Immigration Policy and Sustainability of Social Security in Japan ‡Naomi Miyazato 
Nihon University

Abstract
The aging of the population in Japan is the most severe among all developed countries.
Before the baby-boomer generation started to retire, Japan’s government proposed andimplemented many social security reforms. Unfortunately, it is hard to say if thosereforms will achieve sustainability of Japan’s social security system. There are only two
ways for sound financing of social security: decreasing benefit levels or increasing tax
revenues. Although analyzing and debating the recovery of the birthrate have often
been discussed for increasing tax revenues, immigration policy has barely been
investigated, despite the strong implication for the sustainability of social security.
This paper explores whether an immigration policy could mitigate intergenerational
imbalances and achieve sustainability of the social security system in Japan. I apply adynamic general equilibrium simulation model, which was developed by Auerbach andKotlikoff (1978), to study the effects of immigration policy. By adopting a dynamic
set-up, I’m able to investigate the impact on the financing of social security before andafter the retirement of immigrants. In addition, I am able to analyze the effect that
their descendants would have on the sustainability of social security. Before retirement,
an inflow of working-age immigrants increases tax revenues. When these immigrants
retire, this effect is reversed. Their descendants have the same effect.
I analyze the effects of immigration in Japan by using an over-lapping generation
framework. According to the simulation results, immigration policies, which are both
low immigration and high immigration, have decreasing effects on social security taxes
overall.
Keywords: Immigration, Sustainability of Social Security, Simulation Analysis
JEL Classification:

H55, J11, F22, D58‡ The author would like to thank Naohiko Ijiri, Hisakazu Kato for their helpfulcomments. Needless to say, all remaining errors are my own. Financial support from the
Nihon University (Advanced resarch 08-005) is gratefully acknowledged.

Nihon University College of Economics,
1-3-2 Misaki-cho, Chiyoda-ku, Tokyo, 101-8360 Japan.
Tel/Fax +81-3-3219-3466
E-mail: miyazato@eco.nihon-u.ac.jp
11. Introduction
The aging of the population in Japan is the most severe among all developed countries.
Before the baby-boomer generation started to retire, Japan’s government proposed andimplemented many social security reforms. Unfortunately, it is hard to say if thosereforms will achieve sustainability of Japan’s social security system. There are only two
ways for sound financing of social security: decreasing benefit levels or increasing tax
revenues. Although analyzing and debating the recovery of the birthrate have often
been discussed for increasing tax revenues, immigration policy has barely been
investigated, despite the strong implication for the sustainability of social security.
Razin and Sadka (2000) analyzed the effects of immigrants in a dynamic set-up
which included a pay-as-you-go system. They showed the positive effect of immigrants.
First of all, working-age immigrants make a net contribution to pensioners in the hostcountry. In the next period, these immigrants have retired and receive pensions. The
present value of their pensions may outweigh their contributions during the former
period. However, their children make a positive contribution which is sufficient to cover
the expenses of their parents. Therefore, the burden of the first generation of
immigrants is moved forward into the future. As a result, residents in the host country
receive a one-shot gain. If immigration is repeated in each period, or the gain is spreadout over all the following periods, all the people in the host country could receive gains,in theory.
Borjas (1994) provided an overview of most of the immigration issue: immigration
changes the age composition of the population from the point of view of public finance ina positive direction because immigrants are usually of working age when they arrive inthe host country. At same time, they have, on average, a shorter period as retirees. Then,they have effects on lowering public old-age-dependent expenditures and pension
benefits. On the other hand, immigrants tend to have higher unemployment and lower
wage levels. That means immigrants tend to pay less tax and are a larger fiscal burden.
And there may be several general equilibrium effects. An increase in labor supply may
lower wages relative to capital. Furthermore, the fertility behavior of immigrants isimportant. In general, fertility rates of average immigrants are higher than that of hostcountry residents. Wage levels of immigrant’s children tend to be relatively low.
There are some studies that carry out empirical and numerical calculations on theeffects of immigration. Borjas (1994) computed the net government surplus yielded fromthe cross-section of immigrants currently residing in the U.S. Simon (1984) and Akbari(1989) computed the tax revenues and government expenditures associated withdifferent immigration cohorts. Bonin, Raffelhuschen and Walliser (1997) and Auerbachand Oreopoulus (1999) analyzed the effects of immigration through partial equilibrium
generational accounting approaches for the U.S. and Germany, respectively.
Storesletten (2000) builds a simple computable general equilibrium model to examine
the effects of various immigration policies for the U.S. He finds that selective2

