Download This PDF is a selection from a published volume from... Economic Research Volume Title: NBER Macroeconomics Annual 2007, Volume 22

This PDF is a selection from a published volume from the National Bureau of
Economic Research
Volume Title: NBER Macroeconomics Annual 2007, Volume 22
Volume Author/Editor: Daron Acemoglu, Kenneth Rogoff and Michael
Woodford, editors
Volume Publisher: University of Chicago Press
Volume ISBN: 978-0-226-00202-6
Volume URL: http://www.nber.org/books/acem07-1
Conference Date: March 30-31, 2007
Publication Date: June 2008
Chapter Title: Aggregate Implications of Credit Market Imperfections
Chapter Author: Kiminori Matsuyama
Chapter URL: http://www.nber.org/chapters/c4078
Chapter pages in book: (p. 1 - 60)
1_
Implications
Aggregate
Market Imperfections
Kiminori Matsuyama,
University
families resemble one another. Each unhappy
"All happy
its own
Northwestern
of Credit
way/'
Leo
1
in
family is unhappy
Tolstoy,
Anna
Karenina
Introduction
that the market
It is widely
recognized
investment
credit to the most productive
economy
fails
to allocate
because
credit
the
trans
projects
are subject to agency problems.
In the presence
of such imper
as
net worth?also
known
the balance
sheet
the borrower's
fections,
across
in
crucial
roles
the
credit
entrepre
condition?plays
allocating
level of
neurs, firms, industries, and nations. A change in the aggregate
actions
and a change in the distribution
of wealth
thus affect the equi
Fur
of the credit and hence patterns of investments.
allocation
causes
a
in the investments
the resulting
further
thermore,
change
wealth
librium
in the level and distribution
of wealth, which
leads to a further
in
investments.
the
of
patterns
change
equilibrium
in part by the advances made
in the microeconomics
Stimulated
of fi
change
nancial markets
of credit market
business
and corporate
finance over the last 30 years, the problems
in
have recently found many applications
imperfections
and development,
and international
economics.
has left in its wake a bewildering
array of indi
with seemingly
conflicting results. For example, do the im
cycles, growth
this progress
However,
vidual models
as sug
to the macroeconomic
add persistence
dynamics,
and
Bernanke
Gertler
and
Moore
(1989), Kiyotaki
(1997), and
gested by
as suggested by Azariadis
others? Or, do they add volatility,
and Smith
and Banerjee (2005), and Matsuyama
(1998), Aghion
(2004b)? If they are
perfections
2
Matsuyama
is it because
for causing fluctuations,
the misallocation
of
responsible
or
creates
it
creates boom-and-bust
credit
recessions
because
cycles? Does
credit markets make fluctuations more or less volatile? Does
improving
the credit market
financial globalization
alleviate or exacerbate
imperfec
tions? Do
the rich and the poor help
households?
credit transactions
between
or magnify
to reduce
the inequality among
that credit market
This paper comes out of my conviction
imperfec
a wide
issues.
tions offer the key to understanding
range of important
are
so
rich
of
credit
market
Yet, aggregate
imperfections
implications
and diverse that one should not expect to find a simple answer of any of
come as no surprise that they
manner
inwhich dif
they depend on the
investments
with
each other,
different
interact
ferent agents and/or
and propagation
mechanisms.
which consequently
affects amplification
a particular
fam
This suggests
that the intuition gained from studying
the above
"either-or"
are so rich and diverse
questions.
because
It should
can be misleading
the results may be driven by the
because
made about the set of agents and investment proj
specific assumptions
ects that are competing
for credit.
ily of models
for understanding
This paper offers a road map
aggregate
implica
a diverse set
tions of credit market
By bringing
together
imperfections.
a unified framework,
it
of results (many existing and some new) within
aims
to draw
nections
a coherent
picture
so
that
one
is able
to see
some
close
con
across many
topics that
as unre
viewed
sometimes
results
between
seemingly
conflicting
or even
are ordinarily
treated separately
a simple, highly
of
abstract model
lated.1 To this end, I first develop
to capture all sorts of
is meant
which
credit market
imperfections,
this single model
transactions.
affect
credit
that
Using
agency problems
in se
I examine
the effects of credit market
imperfections
throughout,
or
will
be
The
discussion
ries of relatively
simple equilibrium models.
manners
in which different models
"close the system";
ganized by the
about the sets of agents and of proj
that is, based on the assumptions
in
for the credit and about the price effects of different
ects competing
vestment
mechanisms
and propagation
the amplification
be shown how a wide
range of ag
cause. They in
to the common
be attributed
projects, which determine
Itwill
in these models.
may
gregate phenomena
clude, among other things,
changes,2
development
cessions,
recurrent
technical
investment-specific
of inefficient re
traps, leapfrogging,
persistence
endogenous
boom-and-bust
flows, the rise and fall of inequality
trade. The framework
international
cycles,
reverse
across nations,
is also used
international
and
capital
the patterns of
some
to investigate
Aggregate
Implications of Credit Market
and distributional
equilibrium
credit markets.
One
spond
recurring
finding
impacts
of improving
is that the properties
to
non-monotonically
parameter
3
Imperfections
changes.
the efficiency
of equilibrium
For
example,
often
of
re
increas
net worth first leads to a higher equilibrium
rate of return
ing borrower's
a
to
rate of return; improving
and then
lower equilibrium
credit market
first leads to increased volatility
and then to reduced volatility; produc
first lead to greater inequality and then to reduced
improvements
Such
inequality.
suggests some cautions for studying
non-monotonicity
a
narrow class or a particular
their effects within
For
family of models.
in
to
their
understand
the
effects
of
im
credit
market
attempts
example,
tivity
with no credit market.
Yet,
study models
that the effects of an imperfect credit mar
to those of no credit market.
In their attempts
to under
many
perfections,
there is no reason
ket are similar
authors
to believe
stand the effects of improving
the credit market, many authors compare
with credit market
and models with
the perfect
imperfections
credit market. Yet, there is no reason to believe
the effects of (partially)
are
to
markets
similar
credit
of
those
credit mar
improving
eliminating
ket imperfections
completely.3
models
2 A Simple Model
of Credit Market
A Single Agent's
Perspective
Imperfections:
Let us start with
a simple and
im
highly abstract model of credit market
perfections, which will be used as a building block in all the equilibrium
models
below. Here, we will look at the problem
discussed
faced by a
a
or
in
its
environ
isolation, taking
firm)
single agent (an entrepreneur
ment
as
exogenous.
The world
lasts for two periods: 0 and 1. The agent is endowed with o>
1 units of the input in period 0 and consumes
only in period 1. There
are two ways
of converting
the period-0
con
input into the period-1
can
run
a
the
non-divisible
investment
First,
sumption.
agent
project,
converts one unit of the input in
which
period 0 into R units in con
in period 1 by
1 - a>at the gross market
rate of re
sumption
borrowing
turn equal to r. Second, the agent can lend x <w units of the
input in pe
riod 0 for rx units of consumption
in period 1.
<
The
is to maximize
the period-1
agent's objective
consumption.
By
- co to run
1
the
the
borrowing
project,
agent could produce R units of the
r(l
co)units need to be repaid, so that
consumption
good, from which
= R the period-1
the
(and
consumption
r(l
utility) would be equal to U
4Matsuyama
=
=
rco, the amount that
co) R r + rco.This is greater than or equal to U
rate r, if and
the agent could consume by lending at the gross market
-
only if
>
R
r.
(PC)(1)
the project return needs to be higher than (or equal to) the oppor
the agent eager (or
tunity cost of running the project in order to make
as the analogous
to
borrow
and
invest.
constraint
well
This
(as
willing)
Thus,
in all the models
constraints
Profitability
Even when
later) shall be called
developed
(PC) for
Constraint.
(PC) holds with strict inequality and hence the agent is ea
to
invest, credit market
ger
imperfections
might
keep the agent from
to the
somehow
To obtain credit, the agent must
generate
investing.
is determined
How
the
market.
lenders the rate of return, r,which
by
ever, for a variety of reasons, the entire project output, R, may not be used
it is assumed
To capture this in the simplest manner,
for the purpose.
to
that no more than a fraction, X, of the project revenue can be pledged
for the repayment.
Thus, the agent
the
lenders, if and only if
required by
the lenders
return
can generate
the rate of
XR> r(l
co).(BC)(2)
and
the agent is capable of borrowing
as
in
all
the
the
constraints
analogous
investing.
Constraint.4
for
models
later) shall be called (BC)
Borrowing
developed
is to
is b = 1 - co<XR/r, which
Another way of looking at this constraint
Only when
this constraint
This constraint
ismet,
(as well
value of the
is limited by the present discounted
say that that borrowing
can also be
revenue of the project, XR/r. This constraint
pledgeable
a
states
that
which
rewritten as co>1
XR/r,
sufficiently high net worth
overcome
the credit market
would
imperfection.5
and
to take place, the agent must be both willing
are
satisfied.
when
and
both
to
that
borrow,
is, only
(PC)
(BC)
capable
on X + co. If X + co>
Which
of the two is a relevant constraint depends
1, (PC) ismore stringent than (BC). That is, the agent can borrow when
do not
ever he wants
to borrow. In this case, credit market
imperfections
For the investment
the investment
In this simple,
decision.
highly
If X +
co<
1, on the other hand, (BC) is
more stringent than (PC). That is, credit market
imperfections may affect
investment.
A,
Indeed, if 1 <R/r < (1 co)
(PC) holds but (BC) does not,
investment project
that the agent cannot initiate the profitable
meaning
constraint.
due to the borrowing
affect
abstract model
of credit market
imperfections,
Aggregate
Implications of Credit Market
Imperfections
to capture
the pledgeability,
X, ismeant
restrict the agent's ability to finance the
The severity of these agency problems
factors
industry, or the institutional
5
all sorts of agency problems
that
investment
profitable
externally.
could depend
that determine
on the project, the
the general
effi
en
such as the quality of legal or contractual
ciency of credit markets,
or
more
state
of
the
financial
forcement,
corporate governance,
broadly
I will
of
For
later allow the
the
this
reason,
economy.
development
X, to vary across projects, across industries,
parameter,
pledgeability
across countries
in equilibrium models
with many projects, many
dustries,
or
or
in
countries.
many
In this simple, highly abstract model
of credit market
imperfections,
to capture the entrepreneur's
net
the input endowment,
co, is meant
more
the
firm's
balance
sheet
bor
the
or,
condition,
worth,
broadly,
For this reason, I will
rower's credit-worthiness.
later allow the net
worth
parameter,
heterogeneous
vestment when
co, to vary across agents in equilibrium models with
to depend on the past in
agents. Itwill also be allowed
the
of credit market
dynamic
implications
considering
imperfections.
Remark
1: The microeconomics
of credit markets
offers many different
to
the
that the bor
agency
assumption
justify
rowers cannot
the project revenue.6 The simplest
fully pledge
story
would
be that they strategically
obli
the repayment
default, whenever
cost.
each
exceeds
the
default
is
gation
Alternatively,
project
specific to
the agent and requires his services to generate
revenue.
the maximum
stories
that could be used
the services, the revenue would be reduced. Then the borrower,
towithdraw
his services, can renegotiate
the repayment;
by threatening
see Hart and Moore
Hart
Moore
and
and
(1994),
(1995),
(1997).
Kiyotaki
There is also the costly-state-verification
of
Townsend
(1979),
approach
used by Bernanke
and Gertler
(1989), Boyd and Smith (1997), and oth
ers. See also the moral hazard
and Tirole
approach used by Holmstrom
and
are
A
others.
to the is
number
of
studies
devoted
(1997,1998)
large
sues of the relative merit
of
different
and/or
(conceptual
empirical)
Hart
and
stories; see, for example,
agency
(1995, ch. 5, appendix)
Without
and Karaivanov
I
Paulsen, Townsend,
(2006). In this paper, however,
will not be concerned with
of which
the question
stories offer most
or
causes of
for the microeconomic
plausible
compelling
explanations
credit market
Instead, Iwill simply treat credit market
imperfections.
as
a
fact
of
and proceed with
their ag
life,
imperfections
investigating
or
the
reduced
abstract,
gregate
equilibrium consequences, using
highly
6
Matsuyama
form approach,
lems discussed
ismeant
which
Remark 2: The careful
"loan
and
reader must
have undoubtedly
noticed
the use of the terms such as "debt capacity,"
avoid
liberately
rate,"
to encompass
all sorts of agency
literature.7
prob
in the microeconomic
and
market,"
instead
use
"borrowing
of return," and "credit market." This is because
with
of credit market
aggregate
implications
from broad external financing difficulties. Note
that I de
"interest
constraint,"
this paper
"rate
is concerned
imperfections,
arising
con
that the borrowing
to pledge
the entire
of the borrowers
to the inability
to
the higher rate for the lenders, not because
generate
project
of any arbitrary restriction on the menus
of the financial claims that they
can issue. The main issues addressed
that they
here are general enough
straint
arises due
revenue
are independent
is too ab
of the financial structure.
Indeed, the model
stract tomake ameaningful
distinction
between
the equity, the debt, the
should be viewed
bonds, or any other forms of financial claims, which
as an advantage
of the model.8
3
Partial
Equilibrium
We
have
so far looked
holding
actions
through
3.1
Models
at only the single agent's problem
in isolation,
as exogenous,
about inter
and without worrying
interact
agents
agents. Let us now start letting many
all the prices
among
equilibrium
Homogeneous
Let us now
consider
prices.
Agents:
The Net Worth
a continuum
(Balance
Sheet) Effect
of homogenous
agents with unit mass.
with co< 1 units of the input at period
to the presence
1. In addition
of many
As before, each agent is endowed
0 and consumes
only at period
is that the projects run by the agents convert the
the
difference
agents,
key
the consumption
good
input into capital. Capital is then used to produce
in period 1,with the constant returns to scale (CRS) technology, F(k, Q,
in equi
where k is the total supply of capital (which will be determined
a
in
fixed supply. Let/(fc)
librium), and ? is vector of "the hidden factors"
= ?>.The
=
> 0
factor
F(k, Q, which satisfies/'
competitive
>/" and/'(0)
reward each unit of capital by/'(fc) and the residual,/(fc)
markets
kf'(k)
> 0, goes to the owners of the "hidden factors" in fixed supply.9
the input endowments
of converting
The agents have two means
a
investment
into consumption.
