An Analysis of Government Bond Market and The New Stability Condition for the
Sovereign Bond Market
Naoyuki Yoshino
Professor of Economics,
Keio University
2-15-45 Mita Minato-ku Tokyo, 108-8345, Japan
[email protected]
and
Tetsuro Mizoguchi
Associate Professor of Economics,
Reitaku University 2-1-2 Kashiwa-shi, Chiba, 277-8686, Japan
[email protected]
1
Abstract
In traditional IS-LM analysis, bond market is dropped by Walras Law. Money
market was much more important than bond market during the days of Keynes
and Hicks. However, huge issue of government bond can be seen not only in Japan
but also in Europe and United States. The analysis of the bond market is becoming
much more important than before.
This paper focuses on the analysis of the bond market. When the government
bond marekt is analyzed, traditional research uses the governemtn budget
constraint which is a supply equation for the government bond.
Japan’s government debt to GDP ratio is much larger than Greece and Cyprus.
However, Greece and Cyprus went into bankcrupt and Japanese government bond
market is still sustained. The diffeence between the two is not coming from the
supply of government bond but the demand for government bond.
There are not so many papaers which focused on the bond market especially the
supply and the demand for government bonds. Analysis of the bond market will
cleary addresses the question of the stability of the bond market.
The desired level of government debt should rely on economic conditions so that
the target level should not be fixed at one single number, Instead it should be
changed year by year based on changes in economic activities. The same conclusion
will be obtained in the monetary policy. Recently Governor Kuroda is going to
achieve 2% rate of inflation as a target, however, this paper implicates that the
goal of the rate of inflation (say 2%) should vary from time to time based on
economic conditions.
JEL classification: E42, E63
Key Words: Bond Market,
2
Introduction
The paper analyses the government bond market by focusing on its demand and supply
in Japan. The JGB (Japanese Government Bond) market can be roughly separated into
three periods, namely, (i) the period of high economic growth (1950 to 1985), (ii) the
period of asset price bubble (1986 to 1990), and (iii) the period of economic downturn
after the burst of the bubble (post 1990). During the high economic growth period,
government investment had a strong positive output effect. The infrastructure
investment brought higher economic growth and it increased the tax revenue in the
medium and long run (Yoshino and Nakahigashi (2004). Indirect effect of infrastructure
investment increased the rate of return on private capital stock. It boosted economic
growth and tax revenue increased even further. The budget deficits were kept in lower
level in Japan.
During the period of asset price inflation of the late 1980s, Japanese tax revenue
increased and the budget deficits shrank remarkably.
However, the burst of the bubble brought the Japanese economy into slower growth.
Lower tax revenue and increased government spending due to ageing population
expanded Japan’s budget deficits.
Despite its huge budget deficits, Japanese economy is still sustained and the JGB
market is in calm. This paper will show that the demand for government bonds is
different from Japan and southern European countries such as Greece. High demand for
government bonds in Japan keeps JGB market in stable condition. However, it does not
guarantee the stability of the bond market in Japan.
The government spending rule and tax rule will be needed so as to achieve sustainable
bond market in Japan.
Previous analysis such as Domar (1944) and Bohn (1998,2005) use the government
budget constraint for the stability of the government bond market. Sustainability of
government bond in Japan can be explained by the demand for government bond rather
than the supply. The paper presents a new stability condition for the sustainable bond
market. An numerical example is added to the paper.
There are great concerns about the Japan’s accumulated deficits. As a result of years of
increased social welfare spending due to population ageing and the lower tax revenue
due to slower economic growth, the country's gross public debt went up to twice as
much as the size of its $5 trillion GDP.
In southern Europe, Greece and Cyprus’ budget deficits exploded and it went into
3
bankrupt. Rescue plans are discussed in Europe. Analysis of the bond market becomes
keen interest of various countries.
In traditional macroeconomics where Keynes and Hicks analyze goods market
(IS-market) and money market (LM-market). The bond market is dropped by Warlas’
Law. Thus the bond market was not explicitly analyzed in many literature. The supply
of government bond, namely the government budget constraint is introduced in
macroeconomic analysis (Carl Christ (1979), Blinder and Solow (1973), Yoshino
(1982)).
