‒), PhD and Associate Professor, specialized in urban social geography. E-mail:

Received date: 2021-07-05

  Accepted date: 2021-08-26

  Online published: 2022-02-25

Supported by

National Natural Science Foundation of China(41771184)

National Natural Science Foundation of China(42171234)

Copyright

Copyright reserved © 2021. Office of Journal of Geographical Sciences All articles published represent the opinions of the authors, and do not reflect the official policy of the Chinese Medical Association or the Editorial Board, unless this is clearly specified.
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Abstract

Residential segregation is a dual process of socio-spatial differentiation in residents and spatio-temporal heterogeneity in dwelling. However, most of the existing studies are established from the single perspective of urban residents based on demographic data, which is difficult to reveal the dynamics and complex spatial reconstruction within and between cities. With the characteristics of both stability and timeliness, the rapidly changing housing market is one of the processes and results of socio-spatial reconfiguration, and it is undoubtedly a better lens to observe residential segregation. This paper adopts methods such as multi-group segregation index, multi-scalar segregation profiles, and decomposition of segregation index, with Nanjing and Hangzhou as case cities, and establishes multi-scalar segregation profiles and comparative models based on three geographical scales of census tract, block and grid, and different residential types. A quantitative study was conducted on the degree and pattern of multi-scalar residential segregation in Nanjing and Hangzhou from 2009 to 2018. The paper found that the spatial segregation index is an improvement of the non-spatial segregation index. There are differences between Nanjing and Hangzhou in the evolution process of residential segregation. Nanjing has a higher degree of spatial differentiation as a whole, among which spatial components have a more significant impact.

Key words： residential differentiation; multi-scalar; housing market; housing price; spatial segregation index

Cite this article

SONG Weixuan , HUANG Qinshi , GU Yue , HE Ge . Unraveling the multi-scalar residential segregation and socio-spatial differentiation in China: A comparative study based on Nanjing and Hangzhou[J]. Journal of Geographical Sciences, 2021 , 31(12) : 1757 -1774 . DOI: 10.1007/s11442-021-1921-1

1 Introduction

Exploring the heterogeneity and spatio-temporal dynamic of residential segregation is an effective method of urban geography to measure unbalanced development in large cities (Reardon et al., 2004). As the urban spatial pattern tends to be more mixed and diverse in the post-socialism transition period, large-scale population migration and urban renewal movements (such as suburbanization or gentrification, etc.) temporarily accelerated the social integration of specific regions. However, the widening of income gaps and the transformation of housing commercialization are not reflected in the degree of socio-spatial agglomeration as expected. Such a phenomenon can be seen in many eastern European countries (Clark et al., 2017). On the one hand, it covers up the more complex and fragmented social differentiation phenomenon within cities, which contradicts to the general assumption of traditional residential differentiation theory, i.e., the so-called Paradox of Segregation (Zhou et al., 2015). On the other hand, Reverse of the Paradox is also found in some cities. For example, Copenhagen, Oslo, and Helsinki are among the cities with the lowest level of social inequality globally, but their degree of spatial differentiation is relatively high (Huang et al., 2012). In addition, the similar phenomenon of residential segregation in contradiction to social stratification is also seen in other places of the world. Still, it has not drawn extensive attention until recently (Li et al., 2020).
At the same time, changes in occupational structure brought about by globalization and economic restructuring have intensified the social gap and even polarized spatial segregation within Chinese cities (Zhou et al., 2015; Clark et al., 2017). Urban residents and residential spaces in cities continuously differentiate, interact, integrate, and construct a new urban social space that is becoming more complex (Wei et al., 2005; Li et al., 2020). It is difficult for the traditional study of spatial differentiation based on static section to meet the needs of fine management. The study of spatial differentiation based on multiple spatio-temporal scales help reveal the spatial characteristics, dynamic process and internal mechanism of social re-stratification and residential re-differentiation. In addition, the study of differences among different cities in spatial structure and urban residents can avoid over-generalization of urban experience and spatial pattern, and effectively improve the adaptation of space policy. Moreover, it helps establish the basic system and long-term mechanism of real estate, timely adjust and improve relevant policies, and make efforts to achieve sustained, stable and sound development of the housing market. Therefore, it will become an important research direction for exploring urban spatial differentiation in the future to analyze residential space differentiation from a residential perspective based on multiple spatio-temporal scales and carry out horizontal analysis (Harris et al., 2018; Zhang et al., 2019).

