B31
/^EVWEV
01
M415
working paper
department
of
economics
EMERGING MARKET CRISES:
AN ASSET MARKETS PERSPECTIVE
Ricardo J. Caballero
Arvind Krishnamurthy
No. 99-23
October, 1999
massachusetts
institute of
techinology
50 memorial drive
Cambridge, mass. 02139
WORKING PAPER
DEPARTMENT
OF ECONOMICS
EMERGING MARKET CRISES:
AN ASSET MARKETS PERSPECTIVE
Ricardo J, Caballero
Arvind Krishnamurthy
No. 99-23
October, 1999
MASSACHUSEHS
INSTITUTE OF
TECHNOLOGY
MEMORIAL DRIVE
CAMBRIDGE, MASS. 02142
50
Emerging Market
An
Ricardo
Crises:
Asset Markets Perspective
J.
Arvind Krishnamurthy*
Caballero
This draft: October 08, 1999
Abstract
The whole
sharp
between a mild downturn and a deep
difference
fire sales
of domestic assets
in the balance sheets of
We
Why
and how do
we argue that a poor contractual
build a stylized model that explains the dramatic short run shift
in the interest parity condition
international collateral.
weak domestic
sector.
a parsimonious account of these and related phenomena present in
offers
emerging markets.
and the ensuing collapse
doesn't the private sector take appropriate precautions
to avoid the dear consequences of crises? In this paper
environment
rates,
both the financial and non-financial
And why
such crises materialize?
and possibly exchange
the occurrence of
crisis is
The
collateral, or
—or
—
fire sale
in terms of the
weakening of a country's
lack of precautions, on the other hand,
is
a consequence of
underdeveloped domestic financial markets, which drive a
wedge between the private and
social valuation of assets appealing to foreign investors.
Moreover, domestic banks are the mechanism by which firms with purely domestic
collateral are able to access international markets. Thus, the banks'
endogenous collapse
as domestic assets depreciate, sharply reduces access to international financial markets
and
may
in so doing
Keywords:
trigger a feedback process with multiple equilibria features.
Capital flows,
fire sales,
financial constraints, contractual
and corporate
governance problems, balance sheets, wasted collateral, domestic and foreign spreads,
excessive leverage, collateral underprovision, real depreciation, banks.
'Respectively:
MIT and NBER;
Northwestern University.
Bhagwan Chowdhry, Bcngt Holmstrom, Andres
tional
the
for financial support,
was accomplished,
First draft:
EFG-NBER meetings, WFA meetings, the CEPR
LACEA/UTDT Summer Camp in Interna-
Financial Markets (Gerzensee), and the
Economics and Finance (Buenos Aires)
NSF
thank Daron Acemoglu, V.V. Chari,
Velasco, Luigi Zingales and seminar participants at the Fed
(Board of Governors), Harvard, IMF, MIT, Northwestern,
Summer Symposium on
We
for their
August 1998.
for their
comments and
suggestions. Ricardo Caballero thanks
and the AEI and Research Department at the IMF, where part of
this
work
hospitaUty and support. E-mails: caball@mit.edu, a-krishnamurthy@nwu.edu.
Digitized by the Internet Archive
in
2011 with funding from
Boston Library Consortium IVIember Libraries
http://www.archive.org/details/emergingmarketcrOOcaba
Introduction
1
Following the recent experiences in emerging markets, the merits of an open capital account
are once again being called into question.
inflows
Weighed against the obvious
the specter of capital market instability.
is
was dramatically worsened by the reluctance
internal
and external demand
fell,
in
East Asian countries
of international investors to provide the re-
smooth the impact of a combination of
sources needed to
As
The downturn
benefits of sustained
and external
internal
—and capital flows
external credit
in general
many
leading
and currency depreciations took unexpected proportions,
asset deflation
observers to assert that [the declines were] "well beyond
by any reasonable reassessment of economic fundamentals, even
(IMF World Economic Outlook, May
The
— van-
As symptoms
ished, bringing the real sector, especially nontradeables, to a virtual halt.^
and consequences,
deficiencies.
what was
justifled
in the light of the crisis."
1998, p.4.)
emphasis from problems of the current account to those of the capital ac-
shift in
count has led to a rethinking of the traditional "goods markets" view of external
A
misaligned real exchange rate
ternal imbalance
imbalances.
and
is
no longer the central element in understanding an ex-
in guiding policy responses to avert
Although certainly an important factor
economy, this relative price ingredient
asset prices
and
is
and
we
in the long
- a
run readjustment of an
and our
link which, in our view,
movements
is
in
at the core
ability to control them.^
present an "asset markets" view of external crises, in which asset values
their feedback into real activity take center stage.
financial links,
harmful consequences of these
often subordinate to the short run
their feedback into real activity
of understanding the magnitude of crises
In this paper
crises.
We
show that weak international
when combined with underdeveloped domestic
financial markets, provide a
parsimonious account of the chief features of systemic crises and the scenarios where they
develop.
The paper proceeds
• First,
'For the
we provide a
first
round of
in three steps:
framework that captures the main features of
stylized
crisis-countries
was probably higher
since "errors
and
— Indonesia, Korea, Malaysia, the Phihppines and Thailand — net
capital flows declined from 73 billion dollars in 1996 to
inflows
real
minus
11 billions in 1997.
and omissions" went from
The
-8.5 billions in
actual decline in net
1996 to -19.5 billions in
1997.
^The
literatures
on debt
crises,
currency speculation, and bank-runs, offer important insights on different
aspects of assets markets during crises.
more
likely
by the issues we emphasize
Most of the
effects in these literatures are either
in this paper.
For papers on currency speculation
(1994, 1996); on debt crises see, e.g., Calvo (1988), Giavazzi
amphfied or made
see, e.g.,
Obstfeld
and Pagano (1990), Cole and Kehoe (1996);
on bank runs see the canonical Diamond and Dybvig (1983) and the apphcations to open economies by
Goldfajn and Valdes (1998) and Chang and Velasco (1998a).
interesting discussion
Also see Calvo (1998) for an overview and
on implications and sources of capital market
crises in small
open economies.
financial variables during a crisis.
A
weakening of international financial
links
-
represented in our model as a small negative shock to international collateral- can
lead to
falls in
asset prices
below fundamentals and contractions
The
in real activity.
response of the economy to these shocks can be very non-linear depending on the
condition of the aggregate balance sheet of the country.
•
We move
on to develop the dynamic implications of our framework and arrive at our
main conceptual
oped domestic
collateral
result.
financial
We
show that domestic agents
markets
—represented
in
in
economies with underdevel-
our model as a scarcity of domestic
— systematically underestimate the social value of their access to interna-
tional capital markets.
As a
and experience more costly
framework
• Finally, the
is
result, these
economies arrive to downturns unprepared,
crises.
enriched to include a banking system, as banks have played
We
central roles in recent emerging markets crises.
show that the
fall in
asset prices
can compromise the banks' balance sheets, resulting in a domestic "credit crunch"
which amplifies the shock to international
collateral
and brings about the
possibility
of multiple equilibria.
An
emerging economy, almost by
resources to carry on with
as the
inadequacy
its
normal
definition,
activities.
is
one which requires substantial foreign
Weak international
financial links, reflected
on
(real or perceived) of a country's international collateral, place limits
the country's ability to acquire international financing.^
During
crises, as triggered
by a
decline in terms of trade or a tightening in international financial markets, the country's
international collateral proves inadequate to finance normal operations.
Domestic
firms,
needing foreign funds, willingly exchange domestic assets for international collateral at
sale prices."*
Domestic
interest rates surge, not to
increased default probability, as
first
form concept
myriad
for higher
for
expected inflation or an
and second generation models would have
ration the scarce international collateral.^
on, as well as the
compensate
Our quote from the IMF's
WEO
'Witness current account
expect
By
if
it,
but to
(1998) earlier
stories of sharp declines in "risk-appetite" (a practitioners'
reduced
expected return) in the aftermath of systemic crises in emerging
markets, seem to provide widespread support for this central implication.^
may
fire
deficits of at largest
15%
of
GDP
as opposed to the
150%
The meltdown
of
GDP
that one
capital markets were fully integrated. See Kletzer (1988) for a similar argument.
a fire sale,
we mean a
similar to that in Shleifer
decline in the price of an asset
and Vishny
beyond
(1993), although in our
its
fundamentals. This definition
model the
fire sale
price
is
determined
is
in
equilibrium rather than by the exogenous bidding price of an inferior user.
''The modeling choices highlight this rationing aspect of the rise in interest rates.
believe that devaluation
This
is
Though, we certainly
and default expectations are important factors as well.
first and second generation models are not important,
not to argue that the insights of so called
and aggregate
of balance-sheets
firms
—
those with limited international collateral
i.e.
nontradeables sectors and small
activity, especially in the
While shortages of international
collateral
—
is
just another facet of this process.
can characterize
crises,
the incidence of these
shortages arises from underdeveloped domestic financial markets, which reflect the inad-
equacy
domestic
(real or perceived) of
domestic collateral creates
Insufficient
collateral.
a spread between the internal rate of return on a good project in the economy and the
rate of return that can be credibly promised to outside domestic financiers.
tic
spread
is
just the dual of
an
This domes-
domestic capital allocation process - or poor
inefficient
In a dynamic setting, the domestic spread leads
collateral aggregation in our language.
The reasoning
is
a shortage of international collateral, abating
it
to an undervaluation of international collateral that exacerbates crises.
straightforward. Since in a crisis there
is
requires an ex-ante decision to carry an extra unit of international collateral into the crisis.
However, doing so provides the holder
collateral -in fact, the shortfall
is
less
than the
full social
return on this international
proportional to the domestic spread. Anticipation of this
reduces the private sector's incentive to accumulate and provision international collateral.
The
fragility resulting
We
costly.^
show that
from such under-accumulation, or over-leverage, makes
this inefficiency
is
due to a pecuniary externality. Thus,
efficiency in domestic financial markets, rather
links alone, that
may
justify capital controls
crises
it is
more
the in-
than the weakness in international financial
and equivalent measures.^
In emerging markets, liquid domestic debt markets are the exception rather than the
rule. Invariably, the financial
system
is
bank based. Banks
issue claims to foreign investors
against balance sheets that are partially backed by international collateral, and lend domestically to those that
do not have direct access to international market. This brings a third
but to highlight a significant difference between "solvency" type models where interest rate "arbitrage" holds
and models where
it
does not, as
Tirole (1998b). Note that
class, since
return
is
is
the case in ours or in Shleifer and Vishny (1997), or Holmstrom and
Diamond-Dybvig
type models also belong to the solvency-arbitrage
"illiquidity"
the real costs of the run validate the run, by which
fair in
the bad equilibrium as well.
Later on
we
it is
often
meant that the equilibrium required
discuss the natural complementarities between
these two classes of models.
^Alternatively,
shocks
may be
if
domestic financial markets are extremely primitive, volatility costs due to external
replaced by depressed growth and over-exposure to domestic shocks as the economy
to aggregate internal resources
and use
its
international collateral. Similarly,
limited to start with, international leverage disappears and with
shocks.
We
do not emphasize these cases as our purpose
than stagnation and traditional domestic business
financial fragihty arises
cycles.
is
it
if
is
international collateral
unable
is
very
so does volatility with respect to external
to emphasize crises in
Also, see
Aghion
open economies rather
et al (1998), for a
model where
from the mechanics of debt accumulation rather than from the undervaluation of
collateral provision. Interestingly, they also find that
growth
volatility
is
maximized
for
intermediate levels
is
also central to the
of financial development.
In Caballero and Krishnamurthy (1999)
debate on the virtues and
we argue that
pitfalls of alternative
this simple observation
exchange rate systems.
balance sheet
tion.
in
—that of the banking system— into
As the country
faces
an international
crisis
tiie story,
and
and with
further amphfica-
it
asset prices collapse, the deterioration
banks' balance sheets limits their ability to intermediate foreign funds into the domestic
system, further deepening the
crisis,
and so
on. If this feedback
is
strong enough, the size
depends on the extent of pessimism, as the model exhibits multiple
of the crisis
The framework we
equilibria.
use gives central roles to credit market constraints arising from mi-
croeconomic contractual problems in the process of creation and aggregation of international
collateral.^
There
are, in principle,
many factors behind the
incomplete development of both
domestic and international financial links in emerging economies, ranging from macroeco-
nomic and
political instability to
Our model emphasizes the
weak corporate governance and contractual environment.
both because they are
latter factors
less well
understood within
the context of sovereign risk and because their importance has been heightened by the
recent Asian
crisis.
Relation to the literature.
opment
of
The Latin American debt
crisis of
the 1980s led to the devel-
of formal models of sovereign debt renegotiation, which posed the central question
what can international lenders threaten sovereign countries with
fault (see
Eaton and Gersovitz (1981), Bulow and Rogoff
in the event of a de-
(1989)). This
is
closely related to
our identification of international collateral. Since in this literature default and
its
costs are
mostly modeled as a country-wide phenomenon, the question immediately arises on whether
the domestic private sector internalizes the effect of their actions on the likelihood of these
events.
Bardhan
(1967), Harberger (1985)
and Aizenman (1989) advocated taxing capital
flows on the grounds that individual agents do not
pay
for the increase in a country's aver-
age cost of capital brought about by their international indebtedness. While our results on
collateral underprovision are related to theirs, our externality
stems from
imperfections in the domestic financial system rather than from the country's
monopsony
capital flows
power
and
in international financial martkets or
any sovereign
Although we touch on many of the insights of the
eling
and conceptual
^According to the
differences with
IMF
it
are large.
