Immigration Policy and Demographic Dynamics: Welfare Analysis of an Aging Japan *Akira Okamoto**
Okayama University
May 14, 2021

Abstract
This paper quantified the effects of immigration policies in an aging anddepopulating Japan. Under a constant total number of immigrants, it focused on
the optimal period for an immigration policy that maximized the per-capita utility.
Simulation results, based on an extended lifecycle simulation model withendogenous fertility, showed that a longer period immigration policy increased thefuture population and enhanced long-run economic growth. Conversely, a shorter
period immigration policy enhanced economic growth in earlier years but less soin the long run. This paper found that an optimal duration for an immigration policy,
under the standard parameter settings for Japan, was nine years; this was derived
by the reconcilement of merits and demerits between shorter period and longer
period immigration policies.
Keywords: Immigration policy; aging population; welfare analysis;
dynamic overlapping generations model; simulation analysis.
JEL classification: H30; C68*

I am grateful for the insightful comments and suggestions of Professors Alan J. Auerbach, Ronald D. Lee,and Emmanuel Saez (The University of California, Berkeley). In addition, I want to thank Associate Professor
Yoshinari Nomura (Okayama University), who helped me in writing the computer program used for thesimulations. Finally, I also wish to acknowledge the financial support from the Social Science ResearchCouncil under an Abe Fellowship and the Ministry of Education, Culture, Sports, Science and Technology inJapan (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 aging at an unprecedented speed for a developed nation, and the
population is simultaneously decreasing, which has become one of Japan’s most important
problems. Figure 1 presents old-age dependency ratio projections (defined as a ratio of the
population aged 65 or older against that of 20–64) for five advanced countries. The ratio will rise
sharply and stay at an elevated level throughout the century. As the figure shows, the speed andmagnitude of demographic aging in Japan are remarkable, even compared to other countries thatface similar challenges. Thus, the projections of future fertility rates and survival probabilities inJapan indicate a severe reduction in both the total and working-age population. Regarding the
problems associated with aging and depopulating societies, increases in childcare allowances areoften discussed as one effective countermeasure. Another method for mitigating rapid population
decreases in Japan is an enhanced immigration policy.
In reality, advanced countries such as the United States (US) and Germany have accepted many
immigrants and have used the immigrant population to maintain the population level or to promoteeconomic growth. As Imrohoroglu et al. (2017) pointed out, however, Japan has been historicallyinsular concerning immigration and has followed insular policies for centuries, relying mainly onnative-born workers for economic growth. The annual inflow of immigrants to Japan is currently
low; according to data from the United Nations (2021), the stock of immigrants in Japan was only
1.97% of the total population (i.e., 126 million people) in 2019. Conversely, the stock of immigrants
in the US was 15.40% of the total population (i.e., 328 million people) in 2019.
During our research, we used the lifecycle general equilibrium simulation model ofoverlapping generations, developed by Auerbach and Kotlikoff (1983a, 1983b) and similarly
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), Okamoto (2005, 2010, 2013), and so on.
Okamoto (2020) extended the simulation model to introduce the number of children freely chosen
by households, thus incorporating endogenous fertility and future demographic dynamics.
In 2014, the Japanese government stated that it would consider a guest worker program thatwould bring 200,000 foreign workers to Japan annually over 10 years, eventually accumulating a
total of two million guest workers. To investigate the quantitative effects of an enhanced2

immigration policy, we extended the simulation model to freely set or choose the numbers andtimings of immigrant inflow. Alternative immigration policies have different durations and annual
numbers of immigrants. This paper analyzes the quantitative effects that increased immigration to
Japan might have on the future population and per-capita household welfare. It specifically focuseson the optimal immigration policy duration, under a constant total number of immigrants (withequally distributed immigrants each year). Here it should be noted that this result is obtained under
the current level of government childcare subsidies and under the assumption that the immigrants
are completely identical to the Japanese natives.
Regarding government childcare subsidies, in 2014, the Japanese government set a target
population of approximately 100 million in 50 years, whereas the population is projected by the
National Institute of Population and Social Security Research (2017) to reach only 88 million in
2065. This was the first time in history that the government formally expressed a numerical target
for the future population, revealing a sense of impending crisis. To realize the desired fertility rateof 1.8 the government began devising countermeasures for the falling birth rate. When the subsidies
increase, an optimal period for immigration policy may change. Therefore, we will examine theeffects of alternative immigration policies in a situation where child allowances increase.
Although our baseline simulation results are obtained under the assumption that the immigrants
have completely the same features as the native Japanese, immigrants to Japan tend to have higher
fertility, a shorter life expectancy, and lower labor productivity than Japanese natives; these threecharacteristics of immigrants may change an optimal period for the immigration policy. Therefore,
we will evaluate the effects of each atypical characteristic.
Our study also introduces an additional government institution, the Lump Sum Redistribution
Authority (LSRA), as shown in Okamoto (2020). Alternative immigration policies generally
improve the welfare of some generations but reduce the welfare of others. If combined withredistribution from winning to losing generations, such policies may offer the prospect of Pareto
improvements. Without implementing intergenerational redistribution, however, potential efficiency
gains or losses cannot be estimated. Therefore, like Auerbach and Kotlikoff (1987) and Nishiyama
and Smetters (2005), we introduce LSRA as a hypothetical government institution. Thisdistinguishes potential efficiency gains/losses from possible offsetting changes in the welfare of3

different generations. To isolate pure efficiency gains or losses, we consider simulation cases via
LSRA transfers where alternative immigration policies are implemented. 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 as well, which will allow us to present
concrete and useful policy proposals.
The remainder of this paper is organized as follows: Section 2 describes literature related to ourstudy; Section 3 identifies the basic model applied in the simulation analysis; Section 4 explains themethod and assumptions of simulation analysis; Section 5 evaluates the simulation findings anddiscusses policy implications; Section 6 summarizes and concludes.

2. Related LiteratureThis paper is contributing to the literature on immigration policy; the main literature related to ourstudy is:Auerbach and Oreopoulos (1999) reconsidered the fiscal impact of immigrants over time, using
the technique of generational accounting, and obtained two conclusions. First, whether immigration
contributes to (or helps) alleviate fiscal stress depends on the extent to which that stress will beshouldered by future generations. If the entire fiscal imbalance currently estimated for the US isplaced on future generations, then the presence of new immigrants reduces the burden to natives.
Second, the impact of immigration on fiscal balance is extremely small in relation to the overall sizeof an imbalance. Therefore, immigration should not be viewed as a major source of an existing
imbalance nor as a potential solution to one.
Storesletten (2000) used a general equilibrium model with overlapping generations, calibrated
to the US economy, and estimated the long-run fiscal impact of immigrants. Explicitly considering
the differences between immigrants and natives, the study argued that a large immigration policy(about 1.6 million annual flow starting in 2000) of high- and medium-skilled immigrants could
resolve fiscal problems. It found that the fiscal impact of immigration on the host country was
positive, even when taking into account the ages and skill levels of immigrants.
Lee and Miller (2000) analyzed the fiscal impact of immigration and found that 100,000 more
immigrants per year would initially raise taxes for nonimmigrants, later reducing them by amounts
4less than one percent of current tax levels. A higher rate of immigration would benefit OASDI (OldAge, Survivors, and Disability Insurance), even though many immigrants might have lower
education. As with other fiscal impacts, however, the effect was quite small. Their results alsosuggested that a policy of admitting only highly educated immigrants from young working ages
could be highly beneficial fiscally, which was consistent with the findings of Auerbach andOreopoulos (1999) and Storesletten (2000).
Storesletten (2003) used an accounting model for Sweden and calculated the net public gain of
a new immigrant as the discounted value of future tax payments, minus transfers and additional
government consumption. Consequently, the study found potential gains to be large, atapproximately $20,000 per new immigrant.
Fehr, Jokisch, and Kotlikoff (2004) developed a three-region overlapping generations modelfor the US, Japan, and European Union, and analyzed whether immigration could mitigate thenegative impacts of demographic transition on an economy. Their baseline experiment called for anannual flow of 54,000 immigrants (with the same amount of capital and children as their nativeborn counterparts), and an alternative of 108,000 only high-skilled immigrants. Their overall
conclusion was that there were small welfare effects and that the impact would be “too little toolate.” In other words, immigration would not alter the major negative impacts of demographictransition, regardless of the immigrants’ skill levels.
Our paper is contributing especially to the literature on immigration policy in Japan, as few
previous studies analyzed the quantitative effects of immigration policy for Japan. Both Shimasawa
and Oguro (2010) and Imrohoroglu et al. (2017) investigated using a lifecycle dynamic simulation
model with overlapping generations, revealing that more immigrants or high-skilled guest workers
would benefit the Japanese economy and that even more immigrants were needed to improve thefiscal balance of the government.
Shimasawa and Oguro (2010) used a 16-country/region overlapping generations model inwhich immigrants could not be distinguished from natives upon entry. Based on this assumption,
like Fehr, Jokisch, and Kotlikoff (2004) and other studies, immigrants’ labor productivity was thesame as their native counterparts, and they were eligible for pensions and public health insurance.
Their baseline immigration policy brought 150,000 immigrants annually, and the foreign-born
5

