Global COE Hi-Stat Discussion Paper Series 179

Research Unit for Statisticaland Empirical Analysis in Social Sciences (Hi-Stat)

Institution-Induced Productivity Differences andPatterns of International Capital Flows

Hi-Stat Discussion Paper

Kiminori Matsuyama

March 2011

Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp

©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

Institution-Induced Productivity Differences and Patterns of International Capital Flows1

By Kiminori Matsuyama

Last revised: March 14, 2011

Abstract
This paper presents a stylized model of the world economy to study how the crosscountry differences in the institutional quality (IQ) of the domestic credit markets
shape the patterns of international capital flows when such IQ differences also
cause productivity differences across countries. Institution affects productivity bychanging the composition of credit across heterogeneous investment projects withdifferent productivity. Such institution-induced productivity differences are shownto have effects on the investment and capital flows that are opposite of exogenous
productivity differences. This implies that the overall effect of IQ could generate
U-shaped responses of the investment and capital flows, which means, among
other things, that capital flows out from middle-income countries and flows into
both low-income and high-income countries, and that, starting from a very low IQ,
a country could experience both a growth and a current account surplus after asuccessful institutional reform. More generally, it provides some cautions wheninterpreting the empirical evidence on the role of productivity differences andinstitutional differences on capital flows.
Keywords: Institution-dependent productivity-agency cost trade-off, Endogenous
productivity through the composition of credit across heterogeneous investment
projects, Pledgeability approach to modeling credit market imperfections, Reverse
capital flows, Chains of comparative advantage in intertemporal trade; Strict logsubmodularity, Envelope Theorem
1This paper has a long gestation lag. Yet, I was lucky enough to be given the opportunity to present the idea atvery preliminary stages under different titles without any written draft at the following places: Bank of Japan,
UPF/CREI, DBJ-RICF, FRB of Chicago, GRIPS, Hitotsubashi, Keio/GSEC, KIER, Harvard, MIT, Tokyo, andZurich. I would like to thank seminar participants at these places for listening to me and giving me constructive
comments, which helped me to write up this paper.
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows1.

Introduction
It is now well established that capital often flows “upstream,” i.e., from poor to richcountries, contrary to the prediction of the standard textbook neoclassical model.2 To explainsuch reverse flows, one needs to abandon the central tenet of the neoclassical paradigm; countries
differ in per capita income due to the differences in the capital/labor ratios. In reality, of course,many other factors can account for the difference in per capita income. For example, somecountries may be richer than others because they are more productive. Then, capital would flow
upstream, because the lenders would get higher return in the rich countries. Or, some countries
may be richer due to their superior credit market institutions. Then capital would flow upstream,
because rich countries do better jobs protecting the interest of lenders. Indeed, a simple
theoretical model can be used to show how exogenous cross-country variations in productivity or
in institutional quality can generate reverse capital flows (as will be demonstrated in section 3).
One might think intuitively that this logic should carry over even if the rich countries are moreproductive owing to their superior institutions. This paper aims to show theoretically that
productivity differences that arise endogenously due to institutional differences have effects on
capital flows that are opposite of exogenous productivity differences, and that institutional
differences might have non-monotonic effects on capital flows through their effects on
productivity. 3
In the model presented below, countries differ in the institutional quality (IQ) of theirdomestic credit markets. Saving flows freely across countries, equalizing the rate of return.4 In
each country, entrepreneurs have access to a variety of heterogeneous investment projects withproductivity-agency cost trade-off: a more productive project comes with a bigger agency cost.
As entrepreneurs compete for funding, credit goes to the projects that generate the highest returnto the lenders (net of agency cost), which are not the most productive ones. The key feature of

2See, for example, Gourinchas and Jeanne (2007) and Prasad, Rajan, and Subramanian (2007).
To economize language, we simply say “exogenous productivity differences” to mean productivity differences
caused by factors unrelated to the institutional quality of domestic credit markets, which also include endogenous
productivity differences, for example, due to human capital externalities discussed by Lucas (1990).
4
Thus, this is not a model of international financial market imperfections. A country’s poor IQ reduces the rate of
return to lending to its entrepreneurs, regardless of the nationality of lenders. All lenders from all countries earn
the same rate of return. In reality, of course, there might be a significant cost of lending to foreigners. However,Page 2 of 28
3

©Kiminori Matsuyama, Institution, Productivity, and Capital Flowsthe model is that the agency cost of each project depends not only on the nature of each project,
but also on the country’s IQ. More productive projects, due to their bigger agency problems, aremore affected by the country’s IQ. In this setup, productivity differences arise endogenously due
to IQ differences, because IQ affects the productivity-agency cost trade-off, hence the types ofprojects financed in each country. And it is shown, perhaps counter-intuitively, that an institutioninduced productivity improvement, though it leads to a higher output and a higher wage just likean exogenous one, leads to a lower investment and a current account surplus (i.e., capitaloutflow), unlike an exogenous one.
Why do investment and capital flows respond differently to endogenous productivity
changes? Let me try to offer verbally an intuition to this rather counterintuitive result. (Later,
this will be shown more formally, which is precisely one of the main goals of the model.)Although it is often overlooked, higher productivity generally has two effects that work in the
opposite directions. The first effect is that more output can be produced with less investment.
The second effect is that a higher rate of return makes the lender willing to finance moreinvestment. In the exogenous case, both effects operate. However, under the relatively mild
assumption, satisfied for example when the production function is Cobb-Douglas, the second
effect dominates the first, which means that higher productivity leads to a higher investment, andhence to a current account deficit (i.e., capital inflow). When productivity rises in response to abetter IQ in our model, it is because the composition of credit shifts toward more productive
projects, which come with bigger agency problems. This offsets any effect on the rate of return to
the lender (i.e., net of the agency cost) that the resulting productivity improvement might have.5
This means that the first effect dominates the second, hence a lower investment and a current
account surplus (i.e., capital outflow).
Note also that this makes an overall effect of IQ on capital flows generally ambiguous,
because two effects work in the opposite directions. First, holding productivity constant, a better
adding such barriers to international capital flows into the model would reduce the volume of flows, but would notchange the direction of flows.
5
The alert reader might notice that this is nothing but the envelope theorem, as will be shown more formally later.
The market always selects the project that maximizes the rate of return to the lender, holding IQ constant. When achange in IQ changes the project selection, the effect on productivity is of the first-order, but the effect on the rateof return to the lender is of the second-order.
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

