Model design
Actuarial science studies the effects of uncertain future events. As an important application of actuarial science, medical insurance mainly includes the experiential data of the population, society, economy, and fund operation to forecast and evaluate fund revenues and expenditures in the future to analyse the solvency, risk status, and long-, medium- and short-term financial status of medical insurance funds.
A dynamic actuarial model of the URRBMI fund was established to evaluate the sustainability of URRBMI fund operation in the target period. The model includes two parts: the income and expenditure forecast model and the accumulated balance model. The former is mainly used to analyse the URRBMI fund income and expenditure, and it can be divided into the income forecast model and expenditure forecast model. The latter is used to investigate whether the URRBMI fund has the ability to operate sustainably. When the accumulated balance is greater than 0, the fund can still self-regulate, and its overall operation is stable. However, if the accumulated balance is less than 0, the URRBMI fund is no longer capable of providing adequate medical security and running sustainably.
Income forecast model of the funds
Since 2013, provinces have started to integrate the URBMI and NCMS according to the national requirements to establish a unified URRBMI, but this integration is not yet fully complete. On this basis, this study adopted a separate calculation method to obtain the URRBMI fund income. This means that the income of the URRBMI fund in year t in this study should be equal to the sum of the income in year t of the NCMS fund and that of the URBMI fund. The income of the NCMS fund in year t is equal to the number of NCMS participants in year t multiplied by the per capita financing standard in year t. The income of the URBMI fund in year t is equal to the number of URBMI participants in year t multiplied by the per capita financing standard in year t, as shown in formula (1):
$$ {\displaystyle \begin{array}{l}{(AI)}_t=\left(\sum \limits_{x=0}^{100}{N}_{t,x}^{r,m}+\sum \limits_{x=0}^{100}{N}_{t,x}^{r,f}\right)\times {(PI)}_t^r+\left(\sum \limits_{x=0}^{100}{N}_{t,x}^{u,m}+\sum \limits_{x=0}^{100}{N}_{t,x}^{u,f}\right)\times {(PI)}_t^u\\ {}=\left(\sum \limits_{x=0}^{100}{N}_{t,x}^{r,m}+\sum \limits_{x=0}^{100}{N}_{t,x}^{r,f}\right)\times {\left[{(PA)}_{2020}^r\times \prod \limits_{i=2021}^t\left(1+{\alpha}_i^r\right)+{(PB)}_{2020}^r\times \prod \limits_{i=2021}^t\left(1+{\beta}_i^r\right)\right]}_t^r\\ {}+\left(\sum \limits_{x=0}^{100}{N}_{t,x}^{u,m}+\sum \limits_{x=0}^{100}{N}_{t,x}^{u,f}\right)\times {\left[{(PA)}_{2020}^u\times \prod \limits_{i=2021}^t\left(1+{\alpha}_i^u\right)+{(PB)}_{2020}^u\times \prod \limits_{i=2021}^t\left(1+{\beta}_i^u\right)\right]}_t^u\end{array}} $$
(1)
Where (AI)t is the URRBMI fund income in year t. \( {N}_{t,x}^{r,m} \) and \( {N}_{t,x}^{r,f} \) are the populations of males and females of X years of age who were insured by the NCMS in the year t, respectively. \( {N}_{t,x}^{u,m} \) and \( {N}_{t,x}^{u,f} \) are the populations of males and females of X years of age, respectively, who were insured by the URBMI in year t. (PI)tr and (PI)tu are the per capita financing standards in year t of the NCMS and URBMI, respectively. \( {(PA)}_{2020}^r \) and \( {(PA)}_{2020}^u \) are the subsidies of per capita financing of the NCMS and URBMI, respectively, from public finance in 2020. \( {(PB)}_{2020}^r \) and \( {(PB)}_{2020}^u \) are the individual contribution amounts of the insured population of the NCMS and URBMI, respectively, in 2020. αir and αiu are the average annual growth rates of the financial subsidy part in the per capita financing standard of the NCMS and URBMI, respectively, in year i (i ≤ t). \( {\beta}_i^r \) and \( {\beta}_i^u \) are the average annual growth rates of the individual contribution part in the per capita financing standard of the NCMS and URBMI, respectively.