2 Literature review

Since Duncan proposed the residential differentiation index in 1955, the index has developed into over 40 types. The frequently-used residential differentiation measurement methods, such as Gini Index (Dorfman, 1979), Atkinson Index (Atkinson, 1970), Dissimilarity Index (Duncan et al., 1955), Exposure Index (Morgan, 1983) and Information Theory Index (Theil et al., 1971) are classified as non-spatial indices (White, 1983; Massey et al., 1988), laying the framework and foundation of indicator systems for follow-up studies. Non-spatial indices are simple and practical, but fail to take into account the relationship between spatial patterns and scales between residential locations (Chen et al., 2020). Due to checkerboard problem① (① Checkerboard problem refers to the issue that non-spatial segregation index ignores the spatial proximity of neighborhoods and only pays attention to the group composition of neighborhoods. For easy understanding, we may imagine a checkerboard, where each square represents an exclusively black or white community. If we move all black squares to one side and all white squares to the other, such change shall be recorded as intensified segregation. It is difficult to distinguish these two segregation patterns based on non-spatial segregation index, because the group composition of each community is the same in these two cases.)(Morrill, 1991) and Modifiable Areal Unit Problem (MAUP)② (② Modifiable areal unit problem refers to the issue where resident population data is usually collected, clustered and released with regards to administrative boundaries or social space units (such as census tracts) that are divided in advance and can no longer be divided. The implicit assumption of such data collection scheme is that the social distance between groups living in different space units are relatively far, but the social distance between groups living in the same space unit is farther. Although non-spatial index is sensitive to the changes in the quantity of census tracts and groups, it is difficult to reflect such problem of spatial proximity.)(Openshaw, 1977; Wong, 1997), it has always been criticized (Reardon et al., 2002; Wong, 2002). Therefore, the spatial segregation index is increasingly being prioritized.
Morrill (1991) held that the traditional segregation index lacks boundary interaction, hence adding the neighborhood matrix to reflect the neighborhood correlation. As the concept of neighborhood matrix can only tell whether the neighborhood connects, there lacks consideration on contact boundary. Therefore, Wong (2004) further considered the neighborhood area and boundary shape on this basis, and proposed to measure the segregation index based on Ellipse-based Measure. As a global measure, the segregation index represents regional overall differentiation rather than local or even microscopic scale (Wong, 2002). Therefore, Feitosa et al. (2007) proposed the local index through the concept of local population density. Reardon et al. (2009) continued to lead the study of spatial segregation from the perspective of small local space, promoting the way to replace the global measure index with the segregation index for measuring local units, and also devoting themselves to studying the segregation phenomenon in small scales, areas and units, and that in small local space at a micro level through human activity space (Reardon et al., 2009).
The rapid urbanization and population suburbanization seemed to lower many macro-scale dissimilarity indices (Peach, 1996), while the contradiction and segregation degree within space continue to worsen (Morrill, 1991; Wong, 1997), forming the Paradox of Segregation (Krupka, 2007). Therefore, it is necessary to transform from a single scale to a combination of multiple macro and micro scales in the study of urban space differentiation. The multi-scalar research perspective is expected to provide a research framework for the integration of macro stability and micro diversity of complex urban systems (Lichter et al., 2015). In order to overcome the modifiable areal unit problem in the study of socio-spatial differentiation, Reardon (2008) provided a scale-sensitive measure by analyzing the spatial segregation profiles and the ratio of macro to micro segregation. O’Sullivan and Wong (2007) attempted to simulate spatial segregation and scale effect based on kernel density estimation. Fowler (2017) further demonstrated the critical assumption of multi-scalar segregation measurement. Manley (2015) used a multi-level framework to explain the changes of residential differentiation in Auckland, New Zealand at macro, meso and micro scales from 2001 to 2013. Johnston et al. (2016) proposed a segregation model that takes into account both macro stability and micro diversity. Hennerdal and Nielsen (2017) developed a method based on k-Nearest Neighbors to measure the degree of exposure in groups at different scales. Thus, it can be seen that these studies have highlighted the changes of residential differentiation with time and scale.
Given the dynamic spatio-temporal characteristics and geographical scale effect of residential space differentiation (Catney, 2017), the residential heterogeneity of a city in different periods and at different geographical scales may tend to have different spatial patterns (Manley, 2015). As it is difficult to fully explain the socio-spatial differentiation model of the whole city if analyzed from the perspective of single scale or time, it is necessary to analyze residential segregation at multiple spatio-temporal scales. Meanwhile, different cities may have significant differences in residential differentiation pattern, process and mechanism due to different natural and humanistic social environments (Barros et al., 2017). Therefore, it is necessary to explore multiple similar cities and adopt the same research framework to carry out joint analysis and comparative study in a normalized way, and reveal the common regularity and characteristic differences of residential segregation.
In view of this, this paper takes Nanjing and Hangzhou as case cities, adopts methods such as multi-group segregation index and multi-scalar segregation profiles based on the urban housing market data from 2009 to 2018, looks into the degree of residential differentiation in Nanjing and Hangzhou and the evolution process at multiple scales from a housing perspective, compares the structural differences in residential differentiation between Nanjing and Hangzhou, and explores the way of giving new vitality to and deepening the study of residential segregation by expanding study perspectives, measure methods and empirical fields of residential segregation.

