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: Comment on "Aggregate Implications of Credit Market
Imperfections"
Chapter Author: Nobuhiro Kiyotaki
Chapter URL: http://www.nber.org/chapters/c4080
Chapter pages in book: (p. 71 - 77)
Comment
Nobuhiro
1
Kiyotaki,
Princeton
and NBER
University
Introduction
What
duction
are the implications
constraint
of borrowing
for aggregate
pro
answer has
and income distribution?
Kiminori Matsuyama's
two aspects. First, concerning
the behavior
of an individual
producer,
a
constraint has
the borrowing
the invest
fairly robust prediction?that
ment of each producer
in addition
to the
upon its net worth,
depends
cost of capital and the expected marginal
product of capital. Secondly,
the author argues that there is no
the aggregate
outcomes,
concerning
and that the borrowing
constraint
leads to a variety
simple prediction,
on
of aggregate predictions,
the
environment
(in
depending
underlying
to the borrowing
addition
The
constraint may
constraint).
borrowing
generate
persistent
movement
of
aggregate
quantities,
or
may
cause
or
may expand during recessions
volatility. The inefficient production
be aggravated
booms.
The
of
the
financial
during
improvement
of aggregate
before
system may first increase the volatility
production
may
it.
reducing
At one level, this is an impressive
piece of work?a
toMatsuyama.
Like a screwdriver with exchangeable
ematically
simple framework with borrowing
eties of results in business
cycles, development,
on the attachments.
pending
world
according
heads, one math
constraint brings in vari
and capital
At another
is complicated
level, I find that the model
even
if
it
in
be
terms
of
mathematics.
ory,
may
simple
as
as
to
be
critical
in
to highlight
order
going
possible
between
the author
and me,
even
though
I agree
first lay out the key assumptions
de
in terms of the
Hereafter
I am
the differences
to many
arguments.
Let me
flows,
of his basic model:
of his
72 Kiyotaki
are
1. Agents
2. Projects
homogeneous.
are indivisible
and there is no lottery.
3. Agents
face borrowing
4. Agents
receive
5. Overlapping
constraints.
credit by the rule of the first-come-first-serve.
generations
with
model
each agent
living
for two pe
riods.
6. Agents
choose
one project
(a) Productive
versus
(b) Pledgeable
versus
(c) Produce
Do we
from amenu
of projects.
unproductive;
not-so-pledgeable;
capital versus
produce
consumption
goods.
really need
all six of these assumptions?
of (1) ho
Assumptions
indivisible
and
credit
(4)
mogeneous
agent, (2)
project,
rationing are not
essential. Here, because
the agents are homogeneous,
there are neither
nor
natural lenders
borrowers.
The only reason for borrowing
is that the
scale of investment
is larger than the saving of an individual
no
is
and
there
agent
lottery. (If there were a lottery so that the winner
could get enough
funds to finance the project, there would
be no need
earn
returns
if they receive credit
for borrowing.)
Because people
higher
minimum
to finance
constraint
is binding,
the borrowing
credit
the project when
in
in
is
the
this
needed
the
role
of
finance
Thus,
rationing
equilibrium.
are
in
to
from
those
who
back
the
is
transfer
the
power
paper
purchasing
are
in
to
front
of
the
those
who
queue
queue
(lucky
(unlucky agents)
ones).
there are many
is a complicated
theory of credit, because
more
to
it
is
that the fi
think
natural
consider
assumptions.11
This
auxiliary
nancial system transfers funds from those who have
the producers
because
have investment
opportunity,
them to those who
and consumers
are
heterogeneous.
ismore substantial
of (5) overlapping
Assumption
generations model
the overlapping
of (1), (2), and (4). But, because
than the assumptions
to
it
is
model
is rich by itself,
difficult
clearly understand
generations
genuinely
how many of the results
the overlapping-generations
are due
to the borrowing
constraint
instead
of
model.
an argument
similar to the author's, only with the as
Can we develop
constraint with heterogeneous
agents? Here,
sumption of (3) borrowing
we can use the insight that the overlapping-generations
is iso
model
to some credit-constrained
(See, e.g., Woodford
economy.
morphic
Then
the
and
[1989, 1992]).
[1986, 1990]
genera
overlapping
Aiyagari
73
Comment
be a result of the borrowing
tions feature would
constraint,
not
the as
sumption.
2
Alternative
Model
an infinite horizon
economy with homogeneous
output,
are two (even and odd) types of a
at
and
each
date.2
There
labor
capital
size of each type of
continuum
of infinitely lived agents. The population
We
consider
as unity.
is normalized
agents
elastically
and has
technology
Each even-type
to invest goods
labor in
agent supplies
in every even number of
as:
date
(1)
yt=f(kt)=Akf,0<A,0<a<l.
on
output at date t and kt is gross investment
capital at
t -1 is an even number.3 Each odd-type
agent supplies
in every odd number of date.
labor and invests on the same technology
where
date
Both
yt is gross
t -1, where
types have
00
the preference
=
U( Xr'lncs,0<p<l
c$ is consumption
storable between periods
where
as
(2)
at date
s and In c is natural
c. Goods are
log of
<
with the gross rate of return B
1/p.
