Research on the Impact of the Optimal State-owned Capital Allocation,Tax Deferral and Delayed Retirement on the Replacement Rate of Pension and Policy Optimization

Abstract

In order to cope with the aging population, China has implemented individual tax deferred policy and state-owned capital allocation, and plans to raise the retirement age. Firstly, this paper comprehensively considers the above three policies and develops an overlapping generation model with three sectors: the household sector, consisting of one agent concerned with the individual tax deferred policy; the production sector, composed of state-owned and privately-owned enterprises; and the public sector responsible for comprehensive policy arrangements. Then we discuss the impact of three policies on the total replacement rate of pension benefits under the steady state and conduct the parameter sensitivity analysis. Secondly, the relationship between the three policies is explored when we set the target replacement rate. Finally, under the premise of maximizing individual’s utility and a certain pension benefits replacement rate, we find the optimal solution when one of the policies is fixed, and the remaining two are allowed to be adjusted. The study finds that the tax deferred policy has the greatest impact on the pension benefits replacement rate, and each of the policies presents inverse relations under a certain pension benefits replacement rate. When comparing with delayed retirement, individuals prefer the tax deferral and state-owned capital allocation under a certain replacement rate.

JEL Classification: F842.67

Introduction

The aging population has become a significant demographic factor that has accompanied the long-term development of Chinese society. According to the seventh national census data, the population of China aged 60 and above exceeds 264 million, accounting for 18.7% of the total population and far exceeding the international standard of 10% population aging. The continuous increase in the proportion of the elderly population not only poses severe challenges to China’s economic development, but also puts enormous pressure on China’s pension benefits payment system.

One important purpose of establishing a pension system is to ensure the basic living of retired elderly people. Since the 18th National Congress of the Communist Party of China, the number of people participating in basic pension insurance in China has increased from 790 million in 2012 to 1.05 billion in 2022. The coverage rate of basic pension insurance has significantly increased, and the social security industry has achieved significant results. Driven by the goal of common prosperity, in order to promote the sustainable development of the pension system, in addition to expanding the scale of participation and ensuring the basic livelihood of more elderly people, it is also necessary to increase the replacement rate of pension to improve the quality of life of the elderly.

According to the World Bank’s calculations, maintaining the living standards of elderly individuals post-retirement requires a pension replacement rate of 70%. However, in 2019, the replacement rate of the basic pension for urban employees in China was a mere 43.97%, falling below the 55% threshold set by the International Labour Organization. As the process of population aging intensifies, an increasing number of elderly individuals will need pension support, while the workforce contributing to the pension system is gradually diminishing. This trend suggests a potential further decline in China’s pension system replacement rate in the future, posing additional challenges to the nation’s pension framework.

To alleviate the pressure on pension benefits payments and enhance the replacement rate of endowment insurance, China has implemented a series of significant initiatives. In 2017, the State Council, China’s cabinet, introduced an executive plan for allocating state-owned capital to the pension fund. This plan tentatively mandated that large and medium-sized state-owned and state-controlled enterprises, as well as financial institutions, allocate 10% of their equity to the pension fund. Additionally, the plan clarified the roles of the transferor and the transferee in written agreements.

In May 2018, the Ministry of Finance issued a notice on the pilot program for individual tax-deferred commercial endowment insurance, selecting Shanghai, Fujian Province, and Suzhou as pilot areas. Building upon this directive, the tax-deferred policy was relaxed for a one-year period.

Furthermore, the report from the 20th National Congress of the Communist Party of China explicitly proposes a gradual increase in the statutory retirement age. The delayed retirement is positioned as an inevitable choice for China to address the challenges posed by its aging population in the future.

Enhancing the well-being and improving the quality of life for the people is not only a key focus outlined in the 20th National Congress report but also a longstanding commitment of the Chinese government. Pensions constitute the primary means of support for elderly retirees, and elevating the pension replacement rate stands as a crucial avenue to enhance the quality of life for this demographic. Presently, three policies—state-owned capital allocation, tax deferral, and delayed retirement—are directly capable of significantly impacting China’s pension replacement rate. Hence, a more pragmatic approach involves integrating these three policies into a unified model to comprehensively explore their combined impact on the pension replacement rate. What consequences will the implementation and adjustments of policies like state-owned capital allocation, tax deferral, and delayed retirement have on China’s pension replacement rate? How can these three policies be synergistically and optimally combined to create a win-win scenario, improving the living standards of the elderly and maximizing individual utility? These critical questions warrant thorough consideration and research. Consequently, leveraging the overlapping generations (OLG) model, this paper elucidates the evolution of the pension replacement rate under the collective influence of the three policies. It further examines the optimal combination of these policies, taking into account individual utility maximization and various target pension replacement rates. The findings serve as a valuable decision-making reference for the active implementation of the national strategy in response to population aging during the new development stage.

Countries other than China are more advanced in the practice of delaying retirement, and research on related issues is more comprehensive. Cabo and García-González (2014) emphasized that delaying retirement can prevent the social security deficit from escalating to an unsustainable public debt level. Martín et al. (2019) discovered that raising the retirement age can stimulate social demand and boost employment. Chen (2018) observed significant variations in the effects of delayed retirement policies among different resident groups (Bronshtein et al., 2020), with the most adverse impact on low-income groups (Xie et al., 2021). Chen et al. (2020) found that the positive and beneficial effects of the delayed retirement policy may not be universally applicable to alleviate pension payment challenges, constituting only about 15% of the overall impact. Bazzana (2020) demonstrated that delayed retirement can moderately alleviate the strain on pension benefit payments caused by the continual increase in the aging population, enhancing the sustainability of pension funds (Kalemli-Ozcan & Weil, 2010; Li & Lin, 2016).

Research conducted by scholars from various countries indicates that the tax deferral policy can not only optimize residents’ welfare and alleviate financial burdens but also enhance the replacement rate of endowment insurance. Venti and Wise (1990) assert that adopting tax deferral encourages increased savings without crowding out other types of savings (Gomes et al., 2009). Empirical analysis by Creedy and Guest (2008) demonstrates that the EET-type endowment insurance is advantageous for promoting intergenerational equity and enhancing residents’ welfare. Mishra and Chang (2011) examined factors influencing individual tax-deferred endowment insurance among American households, concluding that higher household income levels result in more significant tax incentives (Blanc & Scholl, 2017; Yu et al., 2020). Nishiyama (2011) found that tax-deferred accounts contribute to long-term increases in national wealth and total output (Ho, 2017). Ghilarducci et al. (2012) investigated the impact of eligibility changes in participating in 401 k plans, discovering that lowering the entry threshold significantly increases pension balances without residents reducing other assets.

