Vulnerability to Poverty in Chinese Households with Elderly Members: 2013–2018

Abstract

In Chinese households, there is a significant shift away from basing poverty alleviation on the relative poverty line as opposed to the absolute poverty line. Based on VER and the concept of poverty capacities, this study evaluated the impact of development capacities and indicators on the vulnerability to poverty of elderly households. The three most important findings are as follows: (1) This study employed the multidimensional vulnerability methodology to evaluate the effects of potential factors on the Chinese elderly household’s vulnerability. Rather than analysing current poverty, this study focused on the estimation of future poverty, which is prospective. (2) Contrary to the expectations of empirical studies, the application of difference-in-difference and propensity score matching in this study revealed that the government’s institutional pension reform decreases the vulnerability rate further. (3) Both development capacities and indicators are critical determinants of further poverty, and in order to effectively alleviate poverty, policymakers should strengthen capacities and grant rights to vulnerable households.

1. Introduction

The first peak in the birth rate in China appeared in the 1950s. The one-child policy, which aimed to restrict the number of children, was introduced in the 1980s [1]. Under dual effects, China is rapidly transforming into an ageing nation. In 2010, there were 111 million individuals aged above 65, accounting for 8.2% of the total population. The figure is expected to reach 400 million in 2050, which will likely constitute nearly 30% of the total population [2,3].

The traditional Confucianism that is deeply rooted in China calls for younger generations to respect and take care of the elderly in the household [4]. However, in recent decades, the rapid development of urbanisation and the implementation of the one-child policy have induced an extreme outflow of labour in rural China [5]. All of this has forced young generations to leave their hometowns and has posed great challenges for adult children about providing their parents and children with adequate care, pushing the elderly towards a dilemma in which they heavily rely themselves on welfare schemes such as pension and medical insurance, as well as suffering the dual burden of taking care of offspring and spouses.

The issue of China’s ageing population has become a focal point of numerous empirical discussions. Cheng et al. [6] analysed China’s regional pattern of population ageing using data from the 2000 and 2010 censuses. They discovered that the impact of low educational attainment and poor health on urban vulnerable households in the inland is more remarkable than on urban vulnerable households in the east with the same conditions. Kong and Yang [7] evaluated the impact of old-age care policies on vulnerable elderly households and concluded that, as of 2013, the vulnerability rate in urban households was higher than anticipated, and the effectiveness of related policies was limited. Zhou et al. [8] analysed the influence of chronic illness on the medical expenses of the elderly. They concluded that higher medical costs increase the risk of rural households being poor, especially for households with more than two elders, and they questioned the efficacy of the New Cooperative Rural Residents’ Medical Scheme in easing the financial burden of rural residents. Finally, Hu et al. [9] investigated the potential factors that influence the Chinese elderly’s household consumption and found that household welfare has a limited impact on reducing vulnerability in urban households but a remarkable effect in rural households with the same conditions.

Prior research on the ageing population in Chinese households has primarily focused on single-dimensional issues, such as policy evaluation and the assessment of developmental capacity, as opposed to multidimensional issues. Nonetheless, poverty encompasses not only development capacities but also the assessment of vulnerability indicators; thus, the measurement should be derived from multiple perspectives instead of a single one [10]. Consequently, this study examined the impact of individual development capacity on household vulnerability to poverty, the effect of pension reform on reducing vulnerability, and the contribution of deprivation of indicators to the household’s vulnerability. This paper constructed a comprehensive picture of the vulnerability of Chinese elderly households by combining three methodologies.

The paper is structured as follows. The Section 2 lists all types of welfare schemes that are closely related to elders’ well-being, such as pension and medical insurance, and discusses the advantages and disadvantages among them. The Section 3 describes the variables employed in this paper as well as the reasons for choosing them. The Section 5 explains how the relative poverty line is used to measure the impacts of different types of development capacities upon the vulnerability level of elderly households in urban and rural areas, respectively, evaluates the impact of the 2015 pension reform on household vulnerability, and uses multidimensional vulnerability analysis to show how the deprivation index affects the vulnerable household. The Section 6 provides the findings and recommendations for policy-makers.

There are three contributions in this study. (1) We employed the multidimensional vulnerability methodology to evaluate the effects of potential factors on the Chinese elderly household’s vulnerability. Rather than analysing current poverty, this study focused on the estimation of future poverty, which is prospective. (2) Contrary to the expectations of empirical studies, the application of difference-in-difference and propensity score matching in this study revealed that the government’s institutional pension reform decreases the vulnerability rate further. (3) Development capacities and indicators are both critical determinants of further poverty, and in order to effectively alleviate poverty, policymakers should strengthen capacities and grant rights to vulnerable households.

2. Literature Review

2.1. Discussion about Pension Reform in China

Table A1. Policy measures against urban elder poverty—Pension Scheme.

Name of Pension	Target	Contents
Universal Pensions
Rural Residents’ Pension (RRP) [12]	Rural residents who enrol in this programme voluntarily.	Individual and collective subsidies and local fiscal contribute to residents’ pension account. The average pension in this programme is higher than that in the Old Rural Pension programme.
Urban Residents’ Pension (URP) [11]	Residents who do not have any type of pension in urban areas.	Both residents and local fiscal contribute to this pension account, and residents are able to receive a relatively low pension when they are aged above 60.
Job-Related Pensions
Government and Institutions Pension (GIP) [86]	People should have a long contract and be employed by government or public institutions.	There are no payments during employment, and they receive a relatively high pension after retirement. The exact percentage varies among regions.
Enterprise Employee Pension (EEP) [12]	People should work in an enterprise and satisfy the re-equipment of minimum years.	Both employers and employees should contribute a certain percentage of their wages to the Social Pension Funds. There is more pay during employment, and they receive more after retirement.
Private Pensions
Commercial Pension [87]	Insured people in insurance companies.	Payments and earnings depend on the insurance programme.
Life Pension [87]	Insured people in insurance companies.	Payments and earnings depend on the insurance programme.
Other Pensions
Old Age Pension Allowance [11]	Residents who are aged above 60.	There are free bus/train tickets, free visits, and so on. Exempted activities are varied across cities.

summarises the main types of pensions applied in Mainland China. The Universal Pension, Rural Residents’ Pension, and Urban Residents’ Pension are known to have no entry requirements. However, they have been widely criticised for their smaller pension amounts, which are unable to meet residents’ minimum living needs [11,12]. The Enterprise Employee Pension (EEP) was founded in 1997 and was developed from the traditional pension system under the planned economy into a social insurance system under the market economy [13].

In the earlier phases, it only covered employees in state enterprises. Until 2005, its coverage expanded to employees in private enterprises, the self-employed, migrant workers, and other non-standard employees from informal sectors [14]. Literally, this system is combined with social pooling and individual accounts, and the social pooling aspect is a ‘pay as you go’ system, which is financed by 20% of contribution wages from employers or 12% of contribution bases from the self-employed, while the individual account is financed by 8% of contribution wages from employees.

However, there are two limitations in the practice of the EEP. The first limitation is the relative restriction requirement for contribution years. In most urban areas in China, employees should contribute to their private account continually for more than 15 years, as this is the prerequisite for receiving pension after retirement. Secondly, the contribution base varies from 60% to 300% of an employee’s wage, depending on the type of enterprise. Furthermore, in practice, these contributions are often suspended for some unexpected reason, and have to be paid at the lowest base, which means that the actual contribution rate is quite far below the literal policy rate.

