Fiscal sustainability in Japan∗

Masaya Sakuragawa and Kaoru Hosono ∗∗Abstract
We investigate fiscal sustainability of Japan by providing a dynamic stochastic generalequilibrium (DSGE) model that features low interest rates of government bonds relative
to the economic growth rate. We evaluate sustainability by testing whether the expecteddebt-to-GDP ratio stabilizes or increases without bound. The simulated debt-to-GDP
ratio depends on the intermediation cost, the elasticity of intertemporal substitution, theprojected growth rate, and on the specified fiscal policy rule. If the fiscal policy ruleestimated over the past 30 years goes over in the future, the debt-to-GDP ratio will
increase without bound, and in this sense the fiscal policy is not sustainable. We
investigate alternative fiscal policy rules to avoid possible fiscal insolvency.

∗

We are grateful to Takero Doi, Toshihiro Ihori, Eric Leeper, Shin-ichi Fukuda, andparticipants at the TRIO conference and seminars held at Hitotsubashi and Keio University.
∗∗* Keio University, Mita 2-15-45, Minato-ku, Tokyo, 108-8345, 81- 03-5427-1832,

masaya@econ.keio.ac.jp, ** Gakushuin University, kaoru.hosono@gakushuin.ac.jp,

11. Introduction
Whether government debt is sustainable in Japan has become a great concern.
Japan’s government debt outstanding is close to the double of annual GDP, which is thehighest among the developed countries and in its own post-WWII history. Though theJapanese government (Cabinet Decision, 2010) declared its target at turning fromprimary deficit to primary surplus by 2020 and lowering the debt-to-GDP ratio from2021, the weak economic recovery and unstable political situations are undermining its
feasibility and credibility. We investigate the sustainability of Japanese government
debt under the fiscal policy observed in the past thirty years and some alternative policy
rules.
Investigating fiscal sustainability, however, entails facing a puzzling fact. Interest
rates on government bonds have remained quite low relative to the economic growthrate in Japan. Figure 1 illustrates the time series of the Financial bill rate, the interest
rate of the long-term bond, and the economic growth rate for the period of 1981–2009.
All figures are measured in real terms in terms of GDP deflator. The averages of thelong-term bond and the Financial bill rates are 3.6 percent and 1.9 percent, respectively,
while the average of the growth rate is 2.2 percent.
With the annual discount factor that is extensively used in the business cycle
literature (namely, 1 / 1 .03 , e.g., Christiano and Eichenbaum, 1992 and Christiano, et al,2005),

both the exogenous growth model and the endogenous growth model with2

log-utility predict that the interest rate should be 3 percent above the growth rate.
Understanding a “low” interest rate is crucial to investigating fiscal sustainability.1
To account for low interest rates of government bonds, we provide a dynamic
stochastic general equilibrium (DSGE) model incorporating financial friction and theheterogeneity in the access to production among agents (e.g., Woodford, 1990 and Bohn,
1999). The introduction of the intermediation cost gives rise to declines in both theeconomic growth rate and the interest rate of government bond, allowing the model tomimic the actual data with the gap increasing or decreasing depending on the elasticity
of substitution on consumption. If the elasticity is nearly less than 2, the intermediation
cost decreases the gap, and hence improve sustainability.
We evaluate sustainability by testing whether the debt-to-GDP ratio stabilizes orincreases without bound. The simulated debt-to-GDP ratio depends on theintermediation cost, the elasticity of intertemporal substitution of consumption, theprojected growth rate, and the specified fiscal policy rule. Of particular importance isthe elasticity of intertemporal substitution. Our estimate is within the range over which
the high intermediation cost leads to a decline in the gap between the growth andinterest rates, contributing to the improvement of fiscal sustainability. At least as for theJapanese case, our approach that explains low interest rates imposes a looser condition
on sustainability than the standard model otherwise.
The specification of the fiscal rule is crucial to evaluate fiscal sustainability. If the
fiscal rule that has been adopted over the past thirty years goes over in the future, the1This tendency is common to many countries. The average realized real rates of return on

government bonds in major OECD countries over the past 30 years have been smaller than thereal growth rate (e.g., Blanchard and Weil, 2001).

3

expected debt-to-GDP ratio would reach 11.5 in 100 years and afterwards would
continue to grow unboundedly. The probability that the debt-to-GDP ratio will diverge
is greater than 50 percent in 20 years and later, and we have to judge that the Japanese
fiscal policy is not sustainable. If the fiscal rule incorporates Bohn’s idea that a rational
government should increase the primary surplus when the debt-to-GDP ratio is high,sustainability improves.
We do not rely on the risk-premium approach to explain low interest rates for two
reasons (e.g., Mehra and Prescott, 1985, and Weil, 1989).2 First, this approach explains
only the low interest rate of the safe bond but does not explain low rates of thegovernment bonds as a whole. Secondly, as the literature on the “risk-free rate puzzle”(e.g., Weil, 1989) points out, classes of simple utility functions do not explain the lowinterest rate within admissible parameter values.
This paper contributes to the literature on methodology to test fiscal sustainability.
We do not use the approach of checking the intertemporal government budget constraint
in two respects. First, the latter approach constitutes only a necessary condition forsustainability. Secondly, in the presence of intermediation costs, among various menusof government bonds, any interest rate and/or their combination is not appropriate fordiscounting the future correctly.

2

Abel et al. (1989) and Bohn (1995) provide stochastic growth models in which the risk

premium drives down the safe interest rate, often below the economic growth rate. Theirargument demonstrates that the no-Ponzi condition for the intertemporal government budget
constraint holds, even if the safe interest rate is below the growth rate.

4Hamilton and Flavin (1986), Ahmed and Rogers (1995), and others use theapproach of investigating the intertemporal government budget constraint.3 Bohn
(1995) criticized this approach for the reason that safe government bonds do not reflectcorrect discounting. Observing the lower interest rates of the US government bondrelative to the growth rates in many periods, Bohn (1998) proposed a simple test to
check whether the debt-to-GDP ratio displays a mean-reversion property.4 Ball et al.
(1998), in their famous paper entitled “Deficit Gamble,” projected future growth rates
and interest rates from past data and calculated the probability under which thedebt-to-GDP ratio would enter a dangerous zone. Our approach is similar to the latterapproach. In our model, when there is a significant intermediation cost, the government
can run the Ponzi strategy, but even then, if the debt-to-GDP ratio is constant, the fiscal
policy is sustainable.
Recently, some literature has studied fiscal sustainability by applying a dynamic
stochastic general equilibrium (DSGE) model. Mendoza and Oviedo (2004, 2006)
develop small open economies to investigate how macroeconomic shocks affectgovernment finances and estimate the amount of sustainable public debt in emerging
market economies. Arellano (2008) also develops a small open-economy model to study
sovereign default risk and its interaction with output and foreign debt. Sakuragawa and3

Other works include Wilcox (1989), Trehan and Walsh (1991), Hakkio and Rush (1991),,

Uctum and Wickens (2000), and Polito and Wickens (2005).
4

Bohn (2005) applies his test to the historical data of the US and finds evidence supporting

fiscal sustainability (see also Greiner and Kauermann, 2007). Mendoza and Ostry (2008) apply
Bohn’s test to industrial and emerging countries and finds evidence of fiscal solvency in bothtypes of countries. Galí and Perotti (2003) and Wierts (2007), among others, apply Bohn’s test
to European countries.

