Longevity, social security and endogenous retirement theory and policy implications

This paper employs a two-period overlapping generations OLG model to study the impact of an unfunded social security on retirement decision by incorporating uncertainty in life longevity

LONGEVITY, SOCIAL SECURITY AND ENDOGENOUS RETIREMENT: THEORY AND POLICY IMPLICATIONS

ZENG TING

A THESIS SUBMITTED FOR

FOR THE DEGREE OF MASTER OF SCOCIAL SCIENCES

DEPARTMENT OF ECONOMICS

NATIONAL UNIVERSITY OF SINGAPORE

2011

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ACKNOWLEDGEMENTS

First of all, I owe my deepest gratitude to Professor Zhang Jie who guided me as

my supervisor, and offered inspiration and encouragement throughout the process I appreciate Dr Zhu Shenghao for his suggestion on the improvement of my thesis, and

my future research direction I would also like to thank my fellow classmate, Mr GaoXinwei, for his valuable comments, and administration staff, Ms Nicky Kheh and

Ms Sagi Kaur, in the Economics Department for their kind help And lastly, I want to extend my regards and blessings to my family and all those friends who supported me

in any respect during the completion of the thesis

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TABLE OF CONTENTS

1 Introduction 1

2 The theoretical model 8

2.1 Individual’s problem 13

2.2 Comparative statics 14

2.3 Impacts on the economy 15

3 Calibration 20

4 Policy implications 26

4.1 Universal vs individual specific benefit plan 26

4.2 Age-specific vs uniform contribution schemes 29

5 Concluding remarks 32

Bibliography 34

Appendices 36

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SUMMARY

Many existing studies predict that raising life longevity tends to increase retirement age However, empirical observations of cross-country effective retirement age show the reverse trend This inconsistency is believed to be caused by the existence of social security pension system This paper employs a two-period overlapping generations (OLG) model to study the impact of an unfunded social security on retirement decision by incorporating uncertainty in life longevity Analytical results confirm that retirement is negatively related to life longevity but positively to social security generosity Numerical results from calibration illustrate the effect on retirement age, welfare and steady-state capital levels for various life longevity and payroll tax (pension benefit) levels In addition to the baseline model, the paper also compares the retirement incentives induced by different social security contribution and benefit schemes, and thus draws implications for policy making on social security reform

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LISTS OF TABLES

Table 1 The historical U.S social security contribution rates 5

Table 2 Quantitative impacts when  0.5 21

Table 3 Quantitative impacts when  0.75 21

Table 4 Quantitative impacts when  1 22

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LISTS OF FIGURES

Figure 1 Trends in life expectancy at age 65 and at age 80, males and females,

OECD average, 1970-2007 2

Figure 2 OECD average effective age of retirement, 1970-2009 4

Figure 3 Pension generosity and retirement age in OECD countries, 2009 6

Figure 4 Payroll tax and retirement decision 22

Figure 5 Payroll tax and welfare 23

Figure 6 Payroll tax and saving rate 23

Figure 7 Payroll tax and steady-state capital per worker 24

Figure 8 Payroll tax and steady-state output per capita 24

Figure 9 Individual vs universal benefit plans 29

Figure 10 The stability of the unique steady-state capital-labor ratio 38

Figure 11 The impact of on k 40

Figure 12 The impact of on y 42

Figure 13 The impact of on U 44

Figure 14 The impact of on U 45

b social security pension benefit in the baseline model

payroll tax rate, or social security contribution rate in the baseline model

U lifetime utility for agent born at period t

coefficient of time preference, or discounting factor, exogenous

 relative taste of leisure to consumption in old age, exogenous

t

Y aggregate output level at period t

A coefficient of total factor productivity, exogenous

L aggregate labor force at period t

capital’s share of output

b social security pension benefit in universal benefit plan

z total retirement time under universal benefit plan

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1 Introduction

The motivation of my paper is obtained from the 2010 French strikes and protests which were against the rise of the legal minimum retirement age from 60 to 62 People defended their rights for not working, but showed little concern about who pays for the early retirement Pension promises are easy to make, but hard to keep due to the increasingly high cost of provision The escalating costs of maintaining pension system have crowded out other public priorities with great importance In 2010, the pension benefit paid in the state of California, the U.S., was over $6 billion, which exceeded what the state spent on higher education (Schwarzenegger, 2010)

