A Three-Component Decomposition of the Change in Relative Poverty: An Application to China

Abstract

China has eliminated absolute poverty and begun to tackle relative poverty, yet the change in relative poverty in China has been less studied. In this paper, we develop a three-component decomposition of the change in relative poverty and apply it to analyze the relative poverty in China. The change in relative poverty is decomposed into identification, growth, and redistribution components. We compare the three-component decomposition with other decomposition methods in the existing literature and show the advantages of the former. Our study, using the China Family Panel Studies (CFPS) 2010–2018 data, shows that relative poverty is rising. Examining the periods of 2012–2014, 2014–2016, and 2016–2018, we show that the three components differ in their contribution to relative poverty. The identification component rises with income growth and increases relative poverty by 8.42%, 12.19%, and 12.55%, respectively. The growth component reduces the incidence of relative poverty by 8.34%, 11.24%, and 12.18%, respectively. In comparison, the redistribution component increases the incidence of relative poverty by 2.88%, 1.12%, and 6.60%, respectively.

1. Introduction

The incidences of extreme poverty in the world have been declining, mainly due to the continuous decrease in the number of absolute poor in developing countries [1]. However, poverty remains the most severe challenge in the world so far. According to a report by the United Nations, 71 million people in the world may return to extreme poverty in 2020 due to the impact of COVID-19, the first increase in the number of people in poverty since 1998. By 2030, 207 million more people in the world may fall into extreme poverty, bringing the total number of people in extreme poverty above 1 billion. People who have just emerged from poverty are more vulnerable to adverse external shocks and face a greater risk of returning to poverty. At the same time, although the number of poor people measured by global absolute standards has decreased year by year (2020 is an exception), the number of poor people is still large according to the relative poverty standards of specific countries.

As the largest developing country in the world, China has made the greatest contribution toward global poverty reduction and achieved the United Nations 2030 Agenda for Sustainable Development poverty reduction goal 10 years ahead of schedule. Over the past 40 years, China has lifted 770 million people out of poverty, accounting for about 3/4 of the global poverty reduction population in the same period [2]. However, in 2022, a huge number of people in China live just near the absolute poverty line. Although they are classified as non-poor under the current absolute poverty criteria, they are still relatively poor because of their low income. Moreover, with the ongoing changes in the poverty line, “new poor” people may appear. Therefore, completing the historic task of eliminating absolute poverty starts a new era in the battle against relative poverty. We would produce a quantitative decomposition method to reveal the main components of poverty changes and calculate their contributions. More quantitative studies on poverty change and potential decomposition can provide clues as to how China has completed such a large-scale task of poverty alleviation in a relatively short time and provide lessons for other developing countries.

Most researchers decompose poverty changes into growth and redistribution components in the existing literature [3,4,5]. This method is suitable for absolute poverty when the poverty line remains unchanged but is not applicable for relative poverty when the poverty line varies from year to year. China has entered the stage of dealing with relative poverty, leading to the urgency of solving the deficiencies of existing decompositions. Our research incorporates the endogenous change in poverty lines and fills in the gap through a comprehensive examination of the identification, growth, and redistribution components.

This paper contributes to the literature in the following aspects. Firstly, we construct the “identification-growth-redistribution” decomposition framework of poverty change, which can be applied to both absolute and relative poverty and provides a complete decomposition. Secondly, based on the decomposition framework, we decompose the change in relative poverty to analyze the factors that lead to changes in relative poverty in the context of China. Thirdly, we study the contribution of relative lines, economic growth, and income redistribution to relative poverty empirically.

The rest of this paper is organized as follows: Section 2 provides a review of the relevant literature. Section 3 sets out dynamic measurements of relative poverty using the CFPS (2010–2018) database. Section 4 constructs the quantitative framework of “identification-growth-redistribution” decomposition and calculates the contribution of each component to poverty changes. Section 5 concludes with the policy implications.

2. Literature Review

2.1. Poverty and Its Measurement

Absolute poverty is mostly measured in developing countries, where it coexists with absolute and relative poverty, with more emphasis on the former. Relative poverty is often measured in developed countries when absolute poverty has been eliminated. However, poverty measurement is much more complex than considering income or consumption. One strand of the literature on the measurement of poverty ties it to human capabilities. The essence of poverty is that people are incapable or “deprived” of the ability to change their living conditions, resist various risks in production or life, seize economic opportunities, or gain economic benefits [6]. The absolute deprivation of capability is absolute poverty. Being absolute in the capability space may imply being relative in the commodity or income space. However, relative poverty is also correlated with income inequality. Another strand emphasizes the (relative) costs of social inclusion [7]. These approaches imply the existence of a relative poverty line. Ravallion (2020) regards poverty as an objective economic deprivation that is low economic welfare or living standard, which is consistent with Sen’s view [1].

