IMES DISCUSSION PAPER SERIESFiscal Policy Switching:
Evidence from Japan, the U.S., and the U.K.

Arata Ito, Tsutomu Watanabe, and Tomoyoshi Yabu
Discussion Paper No. 2007-E-2

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IMES Discussion Paper Series 2007-E-2
February 2007

Fiscal Policy Switching:
Evidence from Japan, the U.S., and the U.K.
Arata Ito*, Tsutomu Watanabe**, Tomoyoshi Yabu***
Abstract
This paper estimates fiscal policy feedback rules in Japan, the United States, and theUnited Kingdom for more than a century, allowing for stochastic regime changes.
Estimating a Markov-switching model by the Bayesian method, we find the following:First, the Japanese data clearly reject the view that the fiscal policy regime is fixed, i.e.,that the Japanese government adopted a Ricardian or a non-Ricardian regime
throughout the entire period. Instead, our results indicate a stochastic switch of thedebt-GDP ratio between stationary and nonstationary processes, and thus a stochastic
switch between Ricardian and non-Ricardian regimes. Second, our simulation exercises
using the estimated parameters and transition probabilities do not necessarily reject thepossibility that the debt-GDP ratio may be nonstationary even in the long run (i.e.,
globally nonstationary). Third, the Japanese result is in sharp contrast with the results
for the U.S. and the U.K. which indicate that in these countries the government's fiscal
behavior is consistently characterized by Ricardian policy.

Keywords: Fiscal Policy Rule; Fiscal Discipline; Markov-Switching Regression
JEL classification: E62*Graduate Student, Graduate School of Economics, Hitotsubashi University (E-mail:ged1102@srv.cc.hit-u.ac.jp)**Professor, Institute of Economic Research and Research Center for Price Dynamics,
Hitotsubashi University (E-mail: tsutomu.w@srv.cc.hit-u.ac.jp)***Economist, Institute for Monetary and Economic Studies, Bank of Japan (E-mail:tomoyoshi.yabu@boj.or.jp)
We would like to thank Hiroshi Fujiki, Ippei Fujiwara, Kiyohiko Nishimura, Masashi Saito,
Matthew Shapiro, John Taylor, Toshiaki Watanabe, and David Weinstein for useful suggestions
and comments. Views expressed in this paper are those of the authors and do not necessarilyreflect the official views of the Bank of Japan.

1Introduction

Recent studies about the conduct of monetary policy suggest that the ﬁscal policy regime has important implications for the choice of desirable monetary policy rules, particularly, monetary policy
rules in the form of inﬂation targeting (Sims (2005), Benigno and Woodford (2006)). It seems safe
to assume that ﬁscal policy is characterized as “Ricardian” in the terminology of Woodford (1995),
or “passive” in the terminology of Leeper (1991), if the government shows strong ﬁscal discipline. If
this is the case, we can design an optimal monetary policy rule without paying any attention to ﬁscal
policy. However, if the economy is unstable in terms of the ﬁscal situation, it would be dangerous
to choose a monetary policy rule independently of ﬁscal policy rules. For example, some researchers
argue that the recent accumulation of public debt in Japan is evidence of a lack of ﬁscal discipline on
the part of the Japanese government, and that it is possible that government bond market participants
may begin to doubt the government’s intention and ability to repay the public debt. If this is thecase, we may need to take the future evolution of the ﬁscal regime into consideration when designinga monetary policy rule.
Against this background, the purpose of this paper is to estimate ﬁscal policy feedback rules forJapan, the United States, and the United Kingdom for a period spanning more than a century, so as
to gain a deeper understanding of the evolution of ﬁscal policy regimes. One of the most importantfeatures of recent studies on ﬁscal policy rules is the recognition that ﬁscal policy regimes are notﬁxed over time, but evolve in a stochastic manner.1 For example, Favero and Monacelli (2005) and
Davig and Leeper (2005) estimate ﬁscal policy rules for the United States during the postwar period
under the assumption that there are two alternative ﬁscal regimes, i.e. a “passive” and an “active”
regime, and that stochastic ﬂuctuations between the two regimes may be characterized by a Markov
process. They ﬁnd that ﬁscal regime switching occurred fairly frequently: Davig and Leeper (2005)
report that there were twelve ﬁscal regime changes during the period of 1948-2004, while Favero andMonacelli (2005) found that ﬁscal policy was even more unstable than monetary policy.2
However, these pioneering works still have some shortcomings. First, they do not make an empirical distinction between locally and globally Ricardian policy rules. For example, Favero and Monacelli
1 A comprehensive list of recent empirical studies on ﬁscal policy rules is provided by Afonso (2005).
2 These studies are in sharp contrast with research on ﬁscal sustainability initiated by Hamilton and Flavin (1986)
about two decades ago, which typically investigates whether ﬁscal variables such as the debt-GDP ratio are characterized
by a stationary or a nonstationary process without any break (Trehan and Walsh (1988, 1991), Wilcox (1989), Ahmedand Rogers (1995)).

1

(2005) specify a locally Ricardian rule and ask whether the U.S. government has followed this rule ordeviated from it. However, as pointed out by Bohn (1998) and Canzoneri et al. (2001), the transversality condition may be satisﬁed even if the debt-GDP ratio does not follow a stationary process, or
equivalently, even if a government deviates from a locally Ricardian policy rule. Second, the studies
by Davig and Leeper (2005) and Favero and Monacelli (2005) do not pay much attention to governments’ tax smoothing behavior. As pointed out by Barro (1986) and Bohn (1998), tax-smoothing
behavior may create a negative correlation between public debt and the primary surplus. Without
properly controlling for such behavior when estimating a government’s reaction function, researchers
may easily obtain biased estimates of ﬁscal policy reactions to a change in public debt. Third, theempirical approach of these studies is based on maximum likelihood estimation and implicitly assumes
that the debt-GDP ratio is stationary at least in the long run (i.e., that it is ”Harris recurrent”). Thiscondition is satisﬁed if, for example, the debt-GDP ratio switches between two AR (p) processes,
one stationary and the other nonstationary, but the nonstationary regime is not visited too often orfor too long (Francq and Zakoian (2001)). However, there is no a priori reason to believe that thiscondition is indeed satisﬁed for the debt-GDP ratio; it is possible that a non-Ricardian regime isvisited frequently and/or for a long time, depending on the transition probabilities. If this is the case,maximum likelihood estimators will fail to follow a standard normal distribution even asymptotically(Douc et al. (2004)).
We derive an estimating equation based on a model of optimal tax smoothing, paying particularattention to diﬀerences between locally and globally Ricardian rules, and then estimate the equationby the Bayesian method. The main ﬁndings of the paper are as follows. First, the Japanese dataset, covering the period 1885-2004, clearly rejects the view that the ﬁscal policy regime was ﬁxed
throughout the sample period, i.e., that the Japanese government adopted only one policy stance Ricardian or non-Ricardian - throughout the entire period. Rather, our empirical results suggest thatthe ﬁscal policy regime evolved over time in a stochastic manner, and that the debt-GDP ratio is welldescribed by a Markov switching model with two or three states. Speciﬁcally, Japanese ﬁscal policy ischaracterized by a locally Ricardian rule in 1885-1925 and 1950-1970. The former roughly corresponds
to the period when Japan had adopted the gold standard, under which the government was forced tomaintain a balanced budget. Japan left the gold standard in 1917. The latter period corresponds tothe period of ﬁscal restructuring just after WWII, when the Japanese government, under the direction2

of the Supreme Commander for Allied Powers (SCAP) introduced a balanced budget system as partof the so-called ”Dodge Line” in order to stop runaway inﬂation. On the other hand, Japaneseﬁscal policy is characterized by non-Ricardian rules in 1930-1950 and 1970-2004, suggesting that theJapanese government abandoned ﬁscal discipline not only during WWII, but also in the most recent
period starting in 1970. These empirical results are conﬁrmed as being quite robust to changes in
empirical speciﬁcations.
Second, given that the Japanese debt-GDP ratio switches between stationary and nonstationary
processes, one may wonder to what value the debt-GDP ratio goes to in the long run. To address
this question, we conduct stochastic simulation exercises using the estimated transition probabilities,
and ﬁnd that the debt-GDP ratio is quite likely to increase over the next 20 years, but will start
declining after that and ﬁnally converge to zero. This implies that the debt-GDP process is “globallystationary” (i.e., stationary across regimes), although it may not necessarily be locally stationary (i.e.,
stationary within each regime).3 However, we also ﬁnd that this result is not very robust to changes
in the speciﬁcation of the estimating equation, such as the number of possible “states,” and in somecases, we ﬁnd global nonstationarity.
Third, we apply our methodology to U.S. and U.K. data sets to ﬁnd that the ﬁscal behavior of
the U.S. government throughout the entire sample period, 1840-2005, may be described as switching
between locally Ricardian policy rules, while the behavior of the U.K. government during the entire
sample period, 1830-2003, can be characterized as switching between globally Ricardian policy rules.
Thus, the U.S. and U.K. results are in sharp contrast with the result for Japan. The U.S. result is
consistent with Bohn (1998, 2005), but diﬀers from Favero and Monacelli (2005) who report that U.S.
government behavior deviated from Ricardian policy for most of their sample period, 1961-2002.
The remainder of this paper is organized as follows. Sections 2 and 3 explain our empiricalapproach, while Section 4 explains our data set. Section 5 presents the regression results. Section 6
concludes the paper. A detailed explanation of our data set is provided in Appendix.

3 The recent behavior of investors in the Japanese government bond market seems to be consistent with this as theyshow no hesitation to purchase government bonds even though the government is lacking ﬁscal discipline and rapidly
accumulating public debt.

3

2

Ricardian ﬁscal policy

2.1

The government’s budget constraint

We start by looking at the government’s budget constraint. Let us denote the nominal amount ofpublic debt and base money at the end of period t by Bt and Mt . Also, we denote the one-period
nominal interest rate starting in period t − 1 by it−1 , the nominal government expenditure (excludinginterest payments) and the nominal tax revenue in period t by Gt and Tt . Then the consolidated ﬂow
budget constraint of the government and the central bank takes the following form:
Mt + Bt = (1 + it−1 )Bt−1 + Mt−1 + (Gt − Tt ).
Dividing both sides of this equation by nominal GDP, Yt , we obtain:
mt + b t =1 + it−11
bt−1 +
mt−1 − st ,1 + nt1 + ntwhere mt , bt , st , and nt are deﬁned by
mt ≡

Mt
Bt
Tt − Gt
Yt − Yt−1; bt ≡; st ≡; nt ≡
.
Yt
Yt
Yt
Yt−1

Denoting the total consolidated liabilities by wt (≡ mt + bt ), the transition equation for wt can be
expressed as:
·
¸
it−1
nt
it−1
wt − wt−1 =wt−1 −
wt−1 −
mt−1 + st .
1 + nt1 + nt1 + nt(1)

it−1Note that 1+n
mt−1 represents seignorage and that an increase in the primary surplus st or seignoraget

reduces total liabilities. Also note that an increase in the nominal growth rate nt contributes to lownt
ering total liabilities through the second term on the right-hand side, − 1+nwt−1 , which is sometimestcalled the “growth dividend” (Bohn (2005)).
Equation (1) can be rewritten as
wt = qt [wt+1 + st+1 ] +where qt represents a discount factor that is deﬁned by
qt ≡1 + nt+1.
1 + it4it
mt ,1 + it(2)

Integrating equation (2) forward from the current period and taking expectations conditional on
information available in period t, we obtain a present-value expression of the budget constraint:
Ã
!µ
Ãj−1
!
!
ÃT −1
¶
T
−1 j−1
T
Y
Y
X
X
Y
it+j
qt+k
qt+k st+j + Et
wt = st + Et
mt+j + Et
qt+k wt+T .
1 + it+j
j=0
j=1
k=0

k=0

k=0

This implies that the transversality condition is given by
!
ÃT −1
Y
qt+k wt+T = 0.
lim Et
T →∞

2.2

(3)

k=0

Locally Ricardian policy rules

Woodford (1995) proposes that a ﬁscal policy commitment be called “Ricardian” if it implies that thetransversality condition, equation (3), necessarily holds for all possible paths of endogenous variables(in particular, prices). More speciﬁcally, Woodford (1995, 1998) proposes two types of Ricardian ﬁscal
policy rule.
The ﬁrst type, which is referred to as “locally Ricardian,” can be expressed as
·
¸
it−1
it−1
st +
mt−1 = λt +wt−1 + νt ,1 + nt1 + nt(4)

where λt is a time-varying parameter satisfying 0 < λt ≤ 1, which represents the government’s
responsiveness to changes in total liabilities, and νt is an exogenous stationary variable. Note thatthe left-hand side of equation (4) represents the sum of the primary surplus and seignorage. Equation(4) requires the government to create a surplus in period t great enough to cover its interest payment
it−1
in that period, 1+nwt−1 .
t

By substituting (4) into (1), we can fully characterize the dynamics of wt :·wt = 1 − λt −¸nt
wt−1 − νt .
1 + nt(5)

Under the assumption that nt is an exogenous process (i.e., the government treats nt as exogenously
given when making a ﬁscal decision in period t),4 this equation implies that wt would be a stationarynt
process and thus satisﬁes the transversality condition if the sum of λt and 1+nlies between zero andt

4 It is possible that n could be an endogenous variable in the sense that the government’s ﬁscal behavior could havet
non-negligible consequences on the path of nt . For example, as argued by Woodford (2001) among others, it might
be possible that if the government does not react at all to changes in total liabilities (that is, λt = 0), then inﬂation
endogenously emerges (nt > 0), and consequently the coeﬃcient on wt−1 in equation (5) becomes less than unity.