5

Hosono (2009) develop a closed economy model of an exchange economy to test fiscal
sustainability of the Japanese economy. In the present paper, we extend their model byincorporating the AK-type production technology, which enables us to investigate theeffect of the financial intermediation cost on the growth-interest rate relationship. We
also expand the range of fiscal policy rules that we simulate, based on the observed ruleover the last thirty years.!Sakuragawa et al (2010) use a closed economy model of a
production economy to test fiscal sustainability of the US.
This paper is also related to the theoretical literature that combines financial
frictions with the heterogeneity in the access to production among agents to have
implications for the lower interest rate than the growth rate. The literature includes
Woodford (1990), Bohn (1999), Kiyotaki and Moore (2008), Hellwig and Lorenzoni(2009) and Kocherlakota (2009).
This paper is organized as follows. In Section 2, we outline the model. In Section 3,
we develop the theoretical analysis. In Section 4, we describe the simulation procedure.
In Section 5, we investigate the sustainability of the Japanese public debt.!Section 6
concludes.

2. ModelConsider an economy made up of two types of agents that live infinitely, with thenumber of each normalized to be unity, and the third type of agents that live for two

6periods and act as intermediaries. We consider heterogeneous agents and financial
friction in order to provide implications for low interest rates.5
Type E agents have access in all even periods to an AK production technology thattransforms K t units of the final good into random (1 + xt +1 ) Kt units after one period,
while type O agents have access in all odd periods. Two reasons motivate theintroduction of the AK model. First, fiscal sustainability is a long-run problem. Second,
the AK model enables one to have the positive link between interest and growth rates
that is observed in the time series. The rate of return on capital, xt +1 , is a random variable
that follows a Markov process and takes values in a set, X t . The history of theeconomy up to time t is denoted by ht = ( xt , xt −1 , …), which takes values in a set H t .
Denote the probability of a variable, xt +1 , given a history ht , by π ( x ht ) .
To simplify the notation, let there be one representative agent of each type so thatthe individual income (1 + xt +1 ) Kt denotes the aggregate income. There is no population
growth. Both types have identical preferences over consumption and maximize
Ct1−α , where
α is the inverse of the elasticity of substitution of consumptions
E0 ∑ β
1−α
t =0
∞

t

across periods, β (0< β <1) is the discount factor, and E0 is the expectation operator.
We impose the relevant condition on bounded utility by Et {β (1 + g t +1 )1−α } < 1 , where

gt is the growth rate of the aggregate income argued below. The government spending,5

Aiyagari and Gertler (1991) and Heaton and Lucas (1996) construct models withintermediation costs and heterogeneous agents.

7

Gt , is a constant share of GDP to meet Gt = zYt . The government finances its spendingby imposing lump-sum taxes Tt and by issuing public debt.
At each period, finite N agents who act as intermediaries are born and live for two
periods. They are endowed with a specific skill of intermediating finance between
private agents, and maximize the second-period consumption less the amount of effort
exerted by them.
We introduce financial friction by supposing that these agents have to bear a
proportional intermediation cost, κ > 0 , per unit of funds. The cost is measured in termsof the loss of effort. One may interpret κ as a cost of monitoring or identifying aborrower, or of verifying credit.

3. Theoretical Analysis
The intermediary issues securities that request the rate of repayment rtb to firms andguarantee the rate of return rt to investors. In a world of competitive intermediation,intermediaries finally have to earn zero profit to satisfy(1)(1 + rt )(1 + κ ) = 1 + rtb

for any xt . Note that both assets are risky in the sense that the rate of return depends on
the productivity. We take an approach of the incomplete bond market where the8government can issue only one-period bonds and private agents cannot insure away the
income uncertainty.6
At the beginning of an even period t , type E agents face a shock xt , receive
capital income (1 + xt ) Kt −1 , repay (1 + rtb ) Bt −1 , consume Ct , pay taxes Tt , and invest
the remaining in the private security Wt and the public bond Dt . They maximize thefollowing value function:
(2)

Ct1−α
+ β ∑π (xt +1 ht ) V~(Wt , Dt , xt +1)
V ( Bt −1 , Kt −1, xt ) = max
Ct ,Wt , Dt 1 − α
xt +1∈X t +1

subject to the budget constraint(3)(1 + xt ) K t −1 − (1 + rtb ) Bt −1 = Ct + Wt + Dt + Tt .

On the other hand, at period t , type O receives interest incomes from the private
security (1 + rt )Wt and the public bond (1 + Rt ) Dt −1 , and transfers Πt from~intermediaries. They consume Ct and invest the remaining in capital to produce in theodd period. They maximize the following value function:~ 1− α(4)Ct~
V (Wt −1, Dt −1, xt ) = c~max
,K ,B
t

t

t

1−α

+β

∑ π (xxt + 1∈ X t + 1

t +1

ht ) V ( Bt , Kt , xt +1 )subject to
(5)

6

~
Πt + (1 + rt )Wt −1 + (1 + Rt ) Dt −1 + Bt = Ct + Kt ,Some studies cast doubts on the presence of complete bond markets. For example, Marcet andScott (2009) find the persistency of the data for the US government debt, which is supportive of
incomplete markets but is inconsistent with complete markets

9where Rt is the interest rate on the government bond, and Πt (≡ κ (1 + Rt )Wt −1 ) is theintermediary’s profit that is transferred to them. The intermediary is compensated forthe loss of effort by income, but the income accruing to the intermediary is transferred
to households in a lump-sum fashion.
Assume that the equilibrium has an interior solution. Equilibrium conditions on

Kt +1 , Wt +1 , Bt +1 , and Dt +1 , together with envelope conditions, lead to∑ π ( xt +1 ht )(1 + xt +1 )~{C ( ht )}α{C ( xt +1 ht )}α

(6)

1= β

(7)

1= β

∑ π ( xt +1 ht ){1 + r ( xt +1 ht )} ~1= β

∑ π ( xt +1 ht ){1 + R ( xt +1 ht )} ~(8)

x t +1 ∈ X t +1

{C ( ht )}α{C ( xt +1 ht )}αx t +1 ∈ X t +1~
{C ( ht )}α
1 = β ∑ π ( xt +1 ht ){1 + r b ( xt +1 ht )},{C ( xt +1 ht )}αx t +1 ∈ X t +1

and
(9)

x t +1 ∈ X t + 1{C ( ht )}α.
{C ( xt + 1 ht )}αThe market clearing in the good market is expressed as(10)~
Ct + Ct + Kt + zYt = (1 + xt ) Kt −1 .

