Notional Defined Contribution Pension, Fertility, and Efficiency Wages in an Overlapping Generations Economy Leran Wang†

Abstract This study analyzes how fertility is affected by social security systems when labor market frictions are considered in an overlapping generations model of a small open economy, where unemployment exists due to the efficiency wages. It reveals that the effects of social security on unemployment and fertility depend on whether notional defined contribution pension (NDC) account return rate outnumbers market interest rate. When the former is higher, which means the expectation of individual future total income is higher with pension than with saving by oneself, the acceptable wage criteria that ensures no shirking behavior during work decreases. This leaves more room for firms to hire more workers, thus improving the employment status and fertility rate.

Keywords: fertility, efficiency wages, unemployment, NDC pension JEL: J13, J18, J31, J65

†

Faculty of Economics, Keio University. Address: 2-15-45Mita, Minato-ku, Tokyo, Japan, 108-8345; Email: [email protected]. 1

1.

Introduction

Population aging, which is believed to be caused by the decrease in fertility and increase in longevity, has become an increasingly important global challenge. Demographic aging has been exacerbated by the retirement of baby boomers, born in 1950s and early 1960s and the claim of decline in their retirement age. As a result, the decreasing working force have to bear the heavy burden of social security from the increasing elderly population, thus causing widespread concern and global challenge in the debates among researchers and policy makers. Numerous studies have discussed the relationship between social security systems (SSS) and fertility in competitive labor markets. Employment status, as one of the most important financial outcomes of rearing children, should not be ignored. Therefore, taking into consideration unemployment due to labor market friction is necessary for the analysis in this field. However, unemployment, which is traditionally thought of as a periodic phenomenon and often regarded as resulting from the mismatch between jobs and jobseekers or business cycle, is thus barely researched together with fertility. Nevertheless, unemployment has persisted for a long time. Consequently, in this research, I approach this issue by regarding unemployment as a long-run phenomenon, which is caused by imbalance between labor demand and supply, and the cause has been identified as efficiency wages. With regard to long-term unemployment, it is often asked why the high unemployment in society is not self-corrective through falling wages. The efficiency

2

wage model provides an explanation. Efficiency wage is the wage set over and above the going wage rate by firms, as firms find the increase in the wage boosts productivity. If firms reduce the income, the productivity will be negatively affected. First, reduced income restrains morale (gift exchange model by Akerlof, 1982) and phases out trained workers (labor turnover model by Salop, 1979). The loss of productivity may exceed the savings made through lower wages. In addition, the inability to monitor workers’ efforts requires involuntary unemployment to be a penalty for misdemeanors (shirking model by Shapiro and Stiglitz, 1984). Also, firms raise wages to attract better applicants (adverse selection model by Weiss, 1980). Since rearing children is income-related, it is expected that the effects of SSS on fertility should vary with the wage setting.2 This research follows the strand of shirking model, and assume that firms set the efficiency wage (over the on-going wage) in order to avoid employees’ shirking behaviors. Employees will decide whether they will shirk when they enter the work force, and weigh whether to take effort or risk to be found out shirking and fired. Pension in this study is assumed to be a notional defined contribution (NDC) plan. NDC pension, which initiates in Sweden, is designed to address the fiscal instability

of

traditional

plans.

It

mimics

the

characteristics

of

funded

defined-contribution plans while retaining PAYG pension financing. Specifically, the workers of this plan are told that their contributions will be credited to an account, and will be given back until they retire. But actually, the pension contributions are

