Journal of Business & Economic Policy

Vol. 2, No. 4; December 2015

Effects of Direct Underwriting of Public Bonds by the Central Bank in Japan
Motonori Yoshida
Associate Professor
Graduate School of Economics
Osaka Prefecture University
1-1 Gakuen-cho, Naka-ku, Sakai-city
Osaka, 599-8531
Japan

Abstract
This study uses a dynamic computable general equilibrium OLG (overlapping generations) model to elucidate theeffects of direct underwriting of public bonds (DUPB) by the central bank, which has the potential to support theJapanese economy and government finance and to improve the efficiency of added-value distribution. The results
demonstrate that the Japanese economy and government finance become sustainable through DUPB by thecentral bank but, on the other hand, collapse when public bonds are absorbed by the market. This is due to thefact that in the former case, payment of the central bank’s seignior age to the national treasury improves thegovernment’s finance situation.

Keywords: Fiscal sustainability, Direct underwriting of public bonds, Central bank, Seignior age, Dynamic
computable general equilibrium, overlapping generation’s model.

1. Introduction
Currently, many experts are questioning the sustainability of the Japanese economy and government finance. In
fact, the ratio of fiscal balance of the general government 1 to GDP and that of the general government’s
outstanding debt to GDP were approximately -9.8% and 218.8%, respectively, in 2012. Moreover, both figures
were the worst among the G7 countries.2 Accordingly, in order to examine this issue in detail, I show thetransitions in the balance of net lending (+)/net borrowing (-) in Figure 1, which explains the following points: 1)
Among the various sectors in Japan, the public sector’s balance of flow continues to be in extremely poor
condition. 2) However, in the Japanese economy as a whole, the buoyant financial situation of the private sector
sufficiently compensates for the poor performance of the public sector. 3) In particular, as a result of 2), Japan’s
external asset balance is the highest in the world as of 2012 (concretely, Japan has the largest amount of net
balance at 3,423,625 million U.S. dollars, which is approximately 1.83 times that held by China, having thesecond largest amount).3Hence, taking all these points into consideration, we can perceive the fact that Japan ispoorly distributing its own added value under its global top-class economic power.
Furthermore, the following key points must be considered:4 1) The monetary-easing policy implemented
continuously by the Bank of Japan (BOJ) since 1998 has kept rapidly increasing the outstanding Japanese
government bonds (JGBs) among the BOJ’s assets; the amount of outstanding JGBs held by the BOJ soared from64,266 to 198,337 billion yen during FY2008-13 (the ratio of JGB to BOJ’s total assets grew from 0.519 to
0.821).5 2) Most of the BOJ’s receipt of interest on JGBs (the BOJ’s seignior age) is paid to the national treasury,6
and this amount increased from 255 to 579 billion yen during FY2008–13. 3) At the same time, expenditure on
public bonds accounts for an extremely high proportion of the central government’s annual expenditure (thisproportion is 0.240 in FY 2013). On the basis of the above observations, Japan needs to consider the
implementation of direct underwriting of public bonds7 (DUPB) by the BOJ, although this policy may initiallyseem reckless.8 Such a policy seems necessary because it has the potential to support the Japanese economy andgovernment finance and to improve the efficiency of added-value distribution in Japan as a whole, via the channelof the BOJ’s-seignior age payment to the national treasury.
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Many prior studies have demonstrated negative simulation results in relation to the sustainability of Japanese
government finance, including Ihori et al. (2001), Doi et al. (2011), Hoshi and Ito (2014), Ihori et al. (2006), andShimazawa and Oguro (2010). Moreover, such studies have indicated the need for Japan to raise the ratio ofgovernment revenue by taxes and pension contributions (referred to as “GRTPC”) to GDP to roughly 50% or to
drastically cut public annual expenditure in order to maintain government finance. However, to the author’s
knowledge, no research has used a dynamic computable general equilibrium OLG (overlapping generations)model (DCGE-OLG model) to examine the effects of DUPB by the BOJ. Therefore, I have decided to attempt thisapproach. The rest of the paper is organized as follows. In Section 2, related literature and the aim of this study
are explained. Section 3 describes the model used in this study. Section 4 provides an explanation of theparameters and data used in the study. Section 5 presents the simulation results. Finally, Section 6 concludes thepaper．
Figure 1: Net Lending (+) / Net Borrowing (-) by institutional sectors of Japan(% of nominal GDP)
15.0

10.0

5.0

0.0

-5.0

-10.0

FY
-15.0
1. Non-financial corporations

2. Financial corporations

3. Households

Subtotal of 1-3

4. General government

5.Rest of the world

Note: Households include private unincorporated enterprises and private non-profit institutions
serving households.
Source: By the author, using data from the National Accounts (Cabinet Office).

2. Related Literature and Aim of Study
This study is related to the following research fields: 1) fiscal sustainability analysis in the context of population
aging, 2) monetization of government debt, and 3) analysis using the DCGE-OLG model. Accordingly, Section
2.1 provides an overview of the related literature in these areas. Next, Section 2.2 states the position and aim of
this study.
2.1 Related literature
2.1.1 Government fiscal sustainability
First, Hamilton and Flavin (1986) indicated that if the discounted present value of indefinitely rolled-overoutstanding government debt converges to zero, such fiscal management is sustainable. Furthermore, they
demonstrated that the U.S. government implemented sustainable fiscal management during the period of 1960–84
by empirical analysis based on their theory. In addition, Fukuda and Teruyama (1994) used Hamilton and Flavin(1986)’s method to analyze the sustainability of Japanese government finance between 1888 and 1992, and theyrejected the fiscal sustainability during the prewar and wartime periods. Next, Bohn (1998) presented a method
for examining the sustainability of government finance by regressing the ratio of outstanding public debt (OPD)
to GDP on the ratio of primary balance to GDP. His empirical analysis demonstrated that if the ratio of OPD to
GDP rose, the U.S. government would improve the primary balance to a surplus during the period of 1956–98.
Furthermore, Ihori et al. (2001) utilized Bohn (1998)’s method to examine the sustainability of Japanese centralgovernment (general account) finance and rejected any such sustainability during the period of 1956–98. Then,
Broda and Weinstein (2005) demonstrated a ratio of GRTPC to GDP that could ensure the sustainability ofJapanese government finance.
110Journal of Business & Economic Policy

