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02-
DEWEY
Massachusetts Institute of Technology
Departnnent of Econonnics
Working Paper Series
A
"VERTICAL" ANALYSIS OF
MONETARY POLICY
IN
EMERGING MARKETS
Ricardo J. Caballero
Arvind Krishnamurthy
WORKING PAPER
02-1
March 2002
Room
E52-251
50 Memorial Drive
Cambridge, MA 02142
paper can be downloaded without charge fronn the
Social Science Research Network Paper Collection at
This
http://papers.ssrn.conn/abstract-xxxxx
Massachusetts
Institute ot
Technology
Department of Econonnics
Working Paper Series
A
"VERTICAL" ANALYSIS OF
MONETARY POLICY
IN
EMERGING MARKETS
Ricardo J. Caballero
Arvind Krishnamurthy
WORKING PAPER
02-1
March 2002
Room
E52-251
50 Memorial Drive
Cambridge, MA 02142
paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
This
http://papers.ssrn. com/abstract=xxxxx
rMASSACHUSEffs'lNSTitLfrr
OF TECHNOLOGY
A
"Vertical" Analysis of
Monetary Policy
in
Emerging
Markets
Ricardo
J.
Arvind Krishnamurthy*
Caballero
This draft: March
8,
2002
Abstract
During emerging market
crises,
domestic agents might have sufficient collateral to
borrow from other domestic agents, but they are unable to borrow from foreigners
because the country, as a whole, lacks international
show that an
collateral.
(ex-post) optimizing central bank's response to an external crisis
tighten monetary policy to support the exchange rate.
be rationalized ex-post,
markets are underdeveloped:
It
policy.
If
central
this response
when domestic
a central bank could commit,
to
can
financial
it
should instead
Indeed, lacking the willingness, credibility, or feasibility to
implement an expansionary monetary policy during
means that the
is
reduces the already insufficient private sector incentives
to insure against external crises.
expand monetary
Although
has negative ex-ante consequences
it
we
In this setting,
bank must
crises
has important drawbacks.
resort to other, potentially
more
It
costly instruments to
address the underinsurance problem, such as capital controls and international liquidity
requirements
JEL Codes:
Keywords:
EO, E4, E5, FO, F3, F4,
External shocks, domestic and international liquidity, monetary policy,
interest parity departures,
credibility,
'Respectively:
jan, Roberto
exchange rate overshooting, fear of
MIT
and NBER; Northwestern University.
Rigobon and Andres Velasco
ME-NBER
floating,
commitment,
underinsurance.
University of Chicago, Columbia, IMF,
the
Gl
group.
for their
We
thank Stavros Panageas, Raghuram Ra-
comments, as well as seminar participants
MIT, Federal Reserve Bank
Caballero thanks the
NSF
for
of
New
financial support.
at
Brown,
York, the World Bank, and
E-mails:
caball@mit.edu, a-
kTishnamurthy@nwu.edu. This paper expands and replaces: "A Vertical Analysis of Crises and Intervention:
Fear of Floating and Ex-ante Problems," April 2001.
Introduction
1
This paper investigates central bank policy
to
its
A
external supply of funds.
asset prices
fall.
We
The question
an emerging economy that experiences shocks
negative shock can lead to a
crisis in
study central bank behavior during such a
undertaken prior to the
policies
in
crisis
which output and
and the preventive
crisis.
of optimal policy during a crisis has received renewed attention in the
literature (see, e.g.,
Furman and
spedes
Gertler et al (2001), and Christiano et
et al (2000),
Aghion
Stiglitz (1998), Fischer (1999),
the central bank defend the value of
its
(2000)).
al.
currency, or should
it
et al (2000),
They
Ce-
ask, should
lower interest rates?
In a
developed economy this question has a clear answer: the central bank will lower interest
rates in a deep recession to stimulate the economy. Thus, the
whether the structure of emerging markets leads to a
how does
developed economies,
much debated
different answer.^
issue should
That
is,
be
vis-a-vis
the presence of financial constraints alter the conclusion
that one draws?
To answer
these questions,
we
by modehng the presence of two
distinguish between developed
distinct financial constraints. If agents
either domestic or foreign lenders, then there are
First,
from
an agent
may have
investors.
is
two types of financial
We
and domestic agents thus are constrained
argue that the second type of constraint
the distinguishing feature of emerging markets'
is
bank policy
is
to expand the
and thus increase output.
This
is
money supply
Gertler,
in
and
most of the macroeconomics
Gilchrist, 1989,
When
limited
borrowing from foreign
unique to emerging markets, and
at the micro-level, then the optimal
model of microeconomic
literature
Our model
financial constraints
on credit constraints
1997).
As
is
(e.g.,
Bernanke,
widely communicated
and thereby increases aggregate output. In
money supply accomplishes
this task.
the financial constraint exists at the coimtry
level, this logic fails
because mon-
etary policy only regulates the borrowing of a domestic agent from a domestic lender.
^This question has not found a clear answer from either academics or policy-makers. See,
et al (2000) for a survey of the
of
worth of borrowers enables them to receive additional
credit from either domestic or foreign lenders
our model, expanding the
in
may have
in order to relax the financial constraint
and Kiyotaki and Moore,
in that literature, increasing the net
whole
the recipe for a developed economy.
this case corresponds closely to the standard
emphasized
frictions to consider:
crises.