IQ causes to a current account deficit (i.e., capital inflow), because it makes the country a more
attractive place to invest. Second, induced productivity improvement causes a current accountsurplus (i.e., capital outflow), because the country needs less investments to produce more output.
This means that, even if the rich are more productive and have better IQ than the poor, there is no
reason to expect large capital flows in either direction. Or the lack of such capital flows should
not be interpreted as the prima facie evidence for the presence of significant barriers forinternational capital flows.
Some parametric examples also suggest that improving IQ, while monotonically increasing
the capital stock and wages, leads initially to a lower investment and a current account surplus(i.e., capital outflow) and then to a higher investment and a current account deficit, (i.e., capital
inflow). Such an U-shaped response of capital flows to IQ implies that, if countries inherently
differ only in IQ, middle-income countries run a current account surplus (i.e., capital outflow),while high-income and low-income countries run a current account deficit (i.e., capital inflow).
However, these countries experience capital inflows for different reasons. High-income countries
experiences inflows because they do better jobs protecting the interest of lenders, while lowincome countries experiences inflows because they are less efficient in allocating the investment.
It also suggests that, starting from very low IQ, an institutional reform would help low-income
countries to experience both a growth and a current account surplus at the same time.
Even if the indirect effect of IQ through productivity is not large enough to offset its direct
effect, hence unable to generate non-monotonic effects, the prediction that institution-induced
productivity differences have the effects on the patterns of capital flows opposite fromproductivity differences due to other factors should provide some cautions when interpreting theempirical evidence. For example, imagine that the rich countries are more productive partly due
to their better IQ and partly for other reasons, say, human capital externalities. Then, one’s
failure to properly separate the two sources of productivity differences could lead one tooverestimate the effects on capital flows of IQ differences and to underestimate those of
productivity differences due to human capital externalities.
Many studies have already examined the effects of domestic credit market imperfections
on international capital flows. In models of Gertler and Rogoff (1990) and Matsuyama (2004,
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows2005), countries do not differ in their institutional quality, but the presence of credit market
imperfections give advantage to those entrepreneurs with higher net worth when competing for
credit, which could cause reverse capital flows. In models of Sakuragawa and Hamada (2001),
Caballero, Farhi, and Gourinchas (2008), and Ju and Wei (2010), among others, reverse flows
occur because countries differ in their IQ, but productivity does not respond to the IQ.6
Productivity responds endogenously through a change in the composition of credit across projects
with different productivity in the closed economy dynamic macro model of Matsuyama (2007),
but the reason why the composition changes is due to an endogenous movement of borrower net
worth over time, not due to a change in IQ.7
The non-monotonic patterns of capital flows implied by the U-shaped response to IQ, i.e.,current account surpluses of the middle-income countries finance current account deficits of thelow- and high- income countries, might be somewhat reminiscent of the empirical finding by
Gourinchas and Jeanne (2007), who called it the “allocation puzzle.” It should be noted,
however, that the primary goal of this paper is not to account for the observed patterns of capital
flows. Rather, it is to clarify a mechanism (previously unknown, to the best of my knowledge),
through which the quality of domestic financial markets affects productivity, the aggregate
investment, and the patterns of capital flows. To this end, the model developed below deliberately
abstracts from many other factors that affect the patterns of capital flows. In particular, the model
is set up in such a way that the aggregate saving does not respond to changes in IQ nor inproductivity. In this respect, the recent studies by Song, Storesletten, and Zilibotti (2011) and
Buera and Shin (2010) are noteworthy. Partly motivated by the allocation puzzle, they haveshown that, when the economy starts booming after an economic reform that triggers the processof reallocation from the old and less efficient to the new and more efficient sectors, it experiences
a current account surplus (i.e., capital outflow) because the aggregate saving grows faster than
the aggregate investment, under the assumption that the new and more efficient sectors areborrowing-constrained due to the domestic credit market imperfections. This might lead some to

6

Strictly speaking, reverse flows in the Caballero-Farhi-Gourinchas model occurs because some countries have alimited supply of saving vehicles. However, they suggested that this could be attributed to the country’s
institutional problem.
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flowssuspect that their mechanisms would be weakened, if the institutional quality of domestic credit
markets improves as a result of the very economic reform that triggers the boom. The result
obtained here, however, suggests that such an improvement could even magnify capital outflows
generated by the economic reform.8 In this sense, the present study is complementary to theirstudies.
The rest of the paper is organized as follows. After setting up the model in section 2,
section 3 briefly discusses the patterns of international capital flows when both productivity
differences and IQ differences are exogenous. Section 4 shows how productivity responds to IQ
through its effect on the composition of credit and explains why such endogenous productivity
differences have opposite implications on the investment and capital flows. Section 5 looks at thepatterns of international capital flows when countries differ only in IQ but IQ differences causes
productivity differences, first for the case with two projects and then for the case with acontinuum of projects. From section 2 through section 5, the model is described as a two-sector,
two-period model for the ease of presentation. However, the model can also be given a onesector, and infinite-period interpretation, as explained in Section 6. Section 7 concludes.

2.

The Setup; A Two-sector, Two-period Interpretation
There are two periods: t = 0, “today” and t = 1, “future.” (Section 6.2 shows how thistwo-period setup can be reinterpreted as an infinite period model within an overlapping
generations framework.) In t = 0, the endowment is allocated between consumption in t = 0 andinvestment projects. In t = 1, these investment projects generate capital, K, which are combinedwith labor, L, available in fixed supply, to produce the consumption good with CRS technology, Y= F(K, L) ≡ f(k)L, where k ≡ K/L is the capital-labor ratio and f(k) is output per labor, satisfying
the usual properties, f ' (k ) > 0 > f " (k ) and f ' (0)   .

