2.1. Summary of the Evolution of the Long-term Care Insurance System

The original LTCI model originated in the United States in the 1970s. With the deepening of domestic aging in the United States, the care needs of the elderly are increasing year-by-year. In 1996, the Health Insurance Portability and Accountability Act came out and made a far-reaching reference to long-term insurance costs. Subsequently, many countries in Europe and Asia also have different forms of LTCI [1–4]. For example, in the dual mechanisms represented by France, although critical illness insurance covers most of the hospital’s health expenditures in its medical system, the direct funding of family assistance only accounts for 9%, requiring the introduction of compulsory care insurance. Commercial nursing insurance was introduced as a supplementary mechanism in subsequent years [5]. In the universal social security system represented by Japan, the form of payment is to provide benefits regardless of income or family status [6]. Generally speaking, the European region is mainly represented by the compulsory insurance of Germany and France, while the more developed countries in Asia are mainly Japan. The overall trend of global LTCI development is to change from the early government-sponsored model to a government-led corporate business model and then to a market-led corporate business model.

There is no mandatory LTCI system in the United States. The market-oriented model represented by the United States is essentially a joint guarantee of social insurance and commercial insurance, it is mainly operated by commercial insurance companies in the insurance market, with government intervention and subsidies. There are three main categories in social and commercial insurance [7]. The government mainly provides limited care protection to certain groups of people through Medicare and Medicaid, while the rest of the population is covered by commercial LTCI:

1. (1)

   Medical care (Medicare), which mainly covers the elderly above 65 years old, providing nursing care for the elderly for daily medical treatment, medication, and hospitalization within a certain number of days, individuals do not need to bear the cost.

2. (2)

   Medical assistance (Medicaid) is mainly operated by institutions, and the implementation subject is still the government. The subsidy fee is mainly for the operator of the institution since its original intention is to medical help, participants do not need to make personal payments.

3. (3)

   Long-term care cooperative plan is a form of cooperation between the government and the enterprise: The government takes care of the bottom line, the company conducts private operations, and the insured voluntarily insure, and the cost of insurance is higher than the previous two forms. The form of commercial insurance is mainly operated by commercial insurance companies, it is aimed at middle- and high-income groups and it is also a supplement to social insurance and aims to meet the willingness of higher-demand groups to purchase insurance.

Next is the universal social insurance model represented by Japan. The Japanese government introduced the “Long-term Care Preventive Measures” in 2006. In the past 10 years of development, several bills have been introduced [8]. Among them, the “Long-term Care Insurance Law” was reformed in 2015, covering all people above 40 years of age. There are two types of insurance subjects, divided by age: nationals between 40 and 65 years old are called No. 2 insurers, and nationals 65 and above are called No. 1 insurers; among them, according to the family and income, it is divided into five levels, as shown in Table 1. While providing long-term care protection, this measure is organizing community salons for the elderly above 65 years old. The cost of participation is relatively low, which can effectively screen them regularly to identify high-risk groups and promote social activities for the elderly.

2.2. Research Progress of Long-term Care Insurance Demand Theory

In the early discussion of LTCI theory by foreign scholars, it was mainly based on the assumption of rational people [9,10]. Most of them are thinking about the family’s intergenerational relationship. It is found that the consumption of LTCI is affected by the income level of the children. Low-income children are more inclined to take care of their parents in person [11–14] using HRS data analysis found that children’s care for their parents will be replaced with income. Some scholars, based on the sociology of population, found that individuals with higher incomes and married people have more urgent needs for LTCI [15,16]. Although China’s LTCI theory research started late, the results of research on aging are relatively rich, and it is generally believed that my country’s aging has three major characteristics [17]. Firstly, is get old before getting rich. Our country has entered an aging society when the overall national strength is not high. Secondly, is unprepared to get old. China’s pension system will face the strong impact of aging when it is not perfect. Thirdly is loneliness. Due to the widespread phenomenon of “fewer births” today, the elderly are prone to getting old and difficult to support due to various reasons such as disease and loneliness. In the government’s response strategy, in the face of a major change in the demographic structure, the government needs to build strong public service measures for elderly care, centering on the actual needs of the elderly to ensure the quality of elderly care. Furthermore, with the acceleration of aging in China, the concept of “long-term care” has begun to be studied in depth. Many scholars have compared the experience of foreign LTCI implementation and believe that China should establish a LTCI mechanism with Chinese characteristics [18–21]. In recent years, the content of the current development model across the country is quite different, the development of LTCI can be carried out by providing customers with protection and avoiding moral hazard [22].