5

unity.5 Note that the assumption of a locally Ricardian policy requires that 1 − λt is smaller thanunity, while stationarity of w requires that the coeﬃcient on wt−1 in (5) is less than unity. These two
conditions are closely related but not identical except for the case of nt = 0.
An alternative speciﬁcation to equation (4) would be:
·
¸
it−1
it−1
nt
st +
mt−1 +
wt−1 = λ̂t +wt−1 + νt .
1 + nt1 + nt1 + nt(6)nt. Now the government seeks to adjust the sum of the primary surplus,
Note that λ̂t ≡ λt + 1+nt

seignorage, and the growth dividend in response to changes in total liabilities. An important diﬀerence
from equation (4) is that the government reduces the primary surplus when the growth dividend ispositive, for example, due to high inﬂation, and increases it when the growth dividend is negative; on
the other hand, equation (4) requires the government to create a primary surplus independently of
the level of the growth dividend. It can be easily seen that the transition equation corresponding to(5) is now given byhiwt = 1 − λ̂t wt−1 − νt ,(7)

and that wt is a stationary process if λ̂t satisﬁes the condition that 0 < λ̂t ≤ 1.
Favero and Monacelli (2005) adopt a policy reaction function very close to equation (6). According
to their deﬁnition, a government with ﬁscal discipline seeks to keep the primary deﬁcit lower than the“debt-stabilizing deﬁcit”, which is given by
·
¸
it−1
nt
−
−
wt−1 .
1 + nt1 + ntGiven this deﬁnition, the debt-stabilizing deﬁcit becomes positive if nt takes a suﬃciently large positive
value, implying that the government can run a deﬁcit.

2.3

Globally Ricardian policy rules

The idea that the government should maintain a surplus large enough to at least cover interest
payments seems to be a useful one from a practical point of view,6 but the transversality condition
5 Note that, from an econometric point of view, w is a stationary process if the coeﬃcient on wt
t−1 in equation (5)ntlies between -1 and 1 (−1 < 1 − λt − 1+n< 1). However, it seems safe to rule out the possibility that w converges overttime to a constant value with oscillation, so that we can concentrate on the condition that the coeﬃcient lies between
nt
0 and 1 (0 ≤ 1 − λt − 1+n < 1).
t

6 If we rewrite equation (4) as s − it−1 b= λt wt−1 +νt , we see that the rule requires that not the primary surplust
1+n t−1t

but the traditional ﬁscal surplus (i.e., primary surplus less interest payment) be adjusted in response to a change intotal liabilities, which is the idea underlying the Maastricht Treaty and the Stability and Growth Pact. See Woodford(2001) for more on this issue.

6does not necessarily require it. Speciﬁcally, as shown by Bohn (1998) and Canzoneri et al. (2001),
the transversality condition could be satisﬁed even if the government reacts to an increase in total
liabilities by less than the amount needed to cover its interest payments. This is the second type ofRicardian policy, which is referred to as “globally Ricardian.”Globally Ricardian policy can be expressed as
st +

it−1
mt−1 = γt wt−1 + νt ,1 + nt(8)where γt is a time-varying parameter satisfying 0 < γt ≤ 1. Note that equations (4) and (6) require
the government to generate a primary surplus that is suﬃcient to cover its interest payments in eachperiod. Here, however, the government can now issue additional debt to pay interest on the existing
debt at the beginning of that period. Under this policy rule, the dynamics of wt are now given by
·
¸
nt
it−1
wt = 1 − γt −+wt−1 − νt(9)
1 + nt1 + nt
or
wt =

·

1
qt−1

¸
− γt wt−1 − νt ,

(10)

1 7
which implies that the transversality condition (equation (3)) is satisﬁed if 0 < γt ≤ qt−1
. Notethat this condition does not necessarily guarantee that wt is a stationary process; in fact, it allows wt
to grow forever, but at a rate lower than the interest rate in each period. In that sense, a globally
Ricardian rule imposes a weaker condition on government behavior than a locally Ricardian rule.
Bohn (1998, 2005) adopts a policy reaction function very close to equation (8) and looks at U.S.
data to determine whether γt is positive.8 Equation (8) is an appropriate estimating equation when
the government adopts a globally Ricardian policy or when it actually adopts a locally Ricardianpolicy but interest rates do not ﬂuctuate much during the sample period. In the latter case, we would
be able to empirically distinguish between a locally and a globally Ricardian policy just by looking at
whether the estimated coeﬃcient on wt−1 is greater than the sample average of the nominal interest
rate. However, if the government adopts a locally Ricardian policy and ﬂuctuations in interest rates
are not small, then Bohn’s speciﬁcation may not be appropriate. For example, the estimated coeﬃcienton wt−1 may become biased towards zero if ﬂuctuations in interest rates are quite large during thesample period while those in public debt are negligibly small.
7 Again, we rule out the possibility that the coeﬃcient on w

t−1 in (9) or (10) is below zero.
8 However, Bohn (1998, 2005) does not consider the possibility that the ﬁscal regime evolves over time in a stochastic

manner.

7

3

Estimation method

3.1

Estimating equations

Given the two deﬁnitions of Ricardian ﬁscal policy above, we estimate an equation of the formbt = µ0 + (α0 + ηt )bt−1 + u0t ,µ1 + (α1 + ηt )bt−1 + u1t ,if

St = 0(11)

if

St = 1

where uit = εit − νt with εit ∼ i.i.d.N (0, σi2 ). {St ∈ (0, 1)} is a two-state Markov chain with transition
probabilities pij = Pr(St = j | St−1 = i). Note that, given that the current regime is i, the expected
average duration of staying in the same regime is (1 − pii )−1 . Also, note that we use public debt issued
by the government bt as the dependent variable rather than the total liabilities wt , assuming that theamount of base money mt is small relative to the public debt and that ﬂuctuations play a much lessimportant role in seignorage than in the primary surplus.
We specify four diﬀerent estimation equations based on diﬀerent deﬁnitions of the observablevariables, ηt and νt .
Speciﬁcation 1

ηt = νt = 0:This is the benchmark case in which no exogenous variables areincluded. Hence, bt follows a simple Markov-switching AR(1) process.
Speciﬁcation 2 ηt = 0, and νt = −gtm : This is a case in which government tax smoothing behavior
is incorporated through gtm (military expenditures relative to GDP). As pointed out by Barro (1986)
and Bohn (1998), the government’s tax-smoothing behavior may create a negative correlation between
public debt and the primary surplus. To illustrate this, consider a situation in which the government
increases its expenditures, but only temporarily (such as in the case of a war). The government
could increase taxes simultaneously by the same amount as the increase in expenditures, but it iscostly to change marginal tax rates over time, since doing so increases the excess burden of taxation.
Recognizing this, an optimizing government would seek to smooth marginal tax rates over time.
This implies that a temporary increase in government expenditures would lead to a decrease in the
primary surplus and an increase in public debt. Bohn (1998) argues that such a negative correlation
between the primary surplus and public debt should be properly controlled for when estimating thegovernment’s reaction function; otherwise researchers may easily obtain imprecise estimates of ﬁscal
8policy reactions to an increase in public debt. Bohn (1998, 2005) shows that empirical results for the
U.S. sharply diﬀer depending on whether or not temporary government expenditures are included as
an independent variable, while Iwamura et al. (2005) report a similar ﬁnding for Japan during thepost-war period.

Speciﬁcation 3nt
ηt = − 1+n, and νt = −gtm :tThis speciﬁcation corresponds to equation (5)with αi = 1 − λi . Note that when nt is very close to 0, speciﬁcation 3 reduces to speciﬁcation 2.
This condition might hold in a very stable economy without any experience of high inﬂation, but
unfortunately, this is not the case for Japan, which experienced three-digit inﬂation rates just after
the end of WWII. Of course, Japan is not an exception, and one can easily ﬁnd other examples inwhich the accumulation of public debt leads to uncontrollably high inﬂation. For such countries,
speciﬁcations 2 and 3 are not identical.

Speciﬁcation 4

it−1ntηt = − 1+n+ 1+n, and νt = −gtm :ttThis corresponds to equation (9) withit−1
αi = 1 − γi . This speciﬁcation diﬀers from speciﬁcation 3 in that interest payments, 1+n, aret

included in ηt , reﬂecting the fact that the government is not required to create surplus to cover its
interest payments. Note that a globally Ricardian policy requires αi to be less than unity, implying
that, when nt is always equal to zero, bt could continue to grow forever, but at a rate lower than the
borrowing cost in each period.

3.2

Estimation

We estimate equation (11) by employing a Bayesian approach via the Gibbs sampler instead of aclassical approach based on maximum likelihood estimation. The Bayesian approach has the following
advantages. First, the maximum likelihood estimator (MLE) has the potential disadvantage thatinference on St is conditional on the estimates of the unknown parameters. We estimate the parametersof the model and then make inferences on St conditional on the estimates of the parameters as if weknew for certain the true values of the parameters. In contrast, the Bayesian approach allows boththe unknown parameters and St to be random variables. Therefore, inference on St is based on the
joint distribution of the parameters and St (see Kim and Nelson (1999)).
Second, for the Markov switching models, the likelihood is often not uni-modal but multi-modal.
Therefore, numerical algorithms such as Expectation Maximization (EM) and Newton-Rapson algo-9rithms sometimes converge to a local maximum on the likelihood surface. This is a typical problem
encountered with data in practice, regardless of which optimization algorithms are used. Maddala andKim (1998) argue that the maximum likelihood estimation method is fragile as multiple local maxima
are often found.
Third, MLE follows a non-standard limiting distribution when the process is nonstationary in thelong run (or globally nonstationary). To our knowledge, such limiting distributions have not been
derived for Markov-switching models. On the other hand, the Bayesian method can approximate thejoint and marginal distributions of the parameters and St via a Markov chain Monte Carlo (MCMC)
simulation method such as the Gibbs sampler. The method is valid even when the observed process
exhibits non-stationarity (or explosive) behavior in the long run. To illustrate this point, let us
suppose there are two ﬁscal policy regimes: one is a stable regime in which the debt-GDP ratio ischaracterized by a stationary process, and the other one is an unstable regime in which the debt-GDP
ratio is characterized by a nonstationary process. Note that the mere existence of an unstable regime
does not necessarily imply global instability: The system could still be globally stable if the unstableregime is not visited too often or for too long. In this sense, the transition probabilities of the Markov
chain are important determinants of global stability or instability. On the other hand, as shown byFrancq and Zakoian (2001), it is possible that the system is globally unstable even when both of thetwo regimes are stable. An important point to be emphasized here is that it would not be appropriate
to employ MLE if it is uncertain whether the system is globally stable.9

3.3

MCMC simulation

The ﬁrst time the Gibb sampler was used in a Bayesian analysis of Markov switching models wasin the study by Albert and Chib (1993). The Gibbs sampler is used to approximate the joint andmarginal distributions of the parameters of interest from the conditional distributions of the subsetsof parameters given the other parameters (see Kim and Nelson (1999) for an introduction to Gibbs
sampling). It is useful in this case because the joint distributions are diﬃcult to obtain.
We follow Kim and Nelson (1999) to estimate a model of the form:

9 An alternative empirical framework to study ﬁscal regime shifts would be to use the methodology proposed by Bai
and Perron (1998), in which a multiple linear regression model with l breaks (or l + 1 regimes) is examined within theclassical framework. However, this approach requires the process to be weakly stationary in each regime. Therefore,
their method cannot be applied in our context.

10b∗t =

 µ0 + α0 bt−1 + ε0t ,µ1 + α1 bt−1 + ε1t ,if

St = 0if

St = 1

where b∗t = bt − ηt bt−1 + νt and εit ∼ i.i.d.N (0, σi2 ) for i = 0, 1 with σS2 t = σ02 (1 + h1 St ) and h1 > 0.
{St ∈ (0, 1)} is a two-state Markov chain with transition probabilities pij = Pr(St = j | St−1 = i).
Note that the two states are assumed to be identiﬁed not by αSt but by σS2 t , simply because we wantto know if there is any diﬀerence between the two states in terms of αSt .
3.3.1

Prior distributions

Next we describe the choice of priors for the unknown parameters. Let eh1 = 1 + h1 with h1 > 0. Thenthe priors are the following:

µi
σ02
p11

∼ N (ψ, ω −1 ), αi ∼ N (φ, c−1 ),υ δυ δ∼ IG( , ), eh1 ∼ IG( , )1(eh1 >1) ,2 2
2 2∼ beta(u11 , u10 ), p00 ∼ beta(u00 , u01 )The parameters used are ψ = 0, ω = 25, φ = 0, c = 1, (υ, δ) = (0, 0), u00 = u11 = 8, andu10 = u01 = 2. Hence the prior of σi2 is non-informative. The other parameters are chosen so thatthe priors are informative but relatively diﬀused. The means and standard deviations of the priordistributions are presented in the following table.
Priors for the parameters

µi
αi
pii
σ02
e
h1
3.3.2

Distribution
NormalNormalBeta
Inverted Gamma
Inverted Gamma

Mean
0.00
0.00
0.80
—
—

Std. Dev.
0.20
1.00
0.12
—
—

Computational algorithm

The needed posterior conditional distributions for implementing Gibbs sampling are easily obtained
from the priors and the assumptions of the data generating process. The following steps 1 through 5
are iterated to obtain the joint and marginal distributions of the parameters of interest.
11

Step 1: Generate p11 and p00 conditional on SeT = (S1 , ..., ST ). Let nij refer to the total number oftransitions from state i to j, which can be counted from SeT . Then
p11 | SeT

p00 | SeT

∼ beta(u11 + n11 , u10 + n10 )∼ beta(u00 + n00 , u01 + n01 )Step 2: Generate µi conditional on SeT , σi2 , and αi . We have the regression yt = µi + εit whereyt = b∗t − αi bt−1 for t ∈ {t : St = i}. Hence, the posterior distribution is µi ∼ N (ψ∗ , ω∗−1 ) where


X
X
2
2
−1 
yt /σi + ωψ ω∗ =1/σi + ω, ψ∗ = ω∗t∈{t:St =i}t∈{t:St =i}

Step 3: Generate αi conditional on SeT , σi2 , and µi . Let d∗t = b∗t − µi , then we have the regressiond∗t = αi bt−1 + εit for t ∈ {t : St = i}. Hence, the posterior distribution is αi ∼ N (φi∗ , c−1i∗ ) where


X
X

bt−1 d∗t /σi2 + cφb2t−1 /σi2 + c, φi∗ = c−1ci∗ =i∗t∈{t:St =i}t∈{t:St =i}

Step 4: Generate σ02 and σ12 conditional on SeT , µi , and αi . We ﬁrst generate σ02 conditional on
h1 and then generate e
h1 = 1 + h1 to indirectly generate σ12 . Conditional on h1 , the posterior

distribution of σ02 is as follows:

σ02 ∼ IGµ

υ0∗ δ0∗
,
2
2

¶

where

with RSSi =with T1 =

= υ+T

δ0∗

= δ + RSS0 + RSS1 /(1 + h1 )P∗
2t∈{t:St =i} (bt − µi − αi bt−1 ) .

e
h1 = 1 + h1 is as follows:
where

υ0∗

e
h1 ∼ IGµ

Conditional on σ02 , the posterior distribution of

υ1∗ δ1∗
,
2
2

¶

1(e
h1 >1)

υ1∗= υ + T1

δ1∗

= δ + RSS1 /σ02PT2et=1 St . Once h1 is obtained, we can calculate σ1 .