On
constraint.-^"
debt-crisis literature,
both our mod-
these aspects, our approach
(1998, pp. 63-64), a distinguishing characteristic of the Asian crisis
macroeconomic considerations played a
lesser role
than
in previous crises. Also, see
Johnson, ct
is
contractual environment) in an
economy and the incidence
of the current crisis.
more
that purely
al.
evidence on the correlation between weak corporate governance and institutional environment
is
(1998) for
(i.e.
a weak
As the corporate finance
hterature has demonstrated, weak corporate governance and, more generally, weak contractual enforcement
go hand in hand with credit market constraints.
'"Similarly, our policy
recommendation
to increase collateral availability
ment
in the
is
— while not
its
origin
—
in favor of subsidizing the tradable sector
akin to Borensztein and Ghosh's (1989) advocacy for subsidizing invest-
export sector. See Fernandez-Arias and Lombardo (1998) for a recent model of sovereign risk
and overborrowing.
closely related to the
new
literature
and Moore (1997) place the
on the
role of collateral in
collateral role of a fixed input
macroeconomics. Kiyotaki
—land— and
its
distribution
across agents at the center of their amplification mechanism.^ ^ Krishnamurthy (1998) shows
how a
richer set of contracts than that allowed
by Kiyotaki and Moore
shifts the relevant
constraint from that which applies to individual agents to the total availability of collateral
in the
Holmstrom and
economy.
Tirole (1998a) argue that the stock market alone
provide insufficient collective collateral
if
They
not aggregated properly.
even when wasted corporate collateral (liquidity)
is
also
may
show that
not an issue, public supply of
it
may
be
required in the presence of large shocks.
In terms of our modeling choices, our paper
canonical model of liquidity, and particularly to
model
As
in the context of firms.
is
related to
Diamond and Dybvig's
Holmstrom and
in that paper, firms in
Tirole's departure
(1983)
from
this
our economy receive a production
shock that they must cope with by mortgaging collateral in order to borrow additional
The
fimds.
Analogously, firms in the model of Holmstrom- Tirole can borrow funds either
investors.
from other firms
the
first
can be obtained from other domestic firms or directly from international
latter
in the corporate sector or directly
and
efficiency of the second transaction.
transactions encounter frictions in our model.
on
many
differences in terms of substance
Indeed, and
more
In contrast, both
generally, while there
and modeling aspects with each of the
articles
and macroeconomics mentioned above, our central theoretical departure with
collateral
them
Intermediation renders
transaction frictionless in Holmstrom-Tirole and their macroeconomic analysis
focuses on the implementation
are
from savers.
as a group
is
our focus on the presence of two collateral constraints
an international one
— and
Our underprovision
their rich static as well as
dynamic
—a domestic and
interactions.
of collateral results are analogous to the free rider problems
and un-
derprovision of liquidity studied in the banking literature (see Jacklin (1987), Bhattacharya
and Gale
model
is
However, the source of the externality behind
(1987)).
this inefficiency in
our
the endogenous result of imperfect contract laws and institutions, while theirs
the exogenous divergent ex-post valuation of liquidity by consumers.
from these models
is
A
is
second departure
our focus on markets rather than on banking arrangements and their
key sequential servicing constraint. While we do believe that bank failures and runs can
aggravate
of crises
crises, as
and
we
discuss in section 4, our
their prelude arise even
ply liquidity. Moreover, the
fire sale
model points out that the basic features
when no agent
or institution
is
committed to sup-
mechanism we emphasize boosts and
feeds from the
likelihood of banking crises themselves.
Outline.
Section 2 follows this introduction with a description of the basic model and
See Bernanke et
nomics.
al (1999) for
a thorough survey of the literature on credit constraints and macroeco-
weak connections with international
discusses the aggregate implications of
kets. Section 3 highlights the implicit transactions in collateral aggregation,
frictions in
financial
mar-
and introduces
domestic financial markets. Banks as collateral aggregators and as a source of
amphfication and multiple equilibria are discussed in section
4.
Section 5 concludes, and
is
followed by an appendix.
A
2
Time-to-build model with limited international collat-
eral
In our view, there are two central ingredients behind the recurrent crises affecting emerging
economies: weak international financial links and underdeveloped domestic financial mar-
We
kets.
start
with a discussion of the
ingredient in isolation, while the next section
first
brings into the analysis frictions in domestic financial markets.
The Economy
2.1
Our goal
Time.
in this section
is
to highlight the consequences of suffering insufficient
(perceived) international collateral during crises, as well as to understand motives for un-
dertaking precautionary measures in anticipation of more stringent international financial
conditions.
lem
in
Our timing assumptions
are designed to capture these two aspects of the prob-
a minimalist framework.
The world
flexible period
and portfolio
lasts three periods.
when economic
allocations.
shift resources
indexed as
t
=
0,1,2.
Date
is
the fully
agents design the productive structure, ownership structure,
Date
when
Heterogeneity
cial frictions.
is
1 is
the
crisis
period,
when economic
agents struggle to
from the future to cope with shocks in the present. Date 2 represents the
unconstrained future,
Agents.
Time
the economy
among
agents
is
is
(relatively) rich in resources.
required to understand the consequences of finan-
We have two dimensions of heterogeneity:
consumers and foreign
financiers,
The domestic economy
is
one between domestic entrepreneurs-
and another one among domestic entrepreneurs.
populated by a continuum of unit measure of agents with
Cobb-Douglas preferences over date 2 consumption,
u''
where,
ct is
(ctc„)l/^
consumption of tradeable (T) goods at date 2 and c„
tradeables (N) at date
N-goods as
=
e.
By
2.
We
is
consumption of non-
denote the date 2 real exchange rate of T-goods in units of
specifying preferences over date 2 consumption only,
we remove from
our analysis standard intertemporal substitution and smoothing arguments which are not
central to our approach.
The
world
rest of the
is
represented by foreign investors
consumption of tradeable goods at
The
=
Ct,0
+ Ct^l + Ct,2may be
contrast with domestic agents arises because foreign investors
supply tradeable goods in the date
They have
period.
called
period as well as during the date
1 crisis
endowments of T-goods
large
preferences over
dates,
all
u^
who have
at all dates.
pre-crisis
we assume
Additionally,
down
that they do not discount the future so that the preference structure pins
on to
the gross
international interest rate at one.
At date
Endowments and production.
0,
ex-ante homogenous domestic agents are endowed
with resources of wq T-goods which can be invested or stored.
resources by taking on foreign debt of doj
has a time-to-build aspect. Investments are
at date
Let
2.
fc„
and
the firms in the N-sector
N-goods at date
of
be
offset
realize
2.
is
The
fc„
+ kt
make saving
T-sector
is
<
l
in
both
N
»
Rail
in
-
manner -
of production units
shocks to the N-sectors.
is
1,
realized
and
T
at
kt requires
a fraction
1
—p
of.
A„ =
/?„
— r„ >
0,
which can
we assume
result in substantial additional
Production per unit of capital in the
critical link
1
below.
between financing and production
any economy have ongoing capital needs (working
is
our
down production
crisis.
The dual
many
capital, etc.).
units in a potentially
of this shutting
that the marginal value of capital during a crisis
implication of our modeling underlies
is
down
very high. This
of the key results in the paper.
'^Nonetheless, there are a few interesting peripheral issues that arise once the T-sector
idiosyncratic shocks. For example, a Kiyotaki
that,
p)
illustrated in figure
to anticipate results, this
is
At date
N
and
fc„
is
-tMiKn-
and T-sectors does not
Starving firms of capital has the effect of shutting
wasteful
creating capital of
= Vn + ^n"n)kn ^
simply Rt-^^ The time-line
Firms
Then
distressed production units sufficiently profitable,
restrict these
crisis.
and output
of kn, in units of the tradeable good, in order to
This time-to-build structure underlines a
during a
1,
of:
Because having shocks
we
0.
rest experience a productivity fall,
A„
insights,
Production
this shortly.
spared of further investment and go on to produce Rnkn units
Rniynjkn
In order to
and
at dates
units of tradeable goods.
by reinvesting a fraction On
output at date 2
made
inherited from date
1,
investment totaling
a date
expand on
shall
increase these
denote the total amount of capital devoted to sectors
kt
the beginning of date
we
-
They can
and Moore (1997) type multiplier may
arise.
is
subject to
The domestic economy
have no tradable goods at date
will
1
to contribute
and
capital
needs can only be accommodated by an increase in imports. In order to finance this increase,
domestics must access international capital markets.
DateO
Date
—I
Date 2
1
+
Borrowing
+
Repayment
Consumption
Crisis
Investment
Budget Constraint:
Date
T-Production:
do
f
+ Wo =
+
k„
k,
k,
>
R,k,
^
Rnkn
N- Production: Time-to-build
(INTACT)
k„
Prob = p
(DISTRESSEDT'
Need
rnkn+ A„0„
additional investment of
e„ k„
Our assumptions on
with capital of
this
kt
1
:
K
Time Line
Foreign investors extend finance only with the security of col-
Collateral Constraints.
lateral.^"*
= RnOn)
T-goods
Figure
k„
collateral are two- fold. First, a firm in the tradeable sector
We
expects output at date 2 of Rtkt-
assume that only a fraction
Aj of
output can be valued and seized by foreigners in default.^' Second, we assume that
foreigners can only value
collateral to foreigners.
and
seize
output of the T-sector, while the N-sector provides no
Thus, the quantity XtRt^t constitutes the international collateral
of the economy.
Almost by
however the
definition,
an emerging economy
is
ability to access international capital
in
which project returns are high,
low.
These features are captvired by
one
is
assuming that,
Rt
This collateral
'"We appeal
to
justification of the
may be
>
but
1
explicit or implicit, as
agency conflicts
in
making
XtRt
<
1.
the case in a surplus-sharing bargaining equilibrium.
is
this "high-level" assumption.
assumption based on costly state
verification. It
is
See the appendix for a deeper
costly for a foreign investor to verify
and liquidate the output of Rtkt- This implies that only a fraction of the output can be used as
Also, see
La Porta
et al.
managers from
collateral.
(1998) for worldwide evidence on the high positive correlation between corporate
governance problems and ownership concentration
to prevent
(1)
(in their interpretation,
stealing).
8
higher concentration
is
needed
While the capital market has weak international
that the domestic capital market
N
of output in both
is
for
domestic
with A„
collateral,
The asymmetric
the rest of the world.
valuation of goods
full
value
XnRn^n
of this output constitutes
1.
collateral constraint identifies the domestic
Much of the
economy
as distinct
from
international economics literature assumes an' asymmetric
—foreigners only value T-goods, while domestics value both T and N-
In contrast, the collateral restriction
goods.
until the next section
example, a firm in the N-sector with capital of
kn (at date 1) expects output at date 2 of Rnkn- Then,
=
we assume
Residents accept as collateral the
frictionless.
and T-sectors. Thus,
links,
is
that domestic residents extend finance to
either tradeable or nontradeable firms, while foreigners accept as collateral only claims
the tradeable sector.^^
It is
on
important to point out that this assumption does not correspond
to the empirical restriction that
we should only observe
foreign credit extended to firms in
the T-sector. In our model, foreigners are willing to hold claims on the N-sector but only
as long as their
market
is
"liquid, " in the sense that there are
to allow an instantaneous trade.
1,
The
in a crisis state, they will always
restriction implied
swap these
for claims
enough claims
by the assumption
in the T-sector
is
that at date
on the T-sector with a party that
does value N-claims ("residents").
The
international economics literature has long recognized the importance of interna-
tional collateral
and
its
Formal models of
relation with a country's tradeable sector.^^
sovereign debt renegotiation are built around the question of what international lenders can
threaten sovereign countries with in the event of a default (see Eaton and Gersovitz (1981),
Bulow and Rogoff
In this literature, international collateral
(1989)).
is
typically taken to
be some fraction of exports.
While similar
in spirit to this identification, our
than aggregate. Liquidation and seizure of output
foreigners than
For instance,
they make
crisis,
that
it
when
it
it is
it is
by the
fact that cash revenues
back into the country.
received.
revenues were
In
many
'^See, e.g.,
N
is
harder for
disadvantage disappears.
from exports can be seized before
part of the collateral backing the liquidity package
instances the bias
first
is
directly justified
principles
sector to be infinite for foreigners, while
Simonsen (1985).
microeconomic rather
This feature was used by Mexico during the 94-95
made
'^This assumption can be justified from
output in the
is
in the non-tradeable sector
for domestics, while in the tradeable sector this
justified
its oil
assumption
by mandates on foreign
by taking the cost of verifying and liquidating
it is finite
for domestics.
on
institutional investors (e.g. limits
Alternatively, this assumption
cations of an
an
is
expanded model where
ment
and Krishnamurthy
is
only against a fraction of
affect the
sector.
times." In the churn of any economy, there are
Thus, there
is
(see
an
economy
at date 1
and take two
an idiosyncratic shock that demands reinvest-
is
N
p of the firms in the
resources than others.
to capture the central impli-
(1998)).^^
Shocks
we described above, there
in a fraction
mechanism
foreigners' collateral-bias
Aggregate and idiosyncratic shocks.
forms. First, as
efficient
^^
and current production of perishable nontradeable goods
firms -in either sectorearlier draft, Caballero
real estate investments).^^'
The
idiosyncratic shock reflects "normal
some production
units which require
more
a constant need to attract and reallocate resources
from some production units to others.
