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Department of Economics
Working Paper Series
MIT,
International Liquidity
Management:
Sterilization Policy In Illiquid Financial
Ricardo
J.
Caballero,
Markets
MIT and NBER
Arvind Krishnamurthy, Northwestern University
Working Paper 00-04
May 2000
Room
E52-251
50 Memorial Drive
Cambridge,
MA 02142
http://papers.ssrn.com/paper.taf?abstract
id=xxxxxx
lI^SAWiKETfslN&flTDTn
OF TECHNOLOGY
OCT 2
5 2000
LIBRARIES
MIL Department of Economics
Working Paper Series
International Liquidity
Management:
Sterilization Policy In Illiquid Financial
Ricardo
J.
Caballero,
Markets
MIT and NBER
Arvind Krishnamurthy, Northwestern University
Working Paper 00-04
May 2000
Room
E52-251
50 Memorial Drive
Cambridge,
MA 02142
http://papers.ssrn.com/paper.taf?abstract
id=XXXXXX
Management:
International Liquidity
Sterilization Policy in Illiquid Financial
Ricardo
Arvind Krishnamurthy*
Caballero
J.
Markets
May
17,
2000
Abstract
During the booms that precede
and
struggle to limit capital flows
tool for this task
lic
bonds.
with
many
is
arguing that
is
it
may be
traditional
forces account for the private sector's reaction
paper we provide a model to discuss these
this
emphasize the international
this policy,
counterproductive once the (over-) reaction of the
But what
remain largely unexplained. In
We
policy
a swap of international reserves for pub-
an extensive debate on the effectiveness of
is
considered.
The main
their expansionary consequences.
sterilization -essentially
However, there
private sector
emerging economies, policy makers often
crises in
liquidity
management aspect
issues.
of sterilization over the
monetary one, a re-focus that seems warranted when the main concern
We
external crisis prevention.
first
is
demonstrate that policies to smooth expansions in
anticipation of downturns can be Pareto improving in economies where domestic financial
markets are underdeveloped.
policy
is
most needed - that
is,
We then discuss
The
of this policy via sterilization.
the implementation and effectiveness
greatest risk of policy arises in situations
when
financial
markets are
illiquid.
where
Our mechanism
is
akin to the "implicit bailout" problem, although the central bank acts non-selectively
and only intervenes through open markets
tion
in
our model.
Illiquidity replaces corrup-
and ineptitude. In addition to an appreciation of the currency and the emergence
of a quasi-fiscal deficit, the private sector's reaction to sterilization
may
lead to an
expansion rather than the desired contraction in aggregate demand or nontradeables
investment and to a bias toward short term capital inflows. The main insights extend
to international liquidity
JEL
Classification
Keywords:
management
issues
more
generally.
Numbers: E590, F310, F340, G380
Capital flows, sterilization policy, monetary policy, financial constraints,
balance sheets, excessive leverage, short term capital flows, debt maturity, quasi-fiscal
deficit,
sovereign
'Respectively:
risk, illiquidity.
MIT and NBER;
Northwestern University.
We thank Adriano Rampini,
Sergio Rebelo and seminar participants at Northwestern for their comments,
financial support. E-mails: caball@mit.edu,
a-krishnamurthy@nwu.edu.
and the
Roberto Rigobon,
NSF
(Caballero) for
Introduction
1
During the booms that invariably precede
struggle to limit capital flows
monetary
tight
open market
These
and
crises in
emerging economies, policy makers often
They primarily
their expansionary consequences.
sale of domestic
bonds or increased reserve requirements.1
can be extremely
sterilized interventions
— amounting to around seven percent of
inflow
on
In particular, they attempt to sterilize capital inflows through an
policy.
large.
During the early 1990s
example, the exchange intervention meant that over three quarters of
for
rely
The
reserves accumulation at the central bank.
GDP
its
per year
its
in Chile,
large capital
— went to international
sterilization of this intervention increased
the ratio of international reserves to monetary base from 3.5 around 1990 to over 6.0 by
1993. This pattern
was repeated
in
many emerging economies
capital flows to the developing world surged. In fact
during the early 1990's, when
most of the economies involved
second half of the 1990's had heavily sterilized inflows.
crises of the
Illustratively,
in the
many
of
these countries' central banks exhausted their stock of treasury securities in the process,
and had to
While
that
it
resort to alternative sterilization
sterilization
a widely used
tool,
comes along with a number of
Fleming
many
logic,
are integrated
central
is
is
(see e.g. Glick (1998)).
both policy makers and academics have warned
difficulties
argue that sterilization
and there
mechanisms
and
Building on the Mundell-
risks.
When
at best, ineffective.
is,
a simultaneous attempt to stabilize the exchange rate, the
bank has no control over the money supply because the private
open market
sale of
bonds
for
increase in capital inflows that
that fuel what
is
money (Mundell
accompany
(1962)).
The
is
sector can
sterilization, argues that since
counterproductive
Corbo and Hernandez 1996, Massad 1997) ?
(e.g.
Calvo
undo an
policy literature, noting the
perceived as an excessive expansion in aggregate
overvaluation, sterilization
capital markets
it is
these flows
demand and exchange rate
et al.
1993, Williamson 1995,
Building on Sargent and Wallace's (1981)
unpleasant monetary arithmetics, Calvo (1991) formally shows that, by raising domestic
1
Calvo
E.g.,
et al.
(1993) p. 146 write: "Sterilized intervention has been the most popular response to
the present episode of capital inflows in Latin America."
"Sterilization
among
2
was the most widely and
And
so does the
World Bank
181:
(1997), p.
intensively used policy response to the arrival of capital inflows
The sample included 22 emerging economies.
statement on behalf of the Latin American Governors of the Fund at the
the countries in our sample."
In his
annual meeting of the Board of Governors held in Hong
return on capital in a
booming economy
Kong
rapid productivity growth. Capital flows stimulate domestic
The probable outcome
will
resulting risk of widening the current account deficit,
reversed, should
writes:
is
some negative external shock
World Bank
"The high
-
IMF
rate of
These inflows are further
characteristic of economies experiencing
demand and could push up domestic
monetary authority safeguards domestic equilibrium.
incentive for capital inflows.
Massad
attracts large inflows of external resources.
encouraged by the appreciation of the domestic currency, which
rates if the
(1997),
joint
interest
This, in turn, could provide a further
be continued appreciation of the local currency, the
and the greater danger that these capital
occur." (page 4, our emphasis).
flows will
be
interest rates, the
its
debt-service burden
may jeopardize the very stabilization attempt
deficit that
by the
government increases
that
is
and creates a
quasi-fiscal
supposedly being protected
sterilization.
