International Trade and Capital Movement under
Financial Imperfection ∗Taiji Furusawa†

Noriyuki Yanagawa‡

Hitotsubashi University

University of Tokyo

June 2013

Abstract
We construct a simple two-country model that enables us to examine the interactions
between trade in goods and international capital movement under ﬁnancial imperfection. We show that they are complements in the sense that trade in goods facilitates
capital outﬂow from the South, which is either ﬁnancially less-developed or endowed
less capital than the North. This complementarity disappears if ﬁnancial institution
is perfect or almost perfect; trade in goods and capital movement are substitutes as
traditional literature shows in such cases. We also show the possibility that capital
account liberalization entails capital leakage from the manufacturing industries to an
inferior investment opportunity.
JEL Classiﬁcation: F12, F21, G20, G30
Keywords: Financial imperfection, complementarity, trade, capital movement∗

We are grateful for helpful comments to Martin Davies, Motonari Kurasawa, Kiminori Matsuyama, Yasuhiro Sato, Thierry Verdier, participants of the Asia Paciﬁc Trade Seminars 2008, the 2009 Far Easternand South Asian Meeting of the Econometric Society, the European Trade Study Group meeting (2009),
Hitotsubashi COE Conference on International Trade and FDI 2009, Hitotsubashi-UNSW Conference on
International Trade and FDI 2011, the IEFS China Inaugural Conference (2009), the 2008 annual meetingof Japan Society of International Economics, Midwest International Economics Group Meeting (Fall 2009),
Second Keio/Kyoto International Conference on Market Quality Economics (2009), and seminar participantsat Copenhagen Business School, Dartmouth College, GATE, Keio University, Kobe University, Kyoto University, Kyung-Hee University, National Taiwan University, Paris School of Economics, Sogang University,
Universite de Caen Basse-Normandie, University of Tokyo, and Yokohama National University. Part of theanalysis was conducted when Furusawa was a research associate of the Program on U.S.-Japan Relations at
Harvard University. Furusawa gratefully acknowledges their hospitality and ﬁnancial support from the Abe
Fellowship.
†
Graduate School of Economics, Hitotsubashi University. Email: furusawa@econ.hit-u.ac.jp‡
Faculty of Economics, University of Tokyo. Email: yanagawa@e.u-tokyo.ac.jp

1

Introduction

Whether a country should liberalize capital account has been a long-standing, important
issue for policy makers, as well as for researchers.1 A conventional wisdom suggests thatcountries should liberalize capital account to eﬃciently utilize capital worldwide. Even developing countries, which tend to be scarce in capital, are considered to beneﬁt from being
open to the world capital market since capital would ﬂow into such capital-scarce countries,
thereby achieving economic development. In practice, however, most developing countries
are reluctant to liberalize capital account. They are afraid of exposing themselves to volatile
capital market, for example. History suggests that their concern is legitimate. Developing
countries sometimes experience sudden capital ﬂight in a large scale; Indonesia, Thailand,
and South Korea, for example, had severe economic crisis after sudden capital ﬂight in 1997
(Asian economic crisis). Indeed, capital often ﬂows from the South to the North, contrary
to the traditional prediction, which is often called the Lucas Paradox (Lucas, 1990). It is far
from clear that capital account liberalization leads to economic development for developing
countries.
Causes of the Lucas Paradox has been extensively examined, and so has been the impact
of capital account liberalization on economic growth.2 However, researchers have not fully1

Rodrik (1998) is skeptical about positive impact of capital account liberalization on economic growth,whereas Henry (2007), for example, ﬁnds evidence that ﬁnancial globalization contributes to economic
growth. Eichengreen (2001) provides insightful summary of the debate on the impact of capital accountliberalization on economic development.
2Gertler and Rogoﬀ (1990), Caballero, et al. (2008), Aoki, et al. (2010), for example, develop theories to
explain the Lucas Paradox, emphasizing the role of some sorts of ﬁnancial imperfection. Economic institutions, which include ﬁnancial and legal institution in a broad sense, have been considered as a key factor thataﬀects the eﬀect of capital account liberalization on economic growth. Klein (2005) shows that countries with
better (but not the best) institutions exhibit positive eﬀects of capital account liberalization on economic
growth. Kose, et al. (2006) argue that countries that meet threshold conditions (about institutional quality
and trade openness, for example) are better able to reap the growth and stability beneﬁts of ﬁnancial globalization. Financial development itself depends on general institutional quality and political and economic
environment. Chinn and Ito (2006) ﬁnd evidence that capital account liberalization leads to equity market
development only if a threshold level of legal development has been attained and that trade openness is aprerequisite for capital account liberalization. Rajan and Zingales (2003) and Do and Levchenko (2007) ﬁnd
that trade and international capital movement induce ﬁnancial development. Indeed, the quality of ﬁnancial
institution has long been recognized to be critical to the economic prosperity. McKinnon (1973, 1993), forexample, emphasizes that less-developed countries and countries in transition from socialism to democracy
should develop reliable ﬁnancial institution in order to achieve economic growth. He argues that countries
should ﬁrst improve their internal ﬁnancial institutions before opening to trade in goods. Rajan and Zingales

1explored the eﬀect of capital account liberalization in conjunction with its interaction with
openness of international trade in goods. It is often thought that trade openness is a key toattract foreign capital, which fosters economic growth. Emerging economies in the Southeast
Asia, for example, have liberalized trade substantially in recent decades, attracting foreign
capital to successfully grow. On the contrary, some countries in the Sub-Saharan Africa
adopted import-substitution policy, and at the same time failed to attract foreign capital
especially to their manufacturing industries (Overview and Chapter 4, Economic Commission
for Africa, 2006). But can we conclude from these evidences that trade openness is necessary
for attracting foreign capital and for achieving economic growth? It seems too early to reachthis conclusion. Even those Asian countries that are relatively open to international tradesuﬀered capital ﬂight in a large scale and resulting economic downturn during the Asian
economic crisis in 1997, for example. We need more studies on the relationship between theeﬀect of capital account liberalization and trade openness in order to derive useful insights
for countries (especially developing countries) to achieve sustainable growth. Does trade
openness help countries attract foreign capital especially into manufacturing sectors, which
contributes to economic growth? How does the answer to this question depend on economic
structure and economic (and legal) institution of the country?
To answer to these questions and more broadly to ﬁnd the relationship between the effect of capital account liberalization and trade openness, we build a simple model in which amanufacturing sector relies on external ﬁnance through an imperfect ﬁnancial market. The
diﬀerence in ﬁnancial development across countries is a source of potential capital ﬂight inthis model, similarly to those by Gertler and Rogoﬀ (1990), Caballero, et al. (2008), Aoki,
et al. (2010). In addition, however, we design the model so as to be able to investigate theinteraction between capital account liberalization and trade openness. Thanks to the additional feature of the model, we are able to ﬁnd that the degree of ﬁnancial development playsa critical role in the relationship between capital account liberalization and trade openness.
More speciﬁcally, we ﬁnd that under imperfect ﬁnancial institution, freer international trade(1998) ﬁnd evidence that ﬁnancial development contributes positively to the economic growth. Kose, et al.
(2006, 2009) provide excellent surveys of the studies on the economic impacts of ﬁnancial globalization.