The market clearing in the credit market is expressed as(11)

Wt = Dt .

Finally, the government’s budget constraint is given by(12)

Dt = (1 + Rt ) Dt −1 − Tt + Gt .

As has been suggested by Barro (1979), Kremers (1989), and Bohn(1991), we impose
an additional feasibility constraint restricting the government’s taxable income to belimited to some fraction of the aggregate income. We simply call a fiscal policy feasible
if the tax revenue does not exceed a fraction τ of GDP, that is,
10

(FC)

Tt ≤ τYt

at any time and at any state s .
The competitive equilibrium is defined as a sequence of nine variables!

~
Ct +1 Ct +1 Kt +1 Wt +1 Bt +1 Dt +1
{
,~ ,
,
,
,
, rt , rtb , Rt }t∞=0 , satisfying nine equations (1), (3),(6)–(12),Ct Ct +1 Kt Wt Bt Dt(FC), and relevant non-Ponzi-game (NPG) conditions, given the sequence of randomvariables {xt }t∞=0 and the sequence of the policy rule {Tt , Dt }t∞=0 , and given K 0 and D0 .
The fact that two-period-lived intermediaries have no intertemporal consideration
simplifies the link among several interest rates. As for the link between xt and rtb ,bcompetitive intermediation should lead to xt = r ( xt ) for any xt . Jointly with (1), theinvestors’ rate of return rt should also be dependent on xt to satisfy
rt = (1 + r b ( xt )) (1 + κ ) − 1 ≡ r ( xt ) . Equations (6) and (8) imply that the private security

issued by the intermediary and the government bond are perfect substitutes for investors
so that, without loss of generality, we may set R( xt ) = r ( xt ) for any xt . We haveR( xt ) < r b ( xt ) ; the government can borrow at a lower rate than private agents. The
reason behind this finding is that loans to the government can be monitored with no cost,
while loans to private agents need intermediation cost.
We use these features on several interest rates to argue on the non-Ponzi-game(NPG) conditions that formalize the limited willingness of agents to lend. The NPG
condition for agents who have access to production at the current period and those whohave no access are, respectively,
11

(NPG1)

Et lims →∞K t + s − Bt + s= 0,(1 + r )(1 + rt + 2 )(1 + rtb+3 )...
b
t +1

and

(NPG2)

Wt + s + Dt + s=0.
s → ∞ (1 + r )(1 + r b )(1 + r )...
t +1
t +2
t +3

Et lim

We assume that both conditions are satisfied. The agent alternates between a lender anda borrower every other period and discounts the future at rate

(1 + rt )(1 + rt b+1 ) − 1 (or(1 + rt b )(1 + rt +1 ) − 1 ).

We investigate sustainability conditions for the fiscal policy. We argue that
evaluating sustainability in terms of the intertemporal budget constraint is not
appropriate in two respects. First, when agents discount the future at a higher rate than
the government, checking the government budget constraint does not establish acondition for sustainability. The discounted value of debt that the government can earn
by a Ponzi strategy is(PG)

Dt + ss → ∞ (1 + R )(1 + R
t +1
t + 2 )...(1 + Rt + s )...

Et limwhich is derived from the government budget constraint. On the other hand, thegovernment cannot run a Ponzi strategy so long as agents do not find it optimal to be on
the lending side of the Ponzi scheme. The latter condition is expressed as
Dt + s= 0 , which is a weaker condition than the one unders → ∞ (1 + r )(1 + r b )(1 + r )...
t +1
t +2
t +3

Et limwhich (PG) converges to zero since, by using (1) and rt = Rtb , we rewrite the agent’s
NPG condition as
12(NPG3)

Dt + s= 0.
s → ∞ (1 + κ )(1 + Rt +1 )(1 + Rt + 2 )...(1 + Rt + s )...

Et lims 2

Secondly, even checking the agent’s NPG condition is not sufficient to establish acondition for sustainability. The condition (NPG3) restricts the debt to grow no fasterthan the rate of discount (multiplied by the term (1 + κ )1 2 ), but when the interest rate is
greater than the economic growth rate, it permits the debt to grow faster than theeconomy as whole. An unbounded debt-output ratio cannot be ruled out only by the
NPG condition (e.g., McCallum, 1984).
We impose an additional constraint of feasibility, (FC). Accordingly, it makes sense
to define fiscal sustainability more narrowly. A fiscal policy rule is defined to besustainable if the following two conditions are satisfied. First, the NPG condition ofprivate agents, (NPG3), is to be satisfied. Second, the government’s budget is to befeasible, i.e., (FC) is satisfied at any time and at any state. We have the following.

Proposition: If fiscal policy is sustainable, then E t

Dt + sis bounded above.
Yt + s

Proof. See Appendix A.

The intuition behind the proof is as follows. Suppose that the debt-to-GDP ratio
grows unboundedly. The government will either let debt grow further without
increasing taxes, or constraint debt by increasing taxes. In the former case, debt will
eventually exceed the amount that the private agents are willing to lend to thegovernment (NPG). In the latter case, tax revenues required will exceed the limit oftaxability (FC). To satisfy both (NPG) and (FC), the debt-to-GDP ratio must bebounded above.
13

An example of the deterministic economy shows that the sustainable fiscal policy
requiresDt (τ − z )(1 + g )<. Suppose, for example, that R = 0.02, z = 0 .1 , τ = 0 .3 ,YtR−g

and g = 0 .01 , then the upper bound becomes, Dt Yt < 20.2 which is extremely high sothat the latter condition seems virtually not restrictive if the debt-to-GDP ratio is stable.
Therefore, we may safely say that if the debt-to-income ratio does not growunboundedly but converges to some level, the fiscal policy is sustainable.