Second, we introduce an external shock at date
1
that affects, in the aggregate, the
economy's ability to attract resources from foreign investors. XtRth represents international
collateral
LJ
with respect to foreign investors. There are two states of the world at date
e {B,G},
differentiated
by a low amount of international
That
of international collateral.
collateral
1,
and a high amount
is,
X^
R^
<
kt
Xt
Rt
kt
Shocks to international collateral can, in principle, arise either as a shock to Rt or a shock to
Af.
Terms
capital
of trade shocks are declines in Rt, while a shortage in the supply of international
a decline in Aj.^"
is
To
simplify the exposition,
'^Of course there are important exceptions
(e.g.
"too big to
we
focus only on shocks to At. In
fail" utilities),
but
see, e.g.,
Kang and
Stulz
(1997) for systematic Japanese evidence showing that, for small firms, those that are export oriented are
favored by foreign investors.
See, e.g.
Blommestein (1997),
for a discussion of
how
real estate
assets considered highly illiquid or exposed to exchange risk are generally avoided (sometimes
by foreign institutional investors.
rating, are for
is
crisis
sector.
by the World Bank, describes firms that borrow in
foreign currency as "predominantly large exporting firms with ties to foreign companies,
of those firms that
crisis..."
borrow
(box
4.3,
page
62).
The 1997
The same
in foreign currency, 88 percent export,
statistics for firms that
do not borrow
and they have
Industrial Survey in Thailand reflected that
have an average of 818 employees, a debt-
equity ratio of 3.12, a relatively high capacity utilization and optimism during the
respectively.
by
bounded from above by that country's
companies which belong to the export
"'The September 1998 report on the Asian
better adjusted to the
by mandate)
Interestingly, the very few exceptions to the sovereignty principle,
which the rating on debt issued by a country's corporate sector
government debt
and other
in foreign
crisis,
70 and 37 percent
currency (75 percent of firms) are:
46 percent, 139 employees, 2.36, 61 percent and 19 percent. See Dollar and Hallward-Dreimeier (1998).
'^There
1991),
is
an extensive literature documenting "home bias" in asset holdings
matched by asymmetric information explanations
reasons behind
home
bias, as
Zhou
(see, e.g.,
1998).
French and Poterba
There are also institutional
most countries hmit foreign ownership of domestic companies. These
range from constraints on a few "strategic" sectors
(e.g.
across-the-board constraints, as in pre-crisis Korea.
^°A
(see e.g.
"collateral squeeze" versus a "credit crunch."
10
oil
and telecommunications),
limits
as in the U.S., to
fact,
any shock to international
Firms can
Financial structure.
We
foreign investors.
either
by domestic
Since
free,
we can
likely to
is
be a combination of these two shocks.
and date
raise finance at date
assume that
all
1
from either domestic or
finance must be default free and fully collateralized
-
collateral in the case of domestics, or international collateral in the case
of foreign investors.
contracts.
collateral
all
Without
loss of generality, this allows us to focus
firms are
homogeneous
will involve
free debt
and since debt contracts are default
at date
borrowing from foreign investors.
also restrict attention to date
borrowing between domestics
on default
no net transfers
at either date
Any
date
or at a later date
and can therefore be ignored.^^
Balance Sheets and Financial Contracts
2.2
Balance
Each entrepreneur has a firm
sheets.
in
each sector. While he can issue claims
separately on each firm, the entreprenem: consolidates their financial resources in case of
We
distress.
firms at date
Date
start our characterization of equilibrium
1,
and by highlighting
their
dependence on asset prices and exchange
decisions result in firms arriving at date 1 with installed capital of kn
foreign debt of doj.
At date
that escapes the shock
is
1,
intact
a firm that receives a shock
The balance
(I).
kn and foreign debt of doj. However, not
value.
by studying the balance sheets of
On
all
is
and
rates.
and
kt
distressed (S), while a firm
sheet of an intact firm has assets oikt and
of these assets have international collateral
one hand, incentive constraints determine that only a fraction At of the shares
On
of kt are internationally pledgeable.
the other, shares of
/c„
possibly
may be
converted
domestically into international collateral at a discount. LetL'^ be the market gross interest
rate applied to a -collateralized- claim
world
Date
u!.
2 output of
^^^
on one unit of N-goods
can be exchanged at date
at date 2, in state of the
1 for
^^
units of date
T-
1
goods, or equivalently, claims on date 2 T-goods. Then, the international collateral value
of the assets of this firm
is,
XtRtkt
The debt
of this firm with respect to foreigners
of the intact firm as the difference between
<it
The
+
=
>^rRtkt
its
+
^.
is
dgj. Hence
assets
and
we can
define the equity value
liabilities, in
terms of T-goods, as
^-doj.
(2)
condition of balance sheets play a more central role for distressed firms, since
determines their debt capacity (and from
This assumption
among domestic
is
relaxed in section 4
now we
use these terms interchangeably).
when we introduce domestic banks and
agents.
11
it
A
therefore lose homogeneity
distressed firm suffers a production shock that requires
goods
in order to attain
units of N-goods at date
Rnkn
The debt
the firm realizes a lower output of Rn{dn)kn-
Qs
-\
+
i^tt-t
it
2.
to reinvest resources of
Investing 6nf^n
<
fcn
capacity of such a firm
compromise balance
As we show below,
reinvestment for the distressed firm at date
Debt contracts.
Lenders at date
do not know
and therefore
if
a firm will be distressed or intact.
1 is
non- verifiable. Thus lenders
on being distressed or
intact.
Purely for
simplifying asstmiption that debt contracts are also not
written contingent on the aggregate shock
when
appendix, are preserved even
collateral
inter-
1.
are unable to write debt contracts contingent
we make a
N
High
this translates directly into constrained
Moreover, the realization of the idiosyncratic shock at date
expositional purposes,
is:
[i]
exchange rates decrease the value of
sheets.
T-
means that
do,/-
^^^^
This expression hints at the sensitivity of balance sheets to asset prices.
est rates or depreciated
A:„
— in
fact,
most of our
results, as
we show
in the
contracts are fully contingent. Lenders impose the no
default constraint that,
This ensures that firms always have sufficient resources to repay debts at date
no reinvestment takes place. Debt
levels
above
this
1
even
if
Hmit introduce considerations of debt
overhang and bankruptcy costs which, while relevant and interesting, are not central to our
main concerns. ^^
The
than
foreign debt constraint requires that (worst-outcome) marketable assets be greater
liabilities.
N-assets. This
It is
is
important to note that these marketable assets includes both T- and
the sense in which the collateral assumption that
imply that foreign credit
2.3
Date
its
will only
we have made does not
be extended to T-firms.
Microeconomic Decisions and Equilibrium
1
Consider the problem of a distressed firm in raising funds to alleviate
problem.
production shock.
A
choice of O^kn will result in output at date 2 oi
Rn{6n)kn N-goods. Sincc
T-goods
e'^ is
the real exchange rate at date
2,
Rth T-goods and
the value of this output in
is,
This constraint
is
tighter
than
it
needs to be since the firm in principle could borrow against the
pledgeable component of the reinvestment option.
since even the tighter constraint
is
non-binding
in
Absent renegotiation,
equilibrium (see below).
12
this omission is not
important
In order to retool a fraction
T-goods.
ff^kji
can do
It
collateral at date 1 that
it
6"^
of the distressed unit, the firm must raise finance and reinvest
this in
two ways.
may have some
First, the firm
can use to borrow directly from foreigners. That
international
is
the firm can
always raise directly,
</ <
The
latter quantity
can raise at date
1.
The
rest
must come from
distressed firm can use
intact firms.
doj.
always positive (see below), and represents the
is
investors since their capacity to
A
-
>^tRth
intact firms,
borrow abroad at date
its
minimum
that a firm
which also have access to foreign
also
1 is
X^Rtkt
—
doj.
N-collateral to access the international collateral of the
>
In equilibrium, the latter discount the N-collateral at a rate of L'^
providing international collateral. Through this "credit chain," the distressed firm
to aggregate the international collateral of the
raise resources for date 1 reinvestment. Let d-^ j:
debt
(in imits of
y-
=
s.t.
{i)
max,^,<i^^^,<i^_^
(z)
is
the foreign and domestic
1.
We
can then write the
+ ^^^^S^-doj-dlf-d-,,
= X^Rth - doj + "^j^lil"" > dlf + §f
(ts
6^^K = dl^ + %i
{ii) reflects
resources received by the firm at date
is
this to foreigners to
1.
a balance sheet constraint (net marketable assets greater than
while constraint
able
R^kt
K<
iiii)
liabilities),
d'^^ represent
in
as,
(ii)
Constraint
and
T-goods) contracted by a distressed firm at date
problem of a distressed firm
(PI)
economy and pledge
is
1
that
1 in
new investment must be
fully
new
paid with the
taking on debts of d^y and d^^. Constraint {in)
purely technological.
An
intact firm at date
distressed firm.
1
has only one decision:
Suppose that the firm accepts claims at date
T-goods) in return
for
making a date
1
contribution of ^if
=max,^_^
Vr
(P2)
R^kt
problem.
At date
either distressed or intact,
Thus the
decision at date
(P3)
0,
+
X^Rtkt
s.t.
Date
how much
,
1
oixid
(face value of date 2
^+x^-^
- doj - 5r >
1
can expect to find
is,
s.t.
E.E{G,B} ^'^ipVs^
doj
kn
extend to the
itself as
good or the bad aggregate state of the world.
in either the
maxfc„,fc,,rf„^
it
then,
a firm looking forward to date
and
finance will
<
+
min^{X'^ Rth
+ kt = Wo + doj.
13
(1
+
-
pWH
^}
where
vr'^
represents the probabiUty that state
Market clearing
Equilibrium.
uj
occurs.
domestic debt market at date
in the
1
(capital letters
denote aggregate quantities) requires that the aggregate amount of domestic debt taken on
by distressed firms
is
fully
funded by intact firms:
^M
= P<d
Therefore, market clearing,
Dla = Xr,„
determines the gross discount rate
The
real
exchange rate at date
(4)
L'^.
2, e'^, is
determined by goods-market clearing at date
2.
Given the Cobb-Douglas preference structure, the exchange rate only depends on aggregate
consumption. The
first
order condition for a representative consumer yields,
e^
= 9^,
c:
(5)
with
G;:
An
=
{Rn
+ p^n{On "
economy
equilibrium of this
Cr = RtKt -
and
1))^-^-
and date
consists of date
1
pe';:Kn.
(contingent) decisions,
{kn,kt,doj) and {9';^,d'^j,d'^^a,d'^^a)^^^^'^\ respectively, and prices (e",L'^)'^s^'^'^>. Decisions are solutions to the firms' problems (PI), (P2),
market clearing conditions,
Crises
2.4
With the
and Fire
and
(4)
and (P3) given
prices,
(5), hold.
we can now
basic setup behind us,
1,
characterize crises.
as stated in (PI).
Consider the problem
Halting the productivity decline of a
production unit in the N-sector generates a date 2 return of
1
At these
Sales
of a distressed firm at date
date
prices.
A„
N-goods, but requires a
investment of one T-good. Since foreign lenders charge a gross interest rate of one
on collateralized loans, the firm
foreign lenders as long as
^
>
will
1
choose to pledge
and
6':^
<
l-
all
"
much
>
1
from
as possible
=>
e^
d^f
For financial requirements above this
lateral. Since foreigners
do not accept
=
level,
its
international collateral to
Our assumption that A„
allows us to focus on the case where saving distressed units
so that firms borrow as
of
is
>>
always profitable and
—
p)
^>
1,
foreigners:
min[kn, XI^Rth
-
d^j].
the firm has to mortgage
(6)
its
this collateral directly, distressed firms
14
Rn{l
domestic
col-
must borrow
from intact firms
in order to access foreign resources. In equilibrium, domestic collateral
discounted at the rate of 1/L^ so that the firm sets
as long as An/e'^
choice
> L^ and
<
0^!^
The
1.
firm
domestic debt as high as possible
its
the marginal product of investing for the firm
if
and debt
indifferent in its investment scale
is
is
is
equal to the domestic discount
rate:
<
<_d
However
>
(4?
if
the marginal product of investing
L'^), this
-
L"^ max[fc„
The
expression holds with equality.
0].
above the domestic discount rate
strictly
is
cally held international collateral, d^r, needs to
this,
d^f,
distressed firms'
demand
domesti-
for
be paired to intact firms' supply of
consider the problem of an intact firm at date
1,
The
as portrayed in (P2).
it.
For
firm lends
to the distressed firm at a gross interest rate of L'^. It accepts debt claims at date 2 with
x^^ and pays
face value of
solution to this problem
for this
equilibriimi value L'^,
l
^
determined by market clearing condition,
is
international collateral as long as L'^
is fiat
L =
at
Demand, on the other hand,
when reinvestment
mild
—and
is
1
is
>
and
-^. The
1.
=
(4).
Distressed
while intact firms supply
all their
Figure 2 portrays a simple supply and
demand
vertical
pdi^d-,
when
all
international collateral
is
used up.
mildly declining and equal to the marginal product
incomplete, and
less interesting
rate induced
gets from foreigners) of
xl^<XtRtkt-doj.
firms issue domestic debt claims totaling Di^d
diagram. Supply
it
straightforward:
is
L- =
The
with T-goods (which
— decline
falls
is
sharply as
full
reinvestment
due to the depreciation
by increased reinvestment. The sharp
decline,
fact that protecting the capital of financially distressed
is
financed.
in the long-run
on the other hand,
companies
is
A„/e
The
exchange
reflects the
a very high return
project.^^
The
figure illustrates
In panel
so there
is
Since did
two scenarios.