First, each agent can run non-divisible
Implications of Credit Market
Aggregate
Imperfections
7
converts one unit of the input in period 0 into R units of
project, which
con
1 - coat the market
in
rate, r,which
capital
period 1 by borrowing
as exogenous.10
Since each unit of capital earns/'(A:)
in consumption,
each project generates Rf'{k) units of the consumption
can lend the input endowment
in period 0 at
good. Second, each agent
as
to
rate
return
total
of
the
before. Finally, the
r,
equal
supply of capi
n is the number
tal is given by k = Rn, where
(or the fraction) of the
= Rn are determined
in
agents who borrow and invest. Both n and k
tinues
to be treated
equilibrium.
1 - co to run the project, the agent can consume
17 =
By borrowing
rate, r, the agent can consume
r(l
co). By lending at the market
Rf'(k)
U = rco. By comparing
the two, (PC) now becomes
Rf'(k)
On
>
r.
(BC) is now
the other hand,
XRf'(k)>r(l-(o).
(PC)(3)
given
by
(BC)(4)
in this model,
that the two constraints
(3) and (4), differ from those
in the single agent's problem,
and
(1)
(2), only in that the project revenue,
now
is
hence
become endogenous.
and
R,
replaced by Rf'(k),
In equilibrium
the investment
takes place until one of the (BC) and
so that
(PC) becomes binding,
Note
=
Rf'(k) Max 1,
This determines
-^^
\r
the equilibrium
+ (BC)(5)
(PC)
value
of fc.11
When
X +
co<
1, (5) be
comes
Rf\k)
=
(~^-\r>r.
(6)
Thus, (BC) is binding but (PC) is not; the project
than the opportunity
cost of the project. All the
no
more
but
vest,
agents can borrow and invest,
In
olate (BC).
short, there is too little investment.
return
is strictly higher
agents are eager to in
vi
because
that would
In this case, improving
an increase in X,
the credit market,
to a higher
leads
invest
obviously
ment. A higher co also leads to a higher investment.
This is the net worth
the agents
(or balance sheet) effect. As the borrower net worth
improves,
need
to borrow
more
investment
(5) becomes
eases the borrowing
and hence
less, which
constraint,
will be financed. When
X + co> 1, on the other hand,
8
Matsuyama
Rf\k)=
(7)
r>(^^y
Thus, (PC) is binding
there is no net worth
and the level of investment
effect; a higher
cowould
is optimal. In this case,
not affect the investment.
Remark 3: In this model,
only the fraction n of the agents invests in equi
that the fraction 1 - n of them becomes
the lenders.
librium, which means
This obviously
"How can the credit be allocated only
raises the question,
to a fraction of homogeneous agents?" When X + co> 1, this is not a
prob
= r.
lem, because
Thus, the agents are indifferent
(PC) is binding; Rf'{k)
and lending. However,
when X + co< 1, (PC) is not
borrowing
> r, so that the
to lend
agents strictly prefer borrowing
binding, Rf'{k)
are
we
two
There
resolutions
for
this.
think
that
First,
may
ing.
possible
between
the equilibrium
allocation
case. The credit is allocated
in this
involves
credit rationing
n of the agents, while
to
the
fraction
randomly
are denied credit.12 The latter have no choice but to
necessarily
the rest of the agents
the lenders; they would not be able to entice others to switch and
a
become
lenders by promising
higher return because that would violate
we
as the limit
the
view
Second,
(BC).
may
agent model
homogeneous
case of some heterogeneous
models.
For
the
agent
agents may
example,
become
in their endowment,
to G(co). Then, the equi
distributed
according
librium is given by the threshold
level of the endowment,
coc, such that
are lower (higher) than cocbecome
the agents whose
endowments
the
a
we
at
will
with
lenders (borrowers).
look
such
model
Indeed,
shortly
as the
endowments.
The above model may be obtained
heterogeneous
to a single mass point.
limit when G(co) converges
differ
Remark 4: Just in case one might
suspect that the results here may be
driven by the indivisibility
of the projects, not by credit market
imper
here ismore subtle than
fections, the role of the indivisibility
assumption
one might
think. In the literature, it is often argued that the equilibrium
is fundamentally
difficult be
imperfections
analysis of credit market
cause it is necessary to model
in
for credit
order
agents
heterogeneous
transac
to take place. This is not true; credit market
market
transactions
are
some
if
there
tions can take place even among homogeneous
agents
In what follows, I find it useful to assume the
the effects of
within
each economy when exploring
homogeneous
agents
across countries. The in
across projects or heterogeneity
heterogeneity
to
is
active even among
the
market
assumed
credit
keep
divisibility
only
indivisibility
constraints.
Aggregate
Implications of Credit Market
Imperfections
9
the homogeneous
agents. To ensure that the results are not driven by the
of the projects per se, it is assumed
that a continuum
of the
indivisibility
access
to
have
the
identical
This
(indivisible)
agents
projects.
helps to
the
said
this, how
aggregate production
convexify
technologies. Having
ever, let us now
3.2
Heterogeneous
look at some examples
Agents:
with
Distributional
heterogeneous
agents.
Implications
Let us first allow
or the net
the agents to differ in the input endowment,
co is distributed
to
model
the
worth, where
Otherwise,
G(co).
according
is the same as above. In particular,
the agents share the same R, that is,
as entrepreneurs.
they are equally productive
With
different
face different
endowments,
heterogeneous
agents
co> coc= 1 can
(BC). For a given level of k, only those with
XRf'(k)/r,
borrow. If (PC) holds strictly, Rf'(k) > r, all of these agents invest. Hence,
the total supply of capital is equal to R times the fraction of the
agents
so
that
(BC),
satisfying
T
/
.
k = R 1 - Gil-LX1XRf'(k)Y(8)
As
the RHS of (8) is decreasing
in k, this equation determines
k uniquely.
> r holds at this solution,
as
it
is
indeed
the
long
Rf'(k)
equilibrium
value of k. If not, the equilibrium
is given by Rf'(k) = r. Inwhat follows,
As
let us assume
are such that the
that the parameters
is char
equilibrium
by (8)with Rf'(k) > r.
Both a lower r and a higher X increase the RHS for a
given k. Hence,
both lead to a higher k. The reason is
These
simple.
changes increase the
discounted
value
of
the
raises the
revenue, which
present
pledgeable
acterized
limit. Hence, more agents can finance the
project. One can
that k goes up, when
the distribution
of the net worth
shifts to
the right in the First-Order-Stochastic-Dominant
manner.
This is a gen
eralized version of the net worth effect discussed
earlier.
Let us now see the distributional
of
the credit
implications
improving
"-" denotes
market. Let X go up from X~ and X+.
the value
(Superscript
" "
the change
+
before
and superscript,
denotes
the value
after
the change.) As noted above, an increase in X leads to an increase in k
from k~ to k+. This increase
in k occurs because
a
larger fraction of
the agents are now able to finance their
means
which
that the
projects,
threshold
level of the net worth has declined
from co;= 1 - X Rf'{k~)/r
to
=
three classes of
Therefore, we need to distinguish
coc+ 1 X+ Rf'(k+)/r.
borrowing
also show
10
Matsuyama
u(co)yf
*
'
'
Rf\K)-r'
s
'
Rf{k+)~r
S\ \
T
'
\S\
O coc+
Figure 1.1
Distributional
s
o)c
Impacts
co < co/ invest neither before nor after the
their
before and after the
change. Hence,
utility (period-1 consumption)
=
= rco.
< co<
are
those
with
Second,
(i+(co)
co/
given by U~(co)
change
co~ invest only after the change. Hence,
their utility increases from U~(co)
= rco to
=
>
IT(co)
co).
r(l
Rf'{k+)
Finally, those with co co~invest both
their utility declines from U~(co) =
before and after the change. Hence,
=
declines
from
r(l
co), before/'(fc)
co) to IT(co)
r(l
Rf'(k-)
Rf'{k+)
agents.
First,
those with
effects.13
f'(k~) to/'(/c+). Figure 1.1 illustrates these welfare
from
the
credit
market
The
Thus, not everyone
gains
improvement.
middle
class gains (as well as the owner of the hidden factors, which are
of the consumption
inputs to capital in the production
complementary
reason
the rich lose. The
is that credit market
imperfections
good), while
like
barriers.
The
should be
operate
entry
political economy
implications
clear. If the political power is in the hands of the rich who have easy access
to credit, the government
has an incentive not to improve the credit market.
33
Heterogeneous
Let us now
Agents:
Replacement
the case where
Effects
the agents differ also in their pro
each agent is identified by (co,R) distributed
ductivity. More specifically,
to
G(co, R). Figure 1.2 illustrates the two constraints
according
consider
Aggregate
Implications
of Credit Market
Imperfections
11
i
1
V
a|
B
i-r.:v...i
^X
.
X
i-r.i.w
X
\
_I_i_V*
0
^X
N
> r
r/f{lf) r/f{k+) r/l+f(k+) r/X~f{k~)
1.2
Figure
Effects
Replacement
Bf'(k)/r>l (PC)(9)
= 1co> coc(fc,
R)
XRf{k)/r. (BC)(10)
The agents
(PC), while
XRf'(k)/r,
satisfy
aggregate
supply
lowing
=
line, R
r/f'(k), satisfy
=
= 1line, co coc(fc,R)
satisfying both invest. Thus, the
to the right of the vertical
the agents above the negative-sloped
located
(BC). Only
of capital
the agents
is given by
the unique
solution
to the fol
equation:
00
k= \
R \
r/[f'(k))
00
?(co,R)dcodR(11)
lJG>c(k,R)
it is straightforward
to show that k goes up in response to a lower
Again,
a
a
First-Order
Stochastic-Dominant
shift of the net
r, higher X, and
to the right.
worth distribution
Let us look at the effects
An
increase
hence
of an improved
credit market more closely.
in X from X" to A,+ leads to an increase in k from k~ to k+, and
to a decline
the
in/'(fc) from/r(fc~) to f'(k+). These changes move
line to the right, and the negative-sloped
line to the left, as
shown by arrows in figure 1.2. This means
that four classes of the agents
in
A
be
Those
in
may
distinguished.
stop investing. Those in B continue
vertical
vesting. Those in C start investing. The rest never invest. This means
the rich but less pro
that, as a result of a credit market
improvement,
12Matsuyama
inA are replaced by the poor but more productive
agents
now able to bor
are
in C.14 Clearly, those in C are better off because
they
row and invest in the profitable
those in A and in B are
project, while
ductive
worse
agents
off because
their projects
become
less profitable
due
to the entry
by the agents in C.
To explore further
let us now look at amore specific ex
implications,
are only two types of agents. Their relative
that
there
ample. Imagine
<
> co2, so that
and net worth
R2, coa
type-1
satisfy R:
productivity
are
than
Let
6
denote
the
richer
but
less
agents
type-2 agents.
productive
and
that 1 - coa< (R1/R2)(l
furthermore
share of type-1. Suppose
co2)
1 - co1< X' <
consider the effects of an increase in X from X~ to X+, where
<
< 1 - co2. Then, for
co2) X+
type-1, (PC) ismore stringent
(RJRJil
than (BC) both before and after the change, and, for type-2, (BC) ismore
than (PC) both before and after the change. Furthermore,
stringent
when 0 and r are chosen to satisfy the inequalities,
1 - co2 f'(Rfl)
^
^
X~R2
one can show
r
1
^ /'(R2(l
R1
that the equilibrium
r
0)) ^ 1 co2
'
X+R2
takes the following
form:
the change (X = X~), RJ'{k~) = r,where k~ < Rfi. That is, (PC)
for type-2. Some type-1 in
is binding
for type-1 and (BC) is violated
vest, but no type-2 invest.
<
After the change (X = X+), X+R2f,(k+) = r(l
0).
co2),where k+ R2(l
for type-1. Some
for type-2. (PC) is violated
That is, (BC) is binding
no type-1 invest.
type-2 invests, but
Before
=
but rich agents invest, none of
X~, only the unproductive
Thus, with X
=
but poor
With X
is credit-constrained.
whom
X+, only the productive
are
all
credit-constrained.
whom
of
Furthermore,
aggre
agents invest,
(the total amount of the inputs going into the projects)
gate investment
in the credit market. This is
may decline as a result of an improvement
as the credit
investment
improve endogenously,
technologies
more
to
the
from the less productive
agents.
productive
agents
a
feature of the above example. More
This is by no means
peculiar
a better credit market does not necessarily mean that there are
generally,
the two ex
the active firms. Consider
less credit-constrained
among
is perfect so that no firms are
treme cases. If X = 1, the credit market
shuts
If X = 0, on the other hand, the credit market
credit-constrained.
down completely. Hence, only the firms that can self-finance
entirely op
because
shifts
Implications of Credit Market
Aggregate
erate so that no active
diate
cases should we
Imperfections
13
firms are credit-constrained.
expect
some active
Only in the interme
firms to be credit-constrained.
so far have been in partial equilibrium
in that the market
the models
rate of return required by the lenders, r, is treated as exogenous.
It is now
in
general equilibrium.
endogenized
All
4
General
Deepening
with
Equilibrium
versus Net Worth
Endogenous
Effects
Saving:
Capital
Let us go back to the homogeneous
case, where all (investing) agents have
the same R and co. In this section, we call them "entrepreneurs,"
because
we also add some agents, "savers," who have no access to the investment
co?units of the input. In addition
projects. The savers are endowed with
to the period-1 consumption,
they also consume some of the inputs in pe
riod 0.More specifically,
U? = V(C?0) + C?, subject to the
they maximize
=
r(co? Co0),where Vis an increasing, concave func
budget constraint, C?
tion. Then they choose their saving, S? = co? C?Q,such that V (co?- S?) = r,
which defines their saving function, S?(r) = w?- (V'y\r). Since the entre
the aggregate
preneurs save all of their endowment,
saving of this econ
or
to
in
the
total
used
the
available
be
omy,
inputs
projects, is given by S(r)
= co+ co?= co+
into cap
S?(r)
(V)_1(r). Since these inputs are converted
ital at the rate equal to R, the aggregate
of
is
supply
capital
given by
k = RS(r) = R[co + co?- {V')-\r)l
(RQ(12)
where
(RC) stands for the Resource Constraint of the economy.
are given
and
(PC)
(BC) of the entrepreneurs
by
=
Rf'(k) Max 1,
i^
r
~
co+ co?
