Examining Vulnerability Factors to Natural Disasters with a Spatial Autoregressive Model: The Case of South Korea

: Socially and economically marginalized people and environmentally vulnerable areas are disproportionately affected by natural hazards. Identifying populations and places vulnerable to disasters is important for disaster management, and crucial for mitigating their economic consequences. From the ﬁelds of geography, emergency management, and urban planning, several approaches and methodologies have been used to identify signiﬁcant vulnerability factors affecting the incidence and impact of disasters. This study performs a regression analysis to examine several factors associated with disaster damage in 230 local communities in South Korea, using ten vulnerability indicators for social, economic, and environmental aspects, and a single indicator for disaster characteristics. A Lagrange Multiplier diagnostic test-based spatial autoregressive model (SAM) was applied to assess the potential spatial autocorrelation in the ordinary least squares (OLS) residuals. This study compared the OLS regression results with those of a spatial autoregressive model, for both presence of spatial autocorrelation, and model performance. The conclusion of this study is that Korean communities with a higher vulnerability to disasters, as a result of their socioeconomic and environmental characteristics, are more likely to experience economic losses from natural disasters.


Introduction
Despite similar magnitudes, the impact of natural disasters is unevenly distributed among communities with different social and physical aspects [1,2]. Economically low-income countries are more vulnerable to natural disasters [3]. According to the Centre for Research on the Epidemiology of Disasters (CRED), disaster victims in developing countries accounted for 69.9% of the world's total damages from natural disasters [4].
The identification of vulnerable people and places is key to enabling local communities to assess their vulnerability to natural disasters, improve their emergency management, and mitigate losses when a natural disaster occurs [1,5,6]. In the fields of geography, urban planning, and emergency management, a vulnerability index has been developed by combining vulnerability indicators to identify areas having a high vulnerability to natural disasters [1,7,8]. Vulnerability factors related to people and communities have been examined, and their relationship with disaster damages identified, using traditional regression methods such as the ordinary least squares (OLS) regression model [1,9]. In addition to the OLS regression analysis, machine-learning approaches were applied to identify factors determining vulnerability to natural disasters, focusing on South Korea [2]. However, previous

Literature Review
Previous studies in the fields of geography, emergency management, and urban planning have defined vulnerability in several ways; one definition is the probability that damage would be incurred, in terms of both human lives and property [18]. Vulnerability has also been defined as a measure of the potential loss from a hazard [7,19], an inherent predisposition to be exposed to disaster damage [20], the extent of a community's inability to manage stress from the outside and from shocks [21,22], and a weakened adaptive capability [23]. Vulnerability has been understood as exposure and susceptibility to disasters, and the community's ability to prepare for and recover from a disaster [24,25].
The level of vulnerability is determined by the social and physical characteristics of a community [1,2,26]. Demographic patterns and economic status are factors related to social vulnerability [7,26], and geographic and intrinsically vulnerable traits lead physical vulnerability to vary across different geographic regions [26,27]. Regions with a large portion of children, elderly, less educated, and ethnic minorities tend to be more vulnerable to natural disasters, because they seem to have less physical and mental capacity to cope with them [7,26]. Economic conditions also affect the level of vulnerability. Low-income people tend to be more vulnerable to natural disasters, due to limited access to the resources needed to recover from disaster losses [26]. The poor may have difficulties in placing their dwellings in safe areas, leading them to live in hazard-prone areas [26]. Regarding the physical environment, building characteristics can also be a determinant of vulnerability to natural disasters, especially earthquakes [26]. Construction materials, building size, and building age are the main factors determining building vulnerability [1,26]. Geographical characteristics, including forests, open spaces, buffer zones, and slopes, are also determinants of vulnerability to natural disaster [26,28].
