Substitutability of Savings by Sectors: OECD Experiences
Yoichi Matsubayashi∗

Takao Fujii†This version: August 21, 2012

Abstract
This paper investigates empirically the substitutability of savings among thehousehold, corporate and government sectors in OECD countries. First, theoretical micro-foundations are constructed, wherein, each sector behaves under intertemporal optimization. Second, empirical investigations are conductedbased on this theoretical formation. Optimal consumptions is then derived basedon the theoretical relationship between household consumption and corporate
and government savings. Empirical results indicate that changes in corporatesavings marginally oﬀset household savings in OECD countries. This empirical evidence somewhat supports the assertion that households partly pierce thecorporate veil and that other factors, such as ﬂuctuations in disposable income
and precautionary motives, contribute to the relation between household andcorporate savings. However, substitutability of savings between the households
and the government is not clearly evident.

Keywords: Savings by Sectors, Pierce Corporate Veil, Ricardian Equivalence Theorem
JEL Classiﬁcation: E21, E62, F01∗†

Graduate School of Economics, Kobe University. E-mail: myoichi@econ.kobe-u.ac.jp
Graduate School of Economics, Kobe University. E-mail: fujii@econ.kobe-u.ac.jp

1

Introduction

Much attention has been focused on the trend of worldwide external imbalances’global imbalances’. When taking medium and long-term views of these imbalances
as they pertain to savings and expenditures, we must scrutinize savings trends fornational economies. Unfortunately, doing so often causes arguments to centre uponhousehold savings, and insuﬃcient consideration is given to the relations amonghousehold, corporate and government saving. In the US and Japan, for example,
declining household savings have been widely and fearfully discussed. However, thetilting of those discussions may have the redeeming feature of exposing alternative
ways to view savings in other sectors and thereby promote multi-angled examinationsof national savings, and not merely that of imbalances in saving and expenditure.
In today’s market economy, households, ﬁrms, and governments save independently, e.g. personal savings by households, cash ﬂows in ﬁrms and ﬁnancial surpluses
among governments1 . However, sacriﬁce theories argue that households (shareholders) own corporations and governments are surrogates for households (citizens),
therefore corporate and government savings are merely substitutes for householdsavings. From this notion emerges the question of whether savings by one sector of
the economy suubstitute for savings in other sectors.
This paper will empirically examines these issues and shows the theoretical relationships of substitutability between sectors by focusing on dynamic decision-making
by households, ﬁrms and governments. This paper is structured as follows. The next
section reviews relevant research and summarizes the original characteristics of thepresent analysis. Section 3 constructs a theoretical model based on empirical analysis, while Section 4 examines savings trends, Section 5 and 6 oﬀer a detailed empiricalanalysis. Section 7 elabourates upon further points and Section 8 summarizes theconclusions of the analyses.
1

Government savings is the diﬀerence between revenues and government consumption, not net ofgovernment investment(in public capital formation). Accordingly, their levels are not the same as”ﬁscal balances”. However, because ﬂuctuation patterns in government savings and ﬁscal balances
match, in this paper we treat both of these as essentially the same concept.

1

2

Overview

First let us review relevant previous research into this topics. Denison (1958) obserbed post-war US data and concluded that ﬂuctuations in private savings were
smaller than ﬂuctuations in household and corporate savings. Now known as the
Denison’s Law, his report was the ﬁrst to imply substitutability between household
and corporate savings.2 Few scant attempts at computational analysis followed Denison (1958). Using UK data from 1946 to 1968, Feldstein and Fane (1973) concluded
that corporate savings have eﬀect on household savings. Other papers sceptical
about substitutability include Feldstein (1973, 1978), David and Scadding (1974),
von Furstenberg (1981), and Pitelis (1987). On the other hand, using US data from1948 to 1986, Poterba (1987) reported that household savings could, to an extent,
substitute for corporate savings. Thornton (1998) obtains similar results with annual
panel data from 1980 to 1993 for ﬁve OECD countries: Canada, France, Japan, theUK and the US. Bhatia (1979) and Hendershott and Peek (1987) hint at the possibility of substitutability.3 Using aggregate and microeconomic data, Iwaisako andOkada (2010, 2012) suggest that Japan’s declining savings rate, particularly a nonlinear movement, cannot be attributed solely to population aging and productivity
shocks and underscore the importance of income distribution. Examining corporatesaving, they cite the substitution between household and corporate saving as evidence of a shift in income distribution from labour to shareholders after Japan’s
ﬁnancial crisis in the 1990s. Jongwanich (2010) investigates determinants of household and private savings in Thailand and ﬁnds that corporate savings is one of theimportant determinant of household savings and suggests substitutability between
corporate and household savings.
The relation between household and government savings, which we elabourate
later, helps explain how the Ricardian Equivalence Theorem can be possible when as2

However, Keynes (1936), in his eighth chapter, has already acutely noted that household savings

cannot substitute for corporate savings.
3
Chapter 4 of Sachs and Larrain (1993) contains a simple explanation of substitutability between
household and corporate savings.

2

sessing the eﬀectiveness of government policy. Beginning with Barro (1974), scholars
have analysed the theorem and drawn many conclusions.4 Jongwanich (2010) empirically investigates the relation between household and public saving, and ﬁnds thathousehold saving does not fully crowded out by public saving, suggesting that Ricardian equivalence does not hold. Monogios and Pitelis (2004) ﬁnd that the prefectsubstitution between household savings and government savings, corporate savings,
or both cannot be supported. They conclude that each agent’s rational behaviour is
not satisﬁed.
Several implications arise from previous research. First, evidence of substitutability between household and corporate savings is undeniable among primary advanced
economies, including Japan. Second, substitutability between household and government savings cannot be clearly observed. However, research either relies on simple
observations of data or employs orthodox regression aanalyses. None have closely
scrutinized the time-series data from a strictly theoretical basis.

3

Model

In this section, we show theoretical substitutability among sectors by consideringintertemporal decision-making by households, corporations and governments.

3.1

HouseholdBased on budgetary constraints at diﬀerent times, households choose a period-speciﬁc
consumption proﬁle that maximizes the discounted present value of a utility stream
as shown in Equation (1). Their budgetary constraints can be expressed by Equation(2).
4

For example, research by Brittle (2010), Cohn and Kolluri (2003) and Kessler et al. (1993)

partially supports the theorem, whereas Cebula et al. (1996), Eisner (1994), Jaeger (1993), Domenech
et al. (2000) and Drakos (2001) dispute it. For developing countries, refer Leiderman and Razin(1988), Gupta (1992) and Khalid (1996). See Buiter and Tobin (1979), Bernheim (1987), Leiderman
and Blejer (1988), Barro (1989), Seater (1993), Elmendorf and Mankiw (1999), Ricciuti (2003) andAdji (2007) for overviews of theory and empirical analysis.

3

Et

∞
∑

β s−t U (Cs )

(1)

s=t

β=

1
1+µ

At+1 + Vt χt+1 = (1 + r)At + Vt χt + dt χt + W Lt − Ct

(2)

W Lt = Y Lt − T Ht
At = Btg + Btp
In Equation (2), At is the non-stock ﬁnancial wealth at the beginning of period t,
Vt is a corporation’s market value at beginning of period t and χt is the share ownership ratio at the beginning of period t. In addition, r is the rate of return on ﬁnancial
wealth, dt is total dividends at period t and µ is the discount rate (0 < µ < 1). Y Lt
is labour income before taxes and W Lt is labour income after taxes. T Ht denotes
household tax payments and Ct denotes household consumption. Households’ nonstock ﬁnancial wealth is assumed to be held as government bond(Btg ) and other safe
assets(Btp ), and their rate of return is assumed to be identical.5 All variables are expressed in real terms. After considering optimization of the necessary conditions andby substituting Equation (2) successively, the budgetary constraints can be rewritten
as Equation (3).
∞ (
∞ (
∑
∑
1 )s−t1 )s−tEt
Cs = (1 + r)At + Vt χt + dt χt + Et
W Ls
1+r
1+r
s=t
s=t

(3)

Equation (3) can be interpreted as future consumption being determined by the
total equity and ﬁnancial wealth held in the current period (non-human capital) andfuture labour income after taxes(factor endowments). In regards to consumption
expenditure and labour income after taxes, it is impossible, in the present, to observe
5

In Equation(2), market value in period t, Vt , does not change. It is assumed that the ownershipbalance of equity can be altered by adjusting household income via the ownership ratio (χ). Obstfeld
and Rogoﬀ (1996) (2-5-1) share this assumption.

4

future ﬂows, but it can be assumed as a stochastic variable. In Equation (3), theconditional expected value (Et ) appears based on the information set established for
period t.
If we specify a utility function, we can derive an optimal decision function asshown below.6
∞ (
[
]
∑
1 )s−tCt = α (1 + r)At + Vt χt + dt χt + Et
W Ls
1+r
s=t

(4)

α>0
Equation (5) is a formulation of the Permanent Income Hypothesis, which argues
that household consumption for each period embodies expectations of its permanent
income, the sum of human and non-human capital.

