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Institute of
Trade and Capital Flows:
A Financial Frictions Perspective
Pol Antras
Ricardo
J.
Caballero
Working Paper 08-06
November 2, 2007
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.M415
09 6
1
Trade and Capital Flows:
A
Financial Frictions Perspective
Pol Antras and Ricardo
November
2,
J.
Caballero*
2007
Abstract
The
classical
Heckscher-Ohlin-Mundell paradigm states that trade and capital mobility are
substitutes, in the sense that trade integration reduces the incentives for capital to flow to
capital-scarce countries.
In this paper
we show that
in
a world with heterogeneous financial
development, the classic conclusion does not hold. In particular,
in less financially
developed
economies (South), trade and capital mobility are complements. Within a dynamic framework,
the complementarity carries over to (financial) capital flows.
deepening trade integration
It also
in
South
raises net capital inflows (or reduces net capital outflows).
implies that, at the global level, protectionism
capital flows,
when
This interaction implies that
may
backfire
if
these are already heading from South to North.
the goal
Our
is
to rebalance
perspective also has
implications for the effects of trade integration on factor prices. In contrast to the Heckscher-
Ohlin model, trade liberalization always decreases the wage-rental
Samuelson
in
South: an anti-Stolper-
result.
JEL Codes:
Keywords:
E2, Fl, F2, F3, F4.
Trade, capital mobility, capital flows, globahzation, financial frictions, comple-
mentarities, factor payments, saving rate, global imbalances, protectionism.
'Harvard and NBER, and MIT and NBER, respectively. We are grateful to Arnaud Costinot, Davin Chor,
Elhanan Helpman, Kalina Manova, Jim Markusen, Roberto Rigobon, Jose Tessada and seminar participants at
Banco Central de Chile, Boston College, Brown, Connecticut, Gerzensee, Harvard, Michigan, MIT, LSE, NYU-New
York Fed, Princeton, Stanford, Vanderbilt, Virginia and the 2007 NOITS conference for useful comments. We thank
Sergi Basco and especially Eduardo Morales for valuable research assistance. Caballero thanks the NSF for financial
support. First draft;
May
11, 2007.
Introduction
1
The process
economies.
of globalization involves the integration of goods
and
financial markets of heterogeneous
While these two dimensions of integration are deeply intertwined
economics literature has kept them largely separate.
in practice, the
International trade deals with the former
while macroeconomics with the latter. In this paper we argue that such separation
when
is
not warranted
an important source of heterogeneity across countries and sectors.
financial frictions are
In particular, we show that in this context trade and net capital flows are complements in
A
financially developed economies.
account without liberalizing trade
liberalization
financially underdeveloped
is
likely to
economy that opens the
An
experience capital outflows.
can reverse these outflows. At the global
level,
less
capital
aggressive trade
a rise in protectionism
may
exacerbate
rather than reduce the so called "global imbalances."
While some of these implications may resonate with practitioners, they are
those that follow from the classical Heckscher-Ohlin-Mundell paradigm
in stark contrast
(HOM).
with
In the neoclassical
two-good, two-factor model, provided that a smaU open economy produces both goods, free trade
When
brings about factor price equalization (FPE) with the rest of the world.
international capital mobility
economy
sets a
tariff'
restored. In sum, in
on
irrelevant.
import sector,
its
HOM
becomes
By
the
same token,
if
this
a capital-scarce small open
which
triggers a capital inflow to the point at
it
happens,
FPE
is
trade and capital inflows are substitutes: trade integration reduces the
incentives for capital to flow to capital-scarce countries.
The key
difference
between our model and the
HOM one,
aside from the
dynamic aspects that
allow. us to talk about financial flows rather than just physical capital mobility,
of financial frictions.
(1997),
(1998),
Manova
of heterogeneity in financial frictions.
is
cross- sect oral heterogeneity.
system, producers in certain sectors find
in others sectors. Paraphrasing
financial infrastructure
it
close the trade channel, then
ability to
higher in rich "North" than in developing "South."
Even when operating under a common
Rajan and Zingales
than others. In
The
financial
more problematic to obtain financing than producers
(1998),
this context,
mechanisms to circumvent the misallocation
we
and many others, we highlight two dimensions
(2007),
First, there is cross-country heterogeneity.
pledge future output to potential financiers
is
the presence
Motivated by the findings of King and Levine (1993), Shleifer and Vishny
Rajan and Zingales
Second, there
is
some
sectors are
more "dependent" on
both trade and capital flows become market
of capital induced
by financial
frictions in South.
If
both physical and financial capital outflows from South become
the vehicle through which the return to savers and the sectoral allocation of capital are improved
in South. In contrast, with free trade,
it is
the reorganization of domestic production in South that
does the heavy- lifting, and by doing so raises the return on capital in South and palliates or even
reverses capital outflows.
In order to formalize these insights, in section 2
sector) general equilibrium
model
produce two homogenous goods.
countries and sectors in
tlie
we develop a standard
of international trade in
To capture the
simplest possible way,
2x2
(two-factor, two-
which firms hire capital and labor to
role of heterogeneous financial frictions across
we enrich the standard model by incorporating a
market imperfection
financial
in every other respect.
affected
We
by
The
one of the sectors, while
initially
financial friction limits the
amount
in
making the two
symmetric
sectors
of capital allocated to the sector
it.
consider the autarkic equilibrium of this simple
first
markets have to clear domestically.
economy
in
which goods and factor
In such a case, countries with worse financial institutions
feature a lower relative price of the unconstrained sector's output (since a disproportionate share
of resources ends
up being allocated
returns to capital.
If
we now allow
to this sector)
capital to
and
move
also featvue relatively depressed
wages and
across countries that differ only in financial
development, capital flows from the financially underdeveloped South to the financially developed
North.
These closed
(to trade)
economy outcomes
trade with a financially developed North.
in the unconstrained sector
when South can
are in sharp contrast to those
We show that in that case South
freely
(incompletely) specializes
and thus becomes a net importer of the output of the
"financially
dependent" sector. From the point of view of South, trade integration raises the relative price of
the unconstrained sector's output and the real return to capital. Trade does not bring about factor
price equalization
and the rate of return to capital ends up being higher
This "overshooting" follows from a depressed wage
effect:
South than in North.
in
In the free trade equilibrium wages in
the South remain depressed relative to those in North, which
when combined with goods
price
equalization (a condition absent in the closed economy), ensures that capitalists earn a higher real
return in South than in North.
Although we
initially derive
our conclusions for the case in which South
and preferences and technologies are Cobb-Douglas, we
later
a small open
is
economy
demonstrate that the complementarity
between trade and return to capital (and hence capital mobility)
is
fully general. In particular, in
a world in which countries differ only in financial development and sectors differ only in financial
dependence, trade integration reduces the gap between the real return to capital
and with
free trade, the real return to capital
is
section
we characterize the equilibrium with
capital mobility
3,
between trade and net capital inflows works
flows to the unconstrained sector in South
All the statements
flows involve
model that
is,
up
movements
to
both
and show that the complementarity
directions, in the sense that
and increases trade flows between
follow from a static
so,
we
Northern capital
countries.
model where the only possible type of capital
In section 4
our mechanism has similar implications
ownership claims). In doing
North and South,
higher in the less financially developed South. In
of physical capital across countries.
illustrates that
for flows of
now
in
in
we develop a dynamic
for financial capital flows (that
build on the overlapping-generations framework
developed by Caballero, Far hi, and Gourinchas (2007). Under the plausible assumption that neither
labor income nor entrepreneurial rents are capitalizable, our model implies that countries with
underdeveloped financial markets feature relatively low interest rates under trade and financial
autarky, but relatively high interest rates with free trade and financial autarky.
again, trade and financial capital inflows are complements in South.
illustrates the effect of trade integration
on the steady-state distribution
It follows that,
Our dynamic model
also
of wealth in the economy,
which
endogenous changes
in turn generates
Our benchmark model
financial frictions
in the tightness of the financial constraint.
isolates the effects of cross-country
on the structure
and capital
of trade
and cross-sectoral heterogeneity in
we introduce Heckscher-
flows. In section 5
We
Ohlin determinants of international trade into our static model.
relevant case in which the financially underdeveloped South
is
focus on the empirically
also relatively capital scarce
and the
constrained sector features a higher elasticity of output with respect to capital than the unconstrained sector.
Under these circumstances, we show that our main
between trade and net capital flows generally goes through and
result
is
on the complementarity
often reinforced.^
Further-
more, regardless of relative factor endowment differences and relative factor intensity differences,
our model generates a decrease in the Southern wage-rental ratio after trade liberalization:
anti-Stolper-Samuelson
Our paper
an
effect.
relates to several literatures in international finance
and international trade. Prom
the point of view of international finance, the closest models are those studying the role of financial
frictions in
shaping capital flows. These models are typically cast in terms of one-sector models,
where capital flows
the only
is
mechanism
to increase the return to capital in financially under-
developed countries. The literature highlighting
this
mechanism
is
large
and includes Gertler and
Rogoff (1990), Boyd and Smith (1997), Shleifer and Wolfenzon (2002), Reinhart and Rogoff (2004),
Kraay
et al. (2005), Caballero, Farhi
and Gourinchas (2007),
as well as the recent (working) papers
by Aoki, Benigno and Kiyotaki (2006), and Mendoza, Quadrini and Rios-Rull (2007). There
also a trade hterature
dependence
financial
emphasizing the role of the interaction between financial development and
in
shaping international trade fiows.
Kletzer (1987), Beck (2002),
Matsuyama
(2005),
Wynne
These papers, however, focus on deriving (and
(2007).
do not allow
for capital mobility.^ In
It
includes the work of
(2005), Ju
and Wei (2006), and Manova
testing) implications for trade flows
who shows
the
which comparative advan-
not driven by difl^erences in capital-labor ratios across countries. In our paper, we focus on
first
in his
and
that our second level of complementarity (from
capital mobility to trade flows) can be derived in a variety of models in
is
Bardhan and
terms of complementarities between trade and capital flows,
our paper shares with Markusen (1983)
tage
is
type of complementarity going from trade integration to capital mobility, which
framework. Another difference between Markusen (1983) and our paper
is
is
absent
that he did not
explore the role of financial frictions, which are of course central in our context.'^ Finally, in terms
of comparative statics, our extended
model with Heckscher-Ohlin elements have some
Although capital
with the specific-factors model of Jones (1971) and Samuelson (1971).
'in particular,
we show that the autarkic relative price
benchmark mode!, but also
of the forces unveiled in our
forces that
^To be
is
make
labor intensive goods cheaper in
precise, section 2 of
developed
in
Matsuyama
of the unconstrained sector
most cases) because
labor abundant countries.
(in
similarities
is
is
not
lower in South both because
of the standard Heckscher-Ohlin
(2005) includes a discussion of capital flows, but the analysis in that section
terms of a one-sector model and
is
thus more related to the international finance papers mentioned
above.
^Martin and Rey (2006) study the
flows,
which
is
absent
in
(modelled as an increaise in market size) on the
Their model empheisizes a risk-sharing rationale for capital
effects of trade integration
likelihood of a financial crash in an emerging country.
our framework.
sector-specific in our model, its allocation across sectors
Amano
erning the tightness of the financial constraint.
is
pinned down by the parameters gov-
(1977), Brecher
and Findlay (1983), Jones
(1989) and Neary (1995) study capital mobility within variants of the specific-factors model, but
the conclusions generally depend on the assumed pattern of specialization and factor mobility.
A
2
we develop our benchmark model.
In this section
paper,
Model of Trade with Financial
Stylized
we make
In order to isolate the
a series of simplifying assumptions that
our benchmark model
is static,
Frictions
we
main mechanism
in the
later relax sequentially. In particular,
imposes a specific log-hnear structure and abstracts from standard
Heckscher-Ohlin determinants of comparative advantage.
The Environment
2.1
Consider an economy that employs two factors (capital
goods
and
(1
informed
The country
2).
capitalists), a
capitalists are
1
—^
of
endowed with
uninformed
/i
oi
capitalists,
and a continuum of
K units of capital and each worker supplies
K
sector I's output, which
in
is
K/L, with a
being "informed" capital and the remaining fraction being "uninformed" capital.
All agents have identical Cobb-Douglas preferences and devote a fraction
Production
of entrepreneurs (or
one unit of labor, so the aggregate capital-labor ratio of the economy
inelastically
^
produce two homogenous
to
inhabited by a continuum of measure
continuum of measure
measure L of workers. All
fraction
is
K and labor L)
we take
Yi
=
perfect substitutes.
to:
Z{K\r{L,)'-'', 1=1,2,
where Ki and Li are the amounts of capital and labor employed
From a
of their spending to
as the numeraire:
both sectors combines capital and labor according
productivity parameter.
rj
(2)
in sector
i
and
Z
is
a Hicks-neutral
technological point of view, informed and uninformed capital are
Notice also that, for the time being, we focus on symmetric technologies to
eliminate any source of comparative advantage other than financial development.
Goods and labor markets
across sectors.
this
economy
If
is
are perfectly competitive, and factors of production are freely mobile
the capital market
is
also perfectly competitive,
straightforward to characterize. In particular, given identical technologies in both
sectors, the marginal rate of transformation
output, p,
L
is
to sector
equal to
1,
then the autarky equilibrium of
1.