Among the various vulnerability studies to natural disasters worldwide, this study summarized social (demographic and economic aspect) and physical (natural and build environment aspect) vulnerability indicators from representative studies in the United States, South Korea, China, India, Nigeria, and Germany in Table 1 [2,[29][30][31][32][33][34][35][36]. Demographic and economic characteristics of communities effectively represent social vulnerability in each country [1,2]. From previous studies, demographic indicators can be categorized into Age, Minority, Gender, Population, Education, and Household [2,[29][30][31][32][33][34][35][36]. The ratio of elderly and younger people are representatives of Age; foreigners and ethnic minorities represent Minority; the sex ratio indicates Gender; the number of dwellings, migration, population density, and growth rate are related to Population; education level, illiteracy rate, and awareness and perception of hazards are connected to Education; and household types (rental, female-only, underground, apartment), living space, and household size comprise Household. Economic aspects are classified as Income, Social capital, and Business [2,[29][30][31][32][33][34][35][36]. The indicators poverty, unemployment rate, household income, household assets, GDP, income of rural households, savings, and distribution of wealth comprise Income; Public assistance, property tax, investments, medical services, budget, subsidies, and resources for disaster prevention, relief, and assistance represent Social capital. Finally, business types (manufacturing, agriculture, small business) and job types (farmer, fishermen) are used as indicators of Business.
Regarding physical aspects, the natural and built environments are used to demonstrate the vulnerability of communities [1,2]. From the vulnerability literature, the natural environment can be largely summarized as Geological characteristic, Meteorological characteristic, and Buffer area [2,[29][30][31][32][33][34][35][36]. Mean slope, stream length, low-lying areas, proximity to higher ground, and distance to a river are components of the Geological characteristic. Precipitation, past experiences, intensity and frequency of natural hazards, and depth of flood waters represent the Meteorological characteristic; and open space, ecosystem, degradation of the environment, soil erosion, rate of protected and organic farm areas, filter and buffer capacity, and water retaining capacity are associated with Buffer area. The last aspect, built environment, can be divided into Land use, Building characteristic, Infrastructure, and Urbanization [2,[29][30][31][32][33][34][35][36]. The ratio of urban and recreational use, industry density, residential area, and dominating type of land use are related to Land use. Building age, number of old buildings, reinforcement concrete building, number of building floors, improper building construction, and building types are indicators of the Building characteristic. Roads, bridges, dams, schools, railways, ports, emergency facilities (police, fire station, hospital, shelter), energy supplies (electricity, water), public transportation system, sanitation/waste discharge sites, and warning systems are components of Infrastructure; and impervious surfaces, urban population, and urbanization rate represent Urbanization. Based on previous worldwide vulnerability studies, this study selects 10 indicators to identify vulnerability characteristics in Korea, which are introduced in the next section.

Study Area
South Korea has a two-tier administrative structure comprising an upper and lower level. The upper-level administrative government agencies include a special city (Seoul), six metropolitan cities (Busan, Incheon, Daegu, Gwangju, Daejeon, and Ulsan), eight provinces (Gyeonggi, Gangwon, Chungbuk, Chungnam, Jeonbuk, Jeonnam, Gyeongbuk, and Gyeongnam), a self-governing special city (Sejong), and one self-governing special province (Jeju) (  ecosystem, degradation of the environment, soil erosion, rate of protected and organic farm areas, filter and buffer capacity, and water retaining capacity are associated with Buffer area. The last aspect, built environment, can be divided into Land use, Building characteristic, Infrastructure, and Urbanization [2,[29][30][31][32][33][34][35][36]. The ratio of urban and recreational use, industry density, residential area, and dominating type of land use are related to Land use. Building age, number of old buildings, reinforcement concrete building, number of building floors, improper building construction, and building types are indicators of the Building characteristic. Roads, bridges, dams, schools, railways, ports, emergency facilities (police, fire station, hospital, shelter), energy supplies (electricity, water), public transportation system, sanitation/waste discharge sites, and warning systems are components of Infrastructure; and impervious surfaces, urban population, and urbanization rate represent Urbanization. Based on previous worldwide vulnerability studies, this study selects 10 indicators to identify vulnerability characteristics in Korea, which are introduced in the next section.