3 Data and methods

3.1 Research subjects

Both Nanjing and Hangzhou are central cities and sub-provincial capital cities in the Yangtze River Delta. They show some similarities in regional position, development stage, economic aggregate and housing price level. However, they also have significant differences in population scale, development pattern and urban structure. To enhance the comparability of both cities, this paper takes the enclosed range of the ring road in Nanjing and Hangzhou as the research area. As shown in Figure 1, the research areas of Nanjing and Hangzhou are 677 square kilometers and 778 square kilometers respectively, both characterized by a river running through the city, old and new urban areas facing each other across the river and an abundance of large mountains and rivers.
Figure 1 Research area and subjects
Residential differentiation actually reflects the imbalance of urban resource elements in geographical space (Wu, 2016), and the superposition of diverse factors such as regional traffic, supporting services, landscape quality, community environment and residential grade (Wang et al., 2015; Wang et al., 2018) shapes a pattern of residential segregation that is diversified, fragmented and spliced within a city. Housing price difference is a comprehensive and market-oriented expression of the differentiation in urban social resource allocation and economic strength of residents, which is also deemed as a relatively reliable indicator and effective tool to measure residential differentiation (Song et al., 2017; Chung, 2021). Therefore, this paper takes the housing price as a classification standard to explore the pattern and mechanism of residential differentiation in Nanjing and Hangzhou.
Data of residential community attributes, including housing price, housing size, geographical location and community support services, are provided by China Real Estate Price Platform (www.creprice.cn). Information available on the platform is collected from the real estate transaction data released and authorized by 9300 real estate websites with up to 50 million users. The real estate listing data dominated by stock housing and supplemented by new housing is obtained, which has time continuity, sample integrity, data accuracy and other advantages. The data is then organized through automatic duplicate removal, rejection and complementation and manually verified again. The platform provides the quarterly average price per unit area of commercial housing transactions in 6932 and 6175 residential communities within the research area of Nanjing and Hangzhou respectively during 2009‒2018 for the study. After eliminating the residential communities with missing information, 2320 and 2303 residential communities in Nanjing and Hangzhou, respectively, are chosen as research samples (Figure 1).

3.2 Spatio-temporal scales

At the time scale, the annual average listing prices per unit area of residential communities are selected as the statistical caliber, and 2009-2018 is taken as the time span to collect 83,911 and 83,502 pieces of quarterly housing transaction market data in Nanjing and Hangzhou separately. Due to insufficient transaction volume of several residential communities in the current quarter, the error in the quarterly housing price data provided by China Real Estate Price Platform may increase. Hence, the annual average data of 36,526 from Nanjing and 36,007 from Hangzhou are used in this study. As shown in Table 1, 2009-2018 is a decade for a rapid rise in residential prices in Nanjing and Hangzhou, of which the housing prices within the research area of Nanjing and Hangzhou separately rose from 10,733 yuan/m2 and 16,051 yuan/m2 in 2009 to 33,982 yuan/m2 and 36,307 yuan/m2 in 2018, and the median prices separately rose from 10,656 yuan/m2 and 15,143 yuan/m2 in 2009 to 32,000 yuan/m2 and 35,103 yuan/m2 in 2018 (Table 1).
Table 1 Average and median housing prices of Nanjing and Hangzhou from 2009 to 2018 (yuan/m2)
Year 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Average housing price of Nanjing 10733 13975 15516 15516 17753 19661 20159 24955 30685 33982
Average housing price of Hangzhou 16051 21194 22613 20848 21656 20372 19083 20652 29714 36307
Median housing price of Nanjing 10656 13855 15405 15372 17311 19107 19756 23309 29043 32000
Median housing price of Hangzhou 15143 20354 21971 19900 20847 19516 18129 19673 28750 35103
At the spatial scale, based on the dotted data of residential communities, the selection of spatial scale units can be more flexible and detailed. After taking into account overall consideration factors such as the dialogicality with existing research results, the similarity of living space in the same block and the spatial heterogeneity of residential communities, this paper analyses three spatial scales, i.e., census tract, block and grid. On the census tract scale, Nanjing and Hangzhou are divided into 60 and 62 space units respectively according to the unified administrative division for census tracts given in the 6th national population census in 2010; on the block scale, Han et al. (2020) proposed to use urban main road boundaries and road intersections, use Topology tools and Feature to Polygon command in ArcGIS to divide block units, and merge blocks based on visual interpretation of remote sensing imagery, so as to get 258 space units in Nanjing and 262 space units in Hangzhou; on the grid scale, the Create Fishnet tool in ArcGIS is used to divide the research area into 1 km*1 km grids, and get a total of 702 unit grids in Nanjing and 792 unit grids in Hangzhou (Figure 2).
Figure 2 Spatial units between Nanjing and Hangzhou on census tract, block and grid scales