Expenditure forecast model of the funds
The URRBMI fund expenditure in year t should be equal to the sum of the expenditure in year t of the NCMS fund and URBMI fund; this is the same principle used to construct the income forecast model of the fund. The NCMS fund expenditure in year t is equal to the insured population of the NCMS in year t multiplied by the corresponding per capita compensation expenditure, and the URBMI fund expenditure in year t is equal to the insured population of the URBMI in year t multiplied by the corresponding per capita compensation expenditure, as shown in formula (2):
$$ {\displaystyle \begin{array}{l}{(AC)}_t=\left(\sum \limits_{x=0}^{100}{N}_{t,x}^{r,m}+\sum \limits_{x=0}^{100}{N}_{t,x}^{r,f}\right)\times {\left(\overline{PC}\right)}_t^r+\left(\sum \limits_{x=0}^{100}{N}_{t,x}^{u,m}+\sum \limits_{x=0}^{100}{N}_{t,x}^{u,f}\right)\times {\left(\overline{PC}\right)}_t^u\\ {}\hfill =\left(\sum \limits_{x=0}^{100}{N}_{t,x}^{r,m}+\sum \limits_{x=0}^{100}{N}_{t,x}^{r,f}\right)\times {\left(\overline{MC}\right)}_{2020}^r\times \prod \limits_{i=2021}^t\left(1+{k}_i^r\right)\times {U}_{2020}^r\hfill \\ {}\hfill +\left(\sum \limits_{x=0}^{100}{N}_{t,x}^{u,m}+\sum \limits_{x=0}^{100}{N}_{t,x}^{u,f}\right)\times {\left(\overline{MC}\right)}_{2020}^u\times \prod \limits_{i=2021}^t\left(1+{k}_i^u\right)\times {U}_{2020}^u\hfill \end{array}} $$
(2)
(AC)t represents the URRBMI fund expenditure in year t. \( {\left(\overline{PC}\right)}_t^r \) and \( {\left(\overline{PC}\right)}_t^u \) are the per capita compensation expenditures in year t of the NCMS and URBMI, respectively. \( {\left(\overline{PC}\right)}_t^r \) is equal to the per capita medical expenses in year t of the NCMS multiplied by the actual compensation ratio of the NCMS (\( {\left(\overline{PC}\right)}_t^r={\left(\overline{MC}\right)}_t^r\times {U}_t^r \)). \( {\left(\overline{PC}\right)}_t^u \) is equal to the per capita medical expenses in year t of the URBMI multiplied by the actual compensation ratio of the URBMI (\( {\left(\overline{PC}\right)}_t^u={\left(\overline{MC}\right)}_t^u\times {U}_t^u \)).
The reason for choosing the actual compensation ratio is that according to previous studies [25, 26], the actual compensation ratio can reflect the actual guarantee level of the URRBMI more accurately than the policy compensation ratio. This is also applicable for the horizontal comparison of guarantee level between different systems, different regions and groups of people. \( {k}_i^r \) and \( {k}_i^u \) are the average annual growth rates of the per capita medical expenses of the NCMS and URBMI, respectively, in year i. The meanings of the other parameters are the same as above.