It is
is
equal to
—1 and thus the
relative price of sector 2's
then easily verified that the economy allocates a fraction
and the remaining fraction
1
—
77
to sector
2.
If this frictionless
international trade and faces an exogenously given relative price p, then
it
rj
economy
oi
is
K
and
open to
completely specializes
in sector 1
if
p <
1
and completely
specializes in sector 2
if
p
>
1.
Financial Friction
2.2
We
market has a
shall assume, however, that the capital
literature discussed in the introduction,
two
effect in the
To
sectors.
we assume that the
simplify matters,
Consistently with the empirical
friction.
we assume
that financial contracting in sector 2
perfect in the sense that producers in that sector can hire any desired
equilibrium rental rate, which
Conversely, there
is
we denote by
"human
sector
capital"
(i.e.,
essential),
is
We
that only entrepreneurs
and
appeal to this complexity to justify the
know how
to
amount
of capital.
capital market friction in a stark (though standard in the literature)
are only willing to lend to entrepreneurs a multiple ^
z's
investment
is
produce
in sector 1
—
1
We
commitment
It
capture the latter
way by assuming that
of the entrepreneur's capital
dK'
=
0K,
for
lenders
endowment,
9>1.
(3)
For the purposes of this paper we need not take a particular stance on what
borrowing constraint.
their
constrained by
r<
this
(i.e.,
that because of informational frictions, producers in that
(ii)
entrepreneurs) can only borrow a limited
so entrepreneur
of capital at the
which we associate with the production
1,
process in that sector as being relatively "complex."
(i)
amount
is
S.
a financial friction in sector
following two assumptions:
an asymmetric
financial friction has
is
the friction behind
could be related to an ex-post moral hazard problem, to limited
or to adverse selection. In
Appendix
A.I.,
we develop a simple microfoundation
for
the financial constraint in a model with limited commitment on the part of entrepreneins.^
Regardless of the source of the constraint,
neurs are able to jointly allocate a fraction
i]
it is
interesting case in
Assumption
Closed
2.3
We
tion
1:
fiO
<
which
6
is
if
9
is
sufficiently large,
of capital to the constrained sector
constraint (3) does not bind and the equilibrium
more
clear that
is
low enough so that
(3) binds.
In such a case,
1.
as described above. Hereafter
then entrepre-
we
focus on the
This requires:
rj.
Economy Equilibrium
next turn to explore the autarky equilibrium of this economy. As noted above, under Assump1
the financial constraint (3) binds, each entrepreneur invests an
''a simplifying
assumption
in
our setup
is
that the credit multiplier d
is
amount
OK
independent of
5,
(of
which
{d
— l)K
Aghion, Banerjee and
Piketty (1999) provide a microfoundation for this rental-rate insensitivity in a model with ex-post moral hazard and
costly state verification. Our model in Appendix A.l can also deliver such insensitivity, but we show that our main
results are preserved in an alternative formulation in
overview of different models of financial contracting.
which 6
is
a function of factor prices. See Tirole (2006) for an
is
borrowed), and the aggregate amount of capital allocated to sector
Ki = iiOK <
Because labor can
move
freely
product, which using
across sectors,
it
is
r]K.
(4)
allocated to equate the value of
its
marginal
(4) implies
where, remember, p denotes the price of good 2 in terms of good
Prom
1 is:^
the consumer's
first
1
(the numeraire).
order condition and goods market clearing
we have
(l-77)Z(/x0Ar(il)'"-"=P7?Z((l-^0)/^)°(L-Ll)l-^
which together with the labor market condition
Li
(6)
in (5) implies that
=
rjL
and
(7)
a
where the inequality follows again from Assumption
As indicated by equations
(4)
and
(7), in
1.
our benchmark model financial frictions do not distort
the allocation of labor across sectors but shift capital to the unconstrained sector (sector
result, sector 2's
output
is
"oversupplied" and
its
relative price
p
is
down by
labor and uninformed capital (in terms of the numeraire) are pinned
in the
unconstrained sector, which using
As a
depressed.
Financial frictions also have significant effects on equilibrium factor prices.
marginal products
2).
The rewards
to
the value of their
(8) yields:
and
,9(i-,)^^/M?^r-'
,j„)
Note that both
Other things equal,
w
and
5 are increasing functions of the degree of financial contractibility 9.
less financially
developed economies feature depressed wages and depressed
returns to uninformed capital.
The
effect of
a
fall in
9
on the rental rate of uninformed capital
is
clear:
the tighter borrowing
constraint reduces the availability of this type of capital in the constrained sector, thus increasing
^This imposes that entrepreneurs invest
all
their
endowment
of
K
in sector 1.
But
the equilibrium since, as we will see shortly, they can always obtain a higher return
in
this
is
necessarily a feature of
that sector.
the capital-labor ratio in the unconstrained sector and reducing
sector 2 output
(i.e.,
reducing
rental 5 drops with the
I's
fall
5/p).^^
Because the relative price p
in 6 not only in
terms of sector
its
is
marginal product
an increasing function of
output but also
2's
terms of
in
in
0,
the
terms of sector
output.
The changes
in sectoral capital-labor ratios are crucial for
6 on the remuneration of workers. Wages
the capital-labor ratio in that sector
capital-labor ratio rises in sector
2,
is
lower
we have
when
that
understanding the
terms of sector
fall in
9
w/p
is
lower.
1
one can show that the real purchasing power of wages, that
is
a
fall
in
output (the numeraire) because
By
the same token, and since the
with the decline in
rises
effects of
w/p^~'^
,
falls
0.
All in
all,
however,
with a decline in 6 J
This discussion hints that uninformed capital suffers disproportionately more from a low value
of
6.
In order to see this formally, notice that (9) and (10) imply that the wage-rental ratio
w
[I
6
is
decreasing in
6.
In sum, labor
is
- a) {I - iiO) K
a(l-^)
L
hurt by the financial constraint but less so than capital because
the capital-labor ratio rises in sector
2, offsetting
the
downward pressure on wages due the
decline
in p.
So
far
we have been
frictionless
silent
on the return obtained by entrepreneurs
informed capital). In the
(or
economy, informed and uninformed capital are perfect substitutes and both obtain a
common rental
rate
S.
However, when the borrowing constraint
(3) binds,
informed capital becomes
and entrepreneurs obtain a premium over the return
relatively scarce in sector 1
investors in that sector. In particular, their return per unit of capital
of
is
R^6 + Xe,
where A
is
uninformed
(11)
the Lagrange multiplier corresponding to the financial constraint (3).^ In equilibrium,
the marginal product of capital in the constrained sector
1
needs to equal 6
+
X,
from which we
obtain:
which
is
strictly positive
of entrepreneurial capital
(11),
is
1)
and
also decreasing in 6. Hence, the
whenever the
it is
shadow value
higher in economies with less developed financial markets. Note from
however, that this does not imply that the welfare of entrepreneurs
in 6. In particular,
in
(under Assumption
is
necessarily decreasing
straightforwajd to verify that entrepreneurs would always favor an increase
initial 9 is
low and a
is
large enough.
^Note that 6/p = aZ ((1 - /.t^) K/ ((1 - r?) L))""' is increasing in 9.
'This follows from the fact that w/p^~^ cc {ij.9)'"' (1 - ^5)°'''^'' which is increasing in 9 under Assumption 1.
*The return R follows from R = 9(5 + X) — (9 — \)5. Notice that the fact that R > S justifies our assumption above
that entrepreneurs invest all their endowment of capital in sector 1. Furthermore, given that we have constant returns
to scale in all factors, the Lagrange multiplier A would be common to all entrepreneurs even if their endowments of
were not identical. This feature will become useful in the dynamic version of the model.
,
K
Finally,
because
all
agents in the economy share identical preferences, aggregate welfare
by total income in terms of consumption
units.
That
wL + 5{l-
Using the expressions above,
as argued above
is
it is
attain higher welfare levels.
We
fj.)K
+ RfiK
U
is
proportional to w/p^~'^, which
sum, economies with more developed financial systems
summarize our
results as follows:
Proposition 1 In
the closed
following effects:
raises the relative price of the unconstrained sector, the real return to
it
capital, real wages,
economy
and welfare;
it
given
is
straightforward to check that
strictly increasing in 6. In
is
equilibrium, an increase in financial contractibility 9 has the
lowers the wage-rental ratio, and
it
uninformed
has an ambiguous
effect
on
entrepreneurial income.
Open Economy Equilibrium
2.4
Consider now a situation
in
which the economy we are studying, which we
refer to as South,
we
to international trade with the rest of the world (or North). For expositional simplicity,
for
p.
now on
the case in which South
As we show
later,
small, in the sense that
is
it
it is
South and
our substantive implications do not depend on this assmnption.
2.4.1
p>
<
We
think of
same production technologies
in sector
Later, however,
1.
focus
we
1.
For these reasons,
briefly discuss the case in
I.
Trade and factor payments
As argued
at the
end of section
specialize in the production of
this
which p
natural to focus on a situation in
which
though smaller,
also facing a financial friction,
open
faces a fixed world relative price
the rest of the world as having the same preferences in (1) and the
in (2) as
is
2.1,
good
whenever p <
1.
a
1,
frictionless small
South would
However the borrowing constraint
like to fully
in that sector prevents
by hmiting the aggregate allocation of capital to that sector to be no larger than p,6K. Thus,
the distribution of capital across sectors
is
identical to that in the closed economy.
Conversely, the allocation of labor across sectors
in goods.
Condition
(5)
is
affected
by the access
to international trade
equating the value of the marginal product of labor across sectors
still
needs
to hold in equilibrium, but the allocation of labor no longer needs to be consistent with goods market
clearing as dictated
in the model:
it
by equation
(6)
above. This
is
the distinguishing effect of international trade
detaches the allocation of factors across sectors from local
demand
conditions.
Instead, South faces an exogenously given relative price p, and thus (5) yields
^
The amount
{i-fi9)p^/»
+ fie'
of labor allocated to the financially constrained sector
^
1
is
'
decreasing in p and
increasing in
Intuitively, a larger
9.
thus pulling labor away from sector
to the unconstrained sector
2,
p
1.
raises the value of the
marginal product of labor in sector
amount
Similarly, a lower 6 increases the
Li coincides as well with the autarky allocation,
i.e.,
=
Li
allows South to face a less depressed relative price p, South
unconstrained sector
The
2,
of capital allocated
thus again raising the marginal product of labor in that sector.
the world relative price p happens to coincide with South's autarky price
When
equation (8)), then
(in
But when international trade
tjL.
tilts
2,
the allocation of labor toward the
thus specializing in the less "financially dependent" sector.^
equilibrium rewards to labor and uninformed capital are again pinned
and
ginal products in the unconstrained sector, which using (4)
down by
(13) can be expressed
their
mar-
as:
w^{i-a)z(({i-^ie)p"^ + iMe)^X
(14)
and
= aZp"''[({l-,l6)p'/- + ^ie)^X
5
It is
p.
A
w
straightforward to verify that both
larger
p
and
(15)
.
5 are increasing functions of the relative price
raises the incentive to shift resources to the unconstrained sector.
the financial constraint in sector
first
order condition for capital in sector
1
in
we have
terms of sector
is
strictly decreasing
mp}^
of labor
Another way
and
(16)
In sum, by allowing South to specialize in the sector with lower
is
by studying the
effect of
an increase
capital-labor ratios.
As shown above, an increase
reduces KilL2-
then clear that the marginal product of labor in sector
in
p reduces L\ and thus
the marginal product of capital in sector 2 (and hence
follows immediately that 5
is
also increasing in p.
in sector 2 leads to a fall in the
fall
of w/p),
it is
underdevelopment
capital.
to understand this result
It is
output.
,
financial frictions, international trade reduces the negative impact of financial
on the rewards
I's
(after replacing 5 in it)
A=(l-//")az(((l-M^)pi/" + Me)^)"
which
shift relaxes
and consequently reduces the premium remuneration obtained
1,
by entrepreneurs, and increases the remuneration of labor and capital
Formally, from the
This
(5/p)
And
in
p on the sectoral
increases
1
Ki/Li and
(and hence w) and
both increase when p increases.
straightforward to show that the real wage w/p^~^''
'Although we have assumed that South
which the financial
is
then
while the decrease of the capital-labor ratio
marginal product of labor in terms of that sectors' output
also apply to the case in
It
is
(i.e.,
a
strictly increasing in p.
relatively financially underdeveloped, the expressions in this section
friction
is
lower
in
South. In the latter case, however, trade integration
leads to a decrease in p in South.
'"in fact, the total return to entrepreneurial capital
(15)
is
necessarily decreasing in p as well.
and (16) to obtain:
R = 5 + \e=
which
is
(e
-
{0
-
i)?'^"^
az U{i -
strictly decreasing in p.
10
ij.e)p'^''
+
fie'^
^^
To
see this, use equations
Finally, note also that the wage-rental ratio
w _ (l-g) ((l-Mg)p^/° + Mg)
a
5
is
pi/"
strictly decreasing in the relative price p.
capital
more than workers. The
w/S has
capital to sector 2, so
Given equations
(14),
(17)
'
This implies that an increase in p benefits uninformed
straightforward: as p rises, sector
is
new
and
we can
(17),
an increase
is
common
in the
relative price
p but have
also study the effects of
different values of 9 (e.g..
autarky equilibrium we established that
decreasing in
case that an
0.