population eventually reached 37% of the Japanese population by 2100. Despite this large
immigrant population, the fiscal burden was hardly mitigated. The debt to GDP ratio by 2050 was
699%, while it was 719% under the baseline case without immigration. When the consumption tax
rate was raised to 30% under this high immigration assumption, the gains were much larger, and thedebt to GDP ratio also declined to 234% in 2050. Therefore, Shimasawa and Oguro (2010)concluded that immigration policy alone could not alleviate the fiscal burden.
Imrohoroglu et al. (2017) also developed a quantitative overlapping generations model andanalyzed the impact of guest worker programs in Japan. Against a baseline general equilibriumtransition where fiscal sustainability was attained by the consumption tax, the study computed
alternative transitions with guest worker programs. Their results revealed that, with a relatively
manageable increase in the consumption tax, these programs could mitigate Japan’s fiscal
imbalance problem; however, this was dependent on the size and skill distribution of guest workers.
Unlike the two studies above, we focus primarily on studying an optimal period for theimmigration policy (with equally distributed immigrants each year) under a constant total of two
million immigrants. Additionally, we consider the characteristics of immigrants that differ fromJapanese natives, such as their higher fertility, their shorter life expectancy, or their lower laborproductivity, and what effects these differences can have.

3. 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.
3.1. 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 notdistinguish by gender. Each agent enters the economy as a decision-making unit and starts to workat age 21 years, and lives to a maximum age of 105 years. Each household is assumed to consist of6

one adult and its children. The children aged 0–20 only consume, involving childrearing costs fortheir parent. Each household faces an age-dependent probability of death. Let q tj 1| j be theconditional 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   q tj 1| j .

(1)

j 21

The probability q tj 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 21 chooses perfect-foresight consumption pathst( Cst ), leisure paths ( ls ), and the number of born children ( nst ) to maximize a time-separable utility
function of the form:Ut     

1
105
1
1 
1  40 t
( s  21)
t 1 t( s 21)t  t 1


p
(
1


)
n

(
1


)
p
(
1


)
C
l
.
 s
s
s
s
1  ss 21
1   s 21

 

(2)



t

t

This utility function represents the lifetime utility of the agent born in year t . Cs , ls , andnst are respectively consumption, leisure, and the number of children to bear (only in the age 21–40) for an agent born in year t , of age s ;  is the utility weight of the number of children
relative to the consumption–leisure composite,  is the intertemporal elasticity of substitution, is the adjustment coefficient for discounting the future, and  is the consumption share parameterto leisure.
As shown in Okamoto (2020), fertility choice in the model is only based on the direct utility
that households obtain from their offspring, 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 theinvestment aspect of children socialized, as Groezen et al. (2003) pointed out. This creates thepossibility for households to free-ride on the scheme by rearing fewer or no children, still being
entitled to a full pension benefit. 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 of 21–40.
7tLetting As 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 1  {1  rt  s (1   r )} Ast  (1   w   tp s ) wt  s es {1  lst  tcst (nst )}  ast  orst

 bst ({1  lut  tcut (nut )}uRE21 )  (1   tc s ) Cst  (1   tc s )ts ,(3)

where rt is the pretax return to savings, and wt is the real wage at time t ;  ,  , and  t arewrp

is thethe tax rates on labor income, capital income, and consumption, respectively.  tccontribution rate to the public pension scheme at time t . All taxes and contributions are collected
at the household level. tc(n) is the time cost for childrearing. a is the bequest to be inherited,and or is the childrearing cost for orphans. There are no liquidity constraints, and thus the assets

As can be negative. Terminal wealth must be zero. An individual’s earnings ability es is an
exogenous function of age.
The public pension program is assumed to be a PAYG scheme similar to the current Japanesesystem. The pension benefit is assumed to comprise an earnings-related pension:

H t ({1  lut  tcut (nut )}uRE21 ) ( s  ST )bst ({1  lut  tcut (nut )}uRE21 )  ,( s  ST )
0

(4)

where

H t ({1  lst  tcst (nst )}sRE21 ) RE1 wt s es (1  lst  tcst (nut )) .
RE  20 s21

(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 is  . The
H t ({1  lut  tcut (nut )}uRE
21 )symbol bst ({1  lut  tcut (nut )}uRE21 ) signifies that the amount of public pension benefit is a functionof the age profile of labor supply, {1  lut  tcut (nut )}uRE21 .
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 0–20
years old. Regarding the childrearing costs, the model takes account of both monetary and time
costs. The children aged below 21 years old do not conduct an economic activity independently, andchildrearing costs for their parent arise until they become independent of their parent. The financial
cost for rearing the children, for the parent born in year t and s years old, is represented by8 s tt   (1   t  s )nk ( s  21, 22,, 40)k  21, (6) ts   40tt
 (1  t  s )nk ( s  41, 42,, 60)k s  20

 ts  0 ( s  61, 62,,105 ) ,(7) t  NW t ,(8)where  t 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 coststto the net lifetime income, NW , of the parent born in year t .
The number of children affects the available time endowment for a parent, because of the timerequired for childrearing. The time cost for rearing the children for the parent born in year t , of age

s , is represented by
tcst  nst ,(9)

where  is the parameter that shows the relation between the number of children and the timerequired for childrearing, which is assumed to be proportional to the number of born children.
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 households at time t . When BQt is the sum of bequests inherited byhouseholds at time t , the bequest to be inherited by each household is defined by(1   h ) BQt  sa ,
Et  s
t
s

(10)

where
105

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

(11)

s 21

 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 is the number of the households conducting an
economic activity independently, aged 21 and older. The number of the generation born in year t ,of age s , is represented by

N st  pst N 0t ,(12)9

Total childrearing cost of the orphans, who are inevitably generated as a consequence ofparents’ uncertainty over length of life, is distributed equally among all surviving households attime t . When ORt is the sum of childrearing costs incurred by households with age s years attime t , the childrearing cost for orphans for each household is defined byorst 

ORt  s,Et  s

(13)

where
60

ORt   ( N st 1s  N st s ) tss .

(14)

s 21

Therefore, the net amount of bequests is represented as a  or . 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:ttt 0  ls  1  tcs (ns ) t ls  1(21  s  RE )( RE  1  s  105 )

.