(W(r) - S(r)= I(r)- I(/')-if Max 1,
1.3 depicts
+ (BC)(5)
(PC)
k and r. These
(5) and (12) jointly determine
Equations
as
ditions may be rewritten more compactly
As before,
equilibrium
Jj\
con
(13)
of the upward
(13) by the intersection
equation
and
the
sloping aggregate
saving schedule, S(r),
ag
downward-sloping
on the aggre
schedule,
l(r).15Note that S(r) depends
gregate investment
co + co?,while
on the entrepreneur's
en
I(r) depends
gate endowment,
Figure
dowment,
co.
14Matsuyama
J
RKJ { V X \R)
r
^V
/S(r)
=
co+a)?-(Vyl(r)
_
k/R
O
Figure
General
1.3
Equilibrium
with
Endogenous
Saving
the effect of a higher endowment
of the savers,
Figure 1.4 shows
to the right, while keeping
the invest
which
shifts the saving schedule
An
in
fi
ment
intact.
schedule
increase
the aggregate
saving, which
nances the aggregate
that more capital is produced.
investment, means
to diminishing
of capital de
returns, the marginal
productivity
a
rate
In
to
return.
of
this
is
the standard
leads
low
which
essence,
clines,
Due
neoclassical
capital deepening effect.
The effect of a higher X,when
(BC) is binding
(X + co< 1), is shown in
to the right, while
the saving
1.5.
schedule
investment
shifts
The
figure
intact. By easing the borrowing
constraint, more en
could borrow to finance their investment. With the upward
trepreneurs
rate of return. Re
sloping supply of saving, this raises the equilibrium
=
savers to the entrepreneurs
the
the
wealth
from
(Aco -Aco?
distributing
> 0) would have the same effect,
through the pure net worth effect.
schedule
remains
The effect of a higher net worth of the entrepreneurs
(Aco > 0), when
the offsetting
(X + co< 1), without
(BC) is binding
change in the saver's
a
as
two
effects discussed
combination
the
be
viewed
of
wealth, may
above:
the capital deepening
effect, due
to an increase
in the aggregate
Aggregate
Implications of Credit Market
Imperfections
.r S(r)
=
15
co+co?-(V)-\r)
"?]-"m
Figure
1.4
Capital
Deepening
Effect:
Aco0 > 0
-
k/R
O I
Figure 1.5
Net Worth
Effect:
Aco = -Aco0 > 0 (and AX > 0) for X + co < 1.
increases the aggregate
in
saving, and the pure net worth effect, which
vestment. When
the latter dominates
the former, as shown in figure 1.6,
rate of return goes up.16 However,
once the entrepre
the equilibrium
neur's net worth becomes high enough
to make
(BC) irrelevant
(X + co
> 1), a further increase in co reduces
the rate of return, because
only
the capital deepening
In short, the equilibrium
effect is at work.
rate
of return may
to the borrower
net worth.
respond non-monotonically
a
rate
return
in
a sign of
low
of
be
could
generally,
equilibrium
either good or bad economic
In section 6, we will explore
conditions.
More
16Matsuyama
?-
Figure 1.6
Combined
Effects:
further
Aco>
implications
0, for X +
"*
co< 1.
of this feature of the model
in the context
of a global
economy.17
5
General
It has been
Equilibrium
assumed
Let us now
project.
ect to invest.
with
Heterogeneous
Projects
so far that each agent has access to
one type of
only
where agents can choose which proj
look at amodel
with
the world with homogenous
entrepreneurs
Again, we consider
unit mass, each of whom
is endowed with counits of the input at period
0 and consumes only at period 1. To keep it simple, we assume that there
are no outside agents, "savers." Despite
that this makes
the aggregate
and the net worth
saving inelastic, credit market
imperfections
the composition
affect the equilibrium
allocations by changing
can still
of credit
flows.
can choose
one (and
Entrepreneurs
=
A
1,2,...,/).
projects
(;
Type-j project
puts in period 0 into m;R; units in capital
tion good. Thus, the projects may differ
as well as the types of the goods produced
only one) of / non-divisible
converts m. > counits of the in
and
units in the consump
m]B]
in the set-up cost, productivity,
(and their compositions).
By
=
+
can
consume
a
the
co)
agent
running
project-/,
B;] r(m;
m.[JR;./'(fc)
+ rco in
+
can always consume
period 1. Since the agent
B; r]
mj[Rjf'(k)
rco by lending,
the Profitability Constraint for a Type-j Project (PC-;) is
given
by
Aggregate
Implications of Credit Market
Imperfections
(BC-j) /
n(co)
Rjf'{k)+Bj-/
i
i
^/
4
17
(PC-j) /
I
|
**^
XiRjfW+MjBj
\
__?
I
?
CO
o
Figure
1.7
?,./'(*:)+ B;>r. (PC-;)(14)
the credit market
that only a
imperfections
by assuming
X. of capital and a fraction of
of the consumption
good are
jul;
to
a
the
lenders.
the
Constraint
Then,
pledgeable
Borrowing
for Type-] Proj
ect (BC-j) is given by
We
introduce
fraction
mfcRf'ik)
Both
+
>
Mj-B,] r(mj co).(BC-/)(15)
(PC-;) and
(BC-/) need
type-/ projects.
Figure 1.7 shows
= Min
r(co)
1
the graph
u.B.
'JLR,/'(*)
' >J + ^>
II
?
co/m
to be satisfied
for the credit
to flow
into
of
.
+ B,' (16)
',Rf'(k)
J
<
In other words,
(PC-j) and (BC-/) are satisfied if and only if r
/^(co).
this graph shows the maximal
rate of return that a type-; project can gen
erate to the lenders without
(PC-/) nor (BC-;). As shown, the
violating
co
is
in
when
is
the relevant constraint. The rea
graph
increasing
(BC-;)
son is that a
eases
net
worth
the
constraint as the en
higher
borrowing
need to borrow
less. This makes
it possible
for them to
trepreneurs
a
rate
return
to
of
the
lenders.
The
promise
higher
graph is flat when
is
the
relevant
constraint.
(PC-;)
Both
the equilibrium
let n. denote
the measure
of
formally,
initiated
of
the
who
in
invest
(and
type-; projects
agents
type-; projects).
Since each type-; project requires m. units of the
sav
input, the aggregate
the
if
investment
and
if
ing equals
aggregate
only
To describe
18Matsuyama
<0= 5>;"> (17)
j
Since each type-; project
of capital is given by
k=
produces
m;R;
units
of capital,
the total supply
(18)
5>,R,*,.).
can
compete with one another for credit and they
to
the
credit
all
the
goes only
projects
projects,
freely among
rate of re
the highest
and hence generate
which have the highest
jj(co)
as
can be expressed
turn to the lenders, which
Finally,
choose
as the agents
r = Max
=
>
(j;.(co)} r.(co) Min
; ]
\X.RJ'(k)
_
+ u.B.
^
1
],R.f'(k) + Bj ;
(19)
=
l,2,.../),
n,=>0(;
the two
where
conditions.
inequalities
The equilibrium
slackness
in (19) are the complementarity
is fully characterized
of this economy
by
(17)-(19).
Let us now
5.1
A Model
look at some
with
Investment-Specific
Suppose
projects
special
cases.
Pure Capital Projects:
Technical Change
Endogenous
=
= 0 for
as inMatsuyama
1,2,...,/,
all;
B;.
of the output;
do not differ in the compositions
homogeneous
capital.
In this case,
(16) is simplified
(2007). Thus, the
they all produce
to
4^ =Mini?^?,lk (20)>
f'(k)
J
[l-co/m/
to the RHS of (20), which
that the projects can be ranked according
of the
of the allocation
is independent
of fc, and hence
independent
has a
credit
allocation
of
the
means
that the equilibrium
credit. This
Note
all the credit goes to only
feature. That is to say, generically,
bang-bang
a
and when
one type of project at each given
level of the net worth
is
the
effect
credit
net
in
affects
the
the
worth
composition,
change
from one type to an
the
switches
credit
drastic:
and
completely
abrupt
to say, this is neither realistic nor robust feature of the
other. Needless
the exposition.18
it
but
model,
greatly helps to simplify
5.1.1
where
the case
Let us begin with
Change
Productivity
Procyclical
= 2 and
are
>
be
trade-offs
In
there
words,
/
X2R2.
R2> R1> Xftx
Aggregate
Implications of Credit Market
tween productivity
hence
and agency problems.
Project 2 ismore productive,
to the borrowers, while Project 1 offers more
pledge
unit of investment,
which makes
them potentially
appealing
return per
"safer" or a "more
able
can be
important
19
Imperfections
secure"
when
alternatives
some
for the lenders.
advanced
technologies may be subject to bigger
dane projects that use well-established
projects
agency
Such
tradeoffs
that use
problems
leading edge
than some mun
technologies.
inwhich
the graphs of (20) for; =
Figures 1.8 and 1.9 show two ways
1 and 2 could intersect with each other. In both cases, there is a critical
net worth
all the credit flows to type-1 projects
level, coc,below which
= 1=
and
above
which
all the credit flows to type-2 projects
n2
1)
(nx
r2{(o)lf\k)
R2-_
R/
hRi-
Figure
7
n((o)/f'(k)
A
/
j
^^
hRi
\
o
-7\-*
Wc
1.8
r2(co)/f'(k)
R;
R'
T^
hRi-y\
^
hRi
Figure
1.9
\
n(co)/f'(k)
e>
20Matsuyama
Rico
/
/
R\co
*<?
-TT"
Figure
1/
O coc
1.10
Procyclical
Productivity
Change
=
=
0). Then,
l-n2
(n1
rium supply of capital
from (17) and (18), we
can show
that the equilib
is
fl
ifco<coc,
(21)
[2
ifco>coc,
as shown in figure 1.10. Thus, a higher net worth can raise the productiv
used from Rx to R2. In short, the invest
ity of the investment
technologies
ment productivity
changes procyclically
through the credit channel. The
k=
where
Rm<o,
/(co)
=
a low net worth,
the agents have to rely
the
into
flows
heavily
borrowing.
saving
type-1 projects, which
rate
net worth
im
the higher
return.19 When
of pledgeable
generate
the borrowers
need to borrow
enables the entrepre
less, which
proves,
neurs to offer the
higher return to the lenders with type-2 projects, despite
intuition
should
on
that they generate
The equilibrium
=
r(co)
be clear. With
Thus
return per unit of investment.
the lower pledgeable
rate of return is now given by
RRJ'(Rma>) (22)
Mini?-^f-,
[ 1 co/m/(co)1}J
rate of return
that a higher net worth
affects the equilibrium
to pledge
it
three
allows
the
borrowers
channels.
First,
separate
through
more to the lenders per unit of lending. Second,
the credit composition
Note
may shift toward more productive
projects. These two channels work in
this is the usual capi
the direction of a higher rate of return. Offsetting
in the direction of a lower return. The
tal deepening
effect, which works
overall
effect can go either way.
Implications of Credit Market
Aggregate
Imperfections
21
Let us briefly consider the implications
of an increase in
One may
Xr
or
that a better corporate
contractual
enforcement
governance
cause
more
to
into
would
the
credit
flow
the
invest
always
productive
think
ment
raises X2. But
projects. That is certainly the case, if the improvement
if it raises Xxl Look at figure 1.9. In this case, a higher X1 leads to a
higher coc.This offers some cautions. If an attempt to improve corporate
what
ismore effective for the well-established
industries, where
governance
are
the nature of the agency problems
well
understood
relatively
(type-1
itwould
end up preventing
the saving from flowing into new,
projects),
but more
productive
technologies,
the nature of the agency problems
Dynamic
run
by small venture capital, where
are less understood
(type-2 projects).20
Implications:
Credit Traps
so far treated
coas exogenous.
Let us now explore the dynamic
of
implications
procyclical
investment-specific
technological
changes by
some positive
feedback from k to co.To keep it simple, we fol
allowing
low Bernanke and Gertler (1989) and consider the world where
the econ
We have
a la Diamond
of a sequence
of overlapping
generations
=
zero
Time
is
to
discrete
and
extends
from
(1965).
0,1,2,...).
infinity (t
In each period, a new generation
of the homogenous
agents arrives and
(those "born" in period t),
stays active for two periods. For generation-f
omy
consists
their "period 0" is period t and their "period 1" is period t + 1.
They dif
fer from the two-period
in
discussed
above
instead
of
that,
agents
only
a
are
endowed
with
fixed
endowed
with
the
"hidden
co, they
being
?,
factors" in fixed supply, which are used with the capital stock produced
of the final good, F(kt, Q, (where
-1), kt, in the production
by generation-(f
the final good may be used both as the consumption
good and the input
=
for the investment
earn
save
thus
and
co, f(kt)
project). They
kj'(kt)
=
t. Then, at the end of period
t, they enter the
W(kt) during period
credit relationship
and produce
among themselves
kt+1,which will be
come available
in period t + 1, and used to
the final good with
produce
+ 1). The
factors" in fixed supply supplied by generation-^
of this overlapping
dynamics
economy are described
generations
simply
co
and
k
in
(21), which becomes
by replacing
by W(kt)
by kt+1
equation
the "hidden
=
=
K+i V<jy>W(fc*)'where /(?>)
fl
if co< coc,
(23)
[2
if co> coc.