Accumulated balance (or accumulated deficit) forecast model
The accumulated balance (or accumulated deficit) of the URRBMI fund in year t is equal to the sum of the accumulated balance (or accumulated deficit) in year t of the NCMS fund and URBMI fund. The former is equal to the sum in the NCMS fund of the accumulated balance (or accumulated deficit) of year t-1 and the current balance (or current deficit) in year t, while the latter is equal to the sum in the URBMI fund of the accumulated balance (or accumulated deficit) in year t-1 and the current balance (or current deficit) in year t, as shown in formula (3):
$$ {\displaystyle \begin{array}{l}{S}_t={S}_t^r+{S}_t^u\\ {}=\left({S}_{t-1}^r+{S}_{t-1}^u\right)\times \left(1+{\sigma}_1\right)+\left\{\left[{(AI)}_t^r-{(AC)}_t^r\right]+\left[{(AI)}_t^u-{(AC)}_t^u\right]\right\}\times \left(1+{\sigma}_2\right)\end{array}} $$
(3)
\( {S}_t^r \)and \( {S}_t^u \) are the accumulated balances (or accumulated deficits) of the NCMS fund and URBMI fund, respectively, in year t. \( {(AI)}_t^r-{(AC)}_t^r \) and \( {(AI)}_t^u-{(AC)}_t^u \) are the current balances (or current deficits) of the NCMS fund and URBMI fund, respectively, in year t. σ1 and σ2 are the interest-bearing interest rates of the accumulated balance and current balance during the forecast period, respectively. According to these hypotheses, σ = σ1 = σ2. Because the accumulated balance (or accumulated deficit) and the current balance (or current deficit) may not coincide with each other, the accumulated balance (or accumulated deficit) forecast model of the URRBMI fund should include the following three situations:
Situation 1
When the current balance is greater than 0 and the accumulated balance is also greater than 0. Assume that when t = 2021,2022,...,t + x-1, the current balance and accumulated balance of the URRBMI fund are both greater than zero. Therefore, the accumulated balance of the URRBMI fund in year t should be equal to the sum of the current balance of the URRBMI fund (including the amount of interest) in year t and the accumulated balance of the URRBMI fund (including the amount of interest) of year t-1, as shown in formula (4):
$$ {S}_t=\sum \limits_{m=2021}^t\left\{\left[{(AI)}_m^r-{(AC)}_m^r\right]\times {\left(1+\sigma \right)}^{t-m+1}\right\}+\sum \limits_{m\hbox{'}=2021}^t\left\{\left[{(AI)}_{m\hbox{'}}^u-{(AC)}_{m\hbox{'}}^u\right]\times {\left(1+\sigma \right)}^{t-m\hbox{'}+1}\right\}+\left({S}_{2020}^r+{S}_{2020}^u\right)\times {\left(1+\sigma \right)}^{t-2020} $$
(4)
Situation 2
When the current balance is not greater than 0 and the accumulated balance is greater than 0. Assume that when t = t + x,t + x + 1,...,t + y, the current balance of the URRBMI fund begins as less than 0, which means a deficit for the current period. However, at this time, the accumulated balance is still greater than 0. Therefore, at this time, interest would only accrue on the accumulated balance, and no interest would accrue on the current deficit, as shown in formula (5):
$$ {\displaystyle \begin{array}{l}{S}_t=\sum \limits_{m=2021}^{t+x}\left\{\left[{(AI)}_m^r-{(AC)}_m^r\right]\times {\left(1+\sigma \right)}^{t+x-m+1}\right\}+\sum \limits_{m=t+x+1}^{t+y}\left[{(AI)}_m^r-{(AC)}_m^r\right]\\ {}+\sum \limits_{m^{\prime }=2021}^{t+x}\left\{\left[{(AI)}_{m^{\prime}}^u-{(AC)}_{m^{\prime}}^u\right]\times {\left(1+\sigma \right)}^{t+x-{m}^{\prime }+1}\right\}+\sum \limits_{m^{\prime }=t+x+1}^{t+y}\left[{(AI)}_{m^{\prime}}^u-{(AC)}_{m^{\prime}}^u\right]+\left({S}_{2020}^r+{S}_{2020}^u\right)\times {\left(1+\sigma \right)}^{t+x-2020}\end{array}} $$
(5)
Situation 3
When the current balance is not greater than 0 and the accumulated balance is also not greater than 0. Suppose that when t = t + y + 1,t + y + 2,...,2030/2050, the current balance and accumulated balance of the URRBMI fund all begin as less than 0, which means that there are current deficit and accumulated deficit successively. Then, neither accrues interest at this time, as shown in formula (6):
$$ {\displaystyle \begin{array}{l}{S}_t=\sum \limits_{m=2021}^{t+y+1}\left\{\left[{(AI)}_m^r-{(AC)}_m^r\right]\times {\left(1+\sigma \right)}^{t+y+1-m}\right\}+\sum \limits_{m=t+y+2}^{2030}\left[{(AI)}_m^r-{(AC)}_m^r\right]\\ {}+\sum \limits_{m^{\prime }=2021}^{t+y+1}\left\{\left[{(AI)}_{m^{\prime}}^u-{(AC)}_{m^{\prime}}^u\right]\times {\left(1+\sigma \right)}^{t+y+1-{m}^{\prime }}\right\}+\sum \limits_{m^{\prime }=t+y+2}^{2030}\left[{(AI)}_{m^{\prime}}^u-{(AC)}_{m^{\prime}}^u\right]+\left({S}_{2020}^r+{S}_{2020}^u\right)\times {\left(1+\sigma \right)}^{t+y-2019}\end{array}} $$
(6)
Data processing and parameter specification
The data in this study were mainly sourced from national data of China such as the Sixth National Census and annual National Statistical Yearbook. This study also in the light of research [27,28,29,30,31] in China to modify the relevant data and determine the following parameters.