12

Step 5: Generate SeT = (S1 , ..., ST ) conditional on the other parameters. This is conducted using

multi-move Gibbs sampling, which was ﬁrst introduced by Carter and Kohn (1994) in the context
of a state-space model. Here the procedure for generating SeT using the multi-move Gibbssampling is the same as that in Kim and Nelson (1999).

We iterate steps 1 through 5 M + N times and discard the realizations of the ﬁrst M iterations
but keep the last N iterations to form a random sample of size N on which statistical inference canbe made. M must be suﬃciently large so that the Gibbs sampler converges. Also, N must be large
enough to obtain the precise empirical distributions. Taking these aspects into consideration, we set
M = 5000 and N = 10000.

4

Data

We construct a data set covering the period 1885-2004 for Japan, 1840-2005 for the United States,and 1830-2003 for the United Kingdom.10

4.1

Japan

Public debt

Public debt is deﬁned as the amount of gross debt issued by the central and local

governments at the end of each ﬁscal year.11 To convert the ﬁgures reported in various budget
documents into a format consistent with the SNA, we make adjustments by excluding the amount ofdebt issued under the Colonial Special Accounts and the Public Enterprise Special Accounts, both ofwhich are outside the general government according to the SNA deﬁnition.12

Nominal GDP A single data set covering the entire sample period is not available, so that wecollect data from various sources and link them in a consistent way. For the period after FY1936,
we use a data set produced by the Japanese government (various versions of the SNA), while for the
10 See Appendix for details. All data we use are available upon request.
11 The data for the debt issued by the central government are taken from various documents published by the Ministryof Finance, including “Japanese Government Bonds Statistics,” “The Financial History of the Meiji and Taisho Period
in Japan,” the “Annual Report on Japanese Government Bonds Statistics,” and “Budget Statistics,” while the data
for the debt issued by local governments is taken from documents issued by the Ministry of Finance and the Ministryof Home Aﬀairs (Ministry of Internal Aﬀairs and Communications), including “The Financial History of the Meiji andTaisho Period in Japan,” “Local Government Bonds Statistics,” the “Annual Publication on Local Public Finance,”
and the “Annual Report on Local Public Finance Statistics.”
12 We use various deﬁnitions of the general government: For 1885-1954, we use the deﬁnition by the Economic
Counsel Board, for 1995-1969, the OLD SNA, for 1970-1979, the 68SNA, and for 1980-2004, the 93SNA. Note thatthese deﬁnitions slightly diﬀer from each other, because special accounts held by the central government and businessaccounts held by local governments are sometimes classiﬁed as part of the general government and sometimes not.

13

period before FY1935, we basically use Ohkawa et al. (1974). However, since data are completely
missing for the ﬁnal stage of WWII (FY1944 and 1945), we estimate the real GDP in these twoyears by using the index of industrial production and the index of agriculture, forestry and ﬁsheryproduction,13 and the GDP deﬂator by using the agricultural price index, the production goods priceindex, and the consumer price index.

Government interest payments The data for government interest payments for FY1885 to 1929
are taken from Emi and Shionoya (1966) for FY1885 to 1929, while those for FY1952 to 2004 are fromvarious documents published by the government, including the “White Paper on National Income,”
the “Annual Report on National Income Statistics,” and the “Annual Report on National Accounts.”
As for the period between FY 1930 and FY1951, we estimate interest payments closely following themethodology adopted by Emi and Shionoya (1966).

Military expenditure

For the years after FY1947, we use the ﬁgures referred to as “National

Defense and Related Aﬀairs” in various issues of the “Settlement of General Account Revenues andExpenditures” published by the Ministry of Finance. The data for FY1946 are taken from Economic
Counsel Board (1954), while for the years before FY1946, we use the data from Emi and Shionoya(1966).
As for military spending during wartime, that is, FY1937 to FY1945, we deﬁne this as expenditures
spent only by the forces at home, and do not include expenditures spent by the forces overseas. Thisis consistent with our deﬁnition of public debt in which those debts issued under the ﬁve Colonial
Special Accounts (namely, the Chosen Government, Taiwan Government, Kwantung Oﬃce, Karafuto
Oﬃce, and Nanyo Oﬃce) are not included.14

13 This methodology closely follows the one used by the Japanese central bank in its various publications on ﬁnancial
and economic activities around the end of the WWII (see, for example, Bank of Japan (1950)).
14 However, as one might imagine, a non-negligible portion of expenditures spent by the forces overseas was ﬁnancedby the central government through the issue of public debt, especially at the ﬁnal stage of WWII. Ideally, this portion
should be included in our deﬁnition of military expenditure, but we do not do so because reliable ﬁgures for that portion
are not available. However, to see how sensitive our empirical results are to this treatment of military expenditures, wecreated an alternative series of military expenditures using a tentative estimate by Emi and Shionoya (1966) for militaryspending by the forces overseas that were ﬁnanced by the central government through the Colonial Special Accounts,
and repeated the same empirical exercise as in Section 5. We were able to conﬁrm that the basic empirical ﬁndings are
not sensitive to the deﬁnition of military spending.

14

4.2

The U.S. and the U.K.

For the United States, the data are taken from the “Historical Statistics of the United States” (Carter
et al. (2006)) and the “Historical Tables, Budget of the United States Government” published by
the Oﬃce of Management and Budget. For the United Kingdom, the data sources are the “British
Historical Statistics” (Mitchell (1988)), the “Annual Abstract of Statistics” published by the Oﬃce
for National Statistics, and the Public Sector Finances Databank by HM Treasury.

5

Empirical results

5.1

Preliminary analysis

The trend in the debt-GDP ratio for Japan, the U.S., and the U.K. is shown in Figure 1. We seethat there are three major periods of debt accumulation in Japan. The ﬁrst period, 1904 to 1905,is the period of the Russo-Japanese War (1904-1905). Reﬂecting a substantial increase in military
expenditure, the debt-GDP ratio increased to over 50 percent at the end of 1905; however, it started
to decrease again right after the end of the war and the decline continued until, in 1918, the debt-GDP
ratio had returned to the pre-war level. Given that there was no remarkable growth dividend during
this period (the nominal growth rate in 1906-1915 was 5.4 percent per year on average), one cansee that this downward trend mainly came from ﬁscal reconstruction, including substantial spending
reductions.15 As pointed out by many researchers, the government during this period had a strong
political will to restore budget balance so as to avoid the risk of a massive outﬂow of gold under thegold standard system.
The second phase of debt accumulation was 1920 to 1944, i.e., the period that includes WWII.
The increase in the debt-GDP ratio accelerated following the outburst of war with China in 1937,
and the ratio eventually reached 1.8 when the war ended in 1945. However, as can be seen in Figure
1, the debt-GDP ratio dropped precipitously right after the end of the war, all the way to a level
very close to zero. This is an episode of inﬂationary erosion of the debt, or “partial default,” due tohyper-inﬂation during this period.16
Finally, the most recent phase of debt accumulation started in the early 1970s and continues until
today. A series of reforms in the social security system, including the introduction of indexation in the
15 Although Japan won the war, it received no war reparations from Russia.
16 The rate of inﬂation in terms of the GDP deﬂator was 273 percent in 1945, 175 percent in 1946, and 154 percent

in 1947.

15

public pension system, have been implemented since the Tanaka administration declared a changeoverto the welfare state in 1973. This accumulation of debt continued until the government ﬁnally started
ﬁscal reconstruction in the latter half of the 1980s, including a substantial cut in spending and theintroduction of a consumption tax in 1989. However, the debt-GDP ratio started to increase again in
the 1990s, at least partially due to the collapse of the asset price bubble in the early 1990s.
Turning to the U.S. and the U.K., we see that the main cause of debt accumulation was increases inmilitary expenditures during wartime. Speciﬁcally, the U.S. debt-GDP showed a rapid and substantial
increase in 1861-66, 1916-19, and 1941-46, respectively corresponding to the Civil War, WWI, andWWII periods. The debt-GDP ratio for the U.K. is also characterized by three spikes, created by the
Napoleonic War, WWI, and WWII. A notable diﬀerence with the Japanese data is that in both of thesecountries there was no major inﬂation comparable to Japan’s hyper-inﬂation in 1945-47. It should
also be noted that the U.S. and the U.K. have never experienced an uncontrollable accumulation of
public debt during peacetime, which again is in sharp contrast with the Japanese experience since theearly 1970s.
Table 1 presents a standard ADF test for the debt-GDP ratio in Japan, the U.S., and the U.K.
Speciﬁcally, we run an AR (p) regression of the form
bt = µ + αbt−1 +

p−1
X
j=1

φj △bt−j + ut

(12)

for the entire sample period with no break. We repeat this with various lag lengths (p = 1 to 10) to
ﬁnd that the estimates of α are very close to unity, and thus the null hypothesis H0 : α = 1 cannot
be rejected for each of the three countries.
But does this necessarily imply that the debt-GDP ratio follows a unit root process throughout theentire sample period? In order to examine this, we conduct a rolling regression of equation (12) with awindow of 40 years; for example, the estimated value for 1925 is from a regression conducted over theperiod 1885-1925. The lag length is set to p = 2. The results are shown in Figure 2 and show for Japanthat the estimate of α ﬂuctuates substantially in a range from 0.6 to 1.1, suggesting that the timeseries properties of the debt-GDP ratio changed signiﬁcantly at least several times. Speciﬁcally, theestimate of α shows a sharp rise during WWII, indicating that the Japanese government abandoned
ﬁscal discipline during this period. On the other hand, α shows a sharp decline during the period
just after the war, probably reﬂecting the fact that hyper-inﬂation during that period quickly reduced
16

the real value of public debt. It should also be noted that the value of α has stayed very close to (orslightly above) unity since the latter half of the 1980s, suggesting that the debt-GDP ratio has been
following a unit root process or even an explosive process during this most recent period.
In contrast with the Japanese result, the estimates of α for the U.S. and the U.K. do not show
large ﬂuctuations. Basically, the estimates stay below unity, except that the U.S. estimate shows asharp rise during WWII.17

5.2

Empirical results for Japan

Table 2 presents the regression results for Japan obtained from a two-state model. Panel A of the tableshows a benchmark regression in which no exogenous variables are included (namely, speciﬁcation 1).
The estimate of α in regime 0 is 0.517, indicating that the debt-GDP ratio is characterized by astationary process that converges to its mean quite quickly. On the other hand, the estimate of α
in regime 1 is 1.116. Since its lower bound (1.067) exceeds unity, we cannot reject the null that thedebt-GDP ratio follows an explosive process. Figure 3 presents the estimated probability of regime
1 in each year of the sample period, as well as the estimated coeﬃcient on bt−1 , which is calculated
as a weighted average of the coeﬃcients in regimes 0 and 1, with the estimated probabilities of eachregime being used as a weight. The shaded area represents the 95 percent conﬁdence interval. Figure
3 shows that the years except 1945-1970 fall under regime 1 and that the coeﬃcient on bt−1 exceeds
unity except during the period 1945-1970.
Panel B of Table 2 shows the results of a similar regression, but this time we added military
expenditures as an exogenous variable (speciﬁcation 2). Again, the debt-GDP ratio is characterized
by a stationary process for regime 0 and an explosive process for regime 1. The estimated coeﬃcienton bt−1 , shown in Figure 3, looks quite similar to the previous case, except that the coeﬃcient is now
lower than unity in 1890-1905 (the period of the Sino-Japanese and the Russo-Japanese Wars) and
1915-1920 (the period of WWI).
Panel C of Table 2 reports the regression result for the case in which military expenditure andnt
the growth dividend, − 1+nbt−1 , are included as exogenous variables (speciﬁcation 3). Again, we seetthat regime 0 is characterized by a stationary process and regime 1 by an explosive process. But a

17 In addition, α shows a sharp decline during high inﬂation periods (the 1920s in the U.S. and the U.K., and the1950s in the U.K.), again probably reﬂecting the fact that the real value of public debt quickly decreased due to highinﬂation.

17notable diﬀerence from the previous two speciﬁcations is that the estimate of α in regime 0 is now
much closer to unity, indicating that convergence to its mean is much slower. Speciﬁcally, the estimateof α in speciﬁcation 1 (0.5177) implies that the debt-GDP ratio declines to half of its initial value
after about 1.05 years, while the one in speciﬁcation 3 (0.9178) implies that the half-life is 8.08 years.
The surprisingly quick decline in the debt-GDP ratio found in speciﬁcations 1 and 2 mainly reﬂects
the fact that the debt-GDP ratio fell very quickly during the hyper-inﬂation period in 1945-47. This
problem is now ﬁxed by properly controlling for the growth dividend. Figure 3 now shows that theprobability of regime 1 is close to unity in 1930-1950 and 1970-2004, while the probability of regime 0
is high in 1885-1925 and 1950-1970. These results suggest that the former periods are characterized
by a lack of ﬁscal discipline, while the latter periods are characterized by a locally Ricardian rule.
³

Finally, Panel D of Table 2 reports the results for the case in which military expenditure and
´
it−1
nt
−
1+nt
1+nt bt−1 are included as exogenous variables (speciﬁcation 4). The results are basicallythe same as those for speciﬁcation 3, except that the estimates of α in regimes 0 and 1 are both

lower, conﬁrming that the assumption of a globally Ricardian policy is weaker than that of a locally
Ricardian policy.
In sum, we ﬁnd that the Japanese government made several large changes with respect to its ﬁscal
behavior over the past 120 years. Speciﬁcally, Japanese ﬁscal policy is characterized by a locally
Ricardian rule in 1885-1925 and 1950-1970. The former largely corresponds to the period in which
Japan had adopted the gold standard under which the government was forced to maintain a balanced
budget until Japan left the gold standard in 1917, following the same move by the core countries ofthe system.18 The second period follows the ﬁscal restructuring ushered in in December 1948, when
SCAP instructed the Japanese government to implement a balanced budget in order to stop runaway
inﬂation. 19 On the other hand, Japanese ﬁscal policy is characterized by a non-Ricardian rule in
1930-1950 and 1970-2004, suggesting that the Japanese government abandoned ﬁscal discipline not
only during WWII, but also in the most recent period starting in 1970.