Vol. 2, No. 4; December 2015

Here, they used a simulation analysis based on the government’s intertemporal budget constraint and the givensocioeconomic variables (simulation period of 2000–2100). They indicated that the required ratio of GRTPC to
GDP remains at the level of typical EU nations (i.e., the Japanese economy and government finance will notcollapse if Japan’s tax rate is raised from the current relatively low level, in comparison to the average ofdeveloped nations, to a reasonable level). Furthermore, Doi et al. (2011) considered additional real-world
constraints, such as social-security payment obligations, and updated Broda and Weinstein (2005)’s analysis.
Consequently, they argued the need for a higher ratio of GRTPC to GDP compared with Broda and Weinstein(2005). Next, Hoshi and Ito (2014) simulated the dynamics of Japan’s OPD and private financial assets byassigning various socioeconomic variables exogenously to the transition equations of OPD and private financial
assets. Accordingly, they demonstrated that OPD will exceed private financial assets in 2024 and also that it isnecessary to raise the ratio of GRTPC to GDP to 43–50% in order to attain fiscal sustainability. Finally, Kato
(2002), Ihori et al. (2006), and Shimazawa and Oguro (2010) used a DCGE-OLG model to analyze various issues
related to the sustainability of Japanese government finance. These works argued the need for drastically raisingtaxes and cutting annual expenditures to achieve fiscal sustainability. For example, Ihori et al. (2006)
demonstrated that the ratios of tax burden and social-security burden to GDP will rise significantly to 35.93%(2002 actual value = 15.62%) and to 23.27% (2002 actual value = 9.69%), respectively, by 2050.
2.1.2 Monetization of government debt
First, Sargent (1999) explained the basic concept of monetization of government debt as follows. Althoughgovernment annual expenditure (including payment of interest on public bonds) should be covered first by tax
revenue and then by revenue from public bonds, the residual that these two forms of revenue cannot cover has tobe met by revenue gained by increasing the money supply (namely “seignior rage”); in other words, in this case,the central bank is inevitably forced to monetize government debt. Next, Detken (1999) used an OLG model toexplain how intergenerational wealth redistribution changes in the case where the government relies on seignior
rage revenue, via the monetization of government debt by the central bank, and demonstrated the occurrence ofwealth redistribution from the current generation to future generations. Finally, Broda and Weinstein (2005) also
inspected the impact of monetization of Japanese government debt on the sustainability of government finance.
They measured the effect of the BOJ monetizing 50% of the initial OPD during the first five years of thesimulation period and showed that the monetization of government debt is not particularly effective in terms ofenabling sustainable finance. 9
2.1.3 DCGE-OLG model
The DCGE-OLG model,10 which was developed by Auerbach and Kotlikoff (1983, 1987), has been used invarious prior works, especially in the context of population aging because it has the following advantages,
differing from simulation analysis which only assigns various socioeconomic variables exogenously. 1) Thismodel is able to closely observe and examine reactions of the respective economic agents to changes in
exogenous variables such as fiscal policy, repeated effects of endogenous variables on the government sector,
mutual influences between economic agents and changes in society as a whole, the transition process of society,and welfare and financial burdens of each generation. Furthermore, 2) being a numerical simulation model, it ispossible to construct a model that conforms to actual social structure in accordance with the analysis objective.
2.2 Position and aim of this study
As reviewed so far, existing studies, in the context of the sustainability of the Japanese economy and government
finance, have analyzed only the effects of raising various national-burden ratios, lowering public expenditures,and partial monetization of government debt. Accordingly, I aim to analyze the effects of DUPB by the BOJ as
another policy to maintain the current level of government expenditure and the public pension system and toprevent the collapse of the Japanese economy and government finance. The detailed reasons for examining thispolicy are as follows. 1) In spite of the existence of the market-absorption principal of JGBs stipulated by Article
5 of the Public Finance Act, in practice, the BOJ has continued to purchase JGBs from the market for intensemonetary easing (Section 1). 2) The BOJ pays the majority of its seigniorage,11 namely the difference between
interest revenue on interest-bearing financial assets (of which JGBs account for the vast majority) and the cost ofadministrating issued currency (liabilities, i.e., BOJ banknotes) to the national treasury, based on Article 53 of the
Bank of Japan Act (Section 1).12 3) As shown in points 1) and 2), DUPB by the BOJ has both positive andnegative effects on Japan’s economic mechanism.
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Thus, quantitative measurement of these effects in both directions is extremely meaningful in evaluating theeffectiveness of this policy for the sustainability of the Japanese economy and government finance and forJapanese citizens’ welfare over generations. In addition, I chose a DCGE-OLG model to quantitatively measure
the above effects because of its advantages as explained above.

