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Technology
Department of Economics
Working Paper Series
Massachusetts
Institute of
SMOOTHING SUDDEN STOPS
Ricardo
J.
Caballero
Arvind Krishnamurthy
Working Paper
July
5,
01 -26
2001
Room
E52-251
50 Memorial Drive
Cambridge,
MA 02142
paper can be downloaded without charge from the
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T^ssfflilr
Technology
Department of Economics
Working Paper Series
Massachusetts
Institute of
SMOOTHING SUDDEN STOPS
Ricardo
J.
Caballero
Arvind Krishnamurthy
Working Paper
July
5,
01 -26
2001
Room
E52-251
50 Memorial Drive
Cambridge,
MA 02142
paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
This
http://papers.ssrn.com/paper.tafSabstract id=xxxxxx
Smoothing Sudden Stops
Ricardo
J.
Arvind Krishnamurthy*
Caballero
July
5,
2001
Abstract
Emerging economies are exposed to severe and sudden shortages of international
financial resources.
Yet domestic agents seem not to undertake enough precautions
against these sudden stops.
Following our previous work,
the central role played by limited domestic development
in
we
highlight in this paper
ex-ante (insurance) and ex-
post (spot) financial markets in generating this collective undervaluation of external
resources and insurance.
Within
this structure, this
policies to counteract the external underinsurance.
paper studies several canonical
We
do
this
by
first
solving for
the optimal mechanism given the constraints imposed by limited domestic financial
development, and then considering the main - in terms of the model and practical
relevance - implementations of this mechanism.
JEL Codes:
Keywords:
E0, E4, E5, F0, F3, F4,
External shocks, domestic and international collateral, underinsurance,
credit lines, liquidity requirements, asset
'Respectively:
MIT and NBER;
Duke Research Workshop
their
comments, and
Gl
to
market intervention.
Northwestern University.
We
are grateful to the participants at the First
especially to V.V. Chari for
in International Economics, Venice, June 2001, and
Adriano Rampini
for helpful conversations.
Caballero thanks the
Written
support. E-mails: caball@mit.edu, a-krishnamurthy@nwu.edu.
NSF
for the First draft:
for financial
May
2001.
Introduction
1
To a
first
order, an emerging
economy external
can be described as an event
crisis
which a country's international financing needs significantly exceed
its
in
international financial
resources. Given that these events are a "fact-of-life" in these economies, it is puzzling that
domestic agents do not undertake measures to precaution against them. Indeed, quite the
contrary, they often increase the likelihood of these events
booms, contracting dollar
inflow
A common
anticipated
is
and so
explanation for this behavior
official
is
over- borrowing during capital
on.
that
due to distortions created by
it is
interventions, such as crony capitalism, fixed exchange rates,
and IFI's
1
bailouts.
We
liabilities,
by
have argued elsewhere that the external underinsurance problem in these economies
more structural
interventions.
nature than one concludes from just pointing at potentially misguided
in
Underdeveloped financial markets, a basic feature of emerging economies,
leads to a distorted valuation of international resources that in turn leads to external un-
derinsurance. In this paper,
we take
this structure as given,
and explore a
solutions to the underinsurance problem. Since the strategies
ing form
by governments
on which strategies
gies that
in
we
discuss are
emerging markets, our main interest
may work
is
better under different constraints.
work within our model and discuss some of the
series of canonical
difficulties
all
used in vary-
in providing
We
guidance
identify the strate-
they
may
encounter in
implementation.
In our framework,
when a country's international
collateral (or liquidity), the
collateral (or liquidity).
phenomenon.
of this
A
financing needs exceed
domestic price of the latter
rises vis-a-vis
depreciation of the exchange rate, for example,
international
that of domestic
is
a manifestation
2
However, when domestic financial markets are underdeveloped
when
its
the domestic collateral value of projects
is less
—
in
our terminology,
than their expected revenues - agents'
external insurance decisions are distorted.
The reason
external resources cannot transfer the
surplus generated by these resources to other
full
is
that domestic agents in need of
participants in domestic financial markets that do have access to the scarce external funds.
Thus,
in equilibrium,
the scarcity value of external resources
sions are biased against hoarding international liquidity
events.
The underinsurance with
'See. for example,
Krugman
is
depressed, and private deci-
and thereby insuring against these
respect to external shocks takes
(1998), Burnside,
See Caballero and Krishnamurthy (2001c).
Eichenbaum and Rebelo
many
(2000). or
forms:
excessive
Dooley (1999).
external borrowing during booms, a maturity structure of private debt that
toward the short term, dollarization of international
lines,
and
so on.
distorted
is
limited international credit
liabilities,
3
In this paper
we study
in
a unified framework several of the main solutions to this
underinsurance problem. Section 2 presents the environment that we have used in earlier
work, and reproduces the result of collective external underinsurance in the competitive
equilibrium with only spot loan markets.
suppress
all
aggregate shocks.
The
One
reasons
to deal with the underinsurance problem.
is
model
difference in the current
that our focus
To keep matters
is
that
is
we
on domestic arrangements
simple,
we do not
discuss at
all
4
international credit lines and other valuable insurance mechanisms that involve foreigners.
