TITLE:

An Optimal Rate of the National
Burden in an Aging JapanAUTHOR(S):Okamoto, Akira

CITATION:

Okamoto, Akira. An Optimal Rate of the National Burden in an Aging
Japan. The Kyoto Economic Review 2006, 75(1): 13-34

ISSUE DATE:
2006-06

URL:
https://doi.org/10.11179/ker.75.13
RIGHT:

The Kyoto Economic Review 75(1): 13–34 (June 2006)

An Optimal Rate of the National Burden in an
Aging Japan
Akira Okamoto1
1 Associate Professor, Faculty of Economics, Okayama University.
E-mail: okamoto@e.okayama-u.ac.jp

This paper examines an optimal rate of the national burden to establish guidelines
for fiscal reform in Japan’s graying society. The paper looks at Japanese tax and social security systems through an extended life-cycle general equilibrium simulation
model. It explicitly considers the benefits that the government provides to households,
which enables us to comprehensively evaluate the balance between benefits and burdens. Simulation results show that an optimal rate of the national burden is high whenhouseholds put a great utility weight on the benefits coming from public services, andthat it is low when the degree of publicness of government expenditure is high. The
results also suggest that an optimal rate of the national burden would rise as Japan ages
and may exceed 50% during the rapid aging of its population.
Keywords: aging population, national burden rate, government expenditure,
tax reform, life-cycle general equilibrium simulation model
JEL Classification Numbers: H20, C68

1. Introduction
With a population that is aging faster than any other in the world, Japan faces
serious problems with its public finance, particularly when it comes to tax andsocial security issues1) . Structural reforms are urgently needed to accommodate
the impending demographic change. There has recently been increased discussion
about the “rate of the national burden” in Japan. When reconstructions of publicfinance or fiscal structural reforms were implemented in past years, one of the government’s aims was to keep the rate of the national burden below 50%. One of
the main reasons for this is that, as the rate of the national burden becomes high,economic vitality is diminished.
1) Japan’s population has the highest old-age dependency ratio.

currently the fastest aging country in the OECD member countries.

However, the Republic of Korea is

14 A. Okamoto

Several recent studies, however, have suggested that the size of the welfare
state has no relation to the rate of economic growth. For example, Atkinson (1999)
reported that the results of econometric studies of the relationship between socialtransfer spending and growth rates are mixed: some find that high spending onsocial transfers leads to lower growth, others find the reverse, and thus that thestudies of the aggregate relationship between economic performance and the sizeof the welfare state reviewed in his book do not yield conclusive results.
This paper aims to establish guidelines for fiscal reform in Japan’s graying society by looking at Japanese tax and social security systems through an extended
life-cycle general equilibrium simulation model. Many papers have studied tax reforms using this kind of model; for instance, Auerbach and Kotlikoﬀ (1987), Altig
et al. (2001), and Ihori et al. (2005). However, these papers incorporate taxes into
their models but do not take account of the fact that government expenditure enhances households’ utility. Moreover, few studies have examined an optimal rate of
the national burden, taking full account of the benefits that the government provides
to households.
Therefore, we explicitly consider that public services improve households’ welfare, which is the main contribution that this paper aims to make. This enables us
to comprehensively evaluate the balance between benefits and burdens, and thus toinvestigate an optimal rate of the national burden. We explore an optimal rate of
the national burden during the rapid aging of the Japanese population.
When taking account of the fact that households receive benefits coming fromgovernment spending, there are two crucial aspects. One is to what degree households put a utility weight for the benefits coming from government expenditure,compared with their private consumption. The other is to what degree the goods
and services that the government provides to households take on the character ofpublic or private goods. If government expenditure takes on the character of public
goods, its benefits to households are widespread. On the other hand, if it takes on
the character of private goods, its benefits to households are restricted. Because
simulation results depend substantially on the parameter values that determine theabove degrees, we undertake sensitivity analyses for changes in these parametervalues.
This paper is organized as follows. The next section identifies the basic model
employed in the simulation analysis. Section 3 explains the method of simulation
analysis and the assumptions adopted. Section 4 evaluates the simulation findings
and discusses policy implications. Section 5 summarizes and concludes the paper.
2. Theoretical Framework
The life-cycle growth model employed in this paper is grounded in the microeconomics of intertemporal choice, and the macroeconomics of savings andgrowth. The simulation model has three features. First, aggregate assets of theeconomy in each period consist of the assets of diﬀerent generations that maximize
their lifetime utility. This allows us to rigorously analyze changes in the supplyAn Optimal Rate of the National Burden in an Aging Japan15of assets caused by demographic changes. Second, assets in the capital market,
where aggregate assets appear as real capital, aﬀect the production level. Third,
it is possible to estimate realistic consumption-savings profiles for the elderly, byincorporating life-length uncertainty and unintended bequests into the model.
We calibrate the simulation of the Japanese economy by employing population
data estimated by the National Institute of Population and Social Security Researchin 2002. The model has 75 diﬀerent overlapping generations. Three types of agentsare considered: households, firms, and the government. The basic structure ofhouseholds is as follows.
2.1. Household Behavior
Households are divided into three income classes: low, medium, and high2) .
A single household type represents each income class. Each household has thesame mortality rate and the same utility function. Unequal labor endowments,
however, create diﬀerent income levels. Each household appears in the economy asa decision-making unit at the age of 21 and lives to a maximum of 95. Households
face an age-dependent probability of death. Let q j+1| j be the conditional probability
that a household of age j lives to j + 1. Then the probability of a household of age
21 surviving until age s can be expressed by
ps =

s−1


q j+1| j .

(1)

j=21

The probability q j+1| j is calculated from data estimated by the National Institute ofPopulation and Social Security Research (2002).
The utility of each household depends on the levels of consumption and the
public services that the government provides to each household. There is no choice
between leisure and labor supply. Each household works from age 21 to RE, theretirement age. The labor supply is inelastic before retirement and zero after retirement (see the first comment in Section 4.2 for the explanation of this assumption).
Each household that maximizes the expected lifetime utility makes lifetime decisions at age 21 concerning the allocation of wealth between consumption andsavings. The utility function of a representative household of income class i, theform of which is assumed to be time-separable, is95
1− γ1  i  1− γ1

Gt
1 
i
−(s−21)  C s,p s (1 + δ)
+µ
Ut =
(2)
ρ
1
ANt
1 − γ s=21
where C is represents consumption (or expenditure) at age s, δ the adjustment coeﬃcient for discounting the future, and γ is the intertemporal elasticity of substitution2) Okamoto (2005a) also incorporated three representative households with diﬀerent earnings abilities.

