Intergenerational Earnings Mobility and Demographic Dynamics:

Welfare Analysis of an Aging Japan

Akira Okamoto (Okayama University)
June 30, 2021
Okayama University Discussion Paper No. I－112

0Intergenerational Earnings Mobility and Demographic Dynamics:
Welfare Analysis of an Aging Japan*
Akira Okamoto**
Okayama University
June 30, 2021

Abstract
This paper simulates the effects of intergenerational earnings mobility on
individual welfare and future demography in an aging and depopulating Japan. A
simulation analysis finds that increased intergenerational mobility across income
classes promotes economic growth, and from a long-term perspective, a higher
mobility potentially achieves Pareto improvements. In the long run, however, it
will hinder economic growth. This is because increased mobility increases the
population share of individuals with a higher labor productivity, enhancing
economic growth in the initial stage, but because of their lower fertility, an increasein their population ratio negatively effects the total population over time.
Keywords: Intergenerational earnings mobility; depopulating and aging societies;
demographic dynamics; Pareto improvements; welfare analysis.
JEL classification: H30; C68*

An earlier version of this paper was presented at the International Symposium on Business and Economic
Studies held at Okayama University in November in 2019, with the title of “Simulating the Comprehensive
Effects of Intergenerational Earnings Mobility in an Aging Japan.” I am grateful for the insightful comments
and suggestions of Professors Alan J. Auerbach, Ronald D. Lee, and Emmanuel Saez (The University ofCalifornia, Berkeley). In addition, I want to thank Associate Professor Yoshinari Nomura (Okayama
University), who helped me in writing the computer program used for the simulations. Finally, I also wish toacknowledge the financial support from the Social Science Research Council under an Abe Fellowship andthe Ministry of Education, Culture, Sports, Science and Technology in Japan (Grant-in-Aid for Scientific
Research (C) No. 20K01679).
**
Professor, Faculty of Economics, Okayama University, Japan. Tsushima-naka, Okayama 700-8530, Japan.
E-mail: okamot-a@okayama-u.ac.jp

11. Introduction
Japan’s population is currently rapidly aging at a speed unprecedented for a developed nation, andsimultaneously, the population is decreasing, which has become one of Japan’s most important
problems. Furthermore, currently, the problem of economic disparities, or income gaps, has become
more and more significant. Particularly, it is often pointed out that the parents’ inequality is more
likely to be passed down to their children. For instance, Hashimoto (2018) and Kikkawa (2018)
found that this trend is gradually becoming stronger in Japan, based on the 2015 Nationwide Survey
on Social Stratification and Social Mobility (SSM2015). Corak (2016) found in 22 countries that
more inequality at a point in time is associated with less generational earnings mobility (see Figure
1, reprinted from Corak 2016). Figure 2 (also excerpted from Corak 2016) shows comparable
estimates of the intergenerational elasticity between father and son earnings for 22 countries. Figure
2 indicates that Japan has modest income inequalities and intermediate intergenerational earnings
mobility (the intergenerational elasticity between father and son earnings is 0.34).1
As illustrated in Figures 1 and 2, most advanced countries, such as the United States (US) andthe United Kingdom (UK), face widening income inequalities and increasing disparities, except for
Scandinavia. In an aging Japan, it is expected that elderly poverty will become a more serious
problem in the near future because cohort income disparity increases with age.2 For example, theUS is an advanced country and known for its significant income inequality and wherein the top
income class with a very small population ratio currently takes an extremely large share of theoverall income and wealth while there also exists a serious poverty problem.3
The problem of economic disparities, or income gaps, will become even more important inJapan for four reasons. First, with a rapidly aging and shrinking population, future high economic

1

Ueda (2009) estimated the intergenerational mobility of economic status in Japan, using predicted parental
income. The intergenerational elasticity is estimated at 0.41–0.46 for married sons and 0.30–0.38 for marrieddaughters.
2 Ohtake (2003) suggested that income inequality in Japan has been recently expanding and thatcountermeasures must be implemented especially for younger generations. Ohtake (2003) also found that,compared with the US, Japan has a lower mobility across income classes and a lower possibility of “reversal,”
resulting in a larger gap in lifetime income.
3 According Stebbins and Comen (2020), the top 1% of earners in the United States account for about 20% of
the country’s total income annually. Meanwhile, the lowest-earning quarter of Americans account for just
3.7% of income every year.

2

growth is no longer expected. Since increases in the whole pie cannot be expected in a society withlow economic growth, the problem of income redistribution becomes more important because of alimited total income. Second, as reported by the Organization for Economic Co-operation andDevelopment (OECD) (2020), Japan’s public expenditure on education is the lowest level in theOECD. This suggests that, compared with other developed countries, Japan relies on private
education rather than public education. Additionally, non-regular, contingent, and part-time workers
are increasing in Japan. Their salary is relatively low, and their life is unstable and precarious.
Japan’s child poverty rate is considerably high; it is 14.0% (new standards) in 2018 (Ministry of
Health, Labour and Welfare 2019). Thus, the so-called ‘a chain of the poverty’ is gradually
becoming a serious social problem. Third, Iwamoto (2019) found the preponderant problem of
artificial intelligence (AI) and employment is economic disparity. Since AI replaces high-skilledroutine work, medium-skilled workers are taken jobs and drop down to become low-skilledworkers. If the total number of low-skilled workers remains unchanged, their wages will decrease
and their jobs will become precarious, exacerbating economic disparity. Fourth, Fisher and Bubola(2020) reportedthat COVID-19 has exacerbated economic inequality, because it burdens many
people in the lower economic strata, who are more likely to catch the disease and to die from it.
Furthermore, even the healthy are likely to suffer loss of income or health care because ofquarantine and other measures. This may also hold true for Japan.
Next, we describe our research method. We use the lifecycle general equilibrium simulation
model of overlapping generations, developed by Auerbach and Kotlikoff (1983a, 1983b) andsimilarly applied in Auerbach and Kotlikoff (1987), Seidman (1983), Auerbach et al. (1989), Altig
et al. (2001), Homma et al. (1987), Ihori et al. (2006, 2011), and Okamoto (2005, 2010, 2013).
Okamoto (2020) extended the simulation model to introduce the number of children freely chosen
by households, thus incorporating endogenous fertility and future demographic dynamics.
Because our paper examines the quantitative effects of changes in intergenerational mobility inJapan across income classes, the mobility between parents and children must be introduced into themodel. Therefore, from Okamoto (2020), we incorporated the mobility probability into thesimulation model with endogenous fertility, enabling us to analyze intergenerational earnings
mobility, which is our main contribution to the literature. Since this model extension is performed in3

a model framework with endogenous fertility, it can also analyze the quantitative effects of changes
in intergenerational income class mobility on the transition of the population of each income class.
This extended simulation model is a useful analytical tool because it can rigorously examine thequantitative effects of changes in intergenerational income class mobility from parents to theirchildren on individual welfare and demographic dynamics. Thus, this model allows for a discussionof countermeasures for the impending problems concerning widening income disparities andincome class stratification in a depopulating and aging Japan.
Therefore, we introduce the descendent income inequality from parents to their children into
the simulation model with endogenous fertility and specifically incorporate two representative
households, low- and high-income classes into a cohort. Our model treats intergenerational earnings
mobility as intergenerational income class mobility. The model also allows the degree of income
class stratification to be freely set or chosen by an exogenously probability matrix, which
determines the mobility probability from low-income parents to low- or high-income children andthat from high-income parents to low- or high-income children.
Our paper will investigate the quantitative effects of changes in intergenerational income classmobility on individual welfare and future demography, using an extended dynamic simulation
model of the Auerbach–Kotlikoff type. First, we extended the simulation model to introduce thenumber of children into the utility function, which enables future demography to be determined
endogenously (Okamoto 2020). Furthermore, into our extended framework with endogenous
fertility, we introduced the descendent link between a parent and children and gave the exogenoustransition probabilities from the parent’s income class to the same (or the other) income class that
their children will belong to.
Finally, as shown in Okamoto (2020), our study introduces an additional government
institution, the Lump Sum Redistribution Authority (LSRA). Changes in the intergenerational
mobility across income classes generally improve the welfare of some generations but reduce thatof others. If combined with redistribution from winning to losing generations, such changes may
offer the prospect of Pareto improvements. Without implementing intergenerational redistribution,
however, potential efficiency gains or losses cannot be estimated. Therefore, like Auerbach andKotlikoff (1987) and Nishiyama and Smetters (2005), we introduce the LSRA as a hypothetical4

government institution. This distinguishes potential efficiency gains/losses from possible offsettingchanges in the welfare of different generations. To isolate pure efficiency gains or losses, weconsider simulation cases via LSRA transfers where the probability of intergenerational income
class mobility is increased/decreased. The introduction of LSRA transfers enables us to examine
policy proposals from a long-term perspective, considering not only the welfare of current
generations but of future generations. Because of its ability to quantify alternative policies from along-term perspective, we will be able to present concrete and useful policy proposals.
The remainder of this paper is organized as follows. Section 2 identifies the basic model
applied in the simulation analysis. Section 3 explains the method of simulation analysis and its
assumptions. Section 4 evaluates the simulation findings and discusses policy implications. Section
5 summarizes and concludes.

2. Theoretical Framework
We calibrate the simulation of the Japanese economy by applying population data from 2017,
estimated by the National Institute of Population and Social Security Research. The model includes
106 overlapping generations, corresponding to ages 0–105 years old. Three types of agents areincorporated: households, firms, and the government. The following subsections describe the basic
structures of households, firms, and the government, as well as the market equilibrium conditions.
Our model incorporates intergenerational mobility across income classes based on Kikkawa(2009) who found that Japan’s income disparity stems fundamentally from different educational
backgrounds between high school and university graduates. On the basis of his study, our model
introduces two types of representative agents: the low-income class (i.e., (just) high school
graduates) and the high-income class (i.e., university graduates) into a cohort. In this section, we
describe the behavior of the low-income class household in the model (see Appendix A for the
behavior of the high-income class).

