Influences of the Plot Area and Floor Area Ratio of Residential Quarters on the Housing Vacancy Rate: A Case Study of the Guangzhou Metropolitan Area in China

Abstract

Factors affecting the housing vacancy rate (HVR) vary, but few studies have considered the relationships between the HVR and plot area (PA) and floor area ratio (FAR). This study thus considered 212 residential quarters in the Guangzhou metropolitan area as the research object, and we constructed a regression model of the factors impacting housing vacancies. The model includes two explanatory variables, PA and FAR, and the remaining six impact factors as control variables. In this study, the influences of PA and FAR on the HVR was analyzed by combining the traditional ordinary least squares (OLS) and two spatial regression models: the spatial lag model (SLM) and spatial error model (SEM). The results indicate that (1) the HVR in the Guangzhou metropolitan area shows spatial difference characteristics of the low central area and high edge, and there is spatial autocorrelation. (2) The PA of the residential quarters gradually increases from the central to the edge area, but the spatial pattern of FAR is the opposite. (3) The SLM results indicate that the PA and FAR of the residential quarters have significant positive correlations with HVR; that is, the larger the PA and FAR, the larger the HVR of the residential quarters, which is in accordance with the expected direction of the theory; furthermore, basic education convenience, road density, and waterfront accessibility have significant negative effects on HVR. This conclusion provides a reference for government departments to formulate reasonable and effective housing policies aimed at the current housing vacancy problem and should help alleviate urban housing vacancies.

1. Introduction

Housing is the basic demand of residents, and housing problems are related to people’s livelihoods and well-being, which has always been a hot topic for urban geographers. However, housing vacancies are a manifestation of housing problems, and these have received relatively little attention compared to housing prices, housing rents, and price-to-rent ratio. According to internationally recognized standards, the reasonable housing vacancy rate (HVR) ranges from 5% to 10%, and >20% is regarded as a high vacancy. The relevant statistics available say that the HVR proportion in China has exceeded 20%, which shows that the housing vacancy problem is very serious there. High HVR brings numerous problems, such as the imbalance of housing supply and demand in some cities. This leads to the appearance of “ghost cities”, “sleeping cities”, and “empty cities”, which waste land resources [1,2]. There are also many population outflows in some cities, resulting in urban shrinkage [3]. However, when the HVR is high, it happens that many people cannot afford housing; these forces contradict each other and hinder urban development. To alleviate this serious housing problem, national and local governments have successively issued relevant regulatory policies. Therefore, based on this backdrop, research on urban housing vacancies conforms to the national policy orientation, which cannot only provide an effective decision-making basis for accurate housing policy formulation, but also help to alleviate the contradiction between urban housing vacancies and housing pressure.

Existing studies have proven that the impact factors of housing vacancies stem from many aspects, which can be summarized as housing itself (including housing and residential quarter), community factors, and urban or regional factors. Among them, housing and its external factors are the important factors that affect urban housing vacancies, such as property value, age, size [4], quality, pattern, area, building structure [5,6], number of floors, greening environment, living facilities, convenience characteristics (employment convenience, basic education convenience, medical convenience, transportation accessibility [7], commercial services, surrounding landscape level (waterfront, park and green space, famous landmark landscape, etc.), surrounding environmental quality (disgusting municipal facilities, factories, logistics centers, etc.), and location. Generally, old, small, broken, cheap, and poorly maintained houses may have higher vacancy rates [8,9,10,11]. Han and Jung and others found that poor conditions and infrastructure of the community also promote the emergence of HVR [12,13]. These factors mainly promote the rise of HVR by influencing residential choices.

