Discussion Paper No. 649

CAPITAL INCOME TAXATION AND
SPECIALIZATION PATTERNS:INVESTMENT TAX VS. SAVING TAX

Yoshiyasu Ono
andAkihisa Shibata

March 2006

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Capital Income Taxation and Specialization
Patterns: Investment Tax vs. Saving Tax∗
Yoshiyasu Ono† and Akihisa Shibata‡
March 2006

Abstract
Unless free international lending/borrowing is allowed, domestic saving equals domestic investment and hence saving and investment taxes
have the identical eﬀect, as is the case in a closed-economy context.
However, if it is allowed, households can accumulate foreign assets besides domestic capital and hence saving and investment are separated,causing the two taxes to have diﬀerent eﬀects. Using a two-sector
growth model, we show that the two taxes generate completely diﬀerent eﬀects on industrial structure. The investment tax always shrinks
the capital-intensive sector whereas the saving tax may well expandit.
Keywords: saving tax, investment tax, two-sector growth model,
industrial structure, financial asset trade
JEL Classification Numbers: F41, E62∗

The authors would like to thank Makoto Mori, Yoshihiko Seoka and seminar participants at Osaka University of Economics for their helpful comments and suggestions.
This research is financially supported by the 21st Century COE programs, Ministry of
Education, Culture, Sports, Science and Technology.
†
Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki,
Osaka 567-0047, Japan. E-mail: ono@iser.osaka-u.ac.jp. Tel: +81-6-6879-8578.
‡
Institute of Economic Research, Kyoto University, Yoshida, Sakyo-ku, Kyoto 606-8501,
Japan. E-mail: shibata@kier.kyoto-u.ac.jp. Tel: +81-75-753-7126.

1

Introduction

In a closed-economy context domestic real capital is the only available asset
when people accumulate wealth. Therefore, wealth accumulation (saving)always equals real capital accumulation (investment) although they are independently determined by diﬀerent agents —i.e., the former is decided byhouseholds whereas the latter is by firms. It implies that saving taxation has
the same policy implications as investment taxation.
The same property is valid even in an open economy context unless international asset trade is allowed. In this case a country’s current account has tobe always balanced, and hence saving equals investment in the country. Thisis actually the case in most open-economy two-sector growth models suchas Oniki and Uzawa (1965), Stiglitz (1970), Manning (1981), Chen (1992),
Manning, Markusen and Melvin (1992), Mountford (1999) and Brecher, Chen
and Choudhri (2002).1
If free international asset trade is allowed, however, saving is separated
from investment since people can accumulate foreign asset along with domestic real capital. The gap between saving and investment equals the current
account.2 Therefore, the eﬀect of a saving tax may significantly diﬀer fromthat of an investment tax. In fact, we shall show that their eﬀects on industrial structure can be just opposite to each other. Judging from therecent expanding trend of international asset trade, it should be importantto analyze the diﬀerence in the eﬀects of the two taxes in the presence ofinternational asset trade.3
In the literature on international taxation two taxation principles are con1

Exceptions are Fischer and Frenkel (1972), Matsuyama (1988), Ono and Shibata (2005,
2006) and Futagami et al. (2006). They develop open-economy two-sector growth models
with international trade of financial assets.
2
Even in this case world saving must equal world investment. This is because a country’s current account equals the minus of the other country’s current account in a twocountry setting.
3
Since the influential work by Feldstein and Horioka (1980) a large body of researchers
have investigated the degree of international capital mobility. Obstfeld and Taylor (2004),
among them, persuasively showed that the degree of capital mobility was high before
World War I, rapidly declined in the Great Depression period, then turned to increase
after World War II and sharply accelerated in the final decades of the 20th century.

1

sidered; one is the residence principle and the other is the source principle.4
Under the former principle the home country’s government applies a uniformtax rate to residents’ income from capital regardless of where the capital islocated. It however imposes no tax on nonresidents’ income from capitaleven if it is located in the home country. Under the latter principle a uniform tax rate is applied to income from capital installed in the home country
regardless of the residency of the income recipients. These two tax principles
can be regarded as saving and investment taxation respectively, as shown by
Summers (1988) and Giovannini (1990).5
Comparing these two principles in overlapping generations models of asmall open economy, Iwamoto and Shibata (1991) and Bovenberg (1992)
show that a rise in the residence-based tax rate leads the country to a current
account deficit while an increase in the source-based tax rate makes thecountry run a current account surplus. Sorensen (1990) and Ihori (1991)
use two-country models with capital mobility and show that a rise in theresidence tax of the home country reduces capital stock in both countries
while a rise in the source tax decreases capital stock in the home country but
increases it in the foreign country. Thus, it is well recognized that the eﬀect
of an investment tax significantly diﬀers from that of a saving tax in various
respects.6
However, these models cannot be used for analyzing industrial structuresince they either employ a one-commodity model or assume that each country produces only one commodity. Most of the open-economy two-sector
growth models can neither be used for the present analysis since they ignore
international trade in financial assets, causing a saving tax to be equivalent
to an investment tax.
4

See Chapter 2 of Frenkel, Razin and Sadka (1991) and Chapter 6 of Turnovsky (1997)
for more detailed explanations on the economic implications of the residence and source
principles. See also Iwamoto and Shibata (1999) for the deviations of the actual tax
systems from the two principles.
5
Strictly speaking, the source tax would aﬀect not only investment but also saving
through changes in the wage rate.
6
See also Bianconi (1995) and Lejour and Verbon (1998), who analyze the international
spillover eﬀects of both source-based and residence-based taxation in one-commodity Ramsey type models.

2

To fill this void, we develop a dynamic two-sector model with free international asset trade and compare the eﬀects of saving and investment
taxes on industrial structure. It is found that an increase in an investment
tax of a country moves labor from the capital-intensive sector to the laborintensive sector in both countries. Particularly the country that imposes
the tax eventually specializes in the labor-intensive sector while the othercountry produces both commodities. In contrast, a saving tax of the morepatient country may move labor from the labor-intensive sector to the capitalintensive sector in both countries. It is indeed the case when the subsistence
demand for the capital-intensive commodity is significantly larger than thatfor the other commodity. Moreover, a saving tax of the less patient country is found to have no eﬀect on specialization patterns. Thus, the eﬀect
on specialization patterns of a saving tax is quite diﬀerent from that of aninvestment tax.

2

The Model

We introduce endogenous capital accumulation into the standard HeckscherOhlin (HO) model. In each of the two countries, h and f , there are two
production sectors 1 and 2. Sector j (j = 1, 2) hires labor and rents capital toproduce commodity j unless it incurs negative profits. The two commodities
are both tradeable whereas the two factors are immobile across countries but
mobile within each country. There is another sector, called sector 3, whichuses commodity 1 to accumulate capital and rents it to the two production
sectors.7 Thus, each country’s capital varies over time.
The population of country i is Li (i = h, f ) and each household’s laborendowment is unity. Households consume both commodities and accumulate
wealth so as to maximize their lifetime utility. The government of country
h imposes investment tax sI (> 0), saving tax (or equivalently asset-holdingtax) sA (> 0) and commodity tax τ on commodity 2 whereas that of country
7

Even if we assume that sectors 1 and 2 themselves accumulate capital, we can obtainessentially the same results as derived below.

3f imposes no tax, for simplicity.

2.1

Firms

The two countries have the same production functions that satisfy constantreturns to scale:f1 (k1i )Li1 and f2 (k2i )Li2 ,i = h, f,where kji is the capital-labor ratio and Lij the labor input of sector j in country
i.8 Given capital rent ri , wage wi and relative price p, where commodity 1 istaken as the numeraire, each firm in country i maximizes profits and hence,
if country i produces both commodities, k1i and k2i satisfy
ri = f10 (k1i ) = pf20 (k2i ),

(1)

£
¤
wi = f1 (k1i ) − f10 (k1i )k1i = p f2 (k2i ) − f20 (k2i )k2i .

(2)From these two equations, if both countries are imperfectly specialized, we
have

(k2 )
,
k1h = k1f = k1 (p), k10 (p) = f 00 (kf2)(k−k )1

k2h = k2f = k2 (p),
h
f
r =r

1

2

1

f1 (k1 )k20 (p) = p2 f 00 (k,2 )(k2 −k1 )2
f20= r(p), r (p) = k2 −k1 ,
h
f

(3)

w = w = w(p).

Since commodity 1 is used for investment as well as consumption, we naturally assume sector 1 to be more capital-intensive than sector 2:
k1 (·) > k2 (·).

(4)

The optimal behavior of sector 3 is formalized to maximize
Z ∞
Z t
¡ i¢
K̇ i
i
i
i
i
i
[r − (1 + sI )h ]K exp(−Rds)dt s.t.
=
g
h ,
V =
Ki
0
0

(5)

where R is the equity rate of interest, hi is the investment ratio that equals
I i /K i , siI is the investment tax, and g(·) is the inverse of the adjustment cost
8

The case of asymmetric technologies is examined by Ono and Shibata (2006).

4

function of investment that satisfies9
g0 > 0, g 00 < 0, g 0 (0) = 1, g(0) = 0.

(6)Note that investment tax siI can be regarded as a source-based tax, as provenin Appendix 1. Country f does not impose the investment tax and henceshI = sI > 0,

sfI = 0.

(7)Equity rate of interest R is internationally the same under free trade ofinternational financial assets whereas capital rent ri is not always the sameacross countries since real capital is internationally immobile and its rent isdetermined in each domestic market.10
As the result of sector 3’s optimal behavior represented by (5), the dynamic path of real capital accumulation in country i is determined so that
1 + siI = λi g0 (hi ),(8)λ̇ = [R − {g(hi ) − g 0 (hi )hi }]λi − ri ,

(9)

i

i
i
∞
for given {R(t)}∞0 and {r (t)}0 , where λ represents the co-state variable of

K i.

2.2

Households

The government of country h imposes tax sA (> 0) on the household sector’s
asset holding and tax τ on its purchase of commodity 2, and gives lump-sumtransfer z to it while that of country f neither imposes any tax nor gives any
transfer. Under the balanced budget of the government of country hz = sA ah + pτ C2h + sI hh K h ,9(10)Without adjustment costs of investment the dynamic paths of K h and K f are notdetermined since the indeterminacy problem pointed out by Mundell (1957) arises.
10
When one of the two countries specializes in a sector, capital rents rh and rf generally
diﬀer from each other in transitional states, although they eventually converge to thesame level. When both countries are imperfectly specialized, rh and rf take the samevalue because of the factor price equalization mechanism, as (3) shows. See also Niehans(1984, pp.130) for the diﬀerence in implication between real capital mobility and financial
asset mobility.

5where Cji is country i’s consumption of commodity j (j = 1, 2) and ai is
its non-human wealth (= foreign assets + equities) whose interest rate is R.
The flow budget equation of each household is thenȧh = (R − sA )ah + wh − C1h − p(1 + τ )C2h + z,ȧf = Raf + wf − C1f − pC2f .

(11)
(12)

Note that saving tax sA can be regarded as a residence-based tax, as shownin Appendix 1.
Without loss of generality, households of country i are assumed to havethe following log-linear instantaneous utility:11iiαln(C1i − C 1 ) + (1 − α)ln(C2i − C 2 ),iwhere C j is the minimum level of commodity j required by each householdof country i to survive.12 This formulation follows recent empirical evidence
that supports the existence of the minimum requirement of consumption.13
Subject to flow budget equation (11) or (12) the representative household ofcountry i (i = h, f ) maximizes
Z ∞
i
i
i
i
[αln(C1i − C 1 ) + (1 − α)ln(C2i − C 2 )]e−ρ t dt,
U =

(13)

0

where ρi is country i’s subjective discount rate.
The first-order conditions for optimality areĊ1h= R − sA − ρh ,hC1h − C 1
11

Ċ1f
f
C1f − C 1

= R − ρf ,(14)

As shown later in Proposition 1, the steady-state relative price takes a unique common
value under all possible specialization patterns. This proposition is derived only from theproperties of subjective discount rates and production functions.
12
In order to assure the existence of the equilibrium path, we assume that the initiallevels of capital in the two countries are so large and the subsistence levels are so small thatthe worldwide production of each commodity always exceeds the worldwide subsistencelevel of it.
13
See, for example, Rosenzweig and Wolpin (1993), Atkeson and Ogaki (1996), Ogaki
and Atkeson (1997), Ogaki and Zhang (2001) and Zhang and Ogaki (2004). Moreover, themacroeconomic implications of subsistent consumption are widely examined in the literature. Using growth models with heterogenous agents, Chatterjee (1994), Chatterjee andRavikumar (1999) and Obiols-Homs and Urrutia (2003) study the transitional dynamics
and wealth distribution in the presence of subsistence consumption. Easterly (1994) andSteger (2000) introduce subsistence consumption into an endogenous growth model.

6hC1h − C 1h
C2h − C 2f

= (1 + τ )γp,

C1f − C 1f
C2f − C 2

= γp,where γ =

α
,
1−α

(15)

and the transversality condition is

lim q i (t)ai (t) exp(−ρi t) = 0,

t→∞

(16)

where q i is the co-state variable of ai . Equations (11) - (16) give the dynamic
paths of consumption and financial asset accumulation for given {R(t)}∞0 ,∞i{wi (t)}∞0 and {p(t)}0 . Note that the path of financial asset a is determinedas the result of households’ optimal saving behavior while the path of realcapital K i is determined as the result of sector 3’s optimal investment be-havior represented by (8) and (9). The two paths generally diﬀer from eachother since households can hold foreign assets as well as domestic equities.
From (14) we obtainĊ1hh
C1h − C 1

TĊ1f⇐⇒ sA + ρh S ρf .

f
C1f − C 1

(17)This implies that sA works as if the subjective discount rate rose by sA
and that the country of which the sum of the subjective discount rate andthe asset-holding tax rate is higher than the other’s gradually decreases its
expenditure share in the world market and eventually consumes only its
subsistence levels of the two commodities while the other country consumes
all the rest.

2.3

Market Equilibrium Conditions

In the factor markets of country i
K i = k1i Li1 + k2i Li2 ,(18)

Li1 + Li2 = Li for i = h, f.

(19)

Since K i accumulates following (8) and (9), Lij ’s change over time and eventually perfect specialization may arise. It is in sharp contrast to the standard Heckscher-Ohlin (HO) model since in the HO model neither K i nor
7Lij ’s change over time and hence the two countries stay to be imperfectly
specialized.
Since total demand for commodity 1 equals the sum of world consumption
C1h Lh + C1f Lf

and world investment hh K h + hf K f , its market equilibrium

condition is
C1h Lh + C1f Lf + hh K h + hf K f = f1 (k1h )Lh1 + f1 (k1f )Lf1 .

(20)

The market equilibrium condition of commodity 2, which is used solely for
consumption, is
C2 (≡ C2h Lh + C2f Lf ) = f2 (k2h )Lh2 + f2 (k2f )Lf2 .

3

(21)

Specialization Patterns

Since there is no investment in the steady state of the present dynamics,
hi = 0,(22)

C1 (≡ C1h Lh + C1f Lf ) = f1 (k1h )Lh1 + f1 (k1f )Lf1 .

(23)

and then (20) reduces to

From (6), (8), (9) and (22),λh = 1 + sI ,(24)

R = rh /(1 + sI ) = rf .
As long as sI 6= 0, the second equation of (24) is inconsistent with thecondition of factor price equalization given by (3). Therefore we obtain14

Proposition 1. As long as a non-zero investment tax-cum-subsidy is imposed, at least one country eventually leads to perfect specialization.
14

In the presence of an international diﬀerence in the relative productivity between
the two sectors, no matter how small the diﬀerence is, imperfect specialization of bothcountries never obtains. See Baxter (1992) and Ono and Shibata (2006) for details.

8Proposition 1 implies that the case of both countries’ imperfect specialization, viz. the standard HO world, never arises. Furthermore, in the steadystate real capital stays constant and hence production of each commodity
stays at each steady-state level. Thus, from (14) and (24) we obtain15
R = rh /(1 + sI ) = rf = ρmin ≡ min(sA + ρh , ρf ).

(25)

Since we consider the case where investment tax sI is positive, from (25) rh >rf , which causes capital accumulation in country h to be less advantageousthan in country f . Therefore, country h (or f ) never specializes in sector
1 (or 2). Only the following three cases are possible, viz. (i) Country h’s
specialization in sector 2 and country f ’s imperfect specialization, (ii) country
h’s specialization in sector 2 and country f ’s specialization in sector 1, and(iii) country h’s imperfect specialization and country f ’s specialization in
sector 1.16
In the arguments below, for simplicity, we ignore commodity tax τ
(26)

τ =0

until we examine its eﬀect in section 5. Thus, from (15) and (26), world
demand for each commodity, C1 and C2 , has to satisfy
C1 − C 1= γp,
C2 − C 2h(27)fwhere C j ≡ C j Lh + C j Lf .
Using these properties we obtain steady-state conditions for each of the threecases.
Case (i): Country h’s imperfect specialization and country f ’s perfect specialization in sector 1
15

The equality between the steady-state interest rate and the subjective discount rate of
the most patient country is shown by Becker (1980), Blanchard and Fischer (1989, pp.6970) and Ikeda and Ono (1992) in a multi-country context. The present result is a simple
extention of it to the case with saving and investment taxes and subsistence consumption.
16
If sI < 0, there are the following three cases: (i) country h’s perfect specialization in
sector 1 and country f ’s imperfect specialization, (ii) country h’s perfect specialization in
sector 1 and country f ’s perfect specialization in sector 2, and (iii) country h’s imperfectspecialization and country f ’s perfect specialization in sector 2.

9In country h (1) and (2) are valid and hence from (25) p equals ph thatsatisfies(1 + sI )ρmin = f10 (k1h ) = ph f20 (k2h ),£¤f1 (k1h ) − f10 (k1h )k1h = ph f2 (k2h ) − f20 (k2h )k2h .

(28)

Since country f specializes in sector 1 and rf = ρmin from (25),
Lf1 = Lf , Lf2 = 0,ρmin = f10 (k1f ).

(29)

Therefore, from (18), (19), (21), (23) and (27),
Lh1 = Lh1-(i) =Lh2Khγph [f2 (k2h )Lh − C 2 ] − [f1 (k1f )Lf − C 1 ],f1 (k1h ) + γph f2 (k2h )f1 (k1h )Lh + f1 (k1f )Lf − C 1 + γph C 2=,
f1 (k1h ) + γph f2 (k2h )= k1h Lh1 + k2h Lh2 ,K f = k1f Lf .

(30)

Case (ii): Country h’s perfect specialization in sector 2 and country
f ’s perfect specialization in sector 1
In this case
Lh1 = 0, Lh2 = Lh ,Lf1 = Lf , Lf2 = 0.

(31)

In country h capital rent rh equals the marginal productivity of capital insector 2 while in country f capital rent rf equals the marginal productivityof capital in sector 1. Therefore, from (25) we obtain(1 + sI )ρmin = ps f20 (k2h ),ρmin = f10 (k1f ),

10

(32)

where ps is determined so that the production of commodity 1 (which equals
C1 ) and that of commodity 2 (which equals C2 ) satisfy (27):f1 (k1f )Lf − C 1 = γps [f2 (k2h )Lh − C 2 ].

(33)

From (18) and (31),K f = k1f Lf .

K h = k2h Lh ,(34)

Case (iii): Country h’s perfect specialization in sector 2 and country f ’s imperfect specialization
Country f is imperfectly specialized and hence (1) and (2) are valid.
Therefore, from (25) p equals pf that satisfies
ρmin = f10 (k1f ) = pf f20 (k2f ),hi
f1 (k1f ) − f10 (k1f )k1f = pf f2 (k2f ) − f20 (k2f )k2f .

(35)

In country h only sector 2 operates and thus

Lh1 = 0, Lh2 = Lh ,(1 + sI )ρmin = pf f20 (k2h ),(36)

where pf is given by (35). Therefore, from (18), (19), (21), (23) and (27),
Lf1 =
Lf2

=

Kh =

γpf [f2 (k2h )Lh + f2 (k2f )Lf − C 2 ] + C 1,
f1 (k1f ) + γpf f2 (k2f )[f1 (k1f )Lf − C 1 ] − γpf [f2 (k2h )Lh − C 2 ]f,
L2-(iii) =f1 (k1f ) + γpf f2 (k2f )k2h Lh ,K f = k1f Lf1 + k2f Lf2 .

4

(37)

Investment Tax vs. Saving Tax

Using the steady-state conditions for the three cases obtained in the previous
section, we examine the eﬀect of investment tax sI and that of saving tax sA
on specialization patterns.
11

4.1

Investment Tax

By comparing Lh1-(i) in (30) with (33), we find that (33) is valid when Lh1-(i)equals zero. Also, since (32) in case (ii) is valid if (28) and (29) in case (i)are valid, we find pf = ps when Lh1-(i) equals zero. Therefore, the two cases
coincide with each other when Lh1-(i) equals zero. Analogously, when Lf2-(iii)in (37) equals zero, (33) is valid, implying ph equal to ps , and then cases (ii)and (iii) coincide with each other. Therefore, if a change in sI makes Lh1-(i)(or Lf2-(iii) ) zero, it changes specialization patterns from case (i) to (ii) (orfrom case (iii) to (ii)). We shall below show this property.
From Lh1-(i) in (30) and Lf2-(iii) in (37), case (i) arises when Lf /Lh is smallenough and case (iii) does when Lf /Lh is large enough. It implies that thecountry with a much larger population tends to be imperfectly specialized
and that the other tends to specialize in a sector. It is naturally understoodsince a supply shortage of the other commodity occurs if the country with amuch larger population specializes in a sector.17
Now suppose that Lf /Lh is so small that case (i) arises and that the
government of country h raises the investment tax. From (28) and (29), ph ,k2h and k1f are all independent of Li ’s or γ and satisfy
dph
< 0,
dsI

dk1f
= 0,
dsI

dk2h
< 0,
dsI

which implies that an increase in sI reduces the numerator of Lh1-(i) in (30).
Therefore, if Lh1 is small enough, an increase in sI makes it zero, causing
specialization patterns to move from case (i) to case (ii).
Suppose next that Lf /Lh is so large that case (iii) arises. From (35) and(36), pf , k2h and k1f are all independent of Li ’s or γ and satisfy
dpf
= 0,
dsI

dk1f
= 0,
dsI

dk2h
< 0,
dsI

which implies that a decrease in sI reduces the numerator of Lf2-(iii) given in(37). Therefore, if Lf2-(iii) is small enough, a decrease in sI makes it zero —i.e.,
an increase in sI moves specialization patterns from case (ii) to case (iii).
17

See Ono and Shibata (2006) for this point.

12In sum, an increase in sI varies specialization patterns as stated below.18

Proposition 2. An increase in an investment tax of country h leads thecase of country h’s imperfect specialization and country f ’s specialization in
the capital-intensive sector to the case of country h’s specialization in thelabor-intensive sector and country f ’s specialization in the capital-intensive
sector. A further increase in the tax leads to the case of country h’s perfectspecialization in the labor-intensive sector and country f ’s imperfect specialization.
Intuitively, in country h an increase in sI raises capital rent rh (= (1 +sI )ρmin ) and makes the capital-intensive sector less advantageous whereas
in country f capital rent rf remains equal to ρmin . Therefore, if initiallycountry h is imperfectly specialized and country f specializes in the capitalintensive sector, country h reduces, and eventually stops, production of thecapital-intensive commodity as sI rises. Then, country h specializes in thelabor-intensive sector while country f does in the capital-intensive sector. A
further increase in sI reduces country h’s capital stock more and decreases
production of the labor-intensive commodity, the only commodity that country h produces. Therefore, country f starts producing the labor-intensive
commodity as well. Figure 1 depicts a typical case of the investment-tax
eﬀect on specialization patterns.

4.2

Saving Tax

In the case where foreign-asset holding is not allowed, including the closedeconomy case, a saving tax is equivalent to an investment tax since people as18

Dependent upon the values of technological, preference and population parameters,
the changes in specialization patterns mentioned in proposition 2 may not occur evenunder a suﬃciently large change in the investment tax. For example, if Lf /Lh is verylarge, country f cannot perfectly specialize in the capital-intensive sector and hence only
case (iii) is valid. In fact, from (35), (36), and Lf2-(iii) in (37) we find Lf2-(iii) to stay within(0, Lf ) for any positive sI . However, we can definitely say that the shifts in specialization
patterns opposite to what proposition 2 states never arise.

13

a whole has no other choice than domestic real capital when saving. However,unless foreign-asset holding is restricted, saving and investment are separated
from each other. Therefore, the eﬀect of a saving tax should diﬀer from thatof an investment tax. This section examines the eﬀect of a saving tax andcompare it with that of an investment tax obtained in the previous section.
Whether the country that imposes saving tax sA is more time-patient orless results in a quite diﬀerent eﬀect on production and specialization patternsof the two countries. It is in sharp contrast to the eﬀect of investment tax sI
summarized by proposition 2, which is independent of which country is morepatient.
First, we analyze the case where the less patient country imposes sA andobtain the following proposition:
Proposition 3. An increase in the less patient country’s saving tax aﬀects
neither specialization patterns nor demand patterns in the steady state.
Proof. Suppose that country h is the less patient country, i.e., sA + ρh > ρf .
Then, an increase in sA does not aﬀect ρmin (= min(sA + ρh , ρf )). Therefore,
the steady-state conditions in the three cases presented in section 3 are allleft unaﬀected. Q.E.D.
If sA + ρh < ρf and thus country h is more patient than the other, an
increase in its saving tax raises the steady-state world interest rate ρmin (=sA + ρh ) and harms the capital-intensive sector in both countries. In thiscase we obtain the following proposition:19
Proposition 4. Suppose that country h imposes an investment tax so thatit never specializes in the capital-intensive sector. Under Cobb-Douglas production technology, if the worldwide subsistence level of the labor-intensive
19

As mentioned in footnote 18, dependent upon the values of technological, preference
and population parameters, the changes in specialization patterns mentioned in proposition 4 may not occur even under a suﬃciently large change in the investment tax. For
example, if Lf /Lh is very large, country f cannot perfectly specialize in a sector. In fact,
Lf2-(iii) in (37) stays within (0, Lf ) even if sA (and hence ρmin ) is very large. However, we
can definitely say that the shifts in specialization patterns opposite to what proposition 4states never arise.

14

commodity is suﬃciently small while that of the other commodity is not, an
increase in a saving tax of the more patient country changes the case ofcountry h’s perfect specialization in the labor-intensive sector and country
f ’s imperfect specialization to the case of country h’s specialization in thelabor-intensive sector and country f ’s specialization in the capital-intensive
sector. A further increase in the tax leads to the case of country h’s imperfectspecialization and country f ’s specialization in the capital-intensive sector.
If the subsistence level of the capital-intensive commodity is suﬃciently small
while that of the other commodity is not, an increase in a saving tax of themore patient country generates just the opposite transition in specialization
patterns. Note that the results hold true regardless of which country is morepatient.
Proof. See Appendix 2.
Propositions 2, 3 and 4 show that the eﬀect on specialization patterns ofa saving tax completely diﬀers from that of an investment tax. Particularly
if the subsistence level of the labor-intensive commodity is suﬃciently small
while that of the other commodity is not, under Cobb-Douglas production
functions the more patient country’s saving tax generates an eﬀect opposite
to what its investment tax does —i.e., the saving tax moves labor to thecapital-intensive sector and hence changes specialization patterns from case(iii) to case (ii) and from case (ii) to case (i) whereas an increase in theinvestment tax moves labor to the labor-intensive sector and hence changes
specialization patterns from case (i) to case (ii) and from case (ii) to case(iii). Figure 2 illustrates the saving-tax eﬀect on specialization patterns inthis case.
An investment tax raises the capital rent and makes the capital-intensive
sector less advantageous only in the country that imposes it. Therefore,changes in specialization patterns are generated by the labor movement fromthe capital-intensive sector to the other only in the country. In contrast,
an increase in the more patient country’s saving tax globally raises the capital rent and makes the capital-intensive sector less advantageous in both15

countries. It also reduces the steady-state level of capital stock. Therefore,
if prices were fixed, labor would move from the capital-intensive sector to
the labor-intensive sector in both countries (the Rybczynski eﬀect). As thecapital-intensive commodity is less produced, however, the price elasticity ofdemand for it decreases in the presence of the subsistence level, and thus themagnitude of the price rise increases, attracting more labor to the capitalintensive sector. Specialization patterns depend on the relative strength of
the two opposite eﬀects on labor movement.
Particularly if C 1 is much larger than C 2 , demand for the capital-intensive
commodity remains large and hence the rise in its price is so high that thelatter eﬀect dominates the former, causing labor to move from the laborintensive sector to the capital-intensive sector. Thus, in the case wherecountry h specializes in the labor-intensive sector and country f is imperfectly specialized, labor moves to the capital-intensive sector in country f
and eventually country f specializes in the capital-intensive sector. Notethat country f has comparative advantage on the capital-intensive sector
when country h imposes an investment tax and thus country f reallocateslabor to the capital-intensive sector before country h does so. Once all labor moves to the capital-intensive sector in country f , a further increase in
the saving tax reduces the country f ’s production of the capital-intensive
commodity beyond worldwide demand for it, and thus country h starts producing the capital-intensive commodity, which leads the country to imperfectspecialization.
If C 2 is much larger than C 1 , on the contrary, demand for the laborintensive commodity remains large so that the price rise of the capitalintensive commodity raises demand for the labor-intensive commodity. It
moves labor from the capital-intensive sector to the labor-intensive sector.
Thus, in this case a saving tax changes specialization patterns in the same
direction as an investment tax does.

165

Commodity Tax

In steady state the representative household of the less patient country consumes the subsistence levels of the two commodities regardless of whether acommodity tax is imposed or not in the country. Since the tax does not aﬀect
the domestic prices in the other country, there is no international spillover
eﬀect. Thus, a commodity tax imposed by the less patient country generates
no eﬀect.
We next examine the case where the more patient country imposes commodity tax τ . Naturally, it will be found that an increase in τ stimulates
production of commodity 1 and harms production of commodity 2 if bothcommodities are produced.
Without loss of generality, suppose that country h is more patient andimposes commodity tax τ on commodity 2. Then, γ in (15) is replaced byγ(1 + τ ), implying that in country hhC1h − C 1

= γ(1 + τ )p,h

C2h − C 2(38)

while in country fff

C1f = C 1 , C2f = C 2 .
Therefore, γ(1 + τ ) replaces γ in (30) and (37). All equations that represent
firms’ behavior remain unaﬀected, implying that k2h , k1f , k2f and pf given by(35) and (36) and k1h , k2h , k1f and ph given by (28) and (29) are all unchanged.
Replacing γ by γ(1+τ ) in (30) and (37), diﬀerentiating them with respectto τ and applying (21), (23), (29) and (36) to the results yield
£
¤
h
h
h
γ
(C
−
C
)f
(k
)
+
(C
−
C
)f
(k
)
p
2
2
1
1
1
2
1
2
> 0,
dLh1-(i) /dτ =¤2£
f1 (kh ) + γ h ph f2 (k2h )hipf γ (C2 − C 2 )f1 (k1f ) + (C1 − C 1 )f2 (k2f )< 0.
dLf2-(iii) /dτ = −[f1 (k1f ) + γ h pf f2 (k2f )]2
This implies the following property:

17Proposition 5. Suppose that the more patient country (which we call country h) imposes an investment tax so that it never specializes in the capitalintensive sector. An increase in its commodity tax on the labor-intensive
commodity changes the case of country h’s perfect specialization in the laborintensive sector and country f ’s imperfect specialization to the case of country
h’s perfect specialization in the labor-intensive sector and country f ’s perfectspecialization in the capital-intensive sector. A further such change eventually results in country h’s imperfect specialization and country f ’s perfectspecialization in the capital-intensive sector.

6

Conclusions

Unless international asset trade is allowed, saving always has to equal investment within a country, as in the case of a closed economy. Therefore, asaving tax has the same eﬀect on each country as an investment tax does,
although households’ saving decisions are determined independently of firms’
investment decisions. Once free international asset trade is allowed, households have a choice of asset accumulation between real capital and foreign
asset holdings —i.e., domestic saving is used for not only domestic investment
but also foreign asset holdings. Therefore, the eﬀect of a saving tax may
diﬀer from that of an investment tax. This paper shows that the eﬀect of asaving tax on specialization patterns in fact significantly diﬀers from that ofan investment tax. They can even be opposite to each other.
An investment tax raises the capital rent and reduces capital accumulation only in the country that imposes the tax. It makes the capital-intensive
sector less advantages than the labor-intensive sector. Therefore, possible
specialization patterns are only the following: (i) the country’s imperfectspecialization and the other country’s specialization in the capital-intensive
sector, (ii) the country’s specialization in the labor-intensive sector and theother’s specialization in the capital-intensive sector, and (iii) the country’s
specialization in the labor-intensive sector and the other’s imperfect specialization.
18

If the country raises the investment tax in case (i), labor moves fromthe capital-intensive sector to the other and eventually makes the country
specialize in the labor-intensive sector, which is case (ii). Since the othercountry faces a lower rent of capital, it specializes in the capital-intensive
sector. After the country that imposes the investment tax specializes in thelabor-intensive sector, a further increase in the tax reduces production in thelabor-intensive sector and generates a global shortage of its supply. It leads
the other country to start producing the labor-intensive commodity, whichis case (iii).
A saving tax has a completely diﬀerent eﬀect from that of an investment
tax. Its eﬀect is equivalent to that of an increase in the subjective discountrate of the country that imposes the tax. Since the steady-state interest
rate equals the more patient country’s subjective discount rate, a saving
tax of the less patient country has no eﬀect. However, a saving tax of themore patient country globally raises the capital rent in the two countries andaﬀects labor allocation between the two sectors. Consequently, specialization
patterns change. We find that the eﬀect on specialization patterns depends
on the subsistence levels of the two commodities and the shapes of production
functions.
For example, suppose that production functions are of the Cobb-Douglas
type and that the subsistence level of the labor-intensive commodity is suﬃciently small while that of the other commodity is not. Suppose also that themore patient country imposes an investment tax and perfectly specializes in
the labor-intensive sector while the other country is imperfectly specialized,
which is case (iii). Then, an increase in a saving tax by the more patient
country leads both countries to perfect specialization, which is case (ii), andeventually to the country’s imperfect specialization and the other’s specialization in the capital-intensive sector, which is case (i). Thus, it generates
just the opposite eﬀect on specialization patterns to what is generated byan increase in an investment tax. In contrast, if the subsistence level of thecapital-intensive commodity is suﬃciently small while that of the other isnot, it generates the same transition in specialization patterns as generated
19

by an increase in an investment tax.

20

Appendices
Appendix 1: Residence-based and Source-based Taxation
In this appendix we show that the saving and investment taxes formalized
in the text are respectively equivalent to the source-based and residence-basedtaxes in the literature on international taxation.
Let us assume that in country f no tax is imposed and the financial
interest rate is R. In country h residence-based tax θh and source-based tax
η h are imposed and the financial interest rate is Rh . From the no-arbitrage
condition in country h:
#
h
h
V̇
+
Div
,
(1 − θh )R = (1 − θh )(1 − η h )RH = (1 − θh )(1 − η h )Vh"where V h and Divh are respectively the firm value of the investment sector
and its dividends:
Div h = [rh (t) − hh (t)]K h (t),(A1)

R = (1 − η h )Rh ,(A2)

we deriveRV̇ h + Divh=.
1 − ηhVh(A3)Note that (A1) also implies the no-arbitrage condition for foreign investors
between the two countries’ financial assets.
From (A1) and (A3), the investment sector’s behavior is formalized tomaximize
h

V =

Z ∞
0

µ Z t
¶
R(s)
[r (t) − h (t)]K (t) exp −
ds dt
h
0 1−η
h

h

s.t.

h

¡ h ¢
K̇ h (t)=gh (t) ,K h (t)of which the optimal conditions are

1 = λh g0 (hh ),
21

∙

¸
© h
ª h
R
0 h h
λ̇ =
− g(h ) − g (h )hλ − rh .
1 − ηhh

In steady state they reduce to

rh =

R
.
1 − ηhWe find it to be equivalent to (24) by replacing sI by η h /(1 − η h ) in (24)—i.e., investment tax sI is equivalent to source-based tax η h .

In the presence of residence-based tax θh and commodity tax τ the flow
budget constraint of the representative household isȧh = (1 − θh )Rah + wh Lh − C1h − p(1 + τ )C2h + z,
which is equivalent to (11) where sA is replaced by θh R. Thus, saving tax sA
is found to be equivalent to residence-based tax θh .

Appendix 2: Proof of Proposition 4
We prove Proposition 4 by assuming production functions to be of thefollowing Cobb-Douglas type:f1 (k1 ) = A(k1 )θ ,f2 (k2 ) = B(k2 )ν ,(A4)

where A and B are positive constants. Factor-intensity condition (4) reducestoθ > ν.
Under production functions (A4) k1f , k2h and ph in case (i) are
k1f
ph

1 µ
¶ 1−θ
¶
ν
Aθ
1−θ
=
,
·
,
(1 + sI )ρmin
1−ν
θ
µ
¶1−ν
1−ν
ν
(Aθ) 1−θ
1−θ
=
.
(A5)
·
θ−ν
θ
Bν[(1 + sI )ρmin ] 1−θ 1 − ν

µ

Aθ
ρmin

1
¶ 1−θ

k2h =

µ

Substituting (A5) into Lh1-(i) given in (30) gives
Ã
Ã
!
!
θ
h
h
h
1−θ (1 − ν)Lf
(1
+
s
[f
(k
)L
−
C
]
)
p
2
2
I
2
γ−
Φ(ρmin ) ,Lh1-(i) =(1 − θ)Lh
f1 (k1h ) + γph f2 (k2h )22where
min

Φ(ρ

−θ
b1
(ρmin ) 1−θ − C

) =

,
−θ
ν−θ
ν
b2
(ρmin ) 1−θ − (1 + sI ) 1−θ (ρmin ) 1−θ C
C1
C2
b2 =
=
, C
.
ν
1
θ
ν
ν Lh
B(Aθ) 1−θ ( 1−ν· 1−θ
)A 1−θ θ 1−θ Lfθb1
CDiﬀerentiating Φ(ρmin ) with respect to ρmin yields
−ν

ν−θ

0

min

Φ (ρ

ν

b1 + (θ − ν)C
b1 C
b2 − (1 + sI ) 1−θ θC
b2 (ρmin ) 1−θν(ρmin ) 1−θ C
)=
h
i2 .
−ν
−θ
ν−θ
1
ν
min
min
min
b
1−θ
1−θ
1−θ
1−θ
1−θ
(ρ )
(1 + sI ) (1 − θ)(ρ )− (1 + s) (ρ ) C2

Thus, when Lh1-(i) is small enough,dLh1-(i)dρmindLh1-(i)
dρmin

( =
( =

dLh1-(i)dsA
dLh1-(i)dsA) > 0 if C 1 > 0 and C 2 = 0,
) < 0 if C 1 = 0 and C 2 > 0.

(A6)

Under (A4) k1f , k2h and pf in case (iii) are
k1f
pf

¢ 1 µ
¡
¶
Aθ/ρmin 1−θ
ν
1−θ
·
,
=
,
1
1−ν
θ
(1 + sI ) 1−ν
µ
¶1−ν
1−ν
ν
(Aθ) 1−θ
1−θ
=
.
·
θ−ν
θ
Bν(ρmin ) 1−θ 1 − ν
µ

Aθ
ρmin

1
¶ 1−θ

k2h =

(A7)

Substituting (A7) into Lf2-(iii) given in (37) gives
pf [f2 (k2h )Lh − C 2 ]Lf2-(iii) =f1 (k1f ) + γpf f2 (k2f )ÃÃν

(1 + sI ) 1−ν (1 − ν)Lf
(1 − θ)Lh!

Ω(ρmin ) − γ

!

,

−θ

min

Ω(ρ

)=

b1
(ρmin ) 1−θ − C

−θ
ν−θ
ν
b2
(ρmin ) 1−θ − (1 + sI ) 1−ν (ρmin ) 1−θ C.

Diﬀerentiating Ω(ρmin ) with respect to ρmin yields
0

min

Ω (ρ

ν−θ
−ν
ν
b1 + (θ − ν)C
b1 C
b2 − (1 + sI ) 1−ν
b2 (ρmin ) 1−θθC
ν(ρmin ) 1−θ C
)=
h
i2 .
−ν
−θ
ν−θ
1
ν
min
min
min
b
1−ν
1−θ
1−θ
1−ν
1−θ
(ρ )
(1 + sI ) (1 − θ)(ρ )− (1 + s) (ρ ) C223

Thus, when Lh1-(i) is small enough,dLf2-(iii)dρmindLf2-(iii)
dρmin

( =
( =

dLh1-(i)dsA
dLh1-(i)dsA) < 0 if C 1 > 0 and C 2 = 0,
) > 0 if C 1 = 0 and C 2 > 0.

(A8)(A6) and (A8) imply the changes in specialization patterns mentioned inproposition 4.
In the above analysis we assume that the country that imposes investment
tax sI also imposes saving tax sA . However, even if the country that does
not impose an investment tax imposes a saving tax, it raises ρmin in the same
way as long as the country is more patient. Thus, as long as the more patient
country imposes a saving tax, all of the above results hold true regardless ofwhich country is more patient.

24

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28

f: specialization in sector 1

f: specialization in sector 1

An Illustration of the effect of s I

hf: imperfect specializationh: specialization in sector 2

on specialization patternFigure 1

h: specialization in sector 2

h: imperfect specializationsIhf: specialization in sector 1

f: imperfect specialization

f: specialization in sector 1

h: imperfect specializationsA

An Illustration of the effect of s A on specialization pattern under CES technology (when C 2 is sufficiently small and C 1 is relatively large)

Figure 2

h: specialization in sector 2

h: specialization in sector 2