Is Japanese Public-Sector Finannce Sustainable?
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言語: English
出版者:
公開日: 2019-10-15
キーワード (Ja):
キーワード (En):作成者: Yoshida, Motonori
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https://doi.org/10.24729/00016629

Discussion Paper New Series

Is Japanese Public-Sector Finannce
Sustainable?

Motonori Yoshida
Discussion Paper New Series No.2019-3
October 2019

School of Economics

Osaka Prefecture University
Sakai, Osaka 599-8531, JapanIs Japanese Public-Sector Finance Sustainable? ∗Motonori Yoshida
Graduate School of Economics, Osaka Prefecture University ∗∗Abstract

Although the Japanese economy might enjoy the world’s best financial status, its public-sector
finance has remained mired in an unsound condition for decades: the Japanese general
government’s debt/GDP ratio is the worst among the G7 countries. Therefore, I estimated the fiscal
reaction functions (originating from Bohn, 1998a, 2005) with time-varying parameters of all
Japanese public sectors (for FY1970-2017) to examine the fiscal sustainability of them. In mymodel, a positive reaction of primary-surplus/GDP to the increase of debt/GDP constitutes asufficient condition for the fiscal sustainability. This study’s results demonstrate that the general
government (or the central government) has failed to meet Bohn’s (1998a, 2005) sufficientcondition for the fiscal sustainability since the end of the 1990s. The Japanese public sector as awhole has probably continued an unsustainable fiscal policy in recent years.

Keywords: Fiscal sustainability, Fiscal reaction function, Bohn, Time-varying parameters, Statespace model, Kalman filter
JEL Classification Numbers: E61, E62, H11, H61, H62, H63, H72, H74, H77∗

I am grateful for financial support from the Japan Society for the Promotion of Science, Grant-in Aid for
Science Research (C), 19K01720.
∗∗
Professor of Graduate School of Economics, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakaicity, Osaka, 599-8231, Japan. E-mail address: myoshida@eco.osakafu-u.ac.jp.

11. Introduction

The Japanese economy probably enjoys the world’s best financial status at present. It has
maintained its current account surplus for the last 40 years (as of 2017). Table 1 shows its
current surplus situation for about the last two decades. Figure 1 shows that its externalfinancial asset balance is the highest in the world. However, the Japanese public sector, oneof the subsectors of the Japanese economy, has been mired in a critically untenablesituation for decades. The ratio of the Japanese general government (“general government”
is referred to as GG henceforth) 1 debt to the gross domestic product (GDP) was 235.0% in
2017: the worst among all the G7 countries. 2 However, not all of the public subsectors thatcomprise the Japanese general government have been mired in the same bad state. Eachpublic subsector faces a quite different fiscal condition. Table 2 indicates that just only thecentral government (CG) has a large primary deficit, unlike the whole of the local
governments (WLG) and the whole of the social security funds (WSSF). 3 In addition, eachpublic-sector-expenditure/GDP is graphed in Figure 2. The WLG and the WSSF (rather
than the CG) function more massively in the Japanese economy. Then, scrutinizing theJapanese public finance system reveals the following facts. (1) The WLG and the WSSF
finances are heavily supported by grants and subsidies from the CG (e.g., local allocation
tax and national treasury disbursements). Actually, the CG pays around 54 trillion yen of
the net current financial transfers to other public subsectors; on the other hand, the WLG
and the WSSF respectively received about 19.5 and 34.5 trillion yen from other public

1

The general government consists of a central government, local governments, and social security funds.
Italy had the second worst figure: 131.3%. These figures are reported by Ministry of Finance: URL:
https://www.mof.go.jp/tax_policy/summary/condition/a02.htm. (Accessed in September 2019.)
2

3

In this paper, “public sector” denotes the GG and “public subsector” denotes each subsector from which
the GG is comprised: the CG, the WLG, and the WSSF. “Government sector” is used for explainingsome issues with all four government-related objects of the GG, the CG, the WLG, and the WSSF asargument targets.
2

subsectors (see Section 4 for the details) in FY2017. (2) The CG issued about 21 trillion
yen to finance the total deficit of the public sector in FY2017.
Some studies assessed the fiscal sustainability of Japanese government by examining thereaction of the primary-balance/GDP ratio to the increase of the government-debt/GDP
ratio, i.e., Bohn’s (1998a, 2005) method, concerning about the situation that the Japanese
government finance is quite unfit among OECD countries. The Japanese GG-deficit/GDP(%) is -2.95 (all the OECD countries’ mean is -0.82) and its performance was ranked 36th
among 42 countries in 2017, and this situation has continued over the last decade. 4 Ihori etal. (2001) rejected the sustainability of Japanese CG finance using FY1965-1998 data withthe general account as their research target. Doi and Nakazato (2004) did not support thesustainability of the total finance of the CG (the general account) and the WLG (theordinary accounts 5) using FY1965-2000 data, and Doi et al. (2011) also obtained the same
result for the GG for the period 1980Q1-2010Q1 (Q denotes a quarter), allowing for the
possibility of regime changes. However, Fuji (2010) described the CG’s fiscal sustainability
with 1992Q2-2007Q1 data and Mochida (2015) for the WLG’s fiscal sustainability with
1980Q1-2011Q4 data. However, to the best of my knowledge, the existing researches,
which examined the fiscal sustainability of the Japanese public sector and subsectors by
Bohn’s (1998a, 2005) method, suffer from the following shortcomings. (1) The existing
researches (except Doi et al., 2011) failed to deal with the GG, and no research
simultaneously scrutinized all the public subsectors (i.e., the CG, the WLG, and the WSSF).
(2) The results vary depending on the used data set. (3) Most researches (except Yoshida,2018) did not completely investigate the stationarity and the cointegration relationships on
the variables despite using time-series data. (4) Most researches (except Yoshida, 2018) did

4

These figures were reported by OECD. URL: https://data.oecd.org/gga/general-government-deficit.htm.
(Accessed in September 2019.)
5
An ordinary account is the sum of the budgets of the general account and a part of the special accounts.

3not take the effects of fiscal transfers among public subsectors into account. (5) No research
has investigated the time-varying parameter models 6 by the state-space model and theKalman filter as did Burger et al. (2012), Nguyen et al. (2016), and Paniagua et al. (2017).
Therefore, I estimated the fiscal reaction functions that overcame the above shortcomings
using the unit-root test with multiple structural breaks (Lee and Strazicich, 2003), the statespace model, and the Kalman filter. My main findings are the following. (1) The order ofintegration among all the variables is generally less than or equal to one. (2) Somecointegration relationships among I(1) (i.e., integration of order one) variables exist. (3)The effects of fiscal transfers among public subsectors were not recognized except whenestimating the time-invariant parameter model of the WLG. (4) Based on the results of thetime-varying parameter model, the GG and the CG have not implemented sustainable fiscal
policies since the end of 1990s (on the contrary, the WLG and the WSSF have maintained
sustainable fiscal postures). Hence, this fact indicates that as a whole, the Japanese publicsector finance is probably unsustainable.
The rest of this paper is organized as follows. Section 2 reviews related literature andexplains the aim of this study. Section 3 presents the theoretical backbone of Bohn’s(1998a, 2005) method. Section 4 explains my empirical model and data. Section 5 offers
analysis results and Section 6 concludes the paper.
[Table 1 about here][Figure 1 about here][Table 2 about here][Figure 2 about here]

6

A function (or model) with only time-invariant parameters is referred to as a time-invariant parameter
function (or model) and one with both time-invariant and time-varying parameters is as a time-varying
parameter one in this paper.

