# The choice of pension and retirement systems when post-1960s baby boomers start to retire in China

## Abstract

### Background

Around 2015, with the alternation of population generation, post-1960s baby boomers start to retire and post-1990s and 2000s baby busters successively enter into labor market in China, which has led to the decrease of working-age population, the increase of pension burden.

### Methods

We use dynamic programming method by improving the traditional OLG model.

### Results

This paper finds that a combination of immediately delayed retirement and accumulated pension system should be implemented if based on the goal of maximizing output, while a combination of undelayed retirement and accumulated pension system should be implemented if based on the goal of maximizing utility. Certainly, with using efficiency of elements unchanged, with the decrease of working-age population caused by the alternation of population generation, the increase of pension burden and the disappearance of capital dividend, a sharp decline of future economic growth cannot be changed no matter what kind of pension and retirement systems are implemented.

### Conclusions

In view of the substitutability of family utility and social output and synthesizing reform resistance, a combination of gradually delayed retirement and accumulative pension system should be implemented. At the same time, on the premise of stabilizing short-term economic situation, we should look for a new engine for economic development by system reform in the long run.

## Keywords

Retirement system Pension policy Post-1960s baby boomers Social output and family utility## Background

Along with the implementation of the new farmers’ security in 2009, new endowment insurance for urban residents in 2010, and pension reform of public institution in 2015,, China has formed a unified mode of the combination of social pooling and individual account, namely, the current system of supporting for the elderly is a mixture of family support and social pension; social pension system is a hybrid scenario of pay as you go system and funded system. China’s current retirement system has been formed in 1978, the document stipulates that male workers and cadres retire at the age of 60 years old, female cadres retire at the age of 55 year old, female workers retire at the age of 50 years old, and the average retirement age is about 55 years old. Of course, there are a lot of contents on the reform of the pension and retirement system. Here, the author pays more attention to the reform of intergenerational distribution effect of pension system, and retirement mode choose according to retirement age. Based on the above key points of research, two important reforms on China’s pension and retirement system are as follows, whether we should delay the retirement, or not and whether we should increase the accumulation effect of pension and the proportion of personal account in order to establish fully funded pension system, or not.

For the above two scientific problems, different scholars have different opinions, for example, Yuan (2014) thought that delayed retirement could mitigate the gap size of pension and lessen finance stress for the government, the study on OECD countries showed that continued employment of the aged would not result in taking more positions which belong to the young (Kalwij et al. 2010), in fact, there is the complementarity between the employment of the aged and the employment of the young. Yang and Xie (2014) thought that, after entering into new normal, continued employment of the retiree would increase employment pressure on the young; Michello and Ford (2006) thought that delayed retirement would result in taking more positions which belong to the young, especially in those sections which already have surplus workers, et al. Therefore, whether delayed retirement should be implemented, or not, which is a question to answered explicitly. Different pension systems certainly have different features. Gayane (2015) thought funded pension system is more vulnerable to inflation risk, while in contrast, pay-as-you-go system does not have this problem. The future studies showed that in reality, if based on the perspective of maximizing investment and output, funded pension system is superior to pay-as-you-go system (Chybalski 2011); family support system exists widely in China’s vast rural area; during the period of demographic dividend, we should universally implement pay-as-you-go system (Ke and Yuan 2004); what kind of pension mode should be chosen is a question which need to be answered urgently when post-1960s baby boomers start to retire in China.