2

induces capital to reallocate from the South to the North. International trade and capital
movement are complements in the sense that trade induces (further) capital movement fromthe South to the North. If the ﬁnancial institution is perfect or almost perfect, on the other
hand, trade and capital movement are substitutes as the traditional literature predicts. This
result gives an important lesson to policy makers in the South; globalization of the goods andcapital markets should be accompanied by ﬁnancial development in order to attract foreign
capital or to avoid capital outﬂow. Our result is consistent with a commonly-held view thatthe development of economic institution is a key to an economic success of a country. The
following quotes are suggestive.
The trend of overall private ﬂows to Tunisia mirrors the East Asian experience inthat substantial increases in capital ﬂows seem to follow improvements in policies,
institutions and physical and human infrastructure in an open export-oriented
economy. (p. 145, Economic Commission for Africa, 2006)
Nigeria provides an example of a country which, because of policy failures, failed
to achieve sustainable growth and economic transformation despite substantial
FDI inﬂows combined with a sound human capital base. (p. 149, Economic
Commission for Africa, 2006)
The case of Nigeria is worth further comments. Eichengreen (2001) points out that “capital
may ﬂow to sectors in which the country has a comparative disadvantage”. In the caseof Nigeria, capital ﬂows disproportionately into oil industry rather than manufacturing.
Indeed, “the contribution of manufacturing to GDP fell sharply from a peak of 9 per centin 1980-1984 to 4.1 per cent in 2000-2003” at least partly due to “severe constraints” that
include “inadequate access to ﬁnancing” (pp. 149-150, Economic Commission for Africa,2006). Our model shows that ﬁnancial under-development severely hinders capital inﬂow
into manufacturing sectors.
We are not the ﬁrst to theoretically examine the relationship between trade and capital movement under ﬁnancial imperfection.3 Antràs and Caballero (2009) also show the3

More generally, international trade issues in the presence of ﬁnancial imperfection have not been well3

complementarity between international trade in goods and capital movement under ﬁnancial
imperfection. They show that trade in goods and capital movement are complements in thesense that trade in goods induces capital to ﬂow into a ﬁnancially-less-developed country(i.e., the South), the result that encourages (rather than discourages) the South to liberalize
trade as well as its capital account. Their model and ours share a prediction that tradein goods induces international capital reallocation. But the direction of resulting capital
movement is completely opposite; their result appears to contrast sharply with ours. Antràs
and Caballero (2009) build a model with two sectors that have diﬀerent degrees of ﬁnancial
dependence. The South, which is less ﬁnancially developed, naturally has a comparativeadvantage in the ﬁnancially-unconstrained sector. They show that after trade liberalization,
capital ﬂows into this ﬁnancially-unconstrained sector in the South. In contrast, we builda model with one ﬁnancially-dependent sector under monopolistic competition, which canbe considered as manufacturing. The model is designed to capture a ‘competition eﬀect’
within an industry, through which opening to trade aﬀects returns to capital, thereby inducing capital reallocation. In such an environment, we show that after trade liberalization,
capital ﬂows out of the ﬁnancially-dependent sector in the South to the one in the North. In
summary, our analysis should be viewed as a complement to theirs, rather than a competing
substitute. They predict that trade induces capital inﬂow to the ﬁnancially-unconstrained
sector in the South. On the other hand, we show a channel through which trade induces
capital outﬂow from the ﬁnancially-dependent sector in the South.
Our study here is also related to the one in the companion paper (Furusawa and Yanagawa
explored. Kletzer and Bardhan (1987), Beck (2002), Matsuyama (2005), Wynne (2005), Levchenko (2007),Ju and Wei (2011), and Antràs and Caballero (2009), for example, ﬁnd that the cross-country diﬀerencesin the quality of ﬁnancial institutions signiﬁcantly aﬀect the structure of countries’ comparative advantage
and trade patterns. Chaney (2005), Manova (2013), and Suwantaradon (2008) develop models in whichheterogeneous ﬁrms are faced with credit-constraints when they ﬁnance trade costs. Their models predictthat more-productive and wealthier ﬁrms engage in export, while others sell their products only domestically.
Indeed, Manova (2008) and Chor and Manova (2012) ﬁnd evidence that credit constraints are an important
determinant of international trade ﬂows. Foellmi and Oechslin (2010) also theoretically investigate theeﬀect of international trade on exogenously-heterogeneous ﬁrms within an industry and show that rich
entrepreneurs win while poor ones lose from opening to trade. Despite that these studies in the ﬁeld ofinternational trade reveal many important features and mechanisms that appear under ﬁnancial imperfection,
we have yet to analyze many aspects of international trade and capital movement in the economy withimperfect ﬁnancial institutions.

42012), which investigates the impacts of trade and capital account liberalization on the
productivity distribution of the industry that depends on external ﬁnance. The main purposeof the companion paper is to explore the relationship between the ﬁnancial development andﬁrm heterogeneity in their productivity (which is absent in this paper) and to show that
trade and capital account liberalization leads to the global convergence in the productivity
distribution in. This paper, on the other hand, examines the substitutability between tradein goods and international capital movement, a traditional and fundamental question ininternational trade.
In the next section, we set out a two-country, one-sector model with ﬁnancial frictionin order to examine the relationship between trade and capital movement under ﬁnancial
imperfection. In Section 3, we examine the case in which two countries are diﬀerent in theirﬁnancial development. We show that capital ﬂows from the South, which is ﬁnancially lessdeveloped, to the North and that trade in goods ampliﬁes this capital outﬂow from the South.
In Section 4, we examine a more traditional case in which the two countries are diﬀerent
in their wealth (or equivalently capital) distributions across individuals such that the Northhas more rich individuals than the South, while the degrees of ﬁnancial imperfection are
the same between the two countries. Then, we show that although capital moves from theNorth to the South, i.e., from the capital-abundant country to the capital-scarce country,
trade in goods induces capital reallocation from the South to the North also in this case.
Therefore, we conclude that trade and capital movement are complements in the sense that
trade induces capital reallocation from the South to the North in both cases.
Trade induces capital outﬂow from the South because trade beneﬁts ﬁrms in the Northand harms those in the South (the positive market expansion eﬀect outweighs the negativecompetition enhancement eﬀect for ﬁrms in the North but not for ﬁrms in the South) sothat it pushes up the rental rate in the North but pushes down the rental rate in the South.
That is, the key to our complementarity is the competition eﬀect in the industry. Ourcompetition eﬀect is relevant and important especially for contemporary trade because the5proportion of intra-industry trade to inter-industry trade is higher than ever before.4 In
Section 5, we examine why ﬁnancial imperfection matters in the prediction of international
capital ﬂow induced by international trade, by showing that trade and capital movement
are substitutes in the case where ﬁnancial institution is perfect or almost perfect. A key
to understand the diﬀerence in the prediction between the two cases is that capital moves
internationally according to the diﬀerence in its returns between the countries under perfectﬁnancial institution, whereas pledgeability of its return critically matters under imperfectﬁnancial institution. Section 6 uses the basic model to show how the impact of ﬁnancial
crisis in the North varies with the wealth distribution in the South. Section 6 also extends
the basic model by including an alternative investment opportunity and shows that capital
account liberalization may induce part of capital to be used in a less-proﬁtable investment
opportunity in the North. Section 7 concludes the paper.

2

Model

There are two countries, which we call North (N ) and South (S). In country k ∈ {N, S},
there is a mass mk of individuals; we normalize the population such that mN + mS = 1.
Each individual owns one unit of labor and a wealth (or capital) of ω that is distributed
according to the cumulative distribution of Fk . All individuals share the same utility function
over the two goods, a diﬀerentiated manufacture good X and a numeraire good Y , which ischaracterized byu = log ux + y,
where

[∫

ux =

x(i)

σ−1
σ

] σ

di

σ−1

, σ > 1,(1)

Ωkdenotes the subutility derived from the consumption of continuum varieties of good X,{x(i)}i∈Ωk (where Ωk denotes the set of all varieties available in country k), and y denotes
the consumption level of good Y . The numeraire good is competitively produced from labor4

Our result can be considered to be in contrast to Krugman’s (1979) substitutability result, just as Antràs
and Caballero’s (2009) complementarity is in contrast to Mundell’s (1957) substitutability result.