When Hicks initiated IS-LM analysis, money market and goods market were analyzed
since the deposit market (which is major part of money supply) was much more
important than bond market in those days. However an increase of government debt
addresses the importance of analyzing the bond market explicitly in macroeconomic
analysis.
The paper is constructed as follows.
Section 1 will explain an increase of government bonds in various countries.
Section 2 describes the supply of government bond and the demand for government
bond.
Section 3 constructs very simple macroeconomic model and proposes government
spending and tax revenue rule so as to achieve stability of the bond market.
Section 4 concludes the paper.
Section 1.
Bond Market of Selected Countries
Figure 1 depicts the debt to GDP ratio of selected countries. Japanese debt to GDP
ratio exceeds much higher than Greece and southern European countries. Japan’s gross
4
debt rose from 64% of GDP in 1991 to more than 200% in 2013.
<footnote, 1>
<Footnote 1>
Footnote 1, The figure 1^1 compares the grow debt to GDP ratio rather than net debt to
GDP ratio. The reason is that the net debt is defined as gross debt minus government
wealth. However, the computation of government assets seems not consistent from
country to country. For example, Japan’s government assets are over stated. There are
three bridges were constructed between main land of Japan and island of Shikoku.
These three bridges are not making profits, however the asset values are positive. Since
the value is computed based on how much costs were spent to construct three bridges.
The market value of three bridges might be below zero based on their daily use.
Therefore the gross debt to GDP ratio is used in the paper.
Figure 1.1 Gross debt/GDP ratio
Figure 1.1: Gross in selected OECD countries (source: OECD)
In figure 1.2 shows the ownership of government bonds in Japan. It shows that about
5
93% of JGBs are held by domestic investors such as commercial banks & post office
savings (42.7%), insurances (19.2%), pension funds (10.1%), the Central Bank of Japan
(12%) and households (2.5%). The Foreign Investors hold JGB only about 9%. In total,
about 91.3% of JGB is held domestically (figure 1.2).
Figure 1.2: Ownership of JGB in Japan 2012 (December) (Ministry of Finance, Japan).
Accumulated government debt now amounts to more than 200 percent of GDP and it
will be difficult to issue further unless the Central bank of Japan purchase JGBs.
6
Despite its huge budget deficits, Japanese economy can sustain the stability of the bond
market. This paper explains this puzzle. It lies in the demand for bond rather than the
government budget constraint.
Until 1965, a balanced budget policy is maintained in Japan. However the primary
balance gap increased at the time of the 1st oil shock in 1973 and 1974. According to
Ihori and Nakamoto (2005), the source of fiscal deficit divided into three factors: (i) the
social welfare program (in the first half of 1970s); (ii) the public investment (in the
second half of the 1970s); and (iii) the great reduction of tax revenues. At this time, the
policymaker such as Prime Minister Miyazawa (199?) believed that the Keynesian
fiscal policy was still effective like in the 1960s.
Japanese government significant reduced its accumulated deficit by introducing
exercise tax at 1986.1 However, after bubble burst (in 1991), the tax revenue decreased
significantly (figure 1?). As a result, bond-financing became a very important method to
financing in Japanese government spending. At 1991, the bond-dependency ratio was
lower (9.5%) but after 1991 the bond-dependency ratio increased upwards. At 2009, the
bond-dependency ratio attained the highest level (52%) (see in figure 1.2). Because of
the reduction of tax revenue and several stimulus economic policy packages, the deficit
of the general government balance is worsening. At 2013, the gross public debt hit over
200%, the highest level of OECD countries (figure 1.2). A comparison of these fiscal
situations between OECD countries indicates that the fiscal situation in Japan drastically
worsened at the beginning of 2000.
1
Yoshino and Mizoguchi (2010) classified this era as the asset bubble period and discussed the
bond-financing for the purpose of economic stimulus.
7
Figure 2.2: Government bond issues and bond dependency ratio (source: Ministry of
Finance)
There are several debt-raising factors in Japan. As we mentioned earlier, Japanese
government launched a series of economic stimulus packages in both 2008 and 2009.