3. ModelThis section describes the study’s model, i.e., a DCGE-OLG model with six main parts: 1) households, 2) firms,
3) government, 4) public pension, 5) central bank, and 6) market equilibrium. In addition, each respective market
is in perfect competition; this model adopts the closed economy model based on the study aim; and the model
does not explicitly handle the issue of bequests for simplification.
3.1 Households
Respective households exist in each generation and are considered as follows. 1) Their preferences are the same
throughout all generations. 2) They originate at age 21 (1st period), retire at age 64 (44th period), and decease atage 105 (85th period);13 each household in elastically supplies one unit of labor during the 1st–44th periods. 3)
They possess perfect foresight and form rational expectations in a forward-looking manner. 4) Their utility
function with constant relative risk aversion is additive and separable over time.
Consequently, their life-cycle utility function is specified as follows:
=

1
1+

1

=

1−

1
1+

1

,

1−

(1)

where and denote the generation and the life period, i.e., age (20 + years old at the th period). Furthermore,
and represent the utility and the consumption of the th period of generation , respectively. ρ represents therate of time preference,γ the intertemporal elasticity of substitution, and the assumed final period of eachhousehold (here, = 85). Next, the budget constraint equation of generation in year is as follows:
(1 −
2 )
)(1 −
)
)
= [1 + (1 − ) (1 −2 )]
+ (1 −− (1 +
(
)
+ 1−
,
(2)
where
represents the assets at the end of the th period, the wage profile in the th period, the pension
14
benefit,the public pension contribution rate in the th period, the interest rate,
the wage rate,theinterest income tax rate,
the labor income tax rate,
the consumption-based tax rate,
the pension income
tax rate in year , and2 the ratio of OPD held by the central bank (i.e., BOJ) to outstanding national assets(ONA,
2 = 0 in the scenario of not implementing DUPB by the BOJ). 15In addition, the relationship between
year, generation, and age is as follows: = + − 1. Moreover, specified as a function of age andare asfollows:=+ (20 + ) + (20 + ) ,
(3)
=
+
=
+
,
(4)
where
represents the fixed amount portion,
the remuneration-based portion in the th period,
theaverage annual labor income of working period converted into the value at the pension-receipt time using theinterest rate, andthe rate used to calculate the remuneration-based portion in year . Furthermore, the in
tertemporal budget constraint of generation from Equation (2) is obtained as follows. In the equations below,
is a discount factor for converting the value of generation in the th period into the value at the time of the
1st life period:
(1 +

112

)

=

(1 −

)(1 −

)

+

(1 −

)

,

(5)

Journal of Business & Economic Policy

Vol. 2, No. 4; December 2015

1
=

∏
1

[1 + (1 −

)

(1 −

)]

2

if ≥ 2(6),.

if = 1

Maximizing Equation (1) subject to Equation (5),households obtain the following Eular equation on consumption
per period:
=

(

) (

γ

)

.
(7)

3.2 Firms
A representative firm exists in the private sector. Its productive structure is expressed by the Cobb-Douglas
production function with constant return to scale, and its structure and the transition of physical capital stock(PCS) are as follows.
[(1 + ) ]==,(8)
= + (1 − ),(9)where represents output,
the PCS, effective labor (labor measured by efficient-labor units), the grossprivate investment in year , the scale parameter, the capital share in production, the rate of Harrod-neutral
technological progress, and the depreciation rate of physical capital. In addition, the products are used both as
consumer and investment goods;
and are supplied by households. Moreover, profit maximization behavior
generates the following production-factor demand equations, where represents the PCS per efficient-labor unit:
(

=

(

)

)

−

(

=

)

−

,

(10)
= (1 − ) (1 + )()= (1 − ) (1 + ).

(11)
3.3 Government
The central government, local governments, and social security funds excluding the pension are specified as thegovernment. Accordingly, the factors of the government are set in turn. First, total tax revenue and total annual
revenue in year are expressed as follows.
=

=

+

+

2

(1 −

2 )+

+

,

(12)

.
(13)

In these equations,represents the total tax revenue,
the total annual revenue in year ,generation ′ population in the th period, and2 the OPD held by the BOJ in year − 1. In addition,
2 in Equation (13) is the payment of the BOJ’s seigniorage: however, this is zero in the scenario of not
implementing DUPB by the BOJ. Next, total annual expenditure in year is expressed as follows:
=

+

=

+

+

,

(14)

where
represents the total annual expenditure,
the fiscal transfer to the public pension,
the total
annual expenditure except,
the national subsidy rate on the fixed payment portion of public pensions inyear ,
the annual expenditure per person over age 65 in the base year (referred to as “EAE”), andtheannual expenditure per person over age 21 excluding EAE in the base year(referred to as “GAE”).
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In addition,andare fixed at the base year value. From the above, the government’s budget
constraint equation, the public bonds issued, the fiscal balance, and the primary balance are expressed as follows.
) ,= (1 + )
+( −
(15)
) ,
=
+( −
(16)
=
− −
,
(17)
=
−
.
(18)
In these equations,represents the total OPD at the end of year ,the public bonds issued in year ,the fiscal balance, andthe primary balance.
3.4 Public pension
Since the pension system is managed via a modified funding method, its budget constraint equation is expressed
as follows.
(1 −

2

)
= (1 + )(1 −

+

2)

−

+

.

(19)

In this equation,
represents the assets held by the pension sector at the end of year , the first term on theright-hand side the interest revenue on the assets, the second term the public pension contribution revenue, thethird term the government transfer, and the fourth term the pension payment in year .
3.5 Central bankIn order to describe two scenarios of implementing or not implementing DUPB by the BOJ, I formulate the ratioof OPD held by each agent to ONA:
=
1 +
2 ,
(20)
≡
,
(21)
1 ≡

,
(22)

2 ≡

.