Uniformly, this debate has viewed the effects of sterilization as arising from changes in
the composition of the government's
liabilities
(money versus
bonds).- However, as noted
above, in a typical sterilized intervention the central bank also accumulates substantial
international reserves as assets
and some mix of domestic currency and bonds as
while the private sector's balance sheet changes in the opposite direction.
We
liabilities,
argue in this
paper that the impact that sterilization has on the asset side of the government's balance
sheet and on
—
in
its
counterpart in the private sector
understanding
management aspect
We
its
of sterilization over its
is,
it is
— and perhaps the chief factor
we emphasize the
international liquidity
monetary implications.
crisis-prevention rather than day-to-day fine-tuning that typically shapes
macroeconomic
And
policy.
second, external crises are invariably associated with a
3
country's shortage of international liquidity.
of these points (see
debt capacity
is
sterilization as
sovereign debt literature echoes both
(1989)).
tied to its aggregate international collateral (or liquidity),
when
a tool
an intervention
management
The
Eaton and Gersowitz (1981), Bulow and Rogoff
external crises occur
tively
central
build this view on two salient features of emerging economies vis-a-vis developed
ones: First,
their
That
consequences.
is
this external constraint binds.
for international liquidity
in
A
country's
and therefore
This paper studies the use of
management. Since
sterilization
effec-
is
domestic assets markets, an adequate treatment of this liquidity
issue requires us to
be
explicit not only
about the presence of an aggregate
external constraint, but also about the structure of domestic assets and their liquidity.
For a concrete example of the environment and policy issues addressed in this paper,
consider the following: Suppose, that
all
domestic production in the economy requires only
imported goods. In order to put up a building
import
all
downtown Bangkok, a Thai developer must
the raw materials for the building. Suppose that this building
collateral to
will
in
is
not acceptable
a foreigner, so that loans to this developer, against the collateral of the building,
only be forthcoming from other domestics. Lacking any internationally liquid assets
to exchange for the
raw materials,
it
would appear that the
real estate developer
is
in
a
dilemma. However, suppose that foreigners do accept, as internationally liquid assets, claims
on export sector receivables.
Then, construction can proceed as long as the
developer can find a domestic with export sector revenue
who
real estate
will accept the building
See Caballero and Krishnamurthy (1999) for a model of crises based on collateral shortages.
an internationally
liquid asset
is
international investor without suffering a steep discount.
A
shortage of international liquidity means that
the quantity of these assets, net of any pre-existing external debt,
needs.
For us,
one that can be sold (or borrowed against) at a moment's notice to an
is
insufficient to
meet
all
external financial
estate builders take out loans at this low cost of capital to "arbitrage" the government's
short-term liquidity commitment.
borrowing and a
shift in
We
show that
we emphasize the
analysis.
While not addressing
and Holmstrom and Tirole (1998) present models
through changes
to increased external
in public debt.
Government
policies are
in
'
6 7
'
international liquidity
monetary aspect. Changes
sterilization over its
and public debt are central to our
ford (1990)
mismatch leads
the composition of borrowing toward short maturities.5
Unlike the international finance literature,
agement aspect of
this
man-
in international reserves
sterilization,
both Wood-
which policy has
real effects
non-Ricardian because public debt
provides the private sector with liquid assets that they are unable to create for themselves.
Holmstrom and Tirole (1998) show that when there are aggregate shocks the private
may have a
shortage of liquid assets. Public bonds
policy has real effects.
In fact
we
As a
result, policy
assume that
shall
bond, the private sector anticipates a tax
for one.
this shortfall
and government
In our model, on the other hand, issuing public bonds does not
increase private liquidity.
one
make up
sector
liability
if
the government issue a public
which reduces domestic private
liquidity
along the lines of Woodford (1990) or Holmstrom and Tirole
At a more abstract
(1998) will be Ricardian in our model.
level,
nonetheless, our policies
are related to theirs in that government policy acts through changing the liquidity of the
(in
our case, international) assets ultimately held by the private sector.
we
In section 2
lay out our basic model.
We show
that
when domestic
financial
are underdeveloped an externality arises whereby the private sector draws
down
markets
its inter-
national liquidity too fast (over time) relative to the constrained efficient outcome.
This
sets the stage for the policy discussion.
In section 3
We
ments.
we introduce a government/central bank and
demonstrate conditions under which sterilization policy
Pareto improvements and those under which
When
describe
domestic secondary markets are
to a net loss of international liquidity
In section 4
it is
illiquid,
its rights
is
effective
and commitand leads to
completely undone by the private sector.
the government action can backfire, leading
and a Pareto
loss.
we show that our perspective naturally accommodates two
additional sources
public bonds and corporate bonds are imperfect substitutes.
With some
relabeling, this
mechanism can
also
be illustrated via a fixed exchange rate commitment.
Suppose that the government has reserves to sustain a fixed exchange rate over the next year, but has issued
bonds that expire
later.
Then
capital inflows to purchase the
exchange rate unless the bonds can be sold
in liquid
bonds cannot take advantage of the
secondary market in the next year.
If this is
other shorter term assets will be created to take advantage of the government commitment.
private sector finds that there
is
good demand
for
such assets and takes out loans
(i.e.
sells
fixed
not
so,
The domestic
the asset) and
increases real investment.
The
composition of capital inflows during periods of intensive sterilization has been documented
Montiel and Reinhart (1999) and Calvo, Leiderman, and Reinhart (1993).
Dooley (1999) has also emphasized some of the insurance aspects of interventions.
by, e.g.,
7
shift in
anticipate a crisis,
and
not do enough about
still will
The Economic Environment,
2.1
2.1.1
Basic setup
Time.
The world
Assets,
Time
lasts three periods.
is
it.
and Balance Sheets
indexed as
when agents design the productive
fully flexible period
portfolio allocations.
Date
the
1 is
period,
crisis
8
=
Date
is
the
structure, ownership structure,
and
t
when agents must
0, 1, 2.
shift resources
from the
future to cope with shocks in the present. Date 2 represents the unconstrained future,
the
economy
when
(relatively) rich in resources.
is
There are two types of agents:
Agents and heterogeneity.
(i)
a continuum of unit measure
of domestic entrepreneurs-consumers (henceforth, domestics) with linear preferences over
date 2 consumption of a single good, and
with large endowments at
all
is
one. 9
Endowment, Production, Investment, and
with
at date
w
net,
assume that domestic agents are
and access to a production technology.
domestic agents must import materials from the rest of the world in order to
They do
produce.
We
Liquidity.
units of an internationally liquid asset - e.g., the present value
of export sector receivables -
On
foreign financiers (henceforth, foreigners)
dates and linear preferences with no discounting, thus the
international gross interest rate
endowed
(ii)
this
by pledging
their international liquidity to foreigners
foreign debt of do,/- Production has a time-to-build aspect. Investments are
and taking on
made
at dates
realized at date
2.