The huge pension burden is a common problem shared by most of the governments

in developed countries The severe budgetary problem cannot be resolved unless reforms take place Among the potential reform approaches, increasing the official retirement age, the age when workers have the first access to their pension benefit, seems to be the most feasible and least costly method in the short term Raising the legal retirement age would delay pension pay-outs, which buys governments extra time to recover the pension fund

Individual retirement decision, together with the decisions on life-time consumption and labor supply, is largely affected by the expected life longevity We observed a significant improvement of life expectancy since the mid of the twentieth century The upward lines in figure 1 show the life expectancy has increased steadily in OECD countries, truncated at age 65 and at age 80 for both males and female in recent four decades The first question that I intend to answer is whether pushing backward

Source: OECD Health Data (2009)

Many existing literatures have already studied the relationship between life longevity and retirement in various settings Ferreira and Pessôa (2007) studied a finite life economy in which higher life expectancy explains the increases in schooling and retirement age By using a continuous time framework and assuming certain life with exogenous life longevity, their simulation shows that although the total time spent on retirement would increase, the increment is less than that of the life longevity So their model predicts that retirement age will be pushed backward as a result of the rising life longevity Zhang and Zhang (2009) adopt a simple two periods overlapping generations (OLG) model to explain the impact of life longevity on retirement and capital

3 6 9 12 15 18 21

Years

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accumulation They interpret life longevity as the contingent survival rate from young to old age, so the life expectancy is determined by the survival rate despite a fixed maximum age It has been shown that the retirement age is also increasing in life longevity Similar to interpretation of life expectancy by Zhang and Zhang (2009),

d’Albis, Lau and Sánchez-Romero (2010) characterize the recent rise of life expectancy

as a successively reduction in mortality rates at older ages, but in an age-dependent fashion They studied how a mortality change at an arbitrary age affects the optimal retirement age, which also predict that a mortality decline at an older age unambiguously leads to a later retirement age

However, the predictions mentioned do not appear consistent with the empirical observations Over the last four decades, despite a robust gain in life expectancy, workers today retire earlier than they would few generations ago, evident by a decline of OECD average effective retirement age1, with only a small rebound since the early 2000s The transition of OECD average effective retirement age from 1970 to 2009 is shown in Figure 2

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The average effective age of retirement is calculated as a weighted average of withdrawals from the labor market at different ages over a 5-year period for workers initially aged 40 and over (OECD, 2010)

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Figure 2 OECD average effective age of retirement, 1970-2009

Source: author’s calculation based on data from OECD (2010).

I do not intend to override the studies above; rather, I am going to show that the impact of life longevity on retirement in my lifecycle model agrees with the results in those literatures suggest Rather, to explain the puzzle of historical change of retirement,

we must take into account some other institutional factors in one’s retirement decision:

such as the pension adequacy Table 1 shows the historical change of pension contribution in the United State As the taxable earnings pool enlarges, the total contribution rate has increased remarkably since the establishment of the social security Meanwhile, the dependency ratio2 has increased steadily from around 0.15 in 1950s, to 0.21 by 2010, and projected to reach 0.3 by early 2020s (OECD data, 2009) It is very suspicious that the expansion of social security system may be an important causal factor for the declining retirement age

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Table 1 The historical U.S social security contribution rates

Year

Maximum Taxable Earnings (Dollars)

Combined Employer and

Source: Office of the Chief Actuary, Social Security Administration

In a horizontal comparison, the difference between individual pension systems can explain the across-country differences in retirement behavior A rough test of the relationship between pension generosity and effective retirement age using 2009 OECD data is presented in Figure 3 The strong negative correlation gives us a possible candidate that should be responsible for the early retirement

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Note: These rates do NOT include the payroll tax used to finance Medicare, which is 1.45% each on employers and employees There is no ceiling for that tax

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Figure 3 Pension generosity and retirement age in OECD countries, 2009

Source: base on data from OECD (2010)

Social security is a major source of income in one’s old age, and it often

constitutes a large share of family wealth Using the wealth of recent data through the Health and Retirement Survey (HRS), Coile and Gruber (2000) confirm the deterministic

role of social security in one’s retirement behavior In a forward-looking model, they find that the individual’s retirement decision appears to be made based on all the future

streams of social security income, not just the wealth level or income in the next few years

What explains the historical change of actual retirement age? How does the individual make retirement decision, given the prevalent social security system? What is the fair retirement age if we incorporate the rising life longevity? Do the existing policies today distort the retirement decisions by provoking unnecessarily early retirement? What are the long term impacts to the economy? These are indeed the central questions my paper is attempting to answer