Altig et al. (2001) dealt with diﬀerences of lifetime earnings ability by incorporating 12 lifetime-income
groups into a life-cycle model. Furthermore, Okamoto (2005b) introduced numerous representative
households with continuous income distribution in each cohort.

16 A. Okamoto

in diﬀerent years. The superscript i (= l, m, h) stands for low, medium, and highincome classes, respectively.
The goods and services that the government provides to households are incorporated, with reference to Borcherding (1985). Gt is government spending on goods
and services in year t, ANt the size of the households, namely, the total population
at period t, µ a weight placed on the benefits coming from government expenditure(i.e., public services), and the exponent ρ is the degree of publicness. If ρ is zero,then government expenditure, Gt , is purely public. On the other hand, if ρ is unity,
then Gt is purely private. It needs to be noted that, when the value of ρ is large, thedegree of publicness is low.
The flow budget constraint equation for each household at age s is
Ais+1 = {1 + r(1 − τr )} Ais + {1 − τw (wxi e s ) − τ p } wxi e s + bis + ais − (1 + τc ) C is , (3)where Ais represents the amount of assets held by the household at the beginningof age s, r the interest rate, w the wage rate per eﬃciency unit of labor, and e s isthe age profile of earnings ability for the household that belongs to the mediumincome class3) . bis is the amount of public pension benefit, and ais is the amount ofbequest to be inherited at age s. τw (wxi e s ) is the tax rate on labor income, τc that on
consumption, τr that on interest income, and τ p is the contribution rate to the public
pension scheme. xi is the weight coeﬃcient corresponding to the diﬀerent levels oflabor endowments among the three income classes. The medium-income class isused as a yardstick, and thus xm = 1. xl and xh reflect the realistic diﬀerences inearnings ability across the three income classes.
The tax system consists of labor income, interest income, consumption, andinheritance taxes. Labor income is progressively taxed. The symbol τw (wxi e s ) inequation (3) signifies that τw is a function of wxi e s . The progressive tax schedule isincorporated in the same manner as in Auerbach and Kotlikoﬀ (1987): by choosing two parameters labeled α and β, we set the average tax rate τw (wxi e s ) equal
3) To estimate the age profile of earnings ability, e , the following equation is employed:s

Q = a0 + a1 A + a2 A2 + a3 L + a4 L2 ,where Q denotes average monthly cash earnings, A age, and L the length of one’s service for all workers.
Table 8 presents the parameter values estimated using data in the Ministry of Health, Labor and Welfare(2004). Because bonuses account for a large part of earnings in Japan, monthly cash earnings used here
contain bonuses.
Table 8a0

Estimation of the age profile of earnings ability
a1

a2

a3

a4

−0.31291

0.08333−0.00112

0.12496−0.00168(−0.53353)(2.04195)(−3.04843)(2.22492)(−1.12888)

S .E. = 0.0847, R2 = 0.9903.

An Optimal Rate of the National Burden in an Aging Japan17

to α + 0.5βwxi e s for all values of wxi e s . The corresponding marginal tax rate is
α + βwxi e s . Setting β = 0 amounts to proportional taxation. One may make thetax system more progressive, holding revenue constant, by increasing β and decreasing α simultaneously. On the other hand, interest income, consumption, andinheritances are proportionally taxed.
Variables related to the public pension program in a pay-as-you-go system are
represented by ib s = θH i (s ≥ S T ),(4)(s < S T )bis = 0where the age at which each household starts to receive public pension benefits isRE1
S T , the average annual remuneration is H i = RE−20
wxi e s , and the replaces=21

ment ratio is θ. Thus bis rigorously reflects diﬀerent earnings abilities across thethree income classes.
There are unintended bequests caused by uncertainty over the length of life.
The bequests, which were held as assets by deceased households, are handed tosurviving 50-year-old households. Therefore ais is positive if and only if s = 50,
and otherwise is zero. The inheritance is transferred within the households thatbelong to the same income class. When BQit is the sum of bequests inherited by
50-year-old households at period t, ai50 is defined byai50 =
where
BQit = Nt95

(1 − τh )BQit,
Nt p50 (1 + n)−29(p s − p s+1 )(1 + n)−(s−21) Ais+1 ,

(5)

(6)

s=21

Nt is the number of new households entering the economy as decision-making units
at period t, n is the common growth rate of successive cohorts, and τh is the tax rate
on inheritances of bequests.In the steady state of a life-cycle growth model, theamount of inheritances received is linked to the age profile of assets chosen byindividuals.
Let us consider the case in which each household maximizes lifetime utility
under a constraint. Each household maximizes equation (2) subject to equation (3)(see Appendix A). From the utility maximization problem, the equation expressing
evolution of consumption over time for each household is characterized byγ
p s+1 1 + r (1 − τr )i
C is .
(7)
C s+1 =
ps1+δi
If the initial consumption level, C21, is specified, optimal consumption behavior
of all ages can be derived from equation (7). The amount of assets held by eachhousehold at each age can be obtained from equation (3). The expected lifetime
utility of each household is derived from equation (2).

18 A. Okamoto

The social welfare function, which takes account of diﬀerent earnings abilities
and thus provides diﬀerent levels of consumption, is given by
S W = U l + U m + U h.