(a),
excess supply of international collateral in the domestic market
= max[A;„
—
{X^Rtkt
—
doj),
0],
we can
Having a menu of reinvestment opportunities
is
would certainly smooth the sharpness of the
that there are distinct times
when
-
=> L'^
for instance
decline.
But the
=
1.
1.
(7)
by having more heterogeneity among firms
essential point captured
slack rapidly runs out for a large
15
=
rewrite this condition as,
pKn < X^RtKt - Do J
-
and hence L'^
number
by our assumption
of companies.
Notice that the right hand side of this inequality
economy once date
collateral in the
is
the aggregate
amount
of international
We
foreign debts have been paid.
refer to this
constraint as the international collateral constraint.
L=
L=
L=
e
L=
1
1
I
I
'
1
e„=i
Panel
(a)
Figure
Panel (b) illustrates a
2:
:
firms, the latter
:
Supply Shortage
Equilibrium and the International Collateral Constraint
crisis of international collateral,
ceases to hold. In this case, there
interest rate rises
Panel (b)
Excess Supply
is
excess
demand
for
which occurs when condition
funds at date
1
(7)
and the domestic
above one. Moreover, as intact firms lend as much as they can to distressed
compete away
pKr,
all
borrower's surplus:
> X^RtKt - Do J
Let us define the international spread,
s'i,
1
(8)
as
s'^f=L'^Figure 3 illustrates that as the date
^L^ = ^.
1.
realization of A(
16
falls,
eventually the relevant
constraint shifts from (7) to (8)
For small aggregate shocks and
declines in Af, while
and the international spread jumps from zero to
richer specification.^^
demand
jump
in spreads
curve, the sharp nonUnearity
in all the countries involved in the Tequila,
Figure
dramatically
3: Interest
on financing. This
when
there
it
illustrates
is
would survive a
prices has occured
crises.^^
1
*
Rates and International Collateral
good realizations of At the supply of international
attractive terms
from
certainly due to the stylized
Asian and post-Russian
1
"''For
is
Without exception, the non-linear response of asset
L=
all
1.-'
critical level, a contraction in international collateral
causes spreads to blow up. While the abrupt
nature of our collateral
the economy does not suffer at
initial leverage,
beyond a certain
^—
collateral
fully protects their returns
is
plentiful
and borrowers get very
from re-investment. The situation changes
a shortage of international collateral, as credit
is
difficult to
obtain and
all
re-investment returns are transferred to domestic liquidity holders.
^°For instance, suppose there was heterogeneity in reinvestment opportunities
such that the demand curve was smoother.
is
plentiful, shifts in At willl result in
collateral
1
is
In the region where At
no changes
in short supply, shifts will result in
are used to either finance domestic
are sufficient funds,
are in short supply
it is
all
demand
in spreads.
much
is
(i.e.
heterogeneous A„)
high and international collateral
However, when At
is
low and international
bigger changes in spreads. Economically, funds at date
or to purchase tradeable goods (or assets) abroad.
the foreign interest rates which set domestic interest rates. However,
surplus shifts to suppliers and interest rates
on non-heterogeneous demand, heightens this contrast.
^^Without a surge in nominal interest rates, the fire sale
17
is
become very
reflected as a sharp
responsive.
When
there
when funds
Our assumption
exchange rate depreciation.
As the
international spread rises, domestic asset prices collapse. There
is
domestic assets because the domestic opportunity cost of holding these assets
credit
high
is
when
Foreigners are unable to capture these high returns because at times of
scarce.
is
afire sale of
they only hold and arbitrage claims backed by international collateral. While their
crises
arbitrage during normal times keeps the international spread at zero,
That
the international collateral constraint binds.
it is
immaterial
when
the interest-parity-condition shifts
is,
than international arbitrage, holds.
until domestic equilibrium, rather
Fire sales bring about a sharp decline in the balance sheets of distressed firms. In terms of
the program (PI), investment at date
1 is
no longer determined by technological constraints
but by the balance sheet constraint of (i). This
shortage of international resources
firms
—
the rise in
of their production shock, thus
all
L^
is
and competitive
Proposition
Proposition
occurs
In
1
when
=
summarizes the main
=
1.
Conversely, in the
- {XtRtKt - Doj)
results
be in
the international collateral constraint,
this case international
region
fire sales
is
made
(9)
.
upto this point:
The economy can
(Regions).
1
6'^
— are
collateral aggregation, so that
0;^K„
1.
distressed
simply the mechanism by which limited international collateral
consistent with full
bind.
When, pKn < X^RtKt — Dqj,
resolved.
is
the mechanism by which the aggregate
either directly, or through perfect aggregation of the intact firms' collateral
able to fund
1
shift is
one of two regions at date
pKn < X^RtKt — Dqj,
spreads are zero and there
is full
1.
Region
does not
project completion,
Q'1^
=
Region 2 occurs when the international collateral constraint does bind, in which case
international spreads
jump
to
^—
1
>
and distressed projects are downsized: 9t^Kn
=
\{XtRtKt-DoJ)<Kr^.
3
Underdeveloped Domestic
In this section
setup.
We
do
FinanciEil
we introduce underdeveloped domestic
this to
on international
study the date
1 effect
collateral provisioning.
the supply decisions at date
Markets
financial
markets into the previous
of poor domestic collateral on date
That
is,
we
isolate the effect of date 1
decisions
demand on
0.
Distressed firms use their domestic N-coUateral to aggregate the international collateral
in the
economy.
(domestically),
acteristic of
economy.
By assuming
that
we have rendered
of the output in the N-sector can be collateralized
this transaction frictionless.
an emerging economy
Weak
all
is
that
it
However an important char-
does not allocate capital efficiently within the
corporate governance or a weak domestic banking sector are as likely to
18
hinder domestic collateral aggregation as they are to limit the economy's access to foreign
capital. In this section,
ket not only amplify
we show that
and make more
collateral constraints into the domestic capital
mar-
costly the scenarios described above, but also create
pecuniary externalities which make crises more severe and likely than
is
socially optimal.
Basic Setup and Domestic Spreads
3.1
The environment described
in the previous sections needs to
accommodate weak domestic
at date 2
links.
A
firm in the N-sector with output oi
can pledge a fraction XnRnkn, with A„
order to receive financing.
We
be modified only slightly to
retain the
same
<
1,
Rnkn N-goods
as collateral to another domestic in
bias with regards to foreigners - they only
accept claims on the T-sector up to a fraction At of output.
Return to the balance sheet of a distressed
Balance Sheets.
firm, modified
domestic debt constraint. Since the firm can only pledge a fraction A^ of
balance sheet, or debt capacity,
q,
Its
date
1
-
K"
=max,^
s.t.
{{')
(u)
(iii)
The maximum amount
(i')
and
(ii)
is
+
At HtLt
N-output,
its
to:
(lUj
do,/-
jj^
+ ^%">*^ - do J - d^^ - d^^
(^ = XfRtkt - doj + ^"^jfp''" > d^f +
e^K = d^j + f^
Rtkt
0t
<
^
1
of reinvestment that the distressed firm can finance
with equality, and solving
^n^^
which
reduced
the
program must be modified accordingly:
(PI')
combining
is
its
now by
^
A„A„.
for
is
given by
6'^:
yn^th - doj + -J^f^nj
equal to the leverage ratio times the firm's debt capacity. Thus, as long
as,
Ari?tfct-rfoj>(l-^)A;„,
holds, the distressed firm
is
able to finance
all
of
its
(11)
We refer to this constraint as the
needs.
domestic collateral constraint. Unhke the international collateral constraint, which
is
purely
aggregate and hence affects units through equilibrium prices exclusively, the domestic one
affects
microeconomic imits directly through quantity constraints.
that are behind the externalities and excess volatility that
Regions.
Each
lowered. Region
we
It is
discuss below.
of the regions in the previous section gives rise to
1 in
the latter constraints
two new regions as A„
the previous section, where the international constraint
19
is
is
slack, gives
and
rise to regions I
II.
In the former A„
while in the latter the opposite
is
is
is
high so the domestic constraint
true. Similarly, region 2,
is
slack as well,
where the international constraint
and IV, sorted again by whether the domestic constraint
binding, yields regions III
is
slack
or binding, respectively.
Figure 4 provides examples of equilibria within each of these regions.
in
demand and supply
panel (a) represent the unconstrained
(solid lines) is the
unconstrained
the case where A„
=
1.
demand
But when A„ <
can be pledged, which gives
rise to
purchase
where A„
all
L'^
=
i
1 or,
it
L=
A
- it
it
when
needs, even
corresponds to the
demands depicted
is
The
needs.
the latter
>
i
~^\
is
in
available at
is
\
e
L=
1
it
cannot afford
minimum
all
price. In
V
-A
1
dashed hnes. The
zero.
I
\
in
short dashes portray a situation
L
"'^
demand curve
high enough that a distressed firm can
equivalently, the international spread
e
The upper envelope
imable to fully reinvest since
is
solid lines
only a fraction of domestic output that
is
where A„
i
L=
there
the international collateral
the international collateral
both cases
I,
small enough that the firm
is
1,
funds
the constrained
long-dashes represent a case in region
still
for
of Dia-
The
\
\
\
\
\
'\
1
'•..
\
1
1
Panel
(a)
:
Regions
I
and
Panel (b)
II
Figure 4: Equilibrium
when
:
Regions
\<
III
and IV
1
Panel (b) has a binding international constraint. The long dashes represent a situation in
region
III,
where A„
is
large
enough so
all
rents can
20
still
be transferred to collateral supphers
as in the case
with perfect domestic markets. The short dashes, on the other hand, represent
small enough to limit the ability to fully transfer the rents to
a case in region IV, where A„
is
collateral-suppliers, but
high enough to fully aggregate international collateral (unlike
region
still
In both cases L'^
II).
IV both domestic and
is
hence there
1,
now
also a domestic spread, s^,
vestors.^^
When
as in regions II
We
the domestic market
go;
smnmarize the
regions at date
sufficiently
is
underdeveloped, this spread
When A„ <
1)).
spreads are zero and there
1
is full
In
this case,
economy
remain
fails to aggregate all
>
downsized, s^
^''Part of this
economy can
positive,
one of four
he in
0,5^
=
0,6^;^
<
of
zero,
and the domestic
and domestic
both international
project completion,
binding. International spreads
as the
the
collateral constraint (7)
Region II occurs when the international constraint
is
is
1.
collateral constraint (11) are slack.
•
able to promise other domestic in-
is
results of this sub-section as follows:
Region I occurs when both the international
•
in a distressed
and IV.^^
Proposition 2 (Regions (A„ <
We
which we define as
and the return that the distressed firm
1,
a positive international spread
is
between the internal return on investment
reflects the difference
firm at date
a positive international spread. In region
Besides the issue of whether there
d
This spread
is
international collateral constraints bind.
Domestic Spreads.
or not, there
>
is
=
s'^
s'i
=
0,6':^
=
1.
slack but the domestic constraint
however domestic spreads are positive
its collateral
some
resulting in
projects being
1.
wedge may be arbitraged by a resource-consuming bank,
as in
Holmstrom and
Tirole (1997).
revisit this issue in section 4.
^*In fact, emerging economies are likely to spend most of the time between these two regions. Region
corresponding to normal times, while region IV represents deep crises. In region
^—
1.
as the
In region IV, this spread starts to
economy moves
collateral rises.
during
crises,
At, rather
While
at first glance this behavior of domestic spreads
than just the
rise as well, it is
is
and IV rather than
true in region IV.
We
II
economy's
will
A
as
may seem
II
is
any better, but because
at
on
all
domestic
odds with the data
crisis
shock that reduces international collateral
both A„ and
may be one
capture this feature below by letting the economy fluctuate
and IV. In region
More endogenously,
collateral hinders the
is
important to point out that during severe
latter, are likely to fall.
that also reduces domestic collateral.
I
not because the domestic market
the domestic spread
into a crisis the international spread rises as the required interest rate
where they often
between regions
fall,
II,
we develop
I,
no collateral constraint binds, while the opposite
later in the paper,
ability to aggregate collateral
feeds through as a shock to domestic collateral as well.
21
an external shock to international
by compromising the banking
sector.
This
Region III occurs when the international constraint
•
straint is slack. International spreads
The economy aggregates
at zero.
aggregate resources and
IV
• Region
occurs
when
some
jump
of
all
^—
while domestic spreads remain
1,
collateral,
its
projects are downsized,
however there
=
s'^
both the international constraint
are binding. Both, international spreads
projects are downsized,
to
binding but the domestic con-
is
s'^
>
0,s^
>
0,s^
and
<
<
0,9'^
1.
The
What
are the costs of having an undeveloped domestic financial market? Fixing
Externality: Internationcd Collatercd Undervaluation
main
economy
cost to the
resulting in lower investment
is
that in region
and output. But
II collateral is
/c„,/cf
and doj do not remain fixed as A„
over-exposed to the crises brought about by external shocks.
externality in this subsection
The Date
To sharpen the
and
its
At date
Problem.
focus,
we assume
1
that the good state leaves the
bad state
bad
becomes binding as
an entrepreneur /firm
—
e(a;)^/^
=
1
State:
u)
in
In either good or
from production
less
debt
maxltt*^
s.t.
is
ct+Cn/e{u})=W2.}
linear in wealth, production
and financing
is
exactly
reflect.
