Shanghai, the most populous urban area in China, is also China's international economic, financial, trade, shipping, and innovation center. As of 2020, the city had 16 districts under its jurisdiction, with a total area of 6,340.5 square kilometers. The built-up area covers an area of 1,237.85 square kilometers, with a permanent population of 24.2814 million and an urban population of 21.3919 million, with an urbanization rate of 88.10% (Shanghai Statistical Yearbook, 2020). In Shanghai, housing prices have been rising year after year, with the sales price of commercial housing rising from an average of 3,866 Yuan/m² in 2001 to 23,804 Yuan/m² in 2017 (China City Statistical Yearbook, 2001–2017). As one of the largest cities in China, the study of Shanghai can reflect the MWTP of people in the eastern and southern coastal areas of China. Thus, we choose Shanghai as the study area. In addition, to make the research more detailed, Shanghai is divided into 218 tracts based on the sixth National Population Census, as shown in Figure 1.

We focus on air pollutants around residential areas. Figure 2 shows the mean daily concentrations of SO₂, NO₂, and PM₁₀ in Shanghai from 2001 to 2019. Overall, air quality in Shanghai has improved over the years, which is mainly due to the active governance of the Chinese government. The daily concentration of SO₂ across different monitoring sites in Shanghai in 2019 was 7 μg/m³ (attaining the Grade I national standard for air quality), that of NO₂ was 42 μg/m³ (exceeding the Grade II national standard of 2 μg/m³), and that of PM₁₀ was 45 μg/m³ (attaining the Grade II national standard for air quality) (Shanghai Municipal Bulletin on the Status of Ecological Environment, 2019).

The data used in this study include housing price data, air quality data, and other built environment data in Shanghai. All the data used in this paper were collected in 2018 so that the time dimension can be unified.

The housing price information of 27,608 residential areas in Shanghai constituted the housing price data in this study. These data were taken from a platform for real estate transactions in Shanghai (http://cd.lianjia.com/) and included the address, average housing price, construction time, number of housing units, and latitude and longitude coordinates of each community.

The air quality data came from the Shanghai Municipal Bureau of Ecology and Environment. We collected data from 10 national controlled air quality monitoring stations of Shanghai in 2018. These data included the hourly mean concentrations of CO, O₃, SO₂, NO₂, PM₁₀, and PM_2.5, the monitoring time, and the current air pollution levels, which can be used to calculate the annual mean concentrations of air pollutants in different census tracts of Shanghai.

Figures 3–6 show that the air pollutants in Shanghai are diverse, mainly concentrated in the outer suburbs with heavy industries and the city center with heavy traffic. For example, the areas with the highest mean concentrations of SO₂ and PM₁₀ are the Baoshan District, Jinshan District, Yangpu District, and Jiading District, where there are many polluting factories, such as power plants, steel mills, and automobile factories. Furthermore, the large trucks that travel in these areas during the day also contribute to air pollution. The areas with the highest mean concentrations of NO₂ and PM_2.5 are mainly located in the inner ring area because of traffic congestion.

The built environment variables can be measured by the “5 Ds,” namely, density, design, diversity, distance to transit, and destination accessibility (42–44). In this study, the initial environmental data were composed of population data, urban road network data, and point of interest (POI) data. The population data came from the 6th Census of China. The urban road network data of Shanghai were extracted from the Open Street Map (OSM). The POI data were obtained from Baidu.com, which is one of the largest Chinese web mapping service applications. These data provided 14 types of locations, such as schools, restaurants, hospitals, parks, supermarkets, and transportation facilities (45). The total number of POIs in this dataset is 603,085, and for each POI, the basic information includes the name, type, location, and latitude and longitude.

The smallest research unit of this study is one of the 218 census tracts in Shanghai; thus, the three types of data above need to be processed. As shown in Figure 7, this processing mainly includes data cleaning, data analyses, data extraction, and variable calculation.

Based on the existing data and referring to relevant references, we determined the dependent and independent variables of this study and performed a descriptive statistical analysis of all the variables, as shown in Table 2. There are 6 types of air quality data, namely, CO, O₃, SO₂, NO₂, PM₁₀, and PM_2.5 data. The other built environment variables include 18 indicators of the “5 Ds.” In particular, land-use diversity is measured by the entropy index, which ranges in value between 0 and 1, where 0 means that the land use is single and homogeneous and 1 means that all types of land use are evenly distributed (43, 46). The calculation formula of land use diversity is defined as follows:

where E_i is the entropy for land uses within the spatial unit i, p_ij is the proportion of the jth land use at spatial unit i, and N is the number of land use categories. In this study, 14 land uses (restaurants, retail, hotels, tourist attractions, medical facilities, educational buildings, residences, parks, and so on) are considered (N = 14).