For any initial condition,
k0, the entire equilibrium
tained simply by iterating (23) forward.21
trajectory
can be ob
22Matsuyama
y\RiW(k)
R\W(kt)/j
Figure
Credit
|
1.11
Traps
=
ismonotonically
follows, let us assume that W(0)
0, W(k)/k
?
=
o? and
is the
with
0, which
\ivcvk_^JN(k)/k
limjt_>0W(fc)//c
decreasing,
case iff(k) ? ka, with 0 < a < 1. Under
the dynamics
these assumptions,
are characterized
of the form, kt+1 =
convergence
by monotone
R;W(A:,),
In
to the unique positive
with
other
for
fixed
state,
words,
any
/.
steady
or
out heterogeneous
credit
market
the
without
projects,
imperfections,
Inwhat
one-sector
of the economy
look like the standard neoclassical
dynamics
case
a
with (23), because credit mar
la Solow. This may not be the
model
cause endogenous
in invest
ket imperfections
productivity
changes
ment
technologies.
one of three generic cases. It shows the case
Figure 1.11 illustrates
<
<
where fc* kc fc**,where fc*, fc**, and kc are defined by fc*= R1W(fc*), fc**
=
=
coc.There are two stable steady states, fc* and
R2W(fc**), and W(kc)
as a credit trap. In this steady
fc**. The lower one, k*, may be interpreted
so
net
low
that
worth
is
the
the
state,
saving flows into the projects that
return per unit of investment,
the higher pledgeable
although
of
The
lower
less
capital leads to
supply
resulting
capital.
they produce
a lower price of the endowment
of entre
held by the next generation
a
state
the
net
worth.
Which
low
and
hence
economy
preneurs,
steady
generate
on the initial condition.
If the econ
to depends
converge
entirely
to fc*. If the economy
omy starts below kc, it converges monotonically
to A;**. Thus, kc may be
starts above kc, it converges monotonically
as the critical threshold
level for economic development.22
viewed
will
5.1.2
where
now the case
Consider
Productivity
Change
Countercyclical
= 2 with
<
>
and
(1 ^2R2/R1)/(1
/
mjm2
R2>RX>
X2R2 XXRV
Aggregate
Implications of Credit Market
Imperfections
23
r2(co)/f\k)
R,--y
hlR2 **.^f
AiRi
\
\
\
-':-:Wc
O
Figure
co
COcc
1.12
are less productive
and generate
less
XJ < 1. Thus,
type-1 projects
rate
return
of
than
set
cost
the
However,
up
pledgeable
type-2 projects.
ismuch
smaller for type-1 projects, so the agents need to borrow much
less to invest
into these projects, which may give type-1 projects advan
type-2 projects. For example,
type-1 projects could represent
or
other
farms
small
while
businesses,
family operated
type-2 projects
in
sector.
the
investments
the
Or, type-1 projects
represent
corporate
traditional
such as textile and furniture,
represent
light industries,
tage over
which
a
small initial expenditure,
while
relatively
type-2 proj
as
ects represent modern
such
industrial equip
industries,
steel,
heavy
ments,
require
and
petrochemical,
pharmaceutical
industries
that
require
a rel
atively large initial expenditure.
= 1 and 2 intersect twice
Figure 1.12 shows that the graphs of (20) for;
an
with each other. For
intermediate
value of coc< co< cocc,all the credit
= 1= 1.
all the credit goes to
Otherwise,
goes to type-1 projects, nx
n2
= 1= 0.
the
Therefore,
n2
type-2 projects, nx
equilibrium
supply of cap
ital is now given by
r2
k=
Rm<o,
as shown
neurs must
where
/(co)
=
if co< coc
<1
if coc< co< cocc,
[2
ifco>cocc,
in figure 1.13. When
the net worth
almost
rely
entirely on external
(24)
is very
finance,
into type-2 projects that generate more
pledgeable
of investment. As the net worth rises, the entrepreneurs
attractive rate of return with type-1 projects
than with
flows
low, the entrepre
so that the
saving
return per unit
can offer amore
type-2 projects,
24Matsuyama
i
/
//
'
-??--;-1-+C0
O
coc
because
net worth
s
cocc
they need to borrow little for type-1 projects. Hence,
leads to a shift of the credit toward less productive
enough
rises even
type-2 projects.
In this case, a higher
which
the savings flow
a caution when
offers
fections
a rise in the
projects. If
need becomes
small
further, then the borrowing
for type-2 projects that the credit shifts back tomore productive
the net worth
targeted
cocand hence
X1 reduces
into the more productive
thinking about alleviating
the range in
type-2 projects, which
credit market
imper
expands
to small businesses.
Implications:
Leapfrogging
Let us explore the dynamic
by kt+1 in (24) to obtain
implications
Dynamic
'2
=
/
1.13
Figure
K+i
Rico
Rj(W(kt))W(K)>where K?)
=
' 1
,2
and Credit Cycles as a Trap
by replacing
coby W(kt)
and k
if co< coc
if coc< co< cocc, (25)
if co> cocc,
In figure
among many.
Figures 1.14 and 1.15 illustrate two possibilities
=
<
<
<
are
defined
and
A:*
where
1.14, kc
cocand
kc
kcc
kcc fc**,
by W(kc)
=
are
fc*
and A;**,
cocc,and the two stable steady states,
again de
W(kcc)
=
=
fined by fc* RaW(fc*) and fc**
R2W(fc**). If kc<k0< kcc, the economy
>
to
fc*.
If
converges mo
converges monotonically
k0 kcc, the economy
as
as we focus our attention
to the range
to fc**.Hence,
long
notonically
to
it can be
look similar
above kc, the dynamics
figure 1.11. However,
more complicated
starts below kc. After the initial phase
if the economy
Aggregate
Implications of Credit Market
25
Imperfections
45?
kt+\
s
ulL-1?L_i-u+K
m
Figure
1.14
Leapfrogging
kt+\
0|
Figure
Credit
45?
k*
kc
kcck**
1.15
Cycles
as a Trap
to k*, if it falls into the intermedi
of growth,
the economy will converge
ate interval, (kc, kcc).However,
if R2W(kc) > kcc, the economy
could bypass
as
arrows
to
in figure 1.14.
this stage and converge
indicated by the
fc**,
In this case, the long run performance
of the economy
sensi
depends
it suggests
the possibility
tively on the initial condition.23 Furthermore,
of leapfrogging. That is, an economy
that starts at a lower level may take
over another economy
that starts at a higher level.24 In figure 1.15, A:*< kc
<
< fc** and
R2W(kc) < kcc. For kQ< kcc, the economy
these credit cycles, an improvement
nitely.25 Along
causes a shift in the credit towards the less
worth
kcc
that contribute
net worth
causes
less to the future net worth.
the credit
to shift back
fluctuates
indefi
in the current
net
productive
projects
in the
The resulting decline
towards the projects that help
26Matsuyama
more
in the following
the net worth
period. For k0 > kcc, on the
the economy
to the unique stable
converges monotonically
as
another example of
steady state, A:**.Thus, this may also be viewed
credit traps except that the traps here take the form of cycles around kc,
instead of the lower steady state, k*.
to build
other hand,
5.2
A Model
A higher
with
Private
Benefits
net worth might
also shift the composition
of credit toward less
are
the agents
attracted to running
"socially productive"
projects, when
more
some "socially unproductive"
because
projects,
they generate
or
some
satisfaction"
other
consumption
"private benefits,"
"personal
little to the lenders. To capture this idea, let R1 < R2,
values, which mean
and Bx > B2 = 0 with X1 = X2 = 1 and |i1 = \i2 = 0. Thus, capital is fully
at all. type-1
but the consumption
good is not pledgeable
pledgeable,
than type-2, but it is a lot of fun to
projects are less "socially productive"
run type-1 projects. Let AR = R2-Rl>0.
From (17)-(19), one can show
=
=
=
>
<
that k
Rx(o if co coc
R2co if co coc (AR/R2)m1 or AR/'(R2co) >B1;k
> B1 >
and AR/'(Raa)) < Br If co > coc and AR/'^co)
AR/'(R2g>), then
=
means RjCO< k < R2co. Inwords,
all
the
credit goes to
which
Bv
ARf'(k)
cannot
borrow
for
when
the
type-1 projects
agents
type-2 projects either
or the private benefits of type-1 projects are not big enough
to compen
in capital when everybody
else invests in type
sate its low productivity
for
the agents can borrow
2; all the credit goes to type-1 projects when
are
of
and
the
benefits
big enough
type-1 projects
private
type-1 projects
the credit goes to
else invests in type-1. Otherwise,
everybody
the private ben
both types so that the total productivity
(i.e., including
are
and
between
efit)
type-2.
type-1
equalized
case where B1 > ARf,((R1/R2)ARm1).
Then,
Figure 1.16 illustrates the
when
[2
ifco<coc,
k = Rma>,where /(co)=
\ (26)if
[1
co>coc.
that they
In this case, the agents enjoy running type-1 projects so much
are rich enough
to borrow,
that is, co > coc=
will do so whenever
they
(AR/R2)rar
Dynamic
Implications: Credit Cycles
Again, we can look at the dynamic
k = kt+1 in equation
(26). Figure
implications
1.17 shows
co= W(kt) and
by setting
of credit
the possibility
Aggregate
Implications of Credit Market
Imperfections
27
k
I
R2CO
{fT\Bi/AR)
./- \ /
'
\ / s *
\/'
/
M
'
!
j
\i
?co
O(AR/R2)ml
Figure
1.16
kt+\
.
O I
Figure
Credit
45?
k* kc k**
1.17
Cycles
cycles. During booms, a high net worth allows the agents to pursue proj
ects that generate
but less capital, which
satisfaction
slows
personal
the agents cannot pursue
down the economy. During
such
recessions,
to
credit
more
hence
the
that
goes
projects,
generate
projects
capital,
which
leads to the next boom. Note
that the welfare
of these
implications
are
credit cycles
very different from those shown in figure 1.15. Here the
booms occur as a result of the misallocation
of credit, and they end when
a sufficiently high net worth eventually
corrects the misallocation.
If the
credit markets
were
perfect,
and
the agents
could
fully pledge
their
28Matsuyama
to the lenders, the booms would
not occur and with
"private benefits"
out the booms the economy would never experience
In con
slowdowns.
occur
as
a re
in
the
recessions
the
shown
trast,
along
cycles
figure 1.15
sult of the misallocation
of credit.
53
A Model
with
Pure Capital
and Consumption
Projects
let us look at the case where / = 2 with R1 = R > R2 = 0 and Bx = 0
= B.
Thus, type-1 projects produce
<B2
type-2 proj
only capital, while
ects produce only the consumption
good.
The equilibrium
conditions,
(17) through (19), now become
Now
co= m1n1 + m2n2
(27)
k = m^Rnx
(28)
Mini-?-,
[1-co/V
1 \Rf'(k) -
\JKf
r>
Mini-^-,
[l-co/m2
that (29) contains the complementary
type-2. Since only type-1 projects produce
Note
1 B; n22> 0.
V
(29);
J
slackness
condition only
= <*>
ensures
capital,/'(0)
in (29).
the first equality
in the absence of credit market
Figure 1.18 shows the equilibrium
=
=
which
is
1,
1),
jll2
given by
(Xx
perfection
for
nx >
0, hence
Rd)
ifco<cor,
k
R(Oc,
=
(30)
ifco>coc,
k
Rcoc
_.^^^^__^_
co
-L-:-
O COc
Figure
Perfect
1.18
Credit
Case
im
Aggregate
Implications of Credit Market
Imperfections
29
= B.
Thus, all the credit goes to the
by Rf'(R(dc)
return
until
its
becomes
project
equal to the return
capital generating
which
absorbs
all additional
of the consumption
project,
generating
credit.
where
cocis now
5.3.1
Persistence
defined
of
Recessions:
Inefficient
Starting from this benchmark,
fection to the capital-generating
a
small Xv there
sufficiently
Financial
Accelerator
let us introduce
the credit market
imper
< 1 and \i2 = 1).With
type-1 projects
(X1
some of the
is an interval of co, in which
a
that type-1 generates
into type-2 projects
(k < Rco), despite
>
B, as shown in figure 1.19.
higher return than type-2 projects, Rf'(k)
to type-1 projects occurs because
This under-investment
(BC-1) is bind
= B. The
>
over
is
(D/mJ
ing: Rf (k) XxRf (fc)/(l
graph
upward-sloping
a
this interval, because
shifts the credit flows from the
higher net worth
credit flows
consumption-generating
type-2 to the capital-generating
type-1 proj
ects by easing (BC-1).
=
=
kt+1, one can easily see how a credit mar
By setting co W(A:,) and k
ket imperfection
of this kind introduces
persistence into the dynamics.
1.20
1.22
show
three
Figure 1.20 repli
Figures
possibilities.26
through
and Gertler
the key result of Bernanke
(1989). There is a unique
is characterized
Now
steady state, k*, which
by the under-investment.
a
is
that
the
hit
which
one-time-shock,
economy
imagine
by
temporarily
the productivity
of the final goods production.
reduces
the
Without
cates
credit market
state, RW(kc),
the economy would
go back to its steady
imperfection,
after one period. With
the credit market
imperfection,
k
hRf(k)
Rcoc
=
B(\-(o/mfi
,.?\....A_
-i-!-:-
O
1.19
Figure
Under-investment
of Type-1
<?'
co
mx{\-M)
30Matsuyama
ki+\
RW(k,)
^'''/45?
RW{kc)
.mX~"^*\
h
~o[
**W\mi(\-M))
'
1.20
Figure
Financial Accelerator
i
45?
r w(kc).7
?I
y/
Vr\m\(\-Xx))
1.21
Figure
Slow Recovery
its steady
towards
the economy
goes back only gradually
state, fc*, as indicated by the arrow. Even though the shock itself is tem
porary, it reduces the current net worth, which
tightens the borrowing
however,
the future investment.
This in turn reduces future
reducing
or financial acceler
so
on. In short, the credit multiplier
and
ator mechanism
creates an echo effect, transforming
the i.i.d. shocks into
=
In
serial
the
correlations.