=G
this case collateral
is,
2.
solves,
In the good state, neither collateral constraint binds.
That
in region
exclusively to
are taken to maximize the expected value of wealth - which
what (PI) and (P2)
Good
is
where
well.^^
Since the value function over date 2 wealth
decisions at date
economy
I
enough so that the domestic
at date 2 with wealth (output
repayments) of W2 in units of T-goods
in region
Although the negative shock
problem we work backwards from date
arrive at the date
state,
economy
leaves the
international collateral, equilibrium asset prices decline sharply
To
describe the
the economy can be in either a good or a bad state.
collateral constraints bind.
collateral constraint
We
result, the
vulnerability consequences in the next one.
neither of the collateral constraints bind, while the
IV where both
and
not aggregated properly,
with underdeveloped financial markets undervalues international collateral As a
is
fc„, kt
problem, we show that the private sector in an economy
changes. Focusing on the date
economy
and some
are positive
3.2
do J, the
1.
the domestic constraint
and domestic spreads
0,6'^
>
insufficient
is
is
fully
aggregated and that
all
Proposition
1
dictates that in
N-productions units are saved. The only
our scenario a decline in the availabihty of international financing leads to a decline in
domestic "intermediation" as
well.
22
difference
between an intact and a distressed
the fraction of distressed firms
on state
G
firm,
is
that the latter must reinvest kn- Since
the expected (as of date 0) date 2 wealth conditional
is p,
is:
W2{G)
Market clearing
=
Rtkt
+
^-doj-pkn.
at date 2 (condition (5)), yields a real
^
'
(12)
exchange rate of
RtKt - Doj - pKn'
Cp
while both spreads -domestic and foreign- are equal to zero at date
Bad
State:
1.
=B
uj
In the bad state, both collateral constraints bind. Investment
constrained and both
is
the foreign as well as the domestic spread are positive.
The binding domestic
collateral constraint implies that in equilibrium:
e^kn
= ^ [xfRth - Doj +
^f^)
< ^"'
(13)
with
_
1
^
Ar,A„.
'
LBe{B)
while the (aggregate) international collateral constraint implies that:
P
Combining the aggregate coimterpart of
(13)
and
(14)
we obtain the date
1 prices:
A„
T;tiZb
\
l-p\e{B)
.e(S)^e(B)/'
A„
f
where
ry
The
ratio
Z
_
PKn
XfRtKt - Doj
indicates the economy's exposure to crises.
availability of collateral per unit of distressed capital.
As
Z
rises,
there
is
less
aggregate
Other things equal, this means that
the discount of N-claims, L^, rises as well.
The
real
exchange rate at date 2
^
'
is
determined as before:
= CI ^ (^-pAn(l-OK._
Cf
RtKt-p9^Kn-Doj
23
^
'
.
Given these equilibrium prices and
B
date 2 wealth conditional on state
W2{B)
=
availability of reinvestment resources, the
is:
+ -^{R^ - pAr^) -
Rtkt
e{B)
"^ ^^
i^W)
+
The
first line
by date
of the
RHS
/^
„
_L
^"
^[W)~
N
and
T
"
(16)
do,f
^^^"^
~
^^^^'^'
tb\ ^nRnjOn)
) e{B)LB
in (16) reflects the
investment in the
'
"^''^^
,^
^"-
expected wealth, in the bad state, generated
sectors, net of foreign debt contracted at date 0.
In particular, this line corresponds to the expected wealth assuming that
production units are allowed to
in the next
With
lines.
probability
collateral
On
two
The second
[1 — p)
and lends
fail.
the firm
The
intact in
which case
if
the firm
distressed, then
is
units, directly earning the internal return of
its
it
distressed
is
captured
having international collateral.
borrows against the international
to the distressed firm, thereby earning the domestic interest rate
the other hand,
last line reflects
all
value of saving these production units
line reflects the return to
is
expected
^y
borrows to save
it
against
the return to having domestic collateral.
domestic collateral at the domestic interest rate of
its
If
its
oiL^
own production
international collateral.
a firm
L^ and
is
distressed,
it
The
mortgages
uses these proceeds to save
production units, earning ^rgyFollowing the logic of the previous paragraph, we can rewrite (16) directly in terms of
spreads
as,
W2{B)
It is
=
Rtkt
+ -^{R^ - pAn) e[B)
+
(^sf
+
^''^
doj
(17)
+ ps^){X^Rtkt-doj)
e{B)LB
instructive at this stage to construct
two
^--
one
different versions of tW2(-B);
dividual firms and the other for a central planner.
To
construct the former,
for in-
we simply
substitute in (17) the expression for reinvestment implied by the microeconomic domestic
collateral constraint, (13).
To construct the
central planner's version, which
W2{B), we substitute instead the equilibrium collateral constraint,
(14).
we denote by
While separately
these expressions are obscure, their difference clearly highlights the basic externality:
W2{B)
where
tp is
pip
<l
- w*2{B) =
sf
(^p^j^^^kn -
follows from equations (13)
and
(14).
(1
- p^){\fRtkt -
doj)^
(18)
30
the leverage ratio applied to collateral for an individual distressed firm. That
24
,
is, it is
the multipher
At a given equilibrium
in region IV,
W2{B) and
1^2 (-B)
must be
equal.
But
it is
apparent
that individuals and the central planner value a marginal unit of international collateral and
domestic collateral quite
We
differently.
note three things in particular:
domestic collateral more than the central planner.
• Individual firms value
• Individual firms value international collateral less
The divergence
•
At the aggregate
in these valuations are proportional to the
B
domestic spread, s^
the central planner only cares about creating and protecting
level,
international collateral. This
is
because international collateral
However
attract foreign investment.
and international
than the central planner.
microeconomic
at the
level,
can be used to secure financing.
collateral
that can be used to
is all
both domestic
This
is
collateral
the basic tension
between the individual and the central planner's problem.
A positive domestic spread heightens this tension by placing a wedge between the social
and private valuation of collateral. A unit of international collateral generates asocial return
of
^y
at date
1,
while a unit of domestic collateral generates a social return of one at date
At the individual
one.
On the other hand,
difference
an intact
level, for
between
social
domestic collateral generates a return of
firm, a unit of
a unit of international collateral only generates a retinrn ofL^. The
and private valuation of s^
= ^y — L^
The domestic spread prevents
of international collateral.
firms)
1.
from transferring the
results in undervaluation
collateral
demanders (distressed
marginal value of collateral to the collateral providers (intact
full
firms).^^
Underdeveloped financial markets (low values of Ajj)
the systematic mis-valuation of collateral.
have described
is
not of the traditional Bardhan-Harberger type, where individual borrowers
the aggregate collateral constraint.
by distressed
is p,
and
important to realize that the externality we
It is
on collateral that determines how much a firm can borrow.
distressed firms
result in high domestic spreads
then
frtp
X
If
A
simple way to see that
each distressed firm uses a multiple oi
(Value of Domestic
-I-
International Collateral)
firms. In aggregate, however, the country
tp
is
can only borrow against
/^j/)
and
<
the total
its
1 is
to think about
in total the fraction of
amount borrowed
international collateral.
Thus, we must have that,
P'^X (Value of Domestic
or, fnp
+
International Collateral)
<
Value of International Collateral
<1.
Overvaluation of domestic collateral
collateral.
At the individual firm
a return of
^t^-
On
the necessary counterpart of undervaluation of international
a distressed firm, a unit of international collateral
the other hand, a unit of domestic collateral
and generates output of
an excess return of
level, for
is
zero.
^rgt, providing a return of sf
At the individual firm
of domestic collateral, resulting in too
>
0.
level, this
much domestic
At the
is
still
generates
discounted at the interest rate of
mis-pricing causes firms to overvalue the A„r„A:„
collateral relative to international collateral.
25
L*
social level, domestic collateral generates
do not internalize the fact that the country faces an upward slopping supply of foreign
loan.'^^
Indeed, in our setup the economy does face a very steep international funds supply, for the
country
rationed after
is
some
point, but the externality arises only
markets are underdeveloped as
The constrained nature
well.
collateral limits the price that collateral users
arises,
which
reflects
what they can
can
afford.
when domestic
of the domestic
demand
for
In so doing, a domestic spread
the gap between what an extra unit of collateral
Collateral suppliers anticipate such spread,
afford.
financial
is
worth
for
and therefore
them and
see their
provision incentives depressed.
now
establish this result on the undervaluation of international collateral
and
its
dependence on the underdevelopment of domestic financial markets more formally.
We
do
Let us
this in
two
steps. First,
making date
constraints.
we
write
decisions of {Kn,
down
Kt,Dof) subject
We arrive at the constrained
in particular, that these solutions
planner's
is
the problem of a central planner
Pareto
to the domestic
who
has freedom in
and international
collateral
the problem and show,
efficient decisions of
do not depend on A„. Second, we contrast the central
and the decentralized solution and show that the market equilibrium with A„ <
1
constrained Pareto inefficient.
Consider the problem of a central planner
Central planner's problem.
equally weighted
sum
of utilities of agents in the
who maximizes
economy by choosing Kn,Kt and Doj
directly at date 0, subject to the respective collateral constraints. In the
that the solution to this problem
is
max;^„,K.,Do,/
appendix we show
equivalent to the solution of the following program -
which resembles that of the individual
(P4)
the
firm,
with the exception of the expression foru>2(.B):
Ea;e{G,B}'r'^e(w)2ti;*(a;)
wl{B)
s.t.
w*2iG)
=
=
RtKt
+
RtKt
+
- Doj +
- Doj - pK^
^^~4§)"^^"
^
(sf
+
sf ) {X^RtKt
- Doj)
Doj < mm^{Xr RtKt + A„^}
Kn + Kt = Wo + Doj
Propositions (Constrained Optimality)
(a)
Let
{K*,K*,DQf)
These solutions are the constrained Pareto optimal date
{K*,K*,DQf)
(P4).
,
Once we show that
It is
choices of the economy. (6)
are independent of the strength of domestic financial links, A„.
Part (a) see the appendix. Part
Proof:
be solutions to (P4)-
it
(6)
can be done by simple inspection of program
does not depend on the value of A„,
its
solution can't either.
apparent that none of the terms in (P4) depends on A„ but for the constraint on
foreign leverage. ^^
Which
is
However, we
will
show by contradiction that the inequality
not to say that such mechanism
^'indeed, note that {sf
+
sf )
=
is
not important in reahty.
A„/e(S).
26
is
always
strict:
K
Doj < rmn{Xr RtK, +
Suppose
^^^^
"
}•
that,
D,J = min{XtRJU + Xr^^^^^^},
then, the
amount
of international collateral at date
1 in
X^RtKt - Doj <
However
if
this
is
the bad state
is,
0.
the case, then the market for exchanging domestic collateral for interna-
tional collateral will necessarily break down.
must return zero imits
"
Swapping
'
z
units of domestic collateral
of international collateral since the supply of international collateral
not positive. L*^ rises until such a swap does not take place, or until
Undervalued international collateral
Doj < mii\^{XfRtKt}.
Let us contrast the central planners problem with the
decentralized solution. Taking the case where the good state leaves us in region
bad state
in region IV,
(P5)
we can write the program
maxfc„,fc,,do,/
s.t.
is
of a firm at date
I
and the
as:
Ec^G{G,B}7r'^e(w)5u;2M
^
- doj - pkn
= Rth +
= Rtkt + ^^^^^§f^-doj
+ (s] + pi,s^){\fRth-doj)
W2iG)
W2{B)
doj
kn
<
+ Xnj^}
m[ikj{X'^ Rth
+ kt = Wo + doj.
Proposition 4 (Undervaluation of International Collateral)
solutions to the program (P5) in the case
when A„ <
(kn,kt,doj), are constrained Pareto inefficient.
provement by perturbing these decisions
A
1
and s^
>
0.
Let {kn,kt,doj) be
Then
the decisions,
central planner can effect a Pareto im-
to {k'^,k[,d'Q
f),
where at
least
two of the following
inequalities are strict,
doj
<
0^0,/
kn
S
kn
K ^
^t
Proof: see
Appendix
The proof
follows closely from the logic laid out in the previous section.
the only difference between (P4) and (P5)
is
27
in the expressions for
Note that
W2{B) and W2{B).
When
A„
planner's
Pareto
=
1
the domestic spread, s^
and the decentralized
=
0,
and there
is
no difference between the central
market equilibrium
solution. In this case, the
However, when domestic markets are undeveloped, s^
efficient.
>
is
constrained
and there
is
a
divergence in the social and private value of collateral, resulting in the inefficiency.
Excess Volatility and Policy
3.3
Proposition 4 has a straightforward but useful corollary:
Corollary 5
and
solutions {kn,kt,dQj)
What
is
I
and Z' denote
{k'^,k[,d'Q
f)
the indices of exposure corresponding to
and IV,
as
volatile
we have
Figure 5 illustrates
this.
—
Z>
Then,
in proposition 4-
the cost of a higher index of exposure?
economy becomes more
regions
Z
Respectively, let
Z'
.
easy to see that as
It is
economy remains
as long as the
.