4

2. Related Literature and Aim of This Study

Concern about public deficits and debt has grown in terms of both absolute and relative size
to GDP over recent decades in many countries: the U.S. that has faced both the current
balance and the public deficits, the European Union (EU) member countries that face two
restrictions of keeping their public-debt/GDP ratio below 60% and their public-deficit/GDP
ratio below 3%, and Japan, which shows the worst public finance performance among theG7 countries. Many studies have examined government-finance sustainability based on thepast finance management postures of the target countries. Such studies can be classified
into the following three classes, each of which inquires whether the intertemporal budget
constraint (IBC) of government has been satisfied by its own method. The first class uses
unit-root tests on the outstanding debt or the deficit 7 (or each variable’s ratio to GDP). The
second class examines the cointegration between government expenditures and revenues. 8
The third class follows Bohn’s (1998a, 2005) method.
Hamilton and Flavin (1986) is the seminal study of the first class. They showed thestationarity of the primary surplus and the outstanding debt of the U.S. federal governmentfor 1960-1984 by the Augmented Dickey-Fuller (ADF) test and argued for fiscal
sustainability. 9 Wilcox (1989), however, allowed for a time-varying interest rate andderived the opposite conclusion from Hamilton and Flavin (1986) who assumed a timeinvariant interest rate. In addition, Kremers (1988), who investigated the U.S. federal
government finance with an ADF test from 1920-1985 except during WW2, argued that thelarger the sample size, the higher the probability of rejecting the nonstationarity of the7This deficit includes interest payments on debt.
See Hamilton and Flavin (1986) and Nguyen et al. (2016) for the theoretical backgrounds of the methods ofthe first and second classes.
9
Hamilton and Flavin (1986) also estimated the VAR system with a bubble term using Flood and Garber(1980)’s method and reached a similar conclusion as the unit-root tests, which indicates that a no-Ponzi gamecondition held.
8

5

debt/GDP ratio.
Next Trehan and Walsh (1988), who originated the second class, argued for thestationarity of the U.S. federal government’s deficit (i.e., the government financesustainability) by identifying the cointegration between government expenditures inclusiveof interest payments, tax revenues, and seigniorage for 1890-1986 using the Dickey-Fuller
and the Engle-Granger tests. Assuming stationarity of the interest rate, Hakko and Rush
(1991) indicated that (1) the cointegration between the U.S. federal government
expenditures inclusive of interest payments and revenues tends not to be recognized when
the data, whose sample term (1964Q1-1988Q4) was relatively late, were used and that (2) itis recognized when all the 1950Q2-1988Q4 data are used. Moreover, Haug (1991)
investigated the cointegration between the U.S. government debt and the primary surplus
with the 1960Q1-1987Q4 data and argued that IBC held. 10 Quintos (1995), however,proved that (1) the cointegration between government expenditures inclusive of interest
payments and revenues is not a necessary but a sufficient condition to satisfy the IBC andthat (2) it is the necessary condition for the growth rate of the debt not to exceed that of theeconomy by scrutinizing the limit of the debt increment. Quintos also revealed that (1) the
cointegration between the U.S. federal government expenditures inclusive of interest
payments and revenues only held up to 1980 and that (2) the deficit process remains
sustainable despite the failure of cointegration in the 1980s using the method that
endogenously chose the structural breaks in the deficit process. Bajo-Rubio et al. (2008) reexamined the sustainability of the U.S. federal government finance for 1947Q1-2005Q3
using Bai and Perron’s (1998, 2003) approach that endogenously identifies multiple
structural-change dates. Although they support the sustainability up to 1996Q2, they failed
to elucidate whether the IBC was satisfied for 1996Q3-2005Q3 based on their econometric10

He calculates the critical values for cointegration tests with Monte Carlo studies.
6results. Brady and Mazzino (2018a) investigated the sustainability of fiscal policy in a setof 19 European Monetary Union countries (GGs) and indicated the stationarity of thegovernment debt series for the period 1970-2016 by panel unit-root tests considering crosssection dependence. In addition, they showed the government solvency of many countries
in their objects by cointegration tests between the primary balance and the (lagged) public
debt. Brady and Magazzino (2018b) reached the similar results by cointegration tests withthe 1980-2015 data of 28 EU countries. Fukuda and Terayama (1994) supported thesustainability of Japanese CG for1965-1992 and identified cointegration relationships
between government expenditures exclusive of interest payments and revenues.
As reviewed above, the first and second class studies failed to reach a decisive
conclusion on government-finance sustainability. Their results depend on the assumption
about interest-rate properties and the data’s sample period and face a low power problem
when using data whose sample size is not enough large. Hence I review the third classstudies that avoid the drawbacks of unit-root and cointegration techniques using Bohn’s(1998a, 2005) method. Bohn (1998a, 1998b, 2005) claimed that primary surplus reacting
positively on debt accumulation is a sufficient condition to satisfy the IBC. He expressed
the relation between these two variables as a fiscal reaction function with other
determinants. Bohn (2007) proved that the IBC is satisfied if either the debt series or thegovernment expenditure inclusive of interest payment and the revenue series are integratedof arbitrary high order, and that revenues and expenditures do not have to be conintegrated
for the IBC; cointegration is merely a sufficient condition for the transversality condition(TVC). Bohn (1998a, 2005) also showed the sustainability of the U.S. federal government
finance for 1916-84 and 1792-2003. Since Bohn’s (1998a, 2005) method can circumventthe problems of the first and second classes, many studies have followed his work.
Mendoza and Ostry (2008) researched 34 developing countries over 1990-2005 and 22

7

industrially developed countries over 1970-2005 with panel data and reported that thesustainability of GGs is basically supported. Claeys et al. (2008) examined the state
government behaviors of the U.S. for 1962-2000 and Germany for 1970-2005. Theirfindings supported the fiscal sustainability of America’s state governments and rejected thatof the German state governments. Mahdavi (2014) also supported the fiscal sustainabilityof America’s state governments for 1962-2008. Although Bohn (1995a, 2005) used constantparameter models on the fiscal reaction function, the time-varying parameter models by thestate-space model and the Kalman filter have recently appeared. 11 For instance, Burger etal. (2012) examined the South African government over 1946-2008 and argued that the
government implemented sustainable management by the end of the 1980s with a timevarying parameter model. Nguyen et al. (2016) investigated the U.S. situation for 19162012 and reported that the U.S. federal-government fiscal policy has been unstable since2005. Paniagua et al. (2017) studied 11 Eurozone countries for 1970-2014 and indicatedthat the financial management of such countries as Finland, Netherland, and France had
become unsustainable. 12
Finally, I introduce researches that examined Japanese CG, WLG, and some local
governments by Bohn’s (1995a, 2005) method. Ihori et al. (2001) rejected Japanese CG’s
fiscal sustainability with 1965-1998 data. Doi and Nakazato (2004) also rejected thesustainability of the total finance of the CG (general account) and the WLG (ordinary
11

The two-state Marcov-switching model is used to estimate the parameters depending on the economic or
fiscal conditions. For instance, Cassou et al. (2017) argued that with this model, the U.S. federal government
implemented a sustainable fiscal policy during good economic times in the period 1955Q1-2013Q3.
Baharumshah et al. (2017) described the sustainability of the Malaysian government’s fiscal policy for theperiod 1980Q1-2014Q3 except during brief bad economic times. Doi et al. (2011) used this model to examine
Japanese GG’s fiscal sustainability.
12
The fiscal sustainability of developing countries’ governments has also been examined in recent years.
Shastri et al. (2017) showed the cointegration with a structural break between government revenues andexpenditures in five major South Asian economies: India, Pakistan, Bangladesh, Sri Lanka, and Nepal for1985-2014 as do Usman and Adebisi (2017) with the Nigeria government finance for 1961-2013 as theirobject. Martorano (2018) argued that 14 Latin-American governments implemented sustainable policies on
their external debt for 1990-2015 by Bohn’s (1998a, 2005) method and their fiscal policies turned
countercyclical to their economies from the recent Great Recession onward.