It is noteworthy that, since 2015, the Government and Institutions Pension (GIP) gradually merged into the EEP; nevertheless, there is a significant difference between employees in government institutions and employees in other sectors, as the individual account of civil servants is financed by the government, which means that their pension is fully paid by the government, while they receive a relatively high pension after their retirement. Thus, in this study, we discuss the GIP and the EEP separately, aiming to make comparisons between them regarding the impacts on retired employees’ consumption. Moreover, private pension (such as commercial pension and life pension) is bought by individuals, with flexible payments and profit. Compared to other types of pensions in Mainland China, these types of pensions share a relatively small number of participants. Furthermore, local government also provides Old Age Pension Allowance, designed for residents aged above 60 and providing them with different types of exemption, such as free bus and train tickets [15].

2.2. Discussion about Reform of Medical Insurance Scheme in China

Table A2. Policy measures against urban elder poverty—Medical Insurance Scheme.

Name of Medical Insurance	Target	Contents	Additional Notes
Urban Employee Medical Insurance [88]	All urban employees with a long contract.	The insurance is paid by both employers (no more than 6% of the total employee wage) and employees (no more than 2% of the total employee wage).	Male employees pay for 25 years and female employees pay for 20 years, which could benefit medical insurance without any payment after retirement.
Urban Resident Medical Insurance [89]	Urban residents without Urban Employee Medical Insurance.	It mainly depends on individuals’ payments and few local government subsidies.	The insurer should pay year by year, with a minimum year guarantee.
New Cooperative Rural Medical Insurance [90]	All rural residents are eligible for the programme.	In its initial year, the annual premium was USD 3.62 per person, with USD 2.42 from central and local governments and USD 1.21 from household over time, governments gradually increased the subsidies in the programme.	Nobody will be rejected based on health status or other considerations.
Commercial medical insurance	Insured people from the insurance company.	The payment and the percentage of reimbursement depend on the insured program.

summarises the types of medical insurance in Mainland China and makes comparisons among the main types of medical insurance, respectively. There is no doubt that the coverage of the New Rural Cooperative Medical Scheme (NCMS) is larger than that of other types of medical insurance in Mainland China. It was established in 2003, and its fund consists of central government subsidies and county government and individual contributions. Specifically, in its initial year, the annual premium was USD 3.62 per person, with USD 2.42 from central and local governments and USD 1.21 from households. Both the central and county governments gradually increased the subsidies in the individual account [16]. Between 2003 and 2009, the magnitude of subsidies in western China jumped seven-fold, while the subsidies in eastern China roared twelve-fold. With the increasing contributions from governments, the number of participants increased rapidly, and until 2015, more than 1.1 billion rural residents had joined the programme, accounting for the largest population in the world [17].

It is noteworthy that the financing of the NCMS varies across regions in China [18]. More specifically, the central government is subsidised more in western and central regions, while the local county governments contribute relatively less to the individual account. Meanwhile, in highly affluent eastern regions, such as Jiangsu and Shanghai, there is no contribution from the central government; instead, the local county should provide all subsidies, as the local fiscal can perform so. In return, the percentages of reimbursement on inpatient and outpatient services in Chinese regions are varied and could be summarised in four models (there are four models on the reimbursement of inpatient and outpatient services, which are implemented in different rural counties in China. A summary of them is presented in

Table A3. The characteristics of four models about the reimbursement of NCMS.

Characteristics	First Model	Second Model	Third Model	Fourth Model
Rate of coverage	65.2%	6.70%	11.17%	16.87%
Whether a medical savings account is available	Yes	No	No	No
Inpatient services	Yes	Yes	Only reimburse for catastrophic diseases.	Yes
Outpatient services	Yes	No	Only for catastrophic diseases.	No
Extra benefits	There is a deductible and a reimbursement cap for using a medical savings account.	There is a free physical check-up each year for who has not used any medical services that require reimbursement in NCMS.	No	No

) [19,20]. From Table A3, we find that the reimbursement of the NCMS is mainly focused on inpatient services instead of outpatient services.

What is more, the annual free physical check-up is provided in a limited number of counties and is only offered to participants of the NCMS who do not use any medical services that require NCMS reimbursement within that year. This implies that the contribution of the NCMS relieves the individual financial burden on healthcare, which is especially limited for patients with chronic illness.

The following papers argue the effectiveness of the NCMS in increasing the utilisation of care and improving public health. Yip and Hsiao [21] indicated that the medical saving account, which applies to over 50% of counties, as the alternative government-supported scheme, has a tiny impact on the utilisation of outpatient services and increases the amount of self-medication. Wagstaff et al. [22] arrived at a similar conclusion to that of Yip and Hsiao [21] and further figured out that the utilisation of outpatient services, especially for patients with a chronic illness, is disproportionately higher in wealthier households in eastern regions compared to poor households in central and western China. A potential reason could be that of less developed counties offering a lower percentage of real-time reimbursement, with patients in poor households not being able to offer a great amount of out-of-pocket expenses and turning to self-medication.

However, Qin et al. [17] obtained a different conclusion from those of Yip and Hsiao [21] and Wagstaff et al. [22], which illustrates that the NRMS makes significant contributions to alleviate poverty in low-income households, while it has not shown remarkable impacts on middle- and high-income families in rural China. Chen and Pan [23] suggested that, from 2014 to 2017, the outstanding improvement of the NCMS mainly focused on the percentage of out-of-pocket medical payments and the utilisation of inpatient services.

2.3. Discussion about the Impact of Welfare Schemes on Household Consumption

The World Bank established adequate, affordable, and sustainable welfare schemes as the primary goal [24]. Therefore, policymakers should determine the crucial connection between welfare programmes and their effectiveness. Moreover, as a developing country with insufficient domestic demand, China needs to increase domestic consumption and economic growth through expanding welfare schemes.

Nonetheless, the relationship between welfare programmes and household consumption remains contentious. The pension’s net effect on individual savings depends on the degree of the “asset substitution effect” and the “induced retirement effect”. In other words, if the former impact is more significant than the latter, the individual’s savings will decrease; otherwise, they will increase. Moreover, based on the life-cycle model, Leimer and Lesnoy [25] discovered that public pensions slightly impact household savings. Feldstein [26], on the other hand, applied a similar model to US macro data and concluded that the stock of capital would increase by 30 to 50% if there were no pension system.

Based on Feldstein’s [26] framework, Feng et al. [27] proposed a variable titled “pension wealth” and utilised data from the China Household Income Project in 1995 and 1998 to determine its significance. They found that pension wealth has a substantial offsetting effect on household savings. Using their framework, Zhang [28] and Shi and Wang [29] found that pension wealth positively impacts the consumption expenditures of urban Chinese residents. Regarding the impact of pension coverage on household consumption expenditures, Yue et al. [30] noted that residents who participate in the rural pension scheme are more likely to consume than those who do not. Su and Li’s [31] study, which utilised urban household data from Shandong Province, reached the same conclusion.

In recent years, the life-cycle model has always been applied to Chinese data to determine how demographic changes impact household saving rates in China. For instance, Curtis and Lugauer [32] used the standard model of the household life-cycle to simulate an economy populated by 95 generations, in which residents could live up to 95 years, and found that a smaller household size results in higher saving rates in China. Based on their theoretical foundation, Lugauer et al. [33] simulated the infinite lifetime and savings for elderly members after retirement, examining the impact of family composition on household savings. Their findings indicate that fewer adult children in Chinese households correlate to higher household savings.

Although numerous studies have utilised a life-cycle model to simulate the impact of idiosyncratic household elements on household savings or consumption, their efficacy is still being questioned. As they utilised aggregate data, it is difficult to observe the characteristics of each household member. In addition, the simulation based on aggregate data and assumptions could easily result in a biased estimate compared to actual household data. In addition, previous studies covered only one aspect of the welfare system’s impact rather than the entire picture.

Consequently, this study utilised three waves of the China Health and Retirement Survey data to assess the impact of the welfare system on coverage rates and benefit levels among Chinese households based on actual data.