Z
rises
the
fluctuating between
assumed.^''
The
solid lines represent the supply of international collateral in
the bad state and in the good state. In the good state the supply of international collateral
is
at
X9RtKt — Do
=
Given our definition of Zg
''f-
^Y^- Similary in the bad state, since there
constrained at a lower point.
decisions, Z'
?^^
The dashed
—
C "— UQf
Ajg HiKt
,
is less
economy
falls
to
C
varies less across realization of
G
the supply curve turns vertical
international collateral, the supply
lines represent
is
supply at the Pareto improving
at
A during good
states of the
rather than B.
There are two observations we can make from the
L
i
While both economies share the equilibrium
world, the less efficient
since
r.
and
B
First, reading off the y-axis,
figure.
states at Z' than at Z,
we can
see that
asset prices are less volatile. Second, reading of the x-axis, since equilibrium reinvestment
varies less at Z'
there
is little
thus, the
than at Z, investment and output are also
surplus of international collateral
economy
is
left
less volatile.
by
high,
nearly defenseless in the event of a bad external shock.
investment and output
severely
is
even under the best of the scenarios;
While we have stressed the impact of underdeveloped domestic
more
When Z
volatility, it also follows
crisis
when A^
is
financial
markets on
that since reinvestment options are curtailed
lower, the country's stock
market value
suffers
more
as
well.
If
the domestic constraints becomes so tight that,
collateral regions, volatility
e.g.,
the
with respect to external shocks
economy
may
finds itself at all times in the
wasted
disappear altogether, and be replaced by
persistently low reinvestment rates. See our discussion of this issue in the conclusion.
'*In this figure,
we vary Z by changing Kt and Doj, while keeping Kn
only illustrative, as such change in
Z
also changes the date 2
28
exchange
constant. Moreover, the figure
rate,
and hence
shifts
demand.
is
L=A
PVz",
P*^
Figure
Policy.
The constrained Pareto
to policy considerations.
We
5:
Excess and Costly Volatility
inefficiency of
more broadly
discuss policy
(Caballero and Krishnamurthy (1999)). Here
naturally from the previous proposition:
and domestic
market equilibrium
we limit
When
an open invitation
companion working paper
ourselves to pointing out
collateral are warranted; they could
take the form of capital inflows taxation during non-crisis periods (date
collateral
(or,
more
consuming -particularly
requirements
from tmdoing
may
it
follows
market equilibrium leaves the economy
Measures to boost international
investment in the T-sector
what
both international financial links are weak
financial markets are imderdeveloped,
excessively fragile.
in a
is
0); subsidies to
generally, international collateral creators); or taxes
dinring crises- activities.
also work, although supervision
through additional borrowing.
29
is
Mandatory
on
collateral-provision
needed to prevent the private sector
Endogenous Breakdown
4
plification
and Multiple
Am-
in Collateral Aggregation:
Equilibria.
Distressed firms access the international collateral of intact firms by borrowing from these
firms against their N-collateral.
this collateral aggregation
is
The
done
implicit assumption in the preceding analysis
that
is
in a perfectly functioning public debt market. Distressed
firms issue debt claims in the domestic market secured by N-collateral. Intact firms issue
They then use
debt claims to foreign investors secured by international collateral.
the
proceeds from this issue to purchase the debt claims of the distressed firms.
In emerging markets, liquid domestic debt markets are the exception rather than the
rule.
Invariably, the financial
system
is
bank based -
for
good reasons: lack of investor
protection and the necessity of monitoring to alleviate asymmetric information places banks
at the center of the financial system.
Banks
issue claims to foreign investors against balance
sheets that are partially backed by international collateral - both of the distressed and the
intact firms.
These funds are then channeled to the distressed
firms. Implicitly, the intact
firm extends credit to the distressed firms against their domestic collateral.
But unlike the immutable debt markets of the previous
experience sharp
economy's
falls
banks themselves run into trouble.
ability to aggregate its scarce collateral
in asset prices
and
Even worse,
real activity.
this perverse feedback process
if
fits
conventional
can lead to multiple
wisdom
well.
every emerging market's external
among many,
tequila crisis,
4.1
it
is
crisis.
And
equilibria.
its
in its
it
of the early 80s, to
The Banking System: Amplification and
all
reallocation
plays a role in virtually
extreme form of a worst equilibrium
In order to highlight the role of banks, in this section
in
feedback into real activity and asset
reminiscent of Indonesia in the recent Asian
crisis
crisis,
name
Mexico during the
a few.^^
Financial Bottlenecks
we suppress
entirely domestic debt
must be done via the banking system.
need of funds take loans from banks. To attract these funds, banks
market determined interest
enter distress, the
weakened, triggering further declines
is
Arguably, some form of
and Chile during the debt
markets so that
As banks
rate. Intact firms
international collateral to foreign investors
asset prices
banks are undercapitalized at the outset,
This endogenous disintermediation process and
prices
when
sections,
become the
depositors.
Distressed firms
offer deposits at
They mortgage
and then deposit these funds
in the
a
their
banking
See Gclos and Werner (1999) for a study of lending practices by Mexican banks during the postliberalization period.
Among
other things, they document the significant role played by banks in lending
to manufacturing firms without access to foreign funds,
this
mix contributed
significantly to the collapse of the
30
and
their reliance
on
N-collateral.
banking system during the 94-95
They argue
crisis.
that
system.
By
collateral,
intermediating these transactions, the banking system serves to aggregate
which
is
the only role
We
Balance Sheets.
it
has in our model.
unit measure). Suppose that at date
and fund these loans by
of the
bank are a„
T-firms. ^^-^^
bank
consider a representative
0,
banks make loans to firms
issuing debt to foreigners.
this
with d^
both
and
is
N
at face value of
units of foreign debt (in units of
f
the value of capital (entering date 1) in the bank
and
T
Foreigners extend credit to banks against the
''"
date 2 debt on
T
the excess of assets over
goods).
Then
liabilities,
(19)
same no-default constraint
as before,
+at-4j>0.
and
sheets of distressed
(of
sectors
= T:^ + «t-</.
9r
The balance
in
banking sector
In particular, suppose that the assets
face value of date 2 debt of N-firms
Banks fund
in a competitive
intact firms (equations (2)
and
(3))are modified
slightly:
Qi
=
At
Rtk -at+
for the intact firm, while for the distressed firm,
Qs
Both equations
That
is,
do,/.
jjj^
lending from the banking sector.
Notice that we have taken A„ to be one in both balance sheet
any further
in the absence of
to the public debt market with A„
now
-at^
i<-tf-t
it is,
are modified to reflect the date
Capital Constraints.
calculations.
-\
doj
^^^
=
1
and hence
frictions, the
banking system
collateral aggregation
is
is
equivalent
We
frictionless.
introduce capital constraints that limit the capacity of the banking system to aggregate
collateral.
At date
1,
a bank takes in deposits from intact firms of d\ ^ and makes loans of x\ ^
to the distressed firms. Let
respectively.
If
Lx
Lq
and
no other constraint
is
represent the loans' and deposits' interest rates,
present,
both of these are made at the market de-
termined interest rate of L, and the expected date 2 repayment to the bank from this
At date
0,
Thus issuance
not
all
agents in the domestic economy are the same
of domestic debt cannot be netted to zero as
-
there are both banks as well as firms.
we have done
in previous sections. Additionally,
throughout the paper, our firms are conglomerates, each of them with an N-firm and a T-firm
in
it.
We
assume here that each of these mini-firms can contract debt independently.
'*The purpose of this section is to highlight the potential date 1 bottleneck brought about by the deterioration in banks' balance sheets.
There are several interesting date
issues
discussion but which would lengthen this section substantially. For example, one
sign contingent contracts with borrowers
and depositors.
31
which merit an extensive
may
ask
why banks
don't
operation
is
{x\ d
—
d\ ^)L (in units of face value of
T-goods at date
We
2).
assume that
capital constraints restrict the size of this operation. In particular,
>
qt
< a <
where
1 is
value of x\ Juj).^^
there
axl^iuj),
(20)
the capital that banks must hold against making loans with present
If this
Lx
constraint binds,
equal to
is still
L
L^
but
to one since
falls
an excess supply of deposits but a scarcity of loanable funds.
is
Taking as given the market interest rate (on loans) of D^ and date 2 exchange rate of
e'^,
the problem of a bank at date
(P6)
s.t.
- 4,/ - ^t/(^) + (^" -
at
(i)
q^>axl^iuj)
objective of the
bank
L^ and taking deposits
capital constraint
fS
reflects profits
from making loans of x\
^ requires raising deposits
against international collateral of at
—
d\i]^
it
to the appendix.
while in equilibrium
V^ =
1
Banks
is
for
behave exactly as in the previous sections. In
the problem
As
scenario.
is
^
1
the interest rate
(i) is
simply the
resource constraint:
plus attracting funds
investors.
very similar to that of the previous section,
funds
much
is less
fact, as
two regions,
(i)
as they can whenever L'^
Panel
and
>
than loanable funds. Firms
long as constraint
entirely analogous to that in section 2.4.
in that section, there are
the date
from intact firms of d\
will lend as
when demand
reflect
(iii)
from foreign
Since the formal analysis of equilibrium
relegate
and
(ii)
J^lj) at
L^. Constraint
of d\ ^{uj) at the interest rate of
on banks. Constraints
making loans of x\
we
^)AM ' (L^d " l)^ld(^)
4»<d5_rf(a;)+4/(a;)
d\j < at - d^j{u;)
(iii)
of
+
max,.^^(^),,.^^(^)
iii)
The
1 is,
(ii),
(i) is
1,
will
not binding,
(a) in figure 6 depicts this
which are distinguished by
whether or not the international collateral constraint binds.
In practice, capital adequacy requirements are based on both assets as well as
BIS standards assign capital requirements to
sorted
(i.e.
common
stock, preferred stock)
different assets held
liabilities.
For example,
liabilities of
the bank are
and weighted to determine the amount of capital held by the
bank and hence ensure that the capital requirement
principles
by banks. The
is
met. Capital requirements can be justified from
on the basis of moral hazard within the banking
example.
32
sector.
first
See Holmstrom and Tirole (1997),
for
t
A
i
\
L=
\
L=
\
\
\
L=
J
L
\
A
L=
1
\
I
I
'
'
1
„=1
Panel
(a)
:
Regions
(i)
e„=i
and
Figure
The
new
interesting
the economy can
demand from
fall
cases arise
into regions
low and output
is
high.
then interest rates
(iii)
is
that
or (iv) depending on
now
if
Regions
capital requirement
how
line in figure 6 (b)
equilibrium: loan
Conversely,
:
(iii)
and
(iv)
Equilibrium with Banks
when the
(iii)
rise to ration
ingredient to highlight
6:
The dashed
distressed firms.
loans which yields a region
Panel (b)
(ii)
demand
loan supply
is
is
(z)
does bind. In this case
tightly
it
binds relative to
corresponds to a supply of
fully satisfied, interest rates are
constrained by capital requirements,
the scarce supply (dotted
line,
region
(iv)).
The key
the supply curve for loans bends backwards at the point
where the capital requirement binds. This occurs because the value of banks' capital
when
interest rates rise (see equation (19)).
The backward bending nature
differentiates
constraint
there
is
it
from region IV
and a microeconomic
wasted
collateral, in
of supply plays a significant role in region (iv),
in section 3.
aggregation.
While
in
both cases an aggregate
and
collateral
capital requirement bind, in the banking-intermediated case
the sense that not
to the distressed firms. Equilibrium
full
falls
is
all
excess domestic resources are channeled
A
rather than B, where the latter reflects
at point
Constrained banks become a financial bottleneck, which bring about
simultaneously the worst of each scenario described in the previous sections: sharp declines
in asset prices
coupled with collateral waste.
33
Multiple Equilibria
4.2
The
domestic interest rates and
rise in
a cause of the
crisis, it is also
fire sale in
We
crisis.
region (iv)
is
not only a
The
fall
in domestic asset
prices amplifies the impact of the crisis by deepening the credit crunch caused
But
distressed balance sheets."*"
and
it
feasible intermediation brings
and (B)
in the figure represent
is
of the
As we described above,
illustrate this in figure 7.
the contraction in loan supply causes the rise in interest rates.
symptom
by banks'
easy to see that the feedback between asset prices
about the possibility of multiple
equilibria.'^ Points (A)
two equilibria which are distinguished by low
interest rates,
non-binding capital requirements (A) and high interest rates, credit crunch (C). Point (B)
also a possibility in
is
in
The equilibrium
in (C)
<
1
Low
and
is
Pareto inferior to that of (A) and
is
interest rate equilibria are
mechanism
''"This amplification
production units are saved, this
all
or a concave but not rectangular
ranked.
prices
interest rates rise to constrain loan supply to exactly
both (A) and (B)
demand. While
A„
which
is
demand
more
causing the
constraint
efficient
than high rate ones.
similar in spirit to Kiyotaki
fall in
is
on the demand side
is
and Moore (1997)
-
constrained
demand reduces
and further constraining demand. However,
asset prices,
on the supply side
-
in that a fall in asset
In this sense, our
In Kiyotaki
model
rise,
is
model the key
markets during
closer to the amplification
literature (see
also disregarded
and multiple
Lamont
macroeconomic
equilibria that
(1995)).
is
effects of
the strength of firms' balance sheets,
it is
emphasize the balance sheet problems
is
in
More
in firms
another source
introduce a non-convexity in the investment
possible to have multiple equilibria.
