Discussion Paper 2020 E003-

DISCUSSION PAPER SERIESOsaka University Graduate School of Medicine
Department of Health Economics and Management

The Impact of Population Aging on Japan in a Multisector Dynamic General Equilibrium Model

Ryuta Ray Kato

OHEM Secretariat
Graduate School of Medicine Department of Health Economics and Management
OSAKA UNIVERSITY
1-7 Yamadaoka, Suita, Osaka, 565-0871, Japan

The Impact of Population Aging on Japan in a
Multi-sector Dynamic General Equilibrium Model ∗Ryuta Ray Kato†

April 2020

Abstract
This paper tries to expand a static computable general equilibrium (CGE) modelin a dynamic context, and it explores the dynamic impact of population aging on
the Japanese economy with multi-production sectors and overlapping generations. In
particular, aging-related sectors such as the pharmaceutial industry, the medical services, the social insurance and welare, and the long-term care insurance sectors are
considered within the combined model of independently developed static and dynamic
CGE models, and demand for these sectors are estimated to increase by 12.25 percent,19.78 percent, 21.66 percent, and 18.76 percent from year 2020 in a graying Japan,
respectively. Such an increase in demand for their products induces a more labor input
in these sectors, and labor force in the long-term care insurance sector is particularly
expected to smoothly increase from 334 million in year 2018 to 369.21 million in year2034 to fulﬁl the increasing demand for long-term care insurance services.

Keywords: Aging, Japan, Long-term Care Insurance, CGE model
JEL Classiﬁcation: C68, H51, E62, H55, and J16∗
Grant-in-Aid for Scientiﬁc Research by Japan Society for the Promotion of Science (No. 19K01704) andthe research fund by Japan Securities Scholarship Foundation are both acknowledged.
†
Graduate School of Governance Studies, Meiji University, 1-1 Kanda-Surugadai, Chiyoda-ku, Tokyo,
101-8301, Japan (email: raykato@meiji.ac.jp).

11

Introduction

This paper tries to expand a static computable general equilibrium model in a dynamic
context, and it explores the dynamic impact of population aging on the Japanese economy
with multi-production sectors and overlapping generations.
Since Ballard et al (1985) examined the impact of tax reforms on several production
sectors within a static computable general equilibrium (static CGE ) model, the static CGE
model has been applied in several diﬀerent research ﬁelds1 . Auerbach and Kotlikoﬀ (1982
and 1987) numerically investigated the impact of tax reforms with multi-overlapping generations in a dynamic general equilibrium model, which has now been recognized as a dynamic
computable general equilibrium (dynamic CGE) model. Since the research concern of thestatic CGE model was with the impact of policy changes on several diﬀerent production
sectors, it cannot analyze the impact of changes in the population structure dynamically.
On the other hand, a dynamic CGE model was developed to study the dynamic impact ofpolicy reforms over time, and utility is deﬁned over consumption of a single good in diﬀerent
periods over time. Thus, the conventional Auerbach and Kotlikoﬀ model cannot investigate
the impact on diﬀerent production sectors in each time. In reality, each household makes asimultaneous decision over consumption of diﬀerent goods in each time as well as savings overtime. The former decision can be considered in a static CGE model, and the latter decision
can be analyzed in a dynamic CGE model. In order to explore the eﬀect of population aging
on diﬀerent production sectors over time, this paper tries to integrate two independently developed computable general equilibrium models in order to overcome disadvantages of eachmodel2 .
Preference over goods depends on age, and the future change in the demographic structure
1

The GTAP model is considered as one of applied models to the internatinal economy. Naqvi and (1995),
Peter et al (1996), and Adams et al (2000) are also applied models of the static CGE model. Hamamoto and
Nakatani (2007) studied the impact of government expenditures with the Japanese IO table in the context
of population aging of Japan.
2Peter et al (1996) and Adams (2000) can be considered as the integrated models of the static and dynamic
CGE models, but the dynamic optimization behavior has not been considered in their models. Kimura andHashimoto (2010) explored ﬁscal consolidation of Japan in an integrated model.

1induces the diﬀerent impact on demand for goods. This implies that each production sector
will be aﬀected diﬀerently according to population aging. This paper explores the diﬀerent
impact of population aging on each production sector over time. Population aging seems tohave relatively stronger impacts on aging-related production sectors. This paper particularly
focuses on the dynamic impact of population aging on aging-related 5 production sectors;
the pharmaceutical industry, the medical services, the public hygiene, the social insurance& welfare, and the long-term care insurance services sectors. In addition to these 5 agingrelated production sectors, 10 other production sectors are considered. The Input-Output(IO) Table of year 2011 with 190 diﬀerent production sectors is used to construct a social
accounting matrix (SAM) with 15 diﬀerent ﬁnal consumption goods, over which preference
is deﬁned. Re-categorization of the original IO Table with 190 diﬀerent production sectors
to 15 production sectors was made consistent to the data of Family Income and Expenditure
Survey (Kakei Chosa), which provides the information on age speciﬁc consumption patternsof diﬀerent cohorts. In the static part of the model, 15 diﬀerent proﬁt maximizing production
sectors exist each time, and preference of the household over these 15 diﬀerent ﬁnal domestic
goods is deﬁned.
In the dynamic part of the model, in addition to the statically optimal behavior of thehousehold to maximize its utility over the 15 diﬀerent ﬁnal consumption goods, the household
is also assumed to dynamically maximize its lifetime utility, which is deﬁned over composite
goods over time. The composite goods consist of the 15 diﬀerent ﬁnal consumption goods
each time.
A realistic demographic structure is considered over time. Until year 2015, the actual
demographic structure is used. From year 2016, the latest population projection of year2017 by the National Institute of Population and Social Security Research (IPSS) is used. In
the latest population projection, the total population is expected to shrink to less than 60
million in the next 100 years. Reﬂecting rapid as well as high population aging, the futureenvironment for aging-related sectors will change substantially in a graying Japan.
2Regarding the scenarios of the future economic policies, the assumptions in the latest
version of Economic and Fiscal Projections for Medium to Long-term Analysis (EFPMLA:
January 2020) are considered as much as possible to specify the future economy. EFPMLA(2020) numerically embodies the so-called growth strategy, the main policy of Abenomics,
and the actual policy scenarios for several key indicators such as the future GDP, government
deﬁcits and the primary balance are taken into account.
Since Braun and Joines (2015) examined public medical beneﬁts in a graying Japan
within the Auerbach and Kotlikoﬀ (1987) model, ﬁscal sustainability of the public pension,
the national medical services, and the long-term care insurance schemes in an aging Japan
has been explored within the numerical dynamic model in the literature (Kitao (2015a),
Kitao (2015b), Hansen and İmrohoroğlu (2016), İmrohoroğlu et al (2016), Kitao (2017),
Kato (2018), and İmrohoroğlu et al (2019)). While it has commonly been argued in theliterature that population aging of Japan will substantially leave ﬁnancial burdens on theseschemes if the current schemes remain unchanged, the dynamic impact of population agingof Japan on diﬀerent production sectors has not been discussed yet. The main purpose ofthis paper is to study the dynamic impact of population aging on diﬀerent production sectors
over time, by integrating independently developed static and dynamic CGE models.
Several numerical results are obtained as follows: First, population aging indeed stimulates demand for products of aging-related sectors. Compared to the demand in year 2020
with their highest value, or their peak value, demand for the pharmaceutical product, themedical services, the public hygiene services, the social insurance & welfare services, and thelong-term care insurance services will increase by 12.25 %, 19.78 %, 18.93 %, 21.66 %, and18.76 % from year 2020, respectively. The corresponding highest demand levels at their peakare 10,797.08 billion yen, 56,213.90 billion yen, 1,874.34 billion, 10,529.46 billion yen, and10,727.07 billion yen, respectively. Second, while demand for the product of the pharmaceutical sector becomes highest in year 2040, demand for other 4 sectors becomes highest in year
2046. Third, an expansion of demand for these aging-related products induces more demand3for labor in these sectors. In particular, while the combined labor force of both of the social
insurance & welfare and the long-term care insurance services sectors is 431 million in year
2020, it will increase to 467.6 million in year 2034. Finally, based on the estimate of labor
force of the long-term care insurance sector in year 2018 by the Ministry of Health, Laborand Welfare (MHLW; 2018), labor force of the long-term care insurance sector is estimatedto increase to 369.21 million at its peak in year 2034. Since the estimate of labor force of thelong-term care insurance sector in year 2018 by the MHLW (2018) is 334 million workers, it
should increase by 10.5 % from year 2018 to year 2034 in order to sustain the long-term careinsurance sector in a graying Japan. These numerical results indicate that labor mobility inthe labor market should be smooth enough without friction to cope with an expansion ofdemand for products of aging-related sectors.
This paper is organized as follows. The next section introduces the model in detail.
Section 3 explains assumptions about the future economy with the benchmark result, andSection 4 presents numerical results in detail. Section 5 concludes the paper.

2

The Model

2.1

Demographic Structure

An overlapping generations economy in discrete time with a model period of one year is
considered. Households are homogenous within the same cohort, and the representative
household in each cohort is considered. The representative household appears in the economy at age 20 as a decision maker. Although the household faces uncertainty regarding its
death in each period, it dies with certainty at the end of its age of 99 if it is alive until age
99. It is assumed that there is no uncertainty regarding the size of the total population ins∏each period. Denote the survival rate of cohort g by Ps,g , and it is deﬁned by Ps,g =qi,g ,
i=1

where qj+1,g is the conditional survival rate of a j years old household which survives to j +1
years old of cohort g. Ps,g is calculated based on the actual and projected population data.
4

Due to uncertainty of lifetime in each period, accidental/unintended bequests generated bydeath of all cohorts exist in each period, and such bequests are distributed to the surviving household in a particular age. Denote the pre-taxed amount of accidental/unintended
bequests inherited in age s at time t by bqs,t , and each cohort receives the net bequests
denoted by (1 − τq,t ) bqs,t once in its life, where τq,t is the inheritance tax rate at time t. No
bequest motives are assumed so that the representative household of each cohort enters an
economy with no assets. No liquidity constraint is imposed. The age-speciﬁc fertility andmortality rates are time variant, both of which are calculated based on the actual past data
and the projection of year 2017 by the IPSS. This implies each cohort has diﬀerent fertility
and mortality rates over time, and Ps,g diﬀers among diﬀerent cohorts.