When the only financial constraint faced by agents is
central
can borrow from
limited collateral, and therefore be constrained in his borrowing
either domestic or foreign lenders. Second, the country as a
international collateral
and emerging economies
— often contradictory— arguments and empirical evidence.
e.g.,
As
Boorman
long as the marginal lender
when
put. However,
because
another domestic agent, monetary injections increase out-
is
the marginal lender
is
a foreign investor, monetary policy
is
ineffective
does not alter the international collateral of the country.^' ^
it
This distinction between domestic borrowing capacity (domestic liquidity) and international
borrowing capacity (international liquidity)
an emerging market
investment needs.
In Section 2
We
We
the central theme in our analysis. In
the international liquidity of the country
The supply
we develop a
tical constraint.
an event.
crisis
is
of international funds
dual-liquidity
show that
model
in
is
fixed
and
model with one
limited relative to
its
price-inelastic ("vertical").
which a shock may lead to a binding ver-
asset prices, the exchange rate,
also contrast that
is
in
and output
which there
is
fall
during such
no distinction between
domestic and international liquidity.
Section 3 describes the objectives of the centrai bank and derives central bank policy
during a
Although monetary expansions have no output
crisis.
have large effects on the exchange
its
price
that
—the
exchange rate
trading-off output
is
rate. Since the quantity of international
—
is
and an
funds
A
very responsive to monetary policy.
inflation target will see little benefit
significant inflation-target benefits
our model, they
effects in
by contracting. Thus the model
central
bank
by expanding, and
crises, regardless of
the prevailing exchange rate system. (See Calvo and Reinhart (2000) and
flexible
inelastic,
rationalizes the observed
tendency of central banks to tighten monetary policy during external
(2001) for extensive documentation of "fear-of-floating"
is
Hausmann
et al
among emerging economies with
exchange rate regimes.)
In Section 4
we turn to ex-ante optimal
attention to the time prior to the
lessen the extent of the
coming
when
crisis,
crisis.
As
in
(preventive) policies.
That
is,
we
shift
our
private sector and central bank actions could
Kydland and Prescott's (1977) and, Barro and
Gordon's (1983) analysis, we find that the interplay between private sector expectations and
central
bank actions creates a need
for
commitment. However, the concern
with the private sector's preventive measures rather than with
^Chistiano et
al
its inflation
in oiu-
model
expectations.
(2000) address issues similar to those of our crisis monetary policy analysis.
"*
is
In
In their
model, imperfect liquidity substitution stems from imperfect input-substitution, and from the fact that
different inputs are paid in different currencies.
'while
in very different terms,
Dornbusch (2001)
also expresses his uneasiness
emerging economies with access to monetary pohcy can use
it
about the assumption that
to boost activity. For example, in criticizing
the standard view, he writes: "The loss of the lender of last resort [argument]
is
intriguing. This
argument
is
based on the assumption that the central bank - rather than the treasury or the world capital market -
is
the appropriate lender..."
''See
Part
V
in
Persson and Tabelhni (2000) for a thorough review of the inflation-credibility literature.
Also, see Chapter 9 in Obstfeld and RogoiT (1996) for an emphasis on
open economy impUcations of inflation-
our model of emerging markets, the private sector will underinsure against
crisis
events (see
Caballero and Krishnamurthy, 2001a). Moreover, the extent of the underinsurance depends
on the expectations over central bank actions during a
We
crisis.
show that the strategy
of squeezing domestic credit during crises lowers the private return to taking preventive
measures and hence discourages
to counter-cyclical
Our
monetary
As a
it.
resiolt, it is
optimal for the central bank to commit
policy.
analysis links the extent of the underinsurance problem
and the value of monetary
policy as an incentive instrument to the degree of domestic financial development, the
degree of commitment to a countercyclical monetary policy rule, and to the credibility of
the country's post-crisis inflation target.
The
counter-cyclical monetary policy
ment problem, because a
recommendation highlights an unusual commit-
central bank's ex-post optimal response will be to support the
exchange rate by contracting monetary policy. This observation takes us to another normative point. In Section
5,
we show that our framework
offers a solution in the instances
in
which the ex-ante optimal strategy
is
one of underinsurance, either direct or indirect ex-ante measures that induce the
vate sector to carry
more
not credible or
is
Since the primary problem
feasible.
pri-
international liquidity into crisis states will reduce the problem.
Taxation of capital inflows, international liquidity requirements, or large sterilizations of
capital inflows are examples of these measures.
they should be seen as the costs of having
environment of recurrent external
2
While enacting the measures may be
lost
costly,
the ability to use monetary policy in an
crises.
The Private Sector and
Crises
This section lays out a model of the private sector and financial crises based on Caballero
and Krishnamurthy (2001a). Firms hold Hquidity
arise before their projects are completed.
in order to
This hquidity
meet
may be
financial needs that
may
held either as domestic or
international assets. In the vertical view of this paper, the distinction between these two
forms of liquidity
is
central for aggregate outcomes.
view in which the distinction
and
this
view with a horizontal
immaterial for outcomes.
Setup
2.1
We
is
We contrast
study an economy exposed to an external financial
is
followed by a final date 2
credibility considerations.
when
crisis.
The
crisis
occurs at date
firms repay their outstanding debts.
We
1,
start time
with a date
are indexed
by
make investment and
agents
and there
0,1,2,
is
financing
a single (tradeable) good.^
a unit measure of domestic firms that each have access to a production technol-
is
requires
them
Domestic firms have no resources at date
0.
— with
to invest c{k)
— which yields date 2 output proportional to the
>
c"
=
i
ogy. Building a plant of size k at date
and
when
a fully flexible period
is
The periods
decisions.
There
which
0,
size of
They must import the
c(.)
>
0, c'
>
the plant (see below)
capital goods
and borrow
from foreigners to finance their investment. The financing and investment decisions maximize expected plant
who
Each firm
profits at date 2.
is
run by a domestic entrepreneur/manager
has risk neutral preferences for date 2 consumption of the single good.