2.1. Household Behavior
The economy is populated by 106 overlapping generations that live with uncertainty, corresponding
to ages 0–105. Each agent is assumed to consist of a neutral individual because our model does not5distinguish by gender. Each agent enters the economy as a decision-making unit and starts to workat age 18 years, and lives to a maximum age of 105 years. Each household is assumed to consist of
one adult and its children. The children aged 0–17 or 0–21 only consume, involving childrearingt

costs for their parent. Each household faces an age-dependent probability of death. Let q j 1| j be
the conditional probability that a household born in year t lives from age j to j +1. Then theprobability of a household born in year t , surviving until s can be expressed bys 1

pst ( H )   q tj 1| j .

(1)

j 18

t

The probability q j 1| j is calculated from data estimated by the National Institute of Population andSocial Security Research (2017). Since the survival probability is different among agents withdifferent birth year, agents born in different years have the different utility function.
Each agent who begins its economic life at age 18 chooses perfect-foresight consumption paths( Cst ), leisure paths ( lst ), and the number of born children ( nst ) to maximize a time-separable utility
function of the form:Ut (H )



 

1
105
1
1 
1  ( H ) 40 t ( H )( s 18)t ( H ) 1 (H )t (H )
( s 18)t ( H )  t ( H ) 1  ps (1   )ns (1   )  ps (1   )
Cs
ls

1 
s

18
s

18


1









(2)
This utility function represents the lifetime utility of the agent born in year t . Cst (H ) , lst ( H )and nst ( H ) are respectively consumption, leisure and the number of children to bear (only in thefirst 23 periods of the life) for an agent born in year t , of age s ;  (H ) is the utility weight of thenumber of children relative to the consumption–leisure composite,  is the intertemporal elasticity
of substitution,  is the adjustment coefficient for discounting the future, and  is theconsumption share parameter to leisure.
Fertility choice in the model is only based on the direct utility that households obtain from theiroffspring, neglecting the investment element of children. The demand for children as investment
goods played an important role in traditional economies (and still does in developing countries),
where transfers from the young to the old arise within the family. In modern advanced countries,
however, a pay-as-you-go (PAYG) social security scheme makes the investment aspect of children
socialized, as Groezen et al. (2003) pointed out. This creates the possibility for households to freeride on the scheme by rearing fewer or no children, still being entitled to a full pension benefit.
6Therefore, we treat children as ‘consumption goods’ and a parent is assumed to obtain the utility
from the number of children born at each age.
As shown in Okamoto (2020), letting Ast ( H ) be capital holdings for the agent born in year t ,of age s , maximization of Equation (2) is subject to a lifetime budget constraint defined by thesequence:)
Ast ( H {1  rt  s (1   r )} Ast ( H )  (1   w   tp s ) wt  s es( H ){1  lst ( H )  tcst (nst ( H ) )}  ast ( H )  orst ( H )
1





c
t(H )
 bst ( H ) {1  lut ( H )  tcut (nut ( H ) )}uRE
 (1  m)(1   tc s ) ts( H )  m(1   tc s ) ts(U ) , (3)20  (1   t  s ) Cs

where rt is the pretax return to savings, and wt is the real wage at time t ;  w , rand  tc are

the tax rates on labor income, capital income and consumption, respectively.  tp is the contribution
rate to the public pension scheme at time t . All taxes and contributions are collected at thehousehold level. tc(n ( H ) ) is the time cost for childrearing. a ( H ) is the bequest to be inherited, andor (H ) is the childrearing cost for orphans. There are no liquidity constraints, and thus the assets
As( H ) can be negative. Terminal wealth must be zero. An individual’s earnings abilityes( H ) is an

exogenous function of age.
The public pension program is assumed to be a PAYG scheme similar to the current Japanesesystem. The program starts to collect contributions to the scheme from the age of 20, in accordancewith the law. The pension benefit is assumed to comprise only an earnings-related pension:H t ( H ) {1  lut ( H )  tcut (nut ( H ) )}uRE20
bst ( H ) {1  lut ( H )  tcut (nut ( H ) )}uRE20  
0





 (s  ST ) ,( s  ST )

(4)

where



 RE1 19  w e

H t ( H ) {1  lut ( H )  tcut (nut ( H ) )}uRE20 

RE

s 20

(H )
t s s{1  lst ( H )  tcst (nut ( H ) )} .

(5)

The age at which a household born in year t starts to receive the public pension benefit is ST , theaverage annual labor income for the calculation of pension benefit for each agent is, and the weight coefficient of the part proportional to H t ( H ) is
H t ( H ) {1  lut ( H )  tcut (nut ( H ) )}uRE
20

 . The symbol bst ( H ) {1  lut ( H )  tcut (nut ( H ) )}uRE20  signifies that the amount of public pension
benefit is a function of the age profile of labor supply, {1  lut ( H )  tcut (nut ( H ) )}uRE20 .
A parent is assumed to bear children with the upper limit of 40 years old, and expend for them
until they become independent of their parent, namely, during the period when children are fromzero to 17 or 21 years old. Regarding the childrearing costs, the model takes account of both7

monetary and time costs. Here, note that the children aged below 18 or 22 years old do not conduct
an economic activity independently, and childrearing costs for their parent arise until they become
independent of their parent. The financial costs for rearing the children, for the parent born in year

t and s years old, are represented by ts(H ) and ts(U ) , which are the cost for the children who
will become high school graduates and university graduates, respectively:

 s t(H )(1   )nkt ( H ) ( s  18,19,, 35) k 18 s
 ts( H )     t ( H ) (1   )nkt ( H ) ( s  36, 37,, 40) ,k s17
 40 t ( H )(1   )nkt ( H ) ( s  41, 42,, 57 ) k s17(6)

ts( H )  0 ( s  58, 59, , 105 ) ,(7) s t(H )(1   )nkt ( H ) ( s  18,19,, 39)
 

k 18
,
 ts(U )   40
t(H )
t(H )

  (1   )nk (s  40, 41,, 61)k  s  21

(8)

ts(U )  0( s  62, 63,,105 ) ,(9) t ( H )  NW t ( H ) ,(10)

where  t ( H ) is the childrearing cost for the parent born in year t ,  is the rate of government
subsidy (including child allowances) to childrearing costs, and  is the ratio of childrearing costs
to the net lifetime income, NW t ( H ) , for the parent born in year t .
The children who will become university graduates needs more monetary cost than the children
who will become high school graduates simply by the extra four-year (18–21) cost before theindependence from their parents. The mobility m denotes the probability in which the children
will belong to the high-income class (i.e., university graduates) different from their parent, and1  m is the probability in which they will belong to the low-income class (i.e., high school
graduates) same as their parent. The number of children affects the whole available time for aparent, because of the time required for childrearing. The time cost for rearing the children for theparent born in year t , of age s , is represented by

tcst ( H )  nst ( H ) ,(11)

where  is the parameter that shows the relation between the number of children and the time8

required for childrearing, which is simply assumed to be proportional to the number of bornchildren. The time cost is assumed to be same across the two types of children who will become
high school graduates or university graduates.
The model contains accidental bequests that result from uncertainty over length of life. The
bequests, which comprise assets previously held by deceased households, are distributed equally
among all surviving low-income class households at time t . When BQt( H ) is the sum of bequests
inherited by the low-income class households at time t , the bequest to be inherited by each lowincome household is defined byast ( H ) (1   h ) BQt(Hs ),Et(Hs )

(12)

where
105

BQt( H )   ( N st s 1( H )  N st 1s 1( H ) ) Ast 1s 1( H ) .

(13)

s 18

 h is the tax rate on inheritances of bequests. The amount of inheritances received is linked to theage profile of assets for each household. Et( H ) is the number of the low-income class households
conducting an economic activity independently, aged 18 and older. The number of the generation
with age s years born in year t is represented by

N st ( H )  pst ( H ) N 0t ( H ) .

(14)

Total childrearing cost of the orphans, who are generated as a consequence of parents’uncertainty over length of life, is distributed equally among all surviving low-income classhouseholds at time t . When ORt( H ) is the sum of childrearing costs incurred by the low-income
class households at time t , the childrearing cost for orphans for each low-income class household
is defined by
t(H )
s

or

ORt(Hs ) (H ) ,Et  s

(15)

where
57

61

s 18

s 18

ORt( H )  (1  m)  ( N st 1s ( H )  N st s ( H ) ) tss ( H )  m  ( N st 1s ( H )  N st s ( H ) ) tss (U ) .

Therefore, the net amount of bequests is represented as a

(H )

 or ( H ) . When we consider theutility maximization problem over time for each agent, besides the flow budget constraint
9(16)

represented by Equation (3), the following constraint is imposed:t (H )tt(H ) 0  l s  1  tcs (ns ) (18  s  RE ).
 t (H )( RE  1  s  105 ) ls  1(17)

This is a constraint that labor supply is nonnegative, and that each household inevitably retires after
passing the compulsory retirement age, RE .
Let us consider the case where each agent maximizes expected lifetime utility under two
constraints. Each individual maximizes Equation (2) subject to Equations (3) and (17) (seeAppendix B for further details). From the utility maximization problem, the equation expressing theevolution of the number of children over time for each individual is characterized by p t ( H ) 
 t(H )1 ,
Wst ( H )   st ( H1 )  Wr  s 1
p
1

r
(
1


)
t s
 s 


Wst ( H )  ( H )k

1

(18)

1





1

(nst ( H ) ) 

17
21


(1   tc s ) (1  m) ts , g t ( H ) (1   )  m ts , g t ( H ) (1   )
g 0
g 0



,

(19)

1

where ts,0

=1 for g  0 , 

t
s, g

 g

  {1  rt  s1k (1   r )} .
 k 1


Similarly, that for the consumption–leisure composite is represented by pt ( H )  t (H )1 ,
Vst ( H )   st ( H1 )  Vr  s 1
 ps  1  rt  s (1   ) t (H )
s

V







(20)

1

(1   ( H ) ) (Cst ( H ) ) (lst ( H ) )1   (Cst ( H ) ) 1 (lst ( H ) )1.