2.2

The Representative Household

The representative household in each cohort is forward-looking, and future events aﬀect
decisions made today. The representative household faces lifetime uncertainty in each period,
but there is no other uncertainty such as an income shock through its lifetime3 .
In reality, each household makes a simultaneous decision over consumption of diﬀerent
goods in each time as well as savings over time. This paper considers such simultaneous decision making in the following nested model. At the ﬁrst stage, the representative household
maximizes its expected lifetime utility with respect to its consumption of a composite goodand leisure time over time4 . Then, at the second stage, the representative household divides
its consumption of a composite good into diﬀerent domestic consumption goods in order tomaximize its utility deﬁned over diﬀerent domestic goods in each time.
First Stage5 :3

If there is also uncertantiy in lifetime wage income, then precautionary savings motives exist. Thus, withthe assumption of no income shocks, the magnitude of the impact of any policy change on savings, thus on
the capital labor ratio, will be smaller. However, qualitative results should not be aﬀected. On this aspect,see Kitao (2015a), and Kitao (2015b).
4This composite good can be interpretted as GDP minus exports plus the amount used for the intermediate
production process in a national account.
5
The dynamic part of this paper uses the basically similar model to Kato (2018).

5

At the ﬁrst stage, the representative household is assumed to maximize its expected
lifetime utility with respect to consumption of composite goods and leisure time. The household’s expected lifetime utility of cohort g, denoted by E [Vg ], is given by
E [Vg ] =

99
∑

1−ρ
−(s−20) u (cs,t , ls,t )Ps,g (1 + δ)

s=20

1−ρ

,

(1)

where ρ is a reciprocal of the elasticity of substitution between consumption at the diﬀerent
time. δ is the time preference. cs,t and ls,t are consumption of a composite good and leisureof a s years old household at time t, respectively. The deﬁnition of a composite good is given
by:

)
( 1
2
15
,
, Xs,t, · · · , Xs,t
cs,t = cs,t Xs,tiwhere Xs,t(i = 1, 2, · · · , 15) denotes 15 diﬀerent ﬁnal consumption goods produced in 15

diﬀerent production sectors at time t. The list of 15 diﬀerent ﬁnal consumption goods is
given in Table 1. Note that there is a relationship of t = g + s. The felicity function of u isgiven by:

ξ
[ ξ−1
] ξ−1
ξ−1
ξ
ξ
u (cs,t , ls,t ) = cs,t + κls,t,(2)

where ξ denotes the elasticity of substitution between consumption and leisure, and κ denotes
the weight parameter for leisure.
The budget constraint of the representative household is:
as+1,t+1 = [1 + (1 − τr,t ) rt ] as,t + (1 − τw,t − τp,t − τe,s,t ) es (1 − ls,t ) wt
+ (1 − τw,t ) bs,t + (1 − τq,t ) bqs,t − (1 + τc,t ) cs,t − ICs,t − θt LTs,t ,(3)where as,t is the amount of assets held by a s years old household at the beginning of timet. es is the measure of eﬃciency of labor of the household, and es is the eﬃciency measure.
Labor eﬃciency is obtained from the data6 .
6Basic Survey of Wage Structure (BSWS) of year 2011 and Labor Force Survey (LFS) of year 2012 are

6τr,t , τw,t , τp,t ,and τc,t are the interest income tax rate, the wage income tax rate, the public
pension contribution rate, and the consumption tax rate, respectively. τe,s,t is the contribution rate to the long-term care insurance (LTCI), which is applied to the representative
household while it is working in age s at time t7 . After retirement, the representative household still has to contribute to the LTCI. The ﬁxed amount of contributions is denoted byICs,t in age s at time t. Note that an individual starts to contribute to the LTCI once she
becomes age 40 in Japan. Between age 40 and 64, all individuals belong to the second group(age group between 40 and 64), and the amount of their contributions depends on theirearnings. Their contribution rate is given by τe,s,t . Once an individual becomes age 65, thenshe is transferred to the ﬁrst group (age group of 65 and over), in which she still has tocontribute to the LTCI, but the amount of contributions is ﬁxed by ICs,t . This paper takes
into account such a realistic aspect of the LTCI, and the contribution rate for the second
group (age group between 40 and 64) and the ﬁxed amount of contributions for the ﬁrst
group (age group of 65 and over) are both calculated based on A Summary of the Long-term
Care Insurance by the Ministry of Health, Labor and Welfare (MHLW; 2017). LTs,t is thetotal cost of obtaining services through the LTCI, and the θt is the co-payment rate at timet. LTs,t is calculated based on Survey of Long-term Care Beneﬁt Expenditure (SLCBE) ofyear 2014, and LTs,t is assumed to be age-dependent, but time invariant. θt is assumed tobe 0.1 to reﬂect the current rate.
bs,t is the amount of public pension beneﬁts in age s at time t8 . wt and rt are the wage
rate per the eﬃciency unit and the interest rate, respectively. Public pension beneﬁts are
given by)}{ (ϵt Ht + H t ; s ≥ RH,
bt =0; s, < RH

(4)

both used to specify the eﬃciency proﬁle of each worker over time.
7
Precisely speaking, although the retirement age is assumed to be ﬁxed at age 65, the positive rate of
τe,s,t is applied up to age 64, and it becomes zero when the representative household becomes age 65. Whenthe household becomes age 65, it starts paying the ﬁxed amount of contributions.
8
For more detailed studies on the public pension beneﬁts, see, for instance, Yamada (2011) andİmrohoroğlu et al (2016).

7

where RH is the retirement age of 65, and ﬁxed through this paper. This implies thatthe representative household optimally chooses labor supply in intensive margin but not in
extensive margin9 . Public pension beneﬁts are taxed to reﬂect reality. ϵt is the replacement
rate10 . H t and Ht denote the ﬁxed amount of basic pension beneﬁts and earning related
beneﬁts, respectively, and Ht is given by:
1 ∑wt es (1 − ls,t ) .
Ht =RH s=20RH

It is assumed that the representative household maximizes (1) with respect to cs,t andls,t subject to (3), and the ﬁrst order conditions yield the following optimal equations:u′ (cs,t , ls,t ) u (cs,t , ls,t )−ρ =qs+1,g [1 + (1 − τr,t+1 ) rt+1 ] 1 + τc,t1+δ
1 + τc,t+1

× u′ (cs+1,t+1 , ls+1,t+1 ) u (cs+1,t+1 , ls+1,t+1 )−ρ ,[]ξκ (1 + τc,t )ls,t =
cs,t ,(1 − τw,t − τp,t − τe,s,t ) wt es

(5)
(6)

where
u′ (cs,t , ls,t ) =∂ (cs,t , ls,t ).
∂cs,tOnce the initial consumption of a composite good is given, (5) determines the optimal
consumption path over time. The initial consumption is given for the optimal consumption
path to satisfy the lifetime budget constraint.
Second Stage11 :9Kitao (2015a), Kitao (2015b), and Kitao(2017) argue the case of both margins.
There are several deﬁnitions of the replacement rate of the public pension scheme. See İmrohoroğlu etal (2016) in detail. This paper uses the Japanese oﬃcial deﬁnition of the replacement rate, which is deﬁned
as the ratio of pension beneﬁts, which a typical household of a 65 years old husband of category 2 and awife only with the basic ﬁxed amount of pension beneﬁts receives, to average disposal earnings of category
2 male workres. The replacement rate based on this deﬁnition is currently just above 60 %.
11
The static part of this model is close to Kato (2012).
10

8

At the second stage, the representative household divides its consumption of a composite
good, which is optimally chosen by itself at the ﬁrst stage, into 15 diﬀerent ﬁnal domestic
consumption goods in order to maximize its utility in each time. Its utility is given by:
15
) ∑
( 1
i
2
15
α (s)i ln Xs,t,=
, Xs,t, · · · , Xs,tUg Xs,t

(7)

i=1

i
denotes consumption of a ﬁnal domestic consumption good i of a s years old
where Xs,t∑household at time t. 15
i=1 α (s)i = 1 is assumed for all ages. In order to capture the impact

of population aging on diﬀerent production sectors, α (s)i is assumed to depend on ages. idenotes each production sector. The parameter value of each α (s)i is determined by using
the social accounting matrix (SAM) made from the IO Table of year 201112 .
The representative household is assumed to maximize (7) with respect to its consumption
1
2
15
of ﬁnal domestic consumption goods, Xs,t
, Xs,t, · · · , and Xs,t, subject to its budget constraint

such that:15∑() Qi iipt Xs,t = Is,t − Ss,t ,1 + τc,t

(8)

i=1
i
i
where pQt denotes the price of good i at time t. τc,t denotes the ﬁnal consumption tax rateon good i at time t. Is,t , net income of age s at time t, is given by:
Is,t = (1 − τw,t − τp,t − τe,s,t ) es (1 − ls,t ) wt + (1 − τw,t ) bs,t + (1 − τq,t ) bqs,t − ICs,t − θt LTs,t .
Ss,t denotes the amount of savings, which is given by:
Ss,t = as+1,t+1 − [1 + (1 − τr,t ) rt ] as,t .
Note that both Is,t and Ss,t are determined at the ﬁrst stage, and they are exogenously
12
Since the actual SAM and the calculated parameter values of α (s)i are both big data sets, they areprovided upon request.