2

Theoretical and practical evidence shows that besides childrearing costs, parental time is an essential factor for childrearing. We focus on childrearing monetary costs for simplicity. See also Wang (2015, 2016). 3

directly distributed to the elderly of the same period. As a matter of fact, the real account rate of workers is controlled by the government and arranged according to the population aging tendency: the higher fertility rate, the more return rate of accounts, and vice versa. The reasons why the NDC pension plan is employed in this model is that first, NDC has been thought of as a popular reform for the demographic crisis globally. In addition, the feature of this plan that account return rate matters to the population aging status or demographic changes, leads to intriguing discussions and implications on the relationship between endogenous fertility and pension parameters. This study tries to explore how the SSS affects fertility when labor market friction is considered. It analyzes the effects on fertility in a general-equilibrium overlapping generations model (OLG) of a small open economy where unemployment exists due to the efficiency wages. SSS consists of NDC pension plans and unemployment insurances. SSS affects fertility via the channel of unemployment, therefore the effects on fertility is also associated with the effects on unemployment. First, for the effects of SSS on unemployment, it depends on whether the account return rate controlled by the government in NDC pension plan dominates the market interest rate. If the answer is yes, meaning the expectation of individual future total income is higher with pension than with saving by oneself, the acceptable wage criteria that ensures no shirking behavior during work will be relaxed. Therefore, this exogenous shock leaves more room for firms to hire more workers, thus improving the employment status-decreasing unemployment rate. On the other hand, higher unemployment insurance tax burden, leading to a negative expectation of future

4

income, will push the acceptable wage level higher, worsening the employment status. Second, social security affects fertility via the channel of unemployment changes: better employment performance, or decreasing tendency in unemployment implicates lower percentage of people are in poor living condition, increasing the incentive to rear children, and vice versa. Third, the fertility also has feedback effect on social security system: based on the features of the NDC pension system, to balance the payments and benefits, government will arrange the account return rate to adapt to the changing fertility, creating a procyclical relationship between NDC pension and fertility. This paper is organized as follows: Section 2 presents the model. Section 3 discusses the equilibrium of labor market, and endogenous unemployment. Section 4 talks about comparative statics. Section 5 bears the conclusion.

2.

Model

2.1 The individuals Assumption 1 Every employee may lose their job because of uncertain exogenous shock, which is normally indicated by the tightness of job market. This parameter is denoted by 𝜎. Consider a two-period OLG in a small open economy. We assume that everyone decides whether to shirk or not at the beginning of their youth. Specifically, if an individual decides to be a non-shirker, he(she) will either stay employed until retirement or become unemployed due to an exogenous shock(𝜎). If he(she) decides

5

to be a shirker, then the probability of becoming unemployed is higher than that for non-shirkers, because when the shirking is detected(𝜌), he(she) will be fired. Both the exogenous shock and detection by firms will occur once the decisions are made. Therefore, there are three possible states individuals may stay during their youth: work diligently, shirk, or become unemployed. Assumption 2 Children brings the utility to parents as consumption goods because parents have altruism to their children.3 The utility functions of the three states are assumed to be logarithmic, and comprise consumption during youth, old age, and number of children: $ $ 𝑈$ = 𝛼𝑙𝑛𝑐*,, + 𝛽𝑙𝑛𝑐/,,0* + 𝛾𝑙𝑛𝑛,$

where 𝛼 + 𝛽 + 𝛾 = 1 for convenience, and 𝑖 = 𝑎, 𝑏 𝑜𝑟 𝑐, denoting the three states respectively. The lifetime utilities are 𝜙: = 1 − 𝜎 𝑈< + 𝜎𝑈= , and 𝜙> = 1 − 𝜌 − 𝜎 𝑈? + 𝜌 + 𝜎 𝑈= , where 𝑁 and 𝑆 represent no shirking and shirking respectively. The utility maximization problem of non-shirkers is presented as follows: < < 𝑚𝑎𝑥𝑈< = 𝛼𝑙𝑛𝑐*,, + 𝛽𝑙𝑛𝑐/,,0* + 𝛾𝑙𝑛𝑛,< < 𝑠. 𝑡. 𝑐*,, + 𝑠,< = 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 − 𝑚𝑛,< , < 𝑐/,,0* = 𝑠,< 𝑅,0* + 𝜃,0* .