Alternatively, one can think of our discussion as net of these external insurances.
aggregate external constraint will be fully anticipated and
ance, in
its
many
capital inflow
still
A binding
occur. External underinsur-
forms, will simply collapse into excessive international borrowing during
booms.
While aggregate shocks have no
role in the analysis, idiosyncratic ones are central since
they generate the need for domestic financial transactions. Frictions in these transactions
are at the root of the external underinsurance problem.
In section 3,
we show
that
if
domestic agents are able to write complete insurance contracts with each other, the external underinsurance problem disappears.
firms' collateral ex-post,
and hence
More domestic
insurance increases the distressed
their capacity to bid for the external resources held
by
other domestics. In equilibrium, this raises the relative price of international to domestic
collateral, increasing the incentive to
An important
hoard international resources.
aspect of financial underdevelopment, however,
private insurance markets. In section
4,
we assume that
is
the absence of these
idiosyncratic shocks are unobserved
so they cannot be written into insurance arrangements.
We
solve the
mechanism design
problem associated with the private information constraint within our structure, and show
that the social planner can in principle get around this informational constraint and achieve
the competitive equilibrium with complete idiosyncratic insurance markets.
to implementation of the social planner's mechanism.
We
whereby private agents form a conglomerate and extend
this
arrangement
and hence
3
is
is
individually incentive compatible,
it is
We
then turn
begin by analyzing a solution
credit lines to each other.
While
not coalition incentive compatible
not robust to the presence of spot markets, as in Jacklin (1987). Finally
we
See Caballero and Krishnamurthy (2000a) and (2001a).
''See
Caballero and Krishnamurthy (2000a) and (2001b) for discussions of insurance arrangements with
foreigners.
explore two sets of solutions that require government intervention: Capital flows taxation
or
mandated
international liquidity requirements,
and
sterilization of capital inflows.
These
solutions can also work, but they are subject to other forms of the coalition incentive
compatibility problem as well.
A
2
We
model of external underinsurance
begin by laying out the model and describing the external underinsurance in the com-
petitive equilibrium with only spot loan markets. In the next sections
this result
is
by better domestic insurance arrangements, or
affected
we
shall discuss
how
in their absence,
by
centralized arrangements to directly deal with the external underinsurance problem.
The environment
2.1
Consider a three date,
t
classes of agents in the
— 0,
1,2,
economy with a
single
consumption good. There are two
economy: a unit measure each of domestics and
foreigners.
Both
take as objective to maximize date 2 expected consumption of the good,
U=E[c2
Each domestic
is
c2
],
>0.
an entrepreneur /manager who owns and operates a production
nology within a firm. Investing c(k) units of the good at date
where c(k)
is
As part
strictly increasing, positive,
of the
strictly
results in capital of k units,
=
convex with c(0)
0,
—
d(0)
0.
normal ongoing restructuring of an economy, one-half of the firms (ran-
domly chosen) need
j
and
tech-
to re-inject resources into the firm at date 1 to achieve full output. Let
e {i,d} be the type of the firm
at date
1.
Firms that are not
hit
by
this idiosyncratic
shock are i-types ("intact") and go on to produce date 2 output of Ak. Firms that receive
Their output
the shock are d-types ("distressed").
units of good, the d-firm can obtain
A = A
-
a,
and assume that
7A
A >
that
it
maximum
to ak, but by reinvesting I
additional units of goods at date
With
1.
full
obtains the same output as an intact firm, Ak. In
henceforth drop this
falls
reinvestment, I
all
=
k,
2.
We
< k
normalize
a distressed firm
cases of interest below, I
<
k,
thus
we
reinvestment constraint from our discussion (while ensuring
does not bind in our technical assumptions).
The domestic economy has no goods
at either
are
met by importing goods from abroad, which
We
assume that
or date
1.
All investment needs
are paid for with funds raised from loans.
endowments
foreigners have large
date
of goods at all dates,
and have access to
storage with rate of return one.
Firms face
significant financial constraints. Neither the plants nor their expected
are valued as collateral by foreigners.
with
w
units of a good that arrives at date 2
lender courts.
Instead,
i.e.
we assume that each domestic
and can be pledged
domestics can take out loans against
Tangibly,
bank accounts.
we might think
of
w
w
is
output
endowed
as collateral to a foreign
that will be enforced by international
as revenues from
oil
exports that reside in foreign
Assumption
1
(International collateral)
Domestics may take on loans
ofw, and must
international collateral
collateral.
imperfect in the sense that not
+
the
dij < w.
all
However we
assume
up
to
assume that these contracts are also
Ak
is
collateral.
collateral)
that domestic courts are additionally able to enforce domestic (local) debt con-
an amount of Xak where A
do,i
Assumptions
latter as
shall
of the output of
Assumption 2 (Domestic debt and
tracts
from foreign lenders against
domestic can also take on a loan from another domestic. Unlike foreigners, domestics
do accept the plants as
We
1
satisfy a full collateralization constraint:
doj
A
or date
at either date
1
and 2
are
+
dij
how we
<
1
Thus, the domestic lending constraint
.
< Xak + w -
(do,/
+ di,f)
define an emerging economy. Thus,
an economy where pledgable assets are
is:
limited,
we think
of the
and a large share of these assets
are part of domestic but not international collateral.