9

given at the second stage. (3) and (8) imply) Qi i∑15 (i
13
i=1 1 + τc,t pt Xs,t = (1 + τc,t ) cs,t . Since

the optimal cs,t is determined at the ﬁrst stage, (1 + τc,t ) cs,t is exogenously given at the
∑
Qi
i
i
i
second stage. Note that 99
s=20 Xs,t = Xt , and the price of Xt , pt , is measured in a time t
composite good.
The representative household of each cohort is assumed to supply labor in 15 diﬀerent pro)
∑ (iiduction sectors. Denote labor supply in production sector i by 1 − ls,t
, and 15i=1 1 − ls,t =
)
(
∑
i
i
1−ls,t . Denote also the wage rate in production sector i at time t by wti , and 15
i=1 wt 1 − ls,t =iare calculated based on the actual social accounting matrix.
(1 − ls,t ) wt . Both wti and 1 − ls,tiNote that ls,t is optimally chosen at the ﬁrst stage but each ls,tis calculated by using theactual social accounting matrix to make the model consistent to the actual data.
The representative household of each cohort is assumed to maximize (7) with respect toiXs,tsubject to (8) in each time, and the ﬁrst order conditions yield the demand functions

such that:iiXs,t= Xs,t(pi , Is,t , Ss,t ; αi ) =α (s)i (Is,t − Ss,t )) Qi , i = 1, 2, · · · , 15.
(ipt
1 + τc,t(9)Note that α (s)i can be calculated by using (9) and the actual social accounting matrix
so that:) Qi iipt Xs,t
1 + τc,tα (s)i =, i = 1, 2, · · · , 15,Is,t − Ss,t(where both the values of the denominator and the numerator can be obtained from the actual
SAM.

2.3

The Firm

Following the conventional assumption of the static CGE model, the multiple decisions byeach ﬁrm are described by the tree structure in the nested form, where each ﬁrm is assumed
13i
The value of τc,t is given by using τc,t
, which can be calculated from the actual SAM for all i.

10to make a decision over several diﬀerent items in each time. In the tree structure, theoptimal behavior of each ﬁrm which makes a decision over diﬀerent items is described asif the ﬁrm always makes a decision over two diﬀerent items at diﬀerent steps14 . Each ﬁrm
makes a decision over diﬀerent items; the amount of exports of its own product, the amountof imported goods and intermediate goods used for its production, and the amount of laborand capital used in its production. This assumption simpliﬁes a complicated decision over
several items by each ﬁrm.
At step 1, a representative private ﬁrm in sector i (i = 1, 2, · · · , 15) is assumed to use
labor and capital to produce its ﬁrst stage good such as a MVP (minimum viable product),
Yti at time t. Then, the ﬁrm is assumed to produce its good, Zti , by using its own Yti and
Xi,j,t at the second step. Xi,j,t denotes a ﬁnal domestic consumption good produced by ﬁrm
j used by ﬁrm i for its production at time t. Thus, Xi,j,t is the amount of a ﬁnal domestic
consumption good produced by ﬁrm j for the intermediate production process of ﬁrm i. At
the third step, the ﬁrm is assumed to decompose its good, Zti , into an exported good, Eti ,and a good, Dti . This step is concerned about its optimal decision over the amount of its
product to be exported. At the ﬁnal step (the fourth step), the ﬁrm is assumed to produce
its ﬁnal domestic consumption good, Qit , by using its good, Dti , and an imported good, Mti ,at time t. This step corresponds to its optimal decision over how much it uses an imported
good, Mti , and its own goods, Dti , to produce its ﬁnal domestic consumption good, Qit , whichis consumed by the household and the government, and it is also used by the ﬁrm of sector
i in its intermediate production process. The assumption of this tree structure in terms ofdiﬀerent decisions can incorporate ﬁrm’s complicated decisions over the amount of exports
of its own product, the amount of imported goods and intermediate goods which the ﬁrm
uses in its production process, and the amount of factor inputs into the model in a tractableway.
Note that all market clearing conditions are used to determine all prices endogenously
14

For the detailed tree structure, see Kato (2012).

11

in their corresponding markets, and also that at each step the private ﬁrm is assumed todetermine the amount of relevant variables in order to maximize its proﬁt.
By the assumption of the above tree structure, all decision making processes can be
simpliﬁed, and the optimal behavior about all diﬀerent decisions can be incorporated asfollows:
Step 1: The production of the ﬁrst stage good
Each ﬁrm is assumed to produce its ﬁrst stage good such as a MVP by using capital andlabor. Each ﬁrm is assumed to maximize its proﬁt given by:)(
πti = pYt i Yti Kti , Lit − δti Kti − wti Lit ,(10)

where Yti and pYt i denote the ﬁrst stage good produced by ﬁrm i and its price at time t,
respectively. Kti and Lit denote capital and labor used by the ﬁrm in sector i in order toproduce its ﬁrst stage good at time t, respectively. Kti and Lit are both assumed to be sector
i speciﬁc capital and labor, respectively. δti and wti are the rental price of capital and thewage rate of labor in sector i at time t, respectively. The production technology is given by:( )β ( )β)(
Yti Kti , Lit = Ωit Kti K,i Lit L,i , i = 1, 2, · · · , 15,(11)where βK,i + βL,i = 1 is assumed for all i = 1, 2, · · · , 15. Both βK,i and βL,i are assumed tobe time-invariant for all i = 1, 2, · · · , 15. Ωit expresses ﬁrm i’s production technology at time
t. Each ﬁrm is assumed to maximize (10) with respect to labor and capital subject to (11),and the ﬁrst order conditions yield the demand functions such that:) βK,i(Kti = Kti pYt i , δti , wti ; βK,i , βL,i = i pYt i Yti ,δt) βL,i(Lit = Lit pYt i , δti , wti ; βK,i , βL,i = i pYt i Yti , i = 1, 2, · · · , 15.
wt

12

(12a)
(12b)

Note that βK,i and βL,i can be calculated by using (12a), (12b), and the actual social
accounting matrix so that:δti Kti,
pYt i Yti
wi Li
βL,i = Yti ti , i = 1, 2, · · · , 15,pt Yt

βK,i =

where δti Kti , wti Lit , and pYt i Yti can be obtained from the actual SAM of year 2011. The estimated values of βK,i and βL,i for year 2011 are given in Table 2.
Step 2: The production of Zti
Each ﬁrm is assumed to produce its good, Zti at time t, by using intermediate goods andits own good, Yti , which production has been described at step 1. The optimal behavior ofeach ﬁrm in terms of production of its good, Zti , can be described such that:(
M ax πti = pZt i Zti −Yi ,Xi,jst(
Zti = minpYt i Yti −Yti

Xi,j,t,axi,j ayi

)

15
∑

)
pX
j,t Xi,j,t ,j, i = 1, 2, · · · , 15,

where Xi,j,t and pX
j,t denote an intermediate good j used by ﬁrm i and its price at timet, respectively. pZt i is the price of Zti . axi,j denotes the amount of intermediate good j used
for producing one unit of a ﬁnal domestic consumption good produced by ﬁrm i, and ayi
denotes the amount of its own good, Yti , for producing one unit of its good, Zti . Both axi,jand ayi are assumed to be time-invariant for all i = 1, 2, · · · , 15. The estimated values of
ayi for year 2011 are given in Table 315 . Note that the production function at this step isassumed to be the Leontief type. Using axi,j and ayi , and assuming that the market is fully
15
The estimated values of axi,j are not presented in Table 3, since the number of the estimated values
reaches 225. The estimated values are given upon request.

13

competitive, the zero-proﬁt condition can be written by:

pZt i = pYt i ayi +

15
∑

pX
j,t axi,j , i = 1, 2, · · · , 15.

(13)

j

Step 3: Decomposition of Zti into an exported good and a good used for
production of its ﬁnal domestic consumption good
The optimal decision made by the ﬁrm in sector i in terms of the amount of exports of
its own good is described as the the decomposition of Zti (i = 1, 2, · · · , 15) into an exported
good, Eti , and a good for producing its ﬁnal domestic consumption good, Dti . Each ﬁrm isassumed to maximize its proﬁt such that:) Zi i(ps
pt Z t ,− τi,tπti = pet i Eti + pdt i Dti − 1 + τi,t

(14)

where pet i and pdt i denote the price when the good is sold abroad, and the price when its
good, Dti , is used for producing its ﬁnal domestic consumption good, respectively. Note thatpsand τi,t
pet i is measured in the domestic currency. τi,t
are the tax rates of a production tax

imposed on the production of Zti and the subsidy rate at time t, respectively. The values ofps
τi,tand τi,t
are calculated by using the actual SAM, and the calculated values are given in

Table 4 for year 2011. The decomposition is assumed to follow the Cobb-Douglas technology
such that:( )κe ( )κd
Zti = Eti i Dti i , i = 1, 2, · · · , 15,(15)

where κdi + κei = 1 ( i = 1, 2, · · · , 15) is assumed. Both κdi and κei are assumed to be timeinvariant for all i = 1, 2, · · · , 15. Each ﬁrm is assumed to maximize (14) with respect to Eti
and Dti subject to (15), and the ﬁrst order conditions yield

14) Zi i(ps
( ei di Zi p s d e ) κei 1 + τi,t
pt Z t− τi,tpt , pt , pt ; τi,t , τi,t , κi , κi =,ei
pt
) Zi i
(
p
s
d
)
(
1
+
τ
−
τ
κ
i,t pt Ztii,tps, τi,t, κdi , κei =Dti = Dti pet i , pdt i , pZt i ; τi,t
, i = 1, 2, · · · , 15.
dipt
Eti = Eti

(16a)
(16b)