Domestic firms face
of collateral, in the form of receivables arriving at date
goods have collateral value to foreigners
librium default and assume that
At date
0,
when
all
financing
il
1
to
1,
and
w
units
disregard explicit equi-
fully collateralized
debt contracts.
and
/
1 at the rate Iq
to 2, respectively.
1
Financing Needs and Crises
and financing decisions and focus on the
let
us take as given
crisis period.
In a
crisis,
all
date
investment
the financial constraints
for firms.
There are two (aggregate) states of the world at date
probabihties
{tt, 1
—
In the
tt}.
shock.
The
6-state
is
financial constraints
explaining
The
A
how
the
firms
fe-state,
need resources. Financial constraints
from
We
this collateral at dates
For the remainder of this and the next section,
bind
endowed with
firms sign debt contracts with foreigners, the contracted repayments of
from period
Date
2.2
done via
is
is
Only claims against these date 2
2.
prime exports).
(e.g.,
must not exceed w. Foreigners lend against
and
Each firm
significant financial constraints.
crisis state.
may
will prevent
1, co
receive a liquidity shock for which they
them from
fully
absorbing the liquidity
In contrast, in the ^-state there are no shocks and
do not bind. Let us now turn to defining the shock in the
financial constraints
may come
The shock
6-state,
and
to bind.
plants of one-half of the firms receive a shock at date
to a.
G {b,g}, which occur with
only arrives in the 6-state, but
is
1
that lowers output per plant
idiosyncratic in that each firm
receives the shock with probability 0.5.^
^See Caballero and Krishnamurthy (2002) for a model which builds on the distinction between nontradable
and tradable goods. While
this distinction is realistic
qualitatively unimportant for the issues
More
realistically,
due to a decline
in
we
and makes some of our
results a bit less stark,
it is
discuss here.
we can introduce the aggregate shock
as a contraction of international collateral
(e.g.,
terms of trade) or through a rise in the international interest rate faced by the country's
The
output
1)
goods, to give date 2
of,
A{9)k
We
<
productivity decline can be offset by reinvesting 9k (9
=
(a
+ 0A)k <
Ak,
A = A ~ a.
where
assume that the return on reinvestment exceeds the international
interest rate:
A-l>i^
This means that firms will borrow as much as possible to finance reinvestment.
occurs
if
firms are curtailed in their date
A — 1 > Zj
.
ensure that
A
tfiis
<
first
from
1
1,
.
borrows against
its
despite the fact that
Parameter assumptions
is
termed distressed. To cope with the shock,
net international collateral,
foreigners. After this,
it
=w-f
must turn
for
funds to the domestic firms that did not
receive a shock (termed intact). Intact firms have no output at date 1 either, so they
borrow from foreigners
But why would
is,
why
is
crisis
occurs in equilibrimn only in the 6-state (see the appendix).
w"'
directly
reinvestment, 9
In this case firms are financially constrained at date
firm that receives a liquidity shock
the firm
1
A
if
must
they are to finance the distressed firms. They can do this up to
intact firms lend to distressed firms
w"-.
any more than foreigners would? That
the domestic financial market different from the international financial market?
Because we assume that domestic agents accept the output from a firm's plants as
However, since a perfectly ftmctioning domestic financial market
scription of an emerging economy,
and because
collateral.
hardly a good de-
is
this departure has central implications for
our analysis, we assume that only a fraction of the output from the plants can be pledged
We make
to other domestic agents.
this fraction equal to the
firms can use this collateral to borrow
uidity. Likewise, since at
collateral,
2.3
we
date
1 firms
up
to this amount,
we
minimum
refer to
output, ak. Since
ak as domestic
liq-
can borrow from foreigners up to w"' of international
refer to w'^ as the international hquidity
during the
crisis.
The Horizontal View
In the horizontal view, distressed firms are constrained in meeting their financing needs only
to the extent that they have limited liquidity. Their total liquidity of ak
+ w"'
is
insufficient
to meet the production shock.
prime borrowers
6-state
(see Caballero
we would have
to
and Krishnamurthy, 2001a). In
this case, for the crisis to occur only in the
add an incomplete international insurance markets assumption
technological assumption of hquidity shocks that
we made). Our
(as
opposed to the
conclusions would be similar.
Translated into our context, the horizontal view implicitly assumes that the country as
A
a whole, at the margin, has an international liquidity slack.
to extend another loan at
The
i^
to
some domestic
shortfall is in the total liquidity held
firm.
would be willing
foreigner
But the worthy firm
by distressed
is
than
firms, rather
not distressed.
in the country's
international liquidity.
In our model, because intact firms borrow from foreigners against w'" and lend to distressed firms against ak, there
is
excess international liquidity
l^"
Since the international financial constraint
>
if,
lak.
(1)
not binding for intact firms, the interest rate
is
they charge on the loan to a distressed firm against domestic collateral,
is
determined by
the arbitrage condition:
Total reinvestment
is
then determined by the individual firms' financial constraints:
^
=
l
where the superscript
is
all its
The
first
international liquidity, while 9
distressed firms are unable to meet
in a crisis:
(2)
ij
1
H denotes the horizontal equilibrium.
the economy has not used
economy
^^<1^
^V^^<f^>
+
+q
all
inequality shows that
<
1
indicates that the
financing needs because of
their binding financial constraints.
We refer to this as the horizontal view, because the price of loans
quantity. A distressed firm in principle could continue borrowing at
i\,
as long as
2.4
The
its
is
not affected by their
the given interest rate
domestic financial constraint was relaxed.
Vertical
View
In this view, the international supply of funds faced by emerging economies during external crises
is
vertical.
