Multidimensional Relative Poverty in China: Identification and Decomposition

Abstract

This paper aims to study the change and decomposition of multidimensional relative poverty in China. The data we use are from the China Health and Nutrition Survey (CHNS). The data cover 12 provinces in China and span a long period, from reform to precise poverty alleviation. The results show that the multidimensional relative poverty index presents a change pattern of “gradual rise (1991–2004)-decline (2004–2011)-rise again (after 2011)”. The dimensions of education, income, and employment contribute more to multidimensional relative poverty, followed by health and living standards. Multidimensional relative poverty is more severe in rural areas, central and western regions, women, and the elderly. The “incidence of poverty effect” is the main factor in the changes in multidimensional relative poverty, and its contribution is higher than the “intensity of poverty effect”.

1. Introduction

Sustainable development is a prevalent issue in current social research, and poverty is essential to sustainable development. The first goal in the United Nations Sustainable Development Goals is no poverty. Although most countries have solved the problem of absolute poverty, for example, China eliminated absolute poverty by 2020, there are still many countries in the plight of relative poverty. Relative poverty significantly inhibits rapid economic development. What is the standard of relative poverty, how do we reveal the long-term changes in relative poverty from multidimensional perspectives, and how do we decompose multidimensional relative poverty? Research on these issues will help to identify and target the relatively poor in order to adopt targeted public policies.

In previous studies, two significant directions tend to dictate poverty status: the expansion from unidimensional poverty to multidimensional poverty, and the expansion from absolute poverty to relative poverty. Whether it is absolute or relative poverty, it is not only a matter of income dimensions, but also of multiple dimensions and levels. Defining and measuring multidimensional relative poverty is less explored in academia. The main contributions of this paper are: (1) constructing an indicator system of multidimensional relative poverty and developing a measurement. Most existing literature on relative poverty still focuses on the income dimension, usually using a certain percentage of the mean or median income to measure relative poverty; however, these studies lack an analysis of the non-income dimension. Multidimensional poverty is often studied from an absolute perspective but largely lacks relative analysis. This paper combines the above two frameworks to construct a multidimensional and relative analysis perspective and selects CHNS data from 1991–2015 for empirical research. The data span a long period of years and have a rich microsample, which reflects the changes in multidimensional relative poverty in China since 1990. (2) The current literature has two disadvantages when using the Alkire and Foster (2011) (AF) [1] method to analyze multidimensional relative poverty. First, the relativity is usually reflected in the second aggregation cutoff, and the absolute criterion is still used for the first indicator deprivation cutoff. The second cutoff distinguishes the difference between multidimensional absolute poverty and multidimensional relative poverty, but the definition of relativity is subjective. Second, there is no uniform opinion on the absolute criterion of the first indicator deprivation cutoff. Some literature uses the mean to define the first cutoff, which may overestimate the multidimensional relative poverty. This paper takes the median of the indicator distribution as the principle of determining the relative cutoff of indicator deprivation, which is usually lower than the average value. Compared with multidimensional absolute poverty, the indicator relative cutoff method is more objective and is closer to the actual situation. (3) This paper decomposes the changes in multidimensional relative poverty into the incidence of poverty effect and intensity of the poverty effect, measures their contributions to reveal the leading causes of changes in multidimensional relative poverty, and makes feasible policy recommendations.

The remainder of the paper is organized as followed. Section 2 is a review of the related literature. Section 3 measures multidimensional relative poverty. Section 4 presents the empirical results and analysis. Section 5 concludes the paper.

2. Review of Related Literature

2.1. Multidimensional Poverty

Regarding the measurement of poverty, as an advocate of capability poverty, Sen (1976) proposed the “identification-aggregation” approach in which the former distinguishes the poor in the overall population by defining poverty criteria and the latter adds the data of the poor to an overall poverty indicator [2]. Watts (1968) constructed a sensitive and decomposable poverty index that reflects income distribution [3]. Hagenaars (1987) used the social welfare function to expand the poverty index from income to the two-dimensional boundary, including income and leisure. They constructed the first multidimensional poverty index, the HM index [4]. Tsui (2002) [5] extended the poverty indicator proposed by Foster and Shorrocks (1991) [6] from unidimensional to multidimensional. He then expounded the symmetry, replication invariance, monotonicity, stability, and consistency axiom of multidimensional poverty. He stated that from a multidimensional perspective, income may not be an appropriate measure of deprivation because the relationship between income and basic needs is not strong. Bourguignon and Chakravarty (2003) [7] proposed to set a separate poverty line for each dimension. If a person’s situation is below the poverty line of at least one dimension, he is poor. They discussed the combination of poverty lines of different dimensions with the measurement of multidimensional poverty and used the definition of income and education to measure the multidimensional poverty of the rural population in Brazil.

Alkire and Foster (2011) [1] extended the traditional union and intersection approach. They innovatively proposed the “dual cutoff” approach to poverty identification, where the first cutoff is a deprivation cutoff that determines whether an individual is deprived in a dimension. The second is the dimensions of deprivation cutoff that determines whether an individual is deprived or not. Since the AF method satisfies some axiomatic properties, Alkire and Santos (2014) measured multidimensional poverty in 104 developing countries based on the AF method [8]. Subsequently, the United Nations Development Programme (UNDP) adopted this method and published this index annually. Most scholars adopt the AF method to measure multidimensional poverty and mainly construct a multidimensional poverty indicator system from dimensions such as health, education, livelihood, living conditions of children and adolescents, employment, etc. (Shen and Li, 2022; Burchi et al., 2022) [9,10]. Multidimensional poverty also has many applications in Chinese poverty reduction practices. Between 1986 and 2010, China’s poverty alleviation policies mainly addressed the primary survival goals of “food, clothing, and shelter” and adopted the unidimensional “income poverty” criterion. In 2011, the Chinese government promulgated the China Rural Poverty Alleviation and Development Program (2011–2020). They expanded the goal of poverty alleviation to include “rural poor people do not have to worry about food and clothing and have access to compulsory education, basic medical services, and safe housing”. The poverty alleviation policy gradually shifted from a one-dimensional poverty criterion centered on income to a multidimensional poverty criterion (Sun and Xia, 2019) [11].

2.2. Relative Poverty

The setting of the poverty line affects the results of poverty measurement. Regarding the measurement of relative poverty, currently, it is mainly measured by a single dimension of income or consumption. Fuchs (1967) first used the relative approach to estimate the incidence of poverty and proposed that the poverty line in the United States should be set at 50% of the current median income [12]. In addition to the median, the mean is often applied in the measurement of relative poverty; for example, Atkinson (1998) used 50% of the income mean to analyze relative poverty in Britain [13]. Zheng (2001) summarized the methods of related scholars and concluded that there are two measures of relative poverty: one is the percentage of income mean and the other is the percentage of income quantile (median is a particular case of quantile) verified theoretically [14]. Ravallion and Chen (2011) named a fixed percentage of the mean or median of income or consumption as the strongly relative poverty line. They relaxed the assumption and proposed the weakly relative axiom [15]. Ravallion and Chen (2019) further improved weakly relative poverty by considering the Gini coefficient and proposed a weakly relative poverty line that includes upward and downward inequality comparisons [16]. Current research on weakly relative poverty is gradually becoming more popular (Hu et al., 2021; Ma and Lu, 2022) [17,18]. However, in actual economic activities, most countries still adopt strongly relative poverty to measure poverty.

2.3. Multidimensional Relative Poverty

The analysis of multidimensional relative poverty is still mainly based on the AF method. Wang and Feng (2020) proposed that when setting five dimensions to measure multidimensional poverty, any three in five or more dimensions of poverty are defined as “multidimensional absolute poverty”, and any one in five and two in five dimensions of poverty are defined as “multidimensional relative poverty” [19]. Relativity is reflected in the second cutoff. Cheng et al. (2021) [20] and Luo et al. (2022) [21] selected the mean as the relative poverty standard, but the use of the mean may lead to the overestimation of poverty. Wang and Sun (2021) used the 2018 China Household Survey data to analyze multidimensional relative poverty in China. They set 40% of the median income between urban and rural areas as the poverty line in the income dimension, but the deficiency is that there is only one annual dataset [22]. Fang and Zhou (2021) use the “dual cut-off” method to measure multidimensional relative poverty and select a certain proportion for the two cutoffs to define multidimensional relative poverty. Still, the proportion is subjective [23].