In recent studies, welfare and preference have been introduced into the formulation of the poverty line, making the identification results of poverty more accurate and reasonable. One theoretically appealing axiom for any measure of poverty is that individual welfare depends (positively) on both their “own income” and relative income. The welfarist case for using a weakly relative poverty measure rests crucially on this axiom [8]. Ravallion and Chen (2017) propose the welfare-consistent global poverty measurement standard and obtain the real empirical boundary of the measurement of global poverty, with the absolute poverty line as the lower boundary and the weakly relative line as the upper boundary that rises with the increase in the comparison income of specific countries, avoiding the uncertainty of key parameters [9]. Ravallion (2020) critically evaluates the current standards of global poverty, pointing out that the current absolute measures ignore the important impact that society has on welfare, while popular, strongly relative measures ignore the absolute standard of living [1]. Therefore, a new hybrid measure that reflects both survival and social inclusion is needed. Absolute and weakly relative measurements are combined to conform to the national line variation in each country.

2.2. Poverty Criteria and Poverty Lines

The poverty criteria of developed countries are generally the relative poverty lines. However, the relative poverty criteria are not uniform. For example, Japan’s relative poverty line is 50% of the income of middle-income families, the EU is 50% or 60% of the median income of residents, and Singapore regards the lowest 20% of families as relatively poor [10]. The National Academy of Sciences proposed the “quasi relative poverty line”, which is dynamically adjusted across periods based on the necessary subsistence expenditure. European scholars usually regard a certain proportion of a country’s median household income as the relative poverty line, which changes with the change in overall income [11].

China has been dealing with relative poverty since it lifted all the rural poor from absolute poverty. Some researchers have examined the criteria of relative poverty suitable for China’s national conditions. Sun and Zhang (2021) believe that after 2020, China’s relative poverty criteria should mainly consider income standards, supplemented by other measures [12]. The income standard is 40% of rural residents’ median per capita income. Some suggest that in the initial stage of relative poverty in China, the relative income poverty line for urban and rural residents should be set at 40% of the median per capita disposable income of urban and rural residents, respectively [13,14]. Li et al. (2021) suggested that 50% of the median disposable incomes of urban residents and 40% of the median disposable incomes of rural residents should be taken as the relative poverty standards of urban and rural areas, respectively [15]. Chen and Ravallion (2021) show that the Chinese official lines, revised twice since the original 1985 line, are neither absolute nor strongly relative [8]. Instead, they are weakly relative, with a positive elasticity to the mean that is less than unity. They provide a new annual series of weakly relative poverty measures consistent with the official lines. Under this weakly relative measurement, poverty has not vanished in China, but it indicates substantial progress.

Besides the median income, the average household per capita income is another vital reference indicator [1]. Qu (2021) reveals that a population with an income below 30–40% (preferably around 35%) of the average is regarded as relatively poor [16]. Zhou (2020) sets up relative poverty criteria to view an average disposable income below 50% of the national per capita disposable income as relatively poor [17]. He further estimates that the incidence of relative poverty in 2018 was about 22.2%. In a word, the examination of criteria for relative poverty is still in the preliminary stage and far from reaching a consensus.

2.3. Decomposition of Poverty Change

Economic growth and income redistribution are usually the main factors in poverty change. Economic growth (“the size of bread”) determines whether a country has the capability or adequate resources to reduce poverty. Income redistribution is reflected in the redistribution of limited resources across or within groups, which is a problem of how the bread is divided [18]. When a country’s economic growth is not enough to support all people and get rid of poverty, a higher level of income equality may lead to higher incidences of poverty. However, if a country has enough national wealth but does not eliminate poverty, income redistribution (i.e., changing from one distribution state to another) can reduce poverty even without economic growth. Ravallion and Chen (2007) find that the progress of China’s anti-poverty is uneven among the provinces [19]. Provinces with high inequality make slow progress in poverty eradication due to low growth rates and low growth elasticity of poverty reduction.

Datt and Ravallion (1992) divide the change in poverty into two parts: the growth component and the redistribution component [3]. The growth component refers to the change in the poverty index due to the increase in income levels (income distribution remains unchanged), and the redistribution component refers to the change in the poverty index due to the change in income distribution (average income level remains unchanged). This method has been used to study the poverty situation in Brazil and India in the 1980s. Ali (1998) adopted a simple poverty decomposition framework and considered that the change in poverty is the sum of the change caused by economic growth and the change caused by income redistribution [20]. When the poverty line is a function of average income, the elasticity of the poverty line to income plays an important role in determining the change caused by growth. He uses the income data from developing countries to study income inequality and poverty in three developing regions of Latin America, Asia, and sub-Saharan Africa. Shorrocks and Kolenikov (2001) established a model to study the changing trend of poverty in Russia during 1985–1999 and calculated the impact of the mean income, income inequality, and the poverty line on poverty change, respectively [21]. It is found that, taking 1985 as the base period, during 1985–1999, the decline in real per capita income increased the incidence of poverty by 38%, the rise of inequality increased the incidence of poverty by 12%, and the decrease in the poverty line reduced the incidence of poverty by 23%. Therefore, the decline in real income is the decisive factor leading to the high incidences of poverty, but there is still an unexplained residual term in their analysis. Baye (2006) uses a method based on the Shapley value and a household survey of Cameroon to estimate the growth-redistribution components of poverty change and finds that the growth component often dominates the impact of income redistribution and that the distribution-neutral growth of family income has a great potential contribution to poverty reduction [22]. Shorrocks (2013) extends the Shapley decomposition method of the poverty index to eliminate the residual term in Datt and Ravallion (1992), yet the decomposition remains a two-component framework [5]. Jiang and Liu (2017) decomposed the poverty indexes using the CFPS data from 2010 and 2014 and found that economic growth had a positive effect on poverty reduction, while income redistribution worsens poverty [23]. However, their results are questionable since they use the “growth-redistribution” decomposition framework with the poverty line unchanged. China’s government raised the poverty standard in 2011, resulting in a much higher poverty line in 2014 than in 2010. The decomposition may be incomplete without considering the change in poverty lines.