1   tc

(21)

2.2 Firm Behavior
As shown in Okamoto (2020), the model has a single production sector that is assumed to behave
competitively using capital and labor, subject to a constant-returns-to-scale production function.
Capital is homogeneous and depreciating, while labor differs only in efficiency. All forms of labor
are perfectly substitutable. Households with different income classes or different ages, however,supply different amounts of some standard measure per unit of labor input.
The aggregate production technology is the standard Cobb-Douglas form:10Yt  K t L1t  ,(22)

where Yt is aggregate output (national income), K t is aggregate capital, Lt is aggregate labor
supply measured by the efficiency units, and  is capital’s share in production. Using the property
subject to a constant-returns-to-scale production function, we can obtain the following equation:

Yt  (rt   k ) K t  wt Lt ,(23)

where  k is the depreciation rate.

2.3 Government Behavior
As shown in Okamoto (2020), at each time t , the government collects tax revenues and issues debt
( Dt 1 ) that it uses to finance government purchases of goods and services ( Gt ) and interest
payments on the inherited stock of debt ( Dt ). The government sector consists of a narrow
government sector and a pension sector, and a portion of revenues is transferred to the public
pension sector. The public pension system is assumed to be a simple PAYG style and consists onlyof earnings-related pension. Pension account expenditure is financed by both contributions and atransfer from the general account.
The budget constraint of the narrower government sector at time t is given byDt 1  (1  rt ) Dt  Gt  Tt ,(24)

where Gt is total government spending on goods and services, Tt is total tax revenue from labor
income, capital income, consumption and inheritances, and Dt is the net government debt at the
beginning of year t . Dt is gross public debt minus the accumulated pension fund because themodel abstracts the public pension fund, which is represented as a ratio to national income:Dt  dYt ,(25)

where d is the ratio of net public debt to national income.
The public pension system is assumed to be a simple PAYG style. The budget constraint ofpension sector at time t is represented by

Rt  (1   ) Bt ,(26)

where Rt is total revenue from contributions to the pension program, Bt is total spending on thepension benefit to generations of age ST and above, and  is the ratio of the part financed by the
tax transfer from the general account.
The total government spending on goods and service is defined by11

Gt  gYt  Bt  GSt ,(27)

Gt includes transfers to the public pension sector ( Bt ) and the government subsidies to childrearing ( GSt ). The government spending except for the transfers and the subsidies is gYt , which isassumed to be represented as a constant ratio ( g ) of national income. The spending is assumed toeither generate no utility to households or enter household utility functions in a separable fashion.
The total amount of government subsidies (including child allowances) to the childrearing costin year t is GSt :GSt  GSt( H )  GSs(U ) ,

(28)

57
61


GSt( H )   (1  m)  ( RCsa,(t H )  RCsb,(t H )  RCsc,(tH ) )  m  ( RCsa,(tU )  RCsb,(tU ) ) ,
s 18
s 18



(29)

s

a(H )
RC

N kt  s ( H ) t  s ( H ) nkt  s ( H ) ( s  18,19,, 35)

s
,
t

k 18

s

b(H )
t s ( H ) t s ( H ) t s ( H )nk( s  36, 38,, 40) , RCs , t   N kk  s 17

40

c(H )
RC

N kt  s ( H ) t  s ( H ) nkt  s ( H ) ( s  41, 42,, 57 )s,tk  s 17s
a (U )
RC
N kt  s ( H ) t  s ( H ) nkt  s ( H ) ( s  18,19,, 39)

s,t


k 18
,

40
 RC b (U ) N kt  s ( H ) t  s ( H ) nkt  s ( H ) ( s  40, 41,, 61)s,tk  s  21


(30)

(31)

where RCta ( H ) , RCtb ( H ) and RCtc ( H ) are monetary costs for childrearing when the children will
belong to the low-income class same as their parent, namely, they will become high school
graduates, and RCta (U ) and RCtb (U ) are the costs when the children will belong to the highincome class different from their parent, namely, they will become university graduates.
61
57


GSt(U )   (1  m)  ( RCsa,(tU )  RCsb,(tU )  RCsc,(tU ) )  m  ( RCsa,(t H )  RCsb,(t H ) ) ,s  22s  22



(29)’

s

a (U )t  s (U ) t  s (U ) t  s (U )nk
( s  22, 23,, 40)
 RCs , t   N kk  2240

b (U ),
RC
N kt  s (U ) t  s (U ) nkt  s (U ) ( s  41, 42, 43)s,tk  2240

c (U )t  s (U ) t  s (U ) t  s (U )nk
( s  44, 45,, 61) RCs , t   N kk  s  21


(30)’

12

s

a(H )
RC

N kt  s (U ) t  s (U ) nkt  s (U ) ( s  22, 23,, 39)

s,t


k  22,
40
 RC b ( H ) 
N kt  s (U ) t  s (U ) nkt  s (U ) ( s  40, 41,, 57 )s,tk  s 17
(31)’

where RCta (U ) , RCtb (U ) and RCtc (U ) are financial costs for childrearing when the parent is 22
to 61 years old. Once the parent becomes 62 years old, the cost does not exist because all children
are independent from their parent.
The total spending on the pension benefit to generations of age ST and above is representedby

Bt  Bt( H )  Bt(U ) ,(H )where Bt

(U )and Bt(32)
are the expenditure for the two income classes:

105

Bt( H )   N st  s ( H )bst  s ( H ) ,s  ST

105

Bt(U )   N st  s (U )bst  s (U ) .

(33)s  ST

The total revenue from pension contributions and the total tax revenue are represented by

Rt   p wt Lt ,(34)

Tt   w wt Lt   r rt AS t   tc AC t   h BQt ,(35)

where aggregate assets supplied by households, AS t , and aggregate consumption, ACt , are givenbyAS t  AS t( H )  AS t(U ) ,(36)

AC t  AC t( H )  AC t(U ) .

(37)

For the low-income class, aggregate assets supplied by households, AS t( H ) , and aggregate
consumption, ACt( H ) , are given by105

AS t( H )   N st  s ( H ) Ast  s ( H ) ,

(38)

s 18
105

57

61

s 18

s 18

s 18

AC t( H )   N st s ( H )Cst s ( H )  (1  m)  ( RCsa,(t H )  RCsb,(t H )  RCsc,(tH ) )  m  ( RCsa,(tU )  RCsb,(tU ) ) ,(39)
where aggregate consumption consists of adult’s consumption (at age 18–105 years old) andchildren’s consumption or cost (at age zero to 17 or 21 years old).
(U )For the high-income class, aggregate assets supplied by households, AS t
consumption, AC t(U ) , are given by
13, and aggregate

105

AS t(U )   N st  s (U ) Ast  s (U )(38)’s  22

105

61

57

s 22

s 22

s 22

AC t(U )   N st s (U )Cst s (U )  (1  m)  ( RCsa,(tU )  RCsb,(tU )  RCsc,(tU ) )  m  ( RCsa,(t H )  RCsb,(t H ) )(39)
where aggregate consumption consists of adult’s consumption (at age 22–105 years old) andchildren’s consumption or cost (at age zero to 21 or 17 years old).
The total sum of bequests inherited by the households and the total childrearing cost of theorphans at time t are as follows:

BQt  BQt( H )  BQt(U ) ,(40)

ORt  ORt( H )  ORt(U ) .

(41)

Total population (i.e., the population aged zero to 105), the population aged 18 or 22 to 105(i.e., independents financially), and the population aged 65 to 105 (i.e., retirees) in year t are
respectively represented byZt  Zt( H )  Zt(U ) ,(42)

Et  Et( H )  Et(U ) ,(43)

Ot  Ot( H )  Ot(U ) .

(44)

The aging rate (i.e., the old-age dependency ratio), the ratio of the population aged 65 and above tothe total population, is given by Ot / Z t . For the low-income class, the total population, thepopulation aged 18 to 105, and the population aged 65 to 105 in year t are respectively
represented by
105 40Z t( H )   N it  k i ( H ) pkt  k ( H ) nit  k i ( H ) ,(45)

k  0 i 18
105 40Et( H )   N it k i ( H ) pkt k ( H ) nit k i ( H ) ,(46)

k 18 i 18
105 40Ot( H )   N it k i ( H ) pkt k ( H ) nit k i ( H ) .

(47)

k 65i 18

For the high-income class, the total population, the population aged 22 to 105, and the
population aged 65 to 105 in year t are respectively represented by
105 40Z t(U )   N it  k i (U ) pkt  k (U ) nit  k i (U ) ,(45)’

k  0 i  22

105 40Et(U )   N it k i (U ) pkt k (U ) nit k i (U ) ,(46)’

k 22i 22

14

105 40

Ot(U )   N it k i (U ) pkt k (U ) nit k i (U ) .

(47)’

k 65i 22

2.4. Market Equilibrium
Finally, equilibrium conditions for the capital, labor and goods markets are described.
1) Equilibrium condition for the capital market
Because aggregate assets supplied by households equal the sum of real capital and net
government debt,

AS t  Kt  Dt .

(48)2) Equilibrium condition for the labor market
Measured in efficiency units, because aggregate labor demand by firms equals aggregate labor
supply by households,

Lt  L(t H )  L(tU ) ,
RE

N

(49)
t s ( H ) ( H )ss{1  lst  s ( H )  tcst (nst ( H ) )} ,(50)

L(tU )   N st  s (U ) es(U ) {1  lst  s (U )  tcst (nst (U ) )} .

(51)

where L(t H ) 

s 18

e

RE

s  22

3) Equilibrium condition for the goods market
Because aggregate production equals the sum of private consumption, private investment andgovernment expenditure,

Yt  AC t  {Kt 1  (1   k ) K t }  Gt .

(52)

An iterative program is performed to obtain the equilibrium values of the above equations.