Note that κei and κdi can be calculated by using (16a), (16b) for year 2012, and the actualsocial accounting matrix so that:κei = (

pet i Eti
) Zi i ,pspt Z t1 + τi,t− τi,tκdi = (

pdt i Dti
) Zi i , i = 1, 2, · · · , 15,pspt Z t1 + τi,t− τi,tp Zi is Zi iwhere pet i Eti , pdt i Dti , pZt i Zti , τi,t
pt Zt , and τi,t
pt Zt can be obtained from the actual SAM ofyear 2011. The estimated values of κei and κdi are given in Table 5.
Step 4: The Production of its ﬁnal domestic consumption good
Denote the ﬁnal domestic consumption good produced in sector i by Qit (i = 1, 2, · · · , 15)
at time t. This ﬁnal domestic consumption good is consumed by the representative household. The ﬁnal domestic consumption good is assumed to be produced by using its good, Dti ,and an imported good, Mti . This step corresponds to the optimal decision making behaviorof each ﬁrm in terms of the amount of imported goods which are used in its production
process. The production technology at this ﬁnal step is given by the following Cobb-Douglas
function:( )γ m ( )γ d
Qit = Mti i Dti i , i = 1, 2, · · · , 15,(17)

where γim + γid = 1 ( i = 1, 2, · · · , 15) is assumed. Both γim and γid are assumed to be timeinvariant for all i = 1, 2, · · · , 15. Each ﬁrm is assumed to maximize its proﬁt with respect to15

Mti and Dti subject to (17). Its proﬁt is given by:) mi i(di iimi
πti = pQt Qt − 1 + τi,t pt Mt − pt Dt , i = 1, 2, · · · , 15,imiwhere pQt and τi,t denote the price of its ﬁnal consumption goods, Qt , and the import tariﬀ

rate, respectively. The import tariﬀ rate is calculated by using the actual SAM, and it isgiven in Table 4. Then, the ﬁrst order conditions yield)(iiγim pQ
Qi
t Qt
di
m
m
d
i
)
(
,
;
τ
,
p
,
γ
Mti = Mti pm
,
p
,
γ
=
t
t
t
i,t
i
i
i
m
pm
1 + τi,tt) γ d pQi Qi
(
Qi
di
m
m
d
i
= i tdi t , i = 1, 2, · · · , 15.
;
τ
,
γ
,
γ
,
p
,
p
Dti = Dti pm
t
t
t
i,t
i
i
pt

(18a)
(18b)

Note that γim and γid can be calculated by using (18a), (18b), and the actual SAM ofyear 2011 so that:

(
γim =

) mi im
1 + τi,t
pt Mt
i
i
pQ
t Qt

pdt i Dtidγi = Qi i ,
pt Qt

,

i = 1, 2, · · · , 15,

Qi i
di i
i
m mi
i
i
where pmt Mt , pt Dt , pt Qt and τi,t pt Mt can be obtained from the actual SAM. The esti-

mated values of γim and γid are given in Table 6.

2.4

The Government

Since the purpose of this paper is to explore the impact of population aging, three separate accounts of the government sector are explicitly considered; the general account, thepublic pension account, and the long-term care insurance account. The government issues
government bonds, and accumulates the public pension fund. Each account is separately
16

considered as follows.
2.4.1

General Account

The budget constraint of the general account is such that:
DBt − DBt−1 = AGt + rt DBt−1 + P Pt + EEt − Rt ,(19)

where DBt denotes the amount of outstanding government debts at time t. AGt is the total
government expenditure. P Pt is the amount of transfers from the general account to the
public pension account at time t. EEt is the amount of transfers from the general accountto the long-term care insurance account at time t. Rt is the total tax revenue, which is givenby:
Rt = τw,t (wt Lt + ABt ) + τr,t rt ASt + τc,t ACt + τq,t BQt + T Pt + T Mt − SBt ,(20)

The total labor income at time t, wt Lt , is given by:
wt Lt =

RH
∑
s=20

es

15
∑

wti

(

i
1 − ls,t)

P OPs,t =RH∑

es wt (1 − ls,t ) P OPs,t ,

(21)

s=20

i=1

where P OPs,t denotes the total population of age s at time t.
The aggregated values of pension beneﬁts (ABt ), private savings (ASt ), consumption of
a composite good (ACt ), and bequests(BQt ) are given as follows:
ABt =
ASt =
ACt =
BQt =

99
∑

bs,t P OPs,t ,

s=RH
99
∑

as,t P OPs,t ,

s=20
99
∑
s=20
99
∑

cs,t P OPs,t ,bqs,t P OPs,t .

s=20

17

The government imposes a production tax and an import tax on 15 production sectors,
and also subsidies these production sectors. The total production tax revenue (T Pt ) , thetotal import tax revenue(T Mt ), and the total subsidies(SBt ) to 15 production sectors are
given by:
T Pt =T Mt =
SBt =

15
∑
i=1
15
∑
i=1
15
∑

p Zi i
τi,tpt Z t ,m mi
τi,tpt Mti ,s Zi i
τi,tpt Z t .

i=1

The total government expenditure(AGt ) is given by:
15
∑
gi
i
pQ
AGt =
t Xt ,
i=1

where Xtgi denotes consumption of the ﬁnal consumption good i by the government at time
t16 .
2.4.2

Public Pension AccountOn the public pension account, the budget constraint is such that:
Ft − Ft−1 = rt Ft−1 + P Pt + CPt − ABt ,(22)

where Ft denotes the accumulated pension fund at time t. CPt is the total amount ofcontributions collected at time t, which is given by:
CPt = τp,t

RH∑

wt es (1 − ls,t ) P OPs,t .

s=20i
16 Zi mipt , pt , and pQt are all measured in a composite good, ct , at time t.

18

2.4.3Long-term Care Insurance (LTCI) Account

The budget constraint of the long-term care insurance (LTCI) is given by:
T LTt = F ICt + T ICt + OICt + EEt ,(23)

where T LTt is the total expenditure in the account at time t, and it is given by:
T LTt =

99∑

(1 − θt ) LTs,t P OPs,t .

(24)

s=RH−1

EEt is the amount of transfers from the general account to the long-term care insurance
account at time t. LTs,t is the total cost through the LTCI, and the θt is the co-payment rate
imposed on the representative household at time t. P OPs,t denotes the total population ofage s at time t.
F ICt and T ICt , are aggregated revenues contributed by each household at time t, which
are such that:F ICt =T ICt =

RH−1
∑
s=40
99
∑

τe,s,t es

15
∑

RH−1
∑
(
)
i
wti 1 − ls,t
P OPs,t =τe,s,t es (1 − ls,t ) wt P OPs,t ,
s=40

i=1

ICs,t P OPs,t .

s=RH

Note that F ICt and T ICt are the total contributions by the household which belongs to
the ﬁrst group between age 40 and 64, and to the second group between age 65 and over,respectively. To capture the realistic aspect, while F ICt depends on wage income, T ICt is
the total amount of ﬁxed contributions by the second group. The household has to pay apart of the total cost as a co-payment when it receives services through the long-term careinsurance. The current co-payment rate, θ, is 10 %. OICt is the total amount the householdpays by itself when it receives services through the long-term care insurance at time t, which19

is given by:
OICt =

99∑

θt LTs,t P OPs,t .

s=RH−1

In order to reﬂect reality, τe,s,t and ICs,t are both endogenously calculated to satisfy (6) inthe following simulations.

2.5

Mobility of Factor Inputs among Diﬀerent Production Sectors

The assumption on the degree of mobility of a factor input in the factor market is crucial
to determine the equilibrium price of the factor input. It is assumed that sector speciﬁcfactor inputs are used in each production sector so that factor inputs used among diﬀerent
production sectors are assumed to be diﬀerent. This implies that labor and capital canbe assumed to be immobile among diﬀerent production sectors at least in the short run.
However, through the training process of labor and diﬀerent investment behavior over time,labor and capital become more mobile over time if the wage rate and the rental price are
diﬀerent among diﬀerent production sectors. Factor inputs keep moving among diﬀerent
production sectors until the unique equilibrium prices are determined in the whole factor
markets in the long run. Then, this paper considers two diﬀerent assumptions; the shortrun, and the long run. In the short run, both labor and capital are completely immobile
between diﬀerent production sectors, so that diﬀerent equilibrium prices of labor and capitalare determined in factor markets of each production sector. On the other hand, in thelong run, both labor and capital are completely mobile between diﬀerent production sectors,
so that the unique equilibrium prices of labor and capital are determined. Note that the
paper only focuses on the domestic market so that equilibrium factor prices are determinedin domestic factor markets under the assumption that economic environments of the world
economy remain unchanged over time.

20

2.5.1

The Labor Market

The labor market equilibrium condition in each period for all i (i = 1, 2, · · · , 15) is given by:
RH
∑

)
(
i
P OPs,t = Lit ,es 1 − ls,t

(25)

s=20

and the equilibrium wage rate is determined by (25). In the short term, labor is completely immobile and supply of labor in each production sector is completely ﬁxed at aicertain level, ls,t
, and diﬀerent values of wti are determined by (25) for the ﬁxed amount of
(
)
(
) ∑RH
∑RH
i
i
1
−
1
−
l
=
e
e
l
s
s
s,t for all i (i = 1, 2, · · · , 15) . In this case, it is assumed
s,t
s=20
s=20
∑15
∑
17
i
that 15i=1 ϕi = 1 .
i=1 ϕi wt = wt in (3), where ϕs is a weight parameter andIn the long run, the household learns to equip itself with sector speciﬁc labor, and laborcompletely becomes mobile among diﬀerent production sectors. Then the unique equilibrium
wage rate, wt = wti for all i, is determined to satisfy (25). Note that demand for labor by
production sector, i, denoted by Lit , can be diﬀerent among diﬀerent production sectors due
to diﬀerent production technology described by (11). This implies that equilibrium labor
supply in sector i can be diﬀerent among diﬀerent production sectors, and labor supply ineach production sector keeps changing until the unique equilibrium wage rate is determinedin all factor speciﬁc labor markets of 15 diﬀerent production sectors.
2.5.2

The Capital Market

The capital market equilibrium condition in each period for all i (i = 1, 2, · · · , 15) is given
by:

99
∑

i
= Kti ,
Ks,t

(26)

s=20

and the equilibrium rental price is determined by (26). In the short run, capital is completely
immobile and supply of capital owned by the household of age s in each production sectori
is completely ﬁxed at a certain level, Ks,t
, and diﬀerent values of the rental price, δti , are17

The values of ϕi are calculated from the actual SAM.

