Fertility, retirement age, and pay‐as‐you‐go pensions

• Author: Hung‐Ju Chen
• Date: 01 December 2018
• DOI: http://doi.org/10.1111/jpet.12343
• Published date: 01 December 2018

Received: 21 December 2017

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Accepted: 1 October 2018

DOI: 10.1002/jpet.12343

ORIGINAL ARTICLE

Fertility, retirement age, and pay‐as‐you‐go

pensions

Hung‐Ju Chen

Department of Economics, National Taiwan

University, Taipei, Taiwan

Correspondence

Hung‐Ju Chen, Department of Economics,

National Taiwan University, No. 1, Sec. 4,

Roosevelt Road, 10617 Taipei, Taiwan.

Email: hjc@ntu.edu.tw

Abstract

This paper develops an overlapping generations model with

exogenous and endogenous retirement age to examine the

effects of fertility and retirement age on long‐run pay‐as‐

you‐go pensions. For both cases, we find that pensions may

not necessarily increase with the fertility rate. In the case

with exogenous retirement age, a higher fertility rate

(retirement age) raises (reduces) pension benefits if the

fertility rate and official pension age are low, whereas this

result reverses otherwise. In the case with endogenous

retirement age, a higher fertility rate raises pensions if the

fertility rate and costs of raising children are low; otherwise,

such a change decreases pensions. Our numerical results

indicate that, under a reasonable range of parameterization,

raising the fertility rate is more likely to increase pensions in

the case with exogenous retirement age, whereas such a

change tends to reduce pensions in the case with endogen-

ous retirement age.

KEYWORDS

fertility, retirement, OLG, PAYG pensions

JEL CLASSIFICATION

H55, J13, J26

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INTRODUCTION

Many developed countries have witnessed steady declines in their fertility rate and mortality rate over the past

century, leading to concerns about the sustainability of social security systems, particularly the pay‐as‐you‐go

(PAYG) pension system. There is a large strand of literature devoted to possible solutions to the problem of

J Public Econ Theory. 2018;20:944–961.wileyonlinelibrary.com/journal/jpet944

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© 2018 Wiley Periodicals, Inc.

increasing pension burdens caused by aging populations.

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One possible solution is to reform the pension system

from unfunded schemes to funded schemes. Because such a reform would cause a dramatic effect on individuals

during the transition,

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the provision for child allowances and the postponement of retirement have become popular

governmental policies in recent decades, with the common belief that raising the fertility rate or delaying

retirement would lead to a situation where more workers support fewer old people, thus reducing the burden

placed upon government budgets.

3

The provision for child allowances is quite common nowadays in many developed countries such as Australia,

Japan, and Sweden. This provision reduces the cost of raising children, and parents then have stronger incentives to

have more children. With more workers to support old people, the burden placed upon government budgets can be

lessened. Based on an overlapping generations (OLG) model with a PAYG pension system and endogenous fertility

decision, van Groezen, Leers, and Meijdam (2003), Fenge and Meier (2005), and van Groezen and Meijdam (2008)

show that the provision of child allowances raises the fertility rate and has a positive effect on pension benefits.

However, the consensus that an increase in the fertility rate leads to a positive impact on pensions has been

questioned by Fanti and Gori (2012) who analytically examine the effect of fertility on pensions based on a model

with an exogenous fertility rate and find that pensions do not necessarily increase with the fertility rate. Although

increasing fertility raises the labor force and generates a positive effect on pensions, it also causes a negative effect

due to the general equilibrium feedback of the wage rate.

Previous studies concerning the effects of fertility on pensions typically ignore the role of retirement, which

is also an important determinant of pensions. The postponement of retirement means that workers work

longer and benefit from pensions for a shorter length of time. By assuming that the population is constant,

Fanti (2014, 2015), respectively analyzes the effects of an exogenous retirement age on pensions in exogenous

and endogenous growth models with exogenous retirement age and finds that postponement of the retirement

age may be harmful for growth and even for pensions.

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Based on an OLG model with uncertain lifetime and

endogenous retirement decision, Cipriani (2018) finds that population aging (as represented by an increase in

the survival probability to old age) increases the retirement age, but its effect on pensions is generally

ambiguous.

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Miyazaki (2014, forthcoming) examines the influences of retirement on pensions and welfare in

models with exogenous and endogenous retirement age.

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Thus, prior pension crisis studies have shown a

tendency to investigate the effects of fertility and retirement time on pensions separately, thereby ignoring the

interaction between fertility and retirement.

Cigno (2007) argues that “The combined effect of fewer births, longer lives and sluggish retirement age is

putting public pension system, all essentially PAYG, under increasing strain.”This points out that when analyzing

how fertility and retirement age affect PAYG pensions, we cannot ignore the interaction between fertility and

1

The increasing burden of social security likely shifts resources away from the young and toward the elderly. Kaganovich and Zilcha (1999) and

Pecchenino and Pollard (2002) study the interactions between funding for programs benefiting the young (represented by public education) and funding

for programs benefiting the elderly (represented by social security).

2

See Zhang and Zhang (2003) for a comparison of unfunded and funded social security systems. van Groezen, Meijdam and Verbon (2007) examine the

consequence of a switch to a more funded pension scheme based on a two‐sector growth model.

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Introducing international migration may also help reduce the burden of social security. Based on a calibrated general equilibrium overlapping generations

model, Storesletten (2000) investigates whether a reform of immigration policies can solve the increasing burden of social security. Chen and Fang (2013)

analyze the effects of migration policies on economic growth and the burden of social security based on an endogenous growth model with heterogeneous

workers and endogenous fertility.

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Kunze (2014) shows that there is an inverted U‐shaped relationship between retirement age and economic growth in a model where private investment

in human capital is the engine of endogenous growth. However, his analysis abstracts from the theme of pensions.

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The focus of Cipriani (2018) is on population aging and not fertility, and so he assumes that there are no costs of rearing children to simplify the model.

Because rearing children does not incur any time or resource costs, then changes in the fertility rate do not affect an adult’s budget constraint.

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Michel and Pestieau (2013) also consider a model with exogenous and endogenous retirement age. Unlike this paper, which focuses on the interaction

between fertility and retirement age and how this interaction affects pensions, Michel and Pestieau (2013) and Miyazaki (2014, forthcoming) both target

the retirement age and optimal PAYG social security policy. Thus, fertility and population structure are not the focus in their study. While Michel and

Pestieau (2013) demonstrate that the first‐best allocation cannot be achieved in a decentralized economy, Miyazaki (forthcoming) argues that the first‐

best allocation can be achieved in such an economy.

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