immigration policies, involving an increasing inflow of working-age high- andmedium-skilled immigrants, can remove the need for future fiscal reform. In contrast,
an inflow of immigrants with the age and skills composition of average immigrants
cannot induce a long-run budget balance.
There are some studies which concern European countries. Much empirical evidence
was surveyed in Coleman and Rowthorn (2004). Bonin, Raffelhüschen, and Walliser(2000) carried out an analysis for Germany using a generational accounting approach.
They found that the increase in average-skilled immigrations improved the fiscal
condition of Germany, but inflows of high-skilled immigrants will only be able topartially remove the present fiscal imbalance induced by ageing. Roodenburg, Euwals,
and ter Rele (2003) also used a generational accounting approach and found that the
lifetime net contribution of average immigrants is negative in the Netherlands and anincrease in immigration rates would contribute to the sustainability of public finances.
Storesletten (2003) performed a partial equilibrium analysis of fiscal implications ofimmigration to Sweden. He calculated the net present values of immigration effects andshows that average immigrants are not beneficiaries, but some types, 20- to 30-year-old
immigrants, improve fiscal conditions. Schou (2006) performed general equilibrium
analyses of fiscal implications for the Danish. He found increased immigration would
generally worsen the Danish fiscal sustainability problem.
This paper explores whether an immigration policy could mitigate intergenerational
imbalances and achieve sustainability of the social security system in Japan. I apply adynamic general equilibrium simulation model, which was developed by Auerbach andKotlikoff (1978), to study the effects of immigration policy. By adopting a dynamic
set-up, I’m able to investigate the impact on the financing of social security before andafter the retirement of immigrants. In addition, I am able to analyze the effect that
their descendants would have on the sustainability of social security. Before retirement,
an inflow of working-age immigrants increases tax revenues. When these immigrants
retire, this effect is reversed. Their descendants have the same effect.

2. The model
I employ the lifecycle general equilibrium model and make use of the overlapping
generation model developed by Auerbach and Kotlikoff (1987). This allows us torigorously analyze changes in the supply of assets caused by demographic change. The
basic structure of the model is explained below.
2.1 Demographic Structure and Immigration Policies
The model’s households differ by their dates of birth and their lifetime
labor-productivity endowments. Every cohort includes three lifetime-earning groups,
each with its own endowment of human capital and pattern of growth in this3

