3.1. Pension Revenue Model
In general, the revenues of China’s pension system consists of two parts, a pay-as-you-go part and a personal account part. The pay-as-you-go part is equal to corporate payments plus government subsidies. From another perspective, it is also equal to the number of insured employees multiplied by the average salary of the insured employees multiplied by the corporate contribution rate.
Let
be the income from the pay-as-you-go part of the pension system in the
nth year;
is the average annual wage of the employees in the
th year, which is the base period;
is the annual growth rate of average wage;
is the corporate contribution rate;
is the number of insured employees at the age of
x in the
nth year. Then
is the total number of insured employees, where a is the age when the employees begin to contribute to the pension system, and b is the employees’ retirement age. We assume that the average beginning time of employment age in Anhui Province is 20 and μ is the contribution rate of the pay-as-you-go part. We assume the latter is fixed to 20% like it is assumed in the literature referenced above.
3.3. Population Forecast Model
The revenue of the pension system and its expenditure are closely related to the number of insured employees, the number of retirees and the trend of demographic change. Therefore, in order to calculate the revenue of the pension system and pension expenditure of Anhui Province, we should consider the population and pension policies of Anhui Province and predict future population structure, specifically, we should focus on the impact of the “two-child” policy on the fertility rate.
There are many types of population prediction models, including Logistic model, Leslie matrix population prediction model, gray GM (1.1) population prediction model and etc. The problem with the above mentioned models is that the implementation of the “two-child” policy will have a great impact on various parameters in each model, making the model difficult to be accurate, and the prediction result will inevitably be biased. We use in this paper the cohort element method—which can improve the accuracy of population prediction. We use data from the Anhui Provincial Statistical Yearbook and apply MATLAB software to calculate and predict the demographic change of Anhui Province until 2050.
Let denotes the population size of a cohort of age a in year t, a = 1, 2, 3, ..., 100, and at the same time; denotes the mortality rate of people aged a in year t; represents the increase in the number of registered households at the age of a in year t, represents the increase of the migrant population aged a in year t; represents the fertility rate of prolific females at the age of a in year t, assuming 15 ≤ a ≤ 49, the total fertility rate is ; g(t) represents the sex ratio (male to female) of newborns in year t; f represents females and m represents males; the assumptions here are all vector assumptions, X(t) = represents the population structure in year t, (t) = denotes the increased population structure of the registered population in year t, (t) = denotes the increased population structure of the immigrant population in year t, A(t) = represents the survival rate in year t, (t) = is the number of newborns in year t.
The population in year
t + 1 can be expressed as follows:
The number of male newborns and female newborns in year
t + 1 can be expressed as follows:
From the above formulas, we can get the population model as follows:
In China, pensions are received in accordance with the territorial principle. If an individual participates in the pension system, it must be processed in the place where the household registration is located, that is, it cannot be insured in another place. Therefore, this article does not consider the number of immigrants and their pension payments in all following calculations.
3.3.1. Basic Assumptions
As noted above, China’s pension fund is divided into two parts. The individual contributes 8% of its salary to the personal account; the enterprise contributes about 20% of the employees’ salary to the pay-as-you-go part. We mainly focus on the pay-as-you-go part, and the personal account is not calculated here, because all funds in the personal account will be returned when the individual retires, therefore the impact of personal accounts on the overall account is weak. At the same time, the impact of state subsidies on pensions is not considered.
We assume that male employees and female employees begin to work at the age of 20. In recent years, the government releases a progressive delayed retirement plan, but only a few places (Shandong province and Jiangsu Province) have implemented the scheme since the beginning of 2022. Thus, for conservative estimation, the retirement age for male employees is still set at the age of 60 and for females at the age of 55 (In the robustness check part, we will assume an increase in the retirement age and check whether the conclusions still hold). In addition, it usually takes on average 20 years for a newborn baby to be included in the pension system after birth, so we will consider the period 2016–2050.
With reference to the forecast of the average life expectancy of population in China, we refer to the United Nations “World Population Outlook”, and assume that the average life expectancy of the population in China is 80 years, that is, the age of death is 80.
3.3.2. Parameter Introduction
- (1)
Average wage growth rate
Table 1 displays the average wage growth rate of Anhui Province from 2001 to 2018, we observe from the table that the trend of growth rate of average wage is nearly the same as the growth rate of GDP. However, as the economy continues to grow, its growth rate will definitely decline, and accordingly, the growth rate of average wages will also decrease.
It can be concluded from the table that the average wage index ranges between 100–120. Considering China’s future economic situation and GDP growth target, we refer to the CGE model constructed by Xiao (2012) and use the method of changing a certain percentage at regular intervals to define k, the growth rate of average wage per year in Anhui Province [
49], where k is 9% before 2020, 6% from 2021 to 2030, 4% from 2031 to 2040, and 3% from 2041 to 2050.