Let k denote the total amount of capital devoted
to production at the beginning of date
1,
inherited from date
and
and output
1,
investment of
requires a date
increasing, convex
We
is
and
c(/e)
units of imported goods. c(k)
with a simple Bernoulli process. At date
1,
>
which can be
0,
offset
2.
The
R{6)k
=
(r
Firms
in
implied domestic heterogeneity,
rest experiences
<
a productivity
Rk.
critical link
between financing and production
any economy have ongoing capital needs (working
See Caballero and Krishnamurthy (1999) for a similar model with aggregate shocks.
9
The
distinction between foreigners
the economy.
Our
and domestics needs not be as stark as posited
may be grouped with one
fall,
1 of k, in units of the
8
savers, for example,
strictly
of:
+ 6A)k <
This time-to-build structure underlines a
crisis.
its
by reinvesting a fraction 6
imported good, in order to realize output at date 2
during a
assumed to be
half of the firms are spared of further investment
and go on to produce Rk units of goods at date
r
is
creating capital of k
positive.
capture the normal churn of the economy, with
A = R—
Then
0.
capital, etc.).
here.
Domestic
or the other depending on the nature of the shocks faced by
insights can be easily extended to
more complex environments along
this direction.
On
another domestic in order to take on debt.
the other hand,
we assume that rk cannot
be pledged to a foreign investor. Foreigners only lend to a firm against
means that the maximum amount
liquid assets of w. This
take on
is
w. u While much
of this
sovereign aspects that reinforce
it.
its
of external debt the country can
asymmetry can have a microeconomic
We
internationally
origin, there are
return to this issue in the next section.
Assumption 3 (Liquidity Bias)
Domestics lend against
Foreigners lend to domestic firms only against the backing of w.
both
w
and rk.
Firms can
Financial structure and Balance Sheets.
either domestic or foreign investors.
fully
We
raise finance at date
assume that
all
finance
and date
must be default
1
from
free
and
secured debt - either by domestic liquidity in the case of domestics, or international
liquidity in the case of foreign investors.
decisions result in firms arriving at date 1 with installed capital of k
Date
debt of do j.
At date
escapes the shock
is
of domestic liquidity
way
simplest
is
a firm that receives a shock
1,
intact
and
(I)
w
to think of the
.
The balance
is
distressed (S), while a firm that
sheet of a domestic firm has assets of rk units
units of international liquidity,
and
foreign debt of do,/.
w
the other hand, a domestic sees both this quantity as well as rk as assets.
debt constraint with respect to foreigners at date
d
At date
1, if
The
asymmetric treatment of collateral by foreigners and domestics,
to think of foreigners studying a balance sheet of the firm as perceiving only
On
and foreign
,/
<
as assets.
Thus the
is,
w.
a firm takes on additional debt with foreigners, the date 1 debt constraint
do,/
+ dij <
is:
w.
Discussion of main assumptions
2.1.2
Let us pause at this juncture and discuss our main assumptions, starting from the two
borrowing constraints.
We
up to
have assumed a
his
friction that prevents
a domestic entrepreneur from borrowing fully
output from another domestic. Investment at date
produces rk goods at date
2,
and depending on the realization of shocks and reinvestment, an additional Ak of output.
The
stark distinction between domestics and foreigners in their valuation of assets
simplicity.
In reality,
be behind capital
many
flights),
is
only
made
residents behave like our foreigners at time of distress (e.g., households
and many foreigners behave
like
informed and connected with the domestic establishment).
our domestics
(e.g.,
for
may
institutional specialists well
that only a fraction of exports or net exports
On
international collateral.
is
the other hand,
the sovereign debt literature typically just imposes international collateral as an aggregate
We
constraint.
take a microeconomic perspective by assuming that
w
agents in the economy
who can
trade
may
be, here
we have simply posited assumption
Sensible as
an alternative
among themselves and with
we introduce a government and
next section
bias. In the
The
it
it
production shock at date
1.
is
held by individual
foreigners.
3 regarding liquidity
sovereign risk, thereby providing
—and more explicitly modeled— grounding
assumption worth commenting on
last
is
for the
assumption.
the non-observability of the idiosyncratic
Domestic agents are ex-ante identical at date
0.
If
the pro-
duction shock was verifiable, domestic agents would write contracts amongst themselves to
insure that they would be ex-post identical as well.
date
amongst domestics and
1
frictions in the
Assuming non-observability
effect.
is
There would be no heterogeneity at
domestic market would have no economic
necessary to study the impact of these frictions.
The Microeconomic Problem
2.2
Domestics have two sets of decisions. At date
1,
given the date
choices of other firms
(through prices) and the realization of the idiosyncratic shock, a domestic firm must decide
how much
to borrow (lend)
reinvest.
and how much international
invest
induction, starting from date
Date
and
1
problem.
production shock.
At date
0,
liquidity to retain.
a firm must decide how much to
We
solve this
problem by backward
1.
Consider the problem of a distressed firm in raising funds to alleviate
A
its
choice of 6k will result in output at date 2 of R(6)k goods. In order to
save a fraction 6 of the distressed unit, the firm must raise finance and reinvest 8k import
goods.
date
1
It
can do this in two ways.
that
it
First, the firm
may have some
can use to borrow directly from foreigners. That
is
international liquidity at
the firm can always raise
directly,
dij
The
date
latter quantity
1.
The
rest
is
,/.
always positive, and represents the
must come from
since their capacity to
<w- d
intact firms,
borrow abroad at date
minimum
that a firm can raise at
which also have access to foreign investors
1 is also
w — do,/-
A distressed firm can use its domestic liquidity to access the international liquidity of the
intact firms. In equilibrium, the latter discount the domestic liquidity at a rate of L\ > 1
in providing international liquidity.
that
is
L\
is
the date 1 interest rate. It
is
not an interest rate
driven by expectations of default or currency depreciation. Rather,
respectively.
The same
statistics for firms that
do not borrow
it is
driven by
in foreign currency (75 percent of firms) are:
46 percent, 139 employees, 2.36, 61 percent and 19 percent. See Dollar and Hallward-Dreimeier (1998).
10
Equilibrium and Crises
2.3
Market clearing
Equilibrium.
domestic debt market at date
in the
(capital letters
1
denote aggregate quantities) requires that the aggregate amount of domestic debt taken on
by distressed firms
fully
is
funded by intact firms:
2
Therefore, market clearing,
D l4 = X 1<d
(1)
,
determines the gross interest rate, L\.
An
equilibrium of this
(9,d\j,di d,xi
f
t
economy
and
d), respectively,
and date
consists of date
prices
L\}
Q
1 decisions,
(k,doj) and
Decisions are solutions to the firms' prob-
lems (PI), (P2), and (P3) given prices. At these prices, the market clearing condition
(1)
holds.