(15)

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 (15) (seeAppendix A 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 pt  t1 
Wst   st 1  Wr  s 1 ,
p
1

r
(
1


)
t s
 s 

Wst 

k

1

1



t
s



(n )

1



20

(1   )   (1  t s )
c
t s

g 0

t
s, g

(16)

,

(17)

t

1

where ts,0

= 1 for g  0 , 

t
s, g

 g

  {1  rt  s1k (1   r )} for g  1, 2,, 20 .
 k 1


Similarly, that for the consumption–leisure composite is represented by10 p t  t1 
Vst   st 1 Vr  s 1 ,
p
1

r
(
1


)
t s
 s 








(18)

1

(1   ) (Cst ) (lst )1   (Cst ) 1 (lst )1V .
1   tcts

(19)

3.2 Firm behavior
The model has a single production sector that is assumed to behave competitively using capital andlabor, subject to a constant-returns-to-scale production function. Capital is homogeneous anddepreciating, while labor differs only in efficiency. All forms of labor are perfectly substitutable.
Households with different ages, however, supply different amounts of some standard measure perunit of labor input.
The aggregate production technology is the standard Cobb-Douglas form:

Yt  Kt L1t  ,(20)

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 ,where k(21)

is the depreciation rate.

3.3 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. Pension account expenditure is financed by both contributions and a transfer fromthe general account.
The budget constraint of the narrower government sector at timeDt 1  (1  rt ) Dt  Gt  Tt ,tis given by(22)

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 the11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 ,(23)

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

Rt  (1   ) Bt ,(24)

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 by

Gt  gYt  Bt  GSt ,(25)

where Gt includes transfers to the public pension sector ( Bt ) and the government subsidies tochildrearing ( GSt ). The government spending except for the transfers and the subsidies is gYt ,which is assumed to be represented as a constant ratio ( g ) of national income. The spending isassumed to either generate no utility to households or enter household utility functions in a
separable fashion.
The total amount of government subsidy (including child allowances) to the childrearing costin year t is GSt :60

GSt   t  ( RC sa, t  RC sb, t ) ,

(26)

s

a
RC

N kt  s t  s nkt  s ( s  21, 22,, 40)

s,t


k  21,40
t s t s t s
 RC b  N k  nk (s  41, 42,, 60)s,tk  s  20
(27)

s  21

where RCta and RCtb are costs for childrearing when the parent’s age is 21–60 years old. Oncet

the parent become 61 years old, the cost does not exist because all children are independent. N s isthe number of the generation with age s years born in year t .
The total spending on the pension benefit to generations of age ST and above is represented
by
12

105

Bt   N st  sbst  s .

(28)

s  ST

The total revenue from pension contributions and the total tax revenue are represented by
Rt   p wt Lt ,(29)

Tt   w wt Lt   r rt AS t   tc AC t   h BQt .

(30)

Aggregate assets supplied by households, AS t , and aggregate consumption, ACt , are givenby105

AS t   N st s Ast s ,

(31)

s 21
105

AC t   N C
s  21

t s
s

t s
s

60

  ( RCsa, t  RCsb, t ) ,(32)

s  21

where aggregate consumption consists of adult’s consumption (at age 21–105 years old) andchildren’s consumption or cost (at age 0–20 years old).
Total population (i.e., the population aged 0–105), the population aged 21–105 (i.e.,
independents financially), and the population aged 65–105 (i.e., retirees) in year t are
respectively represented by
105 40Z t   N it  k i pkt  k nit  k i ,(33)

k  0 i  21
105 40Et   N it k i pkt k nit k i ,(34)

k 21i 21
105 40Ot   N it k i pkt k nit k i .

(35)

k 65i 21

The aging rate (i.e., the old-age dependency ratio), the ratio of the population aged 65 and over tothe total population, is given by Ot / Z t .

3.4. Market Equilibrium
Finally, equilibrium conditions for the capital, labor, and goods markets are described below:
3.4.1. 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 .

(36)

3.4.2. Equilibrium condition for the labor market
13

Measured in efficiency units, because aggregate labor demand by firms equals aggregate labor
supply by households,
RE

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

(37)s  21

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

Yt  ACt  {Kt 1  (1   k ) Kt }  gYt . (38)
An iterative program is performed to obtain the equilibrium values of the above equations.

4. Simulation Analysis
4.1. Method
The simulation model presented in the previous section is solved, given the assumption thathouseholds fundamentally 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].
Our study assumes the transitional economy of Japan from the initial steady state in 2015 to thefinal steady state in 2300. Alternative scenarios on the immigration policy are assumed to beannounced at the end of 2015. For simplicity, 2015 is set as the starting year, and we simulate thedemography and the economy in the following years. For the generations that were alive in 2015and have survived in 2016, their formation of future expectations is needed to pay attention to. In
2016, 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 profilesof the number of children to bear, consumption, and leisure for these generations, we calculated
their lifetime utility at 21 years.
The LSRA first transfers to each household affected by alternative immigration policies justenough resources (possibly a negative amount) to return its expected remaining lifetime utility backto its pre-change level in the benchmark simulation. For each household that is alive when the14policy is announced at the end of 2015, at its age in 2016, the LSRA makes a lump-sum transfer, toreturn its expected remaining lifetime utility back to its pre-change utility level. For each householdthat enters the economy after a change (from 2016 onward), at its age of 21 years, it makes a lumpsum transfer, to return its expected entire lifetime utility back to its pre-change level.
Note that the net present value of these transfers in 2016 across living and future households
will generally not sum to 0. Thus, the LSRA makes an additional lump-sum transfer to eachhousehold so that the net present value across all transfers is 0. To illustrate, we assume that these
additional transfers are uniform across all future generations. If the transfer is positive, then thechange has produced extra resources after the expected remaining lifetime utility of each householdhas been restored to its pre-change level. In this case, we can interpret that the change has createdefficiency gains, i.e., Pareto improvements. Conversely, if the transfer is negative, then the change
has generated efficiency losses. Thus, the total net present value of all lump-sum transfers to current
and future generations sums to 0 in 2016, satisfying the LSRA budget constraint (see Appendix B in
Nishiyama and Smetters (2005) for further details).
4.2. Simulation cases
This study considers scenarios with different immigration policies in Japan, as well as additional
cases in which LSRA transfers are introduced in alternative immigration policy cases. The
following simulation cases are investigated:
4.2.1. Baseline simulation
The benchmark case simulates the standard transition of the Japanese economy from 2015 to 2300,
in which no immigration policy is assumed in order to isolate the effect of alternative immigration
policies.
4.2.2. Immigration policy proposals
In 2014, the Japanese government mentioned an immigration policy that brought 0.2 million
immigrants annually for 10 years, for a total of two million immigrants. With a constant total of two
million immigrants, we considered the four immigration policy proposals with different durations.
Table 1 shows alternative scenarios with different periods, namely 1, 10, 20, and 30 years,