endowment over its lifetime. The three lifetime-earning groups are the low-skilledgroup, the average-skilled group, and the high-skilled group, respectively.
I used actual demographic structures to achieve realistic simulation results. In thispaper, I analyze the transition path in addition to steady states. Simulation periods are
150 years. Demographic structures from year 0 to year 49 in the simulation correspondto real demography from 1955 to 2004, provided by the Ministry of Public Management,
Home Affairs, Posts and Telecommunications. After the 50-year simulation, I used
population projections for Japan (2007), estimated by the National Institute ofPopulation and Social Security in Japan from 2005 to 2105. Figure 1 shows the total
population in Japan from 1950 through to 2105. This figure reaches the top at 2005 anddecreases after 2005. Total populations are 127,768,000 at 2005, 119,270,000 at 2025,
91,152,000 at 2050, and44,592,000 at 2100, respectively. Figure 2 shows the ratio of theelderly population. This index is the ratio of people 65 years old and over to the total
population. These figures are 30.5% at 2025, 39.6% at 2050, respectively. Figure 1 andFigure 2 imply large impacts from immigration into Japan.
The immigrants’ skills take on three values; low skilled, average skilled and highskilled. Skill are exogenous and do not change during their lifetime. It is assumed that
immigrants have children from 21 to 49 years old. The fertility rate of immigrants is
assumed to be same rate in “Population Projections for Japan”. It is assumed that skillsof immigrants’ children are given randomly. Even if immigrants have high skills, one
third of their children become low skill labor and vice versa.
According to OECD (1998), 22,000,000 more immigrants are needed to maintain theratio of elderly population at preset level in Japan. However, this value is impracticalpolicy because Japan’s government has not officially absorbed immigrants yet. So I start
to analyze less number of immigrants. According to OECD (2007), 2,000,000 foreigners
have lived in Japan. Then I start to analyze effects of 2,000,000 immigrants. Case 1 is
inflow of low-skilled immigrants aged 21 to 30. Case 2 is inflow of high-skilled
immigrants aged 21 to 30. The number of immigrants at each age is 20,000, so 200,000
more immigrants (inflow) each year. I assume that immigration policies are
implemented from 2015 to 2025. Therefore, the total number of immigrants is 2,000,000.
Next, I analyze the effects of immigrants increasing permanently. Case 3 is that inflow
of low-skilled immigrants aged 21 to 30 continues permanently from 2015. Case 4 isthat inflow of high-skilled immigrants aged 21 to 30 continues permanently from 2015.

2.2 Households
Households live for 80 periods at maximum and face fatality at each period. Income
classes are divided into three classes. There are the same numbers of each skill type
household among each cohort. Therefore, one third of the cohort is high skill, averageskill and low skill, respectively. Each household is assumed to have the same utility

4

function. However, unequal labor endowments create different income levels. It is also
assumed that each household appears in the economy as a decision-making unit fromthe age of 21 and lives to no more than 100 years. Each j-type (j=1,2,3) household who
begins economic life at date t chooses perfect-foresight consumption paths (c), leisurepaths (l) to maximize a time-separable utility function of the form
1
1 




1
1
1
1  1 1
1  199js  21  j
j


Ui 
PS s ,t  s  21  c s ,t  s  21  l s ,t  s  21   
1  s 
1    21

 


(1)

j = 1,2,3
where α is the utility weight on leisure, γ is the intertemporal elasticity of
substation in the leisure/consumption composite, and ρ is the intratemporal elasticity
of substitution between consumption and leisure. The term β=1/(1+δ) , where δ isthe rate of time preference, is assumed to be the same for all household. PS s,t is
probability of survival at each age. c is consumption. l is leisure. Furthermore, s
represents age, t year.
Letting aj s,t be capital holdings for type j household, of age s, at time t, maximizationof (1) is subject to a lifetime budget constraint defined by equation (2)









a sj1,t 1  1  rt a sj,t  1   tw,1   tw, 2 wt  s x j E  l sj,t  bsj,t  ps sj,t  c sj,t(2)

E  l sj,t

(3)

and
j
a100
,t  0(4)

Where a s,t j represent the amount of assets held by the household at the beginning of ages, r t interest rate, E the time endowment (twenty-four hours), ε s the age profile ofearning ability 1 , xj the weight coefficient corresponding to the different levels of laborendowment.  tw

is wage income tax(  tw,1is public pension tax,  tw, 2is pubic assistancetax respectively). bj s,t is public pension benefits. psj s,t is public assistance. There are no
liquidity constraints, so the assets in (2) can be negative.

