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HB31
.M415
pEWSv;,
Technology
Department of Economics
Working Paper Series
Massachusetts
institute of
EXCESSIVE DOLLAR DEBT: FINANCIAL DEVELOPMENT
AND UNDERINSURANCE
Ricardo J. Caballero
Arvind Krishnamurthy
WORKING PAPER
02-15
March 2002
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/abstract=xxxxx
[^
Technology
Department of Economics
Working Paper Series
Massachusetts
Institute of
EXCESSIVE DOLLAR DEBT: FINANCIAL DEVELOPMENT
AND UNDERINSURANCE
Ricardo J. Cabailero
Arvind Krishnamurthy
WORKING PAPER
02-15
March 2002
RoomE52-251
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/ab5tract=xxxxx
Excessive Dollar Debt:
Financial Development and Underinsurance
(Forthcoming: Journal of Finance)
Ricardo
J.
Arvind Krishnamurthy*
Caballero
This draft: March
1,
2002
Abstract
We
propose that the limited financial development of emerging markets
nificant factor
is
a
sig-
behind the large share of dollar-denominated external debt present in
We
these markets.
show that when
financial constraints affect
borrowing and lending
between domestic agents, agents undervalue insuring against an exchange rate depreciation. Since
more
of this insurance
is
present
when
external debt
is
denominated in
domestic currency rather than in dollars, this result implies that domestic agents choose
We
excessive dollar debt.
also
show that hmited
financial
centives for foreign lenders to enter emerging markets.
development reduces the
The
in-
retarded entry reinforces
the underinsurance problem.
JEL
Classification
Kejnvords:
Numbers: F300, F310, F340, G150, G380
Ciurency mismatch, balance sheets, international
contingent
liquidity,
credit lines, thin markets, limited participation.
*
Respectively:
MIT
and NBER; Northwestern University.
We
thank Philip Bond, Guillermo Calvo,
Bengt Holmstrom, Hugo Hopenhayn, Nisan Langberg, Adriano Rampini, Jean Tirole and an anonymous
referee for
comments.
and the University of
Moore
We
also
Rome
thank seminar participants at
Lsicea's
Summer Camp
in
Buenos
conference on Information and Business cycles for comments.
for editorial assistance.
Caballero thanks the
a-krishnamurthy@northwestern.edu. First draft: June
NSF
1,
for financial support.
2000.
We
Aires,
MIT
thank Sandra
E-mails: caball@mit.edu,
Although observers
still
one factor they agree on
is
debate the causes underlying recent emerging markets'
crises,
that domestic firms' contracting of external debt in dollars as
opposed to domestic-currency creates balance sheet mismatches that lead to bankruptcies
and dislocations.^
The evidence
is
that most contracts between foreign lenders and borrowers in emerging
markets take the form of dollar debt (see Hausmann, Panizza, and Stein (2001)). However,
although foreign lenders must eventually be repaid in dollars, in principle there
is
no reason
that these payments cannot be contingent on the exchange rate. For example, contingencies
can be added explicitly by indexing debt contracts, or implicitly, by foreign lenders receiving
domestic currency payments that they then convert into dollars. As a result, we are
asking
why the choice of dollar debt
On the one hand,
domestic ones.
Is
is
in the best interests of borrowers in
the attraction to dollar debt
On
is
left
emerging markets.
that dollar interest rates are lower than the
the other hand, dollar debt exposes firms to a balance-sheet mismatch.
the low price of dollar debt worth the balance sheet risk for a firm in an emerging market?
Do
prices allocate the risk efficiently?
Should a policy maker be concerned that companies
underprice the risk of dollar debt and therefore take on too
much
of it?
We
address these
questions in this paper.
Analysis of this issue has for the most part centered on the (harmful) incentives of
the government.^ In the context of sovereign debt, Calvo and Guidotti (1990) argue that
once foreign lenders purchase domestic- currency-denominated debt, governments have an
incentive to devalue and reduce the real value of their debt (see also Calvo (1996),
Allen and Gale (2000)).
Foreign lenders rationally anticipate this and avoid purchasing
domestic currency debt. First, these explanations seem most compelling
for
high inflation
countries (Latin America), rather than the Asian countries where chronic inflation
a problem.
Moreover, as Calvo (2000) points out,
private sector debt
difficulties.
if
we
and
it
is
was not
hard to extend this argument to
are interested in the connection between debt choices and financial
The problem
is
that
if
balance sheet mismatches are indeed costly, firms will
prefer to introduce contingencies into their liabilities to avoid them.
In our model,
all
risk of liquidation (or
agents are risk neutral but
demand
insurance because they face a
production interruptions) in bad states of the world and they might
need resources at times when the country faces international borrowing constraints. This
Much
of the analysis of the currency-balance sheet channel assumes that companies choose dollar de-
nominated debt. See,
(2001a);
for
example, Aghion, Bacchetta, and Banerjee (2001); Caballero and Krishnamurthy
Chang and Velasco
(1999);
and Krugman (1999).
Constraints on domestic currency external borrowing
cently, the
borrowing.
may
also
have a domestic policy
origin. Until re-
Chilean tax code penaUzed external borrowing in domestic currency vis-a-vis dollar-denominated
demand
from the observation,
arises
first
made by
Proot, Scharfstein,
and Stein (1993), that
the anticipation of borrowing constraints in a dynamic setting motivates firms to hedge.
Since the exchange rate also depreciates in bad states of the world, borrowing in domestic
currency as opposed to dollars provides more of this insurance.
We show that when
financial constraints affect borrowing
agents, agents' valuation of this insurance
is
because some agents
who purchase
to those
who
provide
it
It limits
than
its social
value.
the insurance will not need
will sell his excess resources to those
friction in this transaction.
less
is
and lending between domestic
who do need
The
it.
the amount that agents
and places a wedge between the
it.
The undervaluation
In this case, the agent
financial constraint places
a
who need insurance can pay
social valuation of insurance
and
the equilibrium return to providing this insurance. In a dynamic setting, agents undervalue
insurance and take on too
Our
result differs
much
dollar debt.
from the sovereign debt literature cited above, because we show that
domestic firms in financially underdeveloped economies
by borrowing
in domestic currency.
The
problem extends to the private
misvalue the insurance afforded
with financial constraints in the private
fault lies
The
sector rather than a misguided government.
will
result also explains
sector's debt choices,
why
the dollar debt
and why the private sector might
undervalue indexing their debt contracts.
In the sovereign debt literature, lenders charge higher prices for lending in domestic
currency because of the sovereign moral hazard.
However, we show that the same mechanism responsible
loans at actuarially fair prices.
for
In our model, foreign lenders extend
underinsurance can also affect the supply decisions of foreign lenders.
We
allow foreign
lenders to pay a fixed cost to enter domestic financial markets. In this case, they are able to
value more of the collateral of domestic agents.
linked to the equihbrium return
states of the world.
As a
We
show that returns on entry are
closely
on providing insurance to domestic agents against bad
result, the distortion in
the valuation of insurance by the domestic
agents also lowers entry by the foreign lenders.
Although our explanation
mechanism,
it
free insurance
is
for dollar fiabilities is also driven
quite distinct from those that point out that fixed exchange rates
and creates moral hazard that
(1997)). In these models, fixing the
in dollars
it is
by an insurance mispricing
and therefore encourages
distorts investment choices (see, e.g.,
exchange rate
offers free insurance to firms that
oflfer
Dooley
borrow
In our model, on the other hand,
dollar borrowing.''
not government misbehavior but financial underdevelopment that creates the private
underinsurance problem.