The main problem
for the
country
is
not insufficient liquidity of
distressed firms, but rather a shortage of country-wide international Hquidity.
Inequality
(1) is reversed:
-w^ < -ak,
2
2
so that distressed firms have
enough domestic
'
liquidity to
of the intact firms. However, international liquidity
k
2
>
w"
1+il
is
pay
for the international liquidity
scarce relative to the financing need:
Since
all
liquidity
investment at date
is all
1 is
eventually financed by foreigners, the stock of international
that determines investment in this region:
aV k
where the superscript
not appear at
V
all in this
= 2w"
(3)
stands for vertical equilibrium. Note that domestic liquidity does
expression.
In the vertical modeling of crises, the interest rate on loans against domestic collateral
departs from
fj.
Since intact firms are borrowing
up
and lending to distressed firms against domestic
foreigners
a dollar-loan,
zf, rises
above
collateral, the
capacity from
domestic price of
i^:
d
In equilibrium, loans collateralized by
ak are made
maximum
to their
at the higher rate of
w
^
are
•*
made
at rate i\, while those collateralized
by
if.
(a) horizontal
(b) vertical
A-1
•d
•
r=i
1
*
1
loans
w
loans
1+L
Figure
Figure
Zj
,
1
1
:
Equilibrium
in
the domestic loans market
represents the equilibrium determination of
if.
The
vertical axis is the price,
d
while the horizontal axis measures domestic loans or domestic reinvestment. For if
_
,•*
However, at
intact firms elastically supply their international liquidity to distressed firms.
the point
w^ /{I +
On
turns vertical.
ij),
the other side of the domestic financial market, the
distressed firms turns
is
intact firms run out of international liquidity,
downward
and hence
insufficient,
sloping
eff'ective
loan
when the domestic
demand
is:
ak/{\
one equilibrium in the horizontal region (panel
cases:
a)
and the supply curve
demand
for
funds by
collateral discounted at
+ if). The
and one
A—
figure represents
1
two
in the vertical case (panel
b).
The
figure illustrates
never exceed
firms
is
A—
A—
1,
A—
1.
This
and as a
However, there
and
1.
is
how
is
Zj rises
above
i\ in
the vertical region. Note also that
Zj
can
because the marginal product of reinvestment for distressed
result distressed firms will never
a large interval for
pay more than
demand within which
%'{
A—
1
lies strictly
for funds.
between
i\
In this case,
ak
While a change
direct effect
(point
on
in domestic liquidity has
if as
no
effect
on output
in equilibrium, it
does have a
long as the economy suffers from shortages in both forms of liquidity
A in Figure 2). A deficit of international hquidity implies that if >
i^,
and a shortage
of domestic liquidity implies that the cost of capital will generally be less than the marginal
product of investment at date
1,
liquidities affect if in this region.
if
< A —
1.
Changes
in the relative
amount
of these
A-1
ak
Figure
The only
2:
Equilibrium domestic dollar rate
equilibrium price in our model
is if.
This
is
the interest rate at date 1 on a
risk free one-period loan against a unit of domestic collateral,
capital for firms in need of funds,
fall in
the date
1
is
and the expected return on loans
Less international hquidity (u;") leads to a higher
means a
and
value of domestic collateral
if.
The
both the dollar cost of
domestic lenders.
for
rise in this interest rate also
"
i+i?'
"^
(
3
Discretionary Monetary Policy during Crises
The
central
bank
affects the
economy through monetary
distributed as "heUcopter" drops to firms,
and redeemed
injections at date
1.
Money
at date 2 with taxes collected
is
by
the government.
We do not provide a detailed description of the government's tax powers and its tax base.
Instead we assume that the government collects T goods via non-distortionary taxation,
and that these taxes do not come from firms. We think of these taxes as resources from a
consumer sector that has a date 2 endowment of y'^
monetary policy
will transfer resources
>
T.
When
it is
effective,
from consumers to the corporate
expansionary
sector.
We focus on
the limit, "nomonetary-frictions" case, because our qualitative conclusions do not depend
on the presence of such
As
in
frictions.^
Woodford (1990) and Holmstrom and
However,
We
mechanism
does not immediately translate into a government tool
in our setup, this
for increasing output.
a
—beyond that of the private sector— to create
that gives the government a special power
liquidity.
we propose
Tirole (1998),
assume that taxation used to fund a monetary expansion does
not alter the international collateral of the country. Foreign investors continue to lend only
against w, and the extent of a crisis
determined only by
is still
back the money supply are not seen as international
to".
collateral,
Thus, the goods that
and monetary
injections
during crises only add to firms' domestic liquidity.
Bank Objectives and
Central
3.1
At the beginning of date
it
redeems
M
level) of:
62
We
M outstanding that
the central bank has
1,
does not inject any more money,
an exchange rate (price
(inflation-target) Credibility
=
central
bank may intervene by
effectiveness of this intervention
credibility considerations into
price level of one
M
M — M_
injecting
depends on
base
is
only
T_
=
1).
and the exchange rate must depreciate
which case
it
^^^
is
Ml
is
all
of its
money and maintain
that
if
M exceeds M.
the
Thus,
it is
possible that the central
bank chooses
If
M<
M, we assume
this
that government
on date 2 so that the date 2 exchange rate remains
at one.
nothing at stake in making this assumption, as opposed to the assumption that
tax revenues are independent of
^See
at date 2: In the high tax revenue
T <T.
I'T
can be viewed as a lower rate of money growth.