1 In this paper, the age profile of earning ability ε s follows values in Auerbach and Kotlikoff(1987) .

5

In this paper, I consider cost of immigration as public assistance. Equation (2)includes this cost. Public assistance follows below:

ps sj,t  zwt

(j=1)

(5)

ps sj,t  0(j=2,3)(6)

where z is probability of pubic assistance recipient ( or welfare recipient), η isreplacement rate of public assitance, and wt is average wage of middle class.
The age at which households start to receive public pension benefits is RE, theaverage annual remuneration is H, the replacement ratio of earning related pension isκ. The variables related to the public pension are represented as follows:

bsj,t  f  H jbsj,t  0H( s ≥ RE )

(7)

(s‹0)



1 RE 1
 wt  s x j E  l sj,tRE  1 s 1

(8)



(9)

f  dwt(10)

where H represents earned income that is used for calculating the amount of pension
benefits. H also reflects the wage rate during the working period. f is basic pension
portion. In this paper, I assume basic pension benefit is average wage of middle class

wt multiple by replacement rate of basic pension portion d.
2.3 The Government
The public pension system is a pay-as-you-go system, and aggregate pension benefits
are equal to aggregate pension insurance payments for each period. The budget
constraint of public pension is:

ABt  APt

(10)

where AP t represents the total revenue from the pension insurance contribution. And

6AB t represents the total public pension benefit to retired generations. AP t is defined asfollows:
3 RE 1

APt    N sj,t tw, j wt  s x j E  l sj,t



(11)

j 1 s  21

where Nj s,t is population of each type.
On the other hand, the total public pension benefit AB t is defined as follows:3

100

ABt    N sj,t bsj,t(12)

j 1 s  RE

There is another budget constraint of government in this paper. Total benefit ofpublic assistance equals total revenue from tax. I assume that this tax collected fromwage income tax. The budget constraint of public assistance is:

TPAt  TPLt

(13)

where TPA t represents the total revenue from public assistance tax. And TPL t
represents the total public assistance benefit to recipients. TPA t is defined as follows:
3 RE 1TPAt    N sj,t tw, 2 wt  s x j E  l sj,t



(14)

j 1 s  21

On the other hand, the total public assistance benefit TPL t is defined as follows:3

100

TPLt    N sj,t ps sj,t(15)

j 1 s  21

2.4 Firms and Technology
Aggregate capital (K) and labor (L) equal the respective sums of individual asset andlabor supplies as indicated in equation (16) and (17).

7

3

100

K t    N sj,t a sj,t(16)

j 1 s  21

3 RE 1

Lt    N sj,t  s x j E  l sj,t



(17)

j 1 s  21

Output is produced by identical competitive firms using constant-returns-to-scale
production technology. In the base case, the aggregate production technology is thestandard Cobb-Douglas form:

Yt  AK t L1t

(18)

where Y t is aggregate output and θ is capital’s share in production. A is production
scale parameter. The competitive pretax rate of return to capital at time t is given by
the marginal product of capitalrt  Ak t 1(19)

3. Simulation Analysis
The model is solved under perfect foresight by households. The simulation model can besolved using the Gauss-Seidel method.
3.1 Specification of the Parameters
First of all, I have to specify the parameters in order to solve the model. All of theparameters have been set so that the actual value could be reproduced as close as
possible. Table 1 shows the value of parameters. The value for δ, the rate of time
preference is set equal to 0.004 to generate a realistic value for the capita-output ratio
in the initial steady state. The values of γ and ρare those in Auerbach and Kotlikoff(1987). The intertemporal elasticity, γ, is set equal to 0.25. I chose α, the utility
function’s leisure intensity parameter, such that, on average household devote about 40
percent of their available time endowment to labor during their working years. Three
lifetime-earning groups are the low-skilled group, the average-skilled group, and thehigh-skilled group. I assume that differences in earnings come from different wage rates.
Furthermore, I assume the wage rate of the low-skilled group is 0.5 times that ofaverage-skilled group, and high-skilled group’s wage rate is 2.0 times the8average-skilled group 2 . That is, I assume x1 is 0.5, x2 1, and x3 2.0 respectively. Recently,
probability of pubic assistance recipient is around 0.02. Then I assume probability of
pubic assistance recipient z is 0.02. According to Basic Survey on Wage Structure(Chingin Kozo Kihon Chosa), average wage is about 300,000 yen in 2005. On the other
hand, public assistance benefits per capita are 148,444 yen in 2005 from National
Institute of Population and Social Security. Then I assume ηis replacement rate of
public assistance η is 0.5.