8

accounts) for 1965-2000. Doi et al. (2011) obtained the same result as the above two
researches for the GG over the period 1980Q1-2010Q1, allowing for the possibility of
regime changes. On the other hand, Fujii (2010) supported the fiscal sustainability of theCG with 1992Q2-2007Q1 data. 13 Mochida (2015) showed the fiscal sustainability of the
WLG with 1980Q1-2011Q4 data. Moreover, Akamatsu and Hiraga (2011) and Mochida(2015) examined the fiscal sustainability of prefectural governments and reported theiraverage sustainability with panel data. 14 Yoshida (2016, 2017) examined ordinancedesignated city governments and core city governments and supported the former’s fiscal
sustainability and rejected the latter’s. Moreover, Yoshida (2018) scrutinized prefecture
governments with 1973-2014 panel data, dealing with the regressor’s endogeneity, andreported the following: (1) the better the fiscal situation, the more sustainable the fiscal
management becomes and (2) adequate fiscal transfers from the CG help each prefecture
government improve its fiscal condition.
Unfortunately, to the best of my knowledge, the existing researches that examined thesustainability of the Japanese public-sector finance by Bohn’s (1998a, 2005) method sufferfrom the following shortcomings. (1) The existing researches except Doi et al. (2011) do
not deal with the GG, and no research simultaneously scrutinized all the public subsectors(i.e., the CG, the WLG, and the WSSF). 15 (2) The results vary depending on the used data
set. (3) Unlike Mahdavi (2014), most researches except Yoshida (2018) did not completely
scrutinize the stationarity and the cointegration relationships on the variables, even though13

In comparison with Ihori et al. (2001), Fujii (2010) has the following features: (1) he divided the analysis
term into two parts based on the result of a structural change test and (2) considered the regressor’s
endogeneity.
14
On the other hand, based on the scrutiny of each prefecture government or each cluster that consists ofprefectures with similar figures on some fiscal indicators, they also demonstrated that the fiscal sustainabilityof some metropolitan prefectures and those with relatively high fiscal power is not supported.
15
Hatano (2009) tested whether Barro’s (1979) tax smoothing hypothesis held in Japan with the GG, the CG,
the total of the CG and the WSSF, and the total of the CG and the WLG as targets (for FY1970-2007) using
the state-space model and the Kalman filter. He regressed the fiscal-deficit (inclusive of interest
payments)/GDP on the debt/GDP, GVAR, and YVAR (see Equation (8) for the latter two variables).

9they used time-series data. (4) Unlike Mahdavi (2014), most researches except Yoshida(2018) did not take the effects of fiscal transfers among public subsectors into account. (5)No research investigated a time-varying parameter model by the state-space model and theKalman filter like Burger et al. (2012), Nguyen et al. (2016), and Paniagua et al. (2017),
considering the fact that the reaction of the primary surplus to variations in debt may betime-varying. Therefore, I address the shortcomings of the existing literature by Bohn’s(1998a, 2005) method, using the unit-root test with multiple structural breaks (Lee andStrazicich, 2003), the Johansen test on cointegration (Johansen, 1988; Johansen andJuselius, 1990), the state-space model, and the Kalman filter. 16 17

3. Theoretical Backbone of Bohn’s (1998a, 2005) Test

3.1 Confirmation of premises
Before examining a government’s fiscal sustainability, researchers need to check whether
the following situations have held in the target economy: (1) the Recardian equivalence
proposition of the concerned government and (2) the dynamic inefficiency of the economy.
If both are established, fiscal sustainability will automatically be satisfied. I adopted thesame assumptions about these two issues as Yoshida (2018) and assumed the following: (1)a failure to hold the Recardian equivalence proposition of the objective governments; (2)16

See Hamilton (1994, ch.13), Harvey (1989, chs. 3 and 4), etc. for the details of the state-space model and theKalman filter.
17
Afonso and Jalles (2017) regressed the primary-balance/GDP ratio on the public-debt/GDP ratio andestimated the time-varying coefficient of the public-debt/GDP ratio with the CGs of 13 advanced countries
including Japan (for 1980-2012) as their objects. However, their study is basically different from mine in thefollowing points. First, they examine Japan as just one of their sample, whereas I scrutinized Japan based on
its properties. Second, they used a two-sided filter that uses the future information as well as the past andcurrent one for the concerned period when estimating the time-varying parameter. On the other hand, I used
only the past and current information for the concerned period since I assume that each government at eachperiod behaves rationally using the information up to the concerned period (see Subsection 5.2). Third, they
did not consider any other determinants except the public-debt/GDP ratio for the primary-balance/GDP ratio.
This point is quite different from this field’s existing researches based on Bohn (1989a, 2005) and mine.
Fourth, I examined not only the CG but also the GG, the WLG, and the WSSF (i.e., all government sectors).

10

the dynamic efficiency of the concerned economy. 18

3.2 Bohn Model
To overcome the above limitations of the unit-root and cointegration methods, Bohn
(1998a, 1998b) provides a sufficient condition for satisfying the IBC and a method to
examine it. Moreover, most studies that belong to the second class in Section 2 claim thatthe sufficient and necessary condition for IBC’s fulfillment is holding a cointegration
between the concerned variables that are I (0). Bohn (2007), however, proved that any finite
order of integration of the debt series is compatible with satisfying the IBC.
Bohn (1998b) showed the sufficient condition for government-finance sustainability
under the case of the GDP (aggregate income) stream with a finite present value as below:

𝑠𝑡 = 𝛽𝑑𝑡 + 𝜇𝑡 ,(1)

where β > 0, 𝑠𝑡 denotes the primary-surplus (i.e., government revenues – expenditures

exclusive of interest payments on debt)/GDP ratio, 𝑑𝑡 is the government debt/GDP ratio (atthe end of period 𝑡 − 1), and 𝜇𝑡 is an error term and follows a bounded stochastic process.
Subscript 𝑡 indexes the periods. He also claimed that Equation (2), which is non-linear, canalso be the sufficient condition if 𝑑 ∗ , which satisfies 𝑓 ′ (𝑑𝑡 ) ≥ 𝛽 > 0, ∀ 𝑑 ≥ 𝑑 ∗ , exists:
𝑠𝑡 = 𝑓(𝑑𝑡 ) + 𝜇𝑡 .

(2)

Bohn (1995) considers a government that finances a stochastic path of government
spending 𝐺𝑡 by levying taxes 𝑇𝑡 and borrowing on financial markets and sets the following
18

See Section 4.1 of Yoshida (2018) for the details of this confirmation.

11

the government budget constraint in period 𝑡:
𝐷𝑡 + 𝐺𝑡 − 𝑇𝑡 =�

𝑠𝑡+1 ∈𝑆𝑡+1

𝑝(𝑠𝑡+1|ℎ𝑡 )𝐷(𝑠𝑡+1|ℎ𝑡 ) .

(3)

In Equation (3), 𝐷𝑡 denotes the government debt at the start of period 𝑡, 𝑠𝑡 is an element ofa set 𝑆𝑡 , which is the state of nature at each period 𝑡, ℎ𝑡 = (𝑠𝑡 , 𝑠𝑡−1 , … , 𝑠0 ) is an element ina set 𝐻𝑡 , which is the history of the economy up to period 𝑡, and 𝑝(𝑠𝑡+1|ℎ𝑡 ) is the price of
securities at period 𝑡. In addition, including the assumption that all individuals are equal,
Bohn (1995) derived the following TVC based on Equation (3):

TVC: lim𝑁→∞ 𝐸𝑡 [𝑢𝑡,𝑁 𝐷𝑡+𝑁 ] = 0,(4)

where 𝑢𝑡,𝑁 denotes the marginal substitution rate between periods 𝑡 and 𝑡 + 𝑁 and 𝐷𝑡+𝑁 =𝑑𝑡+𝑁 𝐺𝐺𝐺𝑡+𝑁 is the level of government debt after 𝑁 periods from 𝑡. 19 Equation (4) can be
reduced to the standard or expected value condition
1(5)

lim𝑁→∞ (1+𝑟)𝑁 𝐸𝑡 [𝐷𝑡+𝑁 ] = 0

if the individuals are risk-neutral or if there is no uncertainty: 𝑟 is, however, a positive andconstant interest rate. Bohn also derived the following IBC:∞

IBC: 𝐷𝑡 = � 𝐸𝑡 �𝑢𝑡,𝑛 (𝑇𝑡+𝑛 − 𝐺𝑡+𝑛 )� ,

(6)

𝑛=1

19

See Bohn (1995) for the details.

12where 𝑇𝑡 denotes the government tax revenues and 𝐺𝑡 denotes the government expenditurelevel exclusive of interest payments on debt. Then Bohn (1998b) proved that Equations (1)or (2) satisfies Equations (4) and (6): the TVC and the IBC. The following equation works
as a key in the proof that Equations (4) and (6) are the sufficient conditions for IBC’s
fulfillment:

lim𝑛→∞ (1 − 𝛽)𝑛 𝑑𝑡 = 0 for 𝑛 > 𝑁.

(7)

If 1 > 𝛽 > 0, then the government debt does not diverge because its growth is reduced bythe (1 − 𝛽)𝑛 factor more than in a Ponzi scheme. Even if |𝛽| is quite trivial, the debt after
infinite periods converges to zero, and the IBC is satisfied.