15

respectively. All policy proposals started in 2016 but ended in different years, which meant different
durations. In each immigration policy case, immigrants were equally distributed each year. We
assumed that immigrants could not be distinguished from natives upon entry and were completely
identical to the Japanese natives. Therefore, the labor productivity was the same as the native
counterparts, and the immigrants were also eligible for pensions.
4.2.3. Cases with LSRA transfers
We regarded the period in which the individual welfare gain was maximized as an optimal duration
for the immigrant policy. To distinguish potential efficiency gains/losses from possibly offsettingchanges in the welfare of different generations, we introduced the LSRA into the alternative
simulation scenarios with different immigration policies. The LSRA transfers produced a leveledand common welfare gain/loss for each household.
4.2.4. Immigration policy with increased government child subsidies
In 2014 the Japanese government set a target population of approximately 100 million in 50 years
and, as such, may increase the subsidy to childcare allowances. Therefore, we evaluated alternative
immigration policies with increased government child subsidies. First, we briefly examined theeffects of increases in the ratio of government subsidies to the overall cost of childrearing, assuming
the ratio in the baseline simulation to be 10% (  = 0.1). From 2016 onward, the ratio  wasincreased from 0.1 to 0.2, 0.3, 0.4, and 0.5, respectively, for each case. In a situation where thesubsidies were increased, an optimal duration for the immigration policy was investigated. Whenthe ratio  was increased, a leveled welfare gain for each household was calculated using the
LSRA method, and an optimal duration for the immigration policy was derived.
Additionally, we considered the combination of increased government childcare subsidies andimmigration policy. We assessed the effects of an immigration policy that brought all immigrants at
one time in 2016, in a situation where the subsidies rate to the childrearing cost was 0.5 (  = 0.5).
4.2.5. Immigrants with characteristics that differ from Japanese natives
In the above simulation, the immigrants were assumed to be completely identical to the Japanesenatives and could not be distinguished from natives upon entry. In reality, however, the immigrants
16were likely to have higher fertility rates, shorter life expectancies, and/or lower labor productivity.
Therefore, we additionally considered an immigrant policy case and evaluated an optimal duration
for the immigrant policy with consideration to each of these three characteristics.
4.2.6. Delayed immigration policy reforms
Furthermore, we also considered scenarios in which the immigration policy bringing all immigrants
at one time was implemented; in the baseline simulation, the immigration policy was conducted in2016, but we considered additional cases in which it was postponed and implemented in 2026 and2036, respectively.
4.3. Specification of the parameters
We chose realistic parameter values for the Japanese economy based on the literature (Nishiyama
and Smetters, 2005; Oguro et al., 2011; Imrohoroglu et al., 2017; Kitao and Mikoshiba, 2020).
Table 2 displays the parameter values assigned in the baseline simulation, and the data source usedin the calibration. Parameter values were chosen such that the calculated values of the model’s
endogenous variables approached the actual data values. Table 3 presents the endogenous variablesin the 2015 initial steady state. Because the simulation results depend on the model setting and thegiven parameters, we must be careful about the effects of any parameter changes.
4.3.1. Demography
The old-age dependency ratio, defined as a ratio of the population aged 65 or older against that of
20–64, will rise sharply and stay at an elevated level throughout the century. Figure 1 illustrates
projections, based on data from the Organization for Economic Co-operation and Development(OECD; 2017), of the dependency ratio in Japan and several other countries. It demonstrates thatthe speed and magnitude of demographic aging in Japan are remarkable, even when compared toother countries facing similar challenges.
Next, we describe how we assigned parameter values for childrearing since our simulation
model incorporated endogenous fertility. The Cabinet Office (2010) indicated the average annual
childrearing costs for a first-born child to annual income for each age. Based on this survey, weassigned the parameter value of  (i.e., the ratio of childrearing costs to parental net lifetime
income) such that the ratio of the annual net childrearing costs to annual labor income for the17

individual was, on average, close to 21.4%. Thus,  was assigned 0.036275.
The OECD (2017) presented public spending on family benefits in cash, services, and tax
measures as a percentage of GDP in 2013. For Japan, public spending ratios on family benefits incash, services, and tax measures to GDP were 0.80%, 0.46%, and 0.23%, respectively.1 We
assigned the value of parameter  (government childcare subsidies divided by childrearing cost)
to 0.1 in the model, as in Oguro et al. (2011). Consequently, the ratio of total government subsidies
to national income was 1.39% in the initial steady state.
Our model incorporated not only the monetary costs of childrearing but also the time costs.
Increases in the number of children diminish the parent’s available time, because of the timerequired for childrearing; more children to bear, more time required for childrearing. The parameter
determining this relation,  , was assigned under the simple assumption that one child required 1 h
per day for childrearing.2
4.3.2. Immigrants
All first-generation immigrants were assumed to enter Japan at age 213and permanently live inJapan. In the baseline simulation, we assumed that the immigrants were identical to the Japanesenatives. As the data in Table 4 shows, however, immigrants to Japan were likely to have different
characteristics in the three previously discussed respects. We consider these characteristics inadditional simulation cases: the first feature is the higher fertility rates of immigrants. Table 4
displays that the (weighted) average total fertility rate was 1.80, which was much higher than that of
the Japanese natives (i.e., 1.45 in 2015). The parameter value of preference to children in the utility
for the first-generation immigrants was assigned in the additional scenario to produce the target of1

In Japan, the ratio of total family benefits to GDP is only 1.49%, whereas it is, on average, 2.43% for the 33
OECD member countries. Thus, the level of governmental support for childrearing is considerably lower inJapan than in the OECD.
2 It is difficult to calibrate the value of parameter,  , which determines the time cost for childrearing in themodel. In the 2015 initial steady state, an average number of children to which a parent gives birth at the age
21–40 is 0.0364 per year. We assume that the parent’s available time endowment is 16 h per day and that thechildrearing time cost for one child is 1 h per day.
3 According to the data on age distribution for immigration excess number (Figure 3-5-4) in the National
Institute of Population and Social Security Research (2017), the age range of immigrants to Japan was
roughly 15 to 35, and most immigrants were around age 21 for both males and females. This data showed ourassumption that all immigrants entered Japan at age 21 was plausible.

18

the total fertility rate, namely 1.80, in the 2015 initial steady state.
The second feature is the shorter life expectancy of immigrants. The (weighted) average life
expectancy was shorter by approximately 8 years than that of the Japanese natives. As Table 4shows, it was only 75.81 years for the immigrants, as compared to 83.84 years for the Japanesenatives. In the additional scenario, the survival probability for the first-generation immigrants was
reduced by a ratio of 75.81/83.84. In Imrohoroglu et al. (2017), the life expectancy of guest workers
was assumed to be 70, which was shorter than that in our study. This was primarily because theirstudy used the life expectancy of male workers while our study used an average of males andfemales.
The third feature is the lower labor productivity of immigrants. In Imrohoroglu et al. (2017), thelabor productivity of immigrants was assumed to be half of the native Japanese counterparts forlow-skilled workers and the same for high-skilled workers. Because we did not distinguish the two
types of workers, we assumed that the first-generation immigrants were 0.75 times as productive as
their native Japanese counterparts. Thus, in the additional scenario, the labor endowments of theimmigrants were reduced by a ratio of 0.75.
In each additional simulation case, one of the different characteristics for the immigrants wasintroduced. To reflect the gradual assimilation process of immigrants, the second-generation
immigrants (children of the first-generation immigrants) were assumed to take a middle position
between the first-generation immigrants and the Japanese natives. Therefore, regarding the threeparameters on the preference to children in the utility function (  ), survival probabilities (ps ),and labor productivity ( xes ), the second-generation immigrants had an average parameter value
between the first-generation immigrants and the Japanese natives, as shown in Table 6.4
4.3.3. Age profile of labor efficiency
The age profile of earning ability was estimated using data from the Basic Survey on Wage
Structure (Chingin Sensasu) by the Ministry of Health, Labour and Welfare for the period (2008–2017). For workers, including both males and females, the labor efficiency profile was constructed

4Here, we assumed that immigrants to Japan, especially the first-generation immigrants, had the threecharacteristics: higher fertility, shorter life expectancies, and lower labor productivity; however, in reality,
these characteristics may be weakened in the Japanese living environment and culture.