(8)This function is derived from a summation of the expected lifetime utilities at age
21 for the three income classes. When comparing steady states, it is not necessary
to take account of the utilities of all overlapping generations existing at period t. A
comparison of the lifetime utility of a single cohort is suﬃcient, because our aim is
to compare the welfare level among simulation cases. The social welfare function
is of the “Benthamite type”, but depends mainly on the utility of the low-income
class, like the “Rawlsian type”4) . It is maximized if all income classes have thesame level of consumption.
With regard to the basic structure of firms, a single production sector is assumed
to behave competitively using capital and labor, subject to a constant-returns-toscale production function. See Appendix B for the basic structures of firms and thegovernment, and market equilibrium conditions.
3. Simulation Analysis
The method of simulation employed in our analysis represents the economy
as a general equilibrium system. We investigate an optimal tax rate on consumption, by comparing the equilibrium solutions that are calculated under given andcounterfactual conditions. This method permits us to numerically calculate various
economic variables and to recognize concrete policy implications. It is especially
useful when examining policy packages, or when there are multiple policies thatwork in a diﬀering direction.
3.1. Method of Simulation
The simulation model presented in the previous section is solved under the hypothesis of perfect foresight by households that correctly anticipate the interest,
wage, tax, and contribution rates. If the tax and public pension systems are determined, the model can be solved using the Gauss-Seidel method (see Auerbachand Kotlikoﬀ (1987) for the computation process). The parameter values α andβ, which determine tax progressivity on labor income, and the tax rates on interest income (τr ) and inheritances (τh ), are exogenously given. Thus, tax revenue
neutrality makes the tax rate on consumption (τc ) endogenous. With regard to the
public pension system, the replacement ratio (θ) is exogenously given. Therefore,
the contribution rate (τ p ) is made endogenous.
4) The model employs a simple utilitarian social welfare function based on the steady state utility for asingle generation. The function is most sensitive to income changes for the low-income class due to theconcavity of the underlying utility function. As the parameter of intertemporal elasticity of substitution,γ, is lower, it depends more on the welfare of the low-income class. It becomes Rawlsian if S W = U l .

An Optimal Rate of the National Burden in an Aging Japan

Table 119

Parameter values characterizing the three steady states
Current steadystate (Cases A)

Aged steadystate (Cases B)

More aged steadystate (Cases C)

Survival probabilities, p s (year)

2005

2025

2050

Parameter

Growth rate of successive cohorts, n

0.0069−0.0047−0.0153

New entrants in period t, Nt

1.21790.82800.5485

Labor supply, Lt

349.6

306.2

260.0

Contribution rate, τ p

13.58%

21.57%

32.61%

3.2. Simulation Cases
We consider three demographic regimes, namely, the 2005 current steady state
and the 2025 and 2050 aged steady states. Case A is the current benchmark of
2005. Cases B and C are the benchmarks of an aged Japan projected for 2025 and
2050, respectively. Cases A, B, and C diﬀer in population structure5) . Diﬀerent
survival probabilities (p s ) and diﬀerent growth rates of successive cohorts (n) create
diﬀerent age structures of the population among the three demographic regimes(see Table 1 for the parameter values characterizing the three steady states).
Under conditions of aged steady states, Japan will face a decline in the proportion of its working population, with a subsequent decrease in aggregate output(Yt ); hence, the ratio of the total tax revenue (T t ) to aggregate output (Yt ) is raised,
representing a substantial increase in the tax burden on an aging society. Under tax
revenue neutrality, there is an extra burden caused by the transition from the current
state (Case A) to the aged states (Cases B and C). In an aging society, tax policies
that stimulate capital accumulation can be required; and for this a consumption
tax promotes capital formation more than other tax regimes (see Okamoto (2004)
for the details). Furthermore, there is the political possibility that the tax rate on
consumption can be raised in present-day Japan. Therefore, in our simulation, aconsumption tax covers the extra tax burden caused by transition to an aging society. Additionally, when maximizing social welfare, we consider cases in which the
tax rate on consumption is adjusted.
The simulation results depend on the weight parameter, µ, placed on public
services in the utility function. The parameter value is assigned to 0.1 in the benchmark cases. Because the setting of the weight parameter is crucial for the aim of
our analysis, a sensitivity analysis is undertaken. We consider simulation cases inwhich it is decreased to 0.01 and increased to 0.3. Also, the results depend on theparameter, ρ, which determines the degree of publicness on government expendi5) Population is the same across Cases A, B, and C. The population AN is assigned to 180.98 in alltsimulation cases.

20 A. Okamoto

Table 2

Simulation results for the three benchmarks for 2005, 2025, and 2050

Weight parameter in utility, µCase A

Case B

Case C(Benchmark for 2005)(Benchmark for 2025)(Benchmark for 2050)

a 0.1

a 0.1

a 0.1

50.96

a 50.96

a 50.96a 6.768%

a 7.167%

a 7.228%

Tax rate on consumption, τc

a 5%

6.54%

9.57%

Tax rate on interest income, τr

a 20%

a 20%

a 20%

Tax rate on inheritances, τh

a 10%

a 10%

a 10%

Government expenditure, G
Tax rate on labor incomeb , τw (wxi e s )Capital-labor ratio, K/L

2.78

3.10

2.93

Interest rate, r

4.54%

3.87%

4.21%

Wage rate, w

1.000

1.020

1.010

Rate of tax burden, T/Y

12.94%

14.61%

17.31%

Rate of social security, B/Y

12.06%

19.30%

29.06%

National burden rate, (T +B)/Y

25.00%

33.90%

46.37%

Social welfare, SW−32.541−35.816−44.008

a The symbol (a ) before the rate indicates that the variable is exogenous.
b The parameter values that determine the tax progressivity on labor income are α = −0.0325,

β = 0.0628 in all simulation cases. The rate presented is an average tax rate on labor income.

ture. The parameter value is assigned to 0.88 in the benchmark cases. We consider
cases in which it is decreased to 0.75 and increased to unity. The following simulation cases are now considered.
3.2.1. Three benchmarks for 2005, 2025, and 2050
Table 2 shows the simulation results for the three benchmarks for 2005, 2025,
and 2050.
Case A (Benchmark of the 2005 current state)
The utility weight, µ, is set to 0.1. The tax system on labor income has a realistic
progressiveness, with an average tax rate of 6.77%. Tax rates on consumption,interest income, and inheritances are 5%, 20%, and 10%, respectively.
Cases B (Benchmark of the 2025 aged state) and C (Benchmark of the 2050 aged
state)The utility weight, µ, is the same as in Case A. The extra tax burden, caused by atransition to an aged society, is covered by a consumption tax. Other tax regimes
remain the same as in Case A.
3.2.2. Cases that maximize social welfare for 2005, 2025, and 2050
Table 3 presents the simulation results in cases that maximize social welfare forthe three benchmarks.