5.3

Sensitivity analysis

AR (2) model

The baseline regressions reported in Table 2 assume that the government adjusts

the primary surplus in period t in response to a change in public debt at the beginning of period
18 See Shizume (2001) for more on the Japanese government’s ﬁscal behavior during the gold standard period.
19 For details on the “Dodge Line,” see, for example, Cohen (1950) and Yamamura (1967).

18

t. Given that we use annual data, this seems to be a good approximation to actual policy making.
However, as often pointed by researchers and practitioners, it usually takes more than one year before
ﬁscal decisions are ﬁnally made. If this is the case, our baseline speciﬁcation may not be appropriate.
To address this potential problem, we change the lag structure of our estimating equation (equation(11)) to

bt =


PK

 µ0 + α0 k=1 ω0k bt−k + ηt bt−1 + u0t , µ + α PK ω b
1
1
k=1 1k t−k + ηt bt−1 + u1t ,where ω0k and ω1k are parameters satisfying

ifSt = 0if

St = 1PK

k=1 ωik = 1 and representing the lag structure of ﬁscal

decision making.20 The estimating equation is now given byPK−1
 µ0 + (α0 + ηt )bt−1 + k=1 θ0k △bt−k + u0t ,
bt =

PK−1
 µ + (α + η )b1
1
t t−1 +
k=1 θ1k △bt−k + u1t ,if

St = 0if

St = 1

where θik ≡ −αi ωi,k+1 . We conducted a lag search to end up with K = 2. The results of theregressions using this equation are reported in Table 3 and Figure 4 and are basically the same as
before. In addition, the coeﬃcient on △bt−1 , denoted by θ in Table 3, is very close to zero in eachregime, indicating that the AR (1) speciﬁcation is not a binding constraint.

Net public debt

The baseline regressions use gross public debt issued by the central and local

governments rather than net debt. This is based on the assumption that governments own only asmall amount of ﬁnancial assets and that ﬂuctuations in the amount of ﬁnancial assets over time are
insubstantial. However, as pointed out by Broda and Weinstein (2004), Japan’s public sector, throughits social security funds, holds non-negligible amounts of ﬁnancial assets. According to their estimate,
net debt held by the Japanese public sector at the end of FY2002 was equivalent to 64 percent ofGDP, while the corresponding gross ﬁgure was 161 percent. Obviously, the diﬀerence is not trivial.
To evaluate how sensitive the baseline results are, we re-estimate our equations replacing grossdebt with net debt. The net debt data we use here are the data published by the Economic and Social
Research Institute (ESRI), Cabinet Oﬃce, which cover the general government, including the central
20 Note that this speciﬁcation diﬀers from a partial adjustment model, such as the one adopted by Favero and Monacelli(2005), in that the coeﬃcient on lagged values of b depends only on the current regime (and not on past regimes).

19

and local governments and the social security funds. Unfortunately, however, the ESRI data cover
only the postwar period starting in 1955, so that the estimation is conducted only for this shorter
sample period.
Figure 5 compares Japanese general government gross and net debt. Although the diﬀerence
between the two in terms of the vertical distance is indeed substantial, we still see a common longterm trend: Namely, both start to increase around 1970 and basically continue to rise over the next
35 years. Comparing the estimation result reported in Table 4 with the baseline result (Table 2), we
see no change in that the debt-GDP ratio is characterized by a stationary process in regime 0 and anonstationary process in regime 1. We may therefore safely conclude that our baseline results are notparticularly sensitive to the deﬁnition of public debt.
Somewhat interestingly, however, if one looks closely at Figure 6, one can see a substantial decline
in the probability of regime 1 during the latter half of the 1980s. Correspondingly, the coeﬃcient on
bt−1 fell below unity during this period in speciﬁcation 3 and more clearly in speciﬁcation 4. The latter
half of the 1980s famously is a period of ﬁscal reconstruction during which the Japanese government
intensively cut expenditure to achieve the target of “no net issuance of government bonds.”21 One
may interpret the decline in the coeﬃcient on bt−1 during this period as reﬂecting the restoration ofﬁscal discipline.22 However, the coeﬃcient on bt−1 started to increase again in the early 1990s andhas remained very close to unity since.

Automatic stabilizers

Recent empirical studies on ﬁscal policy rules emphasize the importanceof automatic stabilizers in explaining ﬂuctuations in the ﬁscal surplus/deﬁcit (see Taylor (2000),
Auerbach (2003), and Bohn (1998)). For example, Taylor (2000), using U.S. data for 1960-1999,
ﬁnds that the cyclical surplus was highly correlated with ﬂuctuations in the output gap but thiswas not necessarily the case for the structural surplus. To control for this eﬀect in our regression
exercise, we add the output gap to the estimating equations. Speciﬁcally, we closely follow Barro(1986) and Bohn (1998) by introducing a new variable, Y V ARt , which is deﬁned as Y V ARt ≡(1 − Yt /Yt∗ )(G∗t /Yt ), where Yt is the real GDP, Yt∗ is its trend component estimated by HP ﬁlter,
21 See, for example, Ihori et al. (2001) for more on ﬁscal reform eﬀorts during this period.
22 Figure 6 shows that the coeﬃcient on b
t−1 during the latter half of the 1980s is slightly below unity but notstatistically diﬀerent from unity in speciﬁcation 3, while it is signiﬁcantly smaller than unity in speciﬁcation 4. Thisimplies that the ﬁscal regime during this period is characterized not by a locally Ricardian but a globally Ricardian rule.
This result is perfectly consistent with the fact that the government indeed aimed at “no net issuance of government
bonds” but had little intention of going further than that, i.e., it had no intention to reduce the debt-GDP ratio to alower level or even zero.

20and G∗t is the trend component of real government spending. The regression results presented inTable 5 show that the coeﬃcient on Y V AR is around 0.7 and signiﬁcantly diﬀerent from zero in both
speciﬁcations, indicating that automatic stabilizers did play an important role even in the Japanesecase. However, the coeﬃcient of main interest to us, α, is almost the same as before, suggesting thatthe baseline result is not sensitive to whether we control for the output gap or not.
No restriction on the coeﬃcient on interest payments As we can see from equations (4) and(8), the sole diﬀerence between locally and globally Ricardian rules is what kind of restriction we imit−1
pose on the coeﬃcient on interest payments 1+n
wt−1 . Locally Ricardian rules impose the restrictiontthat the coeﬃcient should be equal to unity, while globally Ricardian rules impose the restrictionthat it should be zero. The former corresponds to speciﬁcation 3, while the latter corresponds tospeciﬁcation 4. An important implication of these restrictions, whether the coeﬃcient should be zeroor unity, is that these speciﬁcations allow a switching only between locally Ricardian rules and otherrules (i.e., rules that do not belong to locally Ricardian rules) in the case of speciﬁcation 3, and aswitching only between globally Ricardian rules and the other rules in the case of speciﬁcation 4.
These speciﬁcations would be inappropriate if, for example, policy switching occurs between locallyand globally Ricardian rules.
To deal with this potential problem, we conduct a similar regression as before but now do not
impose an a priori restriction on the coeﬃcient on interest payments. Speciﬁcally, we add a newit−1
independent variable 1+nbt−1 to equation (11) witht

ηt = −nt; νt = −gtm .
1 + nt

The coeﬃcient on the new independent variable should be close to zero if the true rule is well approximated by a locally Ricardian rule, and it should be unity in the case of a globally Ricardian rule.
The results are shown in Table 6 and indicate that the estimated coeﬃcient is 0.628 in regime 0 (thestationary regime) and 0.506 in regime 1 (the nonstationary regime). More importantly, the lower
bound in regime 0 is 0.235, rejecting the null of zero, while the upper bound in regime 0 is slightly
lower than unity (0.990), again rejecting the null of unity. This means that the true rule is not wellapproximated by the two extremes (i.e., locally and globally Ricardian rules) but is located between
them. The same results can be seen for regime 1.23 However, the estimated values of α in Table 6
23 These results suggest that neither empirical studies focusing only on locally Ricardian rules nor those focusing only21

tend to fall between those obtained in speciﬁcations 3 and 4 of Table 2, conﬁrming that the main
results regarding ﬁscal policy behavior in Table 2 hold without any substantial modiﬁcations.

Three-state model The robustness of the ﬁndings in Table 2 are examined in Table 7 by extending
the analysis to a three state model. Panel A, which reports the regression results for speciﬁcation 3,
shows that regime 0 is characterized by a stationary process (α = 0.926), regime 1 by an explosive
process (α = 1.081), and regime 2 by another highly explosive process (α = 1.313). Figure 9 showsthat the periods falling under regime 1 in Figure 3 are again classiﬁed as regime 1,24 suggesting thatthe number of regimes allowed in Table 2 (namely, two regimes) is not an inappropriate descriptionof the true model. These results, together with the results for speciﬁcation 4, more or less conﬁrm
the earlier ﬁndings: (1) the periods 1885-1920 and 1950-1970 fall under regime 0 (a regime with ﬁscal
discipline); (2) the period 1920-1950 falls under regime 1 (a regime without ﬁscal discipline).

5.4

Are debt ratios globally stationary or nonstationary?

The regression analysis in this section seeks to determine whether the debt-GDP ratio follows astationary process within a regime. However, as we discussed earlier, even if the ratio is stationary
within a regime, this does not necessarily imply that it is stationary in the long run. This is simply
because regime changes occur stochastically in accordance with transition probabilities. Thus, what
we need to know is where the debt-GDP ratio is headed in the long run given the estimated transition
probabilities, or, put diﬀerently, we need to know whether its distribution converges over time to acertain distribution. A process is said to be globally stationary if the distribution converges to acertain distribution over time, while stationarity within a regime is called local stationarity. Global
stationarity implies that the eﬀect of policy shocks on the debt-GDP ratio becomes smaller and smaller
over time and ﬁnally disappears in the long run. Investors in government bonds markets are interested
in whether this global stationarity is satisﬁed or not, and policymakers, especially central banks, areinterested in this property when designing monetary policy rules.
Francq and Zakoian (2001) obtain a result regarding the relationship between local and global
stationarity that is of some interest in the present context, namely that local stationarity is neither anecessary nor a suﬃcient condition for global stationarity. For example, suppose there are two regimes
on globally Ricardian rules employ an appropriate estimating equation.
24 The exceptions are 1944 and 1970-1980, years in which the debt-GDP ratio recorded an extremely high growth rate,
so that they are classiﬁed as regime 2.

22and one satisﬁes local stationary while the other does not. Even in this combination, the process could
be globally stationary. On the other hand, even if each of the two regimes satisﬁes local stationarity,
this does not necessarily imply global stationarity.25
As we saw in Table 2, the regression results using a two-state model show that one regime satisﬁes(local) stationarity while the other one does not. Also, as we saw in Table 7, the regression results
using a three-state model indicate that one regime satisﬁes (local) stationarity, but the other two donot. Given these results, one may wonder if they imply global stationarity or nonstationarity. To
address this issue, we conduct the following simulation exercise. We generate a time series of bt using

³
´
nt

µ̂
+
α̂
−
if
St = 00 0
1+nt bt−1 + u0t ,
bt =
³
´


 µ̂1 + α̂1 − nt bt−1 + u1t ,if
St = 1
1+nt
for a two-state model and the corresponding equation for a three-state model. Here, parameters witha hat represent the values estimated in the earlier regressions. More speciﬁcally, we randomly draw
policy shocks and policy regimes using the parameters and transition probabilities obtained from theregression of speciﬁcation 3 and generate a replication for the time series of the debt-GDP ratio over1000 years for various paths of the nominal growth rate (nt ) that are exogenously determined. We
repeat this process 5000 times to obtain a distribution of the debt-GDP ratio in every year of the1000 years. We can say that the debt-GDP process is globally stationary if this distribution is stable
over time; otherwise it is globally nonstationary.
Table 8 reports the ﬁrst, second, and third quantiles of the simulated distribution with T = 500(500 years later) and T = 1000 for the two-state and three-state models. In Panel A it is assumed
that the initial regime is a stationary one (i.e., S0 = 0), and that the debt-GDP ratio in period 0
is zero. On the other hand, in Panel B, it is assumed that the initial regime is a nonstationary one(S0 = 1) and that the initial debt-GDP ratio is unity (100 percent). The simulation results from thetwo-state model show that the distribution is stable over time, irrespective of the initial conditions
and the assumed values of nominal growth rates (n), clearly indicating that the debt-GDP ratio
satisﬁes global stationarity. On the other hand, the results from the three-state model show that the
distributions with T = 500 and T = 1000 diﬀer signiﬁcantly for the case of n = 0.00, 0.03, and 0.06,
25 Gali (2006) provides a clear and interesting discussion of the implications of Francq and Zakoian’s (2001) result on

the determinacy of an equilibrium in a monetary economy.

23

implying that the process is globally nonstationary.26
Figure 10 presents a similar simulation conducted to forecast the future path of the debt-GDP
ratio over the next 100 years. To make the initial condition as close to the current situation in Japanas possible, we assume that the initial regime is S0 = 1 and that the debt-GDP ratio in period 0 is 1.7,
which is the actual ﬁgure at the end of 2004. According to the result from the two-state model with
3 percent nominal growth, the “third quantile” line goes up until it reaches 3 with T = 20, indicatingthat a further increase in the debt-GDP ratio is quite likely to occur over the next 20 years. After
that, however, the debt-GPD ratio enters a declining trend as a result of the switch to a stationary
regime and then converges to a quite narrow (and probably tolerable) band within 100 years. On
the other hand, the result from the three-state model with 3 percent nominal growth shows that themedian of the distribution increases quite quickly to reach an unrealistic and intolerable level within
50 years, and that its variance increases over time, clearly indicating global nonstationarity.