Although studies have proven that many factors affect HVR at the residential quarter level, few studies have linked the plot area (PA) and floor area ratio (FAR) of residential quarters with HVR. PA and FAR can reflect the size of residential quarters, and the FAR can better reflect living comfort. The PA and FAR are important aspects of the characteristics of the residential quarter and represent the scale and development intensity of the residential quarter. Theoretically, these two factors also have impacts on housing vacancies. Existing research focuses on the PA and FAR of residential quarters, mainly land price [14,15], land rents [16,17], population distribution [18], urban planning [19], public services, traffic conditions [20], indoor temperature [21], characteristics of spatial and temporal differences [19,22], their relationship with the city center [20,23,24,25,26], and so on. For example, Zong and Ji found that the scale of Chongqing’s residential quarters gradually increased from the city center to the peripheral areas, and planning, transportation, public services, and terrain factors constituted the driving forces for the expansion of residential quarters [20]. Wu et al. used six settlements in Ningbo and found that the floor area ratio has a significant positive effect on residential electricity consumption [27]. Furthermore, Wurm and Goebel found that the FAR decreased gradually from the center to the edge of the city [23]. Li et al. used Internet property data to study the spatial and temporal distribution characteristics of residential floor area ratio in Guangzhou [22]. Li et al. completed a spatial variation analysis of residential floor area ratio in Dalian [19]. Li et al. found that in Singapore, the FAR will have an impact on the indoor temperature [21]. There is current research on plot area and floor area ratio for residential quarters; however, few studies have focused on the impacts of these two factors, namely, PA and FAR, on HVR. PA and FAR are the factors that influence residents’ choice of buying or renting houses, and they theoretically influence the HVR as well. Therefore, it is necessary to research the relationships between PA and FAR, and HVR. However, little research has been conducted in this field.

Housing has always been a prominent problem in the development of many cities, especially in super cities such as Guangzhou. Guangzhou’s economy has developed, and its population has been on the rise recently, which has led to housing problems. However, only a few scholars have focused on the problem of housing vacancies. Guangzhou is also a hot city to which urban geographers have been paying attention. Therefore, as the research object, Guangzhou is a typical and representative example. This study thus provides a reference for identifying housing vacancies in similar cities.

Taking the Guangzhou metropolitan area as an example, we constructed an index system of impact factors in the HVR, including two explanatory variables (PA and FAR) and six control variables. Based on this, we used the spatial regression model to explore the influences of strength and direction of PA and FAR on the HVR. It is hoped that the research results will help urban planning managers to rationally develop and utilize urban land, formulate effective policies to alleviate the problem of urban housing vacancies, and relieve the pressure on urban housing.

The remainder of this paper is organized as follows. The second section introduces the research methods and data, including the research area, data sources, spatial regression model, and index system of impact factors. The research results are then presented. First, the vacant patterns of metropolitan areas are displayed, and then the impact factors PA and FAR are analyzed. Finally, the conclusion and discussion are presented, and policy implications are discussed.

2. Materials and Methods

2.1. Study Area

Guangzhou is located in the south of China, between 22′26″–23′56″ north latitude and 112′57″–114′03″ east longitude. This is the “south gate” of China. As a megacity with a prosperous economy and large population, Guangzhou’s housing problem has always been prominent. Therefore, this study selected the Guangzhou metropolitan area as the research area, which is the central area of Guangzhou, east and north of the Guangzhou Ring Expressway, west of the Guangzhou administrative boundary, and south of the Guangzhou–Gaoming Expressway. According to the reality of Guangzhou’s urban construction and development, and referring to the research results of Wang et al. on the division of Guangzhou’s functional areas [28,29], the Guangzhou metropolitan area is divided into the following four categories: old area, core area, urban district, and suburban, as shown in Figure 1. Taking the typical residential quarters newly built in 2010 as the basic research unit, there are 212 units in total, including 24 in old area, 37 in core area, 70 in urban district, and 81 in suburban.

2.2. Research Design

2.2.1. Research Idea

This study designed a research framework to analyze the influence direction and intensity of PA and FAR of residential quarters on HVR (Figure 2). First, based on the scale of residential quarters, the spatial distribution pattern and spatial autocorrelation characteristics of the residential quarters’ vacancy rate in the Guangzhou metropolitan area were analyzed, and the locations of clusters and outliers were identified. We then analyzed the distribution difference patterns of PA and FAR of the residential quarters in the Guangzhou metropolitan area. Furthermore, taking HVR as the dependent variable, the PA and FAR of residential quarters as the explanatory variables, and six other factors as the control variables, the regression model of impact factors in HVR was constructed. We comprehensively compared the ordinary least squares (OLS), spatial lag model (SLM), and spatial error model (SEM) to determine the best model to analyze the relationship between PA, FAR, and HVR. The model results include the significance, direction, and intensity of the impact factors. Finally, we present and discussed the research results.