3. Simulation Analysis
3.1. Method
The simulation model presented in the previous section is solved fundamentally, given theassumption that households have perfect foresight and correctly anticipate interest, wages, the tax
and contribution rates, and other factors. If the tax and social security systems and other elements
are determined, then the model can be solved using the Gauss–Seidel method (see Auerbach andKotlikoff (1987) and Heer and Maußner (2005) for the computation process).
15

Our study assumes the transitional economy of Japan from the initial steady state in 2017 to thefinal steady state in 2300. Alternative scenarios on the intergenerational mobility across income
classes are assumed to be implemented at the end of 2017. For simplicity, 2017 is set as the starting
year, and we simulate the demography and the economy in the following years. For the generations
that were alive in 2017 and have survived in 2018, we need to pay attention to their formation of
future expectations. In 2018, these generations realized that their previous expectations no longer
apply and thus again maximize their remaining lifetime utility given perfect foresight. Based on the
ex-post age profiles of the number of children to bear, consumption, and leisure for thesegenerations, we calculated their lifetime utility at 18 and 22 years for the low- and high-income
classes, respectively.
The LSRA first transfers to each household affected by the change in the degree ofintergenerational earnings mobility just enough resources (possibly a negative amount) to return its
expected remaining lifetime utility to its pre-change level in the benchmark simulation. For eachhousehold that is alive when a change occurs (at the end of 2017), at its age in 2018, the LSRA
makes a lump sum transfer, to return its expected remaining lifetime utility to its pre-change utility
level. And then the LSRA makes a leveled and common lump-sum transfer to each future householdthat enters the economy after a change (from 2018 onward), at its age of 18 or 22 years, to return its
expected entire lifetime utility back to its pre-change level.
Note that the net present value of these transfers in 2018 across living and future households
will generally not sum to 0. Thus, the LSRA makes an additional lump sum transfer to each future
household so that the net present value across all transfers is 0. To illustrate, let us assume that these
additional transfers are uniform across all future generations, including the low- and high-income
classes. If the transfer is positive, then the change has produced extra resources after the expected
remaining lifetime utility of each household has been restored to its pre-change level. In this case,
we can interpret that the change has created efficiency gains, i.e., Pareto improvements. Conversely,
if the transfer is negative, then the change has generated an efficiency loss. Thus, the total netpresent value of all lump sum transfers to current and future generations sums to 0 in 2018,
satisfying the LSRA budget constraint (see Appendix B in Nishiyama and Smetters (2005) for
further details).
16

3.2. Simulation cases
We investigate alternative scenarios of the degree of intergenerational mobility across income
classes, along with additional simulation cases that add LSRA transfers. According to Kikkawa(2009), the children of high school-graduate parents have a 70% probability of becoming highschool graduates and a 30% probability of becoming university graduates, whereas the children ofuniversity-graduate parents have a 70% probability of becoming university graduates and a 30%
probability of becoming high school graduates. Therefore, the intergenerational mobility probability

m in Japan is 0.3 in the benchmark simulation, indicating that parents and their children are likely
to belong to the same income class. There are two reasons: (1) university graduate parents
sufficiently understand the merits of graduating from a university, whereas high school graduate
parents do not, and (2) university-graduate parents tend to give good education to their children,
whereas high school-graduate parents are likely to provide relatively poor education to theirchildren.
The following simulation cases are investigated:
3.2.1. Baseline simulation
In the benchmark simulation, the intergenerational mobility probability from the low-income classparent to the high-income class children or from the high-income class parent to the low-income
class children is the standard of 0.3, i.e., the normal transitional probability to reach the same
income class between a parent and children is 0.7. The benchmark case simulates the transition of
the Japanese economy from 2017 to 2300, in which the standard intergenerational mobility (0.3)
across income classes is maintained throughout the entire period.
3.2.2. Changes in intergenerational mobility across income classes
We investigate two scenarios in which the intergenerational mobility probability across income
classes increases from 0.3 to 0.5 and reduces to 0 for some reason or other. The former scenario is acompletely shuffled case: children’s future income class (or earnings) is unrelated to their parents’,and thus, the transition of the earnings ability is randomly shuffled between parent and child. In
other words, regardless of the parent’s income class, half of children will belong to the high-income
class, and the other half, to the low-income class. Conversely, the latter scenario is completely
17stratified: children of the high-income class parent will inevitably belong to the high-income class,whereas children of the low-income class parent will always belong to the low-income class.
3.2.3. Cases with LSRA transfers
To distinguish potential efficiency gains/losses from possibly offsetting changes in the welfare ofdifferent generations, we introduce the LSRA into our two alternative simulation cases. The LSRA
transfers will produce a leveled and common welfare gain/loss for each future household in both thelow- and high-income classes.
3.3. Specification of the parameters
We chose realistic parameter values for the Japanese economy on the basis of the literature(Nishiyama and Smetters (2005), Oguro et al. (2011), Imrohoroglu et al. (2017), and Kitao andMikoshiba (2020)). Table 1 displays the parameter values assigned in the benchmark simulation,and the data source used in the calibration. We chose parameter values such that the calculated
values of the model’s endogenous variables approach the actual data values. Table 2 presents theendogenous variables in the 2017 initial steady state.
On the basis of Kikkawa (2009), we assume that the low- and the high-income classes
correspond to (just) high school and university graduates, respectively. Kikkawa (2009) found thatthe population of high school graduates and university graduates is roughly equal today and into the
future. We use the model with two representative households. Specifically, the following threeparameters are crucial for conducting a realistic simulation (the details of assignment of the threeparameters will be described below). First, we need the realistic parameter value on the income
difference between the two representative agents, namely, the difference of age profile of earnings.
Second, we require a realistic parameter value of the difference in birth rates (or fertility rates)
between the two representative agents, namely, the difference of preference on the number ofchildren to bear. Third, we need a realistic population ratio for each agent of the two income classes.
Thus, the realistic parameter values on these three important parameters are available if our model
incorporates two representative agents with different educational backgrounds, on the basis of
Kikkawa (2009, 2018).
3.3.1. Demography
18

Table 3 indicates the population ratio of individuals with a different educational background in2017, which is estimated from the Basic Survey on Wage Structure (Chingin Sensasu) by the
Ministry of Health, Labour and Welfare (2018). Accordingly, the population share of high school
graduates (including junior high school graduates) and university graduates (including technical andjunior college graduates) is 45.5% and 54.5%, respectively. Figure 3 illustrates the age–population
distribution in 2017 based on data from the Ministry of Internal Affairs and Communications(2018a). Figure 3 also denotes the population of high school and university graduates, respectively,
for each age. For the elderly, especially those of advanced age, the number of high school graduates
exceeds that of the university graduates, whereas for the young and the middle-aged, it isapproximately fifty–fifty. For those who are under 18 or 22 years old and undecided to become highschool or university graduates, we assume that their population is the same i.e., fifty–fifty on thebasis of Kikkawa (2009).
Next, we describe how we assign parameter values for childrearing since our simulation model
incorporates endogenous fertility. The Cabinet Office (2010) indicated the average annual
childrearing costs for the first-born child to annual income for each age. Based on the survey in the
Cabinet Office (2010), we assigned the parameter value of  (i.e., the ratio of childrearing costs toparental net lifetime income) such that the ratio of the annual net childrearing costs to annual labor
income for the individual is, on average, close to 19.3%. Thus,  is assigned 0.0385 (the ratio is22.5% for the low-income class and 17.9% for the high-income class).
The OECD (2020) presented public spending on family benefits in cash, services, and tax
measures as a percentage of GDP in 2015. For Japan, the public spending ratios on family benefits
in cash, services, and tax measures to GDP are 0.74%, 0.57%, and 0.30%, respectively,4 When we
assign the value of parameter  (government childcare subsidies divided by childrearing cost) to
0.1 in the model, as in Oguro et al. (2011), the ratio of the total government subsidies to national
income is 1.30% in the initial steady state.
Our model incorporates not only the monetary costs of childrearing but also the time costs.
Increases in the number of children diminish a parent’s available time because of the time required
4

In Japan, the ratio of total family benefits to GDP is only 1.61%, whereas it is 2.40% for the 32 OECDmember countries, indicating that the level of governmental support to households’ childrearing is
considerably lower in Japan than in the OECD.

19

for childrearing. The parameter that makes a connection with the number of children and the timerequired for childrearing,  , is proportional to the number of children to rear. This parameter isassigned under the simple assumption that one child needs 1 h per day for childrearing.5
Table 4 presents the scheduled number of children for young people aged 21 to 40 in Kikkawa(2018), which is based on a large-scale questionnaire survey (SSM2015). The data were used toassign the parameter values that determine the difference of fertility rates between the two income
classes. Table 4 suggests that the scheduled number of children for high school-graduate couples is,on average, 1.14, whereas it is 0.875 for university-graduate couples. The parameter values
determining the fertility were chosen so that the total fertility rate (TFR) is 1.43 in the 2017 initialsteady state, because Japan’s actual TFR was 1.43 in 2017. Consequently, in the initial steady state,
the TFR is 1.59 for the low-income class and 1.27 for the high-income class.
3.3.2. Age profile of labor efficiency
The age profiles of earning ability for the two income classes were estimated with data from the
Basic Survey on Wage Structure (Chingin Sensasu) by the Ministry of Health, Labour and Welfare
for the period (2009–2018). Figure 4 illustrates age–earnings profiles by education. The labor
efficiency profiles are constructed from the Japanese data on employment, wages, and monthly
work hours.
To estimate the age profiles of earnings ability, es

(H )

(U )

and es , respectively, the following

equation is constructed:
Qt  a0  a1 At  a2 At2 ,(53)

where Q is the average monthly cash earnings for high school-graduate workers and universitygraduate workers, respectively, and A is the average age for the workers including both males andfemales. Because bonuses account for a large part of earnings in Japan, Q includes bonuses. For
the high school graduates, the starting age of work is earlier (18 years old), but their age profile ofearnings is flatter than the university graduates and has a lower level. For the university graduates,
the starting age of work is later (22 years old), but their age profile of earnings is steeper with a
Calibrating the value of parameter,  , that determines the time cost in the model is difficult. In the 2017
initial steady state, an average number of children to which a parent gives birth during the period from 18 or
22 to 40 is 0.0364 per year. We assume that a parent is available time of 16 h per day and that the childrearing
time cost for one child is 1 h per day.
5