Our
first
releases labor but not
observation
is
economy with a low value
an improvement in
on equilibrium factor prices. These comparative
in 6,
statics are useful in characterizing the cross-section of factor prices across
a
1
workers.
effect
(16)
(15),
financial contractibility, that
L
to fall for sector 2 to absorb these
The depressed wage
2.4.2
logic
A"
w
and
5
economies that trade at
North and South). Remember that
were increasing
in 6,
that in the free trade equilibrium
it
w/5 and A were
while
can no longer be the
both depressed wages and a depressed
of 9 features
real
return to uninformed capital. In particular, the zero profit condition in sector 2 ensures that
'-"
5{9)Y fw{9y
VI-
a y
where the right-hand
the case that 5
is
side
is
the unit cost in sector
decreasing in
it
high-0-
K/L, under
North
if
w
is
increasing in
9,
then
economy with a lower
must be
it
is
indeed
9 features higher rates of return to
has depressed wages.
The depressed wage
labor ratio
Hence,
Inspection of equations (14) and (15) confirms that this
9.
the case.^^ Put differently, a small-open
capital "because"
2.
follows
from the
fact that,
even holding constant the aggregate capital-
free trade the capital-labor ratio
in both sectors (thus
both
w
and w/p axe lower
with aggregate endowments because South specializes
intensive due to the financial constraint in sector 1.^^
local proof of the effect of
is
an increase in 9
in the
To
lower in the low-0 South than in the
in South).
this
is
unconstrained sector which
see this
more
open economy (that
in the
Note that
consistent
is
capital-
formally, let us develop a
is,
of a
North that has an
infinitesimal financial advantage over South).
We
can decompose the aggregate capital labor
sectoral capital-labor ratios, k\
= K\/Li
and
/c2
ratio, k
=
= K/L,
into a weighted average of the
K2IL2, with weights
i/^i
= L\/L
and
1
—
Vi,
respectively:
ip^ki
+
(1
-
'0i)A;2 == k.
we find that A in equation (16) is decreasing in 6.
Of course, if we instead have a situation where North has a higher aggregate capital-labor ratio, then the depressed
wage result can hold even when the constrained sector's technology is relatively capital-intensive. We return to this
"Similarly,
'^
generalization later in the paper.
11
Total differentiation of this expression yields:
(/C2
Note that the left-hand
toward sector
1 {dipi
than sector 2
(fci
dk2
>
side of (18)
0)
/C2).
=
ki)di)-^
is
tp^dki
+
(1
-
and because the
financial constraint
(18)
associated with specialization
is
makes sector
1 less
Because the value of the marginal product of labor
(p
is
and hence wages are higher when 9
is
is
capital intensive
equated in both
held constant in the exercise), and this sign must
be positive to match the sign of the left-hand side of
0,
i/'i)rf/c2.
positive because a higher 9
and dk2 must have the same sign
sectors, dki
clearly
<
>
-
higher.
(18). In
sum, we have that dki
>
and
^'^
Trade Integration with a More Financially Developed North
2.5
In this section
large
North
we study more
(or rest of the world). In order to isolate the role of financial
trade flows,
we assume that North
development (and
financial
developed.
systematically an equilibrium in which South can freely trade with a
We now
is
We
scale).
identical to
developed North, pins
down
> 9^
in section 2.3 to
so that North
is
more
financially
conclude that this large, financially
the following world relative price
N
?^"
Note that because p^ <
in shaping
in every respect except for the level of
9^'
assume that
shall
can use the analysis
South
development
1,
-
I
I
l-'d" (1
"f " J[
vii-f^e
I
<1-
(19)
both North and South produce both goods
in equilibrium.
The more
developed financial system in North implies, however, that South has a comparative disadvantage
in the constrained sector
1.
Using equations
(2), (14), (15), (16)
and
(19),
we can express imports
of sector I's output in South as
>0,
^(1-Mn
V
J
y
(i-M^^)|S^+M^^y
where the sign follows from 9^ > 9^
Despite the fact that there
attain, since factor prices were
ment
is
diversification in production, factor price equalization does not
shown above
to
depend on the particular
in the corresponding region. Furthermore,
level of financial develop-
from the derivations above, we have the following
result:
'^In our
benchamark Cobb-Douglas model there
anism: In this economy the share of labor
However,
this share
for
is
a given p
<
1,
is 1
—
is
wages are proportional
output increases with the share
increasing with respect to
wage mechoutput (productivity).
and we have shown that
a straightforward alternative proof of the depressed
a, hence
d.
12
to aggregate
of factors allocated to sector
1,
Proposition 2 In
the free trade equilibrium, South produces both goods
"financially dependent" good
and
1.
and
is
a net importer of the
Furthermore, free trade does not result in factor price equalization
leads to
w^ > w'
The
results
features a lower
to informed
it
9.
must have a
A^
<
X'.
North and South share a
relatively lower
and uninformed
Using the results
is
5'
common
relative price
must
allocate a disproportionate
wage
rate,
and
it
with respect to
statics
it
Hence, relative to North,
must feature a
p^ but South
,
amount
of labor
relatively larger return
capital.
in section 2.4,
of view of the South. This
which
<
on the ranking of factor prices follow from the comparative
9 derived in the previous section.
to sector 2,
5^
we can
amounts
to
also study the effects of trade integration
comparing the autarky and
in turn analogous to describing the effects of
open economy equilibrium since 9
>
implies p'^
9
an increase
>
from the point
free trade equilibria in South,
in the relative price
p^, where p^
p
in the small
the autarky relative price in
is
South. As demonstrated in the previous section, this increase in p shifts labor to the unconstrained
sector 2 and raises the real return of uninformed capital in terms of both goods. This positive effect
of trade integration on the real return to capital
and
capital mobility discussed below
Proposition 3 Trade
and hence
is
at the core of the
it is
complementarity between trade
worth restating
it
in the
form of a Proposition:
integration raises the real return to uninformed capital in the financially
underdeveloped South.
As discussed above, trade
integration
(i.e.,
an increase
in p) also raises real
wages in South but
reduces the wage-rental ratio and the return to entrepreneurial capital. Overall, however, one can
show that aggregate welfare
in
South
is
necessarily higher in the free trade equilibrium (see section
2.6.E. for a general proof).
2.6
Robustness and Generalizations
Even though we explore a generalized version
comment on
of our
model
later in section 5, here
we
the robustness and generality of the results stated in Propositions 2 and
briefly
3.
This
discussion helps understanding the mechanisms behind our results.
A.
We
No
Financial Constraints in North
focused above on the case in which North sets a world relative price p lower than
1.
This
is
the natural case to consider in a world in which countries are fully symmetric except for financial
development and the inequality fi9^ <
i]
(analogous to Assumption
13
1)
holds.
Suppose instead
that financial contracting in North
and
a value of A equal to
is
sets a world relative price of
South again (incompletely) specializes
>
not a constraint so that ji9^
p
=
Then, North features
ij.
In the free trade equilibrium,
1.
in the unconstrained sector,
but trade brings about factor
price equalization. In this case, free trade again raises the equilibrium values of the real return of
uninformed capital
The
in South,
but 6
does not "overshoot" the Northern rental
case in which the North sets a relative price higher than
South completely
down by
specializes in sector
2,
relative price
In terms of the results above,
that even
when p >
1
p >
=
0.
Factor prices are piimed
In that case, however, factor prices depend
2.
variables, so factor price equalization generally
on the exact source of the
can be studied analogously. The
which necessarily implies A
the value of their rriarginal values in sector
on Southern
1
5^
fails.
The
direction of failure depends
North.
1 in
we thus have that Proposition
we have that trade and net
3 continues to hold,
complements
capital inflows are
Henceforth, we focus on the case where the financial constraint
is
which implies
binding in North
(i.e.,
in South.
p <
1).
B. General Symmetric Technologies
As shown
in
Appendix A. 3., Propositions
2
and
3 continue to hold
we
if
relax the
Cobb-Douglas
assumptions and assume general homothetic preferences and general symmetric production functions with constant returns to scale
and diminishing marginal products. The key three equilibrium
properties that ensure the generality of the results are as follows:
is
always increasing in
capital intensity
2.
The
is
9;
(b) the real return to
(a)
uninformed capital
the autarky relative price p
is
always increasing in p;
necessarily lower in the constrained sector 1 than in the unconstrained sector
generality of (a) implies that trade integration
which together with
(b) implies that
is
associated with an increase in p in South,
Proposition 3 holds for general symmetric production tech-
nologies. Condition (c) in turn ensures that with free trade the rental rate
in
North (Proposition
2).
Furthermore, property
the financially dependent sector
We
(a) also implies
is
that South
higher in South than
is
a net importer of
1.^"*
can thus conclude that whenever countries
differ only in financial
differ only in financial
development and sectors
dependence, South specializes in the least financially dependent sector, trade
integration raises the real return to capital in South and, with free trade, this rental rate
in
South than
(c)
in the
more
financially developed North.
is
larger
^''^
''This follows from the fact that, with homothetic preferences, the consumption ratio C1/C2
in South is larger in
and thus the production ratio
Y1/Y2 in South is lower in free trade than in autarky. Because consumption and production are equal in autarky and
trade balance must hold in the trade equilibrium, with free trade we must have Ci > Y\ and C2 < 5^2''Conversely, the beneficial effect of trade liberalization on real wages that we obtained in the log-linear model
is not general.
Although Southern wages in terms of sector 1 output always increase with p, once we relax our
Cobb-Douglas assumption, the purchasing power of these wages may or may not increase in p depending on demand
free trade
than
in
autarky.
On
the other hand, the increase in p shifts labor to sector
patterns.
14
2,
A
C.
We
Large South
have so
(19).
far treated
North as a large enough country to
identical to that of
is
two "small" open economies facing a
If
technologies, the equilibrium relative price
Southern and Northern autarkic relative
prices.
The
relative price
clearing at the world
prices:
p^ < p < p^
.
Hence,
p has to
it is still
The reason
the statements in Proposition 2 continue to hold.
common p
and thus cross-sectional comparisons
in equilibrium,
is
between the
fall
the case that trade
integration increases the real return to uninformed capital in South (Proposition
a
in equation
countries differ only in financial development, then for general homothetic preferences
and symmetric production
all
p^
common
now ensure goods-market
with the additional restriction that p should
level.
world prices at
Suppose instead that both North and South are large enough to impact world
equilibrium
p,
fix
Furthermore,
3).
that both countries share
still
follow from studying the
comparative statics with respect to 9 holding p constant.
A
D. Adding Heckscher-Ohlin Features:
What happens when we
Preview
introduce cross-sectional asymmetries in factor intensity as well as cross-
Perhaps surprisingly, we show
country asymmetries in relative factor endowments?
(see also
Appendix A. 3) that an increase
return to uninformed capital.
an increase
p
is
always associated with an increase in the real
Hence, in situations in which trade integration
in the relative price
p
in
South
development and
their level of financial
in
9
>
is
associated with
would be the case when countries
(as
9
in section 5
),
differ
only in
Proposition 3 continues to hold for general
asymmetric production technologies. This leads us to conclude that the complementarity between
trade integration and net capital inflows in South
is
quite general (see section 5 for details).
Consider next the generality of the ranking of factor prices derived in Proposition
whenever both North and South produce good
2.
Note that
2 in equilibrium, the zero-profit condition in that
sector ensures
p
where
C2 ()
is
Hence, unlike
w^ > w^
sector
2,
=
C2
{5^,w^) for j
a general neoclassical unit cost function and
in the autarkic
or 6
we must
>
6
.
On
is
thus increasing in both arguments.
it
must be the case that
either
the other hand, for a general constant returns to scale technology in
also have that
/ I<^j\
ioTJ
(•)
is
(20)
equilibrium case, with free trade
„..7
where &
^ N,S,
=
N,S,
necessarily increasing in i<'2/-^2- Equations (20)
ranking of factor prices
is
(21)
and
(21)
combined imply that the
necessarily as derived in Proposition 2 provided that North operates
the technology in the unconstrained sector 2 at a higher capital-labor ratio than South does,
15
K^ 1^2 > K2/L2, which
is
an empirically
likely scenario.-^'' In section 5
below, we show that for
general asymmetric production functions, this condition holds provided that North
capital
abundant
may be
Model
apparent to the savvy reader that in the region of the parameter space in which financial
constraints bind, our
fact,
we next
model behaves similarly to a two-sector, three-factor
discuss a perfectly competitive three-factor
This
as our model.
will
We
between our framework and a standard
and entrepreneurial (informed)
capital
in sector 2
important differences
also argue, however, that there are
specific-factors model.
now
let
uninformed capital
be distinct factors which are imperfect substitutes
in pro-
combines uninformed capital and labor according to a standard
neoclassical production function: Y2
capital,
model. In
model that features the same equilibrium
Consider a model analogous to the one we developed above, but
Production
specific-factors
prove useful in understanding the mechanics of the model and also in
proving some general welfare results.
duction.
sufficiently
relative to South.