Methods
As vulnerability assessments help planners prepare disaster plans [8] and improve and increase the effectiveness of emergency management [6,12,37], strong efforts have been made to identify areas that are highly vulnerability to natural disasters [1,5,7,8,12,24,[38][39][40]. The Social Vulnerability Index (SoVI) was developed based on 11 factors, using a principal component analysis to identify socially vulnerable counties in the United States [7]. Zhou et al. applied the SoVI method to China to examine the change in county-level social vulnerability in 1980, 1990, 2000, and 2010 [12]. In Romania, Armas and Gavris examined earthquake vulnerability using the SoVI, as well as the spatial multi-criteria social vulnerability index (SEVI model) based on a weighting scheme [13]. Wood et al. employed the social vulnerability index proposed by Cutter et al. [7], and analyzed vulnerability (in terms of social aspects) to Cascadia-related tsunamis in the Pacific Northwest, United States [38]. Azar and Rain used a social vulnerability index for evacuation (SVEI model) based on the SoVI, to identify regions vulnerable to hydrological hazards [39]. Emrich and Cutter identified the spatial pattern of social vulnerability to drought, floods, sea-level rise, and winds from hurricanes, using the SoVI in the southern United States [5]. Myers et al. developed a regional index of social vulnerability based on the SoVI method in the Gulf Coast region, United States [40]. Yoon examined social vulnerability in the Gulf of Mexico, United States, based on the SoVI method, and compared SoVI-based vulnerability with composite social vulnerability based on standardization [1]. Along with introducing a vulnerability index, some studies also examined the Global Moran's I to identify the existence of spatial clusters in the vulnerability index [12,13].
In addition to the vulnerability index, the identification of vulnerability factors to natural disasters is essential to effectively develop and implement mitigation strategies and disaster risk management [5,12]. In the field of geography, Uitto examined vulnerability factors in megacities with high exposures and susceptibility, focusing on social and geographical aspects [8]. The effect of wetlands on flooding was identified using an OLS regression, showing that federal permits allowing development in wetlands can increase flood losses in the United States [29]. Natural wetlands are known to play a critical role in the reduction of flood damage, controlling for biophysical and socio-economic factors [9]. In Tegucigalpa, Honduras, significant factors influencing social vulnerability were identified using an OLS regression [41]. Burton proposed an index representing social vulnerability, and identified the relationship between social vulnerability, hurricane characteristics (hurricane wind and storm surge inundation), and hurricane impact in the Gulf Coast, United States, using multiple linear regressions [42].
Although OLS regression is widely used in vulnerability studies, this method does not consider the existence of spatial autocorrelation in the residuals of the regression model. To control for spatial autocorrelation, Yoon included an adjacent property damage variable to assess the relationship between vulnerability factors and disaster damage [1]. A geographically weighted regression (GWR) was applied to find the spatially-varying relationship between water quality and land use, showing the decrease of spatial autocorrelation in the model residuals [11]. A spatial autoregressive model (SAM) has been used in disaster-related studies, including environmental justice, flood mitigation, and social vulnerability, to account for the spatial autocorrelation in the model residuals or independent variables [14,15,17,40]. Myers et al. identified the relationship between social vulnerability and migration measures using a spatial lag model (SLM) after two hurricanes-Katrina and Rita [40].
This study aims to identify the relationship between vulnerability factors related to social, economic, and environmental aspects, and economic losses from natural disaster. Disaster damage and vulnerability factors are introduced in the following two subsections. This study performed an OLS-based linear regression to examine vulnerability factors influencing the level of disaster damage. Based on the regression results, several assumptions of the OLS regression were checked to examine whether the model violates the assumptions of an OLS regression, such as the absence of multicollinearity among the variables, normality of the errors, and variance homoscedasticity [16,43,44]. The Global Moran's I statistic was used to identify the existence of spatial autocorrelation in the OLS regression model, and a local indicators of spatial association (LISA) analysis was conducted to display significant clusters in the spatially distributed vulnerability index and disaster damage. This study used the SAM to reduce the level of spatial autocorrelation, using the open source program GeoDa (available at https://geodacenter.asu.edu/). An LM diagnostic test was performed to choose the best autoregressive model between the SLM and SEM. The SLM assumes that the dependent variable of a region is related to that of neighboring regions, whereas the SEM supposes that the residuals of a region are influenced by the residuals of neighbors [45]. This study made a comparison between the results of the OLS regression model and SAM, through the value of the log-likelihood, Schwarz criterion (SC), and Akaike information criterion (AIC). The SAM showed improvements over the OLS model, as the log-likelihood increased, and the value of AIC and SC decreased [16,17]. The procedure of examining factors determining vulnerability to a natural disaster with SAM is indicated in Figure 2.