We define an external crisis as a date 1
event in which the financing needs of the economy,
\k, exceeds the international financial resources available to
not central to our concerns and results in this paper,
it,
(w - d
we suppress
all
j). Since they are
aggregate shocks.
external crisis happens despite being fully anticipated. This simplifies our discussion
means that
below).
external underinsurance will only take the form of overborrowing at date
With some abuse
underinsurance.
at date
1
The
of terminology,
we
The
and
(see
will continue referring to the latter as external
following assumptions on parameters guarantee that a crisis occurs
in all the equilibria
we study throughout
the paper, and that there
is
external
underinsurance in the spot loan market equilibrium:
Technical Assumptions 1
(1)
(2)
(3)
2.2
C-i^Aa
> „,_ c (c'-i (-$*•))
^-l ^+a+Aa(A-l) Aa <
w _ c (c /-l( ^+MA-l) j^ A
)
(
Xa < 1
,
Spot loan markets
Let us begin by studying the equilibrium
in this
borrowing via a sequence of spot loan contracts.
domestic insurance arrangements.
economy when agents are
Thus what we
restricted to
rule out for
now
are
All of the investment needs of domestics (date
goods from foreigners. The goods are paid
each firm takes on foreign debt at date
a plant of
there
is
A
its
size k.
by
for
1)
have to be met by importing
Suppose that
issuing date 2 debt claims.
of doj and invests
of these resources in building
all
Since firms are ex-ante identical, without loss of generality we can assume
no domestic debt
firm at date
maximum
and date
1
at time
0.
finds itself either distressed or intact.
If distressed, it
borrows up to
international debt capacity in order to take advantage of the high return of
rebuilding/restructuring the firm:
dij
These resources are then invested
After this,
date
1 either,
it
must turn to
— w-
do j.
until date 2, yielding
intact domestic firms for funds. Intact firms have
so they must borrow from foreigners
This they can do up to their
djjA.
w—
Unlike foreigners, domestics are
slack.
willing to lend to other domestic against their projects. Since firms
to borrow
up to Xak, we
refer to this quantity as
Denote the gross interest rate
out the
maximum
loan as long as
in this
A>
result of domestic
domestic
can use
this collateral
L 1 Then
the firm takes
collateral.
domestic loan market as
.
L\.
d\j
As a
at
they are to finance the distressed firms.
if
d j of financial
no output
=
Xak.
borrowing the firm raises -j^ for investment, to yield
-^ A
at date
2.
Combining the above transactions, and taking into account that date
investment
yielded ak at date 2, the profits accumulating to this firm at date 2 are,
Vd =
(w - d„,/)A
+
^A +
(1
-
X)ak.
Intact firms, on the other hand, have the opportunity to lend to distressed firms at date
1.
As long as Li >
1,
the intact firm will borrow up to
d\j
and invest these resources
in the
=w—
its
maximum
foreign debt capacity,
doj,
domestic loan market to yield Zq
value of date 2 claims that the intact firm purchases.
Then
.
Denote X\ as the face
the intact firm
profits of,
V =
i
xjLj
+Ak + {w- d 0J -
d hf )
=
(w - dQf )L l
+
Ak.
makes date
2
Finally, at date 0, firms are equally likely to
V5 ^ = max
- doj)(Li + A) +
hw
\^
2
1
k,d
j
(
A + (1 -
intact.
A)o
+
V
Thus they
solve,
^AJ/ k
i-i\
doj < w
s.t.
c{k)
The only market
be distressed or
=
do,f.
clearing condition
is
that the loans issued by distressed firms must
equal the loans purchased by intact ones:
~! dl,l
w
2
where the one half
in front of
1
= ^l,
(1)
each microeconomic decision reminds us that distressed and
intact firms form equally sized groups.
Definition. Equilibrium in the economy with only sequential spot loan markets consists
of decisions, (k,d j,dij,dii,x\)
and the domestic
interest rate, L\. Decisions are optimal
given Li, and given these decisions, the market clearing condition (1) holds.
Figure
1
:
Date
1
Market Clearing
for
Domestic Loans
L
i
.
A
>v
•v.
//
/
1
X
/ ^^.
^
L
Increasing
-v
«*
-x
"•»
w-d
f
Domestic loans
.
Figure
1 illustrates
the market clearing.
On
the horizontal axis
the quantity of im-
is
ported goods lent by intact firms /borrowed by distressed firms. The vertical axis
of loans
L\. The supply
is
elastic at
L\
=
their international collateral constraint of
inelastic.
It is
for
Demand
for loans
line is
the middle solid line
1;
the lower dashed line
is
d\j
is
=w
—do,/, at which point
^£f
1.
,
which
the case where L\
is
downward
is
is
sufficient
lies strictly
small and as a result
sloping in L\.
alternatives
domestic collateral
between one and A;
demand
so collateral
is
constrained that intact firms have excess supply of funds and the interest rate
The parameter assumptions in Technical Assumption
L\
into the
A and one -
between
strictly
i.e.
market clearing condition
the solid
lies
is
ensure that equilibrium will have
1
line. In this case,
substituting date
,
—
1.
w-doj
Given
2. If
between these and foreign
=1
c'(k)^j— =
left
and
if
program can be written
this price, the first order condition for the date
where the
1
this is
w were large so that on the margin some
both w and Xak in their portfolio, then again
Alternatively,
domestic investor was holding claims against
hand
as:
&-
*
f
(3)
side represents the expected opportunity cost of the marginal units of
international collateral spent on setting
up a plant
at date 0, while the right
hand
side
the expected marginal revenue associated to the marginal plant.