3.2

Firms

Firms maximize market value, and adjust current period production inputs (employment, materials, etc.) and actual capital stock. In this paper, market value refers to
the income ﬂow of future discounted present value of utility. In a perfect capital markets, this value would match ﬁrms’ equity value. Miller and Modigliani (1958) provethat would be the case in ideal capital markets, regardless of corporate value andcapital structure. Their proof is known as the Modigliani-Miller Theorem(MMT).
Whenever MMT applies, a corporation’s value (market value) as shown by theissuances of stock essentially would be the same as the present value of future ﬂows
of internal reserves. This relation is expressed in Equation (5).

Vt = Et∞ (∑1 )s−t
cashs
1
+
r
s=t

(5)

cashs = πs − ds`
1−1/σ ´If we specify a utility function as a constant relative risk aversion u(C) = C1−1/σ , we fulﬁll
˘¯
a > 0 in Equation (3) based on α = (1 + r) − (1 + r)σ β σ /(1 + r) where (1 + r)σ−1 β σ < 1
65

In this equation, Vt is the market value of a corporation’s equity during period t.
Cashs is cash ﬂow corporate savings deﬁned as post-tax income (πs ) net of dividends(ds ).7 Cash ﬂow is a corporation’s savings, and in situations where MMT strictly
applies, Equation (5) indicates that a ﬁrm’s current market value equals the present
value of future corporate savings under the indicated discounted rate.

3.3

Government

Governments accommodate for the gap between revenues and expenditures by issuingbonds, and budget constraints materialize between periods, as shown in Equation
(6).
g
Bt+1
= (1 + r)Btg + Gt − Tt

(6)

Tt = T Ht + T Ot
Gt represents expenditures for period t, Tt represents revenues, T Ht represents tax
revenues from households, and T Ot represents other revenues. By substituteing
Equation (6) successively, we can express budget constraints as(1 + r)Btg = Et

∞ (∑1 )s−t(Ts − Gs )
1+r
s=t

(7)

We interpret equation (7) as the outstanding balance of government bonds in thepresent that must be redeemed by future budget surpluses and government savings.
7

In the standard corporate ﬁnance model, a ﬁrm’s market value (Vt ), is the discounted present

value of dividends by assuming arbitrage conditions of stock and safe assets. In this case, discounted
present values of future ﬂows can be interpreted as corporate value because dividends, which areincluded in the income of each reporting period, are distributed to shareholders. Intuitively, we saythat share prices rise as dividends increase. However, in this model, not all proﬁt (πt ) is distributed
to shareholders. In other words, dividends (dt ) in this model are not income but deductions fromincome. Accordingly, we see that as dividends decrease, a corporate proﬁt increases after net
distribution of deductions and thus corporate value increases. Additionally, in this analysis, sharevalue (Vt ), which is a corporate market value, is determined by Equation (5). In other words, thisequation can be expressed as a corporation’s market value that is the discounted present value of acorporation’s cash ﬂow (proﬁt less dividends).

6

Thus, it presents an indication of budget constraints over time in the public sector.
Future expenditures and revenue ﬂows cannot be observed; we calculate the expectedconditional value (Et ) based on the information set at t as we did for the household
sector.

3.4

Substitutability of Saving by Sectors

Based on the previous settings, we deﬁne the saving functions for households, ﬁrms,
and governments, we then show the relation among these sectors. Household savingfor period t(Sth ) is the total disposable income net of consumption, as is conventionally deﬁned by Equation (9).

Sth = Y Dt − Ct

(8)

Y Dt = Y Lt + dt χt − T Ht∞[∑
Ct = α (1 + r)Btp + Et
β s−t (T Hs + T Os − Gs ) + dt χt
s=t

+ Et

∞
∑

β s−t (πs − ds )χs + Et

∞
∑

(9)
(10)

]
β s−t (Y Ls − T Hs )

s=t

s=t

In our model, disposable income (Y Dt ) is deﬁned as the sum of labour income anddividends less taxes (Equation (9)). Also, the consumption expenditure standards
for each period (Equation (10)) are provided after considering Equations (4), (5),and (7). We deﬁne corporate savings (Stf ) and government savings (Stg ) as shown
below8 .

8Stf = πt − dt(11)

Stg = Tt − Gt

(12)Tt = T Ht + T Ot

(13)

To abbreviate, we standardize as χs = 1 below.

7First, we observe the relationship between household and corporate saving. Assume that a corporation decreases its dividend (dt ) to shareholders (households) inperiod t. According to Equation (11) and barring a change in income, corporatesavings increase by the amount of the unpaid dividend in period t. The eﬀect ofthe dividend reduction on the household sector will be two-fold, assuming no change
in the share ownership ratio (χt ). First, disposable income (as speciﬁed in (9)) decreases. Second, permanent income and consumption are aﬀected. As we see inEquation (10), dividend reductions reduce permanent income directly. However,when MMT is strictly in eﬀect (Equation (5)), dividend reductions increases in corporate savings increase the value of households equity holdings through increases
in prices (Vt ). In other words, permanent income on the right side of Equation(10) remains unaﬀected and consumption expenditures do not change9 . Expressed
diﬀerently, we observe only a decrease in dividends equal to disposable income, or,consequently, household savings. Private savings remains unchanged. This is theoutcome of households rational response to changes in corporate saving policies andcould be expressed as households unveiling ﬁrms.
Let’s review the conditions under which corporate and household savings aresubstitutes: 1) dividends and corporate savings are negatively correlated; 2) the efﬁcient stock market reﬂect changes in cash ﬂow in the stock prices (or divi- dends);
3) households hold a signiﬁcant amount of a corporation’s assets in stock as ﬁnancial wealth; 4) households regard equity as permanent income on which they baseconsumption and savings.
Next we observe the relationship between household and government saving. We
assume that the government implements taxcut whereby it reduces its tax revenues(T Ht ) from households in period t. From Equation (12), and assuming no changes in
expenditures, government savings decrease by the amount of the tax cuts in period t.
9By writing the permanent income part on the right side of Equation (10),
P
P
s−t
s−t
(1 + r)Btp + Et ∞(T Hs + T Os − Gs ) + dt χt + (πt − dt )χt + Et ∞(πt − dt )χt +
s=t β
s=t β
P∞ s−tEt s=t β (Y Ls − T Hs )it is easily conﬁrmed that dividend reductions in the current period (dt ) does not impact permanent
income.

8

The household sector’s disposable income rises due to the tax decrease. On the other
hand, as Equation (10) indicates, the single-period decrease in T Ht does not aﬀect
permanent income, on the right side of Equation (10), and has no apparent eﬀect
on consumption10 . A reduction in government savings by tax reductiones increased
the household’s disposable income and savings by an amount equal to the tax ofperfect substitutability. It is known in government policy circles, as the Ricardian
Equivalence Theorem or Neutrality Theorem of Debt Burden.

4

Data

Annual unbalanced panel data of 10 OECD countries for 1980-2009:11 Canada(19802009), Finland(1995-2009), France(1995-2009), Germany(1991-2009), Italy(1980-2009),
Japan(1980-2009), Norway(1995-2009), Sweden(1980-2009), the UK(1980-2009) andthe US(1980-2009). Data availability and structural similarities among countries
were the criteria for sample selection12 . Data is sourced primarily from OECD national accounts. The data appendix provides a detailed documentation. We use two
samples: Sample I is composed of G7 countries and Sample II is the G7 plus Sweden,
Norway and Finland.
Figure 1 presents sector-wise savings as a percentage of GDP for each of the 10

10

The fact that permanent income is not aﬀected by a reduction in taxes for that period can beeasily conﬁrmed by the expression in footnote 9.
11
As Haque et al. (1999) point out, to assume parameter homogeneity across countries neglects
heterogeneity and may cause misleading interpretations of results. But it is also true that ourempirical analysis provides the overall picture as stated by Bernheim (1987). Estimating country
by country remains a task for future research.
12
It is extremely diﬃcult to ﬁnd lengthy time series data for household ﬁnancial net wealth. Thisvariable is available only for few countries. Mello et al. (2004) also lament this point.

9OECD countries.13 The ﬁgure reveals several interesting properties.14 This directionality of total savings is evident as upward trending(Norway, Sweden), downward
trending(Italy, Japan, US), ﬂat(France, Germany, UK) or erratic(Canada, Finland).
Total saving rates in Norway and Sweden trend upward but trends in sectoral savings vary. Norway’s household and corporate saving rates remain low but government
saving shows an increase post the Nordic ﬁnancial crisis.15 Swedish corporate andhousehold savings are more cyclical than in Norway, nor does Sweden’s government
saving witness an increase like Norway’s.16
In contrast to those countries, total saving rates and household savings rates in
Italy, Japan and the US trend downwards. Italy’s household saving rate is higher
than those of Japanese or the US, perhaps, reﬂecting the borrowing constraints on
young Italians(Kirsanova and Sefton (2007)). Unlike in Italy, corporate saving rates
negatively correlated with household saving rates in Japan. In Japan, government
saving rates have declined rapidly in recent years unlike Italy which shows improvement in its ﬁscal condition. Moreover, in contrast to Italy and Japan, where trends
in the total saving rates seem to accord with those of household saving, behaviourof the US tatal saving rate may be explained by the government saving behaviour.
Total saving rates in France, Germany and the UK are relatively ﬂat across the
sample period. France’s household saving rate seems negatively correlated with thecorporate saving rate, wherein movements in the government saving rate seem todominate the total saving rate. The UK is almost at par in this regard, although
13

Edwards (1996) states that ”Most empirical studies have associated private savings to house-

hold savings. This is not strictly correct, since in a number of countries corporate savings are an
important component of the aggregate.” An exception is Kirsanova and Sefton (2007), who decompose national savings into household, corporate and public sectors in the UK, US and Italy.
Among lesser developed countries, as mentioned before, Jongwanich (2010) investigates determinants of household and private savings in Thailand and ﬁnds that corporate savings is an important
determinat of household savings.
14
We should, however, bear in mind that we conduct the retroaction of data to the past by using
the growth rate of the older data sets.
15
For more on the Nordic ﬁnancial crisis, see Jonung et al. (2009).
16
Swedish government saving declined drastically in 1993 during the Nordic ﬁnancial crisis. For
details see Bi and Leeper (2010).