An Optimal Rate of the National Burden in an Aging Japan

21

Table 3 Cases that maximize social welfare for 2005, 2025, and 2050
Case A*(2005)

Case B*(2025)

Case C*(2050)

Weight parameter in utility, µ

a 0.1

a 0.1

a 0.1

Government expenditure, Ga 93.38

a 85.71

a 74.03

Tax rate on labor incomeb , τw (wxi e s )a 6.768%

a 7.167%

a 7.228%

Optimal tax rate on consumption, τ∗c20.17%

20.38%

20.45%Tax rate on interest income, τr

a 20%

a 20%

a 20%

Tax rate on inheritances, τh

a 10%

a 10%

a 10%

Capital-labor ratio, K/L

2.78

3.10

2.93

Interest rate, r

4.54%

3.87%

4.21%

Wage rate, w

1.000

1.020

1.010

Rate of tax burden, T/Y

23.71%

24.57%

25.14%

Rate of social security, B/Y

12.06%

19.30%

29.06%

National burden rate, (T +B)/Y

35.77%

43.86%

54.20%

Maximized social welfare, SW ∗−16.346−21.326−33.552a The symbol (a ) before the rate indicates that the variable is exogenous.
b The parameter values that determine the tax progressivity on labor income are α = −0.0325,

β = 0.0628 in all simulation cases. The rate presented is an average tax rate on labor income.

Case A*
In Case A, the tax rate on consumption is adjusted to maximize social welfare.
A rise in the tax rate leads to an increase in government expenditure.
Cases B* and C*
In Cases B and C, the tax rate on consumption is adjusted to maximize social
welfare, which gives Cases B* and C*, respectively.
3.2.3. Changes in the utility weight parameter given for public services for 2005,
2025, and 2050
In contrast to Cases A, B, and C, the weight parameter, µ, given for the benefits
coming from government expenditure is changed to 0.01 and 0.3. Table 4 presents
the simulation results of the transitions of an optimal tax rate on consumption,
an optimal rate of the tax burden, and an optimal rate of the national burden forµ = 0.01, 0.1, and 0.3.
Cases A-1 and A-2
In contrast to Case A, the utility weight, µ, is changed to 0.01 and 0.3, whichyields Cases A-1 and A-2, respectively.
Cases A-1* and A-2*
In Cases A-1 and A-2, the tax rate on consumption is adjusted to maximize social
welfare, which gives Cases A-1* and A-2*, respectively.

22 A. Okamoto

Table 4 Simulation results for cases with diﬀerent utility weights on public services for 2005, 2025,
and 2050
1. Transition of an optimal tax rate on consumption
The utility weight

2005

2025

2050

µ = 0.01

7.48% (Case A-1*)

7.60% (Case B-1*)

7.71% (Case C-1*)µ = 0.1

20.17% (Case A*)

20.38% (Case B*)

20.45% (Case C*)µ = 0.3

29.34% (Case A-2*)

29.61% (Case B-2*)

29.65% (Case C-2*)

2. Transition of an optimal rate of the tax burden
The utility weight

2005

2025

2050

µ = 0.01

14.91% (Case A-1*)

15.46% (Case B-1*)

15.81% (Case C-1*)µ = 0.1

23.71% (Case A*)

24.57% (Case B*)

25.14% (Case C*)µ = 0.3

29.00% (Case A-2*)

30.03% (Case B-2*)

30.74% (Case C-2*)

3. Transition of an optimal rate of the national burden
The utility weight

2005

2025

2050

µ = 0.01

26.97% (Case A-1*)

34.75% (Case B-1*)

44.87% (Case C-1*)µ = 0.1

35.77% (Case A*)

43.86% (Case B*)

54.20% (Case C*)µ = 0.3

41.05% (Case A-2*)

49.33% (Case B-2*)

59.80% (Case C-2*)

Cases B-1, B-2, B-1*, and B-2*
In the 2025 aged steady state, simulations similar to Cases-A are conducted.
Cases B-1, B-2, B-1*, and B-2* correspond to Cases A-1, A-2, A-1*, and A-2*,
respectively.
Cases C-1, C-2, C-1*, and C-2*
In the 2050 aged steady state, simulations similar to Cases-A are undertaken.
Cases C-1, C-2, C-1*, and C-2* correspond to Cases A-1, A-2, A-1*, and A-2*,
respectively.
3.2.4. Changes in the degree of publicness on government expenditure
Table 5 shows the simulation results for diﬀerent degrees of publicness on government expenditure in the 2005 current benchmark case.
Case A-a
In contrast to Case A, the exponent, ρ, that determines the degree of publicness isdecreased to 0.75, which yields Case A-a. In this case, government expenditure
takes on more of the character of public goods.

An Optimal Rate of the National Burden in an Aging Japan

23

Table 5 Simulation results for diﬀerent degrees of publicness on government expenditureρ = 0.75

ρ = 0.88

ρ = 1.00(Case A-a*)(Case A*)

(Case A-b*)

Optimal tax rate on consumption, τ∗c

8.64%

20.17%

37.47%

Rate of tax burden, T/Y

15.80%

23.71%

33.09%

National burden rate, (T +B)/Y

27.86%

35.77%

45.15%

Maximized social welfare, SW ∗−10.919−16.346−27.995

Table 6 Parameter values used in the simulation analysis
Parameter description

Parameter values

Adjustment coeﬃcient for discounting the futureδ = 0.02

Intertemporal elasticity of substitution

γ = 0.25

The degree of publicness of government spendingρ = 0.88

Elasticity of substitution in production

σ = 0.6

Weight parameter in production

ε = 0.2

Scale parameter in production

B = 0.9634

Retirement age

RE = 60

Starting age for receiving public pension benefits

S T = 65

Replacement ratio for public pension

θ = 0.3718

Case A-b
In contrast to Case A, the exponent, ρ, is increased to unity, which gives Case Ab. In this case, government expenditure takes on the character of purely private
goods.
Cases A-a* and A-b*
In Cases A-a and A-b, the tax rate on consumption is adjusted to maximize social
welfare, which gives Cases A-a* and A-b*, respectively.
3.3. Specification of Parameters
This paper examines an optimal rate of the national burden for the economy inan aging Japanese society through comparing steady states. We choose parameter values that are realistic for the economy. Thus, the economic variables in thebenchmark simulation (i.e., Case A), such as the ratio of capital to income (K/Y)
or that of capital to labor (K/L), are close to the values that are suggested by the
Economic and Social Research Institute (2005). The parameter values used in thesimulation are given in Table 6.
First, the weight parameter, µ, in the utility function in equation (2) is assigned
to 0.1 in the benchmark cases. Because no studies have estimated explicitly this24 A. Okamoto