3

In this study, it takes in consideration only financial cost to rear children, not the time cost or the time spent on children can be thought as transferable to formal childcare services. 6

During youth, the employee receives a wage 𝜔, , and incurs a social security tax for public pension (𝜃, ) and unemployment insurances (𝑏, ). The tax rates are 𝜏 and 𝜂, respectively. As assumed by Shapiro and Stiglitz (1984), 𝑒 is the effort level of risk-neutral workers. The rest is used for childrearing costs 𝑚 , consumption during < youth (𝑐*,, ) and savings (𝑠,< ). 𝑠,< and 𝜃, are used for consumption during the

retirement period. Therefore, maximizing the utility of state 𝑎 gives 𝜃,0* , 𝑅,0* 𝜃,0* < 𝑐/,,0* = 𝛽𝑅,0* 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 + , 𝑅,0* 𝜃,0* 𝑠,< = 𝛽 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 − 1 − 𝛽 , 𝑅,0* 𝛾 𝜃,0* 𝑛,< = 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 + . (1 ∗) 𝑚 𝑅,0* < 𝑐*,, = 𝛼 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 +

The utility of this state is 𝜃,0* 𝜃,0* + 𝛽𝑙𝑛𝛽𝑅,0* 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 + 𝑅,0* 𝑅,0* 𝛾 𝜃,0* + 𝛾𝑙𝑛 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 + . (1) 𝑚 𝑅,0*

𝑈< = 𝛼𝑙𝑛𝛼 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 +

The effort level of shirkers differentiates their budget constraint from non-shirkers. For simplification, we assume the effort is 0. ? ? 𝑚𝑎𝑥𝑈? = 𝛼𝑙𝑛𝑐*,, + 𝛽𝑙𝑛𝑐/,,0* + 𝛾𝑙𝑛𝑛,? ? 𝑠. 𝑡. 𝑐*,, + 𝑠,? = 𝜔, 1 − 𝜏 − 𝜂 − 𝑚𝑛,? , ? 𝑐/,,0* = 𝑠,? 𝑅,0* + 𝜃,0* .

Solving this utility maximization problem gives 𝜃,0* , 𝑅,0* 𝜃,0* ? 𝑐/,,0* = 𝛽𝑅,0* 𝜔, 1 − 𝜏 − 𝜂 + , 𝑅,0* 𝜃,0* 𝑠,? = 𝛽𝜔, 1 − 𝜏 − 𝜂 − 1 − 𝛽 𝑅,0* ? 𝑐*,, = 𝛼 𝜔, 1 − 𝜏 − 𝜂 +

7

𝑛,? =

𝛾 𝜃,0* 𝜔, 1 − 𝜏 − 𝜂 + . 𝑚 𝑅,0*

The utility of this state is 𝜃,0* 𝜃,0* + 𝛽𝑙𝑛𝛽𝑅,0* 𝜔, 1 − 𝜏 − 𝜂 + 𝑅,0* 𝑅,0* 𝛾 𝜃,0* + 𝛾𝑙𝑛 𝜔, 1 − 𝜏 − 𝜂 + . (2) 𝑚 𝑅,0*

𝑈? = 𝛼𝑙𝑛𝛼 𝜔, 1 − 𝜏 − 𝜂 +

For the unemployed, the living expenses during youth are funded by 𝑏, , and the consumption during the retirement period is supported by savings and pensions. = = 𝑚𝑎𝑥𝑈= = 𝛼𝑙𝑛𝑐*,, + 𝛽𝑙𝑛𝑐/,,0* + 𝛾𝑙𝑛𝑛,= = 𝑠. 𝑡. 𝑐*,, + 𝑠,= = 𝑏, − 𝑚𝑛,= , = 𝑐/,,0* = 𝑠,= 𝑅,0* + 𝜃,0* .