19

from Japanese data on employment, wages, and monthly work hours.
To estimate the age profile of earnings ability, es , the following equation was constructed:

Qt  a0  a1 At  a2 At ,(39)

where Q is the average monthly cash earnings and A is the average age, for both male andfemale workers. Because bonuses account for a large part of earnings in Japan, Q includes
bonuses.
4.3.4. Taxes and expenditures
Tax rates on labor income, capital income, and inheritances were fixed at the current levels (6.5%,
40%, and 10%, respectively) during the entire period. Tax rates on consumption were endogenously
determined to satisfy Equations (25) and (30). General government expenditures, except fortransfers to the public pension sector ( Bt ) and government subsidies to childrearing ( GSt ), were
proportional to national income ( Yt ) as indicated in Equation (25). The ratio of general expenditure
to national income, g , was assigned 0.1 such that the endogenous tax rate on consumption was
realistic and plausible in the 2015 initial steady state (i.e., 12.16%). The ratio held constant at 0.1
during the entire period.
4.3.5. The public pension system
The public pension program was assumed to be a simple PAYG system similar to the current
Japanese system. The benefit was 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 average annual labor income for each household. General tax revenue finances half of the flatpart, 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 generalaccount in Equation (24) as 0.25, taken from Oguro and Takahata (2013). The replacement ratio (  )for public pension benefits in Equation (4) was 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 from the beginning of the next year.
204.3.6. Government deficits
To make our simulation feasible, net government debt ( Dt ) was assumed to be proportional tonational income. The value of parameter d , which is the ratio of net public debt to national income
as given in Equation (23), was assigned based on data from the Cabinet Office (2017). After 2015,
Japan’s national income is expected to decrease as the population declines. Therefore, theassumption that net government debt was proportional to national income during the entire period
implied that the government would successfully reduce future deficits.
4.3.7. 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 2015 initial steady state, an individual devoted, on average,
approximately 58% of the available time endowment (of 16 h per day) to labor during their working
years (ages 21–64 years).
4.3.8. 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
was assumed to be 0 in the simulation, reflecting Japan’s experience during the past two or three
decades (see Ihori et al., 2006).

5. Simulation Results
The overall results obtained by our simulation analysis revealed that more immigrants generate
more preferable outcomes and more productive immigrants bring about more favorable results, as
shown in Shimasawa and Oguro (2010) and Imrohoroglu et al. (2017). As the previous studies havesuggested, our results showed that a greater number of immigrants enhanced per-capita welfare,indicating that the policy generates favorable economic outcomes. Under the assumption that
immigrants are completely identical to the Japanese natives, the optimal duration for an
immigration policy leading to a maximization of per-capita welfare was nine years, given a constanttotal number of immigrants (with equally distributed immigrants each year).
Our simulation results also found that immigration policies with longer terms produced higher
21

economic growth in the long run; however, during the early years, less favorable economic
outcomes were identified because of fewer initial annual immigrants. Conversely, if all immigrants
entered immediately in a concentrated period, there would be positive outcomes in the early years
but less favorable outcomes in the long run. This was because the utility-maximizing behavior ofindividuals was badly disturbed due to substantial adjustment costs accompanied by sudden andlarge changes in this immigration policy. The optimal immigration policy duration of nine years, asmentioned, was derived by reconciling merits and demerits between shorter period and longer
period immigration policies.
5.1. Baseline simulation
In the baseline scenario, to isolate the effects of immigration policies, no immigration policy was
assumed. Figure 2 illustrates the transition of the total population for the benchmark case (  = 0.1)
and the reform cases in which government childcare subsidies were increased (  = 0.2, 0.3, 0.4,
0.5). As the subsidies were increased, the future population was progressively enhanced.
5.2. Immigration policy proposals
First, we described the simulation results for four experiments on immigration policy, with 1, 10,20, and 30-year durations, respectively. Figure 3 shows the percent changes in the total population
for the four experiments from the benchmark scenario. In the long run, the immigration policy witha 30-year duration created the largest total population, while that with only 1-year duration createdthe smallest total population. By contrast, for approximately the first 50 years after policy
implementation, the immigration policy introducing all immigrants at one time in 2016 brought
about the largest total population. Figure 4 illustrates the percent changes in national income for thefour experiments from the benchmark case. For approximately the first 50 years, the 1-year
immigration policy attained the highest national income, reflecting the transition of total population.
In the long run, conversely, the 30-year immigration policy ultimately achieved the highest national
income. Figures 5 and 6 present the percent changes in capital stock and labor supply, respectively,
for the four experiments.
From the long-term perspective, the 30-year period immigration policy was desirable, as shownin Figure 4. In the long run, the immigration policy attained a 6.5 percent increase from the baseline22simulation for total population, capital stock, labor supply, and national income. Conversely, fromthe short-term perspective, the 1-year-period immigration policy was preferable. Although the 1year immigration policy temporarily provided a large shock to the economy because of many
immigrants at one time, it created the most favorable outcomes on national income for the first 44
years of 2016–2059. From 2060 onward, however, it declined to the worst performance, mainly
because the first-generation immigrants would simultaneously retire in 2060.
Therefore, from the short-term perspective, the immigration policy that immediately brought
all immigrants at one time in 2016 was desirable. Conversely, from the long-term perspective, theimmigration policy that gradually brought fewer annual immigrants for a long period was desirable
because this policy generated a larger future population.
Regarding the four scenarios on immigration policy, Figures 5 and 6 illustrate the percent
changes in capital stock and labor supply, respectively, from the benchmark case. During
approximately the first 50 years, the immigration policy with a 1-year duration attained the highest
levels of capital stock and labor supply.5 Conversely, in the long run, the 30-year immigration
policy achieved the highest level at 6.5 percent, reflecting the total population.
Concerning the four scenarios on immigration policy, Figures 7 and 8 show the percent
changes in interest rates and wage rates, respectively, from the benchmark scenario. For
approximately the first 40 years, the immigration policy that brought all immigrants in 2016 sharply
reduced the wage rates because of sudden increases of immigrant workers, rapidly raising theinterest rates. This 1-year immigration policy dramatically changed the factor prices and thus the
economy. Conversely, the immigration policy proposal with a longer duration, such as 20–30 years,
did not disturb the factor prices so sharply.
Regarding the four scenarios on immigration policy, Figures 9 and 10 illustrate the percent
changes in consumption tax rates and contribution rates, respectively, from the benchmark case. As
Figure 9 shows, these immigration policy proposals fundamentally reduced the tax rates on
consumption (roughly speaking, during the period from around 2035 to around 2100) because of the
5

In the case of the immigration policy that brought all immigrants at one time, just after the reform, thecapital stock slightly decreased in a few years. One of possible reasons for this was the assumption that the net
government debt was proportional to the national income each year, and thus that a rapid increase of the debt,
caused by a sharp increase in national income, decreased the capital stock (see Equation (36)).