Furthermore, in the research methods of LTCI, the existing literature generally focuses on the demand factors of LTCI [23–25]. For example, cross-sectional data from the SHARE database (European Survey of Health, Aging and Retirement) to estimate the determinants of physical health for purchasing LTCI in France, the sample variables include BMI index and disease status, risky behavior and disability experience explain the characteristics of French LTCI demand [25], however, the mechanism design of how to design public policies to encourage the growth of long-term insurance is very lacking [26].

Domestic research is still in a situation of following foreign countries, for example, panel data analysis of the linear relationship between independent variables such as household savings, old-age dependency ratio, and the dependent variable LTCI premium income suggests the trend of the macro demand characteristics of LTCI [27]. Economic factors and education status substitute microscopic investigation Logistics probability model analysis to insure LTCI change factors and whether respondents prefer [28,29]. However, due to the short period of domestic pilot projects and the lack of data compared with foreign countries, domestic scholars mainly use questionnaire surveys to obtain data, and most often use the Logistics model for analysis.

In summary, regardless of the evolution of the LTCI system model or the development of LTCI theory, China lags behind foreign countries. However, domestic urbanization and aging have completed the rapid transformation of more than 300 years abroad in just above 30 years. In particular, the rate of aging is faster than abroad, and the rate of an ultra-high aging population is higher. The mega-urban agglomeration formed in the metropolitan area under the process of urbanization has intensified the demand for insurance driven by the demand for long-term care. In reality, there is an urgent need for LTCI system model reform and LTCI theoretical research to keep up with the needs of actual development, and build a true and worry-free life for the people. Because the LTCI has not been implemented for a long time, the relevant data is still blank, and the relevant empirical analysis is all based on questionnaire surveys, and there are few predictive analyses on the population. This article starts with the aging trend and the nursing needs of the elderly disabled population and uses the GM (1,1) model to predict the population simulation to explore the insurance demand potential driven by the long-term care demand in the process of urbanization.

3.1. A Theoretical Model of Consumer Economic Activity in Demand for Long-term Care Insurance

From the perspective of insurance demand acting on insurance consumption, as the current pilot LTCI in China is mainly social security mode, insurance consumption and welfare payment lag behind. Therefore, this paper puts insurance as a safety service of production and people’s life into the general consumption category, and the demand for LTCI is measured by consumption function.

1. (1)

   The insured behavior is expressed by the production function as the input in the young age [30].

2. (2)

   The payment in the old age is measured by the utility function.

3. (3)

   Assuming that the production factor is a necessary condition of the production function, physical capital can be used as a risk backup when it is not insured, and insurance backup does not require excessive material backup, the insurance compensation (contingent claim) is a kind of market-oriented pre-preparation in advance. Therefore, physical capital and insurance consumption are replaceable. Based on the academic works of related scholars [31,32] this article improves the Cobb–Douglas production function: Q = AL^αK^β. Let K(t) be the capital stock, C(t) be the consumption of general commodities, and E(t) be the consumption of special insurance commodities. Among them, E_R(t) is the consumption of insurance products entering life, and E_P(t) is the consumption of insurance products entering production. Insurance investment cost is measured by consumption.