In 2017, the State Council mandated that state-owned and state-controlled enterprises, along with financial institutions, allocate 10% of their equity to the pension fund. Chinese scholars have extensively researched the impact of this policy. Yang and Gong (2008) discovered that under specific conditions, as the allocation ratio of state-owned capital increased, the overall social welfare level, represented by total consumption, initially rose and then declined. Jing and Zheng (2019) investigated the influence of state-owned capital allocation on the economic growth rate and the replacement rate of basic pension benefits. They found that increasing the ratio of state-owned capital allocation to the pension fund would impede economic growth and raise the replacement rate. Dong and Zheng (2020) calculated a rate based on the minimum contribution rate function. This function requires that the annual basic endowment insurance income, plus the balance from the previous period, not be less than the current expenditure. They found that state-owned capital allocation can reduce the minimum rate of basic endowment insurance (Jing et al., 2020).

In summary, previous studies have investigated the effects of state-owned capital allocation, tax deferral, and delayed retirement policies on pensions and welfare. These studies have explored the mechanisms through which these policies impact pensions and welfare from various perspectives. However, there is a scarcity of research that delves into how policies can be adjusted and combined, considering the target pension replacement rate and maximizing individual utility. Additionally, previous analyses often focus on the impact of individual policies on pensions. In practice, these three policies are typically implemented simultaneously. Studying only one policy might overlook the comprehensive impact of policy combinations, leading to biased results.

In comparison to prior research, this paper contributes significantly in two key aspects: (a) It incorporates state-owned capital allocation, tax deferral, delayed retirement policies, and pension replacement rates into a unified overlapping generations (OLG) model. This quantitative examination comprehensively assesses the impact of each policy on the pension replacement rate, advancing the research landscape in this field. (b) By exploring adjustments and changes in these three policies while maximizing individual utility, the study aims to achieve a reasonable and high pension replacement rate. This provides valuable insights for decision-makers actively responding to the national strategy concerning the aging population in the new development stage

The rest of the paper proceeds as follows. Section “The Model” constructs OLG model and solves the competitive equilibrium. Section “Characterization of the Steady State” describes steady state characteristics. Section “Numerical Simulation and Sensitivity Analysis” explores the impact of the three policies on the replacement rate and the relationship among the three policies. Section “Policies’ Adjustment When the Individual’s Utility is Maximized” finds the optimal combination of three policies and Section “Conclusions” draws some conclusions.

The Model

The overlapping generations (OLG) model unveils the intergenerational structure of the population and the relationships among the same and different generations by categorizing the population into distinct age groups. Consequently, it finds extensive application in the study of public pension systems. This model boasts several advantages: firstly, it incorporates the equilibrium of labor and behavior, capital, etc., across households, production sectors, and public sectors, enabling an examination of the impact of micro-level changes on the overall macroeconomic situation. Secondly, it distinctly illustrates the influence of policy variables on public pensions and the overall economy. The capital-labor ratio permeates various periods within the generational overlap model and exerts a decisive impact on variables such as interest rates, wages, and savings. Changes in the capital-labor ratio can effectively mirror alterations in the overall economy.

The overlapping generations (OLG) model posits the existence of both young and elderly individuals in society, where each representative individual has a defined lifespan. As the lives of the elderly generation conclude, contemporary young individuals transition into the elderly category, while a new generation enters society, assuming the role of young individuals. These two generations are interconnected and undergo constant change. In this model, each representative individual is portrayed as a rational economic agent capable of judiciously managing income and savings for consumption. Furthermore, every representative individual seeks to maximize their own utility and can strategically allocate their consumption throughout both their youth and old age.

The model delineates the division between youth and old age based on an individual’s participation in social labor. Representative young individuals possess the capacity to engage in work, earning wages for current consumption and savings. Upon retiring and ceasing to participate in social labor, the individual transitions into old age, relying on savings accumulated during youth and pension payments to sustain their livelihood. This paper incorporates the assumption of a delayed retirement policy, implying that elderly individuals still need to work for a certain period to qualify for their pension.

Household

Assume that there is only one representative agent in the household who can live up to two periods indexed by $t$ and $t+1$ . Each young individual is endowed with one unit of time which is supplied inelastically to the labor market while receiving wage at the competitive rate $W_t$ . When the individual enters old age, the agent will take part of the time to work and receive wage $W_{t+1}$ in a certain proportion because of the delayed retirement, which means in the second period of their life, their income source includes delayed retirement wage, savings, pooling account pension, individual account pension and commercial pension. So that the budget constraints are given as follows:

$$C_t=W_t(1-r-\theta )(1-i)(1-\delta -s_t)$$

(1)

$$\begin{array}{c}\multicolumn{1}{c}{C_{2t+1}=W_{t+1}L(1-\delta )+I_{t+1}+B_{t+1}+}\\ \multicolumn{1}{c}{R_{t+1}{s}_t{W}_t(1-r-\theta )(1-i)+i{R}_{t+1}{W}_t(1-r-\theta )(1-\pi )}\end{array}$$

(2)

where $0<\theta <1$ is the contribution rate of pooling account to the pay-as-you-go (PAYG) scheme paid by employer and $0<r<1$ is the contribution rate of individual account of endowment insurance paid by current workers. Apart from the basic endowment insurance, the agent will buy tax deferral commercial endowment insurance at the rate of $0<i<1$ , pay individual income tax at the rate of $\delta$ and save at the rate of $0<s_t<1$ . The remaining part is for consumption $C_t$ in the first period. $L$ is the proportion of delayed retirement years in the second period of life, thus the agent will receive income $W_{t+1}L(1-\delta )$ in delaying years. $R_{t+1}$ is the gross real return, so the saving from last period will turn into $R_{t+1}{s}_t{W}_t(1-r-\theta )(1-i)$ . For the part of the pension, the agent will get $I_{t+1}$ from individual account, $B_{t+1}$ from pooling account and $i{R}_{t+1}{W}_t(1-r-\theta )(1-\pi )$ from commercial endowment insurance, and $\pi$ is the part to be deducted when a person receives pension from commercial endowment insurance. These sources of income will be used for consumption in the second period, $C_{2t+1}$ .

The representative agent born at time $t$ solves the following problem subjects to above constraints:

$$U_t=\ln (C_t)+\beta \ln (C_{2t+1})+\gamma \ln (1-L)$$

(3)

where $0<\beta <1$ is the subjective discount factor representing the degree of altruism of next period, and $0<\gamma <1$ is the weight of leisure in the utility function and $\gamma$ is set to be 1.5 in this paper.