1.21,
unique steady state is fc*
positive
figure
constraint,
net worth,
Aggregate
Implications of Credit Market
31
Imperfections
kt+\
R
Figure
Multiple
_,
45?
W(kc).i--7*
1.22
Steady
States
across projects
the marginal
is equalized
RW(kc), in which
productivity
and there is no under-investment.
the
financial accelerator
is
However,
at work at lower ranges. Thus, when
the economy
starts with a low cap
ital stock, the credit market
slows down the recovery pro
imperfection
the inefficient
recessions.
In figure 1.22, this mecha
cess, prolonging
nism is so strong that it creates two stable
steady states, the lower of
is characterized
which
and the economy may
by the under-investment,
a
be permanently
into
All
cases imply per
recession.
of
these
trapped
sistence because
the type of investment
that helps to enhance the future
borrower net worth
is subject to credit market
imperfections.
5.3.2
and Volatility
Let us now
introduce
the
= 1 and
to
<
instead
imperfection
type-2 projects
jli2 l).27
(A,a
With a sufficiently
small |i2, there is an interval of co for which
the credit
continues
to flow into the capital-generating
type-1 projects, even after
the return of type-1 projects becomes
lower than type-2 projects
(k >
as
in
shown
1.23.
This
over-investment
to
Rcoc),
figure
type-1 projects oc
curs because
^
is
that
is, |i2B/(l
(BC-2)
binding,
co/m2)
Rf(k) < B. Note
that the graph is non-monotonic.
It is initially
because
upward-sloping,
all the additional
credit go to type-1 projects because net worth
is too
low for type-2 projects
<
to be financed:
< B.
|H2B/(1
co/m2)
Rf'(R(ri)
net
worth
so
becomes
some
that
credit
Eventually,
sufficiently
high
=
flows into type-2 projects:
<
In
B.
this
|li2B/(1
co/m2)
Rf'{k)
range, the
Inefficient
Booms
credit market
graph
is downward-sloping
because
further
increase
in net worth
shifts
32
k
Matsuyama
=
{\-co/m2)Rf{k) Bn2
AY
-L-1-i-+co
coc
0
1.23
Figure
Over-Investment
m\(l-ju2)
to Type-1
and credit
flow from the capital-generating
type-1 to the consumption
type-2 projects by easing (BC-2).
generating
In
The non-monotonicity
of the graph carries over to the dynamics.
a credit market
into the dynamics,
stead of putting persistence
imper
into the dynamics.
It may generate
or
In
fluctuations.
convergence,
oscillatory
over-shooting,
endogenous
state
is
unstable
and
the
fluctu
its
1.24,
economy
unique steady
figure
ates indefinitely within
the interval I.One can show that the two condi
fection
of this kind
puts
volatility
tions are necessary
for endogenous
fluctuations
(as well as oscillatory
occur.
to
B
to be sufficiently
and
needs
First,
convergence
over-shooting)
never flow into the type-2 projects. Sec
credit would
high; otherwise,
too high nor too low. The intuition
is simple. If
|i2 can be neither
small
suffer
from
(a
jn2),they are
major agency problems
type-2 projects
=
case
never financed.
which
shuts
the
0,
(Just think of
\i2
completely
ond,
credit always goes only to type-1
for type-2.) Hence,
are
If
(a large
projects.
subject tominor agency problems
type-2 projects
are
as
soon
as they become more productive
than
financed
|i2), they
=
us
back to the
type-1 projects. (Just think of the case (i2 1,which brings
occur only for in
fluctuations
credit
market
case.)
Endogenous
perfect
termediate values of |i2. That is, the condition
requires that the agency
with
the
associated
type-2 projects
consumption-generating
problems
down
the credit
are too big to be financed when
is low, but small enough
the net worth
is high.28 Again,
the welfare
to be financed when
the net worth
implica
are similar to the case of figure 1.17 and op
tions of these fluctuations
Aggregate
Implications of Credit Market
Imperfections
33
45?
kt+{
i^y^x\
RW(kc) f.
J
"}*--j-\?-J
i
;
,
-l?_J-i-1-LJ-L>
U
I
/Co
v
^
?**
/
Figure 1.24
Booms
Inefficient
and Volatility
1.15. That is, the misallocation
of credit causes booms,
a
net worth corrects the
borrower
when
collapse
sufficiently high
misallocation
of the credit.
posite
which
of figure
sources of fluctu
is to add some exogenous
interesting extension
ations to this model. For example, suppose
that B may change over time.
Recall that B needs to be big enough
for the graph to look as in figure
1.24. If it is not big enough,
the downward-sloping
part of the graph is
An
far to the right so that the RW(A;,) intersects with
the 45? line at
fc**. If B permanently
to fc**.
converges
stays small, then the economy
once
a
in
B
that
while
to
becomes
However,
every
imagine
big enough
located
the graph look as in figure 1.24. With occasional
arrivals of alter
investment
which
divert
the
credit
away from the
opportunities,
the economy
fluctuates
around k*, below
projects,
capital-generating
small again.
fc**, at least until B becomes
make
native
5.3.3
Cases: Asymmetric
and Intermittent
Hybrid
Cycles
Volatility
cases
The two previous
mar
offer seemingly
views
credit
of
conflicting
one
ket imperfections,
the
other
persistence,
suggesting
suggesting
Indeed, each might
volatility. However,
they are not actually conflicting.
of business
capture different
phases
cycles as the following
hybrid
model
illustrates.
Let / = 3 with Rx = R > R2 = R3 = 0, B1 = 0, B2 > B3 > 0, and Xlf \i2 < 1,
34 Matsuyama
=
there
jli3 1. Thus, type-1 is the only capital-generating
projects, while
are now
two different
of
types
consumption-generating
(type-2 and
the two, type-2 is more productive
than type-3, but
type-3). Between
to
not
is
the
constraint.
One
could
show, under
type-3
subject
borrowing
certain
values,
parameter
irrelevant
type-2 projects become
constraints)
satisfy the borrowing
with
compete
type-3.
type-3 projects become
ductive
type-2 projects
compete with type-2.
In other words,
cessions" model
within
volatility"
The dynamics
can be
co (because they cannot
so that type-1 projects
effectively
for a large co (because more pro
so that type-1 effectively
financed)
re
like the "persistence
of inefficient
the lower range, and the "inefficient booms and
the model
model
irrelevant
for a small
within
now
looks
the higher range.
look like figure
the features
1.25, combining
1.24. In this case, there is no stable steady state.
of figure
is
characterized
The equilibrium
by asymmetric cycles, along which
path
the economy goes through a slow recovery from recessions,
and, once in
a
into re
and then, plunges
booms, experiences
period of high volatility,
look like figure 1.26, com
the dynamics may
cessions.29 Alternatively,
may
1.21 and figure
kt+\
.y-p?r-
?o
Figure
1.25
y
Implications of Credit Market
Aggregate
Imperfections
35
kt+\
45o
k*
1.26
Figure
of figure 1.22 and figure
stable steady state, fc*.
1.24. In this case,
the features
bining
unique
Now
there is a
consider
that the
the following
Imagine
thought experiment.
some
is
hit
i.i.d.
the
shocks, shaking
economy
regularly
by
graph up and
down. Figure 1.26 represents
the situation when
the size of a shock is be
low a certain
threshold
the situation
level, while
figure 1.25 represents
the size of a shock slightly exceeds
the threshold
level. Then, for
most
fluctuates
of the time, the economy
around k*, exhibiting
the
a la Bernanke
financial
accelerator mechanism
and Gertler
(1989).
when
encounters
the economy
bubble like asymmet
However,
intermittently
ric boom-and-bust
it
which
cycles, during
experiences
volatility much
than
that
it.
the
shock
larger
triggers
6
General
and Capital:
We
have
now
with Heterogeneous
Equilibrium
Patterns of International
Capital
so far assumed
look at amodel
different
produce
arises naturally
is homogeneous.
Let us
with
heterogeneous
capital, where different agents
in which
context
of
One
this problem
types
capital.
is the case where
the agents differ in their countries of
and capital
Imagine the world
residence
that capital produced
Agents
Flows
they produce
economy,
are nontradable.30
consisting
of two countries:
North
and
36
Matsuyama
South. The structure
of each country is given by the model with endoge
in section 4. The two countries share the identical
discussed
saving
and
but they may differ in X, co,and co?.To avoid
technologies
preferences,
a taxonomical
us
assume
1 > XN > Xs > 0,1 > coN> cos> 0, and 1
let
analysis,
> co^> co?> 0. Both the
and the consumption
input endowment
good can
nous
the two countries.
be traded between
across
borrow
the borders.
On
(aswell as the hidden factors)
in the North
the entrepreneurs
This allows the agents to lend and
the other hand, it is assumed
that capital
us
assume
is nontradable.
Let
also
that only
(South) know how to produce capital used
in the production
of the consumption
(South).31 We use
good in the North
on
to explore the implications
this model
of credit market
imperfections
the patterns of international
capital flows and economic development.32
The autarky equilibrium
of each country is obtained
= N or
the
S, as follows:
/
by adding
subscripts,
from (5) and (12)
=
=
+
(RC-;)(31)
k, R[Sffl]
R[co; co; (V'y1^)].
=
Rf'(k,) Max\ 1,
Or, from
(PC-/)
-r,
^-^
+ (RC-/)(32)
(13),
= = <33)
SAr/>
| W
+ a>?and
co;
(V')_1(J))
=
where
Sfa)
=
Iff)
= Nor S).
^{fV\Max\l,
now
-^UjO'
that the two countries
become fully financially integrated
Suppose
so that the agents from both countries can lend and borrow their input en
across the borders and repay in the consumption
dowments
good with
costs. By "without additional
costs," ismeant, among other
in
of the lo
each
that
the
country, Xjf is independent
pledgeability
things,
that the
cation of the lenders. Of course, one could think more generally
<
<
can
from
the fraction cpA,.(0
borrowers
cp 1), when borrowing
pledge
the analysis is restricted to the two extreme cases
abroad. Here, however,
=
of the autarky cp= 0 and the full financial integration,
cp l.33
leads to a Rate of Return Equalization
Full financial integration
(RRE)
out additional
across
the
Min\-^?,
two
[1-(BN
countries,
1W
(U
= r=
Mini -^?,
J
[l-<os
1U/' (ks),
J
(RRE)(34)
Aggregate
=
The world
rewritten
kN, ks
=
+
R[aN + co?N cos+ co?s
R[SN(r) + Ss(r)]
is determined
equilibrium
as
=
SN(r)+ Ss(r)
=
^^
37
Imperfections
= o?ensures the interior
solution,
(0)
is
constraint
(WRC)
given by
where/'
resource
kN + ks
Implications of Credit Market
by
> 0. The world-wide
(V)~1(r)].
(34)-(35),
which
(WRCH35)
can also be
IN(r)+ Is(r). (36)
> 1, which
>
also implies ^N/(l
coN) 1, (RRE) be
=
= r=
comes
or
kN
(kN)
f (ks),
equivalently,
ks. In this case,
simply/'
in either country, so that the movement
of interna
(BC) is not binding
inmarginal
tional capital flows is entirely dictated by the difference
pro
a result of financial integration,
in South is
the investment
ductivity. As
When
-
Xs/(1
cos)
and capital flows until the differ
by the lending from North,
inmarginal
eliminated.
is
productivity
in South, the lend
Even when Xs/(1 - cos) < 1, so that (BC) is binding
to
two
if
the
differ
countries
in the
flows
from
North
South
ing
mostly
saver's wealth. This is illustrated by figure 1.27, which assumes XN = XS,
=
share the same investment
coN
cos, co^ > (0?s.Then, the two countries
financed
ence
investment
is located to the right of
schedule
schedule, while North's
South's. Hence,
the autarky rate of return is lower inNorth
than in South
<
are
rates
return
With
financial
of
the
The
(rN rs).
integration,
equalized.
=
=
now
+
rate
return
is
of
given by [SN(r) Ss(r)]/2
IN(r)
Is(r),
equilibrium
Ss(r)
i
View
|
~
1
Figure 1.27
Neoclassical
a^^^^i
of Financial
Integration
1m
B^?a
"
*
h/R
(XN
=
Xs, coN
=
cos, co^ >co?)
38Matsuyama
as shown
by the intersection
the average
saving schedule
of the (common)
investment
schedule
and
dotted
(depicted by the upward-sloping
a rise in its rate of return, which
increases its
curve). North experiences
and hence run a current account sur
saving and reduces its investment,
a fall in its rate of return, which
plus, while South experiences
its saving and increases its investment,
and hence run a current
deficit.
ment.
reduces
account
In short, North's
to South to finance its develop
saving flows
This captures the standard neoclassical
view of the global finan
cial integration.
The reverse flows
than South's.
higher
ing schedule,
while
ifNorth's
occur, however,
autarky rate of return is
In figure 1.28, the two countries share the same sav
North's
investment
schedule is located to the right of
financial
the rate of return is
hence, rN > rs.With
integration,
at
the
level
the
the
intersection
of
(common)
given by
saving
equalized
schedule and the average investment
schedule
(depicted by the down
South's,
its rate of return to
dotted curve). North
(South) witnesses
ward-sloping
to rise (fall), and hence
fall (rise), its saving to fall (rise), and its investment
its current account to turn into a deficit (surplus). In short, the capital
investment. One way inwhich
the sit
flight from South finances North's
=
=
>
in figure 1.28 can occur is XN Xs, coN cos, co^
uation depicted
co^.This
case
captures
stitutional
the view
factors
that weak
contribute
and
governance
corporate
to financial
any
in South
in
other
and hence
insecurity
capital flight from South toNorth. Another way inwhich the situation de
can occur is XN = Xs, coN- cos= co^- co^> 0. In this case,
picted in figure 1.28
lr t
S^r) =Ss(r)
\ \ Mr]
~:
:
:
:
%Ur)
?
ks/R kN/R
Figure
1.28
Capital
Flight
-co?N>0.