For instance, Japanese government would distribute the cash benefits to all households
in part of the ¥26.9 trillion stimulus packages in 2008. Japanese government decided to
distribute ¥12,000 per person in principle while an extra ¥8,000 will be given for each
person 65 or older or 18 or younger. For the purpose of economic stimulus, this cash
benefit is not effective since in the economic downturn, people’s propensity of
consumption is not so high and therefore have tendency to save these cash benefit from
the government. According to Japanese government, the first three stimulus packages
would add 1% of GDP in 2009 and the fourth stimulus package extra 1.9% in 2009.2 In
OECD (2009), Chapter 3. From OECD’s observation, OECD indicates that the average value of
multiplier on series of economic stimulus packages’ spending is around one.
2
8
that sense, the quality of public investment in these government stimulus packages is
very important for the multiplier effect of public works.3
In addition, Japanese society becomes aging society and is suffering the birthrate
decline simultaneously. The government spending will increase to cover elders/retirees
rising medical bills and pension payment. Because of birth rate reduction, weak output
growth in the future makes it difficult to sustain the primary balance. Eastern Tohoku
region of Japan was hit by big earthquake and tsunami on March 11, 2011. Various
special spending to cope with the damage of the region, ??? amount of government
spending increased. Special tax hike was decided to cover some of the government
spending. New Prime Minister Shinzo Abe increased the government spending much
further to enhance economic activities of Japan. .
Figure 2.4 shows the components of FY2010 Budget (general accounts) in Japan. In
general expenditure (57.9%), the social security expenditure (29.5%) is highest because
of aging population. Second highest is public works (6.3%), education and science
(6.1%), National Defense (5.2%). 18.9% of total expenditure is Local allocation tax
grant. Notice that 22.4% of total expenditure is National Debt service. From this
observation, it is important for Japanese government to implement the fiscal
consolidation since the interest payment for bond is also uprising (figure 2.5, 2.6).
- Insert Government Spending
3
See Yoshino and Nakahigashi (2004). Yoshino and Nakahigashi (2004) investigate the relation
between social capital stock and economic growth by estimating the productivity effect of social capital
stock after WWII in Japan. They find that during the high economic growth period, the productivity of the
social capital stock in Japan keeps a high level. However since 1970, because of structural change, it
becomes to a low level standard. From the market quality theory advocated by Yano (2009), we apply
Yano’s view to the effective evaluation scheme of the effective public investments.
9
Fortunately, the decline in the interest payments makes the budget deficit and public
debt not hiked up more. According OECD (2009), gross interest payment fell from 16.8
trillion yen in 2000 to 13.31 trillion yen in 2008 in spite of the increase in public debt.
Notice that the fall in long-term interest rates. The long-term interest rates stay at a low
level. There are several reasons: Japan has so much domestic savings, which are
original funds to keep JGB within Japan. As mentioned earlier, most of JGB is held by
both public and private institutions domestically. Especially, from the point of asset
balance, private institutional investors such as pension funds, insurance companies and
banks are willing to held JGB. Why do institutional investors facilitate JGB holdings?
There are two main reasons: Being introduced to the BIS regulation, the self-capital
ratio of banks is composed of the sound (less-risky) asset. After the bubble burst, banks
promote the JGB holdings more in order to protect their asset devaluation during the
deflation period. In addition, the recent financial crisis caused in a movement to safer
asset, such as JGB, pressure down the interest rate on government bonds in Japan. As a
result, the interest rate of JGB continues to be relatively lower level in Japan (figure ?)
10
.
Figure 2.7: Interest rate by the government (source: Ministry of Finance (2013))
11
Figure 2.8: Gross interest payment (source: OECD (2009))
3. Related Literature
There is substantial numbers of research concerning fiscal sustainability conditions of
the government budget constraint. The sustainability of public debts can be examined
from the government budget constraint in the fiscal policy literature. Most of the fiscal
sustainability conditions are tested by unit root and cointegration test whether time
series are consistent with an intertemporal government budget constraint. For example,
Hamilton and Flavin (1986), Trehan and Walsh (1988,1991), Wickens and Uctum
(2000) investigate whether the public debt series is difference-stationary or whether the
revenue and spending series are cointegrated or not in order to satisfy the intertemporal
government budget constraint. Based on these tests, Bohn (1998) proposed a different
fiscal sustainability test, which estimates transversality condition. He found that an
increase in the ratio of government deficit to GDP increased the ratio of primary surplus
to GDP from 1916 to 1995 in U.S. He concluded that U.S. fiscal policy glutted an
12
intertemporal budget constraint. Bohn (2005) also examines the sustainability of U.S.
fiscal policy, by using the U.S. fiscal record from 1792-2003, critically review
sustainability conditions and their testable implications, and apply them to U.S. data.
particularly emphasize the ramifications of economic growth. A "growth dividend" has
historically covered the entire interest bill on the U.S. debt. Unit root tests on real series,
unscaled by GDP, are distorted by the series' severe heteroskedasticity. The most
credible evidence in favor of sustainability is the robust positive response of primary
surpluses to fluctuations in the debt-GDP ratio.
