TCER Working Paper Series

SUSTAINABILITY, DEBT MANAGEMENT, AND PUBLIC DEBT POLICY IN JAPAN
Takero Doi
Kiyoshi Mitsui
Toshihiro Ihori
August 2006
Working Paper E-6
http://tcer.or.jp/wp/pdf/e6.pdf

TOKYO CENTER FOR ECONOMIC RESEARCH
1-7-10-703 Iidabashi, Chiyoda-ku, Tokyo 102-0072, Japan©2006 by Takero Doi, Kiyoshi Mitsui and Toshihiro Ihori.
All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit
permission provided that full credit, including ©notice, is given to the source.

Abstract
The purpose of this paper is to analyze sustainability issues of Japan’s fiscal policy andthen to discuss the debt management policy using theoretical models and numericalstudies. We also investigate the desirable coordination of fiscal and monetary authorities
toward fiscal reconstruction. We include a potential possibilities of the government
bonds in our theoretical model The public bonds, therefore, cannot be sold when theissuance leads the amount of debt outstanding to be more than a certain level. In thisrespect, the fiscal authority has to take into account the upper limit of stocks of public
debt. This possibility of debt default provides the fiscal authority to issue public bonds
strategically in an earlier period. A strategic behavior of fiscal authority induces themonetary authority, in a later period, to boost output and raise seigniorage revenues toeliminate the distortion of resource allocation due to the limitation on debt issuance.
Therefore, the monetary policy in a later period suffers from an inflation bias from the ax
ante point of view. There are two ways to eliminate this distortion toward successful
fiscal reconstruction. One of them is to make the monetary authority more conservative
than society in the sense that the price stability weight of monetary authority is higher
than that of society. The other way of eliminating the distortion of the resource
allocation is to design an institutional ceiling on the debt issuance. The direct ceilingcan provide a binding constraint of the public bond issuance for the fiscal authority ofJapan because it has accumulated the debt outstanding much more than other countries.

Takero Doi
TCER
andKeio University
Faculty of Economics
2-15-45 Mita Minato-ku, Tokyo
tdoi@econ.keio.ac.jp

Toshihiro Ihori
TCER
andUniversity of Tokyo
Graduate School of Economics
7-3-1 Hongo Bunkyo-ku, Tokyo
ihori@e.u-tokyo.ac.jp

Kiyoshi Mitsui
Gakushuin University
Faculty of Economics
1-5-1 Mejiro Toshima-ku, Tokyokiyoshi.mitsui@gakushuin.ac.jp

Sustainability, Debt Management, and Public Debt Policy in Japan
Takero Doi, Toshihiro Ihori, and Kiyoshi Mitsui
June, 2006

Acknowledgment:This paper is forthcoming in the book “Fiscal Policy and Management in East Asia”
edited by Takatoshi Ito and Andrew Rose. An earlier version of the paper waspresented at the 16th Annual East Asian Seminar on Economics held on June 23-25,
2005, and Conference on New perspective of Fiscal Sustainability, Goethe University
Frankfurt Campus Westend, October 13 and 14, 2005. The authors thank Professors
Dante Canlas, Takatoshi Ito, Anne O. Kruger, Eli Remolona, Andrew Rose, and Jürgen
von Hagen, as well as the participants for helpful comments. Any remaining errors are
our own.

Abstract
The purpose of this paper is to analyze sustainability issues of Japan's fiscal
policy and then to discuss the debt management policy using theoretical models andnumerical studies. We also investigate the desirable coordination of fiscal and monetary
authorities toward fiscal reconstruction.
We include a potential possibilities of the government bonds in our theoreticalmodel The public bonds, therefore, cannot be sold when the issuance leads the amountof debt outstanding to be more than a certain level. In this respect, the fiscal authority
has to take into account the upper limit of stocks of public debt.
This possibility of debt default provides the fiscal authority to issue publicbonds strategically in an earlier period. A strategic behavior of fiscal authority induces
the monetary authority, in a later period, to boost output and raise seigniorage
revenues to eliminate the distortion of resource allocation due to the limitation on debt
issuance. Therefore, the monetary policy in a later period suffers from an inflation
bias from the ax ante point of view.
There are two ways to eliminate this distortion toward successful fiscal
reconstruction. One of them is to make the monetary authority more conservative
than society in the sense that the price stability weight of monetary authority is higher
than that of society. The other way of eliminating the distortion of the resource
allocation is to design an institutional ceiling on the debt issuance. The direct ceilingcan provide a binding constraint of the public bond issuance for the fiscal authority ofJapan because it has accumulated the debt outstanding much more than othercountries.
JEL classification: H63, H21, E63
Key word: fiscal sustainability, debt management policy, debt default, confidence crisis
Takero Doi
Faculty of Economics
Keio University
2-15-45 Mita Minato-ku,
Tokyo 108-8345 Japanand Tokyo Center for Economic Researchtdoi@econ.keio.ac.jp
Toshihiro Ihori
Department of Economics
University of Tokyo
7-3-1 Hongo Bunkyo-ku
Tokyo 113-0033 Japanihori@e.u-tokyo.ac.jp
Kiyoshi Mitsui
Faculty of Economics
Gakushuin University
1-5-1 Mejiro Toshima-ku
Tokyo 171-8588 Japankiyoshi.mitsui@gakushuin.ac.jp

11. Introduction
Currently it is crucial for the Japanese government to implementtight public debt policy, because the Japanese government has issued a veryhuge amount of government debts. Japan’s fiscal situation has deteriorated
rapidly with the collapse of the ‘bubble economy’ in the early 1990s and the
deep and prolonged period of economic recession which ensued, and fromwhich recovery has been slow and modest despite the implementation ofcounter-cyclical Keynesian policy. Since national income did not grow much,tax revenue did not increase either. On the contrary, government spending
has been gradually raised due to political pressures of interest groups,
resulting in large budget deficits.
In 1997, the Japanese government tried to implement the Fiscal
Structural Reform so as to reduce budget deficits. However, in 1998, it
stopped the reform and reduced taxes and increased public investment basedon the traditional Keynesian policy because of the severe economic andfinancial situation, and the defeat of the governing party (the Liberal
Democratic Party) in the Upper House election.
The concern for sustainability of fiscal deficits is a background for the
fiscal reconstruction and structural reform movement by the current
Koizumi Administration.
The "Structural Reform of the Japanese
Economy: Basic Policies for Macroeconomic Development" was decided uponafter acceptance of the report compiled by the Council on Economic andFiscal Policy, an advisory council to the Prime Minister. In this report thecore of policies for the structural reform of the economic society was madeclear. In part of the policies shown, a goal to limit the amount ofgovernment bond issues to less than 30 trillion yen in the fiscal 2002 budget,and afterwards to achieve a primary surplus, was set to show that there
exists a necessity to take on full-scale measures towards fiscal consolidationor fiscal reconstruction. However, in order to cope with the bad situation ofmacro-economy, 1.8 trillion yen of the advance tax cuts was employed with aview to strengthening the competitiveness of industry, facilitating a smoothtransference of assets to the next generation, promoting a shift from “saving
to investment”, advancing effective land use, and so on. The goal to limit
the amount of government bond issues to less than 30 trillion yen in thefiscal 2002 budget was finally abandoned. In the fiscal 2005, newgovernment bond issues are 34.4 trillion yen and the bond dependency ratio
rises to 41.8%.

2

If creditors fear that the government is going to be in a debt trap, thelong-term interest rate begins to rise, reflecting an enlarged credit risk. It isnoted that although the Japanese Government Bonds (JGBs) have been
issued too much, their yields are the lowest among G7 countries in the bondmarket. In this regard, despite its weakening credit ratings, the 10-year JGB
nominal yield of about 1.5% in 2005 remains lower than the U.S. bond yieldof about 1.8% registered during the Great Depression. However, we also
have to pay attention to persistent deflation. Also, the performance in theyield of the JGBs may not accurately reflect its credit risk. The Japanesebanking sector continues to purchase the JGBs simply because short-term
capital gains from the JGBs have been an easy option to offset the existing
stock losses.
The purpose of this paper is to analyze sustainability issues ofJapan's fiscal policy and then to discuss the debt management policy using
theoretical models and numerical studies. We also investigate the desirable
coordination of fiscal and monetary authorities toward fiscal reconstruction.
This paper consists of five sections. In section 2 we survey previous
studies on sustainability issues. In section 3, we evaluate Japan’s debt
management policy by providing a theoretical model to analyze public debt
policy in a second best case as a benchmark. We then implement a simple
numerical analysis based on the smoothing rule derived by the theoreticalmodel. In section 4, we discuss the desirable coordination of monetary andfiscal authorities towards fiscal reconstruction by explicitly investigating
confidence crisis of government debt and spontaneous default of fiscal
authority. Finally, concluding remarks follow in Section 5.