E. Relationship with the Specific-Factors
It
is
=
F2
ij-i^ '^"i)-
uninformed capital and labor according
Production
in sector 1
combines informed
to
Yi=Fifemin|/<^^|,LiV
where Fi
is
in
Assuming that
again a standard neoclassical production function.
perfectly competitive, this
model
yields equilibrium allocations
(22)
and factor prices
our model whenever the endowments of informed and uninformed
and
(1
—
/i.)
K,
respectively.
all
markets are
identical to those
capital are equal to fxK
Because the allocation of the two types of capital to each sector
is
independent of factor prices, the model behaves similarly to a standard specific-factors model in
which 9 governs the
effective relative
supply of the two types of factors to each sector.
Note, however, that there are important differences between our model and the specific- factors
model.
First, the specification in (22)
is
not imposed in an ad hoc manner, but
credit constraints. Second, the financial constraint
capital
to
may move more
move with
it).
easily across borders
Third, as
is
apparent in
mechanism
also sheds light
than informed capital
(22), the
parameter
(it
it
follows from
on why uninformed
does not require individuals
6 not only affects the allocation of
capital across sectors, but also operates as a sector-biased technological parameter in sector 1.^^
As a
result of these features, our
advantage as well as
integration.
model provides sharp predictions
for the incentives for capital to flow across
for the pattern of
comparative
borders with and without trade
Conversely, in the specific-factors model one could obtain just about any pattern of
'^As we showed above, with symmetric production technologies, K^ /L2 > Ki /L^ is ensured by the fact that
North specializes in the constrained sector 1, which operates at an inefficiently low capital-labor ratio.
''Hence, an increase in d is not isomorphic to a simple increase in K' and a commensurate decrease in
For
instance, in a specific-factors model with Cobb-Douglas technologies in both sectors, an increase in K' and a decrease
in K'^ would necessarily decrease the autarky real return to K' and increase that of K'^
This contrasts with our
K
.
result that an increase in 8 can in fact increase the real return to both types of capital.
16
.
comparative advantage and factor mobility by appropriate choices of the endowments of each type
of capital as well as their assumed ease of mobility across borders.
However, the most useful aspect of the analogy with a specific-factors model
terms of
in
is
We argued above that in our benchmark model with Cobb-Douglas preferences and
welfare analysis.
technologies, welfare in South rises
when moving from autarky
The mapping between
to free trade.
our model and a perfectly competitive three-factors model has the implication that this welfare
gain result continues to hold for general (well-behaved) preferences and technologies. Furthermore,
when both North and South
are large, North also gains from trade liberalization with South.
Trade and Capital Mobility as Complements
3
As usual
move
we have studied scenarios
in international trade theory, so far
across countries, but factors of production cannot. In this section
in
we
which goods can
freely
consider the implications
Following the lead of Mundell (1957), we study the
of allowing for physical capital mobility.
interaction of capital mobility and trade integration by comparing the incentives for capital mobility
with and without trade
For simplicity, we develop our results within the log-linear model
frictions.
developed above, but the discussion
more
in section 2.6
should make
it
clear that our
main
results are
general.
Capital Mobility with Prohibitive Trade Frictions
3.1
Consider
first
the case with trade frictions.
the numeraire sector
1
is
mobility, the equilibrium
costless,
is
but trade costs
in sector 2 are prohibitive.
then as described in section 2.3 above.
good, South cannot specialize in
its
From equation
to the autarkic one.
In particular, consider a situation in which trade in
With
Without
it is
one
free trade in just
comparative advantage sector and the equilibrium
(10),
capital
is
then clear that in such a case we have 5
identical
>
6
.
In
words, despite both countries sharing the same aggregate capital-labor ratio, the marginal product
of capital
If
to
is
higher in North than in South.
we then
move
their
allow for physical capital mobility, uninformed capitalists in South have an incentive
endowment
net import of good
in
1
of capital to North.
South
in
exported from South to North. ^*
to flow to
is
North
cumbersome
implicitly given
an amount
The counterpart
The amount
in order to ensure that 5
to compute, but using (5)
of this flow of capital
equal to the rental
payments
is
a positive
of the capital stock
F^'^^ that needs
of non-entrepreneurial capital
converges up to the (unaffected) Northern rental 6
and imposing goods-market
clearing,
we
find that
it is
by
l-a
(^{l-^,e^)rJ-{rJ
+ a{l-rJ))^y[l-^,9'-{l + a{l-v))^y~\e N
1.
1
The assumption
\vO^
that rental payments are settled in sector
2 prices are equalized,
reason
- M^^
we
for this is that in
still
1
output
is
not important. In the case in which sector
obtain that the rental rate for uninformed capital
autarky both 5 and 5/p are increasing
17
in 0.
is
lower
in
South
in autarky.
The
F^^^ /K
Note that
is
necessarily increasing in
9^ and decreasing
in
9^
Hence,
.
larger the
tlie
difference in financial contractibility, the larger the share of Southern capital that flows out to
North. ^^ As a counterpart of this capital flow, South imports good
1 in
an amount
Mf = S^F^^^
This result bears some resemblance to those derived in the literature arguing that financial
tions
may
fric-
help explain the Lucas (1990) paradox (Gertler and Rogoff, 1990, Shleifer and Wolfenzon,
Kraay
2002, Reinhart and Rogoff, 2004,
To the extent that
et al., 2005).
capital-scarce countries
why capital
also are financially underdeveloped, our closed-economy equilibrium can help rationalize
does not flow to those countries.
Notice that we have restricted our analysis to the case involving mobility of uninformed capital.
Because the return to informed capital varies across countries, there might be an incentive
capital to
move
differentials,
when
the
as well. Notice, however, that in order to arbitrage
it is
not sufficient for entrepreneurs to simply
movement
of capital
is
will
for
that
capital return
their physical capital abroad.
accompanied by a movement of entrepreneurial
governance or of the entrepreneur himself,
ability,
Only
corporate
the latter be able to capture some of the return
In practice, the costs involved in the
differential.
move
away informed
movement
outweigh the costs of pure physical capital mobility.
that the effect of 6 on the return to informed capital
may
of these additional factors
far
Regardless, of these considerations, notice
is
ambiguous
and hence
(see Proposition 1),
We
the direction of capital flows under autarky are in general be ambiguous.
briefly return to this
issue in the conclusion.
No
Capital Mobility with
3.2
We next
Trade Frictions
both goods. Conceptually,
analogous
consider the case in which there
is
free trade in
to considering a situation in which there
is
substantial heterogeneity in financial dependence across
the set of goods that are traded in world markets.
we derived above then
indicates that 6^
>
The
6^:
aggregate-capital labor ratio, the return to capital
move
allow uninformed capitalists to
their
this
is
equilibrium without physical capital mobility
even though both countries feature the same
is
endowment
higher in South.
then follows that
It
across borders, capital
if
we
moves from North to
South. Furthermore, because the allocation of capital to the constrained sector in South
is
bounded
above by ^9^K, Northern capital flowing to South only increases the amount of capital employed
in sector 2.
Using equations
equalization
is
now
(5), (10),
and
(15),
(19), the exact capital flow required to
given by
F^^5 _
K
and again vanishes when 6^ -+ 9^
share a
^'if
common
South
is
ensure rental rate
relative price
.
{v
-
119^) [9^
-
9^)
'
0^(1-7?)
Importantly, because the capital flow makes both countries
p and a common rental rate
(5,
wages
w
and the shadow
price A
large enough, this (physical) capital flow has a non-negligible effect on the rental rate 5'^ in North.
In such a case, the required capital flow
F^^^
continues to be increasing in 6'^ /Q^ but
(relative to South's capital).
18
it
is
quantitatively smaller
are also equalized across countries. Hence, as in the classical Heckscher-Ohlin-Mundell model, free
good and factor mobility lead to factor price equalization. The main
difference
is
that our model
requires both types of mobility for equalization to take place.
Our
show
results
from the point of view of South, trade integration and capital inflows
that,
Only when trade
are complements.
capital inflow into South.
is
sufficiently free,
This complementarity
does allowing
reinforced by the fact that the capital inflow
is
South further increases trade flows between North and South.
into
As argued
first.
before, the financial constraint in
amount
flowing to South can increase the
of capital
we can show
In particular,
that capital mobility increases consumption but reduces production of good
production
mobility lead to a
for capital
in South.
1
Consider
South implies that Northern capital
employed only
capital inflow increases the marginal product of labor in sector 2,
in sector 2.
As a
result, this
which leads (by equation
(5)) to
a relocation of labor towards that sector. In sum, the Southern allocation of labor to sector
lower than without capital flows and hence production of sector
other hand, consumption in that sector
Southern income
rises
towards the
is
I's
output
falls in
South.
On
1 is
the
proportional to income, and capital mobility ensures that
level of
Given these
Northern income.^''
results,
we conclude
that capital mobility leads to an increase in trade flows between North and South.
The complementarity between trade
flows
and
capital mobility in our
model
is
in
sharp contrast
with the substitutability present in the standard Heckscher-Ohlin model. As shown by Mundell
(1957), in that
model trade
frictions generate incentives for capital to flow into the capital-scarce
South, while a move toward free trade leads to factor price equalization and therefore eliminates
the incentive for capital to
move
prices, trade integration induces a
to
move
Even when trade does not
across countries.
fully equalize factor
convergence of factor prices and reduces the incentive for capital
across countries. Hence, in the Heckscher-Ohlin-Mundell world, trade and capital mobility
are substitutes.
3.3
Capital Mobility with Intermediate Trade Frictions
The above
results suggest that the real effects of allowing for capital mobility crucially depend,
on the extent of trade integration. In
with intermediate trade
numeraire good
1
that a fraction r e
2, this is
is
frictions.
In order to do
of the
good
is
2 is subject to
friction is in sector
tariff
Because
by considering cases
this insight
we again maintain
lost in transit.
formally equivalent to North levying a
have assumed that the trade
we formalize
so,
but that good
freely tradable,
(0, 1)
this section
the assumption that the
an iceberg transport cost such
in equilibrium
South exports good
on Southern imports. Alternatively, we could
This would lead to identical expressions, but the
1.
trade friction would then have analogous effects to an import tariff levied by South (with the
tariff
revenue being wasted). In either case, we can think of reductions in r as reduction in transportation
costs or as trade liberalizations.
Given our assumption that South
in
""The
South
fact that
is
Southern income
is
a small open economy, the trade friction amounts to South-
rises follows
increasing in the relative price
p,
from the
fact that, in the
and North features a higher
19
small-open-cconomy equilibrium, income
relative price p'^
>
p.
ern producers facing relative prices equal to p
—
(1
not prohibitive and
is
and
fall in
between the
free trade
Because the trade
and autarky
friction r has a
- Paut/v^
1
as
,
continues to be the case that South
it
sector 2's output. Values of r between
As long
Q
35
the trade friction
r) rather than p^.'^^
is
a net exporter of
represent levels of trade integration that
levels.
monotonic
because the rental rate to uninformed capital
on the
effect
relative price
p faced by South, and
increasing in this relative price p,
is
we obtain the
following result:
Proposition 4 There
T
< f we
have 5
exists a
<
S
level of trade frictions
> f we have
while for t
,
<
migrates South when r
unique
f and North
if
>
t
>
S
r 6
6
(0, 1
Paut/P^) such that for
Consequently, (physical) capital
.
<
Furthermore, df/dO
f.
—
0.
Proposition 4 summarizes the sense in which trade and capital mobility are complements in our
model. The particular value
for the threshold integration level
but applying the implicit function theorem to
namely that df/d9^ <
amount
0.
(15),
In words, the lower
we obtain
financial
is
f cannot be derived in closed form,
the last statement in the Proposition,
development in South, the lower
of trade integration needed to ensure that capital flows into
mobility.
The reason
that the wage
is
is
more depressed
South when
the
is
allowing for capital
in regions with less developed financial
markets.
Finally
it is
worth mentioning that with positive trade
frictions,
it
is
no longer the case that
trade integration and free physical capital mobility necessarily lead to factor price equalization.
Even when the
direction of capital flows
is
from North to South, the presence of trade
frictions
ensures that wages in South remain depressed.
Trade and Financial Capital Flows as Complements
4
Up
to
now we have
studied the interaction of financial frictions and trade integration in shaping
the desired location of physical capital.
there
is
an incentive
We
for physical capital to
concluded that when trade frictions are significant,
migrate from the financially underdeveloped South to
the financially developed North, while the opposite
distinct issue
is
that of capital ownership.
this question requires to
capital fiows, which
'If
is
in sector 1,
A
related but
capital located in each region?
Answering
true
owns the
model the implications
what we do
the trade friction was
Who
is
when
trade
is
frictionless.
of our earlier analysis for portfolio decisions
in this section.
and
-^^
then Southern consumers would have to pay a price 1/ (1 — t) when importing
1 in North). The relative price of sector 2's output would
the good (since Northern producers can obtain a price of
again be p'^
^^
(1
Since there
—
r).
is
no concept of
risk
and hence of
diversification in our model,
capital flows.