So far, few researchers have paid attention to how the adjustment of the poverty standard (or poverty line) would affect poverty change. A possible reason is that there have been very few changes in poverty standards when absolute poverty prevails in most countries. For example, China adjusted the poverty standard twice over the 40 years since the reform and opening-up. Decomposing the change in poverty into growth and redistribution components can meet the analytical needs in most cases of absolute poverty. However, relative poverty lines vary frequently as the level and distribution of income change. Therefore, we would consider the impact of poverty line adjustment on poverty change (known as the “identification component” in poverty change because the poverty line is used to identify the poor population) and construct a decomposition framework with “identification-growth-redistribution” components.

The Chinese economy is very dynamic in its growth and structural change, and the relative poverty line changes frequently due to the principle that a boat floats higher when the river rises. It would be inapplicable to use the “growth-redistribution” analytical framework to analyze China’s future poverty changes. Moreover, the poverty line is related to both growth and redistribution. If the changes in the poverty line are not considered, there may be two issues in the “growth-redistribution” decomposition framework. First, the growth and redistribution components of poverty change are not pure. Thus, the effects of economic growth and income redistribution on poverty reduction are biased. Second, besides the growth and redistribution components, there is a residual term that cannot be reasonably explained. That is to say, the sum of the change in poverty caused by growth and redistribution does not equal the total change in poverty.

Several previous studies tried to incorporate the change in the poverty line into the decomposition process of poverty change and expanded the “growth-redistribution” framework [21,24]. However, in the decomposition framework that Shorrocks and Kolesnikov (2001) proposed, there is also a residual term besides the growth, redistribution, and poverty standard components. When using this framework to study the poverty change in Russia, they found that the residual term is not only significant but also more prominent than the components of growth or poverty standards. Therefore, the decomposition is flawed in its unexplained residual term. Fujii (2017) decomposes poverty change into growth and redistribution components, with the difference in the poverty line included in the growth component [24]. Therefore, the growth component is not clean, since identification is not separated from the growth component. The study using the Philippines data shows that the real growth effect on poverty reduction is underestimated in the case of the increasing poverty line. Aristondo et al. (2019) decompose the changes in poverty into poverty line effects and distribution effects without considering how the poverty line varies [25]. The effects of the poverty line contain “new poor” and “old poor” components. The distribution effects are decomposed into a growth component and an inequality component. Luo and Ping (2020) decompose poverty changes into three effects of economic growth, inequality, and total population and analyze the effects of China’s urbanization on urban and rural poverty [26]. We consider the endogenous change in poverty lines and propose a decomposition framework with three parts of identification-growth-redistribution compared with the existing literature. Our method can complete decomposition without residuals and apply to absolute and relative poverty. To clarify the contributions of the paper, we compared it with the existing research in

Table 1. Comparisons with existing research.

Literature	Whether Consider Change in Poverty Line	Type of Poverty Lines	Decomposition Frame	Whether There Is Residual	Countries	Notes
Datt and Ravallion (1992)	No	Absolute	Growth-distribution	Yes	Brazil and India	Incomplete decomposition
Ali (1998)	Yes	Strongly relative	Growth-distribution	No	Latin America, Asia, and South Sahara Africa	Growth component not complete
Shorrocks and Kolenikov (2001)	Yes	Absolute	Growth-distribution-poverty line	Yes	Russia	Incomplete decomposition
Baye (2006)	No	Absolute	Growth-distribution	No	Cameroon	Poverty line change not considered
Shorrocks (2013)	No	Absolute	Growth-distribution	No	-	Poverty line change not considered
Fujii (2017)	Yes	Strongly relative	Growth-distribution	No	The Philippines	Poverty line change not considered
Aristondo et al. (2019)	Yes	Strongly relative	Poverty line-growth-inequality	No	27 European countries	Some results inconsistent
Jiang and Liu (2017)	No	Absolute	Growth-distribution	Yes	China	Poverty line change not considered
Luo and Ping (2020)	No	Absolute	Growth-inequality-population	No	China	Poverty line change not considered
This paper	Yes	Endogenous relative lines	Identification-growth-redistribution	No	China	Complete decomposition and poverty line change considered

.