Subsequently Bohn (1998a, 2005) examined the fiscal sustainability of the U.S. federal
2
government using the regression model below. The regressor of �𝑑𝑡 − 𝑑̅ � observes

whether a higher 𝑑𝑡 causes a government to improve 𝑠𝑡 more:

2𝑠𝑡 = 𝛼0 + 𝛽𝑑𝑡−1 + 𝛽2 �𝑑𝑡 − 𝑑̅ � + 𝛼𝐺 𝐺𝐺𝐺𝑅𝑡 + 𝛼𝑌 𝑌𝑌𝑌𝑅𝑡 + 𝜀𝑡 ,(8)where 𝑑̅ , 𝐺𝐺𝐺𝐺 , and 𝑌𝑉𝑉𝑉 respectively denote the average 𝑑𝑡 during the analysis

periods, 20the government expenditure level, and the business cycle state. The latter two
regressors, which are based on Barro’s (1986b) analysis model of government budget
deficits and control the systematic fluctuations in 𝜇𝑡 of Equations (1) and (2), are also

theoretically supposed to negatively affect 𝑠𝑡 . 2122 Index 𝑡 indicates the FYs.

Bohn (1998a) also examined a model that adopts the regressor of max(0, 𝑑𝑡 − 𝑑̅ ) when adding the squared
term of 𝑑𝑡 to select periods with debt above 𝑑 ∗ .
21
Barro (1986b) utilizes the tax-smoothing model. See Barro (1979, 1986a, 1986b) for the details.
22
If the coefficient of YVAR is negative, then the government finance procyclically reacts to the economy. If
the coefficient is positive, then it shows a countercyclical fiscal policy.
20

13

4. Empirical Model and Data

4.1 Features of empirical models
The empirical models used in this study basically follow Bohn’s (1998a, 2005) model andintegrate the following original features.

Objects of analysis
I researched both the GG and all the public subsectors with Japan as a target using theJapanese National Accounts (NA) data. To the best of my knowledge, no research has
examined both the GG and all the public subsectors. Checking the public sector holisticallyallows the analyzer to finally judge whether the public finance of the concerned country canfunction sustainably going forward.

Testing stationarity and cointegration relationships of variables
Many researches have utilized Bohn’s (1998a, 2005) method. However, despite using timeseries variables, most previous works (except Mahdavi, 2014; Yoshida, 2018) failed to
examine the integration properties of the variables and did not elucidate the validity of theestimation of a fiscal reaction function using time-series variables. Hence, I consider boththese issues.

Methods
First, I use the non-linear least squares (NLS) method for estimating fiscal reaction
functions with time-invariant parameters. Next, I use a state-space model and the Kalmanfilter as Burger et al. (2012), Nguyen et al. (2016), and Paniagua et al. (2017) did for
estimating the time-varying parameter functions. The latter method can help us address the14possibility that Japanese public debt policy might have become unsustainable in recent
years.

Effects of financial transfers among public subsectors
Except Mahdavi (2014) and Yoshida (2018), many studies have failed to examine theeffects of financial transfers among the public subsectors (i.e., the CB, the WLG, and the
WSSF) with Bohn’s (1998a, 2005) method. Therefore, I inspect the effects by following
and extending Yoshida’s (2018) method. I prepared an original variable that well reflects
the Japanese intergovernmental fiscal system as below:

𝑟𝑟𝑡 ≡ 𝑔𝑔𝑔𝑔𝑔𝑔 𝑜𝑜 𝑛𝑛𝑛 𝑔𝑔𝑔𝑔𝑔𝑖𝑖 − 𝑔𝑔𝑔𝑔𝑔𝑔 𝑜𝑜 𝐺𝐺𝐺𝑡 ,(9)𝑔𝑔𝑔𝑔𝑔𝑔 𝑜𝑜 𝑛𝑛𝑛 𝑔𝑔𝑔𝑔𝑔𝑖𝑖 ≡ (𝑛𝑛𝑛 𝑔𝑔𝑔𝑔𝑔𝑖𝑖 − 𝑛𝑛𝑛 𝑔𝑔𝑔𝑔𝑔𝑖1970 )⁄𝑛𝑛𝑛 𝑔𝑔𝑔𝑔𝑔𝑖1970 ,𝑔𝑔𝑔𝑔𝑔𝑔 𝑜𝑜 𝐺𝐺𝐺𝑡 ≡ (𝐺𝐺𝐺𝑡 − 𝐺𝐺𝐺1970 )⁄𝐺𝐺𝐺1970 .

In Equation (9), 𝑛𝑛𝑛 𝑔𝑔𝑔𝑔𝑔 denotes the amount calculated by subtracting the total amountof the general and specific payable grants and subsidies from that of the receivable ones. If

this variable’s WLG and WSSF values are positive (negative), the financial transfer fromthe CG to them is richer (poorer) than the Japanese economic state in the concerned period.
On the other hand, if this variable’s CG value is positive (negative), the financial transferfrom the CG to other public subsectors is richer (poorer) since the net fiscal-transfer
amount (i.e., the receivable financial-transfer amount – the payable one) of the CG isnegative at every period. Considering the financial support system of the CG for otherpublic subsectors, I expect this variable to negatively influence the primary balance of theCGs and positively influence those of other public subsectors by developing them in thesurplus direction.

15

4.2 Empirical models
Next I explain the empirical models. First, the regression model for estimating the fiscal
reaction functions with time-invariant parameters is shown:𝑠𝑡 = 𝛼0 + 𝛼𝑑 𝑑𝑡−1 + 𝛼𝑑𝑑𝑑 𝑑𝑑𝑑𝑡 + 𝛼𝑔𝑔𝑔𝑔 𝐺𝐺𝐺𝑅𝑡 + 𝛼𝑦𝑦𝑦𝑦 𝑌𝑌𝑌𝑅𝑡 + 𝛼𝑟𝑟 𝑟𝑟𝑡 + 𝜀𝑡 , (10)2𝑑𝑑𝑑𝑡 ≡ �𝑑𝑡 − 𝑑̅ � ,𝐺𝐺𝐺𝑅𝑡 ≡ (𝐺𝑡 − 𝐺𝑡∗ )/𝐺𝐺𝐺𝑡 ,𝑌𝑌𝑌𝑅𝑡 ≡ (1 − 𝐺𝐺𝑃𝑡 /𝐺𝐺𝑃𝑡∗ )(𝐺𝑡∗ /𝐺𝐺𝑃𝑡 ),𝜀𝑡 = 𝜌𝜀𝑡−1 + 𝜈𝑡 ,(11)

𝐸(𝜈𝑡 ) = 0, 𝐸(𝜈𝑡2 ) = 𝜎𝜈2 , 𝐸(𝜈𝑡 𝜈𝑠 ) = 0 for 𝑡 ≠ 𝑠.
Here 𝑑𝑡−1 denotes the debt 23/GDP ratio at the end of FY 𝑡 − 1, 𝐺𝑡∗ is the trend of 𝐺𝑡 , and

𝐺𝐺𝐺𝑡∗ is the trend of 𝐺𝐺𝐺𝑡 . The definitions of 𝐺𝐺𝐺𝐺 and 𝑌𝑌𝑌𝑌 follow those of Barro(1986b) cited by Bohn (1998a). 𝜀𝑡 represents the error term, which follows an
autoregressive process of order one (AR1) shown by Eq. (11).

Next, I show the state-space model for estimating the time-varying parameter functions.
It can be expressed by the following system of equations:𝑠𝑡 = 𝛼0 + 𝛼𝑑,𝑡 𝑑𝑡−1 + 𝛼𝑑𝑑𝑑 𝑑𝑑𝑑𝑡 + 𝛼𝑔𝑔𝑔𝑔 𝐺𝐺𝐺𝑅𝑡 + 𝛼𝑦𝑦𝑦𝑦 𝑌𝑌𝑌𝑅𝑡 + 𝛼𝑟𝑟 𝑟𝑟𝑡 + 𝜀𝑡 ,𝜀𝑡 ~𝑁(0, 𝜎𝜀2 ), 𝜎𝜀2 = exp(𝜃1 ).