~
Let Ct Ct ≡ θt denote the consumption ratio between two different types of agents.
Limiting focus on an economy with θ t being constant through time, we have theconsumption growth rate as(13)

C ( xt +1 ht )C (ht )~C ( xt +1 ht )= ~≡ 1 + g ( xt +1 ht ) .
C (ht )We use (13) to rewrite (7) as(14)

1 = β ∑ π ( xt +1 ht ){1 + g ( xt +1 ht )}−α θ α {1 + r ( xt +1 )} ,Xtwhich embodies the relationship between the growth and interest rates. On the other
hand, (8), (9), (13), and (1) jointly imply θ = (1 + κ )1 2α . In the presence of anintermediation cost, agents consume more when they receive income and consume lesswhen they do not. On the other hand, plugging (1) and θ = (1 + κ )1 2α into (14), we
have the following:(15)

1 = β ∑π ( xt +1 ht ){1 + g ( xt +1 ht )}−α (1 + xt +1 )(1 + κ ) −1/ 2 .
Xt

Equations (14) and (15) fully determine the sequence of the growth and interest rates as
the stochastic variable xt evolves.
14

We explicitly solve (14) and (15). We denote the transition probability as

π ( xt +1 = λ j xt = λi ) =φij in the set X = {x1 ,..., xn } . We denote g ( xt +1 = x j ht ) = g j ,which implies that the growth rate of consumption depends only on the current rate of
return on capital. This arises from the fact that the production technology is the “AK”
type and the fact that the proportion of government expenditure in output is constant.
Accordingly, we rewrite (15) asn(16)

1 = β ∑ φij (1 + g j ) −α (1 + x j )(1 + κ ) −1 / 2 for i = 1,..., n .
j =1

We rewrite (14) similarly asn(17)

1 = β ∑ φij (1 + g j ) −α θ α (1 + rj ) for i = 1,..., n .
j =1Equations (16) and (17) constitute 2n equations for solving n growth rates and ninterest rates. We show the case of n = 2 , with X = { x1 , x2 } . We solve four variables{g1 , g 2 , r1 , r2 } from the following four equations:(18)1⎡ (1 + g1 ) − α (1 + x1 ) ⎤⎡φ11−1⎥ = β (1 + κ ) 2 ⎢⎢−α⎢⎣ (1 + g 2 ) (1 + x 2 ) ⎥⎦
⎣φ 21

−1

φ12 ⎤ ⎡1⎤,
φ 22 ⎥⎦ ⎢⎣1⎥⎦

and
−1

(19)

⎡ (1 + r1 )(1 + g 1 ) −α ⎤− ⎡φ11
φ12 ⎤ ⎡1⎤
−1
⎥ = β (1 + κ ) ⎢⎢⎥ ⎢ ⎥.
−α⎢⎣ (1 + r2 )(1 + g 2 ) ⎥⎦⎣φ 21 φ 22 ⎦ ⎣1⎦

Appendix B provides the procedure for solving the general case.
It is interesting to investigate how a change in the intermediation cost κ influencesg t +1 and rt +1 , and their relationship. Equation (18) implies that a one percent increasein κ leads to a decline of g t +1 by approximately 1 ( 2α ) percent for each state. On
the other hand, (19), together with (18), implies that a one percent increase in κ leads
15

to a decline of rt by one percent for each state. If α is sufficiently small (less than0.5), or equivalently, the elasticity of substitution of consumptions is sufficiently large,
the growth rate declines more sharply than the interest rate as κ goes up. Figure 2A
illustrates the case for α = 0.4 .7 By contrast, if α is sufficiently large, the growth rate
declines less sharply than the interest rate. Figure 2B illustrates the case for α = 1(log-utility). Whether higher intermediation costs make fiscal sustainability difficult or
not depends on the elasticity of substitution of consumption.

4. Calibration

In this section and the next, we simulate the model to investigate the fiscal
sustainability of Japan. Our methodology is to update the future fiscal variables byintroducing a specified fiscal rule into the developed DSGE model and to simulate thedebt-to-GDP ratio. The driving force of the growing economy is the rate of return on
capital, which determines the growth rate and the interest rate. We specify the stochastic
process for the logarithm of the gross rate of return on capital by discretizing a simple
AR(1) process with nine states (n = 9) . The AR(1) process is described, with the serial
correlation coefficient ρ and the average log(1 + x a ) , as(20)

log(1 + x t +1 ) = ρ log(1 + x t ) + (1 − ρ ) log(1 + x a ) + e t +1 ,where et +1 for all t are random shocks that are independent and identically distributed
as a normal distribution with standard deviation σ e . Once three parameters, x a , ρ ,7

In Figure 2, we set x a = 0.033. See Table 2 for other parameter values.

16and σ e , have been set, following the method developed by Tauchen and Hussey (1991),
we construct the nine states {x1,...., x9} and the transition probability φij (i, j = 1,...9) .
We use (16) and (17) to solve for 18 variables ( g j , r j ) ( j = 1,...9) , given the specified( x j , φij ) (see Sakuragawa, Hosono and Sano, 2010 for details). We use (20) to obtain thestochastic process for the GDP growth rate as a discretized version of an AR(1) process:(21)

log(1 + gt +1 ) = ρ log(1 + gt ) + (1 − ρ ) log(1 + g ) + ε t +1 ,where ε t +1 (≡ et +1 α ) is a random shock with the standard deviation of σ ε (≡ σ e / α )and g is the steady-state growth rate.
The debt-to-GDP ratio evolves from (12) as(22)

d t +1 =(1 + Rt +1 )d t − st +1 ,(1 + g t +1 )where dt and st are debt and primary surplus divided by GDP, respectively. These
two equations, together with a fiscal policy rule that determines st +1 , provide the fullsystem. Before going on to the fiscal policy rule, we choose parameter values. Data
used to set parameters is described in Appendix C.
First, we choose the preference parameters, β and α . We set the annual discountfactor β to 1/1.02=0.980. The inverse of the elasticity of intertemporal substitution,

α , plays a central role in relating the interest rate to the growth rate, as captured by (19).
To set α , we note from (19) that(23)log(1 + R j ) = α log(1 + g j ) + γ j ,17where γ j is the logarithm of the jth element of the right-hand side in (19). We
regressed the nominal government bond yield on the nominal GDP growth rate using
OLS. The sample used for the estimation below covers the period of 1981-2009 except
for otherwise mentioned. The estimation result is(24)

Rt = 0.023+ 0.565gt , Adj. R2 = 0.651(0.003)(0.077)

where the numbers in parentheses are standard errors. Following (23), we set α at
0.565, implying that the elasticity of intertemporal substitution is set at 1.770. It isnoteworthy that this figure is in the region of parameters in which a rise in theintermediation cost can improve fiscal sustainability.
Next, we specify the technology parameters, ρ and σe . We apply (21) toconduct the OLS estimation of the AR(1) process of the GDP growth8, obtaining(25)

gt +1 = 0.002 + 0.780gt , Adj. R2 = 0.413 0.
(0.006) (0.175)

We set ρ at 0.780 and σε at 0.01996, where the latter is the root mean squared errorof the regression. We use the chosen σε and α to set σe at 0.01128. We set the
average return on capital, xa , at a value that yields 1 percent average GDP growth rate
given the chosen values of β , α , and κ in (16). We find that xa =0.033. The
average GDP growth rate over the whole sample period of 1981-2009 is 2.2 percent, but
this figure seems to be too high for predicting the future growth rate, especially when8

We also estimated the AR(2) process and found that the two-year lagged growth rate is not

significant and the adjusted R2 deteriorates as compared with (25).