Sizes of the population insured by the NCMS and URBMI
According to the model, the sizes of the population insured by the NCMS and URBMI in the forecast period can be calculated. Since both the NCMS and the URBMI have achieved comprehensive coverage, this study assumed that the participation rate of both is 100%. The specific calculation process is as follows. 1) Multiply the population data in the Sixth National Census divided according to age (0–100 years old), sex, and urban and rural residence by the survival probability of the corresponding year to obtain the number of natural population growth for the next year. Referring to the requirements for the age of the population in the Sixth National Census data, this study set the value range of the age of the paying population as 0–100 years old, while individuals 100 years and older are counted as being 100 years old. Besides, this study used the JPOP-1 method for smoothing and employed a survival probability = 1-crude death rate. 2) Multiply the numbers of women of childbearing age obtained in the previous step (divided into urban and rural areas) by the birth probability and sum the results to obtain the population of 0-year-old infants in both urban and rural areas. Then, combine the newborn sex ratio at birth to calculate the newborn population by sex. 3) Calculate the registered population by age, gender, and urban and rural residence in accordance with the household registration urbanization rate. Although urbanization has encouraged some rural residents to work and live in cities and participate in the URBMI, some urban residents have also been included in the management of the NCMS for reasons such as marriage or the coordination of medical insurance between urban and rural areas. Overall, the population insured by the NCMS is the same as the registered agricultural population. Combined with scholars’ research [27] and the actual urbanization of the registered population in China, this study assumed that the urbanization rate of the registered population will increase at the current level at an average annual rate of 1% and reach a peak of 75% in 2050. 4) Subtract the number of UEBMI participants from the number of urban registered populations to obtain the number of URBMI participants. The number of UEBMI participants is equal to the sum of the employed population and the retired population of the UEBMI. The number of employed people is equal to the product of the number of urban registered population, corresponding year employment rate, and UEBMI participation rate. The retired population can be calculated by the cohort element method. In general, this study obtained the number of participants of the NCMS and the URBMI by age.
Total fertility rate
Affected by the economic development level, fertility desire, and other factors, the total fertility rate of urban and rural residents in China has continued to decline in recent years. According to the Sixth National Census data, China’s total fertility rate in 2010 was 1.18, including 0.98 in urban areas and 1.44 in rural areas, both significantly lower than the internationally recognized population replacement level of 2.1. In 2013, the Third Plenary Session of the 18th CPC Central Committee put forward a policy allowing couples to have two children if one parent was an only child, called the selective two-child policy. However, by the end of May 2015, only 1.45 million couples had applied to have another child, accounting for 13% of the amounts of couples applicable to the adjusted policy. Given this, the Fifth Plenary Session of the 18th CPC Central Committee in 2015 proposed the universal two-child policy, also called “the full implementation of a couple can have two children” policy, and put it into effect on January 1, 2016. Considering that scholars generally believed that the total fertility rate calculated based on the data in Sixth National Census is low, this study used the method of previous scholars [28] to revise the total fertility rate. The revised total fertility rate in China was 1.27, including 1.12 in urban areas and 1.42 in rural areas. Finally, according to the “421” family microsimulation model [29], this study calculated the total fertility rates of urban and rural residents under different fertility policies and different levels of fertility desire.