3. Measurement of Relative Poverty in China

3.1. Measurement

We used the China Family Panel Studies (CFPS) dataset, which tracks and collects data at individual, family, and community levels and reflects the changes in China’s society, economy, population, education, and health. The samples cover 25 provinces, cities, and autonomous regions: Beijing, Tianjin, Hebei, Shanxi, Liaoning, Jilin, Heilongjiang, Shanghai, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, Shandong, Henan, Hubei, Hunan, Guangdong, Guangxi Zhuang Autonomous Region, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, and Gansu Province. The target sample size is 16,000 households. CFPS has been officially conducted every other year since 2010. It has been conducted six times so far, of which the data for the first five times are available, and the time spans from 2010 to 2018. This paper takes the family as the unit for analysis and uses family economic data.

This paper uses the data from the CFPS to measure the incidence of relative poverty in China. We set the relative poverty line at 30% or 50% of the average per capita net income of families, respectively. The selection of 30% is mainly based on China’s existing practical experience. Zhejiang was an early province in China to set relative poverty standards. In 2008, Zhejiang began to explore a poverty alleviation standard-setting mechanism related to farmers’ per capita income and set 30% of farmers’ per capita income in 2007 as the poverty alleviation standard. 50% is the most popular proportion in the world at present and is also frequently used in domestic research. Since the average per capita net income of families changes each year, the relative poverty line changes yearly (

Table 2. Relative poverty lines (Yuan) in China.

Year	2010	2012	2014	2016	2018
30% of the mean [median]	3076 [1800]	4028 [2700]	5270 [3240]	7381 [4320]	10,093 [5000]
50% of the mean [median]	5127 [3000]	6713 [4500]	8784 [5400]	12,301 [7200]	16,821 [8333]

Notes: The numbers in square brackets are calculated according to the median.

).

According to the relative poverty line in Table 1, we calculate the relative poverty incidence in each year (

Table 3. Incidence of relative poverty (%).

Year		2010	2012	2014	2016	2018
Relative poverty standard	30% of the mean [median]	25.88 [12.94]	24.14 [16.95]	27.03 [16.95]	25.33 [13.18]	32.75 [12.30]
	50% of the mean [median]	43.98 [24.71]	38.54 [26.71]	41.50 [27.60]	43.57 [24.82]	50.54 [24.99]

Notes: The numbers in square brackets are calculated according to the median.

). In the latest round of the CFPS in 2018, the incidence of relative poverty was 32.75% when the relative poverty line was 30% of the average per capita net income of families. According to the total population of the Chinese mainland in 2018, about 457 million people belonged to relatively poor people. When the relative poverty line is 50% of the average per capita net income of families, the incidence of relative poverty is as high as 50.54%, which means that more than half of the families in China have a per capita net income lower than half of the average income level, and more than 700 million people are in relative poverty.

While the absolute poverty standard increased in 2011, the incidence of relative poverty decreased, indicating that China’s income inequality decreased, and the income of low-income people increased relatively fast between 2010 and 2012. After 2012, the incidence of relative poverty in China has shown an overall upward trend, and the number of relatively poor people is increasing, which shows that the income growth rate of low-income people in China is lower than that of the whole population. With economic growth, absolute poverty decreases continuously, while relative poverty increases at the same time.

Since China eliminated absolute poverty at the end of 2020 under the current poverty standards, China’s focus on poverty has also shifted from absolute poverty to relative poverty. The trend of relative poverty in China from 2010 to 2018 shows that the incidence of relative poverty has shown an upward trend. Therefore, in the transition period from eliminating absolute poverty to reducing relative poverty, the Chinese government is facing big pressure from the increasing number of relatively poor people. How to curb the rising relative poverty becomes a major challenge for China after 2020.

3.2. Comparison of Mean and Median

The mean and median are common statistical indicators to measure relative poverty. Generally, the mean income is higher than the median income. Therefore, setting the relative poverty standard based on a certain proportion of mean income may overestimate relative poverty. Consequently, we also put the relative poverty standard based on the median income, which is co-listed in Table 2 and Table 3. According to the calculation results, the relative poverty line (incidence) set with the mean income as the reference is higher than the result of the relative poverty standard set with the median income. When using the median income to establish the relative poverty line, the changing trend of the incidence of relative poverty is significantly different from using the mean income.