18

we consider the rapid population aging in Japan. We choose the average growth rate to
be 1 percent considering that the average GDP growth rate over the period of 1990-2009
is 1.1 percent.9
Third, we set the financial intermediation cost, κ , at 0.015, the average of net
interest margins between the bank loans and the bank deposits over the period of
2000–2009. We choose the average over the last decade because, as Figure 3 shows, thenet interest margins tended to decline over the last two decades especially at a high ratein the 1990s.
We complete the model by specifying the government’s fiscal policy rule. The
fiscal rule is interpreted as a consequence of the conflict of interests among manypressure groups and so changes little unless the political situation changes drastically.
Based on this idea, we specify the fiscal rule by the regression. We regress the primarybalance as a proportion of GDP on the real GDP growth rate and the one-period lagged
primary balance. The GDP growth rate is expected to capture the business cycle effects.
When the economic boom comes, an increase in tax revenues improves the fiscal stance.
Actually, Figure 4 illustrates a positive correlation between the two. The lagged variable
captures the persistency of the government expenditure and tax revenues. To be specific,
we describe a fiscal policy rule as(26)

st = γ 0 + γ 1st −1 + γ 2 gt .

Using the sample of 1981-200810, we obtain the regression result as

9One percent GDP growth rate roughly corresponds to the “prudent” scenario of thegovernment’s mid-term forecast up to 2020 (Cabinet Office, 2010, 2011).
10

The data of primary balance is available only up to 2008. See Appendix C.

19

(27)

st = −0.021+ 0.658st −1 + 0.577gt , Adj. R2 = 0.759 .
(0.006) (0.160) (0.104)

Based on (27), we set γ 0 =–0.021, γ 1 =0.658, and γ 2 =0.577.
We simulate the model recursively by generating ( gt +1 , Rt +1 , st +1 ) for the stochastic
process of xt +1 , and obtaining dt +1 , given the starting value of dt .
Table 1 summarizes the parameters that we use for the baseline calibration. The
simulation procedure is described in Appendix D.

5. Simulation Results
A. Baseline Forecasts

Table 2 shows the expected debt-to-GDP ratio and the probability that thedebt-to-GDP ratio exceeds d2009 (=1.792)11. Under the baseline parameters, theaverage interest rate is 1.8 percent and the average growth rate is 1.0 percent, with thegap of 0.8 percentage points. The average primary surplus is -4.5 percent of GDP. The
expected debt-to-GDP ratio reaches 11.8 in 100 years and continues to increase
afterwards, suggesting that debt is not sustainable.
The path of the expected debt-to-GDP ratio and the probability that thedebt-to-GDP ratio will exceed its initial value are highly sensitive to the intermediation
cost. If we set κ = 0.0, the average interest rate goes up to 3.33 percent, and the GDP

11

We chose year 2009 as t=0. So, t=20 (“20 years after”), for example, indicates year 2029 inTables 2 to 4 and Figure 6 below.

20

growth rate to 2.34 percent, respectively12. The gap between the two rates goes up from
0.8 to 0.99 percent, and the expected debt-to-GDP ratio increases more rapidly than in
the benchmark case, reaching 13.6 in 100 years (the second row of Table 2). The
smaller intermediation cost makes fiscal sustainability more difficult, since theestimated elasticity of intertemporal substitution of consumption is below two.
The path of the expected debt-to-GDP ratio is sensitive also to the elasticity ofintertemporal substitution of consumption. If we set the inverse of the elasticity ofintertemporal substitution at one (the log-utility case) by keeping the average real GDP
growth rate to 1.0 percent as in the benchmark case, the average real interest rate goesup to 2.26 percent, making fiscal sustainability more difficult to meet: the expecteddebt-to-GDP ratio reaches 15.2 in 100 years.
Incorporating the financial intermediation cost into the model ends up withimposing a looser condition on sustainability, given that the elasticity of substitution on
consumption is less than two. Recent studies report the elasticity of intertemporal
substitution between 1 and 2.13 We may safely judge that Japanese fiscal policy is not

12

In Section 5A (Tables 2), we adjust γ 0 so that the average primary surplus is the same as in

the benchmark case (-4.5 percent of GDP).
13

Abe and Yamada (2005) provide unique micro data evidence of Japanese households,

obtaining the estimated elasticity between 1.50 and 1.78. The other evidences of Japan are basedon aggregate data. Hamori (1996) and Hatano and Yamada (2007) obtained the estimatedelasticity between 1 and 2 in most of their specifications. Sugo and Ueda (2008) and IIboshi etal. (2006) obtained even lower values, which are below 1. Okubo (2003) obtained somewhat
mixed results, obtaining the estimated elasticity between 1 and 2 in half of his four21

sustainable if the expected debt-to-GDP ratio increases unboundedly based on ourmodel with the financial intermediation cost.

B. Alternative GDP Growth Rates

We have thus far assumed that the long-run average real GDP growth rate is 1
percent. Here we examine the effects of higher real GDP growth rates on sustainability
to see if the high growth helps restore sustainability. Specifically, we adjust the average
return on capital, xa , to attain the 2 percent and 3 percent average GDP growth rates.
The other parameters are set as in the baseline case. The 2 percent case corresponds tothe “Growth Strategy Scenario” in the government’s mid-term forecast up to 2020 (inCabinet Office, 2010, 2011; Cabinet Decision, 2010). It is also close to the average real
GDP growth rate over the period of 1981-2009 (2.2 percent). The second and third rowsof Table 3 show that the debt-to-GDP ratio grows more slowly as the average growthrate goes up: in the 1 percent case (the baseline case) the debt-to-GDP ratio reaches 11.8
in 100 years, while the corresponding figures in the 2 percent and 3 percent cases are
6.7 and 3.3, respectively. A higher growth contributes to reduce the future debt-to-GDP
ratio through two channels. First, it increases the primary surplus under the estimatedfiscal policy rule. The average primary surpluses are -2.8 percent of GDP in the 2
percent case and -1.1 percent in the 3 percent case, respectively. Secondly, as thegrowth rate goes up, the average real interest rate also rises, but the gap declines,
resulting in a lower expected debt-to-GDP ratio. The average interest rate in the 2

specifications and above 2 in the other half specifications. As far as we know, Fuse (2004) is the
only study that consistently obtained the estimated elasticity above 2

22percent case is 2.37 percent, and the gap is 0.37 percentage points. In the 3 percent case,the average interest rate is 2.94 percent, and the gap becomes negative, -0.06. It isnotable, however, that even if the economy grows at 3 percent, debt is not sustainablegiven the current fiscal policy rule.