There
introduce (inflation-target)
removes money from the economy. In a growing economy,
also reduces taxes collected
The
In the low tax revenue state, the central bank's tax
The reason we have used the max operator
in
into firms.
monetary policy by assuming that tax revenues are imcertain.
e^OWTAX
M < M_,
M = T.
more money
We
credibility.
bank has enough tax base to redeem
[e2^^^^^^
If it
Y'-
There are two polar states of the (tax) world realized
state the central
held by firms.
planned taxes of T, giving
at date 2 with
normalize this no-intervention exchange rate to one, so that
The
is
Diamond and Rajan
the role of monetary policy in
M.
(2001) and Lorenzoni (2001) for liquidity models of the banking system and
it.
10
The
tax-states occur with probabihty
bank with a
(high tax revenue) and
p
increasing in p.
is
That
the higher
is,
depreciation of 62 in response to a monetary injection
The
central
bank has no reason to
=
e|
where the expression
for e[ follows
In the 6-state, the central
bank
62
inject
central
minus an
bank takes as
exchange rate as
it
injects
is,
the lower the expected
1
Thus,
in the p-state.
(5)
M — M_ into
M
T <T.
firms,
.
and
(6)
T
objective the maximization of aggregate consumption
is
a quadratic
loss function of
the
depreciates from e':*
jcostt„ ^
n'^^^'Cei)
3.2
p
inflation
= \+z\,
In our context, the cost term
inflation cost.
Since a central
from a standard interest parity condition.
= max
its
p-
is.
at date
e\
'
The
money
l,
—
more money without creating
larger tax base will be able to inject
at date 2, credibility
1
_
= ^2
^
/fi
;^
(
-
^
1
" >
)
0-
C^)
'1
Domestic Liquidity and the Interest Parity Condition
Post-injection, a distressed firm has domestic liquidity totalling,
ak
—
+E
.
where the expectation
is
this domestic liquidity
62
,
J
taken over the realizations of the tax base at date
is
exchanged
2.
In equilibrium,
for:
ak
+ E[M/e2]
1 + if
,^.
^
'
units of international liquidity.
For an intact firm to be willing to exchange a unit of international liquidity
money,
ij.
it
must expect a return on purchasing currency equal to the domestic
Thus, the expected appreciation of the currency must equal
if,
which
is
for a unit of
dollar rate,
reflected in the
domestic interest parity condition:
ei
Adding an extra
cost
= (l+zf)(^[l])~\
term related to missing the date
through the interest parity condition.
11
2 target
is
(9)
redundant since 62
is
contained in e\
The
condition differs from the usual one in that there
equivalently, the domestic interest rate
zero)
is
no domestic
is
Adding a monetary
.
interest rate (or
friction
would
result in
a "money demand" and introduce a domestic interest rate into this condition, but
it
would
not add any substantive element to our discussion.
For a fixed value of
62,
a
rise in if leads to
depreciation of the date
+ Zj)
Distressed firms borrow w'^/{l
rate.
from intact
The
firms.
from foreigners and
directly
+ E[M/e2]
l + it
ak
gross output per unit of this investment
is
aggregate consumption by domestic agents in the horizontal region
The
object involving
condition from
(9),
E[M/e2\
of interest in this expression.
is
we can write
A. Adding this output
investments and the consumers' endowment yields an
to the output generated by date
of:
Using the interest parity
this in terms of ei:
M A-jl+il)
^ ^
2
ei
follows that output is increasing with respect to real balances.
The next
money
step in understanding the impact of monetary policy
injections to real balances.
Given a money stock of
Note that a choice of
the inflation cost
is
M greater than T
minimized when
redeem money as long as e^
and by the
>
e^
\
results in 63
>
=
(see (7)
1
1,—
G jl,max
e^
= ;i±iL,
M,
1 if
is
to connect (nominal)
the date 2 exchange rate
and
Thus, 63
(5)).
is:
the low revenue occurs. Since
the central bank always uses
1,
interest parity condition, the date 1
e;
It
exchange
Horizontal View^
3.3
It
1
is
exchange rate
all
either one or
of
its
taxes to
max{l. M/M}.
is:
7(M;rt.(p+(l-p)ml„[l.|]).
(11)
follows that,
^ = M^{M-p)-^.
+
1
el
The term 7(M;p)
decreasing weakly in
is
always
less
M. When
than or equal to one.
multiplied by
12
M,
(12)
Zj
it
It is increasing
weakly
in
p and
measm-es the effectiveness of money
At one extreme, a central bank with
injections in raising real balances.
Mj = min {M,M}.
finds that
Money
no
injections have
=
other extreme, a fully credible central bank {p
when
real effect
1) finds
that
no-credibility (p
M > M.
M7 = M.
=
0)
At the
Thus, money
injections raise real balances one-for-one.
C^
Differentiating
where the term
M, we
with respect to
in parentheses
obtain the benefit of
one minus the
is
elasticity of
money
injections:
7 with respect to M:
M dj{M,p)
oM
7
This elasticity always
at
=
one when p
lies
and
between zero and one.
=
when p
falling to zero
proportionately larger effects on the exchange rate
As long
as
p
>
money
0,
We now
from
stituting the expression for e\
of a
when p =
money
also increasing in
3.4
M > M_.
is
M,
The inequahty
equal to
Vertical
With the
injections have
7(M,p)
with
not credible.
is
is
also increas-
p.^
its inflation cost.
Sub-
= |(7(M;p)-i-l)'.
with the marginal cost highest when p
=
0,
and zero
l.^*^
will inject
and
rises
monetary injection with
Combining costs and benefits we conclude that in
in p,
bank
central
p, starting
(11) into the cost expression, (7), yields:
n-^*(M;p)
is
money
Therefore,
when the
benefit of increasing
must compare the benefit
This cost term
1.
weakly decreasing in
injections raise output. Moreover, since
we conclude that the
ing in p,
It is
its
maximmn
is strict
value
the horizontal region, the central bank
in all cases other
when p =
than p
=
0.