It is worth noting that although the mean and median are the most commonly used comparison incomes in the literature on relative poverty, that does not mean that there are no other alternatives. Some scholars have developed new statistical indicators based on the mean income as a reference. Sheshinski (1972) and Sen (1976) put forward the distribution-corrected mean [27,28]. Ravallion and Chen (2019) set up the theoretical formula of comparison income, including upward and downward relative comparison. Instead of the ordinary mean or median, the model uses a distribution-corrected mean, whose nature depends on whether people tend to look up or down (in terms of income) when assessing their performance relative to others [29]. Ravallion (2020) uses national poverty line data and Gini-discounted means to calibrate a composite measure consisting of the absolute poverty line and the weakly relative poverty line [1]. The mean income can reflect the overall income level of the group, and correcting the mean income by using the Gini coefficient or weight can make up for the disadvantage that it cannot reflect the characteristics of income inequality. It is easy to develop new statistical indicators as comparison income based on the mean. This desirable property makes the mean value widely used in measuring relative poverty. In addition, de Mesnard (2007) and Kampke (2010) also give reasons against the use of the median [30,31]. This paper uses the mean income to discuss the relative poverty standard based on the above considerations.

4. Decomposition of Changes in Poverty

4.1. Decomposition Method

Growth, redistribution, and adjustment in poverty standards can result in changes in poverty indexes. The weights of these components in poverty changes may differ as time goes on and across regions. Economic growth is usually demonstrated as the main path out of poverty when the poor population is large and the “bread” is too small. To identify the effects of growth and income redistribution on poverty, Datt and Ravallion (1992) [3] propose the following decomposition for changes in poverty from time 1 to time 2.

$$\Delta P=P_2-P_1=\left[P\left({\mu }_2,L_r\right)-P\left({\mu }_1,L_r\right)\right]+\left[P\left({\mu }_r,L_2\right)-P\left({\mu }_r,L_1\right)\right]+e$$

(1)

In Equation (1), ${\mu }_i\left(i=1, 2, r\right)$ is the mean income, $L_j\left(j=1, 2, r\right)$ is the Lorenz curve, r represents the reference group, and e is the residual. $\left[P\left({\mu }_2,L_r\right)-P\left({\mu }_1,L_r\right)\right]$ represents the growth component, which is poverty change caused by changes in mean income when the Lorenz curve remains unchanged. $\left[P\left({\mu }_r,L_2\right)-P\left({\mu }_r,L_1\right)\right]$ refers to the redistribution component, which is poverty change caused by changes in the Lorenz curve with mean income unchanged. The decomposition forms a frame for studying poverty reduction policy, and we can decompose the poverty index along with the policy-related dimension [32]. However, there are two problems with the decomposition in (1). One is that the choice of reference will affect the values of the growth component and redistribution component. Another is that the decomposition is not complete, with a residual term unexplained. To overcome the limitations, Kakwani (2000) proposes an axiomatic method to eradicate residuals and give a symmetric estimation for the initial and terminal periods [4]. Shorrocks (2013) proposes a cooperation game theory framework based on the Shapley value [5]. When the framework applied to the growth-redistribution decomposition of poverty changes, the method based on the Shapley value gets the same theoretical and empirical results as Kakwani (2000), which is called Shapley decomposition. The decomposition is as follows.

$$\begin{array}{cc}\Delta P=P_2-P_1=& \underset{growth component}{\underbrace{0.5\left\{\left[P\left({\mu }_2,L_1\right)-P\left({\mu }_1,L_1\right)\right]+\left[P\left({\mu }_2,L_2\right)-P\left({\mu }_1,L_2\right)\right]\right\}}}\\ & +\underset{redistribution component}{\underbrace{0.5\left\{\left[P\left({\mu }_1,L_2\right)-P\left({\mu }_1,L_1\right)\right]+\left[P\left({\mu }_2,L_2\right)-P\left({\mu }_2,L_1\right)\right]\right\}}}\end{array}$$

(2)

In Equation (2), the initial and terminal periods are used as references, respectively, and the growth component and redistribution component are computed by taking the average of both. The reason why the weight for the two components in Equation (2) is 0.5 is that the two components are calculated repeatedly when taking the initial and terminal periods as references, respectively.

In the decomposition in (2), the effect of the changes in the poverty lines on the poverty index is not taken into consideration. Therefore, the decompositions (1) and (2) applied to the cases where the poverty line remained unchanged during the period; however, they are not applicable when the terminal poverty line is different from the initial poverty line. Fujii (2017) studies the growth-redistribution decomposition framework with varied poverty lines; however, the effect of changes in the poverty line is not separate but included in the growth component [24]. Shorrocks and Kolenikov (2001) consider changes in the poverty line and make the following decomposition of growth, redistribution, and the poverty standard component [20]:

$$\begin{array}{c}G=P\left({\mu }_2,L_1,z_1\right)-P\left({\mu }_1,L_1,z_1\right),\hfill \\ R=P\left({\mu }_1,L_2,z_1\right)-P\left({\mu }_1,L_1,z_1\right), S=P\left({\mu }_1,L_1,z_2\right)-P\left({\mu }_1,L_1,z_1\right)\hfill \end{array}$$

(3)

However, when the growth-redistribution-poverty standard decomposition framework was applied to changes in poverty in Russia, the observed total changes in poverty did not equal the sum of the growth component, redistribution component, and poverty standard component. There is an extra residual E, which makes the decomposition incomplete.

$$\Delta P=G+R+S+E$$

(4)