With post-1960s baby boomers starting to reach retirement age and post-1990s and 2000s baby busters successively entering into the labor market, at the same time, the upgrading of industrial structure and the improvement of population quality cannot be realized in the short time. In terms of research questions, few literature, taking China’s special national conditions into account (for example, China’s fertility behavior is strictly controlled by population policy, child-rearing is not only consumer behavior but also is investment behavior, pension system is a hybrid scenario of PAYG system, fund pension system, savings and child support, after 2015, post-60s baby boomers will start to reach retirement age in succession, China implements universal two-child policy) analyzes various pension and retirement systems by considering fertility behavior, retirement system, and pension mode in one-model framework and selects pension and retirement systems which are suitable for future conditions in China based on some policy goals. In terms of research method, existing literatures mostly adopt overlapping generation model (OLG), but, in the next 15 years and short-term, the OLG model of examining intergenerational conversion, which cannot reflect the changes of annual output and family utility according with real situation, also cannot simulate the annual influence of post-1960s baby boomers’ retirement on every aspect of socioeconomic system in the short time. Based on the defects of existing literatures, from the angle of maximizing social output and family utility, this article tries to give some alternative pension and retirement scenarios, and then tries to appraise those pension and retirement systems which may be put into effect by the government in the future by using the dynamic programming model, finally, chooses pension and retirement systems which are suitable for Chinese current and future national conditions.

## Methods

Population can be divided into three types for any period: adolescent, adult, and the aged; the population at the age of 0–15 years old is defined as adolescent, while the age interval of adult and elderly population depends on the retirement system. Adolescents do not participate in social work, and the consumption of maintaining life only comes from parents’ support; in the next period, some adolescents become adult. Adult supply labor for labor income each period, and in order to achieve maximum utility, adults make decision on how to allocate current labor income into consumption, savings, pension, supporting for the elderly, and child-rearing. Some adults become old people in the next period; here, we assume that total social utility is approximately equal to the utility of adult. Elderly population does not participate in work and does not make social decisions, such as fertility decision. Their income comes from pension, adult support, and savings; some elderly people will die in the next period. The utility function of adult includes two parts: current consumption utility stream and utility stream in the next period.

### Theoretical framework

Following Barro and Becker (1989) and Liao (2013), utility function is set as follows, intertemporal substitution elasticity of consumption is *σ*, discount factor is *β*, the proportion of social pooling accounts pension to wage and the proportion of personal accounts pension to wage is *τ* _{1} and *τ* _{2} respectively, and the total proportion of pension to wage is *τ* = *τ* _{1} + *τ* _{2}. For each subsequent period, we uniformity assume that the initial period is *i*, the proportion of family support for each elderly population to wage is *ϕ*, and the proportion of family expenditure for each adolescent to wage is *μ*. Consumption, savings for *i*-th period, and consumption for *i* + 1-th period is *C* _{ i } ^{1},*S* _{ i }, and *C* _{ i } ^{2}, respectively. In the *i*-th period, the number of total population, adolescent, labor population (or adult), and elderly population is *P* _{ i }, *H* _{ i }, *L* _{ i }, and *O* _{ i } respectively. The wage of *i*-th period, the wage of *i* + 1-th period, and interest rates of *i* + 1-th period is *w* _{ i },*w* _{ i+1}, and r_{ i + 1},respectively. Relaxing fertility regulation does not affect human capital level of labor population before 2030. We assume that fertility level is exogenous, fully controlled by a fertility policy, and the fertility level of policy is equal to actual fertility level; according to this assumption, the total fertility rate (referred to as TFR) of universal two-child policy is about 2.

_{ i }for

*i*-th period. The number of labor

*L*

_{ i }for

*i*-th period is calculated according to the population (adult) of each age group and corresponding labor participation rate of each age group. Population at the age of

*i*years old is

*P*

_{ i }(

*j*) for

*i*-th period, labor force participation rate for the population aged

*j*years old is ER

_{ i }(

*j*) for

*i*-th period, in order to simplify the processing; each period, we suppose that labor force participation rate in each age group is fixed on the level of 2010 without affecting analytical results, so total number of labor for

*i*-th period is as follows.