5.5

Empirical results for the U.S.

Table 9 presents the regression results for the United States using a two state model. Results for
speciﬁcation 3, presented in Panel A, indicate that each of the regimes, 0 and 1, is characterized
by a stationary process. This implies that the U.S. government’s ﬁscal behavior during the sample
period can be described as a switching between locally Ricardian policy rules. If we turn to theresults for speciﬁcation 4, presented in Panel B, they again indicate that each regime, 0 and 1,
satisﬁes stationarity, implying that U.S. ﬁscal policy is characterized by a switching between globally
Ricardian rules.
These results suggest that the U.S. government’s ﬁscal behavior consistently has been very close to
locally Ricardian policy throughout the entire sample period. In fact, the estimated coeﬃcient on bt−1 ,presented in Figure 11, consistently and statistically signiﬁcantly remains below unity. If we compare
these results with those reported in previous studies on U.S. ﬁscal policy, we ﬁnd some similarities.
Bohn (2005), for example, regressed the U.S. primary surplus on public debt for a sample period
from 1793 to 2003 and reports that the OLS estimate of the coeﬃcient on public debt is positive andsigniﬁcantly diﬀerent from zero when tax smoothing eﬀects are properly controlled for. Bohn interprets

26 However, when n goes up to 0.10, the distributions with T = 500 and T = 1000 become identical, suggesting thatsuﬃciently high nominal growth could make the debt-GDP ratio globally stationary. The threshold for nominal growth
rates is about 8 percent, which is lower than the sample average (13.7 percent).

24

this result as providing evidence for a globally Ricardian rule; but since the estimated coeﬃcient istypically greater than the average interest rate level, this could be interpreted as suggesting a rulethat is even locally Ricardian. Bohn (1998) conducts a similar exercise using data for 1916-1995 andﬁnds that the coeﬃcient on public debt is signiﬁcantly positive not only for the entire sample period,
but also for ﬁve sub-sample periods, including the postwar period. These results reported by Bohn
(1998, 2005) are consistent with ours.
Favero and Monacelli (2005) estimate an equation that is very close to our speciﬁcation 1 (equation(6)) using the maximum likelihood method and report that U.S. government behavior has been deviating from Ricardian policy for most of the entire sample period (1961-2002), except that it was close
to a locally Ricardian rule during the period of 1995-2001. Although their results cannot be directlycompared to ours because the empirical methodologies diﬀer in several respects, we still attempt todo so by adjusting our sample period to theirs. Panels C and D of Table 9 show the results of aregression that is similar to that underlying Panels A and B, but that now uses data for the postwar
period. The regression results indicate that the estimate of α in regime 0 is less than unity, suggestingthat it is a stationary regime as before, but that the upper bound of α in regime 1 slightly exceeds
unity, so that we fail to reject the null of a unit root. Fluctuations in the estimated coeﬃcient on
bt−1 , presented in Figure 11, show that it has been slightly higher than unity since 1975, implying thepossibility that the U.S. government started to deviate from Ricardian policy around 1975. However,the ﬁgure clearly shows that the estimated coeﬃcient on bt−1 is consistently less than unity during theperiod before 1975 and that there is no evidence for the return to Ricardian policy around 1995 that
Favero and Monacelli (2005) detected. Thus, there are certain inconsistencies between their results
and ours. 27
Given that U.S. ﬁscal policy is characterized by switching between stationary regimes, we may
apply a model with multiple breaks, as proposed by Bai and Perron (1998), to the U.S. data. Thismodel does not require researchers to assume that policy regime switching is a recurrent phenomenon,
and that it has a Markov property. This is an important advantage, but on the other hand it requires
the debt process to be weakly stationary in each regime, so that we cannot apply it to the Japanesedata. The regression results reported in Table 10 show that regime changes occur four times (i.e., there
are ﬁve diﬀerent regimes) with both speciﬁcations 3 and 4. According to the result for speciﬁcation
27 We also estimated speciﬁcation 1, which is very close to the estimating equation employed by Favero and Monacelli(2005), for the entire sample period as well as for the postwar period, but found that both regimes are stationary ones.

25

4, the estimate of α is slightly higher than unity during the wartime period (regime 3, 1917-1943)
but is signiﬁcantly smaller than unity in the other four regimes. These results may be interpreted as
conﬁrming our earlier results obtained from the Markov switching regression.28

5.6

Empirical results for the U.K.

Table 11 presents the regression results for the United Kingdom using a two-state model. Results
for speciﬁcation 3 indicate that regime 0 is characterized by a stationary process, while regime 1 ischaracterized by a unit root process (the upper bound of α slightly exceeds unity). On the other hand,results for speciﬁcation 4 indicate that both regime 0 and regime 1 are characterized by a stationary
process, implying that the U.K. government’s ﬁscal behavior is characterized by switching between
globally Ricardian rules.

6

Conclusion

This paper estimated ﬁscal policy feedback rules in Japan, the United States, and the United Kingdom
for more than a century and allowing for stochastic regime changes. By estimating a Markov switchingmodel by the Bayesian method, we arrived at the following ﬁndings. First, the Japanese data clearlyreject the view that the ﬁscal policy regime has been ﬁxed, i.e., that the Japanese government has
adopted a regime that is either Ricardian or non-Ricardian throughout the entire period. Rather,
our results indicate a stochastic switch of the debt-GDP ratio between stationary and nonstationary
processes and thus a stochastic switch between Ricardian and non-Ricardian regimes. Speciﬁcally,
Japanese ﬁscal policy was characterized by a locally Ricardian rule in 1885-1925 and 1950-1970 but
by a non-Ricardian rule in 1930-1950 and 1970-2004. Second, through simulation exercises using
the estimated parameters and transition probabilities, we showed that the debt-GDP ratio may be
nonstationary even in the long run (i.e., globally nonstationary). Third, the Japanese result stands
in sharp contrast with the results for the U.S. and the U.K., which indicate that in these countries,
government ﬁscal behavior has been consistently characterized by Ricardian policy.

28 However, the results for speciﬁcation 3 are not very informative since α exceeds unity in three out of the ﬁve regimes.

This result may be interpreted as evidence against applying the Bai-Perron method even to the U.S. data.

26

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30

Table 1: Unit Root Tests

p
1
2
3
4
5
6
7
8
9
10

Japan
α
t-stat0.9990 -0.02
0.9607 -1.31
0.9702 -0.94
0.9729 -0.80
0.9756 -0.68
0.9691 -0.82
0.9720 -0.71
0.9824 -0.43
0.9716 -0.67
0.9740 -0.58

U.S.
αt-stat0.9868 -1.04
0.9784 -2.09
0.9818 -1.74
0.9804 -1.86
0.9808 -1.79
0.9806 -1.78
0.9815 -1.67
0.9817 -1.63
0.9839 -1.42
0.9797 -1.81

U.K.
αt-stat0.9864 -1.17
0.9798 -2.21
0.9800 -2.15
0.9817 -1.94
0.9825 -1.84
0.9813 -1.94
0.9853 -1.54
0.9819 -1.91
0.9826 -1.82
0.9827 -1.78

Note: We conduct the standard ADF tests, bt = µ + αbt−1 +P
p−1
j=1 φj ∆bt−j + ut , with various lag length. The null hypothesis is α = 1 and the 10% critical value is -2.57 when the sample
size is 100 (see Hamilton (1994)). The sample periods for Japan,
the U.S. and the U.K. are 1885-2004, 1840-2005, and 1830-2003,
respectively.

31

Table 2: Two-State Model for Japan
Panel A: Speciﬁcation 1

µ
α
σ2
p11
p00

LB
0.03550.47830.00060.91930.7804

Regime 0Mean
0.05120.51770.00100.96580.9078UB
0.06690.55290.00180.9941
0.9811

LB-0.0549
1.06740.0037

Regime 1
Mean-0.0267
1.11680.0050UB
0.0023
1.16490.0068Panel B: Speciﬁcation 2

µ
α
σ2
p11
p00

LB
0.03800.37850.00050.89780.7706

Regime 0Mean
0.05350.41340.00090.95640.8984UB
0.06880.44760.00150.99000.9792

LB-0.08631.04240.0024

Regime 1
Mean
UB-0.0591 -0.0321
1.0821
1.12330.00330.0044

Panel C: Speciﬁcation 3

µ
α
σ2
p11
p00

LB
-0.0133
0.86810.00030.85520.8778

Regime 0Mean
0.00360.91780.00050.93780.9448UB
0.0164
0.97620.00070.98670.9864LB-0.0300
1.01670.0022

Regime 1
Mean
0.00731.06410.0033UB
0.0476
1.11100.0049Regime 1
Mean-0.0150
1.05360.0033UB
0.01931.10030.0050Panel D: Speciﬁcation 4

µ
α
σ2
p11
p00

LB
-0.0067
0.81260.00030.86310.8921

Regime 0Mean
0.00560.85500.00040.94400.9469UB
0.01690.89980.0006
0.9876
0.9831

LB-0.05241.01030.0022

Note: The transition probability, pij , represents Pr(St = j | St−1 = i).
The columns labeled “LB” and “UB” refer to the lower and upper boundof the 95% conﬁdence interval and the columns labeled “Mean” refer tothe mean of the marginal distribution of the parameter.

32

Table 3: AR(2) Model
Panel A: Speciﬁcation 3

µ
α
θ
σ2
p11
p00

LB
-0.00880.85720.02180.00030.87820.8752

Regime 0Mean
0.00690.90040.12270.00040.9454
0.9412UB
0.01850.95780.31500.0006
0.98830.9827

LB-0.0298
1.0151-0.0099
0.0020Regime 1
Mean
0.00751.05580.10090.0030UB
0.0383
1.10280.19990.0045

Regime 1
Mean-0.0125
1.04490.08540.0030UB
0.02481.08710.17450.0045

Panel B: Speciﬁcation 4

µ
α
θ
σ2
p11
p00

LB
-0.00580.80070.03170.00020.86890.8868

Regime 0Mean
0.00790.84290.12130.0004
0.9467
0.9439UB
0.01890.89330.21900.00050.98550.9876

LB-0.0489
0.9979-0.00240.0019Note: The transition probability, pij , represents Pr(St = j | St−1 = i).
The columns labeled “LB” and “UB” refer to the lower and upper boundof the 95% conﬁdence interval and the columns labeled “Mean” refer tothe mean of the marginal distribution of the parameter.

33

Table 4: Net Public Debt
Panel A: Speciﬁcation 3

µ
α
σ2
p11
p00

LB
-0.0333
0.71310.00010.78120.7321

Regime 0
Mean
UB-0.0213 -0.0144
0.9227
0.99160.00020.00030.90400.97830.87990.9674

LB
0.00750.99160.0002

Regime 1
Mean
0.02761.03110.0005UB
0.04151.07370.0010Regime 1
Mean
0.0202
1.01850.0005UB
0.0356
1.05720.0009Panel B: Speciﬁcation 4

µ
α
σ2
p11
p00

LB
-0.0276
0.79610.00010.78550.7159Regime 0
Mean
UB-0.0211 -0.0140
0.8822
0.94120.00020.00030.90520.97880.8701
0.9583

LB-0.0009
0.97700.0003

Note: The transition probability, pij , represents Pr(St = j | St−1 = i). The
columns labeled “LB” and “UB” refer to the lower and upper bound of the 95%
conﬁdence interval and the columns labeled “Mean” refer to the mean of themarginal distribution of the parameter.

34

Table 5: Automatic Stabilizers
Panel A: Speciﬁcation 3

The coeﬃcienton Y V AR
µ
α
σ2
p11
p00

LB
0.4700Regime 0Mean
0.7765

UB
1.1077LB
0.3547

Regime 1
Mean
0.7559UB
1.1602-0.0103
0.86960.00030.86030.89030.00310.91920.00050.93970.94820.01630.96310.00070.98790.9851-0.02631.01170.00240.0152
1.05980.00390.0564
1.10730.0061Panel B: Speciﬁcation 4

The coeﬃcienton Y V AR
µ
α
σ2
p11
p00

LB
0.4811

Regime 0Mean
0.8034UB
1.1901LB
0.3282

Regime 1
Mean
0.7032UB
1.1213-0.0073
0.80540.00030.86260.87960.00670.85050.0004
0.94230.94590.01880.90080.0006
0.98800.9875-0.05140.99920.0025-0.0099
1.04830.00400.0323
1.09480.0062

Note: The transition probability, pij , represents Pr(St = j | St−1 = i). The columns
labeled “LB” and “UB” refer to the lower and upper bound of the 95% conﬁdence
interval and the columns labeled “Mean” refer to the mean of the marginal distribution of the parameter.

35

Table 6: No Restriction on the Coeﬃcient on Interest Payments

The coeﬃcient oninterest payments
µ
α
σ2
p11
p00

LB
0.2351

Regime 0Mean
0.6283UB
0.9907LB
0.1046

Regime 1
Mean
0.5064UB
0.8778-0.0088
0.82280.00030.86680.88260.00520.87720.0004
0.94200.94540.01740.93670.0006
0.98840.9850-0.04311.01550.0022-0.0062
1.06170.00330.0336
1.10750.0048

Note: The transition probability, pij , represents Pr(St = j | St−1 = i). The columns labeled“LB” and “UB” refer to the lower and upper bound of the 95% conﬁdence interval and thecolumns labeled “Mean” refer to the mean of the marginal distribution of the parameter.

