Research on the Intergenerational Transmission of Poverty in Rural China Based on Sustainable Livelihood Analysis Framework: A Case Study of Six Poverty-Stricken Counties

China’s complicated and diverse poverty problems gradually emerged as poverty alleviation efforts deepened and rural urbanization progressed. Among these problems, the intergenerational transmission of poverty (ITP) is the most prominent and is an entrenched issue in rural China. This study selects six typical poverty-stricken counties in the eastern, central, and western regions of China on the basis of geography and uses the transformation matrix method and a regression model to analyze the regional differentiation characteristics of ITP. We further explore its impact mechanisms based on a sustainable livelihood analysis framework with the following results: (1) ITP in rural China exhibits the phenomenon of income-stratified transmission, and the groups at both ends of the low-income spectrum are more prone to having ITP; (2) ITP and the intergenerational mobility of income for different income levels have different spatial distribution characteristics, with these intergenerational relationships exhibiting a reverse variation trend in the eastern region, while exhibiting a codirectional variation trend in the central and western regions; (3) there are differences in the subsistence livelihood capital, which affect ITP in different regions. Financial capital has a significant impact on ITP across all of China. Natural capital has a significant impact on the eastern region, and physical capital plays a significant role in the central region, while the western region is greatly affected by both human and physical capital. In view of the differences in the influence of livelihood capital on ITP in different regions, China should formulate policies to accurately address ITP in order to narrow regional differences and accelerate the comprehensive construction of a financially affluent society.