6such that one unit of labor produces one unit of the good, so the wage rate equals 1.
Each individual chooses a consumption proﬁle of good X to maximize ux subject to∫Ωk p(i)x(i)di ≤ E, where p(i) and E denote the price for variety i and the total expenditureon all varieties of good X, respectively. It is immediate to obtain x(i) = p(i)−σ E/Pk1−σ , where
Pk ≡

[∫

1−σ
di
Ωk p(i)] 11−σdenotes the price index of good X. We substitute this result into (1)to obtain ux = E/Pk , so that an individual’s utility can be written as u = log E − log Pk + y.
Maximizing the utility with the constraint E +y ≤ I, where I denote the individual’s income(which is the sum of her labor income and the investment return from her wealth), we obtain
E = 1. That is, each individual spends E = 1 on good X, so the country k’s aggregate
expenditure on good X is mk .
The diﬀerentiated-good industry is characterized by the monopolistic competition withfree entry and free exit. When a ﬁrm enters, however, it incurs an initial investment of gunits of capital. Each entrepreneur, therefore, needs to raise g units of capital to “ﬁnance”
this investment before the operation. Once entrepreneurs have invested g units of capital,
they operate under the standard monopolistic competition. Since there is a continuum ofvarieties, each ﬁrm’s pricing does not have an impact on the price index, so that ﬁrms selectprices that are σ/(σ − 1) times their individual marginal costs, which we assume are laborcosts of c that is common to all ﬁrms. Let nk denote the mass of ﬁrms in country k. Then,
it is easy to see that the proﬁts for any ﬁrm i in country k in autarky equal
πk (nk ) = mk /σnk ,(2)which is the reciprocal of the per-capita mass of ﬁrms, nk /mk , divided by the elasticity of
substitution, σ.
Individuals in country k decide whether or not they become entrepreneurs, who can
ﬁnance part of the investment externally at a gross capital rental rate of Rk if necessary. If
she decides not to be an entrepreneur or if part of her wealth is left after the investment forher ﬁrm, she will lend out her (remaining) wealth.
The critical feature of the model is that entrepreneurs are faced with a ﬁnancial constraint.
We assume that entrepreneurs in country k can only pledge themselves to repay only a7

fraction θk ∈ (0, 1] of the proﬁts that they will earn, and hence entrepreneur i in country
k can borrow only up to the amount such that the repayment does not exceed θk πk . The
fraction θk represents the quality of the ﬁnancial institution of the country. (Matsuyama
2000, for example, adopts this formulation of ﬁnancial imperfection.5 ) A ﬁnancial institution
is perfect if θk = 1; any entrepreneur with any wealth level can ﬁnance the investmenteﬀectively without any constraint. A ﬁnancial institution is imperfect if θk < 1; individuals
that are endowed with small amounts of wealth may not be able to ﬁnance the investmentin this case. We assume, without loss of generality, that θN ≥ θS .
We can list several reasons why θk can be smaller than one. A natural cause of ﬁnancial
imperfection is the imperfection of legal enforcement.6 If the legal enforcement is perfect, asassumed in the traditional literature, a court can enforce a borrowing contract as long as therepayment under the contract does not exceed the proﬁt from the project, which is denoted
here by π. Empirical evidences show, however, the enforcement power is not perfect (LaPorta, et al., 1998). Thus, in reality, a court may be able to force a borrower to pay only
up to a fraction of the proﬁts, i.e., θk π where θk < 1, even though the realized proﬁts are π.
Hence, unless the non-pecuniary penalty for the default is large enough, the borrower is likely
to refuse to pay more than θk π even if the promised payment exceeds this amount. Thisbehavior is called the “strategic default”. A contract cannot be a perfect commitment device
if the legal enforcement is imperfect; it is diﬃcult for a lender to expect that a borrower will
sincerely make a promised payment. Given that, lenders will not lend more than the amountsuch that the return from the lending equals θk π. Another source of ﬁnancial imperfectionis the agency problem of the lender-borrower relationship, which is explained brieﬂy in a
simple model in the Appendix.
In the economy that we consider, there are two types of the constraints that must be satisﬁed: the proﬁtability constraint and the borrowing constraint. The proﬁtability constraint(PC) πk − Rk g ≥ 0
5(3)

Matsuyama (2007) describes various economic implications of the credit market imperfection of thistype.
6
See for example Hart(1995).

8

simply means that the net proﬁts must be non-negative. The borrowing constraint, on theother hand, can be written as(BC) θk πk ≥ Rk (g − ω),(4)which means that in country k, an entrepreneur with a wealth of ω can rent capital only up
to the amount such that the repayment does not exceed the fraction θk of the proﬁts. It iseasy to see that the proﬁtability constraint is tighter than the borrowing constraint if θk islarge, whereas the borrowing constraint is tighter if θk is small. The borrowing constraint
also tends to be tighter for entrepreneurs endowed with a small amount of wealth.
We investigate the eﬀects of trade and international capital movement under an imperfectﬁnancial institution on the economy and establish the main result that trade and international capital movements are complements in the sense that trade in goods facilitates capitaloutﬂow from the South. To this end, we always assume in the main analysis that θN and θS
are small enough that the borrowing constraints are binding for some entrepreneurs in bothcountries, while the proﬁtability constraints are slack. After all, if θN and θS are large suchthat it is the proﬁtability constraint that binds, the economic performances are the sameas in the case of perfect ﬁnancial institution.7 Note that when the borrowing constraint isbinding while the proﬁtability constraint is slack for some entrepreneurs, individuals whose
wealth is greater than or equal to the wealth of such threshold individuals choose to become
entrepreneurs because in such cases they can enjoy extra proﬁts as a rent if they become
entrepreneurs.
For the clarity of exposition, we ﬁrst analyze the case in which the two countries are
diﬀerent in the quality of ﬁnancial institution, i.e., θN > θS , while they share all other aspects
in common. Then, we analyze the case in which they are diﬀerent only in their wealthdistributions. We assume that the wealth distribution in North has ﬁrst order stochastic
dominance over that in South, i.e., FN (ω) < FS (ω) for any ω. This assumption captures a
traditionally-emphasized diﬀerence in the capital-labor endowment ratio between North and7Section 5 analyzes the case of perfect ﬁnancial institution in order to highlight the role of ﬁnancial
imperfection on the complementarity between trade in goods and international capital movement.

9South, i.e., the capital endowment (or wealth) per-capita is greater in North than in South.
It also represents a diﬀerence in the wealth distribution per se. That is, North has more richindividuals, who do not have to rely (or rely less) on external ﬁnance to establish their ﬁrms
than South does.
We also note here that the numeraire good is always tradable in all cases that we consider,so “opening to trade in goods” here means opening to trade in the diﬀerentiated good as wellas the numeraire good. We need this assumption in order to meaningfully analyze the eﬀectof capital movement. In this static model, the balance-of-payment consideration requires
some goods be traded in order for capital to ﬂow from one country to the other.