To measure the straight-line distance from the city center, we chose the location of the Shanghai Municipal People's Government as the downtown of Shanghai, where there are more than 10 large-scale shopping malls, the headquarters of dozens of well-known corporations, and hundreds of logistics, trade, information technology, and media enterprises.

In addition, the mean-centered method is used to eliminate the dimensional influence of all variables, including house prices. The formula is as follows:

where x_ik is the input value of the model, X_ik is the original value of the k-th characteristic variable at spatial unit i, X¯k represents the original average value of the k-th variable.

Multicollinearity refers to the high linear correlation between explanatory variables, which makes a model difficult to estimate or the regression effect not ideal. To eliminate this phenomenon, we adopted the value of the variance inflation factor (VIF) to filter variables. The VIF is a measure of multicollinearity. Specifically, when the VIF value of a characteristic variable is >7.5, it has problems of multicollinearity with other independent variables and should be removed from the model (50). The VIF of the independent variables is positively associated with the coefficient of determination (r²) for the regression, which can be computed as follows:

Before using spatial regression models, the spatial autocorrelation of the variables should be tested. Moran's I test is often used to verify the spatial autocorrelation of variables (51), and Moran's I can be expressed as follows:

where n is the number of spatial units, w_ij is the spatial weight between units i and j, x_i denotes the attribute value of unit i, and x¯ represents the average value of all units.

Moran's I is a rational number, and it ranges between −1 and 1. Specifically, the larger the positive value of Moran's I, the stronger the spatial correlation. While the value of Moran's I <0 indicates a negative spatial correlation, and the smaller the value of Moran's I, the greater the spatial difference. A value near zero means a spatially random distribution. The null hypothesis of Moran's I test assumes that each explanatory variable is spatially independent, meaning that it is sufficiently close to 0. The Z-score is usually computed to verify the null hypothesis of Moran's I test and is defined as follows:

where E(I) and Var(I) represent the expectation and standard deviation of Moran's I, respectively. The significance level in this study is P < 0.01, and the critical Z-score values are −2.58 and +2.58 when using a 99% confidence level.

GWR models are based on the traditional linear regression model, which attempts to build a linear relationship between a given dependent variable and a set of independent variables (52). The GWR model tries to establish a linear regression equation for each spatial unit by considering the geographical changes among variables. As other observations are closer to the spatial unit, their influence on the coefficient estimation of this spatial unit is greater. This feature of the GWR model takes into account the local specific relationship between the dependent variable and independent variable of spatial variation during modeling. The calculation formula of the GWR model is as follows:

where x_ik is the independent variable, y_i is the dependent variable, (u_i, v_i) are the spatial latitude and longitude coordinate points of spatial unit i, ε_i is the Gaussian error term, εi~N (0,δ2),Cov (εi,εj)=0(i≠j), β₀ (u_i, v_i) is the intercept of spatial unit i (the constant term), β_k (u_i, v_i) represents the relationship weight value of the k-th characteristic variable at spatial unit i, and n is the sample size of the spatial unit.

The implementation process of the GWR model is as follows:

Step 1: Determine the optimal bandwidth.

Bandwidth b is used to explain the functional relationship between w_j (i) (spatial weight function) and d_ij (the distance between spatial unit i and unit j). Excessive bandwidth will generate non-significant differences in parameter estimates between different regions, which will affect the accuracy of model parameter estimation. However, a bandwidth that is too small will lead to a large variation. The Akaike information criterion (AIC) is one of the criteria used to measure the optimal fitness of statistical models (53). In this study, the corrected AIC (AICc) is used to determine the optimal bandwidth. Compared with other methods of determining bandwidth, such as the cross-validation method and designated bandwidth method, the AICc method can usually obtain a better degree of fit. Specifically, the smaller AICc value indicates that the model is better. The calculation formula of AICc is defined as follows:

where σ^ is the maximum likelihood estimate of the variance in the random error term, σ^=RSSn-tr(S), RSS denotes the sum of residual squares, and tr(S) is the trace of S matrix. The S matrix can be expressed as follows:

where Ŷ=[y1^y2^⋮yn^]. Y=[y1y2⋮yn].