This result
may
explain
why
Distortions of private sector incentives due to free insurance
models, such as Burnside, Rebelo and Eichenbaum (2001).
is
the dollar debt problem extends
also behind the
government
bail out type
^
across emerging markets, regardless of exchange rate systems.'*
In methodology, our paper relates to a growing hterature on aggregate liquidity shortages
(Diamond and Dybvig
(1983); Allen
and Gale
(1994);
Holmstrom and Tirole
Krishnamurthy (2000); and Diamond and Rajan (2001)).
The
canonical model in this literature
and the
Each of these papers studies
macroeconomic and asset price consequences of an aggregate
different
on aggregate
effects of runs
is
(1998, 2001);
liquidity shortage.
Diamond and Dybvig, who study banking
structure
Allen and Gale present a model in which
liquidity.
aggregate liquidity shortages affects asset price volatility, and endogenize the links between
market participation, aggregate
and asset
liquidity,
Our modeling approach owes most
relates to that in Caballero
literature
is
when
Holmstrom and Tirole
to the
(1998, 2001)
model
of
Their papers motivate a role for the state in
aggregate liquidity in the context of firms.
the creation of liquid assets
prices.
Our
there are aggregate shocks.
and Krishnamurthy (2001a), whose
basic
model economy
central departure
from the
that they consider two forms of liquidity, one domestic and one international. In
this sense, the
paper also relates to the recent work by Diamond and Rajan (2001) in which
bank's solvency constraints play a role similar to our domestic collateral in determining
domestic asset
In Caballero and Krishnamurthy (2001a), there are two forms of
prices.
because foreign and domestic agents have different technologies to seize collateral
liquidity,
on non-repayment of loans. Aside from the
this paper, the
model of
this
different substantive issue that concerns us in
paper builds the asymmetry between domestic and foreign
lenders from their different valuation of nontradable goods rather than from an
asymmetry
in collateral valuation.
The paper proceeds
Section
as follows.
I
presents our model.
Section
II
discusses
the underinsurance result. Section III explores the connection between underinsurance and
domestic financial development. This section also serves as a transition to section IV, where
we
discuss external supply problems that
arise in this context. Section
of agents, domestic entrepreneurs/firms
are three periods, which
we
define as
V
concludes.
The Model
I.
Our model has two sets
may
t
=
0, 1, 2.
and foreign
All agents are risk neutral
investors.
There
and competitive.
See, e.g., the evidence of external dollar debt in fixed as well as flexible exchange rate systems in
Hausmann
'in
et
al.
(2001).
most currency
in dollars
crises,
governments run out of resources to
end up being badly hurt. Thus we are
left
rational firm can expect the government to provide.
bail out firms
with the question as to
The
free insurance
and the firms that borrow
how much
free insurance a
models require a government with
deep pockets. Our explanation has the advantage of relying only on the resources of the private
sector.
Domestic agents borrow from foreign
and invest
in
production at date
0.
investors, choose the contingency in their Habihties,
Then
at date
1,
there are an idiosyncratic and an aggre-
The
gate shock that determine the funds required to continue production.
agents' abihty to
cope with this shock depends on the vahie of their assets minus contracted habihties. The
question of currency denomination of habihties turns on whether Habihties are sufficiently
At date
contingent to insure against this shock.
2,
debts are fully repaid and
all
agents
consume.
Technology and Preferences
A.
Domestic agents are ex-ante identical and have equal access to the same production technology. All production requires foreign (or dollar) goods
and produces domestic
(or baht)
goods. Domestic agents have no dollars, so they must borrow from foreigners to finance
production. At date
0,
all
a firm borrows b^ dollars from a foreigner and creates capital of k
at a cost of c{k). Thus,
c{k)
To generate an
Once
we assume
interior solution,
created, the capital
is
<
bo
(1)
that the function c{k)
"baht." It generates domestic goods,
is
convex and increasing.
and
its
value as collateral
varies with the exchange rate.
We
note in advance that our model
rate refers to the real exchange rate.
is
is
entirely real. Hence,
We denote the exchange rate as e
(the formal definition
below).
At date
2,
if all
goes well, capital generates
part of the normal churn of the
idiosyncratic shock.
If this
Ak
so,
then
its
output
happens, the firm
is
toa<yl = a-|-Aon
falls
a firm chooses to salvage a fraction ^
—
9)ak
+ 9Ak
units of baht goods.
economy production may be interrupted
<
1
of
Ak
at date
1
by an
baht. If a firm chooses not to do
Thus,
if
capital units, then its date 2 output
is
the capital that
its
However, as
required to import an additional unit of
foreign goods per unit of capital to reahze output of
(1
any allusion to the exchange
is
not salvaged.
and the firm imports 6k units of goods.
Firms that are affected by
this
shock are distressed type, and those that do not are
intact type.
Let
uj
e
{/,
h} be the aggregate state of the world at date
firm suffers from a liquidity shock. However,
need to reinvest. The shock
of firms in the /-state, but
0.5 of being affected
by
it
is
it is
1.
In the /i-aggregate state, no
when the aggregate
countrywide in the sense that
it
state
is
affects
I,
half of the firms
a positive measure
idiosyncratic in that an individual firm has a probability of
in the /-state.
The probabihty
of the /-state
is
n,
and that of the
1
—
At date
2,
/i- state is
date
tt.
and
the domestic entrepreneurs/firms repay the debts accumulated at date
out of production proceeds. They consume the excess. Their preferences are
1
U<i
where c^
is
=
c^
c^,c^>0
+ c'^
consumption of baht goods, and c^
(2)
consumption of dollar goods.
is
Unlike domestic agents, foreigners have preferences only over the consumption of dollar
goods at date
2,
Uf = c^
(3)
and
Foreigners can lend dollars to domestic agents to finance production at both date
date
1.
We
assume they have large endowments of
dollars at each of these dates.
assume that they have access to a storage technology
also
endowments, providing a
for these
down the
gross rate of return of one. These assumptions pin
We
dollar risk-free interest rate at
one.
B.
Liability
Denomination and Contingency
Domestic agents borrow at date
on the aggregate
from foreigners, using contracts that are
fully contingent
state:
Definition 1 (Contingent Liability Contract)
For
uj
6 {l,h}, a date
contingent
liability
investor specifies date 2 repayments,
fi^
contract between a domestic firm
dollars,
foreign investors are risk neutral, competitive,
bo
=
7rf
and date
and
funding of bo dollars.
+ il-n)f^
Flexibihty in specifying liabilities contingent
We
production shock in the Z-state
lenders (Caballero
(4)
mean
that
firms take on so
Definition
1
on the type of firm
is
debt
is
(distressed/intact) could
private information of that firm,
and Krishnamurthy (2001b) examine
all
liability structure of firms.
assume that the identity of firms that experience the date
Although we define the repayments
ically
Since
the dollar interest rate is one,
This definition only allows for aggregate contingencies in the
provide greater insurance.
and foreign
in dollars.
much noncontingent
and
is
not observable by
this issue further.)
in units of dollars, this definition does not
The puzzling question
dollar debt
in
automat-
emerging markets
is
why
from foreigners. Since the repayments
are contingent on the aggregate state, they are not the
of a noncontingent dollar-debt contract.