Introduction
Throughout the history of human development, poverty is consistently one of the problems plaguing all countries of the world.According to the United Nations Millennium Development Goals Report 2015, the total number of people living in extreme poverty around the world decreased by 1.064 billion from 1990 to 2015, with China's contribution exceeding 70% of this total [1].Since China's economic reform and opening, the Chinese government accomplished remarkable achievements in anti-poverty.The number of rural poor people dropped from 770 million in 1978 to 43. 35 million in 2016 (the new poverty line standard: 2300 RMB per person per year basis as of 2010), and the incidence of poverty dropped from 97.5% to 4.5% [2,3], making China a model for promotion all over the world.However, China remains a developing country.It still has the characteristics of a broad poverty area, a deep poverty degree, and a complex overall poverty problem.The reduction of the poverty population does not indicate that the poverty problem is completely solved.The most intractable problem is that poverty-stricken families in rural China often descend into poverty for generations.Poverty monitoring data indicate that the poverty of some rural households entered a vicious circle, with intergenerational transmission of poverty (ITP) becoming increasingly apparent [4,5].The Eighteenth National Congress of the Communist Party of China clearly put forward the grand goal of building a financially affluent society in a comprehensive way by 2020, and the report of the Nineteenth National Congress once again proclaimed that the period from now to 2020 is the decisive time for building a financially affluent society in a comprehensive way.They stated that China should "resolutely win the battle against poverty" and suggested new requirements for solving the problem of rural poverty.To advance new urbanization, as well as promote urban-rural integration and rural redevelopment and construction, we should pay special attention to the current situation of rural construction and the poor populations in rural areas [6,7].Solving the problem of ITP is the key to achieving this goal.
Sen believes that the real meaning of poverty is poor people's inability to generate income and opportunities, meaning that poor people lack the ability to access and enjoy a normal life [8].ITP is a "solidification" phenomenon of poverty and represents a more entrenched problem.Research into this phenomenon began in the early 1960s.When American sociologists studied the problem of the poor, they first suggested the concept of "ITP".This refers to poverty, as well as conditions and related factors leading to poverty, being passed down from parents to children within the family, causing children to repeat their parents' poverty in adulthood and to pass this poverty on to future generations, in a malignant genetic chain [9,10].Some scholars believe that ITP has broad and narrow meanings.In a broad sense, it refers to the idea that related factors that lead to poverty are transmitted from the previous generation to the offspring in the family, community, geographical area (including the country), and the hierarchy, such that the descendants repeat the poverty situation of the previous generation in adulthood.In a narrow sense, it puts more emphasis on the related factors that are passed on from the previous generation to the offspring at the family level, which result in the next generations repeating the poverty situation of the previous generation in adulthood [11].
The early literature on ITP generally focused on developed countries [12][13][14][15].These researchers believed that children from poor families had relatively low levels of education, employment, and health compared to those from wealthy families.The income level of parents also determined the level of human capital of children to a certain extent, which then affected their employment opportunities and improved the probability of falling into poverty [16][17][18].Over the past decade, the research perspective gradually shifted from developed to developing countries [19,20].Drawing lessons from developed countries, more attention was paid to children in low-income families in developing countries.Based on the theory that the employment, income, marital status, and religious beliefs of children's parents at the time of their birth will have an impact on whether they will fall into poverty as adults [21][22][23], improving children's nutrition, health [24], and education [25,26] are considered important ways to reduce poverty and inequality.Some researchers further pointed out that, before offspring are born, poor pregnant mothers can help their children get a good start in life through prenatal care, thus reducing ITP.Mothers also play an important role in the intergenerational mobility of income among children [27][28][29].In the examination of ITP among adults, it is believed that decisions of mothers, such as leaving school, working, and having children, play an important role in the impoverishment of their children [30,31].At the same time, these investigations were concerned about the destructive impacts of regional conflicts and domestic violence on children's poverty [32,33].It is worth mentioning that China's research on ITP pays more attention to the transmission of the economic level.It indicates that the income of rural residents in China exhibits weak intergenerational mobility and strong inheritance, and that the economic situation of offspring is vulnerable to economic disadvantages of their parents [34].The offspring of poor families are affected by their educational level, school opportunities, and employment status.They also have obvious disadvantages in terms of medical insurance and other financial and social factors.Family income exhibits strong intergenerational transmission [35,36].Through research on ethnic minority areas and underdeveloped areas in northwest China [37][38][39], it was found that ITP is very common in rural China, especially at the relative poverty level; it is more prominent, tends to increase, and displays biphasic, long-term, universality, concealment, and complexity characteristics within a district [34,40].
In terms of research methods, some scholars primarily studied income mobility by constructing an income elasticity coefficient [41].However, due to the differences in observations data and processing methods, there are often a number of data errors, leading to inconsistent results [42][43][44].These researchers did not clearly delineate which income class is involved in ITP or how to focus on solving the problem of intergenerational transmission for this class.In addition to using panel data, this research employed micro-data such as family history and life history to explore how the allocation of key assets such as land, healthcare, nutrition, and education among family members affects ITP [45][46][47].
In terms of the causes and mechanisms of ITP, the mainstream theories around the world include the cultural poverty hypothesis, the policy poverty hypothesis (such as welfare dependence), the economic structure poverty hypothesis (such as the labor market), the intergenerational genetic hypothesis, the educational poverty hypothesis, the social exclusion hypothesis, the capacity poverty hypothesis, and so on (such as Thomas [48], Herbert [49], Camp [50], and Sen [51]).The International Center for Persistent Poverty Research points out that the main factors influencing ITP include population and health, social network, education, and living environment [52].Some scholars tended to focus on economic [53], sociological [54], and physiological [55] characteristics, in particular the significant impact of human and social capital, thus paying more attention to individual, parental, and social system factors, while ignoring the systematic investigation of family comprehensive factors.Some scholars found that the low level of education of the household and the family labor ability are the most important factors [56][57][58].At the same time, family assets have significant impact on the long-term poverty situation [59].
In summary, this study argues that ITP mainly refers to the transmission and reproduction of poverty, as well as the factors leading to poverty between two generations.It also asserts that the intergenerational transmission of income is the most direct and fundamental manifestation of ITP.Previous studies paid less attention to ITP data from developing countries.An understanding of this transmission in regions with obvious economic disparities needs to be obtained, and the mechanism of ITP in different regions needs to be clearly explained.In addition, the vulnerability-sustainable livelihood analysis framework is employed in this study to measure absolute poverty [60,61].This is followed by a gradual exploration of the relationship between the sustainable livelihood status of poor farmers and poverty-causing factors, as well as poverty alleviation strategies [62][63][64][65][66].If all five types of livelihood capital (human, natural, physical, financial, and social) are introduced into the mechanism analysis of poverty transmission, it will more comprehensively analyze the influence of familial factors within the same region on ITP.Therefore, this study uses east China (Songxi and Xiapu County of Fujian Province), central China (Pingyu and Xin County of Henan Province), and western China (Gulang and Weiyuan County of Gansu Province) as examples, and, via the participatory rural appraisal (PRA), method obtains 879 questionnaires in order to analyze the regional differentiation characteristics of ITP in China.Based on the sustainable livelihood analysis framework, this study analyzes the impact mechanisms of ITP in China using multiple logistic models and then suggests policy recommendations designed to accurately block ITP.