3.3 Methods

Traditional segregation indices mainly look at two groups, such as blacks and whites, which are increasingly not enough to describe the complex pattern of spatial segregation and integration in a diverse society. Therefore, this paper first adopts multi-group segregation index to calculate multi-scalar non-spatial segregation profiles and spatial segregation profiles, and analyze the differences in the degree and evolution of residential differentiation under different cities, scales and segregation indices; then, it calculates the results according to the segregation indices of different residential types in Nanjing and Hangzhou, identifies main reasons for residential segregation, and adopts segregation decomposition to calculate the contribution of spatial structure component and group attribute component to the differences between Nanjing and Hangzhou in segregation indices, so as to analyze reasons for different residential differentiation levels in Nanjing and Hangzhou.
(1) Multi-group segregation index
Massey and Denton (1988) proposed five dimensions for measuring residential differentiation, i.e., evenness, exposure, clustering, centralization and concentration. Soon afterwards, Reardon and O’Sullivan (2004) argued that there is an overlap between these five dimensions, and further summarized them as two dimensions, i.e., spatial evenness-clustering and spatial exposure-isolation (Figure 3).
Figure 3 Dimensions of residential differentiation
In order to reflect the differentiation and complexity of urban living space, the method of breaking point is adopted to divide residential communities with different prices into five types, i.e., high-priced housing, medium- and high-priced housing, medium-priced housing, medium- and low-priced housing and low-priced housing. The segregation index of these two groups are expanded to multi-group information theory index H (evenness H for short, which refers to the different distribution degree of different groups in spatial units, the greater the value is, the more uneven it is) and multi-group normalized exposure index P (exposure P for short, which refers to the difficulty for a group to be exposed to other group members in the environment, the greater the value is, the less exposed it is) according to unit size and weighting coefficient of residential group proportion:
$H=\sum\limits_{m=1}^{M}{\sum\limits_{j=1}^{J}{\frac{{{t}_{j}}}{TE}}}{{\pi }_{jm}}\ln \frac{{{\pi }_{jm}}}{{{\pi }_{m}}}$
$P=\sum\limits_{m=1}^{M}{\sum\limits_{j=1}^{J}{\frac{{{t}_{j}}}{T}}}\frac{{{({{\pi }_{jm}}-{{\pi }_{m}})}^{2}}}{(1-{{\pi }_{m}})}$
where E refers to global information theory, T refers to the total number of residential communities in all areas, t refers to the number of residential communities in certain unit grid, π refers to the proportion of residential communities, the subscript j refers to spatial unit, and the subscript m refers to different residential communities. tj refers to the total number of residential communities in spatial unit, πm refers to the proportion of residential communities of type m, and πjm refers to the proportion of residential community in spatial unit j.
(2) Spatial segregation index
The above non-spatial segregation index can be regarded as an extremum of spatial segregation index. The non-spatial index implicitly defines local environment as a preset spatial unit, while spatial index defines it as a spatial weight matrix that can theoretically capture meaningful group interaction patterns, so it can better reflect the actual situation (Reardon et al., 2004). Although spatial indices have theoretical advantages over traditional non-spatial indices, they are rarely used due to difficulties in calculation.
The methods for establishing a local environment mainly include fixed coefficient method and method based on an urban road network, of which the latter can better reflect the actual situation. According to a series of evaluation criteria of segregation index, Reardon (2004) proposed that spatial information theory index is more suitable for calculating the residential differentiation based on a road network. In recent years, through the implementation and computational efficiency of GIS and R-package improved differentiation models, some methods have increasingly prominent advantages in spatial econometric analysis and data visualization (Wong, 2003; Apparicio et al., 2013). Based on the local isolation index proposed by Feitosa et al. (2007) and Python spatial analysis library (PySAL) module developed by Rey et al. (Rey, 2019), this paper adopts the spatial weight coefficient and road network space based on kernel function to improve non-spatial indices:
${{L}_{j}}=\sum\limits_{j=1}^{J}{k({{t}_{i}})}$
${{L}_{jm}}=\sum\limits_{i=1}^{I}{k({{t}_{jm}})}$
${{\tilde{\pi }}_{jm}}=\frac{{{L}_{jm}}}{{{L}_{j}}}$
where k refers to kernel function, which is used to estimate the impact of each area l unit on locality. tj and tjm refer to the total number of residential communities in unit j and that of residential community m, respectively. Given the weight by selecting distance decay function and parameters based on the kernel estimation of center of mass placed on statistical unit i, we can calculate the local residential density (Lj) of unit j and that (Ljm) of residential community m, as well as the local proportion (${{\tilde{\pi }}_{jm}}$) of residential community m in spatial unit j. Based on spatial nearness and local environment, the spatial weighted information theory index ($\tilde{H}$) of each unit j is calculated.
$\tilde{H}=\sum\limits_{m=1}^{M}{\sum\limits_{j=1}^{J}{\frac{{{t}_{j}}}{T\tilde{E}}}}{{\tilde{\pi }}_{jm}}\ln \frac{{{{\tilde{\pi }}}_{jm}}}{{{{\tilde{\pi }}}_{m}}}$
where $\tilde{E}$ refers to the local economy; ${{\tilde{\pi }}_{m}}$refers to the local residential communities of type m, and ${{\tilde{\pi }}_{jm}}$refers to the local proportion of residential community m in spatial unit j.
(3) Segregation decomposition
In order to quantify and identify the cause for the formation of difference in residential differentiation indices between Nanjing and Hangzhou, Shapley decomposition is used to measure the contribution of spatial structure component and group attribute component. Compared with traditional decomposition methods proposed by Kakwani and Subbarao (1990) and Datt and Ravellion (1992), Shapley decomposition is more thorough and symmetrical, and the formulas are as follows:
$\Delta H={{C}_{s}}+{{C}_{a}}$
${{C}_{s}}=\frac{1}{2}\left\{ H(s,a)-H(s=\bar{s};a) \right\}+\frac{1}{2}\left\{ H(s,a=\bar{a})-H(s=\bar{s};a=\bar{a}) \right\}$
${{C}_{a}}=\frac{1}{2}\left\{ H(s,a)-H(s;a=\bar{a}) \right\}+\frac{1}{2}\left\{ H(s=\bar{s},a)-H(s=\bar{s};a=\bar{a}) \right\}$
where$\Delta H$refers to the difference of residential differentiation evenness index H or exposure index P of two cities, and Cs refers to the contribution of spatial structure components, which is obtained according to the average differentiation degree by calculating the first modified spatial structure components and the later modified group attribute components; Ca refers to the contribution of group attribute components, which is obtained according to the average differentiation degree by calculating the first modified group attribute components and the later modified spatial structure components (Yamaguchi, 2017).