23

promoted economic growth. Because the policies increased workers who were levied oncontributions and decreased the dependency ratio between retirees and workers, these immigration
policies sharply reduced the contribution rates, as Figure 10 shows.
Figure 11 illustrates the welfare change rates for each generation concerning the above four
immigration scenarios. Broadly speaking, throughout the alternative cases, the generations born
until around 2050 were made substantially better off, while the generations born from around 2060
to around 2150 are made slightly worse off. Initially, new immigrant workers greatly benefited theJapanese natives; however, after the immigrants retired and pension benefits began, it made thenatives slightly worse off for a while.
5.3. Cases with LSRA transfers
The simulation results of cases with LSRA transfers showed that the nine-year immigration policy
was desirable from the viewpoint of per-capita welfare. As Table 5 presents, the leveled welfare
gain for each individual was approximately 0.854 million yen (approximately 7,000 U.S. dollars in2015), which is a considerable amount.6 In terms of efficiency, it is preferable to implement thenine-year-period immigration policy with approximately 0.222 million immigrants annually. One
may expect that an immigration policy that immediately brings all immigrants at one time createsfavorable outcomes not only in the short term but also in the long term because many immigrants inearlier years lead to more children and more descendants, resulting in a larger total population andmore favorable results in the long run. However, this expectation can be wrong and several elements
should be considered.
We assumed the initial steady state in 2015. The generations alive in 2015 and into 2016
realized in 2016 that their previous expectations were wrong and again maximized their remaining
lifetime utility. The immigration policy that immediately brought all immigrants at one time may
severely disturb their utility-maximizing behavior and badly hurt welfare due to sharp, rapid, andunexpected changes and fluctuations. Because there was a large gap between the ex-ante
6

The GDP of Japan in 2015 was estimated to be 516.79 trillion yen by the Cabinet Office (2017), and thelabor force aged 20–64 years was 57.79 million in 2015, according to data from the Ministry of Internal
Affairs and Communications (2017). We calculated the income per worker using these data and also derived
the value for national GDP in 2015 in our model, yielding a conversion rate between actual amounts of yen
and values in the model. Consequently, in 2015, unity in the model corresponded to 5.1614 million yen.

24

expectation in the 2015 initial steady state and the ex-post expectation in 2016, the generations
could not fully maximize their lifetime utility. This entails large adjustment costs, which may also
bring about fewer children to bear.
Also, in the case of immigration policy that immediately brought all immigrants at one time, 44
years later the immigrants would all simultaneously retire because we assumed that they all enteredand started to work at age 21 and retired at age 64. All first-generation immigrants retired at one
time in 2060, which also gave a substantial negative shock to the economy. The wage rate sharply
decreased in 2016, when many immigrants simultaneously enter Japan, and then suddenly jumped
in 2060 when they all retired at the same time. This depends mainly on our simple assumption that
all immigrants enter Japan at age 21, which may be slightly unrealistic. Conversely, the immigration
policy that gradually brought immigrants over a long period could disturb the economy less becauseof the gradual and smooth changes and fluctuations.
Figures 3 and 4 illustrate that the 30-year immigration policy achieved the highest total
population and the highest economic growth in the long run. A reason for this could be that theJapanese population will continue to rapidly decrease, and immigrants in later years take a larger
share in the total population. In later years, immigrants would be more valuable and more beneficial
to the economy. The above results depend on the fertility rate for the immigrants. If we assume
higher fertility for the immigrants, the policy that immediately brought all immigrants at one time
could create more favorable results.
In 2014, the Japanese government mentioned an immigration plan to allow 0.2 million
immigrants annually for 10 years (a total of two million immigrants). We found that thisimmigration policy period was very close to the period suggested as an optimal duration in our
simulation analysis (nine years), which was robust despite the total number of immigrants (for the
total, one to three million immigrants). Note that this result was obtained under the current level ofgovernment child subsidies (  = 0.1) and under the assumption that the immigrants were identicalto the Japanese natives with completely identical characteristics. In reality, in 2014 the government
declared a concrete numerical goal on the future population. Specific countermeasures for the
declining birth rates may be introduced, and government childcare allowances may be actively
promoted.
25

5.4. Immigration policy with increased government child subsidies
Table 5 displays that increases in government childcare allowances reduced the optimal period for
immigration policy. Under the current child subsidies (  = 0.1) an optimal period for immigration
policy was nine years, but six years for  = 0.3 and only one year for  = 0.5. When the Japanese
government increases the subsidies, it would be desirable to simultaneously implement animmigration plan that brings a greater number of immigrants in earlier years. An increase inchildcare allowances would promote economic growth in the long run, but just after the increase,
there would be a decrease in national income for several years. This is because it takes roughly 20
years for the children, who were newly born due to increases in child subsidies, to become adults
and contribute to society.
Therefore, this negative effect could be compensated for by allowing more immigration inearlier years. For example, when  is equal to 0.5, the 1-year period for immigration is desirable
because it can compensate for the large negative effects of high consumption tax rates, induced by
the policy of increases in childcare allowances. There are two ways for maintaining the future
population, namely, immigration policy and child allowances, but the two policies havesubstantially different effects on the economy. The combination of these two policies is desirable
because the immigration policy can successfully compensate for the drawbacks of the government
child subsidies policy.
Regarding the increased government child subsidies policy (  = 0.5), the immigration policythat brought all immigrants at one time in 2016, and their combination cases, Figures 12, 13, and 14
show the changes in national income, capital stock, and labor supply, respectively, from the levelsof the benchmark case. Figure 14 illustrates that increases in the child subsidies (  = 0.5) decrease
the labor supply, mainly because of childrearing time cost, until 2041, after which, the labor supply
begins to increase. Consequently, as Figure 12 shows, increases in child allowances reduce thenational income until 2022, increasing thereafter. This revealed that a large increase in government
child subsidies would be detrimental to the economy during the first several years, thereafter theincrease would have a substantial positive effect. As Figure 12 suggests, the immigration policy thatbrought two million immigrants at one time in 2016 could successfully cover this potential issue

26

with increased childcare subsidies. The policy of increased childcare subsidies alone decreased
national income until 2022, whereas the combination policy of the increased subsidies and thisimmigration plan reduced national income only until 2017.
5.5. Immigrants with characteristics that differ from Japanese natives
The above results were obtained under the assumption that the immigrants had three characteristics
in common with the Japanese natives: the preference for children, life expectancies, and laborproductivity. However, according to the data in Table 4, which shows details of immigrants toJapan, immigrants were likely to have a stronger preference for children, a shorter life expectancy,and lower labor productivity. The differences in characteristics between the immigrants and thenatives brought about different outcomes and thus different optimal duration for the immigration
policy. Table 6 presents the parameter values that determined these characteristics for theimmigrants, and Table 7 shows that each difference shortens an optimal period for the immigration
policy.
First, when a higher fertility characteristic for the immigrants was considered, an optimal
duration for the immigration policy became shorter by four years, from nine years to five years(indicated in Table 7). The per-capita welfare obtained through LSRA transfers enhanced from¥854,000 to ¥986,000, which signified welfare improvement for the Japanese natives. This was
because immigrants with higher fertility contributed more to the future population, which had apositive effect on the economy, especially under a PAYG social security system, reducing
contribution rates by more young workers.
Second, when shorter life expectancies for the immigrants were considered, the Japanesenatives’ welfare was improved. This was because the immigrants were more likely to die earlier,taking less public pension benefits than their Japanese counterparts from the government, thereby
improving the pension finance. Thus, shorter life expectancies in immigrants generated morefavorable outcomes for the Japanese natives. The optimal duration became shorter by two years,
from nine years to seven years, as shown in Table 7. The per-capita welfare increased from¥854,000 to ¥878,000, which meant welfare improvement for the Japanese natives.
Third, when lower productivity characteristics for the immigrants were considered, the27

Japanese natives’ welfare deteriorated. This was because the impact reduced national income. The
optimal duration became shorter by two years, from nine years to seven years, as displayed in Table
7. The per-capita welfare decreased from ¥854,000 to ¥648,000, which signified welfare
deterioration for the Japanese natives. This was caused by less labor supply, measured by efficiency
units, because labor productivity for the immigrant workers was lower than that in the benchmark
scenario.