Therefore, 𝜃,0* 𝑅,0* 𝜃,0* = 𝑐/,,0* = 𝛽𝑅,0* 𝑏, + , 𝑅,0* 𝜃,0* 𝑠,= = 𝛽 𝑏, + , 𝑅,0* 𝛾 𝜃,0* 𝑛,= = 𝑏, + . (3 ∗) 𝑚 𝑅,0* = 𝑐*,, = 𝛼 𝑏, +

The utility of this state is 𝑈= = 𝛼𝑙𝑛𝛼 𝑏𝑡 + 𝛽𝑙𝑛𝛽𝑅,0* 𝑏𝑡 + 𝛾𝑙𝑛

𝛾 𝑏 . (3) 𝑚 𝑡

Therefore, the lifetime utilities are 𝜙: = 𝛼𝑙𝑛𝛼 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 + 𝛾𝑙𝑛

W X

𝜔, 1 − 𝜏 − 𝜂 − 𝑒 +

RSTU VSTU

− 𝜎𝑙𝑛

𝜙a = 𝛼𝑙𝑛𝛼 𝜔, 1 − 𝜏 − 𝜂 + 𝛾𝑙𝑛

W X

𝜔, 1 − 𝜏 − 𝜂 +

RSTU VSTU

RSTU VSTU

RSTU VSTU

+ 𝛽𝑙𝑛𝛽𝑅,0* 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 +

^ YS *Z[Z\ Z]0 STU

𝜃 𝑏𝑡 +𝑅𝑡+1 𝑡+1

_STU



+ 𝛽𝑙𝑛𝛽𝑅,0* 𝜔, 1 − 𝜏 − 𝜂 +

− (𝜌 + 𝜎)𝑙𝑛

^ YS *Z[Z\ 0 STU

8

𝜃 𝑏𝑡 +𝑅𝑡+1 𝑡+1

_STU

RSTU VSTU

+

(4) RSTU VSTU

+

, (5)

We assume that the non-shirkers have a higher utility than the shirkers because of the risks involved in being unemployed; this is referred to as the no-shirking condition (NSC): 𝜙: ≥ 𝜙> (Shapiro and Stiglitz, 1984). Substituting Eq. (4) and (5) into this inequality, 𝜃,0* 𝜃 𝜔, 1 − 𝜏 − 𝜂 + ,0* 𝑅,0* 𝑅,0* 1 − 𝜎 𝑙𝑛 ≤ 𝜌𝑙𝑛 (6) 𝜃,0* 𝜃,0* 𝜔, 1 − 𝜏 − 𝜂 − 𝑒 + 𝑏, + 𝑅,0* 𝑅,0* 𝜔, 1 − 𝜏 − 𝜂 +

This implies that no employee will shirk as far as this condition is satisfied. Then the three states in the beginning will turn to be two: the no-shirking employed and the unemployed.

2.2 The production and the capital market Aggregate output is determined by the Cobb-Douglas production function: 𝑌, = 𝐴𝐾,i (𝑒𝐿, )*Zi , where 𝐴 is a time-independent technology parameter, 𝐾, denotes the amount of capital, and 𝑒𝐿, represents the efficient labor, in which 𝑒 is the effort level of workers. The profit maximization problem of firms gives 𝑚𝑎𝑥𝜋, = 𝑌, − 1 + 𝑟, 𝐾, − 𝜔, 𝐿, . Therefore, 𝑅, = 1 + 𝑟, = 𝛿𝐴𝑒

𝑘, iZ* , (12) 1−𝑢 𝑘, i , (13) 1−𝑢

*Zi

𝜔, = 1 − 𝛿 𝐴𝑒 *Zi

9

where 𝑘, =

oS :S

. We consider a small open economy with perfect capital mobility

both from domestic and foreign markets. Thus, the interest rate is 𝑅 = 1 + 𝑟 = 𝛿𝐴𝑒

*Zi

𝑘 1−𝑢

iZ*

. (12 ∗)

Eq. (13) becomes i

*

i

𝜔 = 𝑒 1 − 𝛿 𝛿 *Zi 𝐴*Zi 𝑅iZ* ≡ 𝜔q = 𝑒𝑁. (13 ∗) where 𝑁 = 1 − 𝛿 𝛿

r Usr

𝐴

U Usr

𝑅

r rsU

U

= 1−𝛿

ti Usr Vr

. The profit-maximizing

wage is defined as the wage of demand side.