Survey of the Study Area
China covers a vast domain, and the poverty situation varies significantly from one region to another.In 2015, the respective numbers of rural poor in the eastern, central, and western regions of China were 6.35 million, 20.07 million, and 29.14 million, accounting for 11.7%, 36%, and 52.3% of the poverty-stricken population, with associated poverty incidence levels of 1.8%, 6.2%, and 10% [67].Gansu Province in western China is one of the most backward provinces in terms of economic and social development, and it has the highest proportion of rural poor, as well as the deepest degree of poverty in all of China.There are still 3.25 million rural poor in Gansu Province and a total of 43 of its counties are key counties in the national poverty alleviation and development effort [67].Gulang and Weiyuan Counties are located in Longzhong and Longnan, respectively (Figure 1).Their characteristics include a poor natural environment, weak infrastructure, large numbers of poor inhabitants, and diverse poverty-inducing factors.Both are dry farming counties in mountainous areas, mainly in the primary industry.These areas are faced with the predicament of a single industrial structure, poor self-development ability, an information blockade, and difficulties alleviating poverty.Henan Province in central China, with a topography consisting of mostly plains, has the country's largest agricultural population and is one of the provinces with the largest rural poverty population, as much as 4.63 million [67].It includes 31 key counties in the poverty alleviation and development effort at the national level.Among these, Pingyu County is a traditional plain agricultural county, and Xin County is a typical forestry county in the old revolutionary area located in the hinterlands of the Dabie Mountains (Figure 1).Both counties are primarily involved in crop farming.Due to the low level of agricultural production, inadequate production input, and poor ability to resist natural disasters [68], as well as the serious constraint of a smallholder ideology lacking any sort of market economy concept or competitive consciousness, poverty and poverty recurrence are prominent.Fujian Province in eastern China is a typical coastal province with both mountains and seas, but its regional development is unevenly distributed.The coastal areas in southeast Fujian are relatively developed, while the mountains in northwest and eastern Fujian are relatively backward, with correspondingly prominent poverty problems and serious non-income poverty [69].At present, Fujian still includes 23 provincial key poverty alleviation development counties [70].Among them, Songxi and Xiapu Counties are located in the concentrated areas of poverty-stricken counties in Fujian Province.The former is a traditional agricultural county in the mountainous areas of northern Fujian Province, while the latter is a typical coastal county with the longest coastline and most islands in the country (Figure 1).These two counties are characterized by a large number of poor inhabitants who returned to poverty due to illness, or to more severe poverty as a result of disasters [71].
Fujian, Henan, and Gansu Province are the typical representatives of the poverty-stricken areas in the eastern, central, and western regions, respectively.The six typical counties mentioned above have the basic characteristics of rural poverty in the eastern, central, and western regions, and they can adequately reflect the current situation of rural poverty in their respective regions and have certain representativeness (Figure 2).

Data Sources
In July, August, and December 2016, three periods of field investigation and household questionnaire surveys were conducted over a total of 40 days in Fujian Province, Henan Province, and Gansu Province, respectively.Firstly, the natural and social statistics of each county were collected from data found on the internet, and then cadres in the sample villages of each county were contacted to lead investigative groups into individual households.The participatory rural evaluation method was used to conduct pre-surveys and questionnaire surveys.The investigators were professionally trained.Each investigator was assigned a local guide to provide directions and translate the language.All questionnaires were completed in person.Due to the large number of questions, each questionnaire took more than 30 min to fill out, and some families were visited and investigated in depth.Since the problem studied in this paper is ITP, it was necessary to form a sample pairing between the father and the child.In this study, the first adult child with income is selected as the research object of the offspring, and the father with income and labor ability is the object of the father's research.In this survey, a total of 900 questionnaires were distributed in three provinces, and 879 valid questionnaires were obtained, with an effectiveness rate of 97.7%.After the questionnaire contents were input into a Microsoft Excel database, a mathematical statistical method and SPSS 22.0 software were used to analyze the data.The sample attributes of the respondents are listed in Table 1.Note: labor capacity = non-labor population (under 14 years old, over 60 years old) × 0 + half labor force (women, children and the elderly who can operate easily) × 0.5 + full labor force × 1.

Variable Selection and Analysis Methods
The population segment analyzed in this study was mainly the rural poor, whose income intergenerational changes mainly consist of three types: when the income of the father is fixed and the income of children is lower than that of parents, that is identified as the intergenerational downward mobility of income; when the income of children is higher than that of their parents, that is identified as the intergenerational upward mobility of income; and when the income level of children and parents is the same, that is identified as the intergenerational transmission of income, which is the most direct and fundamental manifestation characteristic of intergenerational poverty transmission (Figure 3).The research approach mainly employed the transformation matrix method, and it explained influence mechanisms using the logistic regression model of multiple classifications.For the selection of dependent variables in the regression model, upward income flow was taken as the reference group, and five indicators of livelihood capital were taken as independent variables.At the same time, the factors influencing downward income flow and income intergenerational transmission were observed.The main consideration was the downward flow of income, which indicates that the income of the descendants is lower than that of the parents, and that they are falling into the poverty trap, thus becoming a new generation of poverty.A deeper analysis of ITP, as well as an exploration of the factors of downward income flow, will lead to a more in-depth interpretation of ITP.The structure of the logistic regression model for multiple classifications is as follows: where j is the dependent variable, J is the reference variable of the dependent variable, p represents the probability of the intergenerational change type of j income, x k is the independent variable in the table, α j is a constant, and β jk is the partial regression coefficient.

General Characteristics of ITP
The transformation matrix was proposed by Shorrocks in 1978 [72].This method demonstrates liquidity by measuring the changes in the relative position of income, which is the most consistent method of definition of income mobility and the least controversial [42,73].The greatest advantage