Let us
now study
equilibrium in more detail. Starting from date
and investment choices of the distressed firm given (k,doj).
distressed firm
borrow up to
would choose to save as many of
=
w- d0J
the amount raised from international investors,
for restructuring, k,
shortfall. It will
First, if
consider financing
A >
production units as
it
1,
then the
can.
It
may
international debt capacity,
its
dij
If
its
1,
w — doj,
is less
than the funds needed
the firm will have to access the domestic debt market to
choose to do this as long as
the interest rate.
(2)
.
If
A>
L\, or the return
the firm borrows fully up to
its
make up the
on restructuring exceeds
domestic debt capacity,
it
will issue
debt totalling,
d\,d
and
raise funds
reinvestment at date
less
rk,
(3)
with which to pay for imported goods of
the right hand side of
borrow
=
than
its
(2) is
1
and
jf-
•
As long
more than the borrowing need, the firm
all
as the
is
sum
of j&
and
unconstrained in
its
production units will be saved. In this case, the firm will
domestic debt capacity (and perhaps
less
than the international debt
capacity)
Intact firms can tender at
most
their excess international debt capacity of
return for purchasing domestic debt.
They
will
Where we have used
the fact that at equilibrium prices,
12
do,/ in
choose to do this as long as the domestic
interest rate exceeds the international rate of one,
16
w—
L\
>
1.
^^ = d\ j.
where both liquidity constraints are binding. At the aggregate
constrained with respect to foreigners; at the individual
level,
with respect to other domestics since they are selling
aggregation; real investment
rate of L\
for
is
is
all
level,
the economy
is
liquidity
firms are liquidity constrained
of their domestic liquidity in
constrained; domestic spreads are positive; and the interest
above the international interest
the prevention-policy questions
we
rate.
This
the most interesting configuration
is
intend to address in the main section of the paper.
Technical Assumption 1 (Conditions for Crisis)
Assume
c'-
1
that:
f'^±5 + c
1 + A
)
(
c'"
]
1
<r
< A
A + i?\\
1 + A
<w
<
The assumption guarantees that
c
,_ l
fl
A>
in equilibrium
+R
2A
L\
>
+ c\c!-l(l±R
2A
1
<
and
1.
This ensures
focus on a case where both (3) and (4) bind.
Proposition
1
(Crisis
Under assumption
constraint
and
1,
Region)
date
decisions of k and doj are such that both the international
the domestic constraint are binding.
the domestic illiquidity index are positive,
O,0<
The international
liquidity
premium and
and some projects are downsized. L\
> l,Sd>
1.
w
- d(i.r
=k
w-d„
w
"
d (i.r = a k
k = c'Cd,,,)
Figure
Graphically, the solution to (P3)
the budget
set.
This
is
is
2:
(P3)
represented in figure
2.
The
inner curve represents
the set of points of (w—doj, k) such that the date
14
budget constraint
substitute the expression for L\, (5), into the objective of (P4), arriving at an expression
that
is
The program
free of prices.
for a central
max K ,D0i/
(P5)
(R
+ r)K +
w>
s.t.
planner
2A(W-D 0J
)
d,Qj
c(K)
The
is,
= D 0J
solutions to (P5) are the constrained efficient decisions of the economy.
difference
in (P5)
between the programs (P4) and (P5)
from that of (P4) we arrive
sd
At a given equilibrium,
this
is
The
only
in the objective. Subtracting the objective
at,
(j-K-(W-D QJ )y
term must be
zero.
But
it
is
apparent that individuals and
the central planner value a marginal unit of international liquidity and domestic liquidity
quite differently.
Moreover, this misvaluation
is
directly proportional to Sd, the domestic
illiquidity index.
The
first
order condition of (P5) gives,
c'(K)
= R+r
2A
'
while that of (P4) yields,
R + r£
A + Li
c'(fc)
Graphically,
we can
w-d
"
represent the solutions to (P4) and (P5) in figure
o.r
k = c'(d„.f)
Figure
3:
(P4) and (P5)
16
3.
some of the international
to
liquidity held
by the private sector (which needs to borrow abroad
buy the public bonds).
Widespread as
may
it
be, sterilization
perceived as a "risky" strategy, hampered by
is
the possible overreaction of the private sector. But the mechanisms behind this "risk" are
not well understood,
sterilization in
instruments.
alone modeled.
let
In this section
we
offer
a methodic analysis of
an economy with underdeveloped financial markets
We shall begin
for private
and public
by noting conditions under which the private sector completely
undoes the central bank's action.
we demonstrate
In cases where this does not occur,
conditions under which the policy can be Pareto improving, and those under which
Before doing so, however,
results in a Pareto loss.
government,
its
we must introduce the
instruments and constraints, and the implications of
it
(consolidated)
action for asset
its
liquidity.
Preliminaries
3.1
Public Bonds
3.1.1
We
consolidate the central
need
in order to address
bank and the
The minimum number
treasury.
our policy question
is
4,
minimum and
when we
We
we
one public financial instrument and a tax to
finance any quasi-fiscal deficit that the sterilization policy
this
of ingredients
may
generate.
enrich the set of public financial instruments to include
19
We
start with
money
in section
discuss exchange rate systems.
formally describe public bonds in the next assumption, and justify
the preliminaries-section,
when we
it
at the
end of
discuss the key assumptions of this section.
Assumption 4 (Public Bonds)
At date
0,
the
government issues public bonds with face value B:
(Long Maturity) These bonds mature at date
•
markets at date
•
(Illiquidity)
cost
A
but can be bought
and sold
in secondary
1.
sale at date 1 of
ofO<a<
2,
1.
Selling
X
one unit of a date 2 government bond suffers a real
units of bonds only recovers
V~
units of international
liquidity.
19
That
Importantly, taxes are always paid in units of liquidity (either domestic or international).
suppose that a firm has rk units of domestic liquidity at date
on the
firm.
government
government,
Then,
will
this
be
after the transaction the firm will
left
with
T
be
left
is
and that the government
units of domestic liquidity. Thus,
simply reduces
its
liquidity
if
—T
18
a tax of
the firm has a tax liability of
create liquidity.
is,
The
that they alter the balance sheet of a firm by introducing an additional
the firm's ability to raise finance from other agents.
levies
units of domestic liquidity,
with respect to other firms. That
and Holmstrom and Tirole (1998), our government cannot
taxes
1,
with rk
is,
T
and the
T
to the
unlike Woodford(1990)
simplest
liability.
way
to think of
This then affects
sterilization transaction
its
own
would be
action very quickly, policy
undone at date
fully
must
fail.
Essentially the one period bonds are viewed
as perfect substitutes for the reserves they replace. It
require the extreme assumption
Long maturity
because there
of public bonds
is still
is
worth pointing out that we do not
crisis.
not a sufficient condition for imperfect substitutability,
is
a secondary market open and the government
market at date
There are two types of domestic
1.
will inject its reserves
until date 2 are effectively defaulted
1,
and
on to
limit their date
government commits to
into the
market at date
since he
knows he can
foreigners.