On the whole, as the government child subsidies increased, or if each of the three characteristics for
immigrants (higher fertility, shorter life expectancy, and lower labor productivity) was introduced,
the optimal duration for the immigration policy was reduced. If the immigrants were assumed tohave higher fertility or a shorter life expectancy, it would benefit the Japanese economy. This wasprimarily because higher fertility led to a larger future population, which was beneficial to theJapanese natives, especially under a PAYG social security system. A shorter life expectancy meantthat the immigrants received fewer pension benefits, resulting in improved pension finance.
Conversely, the immigrants’ lower labor productivity had a negative influence on the Japanesenatives, and made them worse off, damaging economic growth.
Finally, Table 4 shows that the population share of immigrants from the Philippines to Japan isfairly high (10.2%). Filipinos have a high fertility rate (TFR 2.944) and a considerably shorter-thanaverage life expectancy (68.4 years). Based on the above analysis, it may be beneficial to theJapanese natives to positively increase Filipinos as immigrants to Japan, due to their high fertility
rates and short life expectancies.
5.6. Delayed implementation of immigration policy proposals
In the baseline simulation, the immigration policy that brought all immigrants at one time wasconducted in 2016. We considered additional cases in which this was conducted in 2026 and 2036,
respectively. Although we assumed to immediately start implementing immigration policy
proposals, in reality, the implementation will be likely postponed. To analyze the effects of delayed
implementation, we simulated the additional cases in 2026 and 2036.
Table 8 reveals that a delay in immigration policy implementation decreased the per-capita

28

welfare through LSRA transfers. As the starting year of the immigration policy was postponed from2016 to 2026 and 2036, the per-capita welfare gained by the immigration policy decreased from¥842,000 to ¥777,000 and ¥714,00, respectively. This was mainly because a lower ratio of young
workers to retirees will potentially damage the economy and deteriorate individual welfare,especially under a PAYG social security system. Since more immigrants increased this ratio, theimmigration policy proposal recommended in this study should be executed as early as possible.
5.7. Sensitivity analysis for the time preference
Furthermore, to examine the effect on an optimal duration for the immigration policy, we conducteda sensitivity analysis for the adjustment coefficient for discounting the future. Table 9 shows that, as
the adjustment coefficient for discounting the future,  , was larger, an optimal duration for theimmigration policy grew shorter. The optimal period for the standard value (  = 0.0001) was nine
years. As the value (  ) increased to 0.001, 0.05, and 0.01, it reduced the optimal duration to eight
years, four years, and one year, respectively. Thus, if we assumed a higher time preference forindividuals, an optimal period for the immigration policy was shorter. This was because, when
individuals discounted more the future in their utility function and the present was more important,they preferred more immigrants in earlier years.

6. Conclusions
This study examined the quantitative effects of immigration policies on the future demography andindividual welfare in an aging and depopulating Japan. Using an extended lifecycle generalequilibrium model with endogenous fertility, it quantified the effects of alternative immigration
policy proposals during the period from 2015 to 2300. We focused especially on the optimal
duration for the immigration policy under a constant total number of immigrants. Additionally, toevaluate the pure efficiency gains or losses of these policy proposals, we introduced an additional
government institution (LSRA) and calculated the per-capita welfare.
Our analysis revealed four main findings:
1.

As several previous studies suggested, our simulation results revealed that more immigrants
enhanced the per-capita welfare of future generations, increasing the future population. The
optimal duration for the immigration policy, in which the per-capita welfare of individuals was
29maximized, was nine years under a constant total number of immigrants (with equallydistributed immigrants each year). The result had robustness for a total of one to three million
immigrants. It should be noted that this result was obtained under the current level ofgovernment child subsidies and under the assumption that immigrants had identicalcharacteristics with the Japanese natives.
2.

In terms of economic growth in the long run, a longer duration for the immigration policy was
desirable. An immigration policy with a longer period ultimately generated a larger total
population and higher national income; however, in the early years, just after the immigration
policy started, the policy could not bring about favorable outcomes due to fewer annual
immigrants. Conversely, the immigration policy that immediately brought all immigrants at
one time led to substantially improved performance in the early years, but less so over the longterm. Also, this 1-year immigration policy badly disturbed the utility maximization behavior
for individuals for sudden and large changes on the economy. Therefore, the above optimal
duration of nine years for the immigration policy was led by the reconciling of these two
effects working in different directions.

3.

As the government childcare subsidies increased, an optimal period for the immigration policy
was reduced. If the Japanese government simultaneously implemented these policies (childcare
subsidies increases and the immigration proposal), more immigrants were desirable in earlier
years. This was because an increase in childcare allowances promoted economic growth in thelong run, but, for the years just after the increase, there was a decrease in national income dueto the added childrearing costs spanning approximately 20 years. More immigrants in earlier
years could successfully compensate for this negative effect on the economy.

4.

Immigrants to Japan are likely to have higher fertility, shorter life expectancies, and lower
labor productivity than Japanese natives. The introduction of each of these three characteristics
for immigrants shortens the optimal duration for an immigration policy. The per-capita welfare
gains for the Japanese natives increased when the immigrants had higher fertility or shorter life
expectancies. This was because higher fertility contributed more to the future population,
which benefited the natives, especially under a PAYG social security system. Additionally,
because a shorter life expectancy meant fewer pension benefits received by the immigrants,
30

improvements were seen in pension finance. Conversely, when the immigrants had lower laborproductivity, the welfare gains decreased through damage to the economy.

Appendix A: The Utility Maximization Problem
The utility maximization problem over time for each individual in Section 2 is regarded as the
maximization of U t in Equation (2) subject to Equations (3) and (15). Let the Lagrange function be105

Lt  U t   ts  Ast 1  {1  rt  s (1   r )} Ast  [1   w   tp s ] wt  s es {1  lst  tcst (nst )}  ast  orsts  21RE bst ({1  lut  tcut (nut )}uRE21 )  (1   tc s ) Cst  (1   tc s ) s   st {1  lst  tcst (nst )} , (A1)s 21where ts and  st represent the Lagrange multiplier for Equations (3) and (15), respectively.
The first-order conditions on the number of children nst , consumption Cst , leisure lst , andassets Ast 1 for s = 21, 22, …, 105 can be expressed by20pst (1   ) ( s21) (nst )   ts [1   w   tps ] wt s es  (1   tc ) ts , g t (1  t s )
g 0


1

wt  s es105

   tk

RE  20k  ST st ,(A2)
1

where ts,0

= 1 for g  0 , 

t
s, g

 g

  {1  rt  s1k (1   r )} for g  1, 2,, 20 ,
 k 1  (C ) (l )

 (1   )(C ) (l )pst (1   )(1   ) ( s 21) (Cst ) (lst )1pst (1   )(1   ) ( s21) (Cst ) (lst )1





105

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

1

t 
s



wt s es
RE  20  stts  {1  rt  s (1   r )}ts 1 ,

 st {1  lst  tcst (nst )}  0
1  lst  0

t 1
s

 ts (1   tc s ) ,

(A3)

t 
s

( s  RE ) ,

(A4)
(A5)

( s  RE ) ,(A6)( s  RE ) ,(A7)st  0 .