2.4. Discussion about the Impact of Development Capacities on the Household Vulnerability

This paper also considered development capacities, such as social capital, financial capital, and physical capital, in addition to the essential variables discussed in empirical studies closely related to the welfare system and affecting household savings or consumption.

Initially, family support as social capital is considered the primary source of old-age security in China, especially for rural areas with relatively lower pensions and medical insurance coverage. According to Sung [34] and Gubhaju and Moriki-Durand [35], Confucianism is rooted in Chinese culture, which includes respect, obedience, and gratitude for the parents who provide everything for their children. It encourages adult children to assume greater caregiving responsibilities for their elderly parents.

However, birth rates have decreased significantly since 1995, which means that during the early 1970s, it took six adult children to support one elderly. By 2035, each adult child will be required to support two elderly family members [36,37].

This indicates that adult children increasingly bear the dual care burden compared to previous generations in urban and rural China. It has sparked additional debate as to whether the Chinese family support system will eventually disintegrate and exist only as a conceptual framework, unable to serve as an essential supplement to the formal Chinese welfare system. Li and Wu [38] and Wang et al. [39] suggested that single elders found that it is difficult to receive care from their adult children and that elders are more likely to be cared for by their spouses in urban areas. In other words, seniors receive fewer benefits from the family support system but have to contribute more. Moreover, once they become ill and are hospitalised, their adult children may not be able to assume responsibility for their care, necessitating the hiring of healthcare workers at additional costs.

However, the studies above only discuss the impact of family support on the elder’s physical or mental health from one or two perspectives, which need to be revised to demonstrate how social capital contributes to the elder’s overall quality of life. Consequently, this study took into account all potential family factors, such as the number of elders in a household, whether they are caretakers for offspring, and whether they live with children, to investigate the impact of these social capitals on the vulnerability of ageing households.

In addition, housing choice—specifically rent behaviour or purchase behaviour—is a substantial and long-standing investment in China that is always accompanied by heated debate [40,41,42,43,44].

According to Zeng et al. [40] and Liu et al. [41], who are supporters of renting a property instead of buying one, most rural housing is more susceptible to depreciation than urban housing. This is because, compared to their predecessors, the younger generation is more likely to leave their hometown and settle in urban areas due to the employment opportunities provided by urbanisation. Therefore, on the one hand, there is insufficient need to purchase a home; on the other hand, there is an excess of housing on the market, which could lead to a future decline in housing prices.

Opponents argued that Mainland China lacks a comprehensive rental law, and rentals depend heavily on the landlord, which may increase insecurity and expose tenants to financial risk [42,43,44].

Previous research has primarily focused on the younger generation, making it challenging to observe the effects of housing choices on the elderly. Due to their heavy reliance on insurance and pensions after retirement, senior citizens in both urban and rural areas are less able than the younger generation to face unexpected financial risks. In this study, information regarding the elderly’s financial and physical capital, including the number of fixed assets, whether they own a property, and the property’s value, was considered.

Empirical studies revealed that, in China, Communist Party members, compared to other party members, have a greater proportion of employment in the government sector and national enterprise, receive generous social benefits, and significantly impact the household’s financial decisions [45,46]. Even in rural areas, the median of their salaries is higher than the local mean.

However, few studies have linked Communist Party membership to elderly households’ vulnerability to poverty. In order to fill this gap, this paper examined whether elderly Communist Party members are less likely to fall into poverty than other party members.

3. Data Description

The data in this study came from the China Health and Retirement Longitudinal Study (CHARLS). It contains a high-quality, nationally representative sample of Chinese residents aged above 45 to serve the needs of scientific research on the elderly.

The CHARLS collects data through different methods. Specifically, its applies probability proportion size sampling (PPS) to residents at the county (district) and village level. They utilise electronic mapping software, using a map to make village sampling frames at the household level. Residents are surveyed through a questionnaire, which is designed following several international questionnaires such as the Health, Aging and Retirement Survey in Europe and the England Longitudinal Study of Aging [47].

There are two reasons why we utilised this data set. Initially, real national household-level data could more comprehensively reflect individual actual demographic and household characteristics than stimulation based on aggregate data.

Moreover, 2015 was a watershed year in developing the Chinese pension system [12,13]. In that year, the pension reform was implemented at the national level, and government civil servants are now required to pay a portion of their pension instead of receiving it, benefiting local governments by reallocating funds to low-income groups.

The stratification of Chinese pension arrangements, according to empirical studies, is unreasonable and raises the issue of “incomplete” universalism [39,48]. Before and after the pension reform in the same province should be compared to determine whether the vulnerability rate has changed and whether the pension arrangement stratification has flattened in urban and rural China.

Even though the Chinese Ministry of Human Resources and Social Security announced that the government is drawing up a plan to delay the retirement age, until 2021, the general retirement age in Mainland China was still 55 for male employees and 50 for female employees (the retirement age of males in governmental institutions and divisions is 60 and that of females is 55), which are lower than in other Asian countries, such as Japan and Korea [49]. Furthermore, this study defines the elderly as male and female residents who are aged above 55 and 50, respectively.

Table 1. Summary statistics for urban households.

Variable	n (%)
	2013 N = 1479	2015 N = 921	2018 N = 1099
Demographic characteristics
Females aged higher than 50 years old Or males aged higher than 55 years old	88.44%	90.23%	94.27%
The number of elders in the household
0	11.49%	11.07%	3.37%
1	31.17%	36.16%	38.49%
2	57.34%	52.77%	58.14%
Whether they belong to Chinese Communist Party
Yes	11.83%	17.05%	15.01%
No	88.17%	82.95%	84.99%
Whether they belong to an ethic minority
Yes	7.44%	6.41%	7.83%
No	92.56%	93.59%	92.17%
Whether they are married
Yes	81.34%	78.61%	74.25%
No	18.66%	21.39%	25.75%
Types of employment
Civil servant	8.49%	8.04%	7.18%
Institutional employee	7.16%	8.58%	7.55%
NGO employee	5.07%	5.50%	5.45%
Enterprises’ employee	35.65%	39.12%	35.82%
Self-employed	14.94%	15.97%	23.82%
Farmer	27.07%	20.40%	18.63%
Others	1.62%	2.39%	1.55%
Types of pensions
Without pension	24.07%	28.12%	30.60%
Government and institutional pension	8.45%	7.38%	6.55%
Enterprise employee pension	19.95%	23.34%	24.27%
Commercial pension	0.68%	0.76%	0.55%
Life pension	1.42%	6.62%	3.46%
Rural resident pension	35.43%	21.29%	17.65%
Urban resident pension	5.54%	6.84%	10.10%
Old age pension	4.46%	5.54%	6.82%
ln (annual pension for last year) quartile
Quintile 1(4.09,2.48,4.61)	1.51%	8.03%	3.64%
Quintile 2(4.61,4.61,9.39)	6.68%	10.00%	28.59%
Quintile 3(9.29,9.92,10.23)	74.24%	65.47%	54.29%
Quintile 4(10.23,10.23,12.26)	18.32%	16.50%	13.48
Regular physical examinations
Yes	48.48%	54.94%	35.76%
No	51.52%	45.06%	64.24%
Types of medical insurance
No medical insurance	14.67%	19.65%	12.65%
Urban employee medical insurance	36.03%	35.50%	36.77%
Urban residents’ medical insurance	13.32%	12.81%	18.48%
New Rural Cooperative medical insurance	30.44%	28.01%	26.57%
Private medical insurance	5.54%	4.02%	5.55%
Household characteristics
Whether they take responsibility for caring for children
Yes	60.78%	61.02%	59.87%
No	39.22%	38,98%	40.13%
Whether they live with adult children
Yes	65.99%	72.53%	62.42%
No	34.01%	27.47%	37.58%
Whether they own property
Yes	51.93%	46.04%	38.12%
No	48.07%	53.96%	61.87%
ln (value of owned property) quartile
Quintile 1(0.26,0.41,0.41)	1.42%	1.63%	2.72%
Quintile 2(0.69,0.69,1.39)	59.91%	63.08%	46.86%
Quintile 3(2.30,3.00,3.40)	9.67%	28.35%	21.02%
Quintile 4(3.00,3.69,6.70)	29.00%	6.94%	29.40%
ln (total value of fixed assets) quartile
Quintile 1(4.61,3.91,4.61)	2.37%	2.71%	3.18%
Quintile 2(7.60,8.99,9.23)	45.77%	47.77%	46.86%
Quintile 3(9.90,10.86,11.00)	27.05%	24.32%	25.11%
Quintile 4(10.63,11.66,12.18)	24.81%	25.20%	24.85%

Source: Chinese urban elder household surveys for 2013, 2015, and 2018.

and

Table 2. Summary statistics for rural households.