*L*

_{ i }

*w*

_{ i }in the

*i*-th period. It is spent on consumption

*C*

_{ i }

^{1}, savings

*S*

_{ i }, child-rearing expense

*H*

_{ i }

*μw*

_{ i }, elderly-rearing expenditure

*ϕw*

_{ i }

*O*

_{ i }, social planning pension

*τ*

_{1}

*L*

_{ i }

*w*

_{ i }, and individual account pension expenditure

*τ*

_{2}

*L*

_{ i }

*w*

_{ i }.Consumption

*C*

_{ i }

^{1}happens utility stream (

*C*

_{ i }

^{1})

^{ σ }in the

*i*-th period. In the

*i*+ 1-th period, savings

*S*

_{ i }obtains

*S*

_{ i }(1 +

*r*

_{ i+1}) unit income,

*τ*

_{2}

*L*

_{ i }

*w*

_{ i }(1 +

*r*

_{ i+1}) term is the return of

*τ*

_{2}

*L*

_{ i }

*w*

_{ i }term, \( {\tau}_1{L}_i{w}_i+\frac{\tau_1{L}_{i+1}{w}_{i+1}{\mathrm{RE}}_i}{O_{i+1}}-{\tau}_1{L}_i{w}_i{\mathrm{RE}}_i/{L}_i \) term is the return of

*τ*

_{1}

*L*

_{ i }

*w*

_{ i }. Taking investment culture on pension of bringing up child into account, so child-rearing expenditure

*H*

_{ i }

*μw*

_{ i }and elderly-rearing expenditure

*ϕw*

_{ i }

*O*

_{ i }obtain (

*H*

_{ i }

*μw*

_{ i }+

*ϕw*

_{ i }

*O*

_{ i }) unit income in the

*i*-th period. The term of consumption

*C*

_{ i }

^{1}happens utility stream in the

*i*-th period, the term of

*S*

_{ i },

*τ*

_{2}

*L*

_{ i }

*w*

_{ i },

*τ*

_{1}

*L*

_{ i }

*w*

_{ i },

*H*

_{ i }

*μw*

_{ i }, and

*ϕw*

_{ i }

*O*

_{ i }happens utility stream in the

*i*+ 1-th period. Under the TZPS, annual decision problem which labor population faces is how to choose consumption and savings in order to achieve maximized utility goal of annual labor income. Finally, objective function and constraints for

*i*-th period are as follows.

*s*

_{ i }in the

*i*-th period, then we calculate human capital level

*h*

_{ i }for

*i*-th period according to PWT version 8.0. For each age group, we assume that s

_{ i }(

*j*) is the average years of schooling of each labor population aged

*j*years old for

*i*-th period.

*L*

_{ i }(

*j*) is the number of working people aged

*j*years old for

*i*-th period. Finally, the average year of schooling per labor

*s*

_{ i }for

*i*-th period is as follows.

*s*

_{ i }for

*i*-th period cannot directly enter into production function, we introduce the rate of return on average years of schooling. Finally, we regard human capital level

*h*

_{ i }as a function of average years of schoolings

_{ i }, according to the function provided by Penn World Table 8.0, we can find

*φ*(

*s*

_{ i }) for

*i*-th period is set as follows.

*α*is invariant. In order to simplify analytical process, we use average years of schooling

*s*

_{ i }to characterize human capital level of labor population. According to initial output in 2014, we assume that total factor productivity is a variable which is calibrated. Finally, production function for

*i*-th period and production function for

*i*+ 1-th period is set as follows.

*δ*, savings is equal to investment, and corruption does not exist in the pension. The stock of capital

*K*

_{ i+1}for

*i*+ 1-th period is equal to the sum of current stock of capital

*K*

_{ i }, savings

*S*

_{ i }and pension

*τ*

_{2}

*L*

_{ i }

*w*

_{ i }in the

*i*-th period, and then the above sum deducts depreciation δ

*K*

_{ i }.Finally, according to the above assumptions, the motion equation of capital for each period is set as follows

How to calculate the motion equation of total population or labor population? Here, we follow Lu and Cai (2014)’s work and assume that fertility level is fully controlled by the fertility policy; under this condition, if we know policy fertility level for each period, and will also know initial population distribution and corresponding mortality at each age stage, we will also know future population distribution at each age stage. According to “2014 Chinese population and Employment Statistics Yearbook,” TFR is about 1.3 in 2013, that is TFR of maintaining the fertility policy unchanged, the policy TFR of universal two-child policy is about 2.0.We put population distribution in 2014 for different gender at each age stage as an initial population distribution and put mortality between 2003 and 2013 for different gender at each age stage as population update criteria. Firstly, we calculate population distribution for different gender at each age stage, we get the number of people at each age stage by the sum of the number of population for different gender for each age stage, and then we get the total population by adding the number of the population at each age group. Secondly, the number of newborn babies every year depends on the number of women of childbearing age (aged 15–49) and corresponding fertility level at each age stage.

