Measuring The Value Of Urban Green Space Using Hedonic Pricing Method

Baseline hedonic pricing model

The basic methodology of the study is the hedonic pricing model, which is first brought up by Rosen in 1974. Rosen illustrated that each characteristics of the good could contribute to its prices (Rosen, 1974). Thus, the hedonic pricing model could be represented as:

$P_i=f\left(A_i,\mathrm{}{D}_i,\mathrm{}{E}_i\right)\mathrm{}\mathrm{}$ (1)

where the $P_i$ represents the price of each property $(i$); the $A_i$ represents the basic attributes of the properties, such as the areas of the properties, the number of bedrooms, the age of the property, etc.; the $D_i$ expresses the location characteristics like the proximity to the nearest garden or park, transportation center, public places etc.; while the $E_i$ represents the environmental attributes, such as the number of parks near the property, the areas of green land, the variety of the green species and so on. The basic intuition of the hedonic pricing method is maximum the consumer utility, which is the property’s price in this model.

Statistically, the hedonic pricing model could be represented as:

$P_i={\beta }_{\mathrm{0}}+{\beta }_{\mathrm{1}}{A}_i+{\beta }_{\mathrm{2}}{D}_i+{\beta }_{\mathrm{3}}{E}_i+ϵ\mathrm{}\mathrm{}$ (2)

Model with spatial weight matrix

A spatial weight matrix is a matrix that reflects the interdependence of different geographic regions in space (Seya et al., 2013). The core concept to understand the relationship among districts is the distance-based spatial weights, which is most common used method in spatial econometrics. Euclidean distance, dij is the most familiar case of the distance-based spatial. $d_{ij}=\sqrt{{\left(x_i-x_j\right)}^{\mathrm{2}}+{\left(y_i-y_j\right)}^{\mathrm{2}}}$, for two districts i and j, with separated coordinates $(x_i,y_i)$ and ${(x}_j,\mathrm{}{y}_j)$ (Liberti et al., 2014). In our study we create a spatial weight matrix to describe the closest distance between each city i and neighbouring city j in the sample. We use two spatial weight metrics to represent such distances. The concept of contiguity weight means two spatial units being in actual contact along a boundary or a border (Chen, 2012). The contiguity weight usually can be distinguished into two categories: a rook contiguity and a queen contiguity. For the rook contiguity weights could be represented as:

$w_{ij}=\left\{\begin{array}{c}\mathrm{1}\mathrm{},\mathrm{}\mathrm{}\mathrm{}{l}_{ij}>\mathrm{0}\\ \mathrm{0}\mathrm{},\mathrm{}\mathrm{}\mathrm{}{l}_{ij}=\mathrm{0}\end{array}\right.$ (3)

With $l_{ij}$ notes the length of shared boundary, between $i$ and $j$.

While for the queen contiguity weights are defined by

$w_{ij}=\left\{\begin{array}{c}\mathrm{1}\mathrm{},\mathrm{}\mathrm{}\mathrm{}bnd\left(i\right)\cap bnd\left(j\right)\ne \mathrm{\varnothing }\\ \mathrm{0}\mathrm{},\mathrm{}\mathrm{}\mathrm{}bnd\left(i\right)\cap bnd\left(j\right)=\mathrm{\varnothing }\end{array}\right.$ (4)

$bud\left(i\right)$ represents the set of boundary points of unit $i$.

The spatial weight matrix represents as following:

$W=\left(\begin{array}{cccc}\mathrm{0}& w_{\mathrm{12}}& \dots & w_{\mathrm{1}n}\\ w_{\mathrm{21}}& \mathrm{0}& \dots & w_{\mathrm{2}n}\\ ⋮& ⋮& \ddots & ⋮\\ w_{n\mathrm{1}}& w_{n\mathrm{2}}& \dots & \mathrm{0}\end{array}\right)$ (5)

with: $w_{ij}$= $\left\{\begin{array}{c}\mathrm{}\mathrm{1}\\ \mathrm{0}\end{array}\right.\genfrac{}{}{0pt}{}{\begin{array}{c}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}if\mathrm{}\mathrm{}j\in N_k\left(i\right)\mathrm{}or\mathrm{}i\mathrm{}\in N_k\left(j\right)\end{array}}{\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}otherwise}$

There are three basic spatial econometric models. Spatial autoregression (SAR) model can include spatially related dependent variables and spatially related error terms. The basic representation of SAR model is:

$Y_n=\lambda W_n{Y}_n+\beta X_n+{\epsilon }_n$ (6)

$W_n\mathrm{r}$epresents the spatial matrix. The term $W_n{Y}_n$ considered as “spatial lag”.

The spatial error model (SEM) model describes the spatial disturbance correlation and spatial total correlation. The SEM model is represented as:

$Y_n=\rho Y_n+\beta X_n+\mu$

$\mu =\lambda W_n\mu +{\epsilon }_n$ (7)

The spatial durbin model (SDM) is a combination of spatial lag model and spatial error term model, is a SAR model enhanced by adding spatial lag variable:

$Y_n=\lambda W_n{Y}_n+\beta X_n+\theta W{X}_n+{\epsilon }_n\mathrm{}\mathrm{}$ (8)

$\theta W{X}_n$: exogenous interaction effect.