4 Results

4.1 Segregation indices of multiple spatio-temporal scales

(1) Non-spatial segregation profiles
By calculating the multi-group information theory index H and the multi-group normalized exposure index P of five types of residences on three scales in Nanjing and Hangzhou, the results as shown in Figure 4 are obtained: The two types of segregation indices in different cities and on different scales are mainly distributed between 0.3 and 0.6. According to the European and American standard of dissimilarity indices representing the degree of differentiation (the spatial segregation degree is low if the segregation indices are lower than 0.3, while the spatial segregation degree is high if greater than 0.6) (Denton et al., 1988; Massey et al., 1993), the degree of residential differentiation is “moderate” in Nanjing and Hangzhou; the residential differentiation degree shows a stronger effect on the scale, i.e., the smaller the spatial unit, the higher the segregation degree. As time goes by, the changes in dissimilarity indices on different scales of the same city tend to maintain a relatively consistent waveform. Segregation degree in Nanjing and Hangzhou has changed little in the last decade, and the difference is that the degree of segregation in Nanjing is slightly higher than that in Hangzhou, which was relatively stable in early stages, showed a U-shaped fluctuation during 2014‒2018, and evenness index (H) was always higher than exposure index (P); while the changes in degree of segregation in Hangzhou tended to show a gently inverted U-shaped curve, and evenness index was equivalent to exposure index before 2013, which was increasingly higher than exposure index in the later stage.
Figure 4 Multi-group evenness (H) and exposure (P) between Nanjing and Hangzhou from 2009 to 2018
(2) Spatial segregation profiles
In order to explore the sensitivity of residential segregation degree in terms of scale, the residential evenness index (H) of Nanjing and Hangzhou in 2018 was selected. Linear kernel and exponential kernel models based on road network distance are separately adopted to build spatial information theory profiles from 0 m to 3000 m (Figure 5). The obvious characteristic is found that residential segregation degree continues to decay as scale becomes larger, which is in line with the basic principle, i.e., the larger the scale, the less the segregation (Lee, 2019). Also, H index that is calculated by exponential kernel function decays is faster than H index calculated by linear kernel function. Therefore, the linear kernel function model whose bandwidth is 500 m is finally adopted to calculate the spatial information theory index ($\tilde{H}$) according to the law of segregation indices decaying with scale and in combination with the characteristics of community and neighborhood scales.
Figure 5 Multi-scalar profiles of residential spatial differentiation between Nanjing and Hangzhou in 2018
The calculation results are shown in Figure 6: Spatial index ($\tilde{H}$) is significantly lower than non-spatial index (H). For example, $\tilde{H}$ index of Nanjing on the scales of census tract, block and grid in 2018 was 0.38, 0.48 and 0.59, while H index was 0.48, 0.58 and 0.65, respectively. The trend of spatial indices is basically consistent with that of non-spatial indices, but the spatial index profiles are relatively gentle and differ from non-spatial index profiles in some aspects, indicating that the introduction of neighborhood environmental spatial variables not only generates the decay effect of spatial segregation indices, but may also lead to the calculation results differing from non-spatial indices. For example, the non-spatial index (H) of Nanjing and Hangzhou hit a peak in 2014 and 2013, while the spatial index ($\tilde{H}$) topped in 2018 and 2015, respectively. For another example, the annual average H value of Nanjing was 0.561 during 2009‒2018, which was higher than that of Hangzhou (0.515), while the annual average $\tilde{H}$ value of Hangzhou was 0.506, which was higher than that of Nanjing (0.435).
Figure 6 Multi-group spatial information theory index ($\tilde{H}$) based on road networks between Nanjing and Hangzhou from 2009 to 2018