=
(I): XN > Xs, coN
cos, co^
=
co?;OR Capital
Flight
(II); XN
=
Xs, coN
-
cos
=
co"
Implications of Credit Market
Aggregate
Imperfections
39
a larger share of the wealth
is in the hand of the savers in the South than
in the North. Then, even though the two countries do not differ in the
the "capital flight" occurs from South toNorth. This is
other dimensions,
the firms in the South have weaker
because
the firms in the North.
balance
sheet conditions
the former more
This makes
than
on exter
dependent
in turn makes
nal finance, which
them less credit-worthy. A financial in
tegration forces the firms in the South to compete with those in the North
when
financing their investments, which put the former in disadvantage.
As a result, South's saving flows to finance North's
investment.
=
=
Figure 1.29 illustrates the case where XN Xs, coN> cos, co^
co^. In this
case, North's
saving and investment
If the pure net worth
of
South's.
right
we
have rN> rs.35Again,
ening effect,
schedules
are both
located
to the
effect dominates
the capital deep
that, with financial in
this implies
the
toNorth, because
from
South
flows
the firms in the
tegration,
saving
South have the weaker
financial position
than those in the North.36
Note that, inmany of these cases, kN> ks continues
to hold after the full
so that the marginal
financial integration,
re
of investment
productivity
the assumption
higher in the South: Rf (kN) < Rf (ks). Obviously,
that only the local firms can produce
the capital stock used in the pro
duction of the final good in each country, plays an important role in the
mains
If any firm from any country could operate
at the
analysis.
anywhere
same
in
the
difference
would
be
productivity,
marginal
productivity
some
eliminated
in
which
FDI
to
flows from North
by two-way flows,
South (some agents inNorth produce
capital in South), and at the same
'''
*W* mmm >jK
b^b
^kf*
?-i-:
Figure
Capital
*A* ^W*
u
ks/R
kN/R
1.29
Flight
=
=
(III): A,N Xs, coN > cosco^
1 "^^
co?.
40Matsuyama
time, the saving flows from South to North. Even if their productivity
declines when operating
abroad, the two-way flows may occur, as long
as their financial
to offset the produc
is more
than enough
advantage
of
abroad.37
tivity disadvantage
operating
So far, it has been
assumed
that the two countries
share
the identical
ifNorth
ismore productive
than South, the re
technologies.
Obviously,
verse
could
occur.38
For
if
flows
RN> Rs, the capital
capital
example,
even without
flows from South to North
credit market
imperfections.
it is difficult to draw a sharp distinction
between
the two the
However,
one
on tech
and
based
ories, one based on credit market
imperfections
because
the
differences
differences,
may be
nological
technological
caused by credit market
Recall
that
credit
market
imper
imperfections.
fections may often prevent
the credit from flowing
into the most pro
of section 3.3) or the most productive
agents (in the model
proj
some
models
of
section
(in
5). To the extent that credit market
cause
in investing
it
technologies,
imperfections
endogenous
changes
to tell the two theories apart empirically.
would
be a challenge
ductive
ects
Implications:
Dynamic
Symmetry-Breaking
and Endogenous
In the above
it is shown how the cross-country
analysis,
distribution
(coN, cos) affects the cross-country
Inequality
net worth
dis
of the capital
now
us
Let
feedback
from
introduce
(kN, ks) to (coN,
(kN, ks).
positive
remove
savers
us
it
from
model.
the
the
To
let
By re
cos).
simple,
keep
we
in
obtain
the
k.
and
(31),
dy
by kjt+1
equation
placing
co;by Wj(kjt)
namics of each country in autarky, as follows:
tribution
stock
=
=
kjt+1 RW(kjt) (;' NorS), (37)
which
fc* =
implies
that each country
converges
RW(lfc*).
From equations
(34)-(35), the dynamics
financial integration are given by:
monotonically
of the world
to A:*,where
economy
under
(rre)(38)
Ht^'+^-Mt^'1^^
=
KM + *sm *[W(U
+ W(kst)]r (WRC)(39)
a function of (kNt, kst). Hence,
(kNt+1, kst+1) as
jointly determine
can be
the
from any initial condition,
trajectory
(kNQ,kso),
equilibrium
solved for by iterating (38) and (39) forward.
which
Aggregate
Implications of Credit Market
Imperfections
41
Let us
look at the steady states. In what
let us restrict our
follows,
to the case where XN = XS = X,which means
that the only possible
source of
across countries
is in the initial capital stocks.39
heterogeneity
selves
are binding
in both countries
are given by
constraints
If the borrowing
the steady state conditions
//(M
in steady
nK)
=
state,
(RRE)(40)
l-W(kN)
1-W(ks)
=
kN+ ks R[W(kN)+ W(ks)] (WRC)(41)
1.30 illustrates these conditions
for an intermediate
value of R. It
that there are three steady states. One of them, (SS), is symmetric,
=
(A:*, A:*).The other two are asymmetric,
given by (kN, ks)
(ASN) and
=
=
(ASS), given by (kN, ks)
(kH, kL) and (kN, ks)
(kL,kH),where kH > fc* > kL.
Furthermore,
(SS) is unstable because Xf(k)/[1
W(k)], is increasing at
=
so
k
rate
the
return
that
in
of
each
k*,
pledgeable
country is increasing
in the steady state capital stock. The
instability of (SS) seems to suggest
Figure
shows
(ASS) are stable, if this is the case, the two-country world
under financial integration. Thus, this cap
economy develops
unevenly
tures the structuralist view that poor countries are unable to compete
in
that (ASN) and
integrated capital markets
cial security to the lenders
can offer finan
against rich countries, which
and that the global capital market
contributes
ks
.
,
(WRC)
kL
Figure
I
dpS
f\\)
y
k*kH
=
kN ks
VT\\)
1.30
Symmetry-Breaking
and
the Emergence
of Core-Periphery
Patterns
42Matsuyama
to uneven
of the world
the core
economy,
creating
development
or and the International
Economic
Order, or the
patterns
periphery
of the Rich and the Poor.40
World-System
is suggestive,
the two
While
the above analysis
analytically
verifying
"ifs" above is difficult.41 Instead of the two-country
case, Matsuyama
a
of countries
and
with
continuum
the
above
model
studied
(2004a)
showed
analytically,
as a whole
In autarky, the world
economy
converges
of the initial distribution
ric steady state, regardless
across
to the symmet
of capital stocks
countries.
small X, and for an intermediate
For a sufficiently
range of R, financial
a symmetry-breaking.42
causes
That
is, the symmetric
integration
stable steady
asymmetric
steady state loses its stability and many
states
richer
In any stable steady state,
to emerge.
other countries
than in autarky, while
some
countries
become
poorer
become
than in
autarky.
into the rich and
divided
is endogenously
Thus, the world economy
of these results deserve emphasis.
the poor. Two implications
First, this
a partial improvement
in
market
credit
the
how
demonstrates
example
= 0 to =
could
have
move
X
less
than
while
from
cp 1,
one)
9
(a
keeping
are
to
that
dramatic
distributional
consequences
surprising
perhaps
in
the credit market
financial integration alleviates
imperfections
many;
in
other
some countries and exacerbates
the credit market
imperfections
Second, the instability of the symmetric
steady state and the
an intermediate
occur
states
of asymmetric
only for
steady
across
nations. That
the rise and fall of inequality
value of R. This suggests
R improves over time, the world
is, as productivity
economy may first
as some countries
start taking off, and then fol
divergence,
experience
as other countries start catching up, thereby gener
low by convergence,
across nations.
patterns of inequality
ating the inverted U-curve
above is that "hidden factors" are nontradable.
One key assumption
the fu
in one country would
means
investment
the
This
that
improve
not
same
else
in the
ture net worth
of the entrepreneurs
country, but
in one
If these factors were
where.
freely tradable, then the investment
in any country,
on the net worth
same
effect
the
have
would
country
across countries.
of inequality
the persistence
eliminate
which would
some
of these factors are tradable at
The interesting case would be when
countries.
existence
some positive
costs. Then,
the investment
demand
would
have
bigger
Implications of Credit Market
Aggregate
Imperfections
43
in the neighboring
lead to some
countries, which might
as
as
at
well
the global scale.
effects
contagion
divergence
spillovers
gional
7
General
Equilibrium
Heterogeneous
Projects:
re
with
Heterogeneous
Agents with
Patterns of International
Trade
In all the models
with heterogeneous
agents above, it has been assumed
that each agent has access to only one type of projects. Let us now discuss
amodel with
agents, where each agent has access to a di
heterogeneous
verse set of projects, in the context of international
trade.
a variation of the Ricardian model with a continuum
Consider
of trad
able goods, indexed by z e [0,1], a laDornbusch,
and
Samuelson
Fischer,
a continuum
is populated
of homogeneous
(1977). The economy
by
<
co
1
whom
is
with
each
of
endowed
units
of
the input. Let us
agents,
now call this input labor,
the tradition of the trade literature.
following
are given by symmetric
so that demand
The preferences
Cobb-Douglas,
=
for good z is D(z)
E/p{z), where p(z) is the price of good z and E is the
in this economy. To produce
aggregate
any tradable good,
expenditure
the agents must run a project. Each project in sector z requires one unit
of labor and generates R units of good z. Each agent may run one proj
ect or may simply become aworker, by
the labor endowment
supplying
to other
agents.
Since any project requires one unit of labor, and the labor endowment
of any agent is co< 1, each agent who runs the project must employ 1 - co
units of labor supplied by those who do not run the
project. Let w be the
can
which
the
to
after
rate,
wage
pay to the workers
employers
pledge
the project has been completed
and the output has been sold.
By running
a project in sector z the
earns p(z)R, out of which
entrepreneur
they pay
the wage bill, w(l - co), so that they consume p(z)R - w(l - co).
run
By not
labor, they consume wen. Hence,
ning the project and supplying
any
to run the project in sector z if and
agent is willing
w(l
only if p(z)R
>
co) wco, and equivalently,
p(z)R>w,
where
(PC-z)(42)
(PC-z) stands for the Profitability Constraint for Sector z. This con
straint may not be binding,
can
because
the employers
a
pledge
only
fraction of the project revenue for the wage payment.
The employers
in
sector z can pledge
where
is
continuous
and
X(z)
only X(z)p(z)R,
strictly
the range from zero to one. Because
of the partial
increasing with
the projects in sector z take place if and only if
pledgeability,
they satisfy
44Matsuyama
>
co),(BC-z)(43)
X(z)p(z)R w(l
where
(BC-z) stands for the Borrowing Constraint for Sector
the pledgeable
fraction of the project
revenue,
X(z), is
The
that
it
is
assumption
specific.
strictly increasing means
are
tors
indexed such that the agency problems underlying
ing constraint are bigger in lower-indexed
ensure
The Cobb-Douglas
preferences
z. Note
now
that
sector
that the sec
the borrow
sectors.
that, in autarky, the economy
in
sectors.
all
both
the
Thus,
(PC-z) and (BC-z) must be satis
produces
z.
one
fied for all
for each z,
of them must be binding; oth
Furthermore,
erwise,
p(z)/w
no agent would
=
max{l, (1
-
become
workers.
co)
A(z)}/R.
Therefore,
(44)
in X(z) < 1 - coand constant for X(z) > 1 - co.Note that, for
It is decreasing
X(z) < 1 co, (BC-z) is binding and p(z)R > w. In the sectors plagued by big
in order to as
each project must earn higher revenues
agency problems,
sure the workers
for their wage payment.
The higher prices and higher
are
to
sectors
in
the
these
due
the difficulty of obtaining
project
see
in
restricts
let
which
the
these
sectors.43
To
de
this,
credit,
n(z)
entry
note the number of projects run in sector z. Then, the total output in sec
tor z is n(z)R, which must be equal to D(z) in autarky. Thus, E = p(z)D(z)
=
(44)becomes
p(z)n(z)R. Hence,
revenues
=
co))EM(45)
n(z) min{l, X(z)/(1
in X(z) < 1 - coand constant for X(z) > 1 - co.Since each
is increasing
is
labor endowment
project requires one unit of labor, and the aggregate
resource
in
is
to
constraint
this
the
co,
economy
given by
equal
i
which
[ n(z)dz
= co.
(46)
Summing up (45) for all z and using (46)yields
n(Z)
min{l,Mz)/(l-co)}
^( }
\lmin{l, X(s)/(1 co)}ds
< co for low z and n(z) > co for high z.44 This restricted
implies n(z)
excess
firms to sat
entry and the resulting
profits enable the incumbent
sectors.
in low-indexed
constraints
isfy their borrowing
which
consists of two countries of the
Now, suppose that the world economy
and
South.
North
kind analyzed
above,
They have identical parameters
co.
it
is
that XN(z) = XNA(z) and
assumed
Furthermore,
except X(z) and
=
in z with
the
and increasing
XsA(z), where A(z) is continuous
Xs(z)
Implications of Credit Market
Aggregate
\
1pu{z)lwA
Imperfections
45
ps(z)/ws
.
\/Rvx
.^-^
?-l-[-
O
1.31
Figure
of Absolute
Patterns
A(z)
{\-coN)/XN (\-cos)as
Advantage
to one, and 0 < A,N, A,s < 1. This means
that the agency
two
the
constraint
have
components;
problems
underlying
borrowing
on the
and other sector-specific
factors, and
A(z) depends
technologies
on corporate
and
governance,
XN and Xs depend
legal enforcement,
from zero
range
other
factors that determine
country-specific
in these economies.
In what
cial development
-coN)AN<(l-cos)As.
From (44), the autarky
now given by
prices
=
P/(z)/u;.
max{l,(l-co;.)A7A(z)}/R
in North
(j
the overall
follows,
and South,
=
level of finan
let us assume
(1
pN(z) and ps(z) are
N, S). (48)
-
<
< (1 -cos)
(48) implies that pN(z)/wN
coN)
AN
equation
As,
<
ps(z)/ws for all z and pN(z)/wN
ps(z)/ws for z such that A(z) < (1 cos)/
as
means
in
1.31.
shown
This
that the credit market
Xs,
figure
imperfec
tions effectively
over
become
the source of North's
absolute advantage
Since
(1
South.