Data

In our study, we choose forest cities as our research case. A national forest city is a city whose urban ecosystem is dominated by forest green vegetation and whose forest green space-related indicators can reach national standards. the title of "national forest city" was first awarded by the State Forestry Administration in November 2004. Up to now, 192 cities have been awarded the title of national forest city. In this study, 62 key forest cities were selected as research samples, and the forest green space data of these 62 cities were used for research. We also collected data on residential real estate transactions for these 62 cities between 2010 and 2018: a total of 558 real estate transactions (15 per year). In our model, various characteristics (floors, availability of infrastructure, etc.) were considered as factors influencing the price of housing properties, the most important control variable is the area of green spaces (Table 1).

Results of basic hedonic pricing modeling

Table 2 shows the results of the basic hedonic pricing modeling. To estimate the hedonic pricing models, we used three regression analysis methods: (1) the Ordinary Least Square; (2) the Fixed Effect and (3) the Random Effect. The results of all three methods using demonstrated a positive relationship between areas of green land and the property price. The results revealed that the areas of green land contribute to the house price with significant and robust effects, which are in accordance with previous studies. The OLS model ignores heteroscedasticity; the model variable pGDP measures the level of differentiation of GDP per capita between different cities. In contrast to studies where a similar variable was introduced into the OLS regression model in order to solve the problem of heteroscedasticity, in this study the pGDP variable was used to identify the level of statistical relationship between house price and green area., comparing with the fixed effect model and the random effect model, only one indicator – the built year of the property not represent a significant relationship. In Table 2 the results of fixed effect and random effect are similar.

Results of spatial hedonic pricing modeling

Table 3 shows the results of spatial hedonic pricing modeling. The results also show a positive relationship between house price and GDP per capita. The areas of green land have a positive effect on the price of housing property. In SDM model, the results show that GDP per capita and green area in neighboring cities do not affect the price of downtown housing. The spatial spillover effect does not exist in the spatial correlation with the dependent variables. However, rho equal to 0.404 indicates statistical significance at a 95 percent confidence level, which means that home prices have spatially autocorrelation. Consequently, the cost of housing in one city will be influenced by the price of houses in nearby cities.

The results of these three spatial econometric models indicate that firstly, spatial autocorrelation exits in the prices of housing property. The prices of one city housing property are affected by the prices in neighbor cities. Secondly, the area of urban green space has no spatial autocorrelation, which means the area of urban green space in one city cannot be influenced by such area in the nearby cities. Thirdly, even though there is no spatial autocorrelation in area of urban green space, the spatial spillover effect still exists in spatial hedonic pricing model.

The value of green land in the city

Calculating the economic value of urban green space is the most important part of this paper. The results of the calculation based on the results of the baseline model using the OLS method are that the economic value of urban green space in 62 forest cities is 53 yuan/ $m^2$, the results of the calculation using the fixed-effects model are 31.8 yuan/ $m^2$, and the results of the calculation using the random-effects model are 42.5 yuan/ $m^2$. This result is a basic judgment for understanding the value of urban green space and can provide some reference for policy makers in policy implementation and formulation. However, the OLS results do not reflect well the spatial correlation among forest cities, nor do they avoid the errors brought by spatial heterogeneity on the estimation results. Therefore, we first used fixed effects and random effects to eliminate the problem of spatial heterogeneity. According to the results of the Hausman test, the fixed-effects model is the better model after comparison.

Spatial spillover effects in hedonic pricing model

In order to better analyze the effect of spatial dependence among forest cities on urban green space valuation, we constructed SAR, SEM and SDM models respectively. Comparison of the results of constructing three spatial econometric models, SAR, SEM and SDM, showed that the SDM model was the best regression model (Table 3). Green space area and GDP per capita had a significant positive effect on housing costs in forest cities. However, based on the simulation results, we could not characterize the direct and indirect effects of these independent variables. According to the results, the size of green space has a greater impact on housing prices than GDP per capita. The coefficient of housing prices for the size of urban green spaces is 0.342 higher than the coefficient of GDP per capita. there are several reasons for this situation. First, the government has adopted a series of policy measures aimed at improving the environmental efficiency of green space development management decisions in forest cities. Second, residents of forest cities are more aware than other citizens of the benefits of having green space in the urban environment. According to our calculations, their willingness to pay for the expansion of urban green space is 32 yuan/ $m^{\mathrm{2}}$. The third reason is that there are some positive externalities associated with the development of urban green space. Consistent with our expectations the SDM results also reflect a significant positive spatial correlation between forest cities. From this we can analyze that green space resources in one city have environmental spillover effects and can bring positive externalities to neighboring cities. Comparing the OLS results, we can see that the urban green space valuation after considering the spatial correlation is lower at 32 yuan/ $m^{\mathrm{2}}$than the OLS result of 53 yuan/ $m^{\mathrm{2}}$. This also reflects the fact that urban green space has a spillover effect on other neighboring cities, thus reducing the city's original valuation of urban green space.