4.2 Segregation indices of different housing types

Information theory index (H), normalized exposure index (P) and spatial information theory index ($\tilde{H}$) reflect the degree of overall segregation in multi groups (Figure 6). In order to explore respective segregation characteristics of different residential types, evenness index (H) and exposure index (P) of various residences in Nanjing and Hangzhou are separately measured in order to observe and compare the unbalanced distribution of residential space of different types, as well as the difficulty for such type of residential space to be exposed to other types of residential space.
Given the similarity in waveforms of spatial segregation indices on different scales in Nanjing and Hangzhou, the block scale is selected as analysis subject. The reasons are as follows: on a scale of census tracts, the spatial units are larger, and their segregation indices are lower in calculation results, making it difficult to reveal the actual spatial segregation; the spatial scale of 1 km grids is smaller and the grids are divided rigidly, which may be “distorted” due to excessive amplification of the heterogeneity of living space; the block scale can relatively avoid the above problems and take into overall consideration the road network structure, which can better reflect the actual residential segregation.
As can be seen from evenness (H) and exposure (P) indices for residential spatial differentiation of various types in Nanjing and Hangzhou in Figure 7.
Figure 7 Segregation profiles of different housing groups on block scale between Nanjing and Hangzhou from 2009 to 2018
(1) Low-priced housing shows the highest spatial segregation degree (high evenness and high exposure), i.e., it shows the least evenness in terms of spatial distribution among various housing types, and the least exposure to the residential space of other types; the evenness indices of other types of housing are closer, while exposure indices differ greatly, i.e., the higher the residential grade, the easier to be exposed to other types of housing; as the residential differentiation index waveform is the most similar to the multi-group segregation waveform of low-priced housing in Nanjing and Hangzhou, it is judged that spatial segregation of low-priced housing is the primary factor that leads to the urban overall residential spatial heterogeneity.
(2) Evenness index and exposure index are correlated. As can be seen from Figure 7, the two indices of the same type of housing are extremely similar in waveform, i.e., the higher the degree of imbalance as represented by H index, the higher the difficulty (P) of exposure between different types of housing. At the same time, evenness index is different from exposure index in connotation, and exposure relies more on the relative group size. For example, if the proportion of high-priced housing is small, the probability of exposure to other types of housing is high, and the gap is great in the proportion of various types of housing (Table 2), in which case difference in P index is more significant than difference in H index between various types of housing in Nanjing and Hangzhou.
Table 2 Percentage of different housing groups between Nanjing and Hangzhou from 2009 to 2018
Proportion (%) 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Nanjing High-priced housing 5.10 2.98 2.59 3.90 3.79 3.11 3.14 8.72 2.79 2.43
Medium high-priced housing 19.09 14.87 14.75 15.69 16.21 16.83 17.11 18.17 15.45 15.16
Medium-priced housing 32.14 30.73 30.20 30.91 26.86 25.20 26.96 23.89 24.44 30.23
Medium low-priced housing 23.71 28.34 30.08 26.04 28.91 30.81 29.32 36.18 37.00 43.84
Low-priced housing 19.95 23.08 22.39 23.45 24.23 24.05 23.47 13.04 20.31 27.62
Hangzhou High-priced housing 1.46 0.96 0.79 0.43 0.70 2.48 1.68 2.53 5.13 4.65
Medium high-priced housing 9.17 8.95 7.47 7.66 7.45 10.74 10.19 12.67 16.48 16.67
Medium-priced housing 28.72 31.82 27.16 31.32 25.06 32.27 27.13 28.43 26.09 31.51
Medium low-priced housing 41.54 37.22 39.13 34.82 37.53 31.67 34.44 33.03 32.92 32.78
Low-priced housing 19.12 21.04 25.44 25.77 29.26 22.84 26.56 23.35 19.37 14.39