C. Alternative Fiscal Policy Rules

The above results show that government debt is not sustainable under a wide rangeof parameters given the current fiscal policy rule. In this subsection, we consider
alternative fiscal policy rules. The parameters are the same as in the baseline case
except for the fiscal policy rule.
First, we examine whether or not the government’s fiscal reconstruction target issufficient to restore sustainability. The government

released that it aims at turningfrom the current primary deficit of the central and local governments to a primary
surplus by fiscal year 2020 (Cabinet Decision, 2010) and estimated that it must increaseprimary balance by 4.2 percent of GDP to achieve this goal in their “prudent” scenario(Cabinet Office, 2011). Taking this target into consideration, we assume that the
primary balance as a proportion of GDP linearly increases and reaches zero in 2020 andthat the average primary balance is zero after 2020. The first row of Table 4A reports
the simulation result, showing that the expected debt-to-GDP ratio reaches 5.7 in 100
years and continues to increase afterwards.

Importantly, just realizing zero or slightly

positive primary balance is not sufficient to restore fiscal sustainability.
One simple way to restore sustainability would be to raise the average primary
surplus by raising the value of γ 0 in the rule (26). We find that the primary surplus that23

is 1.96 percent of GDP on average is enough to stabilize the expected debt-to-GDP ratio
at its initial value and, thus, to make debt sustainable14.
A more flexible and maybe more interesting way to restore sustainability is tochange the fiscal policy rule. As Bohn (1998) addresses, a rational government should
increase the primary surplus when the debt-to-GDP ratio is high. We incorporate his
idea into the fiscal rule by assuming that the primary surplus-to-GDP ratio depends on
the lagged debt-to-GDP ratio as well. To be specific, we have(28)

st = γ 0 + γ 1st −1 + γ 2 gt + γ 3dt −1 .
We use the same parameters for γ 1 (= 0.658) and γ 2 (= 0.577) as in the baseline

case, and set γ 3 arbitrarily.15 To compare with the benchmark case, we adjust γ 0 sothat the average primary surplus is –4.5 percent of GDP as in the baseline case if dt −1 isat its value as of 2010.
The second to fifth rows of Tables 4A report the expected debt-to-GDP ratios andTable 4B report the associated expected primary surplus-to-GDP ratios for some valuesof γ 3 . We find that a sufficiently large positive response to the debt-to-GDP ratio

14

In Discussion, we conduct the simple calculation concerning how much consumption tax rate

will be necessary if the primary surplus of 2 percent of GDP is to be achieved only by theincrease by the consumption tax rate.
15

To avoid possible endogeneity, we estimated (28) using d t-2 as an instrument and found thatthe coefficients on dt-1 was positive but not significant. Figure 5 illustrates no significant positive
relationship between st and dt −1 , though it does not control for the GDP growth rate. Bohn
(1995) estimates the determinants of the US primary surplus, finding that the coefficient of thelagged debt-to-GDP ratio is around 0.03 to 0.05, depending on the sample period (Table 1).

24stabilizes the debt-to-GDP ratio and thus makes government debt sustainable.
Specifically, if γ 3 =0.001, the debt-to-GDP ratio increases unboundedly. On the other
hand, if γ 3 =0.01, it eventually stabilizes, though at a high level of 4.9. If γ 3 =0.03 and0.05, the debt-to-GDP ratios stabilize at about 2.7 and 2.3, respectively. As γ 3increases, the required primary surplus becomes initially higher but eventually lower.
A higher γ 3 results in a lower long-run debt-to-GDP ratio, which requires less interest
payment and hence less primary surplus. As γ 3 increases from 0.01 to 0.03 and 0.05,
the long-run expected primary surplus decreases from 4.5 percent to 2.5 percent and 2.2
percent of GDP, respectively. Figure 6 depicts the expected primary surplus-to-GDP
ratio in the case of γ 3 =0.05. It shows that if the debt-to-GDP ratio is to stabilize at 2.3
in the long run, the current primary deficit should turn to a surplus in 10 years, increase
up to 2.2 percent surplus of GDP in 20 years, and keep that level afterwards. If thedebt-to-GDP ratio is to stabilize at a level lower than 2.3, the primary surplus must
increase more rapidly. A delayed fiscal consolidation will result in a higher
debt-to-GDP ratio and make sustainability more difficult to be restored.

6. Conclusion

We investigate fiscal sustainability of Japan by providing a dynamic stochastic
general equilibrium (DSGE) model that features low interest rates of government bonds
relative to the economic growth rate. Although we have proposed a framework that
explains lower intersect rates and provides looser conditions for sustainability than the25standard one, our simulation suggests that the government debt is not sustainable if the
fiscal policy rule taken over the last thirty years goes over in the future. We can safely
say that Japanese government debt is not sustainable unless the fiscal policy rule ischanged.
The usefulness of our approach depends on the estimated elasticity of substitution
on consumption. If it is over 2, our approach incorporating the intermediation cost ends
up with providing a tighter condition for sustainability than the standard modelotherwise. In that case, the standard neoclassical growth model may predict that the
fiscal policy is sustainable even if our model suggests that it is not. Fortunately,
however, the estimates in Japan and the US are both sufficiently less than 2 (e.g.,
Sakuragawa, et.al. 2010). We have to be careful to apply this approach to othercountries.
One useful extension is to incorporate the default cost into the model. The default
cost would make the sustainability conditions more difficult to be met because theinterest rate would be higher and the debt-to-GDP ratio would increase more rapidly.
Discussion: Consumption Tax Rate Required to Restore Sustainability

If fiscal sustainability is to be restored only by raising consumption tax rate, howmuch increase in tax rate is needed?
Eq. (27) implies that the long-run primary deficit (γ 0 + γ 1g
) is 4.5percent of GDP if
1−γ2

the average GDP growth rate is 1 percent ( g = 0.01 ). We can regard this long-run
deficit as structural (i.e., cyclicality- and momentum- adjusted) one. On the other hand,to achieve fiscal sustainability under the 1 percent average GDP growth rate, theprimary surplus must be 2.0 percent of GDP. The difference between the structural and26

targeted primary balance (6.5 percentage points) is a primary surplus that is necessary to
be raised either by a decrease in expenditures or an increase in revenues.
The consumption tax revenue as a proportion of nominal GDP is 2.0 percent on
average during the period of 1997-2009, when the tax rate was 5 percent. If we do nottake into consideration possible effects of the consumption tax on consumption andeconomic growth, we can suppose that raising consumption tax by one percentage point
contributes to a 0.4 percentage increase in primary surplus-to-GDP ratio. Under thisassumption, we can mechanically compute that consumption tax rate must be increased
by 16 percentage points, i.e., from 5 to 21 percent, to raise primary surplus-to-GDP ratio
by 6.5 percentage points. Note that if we do not take into consideration negative effectsof consumption tax rates on consumption or increases in social security expendituresassociated with population aging. If we do so, consumption tax rates required will behigher than 21 percent.