1
same
in
as the repayments
We
prove that in equilibrium,
e'
>
e'*
would be represented under Definition
repayments of
dollar
=
repayments of b^
^
<
=
b^
=
bbaht
and
(i.e.,
bhaht
=
find that f^
high state
=
/''
=
/'
bhaht-
f =
=
1.
ddoiiar-
If
Consider how noncontingent debt contracts
1.
A
noncontingent dollar debt contract specifies
A
noncontingent baht debt contract has baht
we convert
_(miii
Since
e'
>
same
for the
1,
dollar
repayments
in the
the baht contract has lower repayments in the /-state
ddoliar),
we
these to dollar equivalent repayments,
(i.e.,
ddoliar)-
Thus, we look at the hability denomination question as a contingency question:
How
high are dollar contracted repayments in the /i-state compared to the /-state?
Credit Constraints and Collateral
C.
matter because firms face credit constraints.
Liability choices
by requiring firms to post
straints
We
recall that foreigners
We
introduce credit con-
collateral to secure all financing.
do not value any baht goods because they do not consume
these goods. Therefore, eventual repayments to foreigners can never be in the form of baht
goods.
We assume that
goods arriving at date
domestic agents have an exogenously specified endowment of foreign
2 given
define
w
of the output from production
is
by w. Following the sovereign debt
we
literature,
as international collateral.
all
of
w
collateral.
That
is,
production returns
can pledge
all
Although
is
collateral,
we assume that not
(1
—
6)ak
+
of this output to lenders. However,
all
9Ak. In a perfect capital market, firms
we assume
that the reinvestment at date
not observable and verifiable. Thus, courts cannot verify the extra output of {A
1 is
due to reinvestment and can only enforce repayments up to ak. For
is
clearly larger
Assumption
than ak. This limited
w
assnmption
is
>
0, (1
—
9)ak
a)k
+ 6Ak
central to our results.
(Collateral)
1
Lenders demand collateral against
of
collateral
6'
—
dollar goods
and domestic
all loans.
collateral of
capacity of a firm, measured in dollars,
Each domestic firm has international
ak baht goods. Thus, for each
u>,
collateral
the total debt
is
r<-+^
The
collateral value of the firm
(5)
depends on the exchange
rate. Since
as the exchange rate depreciates, the dollar value of this collateral
Since collateral
is
worth
less in
amount
falls.
is
baht
collateral,
Our question
is:
the /-state, and since firms will need resources to finance
their production shocks in this state,
the appropriate
ak
do firms match
this collateral sensitivity
of contingency in their liabilities?
by choosing
We
note that Assumption
1
rules out the possibihty of
equihbrium default
Lenders rationally anticipate the value of a borrower's collateral
and never demand repayments above
The assumption also implies
exceed w. This
contracted debt above w,
anticipate this
and there
it
is
will
our model.
each state of the world,
in
this collateral value.
that in equilibrium, foreign debt repayments of f^ will never
because foreigners only value
is
in
w
have to default on
for
consumption and
if
the country has
this debt. Since foreign lenders rationally
never default in the model, they never
demand repayments above
w.
Assumption
1
is all
that
explain decisions and equilibrium
If
a foreigner
is
However, we can better
required to generate our results.
is
if
we
consider a slight variation of this problem.
repaid in baht goods at date
dollar goods at the exchange rate of
e.
2,
he
will
exchange the baht goods
However, he does not need to wait until date
2.
for
He
could also exchange the claim on the date 2 baht goods for a claim on date 2 dollar goods
at date 0.
That
is,
the foreign lender
is
indifferent
between waiting
of claims against domestic collateral and swapping out of
them
date 2 to swap out
until
at date
0.
Rather than having foreigners lend against ak and then swap these goods at date
some
of the
w
we
dollar goods,
directly
2 for
impose a constraint under which foreigners only
lend against w.
We
collateral of ak.
These two assumptions are unnecessary
impose a similar constraint, that domestic lending be only against the
for the
workings of the model and
our main results, but they do simplify the exposition.
Assumption
la* (Foreign Lending)
All foreign lending takes the
form of
good collateral ofw. Lending
is
liability contracts that are fully
secured by the foreign
default free, so that
f'^<w
Assumption lb* (Domestic
Domestic firms can lend
to
so that agents can only use
Lending)
each other at either date
fully secured by baht revenues.
(6)
or date
All domestic lending
1.
However, the domestic financial market
ak of
the date
2 baht revenues
to secure
is
is
underdeveloped,
financing from another
domestic agent,
/^•"
It
< ak
turns out that since domestic agents are identical at date
(7)
0,
there
domestic agents to borrow or lend from each other against the ak at date
0.
is
no reason
At date
0,
for
/^'^
is
always zero. This
is
convenient, because
denomination of foreign
uncertainty
is
habilities.
Domestic lending can occur
resolved and the contingency issue
is
at date 1, but at this time
moot.
Decisions and Credit Chain
D.
We solve the decision problem of a firm by
60
allows us to restrict our focus to the currencj'
it
funds to create capital of
/i-state,
At date
k.
there are no shocks, and
all
backward induction. At date
0,
the firm borrows
there are two possible states of the world. In the
1,
firms continue to produce Ak. Entrepreneurs repay f^
and consume
= Ak + w-f^
V''
In the ^state, firms divide into distressed and intact groups.
alleviate its production shock.
goods.
To
(8)
A distressed firm raises funds to
A choice of 6k will result jn output at date 2 of {\—9)ak+9Ak
of distressed capital, the firm must borrow and invest 9k
salvage a fraction
imported goods.
The
That
firm can do this in two ways. First,
can go to foreigners to raise additional funds.
it
the firm can always directly raise
is,
Second, the distressed firms can turn to intact firms for loans.
There
is
an as3rmmetry between domestic and foreign agents. Unlike foreigners, domestic
agents value the ak of baht output.
indirectly
Thus, the distressed firm can access foreign funds
by borrowing from the intact
who
firms,
in turn use their international collateral
to borrow from foreign agents. Since the exchange rate
maximum amount
financial
of
^
dollars
from intact
market in our framework.
By
is e',
the distressed firm can borrow a
This credit chain represents the domestic
firms.
using this chain, the distressed firm can aggregate
the resources of the economy and pledge this to foreigners, thus raising resources for date
1
reinvestment.
The
decision problem of a distressed firm
(PI)
Vl
s.t.
=m&yiQjijD
w + ak + 9k{A-a)-f-f[-fP
(i)
fi<w-f
li)
/f < ak
Hi)
9k
straint (iii)
of /{
and
is
/f*.
(z)
and
{i
=
fi
+
^
0<9 <1
(iv)
Constraints
is
are the international
and domestic
collateral constraints.
Con-
that investment must be financed by the resources raised from the debt issues
Constraint (iv)
is
purely technological.
8
An
intact firm at date
^
intact firm lends
ei
dollars at date
constraint
Date
is
At date
= max^D w + Ak + x^-^- f
s.t.
^<w-f
a firm maximizes
0,
and
either distressed or intact,
date
against collateralized baht goods of
1
that the intact firm can at most lend
problem.
in either
w—f
xf
If
the
at date 2 then
dollars to the distressed firm.
expected profits over the events of being
its
the low or the high state. Thus, the decision at
is
(P3)
ma^k,boJ-
-
(1
+ 7r(V^3' + F/)/2
7r)y'^
f\f'<w
s.t.
= nf +
c(fc) < 6o
bo
-
(1
tt)/''
Equilibrium and Exchange Rates
E.