21

determined by (26) for the ﬁxed amount of∑99

is=20 Ks,t =∑99i
s=20 Ks,t for all i (i = 1, 2, · · · , 15).

It is assumed that immobility of capital is caused by the adjustment cost denoted by ξti .
In the long run, the household changes its investment behavior if the rental prices ofcapital are diﬀerent among diﬀerent production sectors, and capital completely becomesmobile among diﬀerent production sectors. Then the unique equilibrium rental price, δt =
δti for all i, is determined to satisfy (26). Note that demand for capital by production
sector, i, denoted by Kti , can be diﬀerent among diﬀerent production sectors due to diﬀerent
production technology described by (11). This implies that equilibrium capital supply insector i can be diﬀerent among diﬀerent production sectors, and capital supply in eachproduction sector keeps changing until the unique equilibrium rental price is determined in
all factor speciﬁc capital markets of 15 diﬀerent production sectors.

2.6

Competitive Equilibrium

For a given sequence of all demographic parameters, {P OPt , Pt−g }∞t=0 , given sequences of all}∞{
government policies, DBt , Ft , τw,t , τr,t , τc,t , τq,t , τp,t , τe,s,t , τe,RH−1,t , θt , bt , ICs,t , ϵt , H t t=0 and{ p m s}∞
τi,t , τi,t , τi,t ; i = 1, 2, · · · , 15 t=0 , and a given sequence of elderly care services, {LTs,t }∞t=0 ,the perfect foresight competitive equilibrium is deﬁned as the sequences of {rt , wt }∞
t=0 ,
}∞
{
∞
i
, which satisfy the following condi{δti , wti ; i = 1, 2, · · · , 15}t=0 , and pQ
t ; i = 1, 2, · · · , 15
t=0tions:
1. The optimal conditions for the representative household, (5) and (6), are satisﬁed for
all generations in each period with the non-ponzi condition.
2. The optimal condition for the representative household, (9), is satisﬁed for all generations in each period.
3. The optimal conditions for the ﬁrm, (12a), (12b), (13), (16a), (16b), (18a), and (18b),
are satisﬁed in each period.
4. Three budget constraints for the government, (19), (22), and (23), are satisﬁed in eachperiod.
22

5. The market equilibrium condition for the ﬁnal domestic consumption good is satisﬁed
in each period for each i (i = 1, 2, · · · , 15) such that:
Qit =

99
∑

i
Xs,t
+ Xtgi +

s=20

15
∑

Xi,j,t + Xtsi ,j=1

where Xtsi denotes the amount of investments by sector i at time t. Note that Xtsi =)δti ( i
Kt+1 − (1 − ϕt ) Kti , where ϕt is the depreciation rate at time t and it is assumed to beQiPt

the same among all production sectors18 ,19 . Note that this paper only considers the domestic
consumption good market20 .
6. The labor market equilibrium condition, (25), is satisﬁed in each period for all i(i = 1, 2, · · · , 15).
7. The capital market equilibrium condition, (26), is satisﬁed in each period for all i(i = 1, 2, · · · , 15).
8. The asset market equilibrium condition is satisﬁed in each period such that:ASt + Ft + Stf = Kt + DBt ,where Kt =∑15 ∑99i=1

i ifs=20 δt Ks,t , and S

denotes the total amount of savings by the foreign

sector, or the deﬁcits in the current account. S f is given by:
f

S =

15
∑

i
i
pm
t Mt −

i=1

15∑

pet i Eti .

i=1i
Since pet i and pm
t are both measured in the domestic composite good, they are also expressed

18

Since the amount of investments by the production sector in the actual Input-Output Table is not
negligibly low for some sectors, the amount of investments is included in this equilbrium condition.
19 sii
Xt and Kt+1
are assumed to be diﬀerent goods.
20This implies that the value of contributions by sector i to the Gross Domestic Product (GDP) is givenby:∑15 Qiei i
iipQ
t Qt + pt Et −j pt Xi,j,t .

23such that:i,
pet i = εt pw,e
t

w,mi
i
, i = 1, 2, · · · , 15,pm
t = εt ptii
are world prices of the exported goodand pw,mwhere εt denotes the exchange rate, and pw,ett

produced in sector i and imported goods used in sector i, respectively. The world prices are
assumed to be exogenously given, and this implies that the exchange rate is endogenously
determined within the model.
9. The eﬃcient market condition is satisﬁed in each period for all i (i = 1, 2, · · · , 15). In
the short run, the eﬃcient market condition is given by:

rt = δti − ϕt − ξti .
In the long run, the eﬃcient market condition is given by:
rt = δt − ϕt ,where δt is the equilibrium rental price determined by (26) in the long run.
10. The sequence of the consumption tax rate, {τc,t }, is endogenously determined tosatisfy (19) from year 2021.
11. The sequence of the contribution rate of the public pension scheme, {τp,t }, is endogenously determined to satisfy (22) until year 2017.
12. The sequence of the replacement rate of the public pension scheme, {ϵt }, is endogenously determined to satisfy (22) from year 2018.
13. The sequence of the revenue instruments of the LTCI, {τe,s,t , τe,RH−1,t , ICs,t }, isendogenously determined to satisfy (23) in each period.

24

3Some Assumptions on the Future Economy

Parameter values have been set to reproduce the values of key variables in the model as
close to real values in year 2011 as possible in the following benchmark for the static partof the model. Regarding the scenarios of the future economic policies, the assumptions in
the latest version of Economic and Fiscal Projections for Medium to Long-term Analysis(EFPMLA: January 2020) have been considered as much as possible to specify the future
economy for the dynamic part of the model. For the dynamic part of the model, year 2018has been assumed to be the benchmark year. EFPMLA (2020) numerically embodies theso-called growth strategy, the main policy of Abenomics, and the actual policy scenarios forseveral key indicators such as the future GDP, government deﬁcits and the primary balance
have been taken into account.

3.1

Demographics

The assumption on the demographics is a key factor. From year 2016 to year 2115, thelatest population projection by the IPSS (2017) is used for age groups of 0 to 10021 . The
medium variant values for fertility and mortality rates are used. From year 2116, the same
distribution as that of year 2115 is assumed for another 100 years. The latest population
projection by the IPSS (2017) shows that the Japanese economy converges to a new steadystate with the high dependency ratio as shown in Figure 122 . In the growing literature
all studies assume that the Japanese economy converges to a new steady state with a low
dependency ratio after experiencing its very high ratio at peak. However, this paper uses
the entire estimates by the IPSS (2017) until year 2115.
Regarding the past demographic structure, the actual data from year 1920 to year 2015 isused23 . The demographic structure before year 1920 is assumed to have the same distribution
21

The populaiton projection by the IPSS consists of the usual estimate for the ﬁrst 50 years and a reference
estimate for another 50 years. This paper uses both estimates for entire 100 years from year 2016 to 2115.
22
The dependency ratio is deﬁned as the ratio of age 65 and over to the total number of age 20 to age 64.
23
The data of age 85 and over from year 1920 to 1946 was calculated based on the actual survival rate of25

as that of year 1920.
Since all parameter values of the total population and the survival rate are calculated byusing the actual and projected data, the demographics in the model can perfectly capture
the actual and projected demographic structure shown in Figure 2.

3.2

Preference and Production

For the static part of the model, all parameter values are given from Table 2 to Table 6
for year 2011. Note that year 2011 is assumed to be the benchmark year for the static
part. From year 2012, all parameter values for the static part of the model are endogenously
calculated consistent to the dynamic part of the model.
For the dynamic part of the model, key parameter values in (1) and (2) are shown in
Table 7 for year 2018. On the values of tax rates and parameter values in the dynamic
part of the model, available values from Hayashi and Prescott (2002) as well as Hansen andİmrohoroğlu (2016) are used. Ihori et al (2006) pointed out that all simulation results arequite sensitive to the value of technological progress (Ωt ). Note that in EFPMLA (2020)
the future economic growth rates are given as targeted values. This paper exogenously gives
the value of Ωt instead, so that the endogenously calculated rate of economic growth in
the model becomes close to the targeted value of economic growth rate given in EFPMLA(2020). Figure 2 shows that the future total population is forecasted to drastically decrease.
This implies that future labor force will drastically decrease as well. While per capita GDP
can still increase even with such a drastic decreasing trend in labor force, EFPMLA (2020),
however, assumes that the even aggregated Japanese economy grows at a stable rate in any
scenario. An assumption of stable growth of GDP seems unrealistic without an assumptionof stable technological progress. In this paper, the value of Ωt is exogenously given, in orderfor the model value of endogenously calculated economic growth rate of GDP to becomeage 85 and over between year 1947 and 1948. The data of all ages from year 1941 to 1943 are missing, andmissing data were recursively calculated based on the survival rates of all ages between year 1947 and 1948
with the data of year 1944.

26

close to the value assumed in EFPMLA (2020). The exogenously calculated value of Ωt isshown in Figure 3. The model values of economic growth calculated endogenously in thebenchmark model will be shown in Section 3-4.