The above literature shows that the research perspectives on poverty have been continuously developed and improved, gradually shifting from a unidimensional income to multidimensions of health, education, and living standards, etc., and from fixed absolute poverty to relative poverty. Most of the current literature on multidimensional poverty mainly focuses on absolute poverty, and the literature on relative poverty also mainly analyses income poverty with fewer multidimensional perspectives. However, in the new stage of shared prosperity, multidimensional absolute poverty and unidimensional relative poverty can no longer meet the needs of poverty research. Combining the concepts of “multidimensional” and “relative” is key to exploring the changes in poverty. The current literature on multidimensional relative poverty is not sufficient. This paper improves the AF methodology to measure the long-term changes in multidimensional relative poverty in China. We then decompose the changes in multidimensional relative poverty into the incidence of poverty effect and intensity of the poverty effect to reveal the causes of poverty changes.

3. Measurement of Multidimensional Relative Poverty

3.1. Multidimensional Relative Poverty Index Measurement Method

The key to the difference between multidimensional relative poverty and multidimensional absolute poverty is that the poverty standard of multidimensional absolute poverty is fixed every year. In contrast, the standard of multidimensional relative poverty can be changed every year. The method used to change this is central in this research. This paper improves the Alkire and Foster (2011) [1] method (AF) to construct a multidimensional relative poverty measurement and decomposition method.

The AF method has two cutoffs. The first cutoff is the indicator deprivation cutoff z, and the second cutoff is the aggregation dimension cutoff k. Therefore, the relativity of multidimensional relative poverty can be considered from two aspects: the indicator deprivation cutoff can change rather than fix, and the aggregation dimension cutoff can change. In current literature, the second approach is mainly used. Still, this approach has two shortcomings: ① there is no unified consensus on the relative proportion of the aggregation dimension cutoff k, which is set at one in five or two in five (Wang and Feng, 2020) [19] or 30% (Wang and Sun, 2021) [22].② In this case, the first cutoff still adopts the absolute criteria. Still, it may happen that even for the same indicator, the absolute criteria used by different scholars are not consistent. This paper uses the first indicator deprivation cutoff to define multidimensional relative poverty. We determine the indicator deprivation relative cutoff z based on the data distribution. This is a significant difference between this paper and most existing literature. In the analysis of relative comparison, the median or the mean is usually set as the object of comparison because the mean is easily affected by the maximum and minimum and the mean is generally higher than the median, and the indicator deprivation relative cutoff defined by the mean is also higher, which leads to a higher incidence of poverty and thus brings great financial pressure on the government to reduce poverty. Based on the above considerations, this paper uses the median of the indicator data distribution to define the relative deprivation cutoff for each indicator, so that the measurement results are more consistent with the actual poverty situation. The specific method is as follows.

Assuming that there are n individuals in the society, the matrix of individual i on the dimension j is:

$$x=\left(\begin{array}{ccc}{x}_{11}& \cdots & x_{1d}\\ ⋮& x_{ij}& ⋮\\ x_{n1}& \cdots & x_{nd}\end{array}\right)$$

(1)

where $i=1,2\cdots n$, $j=1,2\cdots d$.

1. The indicator relative deprivation cutoff. Set z_j (z_j > 0) to denote the relative cutoff of deprivation in indicator j, when the individual is deprived within the indicator, so that $g_{ij}=1$, and vice versa, $g_{ij}=0$, and thus obtain the deprivation matrix:

$$g=\left(\begin{array}{ccc}{g}_{11}& \cdots & g_{1d}\\ ⋮& g_{ij}& ⋮\\ g_{n1}& \cdots & g_{nd}\end{array}\right)$$

(2)

2. Weight of indicators. The weight of each indicator is set as $w_j(0<w_j<1)$, ${\displaystyle \sum }{w}_j=1$. Regarding the index weight, we adopt the practice of most scholars. In selecting indicator weights, to avoid subjective errors due to the different weights of each indicator, the weight of each dimension and each indicator within the dimension is set to be equal, and the individual weighted deprivation matrix is:

$$G=\left(\begin{array}{ccc}{w}_1{g}_{11}& \cdots & w_d{g}_{1d}\\ ⋮& w_j{g}_{ij}& ⋮\\ w_1{g}_{n1}& \cdots & w_d{g}_{nd}\end{array}\right)$$

(3)

The weighted deprivation composite index of an individual i on all d indicators is denoted by $c_i$, which equals the total value of a row of the 𝐺 matrix: $c_i={{\displaystyle \sum }}_{j=1}^d{w}_j{g}_{ij}$.

3. The aggregation dimension cutoff. Set the cutoff k to identify whether the individual $i$ is in multidimensional relative poverty, when $c_i<k$, $g_{ij}\left(k\right)=0$, the individual i is not in multidimensional relative poverty; when $c_i>k$, $g_{ij}\left(k\right)=1$, the individual $i$ is in multidimensional relative poverty, expressed in matrix form as:

$$g\left(k\right)=\left(\begin{array}{ccc}{g}_{11}\left(k\right)& \cdots & g_{1}d\left(k\right)\\ ⋮& g_{ij}\left(k\right)& ⋮\\ g_{n1}\left(k\right)& \cdots & g_{nd}\left(k\right)\end{array}\right)$$

(4)

Based on the above information, this paper can obtain the multidimensional relative poverty index:

$$M_0=\frac{1}{n}{\displaystyle \sum }_{j=1}^d{c}_j\left(k\right)$$

(5)

4. Aggregation. The multidimensional relative poverty index ($M_0$) can be split into H (incidence of poverty) and A (average deprivation).

$$M_0=\frac{q}{n}\times \frac{1}{q}{\displaystyle \sum }_{j=1}^d{c}_j\left(k\right)=H\times A$$

(6)

$q$ denotes the number of people identified in multidimensional relative poverty and $n$ is the overall sample size.

5. Poverty decomposition. The multidimensional relative poverty index ($M_0$) can be decomposed according to different properties such as region, dimension, and urban/rural. Take regional decomposition as an example, where $x$ denotes urban, and $y$ denotes rural, $n\left(x,y\right)$ denotes the total number of people, $n\left(x\right)$ denotes the number of people in rural areas, and $n\left(y\right)$ denotes the number of people in urban areas.

$$M_0\left(x,y,z\right)=\frac{n\left(x\right)}{n\left(x,y\right)}{M}_0\left(x;z\right)+\frac{n\left(y\right)}{n\left(x,y\right)}{M}_0\left(y;z\right)$$

(7)

6. The change in the multidimensional relative poverty index ($M_0$). Drawing on the methodology of Alkire et al. (2017) [24], the change in multidimensional relative poverty over the two periods $t_1$,$t_2$ is as follows.

Change in absolute level:

$$\Delta M_0=M_0\left(X_{t_2}\right)-M_0\left(X_{t_1}\right)$$

(8)

Change in relative level:

$$\delta M_0=\frac{M_0\left(X_{t_2}\right)-M_0\left(X_{t_1}\right)}{M_0\left(X_{t_1}\right)}$$

(9)

Annual absolute level change:

$$\overline{\Delta }{M}_0=\frac{M_0\left(X_{t_2}\right)-M_0\left(X_{t_1}\right)}{t_2-t_1}$$

(10)

Annual relative level change:

$$\overline{\delta }{M}_0=\left[{\left(\frac{M_0\left(X_{t2}\right)}{M_0\left(X_{t1}\right)}\right)}^{\frac{1}{t2-t1}}-1\right]\times 100\%$$

(11)

7. Decomposition of changes in the multidimensional relative poverty index ($M_0$). Since $M_0=H\times A$, based on the studies of Apablaza and Yalonetzky (2013) [25] and Roche (2013) [26], and Shorrocks’ (2013) [27] Shapley decomposition method, changes in the multidimensional relative poverty index can be decomposed into the incidence of poverty effect and intensity of poverty effect.

$$\Delta M_0=\underset{Incidence of Poverty effect}{\underbrace{\frac{A_{t2}+A_{t1}}{2}\left(H_{t2}-H_{t1}\right)}}+\underset{Intensity of Poverty effect}{\underbrace{\frac{H_{t2}+H_{t1}}{2}\left(A_{t2}-A_{t1}\right)}}$$

(12)

Poverty incidence effect contribution:

$${\varphi }_H^0=\frac{\left(A_{t1}+A_{t2}\right)\left(H_{t2}-H_{t1}\right)}{2\Delta M_O}$$

(13)

Deprivation effect contribution:

$${\varphi }_A^0=\frac{\left(H_{t1}+H_{t2}\right)\left(A_{t2}-A_{t1}\right)}{2\Delta M_O}$$

(14)

3.2. Data Source and Description

The data selected in this paper are from the China Health and Nutrition Survey (CHNS), which has a long survey period and large sample size and covers 12 provinces in the eastern, central, and western parts of China. The data can reflect the national situation well. The CHNS survey started in 1989 and ended in 2015 with 10 rounds. The CHNS database is an unbalanced panel data. The data years selected in this paper are 1991–2015. In 1991 and 1993, the data included the eight provinces of Liaoning, Jiangsu, Shandong, Henan, Hubei, Hunan, Guangxi, and Guizhou. In 1997, Liaoning was missed, and Heilongjiang was added, which was still eight provinces. The data included the above nine provinces in 2000, 2004, 2006, and 2009. In 2011, Beijing, Shanghai, and Chongqing were added, a total of 12 regions. In 2015, there were also the above 12 provinces (See Figure 1). According to the indicators selected in the previous section, the household samples were combined with the individual sample data, and we removed the missing data. Finally, we obtained 82,443 observations.