Table 7

Eﬀective tax rates for national income tax and residence tax of wageworkers

Income class

Total amount ofannual income(million yen)Low5xl = 0.7143

177

3.54

Medium7

xm = 1

418

5.97

10

xh = 1.4286

1,041

10.41

High

Weight on Total amount of annual taxes:
labornational income tax andendowments residence tax (thousand yen)Eﬀectivetax rates(%)

Data given are for a couple with two children.
Source: Ministry of Finance (2005).

utility weight parameter, we made reference to Aschauer (1985) as a second-bestmeans. In that study, eﬀective consumption C ∗ is characterized by
C ∗ = C + φG,
where C is private consumption and φ denotes the degree of substitution between C
and G (i.e., government spending). The parameter φ signifies the marginal benefitsof government expenditure. Aschauer’s study estimated φ to lie between 0.2 and0.4.
Second, survival probabilities (p s ) are calculated from the National Institute ofPopulation and Social Security Research (2002). Our model makes no distinction
by sex, and thus this study uses male–female average values for 2005, 2025, and2050. Based on the above data, the percentages of the aged population (65 orover) in the total population (21 or over) in 2005, 2025, and 2050 are 24.90%,
34.63%, and 44.47%, respectively. Common growth rates of successive cohorts (n)are chosen so that the percentages in the simulation equal the estimated values (seeTable 1).
Third, the method of assigning the weight given to labor endowments for thethree income classes is explained. Table 7 shows the data from the Ministry of
Finance (2005). This table presents the eﬀective tax rates of wageworkers on anational income tax and a residence tax, with regard to a couple with two children.
In our model, the three representative households, namely, low, medium, and highincome classes, have diﬀerent earnings abilities. Table 7 suggests that each income
class, which accounts for one third of the total population, corresponds to the representative household earning 5, 7, or 10 million yen, respectively, on an annual base.
The weight on labor endowments for each income class corresponds to the ratio of
its amount of earned income. The medium-income class is used as a yardstick, thatis, xm = 1; xl and xh are assigned to reflect diﬀerent earnings abilities across thethree income classes.
Fourth, the method of assigning the parameter values that determine tax progressivity on labor income, namely, α and β, is described. Table 7 presents theeﬀective tax rate calculated from a national income tax and a residence tax for each
income class. The parameters on labor income are chosen so that the eﬀective tax

An Optimal Rate of the National Burden in an Aging Japan25

rate for each income class in the simulation is close to the estimated value.
Finally, with regard to the public pension system, the replacement ratio of pension payments (θ) in Case A is adjusted so that the contribution rate (τ p ) equals theactual value of 13.58% in employee pension plans (Kosei Nenkin) in 2005.
4. Simulation Results
According to the Ministry of Finance (2005), the rate of the tax burden(= (National taxes + Local taxes) / National income) is 21.5%, the rate of social
security (= Social security / National income) is 14.4%, and thus the rate of thenational burden, which is the sum of them, was 35.9% in 2005. In our benchmark
simulation (i.e., Case A), the rate of the tax burden is 12.94%, the rate of social
security is 12.06%, and the rate of the national burden is 25.00%, as shown in
Table 2. The rate of the tax burden in our simulation is substantially lower than
the actual rate, because our model does not introduce such taxes as corporate andproperty ones. On the other hand, the rate of social security is close to the actual
rate, although our simulation deals only with a public pension scheme. Therefore,
in the setting of our simulation, the rate of the national burden is lower than that inreality in Japan.
This paper investigates an optimal tax rate on consumption to maximize thesocial welfare function. A rise in the tax rate on consumption increases the total
tax revenue, which means an increase in government expenditure. This increaseenhances households’ utility, because our model takes account of the benefits thatthe government provides to households. With regard to the social security system,
our model only considers the current Japanese public pension program operated
in a manner that is similar to a pay-as-you-go style. The replacement ratio in thecurrent public pension system is kept constant in all simulations6) . Therefore, it
should be noted that an optimal rate of the national burden in this paper signifies
the sum of an optimal rate of the tax burden (which is led by examining an optimalrate on consumption) and a constant rate of the public pension (= Public pension /National income).
In this paper, the influence on capital accumulation is regarded as an indicatorof eﬃciency. The reason is that, under the assumption of an inelastic labor supply,
the level of the total output depends solely on the level of the capital stock, as
indicated by equation (14). The social welfare function represented by equation (8)is dependent on the aspects of both eﬃciency and equity.

6) Under a constant replacement ratio of the current Japanese public pension system, we maximize thesocial welfare. This is because, due to the rapid aging of the Japanese population, the benefits to be paid
through the system are not profitable especially for future generations. Therefore, we decided that thecurrent replacement ratio is also maintained in aged simulation cases.

26 A. Okamoto

4.1. Findings and Policy Implications
4.1.1. Three benchmarks for 2005, 2025, and 2050
Table 2 shows the simulation results for the three benchmarks for 2005, 2025,
and 2050. Cases A, B, and C are the benchmarks for 2005, 2025, and 2050, respectively. Under revenue neutrality, a consumption tax covers an extra tax burdencaused by the transition from the current state to the aged states. Therefore, inCases B and C, the revenue-neutral tax rate on consumption is increased to 6.54%
and 9.57%, respectively. As the population ages, the contribution rate to the public pension scheme (i.e., payroll tax) sharply rises under conditions of a constantreplacement ratio. Table 1 suggests that the rate rises from 13.58% (Case A) to
21.57% (Case B) and 32.61% (Case C).
The capital-labor (K/L) ratio increases from 2.78 (Case A) to 3.10 (Case B),
and then decreases slightly to 2.93 (Case C). The K/L ratio is determined by theamounts of capital accumulation and labor supply. Both would decline as the population ages. With regard to capital formation, in an aging society, there are many
cohorts that dissave their assets based on their life-cycle motive. With respect tothe labor supply, it decreases drastically from 349.6 to 306.2 and 260.0 under aconstant population, as shown in Table 1.
The rate of the tax burden rises from 12.94% (Case A) to 14.61% (Case B) and
17.31% (Case C), because there is the extra tax burden caused by transition to theaged states. The rate of social security dramatically rises from 12.06% (Case A) to
19.30% (Case B) and 29.06% (Case C), because the current public pension programis fundamentally a pay-as-you-go style. Thus, the rate of the national burden rises
substantially from 25.00% (Case A) to 33.90% (Case B) and 46.37% (Case C).
4.1.2. Cases that maximize social welfare for 2005, 2025, and 2050
Table 3 presents the simulation results in cases that maximize social welfare
for the three benchmarks for 2005, 2025, and 2050. In the current benchmark,the optimal tax rate on consumption rises drastically from 5% (Case A) to 20.17%(Case A*)7) . As the population ages, it rises slightly to 20.38% (Case B*) and
20.45% (Case C*). The rate of the tax burden rises from 12.94% (Case A) to
23.71% (Case A*). As the population ages, it also rises slightly to 24.57% (Case
B*) and 25.14% (Case C*). Thus, the rate of the national burden rises from 25.00%(Case A) to 35.77% (Case A*). As the population ages, it rises dramatically to
43.86% (Case B*) and 54.20% (Case C*), because of a substantial increase in therate of social security.
Thus, the simulation results suggest that an optimal rate of the national burden
would rise as the population ages and may exceed 50% during the rapid aging of
the Japanese population. When evaluating this simulation result, the fact that the7) The model in this paper does not introduce such taxes as corporate and property ones, while it takes