An
{^1
the distressed firm.
will lend to
it
F/
(P2)
The
how much
decides
1
economy
equilibrium of this
fiT fF^^i')^ respectively, and prices
(PI), (P2),
and (P3) given prices of
The only
equilibrium price
agents, the following
Lemma
1
economy
•
Ifc^,c^ >
•
Ifc^>
The case
and
Decisions are solutions to the firms' problems
At these
prices, the financial
From the
the exchange rate.
is
{k,bo,f'^)
market
clears.
preferences of domestic
true.
0,
but
of c^
The exchange
at date 2:
then e
0,
generates at least
c^ =
=
=
0,
1.
then e
and c^ >
>
1.
:-
can never occur in our model, since production always
some baht and domestic agents must consume
rate
consume both baht
is
one as long as the solution
happens
is
as well as dollar goods. However,
precisely the case
at date
1 in
Equilibrium in the l-state
we
are interested
the low state,
What
of dollar goods? Intact firms have
pins
w-
i.e.,
down
where
in,
e'
if
c^
we
>
=
0,
where domestic agents
the economy runs out of
reflect this scarcity.
construct an equilibrium in which
e'*
=
1.
the exchange rate
f' oi dollar
this baht.
at an interior
is
goods and the exchange rate depreciates further to
Since this
this
e'^.
e'^.
decisions,
1
Let c^ and (P denote the equilibrium consumption of any intact entrepreneur
in the domestic
dollar
must hold
and date
consists of date
when
goods that they
the economy runs out
sell
to distressed firms
to use in production. Distressed firms pay for these dollars by selling
The exchange
firms.
rate
is
the price in this trade
^(--/V
^/f =
This exchange rate
rate
is
one and interest parity must hold, the date
rate divided
we need
to one,
A
a date 2 forward exchange
really
is
by the gross domestic
interest rate.
down the domestic
interest rate.
not pin
we can
call
e" the date
A—
A >
to
By
is
the date 2 exchange
free
=
zz;
—
capital,
its
make up the
fc,
shortfall.
well.
exchange rate of
It will
e'.
We
let
its
A=
much
sum
unconstrained in
its
of
^
its
than the funds needed
for
it
can
w—
f\
up to ak date
sell
is less
have to access the domestic financial market
will
>
e').
2
baht to another domestic at the
The maximum amount
and
u;
—
/' is
of funds raised
is
borrow
than
less
(10)
more than the borrowing need
reinvestment at date
this case, the firm will
is
can against
as
^<^
as the
—a
yl
choose to do this as long as the baht return on restructuring
exceeds the exchange rate (A
As long
capital
/').
then the firm
It
in that
capital. Since the international interest rate
the amount raised from foreign investors,
of
parameter
choosing this interest rate to be equal
the distressed firm chooses to borrow as
1,
international collateral (6i
all
exchange rate
a units of baht goods at date 2 per unit of foreign debt.
one, as long as
salvaging
rate. Since the international interest
international collateral to salvage
its
be the baht return to salvaging one unit of
If
1
(9)
The model has a
exchange rate as
1
distressed firm that borrows against
generates
of baht to intact
fP
1
^
and
in
all
production units
will
of
fc,
the firm
is
be salvaged. In
domestic financial markets.
Intact firms will lend dollars to distressed firms as long as the exchange rate weakly
exceeds one
(e'
collateral oi
w—
If
and
>
The most
1).
that
A >
intact firms lend as
all lent
be salvaged
is
is
their excess international
f.
we assume
which are
that intact firms can lend
e'
>
much
1
,
then distressed firms
as possible.
to the distressed firms.
that |
<w — f
.
A
will
In total, the
borrow as much as they can
economy imports
necessary condition for
For a given equilibrium ^
<
1,
we
all
w—f
goods
production units to
refer to
the constraint
e\<w-f
(11)
as the international collateral constraint.
As long
positive.
as the international collateral constraint does not bind, both c^
From Lemma
1,
we note that
this will
10
mean
that
e'
=
1.
However,
if
and c^ are
the constraint
does bind; the economy will have sold
all
of
dollar goods,
its
and from
Lemma
1,
we
see
that the exchange rate exceeds one.
constrained
demand
1/2
Figure
Figure
1
1
<
international collateral
equilibria at points
A
and
The supply
1).
international interest rate of one,
up
1/2
e k
in the /-state
to
^{w —
of dollars from intact firms
/').
this point, the
is
elastic at the
economy has no more
The
figure represents
and B. The points are distinguished by whether the distressed firms
one. However, in the case
where
w—
/', in
both equilibria 9
(10) does not bind, the
represented by the dashed upper line for
other case (the
At
so the supply of dollars turns vertical.
are credit constrained or not. Given
is
Market Clearing
')
represents the market clearing for the case in which the international collateral
constraint of (11) binds (for ^
case
:
(w-f
downward sloping
is
the same and less than
exchange rate
demand corresponding
is
equal to
A
(this
to point B). In the
solid curve corresponding to point A), the
exchange rate
is
l<e' =
Since
/-state,
we
ak
w-
<
A
are interested in equilibria in which the exchange rate
we assume that the
(12)
fis
depreciated in the
international collateral constraint of (11) binds in this state.
We
are interested in the distinction in outcomes between the cases where (10) does and does
not bind.
Lemma
2 (Exchange Rates)
• In the h-state, the international collateral constraint does not bind.
11
Therefore,
e''
=
1.
In the
•
l-state, the international collateral constraint binds.
I
e
// (10) binds, then e'
We
must
profitable
also
mm
=
<^^
r A
A,
1
-7
1
< A.
make assumptions such that date
and gives an
>
Therefore,
<
interior solution {k
investment in capital
c~^{w)).
We
is
sufficiently
provide the assumptions on
primitives required to generate these equilibria in the appendix.
Underinsurance: Excessive Dollar Debt
II.
Firms contract to make contingent debt repayments
two states of the world and noncontingent
in dollars of /''
and baht debt have
dollar
and
/'.
linearly
There are
independent
repa3anents. Thus, spanning results apply and the contingent repayments of (/'',/') can be
implemented by contracting
debt
when a
central planner
in a
mixture of dollar and baht debt. There
is
excessive dollar
would choose a lower fraction of dollar debt than would private
agents.
Definition 2
and
librium,
and
// /'*
F
and
F
/' are debt
repayment choices in the competitive decentralized equi-
are debt repayment choices of a central planner, then the
has excessive dollar debt
economy
if
^<^
Competitive Equilibrium versus Planner's Choice
A.
To
arrive at the
program
for
a firm at date
and (P2) into (P3) Firms solve
e'
(13)
>
1 (as in
If
Lemma
a firm chooses
the /i-state of
0,
we
substitute the value functions from (PI)
their decision problem, given
exchange rates of
e'*
=
1
and
2).
(fc, /'*,
/'), it will
V^ = Ak + w — f^
make date
(equation
(8)).
2 profits (net of
In the i-state,
if
any contracted debt)
the firm
is
in
distressed, the
date 2 profits are
Fi
{w
—
/') is
The ak
at
A.
^A
(14)
pledged to foreigners and the proceeds are invested at the project return of A.
of domestic collateral
If
= (u,-/')A +
the firm
is
is
sold at the exchange rate of
e'
and the proceeds are invested
intact, date 2 resources are
Vl
= {w-
/')e'
12
+ Ak
(15)
f
Combining these
(P4)
results, the
program
date
{l-TT){Ak
maj^kj^f
+ w-
is
f'')+nl(^{A + a^)k + {A + e^){w-
f\f<w
s.t.
c{k)<TTf + {l-Tr)f^
In both h and
I
states the firm can increase its Habihties
benefit of increasing
dollar
by one dollar
used to increase capital by
is
less in
f'^
that the firm raises
is
p^
The
.
increased capital) to cost of increasing /
dollars at date 0. This
tt
that there
is
Now we
consider the
same
at date 0. This dollar
is
.
we
the /-state
used to increase capital by
see that the cost
7r(A
is
7r(A
Comparing these
1
^
C'(fc)
-|-
-pf]^-
e')/2.