3.3. Construction of a Multidimensional Relative Poverty Index System

Many researchers have tried to construct an index for multidimensional poverty. The UNDP selected 10 indicators from three areas to calculate global multidimensional poverty: education (years of schooling, school attendance), health (nutrition, child mortality), and living standards (cooking fuel, sanitation, drinking water, electricity, and housing assets) (UNDP, 2021 [28]). This index has been widely used (Bader et al., 2015) [29]. Coromaldi and Zoli (2012) [30] selected indicators from capacity, consumption deprivation, health, housing facilities, and other aspects for a principal component analysis to analyze multidimensional poverty in Italy. Gerlitz et al. (2015) [31] selected 16 indicators from seven aspects to depict Nepal’s multidimensional poverty: education (literacy, school attendance), health (illness, health care, food consumption, material welfare (assets, dwelling), energy (electricity, cooking fuel), water and sanitation, social capital (political voice, social network), and access to services (markets, hospitals, bus stops). Hanandita and Tampubolon (2016) [32] selected indicators from income, health (illness, morbidity), and education (school, literacy) to research multidimensional poverty in Indonesia. Regarding the selection of multidimensional relative poverty indicators, we referred to the related research (Alkire and Foster, 2011; Wang and Alkire, 2009; Zou and Fang, 2011; Alkire and Fang, 2021; Zhang and Zhou,2015) [1,33,34,35,36]. We followed the principles of scientificity, rationality, and data availability to select the indicators. The multidimensional relative poverty index system contains five dimensions: income, health, education, living standards, and employment, with 11 indicators. The relative cutoffs of deprivation for each indicator are shown in

Table 1. Multidimensional relative poverty indicators and relative deprivation cutoffs.

Dimension (Weight)	Indicator (Weight)	Indicators Deprived of Relative Cutoff
Income (1/5)	Annual household income per capita (1/5)	50% of the median yearly household income per capita
Education (1/5)	Years of education (1/5)	The median number of years of schooling per year
Health (1/5)	Illness (1/15)	Sickness or injury
	BMI (1/15)	BMI non-18.5–24 range
	Medical Insurance (1/15)	Not participating in health insurance
Living standards (1/5)	Drinking water source (1/25)	The median of annual sample distribution (“other”, “ice or snow”, “creek, spring, river, lake”, “open well water (≤5 m)”, “groundwater (>5 m)”, “water plant”, “bottle water”)
	Toilet type (1/25)	The median of annual sample distribution (“no bathroom”, “other”, “earth open pit”, “cement open pit”, “no flush, outside house, public restroom”, “flush, outside house, public restroom”, “no flush, in-house”, “flush, in-house”)
	Cooking fuel (1/25)	The median annual sample distribution (“other”, “wood, sticks/straw, etc”., “charcoal”, “kerosene”, “coal”, “liquefied gas”, “electricity”, “natural gas”)
	Transportation (1/25)	The median number of assets in the annual sample (“tricycles”, “bicycles (including electric-assist bicycles)”, “motorcycles (including three-wheeled motorcycles)”, “automobiles”)
	Household appliances (1/25)	The median number of assets of annual samples (“color TV”, “washing machine”, “refrigerator”, “air conditioner”, “sewing machine”, “electric fan”, “DVD/VCD”, “microwave oven”, “rice cooker”, “pressure cooker”, “telephone”, “cell phone (non-smart)”, “smartphone”, “satellite dish”, “Computer”, “tablet computer”)
Employment (1/5)	Working situation (1/5)	No job (excluding students, retired, too young to work)

, and the details are as follows.

3.3.1. Income Dimension

As the most widely used indicator for measuring poverty, income should generally be covered in the analysis of multidimensional relative poverty, and many scholars try to achieve this (Alkire and Fang, 2019; Feng et al., 2015; Mitra, 2016) [35,37,38]. We set the indicator deprivation cutoff as 50% of the median income. As the difference between the maximum and minimum values of residents’ income is significant and the income gap is noticeable, if it is directly set as the median, the incidence of poverty in the income dimension will be high and not quite in line with the actual situation. In addition, in the unidimensional relative poverty analysis, a certain proportion of the median income (consumption) is usually set to measure. For the proportion, some scholars use 60% (Blackburn, 1990) [39], but the general use is 50% (Fuchs, 1967; World Bank, 2017; Yip et al., 2017) [12,40,41]. Therefore, 50% of the median annual per capita household income is used as the cutoff for the yearly income indicator, and households are considered to be relatively deprived when their annual per capita income is less than this cutoff.

3.3.2. Education Dimension

A low level of education is a prominent cause of poverty. Regarding the educational dimension, some scholars have selected the following indicators: any family member over 18 has not completed five years of education (Wang and Alkire, 2009) [33]; all adults in the family have less than nine years of compulsory education (Shen and Li, 2022) [9]; seven years of formal schooling (Barker, 2008) [42]; no household member (aged 14+) has completed at least eight years of schooling (Vasishtha and Mohanty, 2021) [43]; no household member has completed five years of schooling (Alkire and Seth, 2015) [44]; and no member aged 10 years or older has completed at least six years of schooling (UNDP and OPHI, 2022) [45]. The indicator selected for the education dimension is “years of education” (the question option of “maximum years of schooling” is not chosen here because the length of education involved in “years of schooling” is more detailed and convenient for this study), where the individual questionnaire asks the respondent, “How many years of formal schooling have you had?” Among the options are “1 year of elementary school, two years of elementary school, up to 6 years of a university”. We rank the years of individual education from small to large each year, taking the median years of education as the relative cutoff of that year’s education dimension. When the years of individual education are below this relative cutoff, they are considered to be in relative deprivation.

3.3.3. Health Dimensions

Some families fell into poverty because of the high medical expenses brought by illness. For the health dimension, some scholars chose the indicators as follows: ① child mortality (Stats SA; 2014) [46]; ② disability (Fransman and Yu (2018) [47], if an individual has fewer than two of the following six disabilities: hearing, vision, cognition, ambulation, severe difficulty with self-care (e.g., bathing and dressing), or performing independent tasks (e.g., shopping) (Dhongde and Haveman, 2017 [48]; Glassman, 2019 [49]; Dhongde et al., 2019 [50]; Dhongde and Haveman, 2022) [51]; ③ illness, at least one member stays home because of illness (Shen and Li, 2022) [9]; ④ medical, no health insurance (Wang and Alkire, 2009; Zou and Fang, 2011) [33,34]; the per capita out-of-pocket medical spending accounts for more than 50% of a family’s total medical expenses (Shen and Li, 2022) [9]; ⑤ BMI less than 18.5 (Alkire and Foster, 2011; Guo and Zhou, 2016) [1,52]. Due to the lack of disability information in the CHNS database, this research selects three indicators to measure individual health status, namely sickness, BMI, and health insurance. ① In the case of sickness, respondents were asked in the personal questionnaire, “In the past four weeks, have you ever been sick or injured?” and “Do you have any chronic or acute illnesses?”. Individuals who answered “yes” were considered to be deprived. ② However, with the improvement of people’s living standards, BMI gradually increases, malnutrition gradually improves, and more and more people have normal nutrition or even reach obese. ③ Individuals defined as uninsured with health insurance were considered deprived. It is challenging to quantify relatively for the health dimension due to the data structure, so this paper still adopts an absolute perspective for analysis.