(23)
In these equations,
1 represents the OPD held by households at the end of year ,2 the OPD heldby the BOJ, andthe ONA. Furthermore, for simplification, instead of explicitly handling the money supply,
the effect of DUPB by the BOJ is considered via the situation where the amount directly underwritten by the BOJ
does not become household assets [Equation (20)].
3.6 Aggregation and market equilibrium
Total consumption in year , , total assets held by households at the end of year ,, and the total effective
labor supply in year , , are expressed as follows.
=

114

,

(24)

Journal of Business & Economic Policy

=

=

(1 −

2)

Vol. 2, No. 4; December 2015

,

(25)

.

(26)

Finally, the following market-equilibrium conditions on the effective labor market, the capital market,16and thegoods market must hold in order to close the model structure:
=
,
(27)
+
= +
= +(
1 +
2) ,
(28)
= + +
.
(29)

4. Parameters (estimation and calibration) and Data
Tables 1–3 show the parameter values, how to set the values, and the exogenous-data sources used in this study.
For additional details on these issues, see Section 4 and Appendix in Yoshida (2015),except the parts on data of
total national assets, total assets held by households, and total PCS at initial time. Furthermore, the following
points should be taken under consideration. 1) Since this study considers the government’s fiscal system, the year
units are essentially fiscal years.17 2) The money amount data were deflated by the GDP deflator (2005 = 100)from the National Accounts (NA, Cabinet Office). 3) The respective generations aged 22 or older at the simulationbase year (FY2012) are referred to as “transition generations.”

Table 1: Parameter values
Parameter
Utility function [see Equation (1)]

Value

Parameter
Tax policy parameters [see Equation (2)]

Value

Time preference rate
Intertemp oral elasticity of substitution
Wage p rofile function [see Equation (3)]ργ-0.001
2.00

Labor income tax rate (%)
Interest income tax rate (%)
Consumption-based tax rate (%)

τw
τr
τc

11.5
15.4
9.6 - 13.1

Constant term
Coefficient of first-degree term
Coefficient of second-degree term

φ0
φ1
φ2

5.436
0.099
-0.001

Pension income tax rate (%)
Pension policy parameters[see Equations (2), (4), and (14)]

τp

11.5

Production function [see Equations (8) and (9)]Scale parameter
A
Technology progress rate
λPublic contribution rate (%)
Rate to annual average labor income: for remuneration-based p ension

rp16.6 - 18.3

0.765
0.013

θ

0.233 - 0.313

α
δ

0.300
0.056

National treasury subsidy rate
for basic p ension benefits

sr

0.500

Capital share in production
Depreciation rate of p hysical cap ital

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Table 2: Setting Parameter values
Parameter

Value/Year

M ethod

Parameters of utility function

Data Sources and Notes

Cited

Parameters of wage p rofile function

Prior studies (see Table A1 for details)

Estimated

Using M incer (1974)'s model2012

Calculated"National Accounts" (NA, Cabinet Office)M ean of2000-12Calculated"Gross Cap ital Stock of Private Entep rises" (Cabinet Office)2012

Calibrated

Parameters in the model, total p hy sical cap ital stock (seeTable 3), total effective labor (see Table 3), Gross National
Income (GNI) from NA

Estimated

Using Solow residuals [see Solow (1957)] and following
Kameda and M asuda (2001) and M iy azawa (2008)

FY2012

CalculatedNA

M ean of
FY2010-12

Calculated"M inistry of Finance Statistics monthly " (M inistry of
Finance) and NA

Public p ension contribution rateon the labor income

Cited andCalculated

Default values of Jap an's Emp loy ee's Pension Insurance andvalues p lanned to be raised

Rate used to calculate remuneration-basedp ension benefits from average annuallabor income (2)Calculated

Default values of Jap an's Emp ly ee's Pension Insurance

Cap ital share in p roduction
Dep reciation rate of p hy sical cap ital

Scale p arameter

Technology p rogress rate
Labor income tax rate
= Pension income tax rate
Interest income tax rate
Consump tion-based tax rate (1)National-treasury -subsidy rate for basic
p ension benefits

From FY2009

Cited

Value under imp lemented sy stem

Notes: (1)Values were set to be consistent with the government’s plan to revise the consumption tax rate.
(2) Rate for the generations born in and before 1944 was set to be the same as that of the generation born in 1945.

Table 3: Exogenous-data sources
No.

Data

1

Population: combined total of men andwomen of each age group in for ages 21‐
105

2

Public pension assets

3

OPD

4

OPD related to construction andto deficit-finance5

Total national assets(except tangible non-produced assets)

6

Total assets held by households

7

Total PCS (for private sector)

8Effective labor

9

PCS per efficient-labor unit

10

Assets held by transition generations

11
12

Data/Year

M ethod

Sources"Population Projections for Japan"(PPJ, National Institutionof Population and Social Security Research, 2012)

At end of
FY2011

Calculated

Outstanding financial assets and liabilities from NA

At end of
FY2011

Calculated

Outstanding financial assets and liabilities from NA, datafrom "Debt M anagement Report 2014"(M inistryof Finance) and "White Paper on Local Public Finance,
2014"(M inistry of Internal Affairs and Communications)

At end of
FY2011

Calculated

Closing stocks of assets and liabilities for the nation fromNA, data of items 2-4

Calculated

Population of each age group from PPJ, the wage profile
function

At end of
FY2011

Calculated

Data of items 7-8

At end of
FY2011

Calculated

Savings and liabilities per household (for each age category)from “Annual Report on the Family Income and Expenditure
Survey” (M inistry of Internal Affairs and Communications),
data of items 1 and 6

Fixed payment portion in pension benefits

Cited andCalculated

Default values of National Pension (Basic Pension) andvalues planned to be lowered.