2.2.2. Selection of Indicators

The factors impacting housing vacancies are complex. We thus constructed an index system of impact factors on HVR and selected eight independent variables. PA and FAR are two explanatory variables; the remaining six control variables are office accessibility, basic educational convenience, business service convenience, road density, waterfront accessibility, and distance from central business district (CBD). Specific evaluation methods and expected impact directions are listed in

Table 1. Definitions and evaluation methods for the variables.

Variable	Evaluation Method or Index Composition	Expected Impact Direction
Dependent variable
Housing vacancy rate (HVR)	Housing vacancy rate of residential quarters
Explanatory Variables
Plot area (PA)	The land area of the residential quarter	+
Floor area ratio (FAR)	The floor area of the residential quarter	+
Control Variables—Building and Location Characteristics
Office accessibility	POI data were generated for kernel density and positive standard deviation value examination of the kernel density distribution of office space divided into five levels: residential quarter located outside the mean (1) or residential quarter located at the mean–1 sd (3), 1–2 sd (5), 2–3 sd (7), or 3 sd (9)	−
Basic educational convenience	There are provincial key primary schools with-in the community (9 points), municipal key primary schools within the community (7 points), other communities without provincial key primary schools within 500 m from provincial key primary schools (5 points), other communities without provincial key primary schools within 500 m from provincial and municipal ordinary primary schools (3 points), and other communities without provincial key primary schools within 500 m from all primary schools (1 point).	−
Business services convenience	Performed kernel density analysis and grading using a standard deviation mean plane. Scores were assigned in the same way as for office accessibility	−
Road density	Calculate the road density of the subdistrict where the residential quarter is located.	−
Waterfront accessibility	Calculate the nearest distance (m) from the residential area to the mainstream of the PearlRiver.	−
Distance from the CBD	Distance from the Guangzhou International Finance Center (IFC) (km).	+

Note: The specific treatment methods for office accessibility and business services convenience factors can be found in Wu et al.’s research [30].

.

Independent Variable

HVR is one of the most important indicators for evaluating the health of the real estate market [1]. Given the current serious housing vacancy problem, it is necessary to explore the factors impacting HVR. Housing vacancy is affected by many factors, so we took the residential quarters in the Guangzhou metropolitan area as the research object and HVR as the dependent variable to build a model to determine its impact factors.

Explanatory Variables

The PA directly reflects the size of the residential quarters. The larger the PA, the larger its scale, the more housing supply—even greater than the demand. The imbalance between supply and demand may lead to vacant houses. It has also been found that the PA of the residential quarters changes with the distance from the city center, and the PA of the residential quarters increases from the city center to the edge area [20]; that is, the PA far from the city center is larger, which will affect residents’ choice of buying or renting houses, and then affect the HVR.

FAR affects the living comfort of residents. Generally, the higher the FAR, the lower the comfort. It can be explained that the number of houses in the community with high FAR is large, which can accommodate a large population, and the high-density population will put great pressure on public facilities (fitness places, elevators, fire exits, entertainment centers) in the community, and frequent use will aggravate the aging of the facilities. Residential quarters with high FAR will inevitably lead to high land utilization rate, high floor ratio, low floor spacing, and low greening rate, which will affect the living environment.

Thus, PA and FAR are important factors for residents to consider when buying or renting houses, and they are also factors that may affect HVR. Therefore, we consider them as explanatory variables and focus on analyzing their correlation with HVR.

Control Variables

Office, basic education, business service convenience, and road density are characteristic factors of the convenience of residential quarters. Employment, schooling, shopping, and travel are closely related to residents’ lives and are important factors in their residential choices. Generally speaking, the higher the convenience, the lower the HVR, and the higher the vacancy rate. In the neighborhood near the office, the commuting cost is lower, which is more favored by buyers or renters. Whether it is convenient for children to go to school or shop is the key factor in deciding the residence location. Lee et al. found that the existence of schools and supermarkets within 500 m of the residence can reduce vacant houses. The denser the roads, the better the public transport facilities, the higher the travel convenience, and the lower the cost. This type of community is more popular with buyers or renters [31].

With the improvement in living standards, buyers and renters are more inclined to pursue a high-quality living environment. Waterfront accessibility reflects the quality of the living environment. Urban rivers, lakes, and other water systems are important environmental resources that can improve the living environment, improve environmental quality, and make people’s lives more comfortable [32]. Therefore, waterfront accessibility can be used as a factor that affects the vacancy of houses.