Hence, when North and South trade with each other, the equilibrium
so that South
relative wage must satisfy wN>ws,
ad
gains comparative
in
sectors.
indexed
com
1.32
shows
the
of
vantage
Figure
high
patterns
credit market
functions
better and
North, whose
parative
advantage.
are
more
whose
and
richer
hence
entrepreneurs
credit-worthy,
special
izes and exports
in the lower indexed sectors that suffer from
bigger
South specializes
and exports in higher indexed sec
agency problems.
are subject to smaller agency
The relative wage
tors, which
problems.
=
rate and the marginal
are
determined
sector, A(zc)
Ac,
by the balanced
trade
condition.45
46Matsuyama
i
\
_pn(z)
wN/R\.\
ws/R.j.|.^-ps(z)
A(z)
?\-j-'-!-
OJ (\-a>N)IXNAc (\-cos)lh
1.32
Figure
Patterns
of Comparative
8
Advantage
with Pure Price
Equilibrium
A Model
of Polarization
General
Effects:
In all the models
distort
we
the allocation
have
at so far, credit market
In the following model,
of resources,
the allocation
looked
of resources.
imperfections
credit market
and yet, they
do not distort
imperfections
their effects of prices. The
have distributional
through
implications
is clearly very special, but it helps to highlight how the net worth
model
effect could operate through prices rather than quantities.
a continuum
of agents with unit mass, whose
Consider
input endow
In
to lending
to
addition
ment in period 0 is distributed
G(co).
according
<
in period
x
counits of the input in period 0 for rx units of consumption
the
with
variable
1, each agent now has access to an investment
project
converts I units of the input into RI units in consump
scale I>m, which
tion in period 1. To operate this project at the scale equal to I, the agent
rate equal to r.Here, m is the mini
needs to borrow I co at the market
mum investment
that is, investing I<m generates nothing.
requirement,
the period-1 consumption.
As before, each agent maximizes
By running
=
= RI at
the
this project
the scale, I>m,
r(I co)
agent can consume U
= rco.
if R
Therefore,
(R r)I + rco. By lending, the agent can consume U
=
< r, the agent prefers lending; if R
r, the agent is indifferent; and if R >
r, the agent wants to borrow and invest as much as possible.
the agent can pledge only the fraction X of the project
However,
constraint:
enue, hence facing the following borrowing
XRI>r(I-a).
(BC)(49)
rev
Implications of Credit Market
Aggregate
Imperfections
47
If r < XR, the agent would borrow and invest by infinite amount, which
never occur in equilibrium.
would
for XR<r <R, the agent
However,
would borrow and invest up to its borrowing
limit, as long as it also sat
investment
isfies the minimum
that, for XR
requirement, m. This means
the investment
<r<R,
1 ?
=
schedule
by an agent with
the input en
co, is given by
dowment,
I((d)
demand
co if co> coc= m
and zero otherwise.
Aggregate Saving
Therefore,
=
1
-?
the credit market
= F( -? XR\-i
codG(co) J0 1
r
/
\
=
,
Aggregate
equilibrium
r??
is given by
corfG(co)
m(l-XR/r)
(50)
Investment
for XR<r<R.
Figure 1.33 illustrates this condition. The vertical line rep
curve represents
the LHS of (50), while
the downward-sloping
the RHS of (50). For a sufficiently
small X, that is, if X< J0m(1-^codG(co)/Jo
line intersects with the
corfG(co), the vertical
part of
downward-sloping
<
<r
the aggregate
investment
that
in
R
XR
holds
schedule,
ensuring
In
this
the
rich
become
the
borrow
equilibrium.
equilibrium,
relatively
from the relatively poor, who have
ers; they borrow as much as possible
no choice but to lend to the rich. In this model, what
the rich
separates
resents
from the poor is their relative position
in the wealth
distribution.
They
do not have to be rich by any absolute standard, because
the equilibrium
r
R
V
\
V
r
( 1-?ART1
^
I
r)axlG(a>)
r J Ml-AR
XR
?
?
O
^codG(co)
Figure
1.33
48
Matsuyama
rate of return always adjusts tomake sure that some agents would
to become
become borrowers.
lenders, while others would
have
Now suppose that X is reduced further. This shifts down the aggregate
investment
schedule.
the aggregate
investment
does not
However,
change, due to the inelastic aggregate
saving. The overall effect is hence
a reduction
in r such
cocremains
resources,
intact. Thus,
as rmoves
that XIr remains constant, which
that
also means
a
no effects on the allocation of
in
X
has
change
to offset any effect that X might
endogenously
have.
it has
However,
as seen
effects,
for each agent as follows:
distributional
consumption
period-1
'
(\-X)R
I
calculating
the
XR\
ifco>coc^l--j
^r-W7co
U(co)=|
by
/
if co< co = m
rco
1
\
I
XR\
rJ
return of hav
is illustrated by figure 1.34. Note
that the marginal
an
across
additional unit of the input differs
the agents. For the poor,
ing
it is equal to r,which
is strictly lower than the project return, R, because
to in
the credit market
the poor from borrowing
prevents
imperfection
vest. For the rich, on the other hand, it is equal to (1 - X)R/(1 - XR/r),
is strictly higher than R, because of the leverage effect. That is, the
which
rate
enable them to borrow at the market
credit market
imperfections
which
1/
UUo)
\-XRIr
Rco
J
/
/f
/
/
/
/
* yr
?
_?-!O
Figure
1.34
rco
m(\-XR/r)
Aggregate
Implications of Credit Market
Imperfections
49
due to the lever
strictly lower than the project return, R. It is precisely
as
as possible,
to borrow
much
the rich wanting
age effect that makes
that is, equation
is precisely
the reason why their (BC) is binding,
which
arrows
rich.
The
with
for
the
holds
(49)
depict the effects of a
equality
the terms of trade against
reduces r. By moving
lower X,which
this further magnifies
lenders and in favor of the rich borrowers,
parity
of the marginal
returns on wealth
Long-Run
What
Implications
between
the poor
the dis
the rich and the poor.
on Wealth Distribution
if we allow for some
to the wealth
distribution
happen
and
Newman
from (J(co) to co?Following
(1993) and
Banerjee
to
that each agent has an offspring,
and Zeira (1993), imagine
would
feedback
Galor
is an increasing
he leaves the bequest, which
function of (i(co).
the threshold
level of wealth,
the shape of IT(co), including
coc, is a
the dynamic
evolution
of wealth
dis
function of G(co), this determines
=
can be iterated to solve for the long
tribution, Gt+1(-)
<E>(G,(-)),which
run wealth distribution
In some cases, the
from any initial distribution.
whom
Since
run distribution
converges
long
initial distribution.
This occurs
to a single mass point, regardless of the
if a fast wealth
accumulation
by the rich
rate of
and their strong investment
demand drives up the equilibrium
return so much
that the poor lenders could also accumulate
their wealth
by lending, which helps
This is the case where
the credit market.
them to cross over the threshold
level of wealth.
to the poor
"trickles down"
con
the long run distribution
of
the
initial
distribution.
regardless
the rich's wealth
In other cases,
through
verges to a two-point distribution,
causes an endogenous
The credit market
of the society be
polarization
a high level of wealth
the rich and the poor. The rich maintain
in
part because of the cheap credit offered by the poor, who have no choice
but to lend their small saving to the rich. In some other cases, the long
run distribution
on the initial distribution,
the his
depends
exhibiting
tween
tory dependence.46
9
Concluding
Credit market
Remarks
the key to understanding
im
imperfections
many
provide
and
and
interna
portant issues in business
cycles, growth
development,
tional economics.
in these areas, however, has left in its
Recent progress
wake a bewildering
conflict
array of individual models with seemingly
same
the
of credit market
ing results. Using
single model
imperfections
50Matsuyama
this paper brought
throughout,
In so doing,
unified framework.
be
attributed
may
phenomena
clude,
among
other
together
it showed
a diverse
set of results within
a
how awide
to credit market
range of aggregate
imperfections.
They in
technical
investment-specific
recur
recessions,
traps, leapfrogging,
persistent
cycles, reverse international
capital flows, the rise
things,
changes, development
ring boom-and-bust
endogenous
across nations,
and the patterns of international
some equilibrium
to
is also used
and
investigate
distributional
of
the
of
credit
markets.
One
impacts
improving
efficiency
of equilibrium
often respond non
recurring finding is that the properties
and
fall of inequality
trade. The framework
some cautions for
suggests
changes, which
a
of credit market
studying aggregate
implications
imperfections within
narrow class or a particular
of
models.
family
monotonically
Although
cuss many
it is highly
to parameter
the simple framework used in this paper enabled me to dis
issues within
the limited space, it has some limitations. First,
in the dynamic
restrictive
For ex
feedback mechanisms.
it rules out endogenous
agents, and
savings by the investing
ample,
in antici
the net worth
hence the possibility
that they may accumulate
the issue addressed
pation of their future financing needs,
by Green
and Jovanovic
also
(1990), Buera (2006), and others. The model
net worth might depend on
that the borrower's
rules out the possibility
determination
of
the future allocation of credit through the equilibrium
issue
Shleifer
assets
the
the
addressed
owned by
durable
borrowers,
by
and Moore
and Vishny
(1997), and Kiyotaki
(1998). The
(1992), Kiyotaki
wood
in one period.
that all the projects are completed
also assumes
such as
rules out any issues associated with multistage
financing,
as
and
Clementi
and
addressed
terminations
refinancing,
by
project
and Fishman
(1992).
(2006), and Gertler
(2006), DeMarzo
Hopenhayn
model
This
is essential
for such multi-period
projects
allowing
importantly,
of credit market
the liquidity implications
for understanding
imperfec
and
and Kiyotaki
and Tirole (1997,1998)
tions, as shown by Holmstrom
the pledgeability
Moore
X, which mea
(2002, 2005a, 2005b). Second,
sures (inversely)
the severity of agency problems behind the credit mar
To the extent that it re
has been treated as exogenous.
ket imperfections,
we
like to introduce
would
flects the state of financial development,
More
some
feedback mechanisms
from the investments
to the credit market
economic
the two-way
causality between
efficiency
issue
the
addressed
and
financial
by Acemoglu
development,
growth
and Rey
and Smith
and Zilibotti
(1997), Martin
(1997), Greenwood
(1992). To the extent that it reflects the quality of
(2004), and Saint-Paul
in order
to address
Aggregate
or contractual
legal
would
enforcement
Imperfections
and
Finally, aggregate
implications
in the otherwise
been examined
work. While
other
51
institutional
factors, we
some political economy
of credit market
imperfections
neoclassical
frame
competitive
to address
it in order
like to endogenize
issues.
have
Implications of Credit Market
im
for isolating the effects of credit market
to examine how credit market
im
be interesting
interact with other departures
from the neoclassical
this is useful
itwould
perfections,
perfections might
For example,
credit market
framework.
into
introducing
imperfections
the monopolistic
also rich and diverse
in its ag
framework,
competitive
as
gregate implications,
pointed out by Matsuyama
be essential
for understanding
how credit market
the process
of product
economies.
glomeration
Ibelieve
innovation,
(1995,1997),
imperfections
as well
firm entry dynamics,
would
affect
as ag
that incorporating
these additional
into the present
elements
would
the basic message
framework
of the paper.
only strengthen
are
Credit market
in
and
im
rich
diverse
the
imperfections
aggregate
plications
important
a wide
and they provide
the key to understanding
range of
issues. What has been discussed
here ismerely
the tip of the
iceberg.
Acknowledgment
site: http://faculty.wcas.northwestern.edu/~kmatsu/;
This paper
is prepared
[email protected].
on Macroeconomics,
Annual
Conference
March
Web
Email: k-matsu
for the NBER
2007.
22nd
It is a
30-31,
highly condensed version of lecture series given at various places (Kyoto,
LSE, Northwestern,
Toulouse, UCL, and Zurich) over the years, which
has slowly evolved
into its current form. (Most recent lecture slides are
available on my web site.) My special thanks go to the graduate
students
who
attended
ments
these
by the editors,
ference. I thank also
lectures.
This paper benefits greatly from the com
the discussants,
and other participants
at the con
those who attended
the seminars at Chicago
Fed,
Paris-I, and Washington
University
of this paper was presented.
in St. Louis, where
a broad
outline
Endnotes
1. The existing
focus on a few specific areas of
See Bernanke,
surveys
Gertler,
applications.
and Gilchrist
(1999) for business
mechanisms;
cycle propagation
(2005) in
Banerjee-Duflo
Zweimueller
economics;
Bertola,
Foellmi,
(2006, chapter 7) for income dis
development
52Matsuyama
tributions.
it does
teresting
in spirit to this paper, but
13) is closest
(2005, part VI, particularly
chapter
in
Gertler
international
economics.
(1988) offers an in
any applications
Tirole
not
cover
on the state of the field before
glimpse
a major
it became
research
topic.
fluctuations
of TFP to the ex
market
could
endogenous
imperfections
on
I
to
have
tent they affect financing
chosen
of working
focus
investment-specific
capital.
tech
that investment-specific
of some recent studies
technical
change because
suggesting
see
neutral
better
nical changes
than the traditional,
(TFP) technical
changes;
perform
and Fisher
Krusell
Hercowitz,
Greenwood,
(2006).
(1997,2000),
also cause
2. Credit
at least seriously
in the credit market
In my view, anyone who believes
imperfections,
to do research
the impacts of any policy under
in this area, should never examine
enough
one could
that such a policy
the imperfections.
The most
the assumption
could eradicate
the credit market.
is to improve
hope for in any policy
3.
to refer to the Profitability
of agency
theory may want
prefer the language
as the Borrower's
and to
Constraint
Incentive Compatibility
(or Participation)
as the Lenders'
Constraint
Incentive Compatibility
Constraint
the Borrowing
(or Partici
pation) Constraint.