36

Table 7: Three-State Model
Panel A: Speciﬁcation 3

µ
α
σ2
p00
p01
p10
p11
p20
p21

LB
-0.04480.85180.0001
0.79370.00530.00180.83570.00150.0149Regime 0
Mean-0.0018
0.92610.00030.9111
0.05600.03880.92350.06660.1353UB
0.0232
1.06570.00060.97830.15230.10670.9796
0.26670.3272

LB-0.0533
1.04280.0005

Regime 1
Mean-0.0241
1.08190.0007UB
0.0193
1.11220.0011

LB-0.3370
1.18500.0006

Regime 2
Mean-0.0425
1.31360.0081UB
0.04381.54400.0154

LB-0.0624
1.19710.0005

Regime 2
Mean-0.0266
1.27830.0014UB
0.0051
1.34120.0032

Panel B: Speciﬁcation 4

µ
α
σ2
p00
p01
p10
p11
p20
p21

LB
-0.0002
0.79580.0001
0.78390.01030.00620.84980.00150.0317

Regime 0Mean
0.01530.82830.00030.89940.06070.04570.92610.05560.1393UB
0.02620.86730.00040.96980.15480.11550.97390.19030.3257

LB-0.07311.06250.0004

Regime 1
Mean
UB-0.0602 -0.0469
1.08401.10130.00060.0008

Note: The transition probability, pij , represents Pr(St = j | St−1 = i). The columns labeled “LB” and“UB” refer to the lower and upper bound of the 95% conﬁdence interval and the columns labeled “Mean”
refer to the mean of the marginal distribution of the parameter.

37

Table 8: Globally Stationary or Nonstationary?
Panel A: S0 = 0 and b0 = 0
Quantile

Two-State ModelFirst
Median Third

Three-State ModelFirst
MedianThird

0% Growth
T=500-0.1471
T=1000 -0.1593

0.0006-0.00070.15250.1497-1.1E+10-2.5E+21-3.1117-2.7E+07

1.4E+10
2.6E+213% Growth
T=500-0.0751
T=1000 -0.0790

0.0005-0.00110.07720.0786-3.6E+04-5.9E+09

0.04140.6536

4.9E+04
1.1E+10

6% Growth
T=500-0.0569
T=1000 -0.0591

0.0003-0.00120.05740.0584-4.2741-16.665-0.00160.00854.493920.506

10% Growth
T=500-0.0476
T=1000 -0.0478

0.0001-0.0006

0.04630.0466-0.1160-0.11750.00080.00100.12050.1192

13.7% Growth
T=500-0.0423
T=1000 -0.0428-0.0003-0.0004

0.04130.0403-0.0579-0.0598

0.0013-0.0001

0.06150.0592

Panel B: S0 = 1 and b0 = 1
Quantile

Two State ModelFirst
Median Third

Three State ModelFirst
MedianThird

0% Growth
T=500-0.1476
T=1000 -0.1524

0.0017-0.0028

0.16230.1515

6.1E+08
1.0E+19

2.9E+115.2E+228.9E+13
1.8E+26

3% Growth
T=500-0.0800
T=1000 -0.0780-0.0007-0.00070.07800.0751131.324.2E+05

1.7E+05
1.3E+107.2E+079.2E+13

6% Growth
T=500-0.0573
T=1000 -0.0575-0.00030.0006

0.05820.0585-0.2212-1.82120.41990.2312121.10359.11

10% Growth
T=500-0.0481
T=1000 -0.0458-0.00070.00070.04670.0467-0.1082-0.11310.00110.00060.11950.1172

13.7% Growth
T=500-0.0427
T=1000 -0.0400-0.0009
0.00080.0416
0.0413-0.0603-0.0573-0.0009
0.00130.05740.0600Note: We randomly draw policy shocks and policy regimes using the parameters obtained from regressions of speciﬁcation 3 and generate 5000 replications
for the time series of the debt-GDP ratio (1000 years) for various paths of thenominal growth rate (nt ), which are exogenously determined. The ﬁgures inthe table represent the ﬁrst, second, and third quantiles of the simulated distribution with T=500 (i.e., 500 years later) and T=1000. The average growthrate over the entire sample was 13.7 percent.

Table 9: Two-State Model for the U.S.
Panel A: Speciﬁcation 3, 1840-2005

µ
α
σ2
p11
p00

LB
-0.00390.87340.00003
0.84480.8635

Regime 0
Mean-0.00130.88050.000070.91610.9287UB
0.00140.88850.00010.97020.9704LB
0.00550.90250.0004

Regime 1
Mean
0.02420.93930.0007UB
0.04580.97600.0010Panel B: Speciﬁcation 4, 1840-2005

µ
α
σ2
p11
p00

LB
-0.00310.84480.00003
0.81010.8637

Regime 0
Mean
UB-0.00120.00080.85260.85940.00005 0.00007
0.8922
0.95300.92430.9644LB
0.00620.84320.0007

Regime 1
Mean
0.02770.88110.0010UB
0.05180.91650.0014

Panel C: Speciﬁcation 3, 1948-2004

µ
α
σ2
p11
p00

LB
-0.04260.84780.00005
0.82500.7771

Regime 0
Mean-0.01110.88870.00010.92730.9068UB
0.01140.94410.00020.98490.9777

LB-0.0182
0.92610.0002

Regime 1
Mean
0.00850.96990.0004UB
0.0332
1.01890.0006

Panel D: Speciﬁcation 4, 1948-2004

µ
α
σ2
p11
p00

LB
-0.05220.84920.00005
0.83790.7636

Regime 0
Mean
UB-0.0300 -0.0073
0.89070.92850.00010.00020.92920.98330.9024
0.9794

LB-0.04430.93300.0001

Regime 1
Mean
UB-0.0245 -0.0057
0.96531.00040.00020.0004

Note: The transition probability, pij , represents Pr(St = j | St−1 = i).
The columns labeled “LB” and “UB” refer to the lower and upper boundof the 95% conﬁdence interval and the columns labeled “Mean” refer tothe mean of the marginal distribution of the parameter.

39

Table 10: Multiple Break Tests for the U.S.
Panel A: Speciﬁcation 3µαRegime 1-0.00930.95551840-1872 ( 0.0026 ) ( 0.0240 )Regime 21.00091873-1916( 0.0265 )
Regime 3
1.04691917-1943( 0.0125 )Regime 40.9071
1944-1972( 0.0057 )Regime 51.01351973-2004( 0.0079 )Panel B: Speciﬁcation 4µ
αRegime 1-0.01200.91671840-1872 ( 0.0028 ) ( 0.0256 )Regime 20.9781
1873-1916( 0.0283 )Regime 3
1.02641917-1943( 0.0133 )Regime 40.8868
1944-1972( 0.0061 )Regime 50.94501973-2004( 0.0084 )

Note: The constant term is imposed to be identical across regimes. The maximum
number of breaks is 5 with ϵ=0.15. Figures in parentheses denote standard errors.

40

Table 11: Two-State Model for the U.K.
Panel A: Speciﬁcation 3

µ
α
σ2
p11
p00

LB
0.08370.80430.00030.91280.6603

Regime 0Mean
0.10260.82130.0004
0.95440.8175

LB-0.0033
0.79860.00030.9027
0.6323

Regime 0Mean
0.06920.82020.0004
0.94740.7900UB
0.12200.83690.00050.98170.9248LB-0.03410.98840.0004

Regime 1
Mean
UB-0.0264 -0.0180
0.99551.00190.00050.0006

Panel B: Speciﬁcation 4

µ
α
σ2
p11
p00

UB
0.09520.86860.00050.98160.9199LB-0.0411
0.96400.0003

Regime 1
Mean
UB-0.0336 -0.0239
0.97090.97730.00040.0006

Note: The transition probability, pij , represents Pr(St = j | St−1 = i).
The columns labeled “LB” and “UB” refer to the lower and upper boundof the 95% conﬁdence interval and the columns labeled “Mean” refer tothe mean of the marginal distribution of the parameter.

41

Figure 1: Public Debt (Relative to Nominal GDP)

Japan
2.5
2
1.5
1
0.5
0
1825

1840

1855

1870

1885

1900

1915

1930

1945

1960

1975

1990

2005

1930

1945

1960

1975

1990

2005

1930

1945

1960

1975

1990

2005

U.S.
2.5
2
1.5
1
0.5
0
1825

1840

1855

1870

1885

1900

1915

U.K.
2.5
2
1.5
1
0.5
0
1825

1840

1855

1870

1885

1900

1915

42

Figure 2: Coeﬃcient on bt−1 Estimated from Rolling Regressions

Japan
1.2
1
0.8
0.6
0.4
0.2
0
1865 1875 1885 1895 1905 1915 1925 1935 1945 1955 1965 1975 1985 1995 2005

U.S.
1.2
1
0.8
0.6
0.4
0.2
0
1865 1875 1885 1895 1905 1915 1925 1935 1945 1955 1965 1975 1985 1995 2005

U.K.
1.2
1
0.8
0.6
0.4
0.2
0
1865 1875 1885 1895 1905 1915 1925 1935 1945 1955 1965 1975 1985 1995 2005

43

Figure 3: Two-State Model for Japan
Specification 1
1

0.5
Probability of regime 1
0
1885

1.2
1
0.8
0.6
0.4
0.2
0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

Estimated coefficient on bt-1
1895

1905

1915

Specification 2
1

0.5
Probability of regime 1
0
1885

1.2
1
0.8
0.6
0.4
0.2
0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

Estimated coefficient on bt-1
1895

1905

1915

44

Figure 3: Two-State Model for Japan—Continued
Specification 3
1

0.5
Probability of regime 1
0
1885

1.2
1
0.8
0.6
0.4
0.2
0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

Estimated coefficient on bt-1
1895

1905

1915

Specification 41

0.5
Probability of regime 1
0
1885

1.2
1
0.8
0.6
0.4
0.2
0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

Estimated coefficient on bt-1
1895

1905

1915

45

Figure 4: AR(2) Model
Specification 3
1

0.5
Probability of regime 1
0
1885

1.2
1
0.8
0.6
0.4
0.2
0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

Estimated coefficient on bt-1
1895

1905

1915

Specification 41

0.5
Probability of regime 1
0
1885

1.2
1
0.8
0.6
0.4
0.2
0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

Estimated coefficient on bt-1
1895

1905

1915

46

Figure 5: Net Public Debt in Japan (Relative to Nominal GDP)

180
Gross Debt

Net Debt

1960

1970

160
140
120
100
80
60
40
20
0
-20

1955

1965

1975

1980

1985

1990

1995

2000

2005

Sources: Economic Planning Agency, Report on National Accounts, 1955 to 1969, and Cabinet
Oﬃce, Annual Report on National Accounts.

47

Figure 6: Net Public Debt
Specification 3
1
Probability of regime 1
0.5

0
1955

1.2
1
0.8
0.6
0.4
0.2
0

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

1975

1980

1985

1990

1995

2000

2005

Estimated coefficient on bt-1
1955

1960

1965

1970

Specification 4
1
Probability of regime 1
0.5

0
1955

1.2
1
0.8
0.6
0.4
0.2
0

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

1975

1980

1985

1990

1995

2000

2005

Estimated coefficient on bt-1
1955

1960

1965

1970

48

Figure 7: Automatic Stabilizers
Specification 3
1

0.5
Probability of regime 1
0
1885

1.2
1
0.8
0.6
0.4
0.2
0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

Estimated coefficient on bt-1
1895

1905

1915

Specification 41

0.5
Probability of regime 1
0
1885

1.2
1
0.8
0.6
0.4
0.2
0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

Estimated coefficient on bt-1
1895

1905

1915

49

Figure 8: No Restriction on the Coeﬃcient on Interest Payments

1

0.5
Probability of regime 1
0
1885

1.2
1
0.8
0.6
0.4
0.2
0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

Estimated coefficient on bt-1
1895

1905

1915

50

Figure 9: Three-State Model for Japan

Specification 3
1

0.5
Probability of regime 0
0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

1
Probability of regime 1
0.5

0
1885

1895

1905

1915

1
Probability of regime 2
0.5

0
1885

1895

1905

1915

1.5
1
0.5
0
1885

Estimated coefficient on bt-1
1895

1905

1915

51

Figure 9: Three-State Model for Japan—Continued

Specification 4
1
Probability of regime 0
0.5

0
1885

1895

1905

1915

1925

1935

1945

1

1955

1965

1975

1985

1995

2005

Probability of regime 1

0.5

0
1885

1895

1905

1915

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

1925

1935

1945

1955

1965

1975

1985

1995

2005

1
Probability of regime 2
0.5

0
1885

1895

1905

1915

1.5
1
0.5
0
1885

Estimated coefficient on bt-1
1895

1905

1915

52

Figure 10: Globally Stationary or Nonstationary?

Path of the debt-GDP ratio with 3.0 percent growth (Specification 3 of the two-state model)
3
2
1
0
-1
2004 2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

Path of the debt-GDP ratio with 13.7 percent growth (Specification 3 of the two-state model)
3
2
1
0
-1
2004 2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

Path of the debt-GDP ratio with 3.0 percent growth (Specification 3 of the three-state model)
300
200
100
0
2004 2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

Path of the debt-GDP ratio with 13.7 percent growth (Specification 3 of the three-state model)
3
2
1
0
-1
2004 2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

Note: The data of size 120 are generated from Speciﬁcation 3 using estimated values with b0 = 1.7
and S0 = 1. In all cases, we replicate this procedure 5000 times to compute the ﬁrst, second, andthird quantiles.