Proposition
1
Consider two economies indexed by X and
•
A-Li(A)< A-Li(A');
•
Welfare
•
Date
is
s
2)
above the international interest rate of one. The reason for
would imply that L\
must be that L\
decisions
1~-
foreigners were willing to hold claims against Xak, then arbitrage
it
1
Xak
the asymmetry between domestic and foreign agents embedded in assumptions
assets
one.
gives,
Li =
Note that L\
completely
it is
The figure represents three
the case where there
the case where A
the price
to the point that the intact firms saturate
A > L\ >
easy to see from the figure that
A=
up
given by the curve,
is
demand: The highest dashed
that
1
is
increasing in X, so that
V sp°'(A) > V
s
A',
where X
>
A'.
p°*(A');
investment and borrowing are decreasing in X so that k sp? l (X)
Proof: Follows after a few steps of algebra, from
Then,
V spot
,
(2),
and
(3).
<
k spol (X').
is
The proposition
highlights the role of A
the market clearing condition
rises
in
1.
A
firm that decides to borrow
At date
which
1,
As A
prices.
increasing in A.
Thus
Fixing
as
A
of A. This has an important effect
less, is essentially
case, despite the fact that the resources yield
constrained.
0.
1
is
and
k,
from
rises,
L\
on date
"saving" these resources until
these resources are either used internally to yield A, or lent externally,
only internalizes L\ of this return.
date
welfare, decisions,
see that L\
toward the marginal product at date
decisions.
date
we can
on
rises,
to the borrower, the lender
Again, this occurs because the borrower
the spread between
A
and L\
This leads to greater investment at date
rises prices are less distorted
A
1
falls
is
collateral
causing firms to save more at
and welfare increases.
Essentially, as
A
by the credit constraint and the intertemporal savings decision
better reflects marginal products.
Public information of types and date
3
domestic insurance
markets
Our aim in this section is
to
insurance contract at date
l.
5
At
may seem odd
glance this
intuition
is,
may
because at date
way
1
under our spot market equilibrium,
into the
hands of the distressed
and
firms.
suggest that the ex-post allocation cannot be enhanced by further
reallocating domestic collateral to distressed firms since the scarcity
collateral,
of a domestic
that shu- es resources from intact to distressed firms at date
the international resources find their
all of
That
first
show that welfare can be improved through the use
this has already
been
fully transferred.
is
on international
However, in our setup, the welfare
gain from domestic insurance comes entirely from affecting the ex- post price of international
resources, Li, and bringing this closer to
decision of k
to set L\
=
is less
A,
Assumption
The shock
on
A
so that ex-ante the borrowing/investment
distorted. Moreover, reallocating ex-post wealth
affects
V — Vd
1
,
beyond what
is
needed
but not decisions, equilibrium, or ex-ante welfare.
3 (Public information)
at date
public information and insurance contracts can be written contingent
1 is
j.
Consider the following domestic insurance contract: All firms sign a grand insurance
contract at date
xo,i{d)
type-j.
=
>
xo,z
0.
with repayments in date 2 goods of
xqjl{j),
where xoj(i)
Since the types are observable, this contract can be
Repayments are enforceable
made
=
—xq,i
and
contingent on
as long as,
xq,i
<w — doj + Xak
Since there are an equal measure of each type, the insurance payments to distressed firms
are exactly funded by the receipts from the intact firms.
At date
1,
collateral of
its
an intact firm sees the domestic interest rate of L\
w - doj,
and an insurance
liability of xn,/-
>
1
and has international
Suppose that the firm lends
international collateral at L\, then its total resources are date 2 goods
(w - doj)L\
Against this
it
has the
liability of xo,(
1
^Recall that our focus
is
j)Li
of,
of,
+ Ak -xoj.
not on the possibility of more or
less
insurance from foreigners, rather
domestic arrangements given the limited access to international financial markets.
10
of
+ Ak
giving date 2 profits
V = {w-d
all
it
is
on
.
distressed firm borrows against its international collateral of
The
the proceeds in production to yield a date 2 return of A.
w-
and invests
do J
As long L\ < A,
it
borrows
d\j,
in the domestic debt market, satisfying the constraint that,
d\,i
Thus
it
makes date 2
we studied
(4)
a
in the
only loosens
d\j.,
little
[w -
more
do,/)
A+ A-
We know
closely.
previous section and that d\
without
is,
if
loss of generality
the inequality in (4) was
Li)-^ + Xak + x
(
dj
That
(4)
t
profits of,
Vd =
Consider
< Xak +xo i.