3

Diﬀerent qualities of ﬁnancial institution

In this section, we assume that North and South are diﬀerent only in the quality of ﬁnancial
institution, i.e., θN > θS and FN = FS , and derive the result that trade in goods and international capital movement are complements such that capital ﬂight from South is exacerbated
if the countries are open to trade in goods. To establish this main result, we ﬁrst derive theautarkic equilibrium and then analyze the impact of trade and capital movement.
International capital movement directly leads to relocation of ﬁrms between the twocountries. Throughout the analysis, we emphasize this aspect by directly observing theeﬀect of trade and capital movement on the mass of ﬁrms in each country rather than theeﬀect on the amount of international capital movement.

3.1

Autarky

To ﬁnd the autarkic equilibrium, we rewrite the borrowing constraint, expressed by (4), asa function of nk . To this end, we ﬁrst recall the proﬁts for a ﬁrm in country k in autarky
can be written as a function of nk , i.e., πk (nk ) = mk /σnk as shown in (2). Next, we derive
the threshold wealth of individuals who become entrepreneurs as a function of nk . Let ωkdenote the threshold wealth such that the borrowing constraint (4) is satisﬁed with equality.
Since individuals choose to be entrepreneurs if and only if their wealth exceeds ωk , the mass10

of ﬁrms must be equal to the mass of such wealthy individuals, i.e., nk = mk [1 − F (ωk )].
Then, we solve this equation for ωk to obtainωk (nk ) = F

−1

(

)

nk
1−
.
mk

(5)

The function ωk , represented by (5) is decreasing; the larger the mass of ﬁrms, poorer thethreshold entrepreneurs. Now, we can write the binding borrowing constraint (see (4)) asRk =θk πk (nk ).
g − ωk (nk )(6)Figure 1 illustrates the relationship, expressed by (6), between the mass of ﬁrms and therental rate of capital in autarky. The BC curve that depicts this relationship is downwardsloping: the larger the mass of ﬁrms, the lower the rental rate that satisﬁes the borrowing
constraint with equality. There are two factors that contribute to this negative relationship.
The ﬁrst one is the competition eﬀect. If the mass of ﬁrms grows, the market environment
becomes more competitive so that the pledgeable proﬁts for each ﬁrm fall. Then, the rental
rate must also fall so that the threshold entrepreneur can still ﬁnance the project. The second
one is the threshold wealth eﬀect. Given a wealth distribution, the threshold wealth must
decline as the mass of ﬁrms increases. Then, the rental rate must also fall for the less-wealthythreshold entrepreneurs to be able to ﬁnance the project. The rental rate of capital naturally
depends on the proﬁtability of the project that is ﬁnanced, or the proﬁtability for the ﬁrms.
Indeed, as the proﬁtability constraint (3) shows, the competition eﬀect is the only factor
that aﬀects the rental rate if ﬁnancial institution is perfect. Under ﬁnancial imperfection,
however, the threshold wealth eﬀect also plays an important role in determining the rental
rate and hence the international ﬂow of capital. Note further that the BC curve shifts up if
θk increases. Thus, the BC curve for North is located above that for South if nN = nS , forexample.
The equilibrium mass of ﬁrms is determined from the capital market clearing condition.
The total demand for capital equals nk g since capital is used only for the initial investment
by entrepreneurs, while the total supply of capital in country k equals mk ω̄, where ω̄ ≡∫∞0

ωdF (ω) denotes the average wealth. Thus, we obtain the autarkic mass of ﬁrms as
11

Figure 1: The Binding Borrowing ConstraintnA
k = mk ω̄/g for k = N, S. While the mass of ﬁrms is determined solely in the capital market,
the rental rate of capital is determined from both the capital market clearing condition andthe borrowing constraint. As Figure 1 shows, once the mass of ﬁrms is determined in thecapital market, the rental rate is determined from the borrowing constraint. Indeed, we
substitute nA
k = mk ω̄/g into (2) to obtain
πk (nA
k) =

g
.
σ ω̄

(7)

Then, it follows from (5) and (6) that
RkA =

θk g
.
−1
σ ω̄[g − F (1 − (ω̄/g))]A/θN = RSA /θS . Thus, it follows from θN > θS that
Note that RkA /θk is a constant so that RN
A> RSA : in autarky, the rental rate is higher in North than in South because the eﬀective
RN

demands for capital are higher in North that has a better ﬁnancial institution.
Figure 2 depicts the BC curves of both countries in one diagram. The length of the line
12

Figure 2: The Equilibria without Trade (θN > θS )segment ON OS equals nN + nS = (mN ω̄ + mS ω̄)/g = ω̄/g, the total mass of ﬁrms in theworld. Note that the worldwide mass of ﬁrms is constant in the basic model, since (i) capitalis used only for ﬁrms’ initial investment in the diﬀerentiated-good industry, (ii) initial capitalrequirement equals g for any ﬁrm in the world, and (iii) the worldwide capital endowment
is ﬁxed.8
The mass of ﬁrms in South is measured from OS to the left; the BC curve for South istherefore upward-sloping. The ﬁgure shows the autarkic equilibrium points, AN for North
and AS for South, as the intersections between the individual BC curves and the vertical line
at the equilibrium allocation of ﬁrms (shown by z), which is determined by the allocation ofcapital endowment between the two countries (i.e., the length of ON z equals mN ω̄/g). As
we have seen, the BC curve for North is located above that for South at the ﬁrm allocationA> RSA .
point z, such that RN

8

In Section 6.2, we relax the assumption (i).

13

3.2

International capital movement

Since the rental rate of capital is greater in North than in South in autarky, capital moves
from South to North if it is internationally mobile. The total capital endowment is redistributed between the two countries, and so are the ﬁrms. Relocation of ﬁrms caused by
the international capital movement is depicted in Figure 2. If capital in perfectly mobileinternationally, the equilibrium distribution of ﬁrms between the countries is given by theintersection of the two BC curves, which is illustrated by K in the ﬁgure. Capital ﬂight
from South reduces the size of the industry in South and expands it in North. As is well
documented, a country with poor ﬁnancial institution has a risk of losing capital and hence
experiences contraction of industry, if it liberalize the capital account without ﬁnancial development.
In equilibrium when capital is perfectly mobile internationally, the rental rates are equalized between the two countries, and hence we have from (6) thatθN πN (nKθS πS (nK
N)
S)
=
,
K
g − ωN (nN )g − ωN (nKS)(8)

where nKk denotes the mass of ﬁrms in country k in equilibrium under perfect capital mobility. Capital movement from South to North increases nN and decreases nS , which causesA
decreases in πN and ωN and increases in πS and ωS (see (2) and (5)). Since πN (nA
N ) = πS (nS )K
in autarky as (7) shows, these induced changes implies that πN (nKN ) < πS (nS ). Interna-

tional capital movement makes the market in North more competitive than before and thanin South. Consequently, the proﬁts for ﬁrms in North decline and those for ﬁrms in South
increase from the common autarkic level, so that ﬁrms in North have smaller proﬁts thanthose in South in equilibrium under perfect capital mobility.
Lemma 1 Suppose North has a better quality of ﬁnancial institution than in South. Then, if
capital is perfectly mobile internationally, capital moves from South to North, which changes
the competition environment in both countries so that ﬁrms in North earn smaller proﬁts
than those in South.

