Risk of Returning to Multidimensional Poverty and Its Influencing Factors among Relocated Households for Poverty Alleviation in China

: Poverty alleviation through relocation (PAR) is a milestone project in winning the battle against extreme poverty. Its aim is to relocate poor people from inhospitable areas and lift them out of poverty. Assessing the vulnerability to multidimensional poverty (VMP) of relocated households is of great significance for consolidating the achievements of targeted poverty alleviation and preventing a large-scale return to poverty. This study constructed a multidimensional poverty index (MPI) of relocated households and analyzed relocated households’ VMP and its influencing factors using panel data of 1009 households in 16 counties across eight provinces in China. The results reveal that the mean VMP of the relocated households gradually decreased from 2016 to 2020. Moreover, the VMP of the relocated households that have moved into centralized resettlement communities is relatively low compared to those that have moved into decentralized resettlement communities. In addition, the impact of household endowment on VMP is the highest, followed by supporting policies, such as PAR, industrial development, and employment policy. Therefore, the assistance mechanism must be improved to prevent a return to poverty, enhance the sustainable development capacity of relocated households, and optimize follow-up policies for PAR.


Introduction
After eight years of continuous struggle, China comprehensively eliminated absolute poverty by the end of 2020.However, poverty alleviation has not yet been consolidated [1][2][3].Effectively preventing the return to poverty has become an important issue that needs to be solved during the rural revitalization stage, which has also received widespread attention from governments at all levels.Poverty alleviation through relocation (PAR), a milestone project in winning the battle against extreme poverty, aims to relocate poor people from inhospitable areas [4,5].During the "13th Five-Year Plan" period, China built 35,000 settlement communities and 2.66 million housing units for resettled families [6].All 9.6 million poor people who were relocated moved into new homes and were shaken off poverty, laying a solid foundation for eliminating extreme poverty [7,8].However, PAR typically involves the relocation of a large number of people, on a large scale, over a short period, with tight requirements, over a wide range of areas.Coupled with sudden shocks such as COVID-19, multiple challenges remain, such as unreasonable resettlement methods and a lack of follow-up support services [9].In addition, relocated households not only have the characteristics of general anti-poverty households, but also suffer as a result of the transformation of livelihoods, changes in living environment, and disruption of social networks, which makes the risk of returning to poverty even more severe [5,10,11].Therefore, in the stage of advancing rural revitalization across the board, consolidating the achievements of PAR has become the top priority to prevent the return of large-scale poverty.
Agriculture 2024, 14, 954 2 of 19 There are few studies on the return to poverty among relocated households.Some scholars have analyzed the reasons for their return to poverty from the perspectives of difficulties in livelihood transformation, increased living costs, and barriers to social integration [12,13].However, these are mostly qualitative analyses after the fact, which reduce the effectiveness of poverty governance.Poverty is a dynamic phenomenon, and those who have been lifted out of poverty may return to it in the future due to certain risks.Therefore, consolidating and expanding poverty alleviation involves not only taking remedial measures after people have returned to poverty but, more importantly, taking targeted measures in advance to prevent them from falling back into poverty.Poverty vulnerability introduces risk variables into poverty analysis, it measures the probability that a household or individual will fall into poverty in the future, and is an ex-ante intervention in poverty [14].It not only effectively locates groups about to fall into poverty, reduces long-term poverty, and enhances the effectiveness of policies, but also reduces the cost of pro-poor policies.Existing studies often use vulnerability to poverty to reflect the risk of farmers returning to poverty.For instance, Pan et al. [2] established an analysis framework for vulnerability to repoverty (VRP) and further explored the spatiotemporal patterns and obstacle factors of VRP in rural China from 2000 to 2017.Wang et al. [1] assessed the dynamic evolution of multidimensional return to poverty in Chinese rural households based on poverty vulnerability theory and the China family panel studies from 2010 to 2018.
With changes in people's understanding of poverty, its connotations have shifted from income poverty to multidimensional poverty [15].Sen [16] considered poverty as essentially the lack of the ability to resist various risks, to seize opportunities, and obtain economic benefits.Poverty identification should not be limited to the single dimension of income but should also consider other dimensions, such as education, health, social security, and the environment [17,18].In addition, from the perspective of China's practice, the concept of multidimensional poverty is embedded into the two no-worries (not worrying about food and clothing) and three guarantees (guarantee of compulsory education, basic healthcare, and safe housing) for the accurate identification of poor households.Therefore, with the wide acceptance of multidimensional poverty, studies on vulnerability to poverty have extended beyond a unidimensional to a multidimensional perspective [19][20][21].For example, Hernández and Zuluaga [22] applied vulnerability as an expected poverty approach and the MPI to obtain the probability of a household being poor in the future and found that the percentage of vulnerable households was greater than the percentage of poor households.Azeem et al. [23] found that most vulnerable households are accurately identified using exante measures of vulnerability to multidimensional poverty (VMP).Gallardo [24] revealed that Bayesian network classifier models offer an adequate alternative to address the policy challenge of measuring VMP.PAR is a complex systematic project that not only changes the living environment of relocated households but also their production and lifestyle, social network space, and so on.That means that, compared with the general poor households, the risk to poverty of relocated households is multidimensional.Hence, it is important to analyze the risk of relocated households returning to poverty from a multidimensional perspective, but the existing studies have not paid much attention to this point.
Our study explores the risk of relocated households returning to poverty from the perspective of VMP based on the panel data of relocated households in China.The main contributions of this study are as follows.First, this study measured the vulnerability of relocated households to poverty from multiple dimensions.Previous studies have explored the vulnerability of relocated households to poverty based on a unidimensional perspective of income or consumption [25,26].However, this does not truly reflect the risk of returning to poverty because poverty suffered by relocated households is generally multidimensional.Based on China's poverty standard of "two no worries and three guarantees" and the policy objectives of PAR, the risk of returning to poverty is not only in terms of income, but also in terms of education, health, life, and even psychology.Therefore, this paper measures the vulnerability to poverty of relocated households from the multidimensional perspectives, which includes income, education, health, quality of life, and psychology, thereby leading to a more realistic judgment of their likelihood of falling into poverty in the future.Second, this study uses large-scale panel data to measure the VMP of relocated households.Measuring vulnerability to poverty using multi-period panel data is ideal.However, existing studies mostly use cross-sectional data, which inevitably ignore the unobtainable and persistent factors affecting the poverty status of relocated households.This study uses panel data to address these shortcomings and better predict the likelihood of relocated households falling into poverty.Overall, our study more objectively reflects the multidimensional risk of returning to poverty for relocated households.It can provide important an reference for putting forward targeted measures for the central government to prevent the relocated households from returning to poverty.