=
of the agent who
is investing
(even type if t
Let c\ be consumption
=
of the agent who is
even, odd type if t odd) and let chtbe consumption
=
=
even
t
t
if
if
even,
(odd type
odd). The resource con
harvesting
type
can be written
as:
straint of the economy
=
c\ + ct + kt+i + zt+1 Ak? + Bzt,
(3)
zt is storage between date t -1 and date t.
can
see the first best allocation
immediately
starting from the ini
tial capital stock, which
is not very different
from the steady state level,
should satisfy the conditions:
where
We
zt+i
kt+1
=
=
0,
(4)
a(3Afc?,
=
c\ + cht (1
(5)
a(3)Afc?
(6)
(4) implies there should be no storage in the first best alloca
Equation
the rate of returns is less than the time preference
rate.
tion, because
the
rate
constant
is
to
and
(5)
gross saving
Equation
implies
ocp in
equal
74
the efficient
which
allocation,
to the model
is similar
of Brock
Kiyotaki
and Mir
man
(1972).
In the market
in contrast to the first best, each agent faces
economy,
the borrowing
constraint. Following
the author, we assume that the bor
rower can borrow as
as
the debt repayment
of the next period dt+1
long
does not exceed the constant fraction X of returns from the present
in
vestment
kt+1:
(7)
dt+1<XRt+1kt+1,
from
Rt+1 is the gross rate of returns on the capital investment
t to t + 1. The flow-of-fund
constraint of the agent who is investing
at date t implies
where
date
=
c\ + kt+1
wt + lt + Bzt + -^-.
(8)
on consumption
and investment
in
Here, his expenditure
side (LHS) is financed by the wage
income wt, the returns
and storage, in addition to the borrowing
dt+1/rt (where rt is
interest rate) in the right-hand
side (RHS). We conjecture
agent does not store, which
For
the
agent
who
is
returns on the investment
His
debt
in the RHS
is used
the
harvesting,
h?L + Z(+i =
Rtkt
dr
c? +
can be verified
the left-hand
from loan lt,
the gross real
the investing
later.
flow-of-fund
constraint
implies
(9)
of the previous
to finance
the
period after repaying
loan
and
storage
lt+1/rt
consumption,
in the LHS.
The
competitive-market
equilibrium
to the marginal
products:
equal
Rt=f'(kt)
wt
=
=
aAkr\
(1
a)Afc?,
prices
are
(11)
kt is aggregate
capital stock, which
is:
The credit-market
clearing condition
is equal
to kt in equilibrium.
(12)
(3), one of the
clearing is given by equation
not
is
law. The com
by Walras'
independent
is defined as a set of prices (Rt, wt, rt) and quantities
the goods-market
conditions
market-clearing
Although
petitive
the factor
(10)
where
=
lt+1 dt+v
implies
equilibrium
75
Comment
a function
(c\, c\, kt+1, zt+1, dt+1, lt+1) as
which
satisfies the utility maximization
clearing conditions.
of the state variables
of each agent
(kt, zt, dt, lt),
the market
and
can show
constraint
is not tight, that is, X is
that, if the borrowing
is not binding
then the borrowing
constraint
larger than the threshold,
is the first best.
and the allocation
We
constraint
is tight (X is small),
We can also show that if the borrowing
is credit constrained.
The credit-constrained
then the economy
equilib
in his paper.
rium exhibits many
features that the author emphasizes
is an increasing
(a) Investment
function
of the net worth
of the invest
ing agents:
wt +
*??=
lt+ Bzt
c\
l-(XRt+1/rt)
the numerator
' (13)
net
saving of the investing agents?the
The denominator
is the down payment
worth minus
the consumption.
one
for
the
investment
of
unit?the
between
the cost of in
gap
required
where
is the gross
of one unit and the maximum
vestment
amount of borrowing
available.
use
to
the
finance
the
gross saving
gap between
agents
investing
cost of investment
and the amount of external finance.
The
function
(b) Net worth of the investing agents is an increasing
vestment
and storage of the previous period in the equilibrium:
=
wt + lt+ Bzt
(1 a + Xa)Ak? + Bzr
(c) Inefficient storage is used
lower than the time-preference
zt
=
> 0, and
rt
rate to the savers
is
rate:
B<?.