𝛼𝑑,𝑡 = 𝛼𝑑,𝑡−1 + 𝜂𝑡 , 𝜂𝑡 ~𝑁�0, 𝜎𝜂2 �, 𝜎𝜂2 = exp(𝜃2 ).

(12)
(13)

Equation (12) reveals the signal (observe) equation where 𝑠𝑡 is the signal variable, Equation(13) is the state equation that expresses the coefficient 𝛼𝑑,𝑡 of the regressor 𝑑𝑡−1 is a time-

23

This is net debt that equals to “the amount of government financial liabilities minus that of government
financial assets.”16varying state variable. Note that the following. First, I specify 𝛼𝑑,𝑡 as a random walk in thesame manner of Burger et al. (2012) and Nguyen et al. (2016). Second, 𝜎𝜀2 and 𝜎𝜂2 aremodeled to ensure that they are positive. This system of equations was estimated by the
Kalman filter. 24

4.3 Data
This subsection explains the details of the data used in this study. First, all the data weretaken from the NA (the Cabinet Office of the Japanese Government) for FY1998, FY2009,
and FY2017. Second, the analysis term is FY1970-2017. Third, all the variables directly
used in this study and the original data are shown in Table 3. Note that the figures of all thevariables were retroactively revised as follows. (1) The FY1980-1993 figures of FY2009’s
NA were revised by the figures of FY2017’s NA to those of the FY2009 ratios at FY1994
by original data item (in Table 3). (2) The FY1970-1979 figures (FY1969-1979 for theasset-related data) of FY1998’s NA were revised by the figures of FY2009’s NA to those of
FY1998’s NA ratios at FY1980 by original data item. (3) All the public subsector
categories, that is, the CG, the WLG, and the WSSF, adopted the same ratios in the above
terms (1) and (2) as the GG. Moreover, since the primary-balance figures from FY19701979 do not exist, I estimated them using the following figures and processors.

Figures: (1-1) the financial surplus and deficit; (1-2) the payable property income; (1-3)
the receivable property income; (1-4) the average ratio of the interest payments to thepayable property income for FY1980-2009; and (1-5) the average ratio of the interest
receipts to the receivable property income for FY1980-2009.

24

See the appendix of Nguyen et al. (2016) for the outline of the Kalman filter.

17

Processors: (2-1) estimating the interest payments and the receipts from the above data of
Items (1-2)-(1-5); (2-2) adding the estimated interest payments to the above data of Item(1-1) and subtracting the estimated interest receipts from the above data of Item (1-1).
When deriving the FY1970-1979 figures of the government expenditures exclusive ofinterest payments and receipts, the above estimated interest payments and receipts werealso utilized.

Fourth, the amount of data was standardized using GDP deflator (2011 calendar year =100). Fifth, I prepared the trend level of the government expenditures and the GDP by the
Hodrick–Prescott Filter (HP filter). 25 Finally, the data’s descriptive statistics are shown inAppendix. Figure 3 chronologically graphs the primary-balance/GDP, Figure 4 shows thedebt/GDP, and Figure 5 shows the 𝑟𝑟 by government sector. These figures explain thefollowing facts: (1) the primary-balances/GDPs of the GG and the CG have been stagnant
since the 1990s, whereas those of the WLG and the WSSF have remained relatively fit
since FY2000 (this comment applies more to the WLG), (2) the debts/GDPs of the GG and
the CG have been growing over the observation term, whereas those of the WLG and the
WSSF have recently converged to adequate levels (this comment applies more to the
WLG), (3) the unsound condition of the GG finance seems to be attributed to theunhealthiness of the CG finance, (4) the fiscal transfer from the CG to the other public
subsectors has kept increasing in comparison with the development of GDP.
[Table 3 about here][Figure 3 about here][Figure 4 about here][Figure 5 about here]25

See Hodrick and Prescott (1997) for the details. This study also set the penalty parameter of HP filter to 100.

18

5. Results

5.1 Stationarity and cointegration tests
Bohn (2007) argues that even a debt series with any finite order of integration can satisfy
the IBC. As Nguyen et al. (2016) pointed out, the analyzer using Bohn’s (1998a, 2005)
technique with time-series data, however, should examine (1) the sustainability of all thevariables and (2) whether the model is recognized as a cointegration relationship or astandard regression.
First, to investigate the order of integration on all the variables, I implemented the ADF
test and the Lee and Strazicich test (LS test) that allows for the possible presence ofstructural breaks when testing both the null and alternative hypotheses. The latter test was
utilized for my unit-root tests to avoid neglecting the structural breaks in the data as well as
not being biased toward the null that a unit root exists, based on Perron’s (1989) critique.
The test results are shown in Table 4. While the ADF tests suggest that the 𝑑 of the GG and

the CG and the 𝑑𝑑𝑑 of the WLG are I(2), the LS tests show that these variables are also

I(1). According to the LS test results, the 𝑑, 𝑑𝑑𝑑, and 𝑟𝑟 generally are I(1) through all
government sectors and most other variables are I(0), that is, stationary, as Bohn (1998a,
2005) showed.
Subsequently, following the above unit-root-test results, I examined whether the linear
combinations of the level nonstationary variables become stationary: whether cointegration
relationships exist between these variables. Hence, I carried out the Johansen cointegration
tests on the variable combinations of (𝑑, 𝐺𝐺𝐺𝐺, 𝑌𝑌𝑌𝑌) and (𝑠, 𝑑, 𝑑𝑑𝑑, 𝐺𝐺𝐺𝐺, 𝑌𝑌𝑌𝑌, 𝑟𝑟)(Tables 5 and 6). I prepared the former combination to verify Bohn’s (1998a, 2005)

argument that ignoring 𝐺𝐺𝐺𝐺 and 𝑌𝑌𝑌𝑌 , the important systematic components inEquations (8), is problematic when testing the existence of unit root regarding 𝑑. These
19

tables indicate the following: (1) stationarity is accepted on both combinations, and (2) the
result of the former combination is consistent with Bohn’s (1998a, 2005) claim.
Finally, according to the procedures so far, we have to recognize whether the fiscal
reaction function estimated in this study is just a cointegration relationship or a standard
regression, which nests the cointegration among some explanatory variables, depending on
the content of the concerned regression model. 26[Table 4 about here][Table 5 about here][Table 6 about here]

5.2 Fiscal reaction functions

Time-invariant parameter models
First, I estimated the fiscal reaction functions with time-invariant parameters using the
NLS. Table 7 shows the results by government sector and indicates the following:(1) The GG, the CG, and the WLG cannot manage their finances to meet Bohn’s (1998a,
2005) sufficient condition for the IBC since the estimated coefficient parameter of 𝑑 is

not significant. On the other hand, the WSSF can manage its finance sustainably in bothmodels.
(2) The squared term of 𝑑, 𝑑𝑑𝑑, does not work significantly through all the government
sectors.

(3) Based on the 𝐺𝐺𝐺𝐺 and 𝑌𝑌𝑌𝑌 results, the GG and the CG do not worsen theirfinancial conditions by intensive outlays that exceed their trends. They, however, face26

For instance, Model 1 of the GG (in Table7) is recognized as a standard regression, which nests thecointegration among some explanatory variables; Model 2 of the GG is recognized as a cointegration
relationship.

20

deterioration of their primary surplus during economic recessions. This latter fact isprobably attributed to the decline of government revenue and the procyclicalexpenditures to the economy during such a phase. On the other hand, the WLG finance ismore worsened by intensive outlays than economic recessions. This fact probably
indicates that the Japanese fiscal transfer system from the CG to the WLG tends tosupport the WLG finance even during economic recessions. Finally, the WSSF financesuffers from both excessive outlays and economic recessions, which is explained by thefact that WSSF is basically an accounting system for implementing social securities.
(4) 𝑟𝑟 does not affect the primary balance in all the government sectors except the WLG. I
prepared Table 8, which shows the correlation matrices among the dependent andindependent variables, and investigated the cause of this situation. 𝑟𝑟 is strongly

correlated with other variables, especially 𝑑. Consequently, this strong tie between 𝑟𝑟

and 𝑑 seemingly caused the above situation. Therefore, 𝑟𝑟 should be removed from theregressions in all government sectors except the WLG. These correlation coefficients

also suggest that the transfer payments of the CG to other public subsectors worsen the
CG finance; those from the CG mitigate the debt accumulation in the WSSF finance.