As a
2,
any assets held
result, foreigners
holdings to reflect this fact.
must
sell all
In principle,
inject all of the foreign reserves gained during sterilization
1
,
sell
and
assets, corporate assets
government bonds. Since foreigners cannot repatriate payments at date
assets at date
new government
above, but just that a fraction of the
matures after some potential external
liabilities
into this
made
Since the goverment reverses
1.
if
the
back
then a foreign investor would be willing to buy a domestic bond
these at date
the government's reserves.20 Requiring that
1 for
the public reserves are released only on presentation of an invoice for imported goods implies
that the foreign investor cannot, directly, repatriate the return from selling the domestic
bond
at date
1.
Taken together, the two assumptions on sovereign
assets are imperfect substitutes for the foreign assets
and
sterilizations,
this allows
some space
for
risk
imply that domestic
removed from the private sector during
the policy to be non-Ricardian. Finally, the
sovereign risk assumption also provides a deeper foundation for our earlier assumption on
liquidity bias.
Our sovereign
pirically
risk
assumption
difference
is
made
e.g.
that, since decentralization
debt literature simply posits a
actions
similar to that
supported sovereign debt literature (see
The main
financial
is
is
maximum repayment
in the widely accepted
and em-
Obstfeld and Rogoff (1998) ch.
6).
not their main concern, the sovereign
for
a country. In our setup domestic
markets are modeled explicitly and hence we have to be careful about how private
may
affect the
maximum repayment and
perhaps undo government actions. Both
aspects of our assumption, suspension of convertibility and selective default/rescheduling
have been observed in recent years
Mexico
for
Finally,
is
Malaysia
for
the former, and Ecuador, Korea and
the latter).
we
will
be interested
bond market. Our modeling
-
(e.g.
in studying the role of illiquidity in the
of illiquidity - transactions costs incurred for early liquidation
not unusual. As we will see below, illiquidity can exacerbate the impact of the govern-
ment's maturity mismatch on the private sectors' asset liquidity.
°Imagine the following scenario: the government issues
bond
secondary public
at date
for $1.
He
sells this at
date
1,
1
bond
for $1 at
On
date
one hand,
0.
The
illiquidity
is
foreigner buys this
knowing that the government will inject the $1 back into the
market, and this will provide the liquidity for his exit from the country.
20
Debt Markets
Sterilization with Liquid Public
3.3
Let us start our study of the effectiveness of sterilization in a context where private asset
markets are underdeveloped but secondary public debt markets are domestically liquid
(a
=
0).
Lemma
2 (Date
Interest Rates)
government bonds in equilibrium,
// the private sector holds
the date
must
interest rate
satisfy,
>L
LQ
This
is
easy to verify. In order for domestics to hold government bonds, they must be
compensated
A + L\.
in the
However purchasing one bond
an extra Lq A ~^ L
yields
i
.
This gives us the inequality
lemma.
naturally associated with a capital inflow, as either foreigners or domestic
is
buy the high
investors will attempt to
horizons, however. Thus,
and
at date
sell
if
government bonds.
yield
foreigners see a scenario
them back
to purchase the bonds.
Foreigners have short
where they can purchase these bonds
to the domestic private sector at date
They
will
do
1.
Thus the international
buyer of the bonds
short horizons,
it
is
they
will step in
has
liquidity of the public
closely tied to the international liquidity of the private sector.
is
1,
this only to the extent that the private sector
international liquidity to offer at date
bonds
Taking on an extra unit of debt costs
for losing their international liquidity.
Sterilization
some
X
the domestic private sector
itself.
The other
potential
Since this sector does not have
can always take advantage of the high return on the bonds by borrowing
abroad (a capital inflow) to purchase the public bonds. However, once again, the capacity
of the private sector to do so
is
limited by
its
international liquidity. In both cases
liquidity of the private sector that determines the
the
of sterilization.
Liquidity Conservation
3.3.1
Lemma
// the
outcome
it is
3 (Liquidity Bias
government
and Aggregate International
Illiquidity)
sterilizes so that the private sector is internationally illiquid, do,/
=
w,
then foreigners will hold no domestic claims and restrict their holdings to international
claims.
Proof: see appendix.
This
is
the date
effect of future
suspension of convertibility and market
the domestic private sector has no international liquidity to offer a foreigner
domestic claims at date
0.
The
1,
then the foreigner's date
1
liquidity bias extends
illiquidity. If
when he
back to date
foreigner anticipates that there will be a suspension of convertibility at date 1
22
sells
and
^,From the previous proposition,
Taking the other case
(d
j =
w),
we can
sterilization
program
rewrite the
is
ineffective
if
doj
<
w.
as,
+ rA) + (6-T)(l + A)
c(k) + tt = w
maxM
fc(i?
s.t.
The
we know that
-
order conditions for this program yield,
first
LQ c'(k) = -^—t1
+
Now
optimal policy will be such that k
c'(k)
<
c'{k').
Lq
<
LX
we must have
For this to be the case,
k'.
that
satisfies,
,
jR
R + rA
+rA
Rewriting this yields
,
T
L
>
°
R + r£ A + L
R + r±A + Ll
r
Ll
'i
(8)
(8)
-
Consider the market clearing condition for L\
Ll
which we can rewrite
rK + B-T
_
=
Lo
2B
as,
L
1
^-+L ^-= rK + B-T.
1
Lo
l>o
21
Substituting in the government's budget constraint and rewriting,'
rK
—
U-L
Whereas,
L,
If
<
fc
with
this
21
k'
then -g
(8),
The budget
=
x
rK'
_
—
W-D'0J
W - 0(7^) > W - D'of
we can conclude
that Lq
constraint for the government
>
is
L\.
to
Lo
= L\,
pay the
22
We
both
0.
Combining
B
l
^B = B.
When, Lo >
it
must be that
T>
still
in the region
where
L\,
on the government debt.
need to make sure that
A>
L\ after the intervention so that we are
liquidity constraints are binding.
rK <
Since
L x < L\ and B >
22
the budget balances without having to raise taxes.
interest
also
Therefore,
that,
T+L
When
.
K
<
K',
if
the condition
is
-^-B
Lo
= A(W-c(K))
satisfied at the decentralized solution, it
central planner's solution.
24
must
also
be
satisfied at the
and date
bank action at both date
When
sterilization
The
uidity provider.