10

it has a relatively cyclical ﬂow compared with France and Germany. Germany’s
household saving rate is stable compared with other G7 countries(Hufner and Koske(2010)).17
Total saving rates are erratic in Canada and Finland, mainly because they are
dominated by the corporate saving rate that reﬂects the business cycle. 1819
Causal examination of Figure 1 indicates that the household saving rate in many
countries correlates negatively with the corporate saving rate, which inﬂuences thetotal saving rate. We examine these facts statitically. Table 1 presents the coeﬃcientof variation in rates of savings by sectors. The sixth and seventh columns of the table
almost support the above fact known as Denison’s Law(Denison (1958)).
However, the above ﬁndings are based on a casual glance, and an initial descriptive statistics requires further scrutiny through panel cointegration analysis.20 As aprerequisite to testing for cointegration, a panel unit root test is conducted per Im
et al. (2003).
As Table 2 shows, the Im et al. (2003) test fails to reject the null hypothesis forlevels except corporate saving per GDP, and rejects it for ﬁrst diﬀerences. These

17

They suggest that this fact may be what Borsch-Supan et al. (2001) and Borsch-Supan (2002)

term the German savings puzzle.
18
For Canada, Carroll and Summers’s(1987) important paper diﬀers from the analysis here bysample period and purpose of analysis. They seek to explain the divergence between movementsof Canadian and US private savings rates. They suggest that macroeconomic variables such as
inﬂation and unemployment do not suﬃciently explain the divergence and the importance of ﬁscal
policy diﬀerences. Their empirical results show that the increase in budget deﬁcit is oﬀset almost one
for one by increases in private saving. They, however, warn against interpreting the results as theevidence of Ricardian equivalence. For details, see Carroll and Summers((1987), p.272). Moreover,they indicate that corporate saving is not important in explaining the divergence in movements ofthe two countries’ private saving rates.
19
During the mid-1990s, the saving rate of Canada’s government rapidly improved followed byeconomic expansion. Krugman (2012), however, suggests that this experience does not oﬀer evidenceof expansionary ﬁscal consolidations.
20
Previous studies of saving behaviour using panel cointegration analysis include Bandiera et al.
(2000), Sarantis and Stewart (2001) and Hondroyiannis (2006). Their concern is with determinantsof aggregate private saving. See Berube and Cote (2000) and Hufner and Koske (2010).

11

results suggest that the panel data series are I(1).21
Table 3 reports cointegration test results using the panel cointegration tests of
Kao (1999) and Pedroni (1999, 2004).22 Although it is desirable to use Pedroni’s
test because it allows for heterogeneity in slope coeﬃcients across all units, Gutierrez(2003) argues that Kao’s(1999) tests outperform Pedroni’s if the time series dimension of the panel is small from his Monte Carlo results. We therefore use both tests.
Generally, test results support a cointegration relation among any pair of series
except for the pairing of household and corporate savings. These results indicate
an apparent long-run equilibrium among household, corporate and government series. The Kao and Pedroni tests, however, rely on the assumption of cross-sectional
independence and accordingly suﬀer from size distortions(Banerjee et al. (2004);
Gengenbach et al. (2006)). We therefore implement the Westerlund (2007) panel
cointegration test. Table 5 shows these results. After considering cross-sectional
dependence, the cointegration relation still exists, but is less powerful.
To summarize, the analyses indicate only a slight connection among savings bysectors. However, a cointegaration test merely investigtes whether a long-run equilibrium exists among variables.23 We therefore proceed to the next step by estimating
the equation based on structural models.24

21

A careful interpretation of panel unit root tests should be performed. ”In IPS, the alternative isthat at least one of the individual series in the panel is stationary”(Karlsson and Lothgren (2000)).
22
Pedroni (1999) proposes seven tests for panel coitegration: the panel ν-statistic, panel ρstatistic, panel t-statistic(non-parametric), panel t-statistic(parametric), group ρ-statistic, groupt-statistic(non-parametric) and group t-statistic(parametric). From among these, we adopt panelt-statistic(parametric) and group t-statistic(parametric) because a Monte Carlo study by Pedroni(2004) shows that these two statistics are more robust for small samples. We also use the unweighted
statistic as panel t-statistic as per his statement: ”In Monte Carlo simulations, we found that theunweighted statistics consistently outperformed the weighted statistics in terms of the small sample
size properties.”(Pedroni (2004),p.619)
23
Gutierrez (2003) warns about inference based only on panel cointegration tests.
24
Mello et al. (2004) indicate the strengths and weaknesses of reduced-form and structural-form
equations.

12

5Empirical Analysis

5.1

Estimating Method

We focus on the substitutability of savings by sectors, whereas previous studies investigate the determinants of household and private savings. As Loayza et al. (2000)
point out, however, the use of reduced-form saving equations does not necessarily
have a micro foundation. Here, we use the estimation equation based on a micro
foundation.25 Equation (10) is the basis for our analysis, as we set our estimation equation having accommodated the following four points: First, we set house( ∑)s−t (π − d ) as
holds’ rational recognitions for future corporate savings Et ∞
s
s
s=t β
( ∑
)
s−t (T H + T O − G ) as
θ(0 ≤ θ ≤ 1), and for future government savings Et ∞
s
s
s
s=t β
γ(0 ≤ γ ≤ 1). If both θ and γ are 1, households are correctly recognizing corporate
and government savings trends; if both are 0, households are oblivious to the changes
in savings in those sectors’. Second, households confront liquidity constraints, andtheir consumption is thought to depend not only on perceptions of permanent income, but also on each period’s disposable income (Y Dt ). This rate is shown as λ(0 ≤ λ ≤ 1). Third, the share ownership ration (χt ) is assumed to be 1. Giver thesethree points, we rewrite the consumption function of Equation (10) as[

Ct = α (1 + r)Btp + γEt∞∑

β s−t (T Hs + T Os − Gs ) + dt

s=t

+ θEt

∞
∑

β

s−t

(πs − ds ) + Et

∞
∑

(14)

]
β s−t (Y Ls − T Hs ) + λY Dt

s=t

s=t

1
α > 0, β =1+µThe right side of Equation (14) shows government savings, corporate savings, andfuture values for human wealth. Because it is impossible to observe future values
25

Although Lopez et al. (2000), Malengier and Pozzi (2004) and Pozzi and Malengier (2007)

are technically similar to ours in adopting a nonlinear generalized method of moments (GMM)
estimator using panel data, they do not account separately for corporate savings and our analysis
has a diﬀerent purpose. Although not a panel data analysis, Pozzi (2003) estimates a consumptionfunction for Belgium by a nonlinear instrumental variables method.

13

in the present, we cannot directly estimate Equation (14). We use Hayashi’s(1982)
methodology as a fourth modiﬁcation of Equation (14) to allow making these estimations.

g
Cit = (1 + µ)Cit−1 + α[Wit − (1 + µ)(Wit−1 + W Lit−1 )] − αγ(1 + µ)Sit−1f− αθ(1 + µ)Sit−1+ λ[Y Dit − (1 + µ)Y Dit−1 ] + ηi + ²it(15)

where C denotes consumption, W nonhuman wealth, W L after tax labour income,S g government saving, S f corporate saving and Y D disposable income. Subscripts
i and t denote countries and time periods respectively. All variables are real per
capita values.
Within Equation (15), parameters to be estimated are µ, α, λ, θ, and γ, andour parameter space is theoretically constrained. However, Equation (15) speciﬁes acomplex non-linear shape for these parameters. Also, these parameters express theirrepresentative agents behaviours that we validate using macro data. Accordingly, it
is not easy to reach reasonable estimations for all parameters within an appropriate
space range. To amend this situation, we ﬁx the valuee of µ in advance, in estimating
parameters α, λ, θ, and γ as explained below.