4. Those
who
Constraint
to co > 1 - XR/r "the collateral
call the inequality
constraint/'
analogous
or "the
In do
constraint."
call it "the cash flow constraint/'
while
other authors
liquidity
assets or
net worth
held only in collateralizable
that the borrower's
ing so, they assume
the use of
I deliberately
avoid
to satisfy the constraint.
only in liquid assets could be used
with
the question
or "liquidity"
I am primarily
because
concerned
the terms "collateral"
net worth,
abstract
is affected by the (level of) borrower
constraint
of how the borrowing
to say, this is
or liquidity
Needless
holdings.
portfolio
ing from the role of the borrower's
5. Some
authors
an
important
the one used
6. See,
issue, but its careful
in this paper.
for example,
Tirole
treatment
(2005; chapter
would
require
3, supplementary
richer
framework
than
sections).
for this. First,
7. Broadly
there are three reasons
speaking,
even ifwe could identify
them in certain
ket imperfections,
across
amuch
the major
causes
of credit mar
are likely to vary
specific cases,
at least qualitatively
and times. Second,
of credit market
imperfec
implications
investment
countries,
industries,
types,
and equilibrium
of the aggregate
speaking, much
the imperfec
on the specific nature of the agency problems
behind
tions do not depend
reason
one. This reduced
is a practical
the most
tions. The last, and perhaps
important,
this
as the time and effort of the reader. For example,
saves space, as well
form approach
and of
and Gertler
me to reproduce
the key results of Bernanke
enables
(1989)
approach
to explain
the
devoted many
pages and appendices
Boyd and Smith (1997), each of which
one
I needed
In contrast,
state
verification.
under
contract
only
costly
problem
optimal
constraint.
to describe
the borrowing
short paragraph
8. See Tirole (2005, p. 119) who
of credit market
imperfections
the general
of separating
also argues for the benefits
structure.
the questions
of the financial
issues
from
other than sup
factors" play no active role in the economy
factors
income. The hidden
the residual
and absorbing
inelastically
plying
"hid
these
returns
to
to generate
are introduced
here merely
Later,
capital.
diminishing
is embedded
role when
this model
den factors" in fixed supply will be given an additional
net worth.
to endogenize
the borrower
in a dynamic
setting
9. The owners
these
of the "hidden
factors
think that the agents have
10. One may
as amodel
be viewed
this
may
natively,
access
to a storage
of a small
open
of return, r.Alter
technology
or of an industry.
economy
Aggregate
of Credit Market
Implications
11. Equation
assumes
(5) implicitly
53
Imperfections
the interior
can be ensured
which
solution,
by
impos
ing thatRf (R)< r.Then, (5)holds with 0 < k < R, which implies that 0 < n < 1.
12. For
proves
cations
the following
imagine
sequential
example,
n credits on the first-come,
first-serve
basis,
and
are
be denied.
delayed
13. A change
(for some
in rwould
are
straightforward:
tent with
the evidence
facturing
random
have more
a rise in r leads
reasons)
constraint:
those
agents
the market
whose
credit
ap
appli
effects, but its effects on k and coc
in k by raising
consis
coc. This is roughly
and Gilchrist
that small manu
(1994) and others
complicated
to a decline
found
firms are more
will
service
by Gertler
to the tightening
sensitive
welfare
of monetary
policy.
14. Aghion,
some evidence
liber
that, after a financial
(2007) shows
Fally, and Scarpetta
the entry of small firms force larger firms to scale down or to exit
alization,
completely.
as a
15. The partial equilibrium
of the previous
section may be viewed
model
special case,
=
are given
the saver's preferences
is
pC? + C?, so that the aggregate
by U?
saving
the case without
elastic. One may also analyze
the savers by looking at the spe
infinitely
the aggregate
cial case where
is inelastic at S(r) = co.
saving
where
so that the total
the case without
the savers,
is equal to
saving
=
can show that this is
(5), r
co). Simple
XRf (Rco)/(l
algebra
=
= in co in the range, t\/(1 + r\) < co< 1 - X,where
is
t\
increasing
)/log(/c)
log(/'
-kf'/f
the elasticity
of
of the marginal
capital.
productivity
16. For example,
consider
k = Rco and from
co. Then,
in coand co? (as well as X) on k are studied. What
changes
from k to co and co?? Imagine
net
that the entrepreneur's
in period
and the saver's net worth
t, co, and co?, jointly determined
kt+1, as described
which
in turn determines
that co,+1 = W(kt+1) and co?+1 = W?(kt+1).
(This can be jus
our
for example,
into the overlapping
by embedding
two-period
agents
agents
17. Here,
the effects of exogenous
ifwe also allow for some feedback
worth
above,
tified,
as discussed
on how a
of this economy
then depends
framework,
later.) The dynamics
in k affects the distribution
of the wealth
the entrepreneurs
between
and the savers.
change
and Piketty
(1999) conducted
Banerjee,
Aghion,
analysis
along this line in a similar setting,
and found the case of endogenous
of low investment,
cycles, where
periods
during which
the wealth
is shifted
distribution
towards
the savers, alternate with
of high
in
periods
the wealth
distribution
is shifted
toward
the entrepreneurs.
vestment,
during which
18. One
could
remove
this feature
the effects
G(co) and by studying
limit case where
G(co) converges
by letting the endowment
of shifts in G(co). The analysis
to a single mass.
19. One may
call this effect "flight
(2003), who also developed
Barlevy
lower productivity
projects
during
to safety"
amodel
20. Recall
when
21. This
that figure
1.9 is applied
be distributed
here may
to
according
as the
be viewed
to "flight to
(as opposed
quality"),
following
inwhich
the credit composition
shifts toward
recessions.
m2/m1
< (1 ^/(l
X^/RJ
< 1.
to the dynamic
framework
is simple
in part because
the "hidden
fac
durable
such as the land. Otherwise,
the borrower
net worth
assets,
in period
twould
on the asset
in period
on the future tra
t,which
depend
prices
depends
on the investment
which
in turn depends
and the borrower's
net
jectory of the economy,
in period
worth
t. Kiyotaki
and Moore
that such asset
(1997) and Kiyotaki
(1998) argued
make
This conjecture
has been
price movements
amplification
quantitatively
significant.
studied by Kocherlakota
and Quadrini
(2000), Krishnamurthy
(2003), Cooley, Marimon,
and Ripoll
(2004), and Cordoba
(2004).
conversion
tors" do not
include
54Matsuyama
22.
The
associated
(2005b)
space constraint
with poverty
on these issues.
me
prevents
broad methodological
from discussing
issues
many
see Azariadis
and Stachurski
(2005) and Matsuyama
trap models;
23. Mathematically,
for any e > 0, there exist open
intervals,
e I* and
as t?> oo, kt?> k* for
kt?> k** for k0 e I**.
k0
24.
I** c
I* and
(0, e), such
that,
For
that only
textile and other
industries
that
imagine
type-1 projects,
example,
are available
at
some
coun
the
time
of
the
first
revolution
industrial
and
emerged
initially,
in reaching
the steady state, k*. Then, the second
indus
tries, say Britain, have succeeded
some new
trial revolution
arrives and type-2 projects,
like chemi
including
technologies
are born. Britain,
cal and steel industries,
in k*, is unable
to switch
to the new
located
while
some, but not
technologies,
take over the technology
leadership
all,
25. Although
these
form.
period-2
figures
depict
latecomers,
come
say Germany,
by successfully
the new
adopting
and
can take a more
the fluctuations
cycles,
from behind
technologies.
com
plicated
26
As
than
in all these
shown
twice.
This
the graph
intersects with
figures,
can be
same way
as the
in
the
proved
proof
line no more
the 45? degree
inMatsuyama
(2004, p. 865;
lemma).
27. This
cases
the next
and
are based
on Matsuyama
(2004b).
and Piketty
that endogenous
28. Aghion,
(1999) also showed
cycles occur when
Banerjee,
an intermediate
credit
market
has
the parameter
the
of
imperfection
representing
degree
at an intermediate
level of financial de
value. They interpreted
it as saying that countries
are
in the con
This may be an appropriate
interpretation
velopment
subject to volatility.
text of their model,
but not here.
access to many
investment
have
the capital-generating
nancing
that affect
the imperfections
credit
market
credit
29.
flow away from
be more
might
flow
For
agents
the empirical
have
specialized
31. Or,
opportunities
and
projects,
the capital-producing
to financing
at situations
where
constraint
borrowing
(1993),
projects.
such alternative
might
projects,
thereby
evidence
for the business
and Acemoglu
and Scott
cycle
asymmetry,
see,
for example,
when
R, declines
operating
substantially
productivity,
investment.
rules out the foreign direct
Later, some
effectively
will be discussed.
this assumption
32. Prasad, Rajan,
ing) offer overviews
section
2) by adding
33. Of
course,
and Subramanian
of the empirical
the savers.
(2006) and Kose, Prasad,
here
The model
patterns.
Falk
(1997).
the entrepreneur's
assumption
tions of relaxing
into account
the
diverting
is the case where
in which
arises naturally
context
this problem
and capital
in different
industries
and/or
technologies
expertise
or
in a specific
industry
technology.
This
the following
intermediate
the agents
when
fi
we change
happen when
which
divert
the
could
projects,
One could argue that a better credit
seeing what
of alternative
the financing
prone
are looking
face no
and
away.
(1986), Sichel
30. Another
that we
Recall
Rogoff,
extends
and Wei
Matsuyama
different
are
highly
abroad.
implica
(forthcom
(2005a,
in cp, so that
a priori, there is no reason to believe
that the effect ismonotone
the
with great caution. However,
results should be interpreted
dealing with
one would
as
to
have
take
cases would
the
analysis,
substantially
complicate
one for the domestic
and one for the in
two separate borrowing
constraints,
Implications of Credit Market
Aggregate
Kiyotaki
It is assumed
even
55
and Krishnamurthy
Caballero
(2001) and Aoki,
borrowings.
in
issue
models.
small
this
both
studied
economy
(2006)
open
ternational
34.
Imperfections
though
here
for the case without
35. Again,
(2005a,
Matsuyama
are of the
equal size tominimize
is straightforward.
that the two countries
for different
allowing
section
and
the notation,
sizes
country
the saver,
Benigno,
rN> rs if r\/{l
+
=
vi)<(Ds<(0N<l-XN
l-Xs.
See
2).
and Rogoff
that capital
Gertler
hazard model,
(1990) demonstrated
in the imperfect
to the
information
the rich to the poor ismuted
case, compared
case. It is not clear whether
in their
the reverse
information
flows occur
capital
In their moral
36.
flows
from
perfect
In the present model,
the reverse cap
of the poor is negative.
unless
the net worth
model,
is slightly
of the Southern
less than
ital flows occurs even if the net worth
entrepreneurs
that of the Northern
entrepreneurs.
See Ju and Wei
for some related analysis
of the two-way
flows of FDI and
(2006,2007)
a country. Sav
at
at
within
be
work
levels
the lending. Similar mechanisms
regional
might
the local businesses,
flow into big city finan
may
ings in rural areas, instead of financing
into the rural areas by big businesses
the investment
whose
cial centers, which
finance
37.
headquarters
are located
38. Lucas
(1990), for example,
the saving does not flow
why
areas.
inmetropolitan
that human
argued
capital externalities
to the South.
from the North
and Hamada
the case where
(2001) studied
Sakuragawa
in a similar model.
fers from the credit market
imperfections
39.
40. The
intellectual
can be
of this view
origin
traced
back
only
might
one
be the reason
country
to the structuralism
(South)
suf
of Nurske
(1953),Myrdal (1957), and Lewis (1977).
41.
Boyd and
Incidentally,
their two-country
model
of
cation problem.
They found
and two stable asymmetric
same
the exactly
(1997) obtained
dynamics,
on the
the credit market
based
imperfection
costly
numerical
symmetry
examples with one unstable
Smith
in
(38)-(39),
state verifi
steady state
considered
the case
(2006), who
of two countries with unequal
sizes. His simulation
shows
that, if the country
population
sizes are similar, the asymmetric
he also found endoge
steady states are stable. However,
nous fluctuations
around
the asymmetric
the countries
sizes are suffi
steady states, when
ciently
(2005c) discusses
the notion
This means
that the entrepreneurs
in lower-indexed
the
running
project
when
the agents are not indifferent.
44. Note
that the binding
borrowing
The total profit in sector
for X(z) > 1 - co. Summing
the aggregate
profit n is given by n
= wco + n = e.
tive profits.
co and zero
45.
This
See also Kikuchi
different.
42. Matsuyama
economics.
43.
states.
steady
section
credit-based
is taken
explanations
of symmetry-breaking
are not
indifferent
sectors.
See Remark
between
and
its applications
the sectors.
3 for how
to allocate
to
They prefer
the credit
in low-indexed
constraints
sectors give rise to posi
z is
is positive
for X(z) < 1 equal to E wn(z), which
it up across all the sectors and
that
verifies
(46)
using
= E - wco.
the aggregate
income Y satisfies Y
Hence,
from Matsuyama
of the patterns
(2005a, section
of trade include
that looked at
3). Earlier studies
Kletzer
and Bardhan
(1987) and
56 Matsuyama
recent examples.
This
(2006a, 2006b) and Wynne
(2005) for more
(2002). See Manova
that seeks the institutional
is a part of the growing
ad
of comparative
literature
origins
as
and Helpman
such
Costinot
Antras,
(2006),
vantage,
Acemoglu,
(forthcoming),
and Vogel
Levchenko
Nunn
(forthcoming),
(forthcoming),
(forthcoming).
Beck
46.
In essence,
(2000). The literature on the evolution
by Matsuyama
under
credit market
is vast. In addition
imperfections
see
and Bolton
mentioned,
(1997), Freeman
(1996),
Aghion
this iswhat
wealth
of household
is shown
distributions
to the three studies
already
and Ray (2002), and Piketty
(1997). Just as in the macro dy
(2006), Mookherjee
Matsuyama
on the
distri
of the credit market
the implications
namics,
long run wealth
imperfections
on the assumptions
inter
about the way different
households
bution
sensitively
depend
A proper
act with
cannot be explained
each other, which
here due to the space constraint.
a whole
new paper.
of this literature would
require
exposition
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