7

Also related is Buera, Kaboski, and Shin (2010), which shows that productivity responds endogenously to IQ by
affecting the sectoral composition in a two-sector model.
8
Of course, it is important that the reform will not completely eliminate the credit market imperfections for this tobe true. As stressed in Matsuyama (2008), credit market imperfections have generally non-monotonic effects, sothat one should not study the effects of improving the credit market imperfections by making a binary comparison
between a model with the perfect credit market and a model without.
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

The world economy consists of a finite number of countries, indexed by c  C. (For the
moment, however, we suppress the country index to keep the notation simple.) In each country,
there are two types of agents. First, there is a continuum of savers/workers with measure L, eachof whom has ω units of endowment in t = 0 and supplies one unit of labor and earns w(k ) f (k )  kf ' (k ) in t = 1. They seek to maximize the quasi-linear preferences of the form:U s  V (C0s )  C1s ,V > 0 > V

subject to the budget constraint,
C1s  r (  C0s )  w(k ) ,where r is the (gross) market rate of return on their saving. From the first-order condition,
V ' (C0s )  r , each saver/worker consumes C 0s  (V ' ) 1 (r ) in t = 0, so that their total saving isequal to:

S s (r )    (V ' ) 1 (r ) L .
Note that the saving schedule is independent of the wage rate and hence the production side ofthe economy.9 This feature of the model helps us to focus on the primary goal of the analysis, i.e.,
to understand how IQ or productivity changes affect the investment side of capital flows, byremoving the saving channel.
Second, there is a continuum of borrowers/entrepreneurs with measure E, each of whom
may be endowed with (small) ωb ≥ 0 units in t = 0. They consume only in t = 1 and hence save allof ωb in t = 0. Each entrepreneur has access to a set of projects, J. A type-j ( J) project
converts mj units of the endowment to Rjmj units of “physical capital,” by borrowing mj  ωb at
the market rate of return, r. They aim to maximize period-1 consumption.10 By running a

9The two assumptions are responsible for this feature. First, the quasi-linearity ensures that all the income effect isentirely absorbed by period-1 consumption. (In addition, the quasi-linearity rules out the possibility of a backwardbending saving schedule.) Second, the wage income is not earned in t = 0. Considering that t = 1 should beinterpreted to include all future periods, these assumptions are not so unreasonable. However, they are notnecessary to make the saving schedule independent of the wage rate. Alternatively, this can be achieved, forexample, by separating the identity of the savers and the workers, and assuming that the workers do not save.
10
For the moment, we treat the scale of investment mj as a fixed parameter. It should become clear later that
entrepreneurs would not gain even if they were allowed to invest less than mj. In contrast, it is necessary to assume
that they face the upper-bound in order to make their problem well-defined.
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

project-j, they can obtain R j m j f ' (k )  r (m j   b ) = [ R j f ' (k )  r ]m j  r b , which is greater thanor equal to r b (the amount obtained by lending instead of borrowing to running any project) iff
R j f ' (k )  r ,(PC-j):

where (PC-j) stands for Profitability Constraint for a Type-j. This constraint implies thatR j f ' (k ) is the maximal rate of return that they are willing to offer to the lender by running a

type-j project. Furthermore, each entrepreneur has access to any project type-j  J. This means
that, in a world with the perfect credit market, competition among entrepreneurs would drive up
the market rate of return to r  max jJ R j  f ' (k ) and only the most productive projects,
Arg max jJ R j , would be funded.

However, the credit market is imperfect in this world. The imperfections are introducedby the assumption that borrowers/entrepreneurs can pledge no more than a fraction 0 < λj < 1 ofthe project-j revenue for the repayment.11 This condition can be stated as:(BC-j):

 j R j m j f ' (k )  r (m j   b ) ,where (BC-j) stands for Borrowing Constraint for a Type-j. By combining (PC-j) and (BC-j), we
may define the maximal rate of return that an entrepreneur could credibly offer to the lender byrunning a type-j project as follows:
rj (PC-j)+(BC-j):RjMax 1, (m j   b ) /  j m j f ' (k ) .

Again, recall that every entrepreneur has access to any project type-j  J. Hence, competition
among entrepreneurs ensure that, in equilibrium, the credit goes only to the projects with thehighest rj, so that



Rj
r  Maxrj   Max  f ' (k )bj Jj J  Max 1, ( m   ) /  m 
j
j
j





11



See Tirole (2005) for the pledegeability approach for modeling credit market imperfections, and see Matsuyama(2008) for a variety of applications in macroeconomics. Although various stories of agency problems can be told tojustify the assumption that only a fraction is pledgeable, its main appeal is the simplicity, which makes it suitable
for studying general equilibrium implications of credit market imperfections.
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

Note that the ranking of projects may depend on R j ; m j ;  j jJ , but not on k nor r. This meansthat only one project is funded by the credit market.12 By denoting such a project byj*  Arg max jJ r j ,  R j* I R j*,r  Maxr j   
 f 'bjJ
 Max 1, (m j*   ) /  j*m j*   L where I is the aggregate investment, i.e., the total amount of the endowment left unconsumed andallocated to the investment projects in t = 0, which are transformed into capital in t = 1, at the rateequal to R j * , because K  ( R j *m j * )( I / m j * )  R j *I .13
In what follows, we focus on the case where (BC-j) is more stringent than (PC-j). Thiscan be achieved by setting ωb = 0.14

Then, the above expression is simplified to:R Ir  Maxr j   Max j R j f ' k   ( j* R j* ) f ' k  = ( j *R j * ) f '  j *  .
jJ
 L 
In words, the credit goes to the projects that generate the highest pledgeable rate of return.15 This
expression can be inverted to obtain the Aggregate Investment Schedule, which is decreasing in r :(1)

I (r ) L f '1 r 
Rj* R
 j* j* I < 0.