;
t
i
that
=
if xo,i
we can
then x
— 0, we
are back in the situation
Xak. Since increasing
i
can be reduced
until equality, while only
V
1
and
,
but
just,
l(w-d 0J )(A + L + ^(A+
V*"= max
1 )
S.t.
doj
<W
c(k)
=
x o,
Lemma
Vd
welfare (recall that agents are risk neutral). Given this, the date
not decisions or date
is
this point
.
loosening the insurance enforceability constraint and affecting the level of
problem
from
xo,;
set,
= Xak + xqi
strict,
,/
L\
i
a )k
+ l(A-L
Xak
X0
^
1)
1
'
do,/
<w — do,/ + Xak
2 In the insurance market equilibrium:
^=A
Proof:
We
can see this
firms will increase
xo,i
<w—
do,/
two
Suppose that
intact firms at date 1 have
(
fall for
Substituting
Lx —
xo,z
from the program, as long as
xo,j is
=
A >
L\,
the enforceability constraint that
= w — do,/ + Xak — 6,
with 6
>
0.
no international resources, and market clearing
loan market would require that L\
which x0) can
First,
steps.
Second, the only limit on
xo,/.
+ Xak.
in
A. As a comment, there
is
As
in
6
—*
0,
the
the domestic
a large interval within
this to hold.
A
into the
program
gives the
c'(fc)A
Contrasting this expression with the
first
=
first
^p.
order condition for investment,
(5)
order condition in the spot market equilibrium,
(3), implies:
11
Proposition 3 Let k ins
1.
and k 3? 01
be
the solution to (3).
Then:
//A-Zf'X),
k
S
2.
be the solution to (5)
If/S.—L i°
=
0,
spot
>
k
yins
md
ins
the two first order conditions coincide
>
yspot
and decisions as well
as welfare
are the same.
By
signing date
at date 1 until
it
insurance contracts firms bid
reaches A.
As a
result, firms
up
the price of international collateral
borrow
less at
date
leading to a better allocation of external resources across date
the insurance solution leaves no role for
A.
Indeed
by loosening the domestic
and date
1.
Note that
market
insurance market circumvents these
collateral constraint.
12
invest less, thus
this is the point. Since the loan
at date 1 is affected by collateral frictions, the date
frictions
and
4
We
Private information of types and planning solutions
A equal to one, as
shall henceforth set
importantly, from
now onwards we
plays a limited role in what follows.
it
acknowledge the many
shall
difficulties
More
encountered by
domestic insurance contracts in emerging economies and assume:
Assumption 4 (Private information)
The shock
at date
1 is
private information of the firm.
This assumption means that the insurance contracts of the previous section are not
possible since, at face value,
all
However the spot loan market
still
4.1
implement the
full
firms will prefer to claim to be distressed
is still
We now investigate
feasible.
and avoid payment.
whether
it is
possible to
insurance solution.
Mechanism design problem
We take a standard mechanism design approach. The types at date
and must be
1
are private information
by the mechanism. As usual, we appeal to the revelation principle to
elicited
focus on direct revelation mechanisms.
At date
Consider the following mechanism.
collateral to the planner.
The mechanism
0,
0,
of international
defined by,
is
m = {k,yi,yd ,Xi,xd
At date
w
agents hand over
).
the planner hands resources to create capital of k to each firm. At date
1,
agents
send a message of their type, j G {i,d}. They then receive an allocation of international
collateral (or
imported goods) of yj and a claim on date 2 domestically produced goods of
x3Thus the planner
solves the following problem:
V m = max
m
s.t.
-(Ak + yi +
2
c{k)<w
(RC1)
- {yi +
yd )
2
{ICC)
yi
,y d
(RCX)
xi
+
(DCC)
Xi,
(ICd)
+ -(ak + y d A+xd
2
{RCO)
(ICi)
Xi)
+ c(k)<w
>0
xd
<0
xd > —ak
Ak+y +Xi> Ak + y d +x d
ak + yd A +x d > ak + y A + x;
2
t
13
)
The
RCO and RC1
constraints are as follows:
on importing goods
for investment. Since agents
eral to the planner at date 0, the transfer to
can shu- e claims on date 2 goods
—
that this shu- ing does not create
new
maximum
are date
and date
hand over
all
them,
of their international collat-
must be non- negative. The planner
yj,
domestic collateral
i.e.,
—
The
last
On
DCC
requires
states that the
given by their domestic
is
it.
The asymmetry between Assumptions
and RCl.
RCX
1.
two constraints impose incentive compatibility so that
each type prefers the bundle intended for
To import goods
at date
collateral in the aggregate.
the planner can shu- e away from any of the agents
collateral constraint, ak.
resource constraints
1
and 2 are embedded
1
in
can be used - hence
for investment, only international collateral
the other hand, these goods can be shu- ed around
transferring claims against domestic collateral - hence
RCO, RCl and DCC.
DCC. We
among
RCO
domestics by
think this asymmetry
is
a distinguishing feature of an emerging economy. In a developed economy most assets are
both domestic and international
which case we could do away with
collateral, in
DCC
and
rewrite the RC's to include the domestic collateral of ak.
Given
convex,
linearity in y's
we
will
and
x's,
we
will arrive at corner solutions in
have an interior solution in
solution, rewrite the
xd
(xi
+ yi)
+
yd
xd
+ yd
+{A-l)y d >
xi
+ y +(A.-l)y
i
sum everywhere in
we were
compatibility constraint can
be slackened by lowering
yi
=
and
=
2(w -
c(k)),
and xd
an
=
be
at its
0,
yd
x,
and
yt
and increasing
us,
ak,x d
=
gives,
771
first
on
highest value and x d to be at
V = max -(,4 +
k
yi
— 2(w - c(k)),Xi =
and rewriting the optimization problem
.
a) A;
+ A{w -
2
order condition to the planning problem
c'{k)A
is
= A+
2
14
then the incentive
£j.