Variable	n (%)
	2013 N = 2700	2015 N = 4614	2018 N = 4437
Demographic characteristics
Females aged higher than 50 years old Or males aged higher than 55 years old	90.96%	90.98%	92.40%
The number of elders in the household
0	10.63%	10.79%	3.67%
1	30.41%	35.70%	39.10%
2	58.96%	53.51%	57.22%
Whether they belong to the Chinese Communist Party
Yes	7.59%	8.11%	7.05%
No	92.41%	91.89%	92.95%
Whether they belong to an ethic minority
Yes	8.89%	7.20%	7.23%
No	91.11%	92.80%	92.77%
Whether they are married
Yes	79.56%	78.39%	72.26%
No	20.44%	21.61%	27.74%
Types of employment
Civil servant	0.26%	0.63%	0.65%
Institutional employee	0.37%	0.72%	0.38%
NGO employee	0.04%	0.04%	0.07%
Enterprises’ employee	1.41%	1.89%	1.58%
Self-employed	2.33%	3.21%	3.13%
Farmer	63.56%	56.05%	54.97%
Others	1.22%	1.24%	1.33%
Unemployed	30.81%	36.24%	37.89%
Types of pensions
Without pension	20.22%	23.78%	21.82%
Government and institutional pension	1.74%	1.26%	0.43%
Enterprise employee pension	1.74%	3.01%	0.02%
Commercial pension	0.26%	0.13%	0.34%
Life pension	0.30%	1.41%	0.65%
Rural resident pension	67.89%	60.38%	61.48%
Urban resident pension	2.56%	3.88%	14.24%
Old age pension	5.30%	6.16%	1.01%
ln (annual pension for last year) quartile
Quartile 1(3.18,2.48,3.48)	1.85%	12.07%	6.81%
Quartile 2(4.61,4.61,6.73)	2.96%	6.74%	43.61%
Quartile 3(6.49,6.73,7.09)	73.93%	58.45%	30.16%
Quartile 4(10.23,10.26,10.22)	21.26%	22.74%	19.42%
Regular physical examinations
Yes	36.56%	38.19%	30.27%
No	63.44%	61.81%	69.73%
Types of medical insurance
No medical insurance	4.74%	19.18%	4.06%
Urban employee medical insurance	2.37%	5.05%	3.63%
Urban residents’ medical insurance	3.85%	2.45%	13.50%
New Rural Cooperative medical insurance	88.74%	71.82%	76.29%
Private medical insurance	0.30%	1.50%	2.52%
Household characteristics
Whether they take responsibility for caring for children
Yes	60.48%	63.07%	59.34%
No	39.52%	36.93%	40.66%
Whether they live with adult children
Yes	64.48%	67.79%	58.73%
No	35.52%	32.21%	41.27%
Whether they own property
Yes	50.81%	50.63%	36.56%
No	49.19%	49.37%	63.44%
ln (value of owned property) quartile
Quartile 1(0.26,0.18,0.49)	7.44%	6.57%	6.78%
Quartile 2(0.69,0.69,1.10)	56.59%	64.65%	14.85%
Quartile 3(1.61,1.10,2.20)	12.15%	3.38%	53.50%
Quartile 4(3.00,3.69,7.70)	23.82%	25.40%	24.87%
ln (total value of fixed assets) quartile
Quartile 1(4.61,3.91,4.61)	5.56%	5.42%	5.63%
Quartile 2(6.91,7.24,7.25)	40.85%	44.78%	44.38%
Quartile 3(8.70,9.26,9.31)	28.93%	24.97%	24.93%
Quartile 4(10.63,11.66,12.18)	24.66%	24.83%	25.06%

Source: Chinese rural elder household surveys for 2013, 2015, and 2018.

present descriptive statistics across urban and rural households for the variables used in the analysis of household consumption in 2013, 2015, and 2018, respectively.

4. Theoretical Framework

With the development of poverty studies, the concept of poverty no longer only focuses on current poverty but also on poverty in the future. Concerning people’s vulnerability to poverty, three different definitions can be found in empirical studies, which define vulnerability as expected poverty (VEP), explain vulnerability as low expected utility (VEU). and describe vulnerability as the uninsured exposure to risk (VER) [50,51,52]. Compared to the VEP and VEU, VER demonstrates a greater tendency to measure households’ financial ability from the realised risk of shocks rather than the forward-looking measurement. Nevertheless, the VEU measures vulnerability by applying the difference between the utility of the poverty line and the expected utility of consumption in the future but may neglect the differences in household preferences, which are easy to make a few changes from the actual situation of the households. In addition, in China, even in the same province, the utility of the poverty line is not equally suitable for all the residents, which limits its practical application in Chinese households. To contrast this with VER and VEU, VEP methodology, which expects households to be poor by comparison between the relative poverty line and the future household’s consumption, is a better fit for the theme of this study.

The prior poverty studies can be divided into the ensuing three perspectives: firstly, to examine the formation mechanism of vulnerability to poverty from the aspects of theoretical and practical [53]; secondly, to analyse the potential factors that may contribute to the vulnerability to poverty, such as from the demographic outlook, household outlook, and community outlook [54]; and thirdly, to measure the effectiveness of the anti-poverty policy and provide policy-makers with recommendations that enable them to more effectively thwart individual or household vulnerability [52].

According to the consistency of poverty, the major stream is the theory of poverty capacity, which divides poverty into two parts, the lack of development capacity and the deprivation of development indicators [55]. The development capacity consists of objective capacities, which is the talent brought from birth and is restricted by the objective conditions, and the subjective capacity that is constrained by the subjective awareness. Development indicators include production indicators, exchange indicators, and employment indicators [56].

Empirical studies show that the best way to improve current poverty or future poverty is to enhance the development capacity and decrease the deprivation of development indicators [22,57]. Thus, a comprehensive vulnerability analysis should not just assess the anti-poverty policy but should simultaneously consider the residents’ development capacity and development indicators.

5. Methodology

5.1. Feasible Generalized Least Squares

In this study, we define vulnerability as the probability that a household will enter poverty in the future and followed the method suggested by Chaudhuri et al. [50] to estimate the risk of households with elders becoming poor. It is worth noting that this method not only fits cross-sectional data but is also suitable for short-panel data, which this study employs.

A number of empirical studies suggest that the problem of heteroscedasticity exists in cross-sectional data, as the explanatory variables in this type of data vary significantly across observations [58,59,60]. Compared to homoscedasticity, based on the assumption of the Gauss-Markov theory that all the errors have an identical variance, which is described as $Var\left(e_j\right)={\sigma }_{e,j}^2$ for j = 1,2…, n, heteroscedasticity breaches this assumption, as error terms have different variance; thus, using the matrix F as the covariance matrix is not applicable. Instead, we needed to label a new matrix µ, which µ ≠ F.