Since the Aggregate Saving Schedule is an increasing function of r,
(2)



1

 

1



S (r )   b E    V ' (r ) L =   V ' (r ) L ,S > 0the Current Account Schedule, the difference between the aggregate saving and investment, isalso increasing in r:

12

In the case of a tie, the entrepreneurs would pick the project type that is more productive.
Given that each entrepreneur face the upper-bound, mj*, it is necessary to assume that there are sufficiently many
entrepreneurs, E  I / m j* , to ensure the interior solution for I. This is the only role that the parameter E plays in13

the model.
14
In addition, setting ωb = 0 for all countries eliminates the reverse capital flows mechanism that operate throughthe cross-country differences in the borrower net worth, already studied by Gertler and Rogoff (1991) andMatsuyama (2004, 2005) and others.
15
Since r  ( j* R j* ) f ' k   R j* f ' k  , (PC-j*) holds with strict inequality, hence the entrepreneurs have an
incentive to invest as much as possible. For this reason, it is necessary to impose the upper-bound. On the other
hand, entrepreneurs would not gain from investing project-j less than mj.
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

(3)




1
1
 f '1 r  .
CA(r )  S (r )  I (r ) = L   V ' (r ) 
Rj*
 R

 j * j * CA > 0

These schedules are illustrated by Figure 1, the Metzler diagram. If a country were in autarky, its
domestic market rate of return would adjust to equate its aggregate saving and the aggregate
investment, so that
CA(r A )  S (r A )  I (r A )  0 ,where rA is the country’s autarky market rate of return, given at the intersection of its aggregate
saving and investment schedule.16
Instead, imagine that this country can lend and borrow at the rate r = r*, determined at
the world financial market. More specifically, suppose that period-0 endowment is(intertemporally) tradeable at the price r* for a unit of period-1 consumption good, while thecapital stock generated by the project and labor are not tradeable. Then, if rA < r* , as depicted in
Figure 1, this country runs a current account surplus (i.e., capital outflow) in t = 0.17 If rA > r* ,this country runs a current account deficit (i.e.. capital inflow) in t = 0.
To determine r*, let us suppose that saving can flow freely across borders to equate therates of return everywhere. Since the world as a whole is a closed economy, the equilibrium rateof return is given by the condition:cc S (r*)   I (r*)
cC

cC

  CA (r*)  0 ,ccCwhere superscript c  C, the country index, is now made explicit. Recall that
CAc (r )  S c (r )  I c (r ) is strictly increasing in r. Thus, the autarky rates of returns, r cA cC ,dictate “chains of comparative advantage” in intertemporal trade, i.e., the patterns of capital
flows. If we list the countries from the left to the right in the increasing order of their autarky
rates of return, we can draw a line somewhere in the middle such that all the countries on the left
(right) side of the line experience current account surpluses (deficits). In other words, if aNote that rA is independent of L, a feature that turns out to be convenient later in section 6.2.
17
Recall that, in the balance-of-payment accounting, a surplus in the current account, CA c (r )  S c (r )  I c (r ) > 0
16

is a deficit in the financial account (used to be called the “capital account”), FA c (r )  I c (r )  S c (r ) < 0, and hence
a capital outflow.
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flowscountry’s autarky rate of return is higher than another country’s autarky rate of return, the former
would experience a current account surplus (i.e., capital outflow) whenever the latter experiences
a current account surplus (i.e., capital outflow), and the latter would experience a current accountdeficit (i.e., capital inflow) whenever the former experiences a current account deficit (i.e., capital
inflow). In particular, if C = 2, the country with the higher autarky rate runs a surplus (or capitaloutflow) and the other country runs a deficit (i.e., capital inflow).

3.

Patterns of Capital Flows with Exogenous Productivity and IQ
First, let us consider the case where there is one type of the project, hence IQ cannot

possibly affect the composition of credit, and hence productivity of projects funded. By dropping
the project index, j, the aggregate investment schedule, eq.(1), becomes simply:(4)

I (r ) L f '1  r  ,R
 R 

I < 0,which can be used to examine the effects of IQ and exogenous productivity.
For example, a higher λ captures the effect of a better IQ. This unambiguously shifts theinvestment schedule to the right in Figure 1, which leads to a higher rA. Hence, if countries differ
only in IQ, those with better IQs become richer (measured in the wage and per capita income) andrun current account deficits (i.e., capital inflows), while those with worse IQs are poorer and run
current account surpluses (i.e, capital outflows), generating the reverse patterns of capital flows.
In contrast, productivity parameter, R, appears twice in the equation. The aggregate
investment is decreasing in the first R, while increasing in the second R. They capture the two
effects of (exogenously) higher productivity. On one hand, more output can be produced withless investment. On the other hand, the higher rate of return makes the lenders willing to financemore investment. Simple algebra shows d log( I ) / dR  1 /  (k )  1 , where  (k )  kf " (k ) / f ' (k )> 0. Thus, higher productivity leads to a higher investment if and only if  (k )  1 , the condition
satisfied, for example, for the Cobb-Douglas case, f (k )  A(k ) since  (k )  1   . In what
follows, we will focus on the case where this condition holds. Then, a higher R shifts theinvestment schedule to the right in Figure 1, leading to a higher rA. Thus, if countries differ only
in exogenous productivity, those with higher Rs are richer (measured in the wage and per capita
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

income) and run current account deficits (i.e., capital inflows), while those with lower Rs arepoorer and run current account surpluses (i.e, capital outflows), generating the reverse patterns ofcapital flows.

4.

Modeling Endogenous Response of Productivity to Institutional Quality
Let us now go back to the world where entrepreneurs have access to heterogeneous

investment projects. Up to now, we have merely assumed that projects differ both in productivity
and in pledgeability, but have not specified how these differences are related to each other. We
now impose more structures to introduce institution-dependent productivity-agency cost tradeoff. More concretely, suppose that pledgeability of project j in country c is decomposed into two
components, as follows:(5)ccj  [ ( R j )] .