53

Figure 11: Two-State Model for the U.S.
Specification 3, 1840-2005
1

Probability of regime 1

0.5

0
1840

1.2
1
0.8
0.6
0.4
0.2
0
1840

1855

1870

1885

1900

1915

1930

1945

1960

1975

1990

2005

1900

1915

1930

1945

1960

1975

1990

2005

Estimated coefficient on bt-1
1855

1870

1885

Specification 4, 1840-2005
1

Probability of regime 1

0.5

0
1840

1.2
1
0.8
0.6
0.4
0.2
0
1840

1855

1870

1885

1900

1915

1930

1945

1960

1975

1990

2005

1900

1915

1930

1945

1960

1975

1990

2005

Estimated coefficient on bt-1
1855

1870

1885

54

Figure 11: Two-State Model for the U.S.—Continued
Specification 3, 1948-2004
1

0.5
Probability of regime 1
0
1945

1950

1955

1960

1965

1970

1975

1.2
1
0.8
0.6
0.4
0.2
0
1945

1980

1985

1990

1995

2000

2005

1995

2000

2005

1995

2000

2005

2000

2005

Estimated coefficient on bt-1
1950

1955

1960

1965

1970

1975

1980

1985

1990

Specification 4, 1948-2004
1

0.5
Probability of regime 1
0
1945

1950

1955

1960

1965

1970

1975

1.2
1
0.8
0.6
0.4
0.2
0
1945

1980

1985

1990

Estimated coefficient on bt-1
1950

1955

1960

1965

1970

1975

55

1980

1985

1990

1995

Figure 12: Two-State Model for the U.K.
Specification 3
1

0.5
Probability of regime 1
0
1825

1.2
1
0.8
0.6
0.4
0.2
0
1825

1840

1855

1870

1885

1900

1915

1930

1945

1960

1975

1990

2005

1900

1915

1930

1945

1960

1975

1990

2005

Estimated coefficient on bt-1
1840

1855

1870

1885

Specification 41

0.5
Probability of regime 1
0
1825

1.2
1
0.8
0.6
0.4
0.2
0
1825

1840

1855

1870

1885

1900

1915

1930

1945

1960

1975

1990

2005

1900

1915

1930

1945

1960

1975

1990

2005

Estimated coefficient on bt-1
1840

1855

1870

1885

56

Appendix
A.1

Data descriptionJapan

The deﬁnition of “general government” varies over time and there are four such deﬁnitions for thetime span of our sample period: the deﬁnition by the Economic Counsel Board (ECB) for 1885-1954,
the OLD SNA for 1955-1969, the 68SNA for 1970-1979, and the 93SNA for 1980-2004. The ECB’s
deﬁnition is described in Economic Counsel Board (1954) and in the Kokumin Shotoku Hokoku [Reporton National Income] published by the ECB. A detailed classiﬁcation table of government organizationsin the OLD SNA and the 68SNA is provided in Economic Planning Agency (1978). Finally, the 93SNA
deﬁnition is available from the Economic and Social Research Institute, Cabinet Oﬃce website. Ourseries are for calendar years for 1885-1900 and for ﬁscal years for 1901-2004.
A.1.1

Public debt

Central government Central government gross debt consists of government bonds, ﬁnancing bills,
borrowings, and temporary borrowings. For 1885-1899, ﬁgures for these are taken from a table (pp.3132) in Ministry of Finance (1936). For 1900-1962, the ﬁgures are from Summary Table 1 (pp.4-5) in the
Kokusai Tokei Nenpo [Annual Report on Japanese Government Bonds Statistics], FY1975, publishedby the Ministry of Finance. For 1963-2003, the data are obtained from Table 40 (pp.397) in the Zaisei
Tokei [Budget Statistics], FY2005, also published by the Ministry of Finance. Finally, for 2004 they
are from Summary Table 1 (pp.4-5) in the FY2004 edition of the Kokusai Tokei Nenpo.
However, we exclude the Colonial Special Accounts and Enterprise Special Accounts from any
debt held by the central government, because neither is classiﬁed as part of the general government.
There are ﬁve Colonial Special Accounts: for the Chosen Government, the Taiwan Government, theKwantung Oﬃce, the Karafuto Oﬃce, and the Nanyo Oﬃce. As for Enterprise Special Accounts, thenumber of accounts varies over time. The following is a list of special accounts that can be actually
identiﬁed from government debt statistics tables:
For 1890-1954 : Steelworks, National Railway Service, Imperial Railway Service, Foodstuﬀ
Controls, National Forest Service, Telecommunication Service, Communication Enterprise,
Postal Service, Alcohol Monopoly, Taiwan Foodstuﬀ Controls, Chosen Foodstuﬀ Controls,
Printing Bureau, Precious Metals, Fuel Bureau, Demand and Supply Adjustment of Charcoal and Firewood.
For 1955-1969 :Foodstuﬀ Controls, Postal Service, Postal Savings, Alcohol Monopoly,

Old Taiwan Foodstuﬀ Controls, Old Chosen Foodstuﬀ Controls, Silk Price Stabilization.
For 1970-1979 : Industrial Investment, Foodstuﬀ Controls, National Forest Service, Settlers Loans, Postal Service, Postal Savings, Urban Development Loans, Alcohol Monopoly.

57

For 1980-2004 :Industrial Investment, National Schools, National Hospitals, Foodstuﬀ

Controls, National Forest Service, Postal Service, Postal Savings, Urban Development
Loans, International Trade Insurance, Agricultural Mutual Aid Reinsurance, Fiscal Loan
Program Funds, National Center for Advanced and Specialized Medical Care.
The data for government debt by account are obtained from Table 4 (pp.10-13) in the Kokusai Tokei[Japanese Government Bonds Statistics], 1907, published by the Ministry of Finance for 1890-1902.1
For 1903-1907 and 1927-2004, the data are from various issues of the Kokusai Tokei Nenpo, and for
1908-1926 they are from Ministry of Finance (1936).
Local government Local government gross debt consists of ordinary accounts bonds, public enterprise bonds, and business bonds. While ordinary accounts bonds are entirely included in the general
government debt, both public enterprise bonds and business bonds are not always included. This isbecause some public management business accounts sometimes are classiﬁed as part of the general
government and sometimes not. In the ECB deﬁnition, no public management business accounts areincluded as part of the general government. Therefore, for 1885-1954, ordinary accounts bonds are
only included in the general government debt. In the OLD SNA and the 68SNA, public enterprise accounts for hospital projects (HPs) and sewage enterprise services (SESs) and other business accounts
except for those of proﬁt-making business as well as ordinary accounts are classiﬁed as part of thegeneral government accounts. Thus, for 1955-1979 the local government debt is deﬁned as the sumof ordinary accounts bonds, public enterprise bonds for HPs and SESs, and business bonds for thenational health insurance, public-university-aﬃliated hospitals (PUAHs), and public municipal pawnshops. In the 93SNA, the classiﬁcation of HPs and PUAHs was switched from general government
to non-ﬁnancial public corporations. Therefore, for 1980-2004, all bonds issued under these businessaccounts are excluded from the local government debt.
Moreover, we include public enterprise bonds carried under the ordinary account (PEBOAs) in
the general government debt after 1974. However, in order to avoid the potentially severe problemof double-counting some public enterprise bonds issued by HPs and SESs in the local government
debt, we need to subtract the amount of outstanding bonds belonging to these two accounts from thetotal amounts of PEBOAs. Because we cannot directly obtain the data on PEBOAs by business, weneed to estimate them. We do so by ﬁrst calculating the ratio of outstanding public enterprise bonds
to the total sum by business account each year. Then, assuming that the percentage distribution of
PEBOAs by business is equal to the percentage distribution in outstanding public enterprise bonds,
we calculate the amount of PEBOAs held by HPs and SESs using this percentage share multiplied by
the total amounts of PEBOAs.
1 For years before 1901, the statistics report no ﬁgures on government bonds held under the special account for theimperial railway service; therefore, the debt held under this special account is included in the debt held by general
government during this period.

58

The data source for ordinary accounts and public enterprise and business bonds for 1885-1899 is
Table 1 (pp.732) in Ministry of Finance (1937); that for 1900-1911 is a table (pp.7) in Chihosai Tokei[Local Government Bonds Statistics], FY1912, published by the Ministry of Home Aﬀairs; that for
1912-1953 is the Chiho Zaisei Gaiyo [Annual Publication on Local Public Finance] also published by
the Ministry of Home Aﬀairs; that for 1954-2003 is the Chiho Zaisei Tokei Nenpo [Annual Report on
Local Public Finance Statistics] published by the Ministry of Internal Aﬀairs and Communications;and that for 2004 is the Chiho Zaisei Hakusho [White Paper on Local Public Finance], 2006, also
published by the Ministry of Internal Aﬀairs and Communications.2 The 1945 value of ordinaryaccounts bonds is not available from the Chiho Zaisei Gaiyo and we therefore estimate it using thedata on “general local government bonds” reported in Ministry of Finance (1983). Our estimatedvalue is 6451.6 million yen. The data source for PEBOAs is the Chiho Zaisei Yoran [Handbook of
Local Public Finance] published by the Institute of Local Finance.
A.1.2

Interest payments

Turning to interest payments, the data source for 1885-1929 is Table 7a (pp.172-173) in Emi andShionoya (1966). We calculate interest payments of the general government as the sum of interest
payments made by the central government and local governments. For 1885-1900, we construct thecalendar year series using the following calculation: (interest payments in the current ﬁscal year)×3/4+ (interest payments in the previous ﬁscal year)×1/4. For 1930-1951, because we cannot obtain thedata directly from Emi and Shionoya (1966) and various issues of the Kokumin Shotoku Hakusho[White Paper on National Income] published by the Economic Planning Agency, we estimate general
government interest payments closely following Emi and Shionoya (1966). Figures for interest payments by the central government are taken from various issues of the Kokusai Tokei Nenpo. On theother hand, interest payments made by local governments are estimated by multiplying outstanding
local government debt by the average interest rate. We can obtain data on outstanding local government debt for each level of interest rate from the Chiho Zaisei Gaiyo but not data on their weighted
average.3 Unfortunately, Emi and Shionoya (1966) do not provide an explanation of how they obtain
the weighted average of interest rates. We therefore estimate interest payments by local governments
using the values in the appendix table 1 as the average rate for each level of interest rate.4 However,for 1945 we cannot estimate interest payments by local governments because no data on outstanding
2 For 1912-1938, public enterprise bonds issued for electricity and gas supply projects are included in the total
outstanding local government bonds reported in the Chiho Zaisei Gaiyo. We therefore exclude public enterprise bonds
from the total outstanding to obtain the data for outstanding ordinary accounts bonds.
3 Figures on outstanding ordinary accounts bonds for each level of interest rate have been reported in the Chiho
Zaisei Gaiyo since 1950. For 1930-1949, we can obtain nothing but the outstanding data including public enterprisebonds as well as ordinary accounts bonds. Therefore, we use these here.
4 Our estimates are 93.6 for 1926, 107.9 for 1927, 117.3 for 1928 and 125.4 for 1929. The corresponding estimates by
Emi and Shionoya are 94.1 for 1926, 108.2 for 1927, 117.1 for 1928 and 125.0 for 1929. For 1952, our estimated value
is 13460.7 and the estimate by the Economic Planning Agency is 13352.0. The fact that the diﬀerence between ourestimates and the estimates by Emi and Shionoya and the Economic Planning Agency is not large suggests that ourestimates of interest payments by local governments are quite precise.

59Appendix Table 1. Weighted Average of Interest Rates
Period: 1930-1949
Zero percent
0.0000Under 4.0 percent 0.0263
Over 4.0 percent
0.0463
Over 5.0 percent
0.0563
Over 6.0 percent
0.0663
Over 7.0 percent
0.0763
Over 8.0 percent
0.0863
Over 9.0 percent
0.0963
Over 10.0 percent 0.1630

Period: 1950-1951
Under 3.5 percent
0.0238Under 4.0 percent
0.0388Under 5.0 percent
0.0463
Under 6.0 percent
0.0563
Under 7.0 percent
0.0663
Under 8.0 percent
0.0763
Under 9.0 percent
0.0863
Under 10.0 percent 0.0963
Over 10.0 percent
0.1630local government debt for each level of interest rate are available. We estimate interest payments by
the general government using the data on interest payments by the central government. For 1952-1954,
the data source is Table 3 (pp.128) in the Kokumin Shotoku Hakusho, FY1962. For 1955-1969, it is
Account 4 (pp.24-27) in the Kokumin Shotoku Tokei Nenpo [Annual Report on National Income Statistics], 1978, published by the Economic Planning Agency. The source for 1970-1979 is Account 3 andfor 1980-2004 Account 4 in the Kokumin Keizai Keisan Nenpo [Annual Report on National Accounts]
published by the Economic Planning Agency and the Economic and Social Research Institute.
A.1.3

Military expenditure

As for military expenditure, the data source for 1885-1945 is Table 10 (pp.186-189) in Emi andShionoya (1966). We deﬁne military expenditure during this period as the sum of regular defense
expenditure and war expenditure (if any). Note that for the period 1904-1905, we revise the dataon the expenditure by the extraordinary military special account (EMSA), which is included in the
war expenditure. The EMSA expenditure for the period was almost entirely ﬁnanced through bondissues. However, we can clearly observe a somewhat odd relationship between expenditure and bondissues in each year: For 1904, the expenditure is about 200 million yen larger than the issue of bonds,
while for 1905 the issue of bonds is about 200 million yen larger than the expenditure. This is because
total revenues and expenditures under the extraordinary military special account were suﬃcient tobalance out not for one ﬁscal year but for several ﬁscal years. This characteristic of the budget systemprevents us from determining to what extent the increase of bond issuance is caused by a change in
expenditure in one year. We revise the data on the EMSA expenditure by ﬁrst calculating the ratio of
the outstanding value of bonds issued to the total revenues in each year for the period 1904-1905. We
then multiply this ratio by the total EMSA expenditure for the period. Note also that for 1937-1945,
we use the data labeled “Forces in the Home Land.”As for the postwar period, the data source for 1946 is Supplementary Table 25 (pp.283) in Economic
Counsel Board (1954). For 1947-2004, the data are obtained from various issues of the Ippan Kaikei
Sainyu Saishutsu Kessan [Settlement of General Account Revenues and Expenditures]. We deﬁnemilitary expenditure as the sum of Boei Kankei-hi (Expenditures on national defense and related

60

aﬀairs) and Shusen Shori-hi (Expenditures related to the termination of WWII, until 1956).
A.1.4

Nominal GDP

For the period 1885-1954, we construct nominal GDP data series by calculating nominal GNP less net
income abroad. For the period 1885-1935, the data on nominal GNP and net income abroad are takenfrom Ohkawa et al. (1974), while for the period 1936-1950 these data are from the Kokumin Shotoku
Hakusho, FY1963. Furthermore, for the period 1951-1954 they are from the Kokumin Shotoku Tokei
Nenpo, 1978. Note that because for the period 1885-1943, Ohkawa et al. (1974) and the Kokumin
Shotoku Hakusho provide only data on a calendar year basis, we convert the GDP data to a ﬁscal year
series using the following calculation: (nominal GDP in the current calendar year)×3/4 + (nominal
GDP in the following calendar year)×1/4. For the period after 1954, GDP data are directly obtained
from the Kokumin Keizai Keisan Nenpo, 2000. Because oﬃcial nominal GDP data for 1944-1945 are
not available, we estimate the data using our estimated real GDP and GDP deﬂator for these twoyears. Our estimates of nominal GDP are 84907.2 million yen for 1944 and 198068.2 million yen for
1945.
Real GDP for 1944-1945