full account of government expenditure. Therefore, in our simulation, the optimal tax rate on consumption inevitably becomes high. It should be noted that we do not claim that, in the current Japanesesystem, the optimal tax rate on consumption is approximately 20%.

An Optimal Rate of the National Burden in an Aging Japan27

rate of the national burden in the setting of our simulation is lower than the actual
rate needs to be noted.
4.1.3. Changes in the utility weight parameter given for public services
With regard to the weight parameter, µ, given for the benefits coming from government expenditure in equation (2), we assign 0.1 in the benchmark simulation.
To ascertain the eﬀects of diﬀerent weight parameters on the simulation results, weconsider the cases in which µ is changed to 0.01 and 0.3.
Table 4 shows that, when the weight is lowered to 0.01, the optimal tax rateon consumption decreases dramatically from 20.17% (Case A*) to 7.48% (CaseA-1*). As the population ages, it rises slightly to 7.60 % (Case B-1*) and 7.71 %(Case C-1*). When the weight is raised to 0.3, the optimal tax rate on consumption
increases to 29.34% (Case A-2*). As the population ages, it rises slightly to 29.61% (Case B-2*) and 29.65 % (Case C-2*).
Table 4 also presents the simulation results for optimal rates of the tax burden and the national burden for 2005, 2025, and 2050. The results are similar to
those for an optimal tax rate on consumption. When the utility weight parameter ishigh (i.e., µ = 0.3) in 2050, the optimal rate of the national burden is approximately 60% (Case C-2*). The results suggest that, if households think highly of thebenefits coming from government expenditure for their utility, the optimal tax rateon consumption (and thus the optimal rate of the national burden) is high.
To establish the relationship between the assignment of the utility weight parameter µ and the reality of the Japanese economy, an additional simulation was
conducted. The result shows that the current Japanese tax rate on consumption of
5% is optimal when the weight parameter µ equals 0.0052. This means that, only
when the utility weight for public services is this low, is the current tax rate on
consumption justified.
4.1.4. Changes in the degree of publicness on government expenditureWith regard to the exponent, ρ, that determines the degree of publicness on government expenditure in equation (2), we assign 0.88 in the benchmark simulation,with reference to Borcherding (1985). To ascertain the eﬀects of diﬀerent degrees
of publicness on the simulation results, we consider cases in which ρ is changed
to 0.75 and unity. In Case A-a where ρ is 0.75, government expenditure takes onmore of the character of public goods. On the other hand, in Case A-b where ρ isunity, government expenditure is purely private goods.
Table 5 shows the simulation results for diﬀerent degrees of publicness on government expenditure. When government expenditure takes on more of the character of public goods (ρ = 0.75), the optimal tax rate on consumption decreases
dramatically from 20.17% (Case A*) to 8.64% (Case A-a*). Hence, in Case Aa*, the optimal rates of the tax burden and the national burden diminish to 15.80%
and 27.86%, respectively. On the other hand, when government expenditure takes
entirely on the character of purely private goods (ρ = 1), the optimal tax rate on
consumption increases substantially to 37.47% (Case A-b*). Thus, in Case A-b*,

28 A. Okamoto

the optimal rates of the tax burden and the national burden increase to 33.09% and45.15%, respectively.
Therefore, the simulation results suggest that, when the degree of publicness ofgovernment spending is high, that is, as government expenditure takes on more of
the character of public goods, the optimal rate of the national burden is low. These
results are generated by the concavity of the underlying utility function employedin our model.
4.2. Comments
For interpreting the simulation results, the following four comments need to betaken into account. First, our model assumes an inelastic labor supply. Therefore,
there is only a partial impact of progressive taxation and no excess burden. An
elastic labor supply needs to be introduced to comprehensively analyze the eﬀects
of tax reforms. Several investigations, however, showed that labor supply is fairly
inelastic for the after-tax wage rate in Japan. For instance, Asano and Fukushima(1994) reported that the estimated value of compensated elasticity of labor supply
is 0.27 in Japan. It should be noted that their study estimated only the size of thesubstitution eﬀect. If the income eﬀect were also estimated, a still smaller elasticityof labor supply for the after-tax wage rate would be obtained.
An elastic labor supply can be assumed by incorporating leisure into the utility
function in addition to consumption, such as in Auerbach and Kotlikoﬀ (1987),
Altig et al. (2001), and Okamoto (2007):95  1− 1 1− 1ξ  1− γ1
1 ξ−(s−21)
i
ξ
p
(1
+
δ)
+
φ
lis
,
C
U =
s
s
1 − γ1 s=21
1− 1iwhere lis represents leisure at age s, φ the utility weight on leisure, and ξ is the intratemporal elasticity of substitution between consumption and leisure. The weighton leisure φ is assigned to 1.5 in Auerbach and Kotlikoﬀ (1987) and 1.0 in Altig
et al. (2001), respectively. On the other hand, Homma et al. (1987b) estimate theweight parameter to be 0.1 using Japanese data, which is much smaller than thatin the United States. Thus, the parameter φ is assigned to 0.1 in studies on theJapanese economy, such as in Homma et al. (1987a), Iwamoto (1990), and Uemura(2001). Such a large diﬀerence may suggest that, even if elastic labor supply wereintroduced, the simulation results would not change so much as long as we conduct
the analysis on the Japanese economy.
Second, our simulations are limited to the steady states. The model takes account of the eﬀects of demographics, by comparing the three steady states for 2005,
2025, and 2050. Thus, our study lacks a consideration of the transitional path. Tax
and social security reforms have diﬀerent eﬀects on diﬀerent generations. Specifically, current and future generations would experience diﬀerent impacts of theseAn Optimal Rate of the National Burden in an Aging Japan29