Distance from the CBD is a characteristic location factor. Usually, the closer the area is to the CBD, the more public resources abound, such as employment, schooling, medical care, education, and business services, and transportation is then convenient. The closer the community is to the CBD, the more high-quality resources residents can enjoy. In contrast, the farther away from the CBD, the worse the location characteristics, the more imperfect the surrounding facilities, the longer the commute time, the relatively lower the number of people who choose to live at the location, and the more vacant houses.

2.3. Data and Data Sources

The geographic information data of residential quarters were drawn with reference to the AOI (Area of Internet) data of the Baidu map, and the acquisition time was December 2019. The data of residential quarters were from Lianjia.com (https://gz.lianjia.com/, accessed on 16 May 2021) and Cric (http://www.cricchina.com/#/home, accessed on 16 June 2018), which were connected and screened by the names of residential quarters, and there were 212 residential quarters built in 2010–2019.

The HVR data were obtained from the Baidu Street View Map and field survey. The evaluation of the vacancy rate was based on the judgment of the exterior images of daytime housing. The specific data acquisition and evaluation methods were described by Yue et al. [33]; data on PA and FAR were collected from the Fangtianxia website (https://gz.fang.com/, accessed on 27 April 2022) and Baidu (https://www.baidu.com/, accessed on 28 April 2022). Office accessibility, business services convenience, and basic educational convenience come from the POI data of the Baidu map, and the data were from August 2019; the road data of road density factor came from the Baidu map. The Pearl Revier vector data required by waterfront accessibility was drawn according to “Outline of the Guangzhou Urban Master Plan (2011–2020)”. Distance from the CBD factor data takes Guangzhou International Finance Center (IFC)–Zhujiang New Town West Tower as the center of Guangzhou city, and the data came from the Guangzhou POI data set.

2.4. Methodology

2.4.1. Spatial Autocorrelation Analysis

The global Moran’s I was employed to detect the overall spatial characteristics of vacant houses, and it was expressed as follows [34]:

$$I=\frac{{\sum }_{i=1}^n{\sum }_{j=1}^n{W}_{ij}\left(x_i-\overline{x}\right)\left(x_j-\overline{x}\right)}{S^2{\sum }_{i=1}^n{\sum }_{j=1}^n{W}_{ij}}$$

(1)

$$S^2=\frac{{\sum }_{i=1}^n{\left(x_i-\overline{x}\right)}^2}{n}$$

(2)

where I is the global spatial autocorrelation index; x_i and x_j represent the vacancy rates of the ith and jth residential quarters, respectively; and W_ij is the weight matrix of each residential quarter. When the matrix is created using a fixed distance, the weight of the residential quarter is 1, and the rest is 0 within the specified critical distance. The value range of I was [−1, 1]. When I is between [−1, 0), there is a negative correlation between residential quarters and HVR, and the closer I is to −1, the greater the negative correlation. When the value of I is (0, 1], the HVR is positively correlated, and the closer I is to 1, the greater the positive correlation. When I is 0, there is no correlation between vacant residential quarters, and they are randomly distributed. Z is the standardized statistic of I, which is used to determine the degree of HVR agglomeration. The value of Z can be expressed as:

$$Z\left(I\right)=\frac{I-E\left(I\right)}{\sqrt{Var\left(I\right)}}$$

(3)

where Var(I) represents the variance and E(I) is HVR’s mathematical expectation of HVR. When the absolute value of Z is high, it indicates that the positive (negative) spatial correlation of the HVR in the Guangzhou metropolitan area is more significant, and the absolute value of Z tends to 0, which means that the result is not significant, and the HVR is randomly distributed.

2.4.2. Ordinary Least Squares

To explore the influence of PA and FAR in the Guangzhou metropolitan area on HVR, we constructed a model of impact factors. The model uses HVR as the dependent variable, and PA and FAR as the explanatory variables, and the other six control variables are shown in Table 1. We considered three regression models—OLS, SLM, and SEM—and after a comprehensive comparison, we selected the optimal model to analyze the relationships between PA and FAR, and HVR in the Guangzhou metropolitan area.