Thus consider
Applying the same argument to (x d
-ak. Combining, gives
m= (k,yi —
The
interior point
Xi at its highest value.
dictates a solution of y d to
yd
at
i
the program except in this last incentive
compatibility constraint. If
the solution of
as,
+ Vi >
appears as a
is
In order to see which corners determine the
two incentive compatibility constraints
Xi
Note that
k.
them. Since c(k)
a
c{k)).
-ak).
its lowest.
+ yd
)
Thus,
Let k* be the solution. The
last step is to verify that
compatibility constraints. That
the solution
satisfies
the incentive
is,
A(j/d
- Vi) >Xi-x d
>yd -yi
or,
A(w-c(k*))>
ak*
>w-c{k*)
which can be shown to hold under Technical Assumption
1.
Proposition 4 The optimal mechanism under private information of types implements
full- insurance public
the
information solution.
This follows directly from comparing the
first
order conditions in this solution and the
insurance solution of the previous section.
The mechanism works because
it
between distressed and intact firms.
receives
exploits the differential valuation of imported goods
If
a firm claims to be distressed rather than intact
2{w — c(k*)) imported goods, but forgoes 2ak* claims on date 2 goods. The
rate implicit in this choice
where the technical assumption ensures
w - c(k*)
that A > L\ >
borrow at L\ and
intact ones lend at L\.
insurance solution
is
We now
'
A, while the intact firm values
at
Both
it
at one.
Thus
distressed firms effectively
is
enhanced, and the
full-
achieved.
— to act
Domestic credit
first
distressed firm values the
6
turn to the implementation of the planning solution and consider three sets of
private consortium
The
A
l.
types' welfare
alternatives, noting that each requires the planner
4.2
interest
is,
1
imported goods
it
solution
—which in some
instances could be a
(and hence be able to monitor) on a different margin.
lines
we consider
is
a credit-line/banking arrangement akin to Diamond and
Dybvig's (1983) deposit contracts in the context of consumption insurance.
Suppose that
all
firms
hand over
w — c(k*)
to the
bank
at date 0.
with c(k*) for the purpose of building a plant. The bank then
withdraw
6
w - c(k*)
Also note that L\
<
at date
1
L\ since k"
as well as a credit line to
<
k.
15
offers
This leaves each firm
each firm the right to
borrow an additional
w-
c(k*) at
.
the interest rate of L\. Funds not withdrawn at date
date
2.
1
earn the interest rate of L\ until
7
At date
1,
bank and withdraw
distressed firms return to the
w-
In addition,
c(k*).
they choose to take out a further loan against domestic collateral of ak* at the rate of L\.
This gives them imported goods of exactly 2(w
-
c(k*))
which they invest
date 2 at
until
the private return of A.
Since intact firms' alternative use of imported goods returns only one, intact firms choose
not to withdraw their funds at date
return of L*(w
-
c(k*))
=
1
and instead wait
until date 2 providing
to
make any
it
That
side trades.
is
first
pointed
requires the fairly strong restriction that agents not be allowed
is,
all
firms must
be
the bank and be barred from trading in a market.
arrangement
total
ak*
This structure clearly implements the planner's solution. However as was
out by Jacklin (1985)
them a
If
restricted to exclusively trade with
we drop
banking
this restriction, the
no longer coalition incentive compatible and the allocation reverts to the
competitive equilibrium. 8
In our context, Jacklin's critique can be formulated as follows. Suppose that one firm
chooses to opt out of the banking arrangement, and privately makes an investment decision
of k.
At date
1,
the firm
is
either distressed or intact.
suppose that
If distressed,
it
approaches a firm within the banking arrangement and offers to borrow at the interest rate
of L{ against domestic collateral of ak.
Since this return
banking arrangement, the firm withdraws some of
to the rogue firm.
The return
to the rogue firm
Vd = A(w while the firm in the banking arrangement
offers to lend to a firm in
its
as good as the return in the
international collateral
and
offers
it
is,
c(k))
+ 77 A,
unaffected.
is
is
If
the firm
is
intact,
it
instead
the banking arrangement at the interest rate of L*. Once again,
the banking firm accepts, and the rogue firm's profits are,
V*
Combining these
last
=
L\{w -
c{k))
two expressions gives us the date
V T °9^{L\) = max -(u; - c(k))(A +
k
7
L\
We
is left
L\)
program
in
free to adjust in the out-of-equilibria event that
of,
+ - ( A77 + a)
2 \
2.
do not impose a sequential service constraint as
Thus there
+ Ak
Li-y
k.
I
Diamond and Dybvig
(1983). which
more than half of the firms decide
no "bank-run" equilibrium.
8
Thc result that competitive spot markets may undermine insurance arrangements
means that
to
withdraw.
is
See for example. Rothschild and
Stiglitz(1976). Atkeson
16
and Lucas (1992), or
Bisin
arises in
many
settings.
and Rampini (2000).