Sustainability 2018, 10, x FOR PEER REVIEW 6 of 13 dependent variable of a region is related to that of neighboring regions, whereas the SEM supposes that the residuals of a region are influenced by the residuals of neighbors [45]. This study made a comparison between the results of the OLS regression model and SAM, through the value of the loglikelihood, Schwarz criterion (SC), and Akaike information criterion (AIC). The SAM showed improvements over the OLS model, as the log-likelihood increased, and the value of AIC and SC decreased [16,17]. The procedure of examining factors determining vulnerability to a natural disaster with SAM is indicated in Figure 2.

Dependent Variable
Frequently occurring natural disasters in South Korea include typhoons, heavy rains, heavy snow, and snowfall. The dependent variable for this study is the total normalized economic damage per capita from a natural disaster over 10 years (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010) in 230 local communities. This study collected data on historical economic losses caused by a natural disaster from the National Disaster Information Center website (available at http://www.safekorea.go.kr), operated by the Ministry of the Interior and Safety in Korea. Economic damages from a natural disaster include losses from building, shipments, farmland, public facilities, and individual facilities.
Over the 10 years, the top five communities that suffered the most damage from natural disasters were in the Gangwon province, incurring over $12,000 USD per capita (Figure 3). In the same period, there was less disaster damage in Seoul special city, Gyeonggi province, and the metropolitan city of Incheon, where 24 million people (about half of the population of Korea, as of 2010) live ( Figure 3). Damages were normalized for inflation rates (the inflation rate in 2010 was 1) and the population in each community. The dependent variable was log-transformed to obtain a normal distribution.

Dependent Variable
Frequently occurring natural disasters in South Korea include typhoons, heavy rains, heavy snow, and snowfall. The dependent variable for this study is the total normalized economic damage per capita from a natural disaster over 10 years (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010) in 230 local communities. This study collected data on historical economic losses caused by a natural disaster from the National Disaster Information Center website (available at http://www.safekorea.go.kr), operated by the Ministry of the Interior and Safety in Korea. Economic damages from a natural disaster include losses from building, shipments, farmland, public facilities, and individual facilities.
Over the 10 years, the top five communities that suffered the most damage from natural disasters were in the Gangwon province, incurring over $12,000 USD per capita (Figure 3). In the same period, there was less disaster damage in Seoul special city, Gyeonggi province, and the metropolitan city of Incheon, where 24 million people (about half of the population of Korea, as of 2010) live ( Figure 3). Damages were normalized for inflation rates (the inflation rate in 2010 was 1) and the population in each community. The dependent variable was log-transformed to obtain a normal distribution.
Sustainability 2018, 10, x FOR PEER REVIEW 6 of 13 dependent variable of a region is related to that of neighboring regions, whereas the SEM supposes that the residuals of a region are influenced by the residuals of neighbors [45]. This study made a comparison between the results of the OLS regression model and SAM, through the value of the loglikelihood, Schwarz criterion (SC), and Akaike information criterion (AIC). The SAM showed improvements over the OLS model, as the log-likelihood increased, and the value of AIC and SC decreased [16,17]. The procedure of examining factors determining vulnerability to a natural disaster with SAM is indicated in Figure 2.

Dependent Variable
Frequently occurring natural disasters in South Korea include typhoons, heavy rains, heavy snow, and snowfall. The dependent variable for this study is the total normalized economic damage per capita from a natural disaster over 10 years (2001-2010) in 230 local communities. This study collected data on historical economic losses caused by a natural disaster from the National Disaster Information Center website (available at http://www.safekorea.go.kr), operated by the Ministry of the Interior and Safety in Korea. Economic damages from a natural disaster include losses from building, shipments, farmland, public facilities, and individual facilities.