Average annual labor income for transition
generations

Calculated

See below

Labor income in and prior to FY2011 is calculated from the standard labor income in FY2012 in accordance with the number of years
worked until FY2011; the standard labor income is cited from the “Overview of the Employee’s Pension Insurance and National
Pension Service” (M inistry of Health, Labour and Welfare).
Labor income in and after FY2012 is endogenously determined within the simulation.
13

GAE, EAE

FY2012

Calculated

Data from NA and data of item 1

Notes: Regarding population data: 1) the data of medium-fertility and medium-mortality case were used, 2) the population of eachage group in and after 2111 was assumed to be the same as the 2110 values

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5. Simulation
This section explains the simulation scenarios, the sensitivity analysis, and the analysis results.
5.1 Scenarios
I prepared the following two scenarios to examine the effects of DUPB by the central bank (BOJ).18
Scenario 1 (referred to as “UWCB scenario”)
In this scenario, DUPB is implemented by the BOJ from FY2013 onward.
Scenario 2 (referred to as “NOTUWCB scenario”)
In this scenario, DUPB is not implemented by the BOJ. Public bonds are absorbed by the market even after
FY2013, as has been the case until now.
In addition, the following points should be noted. First, fiscal years were used, with the starting (base) year as
FY2012. Second, transition generations are handled as follows: 1) their actual asset values at the end of FY2011
are given; 2) their contributions to the remuneration-based portion of the public pension prior to FY2011 were set
to have been paid under the same income amount as the standard labor income of FY2012; and 3) their behaviors
from FY2012 were endogenously decided. Third, outstanding amounts of national assets, public pension assets,
and public debt (total on both central and local government debt) at the end of FY2011 were given.
Fourth, in order to focus our attention on the effects of DUPB by the BOJ, I did not incorporate factors other thanthe predetermined increase of the consumption tax rate and revisions of the public-pension contribution rates andbenefits. Fifth, this study’s main objective is not to observe the steady state but the transition process of theJapanese economy and government finance, in order to examine the possibility of their sustainability. Accordingly,
a simulation was set to be terminated if the calculation led to the following two situations: 1) their sustainability
has become no longer secured; 2) all public debt has been cleared. Sixth, this study used the PPJ data without any
processing to prevent information loss regarding population. As a result, households leaving the model before theassumed death age are considered to consume their outstanding net assets at the time of leaving.
5.2 Sensitivity analysis
In order to confirm the robustness of this research, I also simulated the cases in which the parameter value of thetime-preference rate of the life-cycle utility function was changed because a shift in this rate effectively influences
the intertemporal consumption and saving patterns of representative households. Table 4 shows the details of thesensitivity analysis.

Table 4: Sensitivity analysis cases and sustainability
Intertemporalelas ticity
of s ubs titution

Economy and public finances us tainability

Cas eTime preference
rate
ρ

γ

UWCB

NOTUWCB

A1

0.021

2.000

No

No

A2

0.010

2.000

No

No

Bas e

-0.001

2.000

Yes

No

A3

-0.002

2.000

Yes

No

Note: Yes and No indicate “sustainable” and “not sustainable”, respectively

5.3 Results of simulation and sensitivity analysis
5.3.1 Future population structure
Figure 2’s graph depicts the future population structure of Japan: 1) Japan’s total adult population (aged 21 andover) will decline from the current level of over 100 million persons to fewer than 40 million persons; 2) the
aging ratio, i.e., the ratio of the elderly population (aged 65 and over) to the total adult population, will rise fromthe current level of approximately 0.300 to a little under 0.500 after approximately 100 years (a society where
each worker supports one elderly person will arise); and 3) the aging speed will be relatively fast until around the
mid-2040s and then become relatively slow.

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Figure 2: Future population structure of Japan(Person)

2111

2108

2105

2102

2099

2096

2093

2090

2087

2084

2081

2078

2075

2072

2069

2066

2063

2060

2057

2054

2051

0.000

2048

0

2045

0.100

2042

20,000,000

2039

0.200

2036

40,000,000

2033

0.300

2030

60,000,000

2027

0.400

2024

80,000,000

2021

0.500

2018

100,000,000

2015

0.600

2012

120,000,000

Pop 1: Working-age (21-64 years old) population

Pop 2: Elderly-age (65 years old and over) population

Total Pop: Pop 1+Pop 2

Pop 2/Total Pop (right axis)

5.3.2 Sustainability
Figure 3 shows changes in the OPD ratio to GNI for the respective cases (see also Table 4). This figure illustrates
the following facts: 1) The Japanese economy and government finance are sustainable in only the UWCB scenarioof the Base and A3 cases. 2) Under the higher time-preference rate, even the UWCB scenario cannot bringsustainability, and a rise in this rate rapidly threatens economic collapse. In other words, it is necessary forsustainability that households assign, to a certain extent, large weight to their future financial condition, and tothat of future generations.
5.3.3 Changes in main economic variables
Changes in GNI, total PCS, GNI per capita, and PCS per efficient-labor unit are shown in Figures 4–7. Thesefigures show the following facts. 1) GNI basically continues to grow until the mid-2030s (the era prior to society
reaching the highest aging level) and subsequently continues to decline after then (see also Figure 2); GNI rapidly
falls after the advent of an economic-failure tendency. 2) In the sustainable cases, GNI starts to grow again fromaround FY2110. 3) GNI per capita and PCS per efficient-labor unit continuously rise in the sustainable cases. 4)
The A3 case attains higher values of GNI than the Base case. The results of items 1)–3) are thought to begenerated by the population’s aging, the population structure fixed at the level of FY2110 after FY2111, and theHarrod-neutral technical progress. In addition, we can consider the result of item 4) to be produced by a process inwhich a downward shift of the time-preference rate prompts a decline in consumption closer to the present;
subsequently, the decline prompts PCS accumulation, and finally this cycle increases production.