3.3.4. Living Standard Dimension

By observing the living standards of households, one can intuitively judge whether households are in poverty or not. This research selects five indicators to measure the living standard status, including drinking water source, toilet type, cooking fuel, transportation, and household appliances. ① In the questionnaire, drinking water sources are classified as “other”, “ice or snow”, “creek, spring, river, lake”, “open wells (≤5 m)”, “groundwater (>5 m)”, “water plant”, “bottled water”, and seven options from the multidimensional absolute poverty study. In multidimensional absolute poverty studies, different scholars set different criteria for the cutoff, such as “open well (less than 5 m), creek, spring, river, etc. or safe drinking water is more than 30 min walking from home, roundtrip” (Alkire and Fang, 2019) [35] or “can not use tap water in-house or in-yard (≥5 m)” (Yu, 2013) [53]. In each case, the cutoff for the same deprivation indicator is different. This paper arranges drinking water sources from poor to good. The drinking water sources distributed in the median each year are the relative cutoff of the annual deprivation of drinking water indicators. ② In the questionnaire, the toilet type considers “no bathroom”, “other”, “earth open pit”, “cement open pit”, “no flush, outside house, public restroom”, “flush, outside house, public restroom”, “no flush, in-house”, and “flush, in-house”. Eight options are given using the same method as the drinking water source question, and the type of toilets are sorted from poor to good. The type of toilets distributed in the median is the relative cutoff of the deprivation indicator. ③ Cooking fuel is divided into “other”, “wood, sticks/straw, etc”., “charcoal”, “kerosene”, “coal”, “liquefied gas”, “electricity”, and “natural gas”. A total eight options are given, and the cooking fuels are ranked from worst to best. The median of the annual distribution is the relative cutoff of deprivation. ④ Transportation includes “tricycle”, “bicycle (including electric-assisted bicycle)”, “motorcycle (including motorcycle tricycle)”, and “automobile”. Four kinds of transportation are given, and the median number of transport assets was the relative cutoff of the deprivation indicator. ⑤ Household appliances include “color television”, “washing machine”, “refrigerator”, “air conditioners”, “sewing machines”, “electric fans”, “DVD/VCD”, “microwave ovens”, “electric rice cookers”, “pressure cooker”, “telephone”, “cell phones (non-smartphone)”, “smartphone”, “satellite dish”, “Computer”, and “tablet computer”. Sixteen appliances were given. The median of the number of assets is used as the relative cutoff deprivation indicator.

3.3.5. Employment Dimension

Employment is directly related to the income level of households. Regarding the employment dimension, some authors choose “all household members aged 15 to 65 years are unemployed (Fransman and Yu, 2018) [47] or “no long-term (more than 12 months) unemployment and formal employment” (Zhang and Zhou, 2015) [36]. The indicator chosen for the employment dimension is whether the individual has a job. Individuals who do not have a job are considered deprived, excluding the three cases of individuals being students, retired, and too young to work. The employment dimension is also limited by the data type and measured using absolute criteria. As seen in Table 1, except for the health and employment dimensions, which continue to use absolute poverty criteria because of the type of data, all other indicators use relative criteria to define the indicator relative deprivation cutoff.

3.4. Relative Deprivation Cutoff

According to the method above, the relative deprivation cutoff $z$ is calculated for each year and the results are shown in

Table 2. The indicators relative to deprivation cutoff in China.

Dimension	Indicator	1991	1993	1997	2000	2004	2006	2009	2011	2015
Income	Annual per capita household income (yuan)	1390	1433	1862	2318	2852	3167	4706	6524	8533
Education	Years of education	6 years of elementary school	6 years of elementary school	6 years of elementary school	2 years of junior high school	3 years of junior high school	3 years of junior high school	3 years of junior high school	3 years of junior high school	3 years of junior high school
Health	Illness	Illness	Illness	Illness	Illness	Illness	Illness	Illness	Illness	Illness
	BMI	<18.5 or >24	<18.5 or >24	<18.5 or >24	<18.5 or >24	<18.5 or >24	<18.5 or >24	<18.5 or >24	<18.5 or >24	<18.5 or >24
	Medical Insurance	None	None	None	None	None	None	None	None	None
Living standard	Drinking water source	Open well water (≤5 m)	Open well water (≤5 m)	Open well water (≤5 m)	Open well water (≤5 m)	Groundwater (>5 m)	Groundwater (>5 m)	Groundwater (>5 m)	Groundwater (>5 m)	Groundwater (>5 m)
	Type of toilet	Cement open pit	Cement open pit	Cement open pit	Cement open pit	Flush, outside house, public restroom	No flush, in-house	Flush, in-house	Flush, in-house	Flush, in-house
	Cooking fuel	Coal	Coal	Coal	Coal	Coal	Liquefied gas	Liquefied gas	Electricity	Electricity
	Transportation	1	1	1	1	1	1	1	1	1
	Household appliances	2	2	3	4	6	6	7	8	9
Employment	Working situation	No job	No job	No job	No job	No job	No job	No job	No job	No job

, which shows that most indicators of relative deprivation cutoffs have changed. The level of relative deprivation cutoff gradually increases over time. ① In the income dimension, the cutoff of the annual per capita household income level rose from 1390 yuan in 1991 to 8533 yuan in 2015, and the income level of residents increased significantly. ② In the education dimension, the number of years of education increased from “6 years of elementary school” in 1991 to “3 years of junior high school” in 2015, indicating that education reform is effective and the residents’ education level is gradually improving. ③ In the living standards dimension, the drinking water has upgraded from “open well water (≤5 m)” in 1991 to “groundwater (>5 m)” in 2015, and the quality of residents’ drinking water has also improved. The toilet type has also improved from “cement concrete pit” in 1991 to “flush, in-house” in 2015. The cutoff of the cooking fuel indicator has changed from “coal” in 1991 to “electricity” in 2015. The number of household appliances increased from “2” in 1991 to “9” in 2015. The cutoff of the number of means of transportation remained unchanged at “1”. The basic quality of life of residents has enhanced significantly. ④ In the health and employment dimensions, the relative cutoffs of deprivation indicators did not change due to the limitation of data to use absolute criteria. The changes in the indicator relative deprivation cutoff reflect the effectiveness of China’s economic development and poverty alleviation, while the standards of multidimensional relative poverty have been raised accordingly as the income and quality of life of residents continue to improve.

4. Empirical Results and Analysis

4.1. Poverty Incidence of Each Dimensional Indicator

Table 3. Incidence of poverty by indicators of multidimensional relative poverty (%).

Dimension	Indicator	1991	1993	1997	2000	2004	2006	2009	2011	2015
Income	Annual per capita household income (yuan)	19.97	20.86	20.05	24.18	24.44	26.32	23.54	24.28	26.65
Education	Years of education	45.17	43.02	41.11	48.64	47.88	45.07	45.36	39.40	35.70
Health	Illness	10.74	6.32	7.64	8.81	16.73	13.61	15.65	17.54	14.01
	BMI	28.93	29.91	33.87	39.09	42.3	43.43	46.23	49.77	54.62
	Medical Insurance	68.87	73.76	75.28	78.44	72.61	50.18	8.91	4.91	2.58
Living standard	Drinking water source	21.55	19.08	10.14	12.83	48.98	45.17	42.92	33.84	34.44
	Toilet type	33.05	30.26	26.94	22.25	46.37	49.50	48.69	36.54	30.58
	Cooking fuel	38.07	39.21	37.52	28.85	25.27	49.88	34.37	45.50	44.00
	Transportation	17.37	16.15	21.83	21.32	25.78	28.02	26.99	27.46	28.36
	Household appliances	38.40	32.81	39.26	40.02	47.00	38.30	38.54	36.28	42.10
Employment	Working situation	9.68	11.19	13.34	16.61	27.05	27.49	26.94	23.55	33.67

presents the change in poverty incidence of each indicator of multidimensional relative poverty from 1991 to 2015. First, the direction and degree of change in relative poverty vary across dimensions. The poverty incidence of the income dimension increased from 19.97% in 1991 to 26.65% in 2015. Although the income level of residents has increased, the relative poverty incidence has also increased, indicating that income inequality among residents has widened. The incidence of poverty in the education dimension decreased from 45.17% in 1991 to 35.7% in 2015, and the residents’ education level not only generally increased, but education deprivation has also improved significantly. In the health dimension, the poverty incidence of health insurance has declined from as high as 68.87% in 1991 to only 2.58% in 2015. Still, the incidence of illness and BMI poverty is increasing, indicating that China’s urban and rural health insurance system has alleviated the problem of access to healthcare for the poor, but illness and poor health are still symptomatic of relative health poverty. In the living standard dimension, the incidence of relative poverty of drinking water, cooking fuel, transportation, and household appliances has increased. These changes indicate that the gap is widening while the living standard of the residents is generally improving. The incidence of relative poverty of the toilet type has significantly decreased, which may reflect the effectiveness of the “toilet revolution” that started in the 1990s (toilet revolution refers to an initiative to transform toilets in developing countries, which was first proposed by UNICEF. A toilet is an important symbol to measure civilization. In 1990, the Chinese government began a campaign to clean up toilets.). In the employment dimension, the incidence of poverty has been on the rise in recent years, indicating that the number of groups with no jobs has increased.