2.3 The government Incomes of the employed are taxed to finance the public pension and unemployment insurances. 𝑁,0* = 𝑁, 𝑛, . In NDC pension plans, the payment of pension to the annuity account invested by the employees can be understood in two ways: the real method actually distributed and the “notional” methods promised by the government. For the notional part, the government promises that the payment will be credited to an individual account as funded defined contribution scheme. When workers are eligible to withdraw the benefits, they will receive benefits including contribution and investment return. 𝜃,0* 𝑁, = 𝜏𝜔, 1 + 𝑔 𝑁, . In reality, however, the benefits to be received in the old age of the workers will be distributed by the generation of their children by PAYG ways: 𝜃,0* 𝑁, = 𝜏𝜔,0* 𝑁,0* .

10

In order to protect the financial balance of this pension scheme, the account return rate will fluctuate to maintain the sustainability of this system. The government will control the return rate based on the population status. 𝜏𝜔,0* 𝑁,0* = 𝜃,0* 𝑁, = 𝜏𝜔, 1 + 𝑔 𝑁, . That is, 𝜏𝜔,0* 𝑛, = 𝜃,0* = 𝜏𝜔, 1 + 𝑔 . Moreover, the unemployment benefits of the unemployed derives from the tax financed by the workers. Thus, 𝜂𝜔, 𝐿, = 𝑏, 𝑁, − 𝐿, .

3.

Equilibrium

Substituting the three equations into Eq. (6), 𝑒

𝜔, ≥ 𝑀− where 𝑀 = 1 − 𝜏 − 𝜂 +

[ *0y VSTU

w 𝑀*Z*Zx

𝜂 1−𝑢 𝑢

w *Zx

≡ 𝜔a

.

where 𝜔> is defined as no-shirking wage, and the subscript 𝑆 represents labor supply. When the wage is set over the no-shirking wage, nobody will shirk. As this equation reveals how the workers would supply their labor according to wages, this wage determines the wage curve of labor supply. When wage level increases, ceteris paribus, the employment will increase- “labor supply curve” (Shapiro and Stiglitz, 1984).

11

Figure 1. Labor Market Equilibrium

3.1 Labor market equilibrium and equilibrium unemployment Labor market equilibrium occurs when wage of labor demand 𝜔q intersects the wage of labor supply 𝜔> . From Figure 1, the intersection of supply and demand curve is the labor market equilibrium point. N is defined as full employment, and the difference between L* and N is equilibrium unemployment, which is endogenous and change as wage level changes. Therefore, endogenous unemployment can be expressed as 1

𝑢=

*Zx w w

𝑀*ZxZ*

w 1 1+ 𝑀*Zx − 𝜂

1−𝛿 where 𝑀 = 1 − 𝜏 − 𝜂 +

[ *0y V

𝐴𝛿 𝑅i

* *Zi

, g is the account return rate, r is the market

interest rate.

12

3.2 Social security’s effect on unemployment Proposition 1. i.)

NDC pension’s effect on unemployment depends on the relative size

between NDC account return rate and market interest rate: when pension tax rate increases, when the account rate is higher, the expectation of individual future total income is higher than just saving, decreasing unemployment rate; when market interest rate is higher, unemployment rate tends to increase. ii.) Increase in the unemployment insurances tax rate will worsen unemployment rate. Proof. 𝜕𝑢 𝜕𝜏 *Zx Z* w w 11 − 𝜎 𝑀 *Zx − 𝜂 𝜌