However, since in the
from that
differs
n
^
dollars
/-state firms
in the /i-state.
From the
Thus, the same benefit-to-cost ratio
last
+
1
^
c'(A:)(A
e')
+
((A
+
two expressions confirms our intuition that since firms
e')/2
However, this cost
is
>
it is
costlier to
have more
will
need
liabilities
1).
lower than that which a central planner would compute. In the
a dollar certainly returns
strictly less
'
^
e')/2
resources to finance their production shock in the /-state,
is
ratio of benefit
is;
-^/c'jk)
in this state
one dollar
exercise in the /-state. Increasing /' by one dollar raises
have to finance their production shock, the cost
objective in (P4)
The
is
is:
^
l-TT
firms
—
cost of doing so
(l-7r)/c-(fc)
state,
1
the h-state, which reduces date 2 consumption by one dollar.
(in units of
in
up to a maximum of w. The
A
when used
than the planners ((A
in production. Since
e')/2
-I-
<
e'
< A,
/-
the cost term for
A). As a result, the planner will have
firms choose to contract less liabilities in the /-state than in the competitive equilibrium
outcome.
We confirm this intuition more formally by constructing the program of a central planner
who maximizes an
equally weighted
sum
of the utilities of the domestic agents, subject to
the domestic and international collateral constraints.
Suppose the central planner makes a date
choice of {K, F^, F') (capital letters denote
the central planner's aggregate quantities). At date
of V'^
=
AK + iu- F^.
2, in
the high state,
all
In the low state, a distressed firm's profits are
(equation (14)). For the planning problem,
we construct an
Substituting the market clearing condition of
e'
=
°'^pt
firms earn profits
{w - F')A
objective that
is
-f
^A
free of prices.
into this profit expression,
we
obtain:
Vl
=
2{w
13
- F^)A
(18)
an intact firm's
Similarly,
in the
profits are
market clearing condition,
[w
efficient
(P5)
+
AK
(equation (15)). After substituting
=
ia
+ A)K
(19)
debt choices in this economy are given by the solution to
{l-Tv){AK + w-F'') +
maxj^ph^pi
TTl(^{A
+ a)K + 2A{w-F^)^
F'',F'<w
s.t.
c{K)
We now
F')e'
becomes:
this
Vl
The
—
<
ttF'
+
(1
-
tt)F''
compare the benefits/costs of increasing
liabilities.
since the objectives corresponding to the /i-state are the
benefit/cost computation for both the planner
and firms
Lemma
w.
=
3 In both (P4) and (P5), F''
f'^
=
Starting with the ^-state,
same across (P4) and (P5), the
in increasing /'' is
the same.
B
Proof: see Appendix.
Since there
no chance of a liquidity shock
is
w
in this state
In the /-state,
Lemma
4
//
and use the proceeds to increase
we confirm that the
A>
e'
,
then F'
is
no reason to leave
much
Optimality requires firms to borrow as
a slack in the debt repayment.
against
in the /i-state, there
<
/',
K at date
as possible
0.
choices over liability diverge:
or debt repayments are set too high in the l-state in
the decentralized equilibrium.
H
Proof: see Appendix.
In the objective in (P4), /'
multiplied by A.
Proposition
1
When
e'
<
multiphed by (A
A, the
latter
is
-f e')/2.
bigger and
we
In the objective in (P5), /'
arrive at the
is
lemma.
(Excessive dollar debt.)
Suppose that the international
tic collateral
is
collateral constraint of (11) binds in the l-state. If the
constraint of (10) binds, so that
debt. If (10) does not bind so that e'
This proposition follows from
=
e'
< A,
then firms contract excessive dollar
A, then debt choices are
Lemma 2.
e'
<
of (10) binds.
14
domes-
efficient.
A only if the domestic collateral constraint
The
B.
The
Externality
planner's choice differs from the competitive equihbrium because of an externahty that
arises
when
there are domestic coUateral constraints.
The market
price of a dollar in the Estate at date
of this dollar in production
for
is
(10) binds, the
demand
for dollars is depressed
its social
The
A
demand
responsible
market price of a dollar
is
relative
up the price of dollars
no distortion.
distorted price affects the quantity of insurance purchased.
The insurance
decision
decision to save one dollar into the /-state. If the firm turns out to be distressed,
a date
A
uses this dollar in production to return
and fetches
less
The
must
sell
if
the firm
is
intact,
the dollar at the price of
than the social marginal product of A.
Ex
e'
<
ante, this translates into
result.^
Financial Development and Underinsurance
III.
The main
However,
at date 2.
firm
underinsurance and the excessive dollar debt
ities
distorts the
and there
the distorted price comes into play:
A
is
value
because the firms in need of dollars
value. If (10) does not bind, then the distressed firms bid
towards their marginal product of
it
The marginal
e'.
A. The difference between these two valuations
are credit constrained. This depressed
is
given by
the underinsurance result.
When
to
1 is
result of the previous section
is
that the excessive share of dollar debt in the
liabil-
of firms in emerging markets arises because credit constraints affect borrowing/lending
relationships
among domestic
agents.
We now
consider an
economy with a mix
of firms
that face no credit constraints in their domestic borrowing and the constrained ones of the
previous section.
We model
financial development as increasing in the fraction of firms that
are not credit constrained.
We
simplify the analysis by ruling out domestic insurance markets contingent
gate shocks, which will naturally arise
when
firms are ex-ante heterogeneous.
on aggre-
The
results
in this section are robust to relaxing this simplification.
®We
note that there
A, distressed firms
sell
is
domestic coUateral at
^
as
opposed to
^. We
overvaluation, relative to the planner, of the collateral created by k investment.
and overinvest
in this
by
paper
is
at date 0. Although,
in
understanding
financial development,
When
e'
<
can show that this
is
an
another factor that reinforces the underinsurance in our model.
their
we do not
how
As a result,
firms overborrow
focus on this aspect of underinsurance because our interest
liabihty choices (as opposed to asset/investment choices) are affected
we can show that when there
are
more than two aggregate
leads to overborrowing but does not affect insuring against the Estate.
15
states, the latter effect
,
Constrained and Unconstrained Firms
A.
Assume
that a fraction A of the domestic firms face no constraints on domestic borrowing.
For these firms the date
domestic collateral constraint
1
fF <
>
For 6
than those of
all
clear that {{l
0, it is
^)a
+ ^^)k
(20)
ak. Thus, these firms are less credit constrained
appendix that since these firms are able to pledge
in the
of their baht output as collateral, the domestic collateral constraint of (20) will never
bind
them.
for
Lemma
5 (20)
will
never bind for unconstrained firms.
Proof: see Appendix.
we
Next,
Ak + w —
the firm
is
— 6)a + 6A)k >
we show
(10). In fact,
-
((1
is
program
consider the date
f^. In the
is
B
'
able to salvage
and generating
A
state, if the firm is intact it
I
distressed
all
it
makes
of
its
profits of VJ
capital units
baht at date
maXfcjHj,
= ak + (A —
-
Tx){Ak
+
{w
— Ak +
— f)e\
dollars at the
— /')e'.