20

higher level.
3.3.3. Taxes and expenditures
Tax rates on labor income, capital income, and inheritances are fixed at the current levels (6.5%,
40%, and 10%, respectively) during the entire period. Tax rates on consumption are endogenously
determined to satisfy Equations (24) and (35). General government expenditures, except fortransfers to the public pension sector ( Bt ), and government subsidies to childrearing ( GSt ), areproportional to national income ( Yt ) as indicated in Equation (27). The ratio of general expenditure
to national income, g , was assigned 0.1 such that the endogenous tax rate on consumption isrealistic and plausible in the 2017 initial steady state (i.e., 11.68%). The ratio is held constant at 0.1
during the entire period.
3.3.4. The public pension system
The public pension program is assumed to be a simple PAYG system similar to the current Japanesesystem. The benefit is assumed to comprise an earnings-related pension, although Japan’s actual
public pension system is two-tiered: a basic flat pension and an amount proportional to the averageannual labor income for each household. General tax revenue finances half of the flat part, whereas
contributions to the pension system fund both the remaining half and the entire proportional part.
We assigned the ratio (  ) of the part financed by the tax transfer from the general account inEquation (26) as 0.25, taken from Oguro and Takahata (2013). The replacement ratio (  ) for public
pension benefits in Equation (4) is equal to 40%, following Braun et al. (2009).
The age at which households start to receive public pension benefits ( ST ) is constant during
the entire period. The compulsory retirement age ( RE ) is the starting age of public pension benefits( ST ) minus 1. Thus, after households retire at the end of the year in which they reach compulsory
retirement, they immediately start to receive pension benefits.
3.3.5. Government deficits
Net government debt ( Dt ) is assumed to be proportional to national income to make our simulation
feasible. The value of parameter d , which is the ratio of net public debt to national income as given
in Equation (25), was assigned based on data from the Ministry of Finance (2018) and the Cabinet
Office (2018). After 2017, Japan’s national income is expected to decrease as the population21

declines. Therefore, the assumption that net government debt is proportional to national income
during the entire period implies that the government will successfully reduce future government
deficits.
3.3.6. Share parameter on consumption in utility
The value of the consumption share parameter,  , in the utility function was assigned based on
Altig et al. (2001). Consequently, in the 2017 initial steady state, an individual devotes, on average,
approximately 56.2% for the low-income class and 58.4% for the high-income class of the available
time endowment (of 16 h per day) to labor during their working years (ages 18–64 or 22–64 years).
3.3.7. Technological progress
The technological progress of private production is significant because it greatly influences
economic growth. Thus, careful attention should be paid to our assumptions. Technological progress
is assumed to be 0 in the simulation, reflecting Japan’s experience during the past two or three
decades (see Ihori et al. 2006).

4. Simulation Results
We assume that the baseline simulation has the standard probability (0.3) on the intergenerational
mobility across income classes. We analyze two alternative scenarios in which intergenerational
mobility is increased to 0.5 and decreased to 0. Furthermore, to isolate the pure efficiency gains orlosses from the changes in the mobility probability, we examine additional cases in which the LSRA
transfers are introduced in the two alternative cases.
4.1. Baseline simulation
Children of the low-income class parent will belong to the low-income class with the transitional
probability of 0.7 and the high-income class with the probability of 0.3. Similarly, children of thehigh-income class parent will belong to the high-income class with the probability of 0.7 and the
low-income class with the probability of 0.3. Figure 5 illustrates the transition of populations foreach class in the baseline simulation with the 0.3 mobility probability. In 2017, the low-income
class has 76.3 million people, and the high-income class has 50.4 million people. After 2017, thepopulation for each class decreases. Throughout the entire period, the population of the low-income22class is greater than the high-income class because the former’s fertility rate is higher.
4.2. Changes in the intergenerational mobility probability
First, we discuss the simulation results for the experiment in which the intergenerational mobility
probability across income classes is increased to 0.5. In this scenario, the two income classes are
randomly shuffled; thus, half the children will belong to the low-income class (or the high-income
class), despite their parent’s income class. Figure 5 illustrates the transition of each population from2017 to 2200 for the two income classes, indicating that around 2070 the populations will converge
to almost the same level for the two classes, and thereafter, they continue to have the same
population. Figures 6 and 7 show changes in the total population and national income, respectively,from the benchmark level. Figure 6 illustrates that an increase in intergenerational mobility results
in a lower population over time, compared with the baseline. This is because a high mobility
probability increases the number of the high-income class but their fertility is lower than that of the
low-income class.
Figure 7 illustrates changes in the national income for the different intergenerational mobility
cases, from the level of the benchmark case. An increase in intergenerational mobility acrossincome classes increases national income. This is due to more workers with a high laborproductivity (see Figure 5). In the very long run, conversely, an increased mobility probability
decreases national income, since after 2134, the negative effect, induced by the decreased total
population (see Figure 6), exceeds the positive effect brought about by more workers with a higher
earnings ability.
Here, we discuss the reason for the first changes in the level of national income from 2017 to2060 in Figure 7, for the different intergenerational mobility cases. After 2060, the national income
becomes higher in the 0.5 intergenerational mobility scenario than in the benchmark 0.3 case, owing
to more workers with a higher labor productivity. From 2017 until 2060, conversely, the national
income for the 0.5 mobility case is slightly lower. A possible reason is that increases in highproductivity workers (i.e., university graduates) entail more childrearing costs and negatively
impact the economy for a while. In the no intergenerational mobility scenario, the reverse occurs
because of relatively more high school graduates.
Next, we discuss the simulation results when the intergenerational mobility probability across23

income classes is decreased to 0. Figure 5 indicates that after 2017 the population of the low-income
class is much larger than that of the high-income class because the fertility rate of the former ishigher than that of the latter. The figure indicates that in 2140 the population of the low-income
class is almost double that of the high-income class, thereafter the gap is gradually increasing. As
indicated in Figure 6, in the no intergenerational mobility scenario, the total population gradually
increases over time, compared with that in the benchmark scenario. This is because the zero
mobility case has relatively more members of the low-income class with a higher fertility.
This scenario increases workers with a lower labor productivity and thus reduces national
income (see Figure 7). In the very long run, conversely, the zero mobility case increases national
income because after 2172, the positive effect caused by a larger total population (see Figure 6)
exceeds the negative effect induced by more workers with a lower labor productivity. Note that theno intergenerational mobility case achieves a larger population in the very long run, with the
population share of the low-income class gradually expanding over time. This may deteriorate percapita welfare, which will be evaluated in the following subsection, Cases with LSRA transfers.
Figures 8 and 9 present the transition of the capital stock and the labor supply, respectively, forthe alternate scenarios. The level of capital stock for the 0.5 scenario becomes higher in 2075 but
becomes lower after 2127 vis-à-vis the benchmark 0.3 scenario. The labor supply level, measured
by efficiency units, for the 0.5 scenario increases in 2057 but decreases after 2138. Increases in thecapital stock and the labor supply are mainly caused by more high-earnings-ability workers inducedby the randomly shuffled intergenerational income classes. In the very long run, conversely, thenegative population effect, caused by the lower fertility of the increased high-income class, exceeds
this positive effect. For the zero mobility scenario, the reverse effect can be observed because of
relatively more high school graduates: The capital stock level for the zero mobility case decreases
after 2070 but increases from 2158, and the labor supply level also decreases in 2055 but increases
after 2181.
Figures 10 and 11 illustrate the transition of interest rates and wage rates, respectively, for thetwo alternate scenarios. In the case of no intergenerational mobility, the population ratio of the lowincome class becomes progressively higher over time (see Figure 5). Since high school graduates
have a flatter age profile of earnings (see Figure 4), an increase in their population ratio leads to24

relatively more capital and less labor (measured by efficiency units), which increasingly reduces
interest rates and increases wage rates over time. Figure 10 shows that after 2052 the interest rate islower in the zero mobility case than in the benchmark 0.3 case, whereas Figure 11 shows that after
2052 the wage rate is higher in the zeromobility case than in the 0.3 case. Conversely, for the 0.5
case, the reverse effect occurs (see Figures 10 and 11).
Figure 12 illustrates the transition of consumption tax rates for the two alternative scenarios.
The tax rate on consumption is lower until 2117 in the 0.5 mobility case than in the standard 0.3
case, because the former has more workers with a higher labor productivity. In the very long run(from 2118 onward), conversely it increases in the 0.5 case because the population ratio of the highincome class increases over time and their fertility is relatively low, resulting in the population
gradually decreasing. A lower ratio of the working population to retirees negatively influences
economic growth especially under a PAYG social security system, resulting in higher endogenous
tax rates on consumption.
Moreover, as Figure 13 shows, in the very long run (from 2098 onward), the contribution rate
to the pension system is also higher in the 0.5 mobility case than in the benchmark 0.3 case.
Conversely, the zero mobility scenario has the opposite effect because the population ratio of the
low-income class with higher fertility gradually increases and the total population progressively
increases over time. A high ratio of the working population to retirees, benefits economic growthparticularly under a PAYG social security system, resulting in lower endogenous tax rates on
consumption and lower contribution rates in the very long run (see Figures 12 and 13).
4.3. Cases with LSRA transfers
We quantified the effects of changes in the intergenerational mobility across income classes on themacroeconomy and demography. Figure 7 indicates the main results for two alternative scenarios.
In this subsection, we focus on the effects of the two scenarios on per-capita welfare. To isolate theefficiency gains or losses from changes in the mobility probability, we introduced LSRA transfers
into the two alternate scenarios. Table 5 presents the welfare gains or losses accompanied withchanges in the transitional mobility, for each future household in both classes. The high mobility

25

probability case ( m = 0.5) generates a per-capita welfare gain of ¥215,0406. A highintergenerational mobility increases the population ratio of the workers with a high laborproductivity, which improves per-capita welfare. This result implies that increased intergenerational
mobility across income classes attains Pareto improvements, and thus, the high mobility is desirablefrom the viewpoint of efficiency. In the very long run, however, in this scenario the total population
is substantially reduced, decreasing national income. Conversely, the zero mobility case leads to a
per-capita welfare loss of ¥294,450. The absence of the intergenerational mobility across income
classes increases the population ratio of the workers with a lower labor productivity, which
deteriorates per-capita welfare. Thus, the no mobility scenario is not preferable from the viewpointof efficiency. In the very long run, however, in this scenario, the total population is significantly
increased, resulting in increased national income.
Therefore, the total population effect dominates in the very long run for the two alternative
scenarios, and the zero mobility case substantially increases the total population, ultimately
increasing economic growth. However, we should note the difference in the population compositionof income classes between the two scenarios: As Figure 5 illustrates, in the 0.5 case, the low- andhigh-income classes have the almost same population share after 2070, whereas in the no mobility
case, the population share of the low-income class with a lower labor productivity continues
toincrease. The difference in per-capita welfare level between the two cases, reflects the differencein the population structure of income classes.
4.4. Policy implications
Our simulation analysis indicates that a higher intergenerational mobility across income classes
generates favorable efficiency results, but in the very long run, it hinders economic growth becauseof a smaller total population. Hence, we offer this policy implication from a very long-term
perspective: A policy that enhances intergenerational earnings mobility should be fundamentally
implemented along with measures to reverse the falling birth rate.