20
we focus only on net but not
gross
By modeling
the net capital flows implications of our view,
we
are also able to connect with
the "global imbalances" literature, which attempts to explain the large capital flows from South
to
North observed
The main conclusion
in recent years.
that emerges from the analysis below
is
that protectionism, an increasingly likely political reaction in North, could exacerbate rather than
alleviate these "imbalances"
A
4.1
financial factors are important determinants of trade patterns. ^'^
if
Dynamic Model
Consider the following dynamic model which essentially integrates the single-good framework of
Caballero, Farhi and Gourinchas (2007) with the trade model in the previous sections.
the
Time
evolves continuously. Infinitesimal agents are born at a rate
same
rate;
population mass
is
4>
per unit time and die at
constant and equal to L. All agents are endowed with one unit of
labor services which they supply inelastically to the market. ^^ Intertemporal preferences are such
that agents save
their
all
at the time of death
assume that the
income and consume only when they die
given by
is
initial
(1).
Physical capital
stock of capital
is
equal to
is
K
tradable and
Instantaneous utility
(exit).^^
the only store of value.
is
We
and we rule out any capital depreciation or
accumulation.
Entrepreneiu's are born as such, and at any given instant they constitute a share
population.
As
in the static
are not capitalizable
(i.e.,
model, they naturally specialize in sector
they cannot be used as store of value).
1.
This
of the
Entrepreneurial rents
is
consistent with our
formulation in Appendix A.I., where these rents stem from the inalienability of the
of entrepreneurs.
^
human
capital
Note that the existence of entrepreneurial rents implies that entrepreneurs (on
average) accumulate more savings than non-entrepreneurs over their life-span, and hence their share
of wealth (that
share by
Jl^
is,
At any point
with
/i(
capital) in the
= KIJK,
where
/<f
economy
is
\x.
no longer given by the parameter
fi.
Let us denote this
the amount of capital owned by entrepreneurs at any instant
t.
determined exactly as in the static model developed above
in time, factor prices are
replacing
is
Nevertheless, in this
dynamic model physical
capital plays a dual role as a
productive factor and also as a store of value. To the extent that claims on this store of value are
allowed to be traded across borders, this dynamic model generates an alternative source of capital
flows across countries.
rental rate
5,
The key
price that determines the direction of these capital flows
differs
from the
static
marginal product of capital,
of capital need not be one in equilibrium (since capital
gains or losses.
q^
not the
but rather the interest rate r in each country before opening the capital account.
This interest rate
Let
is
We
is
fixed)
5,
because the value of a unit
and there could be expected capital
turn next to the determination of interest rates.
denote the value
for
a non-entrepreneur of holding one unit of capital in country j
= N,S
^^See, e.g., The Economist (2006) for a discussion of some of the factors behind the protectionist view,
E.g.,
and multiple Greenspan speeches on the connection between global imbalances and trade imbalances.
http://www.usatoday.com/money/economy/trade/2003-n-20-gspan-protectionism_x.htm
^""To simplify matters we do not distinguish between workers and capitalists in this section. Our previous results
on w, S, and A can be interpreted as applying to the different components of an agent's income.
^^ Caballero, Farhi and Gourinchas (2006) show that the crucial features of the equilibrium described below survive
to more general overlapping generation structures, such as that in Blanchard (1985) and Weil (1987).
21
any instant
at
agents spend
buyers.
The
In equilibrium, qj
t.
their
all
income
in
is
also the
market price of a unit of
capital, since (surviving)
buying capital and non-entrepreneurs are always the marginal
return on holding a unit of capital
is
then equal to the dividend price ratio 5^/gj plus
the capital gain g^/g^:
si
,
qi
rHi + 5-
(23)
Let W/'* denote the savings accumulated by agents of type
(uninformed capitalists)
country j up to date
in
t.
=
i
e (entrepreneurs)
With a
u
savings:
Vi^/-"
=
-4>W^'''
+ {l-f,)wiL + riWt''\
(24)
Vi//-'^
=
-(PW^'^
+ fj,wiL +
(25)
—
fj-l
Xl0^fxlK
+ rjW^'^,
Kf''^ /K.^^
closed capital account,
capital stock at
=
i
Savings decrease with withdrawals (deaths),
and increase with labor income, entrepreneurial rents and the return on accumulated
where remember that
and
it
must be the case that aggregate savings equal the value of the
times:
all
Wr + Wt' - qlK.
Replacing (26) into
and using the sum of
(23),
4>
where the left-hand
side
(wr + Wr)
(24)
and
(25),
= 5iK + wlL +
measures country
j's
(26)
we have that
Xi9^-^iK
^
Y/
aggregate consumption at any instant
and the
t
right-hand side measures aggregate income F/.
Equations (23) through (26) describe the dynamic evolution of the economy, together with the
expressions for factor prices derived above with
steady state of this model. Notice that
interest rate
is
g^
=
/ij
replacing
jj,.
We
hereafter focus on exploring the
immediately implies that the steady-state equilibrimn
given by:
Intuitively, equation (27) captures the fact that a larger share of capitalizable
{6^
K/Y^)
leads to a larger supply of financial assets relative to
its
income
upper bound
Equation
for
symmetric Cobb-Douglas assumption
the interest rate in the economies
(27) also implies that r^
<
</>
we
and hence equations
provide more details on the determination of
necessarily settles at a value lower than r]/9^,
As mentioned
in
footnote
8,
jl^
in (2) that
in
/ij
(24)
(pa.
This
and
is
it
an
(25) necessarily lead to
converging to a constant
Jl^
>
fi.
/x-'
financial constraints bind even in the
given our constant-returns-to-scale assumptions,
22
H =
not binding,
Appendix A. 2, where we show that
and hence
return per unit of capital they hold.
is
price
consider.
a non-degenerate distribution of wealth in the economy with
We
economy
demand, hence lowering the
of these assets and increasing the implied interest rate. If the financial friction
follows directly from the
in the
all
entrepreneurs earn the same
long-run. Intuitively, although entrepreneurs obtain a higher income period
by period, the
finite-
horizon nature of our model implies that the distribution of wealth remains non-degenerate.
also
show
Appendix A, 2. that
in
functions of
jl^
a function of factor prices, which
fi^ is
remember
These interactions between equihbrium factor prices and the tightness of the
.
financial constraint complicates things, but as illustrated below, the analysis remains tractable
yields
new
We
insights.
equations
first
free trade.
the case in which North and South are closed to international trade.
(9), (10),
and
=
^<^:
the autarky steady state share of capital in the hands of entrepreneurs.
js'^^f is
Appendix A. 2., that although the expression
an increasing function
of 9^
.
The
for
trade frictions are large. This
of value
interest rate in
is
autarkic interest rate
is
South
is
jJ^^^O^ is necessarily
thus an increasing function of 9^ which
,
integrates to global capital markets
if it
in
when
assets
is
that the share of output received by uninformed
depressed by the financial friction which pushes uninformed
capital toward the unconstrained sector
and depresses
its
return.
can contrast the autarky result with the polar opposite case where trade
and
(14), (15),
show
reflects the limited availability of assets to satisfy the local store
demand. The reason there are few
Plugging equations
We
the result highlighted by Caballero, Farhi and Gourinchas (2007).
capital, the only capitalizable income,
We
compUcated, the term
/i^^^j is
implies that South experiences a capital outflow
The low
Plugging
(12) into (27) yields:
"dut
where
and
next compute the equilibrium steady-state interest rate in our benchmark
model with and without
Consider
We
are themselves
ripen
is frictionless.
(16) into (27) yields
=
<i><^-q
~1
m—T^
ai\ 1/a
+ (1 - Mipen^^)
P^/"
^^^^
'
^^ipeJ'
where /x^e„
is
the steady state share of capital in the hands of entrepreneurs under free trade.
Although the equation defining A^e„
is
necessarily increasing in
decreasing in 9^
when
trade
The
is
.
That
is,
9-'
.
is
again complicated, we show in Appendix A. 2. that
This in turn implies that the steady state interest rate
South experiences capital inflows
if it
earlier.
By
and thus earns a disproportionately large return. As a
in the
relative to its
is
tightly related to the
specializing in the unconstrained sector, un-
informed capital works with a disproportionate amount of labor
is
now
integrates to global capital markets
higher in South than in North
is
depressed wage mechanism we described
income
is
free."^
result that the interest rate
multipliers
Jj-open^''
in
economies with lower credit
result, a larger share of capital
form of capitalizable "uninformed capital income" and the supply of store of value,
demand,
^''Note also that because
is
higher.
wc showed above that
that trade integration results
in
an increase
in
r{,^(
was lower
in
the South than
the Southern interest rate.
23
in
the North,
it
must be the case
An
additional feature that emerges in the dynamic model
endogenous changes
jj-ipen
is
<
is
in the tightness of the credit constraint.
f^iut (since trade lowers
A
),
that trade liberalization generates
In Appendix A. 2.,
and hence the share of capital
lower in the free trade equihbrium than under autarky.
By
in the
allowing the
we show
that
hands of entrepreneurs
economy
to specialize in
the sector with less financial constraints, entrepreneurial rents are eroded and wealth inequality
reduced in the long run. Naturally,
this implies that,
capital across sectors will not remain unaffected
is
contrary to our static model, the allocation of
by a process of trade hberalization. To be
precise,
the static model in section 2 only captures the "impact effect" of trade opening on factor prices.
As
the
economy
gradually
falls
transitions to the
and that
in sector 2 increases. It
model, these endogenous changes
transition,
new steady
in
Ji
is
straightforward to verify that, in our
benchmark
lead to a gradual tightening of credit constraints along the
which generates further increases
reversal of the initial increase in wages.
We
state, however, the fraction of capital in sector 1
in the real return to
uninformed capital and a partial
^^
next turn to studying intermediate levels of openness, which corresponds to situations with
varying degrees of international specialization.
An
4.2
The
Application: Protectionism Backfires
The
current "global imbalances" have rekindled protectionist proposals.
these proposals
South must
direct logic behind
that by raising trade barriers in North, the magnitude of trade surpluses in
is
We
decline.
argue in this section that
if
the current scenario
is
an equilibrium response
to heterogenous degrees of financial development across the world, protectionism
may
exacerbate
rather than reduce the imbalances.
We
which
interest rate spread,
rises
behind our warning by showing that the pre-integration North-South
illustrate the reason
with trade
is
the
main
factor behind the direction of capital flows in our model,
frictions.
Let us extend the interest rate expression in (28) to cases of intermediate levels of trade frictions.
As
in section 3.3,
fraction r
e
(0, 1)
we consider
situations in which sector I's output can be freely tradable, while a
of sector 2's output melts in transit
the relative price in South
is
p^
(1
—
r)
and the steady-state
/
a[P
,N
,s
Notice that even for a
^
common
when shipped
^^Real consumption
much
less clear-cut
is
in
result,
interest rate in each country becomes:
)
a(p^(l-r))^/"
^
share of entrepreneurs
also decreasing along the transition,
than
As a
h/\l/a
fi
in
neurial wealth in total wealth differs across countries (/i^
are
across countries.
both countries, the share of entrepre-
^
jl^).
An
increase in r impacts the
and hence the welfare gains from trade
the static model. See Chesnokova (2007) for a related point.
24
liberalization
difference
r^ - r^ through
an indirect
effects
is
work
working through the steady state value of
effect
in the
same
< f we
South when r
,
physical capital.
if
r
>
>
It
turns out, however, that both
establish that, for a given p^, the difference
r^ > r^
f we have
r^ — r^
.
—
(0, 1
Vaut/P^) ^"^^^
^f^o.^
for
Consequently, financial capital flows
f.
analogous to Proposition
is
.
unique level of trade frictions f G
while for t
< f and North
This result
fi^
Furthermore, our previous results allow us to conclude that:
exists a
r^ < r^
have
we can
direction and
strictly increasing in r.^^
Proposition 5 There
r
a direct effect apparent in the formula for r^ above, as well as through
4,
but
it
now
applies to financial capital instead of
'^°
Suppose that the
initial level of
trade frictions
is
>
tq
r so that
r^ >
r^.
Then
financial
integration leads to capital outflows from South to North, a situation that captures the current
scenario between emerging Asia and the U.S.
We now
>
integration for different values of trade friction t
the larger
is r,
the larger
is
the gap
r^ — r^
with larger current account surpluses
.
We
in South.
want to compare the impact of financial
It is clear
f.
from the above discussion that
next show that a larger r
may
also
be associated
''^
Notice that financial integration does not affect factor prices and thus the value of production
in South. Hence,
impact changes on the current account follow one-to-one from impact changes
consumption. In our dynamic model, consumption in any instant
fraction
(f)
of agents die
and consume
their wealth.
How
is
in
simply given by (/iW/, since a
does financial integration affect wealth in
South? Note that before opening the capital account we have
Right after opening up the capital account, the interest rate jumps from r^ to r^ and we have
In sum, financial integration leads to a
^^It is clear
from inspection of the formula
Appendix A. 2., we show that
fi^
is
for
fall
in wealth in the South, to
r^ that the direct
effect of
reduced consumption, and
t on r^
decreasing in the relative price faced by South.
A
is
negative.
Furthermore,
larger r then increases jl^
,
in
and
hence further reduces r^
'"We can
also
show that r >
to attract financial capital flows
f,
is
where f
is
such that
5'^
=
5^
.
In words, the required level of trade openess
lower than that required to attract physical capital flows. Hence, a liberalizing
country should first experience financial capital inflows and only later physical capital inflows. Formally, this follows
from the fact that interest rates are proportional to 8^K/Y' Hence, at r = f, we have that r^ = r'^ but still
5^ < 6'^ since income is lower in South.