2. Sustainability Issues and Emergency Reform
2.1. Concerns about sustainability
The events of the 1980s and 1990s in Japan suggest that when agovernment becomes strapped for funds, it will tend to borrow from theworld credit market rather than raise taxes to finance additional public
spending. Indeed, many governments did either not raise broadly basedtaxes, e.g., the Thatcher government in Great Britain or the Reagan andBush Administrations in the United States, or simply could not raise taxes toprevent causing riots, e.g., countries in Latin American and Eastern Europe,and, arguably, France in the reign of Louis XVI. There are long-term

3

concerns about the accumulated fiscal deficit. Important one is whether
such a large deficit can be sustained. The system will be paralyzed if publicfinance collapses under the weight of massive deficit. As a result, thefinancial system and the economy as a whole will be seriously affected. An
extreme case of hyperinflation or default could develop.
The so-called chain-letter mechanism (or a Ponzi debt game) involves
a situation where the future time path of taxes is fixed and debt finance isused to pay for any additional public spending; debt issuance is thus
endogenously determined by the government's budget constraint. If themechanism is sustainable, increased taxation need not necessarily berequired in order to finance increased government spending as the economy
converges to the steady state equilibrium.
If the mechanism isunsustainable, the government will eventually go bankrupt in the sense that
it will be unable to raise enough revenue to finance public spending and debt
repayment. As debt crowds out private capital formation, the economy will
also eventually go bankrupt if the mechanism fails. This suggests thatstudying the chain-letter mechanism and associated sustainability issues isquite important in terms of understanding the effects of government
austerity (fiscal reconstruction) measures on the macroeconomy.
A simple way to evaluate the fiscal sustainability problem is to focus
on the government bond market. In this regard for Japan, despite its
weakening credit ratings, the 10-year Japanese Government Bond (JGB)
nominal yield of about 1.5% in 2005 remains. So far the myth that the
JGBs are risk-free has been somehow propagated. This episode may imply
that Japan’s government solvency is not a serious issue right now. However,Japan has experienced deep deflation, so the real rate of interest is about 2%,
which is not so low. We also have to pay attention to the possibility that theperformance in the yield of the JGB may not accurately reflect its credit risk.
Ihori, Nakazato, and Kawade (2002) attempt a standard approach to test
the fiscal sustainability condition, using the methodology of Hamilton andFlavin (1986). Hamilton and Flavin (1986) define the sustainability of
government debt as follows. Government budget constraint in period t isexpressed as
Gt + (1 + rt)Dt = Rt + Dt+1,
where Gt, Rt, rt, and Dt denote aggregate real government expenditure(excluding interest payment), aggregate real tax revenue, real interest rate,
and aggregate real bonds outstanding (at the beginning of period),4

respectively.

We can rewrite as
n

i

n
1
1
)}S t +i ] + Et [∏ ()Bt + n +1 ]j =1 1 + rt + j
j =1 1 + rt + j

Bt +1 = Et [∑ {∏ (i =1

where primary surplus St ≡ Rt – Gt.
Hamilton and Flavin (1986) define the government budget satisfiesn1)Dt + n +1 ] = 0
j =1 1 + rt + j

lim Et [∏ (
n→∞

(5)

as the condition of sustainability of government bond. The above Equationmeans no Ponzi game condition in dynamic macroeconomic models.
Therefore we can confirm the sustainability of government bond by testing
the following A is significantly equal to 0;n1
lim Et [∏ ()Dt + n +1 ] = An→∞j =1 1 + rt + j

A: constant

Hamilton and Flavin (1986) estimate the following regression to test thesustainability;

Dt = c0 + A(1 + r ) t + c1 Dt −1 + L + c p Dt − p + d1 St −1 + d 2 St −2 + L + d p St − p + ε twhere εt denotes a error term. They assume that (expected) real interest
rate is constant over time, and expectations and error terms of the regression∞

1 i) S t +i ] depends on St–1, St–2, …,
i =1 1 + r

satisfy the relation that the term of Et [∑ (St–p, serial correlation of error terms is eliminated by using the variables, Dt–1,
Dt–2, …, Dt–p. If the estimator of A in the above equation is significantly
equal to 0, they conclude the government bond is sustainable.
Ihori, Nakazato, and Kawade (2002) conduct the empirical analysis
for the Japanese fiscal data from 1957 to 1999. To conduct the test, thevalues for the nominal growth rate, n, and the nominal interest rate, r, mustbe specified. Their strategy is to set various values for r – n and to check
whether the results are sensitive to the values chosen. The estimatedresults imply that the null hypothesis cannot be rejected at a 5% significancelevel, suggesting that government solvency was not a serious problem until
fiscal 1996. On the contrary, the result for the period 1957-1997 rejects thenull hypothesis when r – n is above 0.05, and the results for the period
1957-1998 and the period 1957-1999 also reject the null hypothesis when r –n is above 0.04.
Bohn (1998) proposes a new method different from existing tests forsustainability of government debt. According to Bohn (1998), the test has

5better properties than the tests based on estimating a transversality
condition and on cointegration tests. The condition that fiscal policy
satisfies the intertemporal budget constraint, i.e. the condition onsustainability of government debt, is that the primary surplus to GDP (st)increases with the ratio of (start-of-period) debt to GDP (dt). 1 Strictly
speaking, when we can express a relation between the two as
st = f(dt) + μt
Suppose other determinants, μt, is bounded and the present value of future
GDP is finite. Then, government debt satisfies a transversality condition if
there is a debt-GDP ratio d* such that f'(dt) ≥β > 0 for all dt ≥ d*, where β is apositive constant. We draw a scatter plot of st against dt in Figure 1 (onlythe general account of the central government) and Figure 2 (theconsolidated account of the central and local governments). Until the early
1990s, the Japanese fiscal policy held the quadratic relation between the two.
Recently, the Japanese fiscal policy deviates from the relation excessively.
Doi and Ihori (2003) show that Japanese government debt does not satisfy atransversality condition for fiscal 1965-2000 by estimating β.
**** Insert Figure 1 here ******** Insert Figure 2 here ****
These observations indicate that fiscal sustainability may become aserious issue. The longer the sample period, the more likely we face thefiscal crisis. It follows that the chain letter mechanism will cause the public
1 Broda and Weinstein (2005) point out that using gross debt levels to assess Japan’s
fiscal sustainability is equivalent to treating Japan’s financial assets as worthless.
They assert, therefore, that net debt levels are more appropriate to assess the fiscal
sustainability than gross debt. However, there seem to be following aspects to beconsidered.
Firstly, Broda and Weinstein (2005) calculate the value of net debt of theJapanese public sector by summing together the net debts of the Japanese government,
postal savings, and government financial institutions. Though this net debt of theJapanese public sector includes net debt of social security, the assets of social security
accounts are earmarked for the future pension benefit payouts. Therefore, it is better,from this aspect, to exclude net debt of social security to assess the fiscal sustainability.
Secondly, if fiscal authority and monetary authority act non-cooperatively,
fiscal authority has to take into account the possibility that the monetary authority sellgovernment bonds independently. Therefore, it is important for the independent fiscal
authority to assess the fiscal sustainability without taking account of the government
bonds held by the monetary authority.
Our analysis mainly deals with a
non-cooperative case so that we focus our attention on gross debt levels.

6

debt crisis to occur in the near future. Japan has two serious difficulties interms of sustainability. First, the Japanese primary surplus is apparently
a decreasing function of the debt-GDP ratio since 1990 and hence it does notsatisfy Bohn’s test. Second, the rate of interest is greater than the growthrate in Japan in the 1990s. Hence, it is important to reduce the government
deficit in the near future.
2.2. Non-Keynesian Effect
Many governments prefer to rely on the issuance of debt rather than
explicit taxation in financing expenditures. Recent experience suggeststhat a number of countries are facing potential bankruptcy as a result of
issuing too much debt.
As shown in Ihori (1988), the chain-lettermechanism would most likely be sustainable when the initial interest rateand stock of government debt are smaller or when the propensity to save andthe growth rate are higher.
When the government goes eventually bankrupt, austerity measures
as fiscal reconstruction will be required. This will depend critically on the
response of the private sector to the specific austerity policy and more
specifically the response of capital accumulation. Serious mistakes, which
will possibly exacerbate the bankruptcy problem, may occur if the wrong
action is taken.
The conventional wisdom suggests that either thegovernment must raise taxes or dramatically reduce spending. This iscontingent on an increase in capital accumulation taking place in response to
the change in policy. However, whether these contractions will be affected
through cuts in spending or increases in explicit tax collections, and whenthese actions will be taken is in general unknown. Expectations of future
policy changes are crucial in understanding seemingly counterintuitive
macroeconomic dynamics.
Bertola and Drazen (1993) argue that
expectations about the discrete character of future fiscal adjustments canhelp explain the effects of current fiscal policy. They showed that if
government spending follows an upward-trending stochastic process which
the public believes may fall sharply when it reaches specific 'trigger' points,
then optimizing consumption behavior and simple budget-constraint
arithmetic imply a nonlinear relationship between private consumption andgovernment spending.
The so called "non-Keynesian" effect means that cuts in public
expenditures and/or tax increases contribute to stimulate private demand7under some fiscal situations or macroeconomic environments: that is, when
government spending is inefficient and/or the budget deficit is so large, thisparadoxical effect may occur. If this is the case, it becomes possible toattain simultaneously two policy objectives of fiscal reconstruction andmacroeconomic recovery. This possibility of so-called non-Keynesian effect isconsistent with the experience of several countries.
Such a situation might be relevant for the recent Japanese economy.
A recent line of economic research suggests that private agents realize thatcurrent bond-financed deficits carry with them future tax obligations.
Anticipating higher future taxes, private agents change current spending
behavior to smooth consumption intertemporally.
Although theeconometric study of this issue is still in its infancy, some recent research
indicates that private Japanese behavior has partially offset recent changes
in fiscal policy (see Ihori and Sato (2002) among others).
2.3. Emergency reform for debt repudiation
In reality, however, it may be difficult to employ the standard
austerity measures in a proper time. For example, Japan's fiscal policy inthe 1990s created a problem of a tendency to postpone fiscal reconstruction
reforms. The consensus at the time was that there was no immediate needfor such painful measures as long as government policy prevented theeconomy from slipping into recession. There was, indeed, a widespreadfeeling in the private sector that the government would come to its aid if theeconomic situation worsened. That feeling fostered certain complacency inthe business world, making many corporate managers liable to “moral
hazards” – risks stemming from lack of self-discipline. The continuation of
the short-term stimulus policy, at a time when the economy needed
long-term structural changes, discouraged self-help efforts in the private
sector. Lobbying activities of local interest groups was exaggerated in the
1990s, as showed in Ihori, Doi and Kondo (2001) and Doi and Ihori (2002)’s
empirical evidence. This is also one of the main reasons why Japan's fiscal
reconstruction did not perform very well in the 1990s.
It is thus argued that if the current deficits seem not sustainable,
governments in such countries will be forced to in effect repudiate their debt,
either explicitly through an introduction of partial default or throughinflation depreciation (inflationary taxes). We may call such a policy change
the emergency reform for debt repudiation.
The consequent fiscal