Time-varying parameter models
Based on the results of the fiscal reaction functions with time-invariant parameters, I
removed 𝑑𝑑𝑑 and 𝑟𝑟 from Equation (12) of all the government sectors; the latter regressor
was, however, left in only the WLS’s equation. After this modification, I estimated thetime-varying parameter functions by the Kalman filter. Note the following: (1) I obtained
the estimated values of time-varying parameter 𝛼𝑑,𝑡 by not smoothing up to the last period

but filtering up to period 𝑡 since each government at each period probably behaves

rationally using the information up to the concerned period; (2) I set zero and 0.01 as the21

initial value 𝛼𝑑,0 and the initial variance of the state variable. The results are shown in

Table 9 and Figures 6 and 7. RMSE in Figure 6 denotes the root square mean error; the twodashed lines signify the 95% confidence interval of the estimates. Table 9 indicates thefollowing.

(1) The estimated coefficients of all the regressors except 𝑟𝑟 become significant in contrast
to the results of the time-invariant parameter model. Even in the WLG model, thesignificance of the coefficient of 𝑟𝑟 is rejected, unlike the result of the previous

estimation. These results indicate that the time-varying parameter model is more
appropriate than the time-invariant parameter model: this inference seems consistent withthe variable-level changes shown in Figures 3 and 4.
(2) The estimated coefficients of 𝐺𝐺𝐺𝐺 and 𝑌𝑌𝑌𝑌 are negative as theoretical expectations.
This result shows that both intensive outlays and economic recessions undermine eachgovernment’s finance. The absolute level of the estimated coefficients explains that thistendency is more remarkable on the GG and the CG.
(3) Based on the estimated intercept values, the finances of the GG, the CG, and the WLG
are basically positioned in the primary deficit state.
Next, I obtain the following knowledge from Figure 6.
(1) Except the WSSF, the state variable (𝛼𝑑,𝑡 ) estimates vary greatly and cross negative andpositive areas. This fact seems to explain why I cannot get significant estimates on thecoefficient of 𝑑𝑡−1 with time-invariant parameter models.

(2) The existing researches, which do not use time-varying parameter techniques, haveshown different results on fiscal sustainability depending on the data period. Figure 6
clearly explains the cause of this variance in the results, showing that each government’s
posture on financial management has changed continuously.
(3) Since the end of the 1990s, the GG and the CG have administrated their finances so as

22not to meet Bohn’s (1998a, 2005) sufficient condition for the IBC. Contrary to these two
governments, the WLG has sustainably managed its finance since the end of 1990s andthe WSSF has done so through the analysis term. However, the financial performance ofthe WLG and the WSSF is declining, especially the conspicuous downward movement of
the WSSF estimates has appeared in recent years.

I also compared the actual values, the estimates by the NLS, and those by the Kalman filteron the primary balance/GDP by government sector in Figure 7. Note that every estimate by
the Kalman filter is a one-step-ahead forecast. The estimates by the Kalman filter are
generally recognized to fit the actual values more closely than those by the NLS thoroughall the government sectors.
Finally, taking into account all the findings and the Japanese financial transfer systemfrom the CG to the WLG and the WSSF, we can assess whether the Japanese public sector
sustainably manages its finance as a whole by checking the sustainability of the GG or the
CG finance. This study’s results indicate that the Japanese public sector finance has
probably not experienced a sustainable period since the end of the 1990s.
[Table 7 about here][Figure 8 about here][Table 9 about here][Figure 6 about here][Figure 7 about here]

6. Concluding Remarks
Although Japanese economy might enjoy the world’s best financial status (Table 1 andFigure 1), the Japanese public sector, one of subsectors of Japanese economy, has fallen

23

into an unsound condition for decades (Tables 1 and 2). Especially, the unhealthiness of the
CG finance is quite conspicuous.
Hence, this study examined whether the Japanese public sector has sustainably managed
its finance (for FY1970-2017). This study has the following advantages: (1) unlike existing
researches, it examined all the government sectors: the GG, the CG, the WLG, and the
WSSF; (2) it scrutinized the stationarity of all the variables used in the regression andcointegration among them to confirm whether the estimated fiscal reaction function reveals
just a standard regression or a cointegration relationship; (3) it tested the effects of the
fiscal transfer among public subsectors on primary surplus by extending Yoshida’s (2018)
method; (4) it estimated the time-varying parameter function by the state-space model andthe Kalman filter. Hence, I have elucidated the following. First, the order of the integrationof all the variables is generally less than or equal to one. Second, some cointegration
relationships among I(1) variables exist. Third, the effects of fiscal transfer among the
public subsectors are not recognized except when estimating the time-invariant parametermodel of the WLG. Fourth, based on the results of the time-varying parameter model, theGG and the CG have failed to manage their finances to meet Bohn’s (1998a, 2005)
sufficient condition for the IBC since the end of the 1990s; contrariwise, the WLG and the
WSSF can keep their sustainable fiscal postures. After all, this study’s results indicate that
the Japanese public sector as a whole has probably continued an unsustainable fiscal policy
in recent years.
I think that Japan must focus on the present financial health of its economy. Considering
this advantage and trying to make the allocation of value added efficient through both theprivate and public sectors, Japan might have a chance to create a sustainable economy thatis compatible with the sustainable public-sector finance. But due to Japanese society aging
and the huge amount of outstanding public debt, it can be inferred that Japan should24immediately tackle the necessary reforms to avoid falling into economic and governmentfinance collapse. 27

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Tables and Figures

Table 1 Net Lending (+) /Net Borrowing (-) of Japanese Economy
Sector/ FY
1. Households
2. Financial Corporations
3. Non-financial Corporations
Subtotal of 1-3
4. General Government
5. Rest of World

1994
7.8
-0.4
-1.1
6.3
-3.9
-2.4

1999
5.1
-1.1
5.6
9.6
-7.3
-2.3

2004
1.8
2.5
5.1
9.4
-5.8
-3.6

2005
3.7
1.1
2.3
7.1
-3.7
-3.6

2006
4.2
2.4
0.6
7.2
-3.1
-4.0

2007
2.5
0.5
3.6
6.6
-2.2
-4.5

2008
0.4
1.8
4.7
6.9
-4.9
-2.0

2009
4.8
3.7
4.2
12.7
-9.3
-3.3

2010
3.1
0.4
8.5
12.0
-8.5
-3.6

2011
6.0
2.7
1.5
10.2
-8.5
-1.7

2012
3.5
0.3
4.8
8.6
-7.8
-0.8

2013
1.7
-0.2
5.5
7.0
-6.7
-0.4

2014
4.4
0.3
2.4
7.1
-5.4
-1.6

(Ratio to GDP, %)
2015
2016
2017
1.7
3.5
2.5
-0.7
-0.5
-1.2
4.9
3.8
4.9
5.9
6.8
6.2
-2.6
-2.9
-2.1
-3.3
-4.0
-4.1

Notes: Households includes Private Non-profit Institutions Serving Households.
Source: By author using data from FY2017's National Accounts.

Source: By author using “IMF Principal Global Indicators”(http://www.principalglobalindicators.org/?sk=d36d2560-33bb-4cc5-a92b-363ee5d307c9). (Accessed inAugust, 2019)

Figure 1 International Investment Position (2017Q4)

31

Table 2 Primary Balance by Government Sector in Japan(Ratio to GDP, %)Category/ FY
Total

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

-3.4

-2.5

-2.3

-4.7

-9.3

-8.0

-7.8

-7.1

-6.3

-4.2

-2.7

-2.6

-2.4

1

Central Government

-3.1

-2.4

-1.8

-4.3

-7.7

-6.4

-7.1

-6.2

-5.6

-4.0

-3.3

-3.4

-2.5

2
3

Local Governments
Social Security Funds

0.5
-0.8

0.7
-0.9

0.6
-1.0

0.9
-1.3

0.4
-1.9

0.1
-1.7

0.6
-1.4

0.5
-1.3

0.4
-1.2

0.2
-0.3

0.4
0.2

0.3
0.5

0.2
0.0

Source: By author using FY2017's National Accounts.

Note: Figures are exclusive of net grant receipts among public subsectors.
Source: By author using data from National Accounts of FY1998, FY2009, and FY2017.