For Japanese cases, there are also substantial empirical studies on this issue. Fukuda and
Teruyama (1994) applied the method of Hamilton and Flavin to do empirical test for
no-Ponzi Game condition that is equivalent to the intertemporal budget constraint.
Other studies such as Ihori et al (2001) also investigate the macroeconomic impact of
government debt and the sustainability problem in Japan by using the dynamic game
among interest groups. They also test their model empirically by applying Bohn’s
sustainability condition to Japanese economy. Yoshino and Mizoguchi (2010)
investigate the role of Liberal Democratic Party on the field of public expenditure. In
our previous work, the spending initially fueled Japan's rapid postwar growth and kept
the LDP in power for most of the last half-century. Although after a bubble burst in
1990, the country fell into a long economic malaise, called "lost decade". Considering
the current JGB circumstances in Japan, we introduces the stability condition for
government bond market by taking account of supply by the government and demand
for government bond by financial institutions.
For theoretical studies, Kondo (2007) construct a dynamic general equilibrium model to
examine the equilibrium dynamics of government debt. He shows that the no Ponzi
game condition in his dynamic general equilibrium model is satisfied with the
intertemporal government budget constraint and the determinants of the limitation level
is primary balance, money supply etc. Ito and Hoshi (2012, NBER paper) uses
simulation method to see whether Japan’s budget deficits are sustainable and conclude
that Japan’s fiscal situation is in dangerous zone.
Previous analysis such as Bohn (1998,2005) only uses the government budget
constraint for the stability of the government bond market. In our model, fiscal
sustainability of government bond in Japan can be explained by the demand for
government bond rather than the supply. We consider this reality. Our paper presents a
new stability condition for the bond market.
13
Mathematical Model
The paper describes the equation of both the Government Bond Supply and the Government
Bond Demand based on the model set by Yoshino and Mizoguchi (2010, 2013). Our model is
summarized as follows:
𝐺𝑡 + 𝑟𝑡 𝐵𝑡−1 = Δ𝐵𝑡 + 𝑇𝑡
government bonds
Government Budget Constraint=Supply of
(1)
The disposable income is defined as income (𝑌𝑡 ) plus government transfer to households (𝜃𝐺𝑡 )
plus interest receipt of government bond (𝑟𝑡 𝐵𝑡−1 ) by households minus tax payment (𝑇𝑡 ) as
follows. The disposable income is divided into consumption (𝐶𝑡 )and savings (𝑆𝑡 )
𝑌𝐷𝑡 = 𝑌𝑡 + 𝜃𝐺𝑡 + 𝑟𝑡 𝐵𝑡−1 − 𝑇𝑡 = 𝐶𝑡 + 𝑆𝑡
where 𝑆𝑡 = Δ𝐵𝑡 + Δ𝑊𝑡𝐷 − ∆𝑊𝑡𝐹
(2)
Savings(𝑆𝑡 )=Government bonds(Δ𝐵𝑡 )+Domestic Deposits(Δ𝑊𝑡𝐷 )–Foreign assets(∆𝑊𝑡𝐹 )
̅𝐹
∆𝑊𝑡𝐹 = ∆𝑊
Foreign assets are assumed to be constant
𝐶𝑡 = 𝑐0 + 𝑐1 𝑌𝐷𝑡
Consumption Equation
(4)
𝑊𝑡𝐷 = 𝑑0 + 𝑑1 𝑌𝐷𝑡 − 𝑑2 𝑟𝑡
Deposit Equation
(5)
(3)
From equations (2)-(5), the demand for government bonds can be obtained as follows.