First, 0   ( R j )  1 is the project-specific component, which is common across countries. It
represents the agency problem associated with each project-type, and () is strictly decreasing,which captures the trade-offs between productivity and the agency problem. Second, θc > 0 is thecountry-specific component, which represents the degree of credit market imperfections incountry c, thus the (inverse) measure of its IQ. A bigger θ makes pledgeability smaller,
exacerbating the agency problem. Furthermore, as the credit market becomes perfect, θc  0,

cj  1 for all j, so that all projects become fully pledgeable, and hence the credit would go to themost productive projects. Note that the assumed functional form satisfies the property of strict
log-submodularity in R and θ.18 In words, a more productive project, with its bigger agency
problem, suffers disproportionately more in a country with a bigger institutional problem.
Under this specification, the country’s IQ affects productivity of projects funded. To see
why, recall that the credit goes to the projects that generate the highest pledgeable rate of return.
In other words, the market solves,
18

~
~
~
More generally, let cj   ( R j ;  c )  1 . Then,  is strictly log-submodular in R and θ iff  2 log  / R < 0.

The assumed functional form in (5) is not crucial, as long as it satisfies strict log-submodularity. Nevertheless, eq.
(5) is algebraically simple and more convenient because it can be decomposed into the project-specific and countryspecific components to discuss them separately.
Page 12 of 28

©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

max{ j R j }  max [ ( R j )] R j .
j J

Rj

Figure 2 illustrates this maximization problem. As IQ deteriorates (a bigger θ), thegraph,  j  [ ( R j )] , shifts down. Furthermore, with strict log-submodularity, this negative
effect is disproportionately larger for more productive projects with bigger agency problems,
which is illustrated by a tilting movement of the graph. As a result, the credit shifts towards toless productive projects with smaller agency problems. In other words, the solution, R(θ), is
decreasing in θ.19
By inserting R(θ), the aggregate investment schedule, eq. (1), can be now rewritten as:(6)

I ( r ; ) 



L
r
 .
 f '1 
R ( )
  ( R ( )) R ( ) Note that R(θ) appears three times in the equation. An increase in the first R(θ) reduces theinvestment. This effect, i.e., less investment is needed to produce more output, is of the firstorder. In contrast, the remaining effects are of the second-order, because a change in the second
R(θ) and a change in the third R(θ) offsets each other. This is because R(θ) is chosen to maximize[ ( R )] R . When R(θ) changes due to a change in θ, it is because the composition of credit shifts
towards projects that are not only more productive but also subject to bigger agency problems.
As a result, it has negligible effects on the pledgeable rate of return, which eliminates the usual
effect of making the lenders willing to finance more investment. This is nothing but the envelope
theorem. The credit market always selects the best project for the lenders under the institutional
constraint. Hence, an improvement in IQ has only negligible effects on the lenders. For thisreason, an increase in R(θ) through a change in θ reduces the investment, unlike an exogenous
increase in R.20

19

If there is a continuum of projects with the range of Rj being an interval, as in the case studied in Section 5.2,~
this can also be shown by differentiating ( R;  )  log  ( R;  )  log R with respect to R to obtain
 R ( R( ); )  0 and  RR ( R ( ); )  0 and then by applying the implicit function theorem to obtain~
R ' ( )   R ( R ( ); ) /  RR ( R( ); ) , and hence sgn R ' ( ) = sgn  R ( R ( ); ) = sgn  2 log  / R < 0.
20
It is worth noting that the statement, an increase in R(θ) through a change in θ reduces the investment, is quite
general. It does not depend on J , () , nor f () . Nor does it depend on the assumption of strict logsubmodularity, which only plays a role in determining how R(θ) depends on θ.
Page 13 of 28

©Kiminori Matsuyama, Institution, Productivity, and Capital FlowsThe above paragraph is concerned with the indirect effect of IQ on the investment throughits effect on productivity. In addition, there is the direct effect of improving IQ (a lower θ), which
increases the investment. The combined effect on the investment is generally ambiguous, so weneed to look at some specific examples. In contrast, improving IQ (a lower θ) ambiguously
increases R(θ)I(r, θ), and hence the country’s wage and per capita income.21

5.

Patterns of International Capital Flows with Endogenous Productivity
We now look at several examples to understand how exogenous IQ differences acrosscountries shape the patterns of international capital flows, when IQ differences also cause
productivity differences.
5.1.

A Two-Project Case:
Consider first the case with two projects, J = {0,1}, with R0 < R1 and 1   ( R0 )   0 >( R1 )  1 . Thus, a type-1 project is more productive than a type-0 project, but it is more
subject to the agency problem. Hence, the pledgeable rate of return declines faster for type-1
projects than for type-0 projects when IQ deteriorates (a bigger θ), as shown in Figure 3a.

Only

type-0 projects are financed when   ˆ and only type-1 projects are financed when   ˆ , where
the switch occurs at ˆ  log( R1 / R0 ) / log( 0 / 1 ) . Figure 3b shows R( ) . Note that
productivity, R( ) , jumps at   ˆ , but the pledgeable rate of return,  ( R ( ) R ( ) , changes

smoothly at   ˆ . Thus, when productivity changes as  crosses ˆ , the first effect of
productivity improvement, --less investment is needed to produce more output--, dominates thesecond effect,--lenders are willing to finance more investment. Hence, the investment schedule
shifts to the left, when productivity increases at   ˆ . With the fixed upward-sloping saving
schedule, this translates into a nonmonotone response of rA to a change in  , as depicted in
Figure 3c.22

To see this, for a fixed r  ( R( )) R ( ) f ' (k ) , a lower θ increases  ( R( )) R ( ) and hence k = R(θ)I/L, y =f(k), and w = f(k) ‒ kfˊ(k).
22
Figure 3c is drawn for Λ0 = 1, which implies that the graph is flat for   ˆ . For Λ0 < 1, the graph would have a21

negative slope after it jumps upward at   ˆ . The assumption,  (k ) < 1, ensures that the graph starts at
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

5.1.1: A Two-Country WorldNow suppose that there are two countries, C = {N, S}, where N stands for the rich Northand S for the poor South, with θN < θS. Let us assume that the two countries are identical in allother dimensions.
Figure 4a depicts the case of θN < θS < ˆ . This means that rAN > rAS, which implies CAN <0 < CAS. Thus, capital flows from S to N. In this case, both countries use the same technologies,
but N’s superior institution causes the reverse flows, because the interest of lenders is better
protected in N than in S.