Over the 10 years, the top five communities that suffered the most damage from natural disasters were in the Gangwon province, incurring over $12,000 USD per capita (Figure 3). In the same period, there was less disaster damage in Seoul special city, Gyeonggi province, and the metropolitan city of Incheon, where 24 million people (about half of the population of Korea, as of 2010) live ( Figure 3). Damages were normalized for inflation rates (the inflation rate in 2010 was 1) and the population in each community. The dependent variable was log-transformed to obtain a normal distribution.

Independent Variables
This study selects 10 vulnerability indicators representing the social, economic, and environmental characteristics of each community, based on previous vulnerability studies [2,[29][30][31][32][33][34][35][36] (Table 2). These indicators are standardized using z-score transformations to make all indicators equivalent units of measurement. More detailed descriptions of the selected vulnerability indicators, expected sign for disaster damage, and data sources are shown in Table 2. This study selects two vulnerability indicators to estimate the social aspects of vulnerability. Less-educated people tend to be more vulnerable to natural disasters due to a lack of the knowledge necessary for responding to disasters, which limits their capacity to understand warning information and cope with, and recover from, natural disasters [1,2,[5][6][7]12,13,[34][35][36]46,47]. Education level is a significant factor in determining income levels, health problems, quality of life, and employment status [12,47]. The less-educated population was calculated as the percentage of the population without elementary school education. In addition to educational levels, this study identifies minorities, measured as the percentage of foreigners in Korea, as a vulnerable group. In the United States, minorities, especially non-white people, are considered vulnerable to natural disasters because they may have different languages and cultures, experience difficulties in receiving disaster recovery funds, and live in hazardous areas [1,5,7,30].
Two indicators, property tax and manufacturer establishments, are used to represent the economic aspects of community vulnerability [2,31]. These indicators are selected to represent a community's economic vulnerability as proxies. Communities with higher poverty have more difficulties in storing emergency supplies, purchasing flood insurance, and recovering from disaster damage, which makes them more vulnerable to the impact of a disaster [30,48]. The amount of property tax per capita was used as the tax indicator, and the density of manufacturing establishments per square kilometer was used as the manufacturer indicator.
This study measures four natural environmental indicators related to the degree of disaster damage. The first, precipitation, is measured as the average precipitation from 2001 to 2010, as recorded by 419 stations in the Automatic Weather Station (AWS) operated by the Korea Meteorological Administration (KMA). A simple inverse distance weighting (IDW) method is used to interpolate precipitation, as measured by the 419 stations, to the 230 local communities. The second indicator is frequency, measured as the annual frequency of natural disasters (typhoons, heavy rain, heavy snow, and snowfall), provided by the Korean Ministry of the Interior and Safety (MOIS). Not only precipitation, but also the frequency of natural disasters, are significant natural environment aspects affecting the degree of disaster damage [2,29,34,[48][49][50]. The third indicator was the extent of open space, meaning the green tract of land as a percentage of total land. A green tract of land is a space consisting of trees and other greens, which is called a buffer zone [2,28,36]. Providing a buffer zone helps reduce vulnerability to future consequences of climate impact [48], and prevents surface runoff [28]. The destruction of forest resources increases vulnerability and causes more runoff and flooding [26]. As for the geographic factor related to the level of vulnerability, this study selected the average slope in 230 communities. As a factor related to vulnerability, the location of a community is known to be a determinant of disaster damage [2,26,29,35].
Two vulnerability indicators are used to represent the built environments related to disaster damage. The first, old buildings, measured by the ratio of housing units built in 1959 or earlier, is an important vulnerability indicator related to disaster damage, as old building codes are outdated [1,2,28,33]. The second indicator is housing density, measured as the number of homes per square kilometer. Compact development based on dense housing can maximize open spaces, and is known to decrease vulnerability to natural hazards [51].