M
is
increasing
1.
View
horizontal case as a reference,
we turn now
to the vertical view of crises. Using the
investment expression (3) we can construct aggregate consumption in the vertical region:
,
Differentiating this benefit once
more with respect
d
dp
Since, -^
>
0,
and
^^'^'
'"The marginal cost
It is also
is
<
0,
(dC"\
A 97
\dM
2
J
the marginal benefit
a{'y{M;p)~^
decreasing in p, since 7
is
—
to p,
l)
;v^
T'^^.L
is
we
find that,
A7ae.-,,M
2
dp
dp
increasing in p.
This
is
weakly positive since 7"'
increasing in p, while the elasticity term
13
is
>
1
and e{-y,M)
decreasing in
p.
>
0.
From
case:
this expression,
we reach a conclusion
Expansionary monetary policy has no
has a shortage of international
that contrasts starkly with the horizontal
effect
on aggregate consumption. The economy
liquidity, so reallocating
domestic liquidity has no real
Given this lack of effectiveness, the central bank turns
its
effect.
attention to an inflation target.
Since the exchange rate depreciates in the 6-state, and the central bank takes this to be
costly, its
To
optimal response
is
to contract
money supply and support the exchange
see this, note that the objective of the central
bank
rate.
in the vertical region boils
down
to,
a e\{M)
max-— ( -!-^—r M 2\\^i\
In response to a shock that
may
raise ej
policy to maintain the exchange rate at
1
>
1
Market clearing
^
'
the central bank will choose monetary
recall that:
1+^1
(16)
7(M;p)-
(i+=;)(!^^^^?^)>i+.;-
Equations (16) and (17) yield an expression
e?
are
,
(15)
.
)
at date 1 results in the domestic dollar rate of,
i+.f =
We
^
+ ij. Now
„6
'
+i
V
1
now ready
=
(l
+ tt)
to establish the
for e^
which
'ak')iM-p)-'^
is
(17)
increasing with respect to
M:
+ M\
w"
main proposition
of this section.
Let M"*^ be the
solution to (15). Then,
Proposition 1 In
(M"'^
<
M
Panels
This restricts
).
and defends
the vertical region, the central bank chooses to tighten domestic liquidity
demand for
international liquidity, causing if to fall towards
i^,
the date 1 exchange rate.
(a)
vertical views.
and
(b) in Figure 3
Note that
in their
summarize the
downward
differences
sloping segments,
E[M/e2])/{l+ii).
14
between the horizontal and
demands
are equal to {ak
+
(a) horizontal
(b) vertical
A-1
loans
w
loans
1+L
Figure 3: Domestic liquidity expansion
In the horizontal case, the increase in domestic liquidity caused by expanding monetary
policy raises date
1
investment, leaving if imaffected.
In the vertical region, the
increase in domestic liquidity has no effect on equilibrium investment,
The obvious date
1 policy
conclusion in the vertical region
is
and only
same
raises if.
to contract rather than expand
monetary pohcy.^^
Optimal Monetary Rule
4
Now we show
a date
that the date
commitment
'
'
commitment and the
One can
discretionary monetary policy
is
ex-ante suboptimal.
to a state-contingent date 1 policy, the central
relaxing monetary policy
the
1
more than
it is
With
bank does better by
inclined to do during a crisis.
discretionary solutions occurs because central
The gap between
bank interventions
introduce speculative attack-type effects by letting the probabilities of the different scenarios
change with the
level of
M/T. Our
basic message
speculative effects are suiBciently strong so that
incentive to contract
monetary policy
will
is
unaffected by these considerations, although
M/ei
falls
be enhanced. In extreme cases the latter
of choice even in the horizontal environment.
15
if
the
with an expansionary monetary policy, the
may become
the poUcy
Expectations about this price turn out to be central in determining
affect if.
and investment decisions
discuss
We
decisions.
important to note here that the commitment problem
it is
around policies that
is
affect the private sector's
investment and borrowing
are not concerned directly with the standard inflationary bias emphasized in
we make assmnptions
the inflation-credibility hterature, a-la Barro and Gordon (1983), and
such that this bias does not
This does not mean that inflation-credibility issues are
arise.
irrelevant in our setting, because they restrict the policy options that a central
at date 1; this
on
effects
if,
was one of our themes
there
is
commitment with
is
We
0.
At date
much
It
bank has
simply means that aside from any
at date
1
with an inflation rate different
use the words commitment and credibility to describe
and credibihty with respect to
respect to if
62
=
1,
respectively.
This
primarily about commitment.
Private Sector Date
4.1
in Section 3.
no incentive to surprise firms
from that announced at date
section
financing
at date 0.
In order to avoid confusion,
we
firnis'
0,
Decisions and
the private sector decides
real investment to undertake.
how much
to borrow from foreign investors
The borrowing
domestic firm and a repayment at date
2,
budget constraint
'W^
In the ^-state at date
1
,
(i
all
make
1
amount loaned to a
state
u)
("-"'^'^'^')-
profits of,
In the 6-state, one-half of the firms are distressed
ak
while the other half are intact and
+ E\M/e2]
and they make
w - f\
i+^i;
i+if
make
E {b,g}. Since
investment, and since foreign investors
Ak + {w~ P) + M.
(
[
and how
is,
+ ,5)(i + .;)
firms
contracts specify an
f^, contingent on the date
the fimds raised from this loan are used in date
are risk neutral, the date
if
(expected) profits
M
62
16
'
of.
profits of,
<''
Combining these expressions leads to the following problem
for
a firm at date
0,
PRIV:
- n){Ak + w -
max^fgfb
{1
s.t.