.
,
we focus here on a comparison of the impact effect of financial integration for different values of
However, the mechanism we describe does not depend on initial conditions beyond home bias (which we assume).
Thus, our substantive conclusions carry over to a case where a partial reversal of trade liberalization takes places
during a transition phase from an earlier financial liberalization.
'''For simplicity,
T.
25
to a current account surplus
on impact. The
fall in
+
An
way
alternative
to interpret the result
is
wealth
r-N
\
is
^S
that the ratio q'
when South
of a unit of capital in South, falls on impact
given by
= V' /K'
,
which measures the price
financially integrates with North.
This
decline in the value of domestic capital yields a negative wealth effect that reduces consumption in
South and generates a current account surplus.
We
can now compare the impact
effect of financial integration for different values of r.
Notice
that straightforward differentiation yields:
It is
then apparent that
dAW'
K
dr
r"
for
r
w
f
(35^ fr^
dr \r^
\
(i.e.,
r^
w
\
,s5(r^/r^)\
dr
I
r'), the capital loss in
South worsens with a
in protectionism. This in turn exacerbates the trade surplus recorded in
integration.^^
That
is,
protectionism backfires
(if
the goal
is
rise
South following financial
to reduce North's trade deficits).
In our derivations we have treated South as small relative to North, but
The main
that our substantive results do not depend on this assumption.
it
should be apparent
significant difference
is
that, in the two-large region model, financial integration also reduces the interest rate in North,
thus creating a positive wealth effect that induces North to increase consumption on impact and
increase their trade deficit vis a vis South.
An
4.3
The
Application and Extension: High Saving Rate in Regions of South
implication that regions in South that are
net capital inflows
may appear
as counterf actual
economies in the former region are at
least as
more open
to trade are
more prone
to receive
when comparing Asia and Latin America. The
open
as those in the latter, but they typically
run
current account surpluses that are significantly larger than those of Latin American economies.
However, there
is
no contradiction once one also considers that Asian economies have much higher
saving rates.
Our dynamic model
that South
is
respectively.
split
is
flexible
enough
Because consumption
'"Note that an increase
already very significant.
much space
to
fall
accommodate such
between high and low saving regions —
in
to capture this different propensity to
is
to
in trade frictions
The reason
any instant
consume
may
is
is
for
situations. In particular,
suppose
example, Asia and Latin America,
equal to a fraction
4>
of wealth, a natural
way
to have
reduce the trade surplus in the South when the initial trade friction
does not have
is that, in such case, 5^ is so depressed that
W^
for this result
as a result of financial integration.
26
If all countries in
South have identical financial markets, endowments, technology, and instanta-
neous utihty functions at the time of death, then
it
follows that before opening the capital account
we have
iS,Asia
S.Asia
Now
0'5'.'4s»a
-g
if
sufficiently lower
_
- ^^S,LA
than
(/>^,
S,LA
then
it
^
<^„5,L/1
may
well
be the case that even
Asia
if
is
completely open to trade, we have that
s:S,Asia
^ rW
but
^S,Asia
^ ^N
In words, although trade integration brings the marginal product of capital in Asia above that in
North, the larger propensity to save in Asia makes them net exporters of financial capital in a world
with financial integration. Similarly, even though limited trade integration might not increase the
marginal product of capital in Latin America by
much (and we might have
5^'^^
propensity to save of Latin America makes them net importers of financial capital
account
is
open
(i.e., r'^'-'"'^
>
r^).
More
open to trade than low saving countries
A
5
generally, high savings countries in
<
5^), the lower
when the
South need to be more
in order to experience net capital inflows.^''
Heckscher-Ohlin-Mundell Extension
Our benchmark model
isolates the effects of cross-country
on the structure of trade and capital
cial frictions
and
cross-sectoral heterogeneity in finan-
flows. In this section,
we introduce Heckscher-
Ohlin determinants of international trade into the analysis. The purpose of this extension
On
capital
the one hand,
of preferences
we seek
to explore the robustness of our results to
and technology.
On
the other hand,
we want
to study
more general
how
is
twofold.
specifications
the standard results of
the Heckscher-Ohlin-Mundell model are modified by the presence of imperfect capital markets. For
this reason,
As
we focus on the range
in the previous sections,
In Appendix A. 3,
of parameter values for which the financial constraint binds.
we begin by developing a highly parameterized
we develop a model with general
version of the model.
functional forms, in the spirit of the classical
treatments of the Heckscher-Ohlin-Mundell model.
5.1
Environment
The model
is
a simple extension of our benchmark static model.
to differ in (primitive) factor intensity
'''Our
model
offers
and endow countries with
an alternative explanation
for
We
allow production technologies
different relative
endowments
(that
Latin America attracting larger net capital inflows than Asia
despite being less open to trade. In particular, just as in the case of physical capital, the
amount
of trade integration
needed to ensure net financial capital inflows into South is lower the lower is financial development in South. Hence,
the observed patterns are also consistent with Latin America being less financially developed than Asia.
27
For simplicity, we continue to assume Cobb-Douglas
different aggregate capital-labor ratios).
is,
we now
preferences and technologies, but
allow for a larger output elasticity of capital in sector
Xi^Z {Kip iUy-"^
In words,
intensity
The
we assume that there
and
i
=
1, 2,
with ai
>
a2.
a positive cross-industry correlation between (primitive) capital
frictions in financial contracting.
This specification
is
consistent with available data.^^
closed-economy equilibrium of this two-sector model
frictionless,
acterize.
is
,
For our purposes,
it
1:
—
straightforward to char-
economy would
suffices to indicate at this point that the
amount
is
allocate an
Kr = qai + ^i^^-^K
-77)02
of capital to sector
Assumption
^
1.
For financial frictions to bind, we hence now require:
aO <
1':
1^
(1
°',]'^
,
—
77Qi-|-{l-77)02
Closed Economy Equilibrium
5.2
Under Assumption
1'
the financial constraint binds and equalization of the value marginal product
of labor imposes
We
combine
this condition
with goods market clearing
{1-V)Z [iiOKr
iLi)'-"'
- PVZ
((1
-
f^e)
Kr-
{L
-
Li)'-"=
to obtain
(1
-ai)77-l-
(1
-a2)(l
-?/)
and
As
in our
benchmark model, the
case without financial frictions.
large
amount
price
is
allocation of labor across sectors
Combined with the
of capital to sector 2,
fact that the
we again obtain that good
is
economy
2
is
identical to that in the
allocates
an
oversupplied and
inefficiently
its
relative
depressed.
^^The most widely used cross-industry measure
of financial
dependence
is
given by the share of capital expenditures
not financed with cash flow from operations (see Rajan and Zingales, 1998).
Manova
(2007) reports a positive cross-
and external finance dependance. Importantly, this correlation
which actual capital intensities are more likely to be tightly related to output
sectoral correlation of 0.14 between capital intensity
is
computed using U.S. data, for
The fact that ai >
elasticities of capital.
0:2
is
however perfectly consistent with financially dependent sectors
operating at relatively low capital intensities in financially underdeveloped countries.
28
The
result that the allocation of labor across sectors
is
invariant to the level of financial frictions
depends on our assumption of Cobb-Douglas preferences and technology. Nevertheless,
Appendix A. 3, the
result that the relative price
p
is
as
shown
in
increasing in 9 holds for arbitrary neoclassical
production functions and homothetic preferences.
An
important difference between the present model and our benchmark one
endowment
factor
that relative
differences generate cross-country variation in the relative price p. In particular,
a labor abundant, financially underdeveloped South features a relatively lower
financial frictions but also because sector 2
countries are, ceteris paribus,
We next
is
is
p,
not only because of
labor intensive and autarky wages in labor abundant
lower."''''
turn to describing the equilibrium factor prices of this closed economy equilibrium.
The
rewards to labor and uninformed capital are pinned down by the value of their marginal products
in the unconstrained sector,
which using
(29)
and
(30) yields
^10
K
Ql
^ = (1-"i)^(t^^)
and
Mg(l-r7)
/ ,i9
(31)
a\ —1
K'
'^^^^TT^^^Zl-f^-)
[i-ii0)ri
Ur'i.
As
effect
in our
on
benchmark economy, both
and 5 are increasing
in financial
development
decreasing in
9.
The
intuition for these results
is
analogous to that
financial development, but also in their relative factor
and
but the
{l-ai)T]{l - ji9)K
in
our benchmark economy.
Suppose now that the world consists of two economies. North and South, that
of 9
9,
5 is disproportionate, in the sense that
w _
is
w
(32)
.
also a larger capital-labor ratio
K/ L. We
differ
not only in
endowments. North features a larger value
consider
first
the case of limited trade in which
countries can only trade in the numeraire sector.
Given limited trade,
in
which direction does physical capital flow?
suggests that the larger level of 9 in North implies
North.
to 5
The Heckscher-Ohlin model
<
6
that 5^ >
6
,
and
Our benchmark model
capital flows from South to
instead predicts that, in autarky, the lower
K/L
in
South leads
and capital flows from North to South.
Since this extended model incorporates both effects,
it
is
not surprising that the direction of
As shown in Appendix A. 3, however,
mapping between p and K/L may fail to hold
whenever the elasticity of substitution between capital and labor is much smaller in the unconstrained sector than
in the constrained sector. The condition we derive in the Appendix resembles that derived by Amano (1977) for the
''^This corresponds to the "price version" of the Heckschcr-Ohlin theorem.
for general
production functions
in
the two sectors, this positive
case of the specific-factors model.
29
capital flows
now ambiguous. To
is
where hats denote proportional
differences.
benchmark model. The second term
we can
illustrate this,
The
first
log-differentiate equation (32) to obtain
term
reflects the effect identified in
standard Heckscher-Ohlin
relates to the
effect,
which
is
our
at the
core of Mundell's prediction that trade frictions foster capital inflows into the capital-scarce South.
We
summarize our
result as follows:
Proposition 6 Suppose 9^ > 6^ and
K^ /L^
> K^/L^
Provided that differences in capital-
.
labor ratios are small relative to differences in financial contractibility, with limited trade, capital
flows from South to North.
Open Economy Equilibrium
5.3
Consider now the case in which South
is
small and thus faces exogenous relative prices p.
We
again focus on the case in which North shares the same preferences and technologies as South
and
9
satisfies
Assumption
1'.
This ensures that South does not specialize completely in the
unconstrained sector and allocates an amount iJ.9K of capital to sector
As
in
our benchmark model, the allocation of labor across sectors
by the condition equating the value of the marginal product
is
1.'^''
now
that, just as in the
(33) does not provide a closed
benchmark economy, Li
is
form solution
for Li,
labor-intensive sector, where financial frictions are lower.
its
p not only because of the
larger capital-labor ratio
Letting
ip^
=
is
(33)
.
it is
p,
straightforward to see
When
South
South specializes
in the
9.
Notice that North pins
effect isolated in the
down
sectors:
decreasing in p and increasing in
opens up to trade with a North that pins down a higher relative price
relative price
two
of labor in the
(l-aOZ(^^ ^p{l-a,)Z[-j—^^
Although equation
uniquely pinned
down a higher
benchmark model, but
also because
associated with a larger price of the labor-intensive good.
Li/L, we can next write wages and the rental rate of uninformed capital as a
function of this endogenous variable
South specializes in sector 2 to the point at which financial constraints cease to bind.
model behaves as the standard Heckscher-Ohlin model and, if K^ / L^ is large enough, factor price
equalization attains. As we will see later, however, even in this case trade integration raises the Southern rental rate
relative to the Northern one. This is in sharp contrast to the result obtained in the standard Heckscher-Ohlin
If
9
is
large enough, then
In such a case, the
(5
model.
30
Because
w
that both
and
6 are increasing functions of p, regardless
of differences in factor intensity and factor abundance.
This implies that as in the Heckscher-
tpi is
decreasing in
p, it follows
Ohlin model, trade integration raises wages
(in
terms of the numeraire) in the capital-scarce South.
Nevertheless, contrary to the standard model, the real return to uninformed capital also goes up
Even more
as a result of trade integration.
surprisingly, using (33), (34)
can be written as
w _
{1
6
which
decreasing in p, since
is
wages,
it
ip-^
is
-
a2)
-
{1
iJ.e)
with trade opening, Southern wages increase
A
necessary implication of this result
we have
5
>p>
lu
>
0,
is
that,
terms of the numeraire, but decrease relative to
in
sector 2's prices, while the rental rate of capital goes
(1965) hat algebra,
K
In words, although trade integration raises
p.
even more.
raises the rental rate of capital
w/6
(35), the ratio
L'
a2{l-'tpi)
decreasing in
and
up
in
terms of both goods.
Using Jones'
where hats denote percentage changes. This contrasts
with the ranking dictated by the Stolper-Samuelson theorem:
w >
p >
>
6.
In summary,
we
and
rel-
have derived the following anti-Stolper-Samuelson proposition:
Proposition 7 (Anti-Stolper-Samuelson) Regardless of
ative factor abundance, trade integration with a
North reduces the wage-rental
ratio in South.
differences in factor intensity
more financially developed and
As
capital
abundant
a result, the rental rate increases relative to the
price of both sectors, while wages increase relative to the price of the import sector, but fall relative
to the price of the export sector.