3.3

Government

The Japanese government has been trying to stimulate the Japanese economy based on
the so-called growth strategy. In order to accomplish the growth strategy, the government
documented concrete ﬁgures24 of several key variables such as the future primary balanceand economic growth as targeted ﬁgures25 .
In EFPMLA (2020), there are two assumptions on the future economic environment up
to year 2029; a recovery case and a baseline case. Figure 4-1 to 4-3 show the diﬀerent
assumptions between two cases. In all ﬁgures the actual data is used until year 2018. This
paper follows assumptions made in the baseline case in EFPMLA (2020).
3.3.1

General Account

The future government expenditures and future deﬁcits are both exogenously given. The
future government expenditures are assumed to increase according to population aging basedon the latest Population Projection by the IPSS (2017).
On the future deﬁcits, the assumption made in the baseline case in EFPMLA (2020) is
used until year 2029. After year 2029, the same value as that of year 2029 is assumed tocontinue. The future scenario is shown in Figure 5-1.
The consumption tax rate is assumed to be endogenously calculated from year 2021 in
24

Several oﬃcial documents have been made. This paper follows several assumptions made by the Cabinet
Oﬃce of Japan (Economic and Fiscal Projection for Medium to Long-term Analysis (January 2020)).
25
Miyazawa and Yamada (2015) examined the growth strategy of Abenomics, and they concluded thatthe growth strategy seems diﬃcult to be achieved even under very optimistic assumptions made in one ofthe oﬃcial documents, Economic and Fiscal Projections for Medium to Long-term Analysis (July 2014).
This paper uses several assumptions made in the latest version of EFPMLA (2020) to specify the future
government policy, and expands Miyazawa and Yamada (2015) by separately introducing the government
accounts in a more realistic way.

27

order to satisfy (19)26 . Before year 2021, the consumption tax rate exogenously remains at
10% until year 2019, while the wage income tax rate is endogenously calculated until 2020
to satisfy (19)27 . All other tax rates for the dynamic part of the model are exogenously
given as shown in Table 7. The tax rates for the static part of the model is given in Table
4. Note that the tax rates shown in Table 4 have been obtained based on the actual SAM ofyear 2011. From year 2012, all tax rates for the static part of the model are endogenously
calculated consistent to the dynamic part of the model.
3.3.2

Public Pension AccountThe decreasing trend of the GDP ratio of accumulated public pension fund has alreadystarted since year 2003 in reality. Then, by following the actual plan of decreasing the fundin the next 100 years by the MHLW, the public pension fund is assumed to keep decreasing
down until year 2115. Figure 5-2 shows the actual past trend and the future values given in
the following numerical analysis. Until year 2018, the actual values are used in the ﬁgure.
A half of the total amount of basic pension beneﬁts is transferred annually from thegeneral account in reality, which is Pt in (19) and (22). This paper incorporates this fact28 .
The contribution rate (τp,t ) and the replacement rate (ϵt ) are used as policy instruments
in order to satisfy (22). In order to reﬂect the actual policy change, the contribution rateis endogenously calculated until year 2017 with the ﬁxed replacement rate. Until year 2017
the contribution rate is an endogenous policy instrument to satisfy (22). From year 2018 thecontribution rate is exogenously given at 18.3%, and the replacement rate is endogenously

26

As pointed by Kitao (2015a), the wage income tax is more distortinary to labor supply than the consumption tax, and thus a more welfare loss is generated by the wage income tax. This paper only uses theconsumption tax to ﬁnance the future government policy.
27
The exogenously given values of the consumption tax rate in all simuations are 0 %, 3 %, 5 %, 8 %, and
10 % for before year 1989, between 1989 and 1997, between 1997 and 2014, between 2014 and 2018, andbetween 2019 and 2020, respectively. The wage income tax rate is given exogenously from year 2021 at thesame value of that of year 2020.
28
Until year 2003 the actual transfer rate, deﬁned as the ratio of transfers from the general account to thetotal basic pension beneﬁts, was one-third, and it was gradually increased to 50% from year 2004 to year
2009. Since year 2010, the rate has remained at 50%.

28

calculated to satisfy (22)29 . From year 2018 the replacement rate becomes a new policy
instrument to satisfy (22).
The MHLW reported that the replacement rate in year 2009 was 62.3 %30 , and theexogenous replacement rate is assumed to be ﬁxed at 62.3 % until year 2017. From year 2018
the replacement rate is endogenously calculated, while the contribution rate is exogenously
ﬁxed at 18.3 % afterwards.
3.3.3

Long-term Care Insurance (LTCI) Account

The public long-term care insurance (LTCI) for the elderly was introduced in year 2000. The
expenditures basically depend on the demographic structure and population aging, and theexpenditures are assumed to be exogenous. According to the future demographic structure,
the future expenditures in the LTCI is calculated based on the assumption that the agedependent cost is time-invariant. For given values of expenditures, this paper endogenously
calculates the ﬁxed amount of contributions by the ﬁrst group and the contribution rate forthe second group in order to balance the budget of the LTCI account.
On the revenue side, a 10% of the total cost is paid by the insured as co-payments. A
half of the remaining cost (90 % of the total cost) is covered by transfers from the generalaccount (Et ). Another half of the remaining cost is paid by the insured. A 27 % and a 23%of the remaining cost are currently paid by people belonging to the second group, and theﬁrst group, respectively. Note that the scheme is compulsory so that people between age 40
and 64 have to belong to the second group, and people of age 65 and over have to belong tothe ﬁrst group.
The current ratios of the distribution of the cost between the ﬁrst group (age 65 andover) and the second group (ages between 40 and 64) are 23 % and 27%, respectively. While
29

In the actual plan by the MHLW, it is assumed that the contribution rate remains at 18.3% fromyear 2018, and also that the replacement rate is adjusted to balance the budget with the ﬁxed rate of thecontribution rate of 18.3%.
30Note that this is the oﬃcal replacement rate. See Kitao (2015a) for diﬀerent deﬁnitions of the replacement
rate. The oﬃcial replacement rate used here is diﬀerent from the deﬁnition of the replacement rate used in
Kitao (2015a, 2015b, and 2017).

29

the total ratio paid by the insured remains at 50% (=23 % + 27 %) of the 90 % of the total
cost, the ratios between two groups will be modiﬁed according to the future demographic
structure in the actual future plan by the MHLW. The MHLW announced that the ratios will
be modiﬁed every 3 years, and indeed the actual ratios have been changed since its launchin year 2000. Table 8 shows the actual ratios in the past as well as the future calculated
ratios based on the guideline made by the MHLW. This paper endogenously calculates thecontribution rate (τe,s,t ) for the second group and the ﬁxed amount of contributions (ICs,t )for the ﬁrst group to satisfy (6), based on the given ratios in Table 8.

3.4

Benchmark and Calibration

Year 2011 is assumed to be a benchmark year for the static part of the model. This is becauseparameter values were calibrated by using the actual SAM of year 2011 for the static part ofthe model. Table 9-1 shows the comparison of the ﬁnal domestic consumption goods between
actual and model values31 . Note that the model values in Table 9-1 have been obtained withthe parameter values given in Table 2 to 6.
For the dynamic part of the model, the model was calibrated based on the actual valuesof year 2018, since the latest actual values for key variables for the dynamic part of themodel can be obtained up to year 2018. Table 9-2 shows the comparison of such variables
between actual and model values. Note that until year 2017 the contribution rate of the
public pension is endogenously calculated under the assumption of the exogenous value ofthe replacement rate of 62.7 %, while it is assumed to be exogenously given at 18.3 % fromyear 2018 with the assumption that the replacement rate is endogenously calculated to satisfy
the budget constraint of the public pension account within the model.
In the following numerical experiments, technological progress (Ω) is assumed to follow
the value given in Figure 3, in order to realize the assumption of the baseline case in EFPMLA(2020).
31
The data set of consumption of the household contains 1215 obsersations of each of the actual and model
values, and it can be provided upon request.

30

4Impact of Population Aging

4.1

On Demand

Since the household has age speciﬁc preference over consumption goods, the future change inthe demographic structure aﬀects an economy through the change in demand for goods. It is
expected that population aging stimulates more demand for goods which aged people prefer;the pharmaceutical products, medical services, public hygiene, social insurance & welfare,and long-term care insurance services. This paper particularly pays more attention to theimpact on these 5 production sectors. Figure 6-1 and 6-2 show the impact of population
aging on demand for these 5 production sectors32 . Demand for the medical services sector ismuch higher than other 4 sectors, and it is shown separately in Figure 6-1. Indeed, demand
for all 5 sectors is expected to increase due to population aging. Compared to the demandlevel in year 2020, demand for the medical services, the pharmaceutical, the social insurance& welfare, and the long-term care insurance services sectors will increase to their peak levels
by 19.78 %, 12.25 %, 21.66 %, and 18.76 %, respectively. The corresponding highest demandlevels at their peak are 56,213.90 billion yen, 10,797.08 billion yen, 10,529.46 billion yen,and 10,727.07 billion yen, respectively.
While demand for these 5 sectors will all increase, their peaks will come in a diﬀerent
time. While the peak of demand for the pharmaceutical sector will come in year 2040,
the peaks of other 4 sectors will come in year 204633 . Note that demand for all 5 sectors
will start decreasing after their peak levels due to the fact that the total population will
drastically shrink in the future. The eﬀect of a shrinking population overweighs the impact
of population aging on demand for these 5 sectors34 in the future.
32

Since the economic size of the public hygiene sector is much smaller than other 4 sectors, it is not shownin both ﬁgures.
33
Demand for products of the public hygiene sector will increase by 18.93 % from its level of year 2020 at
its peak in year 2046.
34
While the per capita GDP is forecasted to increase due to the srong assumption in EFPMLA (2020), thetotal GDP will start decreasing due to a drastically shrinking future population. The eﬀect of the shrinking
total population can be observed in a decrease in demand not only for these 5 sectors but also for other 10
sectors in a graying Japan.

31

4.2

On Labor Income

Since demand for these 5 sectors will increase in a graying Japan, more labor inputs areneeded to cope with higher demand. Figure 7-1 and 7-2 show the total labor income of
the 4 sectors. Since the pharmaceutical sector is less labor intensive than others, its labor
income is much smaller. Note also that both of the social insurance & welfare sector andthe long-term care insurance services sector are more labor intensive.