Maximization of equation (3) gives the following function:

$$\frac{1}{c_t}=\beta \frac{R_{t+1}}{c_{2t+1}}$$

(4)

Production Sector

Drawing upon the dual-sector framework established by Jing and Zheng (2019) and Pan and Gong (2015), we assume that the production sector comprises two intermediate goods departments—namely, the state-owned capital sector and the private state-owned capital sector. The final output $Y_t$ is composed of the output of the state-owned capital sector $Y_{g,t}$ and the output of the private state-owned capital sector $Y_{p,t}$ . The production function is expressed in the form of the CES function:

$$Y_t=[\omega {Y_{g,t}}^{\phi }+(1-\omega ){Y_{p,t}}^{\phi }{]}^{1/\phi }$$

(5)

where $0<\omega <1$ is the weight of the output of the state-owned capital sector in the final output of the enterprise. $\phi$ is the substitution elasticity of state-owned capital and private state-owned capital. The two sectors are mutually replaceable when $0<\phi <1$ , and mutually complementary when $\phi <0$ , and the function will degenerate to Cobb-Douglas function if $\phi =0$ .

We assume that all firms in both sectors use C-D technique to product and the production functions is shown as (6)

$$Y_{g,t}={K_{g,t}}^{\alpha }(A{H}_{g,t}{)}^{1-\alpha }$$

(6)

$$Y_{p,t}={K_{p,t}}^{\alpha }(\mathrm{vA}{H}_{p,t}{)}^{1-\alpha }$$

(7)

where $0<\alpha <1$ is the output elasticity of state-owned capital, $A$ represents the total factor productivity in the state-owned capital production that is normalized as 1 in this paper, $v>1$ reflects the private state-owned capital sector has the higher total factor productivity. $K_{p,t}$ and $H_{p,t}$ represent the physical state-owned capital and the human state-owned capital used in state-owned capital sector, respectively, and $K_{p,t}$ and $H_{p,t}$ are the same as those in the private state-owned capital sector. $R_t$ is the common rate of return on state-owned capital, and $W_t$ is the same price of hiring labor in two sectors.

At each period, the enterprise maximizes its profit by choosing the output of the two intermediate product sectors, and the two sectors allocate the physical state-owned capital and the human state-owned capital according to the following profit maximization problem:

$$\frac{H_{g,t}}{H_{p,t}}=\frac{K_{g,t}}{K_{p,t}}=\frac{\epsilon }{1-\epsilon }$$

(8)

$$K_t=K_{g,t}+K_{p,t};H_t=H_{g,t}+H_{p,t}$$

(9)

$$W_t=\mu (K_t/H_t{)}^{\alpha }=\mu {k_t}^{\alpha }$$

(10)

$$R_t=\frac{\alpha \mu }{1-\alpha }(K_t/H_t{)}^{\alpha -1}=\frac{\alpha \mu }{1-\alpha }{k_t}^{\alpha -1}$$

(11)

where $k_t=\frac{K_t}{H_t}=\frac{K_t}{N_t+N_{t-1}L}$ , $\epsilon =1/[1+(\omega v^{\phi (\alpha -1)}/(1-\omega ){)}^{1/(\phi -1)}]$ stands for the state-owned capital proportion in the state-owned sector, and $\mu =(1-\alpha )\omega [\omega +(1-\omega )(v^{1-\alpha }(1-\epsilon )/\epsilon {)}^{\phi }{]}^{(1-\phi )/\phi }$ .

Public Sector

China’s national pooling account follows the PAYG public pension system, characterized by a defined benefit. Meanwhile, the individual account operates under the fund accumulation system, which is payment determined. The government administers a social security program with the following budget constraints:

$$\lambda R_t{K}_{g,t}+\theta W_t{N}_t=B_t{N}_{t-1}$$

(12)

$$I_{t+1}=R_{t+1}r{W}_t$$

(13)

Then we have:

$$\begin{array}{c}\multicolumn{1}{c}{B_{t+1}=\frac{\lambda R_{t+1}\epsilon K_{t+1}+\theta W_{t+1}{N}_{t+1}}{N_t}}\\ \multicolumn{1}{c}{=\theta W_{t+1}(1+n)+\lambda R_{t+1}\epsilon k_{t+1}(1+n+L)}\end{array}$$

where $0<\lambda <1$ is the ratio of state-owned capital allocation to pension fund, and $N_t$ is the population in period $t$ .

The Competitive Equilibrium

China’s national pooling account follows the PAYG public pension system, characterized by a defined benefit. Meanwhile, the individual account operates under the fund accumulation system, which is payment determined. The government administers a social security program with the following budget constraints:

$$K_{t+1}=N_t{W}_t[r+(1-r)i+(1-r-\theta )(1-i)s_t]$$

(14)

The labor-market clearing condition under a neoclassical growth model in which the labor growth rate is an exogenous rate $n$ :

$$N_t=(1+n)N_{t-1}$$

(15)

Then we can obtain the steady-state level of physical state-owned capital per capita:

$$k^{\alpha -1}=\frac{\mu L(1-\delta )+\theta \mu (1+n)+\lambda A\epsilon (1+n+L)+A(1-\epsilon )(1+n+L)+\beta A(1-\epsilon )(1+n+L)}{\beta A\mu (1-r-\theta )(1-i)(1-\delta )+\beta A\mu r+\beta A\mu (1-r-\theta )i+A\mu (1-r-\theta )i\pi }$$

(16)

where $A=\frac{\alpha \mu }{1-\alpha }$ .

Characterization of the Steady State

From the law of motion of $k_{\mathrm{t}}$ in equation (16), we have:

$$\frac{\partial k}{\partial L}=\frac{1}{(\alpha -1)}{k}^{\frac{1}{(\alpha -1)}-1}\frac{\mu (1-\delta )+\lambda A\epsilon +A(1-\epsilon )+\beta A(1-\epsilon )}{\beta A\mu (1-r-\theta )(1-i)(1-\delta )+\beta A\mu r+\beta A\mu (1-r-\theta )i+A\mu (1-r-\theta )i\pi }>0$$

(17)

$$\begin{array}{c}\multicolumn{1}{c}{\frac{\partial k}{\partial i}=-\frac{A\mu (1-r-\theta )[\beta +\pi -\beta (1-\delta )]}{(\alpha -1)}{k}^{\frac{1}{(\alpha -1)}-1}}\\ \multicolumn{1}{c}{\times \frac{[\mu L(1-\delta )+\theta \mu (1+n)+\lambda A\epsilon (1+n+L)+A(1-\epsilon )(1+n+L)+\beta A(1-\epsilon )(1+n+L)]}{{[\beta A\mu (1-r-\theta )(1-i)(1-\delta )+\beta A\mu r+\beta A\mu (1-r-\theta )i+A\mu (1-r-\theta )i\pi ]}^2}>0}\end{array}$$

(18)

$$\frac{\partial k}{\partial \lambda }=\frac{1}{(\alpha -1)}{k}^{\frac{1}{(\alpha -1)}-1}\frac{A\epsilon (1+n+L)}{\beta A\mu (1-r-\theta )(1-i)(1-\delta )+\beta A\mu r+\beta A\mu (1-r-\theta )i+A\mu (1-r-\theta )i\pi }>0$$

(19)

Equations (17) to (19) tell that $k$ increases when $L$ or $i$ or $\lambda$ increases.