We
have simply chosen to
banks where capital constraints are most natural.
done
after the Tequila crisis,
probably exacerbates the problems we have described
making these requirements
by valuing assets at outdated
bank runs can be
is
-
Given the feedback between investment and
specifically to banks, however, increasing capital
liquidity ratios, as Argentina has
latter
debt-overhang problems
the appropriate policy response in this case? To start, the pohcy suggestions in the previous
section apply here as well.
possibility of
concern
in international
both empirically plausible and has been pointed out in the
Debt-overhang problems
of firms as a function of the strength of their balance sheets.
"^What
A
crises.
new public debt
crises.
model has
of amplification
financial
causing bank capital to
mechanism studied in Krishnamurthy (1998).
^'A related mechanism is "the disappearance of markets (and market-makers)" during
often expressed by emerging markets' policy makers in their attempt to place
and Moore
the productivity of assets,
in our
constrained supply causes interest rates to
be compromised, and further constraining supply.
The
with
reinforced by a tightening financial constraint. However, one key diiTerence between our approach
the key financial constraint
and
generally,
function, equilibria can be strictly Pareto
theirs lies in the identity of the agent with the crucial financial constraint.
''^Our
not so in (C).
is
More
(B)."*^'^^
meet
offset
slightly
more
prices, as in Japan).
with improved credit
more comphcated but
lines,
in this section
may
by
adequacy requirements
help avoiding bank runs but
raising a.
At the very
procyclical should be pondered (which
The
perverse impact this
may
often done
have on the possibility of
interbank markets, and lender of
last resort
certainly not impossible in "currency board" scenarios.
34
is
it
least the
mechanisms.
L
j
L=
L=
A
1
1
1
Figure
5
FinEil
1
7:
Multiple Equilibria with Banks
Remarks
Since models are stylized representations of complex realities,
terpret
them narrowly when extracting
their lessons
it
is
always unwise to
in-
and relevance. This applies both to
assmnptions and implications. In the context of our model, there are several implications
and assumptions that deserve further discussion
in order to facilitate their broader inter-
pretation and empirical assessment.
Our
first
central implication
is
the presence of fire sales.
substantial expected excess returns in the midst of a
the form of a sharp
rise in
crisis.
That
is
the emergence of
In the model,
fire sales
take
domestic interest rates, by which we understand the discount
applied to assets that are not good international collateral. There are two related questions
that naturally follow this abstract description of
fire sales:
Do
they include the frequently
observed collapse in the exchange rate? More generally, which observed rates and prices
are the empirical counterparts of the model's rates
Our model
is
and prices?
designed to highlight collateral and balance sheets
we have eliminated a
series of traditional ingredients
35
effects,
and
in so doing
which are needed to pin down exchange
rates during crises, such as [date
and nontradeables,
ables
Ours
is
consumption decisions involving a choice between trade-
monetary decisions that pin down a nominal exchange
or
than on rising
risk
possible
is
Indeed, our emphasis
on
is
premia - although connecting the
if
any combination of these two, are
is
decline in stocks
domestic asset prices. This implication seems highly consistent with the
there
one robust
is
In
many
situations debt
less
than prime
fire sale,
The banks'
instead.
which
is
which
is
assets.
In such cases interest rate surges underestimate the
avail, is also
banks in the post-Russian
crisis is
a fairly well established fact.
is
that
implication,
fire sales
many high marginal product
sharp decline in investment and output. This
The second
is
projects are foregone, resulting
of view of policy,
its
markets
—due to the
is
sector,
which leaves
insufficient
monopsony argument, but
development of domestic finan-
— that renders inadequate the compensation received by collateral providers.
There are several questions that immediately come to mind with respect to
What
the undervalua-
international collateral. This un-
dervaluation stems not from the traditional Bardhan-Harberger
cial
occur, the dual of this
and accumulation by the private
the economy unfit to withstand significant shocks to
from the domestic credit constraint
The behavior
also a central feature of actual crises.
and main one from the point
tion of international collateral creation
when
a good example.
Regardless of the specific mechanism by which the
in the
and quantity constraints
reluctance to lend in the midst of a capital flow reversal, even
decline in asset prices
it is
the practitioners' catch-all term for
partially reflected in rationing
they have plenty of liquidity at their
of Argentine
As we argued
and equity markets are nearly non-existent and most financing
occurs through the banking sector.
extent of the
facts.
and other
fact of crises associated to financial factors,
precisely the sharp decline in "risk appetite,"
a higher required return on
all possibili-
a shift in the "collateral/risk
premium" term. Internal arbitrage must cause a corresponding
if
risk interpre-
given to incentive constraints.''*
is
which are consistent with the model as long as there
in the introduction,
and
from an exchange rate overshooting,
interest parity condition results
or from a sharp rise in domestic rates, or
collateral supply shortages rather
collateral shortage
a more probabilistic interpretation
But whether the new
ties
rate.
a model of a shift in the interest parity condition brought about by collateral short-
ages that hinder arbitrage.
tations
1]
this implication.
are the observable counterparts of the model's domestic financial underdevelopment?
Is there
evidence on the connection between crises and such underdevelopment?
the specific mechanism behind the externality? And, does
The model's
mean
is
have empirical content?
indicator of the degree of underdevelopment of domestic markets
domestic spread, by which we
Where
it
What
is
the
the gap between the marginal product of distressed
the probabilistic term must have an exogenous or endogenous aggregate component. Also, see
Holmstrom and
Tirole (1998b) for a
model of
asset pricing based
36
on
liquidity rather
than
risk premia.
firms
and the domestic
directly has always
been problematic
involve at least one unobservable.
financial markets
time.
Measuring such gaps
interest rate -in the sense described above.
for
What
supporters of credit rationing models since they
is
reasonably measurable, however,
and the bulk of the intermediation that takes place
With these measures
mind, the evidence
in
is
in
is
the size of
an economy over
overwhelmingly in favor of the view that
domestic financial markets in emerging economies are extremely underdeveloped compared
to those of
we
OECD's.
Interestingly,
most of the very few exceptions reside
in Asia, a point
return to below.''^
More
outsiders
generally, our basic insight
is
that a limited ability to transfer internal return to
—the genesis and essence of a
market to suppliers since
financial constraint
effectively reduces its size.
it
— reduces the appeal of that
Our model
limits these suppliers to
domestic producers of T-goods, but in reality international market-makers are also included,
and these
To a
typically dislike markets that do not support significant volumes.
this extension follows the
same
logical steps
and conclusions of our
first
order,
stylized analysis.
Although we have emphasized the implications of underdeveloped financial markets
crises,
an interesting dimension of our model
is
that extremely underdeveloped financial mar-
kets can lead to lower volatility with respect to external financial shocks.
when
equilibrium
falls in
for
the wasted collateral region (region
II), is
The
chief factor
the underdevelopment
of domestic financial markets leading to a failure of domestic aggregation of resources rather
than to the scarcity of external
resources.'*'^
This non-monotonic relationship between do-
—low development
mestic financial development and vulnerability
development and very high
volatility,
and
and high development and low
volatility,
volatility
middle
— connects
our view with two pieces of supportive evidence.
The
one corresponds to the low to middle development range, where correlation
first
between development and
crises is the rapid increase in
of rushed
and
One
volatility is positive.
of the
domestic intermediation. This
careless lending, or the result of some
main empirical predictors
is
of
often interpreted as evidence
moral hazard
As
institution.
Some of that
is
midoubtedly true, but our framework
offers a different angle:
the country moves from region
wasted collateral region) into region IV, where external
factors
may
lead to crises and
II (the
fire sales.
financial
development
rises,
Moreover, since financial underdevelopment means
that private agents undervalue international collateral, they do not take enough precautions
against these crises. Within a range, their increased financing
do not come hand-on-hand with
"The
large spreads for
problems with domestic
banks
in
collateral.
full
emerging economies between deposit and lending rates
These spreads are partly accounted
significant role in determining these spreads as well
al.
possibilities
incentives to take the adequate precautions required
incurred by banks to overcome firms' contractual problems.
'^See Aghion et
and aggregation
—
e.g.
(1999) for similar implication in a
37
for
may
by the monitoring and
also reflect
legal costs
Although undoubtedly other factors play a
inflation, oligopolistic
model of endogenous
banking structures,
credit cycles.
etc.
by higher
leverage."*^
The second one
economies
fairly
why
is
when development
refers to the other end,
is
high.
of Asian
in countries that could achieve such high levels of leverage -reflecting
developed financial markets- were there such dramatic crises?
one of "not enough development."
long stretches of stability.
economies
The puzzle
Financial development gave
short of
Still,
G5
levels of
Our
perspective
is
them much growth and
domestic market development, the
themselves fragile and exposed to crises - albeit imlikely ex-ante - that
left
proved very damaging."*^
The
latter discussion takes us to the externality
ments of the model. In the
latter,
and probably
agents do not worry about the nature
and
relevance beyond the confine-
its
in reality as well, domestic
—domestic or international— of
once the relative prices and market liquidity of these assets
But the central planner does,
savings calculations,
At the
it is
just not in the instrument-mix that the central planner needs.
it is
which
right prices,
is
what happens
in our
when microeconomic
the central planner. But
and
taken into consideration.'*'^
the international collateral constraint
model when domestic
are well functioning, entrepreneurs align their portfolio
prices
collateral per-se,
Individual entrepreneurs do their right microeconomic precautionary
first. ^^
that binds
since during crises
is
microeconomic
interest rates
do not
and leverage
selections with those of
units are credit constrained in equilibrium,
reflect fully the
marginal value of resources. This
the dual of a credit constrained equilibrium, and as such
emerging economies as
financial markets
it
is
simply
appears as a robust feature of
well.
Finally, the third implication
worth expanding on
is
that the above factors can generate
a serious financial bottleneck, with potential multiple equilibria consequences, due to the
collapse of banks' balance sheets.
Is this
channel empirically relevant?
And, does the
underlying amplification mechanism extend beyond banks?
In our model, rather than emphasizing the depositors-lenders maturity mismatches and
the potential runs that
come with
'"'Eventually, however, incentives catch
"^Having said
collateral.
A
this,
it
we have chosen
to emphasize the role of domestic
up with financing opportunities
probably the case that their
is
component
big
realization of this
it,
development continues.
was beyond their international
as financial
levels of leverage
of the crisis, especially right after Thailand, probably
mismatch by international
investors.
had to do with the
Traditional moral hazard arguments
may have
played a role here as well, although we continue to believe that the central problem of emerging markets
too
little
— and too
Note that
volatile
this claim is not inconsistent
class of assets as collateral.
is
— not too much capital inflows.
with our assumption that foreigners do not accept certain
Their aversion to these assets comes from their perception that they have an
informational and incentive disadvantage with respect to certain assets, and hence are priced out of those
markets given their uncertainties.
In a sense, during
one that matters
normal times our model operates with two "currencies," while during
for total
crises
it is
only
reinvestment and activity, while the other one only decides internal transfers.
38
banks
Banks borrow from
in transforming domestic international collateral.
Some
lend to local firms that foreigners would not lend to directly.
foreigners to
of these firms are in
Regardless of the nominal denomination of the domestic loans, banks are
the N-sector.
A
naturally mismatched in their effective denominations.
exchange rates reduces the banks'
ability to intermediate foreign resources into the
and
much whether
there
is
a
crisis or not,
but
its
real-
economy
extreme circumstances, the possibiUty of multiple equilibria
at the worst of times. In
to determine not so
collapse in asset prices
arises
magnitude once embroiled
in the crisis.
This mechanism, as we have argued, plays a role
And
external crises.
in its
into the
bank run type
resources
to
crisis,
name
the early 80s, to
crisis of
Mexico during the tequila
a few. Moreover,
it
crisis
it
reminds us
and Chile during the
complements naturally and feeds
of multiple equilibria, as a reduced balance sheet
means
less residual
This interaction probably had something
to those depositors that run late.
left
emerging markets'
extreme form of a worst equilibrium among many,
of Indonesia in the recent Asian
debt
in virtually all
do with the Argentine bank run of the mid-90s.
But the mechanism we capture goes
well
beyond the banks themselves. In our model,
banks are distinct from corporations in that the
their
T-component and
their
N-component. But
a feature of reality. Once such sharp separation
component
this
is
is
can separate incentive problem in
clearly a
modeling simpUfication not
blurred, a collapse in the value of the N-
of a corporation affects its international collateral as well,
amplification
mechanism
may
internal contagion
the case,
latter
e.g.,
of our banks
also arise
is
when
and the feedback and
extended directly to the corporate
sectors are
complementary
sector. Similarly,
in "production," as
is
with a government whose claims lose their rating, and via the sovereignty
principle, causes a depreciation in the rating of domestic corporations as well.^^
All of our asset price
and
real implications arise
from an abstract liquidity "shock."
How
should these shocks be interpreted in reality? They can arise as pure financial shocks, as
often occurs in the so called "contagion" scenarios. Are these totally imrelated to fundamentals?