Theoretical Analysis
Generally, vulnerability can be defined as a condition of helplessness in which an adverse shock may affect individuals or the household [27].Vulnerability differs from poverty because it is related to the ex-ante risk of being poor, that is, "before the veil of uncertainty has been revealed in a factual realisation of either a poverty or non-poverty state of nature" [24].Over recent decades, poverty research has embraced more comprehensive concepts.It is now widely accepted that a singular focus on income is not sufficient to indicate a household's deprivation in terms of several non-monetary aspects of wellbeing [28,29].Based on existing research on vulnerability and multidimensional poverty [30][31][32][33], we define VMP as the probability that rural families will fall into or remain in multidimensional poverty in the future.The VMP of relocated households depends not only on the external risk shock, but also on the capacity to cope with risk in terms of the government, household, and community (Figure 1).
terms of income, but also in terms of education, health, life, and even psychology.Therefore, this paper measures the vulnerability to poverty of relocated households from the multidimensional perspectives, which includes income, education, health, quality of life, and psychology, thereby leading to a more realistic judgment of their likelihood of falling into poverty in the future.Second, this study uses large-scale panel data to measure the VMP of relocated households.Measuring vulnerability to poverty using multi-period panel data is ideal.However, existing studies mostly use cross-sectional data, which inevitably ignore the unobtainable and persistent factors affecting the poverty status of relocated households.This study uses panel data to address these shortcomings and better predict the likelihood of relocated households falling into poverty.Overall, our study more objectively reflects the multidimensional risk of returning to poverty for relocated households.It can provide important an reference for putting forward targeted measures for the central government to prevent the relocated households from returning to poverty.