6

Japan’s GDP in 2017 was calculated at 531.68 trillion yen by the Cabinet Office (2018), and the labor force
aged 20–64 years was 57.97 million people in 2017 (Ministry of Internal Affairs and Communications(2018b)). We calculated the real income per worker using these data and also derived the value for GDP in2017 in our model, yielding a conversion rate between actual amounts of yen and values in the model.
Consequently, unity in the model corresponds to 4.75917 million yen.

26

4.5 Comments
Because the simulation results depend on the model setting and the given parameters, we must be
careful about the effects of any parameter changes. The following two parameters are especiallycrucial. One is the difference in earnings ability between the low- and high-income classes. As theirlabor productivity gap increases, the labor efficiency effect, caused by changes in the population
ratio of workers with different earnings ability, becomes quantitatively greater. The second
parameter is the difference in the fertility rate between the two income classes. As this increases, thetotal population effect, induced by changes in the population ratio of households with different
fertility rates, becomes quantitatively larger. Therefore, a large labor productivity gap substantially
increases national income in the high intergenerational mobility scenario. Conversely, a large
fertility gap greatly enhances the total population effect in the no intergenerational mobility
scenario. Since the assignment of these important parameter values is crucial, our study assigned
realistic and plausible parameter values using the empirical data.
Next, we offer three challenging tasks for future research. First, our current simulation model
treats only the quantity aspect of children and ignores the quality aspect (see Becker and Lewis(1973) for the interaction between children quantity and quality). In reality, however, many
Japanese parents are interested in the quality of their children and thus eager for their children’s
education. In our model, the costs of raising children are a fixed part of the parent’s net lifetime
income for each of the two income classes, and thus, the absolute level of the expenditure forchildren is unrelated to child quality. Furthermore, since the net lifetime income for the low-income
class is lower than that for the high-income class, the expenditure level on their children is also
lower. Because our model assumes intergenerational mobility probabilities across income classes tobe exogenous, some children of low-income class parents can become university graduates with alower cost, whereas some children of the high-income class parents become just high school
graduates despite of a higher cost. Especially, in the case of randomly shuffled intergenerational
mobility, this setting may be slightly unrealistic.
Therefore, we will introduce parental educational investment into the model in a future paper,
under the assumption that education enhances individual human capital and the quality of children.
In other words, we will extend the model so that the individual human capital is an increasing
27

function of the education level provided by parents (and the government), which makes it more
realistic and plausible. Our current model has exogenous intergenerational mobility probabilities
between the low- and high-income classes. However, we will extend the simulation model toinclude endogenous mobility rates induced by the parent’s educational investment to their children.
Second, compared with other advanced countries, the public education level in Japan issubstantially low, and thus, private education plays a fairly important role. It is well known that the
average annual salary for parents of students at the University of Tokyo in Japan is substantiallyhigher than that for general people in their forties and fifties. (This also holds true for Harvard
University in the US.) Conversely, recently in Japan, contingent and part-time workers have been
increasing. For the poor in the lower economic strata, offering adequate education to their children
is difficult. To explore the possible countermeasures, we will analyze the quantitative effects of thepromotion of public education by the government. The promotion may help poor children gain acertain level of education and obtain a higher labor productivity, which will equalize the distributionof income and produce more favorable societal outcomes.
Third, although the longevity currently increases for almost all advanced countries, it remains
roughly unchanged for the US, mainly because of a short life expectancy for the poor. The National
Academies of Sciences/Engineering/Medicine (2015) noted that the gap in life expectancy between
rich and poor has recently increased in the US. Specifically, the life expectancy of male workers inthe bottom fifth quintile of lifetime earnings does not increase for a period of more than 30 years,
whereas for those in the top fifth quintile it substantially increased by more than 7 years. Therefore,in future research we will introduce the life expectancy gap between rich and poor, although thedata on the difference in life expectancy between university and high school graduates are notcurrently available in Japan, as far as we know.

5. Conclusions
Using an extended lifecycle general equilibrium model with endogenous fertility, this study
quantified the effects of changes in the intergenerational earnings mobility probability on the
demography and individual welfare during the period 2017–2300 in an aging and depopulating
Japan. Our simulation results indicate that a high intergenerational mobility across income classes
28

promotes economic growth, and from a long-term perspective, it potentially attains Pareto
improvements. In this sense, the promotion of intergenerational earnings mobility is desirable. In thevery long run, conversely, the promotion reduces economic growth. This is because the increased
mobility increases the population ratio of individuals with a higher earnings ability, which promotes
economic growth. Because of their relatively low fertility, however, an increase in their population
share gradually diminishes the total population. In the very long run, this negative effect exceeds the
positive effect induced by more workers with a higher labor productivity.
Conversely, the simulation results indicate that no intergenerational mobility across income
classes is relatively harmful to economic growth and from a long-term perspective the absence ofthe mobility deteriorates per-capita welfare. In this sense, policies which hinder intergenerational
earnings mobility are not desirable. This is because the no mobility case increases the population
ratio of individuals with a lower labor productivity, which reduce economic growth. In the very longrun, conversely, it enhances economic growth because they have a relatively high fertility and anincreased population share gradually increases the total population. In the very long run, thispositive effect exceeds the negative effect of increased workers with a lower labor productivity.

Appendix A: Model for the High-Income Class (University Graduates)
Here, we describe the household behavior of the high-income class household (i.e., university
graduates).

A.1 Household Behavior
Each agent enters the economy as a decision-making unit and starts to work at age 22 years, andlives to a maximum age of 105 years with uncertainty of death. The children aged 0–17 or 0–21
only consume, involving childrearing costs for their parent. The probability of a household born inyear t , surviving until s , can be expressed bys 1

pst (U )   q tj 1| j .

(1)’

j 22

Each agent who begins its economic life at age 22 chooses perfect-foresight consumption paths( Cst (U ) ), leisure paths ( lst (U ) ), and the number of born children ( nst (U ) ) to maximize a timeseparable utility function of the form:

29

U t (U )   

1
105
1
1 
1  (U ) 40 t (U )
( s 22 )t (U ) 1 
(U )t (U )
( s 22 )t (U )  t (U ) 1


p
(
1


)
n

(
1


)
p
(
1


)
C
l

 s
 s
s
s
s
1
s 22
s 22

1  







(2)’
where Cst (U ) , lst (U ) and nst (U ) are respectively consumption, leisure and the number of children tobear (only in the first 19 periods of the life) for an agent born in year t , of age s .  (U ) is theutility weight of the number of children relative to the consumption–leisure composite.
Letting Ast (U ) be capital holdings for the agent born in year t , of age s , maximization of
Equation (2)’ is subject to a lifetime budget constraint defined by the sequence:Ast (U1 )  {1  rt  s (1   r )} Ast (U )  (1   w   tp s ) wt  s es(U ) {1  lst (U )  tcst (U ) (nst (U ) )}  ast (U )  orst (U )ct (U )
 bst (U ) {1  lut (U )  tcut (nut (U ) )}uRE
 (1  m)(1   tc ) ts(U )  m(1   tc ) ts( H ) . (3)’22  (1   t ) Cs

There are no liquidity constraints, and thus the assets can be negative. An individual’s earnings(U )ability es

is an exogenous function of age.

The pension benefit is assumed to comprise only an earnings-related pension:t (U )sb

{1  lt (U )u tc (ntut (U )uREu  22)}H t (U ) {1  lut (U )  tcut (nut (U ) )}uRE 220 (s  ST ) ,( s  ST )

(4)’

where



 RE 1 21  w e {1  l

H t (U ) {1  lut (U )  tcut (nut (U ) )}uRE22 

RE

s 22

The average annual labor income for each agent is H

(U )t s st (U )

{1  lt (U )st (U )u tcst (nut (U ) )} .

(5)’



 tcut (nut (U ) )}uRE22 , and theweight coefficient of the part proportional to H t (U ) is  . The symbolbst (U ) {1  lut (U )  tcut (nut (U ) )}uRE 22

 in Equation (3)’ signifies that the amount of public pension

benefit is a function of the age profile of labor supply, {1  lut (U )

 tcut (nut (U ) )}uRE22 .

A parent is assumed to bear children and expend for them until they become independent of
their parent, namely, during the period when they are from zero to 21 years old. Here, note that thechildren aged below 22 years old do not conduct an economic activity independently, and only
childrearing cost for their parent arises until they become independent of their parent. The financial
costs for rearing the children when the parent born in year t is s years old are represented by
 ts(U ) and ts(H ) , which are the cost for the children who will become university graduates and highschool graduates, respectively:30 s t (U )t (U )( s  22, 23,, 40)   (1   )nkk 22
 40,
 ts(U )     t (U ) (1   )nkt (U ) ( s  41, 42, 43)k 22
 40 t (U )t (U )( s  44, 45,, 61)   (1   )nk
k s21( s  62, 63,, 105 ) ,ts(U )  0

(6)’

(7)’

 s t (U )t (U )( s  22, 23,, 39)   (1   )nk
k  22t (H ),
 s   40
t
(
U
)
t
(
U
)

  (1   )nk (s  40, 41,, 57)k  s 17(8)’

ts( H )  0(9)’( s  58, 59,, 105 ) , t (U )  NW t (U ) .

(10)’

The time cost for rearing the children when the parent born in year t is s years old isrepresented by

tcst  nst (U ) .

(11)’

(U )

is the sum of bequests inherited by the high income class households at time t ,When BQt

the bequest to be inherited by each highast (U ) (1   ) BQ
Et(Us)(U )where Et

h

(U )
ts

income class household is defined by

,

(12)’

is the number of the high income class households conducting an economic activity

independently, aged 22 and above, and105

BQt(U )   ( N st s1(U ))  N st 1s1(U ) ) Ast 1s1(U ) .

(13)’

s 22

The number of the generation born in year t , of age s , is represented by

N st (U )  pst (U ) N 0t (U ) .