5.2

Estimation

Equation (15) using OECD countries’ panel dataset is a dynamic panel data model
because it includes a lagged dependent variable, Cit−1 . Thus, the ﬁxed eﬀects model
generates inconsistent estimates under normal conditions(Baltagi (2008)). Therefore,
we use a GMM procedure proposed by Arellano and Bond (1991). As Arellano
and Bond (1991) state, it is preferable to use all lagged values as instruments of
explanatory variables, but practically this preference does not always work well. For
examples, see Tauchen (1986), Alonso-Borrego and Arellano (1999) and Ahn andSchmidt (1999).
In fact, the Monte Carlo work of Ahn and Schmidt (1999) shows that GMM estimation using subset of the moment conditions often performs better than that using
14

of the moment conditions in ﬁnite samples. We therefore use only dependent variables lagged two or more periods as instruments, following Dahlberg and Johansson(2000).26
Moreover, as the equation includes µ, α, λ, θ and γ as estimated parameters
in nolinear form, it is diﬃcult to get reasonable estimates for all parameters. So,
we exogenously set three values for µ, our variable of less interest(0.05, 0.01 and0.001).27
Table 6 reports estimation results. First, we examine λ, representing the proportion of households facing liquidity constraints. This parameter is important as aprerequisite for Ricardian equivalence and is the key to the ﬁscal policy puzzle,28 soit has been researched considerably. Studies employing panel data analysis include
Evans and Karras (1998), Lopez et al. (2000), Malengier and Pozzi (2004) and Pozzi
and Malengier (2007).
Evans and Karras (1998) investigate the severity of liquidity constraints using
annual data for 66 countries between 1970 and 1989. They obtain a robust estimates of 0.25 for λ. Using annual data from 1975 to 1992 for 41 industrial anddeveloping countries, Lopez et al. (2000) get approximately 0.40 as their estimate
for the subsample of 19 industrialized economies and about 0.60 for the 22 developing economies. Malengier and Pozzi (2004) use panel data for 19 OECD countries
spanning 1980 to 1997 and conclude that approximately 25% of consumers are ruleof-thumb households. Moreover, detailed analysis by Pozzi and Malengier (2007)
provides a reliable estimate of λ by estimating a panel data model for 17 OECD
countries over 1981–2003. Their estimate is 0.369.
Our estimates are in line with the above research. In addition, Table 7 indicates
26
27

We do not use the lagged diﬀerence but the lagged level as instruments(Arellano (1989))
A similar approach is taken by Lopez et al. (2000), Malengier and Pozzi (2004) and Reitschuler(2008).
28
As well known, the Ricardian Equivalence Theorem holds under speciﬁed assumptions: noliquidity constraints, identical planning horizons between private and government sectors, nondistortionary taxes and certainty. In addition to these, the theorem does not hold if households havehyperbolic discounting(Laibson (1997)). See footnote 4 for the REP and Gali et al. (2007) for theﬁscal policy puzzle.

15

that our estimates in Sample I are roughly in line with the average value of countryspeciﬁc values given by Evans and Karras (1996) and Evans and Karras (1998).
Although our estimation results in Sample II is diﬀerent from the average of theirresults, our estimate, about 20%, is nearly identical to Malengier and Pozzi’s(2004).
Moreover, it is interesting that estimates of λ in Sample II are lower than for Sample I.
Pozzi et al. (2004) show that a higher government debt ratio causes excess sensitivity,
partly explained by liquidity constraints. As Table 8 reveals, the average government
debt ratio for the three Nordic countries in Sample II is below the G7 average(Sample
I). That is, the lower estimates of λ in Sample II are consistent with the empiricalresults of Pozzi et al. (2004).
Further we discuss the parameters of our primary interest γ and θ. Unfortunately, no previous research concerns these parameters, but most of our estimation
results are statistically signiﬁcant. In other words, household saving substitutes forcorporate and government saving. Note, however, the values are very small, suggesting an extremely low degree of substitutability. These results support Edwards(1996).

6

Robustness Check

This study primarily focuses on the estimates of γ and θ. To check the robustnessof our results, we repeated the analysis along three dimensions. First, we vary thevalue of μ from 0.002 to 0.05 by increments of 0.002 and repeat the analysis. As
we conducted an empirical analysis by setting the value of µ exogenously in theprevious section, it is important for us to reestimate Equation 15 by changing thethe value of µ. Second, we also estimate Equation 15 using households’ ﬁnal consumption expenditures as an alternate measure of consumption. As Graham (1992)
mentions, choosing the consumption measure is important because of its inﬂuenceon the estimation results. Thsu, we exclusively adopt household’s ﬁnal consumption expenditures in place of households’ ﬁnal consumption expenditure as well as

16

expenditures by non proﬁt institutions serving households.29 Third, we use all explanatory variables lagged two and three years as instruments. As mentioned, it ispreferable to use all lagged values as instruments of explanatory variables, but inpractice it causes ﬁnite sample bias. Therefore, as done previously, we dopt only
deppendent variables lagged two or more periods as instruments, following Dahlberg
and Johansson (2000). However, this way of dealing with the issue also presents the
problem that the lagged variables of the all explanatory variables are not used. So,
we use all explanatory variables lagged two and three years as instruments following
Pozzi et al. (2004).
Tables 9, 10 and 11 show the results. Although some estimates take a negativevalues, these results further detail the degree of substitutability between household,corporate and government savings. In particular, estimates of θ, the coeﬃcient ofcorporate saving, tends to be larger than those of γ, representing the coeﬃcient ofgovernment saving. In other words, the degree of substitutability between household
and corporate saving exceeds that between household and government saving. In
addition, the degree of substitutability between household and government saving
is extremely low. As Romer (2011) says, ”the important question on Ricardian
Equivalence Theorem is whether there are large departures from it.” Our results
suggest that the Ricardian equivalence attracts less support than is indicated inthe
previous research, notably Bernheim (1987) and Masson et al. (1998).

7

Discussions

Based on the theoretical model in Section 3 and empirical results obtained in Section
5, we now further consider the relationships among savings by sectors in OECD
countries.

29

Although Graham (1992) indicates the importance of the consumption measure, his argument

is not about the choice between household only or household plus non proﬁt institutions but rather
about the handling of the service ﬂow from consumer durables. Checking the robustness on thispoint remains another important future task due to data availability.

17

7.1

Substitutability of Household and Corporate Savings

First, we re-examine the feasibility of the theoretical model with regard to the substitutability of household and corporate savings. The impact of corporate savingson household consumption (savings) is not large, but is signiﬁcant in both cases. In
other words, there is a slight possibility that in OECD countries it might present
the theoretical model mechanism. Further in this paper, we deepen this discussion
about the investigation of the economic environment that the theoretical model aswell as factors other than the theoretical model.
For household and corporate savings to be substitutable, it is prerequisite that
dividends and corporate savings correlate negatively.
Figure 2 shows the movements of dividend income(DIV) and corporate savings(both given as ratios of GDP) obtained by household sectors in the US, UK andJapan (it was diﬃcult for other countries to obtain dividend series for the same
periods). In the US, until the mid 1990s, high corporate savings were accumulated
against the backdrop of a booming economy, and an increasing trend in dividends wasmaintained, reﬂecting strong corporate performance. However, in the latter half ofthe 1990s, dividend trends correlated negatively with corporate savings. Then, 2000s
onwards, a positive correlation reappeared. In the UK, the two variables showed anegative correlation(−0.625) for the sample period. In Japan, where dividends tohouseholds were weak through the 1990s and early 2000s, corporate savings steadily
increased, producing a negative correlation between the two variables(−0.100). However, from the early, from the early to the late 2000s, dividends and corporate savings
showed roughly identical trends. Data from these three countries thus conﬁrms thenegative correlation between dividends and corporate savings assumed by the theoretical model, however, conﬁrmation depends on the periods observed.
An eﬀective stock market is also an important condition for establishment of thetheoretical model. Determining stock market eﬃciency is an empirical problem, forwhich there are various empirical methods. The most typical is the use of time series
analysis (unit root tests) to determine whether prices follow a random walk.
Narayan and Prasad (2007), and Narayan and Narayan (2007) conducted panel

18

unit root tests, using samples from 17 European countries (January 1988–March
2003), and samples from the G7 (January 1975–April 2003) respectively, which supported the eﬃcient market hypothesis. Narayan and Smyth (2005) further used daily
data (1991–2003) of 22 OECD nations (including the G7), and performed unit root
tests taking into account a one time structural change, and supported the random
walk hypothesis for stock prices.
The mechanism that generates the negative correlation between corporate andhousehold savings does not necessarily depend on rational long term behaviour ofeach economic agent, as shown above. For example, the suppression of wage growth
can result, simultaneously, in both lower household disposable income and higher
corporate proﬁts that could cause negative correlation between corporate and household savings. The empirical analysis in Section 5 conﬁrms that the impact of theliquidity constraint (λ) is signiﬁcant. This means that disposable income and wages
act on consumption and savings in the current ﬁscal period, thus requiring further
attention to the signiﬁcance of this eﬀect.
Figure 3 shows the rate of change in nominal wages of households and corporatesavings for OECD nations, as shown in Figure 1. As Figure 3 depicts, Canada,
France, Japan and the US showing number of periods of negative correlation between
household and corporate savings, but it is possible that the changes in nominal wages
play an important role in this. For example, the growth rate of wages in France
declined during the 1980s. During this period, household savings fell signiﬁcantly
while corporate savings recovered rapidly. No signiﬁcant variations were observedin wage growth through the 1990s and 2000s, as a result, there has been no major
movement in household and corporate savings. A similar trend can be observedin the US during the 1980s, and in Japan during the 1990s. On the other hand,
Sweden, Norway and Finland witnessed no notable decrease in the growth rate ofwages since the 1990s, rendering the eﬀect of changes in wages on corporate savingsand household savings unclear.
Besides mechanisms based on wage changes, factors generating a negative correlation between corporate and household savings can include economic agents’ reactions
to the economy’s rapid deterioration. For example, corporate savings decline during
19

a worsening recession, reﬂecting the decline in earnings. At the same time, economic
uncertainty among households may stimulate precautionary savings. Finland andSweden entered a deep recession during the early 1990s after the economic bubble
collapsed in the late 1980s. As seen in Figure 3, corporate savings during this periodstagnated and household savings increased rapidly, presumably for precautionary
reasons, resulting in a negative relation between savings of these two sectors. This
short term ﬂuctuation functions as a substitute mechanism for savings by sectors.