3.2 Simulation Results
I show simulation results for capital stock, consumption and utility levels, etc from
Table 2 to Table 6. Table 2 shows the no immigration case results. In the no immigrationcase, population structures follow Population Projections for Japan (2007). In the steadystate, the model generates an interest rate of 4.302 percent. Capital stock, labor andconsumption are 186.348, 24.048, and 40.925, respectively. The social security tax rate
is 4.302 percent and the average utility level is -681701.9. In 20 years from the initialsteady state, the interest rate is 3.749. Capital stock is 219.265, labor 23.552,
consumption 41.345. The social security tax rate is 8.52, and the utility level is-705686.1. Capital stock is 224.045, labor 26.692, consumption 38.836 after 60 years.
The social security tax rate is 31.137, and the utility level is -974841.1. Capital stock is
175.952, labor 27.079, consumption 36.816 after 90 years. The social security tax rate is
30.714, and the utility level is -905451.3. Capital stock is 170.569, labor 26.305,
consumption 37.185 after 120 years. The social security tax rate is 21.534, and theutility level is -759463.1.
Table 3 shows the effects of low-skilled immigrants increasing temporarily. In thiscase, I assume that age 21 to 30 low-skill immigrant inflow was from 2015 to 2025
(which corresponds to 61 periods to 70 periods in the simulation). The number of
immigrants at each age is 20,000. Then 200,000 more immigrants (inflow) each year
and the total number of immigrants is 2,000,000 from 2015 to 2025. Results show that
capital stock, consumption, and utility level are lower than that of the no immigrationcase in 2045 and 2075 (which corresponds to 90 periods and 120 periods in thesimulation) 3 . Table 4 shows effects of high-skilled immigrants increasing temporarily.
Results show that capital stock, consumption, and utility level are higher than that of
the no immigration case after 2015 (which corresponds to 60 periods).
Table 5 shows the effects of low-skilled immigrants increasing permanently. In this
2 Okamoto(2004) calculates the weight coefficient corresponding to the different levels oflabor endowment by using the Statistical Year Book of National Taxes (Kokuzeicho
Tokei-Nenposho).
3 In this paper, utility level is higher when it close to 0.

9case, I assume that age 21 to 30 low-skill immigrant inflow was from 2015 to 2105
(which corresponds to 61 periods to 150 periods in the simulation). The number of
immigrants at each age is 20,000. Then 200,000 more immigrants (inflow) each year
and the total number of immigrants is 18,000,000 from 2015 to 2105. Results show that
capital stock, consumption, and utility level are lower than that of the no immigrationcase in 2045 and 2075 and 2105 (which corresponds to 90 periods and 120 and 150
periods in the simulation). Table 6 shows effects of high-skilled immigrants increasing
permanently. Results show that capital stock, consumption, and utility level are higher
than that of the no immigration case after 2015 (which corresponds to 60 periods).
Figure 3 is simulated social security taxes which also includes public assistancetaxes. In the no immigration case, the social security tax in 2005 is 24.224% and it
reaches 34.045% in 2025, 30.714% in 2045. Figure 4 shows difference of social security
taxes between the temporal immigration case and the no immigration case. In low-skill
immigration case, those differences become to be positive (than is, social security taxes
in immigration case are higher than in no immigration case) after 2032. In high-skill
immigration case, those become to be positive after 2054. Figure 5 shows difference ofsocial security taxes between the permanent immigration case and the no immigration
case. In low-skill and high-skill immigration case, those differences become to bepositive continuously after 2054. A climbing power of social security taxes in permanent
immigration is larger than in temporal case.
Figure 6 and 7 show the effects on the net preset value of social security. First of all,
I calculate net preset value of social security as (20).

 bsj,t  s1 1  rt   1  rt  j 1 

NPVt  RE 1

 
s 1

w,1
t  s 1



100

s

s  REj 1

w, 2t  s 1w

 x E  lt  s 1 sj

1  r   1  r sjs ,t  s 1

(20)

t  j 1tj 1

The numerator on the right-hand side of (20) is the net present value of social
security benefits, and the denominator on the right-hand side of (20) is the net present
value of social security payments. Next I calculate the difference in NPV between theimmigration case and the no immigration case for each generation. Figure 6 showsthese results in temporal immigration case. The horizontal axis represents the birthyear. There are some generations whose differences of NPV are negative in high-skill
immigration case. On the other hand, almost generations have negative effects of NPV
in low-skill immigration case. Figure 7 shows these results in permanent immigration
case. Almost generations have negative effects of NPV in low-skill immigration case. On
the other hand, all generations have positive effects in high-skill immigration case.