Appendix A: Proof of Proposition

Suppose that Et lims →∞Dt + sD= ∞ . Then, for some realizations of states, lim t + s = ∞ .
→∞sYt + sYt + sBelow we limit our attention to those exploding paths. The growing debt-to-GDP ratio
should imply that the public debt will crowd out private lending and at some date(denoted by T ), the credit market will disappear. Agents start financing investment
only by their net worth. The NPG condition of agents as of time T is then given by(NPG4)ET lims →∞DT + s=0.
(1 + RT +1 )(1 + RT +2 )...(1 + RT + s )...

27

⎛ 1 + g TD+ s ⎞⎟⎟ < 1 ,Let g tD denote the growth rate of debt. Then, (NPG4) implies that ET lim⎜⎜s →∞ 1 + R
T +s ⎠⎝

which, in turn, implies that there is some δ > 0 , satisfyinglim( RT + s − g TD+ s ) > δ

(A1)

s →∞

for some realizations of states. In addition, given that xt is bounded above, Rt isbounded above from the relationship between xt and Rt (see (A4) in Appendix B).
Therefore, (A1) implies that g tD is bounded above. Let g D denote the upper bound of
g tD .We can rewrite (FC) as(FC’)

Tt Rt − g tD Dt+ z <τ
=Yt
1 + g tD Yt

for all period t and all the realizations of states. For Rt > g tD , (FC’) can also be
rewritten as

1+ g DDt 1 + g tD
(τ − z) , which
(
τ
−
z
)
<
.
The
RHS
is
boundedbyδ
Yt Rt − g tD

contradicts thatDt + sgrows unboundedly. Q.E.D.
Yt + sAppendix B. General Solution for Growth and Interest Rates

We derive the equilibrium growth and interest rates. We first solve for{g1 , g 2 , , , g n } . Letting Gα denote the n × 1 vector with its j th element of (1 + g j ) −α ,Φ denote the n × n matrix with the (i, j ) element of φ i , j , X~ denote the n × n
diagonal matrix with the ( j, j) element of 1 + x j , and I denote the n × 1 unit vector,
1

we can rewrite (16) as I = β (1 + κ ) − 2 Φ X~Gα , which leads to
(A2)

1
2

~
Gα = β (1 + κ ) X −1Φ −1 I .
−128

Next we solve for {r1 , r2 , , , rn } . Letting Ρ denote the n × 1 vector with its jth~element of (1 + r j ) and Gα denote the n × n diagonal matrix with the ( j, j)~−αelement of (1 + g j ) , we can rewrite (17) as I = βθ α ΦGα P , which leads to− ~~P = β −1θ −α Gα−1Φ −1 I = β −1 (1 + κ ) Gα−1Φ −1 I ,(A3)where the second equality comes from (14). Letting X denote the n × 1 vector with its
1

j th element of 1 + x j , we can rewrite (16) as I = β (1 + κ ) − 2 Φ G~ X . Substituting thisαinto (A3), we obtain

P = (1 + κ ) −1 X .

(A4)Finally, we compute the steady-state values of gt and rt . Let the vector λ denotethe stationary distribution of Φ. Then the steady state values of gt and rt are
n

n

j =1

j =1

obtained by g = ∑ g j λ j and r = ∑ r j λ j , respectively, where λ j is the j thelement of λ .

Appendix C. Data

1.

Primary balance is obtained from the current and capital accounts of the systemof national accounts (93SNA, Economic and Social Research Institute) of the general
government as follows:
Primary balance = (Taxes on products and imports + Current taxes on income andwealth + Social burdens + Other current transfers received + Fixed capital depreciation+ Capital transfer received) – (Subsidy + Social benefit except for social transfers in29

kind + Other current transfers paid + Final consumption + Gross fixed capital formation+ Increases in inventories + Net purchase of land + Capital transfers paid).
The primary balance data based on 93 SNA is available only up to 2008. To estimate theprimary balance in 2009 and 2010, we used the government’s estimate that the primarybalances of the central and local governments are -8.1 percent and -6.4 percent of
nominal GDP in fiscal years 2009 and 2010, respectively (Cabinet Office, Midterm
Economic and Fiscal Forecasts, June 22, 2010). To convert the government’s estimate
to the primary balances of the general government (i.e., the total of the central
government, local governments, and the social security funds), we assumed that the
primary balance of the social security funds as a proportion of nominal GDP as of fiscal
year 2008 (-1.1 percent of nominal GDP) did not change constant up to 2010.
2.

Nominal and real GDP are based on 93 SNA, which is obtained from thewebsite of Economic and Social Research Institute.
Nominal and real GDP data are available up to 2009. For the real GDP growth rate in2010, we used the government’s estimate for fiscal year 2010 (2.6 percent, Cabinet
Office, 2010).
3.

Interest rate margin is the difference between the deposit rate and the lending

rate, both of which are obtained from IMF’s International Financial Statistics.
4.

Real yield on financial bills and government bonds are nominal yields on each

asset minus the change in GDP deflator. Those data are obtained from IMF’s
International Financial Statistics.
5.

Government debt is total debt minus financial bills outstanding. Data source ofgovernment debt is Flow of Funds, obtained from the website of Bank of Japan.

30Appendix D: Simulation Procedure

1. Construction of the initial value of dIn the benchmark case and the other cases except for Fiscal Management Strategy
case, we conduct the stochastic simulation from year 2011. To do so, we need toconstruct the initial value of d2010 . To do so, we first construct R2010 by assuming
perfect foresight and substituting g2010 into the deterministic version of (14),(A5)

1
log(1 + R2010 ) = α log(1 + g 2010 ) − log(1 + κ ) − log β .
2Then, we substitute R2010 , g2010 , d2009 and s2010 into (22) to get d2010 (=1.860).
In the case of Fiscal Management Strategy, we conduct the stochastic simulationfrom year 2021. For year 2010, we follow the same procedure as the benchmark caseabove. For the period from 2011 to 2020, by assuming that gt =0.02 (constant) and thatst linearly increases from s2000 (=-0.075) to s2020 =0 , we construct d 2020 using thesimilar formulae of (A5) recursively.