14

3.3

International trade in goods

We turn to the case in which capital is immobile between the countries but goods can be
traded without any costs.
In free trade, all ﬁrms compete in a level ﬁeld in the world market, so ﬁrms earn thesame proﬁts regardless of their locations. Their proﬁts areπw ≡mN + mSg=,
σ(nN + nS )σ ω̄where we have used mN + mS = 1 and nN + nS = ω̄/g. It is readily seen that the proﬁts
in free trade are the same as those in autarky. The competition environment for ﬁrms canbe measured by the per-capita mass of ﬁrms in the market. In this section, we consider
a situation in which the wealth distributions (and hence the average wealth) are the same
between North and South. But this means that the worldwide average of the wealth is thesame as the average wealth of North and South, so the worldwide per-capita mass of ﬁrms is
also the same as those in North and South in autarky. That is why the proﬁts for any ﬁrm
do not change by trade liberalization. For any ﬁrm in any country, beneﬁts from penetrating
the foreign market are completely oﬀset by losses from foreign ﬁrms’ penetration into its
own market.
The borrowing constraint in free trade can be written as
Rk =θk π w.
g − ωk (nk )(9)In comparison with (6), we immediately recognize that the competition eﬀect is now shut
down. With only the threshold wealth eﬀect remaining, the BC curves are ﬂatter than thosein autarky; Figure 3 depicts the BC curves in free trade as dotted curves, which are ﬂatterthan the corresponding solid curves that indicate the BC curves when goods are not traded.
Comparing the borrowing constraints, (6) and (9), we immediately ﬁnd that for each country,
the BC curve in free trade intersects with that in the case of no trade when πk (nk ) = πw . As
we have seen, this happens when ﬁrms are allocated as they were in autarky, i.e., nk = nAk.
Since πk is decreasing in nk , moreover, the rental rate that satisﬁes the borrowing constraint
15

Figure 3: The Equilibria with and without Trade (θN > θS )(9) is smaller (greater) than the one that satisﬁes the autarkic counterpart (6) if and onlyA
if nk < (>)nA
k and they are equal when nk = nk . This critical observation is illustrated in

Figure 3 as the rotation of the BC curves; the BC curve for country k in free trade is locatedbelow (above) the autarkic counterpart if and only if nk < (>)nAk.
In the absence of international capital movement, opening the countries to trade will
not change international ﬁrm allocation. Then, it follows immediately that the equilibrium
points, illustrated by TN and TS in Figure 3, coincide with those in autarky, illustrated byA
T
AN and AS , respectively. That is, we have nTk = nA
k and Rk = Rk , where the superscript‘T ’ signiﬁes the variables in free trade equilibrium without capital movement.
Lemma 2 In the case where countries are diﬀerent only in the quality of ﬁnancial institution, opening the countries to trade will not change the international ﬁrm allocation nor the
proﬁts for each ﬁrm. The rental rates of capital also remain the same as their individual
autarkic levels.
16

In general, opening to trade can change the proﬁts for ﬁrms, and hence aﬀect the borrowing constraints for both countries. This is not the case, however, when the average wealthlevels are the same between the countries and so are the per-capita masses of ﬁrms as a consequence. Since the international ﬁrm allocation does not change by opening to trade, thismeans that the rental rates of capital will also be unaﬀected. Each individual’s income also
does not change, whether an individual is an entrepreneur or not, because neither the proﬁts
nor the rental rate changes as a result of international trade. Despite this fact, however,each individual’s utility increases because international trade allows each consumer to enjoy
more varieties of the manufacture good.

3.4

International trade in goods and capital movement

Since the rental rate is higher in North than in South in free trade equilibrium, capitalmoves from South to North if capital is allowed to move internationally, as in the case where
capital becomes internationally mobile while goods continue to be immobile. We will show
shortly that the amount of capital that moves out from South is greater in the presence ofinternational trade in goods than otherwise; capital ﬂight from South is exacerbated if tradein goods has been liberalized.
It is readily seen that the borrowing constraint when both goods and capital are internationally mobile is the same as the one in the case of free trade in goods without capital
movement, i.e., the borrowing constraint is given by (9). Indeed, whether the borrowing
constraint is written as (6) or (9) hinges on whether goods are allowed to be traded internationally. Capital mobility does not aﬀect the formula for the borrowing constraint,
but induces ﬁrm relocation through international capital movement, which is reﬂected as achange in nk in the borrowing constraint.
As the borrowing constraint (9) applies to this case, equilibrium is illustrated as T K(which signiﬁes ‘trade and capital movement’), the intersection between the two dottedcurves, in Figure 3. We ﬁnd immediately that this equilibrium point is located to the rightof K, which describes the equilibrium when capital is perfectly mobile while goods are not;17

capital ﬂight from South is exacerbated when trade in goods, as well as capital, has beenliberalized.
To show this main proposition of the paper more rigorously, we derive the condition that
determines the equilibrium allocation of ﬁrms by equating the rental rates, RN and RS ,which are given by (9):
θN
θS
=
.
g − ωN (nN )g − ωS (nS )(10)K
Then, it follows from (8) and (10) together with πN (nKN ) < πS (nS ) thatg − ωS (nKTg − ωN (nKT
S )
N )
>
.
K
g − ωN (nN )g − ωS (nK
S)
KT
K
KT
Since nN + nS is constant, this inequality implies that nK
N < nN and nS > nS , i.e., ﬁrm

relocation to North is greater when goods and capital are both internationally mobile thanin the case where only capital is mobile between the countries.
Proposition 1 Suppose North has a better quality of ﬁnancial institution than South. Then,
capital ﬂight from South to North is exacerbated if trade in goods has been liberalized. Tradein goods and capital movement are complements in the sense that trade induces further capital
movement from South to North.
When capital is internationally mobile, capital naturally ﬂows from the ﬁnancially lessdeveloped country, South, to the ﬁnancially developed country, North, since the rental rate
tends to be higher in the ﬁnancially developed country where the eﬀective demands forcapital is higher. Capital movement, however, entails ﬁrm relocation from South to North,which decreases the proﬁts for ﬁrms in North and increases those in South when ﬁrms are
restricted to selling their products only domestically. This in turn tends to lower the rental
rate in North and raise it in South, suppressing the capital ﬂight from South. When goods
can be traded internationally, however, ﬁrms’ proﬁts will not change with the ﬁrm relocation,
so that the factor that counters capital ﬂight from South disappears in this case. Capital
ﬂight from South is exacerbated in the presence of trade in goods as a consequence.
Antràs and Caballero (2009) show that trade and capital mobility are complements in thesense that trade induces capital inﬂow to South, while we show that they are complements in18

the sense that trade induces capital outﬂow from South. In their model, trade liberalization
raises the relative price for the good produced in the ﬁnancially-unconstrained sector inSouth and thereby raises the return to capital that has eﬀectively become speciﬁc (due tothe ﬁnancial constraint) to that sector. That is, capital inﬂow to South in their model is aconsequence of an inter-industry eﬀect of trade. Whereas in our model, trade liberalization
beneﬁts ﬁrms in North and harms those in South, which tends to raise the rental rate ofcapital in North and lower the rate in South. That is, capital outﬂow from South in ourmodel is a consequence of an intra-industry eﬀect of trade. Our model should be viewed as
a complement to their model (as argued in the Introduction) also regarding the mechanismof complementarity between trade and capital mobility.
Is capital ﬂight bad for South? Consider the case in which trade has already been liberalized. Capital account liberalization will not change the proﬁts for ﬁrms while it raises
the rental rate in South. Thus, entrepreneurs’ income decreases while lenders’ increases.
Although this observation suggests that the welfare impact of capital ﬂight is inconclusive
in South, capital ﬂight from South unambiguously decreases the mass of entrepreneurs inSouth, which is certainly bad news to South since entrepreneurs still earn some rents overlenders. The prediction that trade in goods exacerbates capital ﬂight from South can also beinterpreted more broadly beyond the framework of this model. Capital inﬂow is very important for developing countries to build industry, which in turn leads to economic growth. At
the same time, trade openness is also an important factor for growth, as it attracts foreign
direct investment, for example. But the prediction of our model suggests that unless developing countries develop better ﬁnancial institution, capital account liberalization together
with freer trade can lead to capital ﬂight which depletes capital from industry and hence
hampers their economic growth.