1.
succesful, the private sector
is
bank takes over
central
sector has little incentive to
do
so that the private sector has
so. Is it possible to arrive at
little
the private
scenario where both, L\
falls
and the private
incentive to liquidity provision,
sec-
the private sector would free-ride by
If so,
lose international liquidity. In this section
very real possibility
falls,
liq-
provisioning (relative to the case of no-intervention) and on net the
its liquidity
economy would
Indeed, since L\
this job.
tor remains the marginal liquidity provider?
cutting
not the marginal international
is
when domestic markets
are illiquid.
we show that
We
this scenario is
a
demonstrate conditions
shall
under which the capital inflow accompanying sterilization leads not just to a purchase of
government bonds but also to increased lending to the domestic private
At date
1,
government bonds are exchanged
and any potential foreign
sector.
by both domes-
for international liquidity
Distressed firms
sell in
order to
receive funds for investment, while foreign holders sell in order to exit the market.
We now
tic distressed
firms
>
reintroduce a friction in this transaction (a
The
illiquid
secondary market makes
bond and exchange
it
investors.
0).
harder to liquidate the two period government
it
for international liquidity. Transactions costs
must be paid, there are
search costs involved in making the exchange, and potentially even rents must be paid to
market makers. This
will increase the
will further raise the required return for holding
domestic
illiquidity index,
at date
s<*,
bonds at date
0,
and
1.
Backfiring Policy
3.4.1
Suppose that the government
sells
bonds
at date
intervene sufficiently so that the private sector
an attempt to
in
sterilize,
internationally liquid at date
is still
government bonds are sold at interest rate of Lq. Consider the program
bonds at date
to hold b
(P7)
for
0.
B
a firm choosing
0,
(w - d ,/)(A
maxfcido/i6
<w
c(fc) + £ =
+
L)
+ k(R +
r
£
)
+
(&._
T )(l +
(1
- a)£)
doj
s.t.
Lemma
but does not
d
,/.
4 (Government Interest Rates)
The date
interest rate
on government bonds
always exceed the date
will
1
interest rate.
L >Li.
This
lemma
is
easy to
national liquidity. At date
verify.
1, if
Purchasing one government bond costs
the firm
is
distressed the
proceeds invested to yield output at date 2 of
A^2
26
.
If
bond can be
the firm
is
-£-
units of inter-
sold for ^y^
and the
not distressed, the bond
Rewriting this expression, yields
tK-T
The
loss to the
B\
(B
(B
_„
rewrite this expression
1
by substituting
T=B—
in,
imagine that the private sector exactly
That
is
This
jj-.
falls,
is
(10)
)
offsets the
government's reserve accumula-
debt. In this case, the term in the parentheses on the right
would be unchanged by
be that L\
Thus,
as,
B
+ -.
\
/
in taxes.
to say, suppose that for every unit that £- rises, the private sector takes on
an extra unit of date
side
j^B,
,
at the high rate of Lq
must be made up
at the lower rate of L\
rK
(B
_
=W+ (_Do
tion.
B
\
government of intervening by issuing bonds at date
and purchasing bonds at date
Now
„
why
However
sterilization.
if
this
is
the case, and
B >
0, it
hand
must
since the supply of liquidity to purchase private sector assets has risen
The government supports
sterilization backfires.
by
private sector assets and
hence lowers corporate borrowing costs.
The
illiquid
case where the government bonds are fully liquid highlights the key role played by
markets in the previous conclusion. Suppose that
can be sold at date
1
price of L\ at date
1.
without any
B
The government's
0.
=
0,
so that government bonds
friction. In this case, distressed firms sell
Thus append £-
rK
a.
to the left
(B
„
„,
hand
B
bonds at the
side of (10) to arrive at,
„
n
\
reserves go towards purchasing back the
B
bonds that
Sterilization does not bring additional support for corporate assets,
it
issued at date
and hence L\
is
unaffected.
Let us
now
state this result
more
formally.
Proposition 5 (International Liquidity Loss)
Consider the case where
and
(9)
(9)
when
when
B>
B=
and
but doj
a >
let
<
0.
Let
(k' , d'
,
,
L[) be equilibrium choices and prices to (PI)
(k,doj,b,Lo,Li) be equilibrium choices and prices
w. Then, we have
that,
U
<
L\
k
>
k'
doj
>
d oj
Proof: see appendix.
28
+ y-
to
(PI) and
Proposition 6 (Sterilization with Illiquid Markets) There
of
B >
exists a sterilization policy
such that the resulting equilibrium of (k,doj,b, Lq, Li)
is
Pareto superior
to
(k',d' f,L[), as long as,
Domestic markets are
sufficiently liquid (i.e small a),
•
(i)
•
(ii)In the resulting equilibrium, do,/
—w
>
and
so that the private sector
internationally
is
illiquid.
Optimal policy requires
Lq
>
L\,
and
that,
in equilibrium,
the
government
the date 1 interest rate falls relative to
See the appendix for the proof.
The
result
raises date
no -intervention, L\
interest rates,
<
L\.
4. The
PRIV
a function of k (U
), and
can be understood by studying figure
figure traces out welfare for the decentralized equilibrium as
welfare for the equilibrium assuming that the central planner intervenes via sterilization,
and
forces the
economy
to incur the secondary market illiquidity costs (U
cp ).
(JCP [JPRIV
k
Figure 4:
As
in proposition 2,
it is
U cp
and
that
it
clear that the central planner values international liquidity
less.
it is
cost, since firms
must
sell
their
is
beneficial as long
-
point
C on the
That
bonds into an
figure.
The
30
The
is,
K cp
illiquid
when a >
U CP (K CP ) > u PRIV (K PRIV ). But
the size of the externality versus the cost of intervention.
inefficient point
benefit of intervention
choice.
clear that intervention always lowers the welfare function
Intervention
an
Thus the
moves the private sector away from a sub-optimal
However intervention has a
Thus,
c-'(w)
U PR1V
higher than the private sector, and domestic liquidity
is
=
this
<
K'.
market.
0.
depends on
private sector always chooses
cost of intervention
is
that
it
lowers welfare
must be that Lq > L\. Hence, atempting to
on the
large detrimental effects
an
sterilize in
quasi-fiscal deficit, even
illiquid
bond market can have
without the rewards of a higher
domestic corporate borrowing rates and a slowdown in aggregate demand.
Needless to say, this deterioration in the
fiscal situation
can be worsened
if
the reserves
of international liquidity are not targeted back to the private sector in an efficient fashion at
date
This will occur
1.
if
the government receives a return less than L\ on
its
international
reserves.
Excessive Short
4.2
Term
Capital Flows
The observed shortening in the maturity of capital
The
interesting from our point of view.
and long term debt
in defining short
of long term debt as short
in
flows following sterilization
is
particularly
step in arriving at this result from our
One can
terms of their insurance features.
A
term debt plus rescheduling insurance.
model
is
think
simple extension of
the model presented in section 2 shows that agents undervalue the insurance component
of long
<
term debt as long as L\
The
are underdeveloped.
result
A, which
is
when domestic
the case
financial
markets
akin to our previous result on the undervaluation of
is
international liquidity.