Second, there are some ups and downs in the variation of indicators across dimensions. Relative poverty in the income dimension was on an upward trend until 2006, then slightly adjusted back in 2009, and then entered an upward range again. Some indicators of other dimensions, where the incidence of poverty decreased year by year until 2000, jumped after 2000 and 2004 and then began to decline year by year again. This change was related to the change in some indicators’ deprivation relative cutoff in 2000 and 2004 (Indicators with the change in the cutoff in 2000: the cutoff of the indicator of years of education changed from “6 years of elementary school” in 1997 to “2 years of junior high school” in 2000. Indicators with the change in the cutoff in 2004: the cutoff of the indicator of years of education changed from “2 years of junior high school” in 2000 to “3 years of junior high school” in 2004, the source of drinking water changed from “large mouth well water (≤5 m)” in 2000 to “ground water (>5 m)” in 2004, and the type of toilet changed from “open concrete pit” in 2000 to “outdoor non-flushing toilet” in 2004.). Finally, the main factors of multidimensional relative poverty changed over time.

The top three indicators with the highest incidence of poverty among residents in 1991 were health insurance, years of education, and household appliances, which changed to BMI, household appliances, and cooking fuel in 2015. These show that relative poverty has been more prominent in recent years, mainly regarding individual health and living standards.

4.2. Measurement of Multidimensional Relative Poverty

Table 4. Multidimensional relative poverty under different dimensions.

Deprivation of Dimension	Year	1991	1993	1997	2000	2004	2006	2009	2011	2015
$k=1$	$H$	0.578	0.573	0.572	0.636	0.705	0.671	0.622	0.563	0.580
	$A$	0.422	0.417	0.417	0.436	0.473	0.477	0.45	0.452	0.469
	$M_0$	0.244	0.239	0.239	0.277	0.333	0.320	0.28	0.254	0.272
$k=2$	$H$	0.267	0.248	0.25	0.305	0.41	0.388	0.312	0.285	0.321
	$A$	0.547	0.547	0.55	0.563	0.585	0.598	0.583	0.587	0.596
	$M_0$	0.146	0.136	0.137	0.172	0.24	0.232	0.182	0.168	0.191
$k=3$	$H$	0.073	0.064	0.065	0.094	0.165	0.171	0.111	0.104	0.124
	$A$	0.682	0.678	0.694	0.697	0.719	0.725	0.721	0.727	0.727
	$M_0$	0.050	0.044	0.045	0.066	0.119	0.124	0.080	0.076	0.098
$k=4$	$H$	0.008	0.005	0.008	0.014	0.025	0.042	0.022	0.021	0.022
		0.856	0.851	0.845	0.851	0.889	0.863	0.859	0.851	0.843
	$M_0$	0.007	0.004	0.007	0.012	0.022	0.036	0.019	0.018	0.019

shows the incidence of poverty (H), the average deprivation (A), and the multidimensional relative poverty index ($M_0$) under different dimensions. From the results in the table, we know that when two dimensions are deprived, taking $k=2$ as an example, the multidimensional relative poverty index ($M_0$) is 0.191 and the multidimensional relative poverty incidence (H) is 0.321. The average deprivation intensity (A) was 0.596 in 2015. Figure 2 shows the changes in the multidimensional relative poverty index ($M_0$) when individuals suffer from different dimensions of deprivation. As seen in Figure 2, the trend of the change in the multidimensional relative poverty index under different dimensions is generally consistent. The multidimensional relative poverty index declined moderately from 1991–1997, showed a relatively rapid increase from 1997–2004, a sustained and significant decline from 2004–2011, and began to trend upward again in 2011. Compared with 1991, multidimensional relative poverty is more serious in 2015, indicating that solving relative poverty is more difficult at this stage. At the same time, the multidimensional relative poverty index is found to be lower when the individual suffers from more deprivation dimensions. When $k=1$, the multidimensional relative poverty index varies between 20–35%, i.e., approximately 20–35% of the population suffers from one dimension of relative deprivation. When k = 2, the multidimensional relative poverty index varies between 10–25%. When k = 3, the multidimensional relative poverty index does not exceed 15%. When $k=4$, the multidimensional relative poverty index varies by 4%, i.e., only approximately 4% of the population suffers from four dimensions of relative deprivation. When $k=5$, i.e., individuals suffer from relative deprivation in all five dimensions, the multidimensional relative deprivation index is zero and therefore is not shown in the tables and figures.

4.3. Decomposition of the Multidimensional Relative Poverty Index ($M_0$)

4.3.1. Decomposition by Sub-Indicator

Taking two dimensions of deprivation ($k=2$) as an example,

Table 5. Decomposition of multidimensional relative poverty index ($M_0$) by sub-indicators ($k=2$).

Dimension	Indicator	1991	1993	1997	2000	2004	2006	2009	2011	2015
Income	Annual per capita household income	0.206	0.213	0.202	0.211	0.172	0.188	0.200	0.222	0.218
Education	Years of education	0.328	0.321	0.316	0.316	0.281	0.272	0.291	0.281	0.253
Health	Illness	0.021	0.014	0.016	0.018	0.025	0.021	0.028	0.030	0.023
	BMI	0.046	0.052	0.054	0.056	0.055	0.055	0.061	0.064	0.065
	Medical insurance	0.116	0.118	0.112	0.112	0.105	0.076	0.014	0.009	0.004
Living standard	Drinking water source	0.029	0.022	0.013	0.016	0.046	0.042	0.040	0.035	0.032
	Type of toilet	0.041	0.036	0.033	0.028	0.046	0.047	0.045	0.038	0.034
	Cooking fuel	0.040	0.039	0.039	0.030	0.025	0.048	0.034	0.042	0.039
	Transportation	0.024	0.022	0.028	0.023	0.023	0.024	0.025	0.027	0.023
	Household appliances	0.050	0.044	0.050	0.048	0.049	0.042	0.043	0.043	0.045
Employment	Working situation	0.100	0.118	0.136	0.141	0.174	0.186	0.218	0.210	0.265

manifests the contribution of each indicator to the multidimensional relative poverty index ($M_0$). The contribution of the income dimension to the multidimensional relative poverty index was 20.6% in 1991 and rose to 21.8% in 2015, and the relative income deprivation of the population became severe. The contribution of the education dimension to the multidimensional relative poverty index was gradually decreasing from 32.8% in 1991 to 25.3% in 2015, indicating that the relative deprivation of the education dimension is slowing down. However, in 2015 the contribution of the education dimension to the multidimensional relative poverty index was still high, exceeding the contribution of the income, health, and living standard dimensions. In the health dimension, the contribution of illness and BMI to the multidimensional relative deprivation index increased. Still, the contribution of health insurance gradually decreased, indicating that health insurance is more widespread and relevant health insurance policies have had a poverty-reducing effect. In the living standard dimension, the contribution of the drinking water source increased slightly, indicating that there is still much room for improvement in residents’ drinking water safety. The contribution of toilet type, cooking fuel, transportation, and household appliances all decreased, indicating that residents’ living standards have improved in these aspects. The contribution of the employment dimension to the multidimensional relative poverty index has gradually increased from 10% in 1991 to 26.5% in 2015, indicating that the employment deprivation of the population is deteriorating. In summary, the contribution of both income and education dimensions to the multidimensional relative poverty index has been high over the years, while employment deprivation became the most crucial cause of multidimensional relative poverty by 2015. At this stage, addressing relative poverty should focus more on improving income, education, and providing employment.

4.3.2. Decomposition by Rural and Urban Areas

The multidimensional relative poverty index ($M_0$) is decomposed into urban and rural areas.