reforms8) . Therefore, it is necessary to take account of not only steady states but
also the transitional process in an aging society.
Third, the simulation model is solved under the hypothesis of perfect foresight. Households correctly anticipate the interest, wage, tax, and contribution
rates. Without the assumption of perfect foresight, households that maximize their
lifetime utility would have more assets, resulting in more capital accumulation. As
households are more risk averse, this eﬀect is greater.
Finally, because the simulation results are dependent on the given parameters,
we must be careful about the eﬀects of any parameter changes. As shown in Tables
4 and 5, a slight change in the parameters of µ (the weight on public services)and ρ (the degree of publicness) in the utility function has a substantial eﬀect on
the results. Also, a slight change in the parameter of intertemporal elasticity of
substitution, γ, has a great aﬀect on capital formation.
5. Conclusions
This paper examined an optimal rate of the national burden to establish guidelines for fiscal reform in Japan’s graying society. The paper looked at Japanese
tax and social security systems through an extended life-cycle general equilibrium
simulation model. It considers the benefits that the government provides to households, which enabled us to comprehensively evaluate the balance between benefits
and burdens.
The simulation results showed that, when households put a great utility weighton the benefits coming from public services, an optimal rate of the national burden
is high. This implies that, if the government appropriately provides public services that meet the demands of households, the optimal rate is high. The results
also suggested that, when the degree of publicness of government expenditure ishigh, an optimal rate of the national burden is low. In other words, if government
expenditure takes on more of the character of public goods, the optimal rate is low.
Moreover, the simulation results indicated that, as the population ages, an optimal tax rate on consumption rises gradually and the contribution rate to the public
pension program with a pay-as-you-go scheme dramatically rises under conditionsof a constant replacement ratio. Therefore, an optimal rate of the national burden
would rise as the population ages, and may exceed 50% during the rapid aging of
the Japanese population.

8) For example, a change from a labor income tax to a consumption tax creates income transfers among
generations during the transition. At the onset of policy reform, the elderly who had already paid theirlabor income tax will have to pay an additional consumption tax. Because this generation would suﬀer
from a double burden, the transition to a consumption tax is not Pareto improving.

30 A. Okamoto

Appendix A
To consider the utility maximization problem over time for each income class,namely the maximization of equation (2) subject to equation (3), let the Lagrangefunction be
Li = U i +95
λis −Ais+1 + {1 + r(1 − τr )} Ais

s=21+{1 − τw (wxi e s ) − τ p } wxi e s + bis + ais − (1 + τc ) C is ,(9)

where λis represents the Lagrange multiplier for equation (3) and superscripts i (=l, m, h) denote low, medium, and high-income classes, respectively. The first-orderconditions for s = 21, 22, . . . , 95 can be expressed by  − γ1∂Li−(s−21)=p(1+
δ)− λis (1 + τc ) = 0,
C is
s
∂C is

(10)

∂Li
= −λis + λis+1 {1 + r(1 − τr )} = 0.
∂Ais+1(11)

The combination of equations (10) and (11) yields equation (7) that determines thei, equation
slope of the age-consumption profile over the life cycle. For a given C21(7) solves the path for consumption. Transformation of equation (7) leads to thefollowing expression:
C is =

ps
p21

γ 

1 + r(1 − τr )1+δγ(s−21)
i
C21
.

(12)

Integrating equation (3) and using the initial and terminal conditions Ai21 = Ai96 = 0,
caused by no intended bequests, produces the following equation:95{1 + r(1 − τr )}−(s−21) (1 + τc ) C is

s=21

=

RE


{1 + r(1 − τr )}−(s−21) [1 − τw (wxi e s ) − τ p ]wxi e s

s=21

+

95


{1 + r(1 − τr )}−(s−21) bis + {1 + r(1 − τr )}−29 ai50 .

(13)

s=S T
i
To derive C21, equation (12) is substituted into this lifetime budget constraint. Thus,i.
we can find an optimum solution for C21

An Optimal Rate of the National Burden in an Aging Japan

31

Appendix B
Section 2 describes the basic structure of households in the simulation model.
This appendix presents the basic structures of firms and the government, and market
equilibrium conditions.
Firm Behavior
The model has a single production sector that is assumed to behave competitively using capital and labor, subject to a constant-returns-to-scale production
function. Capital is homogeneous and non-depreciating, while labor diﬀers onlyin its eﬃciency. All forms of labor are perfect substitutes. Households in diﬀerent income classes or of diﬀerent ages, however, supply diﬀerent amounts of somestandard measure per unit of labor input.
The production function is assumed to be of the constant elasticity of substitution form:

 1
1− 1
1− 1 1− 1(14)
Yt = B εKt σ + (1 − ε)Lt σ σ ,where Yt represents the total output, Kt the total capital, Lt the total labor supply
measured by the eﬃciency units, B a scaling constant, ε a parameter measuring
the intensity of use of capital in production, and σ is the elasticity of substitution
between Kt and Lt . Using the property subject to a constant-returns-to-scale production function, we can obtain the following equation:
Yt = rKt + wLt .

(15)

Government Behavior
The government sector consists of a narrower government sector and a pension
sector. The narrower government sector collects taxes and spends them on general
governmental expenditure. There is no outstanding debt, and thus balanced budget
policies are assumed.
The budget constraint of the narrower government sector at time t is given by
Gt = T t ,(16)

where T t is the total tax revenue from labor income, interest income, consumption,and inheritances. The public pension system is assumed to be a simple pay-as-yougo scheme. The budget constraint of the pension sector at time t is given by
Rt = Bt ,(17)

where Rt is the total contribution to the pension schedule, and Bt is the total pension
benefit to generations of age ST or over.
Both of these sectors are financed independently and separately. No transfer is

32 A. Okamoto

made between the sectors9) . Gt , T t , Rt and Bt are defined by95

p s (1 + n)−(s−21) g,(18)

T t = LXt + τr rAS t + τc ACt + τh BQt ,Rt = τ p wLt ,95

Bt = Ntp s (1 + n)−(s−21) {bls + bms + bhs },

(19)
(20)

G t = Nt

s=21

(21)

s=S T

where g is annual government expenditure for each cohort, andh
BQt = BQlt + BQm
t + BQt .