*i*-th period and different gender and the number of population for

*i*+ 1-th period and different gender are respectively calculated as follows.

The male and female mortality for *j* years old in the *i*-th period is the variable *d* _{ i } ^{male}(*j*) and *d* _{ i } ^{female}(*j*) respectively, the male and female number of aged *j* years old for *i*-th period is the variable *P* _{ i } ^{male}(*j*) and *P* _{ i } ^{female}(*j*) respectively, and the sub-fertility rate of female for *j* years old in the *i*-th period is the variable TFR_{ i } ^{female}(*j*). It is important to note that this article assumes that people’s lives are limited, the maximum life span is 100 years old, and individuals for more than 100 years old will automatically exit the model. According to the above update law, we calculate the total population by adding the number of population for a different age group and gender in the next 15 years. Considering China law, population are not allowed to take part in labor until 16 years old and the population of less than 16 years old is called adolescent. According to the characteristics of China’s current retirement age, at the same time, we no longer distinguish between urban and rural or for different sectors. We assume that the average retirement age is approximately 55 years old, and the retirement system does not affect the number of working people, but affect the number of the people receiving the pension. So the population of 16–54 years old is called the working-age population, and the population who is over the age of 55 who receive the pension is called the elderly or pensioners.

*j*years old and

*i*-th period is ER

_{ i }(

*j*); here we put labor participation rate of sixth census at each age stage as initial labor participation rate. At the same time, labor participation rate is assumed to be unchanged for subsequent period. If the number of population for

*j*years old and

*i*-th period is

*P*

_{ i }(

*j*). Finally, the motion equations for population are as follows.

*h*

_{2014}, so computational level of human capital for

*i*-th period is

*h*

_{ i }/

*h*

_{2014}in actual simulation. Finally, under the TZPS, annual decision problem which labor population faces is how to choose consumption and savings per year in order to achieve the goal of maximizing utility of labor income in the mechanism of raising children to provide against old age, objective function, and constraints are set as follows every year.

To be sure, under the universal two-child policy, firstly, retirement system affects the number of people who receive a pension each year; for example, according to current average age of receiving pension, if retirement system remains unchanged, the number of people who will retire for *i*-th period is *P* _{ i }(54), so different retirement systems mean different value of *RE* _{ i }. Of course, the above implies an important hypothesis that the number of new pensioners each year is equal to the number of people who will be retiring. Secondly, different parameter combinations imply different pension systems; for example, pension system is the accumulated pension system or personal account pension (fully funded pension system, referred to as APS) when *τ* _{2} is equal to *τ*and *τ* _{1} is equal to 0, pension system is social planning pension or pay as you go system (referred to as PAYGS) when *τ* _{1} is equal to τand *τ* _{2} is equal to 0, and pension system is TAPS when *τ* _{2} > 0 and *τ* _{1} > 0. Technological progress is seen as institutional dividend in this paper; of course, the reform of pension system and retirement system can release productivity level.

### Parameter settings

Various parameters and value setting

## Results and discussions

In view of difference on gender and department of China’s retirement age, meanwhile, the research emphasis of this paper is the comparison of different pension and retirement systems and the hypothesis that retirement age is equal to the age of receiving pension, the average age of receiving pension under the undelayed retirement is uniformly assumed to be 55 years old without influencing analysis results. At the same time, we no longer distinguish the difference on gender and department. According to the above analysis, we choose three types of retirement system: first, undelayed retirement system (referred to as UDR), with average retirement age at 55 years old; second, immediately delayed retirement system (referred to as IDR), with initial retirement age at 55 years old, uniformly put off the retirement age of people who is still on duty until 65 years old, and then fix it; and third, gradually delayed retirement system (referred to as GDR), there is a queue to retire every other year, and retirement age after 2035 is fixed at 65 years old.