7.2

Substitutability of Household and Government Savings

Estimated results in Section 5 assertain that the substitutability of household andgovernment savings was extremely low.30
As discussed, the possibility of substitutability of savings by these two sectors
relates closely to the formation of the Ricardian Equivalence Theorem. Extended
empirical analysis has produced multiple results concerning that possibility, but analysis in recent years has been scattered, showing scepticism about formation of thetheorem. For example, Rohn (2010) conduct panel and individual estimates for 16
OECD countries and six countries (Denmark, France, Germany, Italy, Japan andthe US), and Hufner and Koske (2010) ﬁnd no support to the Ricardian Equivalence
Theorem in OECD countries other than the US and France. Generally, these empirical results support ours. In the event that government savings inﬂuence household
consumption and savings, it is important to consider factors such as the current levelof government savings and how to assess households’ diachronic view of changes intax policy. Even if cutting taxes reduces government savings, households’ consumption for the period will increase because their disposal income increases if they do
not anticipate future tax increases. Also, provided government savings do not sustain major deﬁcits, it is unlikely that future tax increases or spending cuts will be
30

Although not in panel context, Mukhopadhyay (1994) investigates the Ricardian Equivalence

Theorem directly using self-reports of residents in Halifax, Canada. The results show that mosthoseholds do not consider government budget deﬁcits in deciding how much they save, concluding that the Ricardian Equivalence Theorem is not supported. Our extremely low estimates are
consistent with his result.

20

expected. This issue thus requires further investigation.

8

Conclusion

This paper quantitatively analysed the substitutability of savings by sectors using
panel data from OECD countries, producing two signiﬁcant ﬁndings. First, household and corporate saving correlated negatively in most sampled OECD countries.
We surmise that the negative correlation was somewhat explained by short-term
and medium-term intertemporal rational behaviour by households and corporations,along with changes in wages and disposal income, but its eﬀects were marginal. Second, there is no evident, clear relation between the substitutability of household andgovernment saving. Our analysis suggested that the Ricardian Equivalence Theorem held to a degree, dependent on country speciﬁcity and observed time period,
but analysis of the OECD countries as a whole indicated that prospects for the theorem to hold as being low. Most developed countries currently experience declining
birthrate and ageing populations. The savings trend in every sector in such countries, particularly the down trend in household and government saving has drawn
sholarly attention to its medium-term and long-term consequences. Most discussions
are preoccupied with saving trends in individual sectors. If future analysis of substitutability between sectors proceeds in directions suggested by this article, more
research will involve multifaceted angles. Further study is required to assess theimpact of deteriorating government savings on private sector saving. For example,
study of additional long-term issues such as the substitutability of saving by sectors and economic growth could revise and extend the theoretical framework of thisanalysis.
Based on results of this analysis, chances are high that decreased household saving, through numerous routes, is somewhat oﬀset by corporate saving in OECD
countries. Therefore, it is diﬃcult to paint a scenario involving a large decreasein the saving rate for the overall private economy. However, developed countries’
burgeoning government deﬁcits and deteriorating budget balances are worrisome.
National saving could decline if household or private saving does not oﬀset govern21

ment deﬁcits. Extrapolating this trend suggests sustained budget deﬁcits or lack offunds for saving or investing. This problem is serious, particularly for the US andSouthern Europe. This problem cannot be ignored, especially when global imbalances show no indications of setting down. Further, for an in depth understanding of
the global economy research into the substitutability of saving by sectors in emerging
economies is essential. The mechanism of substitutability of saving by sectors may
be critical in the macro performance of the global economy.

Data Appendix
We use annual data for 10 selected OECD countries: Canada, Finland, France, Germany, Italy, Japan, Norway, Sweden, the UK and the USA. Our sample period is
1980-2009. For some of the countries the sample period is shorter, so the panel is unbalanced. Recent data series are primarily taken from the OECD database(OECD.Stat).
We cannot, however, ﬁnd some past series of the variables. Therefore we also use
the previous version of OECD books: National Accounts of OECD Countries Volume IIIa(Financial Accounts Flows 1995-2006), IIIb(Financial Balance Sheets Stocks
1995-2006), Detailed tables Volume II 1980-1992 and Detailed tables Volume II 19841996, etc. The retroaction of data to the past is conducted by using the growth rateof the older data sets. Consumer price index(CPI) is used to construct real values.
• Savings(S)Household saving(S h ), Corporation saving(S f ) and Government saving(S g ) arecorresponding to household saving,net, corporation saving,net and government
saving,net in OECD Annual National Accounts, respectively.
• Consumption(C)Final consumption expenditure of households and non proﬁt institutions serving households• labour Income after tax(W L)
labour income after tax = compensation of employees minus personal current
taxes. Personal current taxes are retrieved from OECD tax statistics.
22• Household Disposal Income(Y D)
Dates are retrieved from Economic Outlook No.73 and No.86. The retroactionof data to the past is conducted by using the growth rate of the net national
disposal income only for UK.
• Net Financial Wealth(W )While dates are mainly retrieved from OECD Financial Accounts, we use theother sources: Bonci and Coletta (2008) for Italy , Statistics Sweden for Sweden
and The Blue Book for UK.
• Household dividend income(DIV )Japanese household dividend income is retrieved from the Cabinet Oﬃce website. For the UK, distributed income of corporations from The Blue Book isused. For the USA, we use personal dividend income from National Income
and Product Accounts(NIPA).

23

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31

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32

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33

Table 1: Coeﬃcients of Variation in Savings by Sectors(as % of GDP)

(1)

(2)

(3)

(3)/(1) (3)/(2)Household Corporation Private(4)Country

PeriodCanada1980-2009

0.625

0.636

0.268

0.429

0.421

1.537

Finland1980-2009

1.347

1.136

0.686

0.509

0.604

1.351

France1980-2009

0.174

1.480

0.155

0.891

0.105

0.927

Germany 1991-2009

0.094

0.953

0.175

1.862

0.184

0.872

Italy

1980-2009

0.500

1.735

0.521

1.042

0.300

0.680

Japan

1980-2009

0.504

0.453

0.205

0.407

0.453

78.026

Norway1980-2009

0.885

0.334

0.356

0.402

1.066

0.651

Sweden1980-2009

0.908

0.446

0.395

0.435

0.886

39.153

UK

1980-2009

1.062

0.741

0.346

0.326

0.467

1.538

USA

1980-2009

0.436

0.262

0.262

0.601

1.000

0.886

Notes: Source: SourceOECD.

34

Government

Table 2: Panel Unit root tests for Savings by Sectors-Im, Pesaran and Shin(IPS)Country Group
Variable

Sample I
Level

Sample II

First diﬀerence

Level

First diﬀerence

Statistics p-value Statistics p-value Statistics p-value Statistics p-value
per GDP
Government

0.18230.5723 −3.6669∗∗ 0.0001-0.2125

0.4158 −4.4659∗∗ 0.0000

Household-0.79240.2141 −2.2933∗ 0.0109-1.21620.1120 −4.0426∗∗ 0.0000

Corporation−2.0744∗ 0.0190 −3.4694∗∗ 0.0003 −2.5568∗∗ 0.0053 −4.7663∗∗ 0.0000

per capita, nominal
Government

2.18810.9857 −2.7065∗∗ 0.0034

1.90570.9717 −3.5650∗∗ 0.0002

Household

0.36630.6429 −2.0470∗ 0.0203

0.66300.7463 −4.3979∗∗ 0.0000

Corporation-0.0082

0.4967 −3.2061∗∗ 0.0007

0.32290.6266 −4.8890∗∗ 0.0000

Government

1.06640.8569 −3.2625∗∗ 0.0006

0.72000.7642 −4.1138∗∗ 0.0000

Household0.56010.7123 −2.0071∗ 0.0224

0.43450.6680 −4.0178∗∗ 0.0000

Corporation-0.9779

0.1641 −3.2307∗∗ 0.0006-0.9703

0.1659 −4.6302∗∗ 0.0000

per capita, real

1. ∗, ∗∗ indicate 5% and 1% signiﬁcance, respectively.
2. A constant is included for variables in levels and in ﬁrst diﬀerences. In all these tests, the lag lengthis set to 3.