8

reconstruction postponement is not free from credibility problems: Will the
additional debt be paid off in full, or will the government find it optimal toresort to higher inflation or partial default to diminish the burden of the debt,
etc? It should be stressed that if the private sector recognizes suchpossibilities of future emergency reforms for debt repudiation, government
bonds and real capital may no longer be regarded as perfect substitutes.
The more likely the current deficits seem not sustainable, the higher the
subjective probability of the future emergency reform.
2.4. Literature on debt Ponzi games under uncertainty
Several important papers investigated debt Ponzi games under
uncertainty. The average riskless rate may be a poor guide as to whether
permanent rollover of debt is feasible when economies are stochastic. Tirole(1985) and Weil (1987a) examine in the overlapping generations framework
deterministic and speculative bubbles which are, like government debt,
intergenerational schemes based on trust. Weil considered a two-statemodel with real capital and a bubble. The bubble has probability θ ofbursting every period. The main result in Weil is that the highest
sustainable bubble (the equivalent of the highest sustainable debt in thepresent paper) decreases with the probability of bursting (debt repudiation).
Calvo (1988) studies models in which debt repudiation is possible andshowed that expectations may play a crucial role in the determination ofequilibrium. See also Chari and Kehoe (1993), and Bulow and Rogoff(1989).
Blanchard and Weil (1992) show that whether or not governments
can rollover debt in dynamically efficient economies depends on whether theissuance of public debt can partially substitute missing markets. Bohn
(1991) shows that the sustainability even of simple policy rules like balanced
budgets or tax rate smoothing should not be taken for granted in a stochastic
economy and that sustainability is often sensitive to assumptions about debt
management. Alesina, Prati and Tabellini (1989) show that the maturity
structure of public debt may influence the likelihood of a confidence crisis on
the debt. The shorter and more concentrated is the maturity, the more
likely is a confidence crisis. See also Giavazzi and Pagano (1989).
2.5. Remarks
Economic theory has begun to catch up with political reality. It has

9done this by not only studying the optimality of fiscal policy in a context
where explicit account is taken of the government's budget constraint but it
has gone a step further by examining the time consistency of optimal policy.
Here, it is the issue of whether it is optimal to keep promises that were
optimal to make in the past. The latter lies at the heart of the credibility
dilemma faced by any serious politician.
Fiscal regimes differ across countries and change over time. At eachpoint in time there is uncertainty about the regime that will prevail fromthen on. A high government deficit financed by debt can be regarded as
unsustainable and therefore may be taken to signal future contractions in
the deficits. The fiscal regime prevailing in an economy, as well as the typeof fiscal relationships expected to arise from such a regime, is an importantfactor in determining the response of private agents to fiscal signals.
The sustainability question in stochastic models is an aspect of fiscal
policy that deserves more attention in future research and in policy-making.

3. Debt Management Policy of the Japanese Government
3.1 Japan's Government Bonds
The Japanese government currently issues government bonds, which
can be classified into six categories: short-term (6-month and 1-year
Treasury bills); medium-term (2-year and 5-year bonds); long-term (10-yearbonds); super-long-term (15-year, 20-year and 30-year bonds); government
bonds for individual investors; and inflation-indexed bonds. The short-term
government bonds are all discount bonds. On the other hand, all medium-,long-, and super-long-term government bonds, except for the 15-year
floating-rate bonds, are the bonds with fixed-rate coupons. The 15-year
floating-rate bonds and the government bonds for individual investors
feature a coupon rate that varies according to certain rules.
The
inflation-indexed bonds are issued as the 10-years bonds to finance funds for
the Fiscal Investment and Loan Program.2
The planned issue amount of each JGB for fiscal 2006 is shown in
The Fiscal Investment and Loan Program (FILP) has been called “the second budget”
because the government initially used FILP to undertake projects it was unable toinclude in the general account budget. Doi and Hoshi (2003) have a good summary of
the structure, components, and history of FILP and PSS, and provide estimates of thecosts FILP has and might impose on Japanese taxpayers; its appendix provides afurther review of the literature. Also see Cargill and Yoshino (2000, 2003).

2

10

Table 1. In the past, there used to be some other types of government bonds.
But after the August 1988 3-year fixed-rate bonds, the September 2000
5-year discount bonds, the February 2001 4-year fixed-rate bonds, the March
2001 6-year fixed-rate bonds, and the November 2002 3-year discount bonds,
these bonds have never been issued. The current maturity structure of thegovernment bonds (outstanding basis) is shown in Figure 3.
**** Insert Table 1 here ******** Insert Figure 3 here ****
3.2. Theoretical Analysis of Debt Management Policy
We construct a theoretical model based on Beetsma and Bovenberg(1997a, 1997b). We include potential possibilities of the government bondsin the model in Section 4. There are households, firms, the fiscal authority(government) and the monetary authority (central bank). The households
live for two periods. The firms produce a private good by using labor, atgiven price level, Pt (t = 1, 2). Their production functions are Yt = Ltη (0 < η< 1), where Yt denotes output, Lt denotes input of labor. Their profits aredescribed as (1–τt)PtLtη–WtLt, where Wt denotes nominal wage rate. The
firms’ output is taxed at a rate τt, as will be described later.
The households organize labor unions, the objective of which is toobtain a target real wage rate. They are assumed to make an expectation to
inflation rationally. We also assume that the unions have monopoly powerin the labor market. We can normalize the logarithm of real wage rate tozero. Therefore, the (log of the) nominal wage rate is set equal to the(rationally) expected price level.
Under such a situation, the logarithm of output yt ≡ lnYt is written asyt =where π t ≡sector.

η
1 −η

(π t − π te − τ t + lnη ) .

Pt − Pt −1, π te denotes the inflation rate expected by the private
Pt

Since

η
1 −η

lnη is a constant, we set v ≡η1–η, and normalize yt as

follows

xt ≡ yt − v lnη = v(π t − π te − τ t )(1)

Equation (1) is the Lucas supply function.

11

In a rational expectations equilibrium ( π t = π te ), if there exist no tax
distortion (τt = 0), the normalized output is given as xt = 0. This normalized
output level corresponds to the natural rate of employment, as mentioned in
Fujiki et al. (1998). Moreover, the socially desirable output, ~xt , without
any distortion of resource allocation is positive, because the socially desirable
employment is allowed to exceed the natural rate of employment, as pointed
out in Beetsma and Bovenberg (1997a, 1997b). Hereafter ~xt is assumed to
be given as a positive constant exogenously.
Next, we describe behavior of the monetary authority.
The
monetary authority decides level of money supply in each period. We
presume that the quantity theory of money is held;3Mt~
Pt = κ X t~
xt ).
where κ is a constant, Mt denotes nominal money supply, and X t ≡ exp( ~~Since X t is given exogenously, the monetary authority determines the
inflation rate directly through controlling money supply. Therefore,
M t − M t −1
= π t in this model.
Mt
Finally, we consider the government’s behavior. The government(or fiscal authority) collects revenues from taxes, bond issuing andseigniorage. Its revenues are used for fiscal expenditures and repayment ofgovernment bond. The government can issue (inflation-indexed) bonds. We
assume that the government can issue only one-period bond and the pure
expectation hypothesis of interest rate is held. In such a situation, thefiscal authority faces the following budget constraint in each period;
P1G1 + (1+rB1)P1B0 = τ1P1X1 + (M1– M0) + P1B1
P2G2 + (1+rB2)P2B1 = τ2P2X2 + (M2– M1)
where Gt denotes real government expenditures, rBt denotes interest rate ofbonds in period t, and Bt denotes the outstanding bonds at the end of period t.
B0, outstanding bond at the end of period 0, is exogenously given for thegovernment. The government chooses Gt, τt, and Bt.
~
Dividing both sides of the above budget constraints by Pt X t gives
the following budget constraints in share of non-distortionary (normalized)
output:An economy in Japan is now mired in a liquidity trap. We would like to focus on thesituation where an economy in Japan escapes from a liquidity trap.