Let the total replacement of the endowment insurance be $T=G+P$ , where $G$ is the replacement of basic endowment insurance and $P$ is the replacement of the commercial endowment insurance, then we have

$$\begin{array}{c}\multicolumn{1}{c}{T=\frac{\theta \mu (1+n)+\lambda A\epsilon (1+n+L)}{\mu }+[r+i(1-\pi )(1-r-\theta )]}\\ \multicolumn{1}{c}{\times \frac{[\mu L(1-\delta )+\theta \mu (1+n)+\lambda A\epsilon (1+n+L)+A(1-\epsilon )(1+n+L)+\beta A(1-\epsilon )(1+n+L)]}{\mu [\beta (1-r-\theta )(1-i)(1-\delta )+\beta r+\beta (1-r-\theta )i+(1-r-\theta )i\pi ]}}\end{array}(20)$$

(20)

Equation (20) indicates that all three policies will have an impact on the replacement rate, at the same time, the three policies will also affect each other. In order to clearly show the relationship between the policies, we give the following function to characterize:

• (1) The relationship between $\lambda$ and $L$ when $i$ is fixed is given by:

$$\lambda =-\frac{E+L[D\mu (1-\delta )+\mathrm{DA}(1-\epsilon )+D\beta A(1-\epsilon )]}{(C+D)A\epsilon (1+n+L)}$$

(21)

where

$$\begin{array}{c}\multicolumn{1}{c}{C=\beta (1-r-\theta )(1-i)(1-\delta )+\beta r+\beta (1-r-\theta )i}\\ \multicolumn{1}{c}{+(1-r-\theta )i\pi }\end{array}$$

$$D=r+i(1-\pi )(1-r-\theta )$$

$$\begin{array}{c}\multicolumn{1}{c}{E=D\theta \mu (1+n)+\mathrm{DA}(1-\epsilon )(1+n)+D\beta A(1-\epsilon )(1+n)}\\ \multicolumn{1}{c}{+C\theta \mu (1+n)-\mathrm{CT}\mu }\end{array}$$

• (2) The relationship between $i$ and $L$ when $\lambda$ is fixed is given by:

$$L=-\frac{\lambda A\epsilon (1+n)G-\mathrm{MG}+\mathrm{rF}+i[\lambda A\epsilon (1+n)J-\mathrm{MJ}+(1-\pi )(1-r-\theta )F]}{[\lambda A\epsilon J+(1-\pi )(1-r-\theta )H]i+\lambda A\epsilon G+\mathrm{rH}}(22)$$

(22)

where

$$\begin{array}{c}\multicolumn{1}{c}{F=\theta \mu (1+n)+\lambda A\epsilon (1+n)+A(1-\epsilon )(1+n)+\beta A(1-\epsilon )(1+n)}\\ \multicolumn{1}{c}{G=[\beta (1-r-\theta )(1-\delta )+\beta r]}\\ \multicolumn{1}{c}{H=\mu (1-\delta )+\lambda A\epsilon +A(1-\epsilon )+\beta A(1-\epsilon )}\\ \multicolumn{1}{c}{J=\beta (1-r-\theta )+\pi (1-r-\theta )-\beta (1-r-\theta )(1-\delta )}\\ \multicolumn{1}{c}{M=[T\mu -\theta \mu (1+n)]}\end{array}$$

• (3) The relationship between $i$ and $\lambda$ when $L$ is fixed is given by:

$$\lambda =-\frac{\mathrm{rQ}-\mathrm{ZS}+i[Q(1-\pi )(1-r-\theta )-\mathrm{ZR}]}{\mathrm{AS}\epsilon (1+n+L)+\mathrm{rA}\epsilon (1+n+L)+i[\mathrm{AR}\epsilon (1+n+L)+A\epsilon (1-\pi )(1-r-\theta )(1+n+L)]}$$

(23)

where

$$\begin{array}{c}\multicolumn{1}{c}{Q=\mu L(1-\epsilon )+\theta \mu (1+n)+A(1-\epsilon )(1+L+n)}\\ \multicolumn{1}{c}{+\beta A(1-\epsilon )(1+L+n)S=\beta [(1-r-\theta )(1-\delta )+r]}\end{array}$$

$$\begin{array}{c}\multicolumn{1}{c}{R=\beta (1-r-\theta )+\pi (1-r-\theta )-\beta (1-r-\theta )(1-\delta ),}\\ \multicolumn{1}{c}{Z=T\mu -\theta \mu (1+n)}\end{array}$$

Numerical Simulation and Sensitivity Analysis

Parameters

This paper refers to Jing et al. (2020) to set the output elasticity of the physical state-owned capital $\alpha$ to be 0.4, the relative total factor productivity of private enterprises $v$ to be 2.829, and the individual income tax rate $\delta$ to be 0.037. With reference to Pan and Gong (2015), the output ratio of state-owned enterprises and the substitution elasticity between state-owned enterprises and private enterprises are set to be 0.49 and 0.33, respectively.

With reference to the research of Wang and Wang (2021),we assume that each period spans 30 years and the annual discount factor is 0.98, then we have $\beta =0.{98}^{30}\approx 0.55$ . According to the Decision of the State Council on Improving the Basic Pension Insurance System for Enterprise Employees, we assume a contribution rate of 16% for the pooling account and 8% for the individual account, with a retirement age set at 60 years old. According to the national population development plan for 2016 to 2030 released by the State Council, we set fertility rate to 0.16. According to the Implementation Plan for Transferring Part of State owned Capital to Enrich Social Security Fund issued by the State Council, we set $\lambda =0.1$ according to the executive plan for state-owned capital allocation to the pension fund. Individuals are required to pay taxes when receiving pensions from commercial endowment insurance, which are deferred when purchasing the insurance.

All the parameters are listed in Table 1 below:

Table 1.