Suppose that only a fraction
foreigners at date
l.
26
Debt that
be viewed as short term debt.
—
1
is
ip,
<
where
Now
suppose that the
2.
A
of (1
—
ip)w at the international interest rate of one.
domestic firm has two choices. (A)
roll this
1
1,
of
— ip
It
w
directly pledgeable to
is
of international liquidity will
rest, tpw,
payment of a monitoring
date
can
<
taken on against this
at date 2, however doing so requires
it
ip
can be seized by foreigners
ofO<e<(A —
cost
l)at
can take on one period debt up to the limit
Then
at date
1, if it
needs the funds,
over and take on additional debt of ipw. However, the interest rate on this
additional debt will obviously be above one to compensate the foreign lenders for bearing
the monitoring cost.
(B) It can take on long term debt against the full w, in which case
the foreign lenders will always pay the monitoring cost to seize the additional ipw. Thus,
domestics face an upward sloping term structure of borrowing.
With option A, only
and draw down
ipw.
firms that are distressed at date
With option B, on the other hand,
extra-collateral ex-ante,
and the
markets are
26
Diamond
model
is
The
latter option
an extra unit of liquidity
the return to intact firms
is
all
take on the additional debt
firms will have pledged their
intact firms will sell the corresponding international funds
at date 1 to the distressed firms.
social value of
1 will
only L\
—
1,
is
A—
1
is
>
clearly socially preferable, since the
e.
The problem,
which could well be below
illiquid. If this last inequality holds,
the equilibrium
is
e if
as before,
depends on aggregate liquidity
32
that
domestic financial
one where no firm values
(1991) develops a model of debt maturity structure based on liquidity risk.
related but the maturity structures
is
risk.
The
sketch of our
In order to lend to the corporate sector at date
from corporations and need to hoard
1
They
per unit of debt's face value.
The
money
central
at date
is
also ^j-.
bank
1.
fully
bankers require domestic collateral
units of domestic
1
are born with
maximum amount
This means that the
corporate sector)
<
\i
0,
M°
money between
dates
and
units of high powered money.
make
of loans that the banking sector can
(to the
28
backs up
M°
with international reserves, which are exchange
Thus, the nominal exchange rate at date
of the exchange rate system prevailing at date
0.
Banks
1,
E\,
is
for
equal to one regardless
are not needed at date
1,
so bankers
can participate directly in the financial markets without holding any money.
Taken together, these assumptions create a transmission mechanism
etary policy via the "lending channel."
29
A
central
for
domestic mon-
or
expands M°//x
bank that contracts
can affect the amount of lending from bankers to the corporate sector. Our assumptions
mechanism on the date
are designed to isolate the impact of this
boom,
as
is
it
apparent that at date
1
the Central
Bank
will
problem of taming the
attempt to ensure perfect
domestic aggregation of international collateral.
Monetary Policy
5.2
We
remove bonds
for
now and
reserve requirements,
None
\i.
Exchange Rate System
in a Flexible
fix
M°,
so
monetary policy takes the form of a tightening
main conclusions
of our
is
by reintroducing bonds
affected
and implementing the monetary contraction via open market operations instead
At date
0,
bankers lend as
much
in
as they can to firms as long as
(see below)
Lq > L\. That
is,
they
supply:
Xq = min
Let
Lq
Xq
=
1
L\.
denote the potential demand
Then the amount
lent,
Xq,
These steps can be disentangled more
goes as follows:
Banks
for loans, defined as
M°
demand
that would arise
= min[X s ,Xr]
finely.
(12)
on taking deposits from
banks can only take in deposits of
—
.
We
savers.
Let
\i
be the reserve
additionally assume that banks
cannot raise funds from savers in any other way than by taking deposits. This means that the
amount
of loans that the banking sector can
that the
rK
That
sales,
29
is
make
of domestic liquidity that firms create
loans to a firm with
some domestic
if
For example, separating bankers from savers, the story
face a reserve requirement
requirement. Then, given
the
is:
X
28
(11)
(to the corporate sector)
is
only tradeable
liquidity can only
among
is
also
—
.
Last
maximum
we assume
the corporate sector and banks.
be made by other firms
(for
example, via asset
trade credit, or mergers), or from savers through the banking sector.
For discussion and evidence of the lending channel in the U.S., see for example, Kashyap, Stein and
Wilcox (1993).
34
Monetary Policy
5.3
Fixed Exchange Rate system
in a
Suppose now that the exchange rate
fixed at
is
one at date
stands ready to swap international reserves for domestic
There are two basic scenarios to consider in
one, foreigners do not value domestic
first
case bankers will offset any
exchange
domestic money. They will do so
for
money
this fixed
exchange rate system.
as collateral.
It is
selling their
Lq
for as long as
is futile.
and the central bank
at the private sector's will.
31
monetary contraction by
Mundell-Flemming, monetary policy
as in
money
as well,
X\
>
In the
apparent that in this
to the central
L\ and X\
>
X\ =
for
This changes once
bank
in
Thus,
0.
then the
bankers are constrained in the same sense as firms were in section 3 in the scenario where
sterilization
worked. The "holy trinity" of open economy macroeconomics establishes that
only two out of the following three are possible: effectiveness of monetary policy, control
of the exchange rate,
that gives back
The other
lateral. In
policy
is
its
and
free capital mobility. It is the
powers to monetary
limit case to consider
that case, neither
useless.
Xq
is
policy.
endogenous canceling of the
latter
32
when high-power money
is
part of international col-
nor X\ can be affected by monetary policy, thus monetary
This case highlights an important aspect of the policy considerations
we
have stressed throughout the paper: In order to be successful in preventing an external
crisis,
the policymaker needs to be able to "hide" some of the private sector's interna-
tional liquidity at date 0. This,
it
will
internationally liquid instruments to
Final
6
A
if it
it
In practice, the
to study this policy.
On
in
main macroeconomic
emerging economies
one hand, the sovereign debt literature
aggregate constraint. But as
sterilization policy.
sterilization policy.
On
external- crisis
it is
identifies the
and therefore
is
the
aggregate
links external
designed to answer a different question, this
markets and
is
therefore unable to study outcomes of
the other hand, the Mundell-Fleming framework directly addresses
However, as
it
essentially ignores all aspects of the external financial
constraint and instead emphasizes the monetary aspect of sterilization,
Recall that bankers need to hold the
mean
is
However, existing models are not particularly well suited
literature suppresses domestic financial
does not
selling highly
tool utilized for such purpose
international constraint as limiting external debt repayments,
31
be
private sector.
its
macroeconomic policy
sterilization of capital inflows.
crises to this
attempts
Remarks
central consideration of
prevention.
not be able to do
money
that foreigners wouldn't accept
at date
money
in order to
as a
method
make
of
it is
best suited
the loans. Hence, this assumption
payment
at date 0, but that
money
in
banks' hands does not count as collateral.