Per capita financing standard
According to the opinions on the integration of the URRBMI issued by the State Council in 2016, the URBMI and NCMS adopt the same financing standards after Integration. However, considering the stability of the system’s development of cohesion, financing growth, and other factors, this study chose the NCMS, which has been established for a long time and has had a relatively stable operation, as a reference to set the corresponding parameters. This means that the average annual growth rate of the per capita financing standard for the URRBMI during the forecast period was set with reference to the average annual growth rate of the per capita disposable income of rural residents from 2010 to 2019. Other parameters were set according to the difference between the two. Additionally, per the National Statistical Yearbook, the average annual growth rate of farmers’ per capita disposable income was 9.68% from 2010 to 2019, slightly lower than the average annual growth rate of per capita GDP (9.74%) in the same period. Considering the current situation of normal economic development in the post-epidemic era, the study assumed that the per capita disposable income of rural residents in China will grow at an average annual rate of 10% from 2021 to 2025 and then decrease by 0.5 percentage points every five years.
Standard for per capita compensation expenditure
According to the model design, the per capita compensation expenditure should be equal to the per capita medical expenses multiplied by the corresponding actual compensation ratio. In this study, the “growth factor” method was used to analyse the factors affecting the growth of the medical expenses of the NCMS and URBMI. To research the impact of the universal two-child policy adjustment, that is, the change in the demographic factor, on the sustainability of medical insurance funds, this study specifically separated the demographic factor from the whole and assumed that it is independent of non-demographic factors. Specifically, demographic factor refers to the increase in medical expenses caused by the increase in population size and the change in the age structure. This study calculated the demographic factor by the insured population by age and the corresponding medical consumption weight index of each age group. Other non-demographic factors were those other than demographic factors influencing the growth of per capita medical expenses, such as the growth of per capita disposable income of urban and rural residents, the improvement of medical technology, etc. According to previous studies [30, 31], combined with the previous setting of per capita financing standards, this study assumed that the average annual growth rate without demographic factors was 1 percentage point faster than the average annual growth rate of per capita disposable income of rural residents in the same period.
Bank interest rate
According to the notice on strengthening the financial management of social insurance funds issued by the Ministry of Finance of China in 2003, the interest of social insurance funds should be calculated by the preferential interest rate stipulated by the People’s Bank of China, namely, the interest rate for three-month fixed deposits. Therefore, this study assumed that the current balance and the accumulated balance of the URRBMI fund are calculated by the latest three months regularly stored at a predetermined rate (1.1%), which was published by the People’s Bank of China on October 24, 2015.
The summary of the aforementioned key parameters is shown in Table 1.
Table 1 The summary of main parameters Measurement process
The selective two-child policy had been implemented for less than two years before it was fully replaced by the universal two-child policy. Therefore, in the subsequent measurement, this study used the strict one-child policy, which can also be called the original policy, as the reference for the subsequent policy adjustment. Although the basic medical insurance system characterized by a pay-as-you-go scheme is a short-term forecast project, considering the time-lag effect of the adjusted fertility policy, 2030 and 2050 were chosen as the endpoints for the analysis.
It has been five years since the universal two-child policy was officially implemented in 2016. Although the number of births rose to 17.86 million in 2016, it then began to decline. The numbers of births in 2017, 2018, and 2019 were 17.23 million, 15.23 million, and 14.65 million, respectively, indicating a significant decline in the effect of the policy. Low fertility desire is undoubtedly a key factor affecting the number of births. Drawing on the study of scholars [32], this study set the current fertility intentions of females in accordance with the universal two-child policy at 40%. Moreover, childbearing willingness may fluctuate in the future, affected by factors such as financial support and maternity security. This study used the URRBMI fund operation under the strict one-child policy as a reference and measured the effect of the universal two-child policy when the fertility intention was 20, 40, 60, 80 and 100%. In addition, we analysed the influence on the URRBMI fund under different fertility policies and fertility intentions to comprehensively analyse the impact of the fertility policy adjustment.