Wooldridge [59] and Greene [61] suggested adopting the White-Hunber standard errors to handle the issue of heteroscedasticity. Nevertheless, this approach cannot fit the construct of vulnerability indicators very well or process the multidimensional vulnerability analysis effectively in Chinese household-level data set. In contrast to this methodology, FGLS enables an estimation of the structure of heteroscedasticity from OLS instead of simply assuming the structure of heteroscedasticity.

In addition, in this study, the error term across the Chinese households varies, as the heterogeneity exists in household consumption. Specifically, the consumption patterns in wealthy Chinese families reveal a greater volatility compared to poor households that have relatively smooth patterns.

With consideration of the above reasons, the feasible generalised least squares (FGLS) method was applied instead of OLS, which avoids the miscomputation of variance of consumption and standard errors and enables the comprehensive construction of the vulnerability indicators.

The stochastic process could then be generated as follows:

$$ln{C}_h=Y_h\gamma +e_h$$

(1)

where $ln{C}_{h,t}$ represents the consumption per capita (and we assume that it is to be log-normally distributed), $Y_{h,t}\gamma$ indicates the household characteristics that contribute to the consumption, and $e_{h,t}$ refers to idiosyncratic shocks with a zero mean.

Given $e_h$, the residual in Equation (1) may raise the problem of heteroscedasticity across households. Its variance is assumed by Equation (2):

$${\sigma }_{e,h}^2=Y_h\alpha$$

(2)

Then, we apply the three-step feasible generalised least squares suggested by Chaudhuri et al. [50] to estimate γ and α. The expected log consumption and the variance of log consumption are then estimated with estimators $\widehat{\gamma }$ and $\widehat{\alpha }$ in Equation (3) and Equation (4), respectively:

$$\widehat{E}=E(\left(ln{C}_h|Y_h\right)=Y_h\widehat{\gamma }$$

(3)

$$\widehat{V}=var(\left(ln{C}_h|Y_h\right)={\sigma }_{e,h}^2=Y_h\widehat{\alpha }$$

(4)

The basic vulnerability to poverty model is given as follows:

$$Vulnerabilit{y}_{h,t}=\mathrm{Pr}\left(C_{h,t+1}\le pl\right)$$

(5)

In Equation (5), $C_{h,t+1}$ is the per capita consumption of household h at time t + 1, pl represents the set poverty line, and $Vulnerabilit{y}_{h,t}$ refers to the vulnerability to poverty of household h at time t, which is defined as the likelihood that $C_{h,t+1}$ is below the set poverty line at time t + 1.

Based on the basic model, bringing the estimations from Equations (3) and (4), the estimated probability of households with characteristics $Y_h$ becoming poor in the future could be written as Equation (6):

$$\widehat{V_h}=\widehat{P_r}\left(ln{C}_h\le lnpl\right)=\phi \left(\frac{lnpl-Y_h\widehat{\gamma }}{\sqrt{Y_h\widehat{\alpha }}}\right)$$

(6)

where $\phi$ stands for the cumulative density of a standard normal distribution. The poverty lines in this study were based on the mean of 60% of the per capita disposable income in the interviewed provinces/municipalities. We calculated them in relation to rural and urban areas, respectively, and the poverty lines also varied in respect of the years (the statistical data came from the Chinese Statistical Yearbook for 2013, 2015, and 2018). With the purpose of the standard of measurement being united in both urban and rural areas, this study applied a mainstream approach that defined the vulnerability threshold at 50% [62,63,64].

Then, we identify the potential factors that induce vulnerability to poverty in elderly households through Equation (7):

$$V_i=\partial +{ϵ}_{x_{h,t}}+{\mu }_{h,t}$$

(7)

where $V_i$ indicates the household vulnerability rate, $ϵ$ and $\mu$ are the coefficients that are normally distributed, $x_{h,t}$ presents the different types of characteristics in individuals and households, and ${\mu }_{h,t}$ is the error term with a zero mean.

5.2. Difference-in-Difference (DID) and Propensity Score Matching (PSM)

Difference-in-difference methodology is considered an effective evaluation tool for public policy [65]. The samples are separated into two groups: the treatment group, which is influenced by the policy, and the control group, which is not affected by the policy. As the dearth of comparability between control and treatment groups, the estimator of difference-indifference may give rise to selection bias [66]. To avoid this problem, the application of propensity score matching (PSM) could benefit the treatment and control group representative and effectively satisfy the common trend hypothesis. Thus, this study applied the DID and PSM methodologies to ensure that the estimator of the experimental and control groups could satisfy the common support conditions and to release dependable results.

(1)

We estimated the propensity score, which is the vulnerability rate of the head of household with government institutional pension before 2015, and it was estimated by the Logit regression; two samples with the same propensity score were matched and, depending on whether they participated in the 2015 pension reform, they were divided into two groups, treatment group and control group.

(2)

Secondly, after the samples of the experimental and control groups were matched and propensity scores were assessed, a proper matching algorithm was selected. The conventional algorithm of k-nearest neighbour matching relies heavily on the number of matched k samples, and when k = 1, the close propensity scores from the control group may not be the best choice due to the large variance. When choosing the algorithm of radius matching, it was not easy in this study to find a correct radius with all the samples with close propensity scores within the radius. Thus, the kernel matching algorithm was adopted, which is a universal matching approach that matches all the individuals in treatment and control groups separately.

(3)

The average treatment effect for the individual in the treatment group was calculated.

$$y_{it}\left(0\right)-y_{i{t}^{\prime }}\left(0\right)$$

(8)

(4)

Then, the average treatment effect for the individual in the control group was calculated.

$$y_{jt}\left(0\right)-y_{j{t}^{\prime }}\left(0\right)$$

(9)

(5)

The estimation of the average treatment effect of the treated groups can be written as follows:

$$A\widehat{T}T=\frac{1}{N_1}{\sum }_{D_i} \left[\left(y_{it}-y_{i{t}^{\prime }}\right)-{\sum }_{j:D_j=1} \varpi (i,j)\left(y_{jt}-y_{j{t}^{\prime }}\right)\right]$$

(10)

$$\varpi \left(i,j\right)=\frac{K\left[\left(p_j-p_i\right)/h\right]}{{{\displaystyle \sum }}_{k:D_k=0}K\left[\left(p_k-p_i\right)/h\right]}$$

(11)

In the above formulation, t and t′ stand for the times at 2013 and 2015, which is prior to and subsequent to the pension reform; $y_{\mathrm{it}}$ represents the vulnerability of household i in the treatment group prior to the pension reform, while $y_{i{t}^{\prime }}$ is the vulnerability of household i in the treatment group subsequent to the pension reform. Similarly, $y_{\mathrm{jt}}$ is the vulnerability of households in the control group before the pension reform and $y_{j{t}^{\prime }}$ indicates the vulnerability of household i in the control group subsequent to the pension reform.

As in the kernel matching, the weights for individuals varied across the control groups; thus, the weights had to be calculated by the kernel functions, which is K ($\cdot$) in Formulation (11). $\varpi \left(i,j\right)$ is the matching weight; $p_j$ and $p_i$ stand for the propensity score for household j in the control group and household i in the treatment group, respectively. h is the bandwidth.

The explained variable is the household’s vulnerability to poverty. With reference to earlier studies, the following five indicators, from the three perspectives natural capital, human capital, and social capital, were selected as explanatory variables. Specifically, X₁ denotes bad health; X₂ represents the amount of annual pension; X₃ reflects the age of the resident; X₄ denotes whether they care for the children in the household; and X₅ represents whether they stay with adult children.

5.3. Multidimensional Vulnerability Analysis

Aiming to analyse how the deprivation of development indicators affects the vulnerable household, this study applied a multidimensional approach. Based on the results of FGLS, the variables that revealed a significant impact on the vulnerability to poverty were selected and categorised into the ensuing four dimensions: economics; health conditions; employment; social security and family support.