Results
This study checked the assumptions of the OLS linear regression. The existence of multicollinearity among independent variables was examined through the value of the multicollinearity condition. As a multicollinearity problem occurs when the multicollinearity condition number is over 30 [16], the OLS regression results showed no multicollinearity among vulnerability indicators (Table 3). Two assumptions, the normality of errors and variance homoscedasticity, were also checked using the Jarque-Bera test and Breusch-Pagan or Koenker-Bassett index, respectively, and showed the OLS linear regression model had no violations. The final test is conducted to check the existence of spatial autocorrelation in the regression residuals as one assumption of the OLS regression. As a frequently used indicator for the presence of spatial autocorrelation, the Global Moran's I was applied to assess the spatial distribution of the model residuals in the 230 communities. The value of the Global Moran's I was calculated using a contiguity-based approach to define the neighbors of a spatial unit. This study used the first-order "queen-based" contiguity approach, assuming that all adjacent regions are considered neighbors. After the consideration of the scope of such neighbors, this study identified the presence of spatial autocorrelation, showing that the Global Moran's I in each model is 0.205, with a 99% statistical significance level (Table 3). This result indicated that the OLS results are likely to be biased because there is evidence of spatial autocorrelation.
In addition to the Global Moran's I test, this study conducted a LISA analysis to identify the degree of spatial autocorrelation in the model residuals in the 230 communities ( Figure 4). The results showed that a spatial cluster exists, with some regions (shown in red in the figure) indicating a hot spot, and others (in dark blue) indicating cold spots for disaster damage.
This study employed a SAM to consider the spatial autocorrelation in the residuals of the OLS regression model. The LM diagnostic test was used to identify a suitable model, showing the best fit between the SEM and SLM. The test indicated that the standard versions of the LM-Lag and LM-Error are statistically significant, whereas only a robust version of the LM-Error is statistically significant (p < 0.01) ( Table 3). Through the LM diagnostic test, the SEM was selected as the best model to account for the spatial autocorrelation in the OLS regression residuals. This study performed two different spatial error models, depending on the neighbor selection: queen-based and rook-based contiguity. The two models solved the problem of spatial autocorrelation, showing that the value of Moran's I was statistically insignificant (p > 0.05) and close to zero, whereas the spatial error parameters were statistically significant (p < 0.01) ( Table 3). The significant vulnerability indicators in the two spatial error models were the same as the OLS linear regression model, whereas the performance of spatial error models was improved. This study showed an increase in the log-likelihood, and decrease in the Akaike information criterion (AIC) and Schwarz criterion (SC), indicating a robust improvement with respect to the OLS linear regression (Table 3). This study analyzed the relationship between 10 vulnerability indicators regarding social, economic, and environmental features and disaster damage using an OLS regression model and spatial error models ( Table 3). The results from the OLS regression model showed that the coefficient on less-educated people is positively related to disaster damage. Minority is also associated with disaster damage, with a positive coefficient (B = 0.072, p < 0.05). Both social aspects are positively related to disaster damage, suggesting that socially vulnerable people are more likely to suffer from disaster damage than others. Economic aspects indicated results in line with previous studies [12,52], showing that poor communities are likely to experience more severe disaster damage. Although tax was not related to disaster damage (B = −0.001, p > 0.05), communities with many manufacturing establishments showed a negative correlation with the extent of disaster damage (B = −0.137, p < 0.01). Regarding the natural environment, precipitation was positively related to disaster damage (B = 0.098, p < 0.01), in line with previous results [49]. The frequency of natural disasters was also positively and significantly associated with the extent of disaster damage (B = 0.104, p < 0.01). The regression results showed that disaster damage is more severe in communities where annual precipitation is high and natural disasters happen frequently. As a buffer zone, open space played a significant role in diminishing disaster damage, showing a negative correlation with disaster damage in the OLS regression model (B = −0.201, p < 0.01). Communities located in steep slopes were more likely to experience damage from natural disasters (B = 0.325, p < 0.01). The findings on built environments showed that communities with a high ratio of buildings older than 60 years showed a positive relationship with disaster damage, but this coefficient was not statistically significant (B = 0.05, p > 0.05). Housing density, however, showed a statistically significant negative relationship with disaster damage (B = −0.254, p < 0.01), meaning that compact communities experience less disaster damage than sprawling communities. In addition to the Global Moran's I test, this study conducted a LISA analysis to identify the degree of spatial autocorrelation in the model residuals in the 230 communities ( Figure 4). The results showed that a spatial cluster exists, with some regions (shown in red in the figure) indicating a hot spot, and others (in dark blue) indicating cold spots for disaster damage. This study employed a SAM to consider the spatial autocorrelation in the residuals of the OLS regression model. The LM diagnostic test was used to identify a suitable model, showing the best fit between the SEM and SLM. The test indicated that the standard versions of the LM-Lag and LM-Error are statistically significant, whereas only a robust version of the LM-Error is statistically significant (p < 0.01) ( Table 3). Through the LM diagnostic test, the SEM was selected as the best model to account for the spatial autocorrelation in the OLS regression residuals. This study performed two different spatial error models, depending on the neighbor selection: queen-based and rook-based contiguity. The two models solved the problem of spatial autocorrelation, showing that the value of Moran's I was statistically insignificant (p > 0.05) and close to zero, whereas the spatial error parameters were statistically significant (p < 0.01) ( Table 3). The significant vulnerability indicators in In summary, the more communities there are with many less-educated people and minorities, high precipitation, fewer manufacturers, fewer open spaces, lower densities, and high slope, the more those regions are exposed to economic losses from a natural disaster.