Figure 3: Ratio of OPD (outstanding public debt) to GNI
20.00

18.00

16.00

14.00

12.00

10.00

8.00

6.00

4.00

2.00

2012
2015
2018
2021
2024
2027
2030
2033
2036
2039
2042
2045
2048
2051
2054
2057
2060
2063
2066
2069
2072
2075
2078
2081
2084
2087
2090
2093
2096
2099
2102
2105
2108
2111
2114
2117
2120
2123
2126
2129
2132
2135
2138
2141
2144
2147
2150
2153
2156
2159
2162
2165
2168
2171
2174
2177
2180

0.00

-2.00
UWCB (Base)118

NOTUWCB (Base)UWCB (A1)NOTUWCB (A1)UWCB (A2)NOTUWCB (A2)UWCB (A3)NOTUWCB (A3)

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Vol. 2, No. 4; December 2015

Figure 4: GNI(Billion yen)
600,000

550,000

500,000

450,000

400,000

350,000

2129

2132

2126

2123

2120

2117

2129

UWCB (A1)UWCB (A3)

2114

2111

2108

2105

2102

2099

2096

2093

2090

2087

2084

2081

2078

2075

2072

2069

2066

2063

2060

NOTUWCB (Base)NOTUWCB (A2)2126

UWCB (Base)UWCB (A2)

2057

2054

2051

2048

2045

2042

2039

2036

2033

2030

2027

2024

2021

2018

2015

2012

300,000NOTUWCB (A1)NOTUWCB (A3)

Figure 5: Total PCS (physical capital stock)(Billion yen)
2,800,000

2,300,000

1,800,000

1,300,000

800,000UWCB (Base)UWCB (A2)NOTUWCB (Base)NOTUWCB (A2)UWCB (A1)UWCB (A3)

2132

2123

2120

2117

2114

2111

2108

2105

2102

2099

2096

2093

2090

2087

2084

2081

2078

2075

2072

2069

2066

2063

2060

2057

2054

2051

2048

2045

2042

2039

2036

2033

2030

2027

2024

2021

2018

2015

2012

300,000NOTUWCB (A1)NOTUWCB (A3)

Figure 6: GNI (per capita)(Million yen)
17.00

15.00

13.00

11.00

9.00

7.00

5.00

UWCB (Base)NOTUWCB (Base)UWCB (A1)NOTUWCB (A1)UWCB (A2)NOTUWCB (A2)UWCB (A3)NOTUWCB (A3)

2132

2129

2126

2123

2120

2117

2114

2111

2108

2105

2102

2099

2096

2093

2090

2087

2084

2081

2078

2075

2072

2069

2066

2063

2060

2057

2054

2051

2048

2045

2042

2039

2036

2033

2030

2027

2024

2021

2018

2015

2012

3.00

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Figure 7: PCS (per efficient-labor unit)(Million yen)
4.50

4.00

3.50

3.00

2.50

2.00

1.50

1.00

UWCB (Base)UWCB (A2)NOTUWCB (Base)NOTUWCB (A2)UWCB (A1)UWCB (A3)

2132

2129

2126

2123

2120

2117

2114

2111

2108

2105

2102

2099

2096

2093

2090

2087

2084

2081

2078

2075

2072

2069

2066

2063

2060

2057

2054

2051

2048

2045

2042

2039

2036

2033

2030

2027

2024

2021

2018

2015

2012

0.50

NOTUWCB (A1)NOTUWCB (A3)

5.3.4 Base caseIn the following, I explain the simulation results in detail, focusing on the Base case. First, the actual values andthe calculated values of the UWCB scenario on key variables in FY2012 are shown in Table 5. This table says thatthe calculated value of PCS per efficient-labor unit exceeds the actual value, especially in the Base case.
We can assume that this result is caused by intensive physical-capital accumulation that depends on householdswith perfect foresight behaving more rationally than in the real-world case. In addition, the comparison of real andcalculated values indicates that the A1 case’s setting more closely fits the real situation than does the Base case’s
setting. Next, Figure 8 shows the changes in OPD, and Table 6 shows the changes in the ratios of OPD to ONA
and PCS per efficient-labor unit. Figure 8 indicates the divergence of OPD in the NOTUWCB scenario. On theother hand, Figure 8 and Table 6 show that OPD will reach zero in the 2180s in the UWCB scenario; that is, thegovernment’s continuous fiscal surplus will first pay off the public debt held by the BOJ in the 2170s and thenalso pay off the initial public debt in the 2180s.
Then, in order to confirm the above facts in detail, I show in Figure 9 the changes in the primary balance (of thegovernment budget) that does not include interest payment on outstanding public bonds and in the final balancethat does include such payment (each balance is defined as the ratio to GNI). This figure explains the following
facts. 1) Although the NOTUWCB scenario achieves a primary balance surplus, it cannot prevent the final fiscaldeficit divergence in the final balance due to the significant burden of interest payment caused by the cumulative
increase in OPD (see also Figure 8). 2) On the other hand, the UWCB scenario first achieves the primary surplus
in the 2060s and subsequently the final surplus in the 2110s. We can assume that this UWCB scenario’s results are
generated by the following process: DUPB by the BOJ creates the central bank’s seignior rage, then the BOJ pays
it to the national treasury, and this payment finally improves the government’s finance situation.

Table 5: Economic and public finance variables in FY2012
Variables
PCS (million yen)
per efficient-labor unit

Actual values

Calculated values of UWCB
(A1 cas e)(Bas e cas e)

2.503

2.527

2.658
442,460

GNI (billion yen)

439,904

435,811

Savings rate to GNI

0.231

0.238

0.411

Ratio of primary balance to GNI-0.075-0.097-0.114

Ratio of Government debt to TA

0.336

0.356

0.346

Note: TA indicates "Total assets (except tangible non-produced assets) held by Japanese people.”