104. Conclusion
I analyzed the effects of immigration in Japan by using an over-lapping generation
framework. According to the simulation results, the social security taxes for theimmigration case are higher than that of the no immigration case after 2054. A climbingpressure of social security taxes in permanent immigration is larger than in temporalcase. In addition, I calculated the difference of the NPV between the immigration caseand the no immigration case for each generation according to (20). There are some
generations whose differences of NPV are negative in temporal high-skill immigration
case. Almost generations have negative effects of NPV in temporal low-skill
immigration case. On the other hand, almost generations have negative effects of NPV
in permanent low-skill immigration case. All generations have positive effects inpermanent high-skill immigration case.

11References
Akbari A H. (1989) “The Benefits of Immigrants to Canada: Evidence on Tax and PublicServices” Canadian Public Policy 15 pp.424-435.
Auerbach A J, Oreopouls P. (1999 “Analyzing the Fiscal Impact of U.S. immigration”
American Economic Review 89 pp.176-180.
Auerbach A J, Kotlikoff L. (1987) Dynamic Fiscal Policy. New York: Cambridge
University Press.
Bonin H, Raffelhüschen B, Wallise J. (2000) “Can immigration alleviate thedemographic burden?” Finanzarchiv 57 pp.1-21.
Borjas G J. (1994) “The economics of immigration” Journal of Economic Literature 32
pp.166-1717.
Coleman D, Rowthorn R. (2004) “The economic effects of immigration into the United
Kingdom” Population and Development Review 30 pp.579-624.
National Institute of Population and Social Security Research (2007) Population
Projection for Japan: 2006-2105 (Estimation in December, 2006), Tokyo: Health andWealth Statistics Association.
OECD. (1998) Trends in International Immigration. Paris: OECD.
OECD (2007) International Migration Outlook. Paris: OECD.
Okamoto, A. (2004) Tax Policy for Aging Societies: Lesson from Japan. Tokyo:
Springer-Verlag.
Razin A, Sadka E. (2000) “Unskilled migration: a burden or a boon for the welfare
state?” Scandinavian Journal of Economics 102 pp.463-479.
Roodenburg H, Euwals R, ter Rele H. (2003) “Immigration and the Dutch economy”
CPB Netherlands Bureau for Economic Policy Analysis.
Schou P. (2006) “Immigration, integration and fiscal sustainability” Journal Population
Economics 19 pp.671-689.
Simon J L. (1984) “Immigrants, Taxes, and Welfare in the United States” Population
and Development Review 10 pp.55-69.
Storesletten K. (2000) “Sustaining fiscal policy through immigration” Journal of
Political Economy 108 pp.300-323.
Storesletten K. (2003) “Fiscal implications of immigration – a net present value
calculation” Scandinavian Journal of Economics 105 pp.487-506.

12

Table 1. Parameters

α
δ
γ
ρ
θ
A
x1
x2
x3
κ
d
z
η

Definition
Value
Utility weight on leisure1
Rate of time preference
0.004
Intertemporal substitution elasticity
0.25
intratemporal substitution elasticity
0.8
Capital share
0.25
Production scale parameter1weight on labor endowments of low income class
0.5
weight on labor endowments of middle income clas
1
weight on labor endowments of high income class2
replacement ratio of earning related pension
0.2
replacement rate of basic pension portion
0.2
probability of pubic assistance recipient
0.02
replacement rate of public assitance
0.5