(A8)

The combination of Equations (A2) and (A5) produces Equations (16) and (17). If the initial value,

n21t , is given, the initial value, W21t , can be derived from Equation (17). If the value, W21t , is specified,31

the value of each age, Wst , can be derived from Equation (16), which generates the value of eachage, nst . If the value, nst , is specified, the childrearing cost for lifetime is calculated, which gives
the lifetime budget constraint represented by Equation (A10).
The combination of Equations (A3) and (A5) produces Equations (18) and (19). If the initialtvalue, V21 , is specified, the value of each age, Vst , can be derived from Equation (18). If Vst is
specified, the values of consumption, Cst , and leisure, lst , at each age are obtained in the methodthat follows.
For s = 21, 22, …, RE, the combination of Equations (A3) and (A4) yields the following
expression:
105 t
 
k wt s es  st  
w
p

(
1




)
w
e

 t  t st s st
RE
20s   t
k

ST
s
t

Cs  l .
 s(1   ) (1   tc s )





(A9)

If the value of lst is given under  st = 0, the value of Cst can be obtained using a numericalmethod, and then the value of Vst can be derived from Equation (19). The value of lst is chosen
so that the value of Vst obtained in the simulation is the closest to that calculated by evolutiontfrom V21 through Equation (18). If the value of lst chosen is unity or higher, the value of Cst is
obtained from Equation (19) under lst = 1. If it is less than unity, the value of Cst is derived from
Equation (A9).
For s = RE+1, RE+2, …, 105, the condition of lst =1 leads to the following equation:


Vst 

  1
t

s
.
c
ts

(1   ) (C )
1

(19)

The value of Cst is chosen to satisfy this equation.
ttFrom Equation (3) and the terminal condition A21 = A106 =0, the lifetime budget constraint fortan individual (= NW ) is derived:
RE

105

105

 st [1   w   tp s ]wt s es {1  lst  tcst (nst )}   st bst ({1  lut  tcut (nut )}uRE21 )   st (ast  orst )s  21s  ST105

40ss  21s  21 k  21s  216040

  st (1   tc s )C st    st (1   tc s ) t (1   t  s )nkt    st (1   tc s ) t (1   t  s )nkts  41 k  s  20

(A10)
32

1

where t
21 = 1 for s
rs = 21,    {1  rt  u (1   )} for s = 22, 23, …, 105.
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35

Table 1 Alternative simulation scenarios on the immigration policy
Duration (years)

Annual immigrants (thousands)

1 (2016)2,000

10 (2016–2025)200

20 (2016–2035)

100

30 (2016–2045)

66.66667

Note: Each scenario has a total of two million immigrants.

36

Table 2 Exogenous variables for the benchmark simulation
Parameter description

Parameter value

Data source

Share parameter for consumption  0.5

Nishiyama and Smetters(2005):   0.47

Weight parameter of the number of children to theconsumption–leisure composite in utility  0.25

Rate of time preference  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):

Ratio of childrearing costs to net lifetime income  0.036275

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

  0.1

Hayashi and Prescott (2002):

  0.25

Oguro and 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  0.81721

Dependency ratio (i.e., aging rate)

O / Z  0.26647

37

Table 3 Endogenous variables in the 2015 initial steady stateParameter description

Parameter value

Interest rate, r

0.07240

Wage rate, w

1.07480

Tax rate on consumption, Contribution rate, 

0.12157c0.14224

p

Capital–income ratio, K / Y

2.45559

Total fertility rate (TFR)

1.45001

Ratio of net childrearing costs to annual labor income

0.21180

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

0.01388

38

Table 4 Origin countries for immigrants to JapanCountry

TFRLife expectancy

Share (%)

1

China

1.569

(years)75.98629.1892

Korea, Rep.

1.239

82.15619.015

3

Philippines

2.944

68.407

10.226

4

Vietnam

1.96

75.778

8.393

5Brazil1.778

74.676

7.593

6

Nepal

2.167

69.973

2.832

7

United states

1.843

78.7412.254

8Rep. of China (Taiwan)

1.12

80.2

2.215

9

Peru

2.427

74.781

2.004

10Thailand

1.497

74.6012.000

11Indonesia

2.437

69.072

1.798

12

Korea, Dem. People’s Rep.

1.968

70.338

1.362

13

India

2.395

68.3491.203

14Myanmar2.177

66.042

0.746

15

Sri Lanka

2.062

74.9530.728

16

United Kingdom

1.81

81.6050.691

17Pakistan

3.55

66.3770.577

18Bangladesh

2.144

72.0010.519

19France2.01

82.671

0.488

20Australia

1.833

82.451

0.436

21Canada1.6

82.1380.421

22Malaysia

1.931

74.8750.381

23

Cambodia

2.595

68.656

0.351

24

Russian Federation

1.75

70.9090.349

25

Mongolia

2.638

69.8210.320

26

Germany

1.5

81.09

0.284

27

Bolivia

2.923

68.74

0.233

28

Turkey2.052

75.426

0.195

29

Iran, Islamic Rep.

1.685

75.591

0.168

30

Italy

1.37

83.49

0.160

(Weighted average)

1.803

75.81197.131

Notes: This is stock data for immigrants in 2016. Japan in 2015: TFR 1.45, Life expectancy 83.844 years.

39

Table 5 Optimal duration for alternative immigration policies under different levelsof government child subsidies
Government child subsidies
ratio (  )Optimal period(years)Welfare gains in yen(thousand)0.1

9853.630.2

82,674.63

0.3

64,635.12

0.4

46,738.37

0.5

19,002.72

Note: The ratio of government subsidy to the total childrearing cost is 0.1 in the benchmark case.

Table 6 Parameter values atypical to immigrants to JapanFirst-generation

Second-generation

Japanese natives



immigrants
0.0729

immigrants
0.058765

0.04463

0.904186

0.952093

1

x

0.75

0.875

1

 : Preference parameter to children in the utility function
 : Weight parameter on survival probabilities (ps )x : Weight parameter on labor efficiency ( xes )Table 7 Welfare gains for the immigration policy in which immigrants have one ofthree features different from Japanese nativesαxOptimal period(years)Welfare gains in yen(thousand)

Benchmark0.0446311

9853.63Higher fertility

0.07291

15

985.52Lower life expectancies

0.044630.9041817

877.81

Lower labor productivity

0.04463

6
1

0.75

7

647.57

Note: Parameters (  , , x ) are described in Table 6, which also presents the parameter values for thesecond-generation immigrants.

40

Table 8 Welfare gains for the immigration policy with different timings ofimplementation
Year ofimplementation

Welfare gains in yen(thousand)2016

842.072026

776.992036

714.07

Note: The results for the simulation case immediately bringing two million immigrants at one time.

Table 9 Welfare gains for the immigration policy under different rates of time
preference
δ

α



x

Optimal period(years)Welfare gains in yen(thousand)

0.0001

0.0446311

9853.630.001

0.044631

1

8824.320.005

0.044631

1

4

706.730.01

0.044631

1

1

589.53

 : Adjustment coefficient for discounting the future in the utility function

 : Parameter that represents the preference to children in the utility function
 : Weight parameter on survival probabilities (ps )x : Weight parameter on labor efficiency ( xes )41

Source: OECD (2017)
Note: The dependency ratio denotes the ratio of the people aged 65 or over against that aged 20–64.

Figure 1

Old-age dependency ratio projections for five advanced countries

Notes: The ratio of government childcare subsidies (  ) is 0.1 in the benchmark case. The ratio isincreased to 0.2, 0.3, 0.4, and 0.5 for the alternative cases.

Figure 2

Transition of total population for the benchmark and four cases ofincreases in government childcare subsidies

42Figure 3

Changes in total population from the benchmark for four immigration
policy scenarios

Figure 4

Changes in national income from the benchmark for four immigration
policy scenarios

43Figure 5

Changes in capital stock from the benchmark for four immigration policy
scenarios

Figure 6

Changes in labor supply from the benchmark for four immigration policy
scenarios

44Figure 7

Percentage-point changes in interest rates from the benchmark for four
immigration policy scenarios

Figure 8

Changes in wage rates from the benchmark for four immigration policy
scenarios

45Figure 9

Percentage-point changes in consumption tax rates from the benchmark forfour immigration policy scenarios

Figure 10

Percentage-point changes in contribution rates from the benchmark forfour immigration policy scenarios

46

Figure 11

Welfare changes of each generation from the benchmark for four
immigration policy scenarios

Figure 12

Changes in national income from the benchmark for immigration policy,
government child subsidy, and their combination

47

Figure 13

Changes in capital stock from the benchmark for immigration policy,
government child subsidy, and their combination

Figure 14

Changes in labor supply from the benchmark for immigration policy,
government child subsidy, and their combination

48