P.f<w
c(fc)<
Our
(,^,,)V,.)
fs
+ M)
(7r/^
+
(l-7r)/.^).
technical assumptions (see the appendix) guarantee that
other words, f^
= w
than investment
in international markets.
=w
/-^
as long as increasing investment in k at date
to absorb the liquidity shocks at date
toward investment at date
0.
It is
1 is
And
f^<was
is
and f^
more
w. In
profitable
long as saving some resources
more valuable than using
all
of those resources
apparent from the private program that
equilibrium price that influences the date
<
if is
the-only
Let us study this connection more
decision.
closely.
Since
k.
/''
At date
=
0,
w, we simply need to consider the tradeoff between increasing /^ and reducing
building a marginally larger plant increases (expected) date 2 profits by,
(i-^M + ^f^ +
^^^^
'^TTzf)-
Building this larger plant requires the firm to raise an additional cf{k) at date
is all
accommodated by increasing
date
1
0.
f^, the cost to the firm is fewer resoirrces to
hquidity shock. Since the probability of a
c^(fe)(i
tt, /**
crisis is
must
Since this
absorb the
rise by,
+ z5)(i+q)
TT
and
results in a fall in expected profits of,
/ A + l+ifW(fc)(l +
[2{l + z*,) )
that can be simplified
f5)(l
+ zt)
to:
c'{k){i+e,)(^^±^Y
The optimal
private sector k equates (19)
the conclusion that follows from them:
decreasing in
is
if; (2)
The marginal
decreasing with respect to
and
(1)
(20).
The
17
note two comparative statics, and
benefit of building a larger plant size
cost of investing
if.
We
(20)
is
increasing in
if.
is
For both reasons, k
4.2
Date
Let us
now
Central
Bank Problem
in the Vertical
turn to the central bank's policy choice at date
for the central
show
this in
two
(aggregate) consumption,
More
to establish that
bank to commit to a looser monetary policy during
by the discretionary solution of Proposition
We
Region
precisely, date 2
steps.
maximized
is
choices are inefficient.
at choices of {k, /^,
/'')
different
private sector's choices. Appealing to the results of the previous subsection,
date
monetary policy can
1
and improve these
affect
inflation cost of the previous section,
Let us
first
it
sector's
for if
choices.
Second,
we
and characterize the optimal poHcy
from the
we argue
that
reintroduce the
choices.
Consumption Maximizing Choices
4.2.1
when
indicated
on maximizing the value of date 2
that the private sector's date
consumption
is
1.
First, focusing purely
we show
than
crises
optimal
it is
present the central bank's program to maximize date 2 aggregate consumption
can directly choose
(fc,
program by eliminating
from
(8) into
/',/'').
if
from
We
show that
this
program
differs
PRIV. We substitute the market
from the private
clearing condition
PRIV:
CENT:
f^,f<w
s.t.
c(fc)< (,^,.)\,^,.) (7r/
The
tradeoff between increasing k versus
benefit of increasing plant size
2j
<A—
1,
this benefit
cost side, borrowing
is
-7r)^
+
strictly lower
very different here than in
more to build
7r-(^
+ a).
On
the
this plant costs,
+ i5)A.
< A — 1, the cost lies strictly above the private sector's computation.
We conclude that as long as if < A — 1 in the competitive equilibrium,
Zj
bank could choose
The
PRIV. The
than the private sector's computation.
c'(fc)(l
For
/'' is
(l-7r)/^).
is,
(1
For
+
{k, f'') directly, its choices
private sector over-invests at date 0,
would
differ
if
from those of the private
and underinsures against the date
shocks.
18
the central
1
sector.
liquidity
The Value of Central Bank Commitment
4.2.2
Since the central bank can affect
choice of
if in its
M,
can use monetary policy to align
it
the private sector's choices more closely with the consumption maximizing choices. Let us
now
characterize the optimal monetary rule from this perspective.
Define U{k) as the value of the objective in
plant
CENT,
a function of the date
Recall that in the private sector's problem, k solves
size.
2V
which yields a
Since in
strictly decreasing
CENT,
the objective
and continuous function
is
fimction. Let k* be the solution in
CENT. We know
To
in
if
1
+ ^1/
k{if) as a solution.
linear while the constraint
other words, total output will increase
value of
choice of
is
that U'{k)
the value of this k
convex, U{k)
<
is less
a concave
is
as long as
A;
>
k*. In
than the private sector's
k.
find the
terms of
monetary policy
p >
if (for
we
result,
first
re-write the central bank's problem purely
0):
max
U{if)-nU^^^\M{zf)),
(21)
if6[if,A-l)
where, if
is
the value of if that prevails
if
the central bank chooses
M=
at date
1
in the
6-state.
The market
As long
w"{if)
as
is
p>
clearing condition at date
0,
the range of
increasing, for every if
an equilibritun with that
terms of
<A—
if.
G
[if,
is
is,
the positive reals. Since k{if)
A—
1]
This allows us to
there exists a choice of
v/rite
decreasing and
M that
will
induce
the central bank's program in (21) in
1,
U'{if)
the objectives in (21) with (15),
>
in (21).
However,
we can
in the central
see the value of
bank objective
no benefit from expanding money. In both programs, the cost term
Proposition 2 The optimal monetary
4.3
is
if.
By comparing
if
M'y{M\p)
in the &-state
1
Inflation-credibility
rule -with comm,itm,ent is M*^
at date 1 there
was
the same. Thus:
>
M"*^.