w

𝑀 *ZxZ* 1−𝛿

=−

𝐴𝛿 𝑅i

* *Zi

w 𝜌 Z/ *Zx − 1 𝑀 w 𝜌 𝝏𝑴 Z* 1 − 𝜎 𝑀 *Zx − * 1−𝜎 𝝏𝝉 𝐴𝛿 *Zi 1−𝛿 𝑅i *Zx / w w

𝑀 *ZxZ*

w 1 1+ 𝑀 *Zx − 𝜂

1−𝛿

where 𝑀 = 1 − 𝜏 − 𝜂 + when 𝑔 > 𝑟,

~• ~[

> 0,

~ƒ ~[

[ *0y VSTU

, and

~• ~[

𝐴𝛿 𝑅i

* *Zi

= −1 +

< 0; when 𝑔 < 𝑟,

~• ~[

*0y V

< 0,

; 𝑅 = 1 + 𝑟. ~ƒ ~[

> 0.

When the account rate is higher, which means the expectation of individual future total income is higher than just saving, the wage level that ensures no shirking

13

behavior during work also decreases. The exogenous shock leaves more room for firms to hire more workers, thus improving the employment status-decreasing unemployment rate. On the other hand, higher unemployment insurance tax burden, leading a negative expectation of future income, will give a negative outside shock of wage level, therefore firms have to increase wage level in order to prevent shirking behaviors, thus worsening the unemployment status, which can be confirmed by the calculation of unemployment insurances gives the same conclusion: *Zx w

−

w 1 𝑀 *Zx − 𝜂/

w

𝑀 *ZxZ* 1−𝛿

𝜕𝑢 =− 𝜕𝜂

𝐴𝛿 𝑅i

+

* *Zi

w 𝑀 *ZxZ/

𝜌 −1 w 𝜌 11 − 𝜎 𝑀 *ZxZ* − 1 − 𝜎 𝜂 𝜌 1−𝜎 𝐴𝛿 1−𝛿 𝑅i

* *Zi

*Zx Z* w

𝜕𝑀 𝜕𝜂

*Zx / w

1+

w 1 𝑀 *Zx − 𝜂

w

𝑀 *ZxZ* 1−𝛿

𝐴𝛿 𝑅i

* *Zi

>0

where 𝑀 = 1 − 𝜏 − 𝜂 +

4.

[ *0y VSTU

, and

~• ~\

= −1.

Comparative Statics

4.1 Endogenous Fertility The fertility of the society is determined by the sum of fertility of both the employed and unemployed. 𝑛, = 𝑛,< 1 − 𝑢 + 𝑛,= 𝑢 =

𝛾 𝜃,0* 𝜔, 1 − 𝜏 − 𝑒 + 𝑚 𝑅,0*

In labor market equilibrium, 𝜔, = 𝜔a = 𝜔… = 𝑒𝑁 Therefore,

14

1−𝑢

𝑛, =

𝑒𝛾 𝜏𝑁(1 + 𝑔) 𝑁 1−𝜏 −1+ 1−𝑢 𝑚 𝑅 U

where 𝑁 = 1 − 𝛿

ti Usr . Vr

4.2 Pension’s effect on Fertility Proposition 2. i.)

The effect of NDC pension on fertility depends on the relative size

between NDC account return rate and market interest rate: when pension tax rate increases, if the account rate is higher, fertility will increase; if market interest rate is higher, fertility will decrease. ii.) The effect of unemployment insurances on fertility is negative. Proof. i.) 𝜕𝑛 1+𝑔 = −1 + 𝜕𝜏 𝑅 When 𝑔 > 𝑟,

~ƒ ~[

1−𝑢

< 0, then

𝑒𝛾 𝑒𝛾 𝜏𝑁 1 + 𝑔 𝑁+ 𝑁 1−𝜏 −1+ 𝑚 𝑚 𝑅 ~† ~[

> 0; when 𝑔 < 𝑟,

~ƒ ~[

> 0, then

~† ~[

−

𝜕𝑢 𝜕𝜏

< 0.