Theoretical Analysis
Generally, vulnerability can be defined as a condition of helplessness in which an adverse shock may affect individuals or the household [27].Vulnerability differs from poverty because it is related to the ex-ante risk of being poor, that is, "before the veil of uncertainty has been revealed in a factual realisation of either a poverty or non-poverty state of nature" [24].Over recent decades, poverty research has embraced more comprehensive concepts.It is now widely accepted that a singular focus on income is not sufficient to indicate a household's deprivation in terms of several non-monetary aspects of wellbeing [28,29].Based on existing research on vulnerability and multidimensional poverty [30][31][32][33], we define VMP as the probability that rural families will fall into or remain in multidimensional poverty in the future.The VMP of relocated households depends not only on the external risk shock, but also on the capacity to cope with risk in terms of the government, household, and community (Figure 1).Risk shocks are triggers of vulnerability to poverty, mainly including accidents, as well as natural, market, and health risks, which negatively affect the VMP of relocated households.In terms of natural risks, the occurrence of meteorological disasters such as droughts and hailstorms can affect the yield and quality of crops of relocated households.In addition, natural risk such as earthquakes and floods can have serious impacts on personal health, family property, and the subjective feelings of relocated households [34].Regarding market risk, unsold agricultural products or plummeting prices have a serious impact on the operating income of relocated households, thereby increasing their probability of falling into poverty.With regard to accidents, the occurrence of unexpected events, such as traffic accidents and deaths, not only leads to a significant reduction in the economic income of relocated households, but also results in a significant increase in their economic burden and sense of insecurity, which increases the VMP of relocated households.Concerning health risks, the presence of a seriously ill patient in a relocated Risk shocks are triggers of vulnerability to poverty, mainly including accidents, as well as natural, market, and health risks, which negatively affect the VMP of relocated households.In terms of natural risks, the occurrence of meteorological disasters such as droughts and hailstorms can affect the yield and quality of crops of relocated households.In addition, natural risk such as earthquakes and floods can have serious impacts on personal health, family property, and the subjective feelings of relocated households [34].Regarding market risk, unsold agricultural products or plummeting prices have a serious impact on the operating income of relocated households, thereby increasing their probability of falling into poverty.With regard to accidents, the occurrence of unexpected events, such as traffic accidents and deaths, not only leads to a significant reduction in the economic income of relocated households, but also results in a significant increase in their economic burden and sense of insecurity, which increases the VMP of relocated households.Concerning health risks, the presence of a seriously ill patient in a relocated household will, on the one hand, affect the employment situation of the labor force in the household, leading to a decrease in household income, while on the other hand, it will increase household consumption and become a significant burden for the household [35], which increases the probability of the household falling into multidimensional poverty.
Government support plays an important role in risk management and response for relocated households.First, the PAR policy enables relocated households to alter their own environmental and location factors, change the state of resource scarcity or strong constraints, improve their livelihood capital space, and enhance their ability to resist risks [11][12][13]36].Second, industrial development policy can reduce production costs, improve the production efficiency of crops, and raise the level of household operating income; furthermore, it can create employment opportunities, help relocated households realize nearby employment, and raise their wage income [7,15].Third, employment policy can provide more employment opportunities for relocated households and increase wages.Simultaneously, it can enhance the employment skills of relocated families, promote the realization of their self-worth, improve their social status and self-confidence, and reduce psychological poverty [37].Fourth, education policy can ensure that children of relocated households have equal opportunities to receive education and break the intergenerational transmission of poverty.It can also enhance the skill levels of families, improve their attitudes and values toward life, and achieve sustainable development [6].Fifth, medical policy can reduce the risk of poverty caused by illness among relocated households by providing basic medical security, improving the level of medical services, reducing the burden of medical expenses, strengthening chronic disease management, and promoting health knowledge education [8].
Household resource endowment refers to the resources and capabilities of an entire household, including household size, non-farm employment, cultivated land scale, social network, and credit availability, and is an important means for relocated households to cope with risky shocks.First, larger households usually have a larger labor force, allowing for greater economic income and resource sharing, which in turn increases their ability to cope with risky shocks [38].Second, non-farm employment can, on the one hand, increase the relocated households' income [7], thereby improving their living conditions, education, and healthcare, which contribute to reducing the likelihood of falling into multidimensional poverty for relocated households in the future [15].On the other hand, it can diversify the relocated households' sources of income [39], reducing the reliance on a single income and enhancing their risk resistance capacity.Additionally, non-farm employment may improve the employment skills and professional development of the workforce [40], strengthening their capacity for sustainable development and reducing the risk of falling back into poverty [37].Third, the cultivated land scale is related to the level of agricultural output and income of relocated households, and a larger arable land size can effectively disperse shocks caused by natural risk, market risks, etc., and mitigate the economic losses of households [15].Fourth, social networks represent the social capital of relocated households, which not only provide relocated households with access to information and channels for resource sharing but also provide them with economic, emotional, and psychological support [41], thereby reducing the likelihood of the family falling into poverty.Fifth, credit accessibility affects household financial capital.The greater the availability of credit, the more funds relocated households can obtain to meet production investments, daily consumption, and entrepreneurship requirements, making it easier for them to cope with various risks and challenges.
The geographical location of the community determines the infrastructure conditions and public services enjoyed by relocated households, which, in turn, affects their ability to resist external risk shocks.First, if the community is closer to the township government, the relocated household is more likely to obtain information on poverty alleviation policies, better enjoy the resources and services provided by the government [38], and better receive timely help and support from the government, improving the household's ability to cope with external shocks [6].Additionally, relocated households living near the township government may easily enter the market to sell agricultural products or purchase production materials, increasing opportunities for economic activities [15].At the same time, relocated households usually have more employment opportunities to increase their family income [40].Second, the distance between the community and the county affects sales channels, employment opportunities, and resource acquisition.If the relocated households' community is closer to the county, they can have more sales channels for agricultural products, obtain more non-farm jobs, and enjoy good education and healthcare resources, which will in turn improve the family's economic status and living conditions [6,15].Third, the distance from the community to the health center affects medical services, the cost of medical treatment, and the health conditions of relocated households.If the relocated household community is closer to the health center, they can obtain quality medical services in time, reduce the cost of transportation and time, and alleviate economic and health risks to their families [15].

Data
The data used in this study were obtained from follow-up surveys of relocated households conducted in 2017, 2019, and 2021.Samples were selected from 16 counties in the eight provinces of Gansu, Guangxi, Guizhou, Hubei, Hunan, Shaanxi, Sichuan, and Yunnan, covering the main implementation areas of the PAR program during the 13th Five-Year Plan in China.The total number of people who relocated in the above-mentioned eight provinces accounts for 82.10% of the national relocated population, which indicates the representativeness of the provinces selected in this study.Next, we used multistage sampling for sample selection.In each province, we selected two counties based on their geographical location and planned relocated population size.Subsequently, considering the planned relocation population and relocation time, three townships were selected in each county, and three villages were selected in each township to balance the relocation time between 2016 and 2019.Finally, 8-16 relocated households were randomly selected within the villages based on official rosters.We conducted a base survey in 2016 and follow-up surveys in 2017, 2019, and 2021 to obtain 1009 panel data.Face-to-face interviews with household heads and village cadres were conducted by well-trained enumerators who spoke the local language following the questions in a predetermined, structured questionnaire.The relocated household-level questionnaire covered basic information about the household, income, consumption, risk situation, community integration, etc.The resettlement communities-level questionnaire included basic information about the resettlement site, industrial development, employment assistance policies, etc.