4. (4)

   Assuming that the production function Y(K, L, E_P) is strictly concave, first-order homogeneous and second-order continuously differentiable. Since the population changes little in the short term, it can be assumed that the labor force L is constant. Then, the production function should be a function of the physical capital K and the insurance consumption E_P(t) (calculated as a cost) into production, set to Y(K, E_P). And there are:

   F(0,EP)=F(K,0)=0,FKEP=FEPK>0 (1)

If consumption is divided into ordinary consumption and special consumption, it is assumed that special consumption is only insurance consumption. Then the total insurance consumption E¯ composed of insurance entering production and consumption and insurance entering life consumption in a certain period, E¯ remains unchanged. Generally speaking, insurance for production and consumption in poor areas is more than insurance for living consumption, developed regions have more insurance for production and consumption. Which is:

Defining the consumption functions U(C, E_R) : R₊→ R₊ is a non-decreasing function, and the consumption function is a second-order continuous differentiable function with diminishing marginal utility. Let ρ be the discount rate, then the utility function is

Then the above problem becomes to solve the following dynamic optimization problem:

Let K(0) = K₀ > 0, C > 0, E_P ≥ 0, λ be the shadow price of capital, δ be the depreciation rate of physical assets, and the depreciation rate of monetary assets is 0, then the Hamilton equation:

The necessary and sufficient conditions for the optimal path are:

Then there is UER=UCFEP , indicating that the marginal utility value of insurance used for personal household consumption must be equal to the marginal utility of ordinary consumption multiplied by the value of the marginal product of insurance for production and consumption of the enterprise.

Let K˙=λ˙=0 , ^* a represents the special solution of the variable in the steady-state, and the results are as follows:

From Equation (8), the left is the total marginal productivity of insurance consumption (VMPEP) , and the right is the marginal cost of insurance products for production and consumption (MCEP) . Then:

It means that the production function is strictly concave, so in the steady-state, there are (1) F_K – δ = ρ is a positive value and UCEP>0 . (2) In the interval [0,E¯] , MCEP is a monotonically increasing function, and VMPEP is a monotonically decreasing function. Then:

Because Equation (7b) shows that FKEP>0 , the insurance of production and consumption is increasing. Therefore, Equations (10a) and (10c) show that when the stock of wealth capital increases, the marginal productivity of wealth capital decreases, and the marginal productivity must be less than ρ + δ .

Moreover, there is an alternative relationship between insurance for production consumption and insurance for life consumption, in other words, there is an alternative relationship between a corporate annuity and personal commercial LTCI.

Also, since U″(·) < 0, then when consumption decreases, U_C must increase. The larger the investment in the early stage of the production function, the greater the welfare for the elderly in the later stage, so the introduction of LTCI is extremely necessary.

As one of the leading cities in the megalopolis, Shanghai has strong regional advantages and economic strength. Policy subsidies and the participation of individuals can increase the benefits for the elderly.

3.2. Analysis and Prediction of the Shanghai Population-based on GM (1,1) Model

The source of the data in this article is the total population of Shanghai registered household registration and the number of elderly people above 60 years of age who are registered in the Shanghai Statistical Yearbook from 2004 to 2017. It can be seen from Figure 1 that the degree of aging in Shanghai has been increasing year-by-year. Especially in 2014, its aging growth rate reached 6.33%. Shanghai has reached a state of deep aging in 2015. Among them, the proportion of the population above 60 years old is 30.21%. According to the data in Figure 1, a corresponding population prediction model is established by the gray prediction analysis theory below.

Figure 1

The growth rate of aging from 2004 to 2016. Data source: Shanghai Statistical Yearbook 2005–2017.

First use the data of the elderly above 60 to form the original sequence:

Accumulate x⁽⁰⁾ once and generate 1-AGO sequence:

Let Z⁽¹⁾ = [Z⁽¹⁾(2), Z⁽¹⁾(3), …, Z⁽¹⁾(14)] be the sequence generated by X⁽¹⁾(k)

where z(1)(k)=12[x(1)(k)+x(1)(k-1)],k=1,2,…,14 .