We estimate real GDP for 1944-1945 using data of an aggregate produc-tion index for 1943-1946. We produce the data on the aggregate production index closely following
the methodology the Japanese central bank adopted in Bank of Japan (1950). The index consistsof two indices: One is an index of industrial production, while the other is an index of agriculture,
forestry and ﬁshery production. These indices are weighted by the share of value-added in the period
1934-1936. The weights are 0.5765 for mining and manufacturing and 0.4235 for agriculture, forestry,
and ﬁshing. The value-added data are taken from Table 8 (pp.42) in Economic Counsel Board (1954).
We use the index produced by the Economic Stabilization Board for the index of industrial production.
The data sources are Tables 9 (pp.67) and 10 (pp.74-75) in the Keizai Tokei Geppo [Monthly Reportof Economic Statistics], October 1951. For the index of agriculture, forestry and ﬁshery production,
we use the index produced by the Ministry of Agriculture and Forestry. The data source is Table 68(pp.648-649) in the Norinsho Tokei Hyo [30th Statistical Yearbook of the Ministry of Agriculture andForestry]. Our estimates of the aggregate production index on the basis of the period 1934-1936 are
137.8 for 1943, 141.2 for 1944, 65.8 for 1945, and 52.5 for 1946. As a result, our estimated real GDP
ﬁgures are 21308.8 million yen for 1944 and 13324.2 million yen for 1945.
GDP deﬂator for 1944-1945 We estimate the GDP deﬂator for 1944-1945 using the data of anaggregate price index for 1943-1946. The data on the aggregate price index for 1943 and 1946 (onthe basis of the period 1934-1936) are obtained from Supplementary Table 5 (pp.100-101) in the
Kokumin Shotoku [National Income], FY1957, published by the Economic Planning Agency. Notethat because for years before 1946 the Kokumin Shotoku provides data only on a calendar year basis,for 1943 we convert the aggregate price index to a ﬁscal year basis using the following calculation:61

(index value in calendar 1943)×3/4 + (index value in calendar 1944)×1/4. However, the data on
the aggregate price index for 1944-1945 are not available. For 1944-1945, we therefore produce thedata on the aggregate price index closely following the methodology the Economic Planning Agency
adopted in the Kokumin Shotoku. The index consists of three indices: the agricultural price index,
the production goods price index, and the consumer price index. These indices are weighted using
the following values, respectively: 0.300, 0.250 and 0.450. First, we use an index of commodities forfamily maintenance (on the basis of the 1937 calendar year) as the agricultural price index. The data
are taken from Table 1 (pp.13) in the Noson Bukka Chosa Hokoku [Survey on Agricultural Prices],
1946-1948, published by the Ministry of Agriculture and Forestry. We change the base year from the1937 calendar year to the period 1934-1936 by multiplying the index by the link coeﬃcient, 1.180.
Our calculated values are 3.655 for 1944 and 12.081 for 1945.
Second, we estimate the production goods price index using the data of the Ministry of Financeeﬀective wholesale price index (on the basis of the period 1930-1934). The data are obtained from
Supporting Table 2 (pp.100-101) in Bank of Japan (1948). However, we revise the index values for1944 and January-August 1945. This is because the 1944 value is produced under the assumptionthat the level of output in 1944, being unknown at the time of estimating the indices, was nearly
equal to that in 1943, and because the January-August 1945 value is produced using data for theperiod 1937-1944. We ﬁrst construct the new value for 1944. Morita (1963), one of those who werein charge of producing the Ministry of Finance eﬀective price index, points out that various economic
statistics published after estimating the eﬀective price index show a clear decrease in production in1944 compared with 1943 and it would be better to use not 115.0 but values around 110.0 for the index
of transactions. Using 110.0 as the transactions index value, our revised eﬀective wholesale price index
is 3.951, which is 0.184 larger than the Ministry of Finance index, 3.767. Then the revised eﬀective
wholesale price index for January-August 1945 is 5.179, which is 0.577 larger than the Ministry of
Finance index, 4.602. We change the base period from the period 1930-1934 to the period 1934-1936
by multiplying the index by the link coeﬃcient, 0.91213. Our estimates of the production goods priceindex are 3.778 for 1944 and 9.825 for 1945.5
Third, we estimate the consumer price index using the data of the Ministry of Finance eﬀective
retail price index (on the basis of the period 1930-1934). The data are taken from Supporting Table
3 (pp.103-104) in Bank of Japan (1948). We adopt the same method to revise the data used for the
Ministry of Finance eﬀective wholesale price index, because the eﬀective retail price index has thesame problem as the eﬀective wholesale price index. As a result of the revision, the eﬀective retailprice index for 1944 is 4.554, which is 0.252 larger than the Ministry of Finance index, 4.302, and that
5 We convert the eﬀective wholesale price index on a calendar year basis to a ﬁscal year series using the following calculation: for 1943, (index value in calendar 1943)×3/4+(index value in calendar 1944)×1/4; for 1944, (index
value in calendar 1944)×3/4+(index value for January-August 1945)×1/4; for 1945,(index value for January-August1945)×5/12+(sum of the seven months from September 1945 to March 1946)×1/12; and for 1946, the simple average
from April 1946 to March 1947. As a result, the eﬀective wholesale price index on a ﬁscal year basis is 3.011 for 1943,
3.884 for 1944, 10.324 for 1945, and 31.236 for 1946.

62

for January-August 1945 is 6.114, which is 0.843 larger than the Ministry of Finance index, 5.271. Wechange the base period from the period 1930-1934 to the period 1934-1936 by multiplying the index
by the link coeﬃcient, 0.94251. Our estimates of the consumer price index are 4.471 for 1944 and21.138 for 1945.6
Finally, we obtain the aggregate price index using these three indices. The values are 3.190 for
1943; 4.053 for 1944; 15.593 for 1945; and 43.910 for 1946. Our estimated GDP deﬂator is 3.985 for1944 and 14.865 for 1945.

A.2

The United States

Public debt

The data source for 1840-1939 is Table Ea584-587 in Carter et al. (2006), Volume 5,

where we use “Public debt” (Ea587), while for 1940-2005, we use Table 7.1 in the Historical Tables,
Budget of the United States Government, Fiscal Year, 2007, published by the Oﬃce of Management
and Budget, where we use “Gross Federal Debt.” All ﬁgures are for the end of the ﬁscal year, that is,
December 31 for 1840-1842, June 30 for 1843-1976, and September 30 after 1977.
Nominal GDP

The data source for 1840-1928 is Table Ca9-19 in Carter et al. (2006), Volume 3,

where we use series Ca10, while that for 1929-1947 is Table 1.1.5 in the National Income and ProductAccounts published by the Bureau of Economic Analysis, U.S. Department of Commerce. Because
these sources for the period before 1948 provide only calendar year data, for 1843-1947 we convert thedata to ﬁscal year data using the following calculation: for 1843, (nominal GDP in the ﬁrst half of theyear)×2; and for 1844-1947, (nominal GDP in the current year)×1/2+(nominal GDP in the previousyear)×1/2. We obtain ﬁscal year data for 1948-2004 from Table 8.1 and for 2005 from Table 1.1.5 in
the National Income and Product Accounts.
Interest payments and military expenditure The data source for 1840-1970 is Table Ea636-643
in Carter et al. (2006), Volume 5. For the period 1840-1953, military expenditure is given by the sumof “Army” (Ea638), “Navy” (Ea639) and “Air Force” (Ea640) expenditure, while for 1954-1970 we use“Total (Department of Defense)” (Ea637). As for interest payments, we use “Interest on public debt”(Ea641) for the entire period. For 1971-2005, the data source for military expenditure and interest
payments is Table 3.2 in the Historical Tables, Budget of the United States Government, Fiscal Year,2007. We use “Subtotal, Department of Defense-Military” (series 051) for military expenditure and“Interest on Treasury debt securities (gross)” (series 901) for interest payments.

A.3

The United Kingdom

Public debt

The data source for 1830-1979 is Public Finance 7 in Mitchell (1988). We calculate

public debt as F U D + U F D for 1830-1868, F U D + U F D + OIB for 1869-1939 and T N D + OIB
6 Using the same calculation to make a ﬁscal year series as the one used for the eﬀective wholesale price index, theeﬀective retail price index on a ﬁscal year basis is 3.504 for 1943, 4.660 for 1944, 26.224 for 1945, 68.925 for 1946.

63

for 1940-1979, where F U D denotes funded debt, U F D unfunded debt, OIB outstanding investment
borrowing, and T N D total national debt. The source for 1980-2003 is Table A10 in HM Treasury’s
Public Sector Finances Databank. All ﬁgures are for the end of the ﬁscal year, that is, January 5 for
1830-1853 and March 31 after 1854.
Nominal GDP

The data source for 1830-1947 is National Accounts 5 in Mitchell (1988). For

1830-1853, we use the calendar year series, because the term of the ﬁscal year is almost identicalto the calendar year. For 1854-1947, we construct ﬁscal year data using the following calculation:(nominal GDP in the current year)×3/4+(nominal GDP in the following year)×1/4. The data sourcefor 1948-2003 is Table A2 in the United Kingdom Economic Accounts published by the Oﬃce for
National Statistics, where we use the series BKTL. For 1948-1954, we construct ﬁscal year data using
the following calculation: (nominal GDP in the current year)×3/4+(nominal GDP in the followingyear)×1/4.
Interest payments and military expenditures

The data source for interest payments for theperiod 1830-1966 is Public Finance 4 in Mitchell (1988). For 1830-1937, we use ﬁgures obtained bysubtracting “Debt Charges (Terminable Annuities)” from “Debt Charges (Total)” and for 1938-1966
we use “Debt Charges (Total).” The data source for 1967-2003 is the Annual Abstract of Statistics
published by the Oﬃce for National Statistics, from which we use the item labeled “Service of the
National Debt.” On the other hand, the data source for military expenditure for 1830-1979 is Public
Finance 4 in Mitchell (1988). We calculate military expenditure as ARM + N AV + EEV for 18301904, ARM + N AV + AIF + EEV for 1905-1937 and ARM + N AV + AIF + CEN + EEV for
1938-1967, where ARM denotes army and ordnance expenditure, N AV navy expenditure, AIF airforce expenditure, CEN central expenditure and EEV gross expenditure on special expeditions, votesof credit, etc. For 1968-1979, we use ﬁgures from the item labeled “Defense.” The data source for
1980-2002 is the Annual Abstract of Statistics. We estimate military expenditure for 2003 using both
the Annual Abstract of Statistics value for 2002 and the Treasury’s value for 2002-2003. The Treasury
value is obtained from Table 3.2 in the Public Expenditure Statistical Analyses, 2006.

Appendix References[1] Bank of Japan, (1948), “Waga Kuni no Infuretion no Gen Dankai ni Tsuite,” [“On the Current
Situation of Inﬂation in Japan”] Chosa Jiho 3, 75-132.
[2] Bank of Japan, (1950), “Antei Seisaku Jisshigo ni okeru Tsuka Ryutsu Jyokyo no Suii,” [“Onthe Circulation of Money Since the Implmentation of the Stabilization Policy”] Chosa Jiho 12,
1-32.

64

[3] Carter, Susan B., Scott Sigmund Gartner, Michael R. Haines, Alan L. Olmstead, Richard Sutchand Gavin Wright (eds.), (2006), Historical Statistics of the United States, Millennial Edition,
Cambridge: Cambridge University Press.
[4] Economic Counsel Board, (1954), Nihon Keizai to Kokumin Shotoku [The Japanese Economy
and National Income], Tokyo: Gakuyo Shobo.
[5] Economic Planning Agency, (1964), Kokumin Shotoku Hakusho [White Paper on National Income
for FY1962 ], Tokyo: Printing Bureau, Ministry of Finance.
[6] Economic Planning Agency, (1978), Shin Kokumin Keizai Keisan no Mikata Tsukai Kata [Howto Read and Use the 1968 System of National Accounts], Tokyo: Printing Bureau, Ministry of
Finance.
[7] Emi, Koichi and Yuichi Shionoya, (1966), Zaisei Shishutsu [Government Expenditure], In Choki
Keizai Tokei [Estimates of Long-Term Economic Statistics of Japan Since 1868 ] edited by
Kazushi Ohkawa, Miyohei Shinohara and Mataji Umemura, Volume 7, Tokyo: Toyo Keizai Shinposha.
[8] Ministry of Finance, (1936), Meiji Taisho Zaisei Shi [The Financial History of the Meiji andTaisho Period in Japan], Volume 11, Tokyo: Zaisei Keizai Gakkai.
[9] Ministry of Finance, (1937), Meiji Taisho Zaisei Shi [The Financial History of the Meiji andTaisho Period in Japan], Volume 12, Tokyo: Zaisei Keizai Gakkai.
[10] Ministry of Finance, (1983), Showa Zaisei Shi Shusen kara Kowa made [The Financial Historyof the Showa Period in Japan 1945-1952 ], Volume 19, Tokyo: Toyo Keizai Shinposha.
[11] Mitchell, Brian R., (1988), British Historical Statistics, Cambridge: Cambridge University Press.
[12] Morita, Yuzo, (1963), “Senji no Bukka” [“Wartime Prices”], in Yuzo Morita (ed.), Bukka [Prices],
81-116, Tokyo: Shunjusha.
[13] Ohkawa, Kazushi, Nobukiyo Takamatsu and Yuzo Yamamoto (1974), Kokumin Shotoku [National
Income], in Kazushi Ohkawa, Miyohei Shinohara and Mataji Umemura (eds.), Choki Keizai Tokei[Estimates of Long-Term Economic Statistics of Japan Since 1868 ], Volume 1, Tokyo: Toyo Keizai
Shinposha.

65