4

Diﬀerent wealth distributions

We have shown in the case where North has a better ﬁnancial institution than South, that
capital movement from South to North is exacerbated if trade in goods has been liberalized.

19

Does this complementarity between trade and capital movement arise because the two countries are in diﬀerent stages of ﬁnancial development? Or does it arise merely because theirﬁnancial institutions are imperfect? To answer to this question, we investigate here the complementarity between trade and capital movement in the case where the two countries haveimperfect ﬁnancial institutions of the same degree, i.e., θN = θS ≡ θ < 1, but have diﬀerent
wealth distributions such that the wealth distribution in North has ﬁrst order stochastic
dominance over that in South, i.e., FN (ω) < FS (ω) for any ω. We will show shortly that
more capital is allocated in North as a consequence of international capital movement if
trade in goods has been liberalized than otherwise. That is, the complementarity between
trade and capital movement in the sense that trade induces capital outﬂow from South exists
even in the case where the two countries are in the same stage of ﬁnancial development; thecomplementarity is a consequence of the ﬁnancial imperfection per se.
Since this section can be considered to establish the robustness of Proposition 1, we
do not attempt here to discuss in detail the equilibrium features for each of the four casesthat we have analyzed in the previous section. Instead, our aim here is to show, mainly
graphically, the complementarity between trade and capital movement.
Let us ﬁrst consider the case in which there is no international trade in goods. The
borrowing constraint that faces country k in this case can be written as
Rk =θπk (nk ),g − ωk (nk )(11)where πk (nk ) is as given in (2) andωk (nk ) = Fk−1

(

)

nk
1−
,
mk

(12)

is slightly diﬀerent from (5) reﬂecting the diﬀerence in the assumptions about the international diﬀerence in wealth distribution (though we use the same notation for simplicity).
The corresponding BC curves are drawn in Figure 4.
Figure 4 shows the autarkic equilibrium points, AN and AS , with the ﬁrm allocation,
depicted by z, under the original capital allocation between the two countries. The ﬁgure
illustrates the case in which the autarkic rental rate is smaller in North than in South. In
20Figure 4: The Equilibria without Trade (FN < FS )general, however, this may not be the case. The rental rate tends to be smaller in North
because the per-capita capital endowment (and so is the per-capita mass of ﬁrms) is greaterin North than in South. But, on the other hand, there are more rich individuals in North
than in South so that the threshold entrepreneurs in North need not rent as much capital as
those in South to start the business. Consequently, the threshold entrepreneurs in North can
aﬀord a higher rental rate than those in South if other things being equal. Figure 4 shows
the case in which the former eﬀect outweighs the latter. It can be shown that this is indeedmax> ωSmax .
the case if Fk is the uniform distribution on the support [0, ωkmax ] such that ωN

Having drawn the BC curves, which express the borrowing constraints (11) of the individual countries, in Figure 4, it is immediate to ﬁnd the equilibrium point when capital isinternationally mobile while goods are not. In equilibrium with capital movement, the rental
rates must be equalized between the two countries. That is, we have from (11) thatπN (nN )πS (nS )=.
g − ωN (nN )g − ωS (nS )
21

(13)

In Figure 4, the equilibrium point in this case is illustrated by K, the intersection between
the two BC curves. Capital moves from capital-abundant North to capital-scarce South in
the case that Figure 4 depicts.9
Regardless of the direction of capital movement, however, we can derive from (13) an
important observation about the proﬁts for the ﬁrms in equilibrium with capital movement:
K
K
K
πN (nKN ) < πS (nS ), and hence ωN (nN ) > ωS (nS ). To show this, let us suppose for now that
K
K
K
K
K
πN (nK
N ) = πS (nS ) and hence nN /mN = nS /mS from (2). Then it follows from (12) andK
FN < FS that ωN (nKN ) > ωS (nS ). Consequently, we ﬁnd from the borrowing constraint,

expressed by (11), that RN > RS , so that capital should (further) ﬂow into North. Thus, inequilibrium, more capital than the assumed level should be allocated in North. That is, we
K
K
K
K
K
have nK
N /mN > nS /mS and hence πN (nN ) < πS (nS ).

Lemma 3 Suppose North is capital-abundant in the sense that the wealth distribution in
North has ﬁrst order stochastic dominance over that in South. Then, in equilibrium under
perfect capital mobility without international trade in goods, ﬁrms in North earn smaller
proﬁts than those in South.
Recall from Lemma 1 that proﬁts are also smaller for ﬁrms in North than those in South inequilibrium under perfect capital mobility when the two countries are diﬀerent in the degreeof ﬁnancial development. In that case, the ﬁnancial institution of better quality attracts
capital to North, so that the market environment there becomes more competitive sincemore ﬁrms operate locally without the possibility of exporting. The reason for the depressed
proﬁts for ﬁrms in North is diﬀerent in this case; the threshold entrepreneurs in North arericher than those in South because of the diﬀerence in wealth distribution, so their proﬁts
can be smaller in equilibrium, which allows more ﬁrms (per capita) to enter the market inNorth than in South. Despite this diﬀerence, what is important is the fact that proﬁts are
smaller for ﬁrms in North than those in South in both cases. When the countries are open to
trade in goods in such situations, ﬁrms in North beneﬁt from the trade liberalization more
9

Capital would move in the opposite direction if the rental rate was higher in North than in South inautarky.

22

than those in South. Capital demands in North increase while those in South decrease as aresult, which leads to capital reallocation from South to North; trade and capital movement
are complements in the sense that trade induces capital reallocation from South to North.
To show this complementarity result more rigorously, we shall derive the equilibria underfree trade with and without capital movement, and compare these equilibria with those wehave derived above. In both cases, the countries engage in free trade so that all ﬁrms earn thesame proﬁts. Since the total mass of ﬁrms in the world equals nN + nS = (mN ω̄N + mS ω̄S )/gand the worldwide population is normalized to 1, the proﬁts for ﬁrms are
πw =

g
.
σ(mN ω̄N + mS ω̄S )(14)

Whether or not capital is internationally mobile, the borrowing constraint for country kwhen the countries engage in free trade can be written as
Rk =

θπw
.
g − ωk (nk )(15)

As in the case where countries are in diﬀerent stages of ﬁnancial development, the competitioneﬀect is shut down when the countries are open to trade. What remains is the threshold
wealth eﬀect in determining the relationship between the worldwide allocation of ﬁrms andthe rental rate. Similarly to the shifts of the BC curves depicted in Figure 3, the BC curves
become ﬂatter when trade is liberalized. In addition, it follows from the comparison between(11) and (15) that the two corresponding BC curves of either country intersect at the pointof ﬁrm allocation such that πN = πS = πw . As shown in Figure 5, these intersections areKto the left of point K, since πN (nKN ) < πS (nS ) in equilibrium under perfect capital mobility

without trade as we have shown above.
The trade equilibrium is illustrated in Figure 5 by TN for North and TS for South. As
in the case of diﬀerent qualities of ﬁnancial institution, international allocation of ﬁrms does
not change with trade liberalization when capital is immobile between the two countries.
But the rental rate increases in North and decreases in South as the proﬁts for ﬁrms in therespective countries change accordingly.