Base Case Parameters and Initial Values.

$\alpha$	$\beta$	$\delta$	$\theta$	$r$	$n$	$\lambda$	$\pi$	$\phi$	$v$	$\omega$
.4	.55	.037	.16	.08	.16	.1	.075	.33	2.829	.49

The Impact of Three Policies on the Target Pension Replacement Rate

The Impact of Policies’ Implementation on the Target Pension Replacement Rate

We perform a numerical simulation of equation (20) and obtain the results in Table 2 below:

Table 2.

The Policies’ Impact on the Target Pension Replacement Rate.

$\lambda$	0	0	10%	0	0	10%	10%
$i$	0	0	0	6%	6%	0	6%
$L$	0	14.3%	0	0	14.3%	14.3%	0
$T$	40.52%	44.72%	44.26%	49.03%	55.32%	48.95%	53.05%

Table 2 reveals that, in the absence of implementing the three policies, the replacement rate is 40.52%. When solely implementing state-owned capital allocation, tax deferral, or delayed retirement, the replacement rate can reach 44.26%, 49.03%, and 44.72% respectively. The independent implementation of these policies can increase the replacement rate by 3.74%, 8.51%, and 4.2%, with tax deferral having the most significant impact. When implementing two policies simultaneously, the combination of tax deferral and delayed retirement can achieve a replacement rate of 55.32%, the combination of state-owned capital allocation and delayed retirement can result in a replacement rate of 48.95%, and the combination of state-owned capital allocation and tax deferral can bring the pension replacement rate to 53.05%.

The Impact of State-owned Capital Allocation on the Target Pension Replacement Rate

If the tax deferral ratio for purchasing commercial endowment insurance and the proportion of delayed retirement years remain unchanged, what impact will the allocation of state-owned capital have on the replacement rate? Table 3 is obtained through numerical simulation to address this question.

Table 3.

The Impact of the State-owned Capital Allocating Ratio.

$\lambda$	2.5%	5%	7.5%	10%	12.5%
$i$	6%	6%	6%	6%	6%
$L$	14.3%	14.3%	14.3%	14.3%	14.3%
$T$	56.45%	57.57%	58.7%	59.83%	60.96%

The replacement rate increases with raising the state-owned capital allocation when fixing $i$ and $L$ when the ratio of state-owned capital allocation increases from 2.5% to 12.5%, the replacement rate increases from 56.45% to 60.96%.

The Impact of Tax Deferring Ratio on the Target Pension Replacement Rate

When the ratio of state-owned capital allocation and the number of years delaying retirement remain constant, changes in the tax-deferred ratio for purchasing commercial endowment insurance will have a certain impact on the replacement rate. The simulated results are presented in Table 4.

Table 4.

The Impact of Tax Deferring Ratio.

$\lambda$	10%	10%	10%	10%	10%	10%
$i$	6%	2%	4%	6%	8%	10%
$L$	14.3%	14.3%	14.3%	14.3%	14.3%	14.3%
$T$	59.83%	52.6%	56.23%	59.83%	63.41%	66.97%

It can be seen from Table 4 that when fixing state-owned capital allocation rate and the proportion of delayed retirement years, the replacement rate increases significantly with the increase in the tax deferring ratio $i$ , when $i$ is augmented from 2% to 10%, the replacement rate increases from 52.6% to 66.97% that has an increase of 14.37%.

The Impact of Proportion of Delayed Retirement Years on the Target Pension Replacement Rate

When the state-owned capital allocation ratio and the tax deferring ratio remain unchanged, the change in the proportion of delayed retirement years also will have a certain impact on the replacement rate. Table 5 shows the simulated results.

Table 5.

The Impact of Proportion of Delayed Retirement Years.

$\lambda$	10%	10%	10%	10%	10%	10%
$i$	6%	6%	6%	6%	6%	6%
$L$	14.3%	3.6%	7.1%	10.7%	14.3%	17.9%
$T$	59.83%	54.75%	56.42%	58.12%	59.83%	61.54%

We observe that the replacement rate rises when the proportion of delayed retirement years is increased while keeping the state-owned capital allocation ratio and the tax deferring ratio constant. As the proportion of delayed retirement years increases from 3.6% to 17.9%, the replacement rate rises from 54.75% to 61.54%, marking an increase of 6.79%. The delayed retirement policy serves to postpone the retirement age of the elderly. On one hand, it boosts labor supply, reduces the number of individuals participating in the pension fund distribution in the pooling account, and increases the number of contributors. This, in turn, elevates the substitution rate of pension funds in the pooling account. On the other hand, elderly individuals can continue accumulating funds in their personal account pension during the delayed retirement period. Therefore, the delayed retirement policy also enhances the personal account pension of the elderly, thereby raising the replacement rate of the personal account pension. In summary, the delayed retirement policy contributes to an increase in the pension replacement rate.

Sensitivity Analysis

In order to verify that the impact of three policies on the replacement rate is not a unique result obtained under the specific parameters, this section conducts a sensitivity analysis on the tax rate $\pi$ , the fertility rate $n$ , the total factor productivity $v$ , and the discount factor $\beta$

The State-owned Capital Allocating Ratio

It can be seen from Figure 1. that the changes in the discount factor $\beta$ , the tax rate $\pi$ , the total factor productivity $v$ , and the fertility rate $n$ will not significantly change the direction and the extent of the impact of the capital allocation on the replacement rate.

Figure 1.

Changing $\beta$ , $\pi$ , $v$ , $n$ to state-owned capital allocating ratio.

The Proportion of Delayed Retirement Years

Figure 2 depicts the impact that when we take different discount factor $\beta$ , tax rate $\pi$ , total factor productivity $v$ and fertility rate $n$ , the direction and extent of the impact of delaying retirement on the replacement rate will not change significantly.

Figure 2.

Changing $\beta$ , $\pi$ , $v$ , $n$ to the proportion of delayed retirement years.

The Tax Deferring Ratio

It is shown from Figure 3 that the impact of three policies on the replacement rate is not a unique result generated by specific parameters, the change in the discount factor $\beta$ , the tax rate $\pi$ , the total factor productivity $v$ and the fertility rate $n$ will not change the impact’s degree and direction.

Figure 3.

Changing $\beta$ , $\pi$ , $v$ , $n$ to the tax deferring ratio.

The Relationship Between Policies Under Target Replacement Rate

State-owned Capital Allocating Ratio and Proportion of Delayed Retirement Years

The relationship between the state-owned capital allocating ratio and the proportion of delayed retirement years when tax deferring ratio is set to be 0 can be obtained by numerical simulation described in Figure 4:

Figure 4.