3

12

g1 + (1+rB1)b0 = τ1 + κπ1 + b1
(2-1)
g2 + (1+rB2)b1 = τ2 + κπ2
(2-2)
G
B
~ ~
where g t ≡ ~t , bt ≡ ~t . We presume that Xt ≈ X t ≈ X (a constant).
X
X
For simplicity, the real interest rate is assumed to be equal to theworld interest rate ρ, which is constant over time. Hence rBt = ρ. From
(2-1,2) we can obtain the integrated government budget constraint asfollows,
g1 +g2
τ + κπ 2+ (1 + ρ )b0 = τ 1 + κπ 1 + 2
1+ ρ
1+ ρ

(3)

3.3. Second Best Solution
In this subsection, we analyze the most desirable case with
distortionary taxes, where the two policy makers are integrated and arecommitted to their policy announcements. We deal with the situation inwhich the government and the central bank are integrated and are crediblycommitted to their policy announcements. The credible commitment
particularly implies that the policy makers announce an inflation rate andcommit themselves to the announced rate at the beginning of each period
before nominal wages are concluded.
The society has the social loss function VS, which is represented byVS =1 2 t −1
β S [α πS π t2 + ( xt − ~x ) 2 + α gS ( g t − g~ ) 2 ]∑2 t =1(4)

where απS > 0, αgS > 0, and βS denotes the discount factor, 0< βS ≤ 1. We
define g~ as the government spending target as the optimal share of thetoutput realized without tax distortions or inflation surprises in period t.
Now, for simplicity of the analysis, g~ is assumed to be constant over time:tg~t = g~ .
The policy makers minimize the above loss function.
The
constraints of each period consist of the Lucas supply function (1), thegovernment budget constraint (3), and the restriction generated by therational expectations formation of the private sector ( π te = π t ).
optimality conditions are given as follows:~
απS
xv2(τt+ ) = αgS( g~ –gt) =π(t = 1, 2)
κ tv
π1 = βS(1+ρ)π2

13

The

(5-1)
(5-2)

~
~
x
x
= βS(1+ρ)(τ2+ )v
v
g~ – g1 = βS(1+ρ)( g~ – g2)

τ1 +

(5-3)
(5-4)

Equation (5-1) is the static optimization condition in each period.
Equations (5-2), (5-3) and (5-4) are the intertemporal optimization conditions
for inflation, tax rate, and government spending, respectively. For example,
if βS(1+ρ) = 1 (the discount rate is equal to the rate of interest), it is desirable
to have the same levels of inflation, tax rate, and government spending overtime, respectively. This is a well known smoothing condition over time a la
Barro (1979). See also Barro (1995, 2003).
Several remarks are useful. Firstly, as Beetsma and Bovenberg(1997a, 1997b) mention, the social loss is affected by the initial level ofgovernment debt outstanding. In the equilibrium, optimal value of VS isrepresented as~
β S + β S (1 + ρ ) + (1 + ρ ) /[1 + β S (1 + ρ ) 2 ] ⎧
K ⎫
~
S
V =
⎨(1 + ρ )b0 + K +⎬,1+ ρ ⎭
κ 2 / α πS + 1 / v 2 + 1 / α gS⎩
from (4) and (5). It means that the larger the initial debt b0 the larger is thesocial loss.
Secondly, the income tax and individual preferences of leisure andlabor affect the production level of the nation.
Intuition is as follows. To maintain the neutrality of bonds towardsocial welfare (social loss), it is necessary to issue bonds to cover the part offiscal expenditures and redemption that cannot be covered from tax revenues
and re-coinage profits while maintaining budget constraints and not
distorting the inflation rate, tax rate, and fiscal expenditures. Issuingbonds should act as a buffer in the budget.
These results are the same as Beetma and Bovenberg (1997a).
3.4. Numerical Analysis
In this subsection, we numerically examine the second best debt
management policy under commitment, which is theoretically analyzed in
the previous subsection. We can easily extend the analytical framework toa more general multi-period model. For the present numerical analysis, weuse a 200-period model and incorporate nominal bonds as well.4
In doing the numerical analysis, it is necessary to specify values of
The reason why we set a 200-period model is to weaken effects of the terminal
conditions which all stock variables are zero, on this numerical analysis.
414some exogenous parameters in the theoretical model. Based on the data ofx = 0.01,
Japanese economy, we set η = 0.7, ρ =0.04, βS =0.964, απS = 2, αgS = 3, ~~and g = 0.1. We also adapt κ = 0.36, as mentioned in Fujiki et al. (1998).
We set the initial outstanding debt to (normalized) output ratio as
100%. Under such values of parameters, we derive numerical results by
expanding the model to 200 periods. Figure 4 shows transitions ofgovernment debt outstanding (to the desirable output ratio) in the upper
figure, and inflation rate (π), government expenditure (to the desirable
output ratio: g), and tax rate (τ) in the lower figure. The upper figuresuggests that it is desirable to reduce the bond dependence ratio gradually toredeem fully in the 200th period. The lower figure indicates the smoothing
effects of these flow variables a la Barro (1979). These figures reflect thesmoothing effect.
**** Insert Figure 4 here ****

4. Debt Management and Fiscal Sustainability
4.1. Default of the government bonds
As analyzed in Beetsma and Bovenberg (1997a, b) among others,
when monetary and fiscal authorities are not cooperative and not able tocommit their policy announcements, an optimally designed conservative,
independent central bank is necessary to establish the second best. The
central bank must be made more conservative than society. They showedthat correcting monetary policy preferences is a direct way to eliminate thedistortions due to the inability to commit. Drudi and Giordano (2000) showedthat since default risk increases as the maturity structure of the debt
shortens, optimal maturity under bankruptcy risk is in general longer thanin the case in which debt repudiation policies can be precommitted or arevery much unlikely. See also Persson, Persson and Svensson (1987, 2005).
If we allow for political distortions, the preferences of the fiscal
authority may depart from the preferences of society. In the presence ofpolitical distortions a debt target is also needed. For example, if thegovernment discounts the future too heavily, the optimal debt target would
de facto act as a ceiling on public debt.
In Japan, the central bank now acts as an independent policy makerand its concern on inflationary targeting is more conservative than the15

government. In this sense, we could say that the central bank behaves in agood manner to attain the second best.
Let us explain this by including confidence crisis of government debt
and spontaneous default of fiscal authority in the model introduced in
Section 3.
Investors of government bonds decide whether they buy bonds
or not in prospect of behaviors of the government. If they can perfectly
expect the government’s default, they do not purchase bonds at all. Hence
we should investigate such a situation using backward induction. It meansthat a subgame perfect Nash equilibrium is adopted as a solution concept inthis section.
The fiscal authority and the monetary authority have individual loss
functions. Loss function of the fiscal authority is written as

VF =1 2 t −1
β S [α πF π t2 + ( xt − ~x ) 2 + α gS ( g t − g~ ) 2 ]∑2 t =1(6)where απF > 0, αgS > 0, and βS denotes the discount factor, 0< βS ≤ 1. Also theloss function of the monetary authority is written asVM =1 2 t −1
∑ β S [α πM π t2 + ( xt − ~x ) 2 + α gS ( g t − g~) 2 ]2 t =1(7)

where απM > απF > 0. It implies that the monetary authority is moreconservative in inflation than the fiscal authority. Each policy makerminimizes the above loss function, taking policies selected by the otherauthority as given. In this section, we set that both policymakers decidepolicies simultaneously in each period. Investors of the government bonds
have the loss function (4).
Now, we describe a situation that the government triggers a debt
default. The government can declare the default before policies are chosen
in this period. When the default occurs, the government does not pay atall.5 However, the production in this economy is deteriorated due to thedefault. In this situation, the Lucas supply function is assumed to include
default costs.
xt = zv(πt – πet – τt)
0 < z <1(1’)
where z is constant over time. It means that the production in default on
the government bond is z times as large as that in the normal situation,
regardless of the amount of the debt.
The real interest rate is assumed to be equal to the world interest rate. In addition,
we exclude the possibility of partial default by assumption. If, therefore, investors
expect the default, the interest rate on the government bonds becomes infinity.
5

16

The constraints of each period consist of the Lucas supply function(1) or (1’), the government budget constraints (2). We also rewrite thegovernment budget constraints as follows,~xx~ (1 − z ) ~K++ (1+ρ)b0 = (τ1+ ) + κπ1 + ( g~ –g1) + b1
(8-1)
vz
vz
~
x
x
~ (1 − z ) ~K++ (1+ρ)b1 = (τ2 + ) + κπ2 + ( g~ –g2)
(8-2)
vz
vz
~
x
~
x v . Note ( xt − ~where K ≡ g~ + ~x ) 2 = z 2 v 2 (π te − π t + τ t + ) 2 from equation (1’),
vzz =1 in the normal situation, and 0 < z < 1 in default of payment.
We assume that, in each period, the monetary authority cannot
commit the inflation rate announced at the beginning of each period before
nominal wages are set. Under this situation, the policy authorities takeinflation expectations as predetermined. Such situation is represented in
Figure 5 as a game tree.
**** Insert Figure 5 here ****

4.2. Policy choice in the second period
To solve for the two-period decision problem, we use the backward
induction method. Thus, we begin with solving for the solution in thesecond period and then proceed to solve for the solution in the first period.
It implies that such a policy is a time-consistent policy, which is analyzed in
Lucas and Stokey (1983), Persson, Persson and Svensson (1987, 2005), Calvoand Guidotti (1990a, 1990b) and so on. In the second period, the fiscal
authority chooses {τ2, g2} to minimize its loss function, subject to the budget
constraint (8-2). Also the monetary authority chooses {π2} to minimize its
loss function, taking as given the expected inflation rate ( π 2e ), without any
regard for the budget constraint (8-2).
4.2.1. The normal case
If the government does not trigger a debt default in the second period,
we obtain the following conditions from the first order conditions for the
choice of {π2, τ2, g2}, taking policies decided by the other authority andinflation expectation and b1 as given,v( ~x – x2) = αgS( g~ – g2) = απMπ2(9)17Moreover, from the above conditions and the government budget constraint
and the restriction generated by the rational expectations formation of theprivate sector ( π 2e = π 2 ), the following relations are held