ii.) 𝜕𝑛 𝜕𝑢 =− < 0. 𝜕𝜂 𝜕𝜂

The effect of NDC pension on fertility can be expressed as follows, which includes the direct and indirect part. 𝑛, = 𝑛

𝜏 0 ‡ˆ Z

15

, 𝑢 𝜏 0‡ˆ –

In the direct part, as shown in the first argument, the pension can be seen as a tax and income, and the tax effect decreases fertility and income effect increase fertility; the relative size of the two effects also depend on that of g and r. In the indirect part, as shown in the second argument, pension affect fertility via the channel of unemployment. Based on the analysis in proposition 1, when pension tax rate increases, the direction of changes of unemployment depend on the relative size between account return rate and market interest rate: when account return rate is higher, the optimistic expectation towards future old-age income act as an exogenous shock for the decline in no-shirking wage level, leading a decrease in unemployment rate. This means more people are hired and live in better condition, and hence fertility will be improved. Therefore, when the relative size of g and r is known, the effect on fertility will be determined simultaneously. The effect of unemployment insurances can also be described as direct and indirect parts. 𝑛, = 𝑛 𝜂 , 𝑢 𝜂 Š

Z

In the direct effect, as shown in the first argument, unemployment insurances can be taken as income or tax and final effect in this part will be determined by the dominant part. However, these two effects are offset because this insurance is transferred intra-generationally, which has no effect for the general product and income. In the indirect part, as the second argument shows, the effect is through unemployment changes: as unemployment insurances gives a pessimistic expectation for old-age income, forcing firms to increase wage level, thus leading to more 16

unemployment; the worsening employment status causes the decline in childbearing incentives.

4.3 Feedback effect of fertility on NDC pension Based on the features of NDC pension plan, the account return rate will be arranged by government in order to maintain the balance of the system. This gives an intriguing implication to the relationship between fertility and pension because if the account rate is higher than the interest rate, fertility will finally increase, and thus leading to a continual increase in the account return rate in the NDC accounts. On the other hand, if the government gives a lower return rate, depressing the future prospect of income, fertility incentive decreases and population aging exacerbates, and financial pressure will load on this system, leading to decreasing account return rate.

5.

Conclusion

The two-period overlapping generations model gives an analysis that when labor market friction is considered, how the effect of social security on fertility will be changed. The implication can be concluded as follows. First, any factors affecting the expectation of future income of individuals will affect their fertility decisions, which the governments should take into consideration when enforcing policies. Second, employment performance, which affects the total household income, is an important factor which should not be ignored when dealing with decreasing fertility.

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References Akerlof, G.A., 1982. Labor contracts as partial gift exchange. The Quarterly Journal of Economics, 97(4), 543-569. Bräuninger, M., 2000. Wage bargaining, unemployment, and growth. Journal of Institutional and Theoretical Economics. 156(4), 646-660. Corneo, G., Marquardt, M., 2000. Public pensions, unemployment insurances, and growth. Journal of public economics. 75(2), 293-311. Fanti, L., Gori, L., 2007. Income taxation, child-rearing policies, fertility and unemployment. Economics Bulletin. 10(18), 1-10. Salop, S.C., 1979. A model of the natural rate of unemployment. The American Economic Review, 69(1), 117-125. Shapiro, C., Stiglitz, J. E., 1984. Equilibrium unemployment as a worker discipline device. The American Economic Review. 74(3), 433-444. Wang, L., 2015. Fertility and unemployment in a social security system. Economics Letters(133), 19-23. Wang, L. (2016). Fertility, Union Wage Setting and Social Security System. International Journal of Economics and Finance, 8(9), 1. Weiss, A., 1980. Job queues and layoffs in labor markets with flexible wages. The journal of political economy, 88(3), 526-538.

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