𝐷
𝐵𝑡 = (1 − 𝑐1 − 𝑑1 )(𝑌𝑡 + 𝜃𝐺𝑡 − 𝑇𝑡 ) + (𝑑2 + (1 − 𝑐1 − 𝑑1 )𝐵𝑡−1 )𝑟𝑡 + 𝐵𝑡−1 + 𝑊𝑡−1
+
̅ 𝐹 − 𝑐0 − 𝑑0 ) (6)
(∆𝑊
By using equation (1) and (2), we obtain temporally equilibrium as follows:
𝑟𝑡 = (𝑐
1
1 +𝑑1 )𝐵𝑡−1 −𝑑2
𝐷
̅ 𝐹 + (𝑐1 + 𝑑1 )𝑇𝑡 + (1 − 𝜃 + (𝑐1 +
[(𝑐1 + 𝑑1 − 1)𝑌𝑡 − 𝑊𝑡−1
− ∆𝑊
𝑑1 )𝜃)𝐺𝑡 + (𝑐0 + 𝑑0 )]
(𝑐 +𝑑 −1)𝐵𝑡−1
] 𝑌𝑡
1
1 𝑡−1 −𝑑2
𝐵𝑡 = [(𝑐 1+𝑑 1)𝐵
𝐵𝑡−1
] (𝑐0
+𝑑
1
1 )𝐵𝑡−1 −𝑑2
[(𝑐
(7)
+ 𝐵𝑡−1 + [1 +
(1−𝜃+(𝑐1 +𝑑1 )𝜃)𝐵𝑡−1
] 𝐺𝑡
(𝑐1 +𝑑1 )𝐵𝑡−1 −𝑑2
𝐷
̅ 𝐹 ) (8)
+ 𝑑0 −𝑊𝑡−1
− ∆𝑊
14
𝑑2
] 𝑇𝑡
+𝑑
1
1 )𝐵𝑡−1 −𝑑2
+ [(𝑐
+
and in the long run, we can obtain steady state level of the government bond and interest rate be
setting Δ𝐵𝑡 = 0.
̅̅̅
𝐵𝑡 =
𝑑2 (𝑇̅−𝐺̅ )
𝑓
̅ 𝐹 −(𝑐0 +𝑑0 )
(1−𝑐1 −𝑑1 )𝑌𝑡 −(1−𝜃)(1+𝑐1 +𝑑1 )𝐺̅ +̅̅̅̅̅
𝑊 𝐷 +𝑊
is the long-run equilibrium level of
government debt. (9)
𝑟̅𝑡 =
̅ 𝐹 −(𝑐0 +𝑑0 )]
(𝑇̅−𝐺̅ )[(1−𝑐1 −𝑑1 )𝑌𝑡𝑓 −(1−𝜃)(1+𝑐1 +𝑑1 )𝐺̅ +̅̅̅̅̅
𝑊 𝐷 +𝑊
𝑑2 𝑇̅−𝑑2 𝐺̅
is the long-run equilibrium level of
interest rate. (10)
Revised Domar condition and the Bohn’ condition combining with the bond market
The Domar condition and the Bohn’s condition are often used to determine whether budget
deficits are sustainable or not.
The Domar condition is obtained from government budget constraints as follows.
𝐺𝑡 + 𝑟𝑡 𝐵𝑡−1 = Δ𝐵𝑡 + 𝑇𝑡 Government budget constraint
(11)
Equation (10) states that government spending (𝐺𝑡 ）＋interest payments （= 𝑟𝑡 𝐵𝑡−1 ）
＝new issue of government bonds（Δ𝐵𝑡 ）＋tax revenue（𝑇𝑡 ）
Divide Equation (11) by GDP (𝑌𝑡 ) and rewrite Equation (11)
𝑏𝑡 − 𝑏𝑡−1 = (𝑟𝑡 − 𝜂𝑡 )𝑏𝑡−1 + 𝑔𝑡 − 𝑡𝑡 The Domar Condition
(12)
where 𝑏𝑡 = 𝐵𝑡 ⁄𝑌𝑡 , 𝜂𝑡 = ∆𝑌𝑡 ⁄𝑌𝑡 , 𝑔𝑡 = 𝐺𝑡 ⁄𝑌𝑡 , and 𝑡𝑡 = 𝑇𝑡 ⁄𝑌𝑡
If 𝑟𝑡 > 𝜂𝑡 then 𝑏𝑡 will become larger and larger, namely the budget deficits explode.
If 𝑟𝑡 < 𝜂𝑡 then 𝑏𝑡 will become small and smaller namely the budget deficits converge.