- (2)
The average replacement rate of the pension system
We use the ratio of the average pension benefit of retired employees to the average salary of in-service employees to calculate the average replacement rate of the pension system.
Average replacement rate of the pension system = average pension income of retired employees/average salary of in-service employees.
It can be observed from
Table 2 that the average replacement rate of pension system in Anhui Province from 2001 to 2018 basically showed a declining trend (except for 71.26% in 2018). The average replacement rate from 2001 to 2009 was 53.41%, and the average replacement rate from 2010 to 2018 was 47.21%. According to the data of the “Pension Development Report” over the years and consider the actual situation in Anhui Province, we use the value calculated by Yang (2017), where the future pension replacement rate is 45% [
50].
- (3)
Participation rate
It can be recognized from
Table 3 that the number of employees participating in the pension system in Anhui Province continues to increase, and the increase in the participation rate reflect the growth rate of revenue of the pension system. The average annual increase of the participation rate for the pension system in China as a whole over the years is 1.66% [
51], on the basis of this value, this article adopts a conservative estimate and assumes that the participation rate in Anhui Province will increase by 1% annually.
- (4)
Number of retirees
The data in
Table 4 shows that the number of retirees in Anhui Province fluctuated, but the general trend is an increase of the number of retirees. At the same time, pension expenditure in Anhui Province increased as the number of retirees rose, and the growth rate of the number of retirees reflects the growth rate of pension expenditure.
- (5)
Contribution rate of the pension system
According to national regulations, the enterprise contributes about 20% of the employees’ salary to the pay-as-you-go part in the pension system. However, the executive meeting of the State Council on 13 April 2016 stipulated that the contribution rate of pension system for the enterprise part should be reduced stepwise to reduce their financial pressure, and could be adjusted from 20% to 19% in the first step. We refer to the practice of other regions in China in 2022 (Fujian Province and Shandong Province in particular) and set the average contribution rate of Anhui Province in the future as 19%.
- (6)
The revenue and expenditure of pension system
Because of the continuous improvement of the pension system and economic development, we can observe from
Table 5 that the income of the pension system in Anhui Province has increased year by year, from 4.7 billion RMB in 2001 to 210.5 billion RMB in 2018. At the same time, the expenditure of the pension system in Anhui Province increased from 5.9 billion in 2001 to 181.7 billion in 2018.
- (7)
Pension adjustment rate
Beginning in 2005, China has repeatedly increased the payments for enterprise employees after retirement. The growth rate in 2006 was 23.7%, since then, the annual growth rate has been around 10% for nearly ten years, and the growth rate was about 6.5% in 2016. Based on related research, this paper adopts the following pension adjustment formula:
, where we use
α and
β values calculated by Yang and Shen [
52]. Then we have
. Among them, ω represents the basic pension adjustment ratio, c is the inflation rate, and w is the growth rate of the average wage.
It can be derived from
Table 6 that the average wage index of urban employees in Anhui Province from 2001 to 2018 ranged between 100 and 120, and the growth rate of wages was relatively stable, the inflation rate fluctuated from 2001 to 2010, but remained relatively stable from 2011 to 2018. Taking into account the actual situation in China and referring to Tang and Wu’s work [
51], we assume that the subsequent inflation rate stabilize at 3% in China.
- (8)
Fertility rate
We adopt the fertility rate of females at childbearing age in the statistical yearbook of Anhui Province.
It can be derived from
Table 7 that the fertility rate has increased after the implementation of the “two-child” policy in 2016, but it is expected to fall back. We refer to Qiao’s (2014) research and assume that the fertility rate will remain constant at 0.35 until 2050 [
53].
- (9)
Sex ratio of newborn children
According to the data of the 2005 sample survey, the sex ratio of newborns was 120.49 nationwide and 133.20 in Anhui Province. According to the data of the sixth national census in 2010, the sex ratio of newborns was 121.21 in China and 131.07 in Anhui Province. Based on the above data and related research, this paper makes the same assumption as Tang and Wu (2016) and the sex ratio of newborns in Anhui Province from 2001 to 2015 is 130. With the implementation of the “two-child” policy, the sex ratio of newborns from 2016 to 2050 will be 115 [
51].
- (10)
Mortality rate
According to
Table 8, the overall mortality rate was around 6‰ in the period 2001–2015. Since 2016, the mortality rate was around 5.95‰. Therefore, in order to simplify the calculation, it is assumed that from 2018 to 2050, the mortality rate will decrease by 0.01‰ each year. At the same time, the population of Anhui Province in 2018 by age and sex is shown in
Table 9.