State-owned capital allocating ratio and proportion of delayed retirement years.

As shown in Figure 4, when the tax deferral ratio is fixed, the ratio of state-owned capital allocation is negatively correlated with the proportion of delayed retirement years under different target replacement rates. The state-owned capital allocation ratio decreases with an increase in the proportion of delayed retirement years. The numerical simulation results are presented in Table 6.

Table 6.

State-owned Capital Allocating Ratio and Proportion of Delayed Retirement Years.

T	T = 45%			T = 50%			T = 55%
$\lambda$	11.99%	5.99%	0.5%	25.4%	18.6%	12.5%	38.81%	31.25%	24.42%
$L$	0	7.1%	14.3%	0	7.1%	14.3%	0	7.1%	14.3%
$i$	0%	0%	0%	0%	0%	0%	0%	0%	0%

From Table 6, it is evident that when the replacement rate is 50% and the proportion of delayed retirement years is 0%, 7.1%, and 14.3%, the state-owned capital allocation ratio needs to be 25.4%, 18.6%, and 12.5%, respectively, showing an inverse relationship. As the replacement rate changes to 45% and 55%, the proportion of delayed retirement years and the state-owned capital allocation ratio continue to exhibit a negative correlation.

Increasing the replacement rate of the pension insurance while maintaining the proportion of delayed retirement years necessitates an increase in the state-owned capital allocation ratio. If the state-owned capital allocation ratio remains constant, then the proportion of delayed retirement years needs to be raised. Simultaneously adjusting both ratios can impact the replacement rate.

Specifically, when the replacement rate needs to be increased from 50% to 55%, the state-owned capital allocating ratio must be adjusted from 25.4% to 38.81% when the proportion of delayed retirement years is fixed at 0. When the proportion of delayed retirement years is increased to 7.1%, the state-owned capital allocating ratio must be increased from 25.4% to 31.25%.

The Tax Deferring Ratio and the Proportion of Delayed Retirement Years

The relationship between the tax deferring ratio and the proportion of delayed retirement years when the state-owned capital allocating ratio is set as 0 can be obtained by numerical simulations described in Figure 5.

Figure 5.

Tax deferring ratio and proportion of delayed retirement years.

Figure 5 illustrates that, with the state-owned capital allocation ratio fixed, the tax deferral ratio and the proportion of delayed retirement years are negatively correlated under different target replacement scenarios. The proportion of delayed retirement years decreases with an increase in the tax deferral ratio The results of the numerical simulation are shown in Table 7 below.

Table 7.

Tax Deferring Ratio and Proportion of Delayed Retirement Years.

$T$	T = 45%			T = 50%			T = 55%
$\lambda$	0	0	0	0	0	0	0	0	0
$L$	15.1%	0.5%	0%	32%	14.12%	2.2%	48.89%	27.7%	13.58%
$i$	0	3%	6%	0	3%	6%	0	3%	6%

Table 7 reveals that, with a replacement rate of 50% and tax deferral ratios of 0%, 3%, and 6%, the proportion of delayed retirement years must reach 32%, 14.12%, and 2.2%, respectively. The proportion of delayed retirement years is negatively correlated with the tax deferring ratio. When the replacement rate changes to 45% and 55%, quantities still have negative relationship.

When increasing the replacement rate, if the proportion of delayed retirement years remains unchanged, the tax deferring ratio needs to be increased. If the tax deferring ratio maintains unchanged, the proportion of delayed retirement years needs to be increased. If both ratios need to be changed simultaneously, it is necessary to adjust both the tax deferral ratio and the proportion of delayed retirement years at the same time. Specifically, when increasing the replacement rate from 50% to 55% with a fixed tax deferral ratio of 0, the proportion of delayed retirement years must be increased from 32% to 48.89%. When increasing the tax deferral ratio from 0% to 3%, the proportion of delayed retirement years must be adjusted from 32% to 27.7%.

The State-owned Capital Allocating Ratio and the Tax Deferring Ratio

The relationship between the tax deferring ratio and the state-owned capital allocating ratio when the proportion of delayed retirement years is set to be 0 can be obtained by numerical simulation described in Figure 6.

Figure 6.

State-owned capital allocating ratio and tax deferring ratio.

As depicted in Figure 6, with a fixed delayed retirement policy, the tax deferring ratio exhibits an inverse relationship with the state-owned capital allocation ratio under various target replacement rates. This implies that the state-owned capital allocation ratio increases as the tax deferring ratio decreases. The detailed results of numerical simulations are presented in Table 8 below.

Table 8.

State-owned Capital Allocating Ratio and Tax Deferring Ratio.

$T$	T = 45%			T = 50%			T = 55%
$\lambda$	12%	0.5%	0%	25.4%	13.43%	2.4%	38.82%	26.34%	14.87%
$L$	0%	0%	0%	0%	0%	0%	0%	0%	0%
$i$	0	3%	6%	0	3%	6%	0	3%	6%

It can be shown in the Table 8, when the replacement rate is 50% and the tax deferring ratio is 0, 3%, and 6% respectively, the state-owned capital allocating ratio needs to reach 25.4%, 13.43%, and 2.4%, respectively. The state-owned capital allocating ratio is negatively related to the tax deferring ratio. When the replacement rate changes to 45% and 55%, the two ratios are still negatively correlated.

When increasing the endowment insurance replacement rate, if the state-owned capital allocating rate maintains unchanged, the tax deferring ratio needs to be increased. If the tax deferring ratio maintains unchanged, the state-owned capital allocating ratio must be increased. Also, if the two ratios change simultaneously, they need to be adjusted together. Specifically, when the replacement rate is increased from 50% to 55%, and the tax deferral ratio is fixed at 0, the state-owned capital allocation ratio must be increased from 25.4% to 38.82%. When the tax deferral ratio is increased from 0 to 3%, the state-owned capital allocation ratio must be increased from 25.4% to 26.34%.

Policies’ Adjustment When the Individual’s Utility is Maximized

In the model we construct, the three policies are negatively correlated with each other. It can be concluded that the maximum individual’s utility under the target replacement rate is also affected by the state-owned capital allocating ratio, the tax deferring ratio and the proportion of delayed retirement years from equation (3).

The reason for choosing to maximize individual’s utility instead of social welfare is rooted in the fact that the measurement of social welfare in the overlapping generations model is associated with a social discount factor. The social discount factor reflects how the social planner cares about the utility of each generation and the factor is calculated under the current policy which already represents or implies the government’s expected target replacement rate of endowment insurance. Opting for social welfare would be contradictory to our original intention; hence, the subsequent content is built upon the maximization of individual’s utility.