π2 =

1

~
[ K + (1+ρ)b1]

NαπS
~
1 ~
x
τ2 + = Nv2[ K +(1+ρ)b1]v
1 ~g~ – g2 =[ K + (1+ρ)b1]
NαgS
where N ≡

(10)

1
1
κ
+ v2 +απM
αgS

Hence, the value of the loss function of the fiscal authority is
1 NF* ~
F
V2 ≡ 2 N2 { K + (1+ρ)b1}2
(11)
1
1
απF
where NF*≡++
απM2 v2 αgS
4.2.2. The case of default
If the government does declare a debt default in the second period,
the government may decrease its value of the loss function. Then, investors
would not buy the government bond in the first period if they can predict the
debt default in the second period. In this situation, the government cannot
issue the bonds in the first period, and does not have any bonds to default inthe second period. Therefore, the government cannot trigger a default inthe second period.
4.3. Policy choice in the first period
In the first period, investors of the government bonds firstly expect
whether the government trigger a debt default.6 If they believe the default
occurs, they do not buy the bonds at all. This situation is confidence crisis.
Under this situation, the government cannot newly issue bonds (b1). If
investors expect the default does not occur, the government bonds are freely
traded.
After that, the fiscal authority chooses {τ1, g1, b1} to minimize its loss
function, subject to the budget constraint (8-1).
Also the monetary
authority chooses {π1} to minimize its loss function, without any regard for
As we mentioned above, the government may default only in the first period, not in
the second period.

618

the budget constraint (8-1).
4.3.1. The normal case under no confidence crisis (Case N)
First, we consider a situation that confidence crisis does not occur.
Under this situation, the government can newly issue an one-period bond (b1).
The fiscal and monetary authorities minimize their loss functions in
consideration of situation in the second period. Thus the authorities in thefirst period have the following loss functions,
1
V1aN = 2[απaπ12 + (x1 – ~x )2 + αgS(g1 – g~ )2] + βSV2a(12)where a = F, M. V2a denotes the value of loss function in the second period.
V2F is defined as (11), and V2M is obtained by assigning (10) to (7).
The monetary authority minimizes (12) regardless of the government
budget constraint, taking policies selected by the fiscal authority andinflation expectation and b0 as given. From the first order condition for the
choice of {π1}, we obtain the following conditionv( ~x – x1) = απMπ1(13-1)
The fiscal authority minimizes its loss function.
~v( ~x – x ) = α ( g~ – g ) = β *[ K + (1+ρ)b ](13-2)
1

gS

1

N

1

where βN* ≡ βS(1+ρ)NF*/N. From the above conditions (13-1, 2) and thegovernment budget constraint, the following relations are held under therational expectations formation of the private sector ( π 1e = π 1 )~
1 ~xτ1 + = Nv2[ K + (1+ρ)b0 – b1]v

1~[ K + (1+ρ)b0 – b1]
NαπM
1 ~g~ – g1 =[ K + (1+ρ)b0 – b1]
NαgS

π1 =

(14)

δ2
~
~
[(1+ρ)b0+ K – βN* K ]1+ρ
1+ρ
where δ2 ≡1+βS(1+ρ)2NF*/N
b1 =Therefore, we obtain the value of the loss function as follows
1 NF* ~
1 NF* ~
2FN
V1 ≡ 2 N2 [ K + (1+ρ)b0 – b1] + 2βS N2 { K +(1+ρ)b1}2
1 NF* 21 ~~= 2 N2 δ 2 {(βN*)2 + βS}[ K +K + (1+ρ)b0]2
(15)
1+ρ

19

4.3.2. The case of default under confidence crisis (Case D)
Next, we consider a situation that confidence crisis occurs. Under
this situation, the government cannot newly issue any bond (b1 = 0), andtrigger a debt default in the first period.
The fiscal and monetary authorities minimize their loss functions.
If once the government defaults on payments in the first period, however, thegovernment has no debt in the second period, that is, there is no default inthe second period. Thus the authorities in the first period have thefollowing loss functions,
1x )2 + αgS(g1 – g~ )2] + βS V2a |b1 =0
V1aD = 2[απaπ12 + (x1 – ~(12’)
where a = F, M, and V2a |b1 =0 : V2a with b1 = 0.
Also the production in this situation is determined by (1’). The
government budget constraint in the first period becomes as follows,~xx~ (1 − z ) ~= (τ1+ ) + κπ1 + ( g~ –g1)
K+
0 < z <1
(8-1’)
vz
vz
The monetary authority minimizes (12’) regardless of thegovernment budget constraint, taking policies selected by the fiscal authority
and inflation expectation as given. From the first order condition for the
choice of {π1}, we obtain the following conditionvz( ~x – x1) = απMπ1(16-1)
The fiscal authority minimizes its loss function (12’), subject to (8-2).
The authority sets policies to satisfy the following condition:vz( ~x – x1) = αgS( g~ – g1)(16-2)
From the above conditions (1’), (16-1, 2), and the government budget
constraint (8-1’), the following relations are held under the rational
expectations formation of the private sector ( π 1e = π 1 )
1 ~ (1 − z ) ~
x
π1 =
[K+
]
HαπS
vz
~
1
x
x
~ (1 − z ) ~τ1 += Hv2z2[ K +]vzvz
1 ~ (1 − z ) ~xg~ – g1 =
[K+
]
HαgS
vz
1
1
κ
+ v2z2 +where H ≡
απM
αgS

(17)

Therefore, we obtain the value of the loss function in this case as
follows

20

*
1 HF* ~ (1 − z ) ~x 2 1 NF ~ 2
V1FD ≡ 2 H2 [ K +] + 2βS N2 K
vz
1
1
απF
where HF* ≡++απM2 v2z2 αgS(18)

4.3.3. Welfare comparison between Case N and Case D
Whether the confidence crisis occurs or not in the first perioddepends on welfare loss of the fiscal authority in each case. If thegovernment defaults on payments, investors of the government bonds facelosses. Thus, they do not buy the bonds at all when they expect that the
government trigger a debt default in the first period.
If V1FN ≤ V1FD, the fiscal authority does not have any incentives todefault in the first period. Hence, investors can purchase the government
bonds. We further analyze this situation.
V1FN ≤ V1FD is satisfied under the following conditions
H F* N 2 ~ (1 − z ) ~x 2~} + βS K 2
{K +
*
2
2+ρ ~
vz
NF H
1
(19)
0 ≤ b0 ≤ –
2K +
(1+ρ)
(1 + ρ )δ 2
( β N* ) 2 + β S
When V1FN ≤ V1FD, that is, condition (19) is held, investors buy thegovernment bonds in the first period. It means that there is no confidence
crisis in the first period under this situation. Otherwise, investors do notbuy bonds at all in the first period. Thus confidence crisis occurs in the first
period.
4.4. Numerical Analysis
In this subsection, we also numerically examine the above situation,
which is theoretically analyzed in the previous subsection. We can easily
extend the analytical framework to a more general T-period model. We will
describe the detail setting of this numerical analysis in Appendix at the endof this paper.
In this numerical analysis we introduce the maturity structure of thegovernment bonds to make it more realistic. We adopt this structure infiscal 2003 (settlement basis) in Japan. The maturity structure of theoutstanding debt is assumed to be given in Table 2. These ratios mean
composition ratios to total amount of debt by remaining years to maturity.
For example, the ratio of the government bonds which has the remaining
year to maturity less than 1 year is about 36%.

21

**** Insert Table 2 here ****We also calculate the transition of policy variables in the realistic
case described the above sections. As we mentioned, in the realistic case,the government may trigger a debt default. Thus can the fiscal authority
avoid a default? Or does the authority have an incentive to default? We
consider whether the government defaults on payment under our calibration
setting.
We set the value of parameters used in this model as the same in thesecond best case in Section 3.4. Also we set z = 0.9.
In the numerical analysis, we calculate the value of loss function of
the fiscal authority in case of default (VtFD) and the value of loss function incase of no-default (VtFN) in each period, and then compare both values. If
VtFD ≥ VtFN, the government in period t does not default. If VtFN > VtFD, thegovernment triggers a default.
In conclusion, under our setting in the 200-period model, we find thatthe fiscal authority could still avoid a default, fortunately. First, the upper
figure of Figure 6 shows the transition of outstanding debts. In this case,the fiscal authority takes such a policy that the outstanding of government
bond increases first and it decreases sharply in the near the last period.
This phenomenon seems to reflect the fact that the fiscal authority issues
government bonds strategically. And it suggests that the outstanding debt
in this situation does not exceed about 120%. It is consistent with nodefault.
The lower figure of Figure 6 shows inflation rate (π), government
expenditure (to the desirable output ratio: g), and tax rate (τ). When theoutstanding of government bonds is large, the issuance of new bonds resultsin the debt default. Therefore, the large amount of outstanding debt limits
the fiscal authority to issue a new government bonds. As a result, issuanceof government bonds leads the fiscal authority to an advantageous position
against the monetary authority. In other words, the issuance of bonds
works as a credible threat to the monetary authority. This mechanism
leads the inflation rate to be higher, comparing to the second best case.
Inflation rate becomes over 6%. In contrast, the tax rate is kept low about
3%.