~
Figure 4b depicts the case of θN <  < ˆ < θS . Again, rAN > rAS, which implies CAN < 0< CAS. Thus, capital flows from S to N. In this case, countries differ both in productivity and ininstitutional quality. However, the institutional quality difference is the cause for the reverse
flows. Although N is more productive than S, it is false to attribute the reverse capital flows to
the productivity difference. Indeed, in this case, endogenous response of productivity partially~
offsets the effect of institutional difference on the capital flows. Figure 4c depicts the case of  <θN < ˆ < θS . This means that rAN < rAS, which implies CAN > 0 > CAS. Hence, capital flows fromN to S. However, the logic behind these capital flows from the rich to the poor is quite different
from the standard neoclassical logic. In this case, S is less productive due to its inferior
institution, and hence it needs to borrow from abroad. Thus, the causality runs from theunderdevelopment to foreign borrowing. It is false to interpret this case as showing that “foreign
capital” somehow undermines South’s development.
Now, imagine that, starting from the case depicted in Figure 4c, S manages to improve its
institution and succeed improving its productivity, but does not catch up with N. This thought
experiment is illustrated in Figure 4d. Capital flows are reversed. S’s current account turns froma deficit to a surplus. (That is, capital starts flowing out, instead of flowing in.) This illustrates
one scenario in which a poor country can experience both a rapid growth and a capital outflow
after the reform.

~  0 above the dotted line, and cross the dotted line at     ˆ . If  (k ) > 1, the graph could stay below the
dotted line for all   ˆ .

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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

5.1.2: A Three-Country World:
Now suppose that there are three countries, C = {N, M, S}, with θN < θM < θS. Again,
assume that these countries are identical in all other dimensions.
~Figure 5a depicts the case of θN<  < θM< ˆ < θS . This means that rAN < rAS < rAM, which
implies CAN < 0 < CAM, so that capital flows into N, and out of M, hence reverse flows between
N and M. Furthermore, among developing countries, capital flows from the more successful M to
the less successful S, which is reminiscent of the allocation puzzle.
~
Figure 5b depicts the case of  <θN< ˆ < θM < θS. This means that rAN < rAS = rAM, which
implies that CAN > 0 > CAM, CAS, so that capital flows from N to M and S. This is because (andnot despite that) the most developed N has higher productivity than M or S.
~
Figure 5c depicts the case of  < θN <θM< ˆ < θS . This implies that capital flows into S
and out of M. Again, among developing countries, capital flows from the more successful to theless successful among developing countries, because (and not despite that) the more successful ismore productive.
Now, consider the thought experiment, in which some developing countries, represented
by M, succeeded in improving their institutions, while other developing countries, represented by
S, are left behind. This is illustrated by Figure 5d, which shows that M’s current account turns
from a deficit to a surplus (capital starts flowing out, instead of flowing in). Thus, M experiences
both a rapid growth and a capital outflow after the reform. Furthermore, N’s current accountcould turn from a surplus to a deficit as a result of M’s growth.

5.2

A Continuum of Projects Case
One might think that the U-shaped patterns obtained above may be driven by the two

features of the set of available technologies assumed, J = {0,1}. First, its discrete nature meansthat the autarky rate of return jumps when the switch occurs. Second, its finiteness means thepresence of the most productive technology, type-1, so that, once a country’s IQ becomes
sufficient good, a further improvement in IQ could not improve productivity. To show that the
U-shaped patterns can arise more generally, this subsection considers the case where there is acontinuum of available projects with no upper-bound on the productivity.
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©Kiminori Matsuyama, Institution, Productivity, and Capital FlowsMore concretely, suppose Rj  [R0,∞) for j  J = [0,∞), with
 1 1  R  
( R j )  exp    j   with γ > 0.
    R0  

Note that  ( R0 ) = 1; 0 <  ( R j ) < 1 for Rj > R0 and  ( R j ) is decreasing in Rj. This captures thetrade-off between productivity and the agency problem.
The market selects the project the generates the highest pledgeable rate of return, i.e., theproject that solves Max{ j R j }  Max[ ( R j )] R j . Thus,
R ( )  R0 /  1 / 

with



[ ( R ( ))] R ( ) = R0 e ( 1) / 



1/ 

for 0 < θ < 1,both of which are decreasing in θ. Thus, as the IQ deteriorates, the credit shifts towards lessproductive projects and the lenders obtain lower rate of returns. Furthermore, lim  0 R ( )   ,so that productivity continues to improve as IQ improves. In contrast,R( ) = R0

with[ ( R ( ))] R ( ) = R0,

for θ ≥ 1, so that the credit goes to the least productive but fully pledgeable project.
Inserting the above expressions toR( ) R ( ) f ' R( ) I   r ,L

and differentiating with respect to θ yield:d log I 1    1  1 
,
d

 

where  (k )  

kf " (k ),f ' (k )for 0 < θ < 1.

If η(k) > 1, I(r;θ) and hence rA are increasing in θ. In this case, capital flows from the rich to thepoor, simply because the more efficient rich needs less investment. This is not an interesting case,as it has nothing to do with the endogeneity of productivity. If η(k) < 1, I(r;θ) and hence rA are
increasing in θ > 1– η(k), and decreasing in θ < 1– η(k).
For the Cobb-Douglas case, f k   Ak  . Then, η(k) is constant and η = 1 – α < 1, andthe investment schedule is given by log I (r ; )  (r )    1   log  for θ < 1, and = (r ) for θ> 1, where (r ) is independent of θ. Note that
I(r;θ) is decreasing in θ < α and increasing in α < θ < 1.
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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows



~
~
~
I(r;θ) > I(r;1) if θ <  and I(r;θ) < I(r;1) if  < θ < 1, where   1 is the second solution~
to h( )    1   log   0 , and satisfies 0     .

With the fixed upward-sloping saving schedule, this translates into U-shaped patterns of the(autarky) rate of return, as shown in Figure 6, despite that R(θ) responds smoothly to θ in thepresence of a continuum of projects, and it is unbounded. Therefore, all the patterns of capital
flows described for the two-projects case in the previous section can also occur for this case as
well.

6.