4.3

On Labor Force

The total labor income of each sector depends on labor force and the wage rate in eachsector. Thus, higher labor income does necessarily not imply more labor force in each sector.
If friction is strong and thus labor cannot move between production sectors smoothly, thenhigher total labor income would be caused by higher wage rates. In this case, even though it
is anticipated that population aging results in higher total labor income, higher demand forthe goods of these sectors could not be fulﬁlled. This implies that stable economic growthof a graying Japan depends on the extent how much the labor market is smooth enoughwithout friction, in order to have enough labor force to fulﬁll increasing demand for goods
elderly people prefer. To see how much labor force is needed for such sectors, the long-run
assumption is imposed in the following experiment; no change in the wage rate. If any othercosts do not change with the inﬂow of labor force into such sectors, then more labor keeps
moving into such sectors until the wage rate settles down to the original level in the long-run,as long as the wage rate is higher than other sectors. Figure 8-1 and 8-2 show the impact of
population aging on labor force under the assumption of the smooth inﬂow of labor force.
Note that the labor force of the pharmaceutical sector is much smaller than other sectors,
and it is separately shown in Figure 8-2. Note also that the experiment was conducted basedon the actual data of Labor Force Survey unyil year 2020. In Labor Force Survey, labor
force of the social insurance & welfare and the long-term care insurance sectors is not shown
separately, so that in Figure 8-1 the integrated values of both sectors are shown. As Figure328-1 shows, the labor force needed in both of the social insurance & welfare and the long-termcare insurance sectors will drastically increase due to population aging. The latest available
data of labor force of both sectors is 431 million workers in year 2020. The needed numberof workers of both sectors at its peak is forecasted to be 467.6 million workers in year 2034.
While it seems diﬃcult to decompose the labor force between the social insurance &welfare sector and the long-term care insurance sector, the Ministry of Health, Labor andWelfare (MHLW; 2018) estimated the labor force of 334 million workers in the long-termcare insurance sector for year 2018 in its simulation analysis. Figure 8-3 shows the futurelabor force of the long-term care insurance sector based on the estimate of year 2018 by
MHLW (2018). Then, in year 2034, the labor force needed in the long-term care insurance
sector is estimated to be 369.21 million workers.

5

Concluding Remarks

This paper integrated independently developed static and dynamic CGE models, and studied
the dynamic impact of population aging on the Japanese economy with multi-production
sectors and overlapping generations.
Numerical results show that population aging indeed stimulates demand for products ofaging-related sectors. In particular, the paper focused on the impact on the 5 production
sectors; the pharmaceutical sector, the medical services sector, the public hygiene sector, thesocial insurance & welfare sector, and the long-term care insurance sector. Compared to thedemand in year 2020 with their highest value, demand for these 5 sectors will increase by
12.25 %, 19.78 %, 18.93 %, 21.66 %, and 18.76 % from year 2020, respectively. The increasein demand also induces higher demand for labor in these sectors, and the combined labor
force of both of the social insurance & welfare and the long-term care insurance services
sectors will increase to 467.6 million in year 2034. These numerical results indicate thatlabor mobility among diﬀerent production sectors should be smooth enough without friction33

to cope with an expansion of demand for products of aging-related sectors in a graying Japanin order to have stable economic growth.

References[1] Auerbach, A and L J Kotlikoﬀ (1987), Dynamic Fiscal Policy, Cambridge University
Press[2] Auerbach, A, L J Kotlikoﬀ, and J Skinner (1983), ’The eﬃciency gains from dynamic
tax reform,’ International Economic Review, Vol. 24, 81 - 100[3] Ballard, C L, D Fullerton, J B Shoven, and J Whalley (1985), A General Equilibrium
Model for Tax Policy Evaluation, Chicago University Press[4] Braun, R. Anton and Douglas H. Joines (2015), ’The implications of a graying Japanfor government policy,’ Journal of Economic Dynamics & Control 57, 1–23
[5] Cabinet Oﬃce of the Government of Japan (2020), Economic and Fiscal Projectionsfor Medium to Long-term Analysis, Cabinet Oﬃce of the Government of Japan (inJapanese)[6] Hansen, Gary D. and Selahattin İmrohoroğlu (2016), ’Fiscal Reform and Government
Debt in Japan: A Neoclassical Perspective,’ Review of Economic Dynamics, 21, 201-224[7] Hayashi, Fumio, and Edward C. Prescott (2002), ’The 1990s in Japan: A Lost Decade,’
Review of Economics Dynamics, 5, 206-235[8] Ihori, T, R R Kato, M Kawade, and S Bessho (2006), ’Public Debt and Economic
Growth in an Aging Japan,’ Chapter 3, in Tackling Japan’s Fiscal Challenges: Strategies
to Cope with High Public Debt and Population Aging, Kaizuka K and A O Krueger eds.,
Palgrave34[9] İmrohoroğlu, Selahattin, Sagiri Kitao, and Tomoaki Yamada (2016), ’Achieving Fiscal
Balance in Japan,’ International Economic Review, 57 (1)[10] —–, ——, and ——– (2019), ’Fiscal sustainability in Japan: What to tackle?,’ Journalof the Economics of Ageing, 14, 1-15
[11] Kato, Ryuta Ray (2012), ’The impact of marginal tax reforms on the supply of healthrelated services in Japan,’ Japanese Journal of Social Security Policy, 9 (1), 1-32
[12] Kato, Ryuta Ray (2018), ’The future prospect of the long-term care insurance in Japan,’Japan and the World Economy, 47, 1-17
[13] Kimura, Shin, and Kyoji Hashimoto (2010), ’A dynamic general equilibrium analysis
of ﬁscal consolidation within the multi-sector overlapping generations model,’ Keizai
Bunseki 183, 1-24 (in Japanese)[14] Kitao, Sagiri (2015a), ’Fiscal cost of demographic transition in Japan,’ Journal of Economic Dynamics & Control, 54, 37-58[15] Kitao, Sagiri (2015b), ’Pension reform and individual retirement accounts in Japan,’
Journal of the Japanese and International Economies, 38, 111-126[16] Kitao, Sagiri (2017), ’When do we start? Pension reform in ageing Japan,’ The Japanese
Economic Review, 68 (1), 26-47[17] Ministry of Health, Labor and Welfare (2018), Simulations of Man-power on Future
Projections of Social Security in Year 2040, Ministry of Health, Labor and Welfare of
the Government of Japan (in Japanese)[18] Miyazawa, Kensuke, and Junji Yamada (2015), ’The growth strategy of Abenomics andﬁscal consolidation, Journal of the Japanese and International Economies, 37, 82-99

35

[19] Naqvi, Farzana and Matthew W Peter (1995), ’MONASH-MRF: A multiregional, multisectoral model of the Australian economy,’ IFAC Modelling and Control of National
and Regional Economies, Queensland, Australia[20] Peter, Mathew W, Mark Horridge, G A Meagher, Fazana Naqvi, and B R Parmenter(1996), ’The theoretical structure of MONASH-MRF,’ Preliminary Working Paper No.
OP-85, Centre of Policy Studies, Monash University[21] Yamada, Tomoaki (2011), ’A politically feasible social security reform with a two-tierstructure,’ Journal of the Japanese and International Economies, 25, 199-224

36

Table 1: The list of final domestic consumption goods
i=

1

2

3

4

5

6

7

8

9

10

Food

HousingFuel, Light &Wager Charge

Furniture &HouseholdUtensils

Clothing &Footwear

Pharmaceutical

MedicalServices

Public Hygene

SocialInsurance &Welfare

11

12

13

14

15

Education

Recreatinal
Services

Other
Consumption
Expenditure

OthersTransportation

Long-term&
Care Services Communication

Table 2 (Static part of the model)
i =

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

𝛽,

0.430839 0.720433 0.323142 0.242593 0.045946 0.684492 0.214598 0.093734 0.076498 0.170567 0.407861 0.140822 0.420927 0.404322 0.344764

𝛽,0.569161 0.279567 0.676858 0.757407 0.954054 0.315508 0.785402 0.906266 0.923502 0.829433 0.592139 0.859178 0.579073 0.595678 0.655236

Table 3 (Static part of the model)
i =
𝑎𝑦

1

2

3

4

5

6

7

8

9

10

0.369496 0.606607 0.496285 0.334325 0.310126 0.363902 0.544265 0.664799 0.678783

11

12

13

14

0.74492 0.338765 0.752842 0.455604 0.598733

15
0.27843

Table 4: Tax Rates for Year 2011 (Static part of the model)
i =

1

2

3

4

5

𝜏,

0.046438 0.047129 0.043652 0.034653 0.028944

𝜏,

0.011303𝜏,

0.122586 0.074455

6

7

8

9

10

11

0.02623 0.016043 0.016572 0.004445 0.022561 0.049094

0.00036 0.003873 1.77E-05 5.63E-05 1.13E-05 0.018181 5.01E-06 2.76E-05 0.003957
0.02539 0.068295 0.122509 0.050353

0

37

0

0

12

13

14

15

0.01273 0.040749 0.026369 0.018751

0.00212 0.001123 0.001082 0.004552 0.003998

0 0.037785

0 0.131171 0.043668

0.0562

Table 5 (Static part of the model)
i =

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

𝜅

0.007450.00604

0.03106

0.07568

0.279450.04784

0.00001

0.00000

0.00000

0.00000

0.15906

0.00249

0.112810.09157

0.13882𝜅

0.99255

0.993960.96894

0.924320.72055

0.952160.99999

1.00000

1.00000

1.00000

0.84094

0.997510.887190.908430.86118

Table 6 (Static part of the model)
i =

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

𝛾

0.09568

0.16252

0.032020.121540.55974

0.208410.00008

0.00000

0.00000

0.00000

0.07789

0.00392

0.14706

0.050480.05919𝛾0.90432

0.837480.96798

0.878460.44026

0.791590.99992

1.00000

1.00000

1.00000

0.92211

0.99608

0.852940.94952

0.94081

Table 7 (Dynamic part of the model)