General Characteristics of ITP
The transformation matrix was proposed by Shorrocks in 1978 [72].This method demonstrates liquidity by measuring the changes in the relative position of income, which is the most consistent method of definition of income mobility and the least controversial [42,73].The greatest advantage of this model is that it can make a corresponding study on the income or class of the father and children of different income levels or strata.Defining the transformation matrix of father-to-child income from y a to y b , we get the following equation: where P(y a , y b ) is the father, i is the income class, the children are in the proportion of the income class j, and n is the income level classification class.The diagonal value in the matrix indicates the proportion of the father and the child's income in the same class.The bigger the ratio is, the higher the income inheritance of the child to the father is.It also means that the higher the intergenerational transmission is, the smaller the mobility is.The value at the non-diagonal position indicates that the child and the father at different income levels.
Based on the field survey data and referring to the absolute poverty line standard in the China Rural Poverty Detection Report 2016, the World Bank's poverty index for developing countries, and the disposable income per capita of rural permanent residents in poverty-stricken areas of China in 2015, the annual income data nodes were defined as 2300, 2900, 8000, 15,000, and 30,000 renminbi (RMB).It should be noted that families with annual incomes greater than 30,000 RMB are generally considered to be non-poor, while the research group in this study consisted primarily of the poor.Therefore, the intergenerational transmission of income for the population segment making more than 30,000 RMB per year was not compared and analyzed.Using the above categories, the 879 observations were divided into income ranks ranging from 1 to 6 (Table 2).A 6 × 6 income conversion matrix was then formed.To explore the intergenerational transmission of income between fathers and children, the distribution of income level between them was differentiated (Figure 4).Across the entire observation group, there was a higher proportion of fathers having lower income levels than their children.The proportion of fathers whose incomes were less than or equal to 2900 RMB was as high as 41.87%, and only 17.52% had income levels greater than 15,000 RMB.The proportion of children's incomes exceeding 15,000 RMB was greater than 50%, but 20% of them still had incomes below 2900 RMB.The above analysis shows that there was a large gap between the income levels of fathers and children.Regionally, the highest proportion of fathers' incomes was less than or equal to 2900 RMB and exhibited a decreasing trend from west to central to east, while the highest proportion of children's incomes was greater than 15,000 RMB, and exhibited a decreasing trend from east to central to west, which is consistent with the gradient pattern of China's economic development.
incomes exceeding 15,000 RMB was greater than 50%, but 20% of them still had incomes below 2,900 RMB.The above analysis shows that there was a large gap between the income levels of fathers and children.Regionally, the highest proportion of fathers' incomes was less than or equal to 2,900 RMB and exhibited a decreasing trend from west to central to east, while the highest proportion of children's incomes was greater than 15,000 RMB, and exhibited a decreasing trend from east to central to west, which is consistent with the gradient pattern of China's economic development.From Table 3 and Figure 5, it can be observed intuitively that the intergenerational transmission of income across the entire observations group was higher in the high-income, middle-high-income, and low-income groups, and exhibited obvious intergenerational transmission characteristics of poverty.Specifically, the highest intergenerational transmission rate was 45.71% in the high-income group, followed by 27.83% in the middle-high-income group, and 19.84% in the low-income group.In terms of income upward mobility, the descendants of a particular income class exhibit an upward mobility trend that gradually strengthens from high income to low, indicating an increasing desire for upward mobility as income decreases.In the process of achieving upward mobility, the lower the income class is, the easier it is to achieve class spanning.Higher income groups, meanwhile, have a lower possibility of achieving class spanning.In terms of income downward mobility, the descendant income class shows a tortuous downward trend from the high-income to low-income  From Table 3 and Figure 5, it can be observed intuitively that the intergenerational transmission of income across the entire observations group was higher in the high-income, middle-high-income, and low-income groups, and exhibited obvious intergenerational transmission characteristics of poverty.Specifically, the highest intergenerational transmission rate was 45.71% in the high-income group, followed by 27.83% in the middle-high-income group, and 19.84% in the low-income group.In terms of income upward mobility, the descendants of a particular income class exhibit an upward mobility trend that gradually strengthens from high income to low, indicating an increasing desire for upward mobility as income decreases.In the process of achieving upward mobility, the lower the income class is, the easier it is to achieve class spanning.Higher income groups, meanwhile, have a lower possibility of achieving class spanning.In terms of income downward mobility, the descendant income class shows a tortuous downward trend from the high-income to low-income groups.Among them, the descendant income downward mobility ratio of the high-income group was as high as 30.48% (not including incomes greater than 30,000 RMB).This reflects descendants whose parents were in the high-income level but, due to income retrogression, are likely to fall into the "poverty trap" and become a new "poor second generation".Note: The white cell indicates that the income of the father is on the same order as that of the children, the dark-gray cell indicates that the income of the father is fixed and the income of the children is upward, and the light-gray cell indicates a downward trend.Note: The white cell indicates that the income of the father is on the same order as that of the children, the dark-gray cell indicates that the income of the father is fixed and the income of the children is upward, and the light-gray cell indicates a downward trend.

Figure 5. Intergenerational mobility of income for generations (all observations)
. Note: The dotted line in the table is an observation of income exceeding 30,000 renminbi (RMB), which is only for reference and not for specific analysis.