Figure 2 Government-Expenditures/GDP by Government Sector

32

Table 3 Data List
Var iable

Ut ilize d Or igin al Dat a

De r ivat io na. Primary balance
Pr im ar y Balan c eb. Financial surplus and deficitc. Interest payments
d. Interest receipts

Ne t De bt Ou t st an din g
Go ve r n m e n t Expe n dit u r e(e xc lu sive o f n e t in t e r e st
paym e n t s)
Ne t Gr an ta. Financial assets
b Financial liabilities

b-aa. Government expendituresb. Interest paymentsa - (b - c)c. Interest receipts
a. Intergovernmental fiscal transfers, receivable
b. Intergovernmental fiscal transfers, payableGDP

a. GDPGDP De flat o r

a. GDP deflatora-b

Source: By author using data from National Accounts of FY1998, FY2009, and FY2017.

Figure 3 Primary-Balance/GDP by Government Sector

33

2.00

1.50

1.00

0.50

0.00

-0.50

-1.00
General Government (GG)

Central Government (CG)

Local Governments (WLG)

Social Security Funds (WSSF)

Note: Debt means “the amount of government financial liabilities minus that of government financial
assets.”
Source: By author using data from National Accounts of FY1998, FY2009, and FY2017.

Figure 4 Debt/GDP by Government Sector

34

Source: By author using data from National Accounts of FY1998, FY2009, and FY2017.

Figure 5 rd by Public Subsector and Growth Rate of GDP

35

Table 4 Unit Root Test Results
Panel A: General Government (GG)
Level
Method
s
d
dsq
GVAR
YVAR
rd

With intercept and no trend
ADF test
LS test
Test critical value
Statistic
P value
Statistic
1%-4.073-2.1450.229-4.227 ***
0.178
0.968
-2.26610%-3.296-0.4980.881-2.30010%-3.2961%-4.0730.035-5.257 ***-3.077 **Break points (FY)
1981, 1997
1994, 2008
2002, 2008
1990, 1994

-4.324 ***0.001-4.710 ***1%-4.073

1986, 2012

-0.4130.898-3.496 *10%-3.296

1998, 2008

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

First DifferenceWith intercept and no trend
ADF test
MethodStatistic
P value Statistic
0.000s-6.476 ***d-3.414 ***

dsq

1.114

rd

-5.322 ***LS test
Test critical value

Break points (FY)

0.015

-4.466 ***1%-4.073

1983, 1992

0.997

-3.748 **5%-3.563

1985, 2010

0.000

-4.354 ***1%-4.073

1989, 2002

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

Second DifferenceWith intercept and no trend
ADF test
MethodStatistic
P value Statistic
***
0.000
dsq
-8.206LS test
Test critical value

Break points (FY)

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

Panel B: Central Government (CG)Level
MethodWith intercept and no trend
ADF test
Statistic
P value Statistic

LS test
Test critical value

Break points (FY)

s
d
dsq

-2.233
0.811
0.638

0.198
0.993
0.989

-2.148-2.0185%
10%
10%-3.563-3.296-3.296

1989, 1997
2000, 2008
1980, 2008

GVAR

-3.416 **0.015-6.830 ***1%-4.073

1982, 2005

YVAR

-4.459 ***0.001-4.851 ***1%-4.0731987, 1992

0.898

-3.496 *10%-3.296

1998, 2008rd

-0.413-3.762 **Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

36

First DifferenceWith intercept and no trend
ADF test
MethodStatistic
P value
Statistic

LS test
Test critical value

Break points (FY)s

-6.863 ***

0.000

d

-3.736 ***0.007-4.437 ***5%-3.563

1989, 2010

1%

-4.073

1989, 2002

dsq

-2.0980.247-3.943 **rd-5.322 ***0.000-4.354 ***1%-4.073

1983, 2005

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

Second DifferenceWith intercept and no trend
ADF test
MethodStatistic
P value
Statistic
dsq-6.677 ***LS test
Test critical value

Break points (FY)

0.000

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

Panel C: Local Governments (WLG)
Level
MethodsWith intercept and no trend
ADF test
Statistic
P value
Statistic-1.9890.291-3.436 *LS test
Test critical value
10%-3.296

Break points (FY)
1998, 2010d-1.8220.365-3.825 **5%-3.5632006, 2008dsq

-2.784 *0.068-2.07810%-3.296

2006, 2011

GVAR

-5.020 ***0.000-5.939 ***1%-4.073

1981, 1999

YVAR

-4.296 ***0.001-4.749 ***1%-4.073

1986, 2012

0.131

-4.564 ***1%-4.073

1982, 2006rd

-2.464

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

First DifferenceWith intercept and no trend
ADF test
LS testMethodTest critical value
Statistic
P value
Statistic
1%-4.073s-5.8250.000-5.581 ***d-2.862 *

0.058

dsq

-3.810 ***

0.005

rd

-6.328 ***0.000-4.014 **5%-3.563

Break points (FY)
1980, 1984
2007, 2009

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

Second DifferenceWith intercept and no trend
ADF test
MethodStatistic
P value
Statistic
0.000
d-8.347 ***LS test
Test critical value

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

37

Break points (FY)Panel D: Social Security Funds (WSSF)
Level
MethodWith intercept and no trend
ADF test
Statistic
P value
Statistic

LS test
Test critical value

Break points (FY)sd-1.313-1.858

0.616
0.349

-1.755-2.72210%
10%-3.296-3.296

2002, 2008
1990, 2011dsq

-2.825 *0.063-1.54010%-3.296

1987, 2009

GVAR

-4.974 ***0.000-3.14610%-3.296

1995, 2008

YVAR

-4.293 ***0.001-4.786 ***1%-4.0732006, 2010

rd

0.286

0.975

-2.37810%-3.296

1999, 2008

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

First DifferenceWith intercept and no trend
ADF test
MethodStatistic
P value
Statistics-6.065 ***d-4.886 ***dsq-4.096 ***LS test
Test critical value

Break points (FY)

0.000

-4.177 ***1%-4.073

1986, 2001

0.000

-6.094 ***1%-4.073

1999, 2010

0.002

-6.180 ***1%-4.073

1999, 2010-3.28710%-3.296

1995, 2007

GVAR

With intercept and trendrd-3.818 ***0.005-6.679 **5%-5.917

1983, 2011

-4.411 ***1%-4.073

1983, 1997

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

Second DifferenceWith intercept and no trend
ADF test
MethodStatistic
P value
Statistic
GVAR-8.608 ***LS test
Test critical value
1%-6.691

Notes: "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

38

Break points (FY)
1981, 2006

Table 5 Selected Number of Cointegration Relationships
by Johansen Cointegration Test with Trace

Government
GG

CG

LGs

SSFs

Object

Test type

a

b

c

d

Data trend

None

None

LinearLinearCointegration
Equation

No Intercept

Intercept

Intercept

Intercept

No Trend

No Trend

No Trend

Trend

2

2

2

0

d, GVAR, YVAR
s, d, dsq, GVAR, YVAR, rd

2

2

1

1

d, GVAR, YVAR

2

1

1

0

s, d, dsq, GVAR, YVAR, rd

3

2

1

3

d, GVAR, YVAR

2

1

2

1

s, d, dsq, GVAR, YVAR, rd

2

2

2

3

d, GVAR, YVAR

3

3

2

1

s, d, dsq, GVAR, YVAR, rd

5

6

3

4

Notes: 1. Above numbers are selected at 5% significant level by critical values based on M acKinnon-Haug-M ichelis (1999).
2. Number of lag-order of differenced endogenous variable is two.
3. GG, CG, LGs, and SSFs indicate general government, central government, local governments, and social security funds, respectively.

Table 6 Details of Johansen Cointegration Test with Trace: Test Type b in Table 5
ObjectGovernment
GG
CG
LGs
SSFs

d, GVAR, YVAR
Statistic
P value
H0 : At most one cointegration vector exists.
21.1830.037
H0 : At most one cointegration vector exists.
39.3030.017
H0 : At most one cointegration vector exists.
39.9120.014
H0 : At most two cointegration vectors exist.
9.819
0.038

s, d, dsq, GVAR, YVAR, rd
Statistic
P value
H0 : Same as the left
82.3340.018
H0 : Same as the left
81.7780.021
H0 : At most one cointegration vector exists.
85.4020.010
H0 : At most five cointegration vectors exist.
10.112
0.033

Notes: 1. Number of lag-order of differenced endogenous variable is two.
2. GG, CG, LGs, and SSFs indicate general government, central government, local governments, and social security funds, respectively.