(14)’

When ORt(U ) is the sum of childrearing costs incurred by the high income class households attime t , the childrearing cost for orphans for each high income class household is defined byorst (U ) 

ORt(Us),
Et(Us)

(15)’

where

31

61

57

s 22

s 22

ORt(U )  (1  m)  ( N st 1s (U )  N st s (U ) ) tss (U )  m  ( N st 1s (U )  N st s (U ) ) tss ( H ) .

(16)’

When we consider the utility maximization problem over time for each agent, besides the flow
budget constraint represented by Equation (3)’, the following constraint is imposed:t (U )tt (U )
 0  ls  1  tcs (ns ) (22  s  RE ).
 t (U )( RE  1  s  105 ) ls  1(17)’

Each individual maximizes Equation (2)’ subject to Equations (3)’ and (17)’ (see Appendix C
for further details). From the utility maximization problem, the equation expressing the evolution of
the number of children over time for each individual is characterized byt (U )sW pst (U1 )  
 t (U )1 ,  t (U )  Wr  s 1
p
1

r
(
1


)
t s
 s 

Wst (U ) (1  

(U )

1

k

(18)’

1



t (U )
s

(n



)

1



17


) (1  m) ts , g t (U ) (1   )  m ts , g t (U ) (1   )
g 0
g 0


21

c
t s

,

(19)’

1

where ts,0

=1 for g  0 , 

t
s, g

 g

  {1  rt  s1k (1   r )} .
 k 1


Similarly, that for the consumption–leisure composite is represented by p t (U )  
 t (U )1 ,
Vst (U )   st (U1 )  Vr  s 1
 ps  1  rt  s (1   ) t (U )
s

V







(20)’

1

(1   (U ) ) (Cst (U ) ) (lst (U ) )1   (Cst (U ) ) 1 (lst (U ) )1.
1   tc

(21)’

Appendix B: The Utility Maximization Problem for the Low-Income Class
The utility maximization problem over time for each low-income class household in Section 2 isregarded as the maximization of U t ( H ) in Equation (2) subject to Equations (3) and (17). Let theLagrange function be

105

Lt ( H )  U t ( H )   ts( H )  Ast ( H1 )  {1  rt  s (1   r )} Ast ( H )  [1   w   tp s ] wt  s es( H ) {1  lst ( H )  tcst (nst ( H ) )}  ast ( H )
s 18





 orst ( H )  bst ( H ) {1  lut ( H )  tcut (nut ( H ) )}uRE20  (1   tcs ) Cst ( H )  (1  m)(1   tcs )ts( H )  m(1   tcs )ts(U )
32





RE



  st ( H ) 1  lst ( H )  tcst (nst ( H ) ) ,

(B1)

s 18

where ts( H ) and  st (H ) represent the Lagrange multiplier for Equations (3) and (17), respectively.
The first-order conditions on the number of children nst ( H ) , consumption Cst ( H ) , leisure lst ( H ) ,and assets Ast ( 1H ) for s =18, 19, …, 105 can be expressed bypt (H )s(H )(1   )( s 18)t (H )
s

(n



)

1



17

 ts( H ) [1   w   tps ] wt s es( H )  (1  m)(1   tc ) ts , g t ( H ) (1   )
g 0


21
105

w e ( H ) m(1   tc ) ts , g  t ( H ) (1   )    tk( H ) t  s s  st ( H ) ,RE  19g 0
k  ST(B2)

1

where ts,0

=1 for g =0, 

t
s, g

 g

  {1  rt  s1k (1   r )} , k 1  (C (1   )(C

pst ( H ) (1   ( H ) )(1   ) ( s18) (Cst ( H ) ) (lst ( H ) )1pst ( H ) (1   ( H ) )(1   ) ( s18) (Cst ( H ) ) (lst ( H ) )1





105

 ts( H ) (1   w   tp s ) wt  s es( H )   tk( H )k  ST



1





1



wt  s es( H )RE  19t ( H )  1s

) (lst ( H ) )1  ts( H ) (1   tcs ) , (B3)t (H ) s  st ( H )) (lst ( H ) ) 

( s  RE ) ,ts( H )  {1  rt  s (1   r )}ts(H1 ) ,st ( H ){1  lst ( H )  tcst (nst ( H ) )}  0
1  lst ( H )  0

(B4)
(B5)

( s  RE ) ,( s  RE ) ,

(B6)
(B7)

 st ( H )  0 .

(B8)

The combination of Equations (B2) and (B5) produces Equations (18) and (19). If the initial value,

n18t ( H ) , is given, the initial value, W18t ( H ) , can be derived from Equation (19). If the value, W18t ( H ) , isspecified, the value of each age, Wst ( H ) , can be derived from Equation (18), which generates thevalue of each age, nst ( H ) . If the value, nst ( H ) , is specified, the child rearing cost for lifetime iscalculated, which gives the lifetime budget constraint represented by Equation (B10).
The combination of Equations (B3) and (B5) produces Equations (20) and (21). If the initialvalue, V18t ( H ) , is specified, the value of each age, Vst ( H ) , can be derived from Equation (20). Ift (H )Vst ( H ) is specified, the values of consumption, Cst ( H ) , and leisure, ls , at each age are obtainedin the method that follows.

33

For s =18, 19, …, RE, the combination of Equations (B3) and (B4) yields the following
expression:105 
tk( H ) wt  s es( H )  st ( H )  
w
p
(H )

(
1




)
w
e



 t ( H ) RE  20  t ( H )  
t s
ts s
k  ST st (H )s  lt (H ) .

Cs 
c

 s
(1   ) (1   t  s )





(B9)

If the value of lst ( H ) is given under  st ( H ) =0, the value of Cst ( H ) can be obtained using a
numerical method, and then the value of Vst ( H ) can be derived from Equation (21). The value oflst ( H ) is chosen so that the value of Vst ( H ) obtained in the simulation is the closest to that

calculated by evolution from V18t ( H ) through Equation (20). If the value of lst ( H ) chosen is unity or
higher, the value of Cst ( H ) is obtained from Equation (21) under lst ( H ) =1. If it is less than unity, thevalue of Cst ( H ) is derived from Equation (B9).
For s =RE+1, RE+2, …, 105, the condition of lst ( H ) =1 leads to the following equation:(1  

Vst ( H ) ) (C )
1   tc s(H )t (H )s  1.

(21)’’The value of Cst ( H ) is chosen to satisfy this equation.
t (H )

From Equation (3) and the terminal condition A18t (H )= A106 =0, the lifetime budget constraint

for an individual (= NW t ( H ) ) is derived:
RE



105



105

 st ( H ) [1   w   tps ]wtses( H ){1  lst ( H )  tcst (nst ( H ) )}   st ( H )bst ( H ) {1  lut ( H )  tcut (nut ( H ) )}uRE20   st ( H ) (ast ( H )  orst ( H ) )s 18s  ST

105

35

s 18

s

40

s

  st ( H ) (1   tc s )Cst ( H )  (1  m)  st ( H ) (1   tc s ) t ( H ) (1   )nkt ( H )  (1  m)   st ( H ) (1   tc s ) t ( H ) (1   )nkt ( H )s 18s 18 k 1857

s 36 k  s 17

40

39

s

 (1  m)   st ( H ) (1   tc s ) t ( H ) (1   )nkt ( H )  m   st ( H ) (1   tc s ) t ( H ) (1   )nkt ( H )s 41 k  s 1761

s 18 k 1840

 m   st ( H ) (1   tc s ) t ( H ) (1   )nkt ( H ) ,(B10)s  40 k  s  21

where t(H )18

=1 for s =18, 

t(H )
s

 s

  {1  rt u (1   r )}
 u 19


34

1

for s =19, 20, …, 105.

Appendix C: The Utility Maximization Problem for the High-Income Class
The utility maximization problem over time for each high-income class household in Appendix A isregarded as the maximization of U t (U ) in Equation (2)’ subject to Equations (3)’ and (17)’. Let theLagrange function be

105

Lt (U )  U t (U )   ts(U )  Ast (U1 )  {1  rt  s (1   r )} Ast (U )  [1   w   tp s ] wt  s es(U ) {1  lst (U )  tcst (nst (U ) )}  ast (U )
s 22





c
t (U )
 orst (U )  bst (U ) {1  lut (U )  tcut (nut (U ) )}uRE
 (1  m)(1   tc )ts(U )  m(1   tc )ts( H ) 22  (1   t  s ) Cs



RE



  st (U ) 1  lst (U )  tcst (nst (U ) ) ,

(C1)

s 22

where ts(U ) and  st (U ) represent the Lagrange multiplier for Equations (3)’ and (17)’,
respectively.
t (U )

The first-order conditions on the number of children nst (U ) , consumption Cst (U ) , leisure ls,

and assets Ast (U1 ) for s =22, 23, …, 105 can be expressed by121
pst (U ) (U ) (1   ) ( s22) (nst (U ) )   ts(U ) [1   w   tps ] wt s es(U )  (1  m)(1   tc ) ts , g t (U ) (1   )
g 0


17

 m(1   )  
c
t

g 0

t
s, g

t (U )(U )105
t (U ) wt  s es
(1   )    k
 st (U ) ,RE  21k  ST(C2)

1

where ts,0

=1 for g =0, 

t
s, g

 g

  {1  rt  s1k (1   r )} , k 1  (C (1   )(C

pst (U ) (1   (U ) )(1   )( s 22) (Cst (U ) ) (lst (U ) )1pst (U ) (1   (U ) )(1   )( s 22) (Cst (U ) ) (lst (U ) )1





105

 ts(U ) (1   w   tp s ) wt  s es(U )   tk(U )k  ST

1  lst (U )  0



1



wt  s es(U )RE  21

ts(U )  {1  rt  s (1   r )}ts(U1 ) , st (U ) {1  lst (U )  tcst (nst (U ) )}  01

t (U )  1s

) (lst (U ) )1  ts (1   tc s ) ,(C3)t (U ) s  st (U )) (lst (U ) )
( s  RE ) ,

(C4)
(C5)

( s  RE ) ,( s  RE ) ,

(C6)
(C7)

 st (U )  0 .