(22)

LXt is the tax revenue from labor income, which is led by a summation of the threeincome classes with the same weight:1
p s (1 + n)−(s−21) αwxl e s + β(wxl e s )2 + αwxm e s
2
s=21

1
1
m
2
h
h
2
+ β(wx e s ) + αwx e s + β(wx e s ) .
2
2

LXt = Nt

RE


(23)

Similarly, aggregate assets supplied by households, AS t , and aggregate consumption, ACt , are obtained by a simple summation of the three income groups:
AS t = Nt95p s (1 + n)−(s−21) {Als + Ams + Ahs },(24)

p s (1 + n)−(s−21) {C ls + C ms + C hs }.

(25)

s=21

ACt = Nt

95

s=21

Market Equilibrium
Finally, equilibrium conditions for the capital, labor, and goods markets aredescribed.
1. Equilibrium condition for the capital market
Because aggregate assets supplied by households are equal to real capital, weget(26)
AS t = Kt .
9) Okamoto and Tachibanaki (2002) incorporate the basic pension (i.e., the flat part) into the public

pension program. In that study, the general tax revenue covers one third of the basic pension, along thelines of the current Japanese tax and public pension systems.

An Optimal Rate of the National Burden in an Aging Japan33

2. Equilibrium condition for the labor market
Measured in eﬃciency units, because aggregate labor demand by firms is equal
to aggregate labor supply by households, we get
Lt = N tRE

p s (1 + n)−(s−21) {xl + xm + xh } e s .

(27)

s=21

3. Equilibrium condition for the goods market
Because aggregate production is equal to the sum of consumption, investment,
and government expenditures, we get
Yt = ACt + (Kt+1 − Kt ) + Gt .

(28)

An iterative program is performed to obtain the equilibrium values of the above
equations.
Acknowledgements
This paper was presented at the 61st Congress of the International Institute of
Public Finance (IIPF) in Korea in 2005, and at the Spring Seminar of the Department of Economics at the University of Wisconsin-Milwaukee in 2006. The author
is very grateful for insightful comments and suggestions by Professors Toshiaki
Tachibanaki, Sunwoong Kim, Mohsen Bahmani-Oskooee, Yoshio Niho, Masaru
Yoshitomi, Yuji Hosoya, Nobuhiko Yamazaki, Masayuki Morikawa, Toshiya
Hatano, Masumi Kawade, Naomi Miyazato, and Syun-ichiro Bessyo. The author acknowledges the financial supports from the Research Institute of Economy,
Trade and Industry (RIETI) in Japan, and from the Ministry of Education, Culture,
Sports, Science and Technology in Japan (Grant-in-Aid for Scientific Research (C)No.15530215). This research is also a part of the International Research Project on
Aging (Japan, China, and Korea) at Hosei Institute on Aging (Hosei University),
supported by the Special Assistance of the Ministry of Education, Culture, Sports,
Science and Technology in Japan.
References
Altig, D., A. J. Auerbach, L. J. Kotlikoﬀ, K. A. Smetters, and J. Walliser (2001) “Simulating
fundamental tax reform in the United States”, American Economic Review 91: 574–
595.
Asano, S. and T. Fukushima (1994) “Some empirical evidence on demand system and optimal commodity taxation”, Discussion Papers in Economics and Business, 94-01, Faculty of Economics, Osaka University.
Aschauer, D. A. (1985) “Fiscal policy and aggregate demand”, American Economic Review
75: 117–127.
Atkinson, A. B. (1999) The economic consequences of rolling back the welfare state. The
MIT Press.

34 A. Okamoto

Auerbach, A. J. and L. J. Kotlikoﬀ (1987) Dynamic fiscal policy. Cambridge University
Press. Cambridge.
Borcherding, T. E. (1985) “The causes of government expenditure growth: a survey of the
U.S. evidence”, Journal of Public Economics 28: 359–382.
Homma, M., N. Atoda, Y. Iwamoto and F. Ohtake (1987a) “Pension: aging society and pension plan”, in K. Hamada, A. Horiuchi and M. Kuroda (eds.) Macroeconomic analysisof the Japanese economy. Tokyo University Shuppankai, pp.149–175 (in Japanese).
Homma, M., N. Atoda Y. Iwamoto and F. Ohtake (1987b) “Life-cycle growth model andsensitivity analysis”, Osaka Economic Papers 36, Osaka University, pp.99–108 (inJapanese).
Ihori, T., R. R. Kato, M. Kawade and S. Bessho (2005) “Public debt and economic growth
in an aging Japan”, COE Discussion Papers COE-F-100, Faculty of Economics, The
University of Tokyo.
Iwamoto, Y. (1990) “Pension plan and bequest behavior”, Quarterly Journal of Social Security Research 25: 388-411 (in Japanese).
Okamoto, A. (2004) Tax policy for aging societies: lessons from Japan. Springer.
Okamoto, A. (2005a) “Simulating progressive expenditure taxation in an aging Japan”, Journal of Policy Modeling 27: 309–325.
Okamoto, A. (2005b) “Simulating fundamental tax reforms in an aging Japan”, Economic
Systems Research 17: 163–185.
Okamoto, A. (2007) “Optimal tax combination in an aging Japan”, International Economic
Journal 21 (in press).
Okamoto, A. and T. Tachibanaki (2002) “Integration of tax and social security systems”,
in T. Ihori and T. Tachibanaki (eds.) Social security reform in advanced countries.
Routledge, London and New York, pp.132–160.
Uemura, T. (2001) Economic analysis of the financial burden: evaluation of tax reform andpension policy. Kwansei Gakuin University Press (in Japanese).

Data
Economic and Social Research Institute (2005) Annual Report on National
Accounts (Kokumin Keizai Keisan Nenpo) 2005, Cabinet Oﬃce, Japan.
Ministry of Finance (2005) Let’s Talk about Taxes, May, Japan.
Ministry of Health, Labor and Welfare (2004) Basic Survey on Wage Structure(Chingin Sensasu) 2003, Japan.
National Institute of Population and Social Security Research (2002) Population
Projections for Japan: 2001–2100 (Estimation in January, 2002), Japan.