Different from existing decomposition, we consider the effects of the endogenous adjustment of the poverty line along with growth and redistribution and set up a three-component decomposition framework.

$$\begin{array}{cc}\Delta P=P_2-P_1=\hfill & \left[P\left({\mu }_2,L_2,z_2\right)-P\left({\mu }_1,L_1,z_1\right)\right]=\left\{\left[P\left({\mu }_2,L_2,z_2\right)-P\left({\mu }_2,L_2,z_1\right)\right]\right\}+\left\{\left[P\left({\mu }_2,L_2,z_1\right)-P\left({\mu }_1,L_1,z_1\right)\right]\right\}\hfill \\ & =\underset{\mathit{identification}\mathit{component}}{\underbrace{\left\{\left[P\left({\mu }_2,L_2,z_2\right)-P\left({\mu }_2,L_2,z_1\right)\right]\right\}}}+\underset{\mathit{growth}\mathit{component}}{\underbrace{0.5\left\{\left[P\left({\mu }_2,L_1,z_1\right)-P\left({\mu }_1,L_1,z_1\right)\right]+\left[P\left({\mu }_2,L_2,z_1\right)-P\left({\mu }_1,L_2,z_1\right)\right]\right\}}}\hfill \\ & +\underset{\mathit{redistribution}\mathit{component}}{\underbrace{0.5\left\{\left[P\left({\mu }_1,L_2,z_1\right)-P\left({\mu }_1,L_1,z_1\right)\right]+\left[P\left({\mu }_2,L_2,z_1\right)-P\left({\mu }_2,L_1,z_1\right)\right]\right\}}}\hfill \end{array}$$

(5)

z₁ and z₂ are poverty lines at time 1 and time 2, respectively, which are closely correlated with the income distribution and are the key to poverty identification. When z₁ = z₂, Equation (5) degenerates into the case of Shorrocks (2013). The first term in the bracket on the right side of the equation is the change in poverty caused by changes in the poverty line, which is called the identification component. The last two items are the same as those in the decomposition of Shorrocks (2013), namely the growth component and redistribution component, respectively.

In the decomposition method above, the identification component uses the terminal period (time 2) as a reference. The selection of reference affects the decomposition result. However, it does not affect the sign of the identification component. Through the identification component that uses the terminal period as a reference, we can know how many people in the terminal poor population are classified as poor because of the rise of the poverty line, to know about the scale of the potential poverty alleviation population. However, the identification component using the base period as a reference has no practical implications. Therefore, we only consider the case where the terminal period is the reference in this paper.

4.2. Quantitative Decomposition of Poverty Changes in China: 2010–2018

To quantify and decompose the poverty changes in China, we first need to investigate the dynamic change process of the national and urban–rural income distribution from 2010 to 2018. Figure 1 shows the kernel density function of the household per capita income distribution in surveys from 2010 to 2018, from which we can see the dynamic change process of the income distribution in China. According to the position of the income distribution curve on the horizontal axis, the income distribution curve gradually shifted to the right from 2010 to 2018, indicating that the overall income level of Chinese households was rising. Therefore, there has been a positive effect of the growth component on poverty reduction. The peak of the income distribution curves became more prominent from 2010 to 2016, and the distribution became more and more concentrated, indicating that the inequality of income distribution decreased gradually. From 2016 to 2018, the peak of the curve reduces significantly, and the curve shape becomes much flatter, indicating an increase in the inequality of income distribution. During this period, house prices rose rapidly, which may be the main reason for the increase in inequality. The increase in inequality brought about by labor income is limited. The prosperity of real estate has made some people’s property income increase rapidly and will make them rich soon. As people got richer, income distribution became more decentralized. China achieved economic growth at the cost of inequality. This is an undeniable fact. In 2016, the income distribution curve presented a tendency for a twin peak, and it moved to a multiple-peak trend by 2018. The peak of the income distribution curve in 2016 is the highest among all survey years, indicating the lowest income inequality in 2016, consistent with the annual change of the Gini coefficient released by the National Bureau of Statistics of China (NBSC). According to data from the NBSC, the Gini coefficients of China were 0.481, 0.474, 0.469, 0.465, and 0.468 in 2010, 2012, 2014, 2016, and 2018. It is worth noting that from 2010 to 2018, the thick tail characteristics of the lower tail distribution gradually disappeared, indicating that the low-income groups in China decreased gradually during this period.

Figure 2 and Figure 3 show the changes in the income distribution in both urban and rural China from 2010 to 2018, respectively. According to Figure 2, the change in the income distribution of the urban population is generally consistent with the changing trend of the income distribution of the whole population, shown in Figure 1. The peak of the kernel density function increased continuously from 2010 to 2016, including three peaks in 2014, and decreased from 2016 to 2018. The kernel density curves shift to the right step by step, indicating that urban income has increased significantly. According to Figure 3, the rural income distribution is quite different from that of the whole population. Except for a right shift from 2010 to 2012, there has been no significant difference in the peaks in the other years, i.e., the right shift of the income distribution is not obvious since 2014. The increase in income is mainly reflected in the narrowing of the lower tail and the thickening of the upper tail, which indicates that the low-income population in rural areas gradually decreases and the medium- and high-income population gradually increases. However, for large-scale rural middle-income groups, the improvement in income level is weak. By comparison, the per capita income gap between urban and rural households is large, and the peak of rural income distribution is always on the left side of urban. The rising rate of urban income is higher than that in rural areas. When the urban income distribution shifts to the right year by year, the rural income distribution has merely shifted and can only be adjusted by the change in the tail distribution. In addition, compared with the improvement in urban income inequality, income inequality in rural areas has not improved significantly.

We incorporate the household income dynamics with the changes in the poverty index since the change and distribution of income may directly affect the identification of poverty. In terms of the incidence of absolute poverty, the poverty index increased from 2010 to 2012. Due to the upward adjustment of the poverty line in 2011, the change in the poverty index can be decomposed into growth, redistribution, and identification components. The growth component has the effect of reducing poverty. The identification component leads to an increase in the poor population. The effect of the redistribution component on the change in poverty depends on whether the distribution is pro-poor or not. The rising absolute poverty incidence from 2010 to 2012 indicates that the identification component has a dominant impact on poverty change. From 2012 to 2018, although the absolute poverty standard remained unchanged, the poverty line was adjusted according to the price index and could be captured by the identification component. Therefore, the change in the poverty index can still be decomposed into the identification, growth, and redistribution components. The stable decline in the poverty index from 2012 to 2018 shows that the growth component is dominant in this period.

As for the incidence of relative poverty, the poverty line is different in each survey year, so the change in the poverty index can always be decomposed into the identification, growth, and redistribution components. From 2010 to 2012, the incidence of relative poverty decreased, indicating that the role of the growth component is larger than that of the identification and redistribution components. From 2012 to 2018, the incidence of relative poverty showed an upward trend, indicating that the role of the identification component is greater compared with the growth and redistribution components. However, since the impact of the redistribution component on poverty change can be positive or negative, i.e., it may reinforce the growth component in reducing poverty or deteriorate poverty incidence, we need a quantitative decomposition to clarify the precise magnitude and direction of each component.

We constructed an “identification-growth-redistribution” decomposition method to decompose the change in the poverty index (absolute poverty incidence and relative poverty incidence) in China from 2010 to 2018. As shown in Equation (5), it is necessary to obtain the average income and Lorentz curve in the five survey years to calculate the decomposition results of poverty change. The average income is obtained while calculating the relative poverty line in Table 2. We further present the Lorentz curves for 2010, 2012, 2014, 2016, and 2018 in Figure 4.

The identification-growth-redistribution decomposition method is used for the absolute and relative poverty changes from 2010 to 2018. The decomposition results are shown in

Table 4. Decomposition of the change in the poverty index: three components.

Periods	Poverty Index (P, %)	Poverty Changes $\mathbf{\left(}\mathsf{\Delta }\mathit{P}\mathit{\right)}$	Identification Component	Growth Component	Redistribution Component
2010–2012	Absolute poverty incidence	↑8.22	7.74	−13.01	13.49
	Relative poverty incidence	↓5.44	8.26	−11.07	−1.89
2012–2014	Absolute poverty incidence	↓1.42	0.74	−17.74	15.58
	Relative poverty incidence	↑2.96	8.42	−8.34	2.88
2014–2016	Absolute poverty incidence	↓7.30	0.44	−20.81	13.07
	Relative poverty incidence	↑2.07	12.19	−11.24	1.12
2016–2018	Absolute poverty incidence	↓1.41	0.03	−19.04	17.60
	Relative poverty incidence	↑6.97	12.55	−12.18	6.60

Notes: The relative poverty standard is set as 50% of the average per capita net income of households.

. We find that the growth component always reduces the poverty incidence (either absolute or relative poverty), while the identification component always increases the incidence of poverty. The impact of redistribution components on poverty may be positive or negative. For example, from 2010 to 2012, the redistribution component sign of the change in absolute poverty incidence was positive, while the redistribution component sign of the change in relative poverty incidence was negative. For all other years, the sign of the redistribution component is positive. We find that the identification components of the relative poverty change gradually increased from 2010 to 2018, indicating that the relative poverty line is rising as the income level increases. We also find that the identification component of absolute poverty changes in 2010–2012, when there was an official rise in the poverty standard, is significantly greater than those in the other three periods, when the poverty standard remains unchanged and the poverty lines change only due to price adjustment.

To compare the relative magnitude of the impact of different components on the change in the poverty index, we calculate the contribution degree (CD) of each component to the change in the poverty index as follows.

$$CD\left(component\right)=\frac{component}{\left[ab\left(I\right)+ab\left(G\right)+ab\left(R\right)\right]}\times 100\%$$

(6)

In the above formula, the component represents the identification component, growth component, or redistribution component, ab (·) represents the absolute value, and I, G, and R represent the identification component, growth component, and redistribution component, respectively. The calculation results are shown in

Table 5. The contribution of identification components, growth components, and redistribution components to changes in poverty.