Figure 8: OPD (outstanding public debt, Base Case)

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Vol. 2, No. 4; December 2015

(Billion yen)
9,000,000
8,000,000
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000

2012
2016
2020
2024
2028
2032
2036
2040
2044
2048
2052
2056
2060
2064
2068
2072
2076
2080
2084
2088
2092
2096
2100
2104
2108
2112
2116
2120
2124
2128
2132
2136
2140
2144
2148
2152
2156
2160
2164
2168
2172
2176
2180

0
-1,000,000-2,000,000
UWCB (ρ=-0.001)_DEBTSUWCB (ρ=-0.001)_DEBT2NOTUWCB (ρ=-0.001)_DEBTS

Note: DEBTS and DEBT2 indicate "Total OPD " and "OPD held by the BOJ," respectively.

Table 6 Public debt ratio and PCS (per efficient-labor unit)UWCBFYNOTUWCB

k

DEBT1
ratio

DEBT2
ratio

DEBTS
ratio

k

DEBTS
ratio

(to TA)(to TA)(Million yen)

(to TA)

0.547

2.503

0.333

(Million yen)

(to TA)

2011

2.503

0.333

2012

2.658

0.346

0.000

0.346

2.670

0.345

2020

3.225

0.247

0.181

0.428

3.347

0.424

2030

3.473

0.195

0.294

0.489

3.707

0.490

2040

3.744

0.169

0.366

0.535

4.055

0.542

2050

3.768

0.155

0.427

0.582

4.141

0.592

2060

3.665

0.146

0.471

0.617

4.092

0.633

2070

3.532

0.141

0.508

0.649

4.009

0.671

2080

3.371

0.140

0.539

0.679

3.903

0.709

2090

3.107

0.141

0.566

0.707

3.674

0.747

2100

2.862

0.142

0.589

0.731

3.384

0.788

2110

2.455

0.148

0.620

0.768

2120

2.931

0.137

0.570

0.708

2130

3.363

0.131

0.506

0.638

2140

3.814

0.126

0.425

0.552

2150

4.283

0.123

0.323

0.446

2160

4.759

0.120

0.200

0.320

2170

5.248

0.117

0.054

0.171

2180

5.830

0.001

0.000

0.001

Notes: (1) "k" indicates PCS per efficient-labor unit.
(2) DEBT1, DEBT2, and DEBTS indicate "OPD held by public sector," "OPD held by the central bank(BOJ)," and "Total OPD," respectively.
(3) TA indicates "Total assets (except tangible non-produced assets) held by Japanese people.”

Figure 9:PB-ratio and FB-ratio to GNI (Base Case)
0.600

0.400

0.200

2012
2016
2020
2024
2028
2032
2036
2040
2044
2048
2052
2056
2060
2064
2068
2072
2076
2080
2084
2088
2092
2096
2100
2104
2108
2112
2116
2120
2124
2128
2132
2136
2140
2144
2148
2152
2156
2160
2164
2168
2172
2176
2180

0.000

-0.200-0.400-0.600UWCB (ρ=-0.001)_PB_ratio_to_GNINOTUWCB (ρ=-0.001)_PB_ratio_to_GNIUWCB (ρ=-0.001)_FB_ratio_to_GNINOTUWCB (ρ=-0.001)_FB_ratio_to_GNI

Note: PB and FB indicate "Primary balance of government budget" and "Final balance," respectively.

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5.3.5 Life-cycle utility level by generation
Finally, this section explains the life-cycle utility level of respective generations in the UWCB scenario of theBase and A3 cases, in which the Japanese economy is sustainable, using an index 19 of 1 plus the equivalentvariation of each generation’s utility level (compared to the base generation’s utility level).
The above equivalent variation excludes the influence of advances in production technology. Then, to help
understand the utility level, the utility level index is divided into two segments: working period (ages 21–64) andretirement period (ages 65–85).20 Furthermore, the former base generation is the generation born in FY2012, andthe latter is that born in FY1967. Figure 10 shows the changes in the utility-level index. This figure explains thefollowing facts. 1) In both the Base and A3 cases, the working-period utility level of future generations exceedsthat of the base generation on a long-run basis, even after excluding the influence of advances in production
technology. We can assume that this is due to the growth of PCS per efficient-labor unit along with the population
aging (see Figure 7). This fact implies that DUPB by the BOJ improves the efficiency of added-value distribution
in Japan. 2) In comparison to the Base case, the A3 case shows higher utility level in the working period of future
generations but lower utility level in their retirement period. We can assume that this is generated by a process inwhich a downward shift of the time-preference rate prompts a decline in consumption closer to the present;
subsequently, the decline prompts PCS accumulation, and finally this cycle increases production.

Figure 10: Equivalent variation
1.400

1.300

1.200

1.100

1.000

0.900

Birth FY

EQVR_65-85 (Base)EQVR_21-65 (Base)EQVR_65-85 (A3)

2135

2131

2127

2123

2119

2115

2111

2107

2103

2099

2095

2091

2087

2083

2079

2075

2071

2067

2063

2059

2055

2051

2047

2043

2039

2035

2031

2027

2023

2019

2015

2011

2007

2003

1999

1995

1991

1987

1983

1979

1975

1971

1967

0.800

EQVR_21-65 (A3)

Note: EQVR indicates "Equivalent variation."