Construct two sets of matrices, respectively:

The vector of coefficients to be estimated as a^=(BTB)-1⋅BT⋅Yn

Establish GM (1,1) gray estimation model, its differential equation is:

After generating the corresponding sequence of time, the corresponding variance is:

That is, the value of a^=-0.00564432,b^=1354.727722 .

Then do cumulative subtraction reduction x^(1)(k+1)-x^(1)(k) to calculate the corresponding value.

In the same way, for the estimation of Shanghai’s registered population, let another original sequence:

Test the two levels:

Similarly, γ(k)=p(0)(k-1)p(0)(k)∈(e-2n-1,e2n-1) . Then use â and σ(k) to test the level ratio deviation value. The value is to meet higher requirements. Therefore, X⁽⁰⁾(k) and P⁽⁰⁾(k) can be used to construct a satisfactory gray prediction model.

Since only the data before 2018 is obtained, this article aims at the medium and long-term forecast, predicting the population distribution in the next 10 years (2017–2027) (Tables A1–A3). It can be seen that because this gray prediction model level ratio deviation value test has reached higher requirements, the population prediction is basically consistent with the original data, and the conclusion that the prediction data is credible can be drawn. The following analysis of the LTCI model is based on this data (Figure 2).

Figure 2

Simulation of the original population above 60 and the predicted population. Data source: Shanghai Statistical Yearbook 2005–2017.

3.3. Calculation of Nursing Needs

3.3.1. Calculation of disability of the elderly population

Based on the above results of using the GM (1,1) gray prediction model, this paper selects the sixth population census in Shanghai, and statistically collates the health and disability of the elderly population.

By calculating the corresponding distribution ratio, age is divided into three stages: 60–79 years old and above 80 years old. Health status is measured by self-care ability, it is divided into the elderly who are not disabled, partially disabled and completely disabled and the latter two are the composition of the disability rate as shown in Table 2.

Age distribution	60–69 years old (%)	70–79 years old (%)	Above 80 years old (%)
Total	100.0000	100.0000	100.0000
Not disabled	94.9725	85.1861	67.2086
Partially disabled	4.1806	11.3786	19.6793
Completely disabled	0.8469	3.4353	13.1121
Disability rate	5.0275	14.8139	32.7914

Data source: The sixth population census in Shanghai.

Table 2

Distribution of disability among the elderly population

According to calculations, among the distribution of the elderly above 60 years old, 87.2711% are not disabled, 9.0208% are partially disabled; 3.7081% are completely disabled, and the disability rate is 12.289%. The number of elderly disabled people and the number of people who need LTCI for the next 10 years from 2016 to 2027 are shown in Table 3.

Year	Population above 60 (10,000 people)	Partially disabled (10,000 people)	Completely disabled (10,000 people)	LTCI demand forecast (10,000 people)	The current number of participants in LTCI (10,000 people)
2016	457.8000	41.2970	16.9758	58.2728	*
2017	481.6100	43.4448	17.8587	61.3036	*
2018	505.2430	45.5767	18.7351	64.3118	23.4
2019	531.9568	47.9865	19.7256	67.7122	49.3
2020	560.0831	50.5237	20.7686	71.2923	*
2021	589.6965	53.1951	21.8667	75.0618	*
2022	620.8757	56.0077	23.0229	79.0305	*
2023	653.7034	58.9690	24.2402	83.2091	*
2024	688.2668	62.0868	25.5218	87.6087	*
2025	724.6577	65.3696	26.8712	92.2408	*
2026	762.9727	68.8259	28.2920	97.1179	*
2027	803.3136	72.4649	29.7879	102.2528	*

Note: Forecast data after 2017. ^*represents data not yet available.

Table 3

2016–2027 Elderly disabled population and long-term care insurance (LTCI) demand forecast

It can be seen from Figure 3 that both the completely disabled population and the partially disabled population are increasing. In particular, the partially disabled population has increased significantly, indicating that the number of people in need of moderate care in the future is relatively large. Under the rising trend of the elderly population in the future, it can be concluded that in the next 10 years, the number of LTCI needs will be about 60, accounting for 1/8 of the elderly population.