𝑏𝑡 − 𝑏𝑡−1 = (𝑟̅𝑡 − 𝜂̅𝑡 )𝑏𝑡−1 + 𝑔𝑡 − 𝑡𝑡
where
𝐷 )
𝜂̅𝑡 = 𝑌𝑡 − 𝑌𝑡−1 ⁄𝑌𝑡−1 = (𝑇𝑡 − 𝜃𝐺𝑡 + 𝐶𝑡 + Δ𝑊𝑡𝐷 )⁄(𝑇𝑡−1 − 𝜃𝐺𝑡−1 + 𝐶𝑡−1 + Δ𝑊𝑡−1
−1
If the equilibrium bond interest rate is bigger than the GDP growth rate, the government
debt will explode. Therefore, the government cannot maintain the fiscal sustainability. Since
previous studies of fiscal sustainability did not include the bond market, the interest rate and
GDP growth rate is not endogenized (Burnside (2005)). In contrast to these studies, our model
includes the market structure into the interest rate and GDP growth rate.
15
If we regard the long-run interest rate given by (9) and GDP growth rate is constant, we can
derive the stock level of bond at time T
𝑏𝑇 = ∑𝑇𝑡=1 {(
1+𝑟̅𝑡 𝑇−𝑡
)
̅̅̅
1+𝜂
𝑡
(𝑔𝑡 −𝑡𝑡 )} + (
1+𝑟̅𝑡 𝑇
) 𝑏0
(13)
̅̅̅𝑡
1+𝜂
where 𝑟̅𝑡 is the long-run interest rate considering the bond demand. We denote that 𝑟̅𝑡 =
̅ 𝐹 −(𝑐0 +𝑑0 )]
(𝑇̅−𝐺̅ )[(1−𝑐1 −𝑑1 )𝑌𝑡𝑓 −(1−𝜃)(1+𝑐1 +𝑑1 )𝐺̅ +̅̅̅̅̅
𝑊 𝐷 +𝑊
.
𝑑2 𝑇̅−𝑑2 𝐺̅
We can also rewrite the equation (13) as:
1+𝑟̅𝑡 𝑇
̅̅̅ 𝑡
1+𝜂
) [∑𝑇𝑡=1 {( 1+𝑟̅𝑡) (𝑔𝑡 −𝑡𝑡 )} + 𝑏0 ]
̅̅̅
1+𝜂
𝑏𝑇 = (
𝑡
(14)
𝑡
If the GDP growth rate is larger than the long-run interest rate, the fiscal deficit can grow out in
the long-run. If the Domar Condition satisfies, the No Ponzi Game (NPG) condition ( lim 𝑏𝑇 ≤
𝑇→∞
0) is automatically fulfilled. The NPG condition means that the fiscal deficit becomes to either
̅̅̅ 𝑡
1+𝜂
𝑡
zero or minus. Otherwise if the following condition (∑∞
𝑡=1 {( 1+𝑟̅ ) (𝑡𝑡 −𝑔𝑡 )} ≥ 𝑏0 ) is satisfied,
𝑡
the NPG condition is fulfilled.
Notice that when the NPG condition is fulfilled with the equality, the NPG condition becomes to
the transversality condition where the current deficit is equal to the present value of the primary
balance.
The Bohn’s Condition (1998): To Check the Stability of Budget Deficits
The Bohn’s condition can be obtained as follows.
𝑃𝐵𝑡 = 𝑔𝑡 − 𝑡𝑡 Primary Balance of Public Finance（PB）
(15)
𝑃𝐵𝑡 = 𝑃𝐵1 + 𝜇(𝑏𝑡−1 − 𝑏0 ) Primary Balance Improvement Rule in Period t
(The Bohn’s Condition） (16)
where 𝜇 > 0, the Bohn’s condition in Equation (15) describes that the primary balance must
improve based on an increase in the levels of debt/GDP ratio (𝑏𝑡−1 − 𝑏0 ). In other words,
either a reduction of government spending or an increase in tax revenue based on an increase in
the level of government debt/GDP will lead to the stability of budget deficits.