13

Table 2. No immigration caseYear

Capital
stock

Laobr
supplyInitial steady state
1
20
60
90
120
150

186.3486
186.3484
219.2652
224.0451
175.9526
170.569
194.4333

24.04884
22.13255
23.55247
26.69247
27.07932
26.30581
24.7562

Consumption Wage rate
40.92528
39.34426
41.34538.83643
36.81663
37.18536
42.58301

1.000011.02098
1.04695
1.02019
0.95693
0.956431.00337

Net
SocialsavingUtilitysecurity tax
rate
0.04302 -0.12828
0.04729 -681702
0.04042 -0.03155
0.0487 -655140
0.03749 -0.05667
0.0852 -705686
0.04051 0.07093
0.31137 -974841
0.04909 0.07484
0.30714 -905451
0.04917 0.03709
0.21534 -759463
0.04258 -0.11702
0.12829 -700079

Interest
rate

Table 3. Low-skilled immigrants increasing case (temporal immigrants)
Net
InterestCapitalLaobr
SocialConsumption Wage rate
Utilitysavingrate
stock
supplysecurity tax
rate
Initial steady state 186.3486 24.04884
40.92528 1.00001 0.04302 -0.12828
0.04729 -681702
1
186.3484 22.11798
39.31976 1.02115
0.0404 -0.03177
0.0488 -655229
20
219.4188 23.55352
41.35012 1.04712 0.03747 -0.0564
0.08518 -705195
60
226.095 26.74631
38.86641.022
0.04030.07370.31089 -1050431
90
173.8478 27.05006
36.30274 0.95432
0.0495 0.08359
0.30758 -918930
120
167.8709 26.3409
36.66163 0.95231 0.04981 0.04809
0.2267 -768882
150
207.191 24.93433
42.7653 1.01762 0.04082 -0.09857
0.13272 -692641
Year

Table 4. High-skilled immigrants increasing case (temporal immigrants)
Net
InterestCapitalLaobr
SocialConsumption Wage rate
Utilitysavingrate
stock
supplysecurity tax
rate
Initial steady state 186.3486 24.04884
40.92528 1.00001 0.04302 -0.12828
0.04729 -681702
1
186.3484 22.11823
39.32011 1.02114
0.0404 -0.03177
0.0488 -655295
20
219.4137 23.55314
41.35022 1.04712 0.03747 -0.05641
0.08518 -705909
60
225.311 26.70058
38.87862 1.02155 0.04035 0.07156
0.31144 -884836
90
178.8859 27.10642
37.47682 0.96066 0.04852 0.06427
0.30663 -906397
120
172.682 26.45405
37.62884 0.95803 0.04892 0.03346
0.22013 -762142
150
207.0366 24.93939
42.7524 1.01738 0.04085 -0.09828
0.133 -693157
Year

14

Table 5. Low-skilled immigrants increasing case (permanent immigrants)
Year

Capital
stock

Laobr
supplyInitial steady state
1
20
60
90
120
150

186.3486
186.3484
219.4704
226.8773
173.0896
159.1011
163.2858

24.04884
22.11174
23.55401
26.76804
27.12714
26.47841
25.15574

Consumption Wage rate
40.92528
39.30981
41.35137
38.87706
35.36687
33.4810735.432091.00001
1.021221.04718
1.02267
0.9526
0.93840.95669

Net
SocialUtilitysavingsecurity tax
rate
0.04302 -0.12828
0.04729 -681702
0.04039 -0.03189
0.04884 -655287
0.03746 -0.05627
0.08517 -704985
0.04022 0.07474
0.31072 -1046215
0.04976 0.10669
0.30707 -1047425
0.05206 0.11821
0.23882 -968138
0.04913 0.03355
0.17411 -928657

Interest
rate

Table 6. High-skilled immigrants increasing case (permanent immigrants)
Year

Capital
stock

Laobr
supplyInitial steady state
1
20
60
90
120
150

186.3486
186.3484
219.3708
224.6676
179.3661
188.2314
245.4358

24.04884
22.12168
23.55326.6793
26.9712926.66598
25.36741

Consumption Wage rate
40.92528
39.3251
41.34884
38.87239
38.70051
41.70017
50.27596