(C8)

The combination of Equations (C2) and (C5) produces Equations (18)’ and (19)’. If the initial value,35t (U ), is given, the initial value, W22t (U ) , can be derived from Equation (19)’. If the value, W22t (U ) , isn22

specified, the value of each age, Wst (U ) , can be derived from Equation (18)’, which generates thevalue of each age, nst (U ) . If the value, nst (U ) , is specified, the child rearing cost for lifetime iscalculated, which gives the lifetime budget constraint represented by Equation (C10).
The combination of Equations (C3) and (C5) produces Equations (20)’ and (21)’. If the initialvalue, V22t (U ) , is specified, the value of each age, Vst (U ) , can be derived from equation (20)’. Ift (U )Vst (U ) is specified, the values of consumption, Cst (U ) , and leisure, ls, at each age are obtainedin the method that follows.
For s =22, 23, …, RE, the combination of Equations (C3) and (C4) yields the following
expression:105 
tk(U ) wt  s es(U )  st (U )  
w
p
(U )

(
1




)
w
e



 t (U ) RE  21  t (U )  tst s sk  ST st (U )s  l t (U ) .

Cs 
c

 s
(1   ) (1   t  s )t (U )

If the value of ls(C9)is given under  st  0 , the value of Cst (U ) can be obtained using a numericalt (U )

method, and then the value of Vst (U ) can be derived from Equation (21)’. The value of ls

ischosen so that the value of Vst (U ) obtained in the simulation is the closest to that calculated byevolution from V22t (U ) through Equation (20)’. If the value of lst (U ) chosen is unity or higher, thevalue of Cst (U ) is obtained from Equation (21)’ under lst (U ) =1. If it is less than unity, the value of

Cst (U ) is derived from Equation (C9).
For s =RE+1, RE+2, …, 105, the condition of lst (U ) =1 leads to the following equation:

Vst (U ) (1  

) (C
1

(U )

t (U )
s
c
ts




  1)(21)’’’The value of Cst (U ) is chosen to satisfy this equation.
t (U )t (U )
From Equation (3)’ and the terminal condition A22= A106=0, the lifetime budget constraint

for an individual (= NW t (U ) ) is derived:
RE

105





105

 st (U ) [1   w   tp s ]wt  s es(U ) {1  lst (U )  tcst (nst (U ) )}   st (U )bst (U ) {1  lut (U )  tcut (nut (U ) )}uRE22   st (U ) (ast (U )  orst (U ) )s  22s  ST105

40ss  22s  22 k  22s  224340

  st (U ) (1   tc s )C st (U )  (1  m)   st (U ) (1   tc s ) t (U ) (1   )nkt (U )  (1  m)   st (U ) (1   tc s ) t (U ) (1   )nkt (U )s  41k  22

36

61

40

39

s

 (1  m)   st (U ) (1   tc s ) t (U ) (1   )nkt (U )  m   st (U ) (1   tc s ) t (U ) (1   )nkt (U )s  44 k  s  2157

s  22 k  2240

 m   st (U ) (1   tc s ) t (U ) (1   )nkt (U ) ,(C10)s 40 k  s 17

where t (U )
22=1 for s =22, t (U )s s  {1  rt u (1   r )}
 u 231for s =23, 24, …, 105.

Conflict of Interest: The author has received research grants from the Ministry of Education,
Culture, Sports, Science and Technology in Japan (Grant-in-Aid for Scientific Research (C)No. 20K01679). However, the author declare that he has no conflict of interest.

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Hayashi, F. and Prescott, E. C. (2002) “The 1990s in Japan: A Lost Decade,” Review of Economic
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Research 17 (2), 163-185.
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Data
Cabinet Office (2010) “The Questionnaire Survey through the Internet for the Child-rearing Cost,”
Cabinet Office Director-general for Policies on Cohesive Society, Japan (in Japanese).
https://www8.cao.go.jp/shoushi/shoushika/research/cyousa21/net_hiyo/mokuji_pdf.html.
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https://www.esri.cao.go.jp/jp/sna/menu.html.
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Sensasu),” https://www.e-stat.go.jp/ (in Japanese).
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https://www.mhlw.go.jp/toukei/saikin/hw/k-tyosa/k-tyosa19/index.html (in Japanese).
Ministry of Internal Affairs and Communications (2018a) “Estimation of the Population (As of 1st Oct2017),” http://www.stat.go.jp/data/jinsui/2017np/index.htm (in Japanese).
Ministry of Internal Affairs and Communications (2018b) “Labour force and labour force participation
rate by age group: Whole Japan,” http://www.stat.go.jp/data/roudou/longtime/03roudou.htm (inJapanese).
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2016–2115 (Estimation in April, 2017), Japan (in Japanese).
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39

Table 1 Exogenous variables for the benchmark simulation
Parameter description

Parameter value

Data source  0.5

Nishiyama & Smetters (2005):

Share parameter for consumption

Weight parameter of the number of children to theconsumption–leisure composite in utility(H )  0.47

 0.04151

 (U )  0.03203

  0.0001

Oguro et al. (2011):   0.01

Intertemporal substitution elasticity

  0.5

Imrohoroglu et al. (2017)

Ratio of government subsidies to childrearing costs  0.1

Oguro et al. (2011):   0.1

Ratio of childrearing costs to net lifetime income  0.0385

Time cost for childrearing  1.7234

Capital share in production  0.3794

Imrohoroglu et al. (2017)

Depreciation rate k  0.0821

Imrohoroglu et al. (2017)

Tax rate on labor income w  0.065

Kato (1998):  w  0.065

Tax rate on capital income r  0.4

 r  0.48 ; Imrohoroglu et al.
(2017):  r  0.35

Tax rate on inheritance h  0.1

Kato (1998)

Ratio of government expenditures to national
incomeRatio of the part financed by tax transfer to total
pension benefitg  0.1

Rate of time preference

Hayashi & Prescott (2002):

  0.25

Oguro & Takahata (2013)

Replacement ratio for public pension benefits  0.4

Braun et al. (2009)

Ratio of net public debt to national incomed  1.3

Imrohoroglu et al. (2017)

Compulsory retirement age

RE  64

Starting age for receiving public pension benefits

ST  65

Ratio of people aged 21 and above to the total
population

E / Z  0.82952

Dependency ratio (i.e., aging rate)

O / Z  0.27742

40

Table 2 Endogenous variables in the 2017 initial steady stateParameter description

Parameter value

Interest rate, r

0.0754

Wage rate, w

1.0624

Tax rate on consumption, Contribution rate, 

0.1168c0.1305p2.4096

Capital–income ratio, K / Y

1.4300Total fertility rate (TFR)(low-income class 1.59; high-income class 1.27)

Ratio of net childrearing costs to annual labor income

0.2246 (low-income class)0.1785 (high-income class)0.01300

Ratio of government childcare subsidies to national income, GS / Y

Table 3 Population ratios among people with different educational backgrounds
Population (thousands)

Population share (%)

Junior high school graduates675.03High school graduates

9,665.36

2.97Share (%)
45.51
42.54

Technical and junior college

4,281.24

18.84

graduates
University
graduates

8,100.33

35.65

Total (in year 2017)

22,721.96

Source: The Ministry of Health, Labour and Welfare (2018)

41

54.49
100
100

Table 4 Scheduled number of children for young people
Number of children
Young female non-university

1.32

graduates
Young male non-university graduates

0.96

Young female university graduates

0.91

Young male university graduates

0.84

Average

1.14

0.875

Source: Kikkawa (2018)
Note: The word “young” denotes the people aged 21 to 40.

Table 5 Welfare gains/losses for each individual for two simulation cases based onintergenerational income class mobility
Intergenerational income classWelfare gains ormobility

losses0.5

0.04518435

215.040−0.06187086−294.45

Equivalent in yen (thousand)Note: The welfare gains/losses for each individual are calculated for changes from the benchmark case (i.e.,
0.3 intergenerational income class mobility).

42

Figure 1

Intergenerational earnings mobility and inequality

Intergenerational Earnings Elasticity

Source: Corak (2016)
Notes: The vertical axis is the intergenerational elasticity between father and son earnings. The Gini
coefficient is obtained from the World Bank. Data points for Italy and the United Kingdom overlap. The
upward sloping line is the least squares fitted regression line.

Figure 2

Intergenerational elasticity between father and son earnings

Source: Corak (2016)43

Figure 3

Age–population distribution in the 2017 initial steady state
Population (thousands)
2,200
2,000
1,800
1,600

1,400
1,200
1,000
800
600
400

Total population

200

University graduates

Year

0
0

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105

Source: The Ministry of Internal Affairs and Communications (2018a).
Notes: The vertical gap between the total population and the number of university graduates is the number ofhigh school graduates for each age. For young people unsure if they will be (just)high school graduates oruniversity graduates, we assume 50/50.

Figure 4

Age earnings profiles based on educational backgroundMonthly earnings in yen (thousand)
650
600

550
500
450
400
350
300

250

Junior high school graduates
High school graduates

200
150

Technical and junior college graduates

University graduates

Age

100

16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64

Source: The profiles are estimated from the Ministry of Health, Labour and Welfare (2009–2018).

44

Figure 5

Transition of population for each income class: Three cases of different
intergenerational income class mobility (0, 0.3, 0.5)
Population (millions)80
Low income class: mobility 0

70High income class: mobility 0
Low income class: mobility 0.3

60High income class: mobility 0.3
Low income class: mobility 0.5

50High income class: mobility 0.5

40

30

20

10

0
2017

Figure 6

Year
2032

2047

2062

2077

2092

2107

2122

2137

2152

2167

2182

2197

Transition of the total population: Two cases of different intergenerational
income class mobility (0, 0.5)45Figure 7

Transition of national income: Two cases of different intergenerational
income class mobility (0, 0.5)

Figure 8

Transition of capital stock: Two cases of different intergenerational income
class mobility (0, 0.5)46

Figure 9

Figure 10

Transition of labor supply: Two cases of different intergenerational income
class mobility (0, 0.5)

Transition of interest rates: Two cases of different intergenerational
income class mobility (0, 0.5)47

Figure 11

Transition of wage rates: Two cases of different intergenerational income
class mobility (0, 0.5)

Figure 12

Transition of consumption tax rates: Two cases of different
intergenerational income class mobility (0, 0.5)48

Figure 13

Transition of contribution rates: Two cases of different intergenerational
income class mobility (0, 0.5)49