Regional Differences of ITP in the Eastern, Central, and Western Regions
The corresponding numbers of observations of fathers and children in the eastern, central, and western regions were 295, 289, and 295 pairs, respectively.From Figure 6b, it can be concluded that the intergenerational transmission rate of income in the high-income group was highest in the eastern region, while the rate in the middle-low-income and low-income groups were highest in the central region.In the western region, the intergenerational transmission rates in the low-income, middle-high-income, and middle-income groups were higher than those in the other two regions (Table 4, Table 5).From the perspective of internal differences (Table 4, Figure 6), in the high-income group, the intergenerational transmission of income decreased from east to west.In the eastern region, more than half of the children's and fathers' income levels were in the same class (53.57%).This income class exhibited obvious characteristics of ITP, and the intergenerational mobility of income was low.In the low-, middle-, and high-income groups, the intergenerational transmission rates of income increased from east to west.The intergenerational transmission rate of income in the western region was found to be higher than the rates in the central and eastern regions.That is to say, the social mobility in the western region was lower than that in the other two regions, thus indicating that the degree of social openness in this region needs to be further improved.It is also .Note: The dotted line in the table is an observation of income exceeding 30,000 renminbi (RMB), which is only for reference and not for specific analysis.

Regional Differences of ITP in the Eastern, Central, and Western Regions
The corresponding numbers of observations of fathers and children in the eastern, central, and western regions were 295, 289, and 295 pairs, respectively.From Figure 6b, it can be concluded that the intergenerational transmission rate of income in the high-income group was highest in the eastern region, while the rate in the middle-low-income and low-income groups were highest in the central region.In the western region, the intergenerational transmission rates in the low-income, middle-high-income, and middle-income groups were higher than those in the other two regions (Tables 4 and 5).From the perspective of internal differences (Table 4, Figure 6), in the high-income group, the intergenerational transmission of income decreased from east to west.In the eastern region, more than half of the children's and fathers' income levels were in the same class (53.57%).This income class exhibited obvious characteristics of ITP, and the intergenerational mobility of income was low.In the low-, middle-, and high-income groups, the intergenerational transmission rates of income increased from east to west.The intergenerational transmission rate of income in the western region was found to be higher than the rates in the central and eastern regions.That is to say, the social mobility in the western region was lower than that in the other two regions, thus indicating that the degree of social openness in this region needs to be further improved.It is also more difficult for children in these income groups to rise into the upper class.In the middle-low-income group, the intergenerational transmission rates of income were generally low, with the rate in the central region greater than the rates in the eastern and western regions.It is worth mentioning that, from Figure 6b, it can be observed that the ratio between the highest-and lowest-income transmission groups was higher in the eastern region than in the central and western regions, confirming the characteristic of highly differentiated income in the rural poor groups of eastern China, a finding that is consistent with the conclusions drawn by other researchers [74].

Figure 6. Intergenerational mobility of income for generations (Eastern, central, western regions).
Note: The dotted line in the table is an observation of income exceeding 30,000 RMB, which is only for reference and not for specific analysis.

Model Variable Selection and Specific Operation
The selection of independent variables in this study was mainly based on the sustainable livelihood analysis framework of the Department for International Development, referring to the quantitative research on livelihood capital performed by Sharp (2003) in Africa [61] and the vulnerability analysis method of farmers and its localization application by Li [75].In this study, we designed the households interviewed in terms of different research units in China for family livelihood capital quantitative numerical measurements (Table 6).

Types of Capital
Measurement Index Index Symbol Assignment

Labor capacity L1
Non-labor population (under 14 years old, over 60 years old) = 0, half labor force (women, children and the elderly who can operate easily) = 0.5, full labor force = 1 Educational years of head of household L2 Educational years (take the logarithm)

Natural capital (N)
Per capita farmland/farming/grazing area of the family N1 Family total cultivated land (cultivated land/farming/grazing area)/total family population (take the logarithm)

Household fixed capital P2
There are several kinds of large machines: none = 1, one = 2, two = 3, three = 4, four or more = 5 There are several kinds of durable consumer goods: none = 1, one = 2, two = 3, three = 4, four or Note: The dotted line in the table is an observation of income exceeding 30,000 RMB, which is only for reference and not for specific analysis.Note: The white cell indicates that the income of the father is on the same order as that of the children, the dark-gray cell indicates that the income of the father is fixed and the income of the children is upward, and the light-gray cell indicates a downward trend.In terms of the intergenerational mobility of income (Figure 6a,c), the upward mobility rates of all income classes in the eastern region were discovered to be higher than the rates in the central and western regions, while the downward mobility rates of all income classes in the western region were higher than those in the eastern and central regions.This trend indicates that the higher the income level and the more developed the economy are, the higher the upward mobility of the children's income class will be.The lower the income level and the more backward the economy are, the more significant the downward mobility of the income class of the children will be.The next generation will enter the struggle to eliminate poverty, making the transmission cycle of poverty from generation to generation longer and more difficult to eradicate.

Model Variable Selection and Specific Operation
The selection of independent variables in this study was mainly based on the sustainable livelihood analysis framework of the Department for International Development, referring to the quantitative research on livelihood capital performed by Sharp (2003) in Africa [61] and the vulnerability analysis method of farmers and its localization application by Li [75].In this study, we designed the households interviewed in terms of different research units in China for family livelihood capital quantitative numerical measurements (Table 6).