22**** Insert Figure 6 here ****
4.5. Intuitions of the analysis and policy implications
According to conditions (19), the fiscal authority has an incentive todefault when the amount of debt outstanding is more than a certain level.
Expecting the debt default, the investors do not buy the public bonds at all.
The public bonds, therefore, cannot be sold when the issuance leads theamount of debt outstanding to be more than the certain level. In thisrespect, the fiscal authority has to take into account the upper limit of stocksof public debt.
This possibility of debt default provides the fiscal authority to issue
public bonds strategically in the first period. Suppose that fiscal authority,in the first period, issues public bonds to be paid in subsequent periods in a
multi-period setting. The amount of issuance is, in addition, supposed to
set to the extent that fiscal authority has to raise tax rate to finance thegovernment spending and/or cut the government spending itself in thesecond period because the additional debt issuance is limited due to thepossibility of the default in subsequent periods.
This strategic behavior of fiscal authority induces the monetary
authority, in a later period, to boost output and raise seigniorage revenues toeliminate the distortion of resource allocation due to the limitation on debt
issuance. Therefore, the monetary policy in a later period suffers from an
inflation bias from the ax ante point of view. Expecting such futuremonetary policy, the fiscal authority has an incentive to issue more publicbonds strategically in an earlier period because it will lead the fiscal
authority to the advantageous position in the game played in a later period.
This strategic bias of the fiscal authority results in the distortion of theresource allocation.7
There are two ways to eliminate this distortion toward successful
fiscal reconstruction. One of them is to make the monetary authority moreconservative than society in the sense that the price stability weight ofmonetary authority is higher than that of society. If the monetary
authority is conservative enough not to raise inflation depending passively
on the strategic accumulation of public bonds, the fiscal authority does not
Since this strategic issuance of government bonds distorts the resource allocation
form the ex ante point of view, it is considered to be one of the time inconsistency
problems.

723engage in the strategic accumulation of debt in an earlier period.
Consequently the central bank should be more conservative to eliminate thedistortion due to the strategic behavior of fiscal authority.
The other way of eliminating the distortion of the resource allocation
is to design an institutional ceiling on the debt issuance. This institutionalframework eliminates directly the distortion stemmed from the strategic
behavior of the fiscal authority. Needless to say, this direct ceiling does notwork effectively if the fiscal authority has not issued public bonds to theextent that the amount of debt outstanding is close to the critical level ofdebt default. It is therefore natural that the direct ceiling might not benecessary for many countries, but it can provide a binding constraint of the
public bond issuance for the fiscal authority of Japan because it has
accumulated the debt outstanding much more than other countries.8

5. Conclusion
If the expansionary trend in Japan's government spending continues
at this pace, the fiscal deficit will inflate further and the ability to raise taxes
in the future will be politically limited. Investors will lose confidence inJapan’s public bonds if they believe that the nation’s public finance is boundfor long-term crisis. The result is that interest rates will rise and fiscal
failure will become a more tangible reality.
This paper has analyzed sustainability issues of Japan's fiscal policy
and then discussed the debt management policy using theoretical models
and numerical studies. We also investigated the desirable coordination of
fiscal and monetary authorities toward fiscal reconstruction.
We have also investigated confidence crisis of government debt andspontaneous default of fiscal authority. The fiscal authority has anincentive to default when the amount of debt outstanding is more than acertain level. Expecting the debt default, the investors do not buy the
public bonds at all. The public bonds, therefore, cannot be sold when theissuance leads the amount of debt outstanding to be more than the certain
One of the reasons why Japan has accumulated the debt drastically is related to thepolitical situation of Japan in the 1990s. Especially after 1993, several parties formeda coalition government. This instability of government party in the Diet resulted in
the delay of fiscal structural reform toward fiscal reconstruction because the politicians
have to take into account the possibility of dropping power when carrying out suchpolices.
824

level. In this respect, the fiscal authority has to take into account the upper
limit of stocks of public debt. Our numerical study suggests that the fiscal
authority could still avoid a default in Japan.
We have also showed that for a country with large stocks of public
debt like Japan, the fiscal authority has an incentive to issue public bonds
strategically. This strategic bias distorts the monetary authority to increaseinflation too much. To eliminate this distortion bias and to attain fiscal
reconstruction, an institutional ceiling on the debt issuance is one of theeffective policy tools.

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McCallum, B.T., 1984, Are bond financed deficits inflationary? A Ricardian
analysis, Journal of Political Economy vol.92, pp.123-135.
Persson, M., T. Persson and L.E.O. Svensson, 1987, Time consistency offiscal and monetary policy, Econometrica vol.55, pp.1419-1431.
Persson, M., T. Persson and L.E.O. Svensson, 2005, Time consistency offiscal and monetary policy: A solution, NBER Working Paper No. 11088.
Samuelson, P.A., 1958, An exact consumption-loan model of interest with orwithout the social contrivance of money, Journal of Political Economy
vol.66, pp.467-482.
Tirole, J., 1985, Asset bubbles and overlapping generations, Econometrica

27

vol.53, pp.1071-1100.
Weil, P., 1989, Overlapping families of infinitely-lived agents, Journal of
Public Economics vol.38, pp.183-198.

28

Appendix

Numerical analysis in a realistic case

In Section 4.4, we also numerically examine a realistic case, which istheoretically analyzed in Sections 4.1-4.3. We can easily extend theanalytical framework to a more general T-period model. Now we introduce
maturity structure of the government bond. The government can issue(inflation-indexed) bonds, and choose their maturity. The pure expectation
hypothesis of interest rates is assumed to be held. In such a situation, thefiscal authority faces the following budget constraint in period t;
t −1

T

s =0

v =t +1

g t + ∑ (1 + ρ ) t − s bs ,t = τ t + κπ t + ∑ bt ,vor~T
x t −1x~ (1 − z ) ~K++ ∑ (1 + ρ ) t − s bs ,t = (τ t + ) + κπ t + ( g~ − g t ) + ∑ bt ,v
vz
vz
s =0
v =t +1(A-1)

where Bst denotes the amount of bonds issued in period s with a prescribedBpayout in period t and bst ≡ ~st . Note z = 1 in the normal situation, andX
0 < z < 1 in default of payment. The initial maturity structure of thegovernment bond {B0v| v ≥ 1} is exogenously given for the government in eachperiod. The government in period t chooses gt, τt, btv (t+1≤ v ≤ T).
A.1. The normal case in the final period
If the government does not trigger a debt default in the final period(period T), we obtain the following conditions from the first order conditions
for the choice of {πT, τT, gT}, taking policies decided by the other authority andinflation expectation as given,x – xT) = αgS( g~ – gT) = απMπTv( ~Moreover, from the above conditions and the government budget constraint
and the restriction generated by the rational expectations formation of theprivate sector ( π Te = π T ), the following relations are held

πT =

1

~
[ K + bT]

NαπS
~
1 ~
x
τT + = Nv2[ K +bT]v
1 ~g~ – gT =[ K + bT]
NαgS

(A-2)

29

T −1

where bT ≡ ∑ (1 + ρ ) T − s bsT . Hence, the value of the loss function of the fiscal
s =0

authority is

1 NF* ~
VTFN≡ 2 N2 [ K +bT]2(A-3)

A.2. Policy choice in period T– 1
In period T– 1, investors of the government bonds firstly expect
whether the government trigger a debt default (in period T– 1 or the periodT). If they believe the default occurs, they do not buy the bonds at all.
This situation is confidence crisis. Under this situation, the government
cannot newly issue bonds (bT–1,T). If investors expect the default does notoccur, the government bonds are freely treaded.
After that, the fiscal authority chooses {τT–1, gT–1, bT–1,T} to minimize its
loss function, subject to the budget constraint (A-1). Also the monetary
authority chooses {πT–1} to minimize its loss function, without any regard forthe budget constraint (A-1).
A.2.1. The normal case (Case N)
First, we consider a situation that confidence crisis does not occur.
Under this situation, the government can newly issue an one-period bond(bT–1,T). The fiscal and monetary authorities minimize their loss functions.
Thus the authorities in period T– 1have the following loss functions,
1x )2 + αgS(gT–1 – g~ )2] + βSVTaN
VT–1a = 2[απaπT–12 + (xT–1 – ~(A-4)
where a = F, M. VTaN denotes the value of loss function in the normal case in
the final period. VTFN is defined as (A-3), and VTMN is obtained by assigning(A-2) to (7).
The monetary authority minimizes (A-4) regardless of thegovernment budget constraint, taking policies selected by the fiscal authority
and inflation expectation as given. From the first order condition for the
choice of {πT–1}, we obtain the following conditionv( ~x – xT–1) = απMπT–1(A-5-1)
The fiscal authority minimizes its loss function and sets policies tosatisfy the following conditions:~v( ~x – xT–1) = αgS( g~ –gT–1) = βN*[ K + bT](A-5-2)
From the above conditions (A-5-1, 2) and the government budget30

constraint, the following relations are held under the rational expectations
formation of the private sector ( π Te −1 = π T −1 )~~ T −2bT–1,T = δT–1[ K + bT–1 – βN*{ K + ∑ (1 + ρ ) T − s bs ,T ]
s =0