Table 3. Definitions and deprivation of the vulnerable indicator.

Dimension	Indicator	Deprivation Cutoff
Economic (1/4)	Household consumption (1/12)	If household consumption is lower than the poverty line, it is 1. Otherwise, it is 0.
	Durables (1/12)	If the total value of durables and financial minus debts is lower than individual poverty line, hen the number of adults is 1; otherwise, it is 0.
	Own property (1/12)	If the household does not own property, it is 1; otherwise, it is 0.
Health (1/4)	Health condition (1/8)	If at least one family member has bad health, it is 1; otherwise, it is 0.
	Regular physical examination (1/8)	If a least one family member does not take regular physical examination, it is 1; otherwise, it is 0.
Employment and social security (1/4)	Stable job (1/12)	If at least one family member is without a job, it is 1; otherwise, it is 0.
	Medical insurance (1/12)	If at least one family member is without any medical insurance, it is 1; otherwise, it is 0.
	Pension (1/12)	If a least one family member is without any pension or they only have old-age pension, it is 1; otherwise, it is 0.
Family support (1/4)	The number of elders in household (1/12)	If there is more than 1 elderly member in the household, it is 1; otherwise, it is 0.
	Marital status (1/12)	If more than 1 family member is divorced, it is 1; otherwise, it is 0.
	Family financial support (1/12)	If they do not receive any financial support from other family members in a survey year, it is 1; otherwise, it is 0.

reveals which households deprived in the following aspects are closely linked to vulnerability. This study also adopted an array of indicators and identified a cut-off point for each indicator, which is suggested by Alkire and Foster [67]. In the meantime, a weight was assigned to each dimension on the grounds of diverse criteria. Dissimilar to those that emphasise the importance of an explicit dimension or variable and assigned a greater weight to one than the others, this study allocated an equal weight to all dimensions and divided them into their nested component equally.

In contrast to the above FGLS test, the multidimensional analysis carefully considered the deprivation dimensions that affect vulnerable households, which may well show the importance of the deprivation of development indicators on effectively improving the households’ vulnerability. Based on the Chinese GDP and degree of the welfare system development, this study defined households with a deprived indicator weight above 0.6 as vulnerable.

6. Results and Analysis

6.1. The Intra-Regional Differences of Vulnerability Rates in Chinese Household

This paper first divided all of the interviewed provinces into the following four districts: central district, including six provinces located in inland China; western district, which consists of eight provinces/municipalities located in mountainous areas and with less transportation; northeast district, including four provinces far away from the economic and political centre; and eastern district, consisting of the Circum Bohai Sea Zone, the Yangtze River Delta, and other coastal regions, which are considered to be economically developed areas (Figure 1).

Figure 2 indicates the comparisons of the vulnerability rate between Eastern urban and rural households. The vulnerability rate in all the provinces in urban eastern China increased from 2013 to 2018, while the majority of the provinces in rural China show a decreasing trend.

Only rural Shanghai and rural Beijing, the political centre and economic centre of China, respectively, displayed a growing trend of vulnerable households. This means that both urban and rural households in Shanghai and Beijing present an increasing number of vulnerable households.

The residents interviewed in this study were all aged above 45, and these two municipalities are characteristic of ageing cities, which have the largest number of residents aged above 55. Meanwhile, these two municipalities share higher per capita disposable income when compared to any other cities in China from 2013 to 2018. This implies that, in these municipalities, the problem of ageing and the disparity between the rich and poor are more urgent tasks than partially seeking rapid economic growth.

Shandong, as a province, mainly relies on the agricultural industry and shares the biggest gap in the vulnerability rate between urban and rural households. Although agricultural support expenditure and social security expenditure in rural Shandong increased rapidly during the interviewed period, more financial support from the government should be added to rural areas, aiming to narrow the vulnerability gap between urban and rural households in this province.

In Figure 3, except for Hubei province, all rural provinces in central China show a decreasing trend in the number of vulnerable households. A potential reason could be related to the Enshi ethnic-minority autonomous prefecture, which is an area with deep-rooted poverty in Hubei with a great number of poor rural households [68,69]. Located within the mountains and lacking an essential transportation network, the residents lack essential financial and human capital, such as fixed assets and low educational qualification. Meanwhile, the relatively isolated community environment hinders the coverage of infrastructural facilities, which hinder the residents’ social connection and further exacerbates the difficulties of poverty alleviation and increasing the vulnerability rate.

Figure 4 shows the trend of the vulnerability rate in western households. From 2013 to 2018, the vulnerability rate in urban households in almost all western provinces was gradually growing, except Yunnan Province. Ethnic minorities probably contribute to decreasing the vulnerability rate, as Yunnan is the province with the largest number of ethnic minorities in China.

Compared to urban western regions with a relatively similar trend in the percentage of vulnerable households, rural western regions showed two opposite trends during the 2013–2018 period. Specifically, rural households in Guizhou, Guangxi, and Xinjiang showed an increasing vulnerability rate, while those in Gansu, Chongqing, Sichuan, and Yunnan displayed a declining vulnerability rate.

The gap between urban and rural households in the vulnerability rate in most western regions was smaller, though Xinjiang and Guangxi presented an opposite trend. Xinjiang and Guangxi also have a larger number of ethnic minorities in comparison to any other provinces in China, and it is worth analysing in the next section whether this nature capital induces the risk of rural households being poor.

Figure 5 displays the comparisons of vulnerability rates between urban and rural households in northeast China. All rural northeast provinces show a declining number of vulnerable households, while urban regions present a growing number of vulnerable households. Simultaneously, the gap in vulnerability rates between urban and rural households is narrowing progressively. These trends are mainly due to the highly similar economic situation, such as per capita disposable income, and resemble economic development patterns in these provinces.

6.2. The Development Capabilities That Contribute to Household Vulnerability

Although the vulnerability rate in both urban and rural households is positively related to the ages of heads of households, with the increasing ages of heads of households, rural households are more likely to be poor than urban households with the same conditions (

Table 4. Regression results of the vulnerability rate in urban households.

Variables	Coefficient	Standard Error
Demographic characteristics
The head of household’s age	0.06 (***)	0.02
The number of elders in the household	0.89 (***)	0.45
Whether the head of household belongs to the Chinese Communist Party	−1.90 (***)	0.35
Whether they belong to an ethnic minority	−0.26 (***)	0.30
The head of household is married	0.99 (***)	0.30
Type of the head of household’s employment
Civil servant	−0.21 (**)	1.09
Institutional employee	−0.37 (*)	1.13
Farmer	10.59 (**)	2.82
NGO employee	1.70 (***)	0.44
Enterprises’ employee	3.80 (***)	0.41
Self-employed	3.08 (***)	0.30
Type of pension
Government and institutional pension	−0.57 (**)	0.48
Enterprise employee pension	−0.51 (**)	0.31
Commercial pension	−1.53	1.19
Life pension	0.54	0.53
Rural residents’ pension	−0.06	0.20
Urban residents’ pension	−0.11 (*)	0.29
Old age pension	0.035	0.36
ln (annual pension for the head of household the last year)	−0.08 (**)	0.04
Regular physical examinations for the head of household	−2.32 (***)	0.24
Type of medical insurance the head of household owned
Urban employee medical insurance	−1.48 (*)	0.98
Urban resident medical insurance	−2.42 (**)	0.97
New Cooperative Rural Medical Insurance	−1.25 (*)	0.74
Private medical insurance	−6.67 (**)	0.041
Household characteristics
Whether the head of household has the responsibility of caring for children	0.48 (***)	0.19
Whether the head of household lives with adult children	2.40 (***)	0.24
Whether the head of household owns property	−1.07 (***)	0.19
ln(value of the head of household owned property)	−1.27 (***)	0.07
ln(total value of fixed assets the head of household owned)	−0.64 (***)	0.06
Integrated variables
Urban employee medical insurance*age	0.83 (*)	0.56
Urban resident medical insurance*age	1.35 (***)	0.58
New Cooperative Rural Medical Insurance*age	0.50	0.44
Private medical insurance*age	4.11 (***)	1.57
Number of observations	3425

* p < 0.05, ** p < 0.01, *** p < 0.001. Source: Chinese urban elder household surveys for 2013, 2015, and 2018.