Types of Capital
Measurement Index Index Symbol Assignment

Labor capacity L1
Non-labor population (under 14 years old, over 60 years old) = 0, half labor force (women, children and the elderly who can operate easily) = 0.5, full labor force = 1 Educational years of head of household L2 Educational years (take the logarithm)

Natural capital (N)
Per capita farmland/farming/grazing area of the family N1 Family total cultivated land (cultivated land/farming/grazing area)/total family population (take the logarithm)

Physical capital (P)
Family housing situation P1 All variables were simultaneously input into multiple multi-classification logistic regression models with Stata.The Hausman test showed that the model was suitable for random effects (the value of p > χ 2 are greater than 0.05) (Table 7); therefore, we could proceed by applying the multinomial logistic model.We firstly conducted a regression analysis.However, due to the mentioned limitations of the multinomial logistic regression model, marginal effects were used for a better interpretation of the results [59] (Table 8).

Model Regression Results and Interpretation
Influencing factors of ITP include human capital, natural capital, physical capital, financial capital and social capital in eastern, central, and western regions.These capitals have different ways of influence and significance in various regions, as shown in Figure 7.
returned to the village to drive the villagers to become wealthy", the proportion of "yes" answers in the eastern region was much higher than the proportions in the central and western regions, while the proportion of "no" answers in the western region was the highest of the three study areas, which also reflected the fact that the eastern region was relatively developed.The higher the proportion of "rural elite" is, the stronger the role of the clan relationship network and the higher the level of intergenerational income transmission between generations are.This indicates that the intergenerational transmission of high income is predominant.It also tangentially indicates that, in the western region, where social capital is generally scarce, the available and accessible social capital is extremely limited, increasing the likelihood of low-income intergenerational poverty transmission.The extremely scarce social capital in the western region makes it more difficult to get rid of poverty, and we should pay close attention to it [80,81].

Conclusions and Discussion
Based on 879 rural poverty questionnaires collected in survey, this study explored ITP in China and the factors affecting it.From this research, we can draw the following conclusions: (1) The income levels of rural fathers and their children are noticeably different.Fathers had the highest proportion of lower incomes in our study observations, with this proportion exhibiting a decreasing "western-central-eastern" trend, while their children had the highest proportion of higher incomes, with this proportion exhibiting a decreasing "eastern-central-western" trend, coinciding with the gradient pattern of China's economic development.
(2) ITP in China is characterized by income class differentiation.Among the low-income groups, the groups at both ends of this income level are more likely to experience ITP.In terms of liquidity, the lower-income generation shows the strongest upward mobility trend, while the higher-income generation shows a more obvious downward mobility trend.
(3) ITP among different strata highlights the solidification of income in the poor strata of society.The intergenerational mobility of income is an important manifestation of the mobility of social income strata, which tends to change in either the same direction or the opposite direction.Among these strata, the economically developed eastern region exhibits a reverse trend, especially for ITP in the high-income group, while the upward mobility of children's income in the eastern region is more significant, which is more likely to block ITP.The economically underdeveloped central and western regions have the most prominent ITP in the middle-and low-income groups, where children's income has a downstream relationship with the income of their fathers.The dynamic trend is more obvious, and it is more likely for children to fall into the poverty trap in these regions.

Impact of Human Capital on ITP
ITP is affected to a certain extent by the family labor capacity and the educational level of the head of the family.Both of these factors play a more obvious role in the western part of China.In western rural poor families, the smaller a family's labor capacity and the lower its education level are, the more likely its children's incomes will be downwardly mobile, thus increasing the likelihood that the next generation will fall into the poverty trap.This makes it more difficult to interrupt ITP and realize the upward flow of income.Families with large labor ability and a father's high education level will reduce 20.1% and 15.2% of the possibility of their child to fall into ITP, respectively.This is also consistent with the conclusions reached by some scholars that human capital plays an important role in ITP [76,77].Gansu Province has the smallest population of the three provinces investigated in this study, with an average of 5.652 people per household, as well as the weakest family labor capacity, with an average of 4.155 people per household.Through the survey data, we also learned that the hollowing out of rural areas in the western region is more serious than expected.The villages are filled with empty nesters, left-behind children, and women.The main labor force decreased, while the number of children increased.Heads of household are consumed with the heavy burden of making a living, leaving them little time to care for their children or to improve their educational level.The inadequate investment of educational capital combined with heavy family labor makes any family resources that can be obtained and absorbed by the descendants in the western region extremely limited, and the lack of human capital increases the likelihood of the intergenerational transmission of low income.

Impact of Natural Capital on ITP
The per capita amount of land owned by a family is the most important factor in a farmer's livelihood.The main source of the income of a farmer depends on the productivity per unit area of land.This variable has a significant impact on ITP in the eastern and central regions.The less natural capital and land income there is, the more prone a region is to ITP.Among these areas, Fujian Province in the eastern region consists of hills and low mountains, with limited arable land.Due to this topography, farms are located mainly on beaches or in shallow seas.Although their income levels are higher than those of farmers in the central and western regions, they are vulnerable to extreme weather events such as typhoons, floods, and heat waves.The instability factors of agricultural output and income dominate in this region (the proportion of non-agricultural/aquatic income last year was as high as 21.7%).This is also consistent with the conclusions reached by some scholars that natural capital plays an important role in ITP in coastal areas [78].Henan Province in central China covers a large area and has a high output of agricultural products, but its main difficulty concerns the low price of these products.The results of a farmer's hard work over the course of a year are sometimes insufficient to pay for land expenditure.In the eastern and central regions, where farming and cultivation predominate, it is common for both parents and children to have farming-related occupations.Their overall income will also be affected by family natural capital and its associated income, resulting in a higher intergenerational transmission rate in the high-income groups of the eastern region, while the intergenerational transmission rate in the middle-and low-income groups is more prominent in the central region.

Impact of Physical Capital on ITP
Physical capital variables include two factors: one is the number and structural type of houses owned by families; the other is the number of large-scale machines and durable consumer products owned by families.The former is an important material way for farmers to obtain a stable life; the latter is the means and methods for farmers to achieve diversified production.From the point of view of the overall observations model, both of these factors played a particular role in ITP.Physical capital had the most significant impact on the western region.In terms of housing structure, only 31.86% of the rural homes in the western region are constructed of brick or steel concrete, while 39.32% are made of adobe.The likelihood of a child with poor family housing falling into ITP will increase by 37%.In terms of large-scale appliances and durable consumer goods, the most basic household durable consumer goods (such as televisions and radios) are still the predominant ones in the western region, while the farmers in the central and eastern regions have new-generation tools and modern production equipment.This factor directly affects the diversification level of farmers' livelihoods and will have a certain impact on the income level of the two generations.Family children with fewer household appliances and durable consumer goods are more likely to fall into ITP by 8.1%.In addition, family housing conditions limit the convertible capital of peasant households available when facing risks, further aggravating ITP among the low-income strata in the western region.

Impact of Financial Capital on ITP
Financial capital had a significant impact on ITP in all three study regions, but there were some differences among them.On one hand, 28.44% of the fathers and children in the eastern region were engaged in fishery production activities, and most of their families' per capita income was concentrated in the 15,001-30,000 RMB range.Therefore, the eastern region, with its higher per capita income, was more likely to have greater income transmission between generations, while the western region, with poor income from land-farming activities, was more likely to have lower income transmission from fathers and children, increasing the likelihood that the children will fall into a vicious circle of poverty.For example, in the central and western regions, families with a per capita income of 2301-2900 RMB had a 22.6% and 29.3% increase, respectively, in the possibility of ITP among their descendants.On the other hand, compared to farmers with credit opportunities, families without credit opportunities were more likely to fall into the intergenerational downward mobility of income, as well as the intergenerational transmission of income, a phenomenon that was more pronounced in the western region.The main reason for this disparity is that the eastern region is located in relatively developed coastal areas, where farmers have more business opportunities, more awareness, and opportunities to obtain credit (71.19% in eastern China, 69.20% in central China, and 59.32% in western China); thus, the ability to enhance financial capital is strong.Farmers in the western region mainly farm the land and work part-time, making the demand for credit less than that in the central and eastern regions.Some farmers who get credit on time just to obtain the interest cannot effectively transform capital and increase income.These factors further contributed to the differences between the levels of ITP in the eastern and western regions.The lack of financial capital led to the deepening of long-term poverty and limited ability to fight poverty [79].

Impact of Social Capital on ITP
Social capital is mainly realized through family politicians and clan networks in rural society, and plays a subtle regulatory role in rural acquaintance society.This variable also exhibited a significant impact on ITP.The poorer a family's social capital is, the greater the possibility of ITP is, which highlights the suffering of poor families in rural areas.When disaster strikes, a poor family's weak social network is insufficient to benefit fully from the help of others and of social teams, leading to more difficulties for poor families, more of a struggle for their descendants to escape the poverty trap, and a greater likelihood of the transmission of poverty between generations.Our survey results demonstrated that this phenomenon was most obvious in the western region.The likelihood of children in western rural families who did not receive credit and social assistance fell into ITP by 7.4% and 9.5% respectively.In addition, when asked whether "the wealthiest people in the village play a helping role with the villagers" and "whether the wealthiest people in the village returned to the village to invest in the village, and whether officials or other successful people returned to the village to drive the villagers to become wealthy", the proportion of "yes" answers in the eastern region was much higher than the proportions in the central and western regions, while the proportion of "no" answers in the western region was the highest of the three study areas, which also reflected the fact that the eastern region was relatively developed.The higher the proportion of "rural elite" is, the stronger the role of the clan relationship network and the higher the level of intergenerational income transmission between generations are.This indicates that the intergenerational transmission of high income is predominant.It also tangentially indicates that, in the western region, where social capital is generally scarce, the available and accessible social capital is extremely limited, increasing the likelihood of low-income intergenerational poverty transmission.The extremely scarce social capital in the western region makes it more difficult to get rid of poverty, and we should pay close attention to it [80,81].