55 60 65 70 75

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The remaining part of the paper proceeds as follows In section two, I build a two-period OLG model based on Zhang and Zhang (2009) with the Pay-as-you-go (PAYG) unfunded social security as the new element Subsequently, the impacts of rising life longevity and greater pension generosity on the economy will be examined carefully

To quantify these impacts, a calibration is followed by using realistic parameters The estimation results are presented in section three I believe a minor difference of policy instrument even within the same PAYG system may bring vast different retirement incentives Based on this idea, section four compares the retirement incentives brought by various benefit and contribution schemes, which aims to draw implications for policy making on social security reform

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2 The theoretical model

First of all, I would like to give a brief overview of the theoretical model The model has infinitely many periods and overlapping generations with identical agents who may live for a maximum of two periods Young workers supply labor inelastically, while the old agent may choose time spent between working and leisure (retirement) This assumption is based on the observation of high and stable labor force participation rates for both men and women between ages 25-50, but high labor force exit rates for ages thereafter in the United States (the U.S Census Bureau, 2000) We can complete a general equilibrium analysis without labor and capital income uncertainty As the agents value leisure only in their old age, retirement in my model is thus a work-life balance choice4 According to characteristics of recent demographic transition, the concept of life expectancy in this two-period OLG model is equivalent to the chance of survival from young to old age

A simple two-period lifecycle model with analytical solutions can be sufficient for

us to understand the relations between behavior and policy motivations Retirement and saving decisions without the existence of social security can be found in Zhang and Zhang (2009) It is served as a benchmark model to compare the impacts brought by social security Please note that only the unfunded PAYG social security system where the benefit is financed by a payroll tax is in my research interest It would be less meaningful

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In a model with labor income uncertainties, retirement (exiting labor market with social security benefits) can be considered as an optimal choice for risk averse agents

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to study an individual’s behavior in a funded system with nonbinding contribution

obligation, because he or she will act exactly in the same way as if there were no social security system at all

Now let’s set up the model formally Consider a simple two-period model with a

constant size of the young population, and each agent is endowed with 1 unit of time each period A representative agent is a working adult in period 1, and become old in the second period Assuming the agent survives for sure upon birth, but the survival from adulthood to old-age is uncertain with an exogenous probability (0,1) An increase of means a rise of the survival rate or a rise of life longevity, so life expectancy can be represented as1 This definition of life longevity in terms of the survival rate is particularly suitable in multiple-period model, where the increase of survival chance in each period is essentially an extension of the life-span For simplicity, we normalize the size of the working adult to be unit 1 in each period, the size of the old-age population is then , and the total population size is therefore1 .

In period t , a young worker allocates his labor income for young age consumption ct and saving s , which is a source of his old age consumption t d t1

When he gets old in period t1, he allocates his time endowment for leisure zt1 and labor 1zt1, where zt1[0,1] The concept of retirement can be directly interpreted as

time spent on leisure in one’s old age

Since there is life uncertainty and no bequest motives by assumption, we need a redistributive mechanism which transfers the assets (i.e savings) of the deceased to those

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who are still alive A complete and competitive life annuity market is therefore assumed

to be in its place functioning both as transfer mechanism and a channel between savings and capital investment If survival is uncertain, it can be shown that a non-altruistic

individual’s optimal choice is always to purchase life annuity with all his saving st5

The annuity intermediary invests s in final goods production, and receives a total return of t

1 1

s r in the following period Subsequently the size of old agents receives annuity payment It1 conditional on survival is equal to 1 r  , which is derived from zero profit condition st1rt1 It1 Notice that a rise of life longevity will lower the annuity return, because there would be more beneficiaries alive in the second period

We assume a PAYG social security system exists in the economy Upon survival from young to old age, the agent can draw total benefit b throughout his old age Due to t

the limitation of the two-period model, we can only assume there is no liquidity constraint

of assessing the social security benefit, so the agent makes fully informed choices by expecting his lifetime resources The social security benefit paid to the old is financed by

a payroll tax at a rate of on wage income for all workers regardless of age The budget must be always balanced in all periods t:

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Notice that the above equation can be also interpreted as the benefit formula6 of a representative agent, since we have assumed the size of young working adult to be unity Let us further assume that the benefit received by the agent at period t is legislated to depend on his own old age labor supply z As we will see soon in section IV, a minor t

difference of the benefit formula provides different retirement incentives

The budget constraints face by the representative agents in both periods are as follows:

where w is the wage rate per unit of labor, and is the payroll tax rate

The agent values only consumption in young age, but both consumption and leisure in old age This setting is reasonable because weaker health and lower productivity are usually experienced among the elderly, leisure is essential for an aged person Besides,

we can focus on old-age labor-retirement decision by simplifying the problem in the

younger age A logarithm utility function is a good candidate to describe an agent’s

lifetime preference as it can give concavity on all arguments and tractable closed form solutions:

share of output The Cobb-Douglas form of production function also has advantages of giving concavity on all factor inputs and satisfying the Inada condition For simplicity, we assume full depreciation of physical capital for all periods Factor prices are determined

in a competitive way Assuming full depreciation of capital, and competitive market implies

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Corner solution z1 exists if  

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 , i.e., the old agent has no

incentive to work at all if the pension benefit is over-generous or the payroll tax rate is too high Also notice that when  , the total retirement time becomes: 0

How does individual’s retirement decision change in response to a change in life

longevity and social security? When interior solution of z exists as in equation (11), time spent on retirement, z, is decreasing in the rate of survival,  , and increasing in the

payroll tax rate, The result is summarized in result 1, and proved in appendix A

RESULT 1 The individual retirement age is positively affected by life longevity , and

negatively affected by social security contribution rate

The intuition follows naturally Rising life longevity lowers the return of life annuity (saving), people have to work more and save more to meet the increased needs for old age consumption As we shall see later, higher saving level tends to raise the wage rate, which also induces a later retirement However, a more generous social security plan (characterized by a higher replacement rate or a higher payroll tax) encourages early

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retirement On the one hand, higher payroll tax rate lowers the real return of labor and cost of old-age leisure; on the other hand, higher social security income reduces the necessity of work in the old age

2.3 Impacts on the economy

We can also investigate the impacts on the economy brought by rising longevity and social security system

If we define saving as a fraction of wage income, i.e., st    , then the sw wt

saving rate can be obtained from equation (9):

t

zs

Notice that the two indicators of savings differ in the term of 1 in the numerator, 

and  sw sy, since wt  1 Y Lt/ t and w Yt / t  Result 2 can be shown easily (see 1appendix B)

RESULT 2: Both saving rate  and saving-to-output ratiosw sy are increasing in life

longevity , but decreasing in social security contribution rate or generosity

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Despite a lower return of saving, individuals save more when they expect to live longer As Bloom, Canning, and Jamison (2004) note: the idea of planning for retirement occurs only when mortality rates become low enough for retirement to be a realistic prospect Rising longevity increases the incentive to save, and provides an incentive that can have dramatic effects on national saving rates The success stories of East Asia

Miracle can be a good footnote of this point The region’s capital accumulation rate is

driven by high household saving levels which often exceed 30 percent of income The rise of life expectancy from 39 in 1960 to 69 in 1990 has largely contributed to the

region’s rapid economic growth However, this incentive of saving for retirement can be

weakened by a PAYG social security by the provision of retirement income As a consequence, capital accumulation is also slowed down by this policy

Since st Kt1 kt1Lt1 kt11(1zt1) , capital-labor ratio evolves according to

The existence and uniqueness of the steady state is evident through the explicit form of k∞

inEquation (15) The stability and characteristics of the steady state can be shown in Appendix C

lower the capital-labor ratio The dominant effect determines the net effect from life longevity

The steady-state per-capita output level can be found as:

The discussion on y shown in Appendix D is summarized in Result 4 below

RESULT 4: The steady-state per capita output level y is ambiguously affected by life

expectancy , but is always decreasing in payroll tax rate

The indeterminacy of dy d is caused by different impacts of rising life longevity on per capita income First of all, rising life expectancy increases the capital level through saving and investment, which directly contributed to the final goods production In addition, higher survival chance from young to old age generates larger old-age labor force, which is also an important factor of production Both effects increase aggregate output level without any ambiguity However, larger population reduces the

Although income per capita is a good measure of the social well beings, a lower income per capita does not necessarily imply a lower social welfare In reality, individual may values longer lifespan despite fewer resources they might hold To investigate the impacts of life longevity and social security on welfare, we shall complete the following procedures

Substituting consolidated lifetime budget constraint into the Euler equation (9),

we can solve for the optimal consumption allocation for a representative agent: