On the Eﬀects of the Development ofInternational Financial Markets When theWorld Economy Is Stratiﬁed
TAIZO MOTONISHI ∗October 2000

Abstract
This paper analyzes global and national growth under imperfectinternational ﬁnancial markets, and evaluates the eﬀects of ﬁnancial
market development using a simple endogenous growth model. The
world economy is assumed to be stratiﬁed. The agents in developed
countries in the face of ﬁnancial market development may lose by
the ’hollowing-out’ eﬀect caused by the capital outﬂows. On the other
hand, for agents in developing countries, the development is beneﬁcial,though it prevents them from catching up with agents in developed
countries.

Keywords: Stratiﬁcation; Hollowing-out; Catching up; Financial market
development; Convergence
JEL Classification: D31, F43, O40, R11∗

Faculty of Economics, Nagasaki University. 4–2-1 Katafuchi, Nagasaki, Japan.
moto@net.nagasaki-u.ac.jp Tel/Fax: 81-95-820-6369. I would like to thank Kazuo Ueda,
Toshihiro Ihori, Makoto Saito, Akihisa Shibata, and seminar participants at Nippon Keizai
Gakkai, University of Tokyo, and Sophia University.

11

Introduction

This paper analyzes the growth of the stratiﬁed world economy under imperfect international ﬁnancial markets, and evaluates the eﬀects of ﬁnancial
market development.
Considering a number of empirical analyses about capital mobility, Obstfeld (1995) concludes: ”As far as industrial countries are concerned, capital
mobility appears substantial when judged by past experience ... Although
the experience of the developing countries is diverse ... it is clear that muchof the developing world still stands outside the nexus of industrial-country
ﬁnancial markets.” (p.255). Actually, the number of ﬁnancial transactions
between developed and developing countries is much smaller than the numberof transactions within the group of developed countries. The international
allocation of credit does not seem to be suﬃcient to equalize capital stocksof countries.
Lucas (1990) presents possible reasons for capital immobility and suggests that it is diﬃcult to fully explain this immobility using the simplest
neoclassical growth model with diﬀerent levels of human capital and related
externalities. Political risk, underdeveloped ﬁnancial technology, and controls on ﬁnancial transactions by policy makers all seem to generate ﬁnancial
market imperfections.
In the ﬁrst half of our paper, it is assumed that the international ﬁnancial markets between developed and developing countries are incomplete. In
addition, our analysis takes into account the fact that the world economy isstratiﬁed in the following sense. Countries are divided into two groups, developed countries and developing countries. Countries within the same groupare close and those within the diﬀerent groups are distant in both geographic
and socioeconomic sense. The productivity of a country is assumed to bestrongly aﬀected by the capital abundance of her group.
In this stratiﬁed world economy, the interaction between the capital abundance and the productivity of countries generate dynamic patterns of global
and national growth.1 The ﬁrst issue that we analyze in this paper relates
to the determinants of the growth of the stratiﬁed world economy underinternational capital immobility.
However, capital immobility is diminishing year by year due to both tech1

Stratiﬁcation is also analyzed in Benabou (1996), which takes up the problem of schoolﬁnance, and their model is closely related to ours.

2nological progress in ﬁnancial transaction and the deregulation of ﬁnancial
markets. The second issue that we analyze in this paper is the impact of thisinternational ﬁnancial market development on the stratiﬁed world economy.
How does the development aﬀect global and national growth rates? Is thedevelopment favorable for both the developed and the developing countries?
We should note here that national policies concerning international ﬁnancial markets are somewhat paradoxical at ﬁrst glance. Developed countries
usually require developing countries to open their capital markets, althoughsubsequent capital outﬂow of the developed countries sometimes leads tothe ”hollowing-out” of their home industries. On the other hand, developing countries usually control capital inﬂow despite all the beneﬁts from thisinﬂow, such as the expansion of production opportunities and positive externalities on the production technology of home industries. Do the developed
and the developing countries want international ﬁnancial markets to be more
open or not?
Our model suggests an answer to the question. As for the agents in developed countries, the development of international ﬁnancial markets aﬀects
their utilities through two channels. First, it enables them to invest theircapital more eﬃciently. Second, it reduces the productivity of their homeindustries because we assume that there is positive externality of capitalon the production of neighbor countries. We call the second eﬀect as the’hollowing-out’ eﬀect. When the hollowing-out eﬀect dominates the former
eﬀect, the development of international ﬁnancial markets reduces the utilitiesof the agents in developed countries. We show in this paper, however, that
it is diﬃcult for the policy makers of the developed countries to prevent thecapital outﬂow.
On the other hand, the lifetime utilities of the inﬁnitely-lived agents indeveloping countries are raised by the development of the international ﬁnancial markets, while the development prevents them from catching up with theagents in developed countries in terms of their period consumption levels.
Boyd and Smith (1997) also analyze the eﬀects of opening international
ﬁnancial markets under the presence of a costry state veriﬁcation problem.
We do not assume informational asymmetry, and show that the stratiﬁcation of the world economy has interesting dynamic consequences. The welfare
implications of the diﬀerent types of ﬁnancial market structures is also analyzed in Devereux and Saito (1997). They argue the eﬀects of moving fromincomplete to complete international ﬁnancial markets by introducing state3contingent claims. In contrast to their analysis our model is deterministic. 2
This paper proceeds as follows: Section 2 presents a basic model, which
is analyzed under the assumption of incomplete ﬁnancial markets. The caseof complete markets is studied in section 3, and the result is then comparedwith that of section 2. Policy implications are shown in section 4, and Section
5 concludes.

2

Stratiﬁcation and Incomplete Financial Markets

2.1

The ModelThis section studies economic growth under incomplete international ﬁnancial markets. Its actual formulation builds on Tamura (1991), which showsthat an endogenous growth model can produce income convergence.
Consider an economy consisting of two groups of countries, developed anddeveloping. ”Developed” countries are type r countries and ”developing”
countries are of type p. The important assumption in this section is thatﬁnancial markets between the two groups of countries are nonexistent. On theother hand, ﬁnancial markets within each group of countries are complete.3
There is a continuum of agents with unit mass within each group ofcountries. Each agent has some initial capital distribution which can be used
for consumption of either real goods or leisure, and for investment in either
human or physical capital. The agents have common preferences, but diﬀer
in terms of their initial capital endowment and their production technology.
The only source of heterogeneity of agents is that the agents in developed
countries have larger initial capital endowments than do agents in developing
countries. This capital distribution determines the production technologythat each agent can exclusively employ. Agents are assumed to be immobile
across borders.

2

Allen and Gale (1995) also analyze incomplete ﬁnancial markets and the eﬀects ofcompletion. Bernanke and Gertler (1989) analyze business ﬂuctuations of a country underimperfect ﬁnancial markets.
3
Actually, in our model, there are no ﬁnancial transactions within each group due tothe homogeneity of agents within a group of countries.

4Each of the agents in type i (= r, p) countries faces the following problem:
∞


max ∞
β t ln Cti ,{Cti, Ht+1i }t=0

subject tot=0 δ (τti Hti )1−δ ,Ht+1i = AHti

(1)

(0 < δ < 1)
Cti = (1 − τti )Hti ,

(2)

given
{H0r , H0p } ,(H0r > H0p ),(3)where Cti , Hti , and τti are the consumption, capital, and savings rate, reti is the
spectively, of every agent in type i country in the t-th year, and H
spillover eﬀect of capital on the production of an agent in type i countries inthe t-th year. The solution to this problem is:τti = τ = β(1 − δ), for all (t, i).

(4)(4) shows that the savings rate, τti , does not depend on time, country type,ti . This result, which is needed to elucidate the roleor the speciﬁcation of H
of international ﬁnancial markets, depends on the assumption of a logarithmic utility function. Under the savings behavior of (4), global and nationalsavings rates are also constant. Therefore, the growth rate of each country isdetermined only by the production eﬃciency in the country, and the global
growth rate is determined by worldwide production eﬃciency.
ti . We introduce the insight
Next we specify the capital spillover eﬀect, H
of Lucas (1990) regarding the assumption of the spillover eﬀect. As he put
it, ”Ordinary experience suggests that while some of the external beneﬁts
of increases in individual knowledge are local, ... others are worldwide inscope.” (p.94). In addition, our model takes geographic and socioeconomic
conditions into account. The world economy is stratiﬁed, in that most of therich countries are located in the North, and the poor countries in the South.
Two countries in the same region are closer than those in diﬀerent regions.
Then the capital spillover eﬀect is formulated as follows.
1−γ γ
 tr = Htrγ Htp, H tp = Htp
Htr1−γ ,H5(5)where γ denotes the degree of stratiﬁcation. We assume .5  γ < 1. (5)implies that an agent’s production is positively aﬀected by another agents’capital holdings according to their distance from the agent. Agents in developed countries beneﬁt greatly from the externality derived from the large
amount of capital around them. The externality beneﬁt is weak for agents indeveloping countries, because human capital is scarce around them. Whenγ is close to 1, the world is severely stratiﬁed, that is, countries of the same
type are very close, and the two groups of countries are very distant, in botha geographic and a socioeconomic sense. When γ is close to .5, the world is
not stratiﬁed at all. (5) also implies that Htr and Htp are complementary inti .
determining H
Next, we focus on the growth rates and the convergence of countries.
From (1), (4), and (5),Ht+1i = Aτ1−δ1−δ(1−γ) δ(1−γ)
HtiHtj= Aτ 1−δ



Htj
Hti

δ(1−γ)Hti .

(6)Therefore, the growth rate of a type i country is given by
Ht+1i− 1 = Aτ 1−δ
gtiI =
Hti



Htj
Hti

δ(1−γ)− 1,(7)where the superscript I denotes that international ﬁnancial markets are incomplete.
The initial diﬀerence in capital endowments reduces over time, due togrowth rate diﬀerences. The rate of convergence is obtained from (4) and
(6).
Ht+1r
=
Ht+1p



Htr
Htp

1−2δ(1−γ).

(8)

The rate of convergence depends on the degree of stratiﬁcation, γ. When
the world is highly stratiﬁed (that is, γ is large), then the diﬀerence in themarginal product of capital is small and convergence is slow. If γ = 1 (theworld is perfectly stratiﬁed), then there is no convergence. Note that theconvergence rate is equal to that of consumption, because aggregate consumption in each country is proportional to the amount of capital in thatcountry as is shown in (4). In the long run, once convergence is complete,
all agents and countries become homogeneous.
6

(3) and (8) implies Htr > Htp for all t. From this and (7),
I
I
< gtp
gtr

for all t.

(9)

I
I
(7) also implies that the diﬀerence between g tr
and gtp
is decreasing in γ andincreasing in (Htr /Htp ).
What can we say about the global growth rate? From (6),t ,
t+1 = Aτ 1−δ H
H(10)t ≡ H .5 H .5 ). The global
t denotes the geometric mean of capital (Hwhere H
tr tp
growth rate of the geometric mean of capital is constant over time. The
degree of stratiﬁcation or capital distribution is irrelevant.
However, a more appropriate measure to capture the growth rate of an
economy is the arithmetic mean rather than the geometric mean. Benabou(1996) pointed out that discriminating between these means is important.4
The arithmetic mean of two numbers is greater than or equal to their geometric mean, and the ratio of the arithmetic mean to the geometric mean
decreases as the two numbers converge. Therefore,
H t+1 < Aτ 1−δ H t

for all t,(11)where H t is the arithmetic mean of capital (H t ≡ (Htr + Htp )/2). In thelong run, once the convergence process is complete, the diﬀerence between
the left hand and the right hand side of (11) disappears. Therefore, gL , thelong run global growth rate measured in H t , coincides with that measured
t .
in H
(12)
gL = Aτ 1−δ − 1.
On the other hand, from (11) and (12), the short run global growth ratemeasured in H t is
I
=
gtW

H t+1
− 1 < gLHt

for all t.

(13)I
We can show that gtW
is increasing in γ and decreasing in (Htr /Htp )using(8) and (10). The economic implications of this result will be discussed in
the next subsection, focusing on the production ineﬃciency that is caused
by incomplete ﬁnancial markets.
4

Tamura (1989) leaves this problem untouched.

7

Finally, we show some results regarding the growth rate of each country.
From (6),I> gL for all t.
(14)gtp
Summing up (13) and (14),I
I
I> gL > gtW
> gtr
gtp

for all t.

(15)

I
I
I
, gtW
, and gtr
converge to their long run value gL by
As time goes by, gtp
capital convergence.

2.2

Sources of Production Ineﬃciency

I
We note that gtW
is aﬀected by two types of production ineﬃciency. The ﬁrst
type of ineﬃciency arises from the absence of international ﬁnancial markets,
which makes it impossible to allocate capital input eﬃciently. Let us assume
γ = .5 by way of illustration. This implies that there is no stratiﬁcation, andall agents employ the same production technology. The capital input of anagent is, however, proportional to his own capital, as we have seen in (4),and this investment behavior generates the ﬁrst type of ineﬃciency. Unequal
capital distribution between countries intensiﬁes this ineﬃciency and lowers
I. When .5 < γ < 1, the developed countries are more productive thangtW
the developing countries. This justiﬁes a portion of the larger investment of
the developed countries, but ineﬃcient capital input still remains.
However, even without the ﬁrst type of ineﬃciency, i.e., even if investment
Ichanges as time passes. This is because webehavior were eﬃcient, g tW
have assumed in (5) that Htr and Htp are complementary in determining
the spillover eﬀect of capital that aﬀects aggregate global productivity. The
global production function, when capital is invested eﬃciently, is calculated
from (1) as follows: tr + H
tp )δ S 1−δ ,Ht+1 = A(Ht(16)

where Ht is the amount of world capital in the t-th year (Ht ≡ Htr +Htp ), andSt is aggregate global capital input. There is no ﬁrst type of ineﬃciency intp ). The second type oftr + H(16) and aggregate productivity changes as (Htp ).
tr + H
ineﬃciency comes about as unequal capital distribution decreases ( H
Discriminating between these two types of ineﬃciencies is important in theevaluation of the eﬀect of ﬁnancial market development in the next section.
8

If γ = 1, the capital input of each agent under nonexistent international
ﬁnancial markets coincides with that under complete markets, and there is noineﬃciency of the ﬁrst type. In addition, H tr and Htp are perfect substitutes
in determining aggregate productivity, and there is no ineﬃciency of theI= gL for all t.
second type. In this case, gtW
The sum of the two types of ineﬃciency is decreasing in γ and increasing
I. In the nextin (Htr /Htp ) because it changes in the opposite direction to gtW
subsection, we apply this result and analyze the eﬀect of γ on the time series,
I
.
gtW

2.3

Stratiﬁcation and Global Growth Patterns under
Incomplete Financial Markets

We can make some predictions about how global stratiﬁcation aﬀects theI, by applying the results in the previous subpattern of the time series, g tWI
is relatively highsection. If the world is highly stratiﬁed (γ is large), g tWat the outset, because the ineﬃciency in production is low. The growthrate, however, does not readily go up as time passes, because the ineﬃciency
lingers due to slow convergence. On the other hand, if the global economyIis low at the outset, however thefaces low stratiﬁcation (γ is small), gtW
ineﬃciency disappears quickly due to convergence and the growth rate rises
sharply.
I
is relatively high at the outset,
In short, if the world is stratiﬁed, gtWI
is relatively low at thebut rises slowly. If the world is not stratiﬁed, gtW
outset, but rises sharply. Numerical examples of this result are shown inﬁgure 1. We set {A, β, δ, H 0r , H0p } = {1.305531, .9,.1,100,20} , γ = .5,.7, and.9.5 These parameter values are used throughout this paper. In the long run,I
converges to gL . The convergence,
when capital convergence is complete, g tWI
however, takes several decades, and gtW at the outset is lower than in theI, is aﬀected by thelong run. We can see that the generated time series, g tW
degree of stratiﬁcation in the same manner as we predicted above.

5

The value of A is adjusted so that gL becomes .08.

9

3

The Creation of International Financial Markets

3.1

The Economy

We have assumed so far that there are no international ﬁnancial markets between the two groups of countries. These markets are, however, developing
year by year due to developments in ﬁnancial technology and by deregulationin developing countries. To consider the eﬀects of this development, we assume in this section that international ﬁnancial markets are complete. Thus
there are no obstacles to ﬁnancial transactions. Comparison of the resultswith those of the previous sections clariﬁes the eﬀect of this developmenton global and national growth rates, on the utilities of agents, and on theinternational payments of countries.
Each agent in countries of type i faces the following problem under complete international ﬁnancial markets:∞
β t ln Cti ,max ∞{Cti, Ht+1i }t=0

subject to

∞

t=0

t=0

 t
Rq−1

× {Hti − Sti − Cti } = 0,

(17)

q=0

 δ S 1−δ ,Ht+1i = AH
ti ti

(18)

given
{H0r , H0p } .
where Sti is the amount of capital input in the t-th year of each agent in a
type i country, and Rt is the market discount factor from year t to t + 1. R−1
is deﬁned to be 1. Note that each agent thinks that his or her decision has
no eﬀect on any of the economy averages or on any other agents’ decisionmaking.
We assume that agents share common perfect-foresight expectation ofcountries’ future capital stocks. Therefore, the expected capital spillover
eﬀect coincides with the investment behavior of agents. Thusγ
tp = Htp
H
Htr1−γ .

1−γ
 tr = Htrγ Htp
,
H

10

(19)

In equilibrium, the following market clearing condition holds.
Ctr + Ctp = Htr + Htp − Str − Stp , for all t.

(20)

The ﬁrst order conditions are
Ct+1r =
1−δ

β
Ctr ,
Rt

tr ,
Ht+1r = {(1 − δ) Rt } δ A δ H
1

Ct+1p =

β
Ctp ,
Rt

(21)

1−δ

tp .
Ht+1p = {(1 − δ) Rt } δ A δ H
1(22)

The conditions that {Rt , Ctr , Ctp , Ht+1r , Ht+1p }∞0 satisfy in equilibrium are(17)∼(22). The convergence rate of human capital is obtained by manipulating (22).
 
2γ−1

Htr
Ht+1r
=
.
(23)
Ht+1p
Htp
Comparing (8) and (23), we can see that the creation of international
ﬁnancial markets advances capital convergence. This is because under complete ﬁnancial markets, convergence is caused not only by the diﬀerences inmarginal productivity between countries, but also by capital ﬂows from developed to developing countries. On the other hand, (21) implies that there isno convergence in consumption, in contrast to the consumption convergence
under incomplete ﬁnancial markets. This means that the creation of international capital markets does not allow agents in developing countries to catch
up with agents in developed countries in terms of annual consumption. The
result is straightforward from the assumptions of perfect ﬁnancial markets
and common utility functions, however, it should be noted that consumption
convergence depends on imperfect ﬁnancial markets.
In the following three subsections, we analyze the eﬀect of ﬁnancial market
creation, focusing more precisely on global and national growth rates, thewelfare of agents, and the international payments of countries.

3.2

Growth Rates

In this subsection we analyze global and national growth rates. From (18)and (22),11tr + H
tp )−δ Stδ .
Rt = {A(1 − δ)}−1 (H(24)

In addition (21) is merged into
Ct+1 =

β
Ct ,
Rt

(25)

where Ct is aggregate global consumption (Ct ≡ Ctr + Ctp ). From (16), (24),and (25),
st+1 = 1 + β(1 − δ) −β(1 − δ)
,
st

(26)

where st denotes the global savings rate, so St = st Ht ,Ct = (1 − st )Ht . If
st < β(1 − δ), (26) implies that capital runs out after some periods andthat ﬁrst order conditions are violated. If st > β(1 − δ), the transversality
condition is not satisﬁed. Thus, we have the following constant global savings
rate under complete ﬁnancial markets:
st = s = β(1 − δ).

(27)(4) and (27) show that the global savings rate is not aﬀected by thecreation of international ﬁnancial markets. Thus we are able to focus on theeﬀect of ﬁnancial market creation on the supply side, that is, the productivity
change.
Under complete markets, the ﬁrst type of ineﬃciency disappears due tointernational capital ﬂows. The second type of ineﬃciency, which is caused
by capital complementarity, decreases quickly because the amount of capitalin each country is quickly equalized due to international capital ﬂows, as
we have seen in (23). Therefore, the global growth rate under completeCI, is always higher than gtW, and lower
international ﬁnancial markets, gtW
than gL , due to the second type of ineﬃciency, under a given initial capital
distribution:
C
I
> gtW
for all t.
(28)
gL > gtWCI
and gtWare shown in ﬁgures
Numerical examples of the relation between g tW
2 and 3. The parameters are set at the same values as before.
Now we discuss national growth rates. Note that under complete international ﬁnancial markets, a country’s capital growth rate diﬀers from its

12

consumption growth rate. From (21), the consumption growth rates of deC
andveloped and developing countries under complete ﬁnancial markets, g tr
CC
gtp , are the same, and they are also equal to gtW .
C
C
C
= gtp
= gtW
gtr

for all t.

(29)

From (15), (28), and (29),
C
I
> gtr
,
gtr

(30)

C
I
< gtp
,
gtp

(31)

for all t under a given initial capital distribution.
The above result does not apply if growth rates under complete markets
are measured in capital. The capital growth rate of developing countries
is higher under complete ﬁnancial markets than under incomplete markets,
due to capital inﬂows from developed countries, and the capital of developed
countries may even decrease at the outset of market completion due to capitaloutﬂows.
In this section, we analyzed the eﬀects of the creation of international
ﬁnancial markets on global and national growth rates. However, a higher
growth rate does not necessarily lead to the higher utility of agents. We
focus on the utilities of agents in each country in the next subsection.

3.3

Utility: hollowing-out eﬀect

Due to the creation of international ﬁnancial markets, capital input becomes
more eﬃcient through borrowing and lending, and this improves agents’ welfare. On the other hand, the spillover eﬀect of capital on the productionof an agent may be increased or decreased by the capital ﬂow. As for the
Agents in developed countries, they beneﬁt from expanded investment opportunities, and at the same time, they face lower capital spillover eﬀects, due
to capital outﬂows following the creation of international ﬁnancial markets.
This second eﬀect is the so-called ’hollowing-out’ eﬀect; developed countries
are damaged by the re-location of home industries to other countries. The
utilities of the agents in developed countries are aﬀected by those two eﬀects,
and parameter values determine the magnitude of them.
For example, if γ = .5, capital location has no impact on the capital
spillover eﬀect. On the other hand, if γ = 1, capital does not move, even13

under complete international ﬁnancial markets. In both cases the creation ofinternational ﬁnancial markets does not bring about the hollowing-out eﬀect.
Therefore, it is in the intermediate case that agents in developed countries
face a loss in utility due to the creation of international capital markets.
On the other hand, agents in developing countries beneﬁt from fully exploiting their production opportunities as a result of the capital inﬂows fromdeveloped countries induced by the creation of international ﬁnancial markets. Moreover, they enjoy increased productivity as a result of this introduced capital. We can prove that the lifetime utility of agents in thedeveloping countries is higher under complete ﬁnancial markets than underincomplete markets.
(32)
UpC > UpI ,where UiC and UiI are the maximized lifetime utility of the representative
agent in type i country under complete and incomplete ﬁnancial markets.
See the appendix for the proof.
We present numerical examples, which show the eﬀects of the openingof international ﬁnancial markets on agents’ lifetime utilities. Table 1 shows
the agents’ utilities under complete and nonexistent international ﬁnancial
markets. We tried two cases: γ = .7 and γ = .9. When γ = .9, thecreation of international ﬁnancial markets reduces the utilities of the agentsin developed countries, since the hollowing-out eﬀect dominates the gains
from eﬃcient investment. On the contrary when γ = .7, U rC > UrI . As fordeveloping countries, the utilities of the agents are higher under complete
international ﬁnancial markets as shown in (32).

3.4International Payments

Under the nonexistence of international ﬁnancial markets, current accounts,
ﬁnancial accounts, trade balances, and income balances are all zero. Afterthe markets have been opened, capital ﬂows from developed to developing
countries, because the developed countries have excess capital compared tothe developing countries. This excess exists even if we take into accountthe higher productivity of developed countries. Thus, the developed countries arrive at current account surpluses and ﬁnancial account deﬁcits, anddeveloping countries accrue current account deﬁcits and ﬁnancial accountsurpluses.
As time passes, productivity diﬀerences between countries decrease. This14

induces new capital ﬂows, and the above deﬁcits and surpluses persist. In
the long run, there is a complete convergence in capital and productivity,and current and ﬁnancial accounts of all countries converge to zero.
We next focus on the composition of the current account to assess longrun eﬀects. Even after all countries attain capital convergence, some of thecapital in the developing countries is owned by agents in developed countries. The interest payment to the agents in developed countries from thiscapital enables them to consume more than they produce at home. On theother hand, agents in developing countries consume less than they produce
at home. This produces trade deﬁcits and income surpluses for developed
countries, and trade surpluses and income deﬁcits for developing countries.
These imbalances persist even in the long run.
Tables 2 and 3 show the results of numerical examples of international
payments of countries. The tables correspond to the cases where γ = .7 andγ = .9 respectively. When γ = .7, the current account surplus (ﬁnancial
account deﬁcit) of a developed country is 24.85% of its Ht immediately after
the creation of international ﬁnancial markets. The current account moves
into a deﬁcit position in 4 years. The country’s long run trade deﬁcit (income
surplus) is 6.58% of its Ht . When γ = .9, the current account surplus(ﬁnancial account deﬁcit) of a developed country is 7.22% of its Ht at theoutset. The current account moves into a deﬁcit position in 7 years. The
country’s long run trade deﬁcit (income surplus) is 7.97% of its Ht .

4

Policy Implications

In this section we endogenize the creation of international ﬁnancial markets
by placing this decision into policy makers’ hands. The policy maker of
each country decides whether to open international ﬁnancial markets in theircountry.
Before analyzing the model, we note here that the actual policy makingof countries regarding international ﬁnancial markets seems somewhat paradoxical at ﬁrst glance. It is common that a developed country’s policy makerrequire a developing country to open her capital market, but the policy makers of the developing country deny the requirement. On the other hand, it
is often pointed out that developed countries in the face of developing international ﬁnancial markets suﬀer from the ”hollowing-out” of manufacturingindustries, while developing countries enjoy expanded production opportuni15

ties, and beneﬁt from externalities generated by the imported capital. Ourmodel can explain these seemingly inconsistent phenomena.
The utilities of agents in developed countries may increase or decrease by
the creation of international ﬁnancial markets. Even if their utilities decrease,that is, the hollowing-out eﬀect dominates, closing the market is diﬃcult for
the reasons presented below.
For an agent in the developed countries, it is always beneﬁcial to violate
international capital transaction controls, because a small agent’s behavior
does not impact on the capital spillover eﬀect. Similarly, the policy makers
of a small developed country, who also cannot aﬀect the economy average,
can beneﬁt agents in their country by allowing them to invest in developing
countries.
Contrary to this, the policy maker of a suﬃciently large developed country
may be able to beneﬁt agents in his country by prohibiting capital outﬂows todeveloping countries because this policy prevents the abatement of the capital spillover eﬀect. In practice, however, the policy maker’s capital controls
are diﬃcult to implement when there exist another suﬃciently small developed country with which the agents in the policy maker’s country can makeﬁnancial transactions. Even if the policy maker prohibited capital outﬂows
to developing countries, the capital of the large country still ﬂows into developing countries via the small developed country, because the policy makers
of small developed countries have no incentive to control capital outﬂows, asargued above.
On the other hand, (32) shows that for developing countries, the creationof international ﬁnancial markets is favorable, although in reality the policy
makers of developing countries often control capital inﬂows. To resolve thiscontraediction, it is helpful to take into account the eﬀect of the creation on
consumption convergence. Under the nonexistence of international ﬁnancial
markets, the consumption of all countries converges in the long run, contrary
to the non-convergence under complete ﬁnancial markets. In other words,
developing countries cannot catch up with developed countries in yearly consumption under complete international ﬁnancial markets. This suggests why
policy makers of developing countries do not open their capital markets.
In summary, a large developed country may suﬀer from hollowing-out
under open international ﬁnancial markets. However, even when the policy
maker of the country tries to control capital outﬂows, there is likely to be aloophole in the regulation. On the other hand, the policy maker of a developing country may prohibit capital introduction in order to catch up with16

developed countries in yearly consumption, although this policy decreases
the lifetime utility of agents in the developing country.

5

Conclusion

We considered a macroeconomic implication of international ﬁnancial market
development using a very simple endogenous growth model. Global andnational growth are aﬀected by the degree of stratiﬁcation and by capital
distribution. We explained the intertemporal and inter-country variability ofgrowth rates by the eﬃciency in capital use.
Next, we analyzed the eﬀect of opening international ﬁnancial markets
between developed and developing countries. The impact on global andnational growth and the international payments of countries are discussed.
The lifetime utilities of the agents in developed countries may be decreased by the creation of international ﬁnancial markets, for they are adversely aﬀected by the hollowing-out of home industries. Prevention of thecapital outﬂow is diﬃcult, however, because investing capital in developing
countries is beneﬁcial for each agent in developed countries and for the policy
makers of small developed countries.
While the lifetime utilities of agents in developing countries are increasedby the creation of international ﬁnancial markets, it also means that the developing countries are unable to catch up with developed countries in yearly
consumption, contrary to the convergence that occurs under the nonexistenceof these markets. Catching up matters, especially for the global economy,
because there is no worldwide legal institution that rules conﬂicts between
countries, and economic power is sometimes important for diplomatic negotiations.
Needless to say, the model used here is very simple and in some respects
does not conform to reality. It should be noted that we assumed the sudden
creation of international ﬁnancial markets. The actual change would be more
moderate than we calculated, but the qualitative results can be applied tounderstand actual ﬁnancial market development.

17

Appendix
This appendix proves (32). We compare the case of complete and nonexistentinternational ﬁnancial markets, with other conditions being equal. Let us denote the value under complete international ﬁnancial markets by superscript
C, and the value under no international ﬁnancial markets by superscript I.
At the outset (t = 0), under a given initial capital distribution {H 0r , H0p }(H0r > H0p ), the amount of capital invested in production in both cases areβ(1 − δ)H0 because the global savings rate is always β(1 − δ) as can be seenin (4) and (27). Then H1C > H1I , because the production technology in eachcase is the same and production becomes more eﬃcient through borrowing
and lending under complete markets.
Next we analyze production in the u-th year under the assumption HuC >HuI , starting from the same initial capital distribution. The aggregate global
up as weur + Hproduction technology in the u-th year is determined by H
ur + Hup is increasing in Hu and decreasing inhave seen in (16), where H(Hur /Hup ). Since(Htr /Htp )C < (Htr /Htp )I

for all t,(A1)

by the diﬀerence in convergence rates, we haveup
ur + HHC

ur + H
up
> H

I

.

(A2)

In addition, the amount of capital input is larger under complete markets
than under the nonexistence of ﬁnancial markets, because β(1−δ)H uC >β(1−δ)HuI . In sum, the agents under complete markets invest large amounts ofcapital, allocating it eﬃciently by borrowing and lending, and employing
C
I
>Hu+1
.
superior technology. Therefore, Hu+1
Thus,
(A3)
HtC > HtI for all t.
by induction.
 I for all t, i.e., the production technology
C > H
From (A1) and (A3), H
tp
tp
employed in developing countries in each period under complete international
ﬁnancial markets is always superior to the production technology employed
under the nonexistence of ﬁnancial markets.
∞C
can realize higher utility than
Therefore, an agent faced with Htp
t=0
∞
I
, under no ﬁnancial transactions and theanother agent faced with H
tp
t=0

18

same initial capital endowment. The utility of the former agent can be raisedeven more by borrowing from developed countries. Thus UpC > UpI . Q.E.D.

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