Alternative Interpretations

6.1

A One-Sector Interpretation
Up to now, the model has been given a two-sector interpretation. That is, theentrepreneurs run projects that produce tangible “physical capital,” in the capital goods sector,
which is rented out to the consumption goods sector. Taken literally, this means that IQ affects
the investment and capital flows through its impacts of the productivity of capital goods sector.
This is consistent with the empirical evidence suggesting that the relative prices of capital goods
to consumption goods are higher among less developed countries.23 Nevertheless, it is not anessential element of the argument, and the mechanism does not rely on the two-sector structure.
To show this, this subsection offers a one-sector interpretation of the model.
Imagine that the economy produces the single consumption good, using the endowment
and labor. In t = 0, entrepreneurs may invest mj units of the endowment to set up a type-j firm. A
type-j firm produces the consumption good in t = 1, using the labor input, n, with a concave
production function, y j   j (n) . Each firm hires labor in the competitive labor market at thewage rate, w, so that its employment would be determined by  j ' (n j )  w . Hence, the profit that
could be earned from running a type-j firm is  j  max{ j (n)  wn} =  j (n j )   j ' (n j )n j .
Suppose that  j (n)  F ( R j m j , n)  f ( R j m j / n)n , where Rj is a parameter. Then, for agiven wage rate, w, the employment and the profit by a type-j firm can be written as n j  R j m j / k
23See, for example, Buera, Kaboski, and Shin (2010), Greenwood, Hercowitz and Krusell (2000), Hsieh andKlenow (2007).
Page 18 of 28

©Kiminori Matsuyama, Institution, Productivity, and Capital Flowsand  j  ( R j m j ) f ' (k ) , where k is defined uniquely for each w by w  f (k )  kf ' (k ) . If a type-j
firm can pledge up to λj fraction of its profit, the pledgeable rate of return for lending to type-j
firms would be  j j / m j =  j R j f ' (k ) , so that the credit flows only to those firms with thehighest λjRj. By denoting such firms by j*  Arg max jJ { j R j } , the equilibrium rate of returnearned by the lenders is
r   j * R j * f ' (k ) .

Since each active firm hires nj* = Rj*mj*/k, summing up across all firms yield the labor market
equilibrium condition,
L   n j*  R j*  m j* / k  R j*I / k ,where I is the aggregate investment. By combining these expressions, we obtainr   j * R j * f ' (k )   j * R j * f ' R j * I / L  ,from which eq.(1) and hence eq.(4) and eq.(6) will also follow. This alternative interpretation
thus gives the same predictions on the relationship between IQ, the investment and capital flows.
According to this interpretation, there is no separate investment good sector. Investment
is an productivity-enhancing expenditure of the consumption goods sector; Rj* = R(θ) is therealized productivity parameter in the consumption good sector; and k represents theorganizational (i.e., intangible) capital per worker, embodied in the firms that set up by
entrepreneurs. The assumption of nontradeability of k might be more natural under thisinterpretation. Furthermore, for f(k) = Akα, AR(θ)α may be viewed as the TFP of the consumption
goods sector firms.24

6.2

An Infinite Period Interpretation in an OLG framework
Some readers may find the two-period setup developed above too restrictive, because

each country’s intertemporal trade must be in balance due to the Walras’ Law, so that CA0 =CA(r) > 0 in t = 0 implies CA1 = ‒CA(r) < 0 in t = 1. Thus, taken literally, any country
experiencing a capital outflow today will experience a capital inflow in the future. However, thePage 19 of 28

©Kiminori Matsuyama, Institution, Productivity, and Capital Flowsabove setup can be given an infinite-period interpretation by embedding the structure into an
overlapping generations framework.25
Imagine now that there is an infinite number of periods, extending from t = 0, 1, 2, …. In
period t, a continuum of savers/workers, with their total endowment ωLt and total labor supply Lt,
and a continuum of entrepreneurs of mass Et are born and live for two periods. Those born in thesame period interact with each other just as described above. Thus, the savers/workers born inperiod-t finance the projects run by the entrepreneurs born in period-t, and the savers/workers
born in period-t work with capital generated by the projects in their second period (period t+1).
In this setup, there is no interaction across different generations. This means that, from theintertemporal budget constraint of each agent, the current account of generation born in period-t(generation-t) in period t+1 must be equal to the negative of the current account of thisgeneration-t in period t.
Consider a particular country whose IQ is given by θ. Then, the investment in period t is
It 



Lt
rt 1
  Lt I (rt 1; ) , f '1
R ( )


(
R
(

))

R
(

)



which differs from eq.(6) only in that Lt may vary over time. Likewise, the saving by generation-t
in period t can be written as:



1



S tt  Lt   V ' (rt 1 )  Lt S (rt 1 ) ,so that the current account by generation-t in period t can be written as:




1
rt 1
1
  Lt CA(rt 1; )CAtt  Lt   V ' rt 1  
 f '1 R( )  ( R( )) R( ) 
Since the current account by generation-(t‒1) in period t must be equal to the negative of thecurrent account by this generation in period-(t‒1),
CAtt 1   Lt 1CA(rt ; ) ,the current account of this country in period t is equal to:

24

The idea that capital can be viewed as a parameter in the production function, representing productivity, with theinvestment being interpreted as any productivity-shifting expenditure, which includes but is not limited to
manufacturing or purchasing capital goods, at least goes back to Uzawa (1969).
25
See Obstfeld and Rogoff (1996, Ch.2) for a survey on overlapping generations models of the current account.
Page 20 of 28

©Kiminori Matsuyama, Institution, Productivity, and Capital Flowst 1t

CAt  CAtt

 CA   Lt 1CA(rt ; )  Lt CA(rt 1; ) .

Suppose Lt  (1  g ) L t 1 , where g > 0 is a constant rate of population (or Harrod-neutral
productivity) growth, which is common across all countries. Then, in per capita term, thiscountry’s current account is:

cat 

CAt
 CA(rt ; )  (1  g )CA(rt 1; ) .
Lt 1

In this environment, the autarky equilibrium path of this country is characterized by aconstant autarky rate of return, rt  r A given by cat  gCA(r A ; )  0 . If this country has accessto the world financial market where it could lend or borrow at rt  r * ,cat  gCA(r*; )  0 if r*  r A ;cat  gCA(r*; )  0 if r*  r A .