The
intuition for this result
factor intensities, as
p
is
analogous to that
rises, sector 1 releases
downwards to accommodate the decrease
in the
benchmark model. Regardless of
labor but not capital to sector
2,
so
w/5 has
relative
to adjust
in capital intensity.
This result bears some resemblance to the result in a specific factors model in which capital
is
sector specific but labor can
move
As
across sectors.
is
well understood, in that type of model,
trade integration increases the real reward of the capital specific to that sector, while having an
ambiguous
effect
on
model, uninformed capital
real wages. '^^ In our
is
not sector-specific, but the
rents obtained by informed capital are sector-specific and this explains the similar predictions that
emerge
in
both models.'^*
5.4
Direction of Capital Flows
So
we have focused on studying the
far
studying an increase in the relative price
South, from which
As a matter
we
p.
Next we explore the
relative factor prices in
North and
learn the (desired) direction of capital flows in the free trade equilibrium.
of fact, in our log-linear model,
higher under free trade. But this result
For similar reasons,
which corresponds to
effects of trade integration in South,
it is
is
we can show that the
real
wage, that
is
w/p^~^,
is
nececessarily
functional-form specific.
easy to verify that the real reward to informed capital goes
liberalization or in terms of Jones' (1965) hat algebra,
p
>
31
>
R.
down
as a result of trade
This analysis amounts to characterizing the comparative statics with respect to 9 and
that both North and South share the same relative price p and are identical
Simple log-differentiation of equations
Q1Q2
w
ai
i
+
^'
Q2
given
in all other dimensions.
(35) delivers:
^'
1-^1
--(i^ a2)ai
"1 + «2 At
=
and
(33), (34)
K/ L,
)^/^
'^+(r—
\i-v^i
1-iJ.OJ
1
Ipl
—
\1
/i0/
—
K/L
'01
1
where remember that
These equations
tp\ is
the share of labor allocated to sector
illustrate that the
country with the larger capital-labor ratio (North) features
a relatively higher wage and lower rental rate of capital. This
is
the Heckscher-Ohlin model outside the factor-price equalization
Furthermore, provided that
V'l
>
1.
A'^''
consistent with the predictions of
set.
holds in both countries, the larger 6 in North contributes
further to ensuring that the rental rate in South settles at a higher level than that in North:
> S .In our benchmark model, this was the only effect at play. There, we had that ip-^—r] and
> ii9 necessarily held in an economy where financial frictions bind. In our more general model,
the condition -01 > M^ ni^-y f^il to hold if ai is sufhciently larger than a2-^^
5
Tj
Still,
even when
ensure that 5
>
5
t/jj
.
<
How
^9, our analysis suggests that large enough differences in
large need differences in
K/L
K/L
always
be? Om: exposition following Proposition
2 in section 2.5 suggested a simple (and in our view plausible) condition that ensures that 5^
namely that North operates sector
5.5
2's
> 5^
technology at a higher capital-labor ratio than South does.
Discussion
In our benchmark model, we derived the result that the difference 6
- 6^
is
negative with limited
trade but positive with free trade. Our extended analysis with Heckscher-Ohlin features illustrates
that neither of these two statements holds for arbitrary capital-labor differences across countries
and
sectors.
Nevertheless, our model does
show that
if
5
—
5
is
positive with limited trade,
larger with free trade. In other words, the incentive for capital to flow towards the South
enhanced by trade integration.
Similarly,
if
with limited trade, and hence the incentives
integration. In sum, in this extended
model
5
—
(5
is
negative under free trade,
for capital to outflow
it
it is
it
is
is
even
always
more negative
from South are reduced by trade
continues to be the case that trade and capital flows
are complements rather than substitutes.
The key
conditions that ensure this result are that
(i)
South features a depressed relative price
''in particular, t^j > fj,0 fails if ai — 02 is large enough to make sector 1 operate at a higher capital-labor ratio
than sector 2. Incidentally, notice that when qi — Q2 is small, Northern exports may well be less capital-intensive
than Northern imports. For example, in our benchmark model with qi = 02 and no differences in K/L, North is
necessarily a net importer of capital services. Hence, credit constraints may provide an explanation for the so-called
LeontiefT paradox (see Wynne, 2005, for more on this).
32
p
closed-economy equilibrium, and that
in the
uninformed capital
South
in
is
in the free trade equilibrium, the rental rate of
(ii)
increasing in the relative price p.
We
showed above that these two
conditions are satisfied whenever preferences and technologies are Cobb-Douglas. In Appendix A.
3,
we show
that condition
(ii)
continues to be satisfied for general neoclassical production functions
and homothetic preferences. This
result in Proposition
As
7.
is
related to the "full" generality of our anti-Stolper-Samuelson
for condition
(i),
we show
in
Appendix A. 3. that
it
also generally
is
except for situations in which the elasticity of substitution between capital and labor
satisfied,
much smaller
in capital
in the
unconstrained sector than
abundance are large
Given these
results,
in
is
the constrained sector and North-South differences
relative to differences in financial development.
we conclude that our model
delivers a robust complementarity
between
trade flows and capital mobihty.
Final
6
Remarks
The main message
dependence are
complements
paper
of this
is
that
significant determinants of
when
variation in financial development and financial
comparative advantage, trade and capital flows become
underdeveloped countries. This complementarity
in financially
is
in
sharp contrast
to the substitutability that arises in the standard Heckscher-Ohlin-Mundell framework,
important practical implications. For example,
South
policies
aimed
indicates that deepening trade liberalization in
it
raises its ability to attract foreign capital.
and has
At the global
at reducing the so called "global imbalances"
level, it
may
implies that protectionist
backfire
and exacerbate them.
And
while we do not analyze the normative aspects of liberalization processes, our framework hints
that
it is
important
for
developing economies to liberalize trade before the capital account,
if
capital
outflows are to be averted.
Our complementarity
of labor to sectors that
underdeveloped country
result follows
is
is
from the
fact that trade liberalization allows
independent of local demand conditions.
able to allocate a disproportionate
amount
As a
result,
and technologies are Cobb-Douglas, we
in a
world in which countries
differ
which South
later
is
a financially
of workers in sectors in which
financial frictions are less severe, thereby increasing the marginal product of capital.
initially derived this result for the case in
an allocation
a small open
Although we
economy and preferences
demonstrated that the result
is
general. In particular,
only in financial development and sectors differ only in financial
dependence, trade integration necessarily reduces (and actually overturns) the gap between the
real return to capital in
North and South. Furthermore, even
after introducing Heckscher-Ohlin
determinants of trade, our complementarity result continues to hold under weak conditions.
In order to keep our analysis focused,
across borders.
we only allowed physical and
However our framework can accommodate mobility
of informed capital.
that in our benchmark model the shadow value of entrepreneurial capital A
North, that
is
A
>
A
.
If
we
allow entrepreneurs (or their
Northern entrepreneurs might want
to migrate (or
33
human
financial capital to flow
is
Remember
larger in South than in
capital) to
move
across borders.
run projects) in South. In practice, however.
the costs of informed capital mobility are likely to be
capital mobility.
Furthermore, Northern entrepreneurs
much
larger
than those of mere physical
will generally find it easier to
borrow
for
domestically-run investments, than for projects performed in foreign countries with weak financial
institutions.
The
fact that foreign affiliates of U.S. multinational firms
country financial institutions attests to this
for future
fact.
We
work.
34
leave a
borrow heavily from host-
more detailed treatment
of these issues
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Jean (2006), The Theory of Corporate Finance, Princeton: Princeton University Press.
Weil, Philippe (1989), "Overlapping Families of Infinitely-Lived Agents," Journal of Public Economics, Vol.
38, Issue 2, pp. 183-198.
Wynne, Jose
(2005), "Wealth as a Determinant of
2005, Vol. 95, Issue
1,
Comparative Advantage," American Economic Review,
pp. 226-254.
36
Appendix
A.
Microfoundations of the Financial Constraint
1
<
In the main text, we simply imposed the assumption that
B'^
5'
K'^
the
is
amount
of capital rented by entrepreneur
we provide a simple microfoundation
for this
and
i,
(6
—
is i's
\) K'^ for
some constant ^ >
endowment. In
capital
this
1,
where
Appendix,
assumption, which builds on limited commitment on the part
of entrepreneurs, along the lines of Aoki, Benigno and Kiyotaki (2006).
In particular,
assume that the entrepreneur can always walk away from the project before production
occurs (but after investment has taken place), and renege on
human
the
capital of the entrepreneur
is
is
inalienable)
ip[K''
i.e.,
+
B'^).
and
all
that investors could recoup
+
6ip (iv'
development. Regardless of the value of
carries out production; but
of withholding his/her
if
B^).
lenders have
human
We
6ip
{K'
+
the
2,
which
is
5B'
if
setting 6
.
way down
new
to 5ip (K'^
their pa.yoff
The
is
+
which
primitive index of financial
does not walk away and
is
B').
able to use the threat
With
full
bargaining
Foreseeing this ex-post
at least as large as the return they could
participation constraint of investors hence imposes
= t^— >
1,
-^^K\
\-p
we have the exact same formulation
associated with a larger collateral value of capital (larger
We can also consider an
(uninformed
as our
B') or
B' <
-
By
this saved collateral in sector 2,
ip
weak bargaining power, the entrepreneur
all
Suppose that
6 (0,1) of the installed capital,
93
capital services to renegotiate the terms of the loan.
obtain in the unconstrained sector
<
a fraction
can think oi
renegotiation, investors only lend to entrepreneurs
so.
the entrepreneur refused
efficiency dictates that the entrepreneur
ip,
power, the payoff to lenders can be pushed
that 6B'
is
Suppose that investors were allowed to rent
would yield them a payoff of
If
from investors, then revenue would be zero (human
to put his/her skills to use after obtaining the funds
capital
debt obligations in doing
all
necessary for production to occur.
as in our
main
text,
with a larger 9 being
93).
alternative formulation in which the collateral value of capital
capitalists) are not completely
unable to produce in sector
1.
is
zero,
but lenders
In particular, suppose that
if
entrepreneur walked away, uninformed capitalists could use the installed capital to produce a fraction
sector I's output.
The
ip is
i/j
negatively related to the complexity of production in sector
of
1.
outside option of lenders in this case would be
1,"
and with
now
In this formulation,
the
full
= max [^Z
(A-
+
B^)" (L)^"" -
wL] = a^Z P"^^'^^ ]
'
"
" [K'
+
B')
,
bargaining power on the part of entrepreneurs, the participation constraint for investors would
be:
.B^<a,z(iiz^)'""''"(A' + Br
In terms of the notation used in the
main
formulation implies
text, this
1=
^
^
n
5-apZ[^l^^y
Notice that the credit multiplier 9
as exogenous, firm behavior
is
is
now a
w
(36)
•
function of factor prices, but because firms take these prices
identical to that in the
main
37
text.
The main
difference
is
that, in solving for
the general equilibrium, one has to be careful
implication of the analysis
that
is
now
acknowledging the dependence of 9{w,S) on
in
w and
An
5.
trade affects the tightness of the constraint.
Despite these nuances, our main result on the complementarity between trade integration and net capital
inflows in South
is
robust to this more general formulation. To see
this,
consider
the equilibrium of a
first
small open economy, where remember that
w
=
{i-a)z
5
=
aZp'^"U{l-^9{w,S))p'/^ + fie{w,5)')-]
Plugging these two expressions into
we end up with a
(36),
+
[(^(1- ij.e{w,s))p^^°'
ij.e(w,6)^YJ
(37)
simple formula for 6
fairly
in
terms of
(p
and
(38)
1/q
"
1
This shows that,
a given
for
formulation. Furthermore,
increases
when
and decreasing
result {S/p
is
Finally,
index
ip
it
this,
is
large
p,
ip
it
countries are also large 9 countries, just as in our previous
a decreasing function of p, and hence the tightness of the financial constraint
follows that overall
increasing in
pas
well).
we must have that
We
Because the rental
p.
is
increasing in
can similarly show that w/6
remains to show that the relative price p increases
it
suffices to
show that the autarky
of financial development (so that
9, this is
relative price
> p^
ip'^
in
p
is
p,
S in (37)
which
is
increasing in p
our complementarity
is
decreasing in
=
{p.9 (1
^
—
p,
which
is
our anti-
77)
/
(1
(77
frictions are reduced.
an increasing function of the primitive
>
implies p'^
—
South when trade
is
equivalent to showing that 9 in (38)
equilibrium autarky relative price p
is
p^).
Because p
increasing in
is
increasing in the
p when
evaluated at the
This yields
p.^)))°.
/J.(l-7])+7?<p^/"
fj,(l
is
5
result.
endogenous tightness
which
(?)
trade liberalization increases the relative price
in 9,
Stolper-Samuelson
To prove
6*
p:
-
+
r])
'
jirjp^l'^
indeed increasing in p. In sum, even accounting for the endogenous response of the credit constraint,
trade integration allows South to trade at a higher relative price p and this necessarily increases the real
return to capital.
A. 2
Detciils
on the Dynamic Model
In this Appendix we provide further details on the determination of the steady-state share of capital in the
hands of entrepreneurs.