35

Table 3: Kao and Pedroni Panel Cointegration Tests for Savings by Sectors(No intercept no trend)

Sample I
Kao

SeriesADF

Sample II
Pedronip-value

Kao

Pedroni

No intercept no trend

No intercept no trend

Within dimension Between dimension

Within dimension Between dimension

ADF

p-valueADF

p-valueADF

p-valueADF

p-valueADF

p-valueper GDP(Government, Household)-0.8146 0.2077 −1.2830† 0.0997 −2.3974∗∗ 0.0083 −2.7251∗∗ 0.0032 −2.7869∗∗ 0.0027 −3.3126∗∗ 0.0005(Household, Corporation)-1.1819 0.1186 -1.0911 0.1376 -1.2174 0.1117 −2.2465∗ 0.0123 −1.4129† 0.0788 −2.1779∗ 0.0147(Government, Corporation)-1.2407 0.1074 −1.4366∗∗ 0.0754 −1.8365∗ 0.0331 −2.6722∗∗ 0.0038 −2.4672∗∗ 0.0068 −2.9926∗∗ 0.0014(Government, Household, Corporation) -0.3656 0.3573 −2.6007∗∗ 0.0047 −3.5290∗∗ 0.0002 −2.8580∗∗ 0.0021 −1.7995∗ 0.0360 −3.3797∗∗ 0.0004
per capita, nominal(Government, Household)−4.2886∗∗ 0.0000(Household, Corporation)−2.5748∗∗ 0.0050 -0.8856 0.1879 -0.0016 0.4994 −1.7233∗ 0.0424 -1.0548 0.1457 -1.1522 0.1248(Government, Corporation)−3.8001∗∗ 0.0001

2.61171.64910.9955 −1.4327† 0.0760 −4.9677∗∗ 0.0000
0.9504 −1.2908† 0.0984 −3.3537∗∗ 0.0004

2.31861.75770.9898 −2.9694∗∗ 0.0015
0.9606 −2.5158∗∗ 0.0059(Government, Household, Corporation) −4.5042∗∗ 0.0000 −2.4068∗∗ 0.0080 −2.3907∗∗ 0.0084 −4.9817∗∗ 0.0000 −2.8306∗∗ 0.0023 −2.8846∗∗ 0.0020
per capita, real
(Government, Household)−4.7113∗∗ 0.0000(Household, Corporation)−3.6084∗∗ 0.0002 -1.0035 0.1578 -0.5082 0.3057 −2.2568∗ 0.0120 -1.1950 0.1161 −1.5781† 0.0573(Government, Corporation)−3.4308∗∗ 0.0003

2.57280.7906

0.9950 −1.7831∗ 0.0373 −5.4798∗∗ 0.0000
0.7854 −1.4409† 0.0748 −3.3220∗∗ 0.0004

2.32880.79120.9901 −3.1039∗∗ 0.0010
0.7856 −2.4940∗∗ 0.0063(Government, Household, Corporation) −4.4991∗∗ 0.0000 −2.2403∗ 0.0125 −3.0670∗∗ 0.0011 −3.4836∗∗ 0.0002 −2.6046∗∗ 0.0046 −3.2360∗∗ 0.0006
Notes: †, ∗ and ∗∗ indicate 10%, 5% and 1% signiﬁcance, respectively.

36

Table 4: Kao and Pedroni Panel Cointegration Tests for Savings by Sectors(Intercept no trend)

Sample I
Kao

SeriesADF

Sample II
Pedronip-value

Kao

PedroniIntercept no trend

Intercept no trend

Within dimension Between dimension

Within dimension Between dimension

ADF

p-valueADF

p-valueADF

p-valueADF

p-valueADF

p-valueper GDP(Government, Household)-0.8146 0.2077 −1.8301∗ 0.0336 −2.4424∗∗ 0.0073 −2.7251∗∗ 0.0032 -0.8398 0.2005 −2.0823∗ 0.0187(Household, Corporation)-1.1819 0.1186 -0.1763 0.4300 -0.7051 0.2404 −2.2465∗ 0.0123 -0.6585 0.2551 −1.6417† 0.0503(Government, Corporation)-1.2407 0.1074 −1.3321† 0.0914 −2.0582∗ 0.0198 −2.6722∗∗ 0.0038 −1.8156∗ 0.0347 −2.6180∗∗ 0.0044(Government, Household, Corporation) -0.3656 0.3573 −1.7936∗ 0.0364 −1.8539∗ 0.0319 −2.8580∗∗ 0.0021 -0.6894 0.2453 −1.6660∗ 0.0479
per capita, nominal(Government, Household)−4.2886∗∗ 0.0000 -1.2571 0.1044 −1.9431∗ 0.0260 −4.9677∗∗ 0.0000 −1.4737† 0.0703 −2.5622∗∗ 0.0052(Household, Corporation)−2.5748∗∗ 0.0050 −3.3019∗∗ 0.0005 -0.3921 0.3475 −1.7233∗ 0.0424 −3.8989∗∗ 0.0000 -0.8456 0.1989(Government, Corporation)−3.8001∗∗ 0.0001 −2.0486∗ 0.0203 −2.4215∗∗ 0.0077 −3.3537∗∗ 0.0004 −2.6102∗∗ 0.0045 −3.2076∗∗ 0.0007(Government, Household, Corporation) −4.5042∗∗ 0.0000 −1.4695† 0.0709 −1.7615∗ 0.0391 −4.9817∗∗ 0.0000 −1.8135∗ 0.0349 −2.0658∗ 0.0194
per capita, real
(Government, Household)−4.7113∗∗ 0.0000 −1.5083† 0.0657 −2.0025∗ 0.0226 −5.4798∗∗ 0.0000 −1.6200† 0.0526 −2.3325∗∗ 0.0098(Household, Corporation)−3.6084∗∗ 0.0002 −5.5801∗∗ 0.0000(Government, Corporation)−3.4308∗∗ 0.0003 −1.7078∗ 0.0438 −1.9408∗ 0.0261 −3.3220∗∗ 0.0004 −2.1974∗ 0.0140 −2.8944∗∗ 0.0019

0.41020.6592 −2.2568∗ 0.0120 −6.4527∗∗ 0.0000 -0.2927 0.3849(Government, Household, Corporation) −4.4991∗∗ 0.0000 −1.4539† 0.0730 −2.5580∗∗ 0.0053 −3.4836∗∗ 0.0002 −1.7844∗ 0.0372 −2.6947∗∗ 0.0035
Notes: †, ∗ and ∗∗ indicate 10%, 5% and 1% signiﬁcance, respectively. The Kao (1999) test results are thesame as those in Figure 3

37

Table 5: Westerlund Panel Cointegration Tests for Savings by Sectors

Sample I
SeriesGτ

Sample II

Gα

Pτ

Pα

Gτ

Gα

Pτ

Pα

per GDP−2.561∗-6.972−6.337∗−6.321†−2.280∗-6.117-4.680-3.978p-value(0.011)(0.533)(0.006)(0.106)(0.039)(0.724)(0.459)(0.571)

Robust p-value(0.015)(0.168)(0.013)(0.058)(0.025)(0.258)(0.443)(0.338)-1.716-7.107-4.815-6.050-1.901−7.749†-6.037−5.986†p-value(0.572)(0.507)(0.161)(0.139)(0.331)(0.362)(0.071)(0.106)

Robust p-value(0.478)(0.180)(0.248)(0.128)(0.235)(0.085)(0.163)(0.095)-2.169-6.351−5.475†−5.710†-1.882-5.856-4.789-4.629p-value(0.125)(0.650)(0.049)(0.189)(0.357)(0.773)(0.416)(0.388)(0.168)(Government, Household)(Household, Corporation)(Government, Corporation)
Robust p-value(0.145)(0.208)(0.090)(0.085)(0.218)(0.233)(0.385)(Government, Household, Corporation)-1.759-7.709-5.117-7.055-1.756-8.224-4.582-4.962p-value(0.786)(0.725)(0.286)(0.287)(0.831)(0.675)(0.791)(0.695)

Robust p-value(0.570)(0.225)(0.265)(0.128)(0.545)(0.135)(0.603)(0.373)per capita, nominal−3.004∗∗−10.546∗-6.381−9.590†−2.400∗−8.026∗-6.332-7.432p-value(0.000)(0.049)(0.005)(0.001)(0.014)(0.304)(0.039)(0.011)

Robust p-value(0.003)(0.010)(0.203)(0.088)(0.023)(0.043)(0.348)(0.170)-1.058-2.844-5.138-6.310-1.269-3.247-6.252-6.383p-value(0.983)(0.982)(0.094)(0.108)(0.963)(0.988)(0.046)(0.063)

Robust p-value(0.910)(0.945)(0.385)(0.418)(0.880)(0.948)(0.333)(0.385)-2.574-7.617-3.357-4.804-2.381-8.110-4.097-4.996p-value(0.009)(0.409)(0.683)(0.366)(0.017)(0.287)(0.686)(0.293)(0.323)(Government, Household)(Household, Corporation)(Government, Corporation)
Robust p-value(0.013)(0.058)(0.620)(0.340)(0.023)(0.030)(0.610)(Government, Household, Corporation)-0.972-1.864-3.069-2.717-1.146-3.302-3.780-2.846p-value(0.999)(0.999)(0.922)(0.932)(0.999)(0.998)(0.944)(0.956)

Robust p-value(0.958)(0.993)(0.718)(0.780)(0.965)(0.980)(0.748)(0.815)per capita, real
−2.808∗−8.260†-6.782-8.224−2.422∗∗-6.876-7.088-7.002p-value(0.001)(0.294)(0.002)(0.009)(0.012)(0.561)(0.006)(0.024)