). Meanwhile, with the increasing number of elders, rural households show a higher likelihood of vulnerability to poverty than urban households. It is interesting to observe that heads of households of an ethnic minority in urban households have a lower probability of being poor, while those of an ethnic minority in rural households are more likely to enter poverty. These findings provide potential explanations for urban Yunnan showing a decreasing trend in the vulnerability rate and rural Xinjiang and Guangxi showing an increasing trend in the vulnerability rate in the section above.

In addition, compared to members of other parties, heads of households belonging to the Chinese Communist Party reduces the household risk of becoming poor in the future in both urban and rural regions. We also found that, if heads of households worked as a civil servant or institutional employee, both urban and rural households have a lower probability of being poor when compared to heads who worked for other industries. These findings are closely connected to each other. Moreover, in both urban and rural households, heads of households with a civil servant pension displayed the smallest likelihood of being poor when compared to other pensions. If we link these three findings together and illustrate that Chinese Communist Party members mainly work in government and institutional enterprises, and compared to other employees, their pension is more generous and the average salary is higher than the medium salary in each province, which is more difficult to be influenced by unexpected shocks when compared to other employees. These findings are similar to the results released by Yu et al. [70] and Cai et al. [71].

The welfare scheme is closely related to elderly household members’ well-being. Not all types of pensions contribute to the incidence of vulnerability in households effectively. Due to the limitation of coverage of the welfare scheme, heads of households with a private pension, such as a commercial pension and life pension, are not significantly correlated with household vulnerability to poverty. Contrasting other types of pensions, the government and institutional pension showed the greatest impact on decreasing the household vulnerability rate. Moreover, heads of households with a universal pension, such as urban residents’ pension and rural residents’ pension, make less contribution to reducing the possibility of entering poverty in both urban and rural households. It is worth noting that the number of residents joining these two types of pension schemes is extremely higher than for other pension schemes in China. Furthermore, the coefficient of the variable of the log of the annual pension amount in both urban and rural households is quite small, further indicating that the actual pension amount is incapable of satisfying the essential living needs of an ageing household.

The influence of urban employee medical insurance (UEMI), urban resident medical insurance (URMI), and New Cooperative Rural Medical Insurance (NCRMI) upon decreasing the incidence of rural household vulnerability was greater than that for urban households with the same conditions, respectively. In addition, the impact of private medical insurance (PMI) upon reducing the urban household vulnerability rate was more than three times that for rural households. The limited coverage and the small number of participants of PMI in rural households could be potential reasons. However, in both urban and rural households, with the ages of heads of households increasing, the impact of universal medical insurance such as URMI and NCRMI upon reducing the household vulnerability rate was decreased. A similar trend was also found for UEMI and PMI in both urban and rural households. This implies that, with age increasing, the impact of such medical insurance upon reducing out-of-pocket expenses is limited and increases the medical financial burden on households.

In both urban and rural households, heads with regular physical examinations could effectively decrease the risk of households being poor, which stresses the importance of implementing compulsory annual physical examinations for all residents.

From the perspective of employment, only heads who are civil servants and institutional employers were negatively correlated with the vulnerability rate. This result could explain why the number of Chinese graduates participating in national civil servant and institutional enterprise examinations has soared in the past decade [72,73].

In both urban and rural regions, households with self-employed heads are more liable to enter into poverty. Empirical studies offer the logical explanation that the self-employed in China pay different types of insurance and pension voluntarily. Their income is unstable, and the ability to resist unanticipated financial risk is lower than employees with a fixed income. Once the payment of insurance and pension ceases due to financial issues, the benefits after retirement are a great deal less than any other type of employment [74,75]. In addition, as the subjects of these survey data are Chinese residents over the age of 45, Wang et al. [76] and Wang et al. [77] discovered that, since 2008, the off-farm labour market in rural areas has been dominated by younger cohorts, and the competition amongst the older rural self-employed has increased, which increases the instability of their income and the probability of becoming poor when they are hit by unforeseen economic shock.

It is worth noting that, if the self-employed off-farm rural residents cease their payment for rural residents’ pension before their retirement and have not participated in any other private pensions but only depend on the basic old-age pension, then they are more likely to become poor even in Beijing and Shanghai. Even though the amount of the old age pension has increased a number of times, in 2021, the monthly basic old age pension for those over 65 was only CNY 1000, equivalent to USD 143.60, which is 2/3 lower than the local subsistence level [78]. The predicament that self-employed off-farm rural residents face ought to receive attention from policy-makers, as they find it difficult to receive other pension benefits and really need additional financial aid from the local government to sustain basic living.

Moreover, households with married heads present a higher likelihood of entering poverty when compared to heads with another marital status. This finding is opposite to that of past empirical analysis [79]. Meanwhile, households with heads taking responsibility for taking care of offspring are positively related to the vulnerability rate.

The reason for households with married heads having a higher propensity to be poor could be explained as most of them are not only the main caregivers of the offspring, but they are also responsible for taking care of their parents. The dual burden imposed on this age group imbalances their work and lives, and once a family member becomes ill or utilises inpatient services, they will probably have to decrease their work hours and act as caregivers, which will bring down income and increase the household vulnerability to poverty.

However, heads of rural households as caregivers of offspring were negatively correlated with the household vulnerability rate. The results imply that rural household income heavily relies on farming and the majority of heads of households working on their own land, which could allow for working flexibly and could facilitate taking care of offspring. Meanwhile, urban household income mainly comes from employers, which means that it is difficult to balance their time between work and family.

Compared to rural households, heads of households owning a property in urban regions make a greater contribution to reducing the incidence of household vulnerability (

Table 5. Regression results of the vulnerability rate in rural households.

Variables	Coefficient	Standard Error
Demographic characteristics
The head of household’s age	0.11 (***)	0.01
The number of elders in the household	1.58 (***)	0.19
Whether the head of household belongs to the Chinese Communist Party	−1.51 (***)	0.12
Whether they belong to an ethnic minority	1.53 (***)	0.13
The head of household is married	1.21 (***)	0.14
Type of the head of household’s employment
Civil servant	−0.06 (***)	0.48
Institutional employee	−0.41 (*)	0.85
Farmer	2.50 (***)	1.39
NGO employee	0.44	0.36
Enterprises’ employee	1.35 (***)	0.20
Self-employed	2.97 (***)	0.008
Type of pension
Government and institutional pension	−0.25 (**)	0.36
Enterprise employee pension	−0.22 (*)	0.27
Commercial pension	0.34	0.69
Life pension	−0.04	0.42
Rural residents’ pension	−0.03 (**)	0.02
Urban residents’ pension	−0.05 (*)	0.14
Old age pension	0.82 (**)	0.16
ln (annual pension for the head of household the last year)	−0.07 (***)	0.02
Regular physical examinations for the head of household	−1.27 (***)	0.67
Type of medical insurance the head of household owned
Urban employee medical insurance	−1.66 (**)	0.86
Urban resident medical insurance	−5.11 (***)	0.62
New Cooperative Rural Medical Insurance	−1.93 (***)	0.31
Private medical insurance	−1.08 (*)	0.60
Household characteristics
Whether the head of household has the responsibility of caring for children	−0.42 (***)	0.08
Whether the head of household lives with adult children	−2.94 (***)	0.09
Whether the head of household owns property	−0.058 (***)	0.07
ln(value of the head of household owned property)	−1.23 (***)	0.05
ln(total value of the head of household’s fixed assets)	−0.49 (***)	0.02
Integrated variables
Urban employee medical insurance*age	0.93 (**)	0.47
Urban resident medical insurance*age	2.92 (***)	0.34
New Cooperative Rural Medical Insurance*age	1.11 (***)	0.18
Private medical insurance*age	1.08 (*)	0.60
Number of observations	11,751

* p < 0.05, ** p < 0.01, *** p < 0.001. Source: Chinese rural elder household surveys for 2013, 2015, and 2018.