Source: China Real Estate Price Platform.

(3) The spatial segregation gap between different types of housing in Nanjing is greater than that in Hangzhou. In terms of evenness, the average H index of low‒priced housing in Nanjing is above 0.86, H index of other types of housing is between 0.3‒0.6, while the evenness index of all types of housing in Hangzhou maintains within 0.3‒0.4; in terms of exposure, P index gap between high-priced and low-priced housing in Nanjing was 0.74 in 2009 and also approached 0.50 in 2018, while the exposure index gap of different types of housing in Hangzhou dropped from 0.61 in 2009 to 0.16 in 2018, indicating that low-priced housing in Nanjing was more uneven and more concentrated in space, while low-priced housing tended to be spatially dispersed and high-priced housing tended to be concentrated in Hangzhou.

4.3 Contribution of difference between Nanjing and Hangzhou

According to the difference between the spatial segregation indices of various types of housing in Nanjing and Hangzhou (Figure 8), it is judged that the spatial segregation indices of different types of housing in Nanjing are higher than those in Hangzhou as a whole, which is especially obvious in high-priced and low-priced housing.
Figure 8 The difference of residential differentiation in different housing groups at block scale between Nanjing and Hangzhou from 2009 to 2018
Therefore, in order to identify structural reasons for the difference and evolution of residential differentiation in Nanjing and Hangzhou, high-priced and low-priced housing types are further selected, Shapley decomposition is adopted to decompose the contribution of the differences of residential differentiation indices in Nanjing and Hangzhou, and the results are shown in Figure 9. The difference in residential differentiation between Nanjing and Hangzhou is generated by the joint effect of spatial structure difference and group attribute difference. The contribution of spatial structure and group attribute components may be positive (i.e., higher differentiation in Nanjing) or negative (i.e., higher differentiation in Hangzhou), and the total contribution of these two types of factors leads to the difference in differentiation indices between Nanjing and Hangzhou. Generally speaking, the contribution of spatial structure difference is higher than that of group attribute difference. As the contribution of spatial structure elements is basically positive, it can be inferred that difference in spatial structure is the primary factor leading to the result that the degree of residential segregation in Nanjing is higher than that in Hangzhou.
Figure 9 The difference and decomposition of residential differentiation index of high and low housing prices between Nanjing and Hangzhou from 2009 to 2018
In order to probe into the structural difference in residential differentiation between Nanjing and Hangzhou, this paper focuses on comparing the spatial distribution patterns of high-priced and low-priced housing types in 2018, as shown in Figure 10. In Nanjing, high-priced housing is mainly concentrated in inner city, including top public primary school catchment areas represented by Lhasa Road Primary School, Lixue Primary School and Langya Road Primary School, Longjiang area in Hexi New Town, areas around the Xuanwu Lake and the east of the Zijin Mountain, while low-priced housing is concentrated in northern Jiangbei New Area. In Hangzhou, high-priced housing is mainly distributed in old towns, including the “famous school” catchment areas represented by Xuejun Primary School, Tianchang Primary School and Qiushi Primary School, areas along Yan’an Road on the east bank of the West Lake, areas around Xixi Wetland and Qianjiang New Town, while low-priced housing is mainly distributed in peripheral areas, especially areas around the ring road.
Figure 10 Percentage of high and low housing groups at block scale between Nanjing and Hangzhou in 2018
From the perspective of difference between Nanjing and Hangzhou, Nanjing tends to show the “single-center” feature with Xinjiekou as the core, while peripheral areas such as the northern part of Pukou District and southern part of Luhe District have always been the low-priced areas due to a relatively big difference in environment from the main urban area such as traffic conditions, supporting services and landscape environment, while Xiaoshan and Xiasha in peripheral areas of Hangzhou have a relatively small difference from the main urban areas in every aspect. Therefore, the high-priced and low-priced houses in Nanjing tend to be more clustered, while those in Hangzhou are relatively disperse, and such structural difference leads to the result that the residential segregation degree in Nanjing is higher than that in Hangzhou.