Robust p-value(0.010)(0.050)(0.168)(0.140)(0.018)(0.148)(0.208)(0.190)-1.507-7.497-5.477−14.768†-1.557-6.711-6.539−13.468∗p-value(0.787)(0.432)(0.049)(0.000)(0.781)(0.599)(0.024)(0.000)Robust p-value(0.662)(0.143)(0.280)(0.055)(0.598)(0.225)(0.268)(0.035)−2.387†-7.126-2.348-3.604−2.282∗−7.507∗-2.986-3.865p-value(0.036)(0.503)(0.932)(0.646)(0.038)(0.416)(0.945)(0.603)(Government, Household)(Household, Corporation)(Government, Corporation)
Robust p-value(0.053)(0.105)(0.740)(0.483)(0.020)(0.043)(0.723)(0.438)(Government, Household, Corporation)-2.052−9.159†−10.478∗−16.589†-1.926−9.048†−12.361∗−16.655†

p-value(0.481)(0.494)(0.000)(0.000)(0.646)(0.515)(0.000)(0.000)Robust p-value(0.323)(0.063)(0.028)(0.083)(0.415)(0.050)(0.018)(0.063)

Notes: Westerlund (2007) investigates panel cointegration tests for the null hypothesis that there is no
cointegration. The tests are implemented with a constant. The lag length and the Bartlett kernel window
width are set to one. All calculations are done using the STATA command ’xtwest’(see Persyn and Westerlund(2008)). The robust p-values, which are robust against cross-sectional dependence, are based on 400 bootstrap
replications. †, ∗ and ∗∗ indicate 10%, 5% and 1% signiﬁcance based on the robust p-value, respectively.

38

Table 6: Estimated Parameters of the Model
SampleParameterαSample Iµ = 0.05
0.0175∗∗0.0199∗∗µ = 0.01
0.0137∗∗0.0106∗∗

Sample IIµ = 0.001
0.0121∗∗0.0132∗∗µ = 0.05
0.0061∗∗0.0050∗∗µ = 0.01
0.0084∗∗0.0065∗∗µ = 0.001
0.0063∗∗ 0.0049∗∗(0.0001) (0.0027) (0.0004) (0.0002) (0.0002) (0.0006) (0.0001) (0.0001) (0.0000) (0.0000) (0.0011) (0.0002)
λ0.4682∗∗ 0.4991∗∗ 0.4905∗∗ 0.4547∗∗ 0.4697∗∗ 0.4674∗∗ 0.1931∗∗ 0.1697∗∗ 0.2078∗∗ 0.2203∗∗ 0.2159∗∗ 0.2202∗∗(0.0014) (0.0145) (0.0108) (0.0019) (0.0004) (0.0041) (0.0003) (0.0011) (0.0001) (0.0001) (0.0039) (0.0006)γθ0.0037∗∗0.0152∗∗0.00240.0332∗∗0.0110∗∗0.0288∗∗(0.0036)(0.0024)(0.0061)(0.0015)(0.0002)(0.0024)0.0377∗∗ 0.0186∗∗ 0.0406∗∗ 0.0106∗∗ 0.0061∗∗ 0.0419∗∗ 0.0215∗∗ 0.0104∗∗ 0.0352∗∗ 0.0183∗∗ 0.0096 0.0250∗∗(0.0052) (0.0064) (0.0107) (0.0003) (0.0010) (0.0125) (0.0001) (0.0017) (0.0013) (0.0014) (0.0083) (0.0010)

Sargan 187.5340 98.6945 196.0871 107.7829 147.8678 165.8652 229.3874† 153.5458 229.7976† 213.1332 221.3138 154.6683
p-value

0.33480.99990.19520.99990.96160.7506

0.0986

0.99530.09530.28190.17980.9943

Notes: This table reports the two-step GMM point estimates. †, ∗ and ∗∗ indicate 10%, 5% and 1%
signiﬁcance, respectively. Standard errors are in parentheses. As is well known, the asymptotic standard
errors of the two-stemp GMM estimator are underestimated in small samples. Therefore, we usually use
the corrected standard errors proposed by Windmeijer (2005). However, as stated by Pozzi and Malengier(2007), the method proposed by Windmeijer (2005) is only available for linear model. As a result, we report
the uncorrected standard errors.

39

Table 7: The Proportion of Liquidity-Constrained Households by Evans and Karras(1996,1998)
Evans and Karras (1996)

Evans and Karras (1998)

sample periodcountry

1950-1990

1970-1989

Canda

0.32

0.44

France0.27

0.40

Germany

0.35

0.39

Italy

0.46

0.43

Japan

0.49

0.23

UK

0.79

0.58

USA

0.52

0.54

Finland

0.24

0.30

Norway0.66

0.22

Sweden

-0.20

0.49

corresponding to ourmeanSample I

0.46

0.39

Sample II

0.39

0.43

Notes: This table summarizes the estimation results by Evans and Karras(1996,1998). We caluclate themean values. Sample I includes Canada, France, Germany, Italy, Japan, UK and USA. Sample II includes
those in Sample I plus Finland, Norway and Sweden.

40

Table 8: Average Government Debt(as % of GDP)country

Net

Gross

Canda

41.37

76.79

France

43.02

47.59

Germany

42.20

59.17

Italy

94.93

107.42

Japan

42.61

110.66

UK

38.15

43.59

USA

44.06

62.49

Finland-105.48

33.36

Norway-54.96

41.02

Sweden

6.50

57.34

mean
G7(Sample I)

49.48

72.53

Three Nordic countries-51.31

43.91

Source: IMF World Economic Outlook Database.
Notes: Average value was calculated over 1980-2009 for Canada, France, Japan, UK, US, Finland and Norwy,
1991-2009 for Germany, 1988-2009 for Italy and 1992-2009 for Sweden.

41

Table 9: The Robustness Check on Estimates of γ and θ

Sample I
µ

γ

0.002

-0.0091

0.004

0.0410∗∗0.006

0.00270.008

0.0137∗∗0.010

0.0152∗∗0.012

0.0126∗∗0.014

0.0278∗∗Sample IIθγ(0.0081)0.0415∗∗(0.0004)

0.0068∗∗(0.0093)0.0422∗∗(0.0001)

0.0341∗∗(0.0024)0.0106∗∗(0.0005)

0.0417∗∗(0.0066)

0.0115∗∗(0.0038)

0.0412∗∗(0.0009)

0.0517∗∗(0.0000)

0.0106∗∗(0.0035)

0.0469∗∗(0.0000)

0.0430∗∗(0.0000)

0.0550∗∗(0.0023)

0.0515∗∗(0.0005)

0.0345∗∗(0.0006)

0.0480∗∗(0.0000)(0.0002)0.0522∗∗(0.0001)(0.0070)0.0295∗∗(0.0000)

0.0061(0.0132)

0.0194∗∗(0.0024)0.0177∗∗(0.0003)

0.0110∗∗(0.0020)0.0068∗∗(0.0039)0.016

0.00260.018

0.0164∗∗0.020

0.0180∗∗0.022

0.0064†0.024

0.0062∗∗0.026

0.0149∗∗0.028

0.0067∗∗0.030

0.0121∗∗

0.032

0.0052∗∗0.034

0.0136∗∗0.036

0.0079∗∗(0.0001)

0.0399∗∗(0.0001)

0.12880.038

0.0134∗∗(0.0000)

0.0495∗∗(0.0002)0.0344∗∗0.040

0.0105∗∗(0.0021)0.0459∗∗(0.0013)0.00450.042

0.0026(0.0062)0.0416∗∗(0.0000)

0.044

0.0115∗∗(0.0007)0.0451∗∗0.046

0.0119∗∗(0.0000)

0.0451∗∗0.048

0.0145∗∗(0.0001)

0.0137∗∗(0.0036)

0.0186∗∗0.050

0.0037(0.0087)

0.0002-0.0015(0.0180)-0.0030(0.0002)0.0102†

θ(0.0000)

0.0248∗∗(0.0001)(0.0068)

0.0415∗∗(0.0156)(0.0006)

0.0144∗(0.0061)(0.0010)0.0201∗∗(0.0013)(0.0002)0.0183∗∗(0.0015)(0.0001)

0.0179∗∗(0.0001)(0.0007)0.0156∗(0.0066)(0.0019)0.0137∗∗(0.0009)(0.0026)

0.0132∗∗(0.0005)(0.0054)0.0141∗∗(0.0009)(0.0006)(0.0007)0.0094(0.0059)0.0147∗∗(0.0076)0.0182∗∗(0.0000)−0.0124∗∗(0.0000)(0.0006)

0.0162∗∗(0.0005)

0.0146(0.0128)(0.0015)0.0123∗∗(0.0002)0.0146∗∗(0.0001)(0.0088)

0.0269∗∗(0.0066)

0.0377∗(0.0151)

0.0046(0.0097)

0.0445∗(0.0176)

0.0394(0.0631)0.0659(0.0654)(0.1451)0.1475∗∗(0.0000)(0.0012)−0.0133∗∗(0.0001)(0.0095)

0.0443∗∗(0.0157)

0.0020∗∗(0.0000)

0.0112∗∗(0.0000)(0.0009)

0.0349∗∗(0.0063)

0.0530∗∗(0.0142)(0.0000)

0.0277∗∗(0.0000)

0.0483∗∗(0.0006)(0.0024)0.0321∗∗(0.0000)

0.0193∗∗(0.0002)(0.0064)0.0332∗∗(0.0015)0.0104∗∗(0.0018)

Notes: This table reports the estimates of γ and θ when the value of µ is set from 0.002 to 0.050.