~
1 ~
x
τT–1 + = Nv2[ K + bT–1 – bT–1,T]
v
1
1 ~
~
= Nv2δT–1βN*[ K + bT–1 +{ K + (1+ρ)3b03 + (1+ρ)2b13}]1+ρ
1 ~{ K + (1+ρ)3b03 + (1+ρ)2b13}]
(A-6)
NαπM
1+ρ
1
1 ~
~
g~ – gT–1 =δT–1βN*[ K + bT–1 +{ K + (1+ρ)3b03 + (1+ρ)2b13}]
NαgS
1+ρ

πT–1 =1

T −2~

δT–1βN*[ K + bT–1 +where bT–1 ≡ ∑ (1 + ρ ) T −1− s bs ,T −1 , δT–1 ≡
s =0

1+ρ
. Therefore, we obtain
1+βS(1+ρ)2NF*/N

the value of the loss function as follows
1 NF* ~
1 NF* ~
VT–1FN ≡ 2 N2 [ K + bT–1 – bT–1,T]2 + 2βS N2 ( K + bT)2

1 NF*~
= 2 N2 δT–12{(βN*)2 + βS}[ K + bT–1 +1 ~ T −2
{ K + ∑ (1 + ρ ) T − s bs ,T }]2
1+ρ
s =0

(A-7)

A.2.2. The case of default in the final period under confidence crisis (Case C)
Next, we consider a situation that confidence crisis occurs. Under
this situation, the government cannot newly issue any bond (bT–1,T = 0). The
fiscal and monetary authorities minimize their loss functions in
consideration of situation in the final period; whether the government faces adebt default or not in the final period.
At first, we consider the case that default occurs in the final period.
When the government does declare a debt default in the final period, thegovernment budget constraint in the final period becomes (A-1) with z ≠ 0.
Under this situation, we obtain the following conditions from the first orderconditions for the choice of {πT, τT, gT}, taking policies decided by the otherauthority and inflation expectation as given,vz( ~x – xT) = αgS( g~ – gT) = απMπT(A-8)
Moreover, from the above conditions (1’) and (12), and the government
budget constraint (A-8) and the restriction generated by the rational
expectations formation of the private sector ( π Te = π T ), the following relations
are held31x~ (1 − z ) ~
[K+
]
HαπS
vz
~
1
x
x
~ (1 − z ) ~τT += Hv2z2[ K +
(A-9)
]
vz
vz
1 ~ (1 − z ) ~xg~ – gT =
[K+
]
HαgS
vz
Hence, the value of the loss function of the fiscal authority is
1 HF* ~ (1 − z ) ~x 2]
VTFD≡ 2 H2 [ K +(A-10)
vz
Next we investigate policy choice in period T– 1. The authorities inperiod T– 1 are written as
1x )2 + αgS(gT–1 – g~ )2] + βSVT–1aD
VT–1aC = 2[απaπ T–12 + (xT–1 – ~(A-11)πT =1where a = F, M. The monetary authority minimizes (A-11) regardless of thegovernment budget constraint, taking policies selected by the fiscal authority
and inflation expectation as given. Since this situation is the same as CaseC, condition with respect to {πT–1} in this case is (A-5-1).
The fiscal authority minimizes its loss functions in consideration ofsituation in the final period. The government decides policies to satisfy thecondition,v( ~x – xT–1) = αgS( g~ –gT–1)(A-5-2’)
Therefore, we obtain the value of the loss function in this case as follows
1 NF* ~
1 HF* ~ (1 − z ) ~x 2
FC2
VT–1 ≡ 2 N2 [ K + bT–1] + 2βS H2 [ K +](A-12)vz
A.2.3. The case of default in period T– 1 under confidence crisis (Case D)
Also, we discuss the situation that the government in period T–1
triggers a debt default under confidence crisis. Under this situation, thegovernment cannot newly issue an one-period bond (bT–1,T = 0).
The fiscal and monetary authorities minimize their loss functions in
consideration of situation in the final period. If once the government
defaults on payments in period T– 1, however, the government has no debt in
the final period, that is, there is no default in the final period. Thus theauthorities in period T– 1 have the following loss functions,
1x )2 + αgS(gT–1 – g~ )2] + βS VTaN |bT =0
VT–1a = 2[απaπ T–12 + (xT–1 – ~(A-13)
where a = F, M. The government budget constraint in this period is (A-1)
with z ≠ 1.
32

The monetary authority minimizes (A-13) regardless of thegovernment budget constraint, taking policies selected by the fiscal authority
and inflation expectation as given. From the first order condition for the
choice of {πT–1}, we obtain the following conditionx – xT–1) = απMπ T–1
vz( ~(A-14-1)
The fiscal authority minimizes its loss function (A-13), subject to(A-1). The authority sets policies to satisfy the following condition:vz( ~x – xT–1) = αgS( g~ – gT–1)(A-14-2)
From the above conditions (1’), (A-14-1, 2), and the government
budget constraint (A-1), the following relations are held under the rational
expectations formation of the private sector ( π Te −1 = π T −1 )
1 ~ (1 − z ) ~x
πT–1 =
[K+
]
HαπS
vz
~
1
x
x
~ (1 − z ) ~τT–1 +]= Hv2z2[ K +vzvz
1 ~ (1 − z ) ~xg~ – gT–1 =[K+(A-15)]HαgS
vz
Therefore, we obtain the value of the loss function in this case as follows*
1 HF* ~ (1 − z ) ~x 2 1 NF ~ 2
VT–1FD ≡ 2 H2 [ K +(A-16)] + 2βS N2 Kvz
A.2.4. Welfare comparison between Case C and Case D
Dose the fiscal authority trigger a debt default under no confidence
crisis? It depends on the value of the loss function of the fiscal authority ineach case.
If VT–1FD ≥ VT–1FC, the government does not trigger a default in period
T– 1. On the other hand, in the case of V2FD < V2FC, the fiscal authority has
incentives to default on payments in period T– 1.
N~
x vz
~
~
The details are as follows. In the case of K >and D > K 2,
1+ z
FD
FC
VT–1 > VT–1 is satisfied under the following conditions~~bT–1 > β S K 2 + (1 − β S ) D − K ,(A-17)
These conditions suggest that the government has an incentive to default
when the amount of debt outstanding is more than a certain level.
A.2.5. Welfare comparison between Case N and Case C or Case D
Whether the confidence crisis occurs or not in period T– 1 depends on
33

welfare loss of the fiscal authority in each case. If the government defaults
on payments, investors of the government bonds face losses. Thus, they do
not buy the bonds at all when they expect that the government trigger a debt
default in period T– 1 or the final period.
If VT–1FN ≤ min{VT–1FC, VT–1FD}, the fiscal authority does not have any
incentives to default in each period. Hence, investors can purchase thegovernment bonds. We further analyze this situation.
VT–1FN < VT–1FC < VT–1FD is satisfied, under the following conditions
1 2~
0 < bN,T–1 < βSD – K 2{γT–1 (1 +) – 1},(A-18)1+ ρ
T −2

where γT–1 ≡ δ T–12{(βN*)2 + βS}, bN,T–1 ≡ (γT–1 – 1)bT–12 + γT–1{ ∑ (1 + ρ ) T − s bs ,T }2 +
s =0

T −2
T −2
1
~
~
)[bT–1+ ∑ (1 + ρ ) T − s bs ,T ],2γT–1bT–1 ∑ (1 + ρ ) T − s bs ,T – 2 K bT–1 + 2 K γT–1 (1+
1+ρ
s =0
s =0

~
~
bT–1 ≤ β S K 2 + (1 − β S ) D − K ,and(A-17’)

γT–1 <

1+ βS D
⎛
1 ⎞
⎟⎟
⎜⎜1 +
⎝ 1+ ρ ⎠2

On the other hand, VT–1FN < VT–1FD < V T–1FC is satisfied under (A-17)
and the following conditions
~
T −2
1 ⎞~
D + βK ⎛T −s⎟⎟ K
0 < bT–1 + ∑ (1 + ρ ) bs ,T <− ⎜⎜1 +
γ T −1s =0⎝ 1+ ρ ⎠and(A-19)

γT–1 <~
D + βS K 2
2⎛
1 ⎞ ~2⎜⎜1 +⎟⎟ K⎝ 1+ ρ ⎠When VT–1FN ≤ min{VT–1FC, VT–1FD}, that is, conditions (A-17’)and (A-18) or(A-17) and (A-19) are held, investors buy the government bonds in period T–
1. It means that there is no confidence crisis in period T– 1 under thissituation. Otherwise, investors do not buy bonds at all in period T– 1.
Thus confidence crisis occurs in period T– 1.