23

Figure 5: The Equilibria with and without Trade (FN < FS )The equilibrium when both goods and capital are perfectly mobile is illustrated by T K,
the intersection between the two countries’ BC curves (shown in this case by dotted curves),
in Figure 5. As the ﬁgure shows, this equilibrium point is located to the right of K, theequilibrium point in the case of perfect capital mobility without international trade. That is,under perfect capital mobility, more capital is allocated in North if trade in goods has beenliberalized than otherwise. To show this important observation more rigorously, we note that
RN = RS implies from the borrowing constraint, expressed by (15), that ωN (nTNK ) = ωS (nTS K )in the equilibrium allocation of ﬁrms, expressed by the masses of ﬁrms in the two countries,
K
nTNK and nTS K . Since ωN (nKN ) > ωS (nS ) in the case of perfect capital mobility without trade,

this means that more capital is allocated to North when the countries are open to trade thanTK
< nK
otherwise so that nTNK > nK
S.
N and nS

Proposition 2 Suppose North is capital-abundant such that the wealth distribution in North
has ﬁrst order stochastic dominance over that in South. Then, trade in goods and capital
24

movement are complements in the sense that trade induces capital to be reallocated fromSouth to North.
We have shown that international trade in goods induces reallocation of capital fromSouth to North in the case where the countries are diﬀerent in their wealth distributions aswell as in the case where they are diﬀerent in the quality of ﬁnancial institution (Proposition
1 and Proposition 2). In both cases, capital movement is insuﬃcient to equate proﬁtability ofﬁrms between the two countries. In the case of diﬀerent ﬁnancial institutions, the diﬀerencein the quality attracts too much capital in North in equilibrium with a common rental rate.
Whereas in the case of diﬀerent wealth distributions, the threshold entrepreneurs are richer
in North so the equilibrium proﬁts, which satisfy the borrowing constraint, are lower inNorth than in South. Opening to trade increases proﬁts for ﬁrms in North while decreases
those in South, which relaxes the borrowing constraint in North while tightens that in South.
Consequently, capital moves out of South into North.

5

Why does ﬁnancial imperfection matter?

In order to deepen our understanding about the reason why the imperfection of ﬁnancial
institution causes complementarity between trade in goods and international capital movement, we examine the impacts of trade and capital movement in the case where the ﬁnancial
institution of either country is perfect or almost perfect such that the proﬁtability constraint
is binding while the borrowing constraint is slack, i.e., both θN and θS are so large thatRk =πk (nk )g(16)

holds for k = N, S. We assume here that North is capital-abundant, i.e., ω̄N > ω̄S to ensure
asymmetry between the two countries.
Figure 6 shows the two PC (proﬁtability constraint) curves for the individual countries.
Each PC curve is ﬂatter than the corresponding country’s BC curve as the threshold wealtheﬀect is absent here. It follows from ω̄N > ω̄S that the per-capita mass of ﬁrms is greaterin North than in South in autarky, i.e., nN /mN = ω̄N /g > ω̄S /g = nS /mS . Consequently,
25

Figure 6: The Equilibria when the Financial Institutions are Suﬃciently DevelopedA
we have πN (nAN ) < πS (nS ) and hence RN < RS in the autarkic equilibrium as illustrated by

AN and AS in the ﬁgure.
If capital is internationally mobile while goods remain immobile, capital moves from
North to South (which accords with the traditional view) until the rental rates are equated.
In Figure 6, this equilibrium is illustrated by K, the intersection between the two PC curves.
Note from the proﬁtability constraint, given by (16), that πN (nN ) = πS (nS ) in equilibrium;
the per-capita mass of ﬁrms are equated between the two countries, i.e., nTN /mN = nTS /mS ,as a result of capital movement, and so are the proﬁts for any ﬁrm between them. Indeed,
the proﬁts are equal to the free-trade equilibrium proﬁts, given by (14), sincenT
nT + nTSmn ω̄N + mS ω̄SnTN= S = N=.
mN
ms
mN + msg(17)

If countries are open to trade while capital is internationally immobile, on the other hand,the proﬁts for any ﬁrm become πw , which is given by (14). In Figure 6, the equilibrium is
illustrated by T ; it follows from (16) and (17) that the equilibrium rental rate is the same26

as the one when capital is internationally mobile while goods are not.
Now, it is immediately seen that when capital is internationally mobile, opening to trade
will not induce further capital movement, in contrast to the case of ﬁnancial imperfection inwhich it does induce further capital movement. When countries become open to trade, ﬁrms
start exporting their products to each other’s markets. But their proﬁts remain the same atπw and so does the rental rate of capital. Indeed, international trade and capital movement
are substitutes in the aspects (i) that trade eliminates an incentive for international capital
movement by equating the rental rates between the two countries and (ii) that international
capital movement equates the proﬁts for ﬁrms worldwide.10 Note, however, that despite thesubstitutability, trade is more beneﬁcial for consumers than international capital movement
since trade allows them to consume foreign varieties as well as domestic ones.
The key to understand why international trade and capital movement is complementary
only when ﬁnancial institutions are imperfect lies in the threshold wealth eﬀect. What is
important under ﬁnancial imperfection is that the pledgeable proﬁts determine the maximum
amount of borrowing, i.e., the amount of borrowing by the threshold entrepreneurs. Indeed,
the rental rate is proportional to the ratio of the pledgeable proﬁts to the maximum amountof borrowing. When countries are diﬀerent in the quality of ﬁnancial institution (i.e., θN >θS ), even if the proﬁts themselves are the same between the two countries, the pledgeableproﬁts become smaller in South. Consequently, the maximum amount that entrepreneurs canborrow becomes smaller in South, which implies that the mass of ﬁrms is smaller and hence
the domestic market is less competitive in South than in North if trade in goods is restricted.
Opening to trade will increase proﬁts for ﬁrms in North and decrease those in South, which
induces further capital outﬂow from South. When countries are diﬀerent in their wealthdistributions, on the other hand, the maximum amount of borrowing tends to be larger inSouth as there are less wealthy individuals than in North. As a result, the (pledgeable)
proﬁts must be greater in South when capital is internationally mobile (so that the rental
10

Although trade eliminates an incentive for international capital movement by equating the rental rates
between the two countries, it would not prevent capital to move from one country to another. Indeed, any
capital allocation between ON and OS in Figure 6 can obtain in equilibrium.

27

rates are equalized) while goods are not. Opening to trade beneﬁts ﬁrms in North and hurts
those in South, and capital is reallocated toward North as a result. Note that such threshold
wealth eﬀect is absent, and so is the resulting complementarity between international tradeand capital movement, if ﬁnancial institutions are (almost) perfect.