(d) Consumption
time:
investing
c\
and the real interest
of in
of individual
agents
is larger at harvesting
time than
1
c\+1 PB
c\
P 1~
Here, because
the aggregate
worth
(XRt+1/rt)
the investing
saving is an
of the investing
agents
agents
save more
function
than harvesting
agents,
of the ratio of the net
increasing
and that of the harvesting
agents.
This as
76 Kiyotaki
sociation
of income distribution
overlapping-generations
overlapping-generations
sume
everything).
Here, as the author
and aggregate
to the
saving is common
even
as
as
it
not
extreme
is
the
though
con
which
the
(in
agents
harvesting
model,
model
the present distribution
af
of wealth
emphasizes,
as seen in (a), and the present
fects the present
investment
investment,
as seen (b). This contemporaneous
affects the future wealth distribution
and
interaction between
the wealth
distribution
and the
intertemporal
investment
is the unique
feature of the credit-constrained
economy.
we
with
the other market
and
(a)
(b)
Combining
clearing conditions,
have:
_= (1
-
a + Xa)Ak? + Bzt
1 - (XaAk^/B)
kt+1
zt+1
=
Ak?
+ Bzt
c\
investment
(14)
kt+1 -c\-
c\.
This dynamic
interaction between
ment may generate rich dynamics
movement
'
(15)
the wealth
distribution
and
invest
of aggregate
economic
activities. The
is persistent
the present
because
of the aggregate
quantities
on the net worth
depends
of the investing
The aggregate
agents, which
is a
function of the previous
investments.
quantities may be
more volatile, because
the net worth
of the investing
agents affect the
the
investment
and
of
the unproduc
compositions
productive
capital
tive storage, which
changes
the total factor productivity
(TFP) endoge
nously.
this alternative model
Although
this model, with
model,
infinitely
erate exotic nonlinear
shares many
lived agents,
features
ismore
of the author's
difficult
to gen
than the author's
genera
overlapping
dynamics
this is the
indivisible
project. But I do not consider
the income distribution
because
of the alternative model,
shortcoming
rate of output during
than the growth
tends to move more
sluggishly
the business
cycle.
tions model
3
with
Conclusion
an alternative
to present
it may be a violation
of etiquette
Perhaps
is impor
constraint
I agree with
the author that the borrowing
model.
ac
tant for understanding
economic
the various
features of aggregate
tivities.
I also consider
the liquidity
constraint)
that the borrowing
constraint
(ormore broadly,
the various
features of
helps in understanding
77
Comment
the monetary
economy
as the medium
is used
that the author did not address. Namely,
as the means
of exchange,
of short-term
and as the unit of contracts.
money
saving,
on the
subject of
in
other researchers
the researchers
Therefore,
communicate
well with
liquidity constraints must
order to have an impact on the way people understand
the economy.
include simplicity
of theory and how
Criteria for good communication
the
well
the simple theory empirically
observations.
explains
Finally,
concerning
simplicity of theory, it is important to explain the wide phe
nomena
as clearly as possible
with
the minimum
of auxiliary
number
as
sumptions.
Endnotes
1. In remark 3, the author argues that the credit rationing
if the initial wealth
is not needed
and the difference
of the investing
is converging
to zero in the limit.
agents are different
I still think it artificial
that agents who have a penny more
in
than the average
However,
less do not invest. If agents have some flexibility
in
vest, while
agents who have a penny
choosing
ligible
the size of project,
become
as the agents
2. This model
3. Thus
follow
is based
or if there
is a lottery,
essentially
on Woodford
then
the borrowing
would
become
neg
homogeneous.
(1990) and Kiyotaki
of date
kt is capital stock at the beginning
the author's notations
of capital investment
and Moore
(2001,2005).
is invested
at date
t,which
as closely as
possible.
t-\.
I
Here,
References
Rao. 1989. Equilibrium
in an overlapping
existence
Aiyagari,
truistic preferences.
Journal of Economic Theory 47:130-52.
-.
1992.
representative
Brock, William,
The discounted
Co-existence
agent
and Leonid
case. Journal
Nobuhiro,
Kiyotaki,
Review 92 (2): 62-66.
-.
2005.
of
a representative
Journal
type equilibrium.
Mirman.
of Economic
and John Moore.
Financial
deepening.
agent
of Economic
type
equilibrium
Theory 57:230-36.
1972. Optimal
economic
Theory 4:479-513.
2001. Evil
Journal
models
generations
growth
is the root of all money.
of the European
with
a non
American
Economic
3 (2-3):
701-13.
Woodford,
Journal
-.
Michael.
of Economic
1990. Public
1986. Stationary
Theory 40:128-37.
debt
as
private
sunspot
equilibria
liquidity.
American
in a finance
Economic
constrained
Review
al
and uncertainty:
Association
Economic
with
80:382-88.
economy.