Measurement of Multidimensional Poverty Index
We used the Alkire-Foster method to measure the multidimensional poverty index (MPI) of relocated households [21].
First, construct the deprivation matrix.Denote a n × d matrix X n,d t for the given period T, where n represents sample size, d the number of dimensions, x t ij the value of household i in dimension j for the given period t, and x t ij ≥ 0. Denote z j as the selected cut-off for dimension j and define it as the minimum achievement required for an individual to be non-deprived.We denote a deprivation matrix G t = g t ij , where g t ij = 1 if x t ij < z j , and g t ij = 0 otherwise.Second, calculate the deprivation score of each individual.Let w j be the weight for dimension j, which is assumed to remain constant in each period t, and ∑ d j=1 w j = 1.Thus, the deprivation score of each individual i for the given period t can be calculated by c t i = ∑ d j=1 w j g t ij .Let k be the "poverty cutoff," which identifies a household as multidimensionally poor, if 0 < k ≤ 1. Denote I t (k) as the function used to identify the multidimensionally poor in the given period t, where I t (k) = 1, if c t i is less than or equal to k, and I t (k) = 0 otherwise.Finally, calculate the MPI: where H t 0 represents the multidimensional poverty headcount ratio in the given period t.A t 0 is the average deprivation score, which represents the intensity of multidimensional poverty.Equation ( 1) can be used to calculate the MPI of relocated households in each period, which can reveal the changing trend of the multidimensional poverty status of relocated households.
Based on the Global Multidimensional Poverty Index 2021 issued by the United Nations, the Outline of Development-driven Poverty Alleviation in China's Rural Areas (2011-2020), the "13th Five-Year Plan" for Poverty Alleviation, and other policy documents, combined with relevant research results and my previous research conclusions [15,19], we selected income, education, health, living standard, and subjective welfare as the five dimensions of the MPI for relocated households.Table 1 details the measurement indicators, deprivation thresholds, and indicator assignments for the different dimensions of multidimensional poverty.Based on existing studies [22,42], we adopted the equal weight assignment method for the weights of each dimension and index.Although the method is somewhat subjective, it is easy to understand.In addition, there is no standardized MPI threshold value.Due to the fact that it is considered as one-third in the Human Development Report issued by the United Nations, we set the basic MPI threshold at 0.3, referring to previous studies [21,42].Note: a Life satisfaction is assigned as follows: very satisfied = 5, more satisfied = 4, average = 3, less satisfied = 2, very dissatisfied = 1.b People's evaluation of their local socio-economic status is obtained by scoring from 1 to 10; the higher the score, the higher the status.c Participation in community public affairs is assigned as follows: frequent participation = 3, occasional participation = 2, no participation = 1.MPI, multidimensional poverty index.

Measurement of Vulnerability to Multidimensional Poverty
The methods for measuring VMP include vulnerability as expected poverty (VEP), vulnerability as low expected utility (VEU), and vulnerability as uninsured exposure to risk (VER).We employed VEP to measure the VMP of the relocated households.
According to existing studies [14,22], VMP is defined as follows: where V it is the VMP of relocated household i in period t, Y i,t+1 is the MPI of relocated household i in period t + 1, and z is the set multidimensional poverty line.V it reflects the probability that a relocated household's future MPI will exceed the multidimensional poverty line.To calculate the VMP for relocated households, it is necessary to obtain the distribution function of the MPI.Since the MPI of the relocated household i in period t + 1 is unknown, assuming that it obeys the normal distribution, it can be defined as a linear function containing a series of observable factors X it , unobservable and non-time-varying influences α i at the level of the relocated household, and special factors e it that lead to different welfare levels of the households.The model is constructed as follows: where X it represents the factors affecting the MPI of relocated households, and β represents the parameter vector to be estimated.According to existing studies [15,25,26], X it includes whether to relocate, relocation time, whether to participate in industrial poverty alleviation programs, whether to participate in employment skills training, whether to enjoy the New Rural Cooperative Medical care system, whether to enjoy poverty alleviation policies through education, household size, number of non-farm employment in the household, cultivated land scale, social network, credit constraint, whether to suffer from a disaster, distance from the household's community to the township government, distance to the county, distance to the health center, and so on.Next, Equation (3) can be used to calculate the expected value Ŷi,t+1 = X it β of MPI Y i,t+1 for relocated households, and the residual term êit = Y i,t+1 − Ŷi,t+1 .It is assumed that the variance of the MPI (the square value of the residual term) is also affected by observable factors X it , that is, these factors affect the fluctuation of the MPI for relocated households.Thus, the square value of the residual term êit which can be expressed as a linear function of the observable household characteristics X it is ê2 i,t = X it γ + µ i .After obtaining the parameter γ through regression analysis, we calculated the variance σ2 = X it γ of the MPI.
Finally, by substituting the expected value and variance of Y i,t+1 into Equation ( 2), the VMP of the relocated households is given as follows: The selection of vulnerability line is important when examining the size of the VMP for relocated households.Based on existing research [15,23,27], this study selected 30% as the low-vulnerability line and 50% as the high-vulnerability line.

Shapley Value Decomposition Method for Influencing Factors of VMP
Based on the measurement of VMP for relocated households, we further examined the factors influencing VMP.The model is constructed as follows: where y i is the VMP of the relocated household i. x 1i is the policy characteristics, including whether to relocate and relocation time based on existing studies [15,25,26], whether the household enjoys poverty alleviation policies through industry, employment, healthcare, and education.x 2i is household characteristics, which include household size, non-farm employment, cultivated land scale, social network, and credit constraint.x 3i is risk characteristics, including natural risk, market risks, accidents, and health risks.x 4i is community characteristics, including the distance from the household's community to the township government, county, and health center.α 0 and α j (i = 1, . . ., 4) are the parameters to be estimated; ε i is the random error term.
To further analyze the contribution of each factor to the VMP of relocated households, we employed the Shapley Value Decomposition method based on regression analysis to examine the relative importance of each factor.According to this approach, the marginal contribution of the nth independent variable x n to the dependent variable y i is defined as the difference in the goodness-of-fit of the regression equation before and after removing the independent variable.
It should be noted that the Shapley value of the independent variable x n is the average of the calculated marginal contribution for all scenarios from which this independent variable is removed.The relative contribution rate of this independent variable is calculated by dividing the Shapley value of this independent variable by the sum of the Shapley values of all independent variables.

Descriptive Statistics
Table 2 presents the descriptive statistics of the factors affecting the VMP of relocated households.In terms of relocation policy characteristics, 93.6% of relocated households moved into resettlement housing, with an average move-in period of 30.3 months.Among the relocated households, 49.5% participated in industrial poverty alleviation projects, 38.7% participated in employment skills training, 99.1% enjoyed the New Rural Cooperative Medical care system, and 95.4% enjoyed poverty alleviation policies through education.On average, relocated households had four household members, two non-farm-employed household members, 5.4 mu of cultivated land, a social network of 17 persons, and 35.8% of relocated households had outstanding loans.Of the relocated households, 13.1% had experienced natural risk in agricultural production, 3.0% had experienced market risks in the sale of products, 2.6% had suffered accidents, and 5.4% had suffered from health risks.The average distance from the community where the relocated households were located to the nearest township government, county, and health center is 10.2 km, 45.5 km, and 1.9 km, respectively.

Vulnerability to Multidimensional Poverty of Relocated Households
Table 3 shows the VMP measurement results for relocated households from 2016 to 2020.In 2016, the mean VMP of the relocated households was of 0.7465, with 99.6% in the high-vulnerability group and only 0.4% in the low-vulnerability group, indicating that many relocated households have a high probability of falling into multidimensional poverty.In 2018, the mean VMP of the relocated households dropped to 0.2997, with only 0.99% in the high-vulnerability group and 47.77% in the low-vulnerability group, indicating that PAR significantly reduces the probability of relocated households falling into multidimensional poverty status.In 2020, the mean VMP of the relocated households decreased to 0.0519, with the proportions of both high-and low-vulnerability groups decreasing to 0. This indicates that the achievements of the PAR are relatively stable and relocated households are less likely to fall into multidimensional poverty.In general, the VMP for relocated households declined over time, and the decline was faster in 2016-2018 than in 2018-2020.This may be because, for farmers with a lower level of poverty, the effect of support measures is more obvious, and it is easier for them to be lifted out and remain out of poverty, and they are less likely to fall into multidimensional poverty.At the later stage of poverty alleviation, the remaining poor households are "the poorest population", and it is more difficult for them to be lifted out and remain out of poverty, and the decline rate of VMP slows down.Table 4 presents the VMP measurement results for relocated households before and after relocation from 2016 to 2020.In 2016, the mean VMP of relocated households that did not move into resettlement housing was of 0.7560, in which the proportions of high-and low-vulnerability groups were of 99.88% and 0.12%, respectively, and the mean VMP of relocated households that moved into resettlement housing was of 0.6958, in which the proportions of high-and low-vulnerability groups were of 98.11% and 1.89%, respectively.In 2018, the mean VMP of relocated households that did not move into resettlement housing dropped to 0.3645, and the proportions of high-and low-vulnerability groups were of 75.09% and 3.16%, respectively, whereas the mean VMP of relocated households that moved into resettlement housing dropped to 0.2743, and the proportions of high-and low-vulnerability groups were of 37.02% and 0.14%, respectively.In 2020, the mean VMP of those who did not move and those who did move into resettlement housing decreased to 0.1152 and 0.0476, respectively.Overall, the mean VMP of relocated households that did not move into resettlement housing is significantly higher than that of relocated households that did move into resettlement housing.In 2016, 2018, and 2020, the mean VMP of relocated households that did not move into resettlement housing was 0.06, 0.09, and 0.07 higher than that of relocated households that did move into resettlement housing, respectively.This finding suggests that PAR can significantly reduce the VMP of relocated households and their probability of falling into poverty status in the future, which is consistent with previous studies [25].After moving into resettlement housing, the production and living conditions around them improved significantly, the level of multidimensional poverty of relocated households decreased significantly [15], and they became less likely to fall into multidimensional poverty in the future.Table 5 shows the VMP measurements for relocated households using different resettlement methods from 2016 to 2020.In 2016, the mean VMP of relocated households under the centralized resettlement method was of 0.7454, and the high-and low-vulnerability groups accounted for 99.52% and 0.48%, respectively, whereas the mean VMP of relocated households under the decentralized resettlement method was of 0.7410, and the high-vulnerability groups accounted for 100%.In 2018, the mean VMP of relocated households under the centralized resettlement method dropped to 0.2937, and the high-and low-vulnerability groups accounted for 45.03% and 0.72%, respectively.The mean VMP of relocated households under the decentralized resettlement method dropped to 0.3030, and the high-and low-vulnerability groups accounted for 51.28% and 0.85%, respectively.In 2020, the mean VMP of households under centralized and decentralized resettlement decreased to 0.0460 and 0.0610, respectively.Overall, in 2016, the mean VMP values of relocated households under centralized and decentralized resettlement were relatively close.With time, the mean VMP of relocated households under the centralized resettlement method declined faster and was lower than the mean VMP of relocated households under the decentralized resettlement method in 2018 and 2020.This result indicates that centralized resettlement significantly reduces the VMP of relocated households, consistent with the work by Li et al. [26].This is because centralized resettlement areas are equipped with relatively complete infrastructure and public services, such as schools, hospitals, and squares, which significantly reduce the likelihood of relocated households falling into multidimensional poverty.

Factors Affecting Vulnerability to Multidimensional Poverty of Relocated Households
To explore the key reasons affecting the VMP of relocated households and provide a decision-making basis for targeted measures to reduce the risk of relocated households returning to poverty, we took VMP as the dependent variable, analyzed the factors affecting the VMP of relocated households using a linear regression model, and then used the Shapley Value Decomposition method to examine the relative importance of each factor.In addition, the multicollinearity problem of independent variables is first tested by using variance inflation factors (VIFs).The results show that the VIF of the independent variables is between 1.02 and 1.43, and the average VIF is 1.14, below the critical value of 10, which means that there is no multicollinearity for the independent variables.

Regression Results of Factors Influencing the VMP of Relocated Households
The regression results for the factors influencing the VMP of relocated households are presented in Table 6.Models (1), (2), and (3) examine the factors influencing the VMP of relocated households without considering relocation policy (whether to relocate and relocation time), considering whether to relocate, and considering relocation time, respectively.

Impact of PAR on the VMP of Relocated Households
Relocation has a significant negative effect on the VMP of relocated households.In other words, compared with relocated households that did not move into resettlement housing, the VMP of relocated households that moved into resettlement housing is lower, which is consistent with the above descriptive statistics.The main reason is that the followup policy in the resettlement area promotes a smooth transformation of the livelihoods of relocated households and significantly increases household income [38].Roads, hospitals, schools, and other infrastructure in the resettlement area improve the production and living conditions of relocated households and significantly enhance their development capacity [11].Public services such as education, medical care, and old-age care in the resettlement area improve the satisfaction, happiness, and sense of gain of relocated households and increase their subjective welfare levels [41].The improvement in income, development capacity, and subjective welfare significantly increases the ability of relocated households to cope with various risk shocks and reduces their probability of falling into multidimensional poverty in the future.
Relocation time negatively affects the VMP of relocated households, indicating that the VMP of relocated households gradually decreases with relocation time.In general, the average time for relocated households to move into resettlement housing is more than 30 months.The longer the relocation time, the more stable the poverty alleviation achievements of relocated households, and the less likely they are to fall into multidimensional poverty.With the gradual enhancement of infrastructure, continuous improvement of the public service level, and an increasingly sound community management system in the resettlement area, relocated households will gradually adapt to the new production and lifestyle, improving their livelihood capacity, satisfaction, happiness, and sense of gain [15].The ability of relocated households to cope with various risk shocks has significantly increased, further easing their risk of returning to poverty.

Impact of other Policy on the VMP of Relocated Households
The policies of industrial development and employment significantly reduced the VMP of relocated households, while education and health policies had no significant impact on their VMP.Specifically, industrial development has a significant negative impact on the VMP of relocated households because participating in industrial projects can not only solve the problems of high costs of production materials, sloppy management, outdated technology and poor sales in agricultural production, and increase households' operating income, but relocated households can also obtain corresponding dividends by using their own resources such as cultivated land, forest land, and houses, and improve the households' property income [7].An increase in household income can significantly improve a household's ability to resist risk shocks and reduce the probability of falling into multidimensional poverty.
Employment policy affects the VMP of relocated households.This finding suggests that participation in employment skills training helps to reduce the risk of relocated households returning to poverty.Stable employment is the main path for relocated households to achieve stable transition, and an important premise of stable employment is to improve employment skills and market competitiveness.By actively participating in various types of skills training organized by the government, such as agriculture, handicrafts, manufacturing, and service industries, relocated households can not only improve their comprehensive quality, achieve long-term stable employment, and increase their wage income [37].They can also stimulate endogenous dynamics and increase the household's capacity for sustainable development, thereby reducing the risk of multidimensional poverty.

Impact of Risk Characteristics on the VMP of Relocated Households
The impact of natural risk on the VMP of relocated households is more obvious, while the impact of market risk, accident, and health risk on the VMP of relocated households is not significant.Natural risk positively affects the VMP of relocated households.This is because relocated households in decentralized resettlement are still mainly engaged in agriculture, and the occurrence of natural risk seriously affects agricultural production activities and income, thus reducing household income and increasing the risk of returning to poverty.Agricultural poverty alleviation projects in resettlement areas are vulnerable to natural risk, which affects the stability of household income and increases the probability of relocated households falling into multidimensional poverty.4. Impact of Household Characteristics on the VMP of Relocated Households First, household size significantly reduces the VMP of relocated households.The main reason for this is that, the greater the number of household members, the relatively larger the number of laborers, the larger the number of income channels, and the higher the resilience to risk shocks.Second, non-farm employment has a significant negative effect on the VMP of relocated households.This is mainly because non-farm employment is the main source of income for most relocated households, and the larger the number of members in non-farm employment, the higher the income level of the household, and the lower the probability of future multidimensional poverty [15].Third, cultivated land size significantly and negatively affects the VMP of relocated households.This is because cultivated land is the main asset for decentralized resettlement households.The larger the scale of cultivated land, the higher the household operating income, and the higher the ability to resist the risk of returning to poverty.Fourth, social networks significantly reduce the VMP of relocated households.The main reason for this is that the larger the social network of relocated households, the more channels there are to obtain information, technology, and other aspects of agricultural production and non-farm employment, which is conducive to household development and thus reduces the risk of returning to poverty.

Impact of Community Characteristics on the VMP of Relocated Households
The distance from the community to the township government or county has a significant positive impact on the VMP of relocated households, indicating that, the further the distance from the community to the township government or county, the more likely that relocated households will fall into multidimensional poverty in the future.This is mainly because the long distance from relocated households to the township government or county, on one hand, is not conducive to their access to advanced agricultural production technology and comprehensive agricultural product sales information, affecting their production efficiency and production income; on the other hand, it is not conducive for them to obtain more non-farm employment information from the outside world, affecting labor transfer employment and non-farm employment income; and lastly, it is not conducive to relocated households enjoying better public services such as education, and medical and old-age care, affecting the stable development of poverty alleviation achievements, and thus increasing the likelihood of returning to poverty.

Decomposition of Factors Influencing the VMP of Relocated Households
The VMP equation for relocated households contains many independent variables.Therefore, using the Shapley Value Decomposition method directly is not effective.To solve this problem, this study referred to the work by He and Wang [43] to decompose the independent variables after proper categorization.We categorized relocation policy (whether to relocate and relocation time), industrial development, employment, healthcare, education as policy support; household size, non-farm employment, cultivated land scale, social network, and credit accessibility as household endowments; natural risk, market risk, accident, and health risk as risk shocks; and the distance from the household's community to the township government, county, and health center as community location.The decomposition results are listed in Table 7.The decomposition results show that household endowment has the greatest impact on the VMP of relocated households, with a contribution rate of 51.48%.In other words, resource endowments such as household size, non-farm employment, and cultivated land scale play important roles in reducing the VMP of relocated households.This finding suggests that household endowment is a key factor for relocated households to cope with various types of risk.To prevent relocated households from returning to poverty, it is necessary to make full use of household resource endowments, cultivate sustainable household development capacities, and firmly maintain the bottom line of preventing largescale return to poverty.The impact of policy support on the VMP of relocated households is second, with a contribution rate of 26.85%.When relocated households are unable to resist risk shocks by relying on their own resources, the government needs to take targeted assistance measures to enhance their risk resilience and reduce the probability of them falling into multidimensional poverty.The contribution of community location to the VMP of relocated households is of 16.28%.This indicates that the community level should be fully utilized to prevent relocated households from returning to poverty.By improving infrastructure and public service levels, the development capacity of relocated households should be enhanced and their probability of falling into future multidimensional poverty should be reduced.The impact of risk shock on the VMP of relocated households is the lowest, with a contribution rate of only 5.39%.To prevent relocated households from returning to poverty, it is necessary to strengthen defenses against various risks and disasters, reduce the exposure of relocated households to various risks and disasters, and reduce their probability of falling into multidimensional poverty.

Robust Check
To test the robustness of the above results, we recalculated the VMP for relocated households and performed regression analysis using the entropy weight method.Table 8 presents the results of the robustness test on the decomposition results.The results show that the order of the contribution of different factors to the VMP is consistent with the basic results, indicating the robustness of the above results.

Discussion
The results of the VMP show that, first, the mean VMP of the relocated households gradually decreased between 2016 and 2020.Second, the VMP of households that moved into resettlement communities is lower than those who did not.These findings align with the research outcomes of Ning et al. [25], who found that relocated households' poverty vulnerability decreases as the relocation time increases.Third, the VMP of relocated households under centralized resettlement communities is relatively low compared to those who under decentralized resettlement communities.This finding is consistent with the work by Li et al. [26], who found that centralized resettlement communities are equipped with relatively complete infrastructure and public services, which could effectively reduce the possibility of relocated households falling into poverty in the future.
Analysis of factors affecting VMP of relocated households shows that, first, the relocation policy, industrial development policy, employment policy, household size, non-farm employment, cultivated land scale, social network, natural risk, distance to township government, and distance to county had greater effects on the relocated households' VMP.This finding aligns with the work by Liu et al. [15], who found that the relocation policy has a significant negative effect on the relocated households' multidimensional poverty, and the longer the relocation time, the more significant the effect.Our finding is also consistent with the work by Leng et al. [7], who found that rural resettlers' income increase was mainly due to agricultural technology training, which confirms that industrial development policy could be effective in reducing the likelihood of relocated households falling into poverty in the future.In addition, Li et al. [38] found that household size affected the quantity of labor in relocated households, which in turn increases their income.This indicates that household size positively influenced the VMP of relocated households, which is in accordance with our study's outcomes.Second, among various factors, household endowments exert the most significant influence on the VMP of relocated households, followed by support policies, community location, and risk shocks.This finding aligns with the work by Hong et al. [34], who found that PAR reduced livelihood vulnerability by lowering exposure and increasing adaptive capacity.Therefore, enhancing the household endowments of relocated households and improving their development capabilities are the fundamental ways to reduce their VMP.
This study has the following marginal contributions: First, this study measured the vulnerability of relocated households to poverty in multiple dimensions, including income, education, health, quality of life, and psychology.Second, this study used a panel data of 1009 households in 16 counties across eight provinces in China to measure the VMP of relocated households.The large-scale panel data could better predict the likelihood of relocated households falling into poverty.Although this study has made some achievements, it still has some limitations.For instance, the current data in this study are only up to the year 2020, which may reduce the effectiveness of our findings in guiding the improvement of existing anti-poverty policies in the long term.In the future, we will continue to conduct follow-up research on sample relocated households to make up for the shortcomings.

Conclusions and Policy Implication
Studying the VMP and its influencing factors of relocated households can help prevent the risk of these households returning to poverty in advance and maintain the bottom line of the scale of returning to poverty in China.On the basis of constructing an MPI for relocated households, this study assessed the VMP of relocated households using the panel data of 1009 households in 16 counties across eight provinces and examined the influencing factors of VMP through the Shapley Value Decomposition method.The main conclusions are as follows.
First, the VMP of the relocated households shows a decreasing trend over time.This means that the achievements of PAR are relatively stable, and the risk of returning to poverty among relocated households is gradually declining.However, poverty is dynamic, so it is still necessary to pay attention to the relatively vulnerable relocated households in the stage of rural revitalization, in order to prevent them from falling back into multidimensional poverty.
Second, households who have moved into new houses have a relatively lower risk of returning to poverty compared to those who have not.In terms of different resettle-ment modes, households that moved into centralized resettlements have a lower level of VMP than those that have moved into decentralized resettlements.These findings also confirm that PAR has a significant effect on poverty reduction, and the effect of centralized resettlements is more obvious.
Finally, regarding to the influencing factors of the risk of returning to poverty for relocated households, household endowments such as household size and non-farm employment have the greatest impact, followed by the impact of support policies such as relocation, industrial poverty alleviation, and employment training.Meanwhile, the community location and risk shock have less impact on the risk of returning to poverty for relocated households.
This study offers three policy recommendations.First, the follow-up support policy of PAR should be improved in the stage of rural revitalization, in order to prevent relatively vulnerable relocated households from returning to poverty.On the one hand, the resettlement community should accurately select follow-up support industries based on its own resource endowment and comparative advantages, continuously extend the industrial chain, and enhance the value chain, so that relocated households can share more dividends from subsequent industrial development and improve their income levels.On the other hand, the resettlement community should provide refined employment services, promote relocated households' search for work, and fully leverage the role of welfare-to-work and public welfare position in rural revitalization, thereby expanding the scale of local and nearby employment.In addition, it is necessary to optimize community management services, promote interactive and emotional communication among relocated households, and enhance their level of social integration.
Second, it is necessary to improve the infrastructure construction and public services for relocated households that have moved into decentralized settlements, so as to reduce their MVP.There is a certain gap between decentralized and centralized resettlement communities in terms of infrastructure construction and public services, which could affect the relocated households' risk of returning to poverty.On the one hand, decentralized resettlement communities should improve their infrastructure construction, including transportation, water conservancy, electricity, and communication, in order to reduce the living costs of relocated households and increase their production potential.On the other hand, it is necessary to raise the level of public services in decentralized resettlement communities, such as education, healthcare, and elderly care, and raise the level of human capital of relocated households to enhance their ability to resist risks.
Finally, the endogenous development power of relocated households should be strengthened to resist the risk of returning to poverty.On the one hand, it is necessary to conduct educational activities related to gratitude and progress in resettlement communities, and to stimulate the morale and confidence of relocated households to change their living conditions through their own efforts.On the other hand, resettlement communities should carry out practical technical skills training in home care, e-commerce, specialty breeding, etc., to enhance the employability of relocated households and reduce their risk of returning to poverty.

Figure 1 .
Figure 1.Risk shock and response capability on VMP of relocated households.

Table 1 .
Measurement indicators, deprivation thresholds, and indicator assignment for different dimensions of MPI.

Table 2 .
Definition and descriptive statistics.

Table 3 .
Measurement results of VMP for relocated households from 2016 to 2020.

Table 4 .
Measurement results of VMP for relocated households before and after relocation from 2016 to 2020.

Table 5 .
Measurements results of VMP for relocated households under different resettlement methods from 2016 to 2020.

Table 6 .
Regression results of factors influencing VMP of relocated households.
Note: Robust standard errors are in parentheses.*** and ** represent significance at the 1% and 5% levels, respectively.VMP, vulnerability to multidimensional poverty.

Table 7 .
Decomposition results of factors affecting VMP for relocated households.

Table 8 .
Decomposition results of factors affecting VMP for relocated households using entropy weight method.