Conclusions and Discussion
Based on 879 rural poverty questionnaires collected in survey, this study explored ITP in China and the factors affecting it.From this research, we can draw the following conclusions: (1) The income levels of rural fathers and their children are noticeably different.Fathers had the highest proportion of lower incomes in our study observations, with this proportion exhibiting a decreasing "western-central-eastern" trend, while their children had the highest proportion of higher incomes, with this proportion exhibiting a decreasing "eastern-central-western" trend, coinciding with the gradient pattern of China's economic development.
(2) ITP in China is characterized by income class differentiation.Among the low-income groups, the groups at both ends of this income level are more likely to experience ITP.In terms of liquidity, the lower-income generation shows the strongest upward mobility trend, while the higher-income generation shows a more obvious downward mobility trend.
(3) ITP among different strata highlights the solidification of income in the poor strata of society.The intergenerational mobility of income is an important manifestation of the mobility of social income strata, which tends to change in either the same direction or the opposite direction.Among these strata, the economically developed eastern region exhibits a reverse trend, especially for ITP in the high-income group, while the upward mobility of children's income in the eastern region is more significant, which is more likely to block ITP.The economically underdeveloped central and western regions have the most prominent ITP in the middle-and low-income groups, where children's income has a downstream relationship with the income of their fathers.The dynamic trend is more obvious, and it is more likely for children to fall into the poverty trap in these regions.
(4) The influence of human, natural, physical, financial, and social capital on ITP varies among the eastern, central, and western regions, with financial capital exerting the most significant influence.In addition, natural capital plays a significant role in the eastern region, where the intergenerational transmission of high income is most prominent.Physical capital predominates in the central region, where the intergenerational transmission of low-and middle-low-income groups is greatest, and both human and physical capital play obvious roles in the western region, mainly characterized by the intergenerational transmission of low income.At present, the influence of human and natural capital is weakened in China's ITP.Correspondingly, family material capital and financial capital will gradually come to play greater roles.Social capital, as a delicate array of networks, plays an important role in rural society, although it is often neglected.This type of capital requires additional attention.
As an important factor affecting ITP, China should explore and summarize the lack of livelihood capital in its eastern, central, and western regions.More attention should be paid to the sustainable construction of livelihood capital in poor peasant households; the diversification of livelihoods should be enhanced, and the stock of "heredity" capital to offspring should be increased.In addition, the problem of ITP is affected by numerous factors, not just the family's five major livelihood capital factors, but also the social system, economic environment, poverty alleviation policies, and other aspects.Future research can strengthen the impact of medium-and macro-factors on ITP.

Policy Implications
Sustainable improvement and development of farmers' livelihoods is an important channel to ensure that farmers reduce poverty and promote livelihood diversification.On the basis of comprehensive consideration of the shortage of capital elements in different regions, several policy recommendations are put forward for ITP.Firstly, we should provide micro-credit to improve farmers' financial capital stock.We should strengthen the guidance of getting rich in precise poverty alleviation, and give full play to the original intention of the government to provide micro-credit.Then, the government can regulate and manage the private credit market through innovation of financial and perfection of systems to make the private lending more legitimate and reduce the ratio of poor farmers borrowing "usury", thereby reducing the possibility of poverty trap.The government can further improve and broaden the financing channels of various financial institutions for household items, gradually reducing the cost of household borrowing, so as to help the poor groups in rural areas ultimately eliminate poverty.Secondly, we should enhance the interpersonal network of rural poor groups and improve the level of information transmission.For example, we can provide social organizations suitable for rural poor groups to help them or we can employ information assistance and labor skill training assistance.Thirdly, the western region should focus on increasing investment in education and basic medical care; particular attention should be paid to girls' education and women's health, actively exerting the power of the government and society.At the same time, strengthening vocational education, and developing vocational education and higher education to enhance the personal ability of children from poor families can truly block ITP.

Figure 1 .
Figure 1.Location map of sample points.

Figure 1 .
Figure 1.Location map of sample points.

Figure 2 .
Figure 2. Per capita disposable income of rural residents in six sample counties and provinces.Source: According to the Statistical Yearbook 2017 of each county.

Figure 3 .
Figure 3. Three types of intergenerational income.

Figure 5 .
Figure 5. Intergenerational mobility of income for generations (all observations).Note: The dotted line in the table is an observation of income exceeding 30,000 renminbi (RMB), which is only for reference and not for specific analysis.
(a) Downward mobility of children income.(b) Intergenerational transmission rate of children income.(c) Upward mobility of children income.

Figure 6 .
Figure 6.Intergenerational mobility of income for generations (Eastern, central, western regions).Note:The dotted line in the table is an observation of income exceeding 30,000 RMB, which is only for reference and not for specific analysis.

Figure 7 .
Figure 7. Influencing factors of intergenerational transmission of poverty (ITP) in eastern, central, and western regions.

Figure 7 .
Figure 7. Influencing factors of intergenerational transmission of poverty (ITP) in eastern, central, and western regions.

Table 1 .
Demographic characteristics of the affected households.

Table 5 .
Comparison of intergenerational income transfer rates in eastern, central, and western regions in China.

Table 4 .
The frequency of intergenerational income transfers in eastern, central, and western regions in China (%).

Table 5 .
Comparison of intergenerational income transfer rates in eastern, central, and western regions in China.

Odds (Outcome-J vs. Outcome-K) Are Independent of Other Alternatives
Y2: intergenerational transmission of income; Y3: intergenerational upward mobility of income.