Discussion and Conclusions
The aim of this study is to analyze the relationship between disaster damage and several vulnerability indicators related to social, economic, and environmental features to pinpoint the factors of uneven distribution of natural disaster impact among communities. The OLS regression model was employed to examine the effect of 10 vulnerability indicators on disaster damage. Several tests were performed to confirm the assumptions of the OLS regression model, and recognized the existence of spatial autocorrelation in the OLS residuals. The LISA analysis showed a space cluster in the model residuals, supporting the presence of spatial autocorrelation. Some regions (east of Gangwon province, parts of Gyeongnam province, and parts of Jeonbuk province) indicated a hot spot, whereas other areas (parts of Gyeonggi and Jeonnam provinces) showed cold spots for disaster damage (Figure 4). The regions located in the same cluster are spatially autocorrelated, having similar features in terms of economic losses. For the reduction of spatial autocorrelation and better model performance, the SAM was employed, and the SEM was identified as the most suitable model, based on an LM diagnostic test. The results of this study are in line with earlier studies in other fields [15][16][17], and confirm that the SAM can be used to identify statistically significant relationships among variables, using the spatially autocorrelated model residuals. Through a spatial error model, this study showed that vulnerable people (less-educated people, minorities) and places (high precipitation, fewer manufacturers, fewer open spaces, lower densities, and high slope) are more likely to experience disaster damage.
The findings of this study have value for policymakers who are developing vulnerability reduction policies for populations and places considered at risk. First, identifying unique vulnerability factors is important in predicting where disaster losses may occur, recognizing the relationship between vulnerability factors and disaster damage. Second, providing education to less-educated people and minorities is key for improving disaster awareness. More education helps vulnerable people access and act on hazard information, which helps them to prepare for, respond to, and recover from natural disasters [12,47]. Third, activities related to risk reduction are necessary to reduce the degree of vulnerability. Risk itself can be removed by understanding the types of hazards in a community, protecting the environment, and preventing development in hazardous areas. Protecting the environment could reduce disaster risk by enlarging the open spaces which function as buffer zones. If development is necessary, compact development in a safe area can be a way not only to preserve open spaces, but also accommodate residents in a safe area. Some significant limitations of this study need to be considered. First, this study has a limitation stemming from its use of indicator-based approaches for the identification of vulnerability factors. There is room for debate on what kinds of indicators should be used [47], and for the study's dependence on statistical analysis, such as the OLS linear regression [46]. Among the various types of candidate indicators, this study selected 10 vulnerability indicators, not only representing social, economic, and environmental aspects, but also satisfying the multicollinearity assumption. Second, this study is limited to finding the local parameters of vulnerability indicators, although both the OLS linear regression and SAM can examine global parameters of independent variables. Although this study found that socially vulnerable people are likely to incur disaster damage, this does not imply that minorities and those who are less educated in Korea are equally vulnerable to a natural disaster [46]. Further studies are needed to examine local vulnerability indicators for local-based disaster management. A GWR model could be an alternative tool for identifying locally vulnerable people and places associated with disaster damage.
Author Contributions: Both authors contributed to the idea of the paper. S.J. analyzed the data, interpreted the results, and drafted the article. D.K.Y. provided core advice and extensive revisions to the manuscript.