Table 6. Decomposition of multidimensional relative poverty index ($M_0$) in urban and rural areas.

Deprivation Dimension	Region	1991	1993	1997	2000	2004	2006	2009	2011	2015
$k=1$	Urban ($M_0$)	0.147	0.153	0.163	0.187	0.221	0.218	0.185	0.152	0.145
	Contribution	0.197	0.187	0.197	0.189	0.204	0.209	0.205	0.251	0.214
	Rural ($M_0$)	0.291	0.274	0.269	0.312	0.383	0.366	0.322	0.328	0.357
	Contribution	0.803	0.813	0.803	0.811	0.796	0.791	0.795	0.749	0.786
$k=2$	Urban ($M_0$)	0.075	0.080	0.090	0.105	0.140	0.143	0.114	0.089	0.081
	Contribution	0.168	0.172	0.189	0.171	0.179	0.19	0.194	0.222	0.170
	Rural ($M_0$)	0.180	0.158	0.157	0.198	0.284	0.271	0.212	0.225	0.265
	Contribution	0.832	0.828	0.811	0.829	0.821	0.810	0.806	0.778	0.830
$k=3$	Urban ($M_0$)	0.023	0.022	0.029	0.037	0.059	0.076	0.052	0.039	0.032
	Contribution	0.147	0.148	0.184	0.160	0.152	0.189	0.201	0.215	0.143
	Rural ($M_0$)	0.063	0.053	0.051	0.077	0.146	0.145	0.093	0.102	0.129
	Contribution	0.853	0.852	0.816	0.840	0.848	0.811	0.799	0.785	0.857
$k=4$	Urban ($M_0$)	0.004	0.003	0.006	0.006	0.008	0.023	0.012	0.008	0.004
	Contribution	0.179	0.167	0.249	0.140	0.106	0.193	0.193	0.186	0.095
	Rural ($M_0$)	0.008	0.005	0.007	0.014	0.028	0.042	0.022	0.025	0.028
	Contribution	0.821	0.833	0.751	0.860	0.894	0.807	0.807	0.814	0.905

and Figure 3 report the rural and urban multidimensional relative poverty indexes and their contributions. When k = 2, the multidimensional relative poverty index is 0.265 in rural areas and 0.081 in urban areas in 2015. The rural multidimensional relative poverty index is approximately 3.3 times of the urban. The contribution of rural areas to the multidimensional relative poverty index is 83% and that of urban areas is 17%. With the increase in deprivation dimensions, the contribution of rural and urban areas to the multidimensional relative poverty index does not change much. Rural areas still have a higher incidence of multidimensional relative poverty than urban areas.

4.3.3. Decomposition by Region

The study decomposed the multidimensional relative poverty index ($M_0$) into eastern, central, and western regions (the central region includes the provinces of Heilongjiang, Henan, Hubei, and Hunan, the eastern region includes the provinces (cities) of Beijing, Liaoning, Shanghai, Jiangsu, and Shandong, and the western region includes the provinces (cities) of Chongqing, Guizhou, and Guangxi).

Table 7. Decomposition of multidimensional relative poverty index ($M_0$) by region.

Deprivation Dimension	Region	1991	1993	1997	2000	2004	2006	2009	2011	2015
$k=1$	Eastern ($M_0$)	0.204	0.208	0.214	0.226	0.272	0.261	0.218	0.172	0.187
	Central ($M_0$)	0.251	0.261	0.234	0.302	0.361	0.350	0.301	0.309	0.335
	Western ($M_0$)	0.285	0.248	0.269	0.296	0.370	0.354	0.332	0.325	0.329
	Eastern Contribution	0.297	0.308	0.218	0.252	0.278	0.279	0.268	0.293	0.287
	Central Contribution	0.373	0.394	0.466	0.478	0.457	0.450	0.459	0.379	0.395
	Western Contribution	0.330	0.298	0.316	0.271	0.265	0.271	0.273	0.328	0.318
$k=2$	Eastern ($M_0$)	0.121	0.113	0.117	0.125	0.170	0.166	0.120	0.093	0.115
	Central ($M_0$)	0.148	0.156	0.135	0.202	0.275	0.265	0.204	0.217	0.249
	Western ($M_0$)	0.173	0.137	0.160	0.177	0.277	0.267	0.231	0.234	0.241
	Eastern Contribution	0.295	0.295	0.207	0.224	0.241	0.246	0.227	0.239	0.252
	Central Contribution	0.369	0.414	0.467	0.515	0.484	0.472	0.481	0.403	0.418
	Western Contribution	0.336	0.290	0.326	0.261	0.275	0.282	0.292	0.358	0.331
$k=3$	Eastern ($M_0$)	0.040	0.038	0.038	0.040	0.071	0.079	0.044	0.036	0.052
	Central ($M_0$)	0.050	0.050	0.043	0.086	0.147	0.146	0.096	0.103	0.120
	Western ($M_0$)	0.062	0.042	0.053	0.062	0.138	0.147	0.105	0.109	0.115
	Eastern Contribution	0.286	0.310	0.207	0.188	0.204	0.220	0.189	0.206	0.242
	Central Contribution	0.364	0.414	0.459	0.572	0.520	0.489	0.511	0.423	0.425
	Western Contribution	0.350	0.275	0.334	0.240	0.276	0.291	0.300	0.371	0.333
$k=4$	Eastern ($M_0$)	0.006	0.004	0.007	0.006	0.013	0.022	0.009	0.009	0.011
	Central ($M_0$)	0.008	0.007	0.007	0.017	0.030	0.050	0.022	0.023	0.028
	Western ($M_0$)	0.006	0.002	0.007	0.012	0.020	0.033	0.028	0.029	0.020
	Eastern Contribution	0.301	0.285	0.250	0.141	0.207	0.210	0.170	0.204	0.244
	Central Contribution	0.429	0.570	0.481	0.607	0.575	0.569	0.496	0.393	0.481
	Western Contribution	0.271	0.145	0.269	0.251	0.218	0.221	0.334	0.403	0.275

reports the multidimensional relative deprivation index ($M_0$) and its contribution in the eastern, central, and western regions. As seen in Table 7, the eastern region has the lowest multidimensional relative poverty index. The central and western regions have high comparative multidimensional relative poverty indexes and are relatively similar in size. The relative deprivation in the central and western regions is more severe than in the eastern region. The central region has the highest contribution to the multidimensional relative poverty index, followed by the region of the west, and the eastern region has the lowest contribution. Figure 4 takes k = 2 as an example. The multidimensional relative poverty index in 2015 was 0.115 in the eastern region, 0.249 in the central region, and 0.241 in the western region. The above results show that the multidimensional relative poverty in the central region was more serious.

4.3.4. Decomposition by Gender

Table 8. Decomposition of multidimensional relative poverty index ($M_0$) by gender.

Deprivation Dimension	Gender	1991	1993	1997	2000	2004	2006	2009	2011	2015
$k=1$	Male ($M_0$)	0.202	0.193	0.195	0.234	0.283	0.270	0.232	0.212	0.231
	Female ($M_0$)	0.283	0.282	0.281	0.319	0.378	0.365	0.322	0.291	0.307
	Male Contribution	0.395	0.389	0.400	0.416	0.405	0.396	0.394	0.391	0.390
	Female Contribution	0.605	0.611	0.600	0.584	0.595	0.604	0.606	0.609	0.610
$k=2$	Male ($M_0$)	0.108	0.092	0.099	0.129	0.185	0.177	0.134	0.126	0.148
	Female ($M_0$)	0.180	0.176	0.175	0.214	0.290	0.280	0.225	0.204	0.228
	Male Contribution	0.356	0.328	0.353	0.370	0.367	0.360	0.349	0.352	0.355
	Female Contribution	0.644	0.672	0.647	0.630	0.633	0.640	0.651	0.648	0.645
$k=3$	Male ($M_0$)	0.033	0.027	0.027	0.046	0.080	0.087	0.055	0.050	0.064
	Female ($M_0$)	0.066	0.059	0.062	0.085	0.154	0.156	0.103	0.098	0.113
	Male Contribution	0.315	0.302	0.296	0.343	0.321	0.331	0.323	0.310	0.323
	Female Contribution	0.685	0.698	0.704	0.657	0.679	0.669	0.677	0.690	0.677
$k=4$	Male ($M_0$)	0.003	0.002	0.003	0.006	0.020	0.025	0.011	0.010	0.011
	Female ($M_0$)	0.010	0.007	0.011	0.018	0.044	0.046	0.026	0.025	0.025
	Male Contribution	0.238	0.197	0.230	0.260	0.288	0.330	0.270	0.262	0.281
	Female Contribution	0.762	0.803	0.770	0.740	0.712	0.670	0.730	0.738	0.719

reports the decomposition of the multidimensional relative deprivation index ($M_0$) by gender. Figure 5 takes k = 2 as an example. When suffering from relative deprivation in two dimensions, the multidimensional relative poverty index in 2015 was 0.228 for females and 0.148 for males. The contribution of females to the multidimensional relative poverty index is 64.5% and the contribution of males is 35.5%. The multidimensional relative poverty index of females is higher than that of males, the contribution is much higher than that of males, and this difference between males and females is relatively stable. The higher the deprivation dimension, the more serious the multidimensional relative poverty of females. The degree of multidimensional relative deprivation of the female group was much higher than that of males.