Notice
first,
from equations
(24)
and
(25), that
Wt'^ ^nd
W^''^
converge to the
following steady-state values:
and
^.,e^
f^-^r
(40)
.
,
where remember that the steady-state
(40),
and using the
fact that rlqj
=
interest rate
Si
in
is
given by
H =
^S-'K/Y^.
From equations
(39)
and
steady state, we have the share of wealth (and capital) in the
38
hands of entrepreneurs
given by
is
M=7-
-^
V
where we have dropped country superscripts and time subscripts
—
Notice that whenever A
With A >
the static model.
share of wealth
varies
jl
that
0,
for simpHcity.
the share of wealth in the hands of entrepreneurs converges to
0,
Importantly, this share
p..
depending on whether the economy
Notice also that the fact that
open
is
> n may
fl
inequality would imply A =
and
either
<
< or jl6 = fi9 >
ij,9
Closed
rj
tj
fi
=
/i is
a function of factor
suggest that Assumption
n, thus contradicting the
Assumption
.
Economy Equilibrium
From equations
(10)
and
prices,
and thus
it
1
is
no longer
we had
first
>
jj.6
rj
ensure
sufficient to
>
jiO,
then the
first
second inequality. Hence, we must have
first
of these cases applies.
the steady-state equihbrium of an
economy that
is
the autarky steady state share of capital in the hands of
/i„,^j
(12),
if
then suffices to ensure that the
1
Consider
Denote by
closed to international trade.
entrepreneurs.
just as in
to international trade or not.
that financial constraints bind in the steady state. Note however that
fi,9
fi,
the higher entrepreneurial income translates into a steady state entrepreneurial
larger than
is
(41)
,
we have that
in the
autarky equilibrium, the ratio X/S
is
given
by
/i,„,^(l-7?)
6
where we have naturally replaced
On
/j.
with
we
/i,
'
/io„t.
the other hand, from equation (27), the ratio r/(p
(12) with /io„t replacing
^
'
is
given by
6K/Y. Using
equations
(9), (10)
and
obtain:
'-'
^
as stated in the
main
(43)
text.
Plugging (42) and (43) into (41) then yields:
(;;|;%;j-i)-HBs^-i)c--)
which implicitly defines
but
in order to
interest rates),
ji^^f as
study the
it
a function of 9 and other parameter values. This expression
suffices to
study
how A =
jj,aut^
varies with
We
next show that
is
A
is
increasing in
increasing in
9, it suffices
rates,
A
as a function of
9.
9{l-A=^9.
1'^l^-;'
right-hand-side
cumbersome,
9.
Multiplying both sides of (44) by 9 and rearranging we can implicitly define
A
is
development 9 on the variables of interest (wages, rental
effects of financial
9.
to
(45)
\
Since the left-hand-side of (45)
show that the left-hand-side
39
is
decreasing in
of (45)
is
9,
while the
increasing in A.
A
few
steps of algebra yield
5(A(1
K^-iS^^(^-^O)
ff(A)
9A
_A-Q+
(a,,
'
1)2
where
5 (A)
=
(1
-
2 (1
-
-
a(l
Hence we need only show that
9 (A)
g'
since
A =
<
fid
of A, which
is
rj.
But
This proves that
(A)
in the
=
(I
-
a)
for all
A
in the relevant range.
= -2 (1 - Q +
7?)(1
a?]
-
>
A)
^i)9
<
- 2q(1 -
rj)
+
a^{l
-
tj)^)
.
But note that
0,
when evaluated
at the highest possible value
(1
-
rj)
(1
-
7]
+ ea - a +
a{Ti
-
611))
>
0.
steady state of our model with endogenous tightness of the credit constraint,
necessarily an increasing function of
equilibrium,
q)(1
from
this follows
(r])
-
-
Hence, we need only show that g (A)
rj.*°
g
still
>
-
a(l
A + A^ +
77))
9.
FVom
jl6 is
inspection of the equilibrium values of the closed-economy
we can immediately conclude that wages, the
rental rate of uninformed capital
and the
interest
rate are larger in a financially developed North than in a financially underdeveloped South. Hence, for large
enough trade
frictions
as financial) to flow
it
continues to be the case that there
is
an incentive
for capital
away from South.
Free Trade Equilibrium
With
determined by equations (27) and
free trade, the equilibrium steady state value of r
(41),
of /iopg„. Using equations (14), (15)
but the equilibrium values of factor prices are now
and
(16),
we have
A
-l/a
P"
_
^
<5
and
Aopen^+(l-Aopen^)p'/"
as stated in the
(both physical as well
main
text.
Plugging these two expressions into (41) yields
1
a0
u
M<.pen«+(l-<"'op,=n»)r>'''',
-1
"''"
a0(
iioper,'»+(l-("'„pcr,»)r'''°
"""We proved above that Assumption
1 is
sufficient to ensure this.
40
-{p-""-^)e{l-^i)
and
fiopen ^^^ still
difl'erent
functions
from which we have that A
As
in the closed
=
fj-open^
economy equihbrium,
hand-side of the above equation
is
increasing in
A
must
for
p
<
to
show that A
increasing in
is
increasing in A. But note that this
Hence, we again have that Aopen^
1.
This result ensures that,
of uninformed capital
is
satisfy
interest rate are decreasing in
9.
to
show that the
A -f
clearly true, since
an increasing function of
wages are increasing
in the free trade equilibrium,
and the
's
is
9, it suffices
—
(1
left-
A)p^/°
6.
in d, while the rental rate
Hence the direction
of
both types of capital
flows are from North to South, just as in the model with "exogenous" credit constraints.
Notice also that
A =
jJop^„9
is
a decreasing function of
p,
which necessarily implies that
/iopg„
<
jj.aut-
^^
words, trade liberalization endogenously tightens the credit constraint in South, and hence trade integration
not only shifts labor from sector
A. 3
The
Static
1
to sector
2,
but also
shifts capital (in the long-run).
Model with General Functional Forms
In this Appendix we extend the static model to general neoclassical production functions and general ho-
mothetic preferences.
identical
In particular,
we assume that each country allows a representative consumer with
homothetic preferences, from which we can express demand
2 as a function k (p) of the relative price p.
technologies to produce goods
1
and
2,
We
also
per worker under each of these technologies by /i
first
(fc)
in sector
assume that both countries have access to the same
and that these technologies feature constant returns
uously diminishing marginal products and no factor intensity reversals. Letting k
Let us
demand
in sector 1 relative to
and /2
to scale, contin-
= K/L, we
denote output
{k).
consider the equilibrium of the closed economy.
As
in the
main
text,
we assume
that 9
low enough to ensure that the credit constraint binds and the amount of capital allocated to sector
Ki = fj,9K
.
The equilibrium
conditions of this
economy
1
is
is
are:
,,,(1^1) . „„„-.../=(i^f)
f'\^J) = '-^
,!,A\^^\-,l,(\^^\iZlt<^
The
first
condition ensures goods-market equilibrium.
in sector 1, while the last
. „
The next two conditions
two ones characterize optimal behavior
solve for equilibrium prices
and the allocation
(46)
in sector 2.
characterize optimality
Although
it is
impossible to
of labor to each sector as a function of parameters,
we can
learn a great deal about the characteristics of the equilibrium by using Jones' (1965) hat algebra approach.
41
Log-differentiating the above system (46)
/
and
+
(5
A
^
J
+
5
-
(1
Q.) /
0-2
=
p
where hats denote percentage changes
=
1
-01
;?
-/j6'
(1
-
-
r
V'l)
02^,
(47)
and the following
in the variables,
Q,
M^
V
- 02)^ +
(1
few manipulations we obtain:
after a
definitions have been used:
f'dk,)kjh{ki)
d In ki
K
These correspond
The system
light
output with respect to capital, sector
to sector i's elasticity of
between capital and labor, and the
(47)
elasticity of substitution in
can be solved to obtain
on the cross-country variation
(p) p//t (p)
w,
p,
in prices
5, A,
as a function of 9
i/^i
and
k.
is
larger in
and
2.
We
North or South. After some
are particularly
fairly
cumbersome
we obtain
(010-2(1
-Q2) -
(1
'
-aQgiao)
^+ ^
It is clear that,
("i'^^ (1
rTTi^^ZZr^
other things equal, the relative price p
financial contractibility
holds more generally.
9.
This
the effect
^:)
larger in an
+
Vicria2)
economy with a higher degree
isolated by our benchmark model, and
it is
of
now apparent that
straightforward to show that, in the case symmetric productions functions, this
It is
immediately implies that p
is
is
-
,^g,
^
_^
it
of substitution
1
These expressions shed
and the allocation of labor under autarky.
interested in exploring whether the relative price p
algebra
and
i's elasticity
consumption between goods
<
1
whenever
financial constraints bind.
The reason
for this is that as 9 rises,
equilibrium values converge continuously to the allocations of an economy where financial constraints do not
bind,
and
in the latter
Equation (48)
also
economy we must have p
shed hght on the
p.
In the Cobb-Douglas case
to
be the case provided that
we had a
=
effects of
1.
a larger aggregate capital-labor ratios on the relative price
positive link
aia2
(1
—
Q2)
between p and K/L. In the general
>
(1
—
(49)
Qi) (7iQ2.
In a frictionless economy, this condition would simply be Qi
42
case, this continues
>
Q2, which
is
our assumption
in the
main
when
text. Similarly,
=
aj
sufficient to ensure that
p
p
K/L.
decreasing in
is
(which
(Tj
is
is
when
Intuitively,
KjL. When a2
sufficiently low,
is
however,
it
and labor are very complementary
capital
> qj
our Cobb-Douglas case), the condition Q]
satisfied in
increasing in
may be
again
is
the case that
an increase
in sector 2,
in the capital stock increases the allocation of labor to that sector almost proportionately (regardless of
factor intensities), and thus expands production in sector 2 relative to production in sector
clear,
in
however, that even when condition (49)
South whenever cross-country differences
We
fails to
be
1.'*^
It
in 6 are larger relative to cross-country differences in
can now move to an analysis of the small open economy. Our goal here
technologies and preferences, the rental rate of uninformed capital
is
to
is
should be
p continues to be lower
satisfied, the relative price
show
K/L.
that, for general
an increasing function of
p.
We
again
use Jones' (1965) hat algebra approach, this time ignoring the goods-market condition and treating p as
parametric. This amounts to solving for w,
value of 5
^
^
5, A,
and
and
as a function of p, 6
•^j
We
k.
focus here on the
:
('j/'itTi
-|-Qig2(l --^i))
(q1(72 (1
-
V"!)
+
(1
-
02)
(qi<72(1 -l/'i) +'!/'iCria2)(l
V'lO-lQ2)
Notice that the rental rate 5
- g^) ai
(i/'i
.
is
This confirms that
necessarily increasing in p.
In fact, the coefficient of
capital.
p
is
strictly larger
-
(QiO-2 (1
61^)
that, provided that trade integration raises the relative price p in South,
uninformed
Qi
^
-
it
than one
(1
-Q2)
-01
it is
)
I
^iC^l Q2)
generally the case
also raises the real
(for
02
<
reward to
and thus J/p
1),
uninformed capital increases
also increasing in the relative price p. In words, the return to
+
in
is
terms of both
sectors' output.
As discussed
in the
main
text, this rise in 5 (and 5/p)
between trade flows and capital flows
5^
>
S'^
in the
the key feature that leads to complementarity
is
model. Whether the increase in 5
is
large
enough to lead to
with free trade depends again on whether relative factor endowment diflFerences are large relative to
factor intensity differences
ensures 6^
>
S'^ is
and
differences in flnancial contractibility.
^1
Or, more simply,
As a matter
of fact, the condition that
completely analogous to that in the model with Cobb-Douglas functional forms, namely:
all
that
we
require
^^
is
^2,
r
1
-W>o.
that North operates sector 2's technology at a higher capital-labor
ratio than South does.
It is
straightforward to show that this condition holds in the case of symmetric (neoclassical) production
functions and no differences in
K/L
across countries. In such a case, the analog of equation (5) equating the
value of the marginal product of labor across sectors
is
f,|!^U,F,('iUi^Vr„,, = ^s,
where Fl{-) denotes the marginal product of labor and F^
preferences and symmetric production functions,
constraint binds in North.
From equation
it
(50), this
(•)
>
0.
(50)
As shown above,
continues to be the case that p
immediately implies that
tpl
<
/ (l
1
—
for general
homothetic
as long as the financial
iplj
>
fiQ^ / (l
—
IJ,6^),
and thus 5^ > 6^
"Our
condition
is
closely related to
Amano's (1977)
analysis of a proportional increase in the
specific factors in the context of the specific-factors model.
43
endowment
of both
Finally, note too that in the case of
symmetric technologies and equal aggregate capital-labor
the last equation of the system in (47) immediately implies that
only in their
the
6''s,
same system
w^ < w^
and thus the sign of dw/d6 has to be the opposite of
(47),
one can also show that
for the case of
.
This
is
ratios,
because countries
the- sign of dS/dO.
symmetric technologies
(i.e.,
differ
Manipulating
qi
=
02 and
c7j
=
all
the statements in Proposition 2 hold for general symmetric production technologies and no relative factor
172)
we
endowment
necessarily have that A
>
A
(details available
differences across countries.
44
upon
request). This completes the proof that