Ordinary least squares (OLS) is a classic linear regression model that can analyze the linear relationship between HVR and eight impact factors. OLS requires independent variables to be independent of each other; that is, there is no linear relationship. It does not consider the mutual influence of the vacancy rates of adjacent residential quarters in space. The OLS model is expressed as follows [35]:

$$y_i=\beta X_i+{\epsilon }_i, \left[ {\epsilon }_i~N\left(0, {\delta }^{2}I\right)\right]$$

(4)

where i = 1, 2, …, 212, indicating the sample number of residential quarters in the Guangzhou metropolitan area, the dependent variable of y_i model—HVR of residential quarters; X_i is the s-dimensional row vector (s = 1, 2, …, 8) of the impact factors in HVR, which indicates the value of the sth impact factor in the ith residential district; β is the row vector of the s dimension, indicating the regression coefficients of the eight impact factors; ε is the random error term of the model; ε_i~N(0, δ2I) means that the error term must obey the normal distribution; and I is the identity matrix.

2.4.3. Spatial Regression Model

SLM is a spatial regression model, which indicates that the HVR of a residential quarter is not only related to its own factors but is also affected by its regional factors, that is, the spatial lag effect. The SLM can be expressed as [36,37]:

$$y_i=\rho {\displaystyle \sum }_{j=1}^n{W}_{ij}{y}_j+\beta X_i+{\epsilon }_i, \left[ {\epsilon }_i~N\left(0, {\delta }^{2}I\right)\right]$$

(5)

where ρ is the value of spatial autoregressive coefficient. W_ij stands the spatial weight matrix.

Considering the spatial correlation of random error terms, SEM shows that the vacancy rate of a residential district is not only influenced by its own factors, but is also related to the influencing factors of neighboring districts and the vacancy rate. The SEM model is expressed as [38]:

$$y_i=\lambda {\displaystyle \sum }_{j=1}^n{W}_{ij}{\phi }_j+\beta X_i+{\epsilon }_i, \left[ {\epsilon }_i~N\left(0, {\delta }^{2}I\right)\right]$$

(6)

In the equation above, φ is the spatial autocorrelation error term in the HVR influencing factor model, and λ is the spatial autocorrelation coefficient of the random error term.

To avoid the influence of dimensional differences, weaken heteroscedasticity, and make the data more stable, we standardized all variables by the logarithm. As there were many values of dependent variables that were 0 or close to 0, referring to Wooldridge’s treatment method, we added 1 to all the values of dependent variables and then log transformed them [39].

3. Results and Discussion

3.1. Spatial Difference Characteristics of Housing Vacancy

The HVR was divided into five categories, and the thresholds were set to 5%, 10%, 20%, and 50%, from small to large. The corresponding vacancy rates are lower, low, medium, high, and higher. The descriptive statistical analysis of HVR is shown in Figure 3. As indicated, there were 93 residential quarters with low HVR (<5%) and nine residential quarters with high HVR (>50%). Overall, there were 54 residential quarters with an HVR >20%, accounting for 25.47%, which shows that the HVR in the Guangzhou metropolitan area is relatively high.

To clearly show the distribution of vacant residential quarters, we used the manual method of ArcGIS10.7 to visually show the spatial pattern of HVR (Figure 4). Residential quarters with low HVR (<10%) are mainly distributed in old area, core area, and inner area of the urban district, whereas residential quarters with high HVR (>20%) are mainly suburban, in the east and south of suburban area. Overall, the HVR in the Guangzhou metropolitan area gradually increased from the central to the marginal area.

The HVR of different residential quarters may influence each other; therefore, we used spatial autocorrelation analysis to explore the distribution characteristics of HVR. The results of the global spatial autocorrelation calculation show that Moran’s I is 0.175768, the Z score is 12.2273, and the p-value is 0.00, which indicate that housing vacancies in the Guangzhou metropolitan area have global spatial autocorrelation. The results indicate that the HVR of some residential quarters may be affected by the HVR of residential quarters in neighboring areas.

3.2. Spatial Difference Pattern of PA and FAR

To visually show the spatial patterns of PA and FAR, we used the quantile method in ArcGIS 10.7 to divide the PA and FAR into four categories and visualize them, as shown in Figure 5 and Figure 6.