Optimal bandwidth b₀ corresponds to the minimum value of AICc, which is obtained as follows:

Step 2: Select the spatial weight function.

In general, spatial weight function w_j (i) is computed by the Gaussian kernel function or the Bi-square kernel function, which are both distance-decay functions. The weight of the Gaussian kernel is continuous and gradually decreases from the center of the kernel but never reaches zero, while the bi-square kernel has a specific range with a non-zero kernel weight, which controls the k-th nearest neighbor distance of each regression position. Furthermore, bandwidth b can be constant (fixed kernel) or variable (adaptive kernel). The adaptive kernel is suitable for creating a nuclear surface based on the density of sample points. If the distribution of elements is close, the coverage of the nuclear surface will be small; otherwise, it will be large.

In this study, we selected the adaptive Gaussian kernel function for the following two reasons. (1) We choose 218 census tracts of Shanghai with different areas, leading to denser tracts in the city center and fewer tracts in the suburbs. (2) Air quality is greatly affected by the distance factor. The adaptive Gaussian kernel function can be expressed separately as follows:

where d_ij is the distance between spatial unit i and unit j, which can be obtained by calculating the distance between the centroids of unit i and unit j by the Toolbox tool in ArcGIS; b is the optimal bandwidth, which can be obtained by Step 1.

Step 3: Compute the regression coefficient

Regression coefficient β_k (u_i, v_i) of spatial unit i can be obtained by the local weighted least square method. The calculation formula of parameter β (i)=[β0 (ui,vi) β1 (ui,vi) … βk (ui,vi)]T is as follows:

where X=[1x11…xk11⋮1x12…xk2⋮⋱⋮x1n…xkn], W(i)=[w1(i)    w2(i)    ⋱    wn(i)]=diag [w1(i)w2(i)…wn(i)].

MWTP represents the change speed of the current willingness to pay, that is, the coefficient of the independent variable (the slope), which means adding one unit of independent variables (such as NO₂, PM_2.5, the density of metro stations and road networks) and how much are residents willing to pay more for the housing price. However, to eliminate the dimensional influence of the independent variable and the dependent variable (the housing prices), the mean-centered method was adopted to normalize the variables in the GWR model. Therefore, the coefficients of the GWR model need to be transformed to calculate the MWTP. The specific formula is as follows:

where MWTP_ik is the MWTP of the k-th characteristic variable at spatial unit i, X¯k represents the original average value of the k-th variable, and Y¯ represents the average value of the dependent variable, which is the housing price in this paper.

First, the Toolbox tool in ArcGIS was used to carry out multicollinearity tests on all the independent variables in Table 2, and the variables with VIF values >7.5 were removed. Then, stepwise OLS regressions were adopted to test the impact of independent variables on housing prices and select the variables with significant performance. Only 10 independent variables were left: the mean concentration of PM_2.5, the mean concentration of NO₂, metro station density, road network density, parking lot density, the percentage of educational service POIs, the percentage of stadium POIs, the percentage of medical institution POIs, the percentage of park POIs, and the straight-line distance from the city center.

The OLS regression results of these independent variables are shown in Table 3. The results show that PM_2.5 and NO₂ have a significant negative impact on housing prices, which are consistent with Chen and Chen (54) and Dong et al. (5), and the coefficients of other built environment variables are basically consistent with the theoretical and expected values. Specifically, Housing prices fall as the residential property move further away from the city center and housing prices rise with the increase of the number of subway stations, schools, and other infrastructures. Furthermore, the VIF values of these 10 independent variables are all relatively small, indicating that the collinearity among the variables is very weak.

The global Moran's I test was conducted to examine whether the 10 independent variables screened above had spatial autocorrelation. Table 4 shows the results, which include Moran's I, the expected index, the Z-score, and the P-value of the independent variables. All independent variables show spatial autocorrelation with a significance level of P < 0.01, and all Z-scores are >2.58. Therefore, it is necessary to use the GWR model to reveal the geographical variability of each variable.

Figures 8, 9 show the actual housing prices and the housing prices predicted by the GWR model, indicating that the GWR model has a high degree of fitting accuracy. To further prove the superiority and feasibility of the GWR model, we compared it with the OLS model, and both models adopted the same explanatory variables mentioned above. We computed the root mean square error (RMSE), mean absolute error (MAE), mean relative error (MRE), R², adjusted R², and AICc values of these two models, as shown in Table 5. From these six indicators, we can find that the prediction accuracy of the GWR model is better than that of the traditional OLS model. Meanwhile, the MAE and R² of the GWR model are 5,029 and 0.876 Yuan/m², respectively, which further reflects the high prediction accuracy of the GWR model. Furthermore, we computed 6 eigenvalues of the estimated coefficients of different variables to describe their influence range, namely, the average value, minimum value, maximum value, lower quartile, median, and upper quartile, as shown in Table 6. From the average value of the estimated coefficient, the GWR model results are consistent with those of the OLS regression as a whole, which shows that the mean concentration of PM_2.5, mean concentration of NO₂, and distance from the city center have negative effects on housing prices and that the other independent variables are all positively correlated. In addition, the value symbols of the maximum and minimum values are the same, proving that there is no directional difference in the influence of different variables on housing prices in Shanghai, and all variables are either promoting or inhibiting factors.

There are many estimates of coefficients output by the GWR model because one important characteristic of GWR models is that the estimated coefficients of each independent variable vary with each census tract, which indicates that each selected variable is affected by local characteristics (49). Therefore, the results of the GWR model can provide a reference for the government to formulate regional policies. In addition, we can calculate residents' MWTP for each variable by Equation (12). This study focuses on the analysis of residents' MWTP for clean air, as shown in Figures 10, 11, and the MWTP for other variables are shown in Figures 12–16.

Figures 10, 11 indicate that residents' MWTP for clean air has obvious spatial heterogeneity, Shanghai residents, on average, are willing to pay 50 Yuan/m² to reduce the mean concentration of PM_2.5 by 1 μg/m³, and the lowest absolute value of MWTP is 16 Yuan/m² in the central Jing'an District and the highest absolute value of MWTP is 163 Yuan/m² in the Pudong New Area. Shanghai residents are, on average, willing to pay 99 Yuan/m² to reduce the mean concentration of NO₂ by 1 μg/m³. The lowest absolute value appears in the Putuo District, where it is 10 Yuan/m², while the highest absolute value appears in the Qingpu District, where it is 250 Yuan/m². In other words, ceteris paribus, our results show that a 1 μg/m³ reduction in the mean concentrations of PM_2.5 and NO₂ results in a 0.1 and 0.2% increase in Shanghai property value, respectively (in 2018, the average housing price in Shanghai was 50,090 Yuan/m², and the mean concentrations of PM_2.5 and NO₂ were 43.19 and 42.33 μg/m³, respectively). Meanwhile, this result is slightly lower than that in developed countries, such as the US (1 μg/m³ reduction in TSPs increases the value of housing by 0.2–0.4%) (9), and it is similar to the study of prefecture level cities in China (a 1 μg/m³ increase in the PM_2.5 is associated with up to a 36 Yuan/m² reduction in housing prices) (19, 20). We speculate that there are two possible reasons: (1) China is currently a developing country, and people pay less attention to air pollution than developed countries. (2) Housing prices in Shanghai are very high, resulting in a small proportion of clean air.

This result shows that Shanghai residents' MWTP for reducing NO₂ levels is higher than that for reducing PM_2.5 levels, which is similar to the OLS model results. The reason is that the effect of NO₂ on Shanghai residents is more obvious. NO₂ is the main pollutant that causes acid rain, and the acid rain frequency was 53.8% in 2018, up 6.2% from the previous year (Shanghai Municipal Bulletin on the Status of Ecological Environment, 2018). Moreover, NO₂ can cause photochemical pollution and swelling of the human lungs (55). Furthermore, residents' MWTP for reducing levels of PM_2.5 and NO₂ increased from the city center to the suburbs. The possible reasons are as follows: (1) There are many factories in the suburbs that emit a lot of air pollutants, especially thermal power plants, machinery manufacturing industry, and automobile factories (Shanghai Municipal Bulletin on the Status of Ecological Environment, 2019), such as heavy machinery manufacturing in Pudong New Area, Shanghai Volkswagen in Jiading District, and petrochemical industry in Jinshan District (Shanghai Statistical Yearbook, 2020). Compared with traffic emissions, air pollutants emitted by these factories are concentrated and visible. Therefore, suburban residents living near these factories may be more disgusted with the air pollution and more willing to pay for clean air (56, 57). (2) Even though there are fewer infrastructure resources in the suburbs, more and more people move from the urban areas to the suburbs in order to enjoy a better quality of life, and these people attach great importance to the living environment (Shanghai Municipal People's Government, 2021). However, residents who live near the city center value other built environmental factors, such as convenient transportation, closer workplaces, and abundant educational and medical resources (1, 5, 24). (3) The result may be different from some previous studies on multiple cities (from a macro perspective) or multiple communities (from a micro perspective) with large economic differences (5, 9, 31). Because our study focuses on each census tract in Shanghai (from a meso perspective), where the economic gaps are relatively small. Even some rich people may prefer to move to the suburbs to enjoy better quality of life, especially in the five new towns.

The density of metro stations and road networks are both important indicators of urban traffic convenience. Figures 12, 13 show the spatial variation in residents' MWTP for the density of metro stations and road networks, respectively, with estimated MWTP ranging from 4,712 to 5,373 Yuan/m² and from 3,136 to 4,126 Yuan/m², respectively. Both indicators are positively correlated with housing prices. In addition, there is a decreasing trend from the suburbs to the city center of residents' MWTP for metro stations and road networks. The possible reasons are as follows: the density of metro stations in the center of Shanghai is relatively dense, with 1 subway station per km on average and 1 subway station per 5–10 km in the suburbs (Shanghai Statistical Yearbook, 2020). The density of road networks in the center of Shanghai is also relatively large, with a dense distribution of secondary trunk roads and branch roads, while it is sparse in the suburbs. Therefore, suburban residents are more eager to increase the density of metro stations and road networks. This result suggests that compared to increasing the density of metro stations and road networks in the city center, increasing these two indicators in the suburbs is more effective for improving the real value of land, especially in areas with poor traffic services.

Figures 14, 15 show the spatial differences in Shanghai residents' MWTP for educational services and medical institutions, with estimated MWTP ranging from 2,133 to 2,377 Yuan/m² and from 419 to 778 Yuan/m², respectively. In general, educational services and medical institutions are positively correlated with housing prices. Spatially, residents' MWTP for educational services is lower in the city center and higher in the suburbs, while it is opposite for residents' MWTP for medical institutions. The reason is probably that China advocates “going to school nearby,” and Chinese residents attach great importance to school district houses, while there are fewer schools in the suburbs, and suburban residents are crazier about school district houses, even though such houses are more expensive. Regarding medical institutions, people are eager to obtain the best medical services when they are sick, and the city center has abundant medical resources. Therefore, both urban and suburban residents are more willing to go to the city center to see a doctor, so residents' MWTP for medical institutions is higher in the city center. For these reasons, it is necessary to promote the balanced development of education and medical care between the city center and the suburbs of Shanghai.

Figure 16 shows the spatial impact of the straight-line distance from the city center on housing prices. In general, the distance from the city center is negatively correlated with housing prices, and the range of the GWR model's coefficient is from −0.0896 to −1.5254. Based on Equation (12), we convert it to MWTP, which ranges from −227 to −3,863 Yuan/m². Spatially, the absolute value of MWTP for the distance from the city center is higher in the inner suburbs, while it is lower in the downtown and outer suburbs. The reason is probably that residents in the inner suburbs are more dependent on downtown resources (such as shopping malls, parks, and stadiums), which will make them tend to buy houses as close to the city center as possible. This result indicates that residents in the inner suburbs are more sensitive to the distance from the city center, while residents in the outer suburbs are more sensitive to other built environmental factors of housing, such as air quality and traffic convenience.

Based on the above estimates, we attempt to compute the actual losses caused by air pollution in Shanghai from the perspective of asset value depreciation in the entirety of the Shanghai housing market. In 2018, the total building area of the housing stock in Shanghai was 594.6 million m² (Shanghai Academy of Social Sciences, 2019). If the mean concentrations of PM_2.5 and NO₂ increased by 1 μg/m³, the estimated losses of the entire Shanghai real estate market would be 29.730 and 58.865 billion Yuan, respectively.

In general, our research proves that air pollution has caused great economic losses in Shanghai. Shanghai residents are very sensitive to air pollution, and residents' MWTP for clean air is lower in the city center and higher in the suburbs, especially in the outer suburbs, such as the Qingpu District, Pudong New Area, and Jinshan District.