1.00001
1.0211
1.04707
1.021020.96250.97696
1.05708

15

Net
SocialUtilitysavingsecurity tax
rate
0.04302 -0.12828
0.04729 -681702
0.04041 -0.03172
0.04878 -655253
0.03747 -0.0565
0.08518 -706108
0.04042 0.07059
0.31162 -888863
0.04824 0.03361
0.30731 -784799
0.04613 -0.03313
0.23827 -639319
0.03642 -0.20865
0.15461 -570040

Interest
rate

16

2105

2100

2095

2085
2090

2080

2075

2065
2070

2060

2055

2045
2050

2040

2035

2025
2030

2020

2015

2005
2010

2000

1995

1985
1990

1980

1975

1965
1970

1960

1955

1950

20.0%

15.0%

10.0%

5.0%

0.0%

2105

2100

2095

2090

2085

2080

2075

2070

2065

2060

2055

2050

2045

2040

2035

2030

2025

2020

2015

2010

2005

2000

1995

1990

1985

1980

1975

1970

1965

1960

1955

1950

thousandFigure 1. Total populations

Total Population

14000012000010000080000
Total Population

60000

40000

20000

0

Figure 2. The ratio of elderly population

Ratio of Elderly Population

45.0%

40.0%

35.0%

30.0%

25.0%

Ratio of Elderly Population

Figure 3. Social Security Tax
0.4

0.35

0.3

0.25
no immigration
low skillhigh skill
high skill (temporal)
low skill (temporal)

0.2

0.15

0.1

0.05

2098
2101
2104

2083
2086
2089
2092
2095

2068
2071
2074
2077
2080

2050
2053
2056
2059
2062
2065

2035
2038
2041
2044
2047

2020
2023
2026
2029
2032

2005
2008
2011
2014
2017

0

Figure 4. Difference between the immigration case and the no immigration case(temporal immigration case)
0.018

0.016

0.014

0.012

0.01
low skill - no immigrationhigh skill - no immigration

0.008

0.006

0.004

0.002

20
00
20
04
20
08
20
12
20
16
20
20
20
24
20
28
20
32
20
36
20
40
20
44
20
48
20
52
20
56
20
60
20
64
20
68
20
72
20
76
20
80
20
84
20
88
20
92
20
96
21
00

0

-0.00217

Figure 5. Difference between the immigration case and the no immigration case(permanent immigration case)
0.045

0.04

0.035

0.03

0.025

low skill - no immigrationhigh skill - no immigration

0.02

0.015

0.01

0.005

20
05
20
08
20
11
20
14
20
17
20
20
20
23
20
26
20
29
20
32
20
35
20
38
20
41
20
44
20
47
20
50
20
53
20
56
20
59
20
62
20
65
20
68
20
71
20
74
20
77
20
80
20
83
20
86
20
89
20
92
20
95
20
98

0

-0.005Figure 6. Effects on net present values of social security (temporal immigration case)
0.006

0.004

0.002

20
00
20
04
20
08
20
12
20
16
20
20
20
24
20
28
20
32
20
36
20
40
20
44
20
48
20
52
20
56
20
60
20
64
20
68
20
72
20
76
20
80
20
84
20
88
20
92
20
96
21
00
21
04

0

-0.002-0.004-0.006-0.00818

low skill - no immigrationhigh skill - no immigration

Figure 7. Effects on net present values of social security (permanent immigration case)
0.02

0.01

20
00
20
04
20
08
20
12
20
16
20
20
20
24
20
28
20
32
20
36
20
40
20
44
20
48
20
52
20
56
20
60
20
64
20
68
20
72
20
76
20
80
20
84
20
88
20
92
20
96
21
00
21
04

0

-0.01

-0.02
low skill - no immigrationhigh skill - no immigration
-0.03

-0.04

-0.05

-0.06

-0.07

19