32
Reisen (1993) argues that the "holy trinity" does not apply
ments rather than open market operations.
We
when
do not find support
36
the central bank uses reserve require-
for
such claim in our model.
and
asset
liability
management,
in the
policies -
management
in practice,
and
on the corporate
its effects
sector. Liquidity
has more layers. Argentina has considered liquidity requirements
banking sector. Central banks often respond to inflows by increasing domestic reserve
requirements. Until recently, Chile required the private sector to hold liquidity against short
term external financing. Each of these actions results
decentralized level.
effective
When
liquidity provisioning
is
in liquidity provisioning at
a more
by the banking system more or
less
than that of the central bank? In assessing the international liquidity of a country,
should we equally weight the holdings of the central bank and those of the domestic banking
system?
These are important questions that
framework to include a domestic banking
require,
sector.
among
other things, enriching the
This remains something we are working
on.
Similarly, while sterilization
cluding external public debt
— and
management
long term solutions to the problems
nature.
international liquidity
Our framework not only
—
we have
may be
management
in general, in-
the tool of choice in the short run,
highlighted are not cyclical but structural in
illustrates the
second best options and policy problems,
but also points at domestic financial underdevelopment as the primitive source of concern.
It is
important when thinking about second best solutions to also ask whether they
have any long run
effects
on the primitive problem. Taxing capital
flows, for
will
example, while
obviously appropriate from the second best point of view, and even useful as a companion
to sterilization, loses appeal once one thinks in terms of the
opment of
for
Flexible exchange rates
financial markets.
Mundell-Fleming reasons
-
but they
may have
medium and
long term devel-
may have an advantage
over fixed
-
long run detrimental effects on financial
markets.
Regardless of the specific answers to these concerns,
increasing realization that a
modern debate on
it
appears to us that there
issues such as the advantages
of dollarization, capital flows taxation, liquidity requirements,
in
for
such a task.
We
are currently exploring
ongoing work.
38
some
and drawbacks
and so on, ought to consider
the asset markets aspects of the problem, and that the structure
a useful tool
an
is
we have proposed here
is
of these structural problems
since they will surely be repudiated at date
Case
0.
34
Suppose the foreigner goes to a domestic investor and
II:
international liquidity. Since cLqj
liquidity
=
Thus, Bj
2.
=
offers
Bj bonds
w, domestics have none, and can only get international
B
bonds to
reserves.
However
by tendering bonds to the central bank. Suppose a domestic tenders
the central bank, shows import goods of
B/L\ and then
receives
B/L\
these reserves will exactly pay for the import goods, hence the domestic will be
no liquidity to
for
with
left
offer foreigners.
Finally let us
show that only
distressed firms will sell
bonds to the central bank
for its
international reserves.
Case
exchange
rK + B — T
Either distressed or intact firms can tender
f of reserves. If intact
,
in
III:
for
some
one domestic claim,
it
firms tender, they onsell the imported goods to distressed firms
rK + B — T
of
it is
Suppose an intact firm tenders
of distressed firms.
which
receives 1/L\ import goods,
L\ domestic claims. Thus
to the government for
indifferent
it sells
to the distressed firm for
between tendering and not. Assume that
does
it
not.
Distressed firms receive
all
imported goods
totalling,
rK + B-T
^From
(7), this is
when only
34
We
!
exactly equal to
L
distressed firms tender, this
is
which
First,
imported goods and liquidate them outside the country
it is
of the government's reserves.
we have
said that foreigners cannot take the
for international liquidity. If there is
goods. That
is
A
1.
reserves.
reserves.
The import goods can be
now be
can receive at
1
I
L
the discount that foreigners
=
L\. This
and
sold to a distressed firm, for -^ domestic claims.
sold to a foreigner to
~
maximum M
bonds so that Lij
to foreigners
is
that
Suppose that a firm can get away with over-invoicing by a multiple of
redeem some of the
reserves.
Thus
by the private sector at date
0.
The
international
international
foreigner's bonds. Foreigners selling
B/ bonds
Bf
B (B
sell their
means that a
j^jjr
let,
^P
L lJ
is
interesting case
During periods of capital-controls domestic firms routinely over-invoice their imported
firm that tenders one unit of domestic claim receives jfa- import goods,
reserves can
This
The more
they claim higher prices than actual ones for their goods, thereby getting their hands on
more valuable international
M>
any liquidation
easy to see that foreigners would prefer not to hold domestic claims, since
they must always bear this cost, while domestics never bear the cost.
of over-invoicing.
Thus
an equilibrium.
have made two unrealistic assumptions here.
cost in this transaction,
is all
bonds
at.
fraction
^
+ Bf )
In equilibrium, foreigners will hold only enough
l
of international reserves can be promised
Over-invoicing creates a leak in the system.
40
away
Consider an equilibrium with L\
From the
is strict.
<
L\ and
=
is
strictly convex, this
can be ruled out by the same
d°,f
>
+
d'oj
where
at least
one of the inequalities
<
—a
cW
=
.
>
a contradiction. The case with L\
is
Hence the only equilibrium
logic.
is,
L\ and
<
L\
L'l7 k
K
>
>
k',
/<"',
and
"
-To-
Proof of Propostion 6
A. 5
when secondary markets were
Proposition 6 derived optimal policy
At date
because
1,
the private sector
When a >
liquidity.
it
when a =
transaction suffers a real cost.
0, this
0,
improvement as long as
more bonds
this cost
U PRIV
into
an
illiquid
costly
market. Policy can
not too high. In the extreme case
as,
max Mo/
(P8)
tf
p
^=
(u;-do,/)(A
< w
=d
,/-
order condition for this program
is,
doj
s.t.
c(k)
The optimal
is
Thus intervention can be
policy always leads to Pareto improvement.
First let us define
first
illiquid.
the government bonds in return for the international
sells
requires the private sector to sell
result in a Pareto
The
-
firm's first order conditions,
m —^
Since c(k)
K < K'
choice
is
denoted
condition remains that of
k'
+
I, 1
)
+
fc(fl
to refer to the no-intervention point.
+ r£)
The market
clearing
(5).
Suppose that a central bank offered
B
bonds
for sale at the interest rate of Lq,
but
bearing the illiquidity cost of a. This program must be altered as follows:
max Mo />6
s.t.
(w
-d
,/)(A
+ L x + k(R + r A) +
)
^ iv
c(k) +
we
- T)(l +
(1
-
a) A)
do,/
±= d
Since
(b
require that the central
,/.
bank
sell
enough bonds so that
do,/
as:
max
fc
,
6
s.t.
£) + ( 6 _ T)(l + (1 = w.
+ ^L
k(R +
c{k)
r
42
a) A)
=
w, we can rewrite
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Date Due
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