The Changes of the Optimal State-owned Capital Allocating Ratio and the Tax Deferring Ratio With the Replacement Rate When Fixing the Proportion of Delayed Retirement Years

As observed in Figure 7, the optimal tax deferring ratio, under the condition of maximizing individual utility, increases with the rise in the target pension replacement rate, assuming the proportion of delayed retirement years remains constant. An elevation in the tax deferring ratio exerts a diminishing effect on the saving rate while also encouraging individuals to invest in commercial endowment insurance. Individuals tend to reduce their savings to compensate for the reduced consumption.

Figure 7.

The optimal tax deferring ratio when fixing the proportion of delayed retirement years.

Consumption in the first period rises with the tax deferring ratio. The reduction in savings outweighs the increased investment in commercial endowment insurance due to the heightened tax deferring ratio, further driving consumption. However, in the second period, consumption declines with the increased tax deferring ratio. This decline is attributed to the fact that the increase in pension obtained from commercial endowment insurance, resulting from the increased tax deferring ratio, is less than the reduction in state-owned capital allocation caused by the increased tax deferring ratio. In summary, to maximize individual utility and promote the pension replacement rate, it is advisable to increase the tax deferring ratio and decrease the state-owned capital allocation ratio. The specific optimal values for each policy are as follows:

When L = 0% (Delaying for 0 year)

When the only policy consideration is the allocation of state-owned capital, the optimal allocation ratio is 12% when the replacement rate is 45%, and it then increases to 25.4% when the replacement rate is 50%. When the replacement rate is 55%, the state-owned capital allocation ratio needs to be 25%, and tax incentives are required by providing a tax deferring ratio of 3.2%.

When L = 3.6% (Delaying for 1 year)

When implementing only the state-owned capital allocation policy, the optimal allocation ratio is 8.9% when the replacement rate is 45%. However, for replacement rates of 50% and above, both the state-owned capital allocation and tax deferral policies are required simultaneously. The optimal state-owned capital allocation ratio is 18.9%, with a tax deferral ratio of 0.7% when the replacement rate is 50%. Similarly, with a replacement rate of 55%, the optimal state-owned capital allocation ratio is 15%, and the tax deferral ratio is 4.7%.

When L = 7.1% (Delaying for 2 years)

When state-owned capital allocation is the sole policy requirement, the optimal allocation ratio is 6% at a replacement rate of 45%. However, when the replacement rate is 50% or higher, both state-owned capital allocation and tax deferral policies are necessary. At a 50% replacement rate, the optimal state-owned capital allocation ratio is 10.3%, and the tax deferral ratio is 2%. For a replacement rate of 55%, the optimal state-owned capital allocation ratio is 6.6%, and the tax deferral ratio is 6%.

When L = 10.7% (Delaying for 3 years)

When the replacement rate is 45%, the sole policy, state-owned capital allocation, requires the optimal allocation ratio to be 3.2%. With a replacement rate of 50%, the optimal tax deferral ratio is 3.4%, and the optimal state-owned capital allocation rate is 1.4%. At a replacement rate of 55%, only the tax deferral policy is necessary, with the optimal ratio being 6.8%.

When L = 14.3% (Delaying for 4 years)

When the proportion of delayed retirement years increases to 14.3%, there is no need to implement state-owned capital allocation and tax deferral if the replacement rate is set to 45%. With a replacement rate of 50% for endowment insurance, only tax deferral is required, and the optimal ratio is 3%. Similarly, when the replacement rate is 55%, the optimal tax deferral ratio is 5.8%.

The Changes of Optimal Tax Deferring Ratio and the Proportion of Delayed Retirement Years With the Replacement Rate When Fixing State-owned Capital Allocating Ratio

Figure 8 illustrates that when the state-owned capital allocation ratio is fixed, with an increase in the target replacement rate for endowment insurance, the optimal tax deferral ratio also rises, and correspondingly, the optimal proportion of delayed retirement years decreases. The escalation of tax incentives will motivate individuals to invest in commercial endowment insurance, enabling them to receive more pension benefits post-retirement, ensuring their living standards and consequently elevating the replacement rate of pension. When the target replacement rate is fixed at a certain level and retirement life is secured, the individual’s preference for leisure surpasses that for labor. In such instances, delaying retirement would diminish the individual’s utility. Overall, it is imperative to raise the tax deferral ratio and reduce the proportion of delayed retirement years to enhance the target replacement rate and maintain the maximization of individual utility.

Figure 8.

The optimal tax deferring ratio when the state-owned capital allocating ratio is fixed.

When $\lambda$  = 0

When the replacement rate is 55% or below, implementing only tax deferral poses no issue. The optimal tax deferring ratio is 10.3% when the replacement rate is 55%, 7% when the replacement rate is 50%, 3.2% when the replacement rate is 45%.

When $\lambda$  = 10%

When the state-owned capital allocation ratio is higher, there is no need to implement other policies except for tax deferral. The optimal tax deferring ratio is 0.7% when the replacement rate is 45%, 4% when the replacement rate is 50%, 7.5% when the replacement rate is 55%.

The Changes of Optimal State-owned Capital Allocating Ratio and the Proportion of Delayed Retirement Years With the Replacement Rate When Fixing Tax Deferring Ratio

Figure 9 shows the relationship between the optimal state-owned capital allocating ratio and the pension replacement rate when the fixed tax deferring ratio is 0 in order to maximize the individual’s utility. As the replacement rate increases, the optimal allocation ratio also rises, leading to a decrease in the proportion of delayed retirement years. Given that state-owned capital allocation can enhance the replacement rate, individuals are disinclined to opt for delayed retirement, as it diminishes their utility while maintaining a fixed target replacement rate. This reluctance stems from the fact that the utility of representative individuals depends on their consumption in adulthood, during their elderly years, and their desire for leisure time. The optimal state-owned capital allocation ratio, ensuring a sufficiently high pension replacement rate, enables representative individuals to meet their second-period consumption needs. At this juncture, individuals seek to enhance their utility through increased leisure. The policy of delaying retirement extends the retirement age for representative individuals, consequently reducing their post-retirement leisure time and diminishing their overall utility level.

Figure 9.

The relationship between the optimal state-owned capital allocating ratio and the replacement rate.