5 Conclusions

This paper focuses on the classic topic of residential segregation and attempts to make innovations in the following aspects: Firstly, study residential differentiation from a housing perspective that is spatially flexible and prospective; secondly, measure the residential differentiation in Nanjing and Hangzhou based on multiple spatio-temporal scales and multi-group segregation index; thirdly, compare the differences in residential differentiation indices between Nanjing and Hangzhou and break down them into the contribution of spatial structure and group attributes. The main conclusions are as follows:
(1) Take the housing prices of residential communities as classification criteria, adopt methods such as multi-group spatial segregation index, and measure the residential segregation from a housing perspective on a material dimension. Due to the advantages of time continuity, strong timeliness, flexible scale division and accurate spatial location, this paper can describe residential differentiation in a more timely, dynamic and accurate manner, better present the complexity and hierarchy of residential segregation truly, and more effectively solve the problem of the so-called Paradox of Segregation.
(2) During 2009‒2018, the residential differentiation indices of Nanjing and Hangzhou tended to show different waveform changes, which increased as a whole; the waveform of non-spatial segregation indices (H and P) is roughly similar to that of spatial segregation index ($\tilde{H}$) of the same city, but there are also some differences, indicating that spatial segregation index can improve the traditional non-spatial segregation indices to a certain extent due to taking into account spatial location and neighborhood environment, so as to more accurately reflect the urban residential segregation degree.
(3) Viewed from the segregation index differences of different types of housing on the block scale, low-priced housing has the highest spatial segregation degree, especially the evenness and exposure indices of low-priced housing in Nanjing are significantly higher than those of other types, indicating that low-priced housing in Nanjing has more unevenness and spatial clustering; the spatial segregation degree of high-priced and low-priced housing types in Nanjing are significantly higher than those in Hangzhou, and the difference can be broken down into cause of spatial structure and cause of group attributes, of which spatial structure components are dominant.
(4) The difference of housing price is the materialized expression of the spatial imbalance in urban resources. Excessive residential differentiation probably means that the space misallocation of urban education resources, jobs and public facilities are intensified. Therefore, the local government shall properly control the degree of residential segregation and ensure the sound and sustainable development of urban social space in the new era by strengthening regulation and supervision of the real estate market, establishing a diversified housing guarantee system, building multi-center urban space structures and promoting equalized configuration of public service facilities.
It is undeniable that this paper has its limitations as an exploratory study. For example, can housing price indices fully represent the material dimension attributes of residential differentiation? What do non-spatial or spatial indices actually mean, and is there a standard for determining residential differentiation? Are residential differentiation indices between different cities comparable? Why do segregation indices tend to show varying waveforms over time? These limitations are the key directions to be further researched in follow-up studies. Therefore, in order to deepen the theoretical and empirical studies of residential segregation in China, it is also necessary to continuously explore the residential differentiation measurement method that can integrate multiple indicators and is suitable for multiple groups and multiple scales, put forward differentiation measurement standards that are in line with China’s national conditions and suitable for different types of cities, and gradually shift the study focus from whether a city has residential differentiation and its degree to exploring the actual meaning of differentiation indices.

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