6

Discussions

6.1

Impact of ﬁnancial crisis in the NorthWe analyze here the impact of ﬁnancial crisis in North on international capital reallocation.
Financial crisis can be represented as a sudden fall in θN in this model. The analysis above
indicates that a fall in θN shifts down the BC curve for North, inducing capital outﬂow from
North to South. The amount of capital reallocation, however, depends on the slope of the
BC curve for South. Figure 7 indicates the impact of a fall in θN on the equilibrium underfree trade and perfect capital mobility. The ﬁgure depicts two cases with diﬀerent slopes of
the BC curve for South.
The BC curve for South is relatively steep in the ﬁrst case. As we can see from theborrowing constraint (15), the BC curve is steep if ωS (nS ) declines sharply with nS . This
happens when the upper-middle income class in South is thin. Individuals in the uppermiddle income class forms a pool of potential entrepreneurs. If there are not many individuals
in this pool, even a small increase of the mass of ﬁrms must be accompanied by a large decline
in the wealth of the threshold entrepreneurs.
Now, a fall in θN shifts the BC curve for North from BCN to BCN′ in Figure 7. The
equilibrium point moves on the BC curve for South, indicated by BCS1 , from point 0 to
1. Capital moves out of North, leading to the contraction of the industry in North andexpansion of that in South. The rental rate that is common between the two countries falls,
reﬂecting the deterioration of the average quality of the ﬁnancial institutions.
If the upper-middle income class in South is thick, on the other hand, capital reallocation
as a result of the ﬁnancial crisis in North is large in scale. In such cases, the BC curve forSouth is relatively ﬂat as curve BCS2 in Figure 7 indicates. The equilibrium point moves from
28

0

2

1

Figure 7: Impact of Financial Crisis in North
0 to 2, indicating that the amount of capital reallocation from North to South is greater thanthat in the ﬁrst case. The rental rate does not decrease much because the new entrepreneurs
in South are relatively rich in this case so that they can aﬀord a relatively high rental rate.
It has been documented that in recent years, the middle income class has become thicker
in emerging market economies. The capacity to absorb capital in these economies has been
increasing and the scale of potential capital outﬂow from North in case of ﬁnancial turmoil
is greater than ever.

6.2

Alternative use of capital

We have assumed that capital is used only in one industry to simplify the analysis. Here, we
relax this assumption by allowing capital to be invested elsewhere. Speciﬁcally, we introduce
an alternative investment opportunity that yields a ﬁxed return of R̄N . The alternative
opportunity may be investment to another (unmodeled) industry or purchasing a government

29

Figure 8: Impact of Capital Account Liberalization in the Presence of an Alternative Use of
Capitalbond (which is also unmodeled). We also assume that this investment opportunity only exists
in North for simplicity.
Let us consider the case in which countries are diﬀerent only in the quality of ﬁnancial
institutions and international trade in goods has already been liberalized. The relevantborrowing constraint, therefore, is given by (9).
Figure 8 describes the impact of capital account liberalization in this case. The equilibrium under free trade without capital movement is illustrated by two points, TN and TS (asthose described in Figure 3 as the equilibrium points in the basic model). We examine thecase in which an alternative investment opportunity yields the return that is greater than
the rental rate in South but is smaller than that in North before capital is allowed to moveinternationally. Capital is not invested in the alternative opportunity in the free-trade equilibrium without capital movement because the alternative opportunity only exists in Northand the equilibrium rental rate in North is greater than its return R̄N . We also focus on the30case where R̄N is greater than the rental rate given by the intersection between the two BC
curves as indicated in Figure 8
Now, we allow capital to be perfectly mobile between the two countries. If there is
no alternative investment opportunity, the equilibrium would be the one described by theintersection between the two BC curves as seen in the previous analysis. But that would
not be equilibrium because the rental rate at the intersection is smaller than R̄N so thatpart of capital would instead be invested in the alternative opportunity. Indeed, although
capital that is to create ﬁrms of the mass ON B is allocated in North, only the mass ON A ofﬁrms will operate in North.11 The remaining g × AB units of capital will be invested in thealternative investment opportunity. Capital account liberalization induces large capital ﬂight
from South. The amount of capital inﬂow into North is so large that the investment returnfrom the diﬀerentiated-good industry would fall short of the return from the alternative
investment opportunity unless some amount of capital is indeed invested outside of thediﬀerentiated-good industry.
The investment return from the diﬀerentiated-good industry is suppressed due to the
reduced eﬀective demands for capital caused by the ﬁnancial imperfection. So the actual
investment return from the diﬀerentiated-good industry may well be higher than that fromthe alternative investment opportunity, i.e., πw /g > R̄N . Indeed, it is easy to see that if
θN or θS is suﬃciently small, the BC curve for North lies below the point KT as depicted
in Figure 8 even though πw /g is greater than R̄N . In such a situation, investment in thealternative opportunity is ineﬃcient, and capital account liberalization causes excess capital
ﬂight from South such that part of capital ends up being invested in this less-proﬁtable
investment opportunity in North.

11

Recall that the horizontal axis of all the ﬁgures in the paper measures the mass of ﬁrms in thediﬀerentiated-good industry rather than the amount of capital allocated in each country. They are closely
related to each other, however, such that if K units of capital is allocated to the industry, the mass ofoperating ﬁrms is equal to K/g.

31

7Conclusion

We have shown the complementarity between trade in goods and international capital movement under ﬁnancial imperfection. We have constructed a simple model that enables us tocapture the eﬀects of international capital ﬂow within the ﬁnancially-dependent industry andto graphically illustrate the formal analysis. We have considered two cases (i) that countries
are diﬀerent only in the quality of ﬁnancial institutions and (ii) that they are diﬀerent in
wealth distributions such that there are more rich individuals in North than in South. We
have found that in both cases, trade in goods facilitates capital ﬂight from South, suggesting that this complementarity prevails even in more-general cases where the countries are
diﬀerent in both aspects.
In recent years, many developing countries and emerging market economies liberalize
capital account as well as trade in goods. It is of their central interest whether such liberalization helps develop manufacturing industries. This analysis oﬀers a caution that in
the world of ﬁnancial imperfection, capital account liberalization when countries are open to
trade in goods will entail capital ﬂight and hence shrink the manufacturing industries in suchcountries. Capital account liberalization that is not accompanied by ﬁnancial development
can cause unintended and unwelcome consequences for those countries.
Financial institution is far from perfect in most (if not all) countries. Given that conventional wisdom may fail to be valid under imperfect ﬁnancial institution as this analysis
suggests, there are still many research agendas left to be explored in this direction.

32

Appendix
A

A Cause of Financial Imperfection

Here, we present a simple model to yield ﬁnancial imperfection of the type that we havestudied in the paper. This model setting is a simpliﬁed version of Tirole’s (2006).
Let us consider a situation in which an agent tries to borrow g from a lender to ﬁnancea proﬁtable project. This project potentially generates proﬁts of π(> Rg) where R is an
exogenous (gross) rental rate. In order to complete the project successfully with a highprobability, however, the agent must exert eﬀort, which is unobservable to the lender. If
the agent exerts eﬀort, the project generates π with the probability 1. If the agent shirks,
one the other hand, the project generates π with the probability pL (< 1) and 0 with theprobability 1 − pL . By shirking, however, the agent can get non-pecuniary beneﬁts bπ, where0 < b < 1.
The agent unambiguously shirks if the entire π goes to the lender. In order to induce
the agent to exert eﬀort, therefore, the lender must abandon some of π, giving a contingent
reward w to the agent; the reward is given to the agent if and only if the project has
successfully generated π. The reward w should satisfy the incentive condition, w ≥ pL w +bπ,
where the left-hand side is the agent’s payoﬀ when she exerts eﬀort, while the right-hand sideis her expected payoﬀ when she shirks. We assume that negative rewards (i.e., penalties) are
not allowed perhaps because the asset held by the agent is limited. This incentive condition
can be written asw≥bπ.
1 − pLThe lender expects to obtain at most {1 − [b/(1 − pL )]}π if he induces the agent toexert eﬀort. Alternatively, he may set w = 0 so that he obtains the expected payoﬀ of pL π.
Consequently, the lender obtains the returns at most θπ, where{}bθ ≡ max 1 −, pL .
1 − pL
Obviously, the lender will not lend g if Rg exceeds θπ. Note that if pL is small enough, θ is33

equal to 1 − [b/(1 − pL )]. Under a developed ﬁnancial institution with a solid legal system,
non-pecuniary beneﬁts tend to be small. The parameter θ can be considered to represent
the quality of a ﬁnancial institution because θ increases as b diminishes.

34

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