Specifically, when the replacement rate is 45%, the optimal state-owned capital allocating ratio is 12%, when the replacement rate is 50%, the optimal state-owned capital allocating ratio is 25%, when the replacement rate is 55%, the optimal state-owned capital allocating ratio increases to 38%. If the tax deferral is asked to be carried out currently, individuals still prefer to raise the state-owned capital allocating ratio but not to delay retirement. Specifically, under the current tax deferring ratio of 6%, maximizing the individual’s utility can be achieved by the following plans: when the replacement rate is 50%, the optimal state-owned capital transfer rate should be set to 2%, when the replacement rate is 55%, the optimal state-owned capital transfer rate should be set to 15%, when the replacement rate is 45%, only tax deferral is required and the optimal ratio should be set to 3.2%.

Conclusions

This paper first comprehensively considers the state-owned capital allocation, individual tax deferral policy and delayed retirement to construct an OLG model to study the impact of these three policies on the pension replacement rate. The model estimates that without the implementation of these three policies, the replacement rate stands at 40.52%. The current 6% tax deferral ratio can elevate the replacement rate to 49.03%, a 10% state-owned capital allocation ratio results in a replacement rate of 44.26%, and a retirement delay of 4 years leads to a pension replacement rate of 44.72%. Implementing any one of these policies individually increases the replacement rate, with the tax deferral showing the most prominent effect.

If the tax deferral policy is implemented concurrently with a 4-year delay in retirement, the replacement rate can reach 55.32%. If we replace the tax deferral with state-owned capital allocation while also delaying retirement by 4 years, the replacement rate can reach 48.95%. Simultaneous implementation of tax deferral and state-owned capital allocation policies can yield a pension replacement rate of 53.05%. If all three policies are implemented simultaneously, the replacement rate can increase to 59.83%. Specifically, keeping the other two policies unchanged, adjusting the state-owned capital allocation ratio from 0 to 12.5% can augment the replacement rate by 5.64%. Increasing the tax deferral ratio from 0 to 10% can augment the replacement rate by 18.02%. Delaying retirement from 0 to 5 years can augment the replacement rate by 8.49%.

Secondly, this paper explores the interplay among the three policies. When a specific replacement rate for one of the three policies is set, the remaining two policies exhibit a negative correlation. Various combinations of policies yield different impacts on the replacement rate.

Finally, under the premise of maximizing individual utility and holding one policy constant, this paper computes and investigates the optimal solutions for the remaining two policies at a specific endowment insurance target replacement rate. With a fixed proportion of delayed retirement years, the optimal tax deferral ratio increases as the target replacement rate rises, reaching its maximum when the individual’s utility is maximized, while the optimal state-owned capital allocation ratio is permitted to decrease. Furthermore, with an increase in the proportion of delayed retirement years, both the optimal tax deferral ratio and the state-owned capital allocation ratio decrease proportionally. When the state-owned capital allocation is fixed, the optimal solution for maximizing utility does not involve implementing delayed retirement, indicating an optimal proportion of delayed retirement years of 0. Instead, the optimal tax deferral ratio increases with a rising replacement rate. Similarly, with a fixed tax deferral ratio, the optimal proportion of delayed retirement years remains 0, and the optimal state-owned capital allocation ratio increases with the replacement rate. This analysis demonstrates that, based on the maximization of individual utility, individuals in society exhibit a preference for tax deferral and state-owned capital allocation over delayed retirement at a specific endowment insurance replacement rate.

On the basis of above conclusions, this paper puts forward the following suggestions:

• (1) Optimize the tax rate appropriately to be paid when receiving pension benefits

In the phase of purchasing commercial endowment insurance, individuals benefit from reduced taxes due to tax deferral, allowing them to obtain the time value of money, and taxes are paid during the receiving stage to bridge the income difference. In 2019, the individual income tax rate significantly decreased with the implementation of the new individual income tax system. While the State Council issued a document to further reduce the tax rate in 2022, the current level of personal income tax deduction remains relatively low, cannot resist a decline in the number of beneficiaries. To broaden the scope of beneficiaries for the individual tax deferral policy and boost individuals’ inclination to purchase commercial endowment insurance, the required tax rate can be further optimized based on the current circumstances. This aims to enhance individual utility and improve the pension replacement rate.

• (2) Adjusting the tax deferring ratio timely

The scale of purchasing commercial endowment insurance and the replacement rate of pension are significantly influenced by tax deferral. Currently, the upper limit of pre-tax deduction for the purchase of commercial endowment insurance is set at 6% of income, as per the existing individual tax deferral policy, which results in an 8.51% increase in the replacement rate. The tax deferral policy exerts the most substantial impact on both the replacement rate and the individual’s utility among the policies. If the public sector aims to further enhance the replacement rate, the tax deferral ratio should be reasonably increased.

• (3) Increasing the state-owned capital allocating ratio properly

The allocation of state-owned capital to the pension fund can enhance the basic endowment insurance system, effectively compensate for the shortfall in pension funds, improve the sustainability of the basic endowment insurance system, and allow individuals to benefit from the achievements of state-owned enterprises. Although the current state-owned capital allocation ratio of 10% increases the replacement rate by 3.74%, it remains a relatively modest contribution. Hence, there is a need to judiciously increase the allocation of state-owned capital to further enhance the replacement rate.

• (4) Giving further consideration to delayed retirement

Based on previous research, it is inferred that delaying retirement by 4 years can boost the replacement rate by 4.2%. However, considering individual utility, it is evident that opting not to delay retirement is the optimal choice. While delaying retirement may enhance the replacement rate at a macro level, it may not be favorable for maximizing individual utility at the micro level. Therefore, the implementation of a delayed retirement policy requires comprehensive consideration and a gradual approach.

• (5) Coordinating the implementation of multiple policies

Individual tax deferral, state-owned capital allocation, and delayed retirement can all increase the replacement rate of pension, but each policy can bring about different improvement and also has different effects on the individual’s utility. Therefore, the public sector must fully consider the impact of these policies in practice and select the best plan which can meet each other perfectly to guarantee the maximized welfare can be brought about to both individuals and society.

Limitations of the study and future work:

This paper, based on the overlapping generations (OLG) model, elucidates the developmental changes in pension replacement rates under the joint influence of three policies. It explores the optimal combination of these policies under individual utility maximization and varying target pension replacement rates. However, the study has some limitations: it does not investigate the impact of the aforementioned three policies on social welfare, nor does it examine the optimal policy combination for maximizing social welfare. This is because the measurement of social welfare in the OLG model is linked to a social discount factor, and the calculation of this factor is highly correlated with the policies implemented in the model. The policies set in the model already represent the government’s expected target replacement rate for endowment insurance, creating a contradiction in selecting social welfare as our primary objective. In future research, we plan to optimize the model, eliminate correlations among various parameters, and explore policy optimization issues under the condition of maximizing social welfare.