34

A.3. Policy choice in period t
In general, in period t, investors of the government bonds firstly
expect whether the government trigger a debt default in subsequent periods.
If they believe the default occurs, they do not buy the bonds at all. Thissituation is confidence crisis. Under this situation, the government cannot
newly issue bonds. If investors expect the default does not occur, thegovernment bonds are freely treaded.
After that, the fiscal authority chooses {τt, gt, bts} to minimize its loss
function, subject to the budget constraint (A-1). Also the monetary
authority chooses {πt} to minimize its loss function, without any regard forthe budget constraint (A-1). The structure of this policy game from period
T– 2 to period T, for example, is shown in Figure A.
**** Insert Figure A here ****
A.3.1. The normal case (Case N)
First, we consider a situation that confidence crisis does not occur.
Under this situation, the government can newly issue bonds. The fiscal andmonetary authorities minimize their loss functions. Thus the authorities inperiod T– 1have the following loss functions,
1x )2 + αgS(gt – g~ )2] + βSVt+1aN
VtaN = 2[απaπt2 + (xt – ~(A-4’)
where a = F, M. Vt+1aN denotes the value of loss function in the normal casein the final period. From the first order conditions like (A-6), the value ofthe loss function of the fiscal authority in period t in the normal casebecomes

Vt
where

FN

t −1
T
⎡~ T
N*
⎫⎤
⎧
= F2 γ t ⎢ K ∑ (1 + ρ ) t − s + ∑ ⎨(1 + ρ ) t − s ∑ bs ,v ⎬⎥2N
s =0 ⎩v =t⎭⎦⎣ s =tγ t ≡ {( β N* γ t +1 ) 2 + β S γ t +1 }δ t2 , γ T = 1, δ t ≡21+ ρ
1 + γ t +1 (1 + ρ ) β N*

,

and

the

(optimizing) newly issued bond in period t isT

∑ bt ,v =v =t +1Tt −1Tδ t ⎧⎪ ~ t −1
⎧
⎫⎤ ⎫⎪
t −s
* ⎡~
t +1− s+ ∑ ⎨(1 + ρ ) t +1− s ∑ bs ,v ⎬⎥ ⎬⎨ K + ∑ (1 + ρ ) bs ,t − γ t +1 β N ⎢ K ∑ (1 + ρ )1 + ρ ⎪⎩s =0
s =0 ⎩
v =t +1⎭⎦ ⎪⎭⎣ s =t +1

A.3.2. The case of default under confidence crisis
Next, we consider a situation that confidence crisis occurs in period t.
Under this situation, the government cannot newly issue any bond in this35

and subsequent periods. If the government triggers debt default in period t,
we also obtain the value of the loss function of the fiscal authority in period t
in default case as follows
2
2
H F* ⎡ ~ (1 − z ) ~
N F*
x⎤
⎡~ T
FD
t +1− s ⎤+Vt , 0 ≡K+
γ t +1 ⎢ K ∑ (1 + ρ )
⎥ ,
vz ⎥⎦
2 H 2 ⎢⎣
2N 2
⎣ s =t +1⎦
from the first order conditions like (A-14-1, 2). Likewise, if the government
defaults in period t+j (0 ≤ j ≤ T– t), from the first order conditions like (A-5-1),(A-5-2’) and (A-9), the value of the loss function of the fiscal authority inperiod t becomes2*(1 − z ) ~x⎤
FDj HF ⎡ ~K+
Vt , j ≡ β Svz ⎥⎦2 H 2 ⎢⎣
22⎧~ T
⎫ t + j −1 h −t ⎧ ~ t −1
N F* ⎡ j +1
⎫ ⎤t + j +1− sh −v⎢ β S γ t + j +1 ⎨ K ∑ (1 + ρ )+⎬ + ∑ β S ⎨ K + ∑ (1 + ρ ) bv ,h ⎬ ⎥2N 2 ⎢
s =t + j +1
h =t
v =0
⎩
⎭ ⎥⎦
⎩
⎭
⎣

We define VtFD ≡ min{Vt,jFD|0 ≤ j ≤ T– t}.
Hence, if VtFN ≤ VtFD, the fiscal authority does not have any incentives
to default in period t. We numerically examine a realistic case based on theabove setting in Section 4.4.

36

Figure 1
Primary Surplus and Government Debt

(The general account of the central government)

Primary Surplus/GDP

3%
6157
91
9088
2% 6256
55
8987
58
60
63
59
1%
92
86
64 73
70
94
69
0%
74
93
68
85
6571
97
72
8384 9596-1% 67
66
-2%
98 99
75
82
76
-3%
78 80 81
77 79
-4%
0%
10% 20% 30% 40% 50% 60%

Government Debt/GDP

37

00
01
02 03
70%

80%

90%

100%

Figure 2
Primary Surplus and Government Debt
(Central and local governments)

4%

Primary Surplus/GDP

90 88
91
89

6157
56
62
6058
59
63 55

3%
2%
1%

87
86
92 85

64 73
69
70
68
6567 74

0%
-1%

84
83 94
93

71
6672

-2%

82

-3%
-4%

75

-5%

80

76
77

78 79

20%

30%

97
96

00

95

98

81

99

01
02 03

-6%
0%

10%

40%

50%

60%

70%

80%

Government Debt/GDP

38

90% 100% 110% 120% 130%

Figure 3
Maturity Structure of Government Bonds(Outstanding Basis)

100%

80%

60%

40%

20%

0%
1965

1970

1975

1980

1985

1990

1995

as of the end of fiscal year
1 yr & less

2-5 yrs

6-10 yrs

39

11-19 yrs

20 yrs & more

2000

Figure 4
Result of Numerical Analysis in the Second Best Case
Outstanding Bonds

Bond to GDP ratio
1.2

1
0.8

0.6
0.4

0.2
0

-0.2
0

10

20

30

40

50

60

70

80

90

100 110 120 130 140 150 160 170 180 190 200

periodTax rate, government spending and inflation rate
5.0%
4.5%
4.0%
3.5%
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
0

10

20

30

40

50

60

70

80

90 100 110 120 130 140 150 160 170 180 190 200πτg

period40

Figure 5
The structure of the policy gameI

If V1FN > V1FDCNC

If V1FN ≤ V1FD

t=1

V1FD

F V1FN
ND

F

D
F, M

F, M

P
t=2

V2F|b1=0

P
F

F

V2F

ND
F, M

ND
F, M

P

P

NC: non confidence crisis, C: confidence crisis, D: default, ND: non default, P: policy
choiceF: fiscal authority, M: monetary authority, I: investors

41

Figure 6
Result of Numerical Analysis in a Realistic Case
Outstanding Bonds

Bond to GDP ratio
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

10

20

30

40

50

60

70

80

90 100 110 120 130 140 150 160 170 180 190 200

periodTax rate, government spending and inflation rate
10%
8%
6%
4%
2%
0%
-2%
-4%
0

10

20

30

40

50

60

70

80

90 100 110 120 130 140 150 160 170 180 190 200πτｇ

period42

Figure AICNC

t = T– 2

F
D

ND

F, M

F, M

F, M

P

P

P

I
t = T– 1

C

F
ND

F, M
P

F

D

D

F, M

F, M

F, M

F, M

P

P

P

P

P

F

D

F, M
P

ND

F, M
F

t=T

NC

D

F, M
P

F, M

F, M

F, M

F, M

P

P

P

P

NC: non confidence crisis, C: confidence crisis, D: default, ND: non default, P: policy choice
F: fiscal authority, M: monetary authority, I: investors

43

Table 1
Planned Issuance of Japanese Government Bonds
Classification by Issuance Methods and Maturity(Billion yen)

FY2005Initial
Budget (a)FY2006
Initial
Budget (b)2,000.09,000.09,600.0
22,800.0
2,000.0
24,000.0
20,400.0
29,961.5–
119,761.5–
119,761.5
3,600.0

2,000.0
10,300.0
9,100.0
24,000.0
2,000.0
25,200.0
21,600.0
28,719.7
600.0
123,519.7
2,658.0
126,177.7
4,400.0

0.0
1,300.0–500.01,200.0
0.0
1,200.0
1,200.0–1,241.8
600.0
3,758.2
2,658.0
6,416.2
800.0

123,361.5
23,043.6
1,000.0

130,577.7
16,557.4–

7,216.2–6,486.2–1,000.0

Fiscal Loan Bonds(transitional measures)

19,300.0

15,200.0–4,100.0

OTC sales at Post Offices
Amount to Public Sector

2,800.0
46,143.6

3,100.0
34,857.4

300.0–11,286.2

169,505.1

165,435.1–4,070.030-year Bonds
20-year Bonds
15-year Floating-rate Bonds
10-year Bonds
10-year Inflation-Indexed Bonds
5-year Bonds
2-year Bonds
Treasury Bills
Auction for Enhanced-liquidity
Subtotal
Non-price Competitive Auction II
Amount to the Market
JGBs for Individual Investors
Amount to Private Sector
Bank of Japan
Fiscal Loan Fund

TOTAL

(x)

(y)

(x)+(y)(b) – (a)Note
1: Figures may not sum up to the total because of rounding.
2: The amount of buy-backs will be 12,800 billion yen in FY2006 (5,500 billion yen fromthe Bank of Japan, 5,500 billion yen from the Fiscal Loan Fund and 1,800 billion yen
from the market).
3: The limit of interest-rate swap transactions will be 300 billion yen on the basis ofnotional principal for FY2005, and will be 1,200 billion yen for FY2006.
4: "Non-price Competitive Auction II" is estimated at 3% of the primary auction.
Source: Ministry of Finance “Planned Bond Issuance for FY 2006”

44

Table 2
Maturity Structure of JGBs in Fiscal 2003
C o m p o sitio n r atio
M atu r ity O u tstan d in g Issu an c e
Y e ar s bas isbasis
1
18.78%
36.25%
2
13.53%
15.86%
3
9.94%
4
11.22%
5
12.03%
16.23%
6
5.09%
7
4.79%
8
4.67%
9
5.03%
10
5.01%
22.00%
11
0.35%
12
0.91%
13
1.39%
14
1.64%
15
1.73%
4.81%
16
0.41%
17
0.64%
18
0.48%
19
0.75%
20
0.83%
3.78%
21
22
23
24
25
26
0.11%
27
0.16%
28
0.07%
29
0.20%
30
0.20%
1.07%

45