Most
short
fist
as given
likely not,
but by now most coimtries know quite well whether they are on the
for a contagion
induced shock. As such, taking our liquidity-shocks-abstraction
and thinking about
its
impUcations - the domestic factors that amphfy them, and
the generic type of policy responses that are most appropriate -
But shocks need not be purely
financial, as the latter
shock to terms of trades, productivity, domestic wages,
'"^Onc of the
main
payments trouble,
it is
Ukely to implement measures
the private sector's repayments as well.
sovereignty principle
is
—
e.g.
may be
loss of
justifications for the sovereignty principle
is
is
a fruitful exercise.
the reflection of a real
competitiveness and a myriad
that as the government finds itself in
suspension of convertibility
— that compromise
Indeed, the very few broad exceptions allowed by
reserved for highly dollarized economies, where
39
S&P
convertibility is difficult to
to the
suspend.
factors that
Each
weaken domestic corporations and a government's credit-quality perceptions.
of these shocks has its
own
idiosyncrasies, but our point of view
financial impact of these shocks, none of
history has offered.
in point.
The
them should have the
real
in isolation - at worst just a 2 or 3 percent
issue
when one
in so
doing compromise
It
fiscal stability,
have omitted
specific episode,
output equivalent shock for a
it
becomes a
the convertibility law, and with
many
it
the private sector
factors that play central roles in specific crises; currency attacks
deficits, to
crises
name a
few.
Our
goal has not been to explain a
can be discussed. The standard intertemporal substitution driven,
analysis of developed economies,
alternative
we
offer
is
is
for
macroeconomic
too distant from emerging markets' reality to be of
a stylized framework that brings to the fore what
much
we view
bone of emerging markets' structure: underdeveloped domestic asset markets
coupled with weak international financial
this structure as, for
we
order
would be abated.
deep markets, neoclassical model, which while useful as a benchmark
as the back
first
but rather, to offer a useful framework within which the economics of
emerging markets
The
a case
seems safe to argue that absent imperfect financial markets considerations,
and unsustainable budget
use.
is
considers the uncertainty that this engenders: Will interest rates soar, and
of this uncertainty
We
consequences that recent
recent bout of uncertainty around Argentina's prospects
country that has growth prospects well above OECD's. However,
much
that absent the
Argentina's loss of competitiveness vis-a-vis Brazil seems a second order issue
when considered
at large?
is
links.
Standard
crises ingredients
can be built on
example, we are doing in Caballero and Krishnamurthy (1999) where
discuss the virtues
and
pitfalls of different
our "asset markets perspective."
40
exchange rate systems within the context of
Appendix
6
Incentive Constrcdnts
6.1
We have
appealed to agency conflicts in order to justify the assumption that entrepreneurs
One
be required to retain a fraction of their shares.
illiquidity
assumption
is
possible formulation to justify this
as follows.
Consider a contract between a firm and a lender at date
one unit at date
[0,
Now assume
oo).
can observe
this
that the realization oi Rt
payment only by paying a
=
where E[Rt]
yields date 2 flows of Rt
is
Suppose that a firm investing
0.
and the support of Rt
Rt,
A
private information of the firm.
cost of c (in units of T-good).
Then,
is
it is
lender
fairly
standard to show that an optimal contract will be a debt contract (see Gale and Hellwig
The
(1985)).
contract will specify a face of /;
Rt
ii
>f
and lenders pay the audit
otherwise, the firm defaults
the firm makes the repayment of /;
and receive Rt
cost
Asstime that each firm has a continuum of such projects each with
Each project
is
^'
This
is
=
E[Rt - f\Rt
/Ifl.
<
<
/]
define,
,
<'
,
f]Prob[Rt
<
f]
+ fProb[Rt >
flProHR, <
/I
_ ^Prom <
f]
^ ^^^^^^^ >
f]
, i _ ,, _ /""IR <
;]
Rt
suppressed the cost
c,
so that this
/]
Rt
the component of firms that can be held by outsiders. In
itself.
Lenders receive
is,
Rt
holds
>
return oi Rt.
of,
scaled by Rt this
is
f]Prob[Rt
Rt
E[Rt - c\Rt
This
>
i.i.d.
the share of each firm that the entrepreneur necessarily holds.
expected flows
m, -
Then
individually financed via a debt contract.
— c.
component
is
oiu:
formulation
we have
simply the complement of what the firm
However, this makes no qualitative difference to the problem.
Derivation of the Central Planner's Program: Proposition 3
6.2
In this section
we show how
to arrive at the central planner's program, (P5) in the text.
Consider a central planner that maximizes the weighted
sum
of utilities of agents in the
economy.
maxX:^:'^ [p«,.<.)^
It is
+
(1
-p)«,c-j5^
easy to show that this can be rewritten in terms of aggregate consumption.
order condition for individual consimiption gives -S^
41
=
The
first
-^. This implies that aggregate
consumption
satisfies,
-C^
<a<
1
P
1
The
-a
central planners objective can then be rewritten as,
P«,s<s)' +
(1
-
pWuA^^ =
(C„(a;)Ct(u;))^
or,
maxX:7r-[KC<j'+(l-/^)«.<.)']=™^E^"(^»H^tM)^Consider next the aggregate consumption relations. In the good state there
is full
project
completion, so that,
In the bad state only
6nKn
is
Cn{G)
= RnKn
Ct{G)
=
RtKt-pKn
completed,
Cn{B)
= kr,{Rn-pAr,{l-9^))
Ct{B)
= ktRt-pe^kn-doj
where,
B
'"=
\?RtKt - Doj
P
Substituting in these relations for aggregate constraints, the central planners problem
{PAl)
maxfc„,fc„d„^^
S.t.
is,
Eu.e{G,B}7r'^(C»(w)Ct(w))^
= Rnkn
Cp = Rth - doj - pkn
C^ = k4R^-pAn{l-e^))
Cj = ktRt — pO^ kn — dgf
C„
aB
_
XfRtKt-Doj
Doj < min^{Xt RtKt + Xn^^^S^ - e^K^}
Kn + Kt = Wo + Doj
A
few remarks
constraints.
first.
(PAl) incorporates both the domestic and international collateral
Thus, the central planner
is
operating under the same constraints as agents
42
in the decentralized equilibrium.
Prices do not appear in either objective or constraints
except for the no-default debt constraint. Moreover, this constraint
\n appears. As we showed
earlier, this constraint will
Let us next rewrite this program so that
(P5),
more
easily.
In doing this
it is
it
is
-
the only one in which
never bind.
can be compared to the decentralized solution,
easier to rewrite
(PAl) and reintroduce
thereby
prices,
getting (P4):
{PA)
Eu;G{G,B}7r^e(a;)2u;*(a;)
max/f„,/c,,z)o,/
wl{B)
s.t.
w*2{G)
=
=
RtKt
RtKt
+
+
^^"4^)"^^"
^
-
Do.f
+
(sf
+ sf)
{X^RtKt - Doj)
- Doj - pK^
Doj < min^{Xr RtKt + A^ ^ff^L""" }
Kn + Kt = Wo + Doj
(P4) arrives from substituting back in expressions for the exchange rate into the
FOC
for
(PAl).
First write
(PAl) as
follows,
max^„,K.,Do,/,c-.,c-.,c5i.,.c^,
s.t.
+ (1 - ^)«i<j2
pd^^, + (1 - /.)<, = cr
p<,, + (l-p)c-, = C^n ~ Rn^n
Cj = Rtkt — doj — pkn
C^ = kn{Rn - PA„(1 - 9^))
Cf = ktRt - pO^kn - doj
Ett'" [p{<,s(^,s)~^
^n
=
p
Doj < min^iXtRtKt +
A^^^g^
-
^^i^n}
Kn + Kt = Wo + Doj
Let
a
=
{Kn,Kt,Doj) be the vector
maxa,c^^_,ej;^,<^,^,<^^
s.t.
where F{a)
reflects the
-A^r(K. +
date
(1
of date
choices,
and rewrite the problem
as,
+ (1 " P)i^,(^A)'
pd^^, + (1 - p)c^, = Cr(a)
pc^_, + (l-p)d;^,, = C-(Q)
F(a) =
E^r'^
constraints.
[/'«.<s)^
Forming the Lagrangian,
- pKs - Q"(a)) - <«,. +
43
(1
- pKs - c^i^))] - /^F^(")
which gives the F.O.C.'s,
&
1
IJ-t
2K«
1
I
c
""'
'
2Vct.
Notice that
Which
this
is
6.3
is
fJ-f
=
]^
=
e{u))2. Substituting this into the last constraint,
just,
the
same F.O.C.
as (P4) gives.
Proof of Proposition 4
Consider the Lagrangian of (P5),
jC=
^
TT'^e{uj)2W2{u;)
-
iJ.{kn
+ kt-wo-doj)
w6{G,B}
Which
gives F.O.C.'s,
5do,/
ddoj
^c^o,/
Denote the solutions to these equations as {kn,kt,doj)- Next consider the F.O.C.'s to the
Lagrangian of (P4),
44
We
can evaluate the partial derivatives in L* at the choices
dC*
dC
dkt
dkt
least
s^
one
>
<7 <
and
1,
+ n^e{B)h^{l-^)XfRt>0
we can conclude
But by the budget
6.4
that welfare can be improved by choosing at
of,
< doj
d'oj
do as
kt,doj).
ddQj
ddoj
Since,
(A;„,
constraint,
if
kn
—
kn
/C(
>
kt
one of these holds
strictly, at least
one of the others must
well.
Contingent Debt Contracts
In this section
we
rewrite the problem of sections 3
written contingent on the state of the world
lj
and 4 to include debt contracts that are
£ {G,B}. The no-default constraint
is
now
written as,
do J
The problem
amount
at date
1 is
<
\ ntkt + jj^
only altered by the fact that date
of date 1 debt international collateral than
decisions result in a different
would be the case
if
debt contracts were
not contingent.
We
can rewrite the date
(P5C)
program
maxfc„,fc,_d^^
s.t.
of (P5) as,
E<^G{G,B}7r'^e(w)2'u;2(a;)
W2{G)
w,{B)
d^j
kn
Allowing
for
economy by
^
- d^j - pkn
= Rtkt +
= R,h+
^^-l^f- -dEj
+ (sf + p^s^){\^Rtkt-dEj)
< X^Rtkt + Xnj^
+ kt = wo + E^[d'^j].
contingency does increase the amount of insurance possible by the domestic
offsetting
some
of the fall of A^.
45
However there
will still
be under-insurance
relative the central planners
problem as the basic externality
the central planners problem for a comparison
is
unaffected.
We
can rewrite
as,
1
(P4C)
maxK„,/c,,D5'_^
E^e{G,B}
^
- D^j + (sf + 5^) {XfRtKt - D^j)
= RtKt +
- D^j - pKn
w*2{G) = RtKt +
D^j < X^RtKt + A„ ^ffj5"
Kn + Kt = Wo + E4Doj]
wl{B)
s'.t.
It is
7r"'e(tj)2w;*(w)
^
apparent that the expressions for W2{B) and W2 are different
-
again reflected in the
domestic spread. For the same reasons as in the text, this will result in undervaluation of
international collateral.
Supporting Formulae
6.5
The
solution to
program (P6)
for
is
Banking Section
determined by the binding constraints.
Constraint
(i)
requires that loans satisfy,
a
Given an amount of loans, the demand
determined by the rate of
for deposits
l
=>
be
x'[^a{u,)<dl^iu;)+at-4j.
Turning next to the decisions of firms, demand
from intact firms follow from the same
for loans
logic as before (see
by distressed firms and deposits
PI and
notational change with respect to sections 2 and
the quantity of debt (supplied by distressed firms and
of face value of date 2 T-goods. In
1
will
interest,
L^ =
we make one
and foreign borrowing by banks
what
3.
P2). For ease of exposition,
demanded by
follows, the quantity of debt
present value of debt. Intact firms extend deposits to banks of
Lf)>
1
^
a:i_d(w)
= X^Rth - doj -
=
1
=>
xi,d(a;)
<
Lf)
Distressed firms take out bank loans of
^>
L"^
^
%=L'^ ^
0(1^^(0;)
di,d(u;)
XfRtkt
- doj -
a:i
intact firms) in units
is
in
^(w),
at
at.
to save production units,
=
max[kn
- <j,0],
di,rf(a;)<max[fc„-d^_/,0].
46
we had denominated
There,
terms of the date
Vis-a-vis the previous analysis, market clearing conditions need to be modified slightly
The aggregate amount
to take into account banks.
must equal the
of deposits in banks
aggregate deposits of the intact firms,
dl^iu)
=
=
D^^iu,)
X.^uj)
Likewise, the total loan supply from banks
=
(1
- p)xrA^)
must equal the new domestic debt issued by
distressed firms.
Taken together and combined with the capital constraint on banks
\tRtkt-4f-do,f<—
''a
XtRtkt-4f-doj>^
Consider the
first
inequahty.
When
=^
diX^) =
=>
d,4{u)
{1
-
this implies that,
p)xiAoj)
'a^
= {l-p)xt^ =
the capital requirement on banks does not bind, banks
aggregate domestic collateral perfectly - they channel
the intact firms to the distressed firms.
all
of the excess debt capacity of
The economy behaves
exactly as
if
A„
=
1 in
a
public debt market (section 2.4). Asset prices and investment depend on the international
collateral constraint,
pkn<XtRtkt-doj-dlf
pkn>XtRtkt-doj-d'oj
When
the capital requirement
depending on how tightly
L^ =
1
it
(i)
^
^
L^^n^^^l
L^ =
binds, the
binds relative to
L^j,
=
0^
^
1
e^<l.
economy can
demand from
=
fall
into regions
(iii)
In this case,
distressed firms.
and:
p{kn-{XiRtkt-doj-At))<^
^
L^ =
p{k^-{XfR,kt-doj-At))>^
^
B^
a
47
=
l
^
et
=
or (iv)
l
e-<l.
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