39

Table 7 Results of Fiscal Reaction Functions with Time-Invariant Parameters

Regression
M odelαcαdGeneral Government(GG)

Central Government(CG)

Local Governments(WLG)

Social Security Funds(WSSF)

1

1

1

1

2
-0.016-0.012-0.010-0.006-0.0060.029(0.038)(0.022)(0.012)(0.015)(0.005)(0.007)(0.005)[-0.677][-0.743][-1.002][-0.689][-1.199][-0.808][6.267]-0.032-0.060-0.021-0.002

0.033

0.023

0.086

[3.944]***0.083(0.066)(0.021)(0.052)(0.036)(0.042)(0.012)(0.033)[-1.020][-0.038][0.917][0.540][7.279][2.557]

0.011

0.001

-0.0930.088(0.080)(0.038)(0.399)(0.247)[0.141][0.021]-0.908-0.807[-0.234]-0.543-0.519**-0.636-0.702***-0.708(0.451)(0.614)(0.595)(1.015)(0.207)(0.188)(0.126)(0.152)[-1.478][-1.357][-0.535][-2.511][-3.381][-5.583][-4.662]-0.181-0.323-0.488-1.409**-3.930***-3.655****-0.454(0.514)(0.543)(1.252)(1.447)(0.291)(0.272)(0.214)(0.237)[-2.604][-2.594][-3.140][-2.525][-0.624][-1.189][-2.280][-1.915]0.010-0.0080.005(0.019)(0.019)(0.002)[0.503]
0.809

***

0.823

[-0.420]
***

0.760

***

0.743

**

0.8217

***

0.870

***

*

0.000
(0.001)[2.438]*****[0.357]***[-1.585]*****(0.007)[-0.901]

α ｒｄ

2

0.027

(0.035)-1.339ρ

2***[-0.891]-0.715α yvar2-0.009α dsq

α gvar2[0.056]
***

0.762

***

0.799

(0.120)(0.150)(0.142)(0.157)(0.106)(0.098)(0.119)(0.119)[6.760][5.488][5.340][4.718][7.716][8.875][6.386][6.716]

Adj. R
S.E.

0.809

0.802

0.772

0.762

0.792

0.800

0.944

0.941

0.014

0.015

0.012

0.012

0.003

0.003

0.003

0.003

DW ratio

2.224

2.179

2.252

2.283

1.723

1.586

1.814

1.840

Obs.

48

48

48

48

48

48

48

48

***

Notes: (1) "dsq" stands for square of (d - average of d), and "rd" is ratio-difference (see Section 4.1 for the details) . (2) DW means DurbinWatson. Standard errors are in parentheses. (3) T-statistics are in brackets. "***," "**," and "*" denote 1, 5, and 10 significance levels,
respectively.

40

Table 8 Correlation Matrices
Ge n e ral Gove rn me n t (GG)
s
s

1.000

d

dsq

Ce n tral Gove rn me n t (CG)
GVAR

YVAR

d

-0.5151.000

dsq-0.223

0.641

1.000

GVAR

-0.425

0.023

0.122

1.000

YVAR

-0.4500.082-0.058

0.163

1.000

rd

-0.616

0.964

0.621

0.213

0.117

rd

s

1.000

Loc al Gove rn me n ts (WLG)
s
s

d

dsq

s

1.000

d

dsq

GVAR

YVAR

d

-0.4731.000

dsq-0.275

0.548

GVAR

-0.440

0.013

0.050

1.000

YVAR

-0.4760.056-0.056

0.095

1.000

rd

-0.597

0.968

0.555

0.217

0.125

rd

1.000

1.000

Soc ial Se c u rity Fu n ds (WSSF)
GVAR

YVAR

rd

s
s

1.000

d

0.465

1.000

dsq

0.108

0.111

1.000

GVAR

-0.500-0.076-0.146

1.000

YVAR

-0.0580.142-0.209-0.0161.000

rd-0.412-0.108-0.174

0.439

0.270

1.000

41

d

dsq

GVAR

YVAR

rd

1.000

d

0.891

1.000

dsq

0.310

0.438

1.000

GVAR

-0.2100.057-0.026

1.000

YVAR

-0.1980.025-0.029

0.318

1.000

rd

-0.805-0.844-0.201

0.074

0.051

1.000

Table 9 Time-Invariant Parameters Estimated by Kalman Filter
GeneralGovernment
(GG)

αc

-0.014(0.004)***[-3.649]

α gvar

-1.052-1.480-0.007(0.002)***-0.656-5.194-0.5630.027(0.001)-0.535***[-4.642]***-0.462(0.470)(1.303)(0.209)(0.273)[-4.386][-3.985][-2.692][-1.694]

α rd

***

(0.115)[-4.143]***

SocialSecurityFunds(WSSF)[4.576]***(0.158)[-3.370]***

Local
Governments(WLG)[-3.551]***(0.439)[-2.868]-2.060***-0.022(0.004)[-5.793]***(0.367)

α yvarCentralGovernment
(CG)

*

0.002
(0.004)[0.620]θ1-8.538***(0.323)

θ2-9.260(0.312)[-26.410]-7.899******(0.000)[-29.724]
***

0.002

-0.029***(0.328)[4.825]***-8.840-13.017[39.641]***-10.393(0.441)(0.448)(0.005)(0.295)[-17.909][-19.714][-5.775][-35.180]

LL

122.229

136.483

191.457

217.360

AIC-4.885-5.478-7.727-8.848

Obs.

48

48

48

48

***

Notes: (1) "rd," LL, and AIC mean ratio-difference (see Section 4.1 for the details), Log likelihood,and Akaike's information criterion, respectively. (2) Standard errors are in parentheses. (3) Zstatistics are in brackets. "***," "**," and "*" denote 1, 5, and 10 significance levels, respectively.

42

Figure 6 Time-Varying Parameter 𝜶𝒅,𝒕 Estimates
43

Figure 6 (Continued)

44

Figure 7 Comparison of Primary-Surplus/GDP:
Actual Values vs. NLS & Kalman-Filter Estimates

45

Figure 7 (Continued)

46

Appendix: Descriptive Statistics of Variables(1) General Government (GG)
Mean

Std. Dev.

Max.

Min.

Obs.

Term in FYs-0.0265

0.03280.0370-0.0935

48

1970-2017d0.42110.41861.2563-0.081848

1969-2016dsq

0.1716

0.19780.69760.001048

1970-2017

GVAR

0.00000.00910.0175-0.022848

1970-2017

YVAR

0.00030.00680.0171-0.0147

48

1970-2017rd (*)

1.73801.18694.07500.000048

1970-2017

Note: "rd" is for the central government.

(2) Central Government (CG)Mean

Std. Dev.

Max.

Min.

Obs.

Term in FYs-0.02700.02530.0212-0.077848

1970-2017

d
dsq
GVAR
YVAR

0.59190.19980.00000.00010.45170.22770.00550.00201.51280.84810.01800.00500.01570.0005-0.0116-0.0041

48
48
48
48

1969-2016
1970-2017
1970-2017
1970-2017rd

1.73801.18694.07500.000048

1970-2017

Max.
0.00930.22900.01180.00930.00541.0748Min.
-0.0198
0.01570.0000-0.0086-0.0060-0.7621

Obs.
48
48
48
48
48
48

Term in FY
1970-2017
1969-2016
1970-2017
1970-2017
1970-2017
1970-2017

Max.
0.00930.22900.01180.00930.00541.0748Min.
-0.0198
0.01570.0000-0.0086-0.0060-0.7621

Obs.
48
48
48
48
48
48

Term in FY
1970-2017
1969-2016
1970-2017
1970-2017
1970-2017
1970-2017(3) Local Governments (WLG)

s
d
dsq
GVAR
YVAR
rd

Mean
-0.0026
0.12410.00490.00000.0001
0.2621

Std. Dev.
0.00750.07050.00350.00400.00250.3155(4) Social Security Funds (WSSF)
s
d
dsq
GVAR
YVAR
rd

Mean
-0.0026
0.12410.00490.00000.0001
0.2621

Std. Dev.
0.00750.07050.00350.00400.00250.315547