38

Figure 1

39

1947
1951
1955
1959
1963
1967
1971
1975
1979
1983
1987
1991
1995
1999
2003
2007
2011
2015
2019
2023
2027
2031
2035
2039
2043
2047
2051
2055
2059
2063
2067
2071
2075
2079
2083
2087
2091
2095
2099
2103
2107

Figure 2

Total Population

140000000

120000000

100000000

80000000

60000000

40000000

200000000

Estimation of year 201740

Figure 3

Technological Progress(The Value of Ω)
1.80
1.70
1.60
1.50
1.40
1.30
1.20
1.10
1.00
0.90
2012 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032 2034 2036 2038 2040 2042 2044 2046 2048 2050 2052 2054 2056 2058 2060

41

Actual value

42

Recovery Case
Baseline Case

2029

2028

2027

2026

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

Figure 4-1

Nominal GDP Growth Rate

4.00%

3.00%

2.00%

1.00%

0.00%

‐1.00%‐2.00%‐3.00%‐4.00%‐5.00%

Figure 4-2

43Actual Value

44

Recovery Case
Baseline Case

2029

2028

2027

2026

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

Figure 4-3

GDP Ratio of Outstanding Governments Debts

250.00%200.00%150.00%100.00%50.00%

0.00%

1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040

Figure 5-1

The Future Scenario of Outstanding Governments Debts

250.00%200.00%150.00%100.00%50.00%

0.00%

Actual Value
Scenario based on the baseline case45

Actual value

46
Scenario

2098

2095

2092

2089

2086

2083

2080

2077

2074

2071

2068

2065

2062

2059

2056

2053

2050

2047

2044

2041

2038

2035

2032

2029

2026

2023

2020

2017

2014

2011

2008

2005

2002

1999

1996

1993

1990

1987

1984

1981

1978

1975

Figure 5-2

GDP Ratio of Public Pension Fund35.00%

30.00%

25.00%

20.00%

15.00%

10.00%

5.00%

0.00%

Table 8:
The Planned Distribution of the Remaining Cost of the Long-term Care Insurance by the MHLW

Year
2000－2002
2003－2005
2006 - 20082009 - 20112012 - 20142015 - 20172018 - 20202021 - 2023
2024 - 2026
2027 - 2029
2030 - 2032
2033 - 2035
2036 - 2038
2039 - 2041
2042 - 2044
2045 - 2047
2048 - 2050
2051 - 2053
2054 - 2056
2057 - 2059
2060 - 2062
2063 - 2065
2066 - 2068
2069 - 2071

Contributins by
1st group 2nd group
17%
18%
19%
20%
21%
22%
23%
23%
24%
24%
24%
25%
26%
27%
27%
28%
28%
28%
28%
28%
28%
29%
29%
29%

33%
32%
31%
30%
29%
28%
27%
27%
26%
26%
26%
25%
24%
23%
23%
22%
22%
22%
22%
22%
22%
21%
21%
21%

1st Group: Age 65 and Over
2nd Group: Age 40 – 64
Remaining Cost = Total Cost (100%) minus Co-payments (10%)

47

Tax
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%
50%

Table 9-1: Actual and Model Values of Year 2011 (Unit: a million yen)

i=

1

2

3

4

Actual

51,311,765.000

84,263,066.000

14,869,917.000

Model

51,311,765.001

84,263,066.003

14,869,917.001

Value Added Actual

33,355,633.000

106,109,375.000

41,282,598.000

Model

33,355,633.001

106,109,375.017

41,282,598.000

Labor Income Actual

13,665,229.000

21,039,644.000

24,355,051.000

Model

13,665,229.000

21,039,644.000

24,355,051.000

Capital IncomeActual

10,344,184.000

54,218,210.000

Model

10,344,184.000

54,218,210.000

GDP

Imports

5

6

7

8

9

10

11

12

13

14

15

9,390,053.000

5,324,630.000

1,104,482.000

41,445,753.000

780,896.000

9,390,053.000

5,324,630.000

1,104,482.000

41,445,753.002

780,896.000

7,847,093.000

8,238,273.000

65,941,196.000

23,766,675.000

56,274,356.000

151,581,036.000

37,924,142.000

7,847,093.000

8,238,273.000

65,941,196.001

23,766,675.001

56,274,356.006

151,581,036.002

37,924,142.005

13,643,503.000

5,759,641.000

4,587,009.000

23,239,086.000

13,643,503.000

5,759,641.001

4,587,009.000

23,239,086.000

952,821.000

5,337,562.000

6,175,231.000

60,028,697.000

26,462,315.000

57,627,965.000

149,495,613.000

26,006,284.000

952,821.000

5,337,562.000

6,175,231.000

60,028,697.002

26,462,315.000

57,627,964.997

149,495,613.005

26,006,284.000

6,892,128.000

1,329,720.000

813,524.000

6,892,128.000

1,329,720.000

813,524.000

18,321,142.000

842,514.000

4,897,379.000

4,997,142.000

26,171,066.000

22,274,987.000

23,236,498.000

79,591,099.000

13,627,196.000

18,321,142.000

842,514.000

4,897,379.000

4,997,142.000

26,171,066.000

22,274,987.000

23,236,498.000

79,591,099.000

13,627,196.000

11,627,451.000

2,207,508.000

64,038.000

1,764,933.000

5,005,951.000

87,140.000

405,674.000

1,027,626.000

18,026,421.000

3,650,952.000

16,890,584.000

54,023,212.000

7,170,178.000

11,627,451.000

2,207,508.000

64,038.000

1,764,933.000

5,005,951.000

87,140.000

405,674.000

1,027,626.000

18,026,421.000

3,650,952.000

16,890,584.000

54,023,212.000

7,170,178.000

Actual

6,291,913.000

23,313,420.000

2,356,211.000

3,370,947.000

3,773,737.000

1,735,393.000

3,620.000

0.000

0.000

0.000

9,349,371.000

136,686.000

12,382,949.000

10,551,695.000

3,888,429.000

Model

6,291,913.001

23,313,420.016

2,356,211.000

3,370,947.000

3,773,737.001

1,735,393.000

3,620.000

0.000

0.000

0.000

9,349,371.002

136,686.000

12,382,948.998

10,551,695.005

3,888,429.000

Actual

501,339.000

783,995.000

2,341,640.000

2,131,308.000

1,292,170.000

347,894.000

234.000

0.000

0.000

0.000

21,726,227.000

86,619.000

10,329,662.000

20,881,621.000

10,521,871.000

Model

501,339.000

783,995.000

2,341,640.000

2,131,308.000

1,292,170.000

347,894.000

234.000

0.000

0.000

0.000

21,726,227.000

86,619.000

10,329,662.000

20,881,621.000

10,521,871.000

Government Actual

239,401.000

2,525,419.000-672.000

789,704.000

504.000

0.000

33,159,023.000

416,088.000

5,819,952.000

7,643,350.000

205,911.000

18,224,475.000

2,290,558.000

39,953,798.000

14,194,133.000

Consumption Model

239,401.000

2,525,419.000-672.000

789,704.000

504.000

0.000

33,159,023.001

416,088.000

5,819,952.000

7,643,350.000

205,911.000

18,224,475.001

2,290,558.000

39,953,798.002

14,194,133.001

Exports

Investment Actual

294,408.000

21,179,091.000

2,748,172.000

745,595.000

81,926.000

56,797.000

0.000

0.000

0.000

0.000

5,910,820.000

0.000

15,564,667.000

13,736,884.000

13,208,138.000

Model

294,408.000

21,179,091.006

2,748,172.001

745,595.000

81,926.000

56,797.000

0.000

0.000

0.000

0.000

5,910,820.002

0.000

15,564,667.005

13,736,884.004

13,208,138.004

48

Table 9-2: Key Parameter Values of Year 2018 for the Dynamic Part of the Model

Variables

ActualModel

GDP ratio of outstanding government bonds

192.00% 192.00%

GDP ratio of public pension fund19.47%

19.47%

GDP ratio of government expenditures

37.33%

37.33%

Primary balance-1.90%-1.90%GDP growth rate (real)

0.30%

0.30%

National burden ratio

48.40%

49.00%

Replacement Rate of the Public Pension*

62.90%

62.83%

Contribution rate of the public pension in year 2017 **18.30%

18.29%

Wage income tax rate

33.24%

33.78%

Sources for the actual values: Ministry of Finance, Cabinet Office, and Ministry of Internal Affairs and Communications*) The replacement rate is of the Kousei-Nenkin**) The contribution rate is of the Kousei-Nenkin.

49

Figure 6-1

Demestic Demand
58,000,000.00

56,213,897.26

56,000,000.00

54,000,000.00

Unit: 1 million yen

52,000,000.00

50,000,000.00

48,000,000.00

46,000,000.00

44,000,000.00

42,000,000.00

40,000,000.00

Medical Services

50

Figure 6-251Figure 7-1

Total Labor Income
19,500,000.00

19,000,000.00

18,500,000.00

Unit: 1 million yen

18,000,000.00

17,500,000.00

17,000,000.00

16,500,000.00

16,000,000.00

15,500,000.00

15,000,000.00

14,500,000.00
2011 2013 2015 2017 2019 2021 2023 2025 2027 2029 2031 2033 2035 2037 2039 2041 2043 2045 2047 2049 2051 2053 2055 2057 2059 2061 2063 2065 2067 2069
Medical services

52

Figure 7-2

53

2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060

Unit: 1 million persons

Figure 8-1

Labor Force

500

450

400

350

300

250

Medical services
Social Insurance & Welfare + Long‐term care services

54

2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060

Unit: 1 million persons

Figure 8-2

Labor Force

16.50

16.00

15.50

15.00

14.50

14.00

13.50

Pharmaceutical Sector

55

2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060

Unit: 1 million persons

Figure 8-3

Labor Force

380

370

360

350

340

330

320

310

Long‐term care insurance sector

56