{w
= nf +
exchange rate of
f'')
+
Tx
({A
firm:
- ^)k + e\w - f))
Efficiency)
collateral constraint binds in the l-state, then
e'
= A,
e'*
jr = jL
Proof: Suppose in contradiction that
maximum amount and
1).
Thus
A >
e'.
Then the
distressed firm will choose to
salvage production units.
^=
|.
1
(21)
We
use
Lemma
5
that (20) will never bind. As a result, distressed firms will issue debt and salvage
=
=
pH
fh
production units [9
e'
{l-n)f>^
and
borrow the
If
because the firm
program of an unconstrained
+w-
Proposition 2 (Financial Development and
and the international
e')fc
V^ =
in the h state,
f^j'<w
c{k)
1
profits of V}
by borrowing k
yields the date
[l
s.t.
If \—
makes
As before
2.
Combining these expressions
(P6)
for these firms.
However, since (11) binds, 6^
=w—
f
and note
all
of their
ioT 9
<
1.
This implies that
^>w-f
which violates market
it
must be that
A=
clearing.
There
is
excess
e'.
16
demand
(22)
for dollars at
date
1.
As a
result,
We
=A
substitute e
into the
maxfcj^ J,
(1
program
- n){Ak + w -
c{k)
is
a firm at date
f^)
+
tt
in (P6).
(^fc + A{w -
f)
f\f<w
s.t.
This program
for
< nf +
(1
-
identical to that of (P5). Hence,
tt)/'^
A
if
=
1,
the economy makes efficient debt
B
choices.
This proposition
fimited to ak in
clarifies
the main result of the previous section:
Assumption
1,
since collateral
firms are constrained in their domestic borrowing.
causes the distortion in prices and results in underinsurance.
of firms can be pledged as collateral,
market prices
When
reflect the social
all
is
This
of the baht output
marginal product and
insurance decisions are chosen optimally.
We
conclude by showing that for the intermediate cases of A
monotone
As
in A.
financial
development
rises
<
1,
the debt choices are
and more firms are unconstrained, the debt
more insurance.
choices feature
Proposition 3 (Financial Development and Underinsurance)
Consider two economies indexed by A and
A',
where A
international collateral constraint binds in the l-state.
>
A'
and
Then for
in both
economies the
both constrained
and un-
constrained firms,
(23)
A'
Proof; see Appendix.
Limited Foreign Insurance: Further Costs of Domestic
IV.
Financial Underdevelopment
The
general principle behind our result
mand
for funds.
Those
by these funds to the
in
We
lenders.
In a dynamic context, the latter find that the business of
far,
is
not profitable and so they transfer their resources
apply this principle to explain the hmited entry of speciahst foreign lenders
into domestic markets
So
that credit constraints leads to constrained de-
need of funds are not credible in transferring the surplus created
lending to firms with bad collateral
elsewhere.
is
(i.e.,
we have modeled
credit line facilities, foreign banks).
foreigners as passive lenders
who make no
lend in either currency. This characterization of foreigners (and
hardly
realistic.
profits
and
many domestic
willingly
savers)
is
This section extends the model to study the effects of financial development
17
We
on foreign lending decisions.
introduce an active margin whereby foreign lenders
may
choose to pay a fixed cost and specialize in lending to the domestic market.
A.
Foreign Specialists
We
return to the model of section
two
classes, specialists
and
III.,
< A <
with
nonspecialists.
The
We
1.
divide foreign lenders into
specialists value baht
goods as do domestic
agents:
U^ = c^ + c^
(24)
Nonspecialists are exactly like the foreign lenders of the previous sections.
dollar goods,
i.e.,
U=
They value only
c^.
Unlike the nonspecialist, a specialist can invest in loans backed by domestic baht collat-
This modification captures the idea that specializing in the domestic market enables a
eral.
foreign lender to receive higher returns on lending to domestic agents.
lenders (both specialists
is
endowment
and nonspecialists) have a date
a continuum of measure a of these
specialists,
a
will shortly
We
of
assume that
w^
dollars.
all
There
be endogenized by positing
a cost of specializing.
B.
Specialist
Lending as Insurance
Definition 3 (Specialist Lending Contract)
A
contract between a foreign specialist and a domestic firm specifies repayments of {fs, fs)
and
initial loan of bo.
boq^il-n)fl + Trfs,
The
>
e'
(25)
collateral constraints for this lending contract are
fs
if the
firm
is
the firm
is
<Ak + w
(26)
unconstrained (in domestic markets), and
f^
if
q
<ak + w
(27)
constrained.
In this definition,
we have accounted
for specialist lending against
baht collateral by
expanding the collateral constraint to include the baht output.
The
required return of the specialist lender
specialist has
is
g
>
e'
a high return investment opportunity in the
good and receive
e'
>
1
baht-goods in return at date
18
2.
(in (25)).
/-state.
If
This
He can
is
because the
lend one dollar-
the specialist converts
all
of
his
wealth into date
1
nonspecialist), he will earn the return of
receive at least this return
on date
on
e'
maxi^jt^jijiji^
0.
[1
s.t.
.
Thus, the speciahst lender must
lending.
and nonspecialists at date
(P7)
w^
his
This firm chooses to borrow from both
Consider the problem of a constrained firm.
specialists
by investing with a risk-neutral
dollars in the /-state (for example,
We
modify (P4) to
- n){Ak + w -
f^
reflect this:
- f^)+
/^/'<u;
0<fl,fs<ak
c{k)
As
in
the previous sections,
<
TT/'
we shorten the
+
(1
-
tt)/''
+
i
+
{jrfs
(1
- n)fl)
.
collateral constraint for specialist loans (the
second constraint) to being constrained only by ak. This
is
without
loss of generality for
the same reason as in previous sections.
The
following
Lemma
lemma
describes the insurance features of specialist lending:
6 (Lending Contract as Insurance)
Consider an economy in which
case,
fg>0
and fg
=
0.
e'
< A and
<a <
e,
where
e is
In addition, the return to specialists
is
positive but small. In this
=
q
\^
.
B
Proof: see Appendix.
In the
economy without
borrowed against. Since
cialists is
specialists, the
baht collateral of firms
specialists value that collateral, their
premium
of g
>
>
e'
nonspecialists lend at the international interest rate of one and /'
increase borrowing from a nonspecialist before
it
h -state
is
never
advantage vis-a-vis nonspe-
lending against the /i-state collateral- This results in /^
Since speciahsts are limited, they charge the
in the
borrows from a
0.
on
their lending. Since
<
w, a firm prefers to
specialist.
firms choose not to borrow against the Z-state from nonspecialists {fg
=
This
is
why
Specialists
0).
provide more contingency and insurance than nonspecialists. In this sense, their lending
is
more domestic currency denominated.
Proposition 4
(Specialist
Lending and Insurance)
Consider two economies indexed by a and a' where
a> a'
.
e^
<
q
<
A
in both economies.
Then
2-^jS{const,unconst} '^jyJj
'
Z-'j£{const,unconst} ^jxJj
JS,ji
'Js,j)
(28)
2-ij£{const,unconst} '^j\Jj
'
Isj)
2^j&{const,unconst} ^jKJj
Q,
19
'
Is,j>
a'
^
Proof: see Appendix.