As can be seen in Figure 5, residential quarters with small PA are mainly distributed in the old and core area, and the residential quarters with large PA are distributed in the urban district and suburban areas, generally showing an increasing trend from the central area to the edge; there are obvious spatial differentiation characteristics. As shown in Figure 6, residential quarters with high FAR are distributed in the old and core area, whereas residential quarters with low FAR are mainly distributed in the suburban areas, showing a decreasing trend from the central area to the edge area, which is contrary to the PA pattern. Possible reasons are that the land resources in the central area of the city are scarce, the land price is high, the population density is high, and the housing demand is high. By improving the land utilization rate, government departments and developers can build more high-rise and super-high-rise buildings on the limited land and increase FAR, which could not only meet the housing demand of more people and relieve the pressure from the government, but also maximize benefits.

3.3. Influence of PA and FAR on HVR

From the above analysis, there are significant spatial differences in the patterns of the HVR, and PA and FAR. To explore the degrees and directions of influence of the latter on the former, we constructed a regression model to analyze the impact factors of HVR. Multiple linear regression requires that there is no collinearity between independent variables; therefore, before the regression analysis, we first tested the multicollinearity of the eight independent variables using SPSS. The results show in

Table 2. VIF collinearity diagnosis results.

Variable	Tolerance	VIF
Plot area (PA)	0.059	1.629
Floor area ratio (FAR)	0.288	1.518
Office accessibility	0.148	6.721
Basic educational convenience	0.600	1.650
Business services convenience	0.195	5.097
Road density	0.373	2.673
Waterfront accessibility	0.804	1.237
Distance from the CBD	0.413	2.350

that the VIF values of the eight independent variables were all <10, indicating that there was no collinearity among them and that they could be included in the regression model.

Then, we used GeoDa software for regression analysis. First, we ran the OLS model to test the optimality of the three models. The fixed distance method was used for weight construction, and the default value was used for the distance threshold. The residual error, Moran’s I (error), of OLS was 0.029, the Z score was 2.5941, and the p-value was 0.0095, which surpasses significance at the level of 0.01, indicating that the residual error of this model had a spatial autocorrelation, so we had to choose the SLM or SEM. Furthermore, by comparing the Lagrange multiplier (LM) and robust Lagrange multiplier of the SEM and SLM models, we found that the Lagrange multiplier (lag) and robust Lagrange multiplier (lag) of the SLM were significant at the level of 0.01, but the SEM model was not. Moreover, R² and log likelihood values of the SLM were larger, and the Akaike information criterion (AIC) was smaller (

Table 3. Comparison of the OLS, SLM, and SEM models.

Model	R2	AIC	Log Likelihood	LM	Robust LM
OLS	0.5186	536.154	−259.077	—	—
SLM	0.5444	528.396	−254.198	0.0047	0.0085
SEM	0.5366	531.221	−256.610	0.2070	0.4642

). After a comprehensive comparison, we selected the SLM to explore the impact factors of housing vacancies in the Guangzhou metropolitan area.

The SLM results in

Table 4. SLM model results.

Variables	Coefficient	Std. Error	t/z-Value	p
W_Y	0.4080 ***	0.1170	3.4862	0.0005
Constant	2.2980 **	1.0021	2.2933	0.0218
Plot area (PA)	0.0935 **	0.0447	2.0914	0.0365
Floor area ratio (FAR)	0.2238 **	0.1135	1.9724	0.0486
Office accessibility	−0.2833	0.1824	−1.5531	0.1204
Basic educational convenience	−0.2874 ***	0.0935	−3.0726	0.0021
Business services convenience	0.2126	0.1662	1.2793	0.2008
Road density	−0.6601 ***	0.1927	−3.4249	0.0006
Waterfront accessibility	−0.1006 *	0.0514	−1.9588	0.0501
Distance from the CBD	0.1644	0.1276	1.2884	0.1976
R2: 0.5444; AIC: 528.396; Log likelihood: −254.198

Note: ***, **, * represent the 0.01, 0.05, and 0.1 significance levels, respectively.

show that, at a significance level of 0.05, the PA and FAR of residential quarters have positive impacts on HVR; that is, when the PA and FAR increase, the HVR of residential quarters also increases, which is consistent with theoretical expectations. Comparing the two coefficient values, it can be seen that when PA and FAR increase by 1%, the impact of FAR on HVR is obviously greater than that of PA. The results show that compared with PA, FAR has a greater impact on HVR, and residents prefer low FAR and high comfort when buying or renting houses. However, PA is the embodiment of the size of residential quarters. In large-scale residential quarters, the supply of houses is greater than the demand, and an imbalance between supply and demand leads to vacancies. Moreover, as the residential quarters with larger PA are generally distributed in suburban areas far away from the city center, remote location is also one of the reasons for the high HVR.