Retirement system does not affect the number of adolescent, but influences the number of adult and the aged. According to the above model setting, we choose three kinds of pension scenarios: first, according to the characteristics of current pension system and the share of capital contribution in China, accumulated pension system led by the government (referred to as APS), *τ* _{2} is equal to*τ* = 0.14, and *τ* _{1} = 0; second, pay-as-you-go system led by the government (referred to as PAYGS), *τ* _{1} is equal to *τ* = 0.14 and *τ* _{2} = 0; and third, the current tongzhang pension system (referred to as TZPS), according to the characteristics of current pension system and the share of capital contribution in China, we give a parameter combination of *τ* _{1} = 0.1 and *τ* _{2} = 0.04. Of course, our study is based on the context of universal two-child policy. At the same time, we assume that actual fertility level is equal to policy fertility level. Based on the above hypothesis, we will examine the influence of various retirement and pension scenarios on social output and family utility and then select suitable retirement and pension scenarios according to some policy goals. Of course, comparative results of different retirement or pension system scenarios are robust for other parameter scenarios. Due to space limitation, author will not list other simulation scenarios; the specific solution process is shown in Additional file 1. Because different retirement system and pension system only affect population structure and parameter value of *τ* _{1} and *τ* _{2}, here, we only give a scenario code under the condition of UDR and TZPS; you can acquire the other simulation results for the other scenarios by giving other population structure and parameter value of *τ* _{1} and *τ* _{2}.

To be sure, the following analyses are obtained under some assumptions such as immigration policy remaining unchanged, the share of capital contribution remaining unchanged, without regard to the differences in sex and between rural population and urban population, investment equaling to savings; no idle pension and no corruption in the pension; the pension of accumulative system all taking part in investment, same returns of savings and pensions; regarding technological progress as reform dividend, exogenous fertility level, factor (labor and capital) reward paid according to marginal output and no industrial updating; the age of receiving pension equaling to retirement age, retirement system which only affects the number of pensioners; and so on.

### Population structure in the future

### Policy selection based on the goal of social output

Why is the per capita output and gross output of PAYGS is the lowest? Firstly, relative to APS and TZPS, after 2015,with post-1990s and 2000s baby busters successively entering into labor market and post-1960s baby boomers just now starting to reach the age of receiving pension, the PAYGS of current young people supporting current old people will make pension outlay of Chinese economy already lack of labor force more bigger, reduce household savings and social investment, which will lead to the decrease of capital stock; secondly, relative to APS and TZPS, the pension of PAYGS does not take part in future production and increase capital stock. Therefore, its output and per capita output is more lower than that of TZPS and APS. Why gross output and per capita output of TZPS is lower than that of APS? TZPS is a pension system dominated by PAYGS, compared to APS. Its cumulative effect and capital increase effect is weaker than that of TZPS. In the case of same number of labor population, TZPS has lower capital stock, so gross output and per capita output of TZPS is lower than that of APS.

Why is output and per capita output of IDR higher than that of GDR? After 2015, in the case of largest post-1960s baby boomers gradually exiting labor market in China, the number of the aged will increase rapidly and the number of working-age population will decrease sharply in the future. According to the attributes of IDR, no working-age population will retire until 2025. Based on the features of GDR, only a wave people will retire each other year after 2015. Working population retires every year for UDR scenario. Under the condition of the same labor inflow, the labor outflow of UDR is stronger than that of GDR, and the outflow of GDR is stronger than that of IDR. So delayed retirement system increases the future number of labor population, reduces pension spending, increases capital stock, and thereby increases output and per capita output. Of course, the output effect of IDR is stronger than that of GDR.