As the mass
of specialists increases, constrained firms raise their borrowing against
the h-st&te. Moreover, these proceeds are used both in increasing k and insuring against
This can happen directly by receiving dollars
the Z-state.
or indirectly
by reducing
/'
the Estate from speciahsts,
in
from the nonspecialists. There
is
an indeterminacy
in
which
lender provides the /-state insurance. However, in total, the Hability structure of the firms
provide more insurance as the mass of specialists
rises.
Equilibrium, Entry, and Financial Development
C.
We
endogenize a and describe how financial development affects a and lending premia.
Assume that
As a
specializing costs C.
and non-entry yields utihty of V"^
result, entry yields
= w^ The
.
expected utility of V^
free entry condition
that
is
a
=
[w^ -C)q
lenders choose
to specialize such that, in equilibrium,
V^ = F""
The
return to specialists of g
is
(29)
a function of both the equilibrium
well as the exogenous level of financial development (A).
amount
In the Appendix,
of entry, as
we prove the
following comparative statics:
Lemma
7
As more
specialists enter the market, q falls:
(q,
As more firms
The
entrant
In
a and X)
in the
first result is
falls,
Lemma
7
and q
we noted
e'
are unconstrained, q
<
0-
ri.ses:
af
'^ ^•
that as more specialists enter the market, the return to the marginal
falls.
this positive relation
show that
economy
d^
We
use previous results to establish the second comparative static.
that q was equal to ^^^ for small a. In the Appendix,
between q and
was increasing
in A.
financial market, firms have
e'
As a
we show
holds more generally for any a. In section
result, q is also increasing in A. In
more domestic
collateral
that
III.
we
a more developed
and the return on lending to these
firms rises.
We
5
=
e
note that the proposition applies only to the case
and unconstrained firms
will also
in
be borrowing from
which q
>
e
.
This
is
because when a
is
large,
specialists in equilibrium. Since these firms are
unconstrained, they are indifferent between borrowing against /i-state collateral or Estate collateral. As a
result, the liability structure is
features of the liabihties. If
indeterminate and we are unable to
we assume
tion continues to hold. In terms of welfare, increasing
between the h and
make statements about
the insurance
that they always borrow against /i-state collateral, then the proposi-
a
/-states.
20
is
always beneficial, since
it
leads to
more insurance
q
k
V
N
\d
^N V
d'
\
\^
V
\\
N
\
\\
V
\
e=Une
N
N.
^
V
V
N.
N
N
N
\
'k
.
\
S.
a
Figure
2:
"»>
N
a
Entry by Foreign Specialists
The
Figure 2 represents the equilibrium for the entry decision.^
demand
for foreign specialist
an economy which
is
more
funds as a function of
financially developed
(i.e.,
q.
A
The
is
solid line
line d' represents
d
is
the
demand
in
higher). Inspection of the figure
leads to:
Proposition 5 (Financial Development and
Specialist Entry)
Financial development increases the entry of specialists into the domestic lending market
(a
is
increasing in X).
Financial Development and Lending Premia
D.
The
limited foreign entry described in the previous section can feed back into the price
charged by foreign specialists through a thin-market externality. Suppose foreign lenders
prefer to lend in a market in
which there are already other foreign
(1994) provide a microeconomic model for this phenomena.
We
lenders. Allen
and Gale
defer to their results,
and
take a reduced form approach to this issue by positing complementarity in foreign entry
^Foreigners require that,
A + e'
1
in order to enter.
As a
result,
a
is
- c
such that the equilibrium exchange rate
21
is e'
=
2
',;
— A.
^\^ d'
d
U^=U"^
!
i
,
i
a
a
Figure
decisions.
Suppose that
C
3:
1
1.
a
Complementary Entry Decisions
a function of the amount of entry:
is
if
a < d
if
a > d
C{a)--
Figure 3 illustrates the effect of complementarity. At the low level of financial develop-
ment corresponding
to d, there
is
the possibility that foreign specialists anticipate limited
entry by others and stay out of the market. However,
(d'), this possibility
themselves.
if
the market
is
developed
sufficiently
disappears, since specialists expect others to enter and therefore enter
Comparing across these two
cases,
we
see that the lending
premia
fall
as
A
rises.
V.
We
Conclusion
began the paper with the following question: The large share of external debt
ing markets that
is
However, since this
dollar
is
denominated has played a central
a private decision,
why do
role in
in
emerg-
most recent
crises.
firms expose themselves to the risks of
dollar debt?
We
answer
this question
equivalent to a choice over
when
by showing that the choice over
how much
international collateral
is
scarce.
liability
denomination was
insturance to purchase against states of the world
The
central result of our analysis
is
that
when
domestic financial markets are underdeveloped, the private valuation of this insurance will
22
be distorted relative to a planner's valuation. The distortion leads to underinsurance.
If
there
is
a drop in returns to providing insurance, then the supply of this insurance
foreign specialists also
foreign credit lines
The
Countries with limited financial development also have fewer
falls.
and foreign lending
by complementarities
in
in
domestic currency. This situation
is
exacerbated
the lending decisions of foreign specialists.
primitive result in our analysis
liabilities in dollars is just
is
one of underinsurance. Denominating external
one manifestation of this underinsurance. Other forms of un-
derinsurance include the limited availability of external credit lines and the large
of short-term external debt in emerging markets.
We
the exchange rate system.
Lastly, the dollar-debt
tigations into the role of
are able to rationalize
We
problem we have discussed
government to correct
is
due to an
this externality
externality.
have proven
Our
fruitful
inves.
We
policies such as capital inflow taxation or
Pareto improving in some situations, although not without draw-
backs (Caballero and Krishnamurthy (2001b)).
We
monetary and international reserve management
Krishnamurthy (2002)). Without a theory
cies, it
among which
are currently investigating this issue.
some canonical government
liquidity requirements as
amount
conjecture that the manifestation of
underinsurance in a particular country depends on institutional factors, chief
is
by-
for
are also able to
policies
can be
show that well-designed
effective (Caballero
why governments may undertake
has not been possible to study the relative merits of these policies.
framework to analyze these issues currently.
23
We
and
these poli-
are using our
Appendix A.
Proof of
Lemma
C*^{l-Ti){AK +
We
3:
form the Lagrangian
W -F^)
+
for (P5),
+ a)A' + 2A(V^-F')) -
7ri((/l
\{c{K) -
-
ttF'
(1
-
7r)F'^)
(Al)
- M^F''
-W)- ^i{F' - W)
First,
1^ =
(1
1^ = _(1 _ ^) + A(l -
TT)
Likewise,
We
=
if [ih
-
+
tt)^
TT^ - Ac'(K) =
(A2)
0,
i^
=
((1
-
7r)A
+
TT
A from above and note that the project
substitute in
to arrive at the inequality.
>
Since ^p-
0, it
A±^ - c'(K))
is
>
(A3)
sufficiently profitable at
must be that F^
=
W
.
date
The same proof
applies for (P4).
Proof of
Lemma
We
4
note that,
°W -"-"'"'
=
F'
(A4)
^''^-i^--)^
f =
(A5)
= A(^(l-7r)yl+^(^ + a))
(A6)
IT
From
the
FOC,
c'{K)
c'{k)
If e'
< A then
c'{k)
> F'.
Proof of Lemma 5
>
=
7^((l--)^+^(^ +
c'{K) and c{k)
>
c{K).