4.3.5. Decomposition by Age

A person is considered an adult at 18 years old. The United Nations classifies people aged 65 and over as the elderly. Considering the multidimensional relative poverty of different age groups, the age groups are divided into three categories: under 18 years old, 18–64 years old, and over 64 years old.

Table 9. Decomposition of multidimensional relative poverty index ($M_0$) by age group.

Deprivation of Dimension	Age Group	1991	1993	1997	2000	2004	2006	2009	2011	2015
$k=1$	Under 18 years old ($M_0$)	0.208	0.183	0.181	0.241	0.326	0.377	0.362	0.385	0.165
	18—64 years old ($M_0$)	0.230	0.225	0.218	0.254	0.308	0.290	0.246	0.220	0.241
	Over 64 years old ($M_0$)	0.425	0.415	0.429	0.453	0.464	0.461	0.427	0.394	0.377
	Contribution under 18 years old	0.062	0.046	0.046	0.051	0.024	0.024	0.015	0.017	0.006
	Contribution of 18–64 years old	0.794	0.800	0.762	0.753	0.760	0.735	0.715	0.698	0.673
	Contribution over 64 years old	0.143	0.154	0.192	0.196	0.216	0.242	0.269	0.285	0.321
$k=2$	Under 18 years old ($M_0$)	0.106	0.087	0.083	0.137	0.233	0.283	0.252	0.314	0.087
	18–64 years old ($M_0$)	0.131	0.120	0.116	0.146	0.212	0.198	0.146	0.132	0.157
	Over 64 years old ($M_0$)	0.335	0.322	0.331	0.365	0.387	0.386	0.343	0.313	0.306
	Contribution under 18 years old	0.053	0.039	0.037	0.047	0.024	0.025	0.016	0.021	0.004
	Contribution of 18–64 years old	0.758	0.751	0.705	0.699	0.726	0.695	0.65	0.636	0.626
	Contribution over 64 years old	0.189	0.211	0.258	0.255	0.251	0.280	0.333	0.343	0.370
$k=3$	Under 18 years old ($M_0$)	0.024	0.020	0.020	0.054	0.115	0.144	0.158	0.191	0.015
	18–64 years old ($M_0$)	0.041	0.035	0.032	0.046	0.094	0.091	0.052	0.047	0.062
	Over 64 years old ($M_0$)	0.163	0.145	0.156	0.203	0.253	0.277	0.205	0.194	0.186
	Contribution under 18 years old	0.036	0.028	0.028	0.048	0.024	0.023	0.023	0.028	0.002
	Contribution of 18–64 years old	0.696	0.677	0.601	0.581	0.646	0.599	0.526	0.502	0.522
	Contribution over 64 years old	0.305	0.295	0.371	0.370	0.330	0.377	0.450	0.470	0.476
$k=4$	Under 18 years old ($M_0$)	0	0	0.002	0.005	0.012	0.044	0.046	0.056	0
	18–64 years old ($M_0$)	0.003	0.001	0.003	0.005	0.014	0.02	0.008	0.008	0.010
	Over 64 years old ($M_0$)	0.050	0.036	0.044	0.064	0.067	0.112	0.069	0.058	0.049
	Contribution under 18 years old	-	-	0.015	0.027	0.014	0.024	0.029	0.034	-
	Contribution of 18–64 years old	0.376	0.272	0.326	0.339	0.509	0.455	0.329	0.376	0.394
	Contribution over 64 years old	0.624	0.728	0.659	0.635	0.478	0.521	0.642	0.590	0.606

reports the multidimensional relative poverty index ($M_0$) and the contribution of each age group. Figure 6 takes k = 2 as an example. Table 9 shows multidimensional relative poverty is the severest for those above 64 years old. Before 2000, multidimensional relative poverty was more serious for those aged 18–64 than those under 18. After 2000, multidimensional relative poverty was more serious for those under 18 than those aged 18–64. Regarding the contribution of each age group to the multidimensional relative poverty index, the 18–64 age group contributes the most, partly probably because this age group involves the largest number of people, followed by those over 64 years old. Those under 18 contribute the least to the multidimensional relative poverty index. Overall, in recent years, older adults have been the more severely deprived group, followed by those aged 18–64, and alleviating multidimensional relative deprivation should focus more on these groups.

4.4. Decomposition of Multidimensional Relative Poverty Changes

Based on the methods of Equations (3) and (10), this paper continues to analyze the changes in multidimensional relative poverty and its change decomposition (see

Table 10. Changes in the multidimensional relative poverty index ($k=2$).

Period	Absolute Change	Relative Change	Annual Absolute Change	Annual Relative Change	Poverty Incidence Effect	Intensity of Poverty Effect	Shapley Decomposition
							Poverty Incidence Effect Contribution	Intensity of Poverty Effect Contribution
1991–1993	−0.010	−0.071	−0.005	−0.035	−0.010	0.000	1.000	0.000
1993–1997	0.002	0.014	0.000	0.002	0.001	0.001	0.595	0.405
1997–2000	0.034	0.249	0.011	0.079	0.031	0.004	0.895	0.105
2000–2004	0.068	0.397	0.017	0.087	0.060	0.008	0.885	0.115
2004–2006	−0.008	−0.033	−0.004	−0.017	−0.013	0.005	1.663	−0.663
2006–2009	−0.050	−0.216	−0.017	−0.078	−0.045	−0.005	0.895	0.105
2009–2011	−0.015	−0.080	−0.007	−0.039	−0.016	0.001	1.082	−0.082
2011–2015	0.024	0.144	0.006	0.033	0.021	0.003	0.886	0.114
1991–2015	0.045	0.310	0.013	0.011	0.031	0.014	0.682	0.318

and Figure 7). Taking $k=2$ as an example, the results show that the multidimensional relative poverty index increased by 0.013 per year on average from 1991 to 2015. Specifically, the direction of change of multidimensional relative poverty was negative in 1991–1993, 2004–2006, 2006–2009, and 2009–2011. The multidimensional relative poverty index decreased, and the multidimensional relative poverty situation was improved. In 1993–1997, 1997–2000, 2000–2004, and 2011–2015, the direction of change of multidimensional relative poverty was positive. The multidimensional relative poverty index increased, and multidimensional relative poverty worsened.

From the two decomposition terms of the change in multidimensional relative poverty, the change in the incidence of the poverty effect is more significant than the change in the intensity of poverty effect. The results of Shapley’s decomposition also show that the contribution of incidence of poverty effect to the change in multidimensional relative poverty index is much higher than that of intensity of poverty effect. The contribution of the intensity of the poverty effect is negative in the periods of 2004–2006 and 2009–2011. The change in multidimensional relative poverty is mainly due to the incidence of the poverty effect. The above results suggest that the alleviation of multidimensional relative poverty should be principally based on the incidence of multidimensional relative poverty to improve the poverty reduction effect.

4.5. Robustness Test

For the robustness test of multidimensional relative poverty index analysis, this paper considers the methods of changing indicator weights, indicator deprivation relative cutoff, and aggregation dimension cutoff. Among them, changing the aggregation dimension cutoff method has been applied in the previous results by presenting the multidimensional relative poverty under different deprivation dimensions. Here, the results of multidimensional relative poverty are measured and compared by ① using the equal indicator weighting method and ② replacing the indicator deprivation relative cutoff defined by the median in the previous paper with the indicator deprivation relative cutoff defined by mean.

4.5.1. Replacing the Indicator Weights

This research sets the same weight of 1/11 for each of the 11 indicators to calculate the multidimensional relative poverty (as shown in

Table 11. Multidimensional relative poverty status under equal indicator weights.