Figure 3

The evolution of the disabled elderly population forecast in Shanghai from 2016 to 2027.

4.1. The Population Who Has Received Reimbursement from Long-term Care Insurance is Inadequate

According to the data published in the “Shanghai Elderly Population and Elderly Career Monitoring Statistics Information” in 2018–2019, the number of people above 60 years old in Shanghai receiving nursing services in 2018 totaled 234,000, accounting for 4.6% of the elderly population, the scope of the pilot program has been greatly expanded in 2019, and the number of elderly people above 60 years old in the city receiving nursing services totaled 493,000, accounting for 9.5% of the elderly population. From the results in Table 3, it can be concluded that the number of people in need of LTCI in 2018–2019 is much greater than the number of people in the pilot, the demand potential of LTCI is huge.

4.2. Supporting Facilities for LTCI are Relatively Absent

It can be seen from the above-predicted value that the difficulty of follow-up by nursing staff and nursing institutions is an important reason for the relatively lagging development of LTCI in China. Firstly, there is a large shortage of nursing staff in LTCI. Combined with the data from the Shanghai Statistical Yearbook and Table 5, the predicted number of nursing home care in 2018 alone will require more than 50,000 people, while the total number of health technicians in 2018 was only 206,500. If we add institutional care and inpatient medical care, it is unrealistic to rely solely on the current 206,500 people. Therefore, it can be judged that there is a huge shortage of nursing staff for LTCI. In terms of salaries, the 2015–2017 salaries of Shanghai residents’ service, repair and other service industries were 33,720, 37,292, and 40,478 RMB per year respectively, which were lower than other industries such as agriculture, forestry, and animal husbandry. Currently, there are relatively few people working in health and social work, and people are more inclined to move to tertiary industries with higher salaries such as wholesale and retail, it can be seen that the promotion of LTCI still needs to be achieved by attracting salary. At the same time, if the government intends to train professional nursing talents, it needs to invest a lot of money. Secondly, the number of nursing institutions is still in a small share. In 2018, the number of elderly nursing homes and hospitals in Shanghai was only 38 and two, and the number of inpatients was 26,001 and 1863. Currently, the people who can participate in institutional care are elderly people with the third type of nursing standard. According to Table 4, the predicted number of people with the third care category in 2018 is close to 20,000, which is equivalent to the overall value of the current elderly care institution. The number is not enough to support the occupancy needs of the elderly with full weight disability, and the elderly with a severe disability still largely rely on home care.

4.3. The Burden Structure of Health Expenses is Under Certain Pressure

Since the implementation of the LTCI pilot program is closely related to medical resources, public health expenditures can be used as a reference standard. As shown in Figure 4, Shanghai’s public health expenditures have been on the rise, and the trend is that the proportion of personal health expenditures has fallen, staying at about 20%, while the proportions of government health expenditures and social health expenditures have been increasing. The health expenses of Shanghai LTCI are mainly paid by the special LTCI Fund, which is a new fiscal expenditure item. The long-term care policy based on aging will have a certain impact on Shanghai’s fiscal expenditure. Correspondingly, due to the impact of the COVID-19 in China in 2020, the national medical resources may further participate in the fight against the epidemic, which will greatly increase the corresponding health expenses. Therefore, the expenditure on health expenditure is uncertain. Despite this, we can still analyze the severity of the elderly population, and more public expenditure on health can be foreseen in the next 10 years (Table A4).

Figure 4

2004–2015 Shanghai health expenditure structure. Data source: Shanghai Statistical Yearbook 2005–2017.

In summary, LTCI needs corresponding aging care needs to exist objectively, meanwhile, the implementation of the policy is under great pressure: the shortage of nursing staff and the low salary, the impact of the special fund for LTCI on fiscal expenditures, and the collateral effect of COVID-19 have increased the uncertainty of public health expenditure.

APPENDIX