6. Concluding Remarks
This study used a DCGE-OLG model to examine whether DUPB by the central bank (BOJ), which has thepotential to support the Japanese economy and government finance and to improve the efficiency of added-value
distribution, is effective. The results are summarized as follows. First, economic collapse occurs in the case where
public bonds are absorbed by the market. On the contrary, under the relatively low time-preference rate ofrepresentative households, the economy and government finance are sustainable in the case where public bonds
are directly underwritten by the BOJ. Accordingly, the payment of the BOJ’s seignior rage to the national treasury
improves the Japanese government’s finance and the economy. Moreover, in the sustainable case, GNI per capita
rises continuously due to the growth of PCS per efficient-labor unit along with the population’s aging and theadvances in production technology. Second, a downward shift in the time-preference rate brings good effects for
economic sustainability and efficiency. That is, this shift promotes the accumulation of physical capital stock, andthus the stock increment promotes production. Third, in the sustainable case, the utility level in the working
period of future generations will exceed that of the base generation on a long-run basis. This fact implies that
DUPB by the BOJ improves the efficiency of added-value distribution in Japan. Finally, some remaining issues
need to be mentioned. First, the rational-expectation assumption (the optimization behavior of representative
households with perfect foresight) may be too strong. Therefore, an analysis under the adaptive-expectation
assumption, and a comparison between its results and this study’s results, should be conducted. Second, a modelthat explicitly handles a bequest element should be developed.
Third, this study’s model should also be expanded into an open-economy model that considers the capital flow
between Japan and other countries.
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Acknowledgement
The author is grateful for financial support from the Japan Society for the Promotion of Science, Grant-in Aid for
Science Research (C), 25380309, and thanks the anonymous referees for their competent comments.
Notes
1. General government consists of the central government, local governments, and social security funds.
2. These financial indicators are based on those of the Ministry of Finance: http://www.mof.go.jp/
tax_policy/summary/condition/(accessed on January 7, 2015).
3. This is based on data from the Principal Global Indicators (IMF):
http://www.principalglobalindicators.org/Pages/Default. aspx (accessed on December 16, 2014).
4. These are based on data from the Ministry of Finance: http://www.mof.go.jp/jgbs/reference/gbb/data.htm(accessed on December 17, 2014), data from the Bank of Japan: http://www.boj.or.jp/about/account/index.htm/(accessed on December 17, 2014), and “Debt Management Report”(issued each fiscal year,
Ministry of Finance)．
5. FY represents fiscal year.
6. This measure is based on Article 53 of the Bank of Japan Act.
7. Hereinafter, as explained here, “public bonds” includes local government bonds, while “government bonds”
refers to bonds issued by the central government.
8. Market absorption of JGBs is obligatory under Article 5 of the Public Finance Act.
9. They explained the reason for this as follows: the main cause of the government’s intertemporal budget
constraint becoming stricter is not the current OPD, which has been reduced by the recent increase in inflation,
but future debt, which is not reduced by this factor.
10. This model has the following characteristics: 1) the respective economic agents possess perfect foresight; 2)owing to 1), the respective economic agents utilize all currently available information and form expectations
in a forward-looking manner (i.e., a forward-looking model); 3) in 2), the respective economic agents carryout optimization behavior, based on a micro-foundation.
11. For the definition of seignior rage, see Neumann (1992), Baltensperger and Jordan (1997, 1998), and Schobert(2000). In regards to the actual magnitude of seignior rage, see Neumann (1992), Reserve Bank of Australia(1997), Schobert (2000), and Oguri (2006).
12. For an explanation of the central bank’s seignior rage and the actual situation in Japan, see Oguri (2006).
13. The age of death is adjusted to the population projection data used in the simulation. Details of this data are
explained in Section 4.
14. Pension benefit strictly means the amount of pension benefit. Hereinafter, owing to space limitations, I omit
the phrase of “the amount of” in the expression of variables implying “amount” in this manner.
15. Such DUPB by the central bank is assumed to have an equal ratio of impact on household assets and on
public pension assets (see Section 3.4).
16. Fundamentally,=+. However, if< 0 , then
=
+
+
(−
).
17. However, in the cases where fiscal year data cannot be used, I used calendar year data instead.
18. In order to create the simulation program, I referred to programs released online, including a program createdby Hashimoto, K. (http://www2.ipcku.kansai-u.ac.jp/~hkyoji/kenkyu/download.htm)
and one created by Oguro, S. and Shimazawa, M. (http://www.nippyo.co.jp/download/535-55664-5/
index.php).
19. This index will be 1 if the utility level of the targeted generation is the same as that of the base generation.
20. Although this study sets households to live over ages 21-105 (85 periods), this lifespan is too long for
calculating the life-cycle utility level. Consequently, I adopted the retirement period of ages 65-85 for theutility-level index.

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Appendix
Table A1: Parameter values of preceding studies

No.

1
2
3
4
5
6
7
8
9
10
11
12
13

AuthorAuerbach and Kotlikoff
Auerbach and Kotlikoff
Auerbach et al.
Iwamoto et al.
Hviding and Mérette *KatoFougère and Merette *Ｍｉｌｅｓ *
Supan et al.
Ｋａｔｏ
Ｓａｄａｈｉｒo and Shimazawa
Supan et al.
Shimazawa and Oguro

Year

1983
1987
1989
1993
1998
1998
1999
1999
2001
2002
2002
2005
2010

Time preference
rate

Intertemporalelasticity
of substitution

Technologicalprogress rate
: Harrod neutral type

ρ

γ

λ

0.020
0.015
-0.040-0.0400.003-0.075
0.003
0.015
0.080
-0.035
0.020
0.011
0.010

1.000
0.250
0.350
0.300
0.250
0.200
0.250
0.750
1/3
0.450
1/1.2
0.500
2.000

0.020

0.024
0.024

0.015
0.010

Notes: (1) "*" indicates studies that cited the values of ρ or γ from Auerbach and Kotlikoff (1987).
(2) If the study uses various values, the base value is indicated.
Source: By the author, using data from preceding studies.

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