Among the six control variables, basic educational convenience, road density, and waterfront accessibility have significant negative impacts on housing vacancies, which is in line with theoretical expectations, but the significance and degree of influence of the three factors are different. Waterfront accessibility and basic educational convenience are significant at the 0.01 level, and the absolute value comparison shows that the influence of road density on HVR is greater than that of basic educational convenience, which shows that “whether it is convenient for children to go to school” and “whether it is convenient for transportation” are the main considerations in housing choice in the Guangzhou metropolitan area. The influence of waterfront accessibility on HVR is significant at the 0.1 level, which indicates that living environment is also a key factor to consider when buying or renting a house. The other three variables, office accessibility, business services convenience, and distance from the CBD, are not significant, indicating that residents in the Guangzhou metropolitan area have not considered these factors when selecting housing.

3.4. Discussion

This study considered residential quarters in the Guangzhou metropolitan area as the research object. Compared with previous studies, this study has a smaller scale and higher precision. The spatial differentiation pattern of HVR in the Guangzhou metropolitan area is high in the central area and low in the periphery, which is consistent with the vacancy patterns of most cities in existing research, such as Detroit [40] and Yichun [41]. The PA shows an increasing trend from the central area to the edge, which is consistent with the research on the plot size of Chongqing by Zong and Ji [20]; however, the spatial pattern of FAR is opposite to that of PA, showing a decreasing trend from the central area to the marginal area, which is consistent with many current studies; that is, FAR tends to decrease from the city center [24,25]. This may be because the closer to the core area, the lower the transportation cost and the higher the land rent; thus, the FAR is also higher [26].

Eight impact factors were selected as independent variables, and an evaluation index system and a regression model were constructed. Through the comparison of three models—OLS, SLM, and SEM, SLM was determined to be the optimal model, and we then used this model for regression analysis. The results show that the influence of the spatial lag effect on the regression results should be considered when analyzing the impact factors of HVR. Compared with the traditional linear regression model, the SLM is more reasonable.

The SLM results show that PA and FAR have a significant positive impact on housing vacancies, which is in compliance with theoretical expectations. Compared with previous studies, this is an innovation of this study, and the spatial heterogeneity of its impact on housing vacancies can be further analyzed in the future. Among the other six variables, basic educational convenience, road density, and waterfront accessibility have significant negative impacts on housing vacancies, which is consistent with theoretical expectations. The results prove once again that schooling [42], travel [43], and waterfront [44] are important impact factors in residential choices. Five factors, including PA, FAR, basic educational convenience, road density, and waterfront accessibility, should be focused in future research on housing vacancies.

It is worth emphasizing that there are still many shortcomings of this study, and future research needs to be further improved. First, we note a difference in the spatial patterns of FAR and HVR demonstrated in this study—that is, high FAR but low HVR in the old area and core area. The reasons for this phenomenon emanate from two main sources. On the one hand, the sample size of residential quarters with high FAR was too small and concentrated in the old area and core area, and the residential quarters of relatively low FAR are mainly distributed in the urban district and suburban areas; and in the global regression, the vast majority of the sample’s residential quarters being distributed in the peripheral zone plays a key role in the regression results. On the other hand, the greater influence of FAR on HVR in the urban district and suburban is engendered by spatial heterogeneity. This contradiction arises due to both sample size and spatial heterogeneity, but the findings are valid for the majority of residential quarters across Guangzhou, suggesting that the higher the FAR, the higher the HVR in the urban district and suburban areas of Guangzhou. We focused on the spatial heterogeneity issue, and in the future, a geographically weighted regression model could be used to comprehensively analyze the spatial heterogeneity of the influencing factors.

Second, the results of the current study only demonstrate that PA and FAR have positive effects on the HVR; that is, the larger the PA or FAR, the higher the HVR, which is only qualitative. The current study has been unable to produce specific data to define a reasonable range of PA and FAR. The clear guidance for housing policy from this current result is that in future housing planning, relevant authorities have to restrict the development of excessively large-scale, high FAR residential quarters, and promote more small plots and developments with suitable (not too high) FAR. In future studies, this issue will be the focus of our attention, and we will conduct an in-depth investigation into the housing vacancy issue to determine the reasonable ranges of PA and FAR, and provide effective policy guidance for housing planning based on concrete data.