Then we recursively solve this Equation (15). We obtain:
16
𝑏𝑇 = ∑𝑇𝑡=1 {(
1+𝑟̅𝑡
̅̅̅𝑡
1+𝜂
− 𝜇)
𝑇−𝑡
(𝑔𝑡 −𝑡𝑡 )} + (
𝑇
1+𝑟̅𝑡
̅̅̅𝑡
1+𝜂
− 𝜇) 𝑏0
(17)
For simplicity, we define the long-run interest rate / GDP growth rate,
−𝑃𝐵1 −(1−𝜇)𝑏0
𝑏𝑇 = (𝜆 − 𝜇)𝑇 (
𝜆−𝜇−1
−𝑃𝐵1 +𝜇𝑏0
)−(
𝜆−𝜇−1
)
1+𝑟̅𝑡
̅̅̅𝑡
1+𝜂
= 𝜆. We obtain
(18)
Now we show the Bohn’s condition satisfies the following transversality condition:
𝑃𝐵
𝑡
∑∞
𝑡=1 (𝜆)𝑡 = 𝑏0
(19)
By using the relationship (18), the left hand side of the transversality condition can be rewritten
as:
𝑃𝐵
𝑃𝐵1 −𝜇𝑏0
(𝜆)𝑡
𝑡
∞
∑∞
𝑡=1 (𝜆)𝑡 = ∑𝑡=1 [
−𝑃𝐵1 −(1−𝜇)𝑏0
(
𝜆−𝜇−1
𝜇
+
𝜇(𝜆−𝜇)𝑡−1 −𝑃𝐵1 −(1−𝜇)𝑏0
𝜇
−𝑃𝐵1 +𝜇𝑏0
( 𝜆−𝜇−1 ) − (𝜆)𝑡 ( 𝜆−𝜇−1
)]
(𝜆)𝑡
−𝑃𝐵1 +𝜇𝑏0
) − 𝜆−1 (
𝜆−𝜇−1
) = 𝑏0 .
=
𝑃𝐵1 −𝜇𝑏0
𝜆−1
+
(20)
So the transversality condition is satisfied under the Bohn’s rule.
Figure shows the trend of the long-term interest rate and nominal GDP growth rate in Japan. As
you can see in the figure especially from year 2003 to 2009, both long-term interest rate and
nominal GDP growth rate is approximately co-moving . Figure shows that the rate of interest
exceeds the growth rate of the economy. It suggests that Japanese budget is on an unstable path,
based on the Domar condition. Applying the Domar condition and the case studies of Polito and
Wickens (2007), the data shows that the unstable case of the stability condition of
bond-financing in Japan. In comparison to the stability condition such as Bohn (1998) and other
studies , our model considers the bond market structure. Since both the interest rate and bond
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supply and demand are endogenized in our model, we can investigate the stability condition
based on the each economic variable in the economy.
Reference
Bohn, H. (1998): “The Behavior of US Public Debt and Deficits,” Quarterly Journal of
Economics, 113:3, 949-963.
Domar, Evsey D., (1944) "The Burden of the Debt and the National Income," American
Economic Review, 34(4), pp.798-827.
Hatano, E (2010): The Economic Analyses of Public Debt and Public Finance Management –
From the Fiscal Sustainability and Nationwide burden, Yuhikaku (in Japanese).
Hoshi, T. and T. Ito (2012), “Defying Gravity: How Long will Japanese Government
Bond Prices Remain High?”, NBER Working Paper Series 18287, National Bureau
of Economic Research.
Nakazato, T. (2011): “The Bond Market and Fiscal Balance an Analysis of Public Subscription
Local Government Bonds,” The Japanese Economy, 38:1, 59-80.
Sakuragawa, M. and K. Hosono (2010): “Fiscal Sustainability of Japan:A Dynamic Stochastic
General Equilibrium Approach, ” Japanese Economic Review, 61:4, 517-537.
Yoshino, N and M. Nakahigashi, “The Role of Infrastructure in Economic Development”, The
ICFAI Journal of Managerial Economics, Vol.9, No.2, May 2004.
Yoshino, N. and T. Mizoguchi (2010): “The Role of Public Works in the Political Business
Cycle and the Instability of the Budget Deficits in Japan,” Asian Economic Papers, 9:1, 94-112.
Yoshino, N., (2011) “Growing Budget Deficits and Sustainability: Why is Japan still
sustainable ?” APEC SME Economic Crisis Monitor, July-2011 Issue, 5-6.
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