From
the
vO
first set
(^')
of equations this also
meai^s that /'
If
the unconstrained firms salvages 6 units of capital by issuing debt
that raises dk dollars, then the
maximum amount
of dollars they can raise
li^:il^A:>.4it
is,
(A8)
e'
e'
Since
y4
we conclude
=
a
+
A>A>e'
that
il^3^L±lAu >
Thus, given any
restructure
(A9)
all
6,
ek
(Aio)
unconstrained firms will always be able to obtain the funds required to
of their capital units.
24
From
Proof of Proposition 3
FOC
(P6), the
an unconstrained firm
for
is
(the "hat"
denotes choices for unconstrained firms),
(1
Note that k
-
strictly decreasing in
is
+
tt)^
decreasing in
(
=
A-^
'
= nw+{l-n)f
(A12)
From the same program
e'.
(All)
e'c'(fc)
I
Also, from the budget constraint
e'.
c{k)
/' is also strictly
TT
for
FOC
constrained firms, the
is
-n)A + n(^^-
(1
Again we conclude that
We know
choices. If
that
and k are
/'
=
if e'
a
A^
^ ^^^'(fc)
strictly decreasing in
(A13)
e'.
A, the private- sector debt choices coincide with the
we take the other
case where
e'
< A,
efficient
the market clearing condition in the /-state
is
Xk
+ ^(1 -
=
A)
(1
want to prove that
This
increasing in A.
is
V
obviously true
However
if
this is true,
then
clearing condition
e'
>
is
e'
-
/'(I
-
-
A)
(A14)
2/'A
both constrained and unconstrained firms)
(for
when
proof by contradiction. Suppose not, then
<
X)tu
fh
We
e'
+
.
Proof of
Lemma
e'
,
For a fixed
6
increasing /^ in (P7), and
raises (1
—
Tr)^
which
compare
more resources
gives a gross borrowing cost of
costs (1
— tt).
/'>/',
fc
>
is
and costs
^^^,
k,
we
consider the
/'>/',
this to the cost in
and incurs
Increasing
f'^
amount
is
>
From the market
fc'.
of
money
raised at date
by
costs of (1
raises (1
—
tt)
—
tt)
in
the objective. This
more resources
0,
but costs
at date
7r^j=j-.
The
and
gross
tt
*^^^
ratio of increasing /'.
in the objective for a gross
e'.
This raises n
borrowing cost of
=
0.
"^^
.
Borrowing from the
dominated by borrowing from the nonspecialist.
return to specialist lending
^^2^
>
fc
we have that
A',
terms of the objective. Increasing fg
However, since specialists lend in equilibrium, fg
=
>
which A
the constrained firm will always choose fg
specialist in the /-state
Thus, q
in
\^
^
resources at date
<
A;',
we construct a
In the other case,
two economies
compare each of these to the cost/benefit
Since ^^^
A.
Increasing fg raises tt^ more resources at date
borrowing cost
We
=
weakly
a contradiction.
at date
q.
for
e'
is
is
>
0.
For small values of a, the
determined by the value of dollars to firms
in the /-state.
Also, at this price, unconstrained firms choose not to
specialists.
25
borrow from
We
Proof of Proposition 4
write the program for an unconstrained firm;
first
- ^)i^k + w-f^-
(1
'^^''kj'^J'JlJ's
fl) +
^[{A-i)k-f's + e^{w-f^))
f\f<w
s.t.
(A15)
0<f^,fs<Ak
<
c{k)
In the region where
all
fg
+
(1
-
n)f'^
+
i
+
{nf's
-
(1
n)f^)
e\ the unconstrained firms will not borrow from specialists. Thus,
lending by specialists must go to constrained firms.
To show that
(1
q>
tt/'
— A)/' + A/'
will rise
We
ratio of /i-state to /-state liabilities rises
falls.
This
is
because we know from
with a, while fg
show the
we show that
=
two
result in
Lemma
with a we need to show that
6 that for the constrained firms,
0.
steps. First
this implies that (1
—
A)/'
we show that
+
A/'
as
e' falls
a
and second,
increases,
falls.
Consider an increase in the mass of specialists of da. Since this increase goes toward
investment and borrowing against the /-state (from
constrained firms altering their date
nonspecialists),
- C)da =
{wf
The market
(1
-
clearing condition in the /-state
Afc
+ ^(1 -
A)
=
-
X)c'{k)dk
(1
-
>
(A16)
2/'A
(A17)
A)7rd/'
is
(1 -f
X)w - /(I -
A)
-
Thus,
iln^l^de'
=
"^ "
,2
If de'
(A16),
>
0,
c//'
<
-
A)c//'
Proof
From
0.
de'
<
(A18),
0,
c/e'
<
<
0,
which
is
0,dk
We
first
<
0,d/'
<
note that q
is
>0,dk>
proportional to
0,
df'
e'.
the region that specialists only lend to constrained firms, q begins at
When there
resulting in g = e'.
linearly.
The proof
However, given
<
>
for
0.
This
"^^
da >
From
is
0.
(A18),
because
in
and decreases
are sufficient specialists, specialists also lend to unconstrained firms,
follows the
same
logic as that of proposition 4. First since specialists lend to
both constrained and unconstrained
{w^
0.
a contradiction. Thus, de'
from the FOC's we know that dk
+ Xdp < 0.
of Lemma 7
(A18)
,2
then from the FOC's we know that dk
Given that
(1
^^—^dk + \dk + (1 - A)d/' + 2\dp.
- C)da =
(1
-
firms,
\)c'{k)dk
+
we note
that
Xc'{k)dk
26
-
(1
-
X)ndf^
- Xndf >
(A19)
>
If de'
for
da >
0,
then from the FOC's we know that dk
<
0.
From (A18)
given (A19), d/'
de'
<
da >
for
means that
this
<
de^
last
^dk + \dk +
=
J^
e
e/2
The
term on the
RHS
is
(1
the
is
non-negative.
first
term on the
<0,dk<
positive for
The proof
RHS
is
<
and
contradiction. Thus, de'
>
for
Parameter assumptions
we have
used.
First,
we
is
However,
0.
a contradiction. Thus,
we can show that
d\ >
df'
dA
We
0,
Thus, we only need to show that the
1.
>
de'
<
for
dA >
However from the FOC's we know that
<
0.
(A20)
because on net, unconstrained firms are
by contradiction. Suppose
positive.
0,d/'
then dk
is
df <
- A)d/ + 2Ad/' + (1 - X)ak(k - 2{w - f))d\
borrowers of dollars in the market at date
term
which
0,
0.
For the A comparative static, after a httle algebra
-de'
0,
<0,dk <
From (A20)
this
means that
de'
<
0,
if
iirst
Then
0.
de'
<
which
0,
is
a
0.
examine the technical assumptions on parameters that
require that
w =
F'^ in (P5), or that the return to investing
domestically exceeds that of investing abroad:
{l-7r)A
Second,
F'
<
we
+ n^-^>c'{w)
require that the solution features
(A21)
some insurance against the
/-state, so
w.
c'HA>
Finally,
we
require that equihbrium has
(l-7r)yl
1
<
e'
+ 7r^^^.
(A22)
< A. The FOC
for the
program
in (P4)
c'{k)^^ = {l-n)A + 7r^(^A + a^^
We
denote the solution to this equation as k{e).
when
that
e
=
1,
and the smallest value when
e
=
Then the
largest value of k
is,
(A23)
is
attained
A. Using this knowledge as well as the market
clearing condition leads to:
7rafc(l)
< A
(A24)
>
(A25)
u;-c(A;(l))
7rafc(A)
w-
c(fc(A))
27
1
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"n
I
i,
0^
i5 ate
Due
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