Periods	Contribution Degree (%)
	Absolute Poverty			Relative Poverty
	Identification Component	Growth Component	Redistribution Component	Identification Component	Growth Component	Redistribution Component
2010–2012	22.61	−38.00	39.40	38.93	−52.17	−8.91
2012–2014	2.17	−52.08	45.74	42.87	−42.46	14.66
2014–2016	1.28	−60.64	38.08	49.65	−45.78	4.56
2016–2018	0.08	−51.92	48.00	40.06	−38.88	21.07

.

In Table 5, we compare the contribution of the three components to the change in absolute and relative poverty, respectively. For absolute poverty, the incidence of poverty increased from 2010 to 2012 (shown in Table 4), which mostly results from the contribution of the redistribution component. The signs of growth components in 2012–2014, 2014–2016, and 2016–2018 are all negative, as opposed to those of identification and redistribution components. The decline in the incidence of poverty mainly results from the large and continuous growth component. Comparing the redistribution component of absolute poverty changes in different periods, we find that the contribution of redistribution components is the largest in 2016–2018 and the smallest in 2014–2016.

For relative poverty, we find that the growth component has always been the main factor in the reduction of relative poverty. Its contribution is as high as 52.17%, which is higher than the effect of the growth component on reducing absolute poverty from 2010 to 2012. Though the contribution decreases in the subsequent years, it is still 38.88% in the 2016–2018 period. On the contrary, the identification component has been the main factor leading to the increase in relative poverty, and its contribution is as high as 49.65% from 2014 to 2016. It is noteworthy that the contribution of the redistribution component differs across the years. Generally, redistribution has a larger effect on the change in absolute poverty than on the change in relative poverty. In all years, redistribution is the main component resulting in raising absolute poverty. In the case of relative poverty, the redistribution component reinforces the growth component in reducing relative poverty from 2010 to 2012; however, the contribution of the redistribution component turns from negative to positive in the subsequent years, which means redistribution as well as identification components, work in the same direction in raising relative poverty.

5. Discussion and Conclusions

Since the reform and opening-up, there has been tremendous concern about China’s absolute poverty. With the rapid economic growth and the improvement in per capita income, China has achieved remarkable achievements in poverty alleviation, and the absolute poor population and the incidence of poverty have continued to decline. The eradication of absolute poverty by 2020 is not the endpoint, and the achievements of poverty alleviation need to be consolidated. On the one hand, the people who get rid of poverty may not have a “firm foothold”, and the new risk of returning to poverty cannot be ignored. On the other hand, the urban–rural gap and regional gaps are still prominent, and people’s attention to poverty will shift from absolute poverty to relative poverty. Efforts should still be made to solve the problem of relative poverty. Getting rid of poverty is an integrated part of realizing long-term inclusive growth and common prosperity. Scientific and reasonable identification of relatively poor people has become the key to solidly promoting common prosperity at this stage. This paper measures the changes in the incidence of relative poverty from 2010 to 2018 using the data from the CFPS. The results show that in the past period, with the decline in the incidence of absolute poverty, the incidence of relative poverty shows an opposite changing trend. In 2018, when China’s absolute poverty population was at a historical low, the relative poverty incidence calculated by using 50% of the average per capita net income of families as the standard exceeded 50%. It can be predicted that China will face greater upward pressure on the incidence of relative poverty after 2020.

Most of the existing decomposition methods for changes in poverty decompose the changes in poverty into growth and redistribution components. This decomposition method does not consider the impact of the poverty line adjustment on poverty change. There is a decomposition method that considers the exogenous change in the poverty line and decomposes the poverty change into the growth effect, redistribution effect, and poverty standard effect, but the remaining residual term makes the decomposition method incomplete. To fill the gap in the literature, this paper considers the endogenous change in the poverty line and decomposes the change in poverty into three components: the identification component, the growth component, and the redistribution component. The change in poverty caused by the endogenous adjustment of the poverty line is called the identification component. Using this decomposition method to decompose the changes in poverty incidence in China in four periods from 2010 to 2018, we found that the changes brought by economic growth can always reduce poverty, the identification component caused by the upward adjustment of the poverty line is always reflected in increasing poverty, and the impact direction of income redistribution on poverty is uncertain. Moreover, the effect of income redistribution on poverty change may change in direction with the dynamic adjustment of the poverty line. Comparing the contribution of each component, we found that the identification component contributes the most to the rise in the incidence of relative poverty.

It can be predicted that in the process of striving to achieve the long-term development goal, optimizing the institutional mechanism of income redistribution and allowing the general public to participate in the process of economic development and share the achievements of economic development fairly will play a positive role in reducing relative poverty. In addition, our work did not consider the contribution of policy on land resource variables as part of the three-component decomposition of the change in relative poverty. Based on the empirical conclusion, an analysis of the impact mechanism of different components, the identification component especially, on poverty change is a future research direction.