### Policy selection based on the goal of family utility

Why per capita utility under delayed retirement is lower than that of undelayed retirement scenario? With average life expectancy unchanged, delayed retirement means the extension of working time, consumption postponement and compulsory savings, and the increase of capital stock, so, it increases output. But under the assumption of an economic man, due to the utility of future consumption per unit is lower than that of present consumption per unit, so per capita utility will decrease according to objective function. That is, every worker under the condition of delayed retirement will have to work longer than before, become more patient with economic prospect and reduce more present consumption to increase savings, and provide more heritages to their children. Delayed retirement also means that the labor population have to work longer, receive much less pension, and carry on less present consumption and private consumption because discount factor is less than 1 and people give larger weight to present consumption and private consumption. Therefore, delayed retirement will decrease per capita utility for every adult.

### Policy selection based on the goal of economic growth

Post-1990s and 20000s are the baby busters in China, with post-1990s and 2000s baby busters gradually entering into the labor market after 2015, even if there is no labor outflow, due to the birth decrease year by year after 1987; 20 years later, the number of entrant entering into the labor market present a decreasing trend. The economic growth will only depend on the growth of labor population when capital growth and technology level remain unchanged. So, accompanied by a decline in the growth of labor population, economic growth will also show a corresponding decline trend. Of course, the delay in retirement and the reform in pension system only reduce the extent of decline, but do not change the decline trend. More seriously, after 2015, if we take successive retirement of post-1960s baby boomers into account, the extent of decline will be greater, ensuing demographic debt as well as gradual disappearance of capital dividend. Under the condition of unchanged production mode, China’s economy will fall into demographic cliff.

## Conclusions

Around 2015, due to the decrease of working-age population and dramatic increase of the aged caused by the alternation of population generation, in order to win time for the upgrading of industrial structure, the improvement of population quality and technological progress, and also to mitigate the impact of fast aging on economic system, it is necessary to look for suitable retirement and pension systems. Of course, there are a lot of contents on pension and retirement reform. In this paper, the author pays more attention to choose pension mode based on intergenerational distribution and choose retirement mode ignoring industry and regional and gender differences.

Simulation results show that no matter under what kind of retirement system, output and per capita utility of PAYGS is the lowest and output and per capita utility of APS is higher than that of TZPS. No matter under what kind of pension system, the output of IDR is the highest, followed by GDR and UDR; while on per capita utility level, no matter under what kind of pension system, UDR is the highest, followed by GDR and IDR. For a country, if based on the goal of maximizing output, a combination of IDR and APS should be implemented. If based on the goal of maximizing per capita utility, a combination of UDR and APS should be implemented. Taking reform resistance, output goal, and welfare goal into account, a compromise scheme which is a combination of GDR and APS should be implemented. Of course, the current TZPS is only a transitional pension system; APS is that we should choose in the aging society. It is gratifying that China is formulating a gradual retirement scheme and will try to carry out fully funded pension system.

Of course, there are a lot of reforms on the pension and retirement system in China. The above study is merely to provide the reader a reform direction on pension and retirement system. Pension and retirement system reform in China is a systematic and complex issue. Only if we take the combination of the pension reform can we achieve the desired policy goals. We not only deal with the relationship between the intergeneration but also have to deal with the relationship between the central and local governments; we not only delay retirement age based on life expectancy but also develop different retirement system for different industries and gender, which are the directions for future research.

## Notes

### Acknowledgements

My deepest gratitude goes first and foremost to peer reviewers, thank you for their constructive comments which help author make paper more perfect. Second, I would like to express my heartfelt gratitude to Prof. Huang Shaoan, Prof. Zhao Wenzhe, and Hu sen, from who the author has received valuable comments. Lastly, my thanks would go to my wife and my mother for their loving considerations and great confidence in me all through these years. All the errors remaining are the author’s.

### Author’s information

Hualei is a PHD candidate in the School of Management, China Agricultural University. He conducted several researches in population economics and public economics.

### Competing interests

The author declares that he have no competing interests.

## Supplementary material

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## Copyright information

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