Deprivation Indicators	Year	1991	1993	1997	2000	2004	2006	2009	2011	2015
$i=1$	$H$	0.914	0.924	0.946	0.957	0.970	0.965	0.949	0.945	0.953
	$A$	0.330	0.317	0.314	0.324	0.398	0.393	0.343	0.326	0.331
	$M_0$	0.302	0.293	0.297	0.310	0.386	0.379	0.326	0.308	0.315
$i=2$	$H$	0.770	0.787	0.804	0.830	0.881	0.862	0.821	0.799	0.816
	$A$	0.375	0.357	0.354	0.360	0.429	0.429	0.382	0.369	0.371
	$M_0$	0.289	0.281	0.284	0.298	0.378	0.370	0.314	0.295	0.303
$i=3$	$H$	0.616	0.618	0.612	0.646	0.756	0.736	0.661	0.617	0.638
	$A$	0.423	0.405	0.408	0.410	0.469	0.471	0.431	0.425	0.424
	$M_0$	0.260	0.250	0.249	0.265	0.355	0.347	0.285	0.262	0.270
$i=4$	$H$	0.456	0.439	0.430	0.453	0.610	0.587	0.490	0.444	0.462
	$A$	0.476	0.459	0.465	0.469	0.517	0.522	0.486	0.484	0.481
	$M_0$	0.217	0.201	0.200	0.212	0.315	0.306	0.238	0.215	0.222
$i=5$	$H$	0.303	0.262	0.265	0.282	0.463	0.436	0.326	0.292	0.304
	$A$	0.532	0.523	0.528	0.533	0.565	0.577	0.548	0.546	0.542
	$M_0$	0.161	0.137	0.140	0.150	0.262	0.251	0.178	0.160	0.165
$i=6$	$H$	0.168	0.130	0.138	0.152	0.301	0.297	0.188	0.170	0.174
	$A$	0.595	0.592	0.595	0.600	0.625	0.633	0.616	0.612	0.608
	$M_0$	0.100	0.077	0.082	0.091	0.188	0.188	0.116	0.104	0.106
$i=7$	$H$	0.065	0.048	0.054	0.063	0.164	0.173	0.096	0.083	0.084
	$A$	0.673	0.671	0.673	0.676	0.691	0.697	0.684	0.681	0.675
	$M_0$	0.044	0.032	0.036	0.043	0.113	0.120	0.066	0.057	0.056
$i=8$	$H$	0.021	0.015	0.017	0.021	0.070	0.080	0.037	0.031	0.029
	$A$	0.750	0.747	0.751	0.754	0.764	0.767	0.759	0.756	0.747
	$M_0$	0.016	0.011	0.013	0.016	0.053	0.061	0.028	0.024	0.022
$i=9$	$H$	0.004	0.003	0.003	0.005	0.023	0.029	0.010	0.009	0.006
	$A$	0.844	0.840	0.851	0.833	0.840	0.838	0.840	0.831	0.827
	$M_0$	0.003	0.002	0.003	0.004	0.019	0.024	0.009	0.007	0.005
$i=10$	$H$	0.001	0.001	0.001	0.001	0.005	0.006	0.002	0.001	0.001
	$A$	0.919	0.932	0.920	0.909	0.921	0.916	0.923	0.909	0.909
	$M_0$	0.001	0.000	0.001	0.001	0.005	0.005	0.002	0.001	0.001

and Figure 8). The results showed that the multidimensional relative poverty index ($M_0$) declined temporarily in 1993, then gradually rose in 2004 and 2006, then started to decline sharply and slowly fell back to the initial level. By comparing the results of multidimensional relative poverty dimensional equal weights and indicator equal weights, it can be found that the trend of the final multidimensional relative poverty changes is consistent for both estimation methods.

4.5.2. Replacing the Indicator Relative Deprivation Cutoff

The indicator relative deprivation cutoff was changed from the median to the mean. The cutoff of the income dimension is 50% of the mean annual income, the cutoff of the education dimension and the living standard dimension was set as the mean of the yearly indicators, and the health and employment dimensions were kept at the same standard due to the limitations of the data type.

Table 12. Multidimensional relative poverty in China (mean cutoff).

Deprivation Dimension	Year	1991	1993	1997	2000	2004	2006	2009	2011	2015
$k=1$	$H$	0.694	0.695	0.741	0.751	0.681	0.721	0.671	0.618	0.751
	$A$	0.454	0.458	0.465	0.477	0.424	0.506	0.476	0.473	0.505
	$M_0$	0.315	0.318	0.344	0.358	0.289	0.365	0.319	0.293	0.379
$k=2$	$H$	0.402	0.405	0.456	0.479	0.349	0.465	0.380	0.342	0.467
	$A$	0.556	0.560	0.564	0.573	0.533	0.612	0.595	0.600	0.619
	$M_0$	0.224	0.227	0.257	0.275	0.186	0.284	0.226	0.205	0.289
$k=3$	$H$	0.150	0.153	0.175	0.194	0.092	0.222	0.149	0.140	0.220
	$A$	0.682	0.681	0.695	0.705	0.675	0.736	0.729	0.730	0.738
	$M_0$	0.102	0.104	0.121	0.137	0.062	0.164	0.109	0.102	0.162
$k=4$	$H$	0.015	0.016	0.021	0.032	0.002	0.063	0.033	0.031	0.043
	$A$	0.860	0.863	0.866	0.868	0.871	0.870	0.859	0.855	0.848
	$M_0$	0.013	0.014	0.018	0.028	0.002	0.055	0.029	0.027	0.037

and Figure 9 show that individuals were deprived when their indicator status was below the indicator deprivation relative cutoff. We conclude that the multidimensional relative poverty index ($M_0$) increased from 1991 to 2000, decreased from 2000 to 2004, began to fall after rising to the highest point in 2006, and then began to increase again in 2011.

The comparison analysis with the results of the median cutoff showed that the multidimensional relative poverty index was higher than that of the mean cutoff. The changes in the multidimensional relative poverty index were more consistent in the overall trend of changes in other years, except for in 2004. The results indicated that the aforementioned results are still robust.

5. Conclusions and Discussion

This paper undertakes a comprehensive analysis of multidimensional relative poverty in China. Based on the 1991–2015 China Nutrition and Health Survey (CHNS) data, this research estimates and deconstructs the multidimensional relativity of China. This study finds that multidimensional relative poverty in China is rising in volatility. The more dimensions of relative deprivation, the more severe the multidimensional relative poverty. Solving multidimensional relative poverty is a long-term task. The poor are generally deprived in terms of income, education, and employment. There are obvious regional differences in multidimensional relative poverty. The multidimensional relative poverty in rural areas is much higher than that in urban areas. This is consistent with the research of most scholars (Wang and Alkire, 2009; Alkire and Fang, 2019; Zhang and Zhou, 2015) [33,35,36]. The multidimensional relative poverty index in the central and western regions is much higher than that in the eastern region. This is consistent with the research of Shen et al. (2018) [54]. There are also significant differences among different groups. The multidimensional relative poverty of females is more serious than that of males, and the multidimensional relative deprivation of children and the elderly is more serious. The decomposition of multidimensional relative poverty changes shows that the change of “the poverty incidence effect “is greater than that of “the intensity of poverty effect”, indicating that poverty reduction should pay more attention to the decrease in poverty incidence.

The research conclusions of this paper provide some theoretical references for the formulation of relevant anti-poverty policies. First of all, the government should focus on improving the income level of residents, reducing the income gap, and establishing and improving the social security mechanism. Especially in health and public services, the government should provide individuals with a complete safety protection network. Secondly, the government should focus on and help multi-dimensional regions and populations with relatively serious poverty. In the central and western regions and rural areas especially, women and the elderly are vulnerable groups in areas with a high incidence of multidimensional relative poverty. Although these people are out of absolute poverty, they are still in multi-dimensional relative poverty and have a significant risk of re-entering poverty.

There are many further analyses on multidimensional relative poverty, and our research is mainly limited by the availability of the CHNS database. (1) The research object of this paper takes the family as the research unit. Rich personal sample data may lead to more targeted research on the multidimensional relative poverty of individuals. (2) In the selection of multidimensionality, we also want to consider some related dimensions, such as mental health and the use of family financial services. Still, relevant data are lacking. If these restrictions can be solved in the future, we can study the multidimensional relative poverty in China more deeply.