2. Stochastic Simulation
Step 1. We generate a series of xt +1 for 1000 periods starting from the initial value
drawn from the stationary distribution of xt .
Step 2. Given a series of xt +1 , we obtain gt +1 and Rt +1 from (A2) and (A4).
Step 3. Given a series of gt +1 , we construct st +1 recursively from the fiscal policy rule(26) with a starting value of s2000.
31

Step 4. We construct dt +1 by substituting Rt +1 , gt +1 , and st +1 into (22) with a starting
value of dt as of year 2010.
Step 5. We repeat Steps 1–4 N times to obtain the distribution of dt +1 . Indexing eachseries by i , the expected value of d t and the probabilities that d t exceeds its
critical values d are computed as E[ d t ] =[1 N∑ di,t andN i =1] N1 ∑ I (d ≥ d ), where d = 1.792 , N = 10000 , andPr ob dt ≥ d =

N

i =1

i ,t

⎧⎪1 if d i ,t ≥ d
I d i ,t ≥ d = ⎨.
⎪⎩0 otherwise()

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38

Table 1. Paramters

Preferenceβdiscount factor
inverse of elasticity of intertemporal substitution

0.980
0.565

average return to capital
serial correlation of return to capital
standard deviation of error term in return to capital
Financial Intermediation
κ
financial intermediation cost
Fiscal Policy Ruleγ0
Constant
γ1coefficient on previous-year primary surplus/GDP
γ2coefficient on GDP growth rate

0.033
0.780
0.011

α

Technology
xa

ρ
σ

0.015
-0.0210.658
0.577

Table 2. Expected debt-to-GDP ratio under alternative parametersAfterbaseline
no intermediation cost
log utility

20 years
3.21(93.9%)
3.32(94.9%)
3.41(99.7%)

50 years 100 years
5.76
11.84
(98.1%)(99.7%)
6.23
13.62(98.7%)(99.8%)
6.53
15.15(100.0%) (100.0%)

500 years 1000 years
582.7949118.59(100.0%)(100.0%)1209.97 229444.07(100.0%)(100.0%)2597.90 1242884.42(100.0%)(100.0%)1. Numbers in the parentheses are the probabilities that the debt-to-GDP ratio
exceeds its value as of year 2009 (1.792)

Table 3. Expected debt-to-GDP ratio under alternative growth rates
After
GDP Growth=1% (baseline)
GDP Growth=2%
GDP Growth=3%

20 years 50 years 100 years 500 years 1000 years
3.21
5.76
11.84
582.7949118.59(93.9%)(98.1%)(99.7%) (100.0%)(100.0%)
2.69
4.00
6.74
74.97
799.67(84.7%)(89.5%)(95.1%) (100.0%)(100.0%)
2.23
2.64
3.31
9.07
17.60
(68.5%)(67.7%)(70.7%)(83.7%)(90.2%)

1. Numbers in the parentheses are the probabilities that the debt-to-GDP ratio
exceeds its value as of year 2009 (1.792)

39

Table 4. Alternative fiscal policy rules
A. Expected debt-to-GDP ratio
After
Average primary surplus/GDP=020 years 50 years 100 years 500 years 1000 years
2.71
3.59
5.71
202.53 16759.50(83.0%)(79.7%)(82.2%)(89.2%)(89.6%)
3.18
5.50
10.42
200.424154.41(93.9%)(98.1%)(99.7%) (100.0%)(100.0%)
2.94
3.94
4.62
4.96
4.91
(94.0%)(97.8%)(99.0%)(99.4%)(99.3%)
2.56
2.65
2.66
2.67
2.65
(93.3%)(94.2%)(94.4%)(94.5%)(94.2%)
2.33
2.32
2.31
2.32
2.32
(92.1%)(91.0%)(91.1%)(91.3%)(91.4%)

Bohn's rule γ3 = 0.001
Bohn's rule γ3 = 0.01
Bohn's rule γ3 = 0.03
Bohn's rule γ3 = 005

1. Numbers in the parentheses are the probabilities that the debt-to-GDP ratio
exceeds its value as of year 2009 (1.792)
B. Expected Primary Surplus-to-GDP Ratio
After
20 years 50 years 100 years 500 years 1000 years-4.03%-3.48%-2.00%
52.63% 1188.60%
Bohn's rule γ3 = 0.001
Bohn's rule γ3 = 0.01
-1.75%
1.34%
3.47%
4.60%
4.46%
Bohn's rule γ3 = 0.03
1.24%
2.43%
2.48%
2.53%
2.48%
Bohn's rule γ3 = 0.05
2.16%
2.04%
2.13%
2.10%
2.15%

Figure 1

Real Financial BIll Rate, Real
Government Bond Rate, Real GDP
Growth Rate: 1981-2009
0.08
0.06
0.04

Real GDP Grwoth Rate

0.02

Real Financial Bill Rate

-0.04
-0.06

40

2009

2007

2005

2003

2001

1999

1997

1995

1993

1991

1989

1987

1985

1983

-0.02

1981

0

Real Government Bond
Rate

Figure 2A.

GDP Growth Rates and Interest Rates
as Functions of Intermediation Costs:
α=0.4
0.04

κ

0.02

-0.02

0
0.006
0.012
0.018
0.024
0.03
0.036
0.042
0.048
0.054
0.06
0.066
0.072
0.078
0.084
0.09
0.096

0
GDP Growth Rates
Interest Rates

-0.04
-0.06
-0.08
-0.1

Figure 2B.

Growth Rates and Interest Rates as
Functions of Intermediation Costs
α=1.0
0.04
0.02

κ

-0.02

0
0.006
0.012
0.018
0.024
0.03
0.036
0.042
0.048
0.054
0.06
0.066
0.072
0.078
0.084
0.09
0.096

0

-0.04
-0.06
-0.08

41

GDP Growth Rate
Interest Rate

Figure 3

Margin between Lending Rate andDeposit Rate; 1981-2009

0.040
0.035
0.030
0.025
0.020
0.015
0.010
0.005

1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009

0.000

Figure 4!

Real GDP Growth Rate and Primary
Surplus/GDP: 1981-2008
0.04

Primary Surplus/GDP

0.02

-0.04

0
-0.02

-0.02

0

0.02

0.04

-0.04
-0.06
-0.08
-0.1
-0.12

Real GDP Growth Rate

42

0.06

0.08

Figure 5

Debt/GDP (t-1) and Primary
Surplus/GDP: 1981-2008
0.04

Primary Surplus/GDP

0.02
0
-0.02

0

0.5

1

1.5

2

2.5

-0.04
-0.06
-0.08
-0.1
-0.12

Debt/GDP (t-1)

Figure 6

Expected Primary Surplus-to-GDP
Ratio under Bohn's Rule (γ3 = 0.05)

4%

2%

0%
1

2

3

4

5

6 7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

years after

-2%

-4%

-6%

-8%

43