The
first
order condition for this program
+ Ll)=J2 +
c'(k)(A
Comparing
< A
L\
is,
planning problem, we can see that
this to the first order condition of the
>
the rogue firm makes a choice of k
A.
k* and attains strictly higher utility
participated in the banking arrangement. Given this, the banking arrangement
if it
for
than
would
unravel.
We
can take this to
its
end by explicitly accounting
logical
trades in the planning problem. This
is
for the possibility of side
done by adding a constraint
that,
ym > yrogue^
Now
the objective in the planning problem
Vm =
=
Substituting in L\
w
^
k .\
,
this
is,
can be rewritten
V™=±(w-c(k*))(A +
Note that
this
objectives in
with the
is
V™
the same as the expression
and
maximum
in
in
VTOgue
yr °9 ue
+ ha + A).
{w - c(k*))A
+ ±(Af; + A)k*.
Ll)
for
as,
V r°9ve
if
evaluated at k
=
weakly exceeding that of
1
is
_
=
to choose k*
Vm
k
.
r °9ve
Given
this,
Since both
maximum,
we can conclude
so that,
ak rogve
w- c(k °9ue
r
)'
These are the same optimality and market clearing conditions that arose
2.2.
.
are strictly concave, they each have a unique
that the best that the planner can do
markets of section
k*
in the spot loan
In summary,
Proposition 5
(a)
The
ner can
credit-line
arrangement implements the full-insurance solution as long as the plan-
restrict agents
restriction,
from making side
the credit-line
trades,
arrangement collapses
loan markets.
17
(b)
to
In the absence of
this exclusivity
the competitive equilibrium with spot
.
Capital inflow taxation/Liquidity requirement
4.3
Let us consider next a tax/ transfer scheme based on date
borrowing (or investment of
Since the primitive problem in the spot loan market equilibrium
k).
borrow /over-invest at date
The planner taxes
proceeds (T) in a
all
0,
that agents over-
a tax has the potential of achieving the optimal solution.
external borrowing at the rate of r and redistributes the
date
lumpsum
is
fashion at date
0,
T = rdoj = rc(k*)
The program
a firm
for
h
wI
max
k
This gives the
first
is,
c (k)-Tc(k)+T)(L 1
+A) + ^ (A + A-^-)k.
2 \
L\ J
order condition,
c'(A:)(l
+
+ A) = (a + Aj-]
t){L x
Thus,
1+T=
2A
^4+f"
LL-
A + Li A + a
where,
U = L\.
It is
straightforward to verify that for L\
An
< A,
alternative, but similar in spirit, implementation of the borrowing tax
-
d oj
of
all
an interna-
foreign borrowings be retained as a liquidity requirement for one-period
until a crisis arises).
Then, since firms choose to borrow c^ j,
saving exactly the right amount until date
While unlike the credit
market
is
suppose that the planner insisted that a fraction,
tional liquidity requirement. For example,
JU
the optimal tax will be positive.
for loans,
line
this
(i.e.,
arrangement has them
1
arrangement each of these solutions can co-exist with the
they do require that the planner observe
all
external borrowings. If agents
could evade the tax/return scheme or liquidity requirement, and trade in the loan market
at date 1,
they would prefer
planner's control since L\
Finally,
date
it
is
to.
Moreover, this incentive
rises
as
more
firms
fall
under the
falls.
worth pointing out that
and then remove the tax
at date
this
1.
If
arrangement requires the planner to tax at
the tax
is left
active for
both periods, the
equilibrium would be exactly as in section 2.2, with the exception that the interest rate on
international collateral would rise to
1
+
t.
In general, this will lead to a worse
than the case of no-taxation.
18
outcome
Proposition 6
planner can observe
// the
external borrowings, a borrowing tax or
all
liq-
implements the full-insurance solution.
uidity requirement
Capital inflow sterilization
4.4
Consider a government that issues b face value of two period bonds at date
Thus the
international reserves of £-.
on these bonds
interest rate
is
L
,
in return for
and
in order to
purchase these bonds, firms increase their external borrowings by -jK
At date
using
the government simply buys the bonds plus claims against domestic collateral
international reserves of ^-. Finally, at date
its
taxes of
1,
T in order to balance its budget.
at the interest rate of 1^, the
2,
the government raises
Since the investment of reserves at date
budget constraint
for
the government
lumpsum
1 is
done
is,
^-L 1 + T=b,
where we note that
L =
if
Li, budget balance
is
achieved without having to raise taxes.
There are two assumptions we make on the government.
tax
liabilities are rationally
Thus the
anticipated
collateral of each firm is
First,
and constitute a reduction
we assume that future
in seizable
endowments.
reduced by T, so that, for example, the domestic loan
capacity becomes,
d\,d
<w-\-ak —
Second,
we assume that the government bonds that
That
they are
is
like
T
are sold are only domestic collateral.
ak and hence foreigners do not purchase these bonds.
In this context, suppose a firm purchases b
bonds
at date 0.