Furthermore, owing to limited research cases, especially regarding this research method, we have only undertaken an empirical study on Guangzhou, and the suitability (or otherwise) of employing this approach to study the housing vacancy problem in different cities remains to be tested in practice, which is a limitation of this study. In the future, we will use the same idea and method to study the housing vacancy problem in other cities to verify the feasibility and rationality of the proffered method.

In addition, this study selected only eight indicators as independent variables, but the impact factors of vacant houses are diverse and complex. In the future, we should start from multiple angles and consider more factors influencing vacant houses. Furthermore, owing to the lack of data acquisition at present, only the impact factors of HVR in the Guangzhou metropolitan area were studied; thus, data on vacant houses in more cities can be acquired in the future, and the characteristics and impact factors of housing vacancies in different cities can be analyzed.

4. Conclusions and Policy Implications

4.1. Conclusions

This study took the HVR as the dependent variable, selected eight impact factors (including two explanatory variables and six control variables) as independent variables, and constructed a spatial regression model to explore the impact factors of the housing vacancy rate of 212 residential quarters in the Guangzhou metropolitan area. The research mainly started from two factors, PA and FAR, analyzed the relationship between them and HVR, and paid attention to the degree and direction of their influence on HVR.

The results indicate that residential quarters with low vacancy rates (<10%) are mainly distributed in the old, core, and inner areas of the urban district; and the residential quarters with high vacancy rates (>20%) are mainly distributed in the east and south of the suburban areas. The results of spatial autocorrelation showed that the distribution of residential quarters in HVR has the characteristics of spatial autocorrelation; low vacant residential quarters were clustered in the old area and the core area and its edge, and high vacant residential quarters in the eastern and southern suburbs. This further indicates that the HVR in the old area and core area of the Guangzhou metropolitan area is low, whereas the HVR in the urban district and suburban areas is high. However, there were significant spatial differences in the distributions of PA and FAR in the Guangzhou metropolitan area, and their distribution patterns were opposite. Residential quarters with large PA are mainly distributed in urban district and suburban areas, and residential quarters with small PA are mainly distributed in old and core areas, showing a decreasing trend from the central area to the marginal areas. However, the residential quarters with high FAR are mainly distributed in the core and old areas, and the FAR of the urban and suburban areas is lower, generally showing that the central area has a higher FAR than the edge.

We selected the SLM model to explore the relationships between PA and FAR, and HVR, and the degree and direction of influence. The model showed that both PA and FAR have a positive impact on HVR, especially at the 0.05 level. With the increase in PA and FAR, the vacancy rate of houses correspondingly increases. By comparing the two coefficient values, it can be seen that FAR has a greater impact on HVR than PA. In addition, other factors (basic educational convenience, road density, and waterfront accessibility) also have negative effects on the HVR to various degrees, all of which are in line with theoretical expectations.

4.2. Policy Implications

The conclusions of this study have important significance for current urban planning and construction, land development and utilization, and policy formulation. The government should (1) guide developers in rational development and not carelessly build large-scale and high-FAR residential quarters in pursuit of high profits. (2) Furthermore, it should restrict the over-exploitation of the real estate market. Starting from the actual housing demand of residents, in the central area of the city, it should improve the land utilization rate, guarantee housing supply, and meet the housing demand of residents to a greater extent. In urban fringe areas, the scale of residential areas should be controlled, the over-exploitation of residential areas with large plots and high floor area ratios should be avoided, and the relationship between supply and demand should be balanced. (3) Large-scale and high-FAR residential quarters should try to build more public service facilities (e.g., kindergartens and shopping centers in service communities) to improve living convenience and attractiveness. (4) The public service level and travel convenience in suburban areas should be improved, and more people should be encouraged to live in suburban areas to reduce the vacancy rate of large-scale residential quarters and high-FAR residential quarters in suburban areas. (5) A rental market should be developed, and both renter and owners should have the same amenities. At present, the floating population accounts for a high proportion of large cities, and most of them rent houses, so we should ensure that renters and buyers enjoy the same rights and interests, such as medical care and education, and help digest the vacant housing market.