). Meanwhile, the influence of the value of fixed assets and property is larger for urban households than rural households in terms of household vulnerability to poverty.

6.3. Results and Discussions about DID and PSM

After the propensity score estimation,

Table 6. Balance test in rural households.

Weighted Variables	Mean Control	Mean Treated	Difference
Vulnerability rate	0.467	0.412	−0.055 ***
$X_1$	0.383	0.370	−0.013
$X_2$	7.428	7.435	0.006
$X_3$	61.022	62.826	1.804 **
$X_4$	0.605	0.543	−0.062
$X_5$	0.612	0.587	−0.025

** p < 0.01, *** p < 0.001. Source: Chinese rural elder household surveys for 2013, 2015, and 2018.

and

Table 7. Balance test in urban households.

Weighted Variables	Mean Control	Mean Treated	Difference
Vulnerability rate	0.343	0.277	−0.066 ***
$X_1$	0.390	0.392	0.002
$X_2$	8.216	8.456	0.240
$X_3$	62.360	63.144	0.784 *
$X_4$	0.580	0.568	−0.012
$X_5$	0.661	0.592	−0.069

* p < 0.05, *** p < 0.001. Source: Chinese urban elder household surveys for 2013, 2015, and 2018.

indicate the balance test for rural and urban households, separately, which are utilized for ensuring the accuracy of propensity score matching. The majority of explanatory variables did not display a significant difference between the control and treated groups, whereas the explained variables showed a significant difference between the control and treated groups. These two tables revealed that, following the PSM, the findings met the criteria of the balance test, allowing the authorization of the subsequent results from difference-in-difference (DID).

The rural households displayed that, prior to the implementation of pension reform, in comparison to the heads of household with other types of pensions, those with government institutional pension were less likely to be poor. After the pension reform, the possibility of the treated group being vulnerable did not increase as expected but rather decreased, and the disparity in the impact of pension between government institutional pensions and other pensions on household vulnerability was further widened. The trend in urban households was similar to that in rural households (

Table 8. Results of difference-in-difference in rural households.

Variable	Vulnerability Rate	Standard Error
Before
Control group	0.467
Treated group	0.412
Difference(T-C)	−0.055 ***	0.007
After
Control group	0.439
Treated group	0.373
Difference(T-C)	−0.066 ***	0.011
Difference-in-difference	−0.011 **	0.013

** p < 0.01, *** p < 0.001. Source: Chinese rural elder household surveys for 2013, 2015, and 2018.

and

Table 9. Results of difference-in-difference in urban households.

Variable	Vulnerability rate	Standard Error
Before
Control group	0.343
Treated group	0.277
Difference(T-C)	−0.066 ***	0.009
After
Control group	0.320
Treated group	0.192
Difference(T-C)	−0.128 ***	0.016
Difference-in-difference	−0.062 **	0.022

** p < 0.01, *** p < 0.001. Source: Chinese urban elder household surveys for 2013, 2015 and 2018.

). The finding reveals that it is contradictory to the aim of pension reform, which is to equalize the pension gap between government institutional pensions and other types of pensions. As a result, the effectiveness of the reform of government institutional pension is questioned.

One potential reason is that an overwhelming percentage of residents who owned government institutional pensions are civil servants; the regression result of 6.2 indicates that, compared to other types of employment, this group has a large advantage over others in terms of lowering vulnerability rates. The pension reform regulates them from no payment during employment to paying less throughout the employment, under the effects of other benefits, such as a generous medical insurance scheme, and the amount of newly added payment has no significant contributions to decrease their living standard and to raise their risk of being poor in the future.

6.4. Results and Discussions about Multidimensional Vulnerability Analysis

Figure 6 reveals the comparison of deprived indicators between urban and rural households. There are 20.89% of vulnerable households in urban areas and 28.39% of vulnerable households in rural areas. It is interesting to discover that routine physical examination is the primary determinant for household vulnerability to poverty in both urban and rural areas. Even in urban areas, more than 50% of households do not take a physical check-up on time, and empirical studies revealed that the early stages of several critical illness such as Hepaticsclerosis and cardiovascular disease are detected upon physical examination [80,81,82]. The deprivation of routine physical health examinations gives elders the risk of their minor ailments changing to major diseases, which can also offer a reasonable explanation as to why bad health is a key determinant that pushes both urban and rural households into poverty.

In addition, the problem of more than one elderly person living in a household also causes vital deprivation in both urban and rural vulnerable households in China, and in urban households, the lack of pension is considered a significant deprivation indicator that is closely connected to vulnerability. This means that the coverage of pension in urban households is still limited, especially for residents over 45 years of age. Once this group of residents retires and has no other opportunities to receive capital, it is almost impossible for them to sustain a basic living standard.

7. Conclusions

This paper adopted the VER and concept of poverty capacity to assess the impacts of different development capacities on household vulnerability. Instead of observing the existed poverty status, the expected household vulnerability rates were estimated.

The first interesting finding is that, even though the government institutional pension was reformed, it still remains in an advantageous position in comparison to other types of universal pension in China. The definitive goal for the implementation of the universal pension ought to be balance and equality, rather than superiority.

In addition, the overall trend regarding the vulnerability rate in urban households from 2013 to 2018 gradually increased, while that in rural targeted households decreased. Several development capacities made contributions to this result, such as the rapid urbanisation process bringing about increased costs of housing in urban regions, and the multiple-caregiver burden on residents aged above 45. In addition, the vulnerability rate in both rural and urban households in Beijing and Shanghai, municipalities with a high economic development, shows an increasing trend, though their relative poverty line is above that of other provinces/municipalities discussed in this study. This calls for policymakers to not only seek soaring economic development but to also consider how to balance the disparity between the rich and poor and benefit the more general elderly residents.

Lastly, the problem of residents’ lack of vital social capital and the deprivation of regular physical check-ups induces households to be poor in the future. These findings recommend the Chinese government to summarise the practice experience from the existing kindergarten and nursing homes effectively, as well as speed up the formulation of elder protection laws and provide old people with more humanisation services such as including a free annual physical examination for elders aged over 55 or 60 years into the universal medical insurance schemes. All these reforms would benefit vulnerable households and decrease their risk of being poor in the future and also strengthen the achievements of poverty alleviation.

8. Limitation and Further Study

In this paper, the problem of endogeneity was considered to be a limitation. In preceding studies, a number of scholars chose a third variable and attempted to prove that it is correlated to independent variables but has no correlation to dependent variables [83,84,85]. Disaster-related variables are frequently used as the third variable, but it is impossible to find comparable variables in this data set. In the meantime, rather than long-time panel data, there are limited-length data in this study that could not resolve the endogeneity issue completely. After 2020, the poverty line applied in the discussion about poverty alleviation in China gradually altered from an absolute poverty line to a relative poverty line, but compared to the relative poverty line, a subjective poverty line would show the true economic situation of each household more comprehensively. Thus, additional study is recommended to apply long time panel data and construct the subjective poverty line for every family. This would enable the endogeneity issue to be solved and the impact of elders’ development capabilities and indicators on poverty alleviation to be explored more effectively.