42

Table 10: Estimated Parameters of the Model for Final Consumption Expenditureof Households
SampleParameterαSample Iµ = 0.05µ = 0.01

Sample IIµ = 0.001µ = 0.05µ = 0.01µ = 0.001

0.0199∗∗ 0.0217∗∗ 0.0144∗∗ 0.0114∗∗ 0.0124∗∗ 0.0117∗∗ 0.0092∗∗ 0.0062∗ 0.0160∗∗ 0.0175∗∗ 0.0173∗∗ 0.0164∗∗(0.0003) (0.0008) (0.0000) (0.0014) (0.0000) (0.0001) (0.0012) (0.0026) (0.0000) (0.0003) (0.0042) (0.0000)

λ0.4413∗∗ 0.4335∗∗ 0.4492∗∗ 0.4628∗∗ 0.4069∗∗ 0.4733∗∗ 0.1731∗∗ 0.2433∗∗ 0.2140∗∗ 0.1834∗∗ 0.2205∗∗ 0.1896∗∗(0.0014) (0.0038) (0.0022) (0.0055) (0.0001) (0.0040) (0.0055) (0.0124) (0.0000) (0.0003) (0.0042) (0.0000)
0.0091∗∗γ(0.0015)θ

0.0331∗∗0.0111∗∗0.0173∗∗0.0027(0.0103)
0.0114∗∗0.0430∗(0.0000)
0.0055∗∗0.0048∗∗0.0058∗∗0.0031(0.0184)0.0429∗∗0.0447†0.0062∗∗(0.0000)
0.0467∗∗0.0414∗∗(0.0000)
0.0430∗∗0.0525∗∗(0.0020) (0.0023) (0.0002) (0.0169) (0.0000) (0.0002) (0.0146) (0.0242) (0.0000) (0.0003) (0.0015) (0.0001)
Sargan 144.7836 147.3170 197.7251∗ 111.6396 116.6281 232.4780∗∗ 179.4825 172.0175 80.3643 263.5456† 111.6258 157.4928
p-value

0.74870.95990.01531.00000.99330.0044

0.9956

0.99861.00000.06961.00000.9999Notes: This table reports the two-step GMM point estimates. †, ∗ and ∗∗ indicate 10%, 5% and 1%
signiﬁcance, respectively. Standard errors are in parentheses. As is well known, the asymptotic standard
errors of the two-stemp GMM estimator are underestimated in small samples. Therefore, we usually use
the corrected standard errors proposed by Windmeijer (2005). However, as stated by Pozzi and Malengier(2007), the method proposed by Windmeijer (2005) is only available for linear model. As a result, we report
the uncorrected standard errors.

43

Table 11: Estimated Parameters of the Model Using Additional Instrumental Variables
SampleParameterαSample Iµ = 0.05µ = 0.01

Sample IIµ = 0.001µ = 0.05µ = 0.01µ = 0.001

0.0509∗∗ 0.0445∗∗ -0.0202 0.0974∗∗ 0.0168∗∗ 0.0630∗∗ 0.0068∗∗ 0.0142∗∗ 0.0024∗∗ 0.0030∗∗ 0.0064∗∗ 0.0018∗∗(0.0000) (0.0020) (0.0000) (0.0000) (0.0007) (0.0004) (0.0009) (0.0000) (0.0002) (0.0006) (0.0002) (0.0001)

λ0.6790∗∗ 0.7797∗∗ 0.3147∗∗ 0.3904∗∗ 0.5697∗∗ 0.5773∗∗ 0.2501∗∗ 0.2644∗∗ 0.2250∗∗ 0.2165∗∗ 0.2114∗∗ 0.1696∗∗(0.0001) (0.0115) (0.0003) (0.0000) (0.0014) (0.0055) (0.0108) (0.0001) (0.0052) (0.0025) (0.0008) (0.0006)
0.0073∗γ

0.0097∗(0.0029)θ

0.0031∗

0.0465∗0.0010∗(0.0000)
0.0227∗0.0244∗0.0053∗(0.0000)
0.0235∗0.0387∗(0.0003)
0.0453∗0.0465∗0.0522∗0.0491∗0.0769∗(0.0151)(0.0029)0.0400∗0.0204 0.0614∗(0.0000) (0.0070) (0.0005) (0.0000) (0.0046) (0.0021) (0.0172) (0.0001) (0.0037) (0.0083) (0.0129) (0.0063)
Sargan 133.3125 154.5000 26.5918 171.4293 144.1128 212.5000 203.0251 212.0081 201.3700 123.2791 153.6372 194.3924
p-value

0.99990.99151.00000.92190.99890.24350.9896

0.96480.99171.00001.00000.9967

Notes: This table reports the two-step GMM point estimates. †, ∗ and ∗∗ indicate 10%, 5% and 1%
signiﬁcance, respectively. Standard errors are in parentheses. As is well known, the asymptotic standard
errors of the two-stemp GMM estimator are underestimated in small samples. Therefore, we usually use
the corrected standard errors proposed by Windmeijer (2005). However, as stated by Pozzi and Malengier(2007), the method proposed by Windmeijer (2005) is only available for linear model. As a result, we report
the uncorrected standard errors.

44

Figure 1: Savings by Sectors(as % of GDP)
Canada(1980-2009)

Finland(1980-2009)

.15

.16

.12

.10

.08
.05
.04
.00
.00
-.05

-.04

-.10

-.08
80

82

84

86

88

90

92

94

96

98

00

02

04

06

08

80

82

France(1980-2009)

84

86

88

90

92

94

96

98

00

02

04

06

08

Germany(1991-2009)

.12

.16

.08

.12

.04

.08

.00

.04

-.04

.00

-.08

-.04
80

82

84

86

88

90

92

94

96

98

00

02

04

06

08

1992

Italy(1980-2009)

1994

1996

1998

2000

2002

2004

2006

2008

Japan(1980-2009)

.25

.20

.20

.15

.15
.10
.10
.05
.05
.00
.00
-.05

-.05
-.10

-.10
80

82

84

86

88

90

92

94

96

98

00

02

04

06

08

80

82

Norway(1980-2009)

84

86

88

90

92

94

96

98

00

02

04

06

08

04

06

08

04

06

08

Sweden(1980-2009)

.28

.20

.24
.15
.20
.10
.16
.12

.05

.08
.00
.04
-.05
.00
-.04

-.10
80

82

84

86

88

90

92

94

96

98

00

02

04

06

08

80

82

84

UK(1980-2010)

86

88

90

92

94

96

98

00

02

USA(1980-2009)

.12

45

.100
.075

.08
.050
.025

.04

.000
.00

-.025
-.050

-.04
-.075
-.08

-.100
80

82

84

86

88

90

92

94

96

98

00

02

04

06

08

80

82

Notes: −：total, ◦：corporation, •：household, ×：government

84

86

88

90

92

94

96

98

00

02

Figure 2: Household and Corporate Saving and Household distributed income(as %of GDP)
JAPAN
.10

.08

.06

.04

.02

.00
1992

1994

1996

1998

2000

2002

2004

2006

2008

2002

2004

2006

2008

2002

2004

2006

2008

UK
.10

.08

.06

.04

.02

.00

-.02
1992

1994

1996

1998

2000

USA
.06

.05

.04

.03

.02

.01
1992

1994

1996

1998

2000

Notes: ◦：corporation, ¨：household distributed income

46

Figure 3: Household and Corporate Saving and Wage(as % of GDP)
CanadaFinland

.16

.16

.12

.12

.08
.08
.04
.04
.00
.00

-.04

-.04

-.08
80

82

84

86

88

90

92

94

96

98

00

02

04

06

08

80

82

84

86

88

90

92

94

96

98

00

02

04

06

08

Germany

France
.16

.10

.12

.08

.06
.08
.04
.04
.02
.00
.00

-.04

-.02
80

82

84

86

88

90

92

94

96

98

00

02

04

06

08

1992

1994

1996

1998

2000

2002

2004

2006

2008

Japan

Italy
.14

.25

.12
.20
.10
.15
.08
.06

.10

.04
.05
.02
.00
.00
-.02

-.05
80

82

84

86

88

90

92

94

96

98

00

02

04

06

80

08

82

84

86

88

Norway

90

92

94

96

98

00

02

04

06

08

96

98

00

02

04

06

08

96

98

00

02

04

06

08

Sweden
.12

.20

.10
.16
.08
.12

.06
.04

.08

.02
.04
.00
.00

-.02
-.04

-.04
80

82

84

86

88

90

92

94

96

98

00

02

04

06

80

08

82

84

86

88

90

UK

92

94

USA

.16

.12

47

.12

.10

.08
.08
.06
.04
.04
.00

.02

-.04

.00
80

82

84

86

88

90

92

94

96

98

00

02

04

06

08

Notes: ◦：corporation, •：household, ¨：wage

80

82

84

86

88

90

92

94