Then
its
program can be
written as,
max
„,
1,
—(w
k,b
2
s.t.
c(k)
Market clearing
c(k)
+
-
b
WT
-r-)(Li
1 /\,
AX
m
+ A) + \ ( Ak + b - T +
,
—A
(ak
+ b - T))
—
<w
La
is,
L\
—
ak
+b-T
There are two cases to consider, depending on whether or not the international borrowing
constraint
9
is
slack or not. Consider first the case that, c(k)
+ £- <
w. Since firms are at
See the appendix in Caballero and Krishnamurthy (2000b) for a model justifying this assumption
terms of a risk of suspension of convertibility.
19
in
an
interior in their purchase of bonds,
must be that Lq
it
—
and therefore
L\,
T =
0.
Substituting this back into the market clearing condition:
—) =
L 1 (w — c(k) +
ak
+b
ak
w—
c(k)
In other words, intervention has no effect in this case.
The other case
sells
where the international constraint binds. Suppose that the government
is
enough bonds so that
As always, the
RHS
c(k*)
+
-^
—
L\ at date
optimahty
Since d{k*)
= "4^°, we
< A, we have that
exactly c(k*)
left,
is
the opportunity cost
d(k*)(L{+A)
Ll
at Lq, sold
Given the intervention,
on these bonds
be,
-
arrive to,
Lo
is
either L\ or A.
for the private sector requires that the interest rate
L° =
For L\
The LHS
be invested in the government bonds
and the proceeds reinvested at
1,
order condition for the private sector
first
the return from an extra unit of k.
is
of these resources. d{k) could otherwise
at
w. The
Lq
>
~
A + ^a 2A
A + a A + Lt Lv
L\. Since after purchasing these bonds the private sector has
amount of
firms invest the optimal
k*
,
and the full-information solution
achieved.
Essentially, the implementation has the
bond with an
interest rate exceeding L\.
investment. However,
On
requires
It
10
endowments,
On
borrowing or
does require that the government be able to tax and issue bonds.
first
power
this tax
the other hand,
arrangement we
it
discussed,
is
not any stronger than what we gave the private
does come with a buried assumption. As in the banking
if
agents had the option to not pay taxes, not buy govern-
ment bonds, but be allowed to trade with the
this option.
10
no knowledge of date
the one hand, since we have assumed that taxes come out of otherwise privately
seizable
sector.
it
government "subsidizing" savings by offering a
As
in the
firms
banking arrangement, the
are paying taxes, they would prefer
sterilization policy
See Holmstrom and Tirole (1998) or Woodford (1990)
20
who
for
is
the converse case.
not coalition incentive
compatible. However,
it
seems reasonable
to believe that coalition incentive compatibility
with respect to taxes
is
easier to achieve
than that of ruling out side trades in a private
banking arrangement.
We
label this policy as sterilization because, in practice,
emerging markets that
sterilize
accumulate international reserves on the one hand, and issue government bonds on the
other.
policy.
However our bond policy
is
"real"
and may seem closer
In Caballero and Krishnamurthy (2001b)
"real" side of a sterilization policy sheds light
only the standard, purely monetary, side of
Proposition 7
we have argued
than to monetary
that emphasizing this
on observed outcomes that are puzzling when
it is
considered.
Sterilizing capital inflows at date
and consequently reversing
to fiscal
by issuing two period
government bonds,
the transaction at date 1, achieves the full-insurance solution as
long as the planner has the power to tax endowments
tional collateral by foreign investors.
21
and bonds are not viewed as interna-
Final
5
As
Remarks
our previous papers, we have synthesized emerging markets'
in
terms of
volatility in
two basic ingredients: weak links with international financial markets and underdeveloped
domestic financial markets. The need for external insurance stems from the former
ciency, while the latter is
The contribution
insuffi-
behind the external underinsurance problem.
of this paper
is
twofold: First,
we have
explicitly
modeled the
infor-
mational constraint on domestic insurance markets and have thereby been able to discuss
the feasibility of contractual arrangements to solve the underinsurance problem.
we have explored
in a unified setting several of the
main
Second,
management
international liquidity
strategies available to these countries.
If
domestics can write complete insurance markets with each other, external underin-
surance disappears. However the mechanism behind this result
channel.
The main problem
allocation of
its
of the
its
not a standard insurance
economy during a sudden stop
limited international collateral but
Domestic insurance improves
is
efficiency
is
not in the domestic
on the aggregate amount
by aligning the price of international
of the latter.
collateral
marginal product. In this sense, domestic insurance relates to our discussion
and Krishnamurthy (2001c) of the incentive
of a countercyclical
monetary policy
in
in
with
Caballero
— as opposed to the standard liquidity— virtues
economies subject to sudden stops. In
there
fact,
we
argue further that such policy could in some instances substitute for the absence of domestic
insurance.
If
that
domestic insurance
it
is
not possible -
when types
are unobservable -
we showed
was possible to design mechanisms that could attain the same aggregate outcomes
and welfare of the
however,
practice
is
full
information case.
their failure to
meet a
The common
Achilles' heel of these solutions,
coalition incentive compatibility constraint;
which
means that they may not be robust to the existence of secondary markets
to opt out of the mechanism.
that bond-policy
is
Among
the solutions of these type
we
studied,
or
in
ways
we argued
probably more robust than the others, but this policy can also have
potentially large drawbacks
illiquid
i.e
if
the intervention
secondary markets during
crises (see
is
not large enough and public bonds have
Caballero and Krishnamurthy (2001b)).
22
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RE.
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24
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