Thus, the country experiences a current surplus (deficit) and capital outflows (inflows) if its
autarky rate is lower (higher) than the world rate, each period. This way, all of the results on theeffects of IQ differences discussed in the two-period setup can be restated in an infinite period
setup.

7.

Concluding Remarks
This paper presented a stylized model of the world economy to study how the cross-country differences in the institutional quality (IQ) of the domestic credit markets shape thepatterns of international capital flows when such IQ differences also cause productivity differences
across countries. Institution affects productivity by changing the composition of credit acrossheterogeneous investment projects with different productivity. Such institution-induced
productivity differences are shown to have effects on the investment and capital flows that are
opposite of productivity differences due to other factors. This implies that the overall effect of IQ
could generate U-shaped responses of the investment and capital flows, which means, among
other things, that there is no reason to expect capital inflows when a country is more productive
and has better institution protesting the interest of lenders, even if saving flows freely acrossborders to equalize the rates of return; that capital flows out from middle-income countries andflows into both low-income and high-income countries, and that, starting from a very low IQ, a
Page 21 of 28

©Kiminori Matsuyama, Institution, Productivity, and Capital Flowscountry could experience both a growth and a current account surplus after a successful
institutional reform. More generally, it provides some cautions when interpreting the empiricalevidence on the role of productivity differences and institutional differences on capital flows.
Furthermore, certain features of the model, such as poor IQ preventing productive technologies
from being adopted, institutional changes causing productivity change, etc., might have wider
applications besides capital flows.

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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

References:
Buera, Francisco J., Joseph P. Kaboski, and Yongskok Shin, “Finance and Development: A Taleof Two Sectors,” Working Paper 2010, forthcoming in American Economic Review.
Buera, Francisco J., and Yongskok Shin, “Productivity Growth and Capital Flows: The Dynamics
of Reforms,” Working Paper, September 2010.
Caballero, Ricardo, Emmanuel Farhi, Pierre-Olivier Gourinchas, “An Equilibrium Model of
Global Imbalances and Low Interest Rates, “American Economic Review, 2008, 358-393.
Gertler, Mark and Kenneth Rogoff, “North-South Lending and Endogenous Domestic Capital
Inefficiencies,” Journal of Monetary Economics, 1990.
Gourinchas, Pierre-Olivier, and Olivier Jeanne, “Capital Flows to Developing Countries: The
Allocation Puzzle,” Working Paper, 2007.
Greenwood, Jeremy, Zvi Hercowitz, Per Krusell, “Long-Run Implications of Investment-SpecificTechnological Change,” American Economic Review, 1997, 87(3), 342-362.
Hsieh, Chang-Tai, and Peter J. Klenow, “Relative Price and Relative Prosperity,” American
Economic Review, June 2007, 562-585.
Ju, Jiandong and Shang-Jin Wei, “Domestic Institutions and the Bypass Effect of Financial
Globalization,” American Economic Journal: Economic Policy 2 November 2010: 173204.
Lucas, Robert E. Jr., “Why Doesn’t Capital Flow from Rich to Poor Countries?” American
Economic Review, May 1990.
Matsuyama, Kiminori, “Financial Market Globalization, Symmetry-Breaking, and Endogenous
Inequality of Nations, Econometrica 2004.
Matsuyama, Kiminori, “Credit Market Imperfections and Patterns of International Trade andCapital Flows,” Journal of the European Economic Association, 2005.
Matsuyama, Kiminori, “Credit Traps and Credit Cycles,” American Economic Review, 2007.
Matsuyama, Kiminori, “Aggregate Implications of Credit Market Imperfections,” NBER
Macroeconomics Annual 2007, University of Chicago Press, 2008.
Obstfeld, Maurice and Kenneth Rogoff, Foundations of International Macroeconomics, MIT
Press, 1996.
Prasad, E.S.,R.G. Rajan, A. Subramanian, “Foreign Capital and Economic Growth,” Brookings
Papers on Economic Activity, 2007.
Sakuragawa, Masaya, and Koichi Hamada, “Capital Flight, North-South Lending, and Stages of
Economic Development,” International Economic Review, 42, February 2001; 1-24.
Song, Zheng, Kjetil Storesletten, and Fabrizio Zilibotti, “Growing Like China,” American
Economic Review, 101, February 2011, 196-233.
Tirole, Jean, Theory of Corporate Finance, Princeton University Press, 2005.
Uzawa, Hirofumi, “Time Preference and the Penrose Effect in a Two-Class Model of Economic
Growth,” Journal of Political Economy, 77, July-August 1969, 628-652.

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©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

Figure 1: Metzler Diagramr
I(r)CA(r*)

S(r)

r*
rA

O

Figure 2: Endogenous Productivity Response to Institutional Quality Change

λj
1Good IQ(small θ)
Bad IQ(large θ)[ ( R j )]
RjPage 24 of 28

©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

Figure 3: A Two-Project Case(Λ1)θR1

R1
Figure 3a(Λ0)θR0

R0

O

ˆ



R1
R0
Figure 3b

O

ˆ



rA
Figure 3c

O

~




ˆ

Page 25 of 28

©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

Figure 4: A Two-Country World

rA

O

rA

θ

N



~ S
 θ ˆ

O

Figure 4a

θ

N

~


ˆ

θ

S



Figure 4b

rA
rA

O

~ N
 θ ˆ
Figure 4c

θS



O

~
 θN θSˆθS

Figure 4dPage 26 of 28

©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

Figure 5: A Three-Country World

rA

rA

O

θN

~
 θM ˆ

~ θN ˆ θM θSOθSFigure 5a

Figure 5b

rA
rA

O

~
 θN θM ˆ
Figure 5c


θS

O

~



θN θM ˆ θM θS
Figure 5dPage 27 of 28

©Kiminori Matsuyama, Institution, Productivity, and Capital Flows

Figure 6: A Continuum of Projects Case

rA

O

~


α

1

θ

Page 28 of 28