Problems and Optimal Monetary Policy
Inflation-target credibihty also influences the extent to
rule can be used to
is
commitment. For
overcome the private
which a commitment to a monetary
sector's underinsurance problem.
19
Proposition 3 Consider two economies indexed hyp andp, where p >
monetary
A
more
bank commits to
A
and higher consumption.
act
more aggressively
means that the
The formal argument
since k{if)
is
any value of
is
at date
1;
this
higher p leads to a lower depreciation in
each choice of if and to a date 2 exchange rate that
policy choice. This
the optimal
if.
(inflation) credible central
results in a higher if
e\ for
>
rule will yield if
Then
p-
cost of raising
i'^
is
more insulated from the date
in (21) falls, allowing for a higher if.
more involved because the program
in (21)
may
> p- We will
not concave. Consider two economies where p
not be concave,
first
show that
for
if:
dU^'*{if-p)
dU^'^{if;p)
^
dif
dif
The marginal
cost in the 73-economy
is.
jLt4,iM;pr'^^\S(l^,'MM:,r'
1+it
dif
J
Consider evaluating this marginal cost for the same value of if for each of the two economies.
If if is to
(p
+
(1
be the same
in the
— p)min< 1,^
[),
two economies, then from market clearing and since 7(M;p)
it
must be that M'y{M;p) and
the two economies. This means that 7(p)
term
in
<
are constant across
the same value of
7(j6) at
parentheses in the marginal cost expression
p{M — M)
is
=
if.
Thus the
first
higher in the p-economy than in the
p-economy.
The second term
reinforces this conclusion. It can
^<"^'""'
By
+
('
be written
+ *wii)W<'-'"lf-
imphcitly differentiating the market clearing condition,
higher in the p-economy than in the p-economy.
money
to affect if
when the
marginal cost of raising
if is
central
as,
bank
is
It
more
we can
easily
show that
^
is
requires a smaller change in nominal
credible.
Thus, we conclude that the
uniformly lower in the p-economy than in the p-economy.
Next, define V{if;p) as the value of the objective in (21). Suppose in contradiction to
the proposition that
if
<
if.
Then, since
if
and
if
are maximizing choices for each of these
economies respectively,
L 9W"2f'^^
-
y(z1;p)-F(if;p)
=
V{if-p)-V{if;p)
= l_'Un^^^^^^^{x)^U'{x-,p)\dx<0.
/,''
20
(x)
U'ix-p)) dx
>
Since the marginal benefit of increasing if
is
independent of
U'{x]p). However, since the marginal cost of raising if
inequalities can hold only
if
if
>
is
p,
must be that U'{x;p)
it
=
lower in the p-economy, these two
QED
if.
Constrained Monetary Regimes
5
There are
three reasons
problem:
implementing comiter-cyclical monetary
limits to
why monetary
policy
may be
have highlighted
unable to solve the private underinsurance
^^
1.
Time
2.
Limited inflation-target
3.
Limited domestic financial underdevelopment.
We
We
policy.
inconsistency of the optimal policy.
discussed the
first
credibility.
two of these factors
explicitly in the previous sections.
stems from the fact that, in om- model, limited domestic collateral
underinsurance problem.
It
third
the source of the
can be shown (see Caballero and Krishnamurthy 2000b), that
as the fraction of capital counted as domestic collateral
market clearing condition of
is
The
(17), the
if falls. ^^ It follows that the cost of
falls, if falls.
domestic hquidity of ak
is
Informally,
reduced to Xak
achieving any given level of if
is
if in
(A
the
<
higher in an economy
with lower domestic financial development, because the central bank has to inject more
and thus depreciate
ei further. So, the central
bank opts
1),
for a lower if in the
program
M
(21),
leaving a larger share of the underinsurance problem unresolved.
Regardless of the reason for such limits, the issue
it is
we address
in this section is
whether
possible to reduce the costs of losing access to an effective countercyclical monetary
Our
policy.
analysis points at a "silver-lining" for these constrained systems: Recognizing
that the cost of losing monetary policy
opposed to the date
'^A fourth
stantial
(2000),
in the
of the central
date
decisions of the private sector, as
bank often emphasized
possibility, extensively discussed in the international
amounts of private debt are
financial
may be
1 inflexibility
is
dollar denominated. This can
economics literature, occurs when sub-
be thought of as another form of domestic
underdevelopment. In this case, rather than lowering interest
defending the exchange rate. See,
and Christiano
et
al.
e.g.,
Aghion
in the literature,
rates, the
output maximizing poMcy
et al (2000), Gertler et al.
(2000), for analysis of this balance sheet channel
(2001), Cespedes et
and arguments
for
al.
and against
the contractionary effects of currency depreciations.
'^A more complete argument requires us to check that the
this conclusion. See Caballero
and Krishnamurthy (2000b)
21
effect of
A on date
for the details.
decisions does not overturn
The
leads to a natural set of policy options.
directly at correcting the underinsurance
that taxing capital inflows at date
central
bank can
problem of the private sector
A—
that
+
{l
Thus the return
remains high.
if)
measures aimed
at date 0.
We
show
one such measure.
is
Recall that the problem induced by not being able to
1 is
institute
commit to expand
credit at date
to hoarding international liquidity
remains undervalued. Of course, this undervaluation arises only in the vertical
until date 1
region, as the aggregate international liquidity constraint does not bind in the horizontal
region.
In our environment, there are two obvious ex-ante policy measures that can deal with
the underinsurance problem: capital inflows taxation during normal times (date 0), and
international liquidity requirements at date
section
Let us return to the analysis of the previous
0.
and characterize the relationship between the optimal ex-ante tax and
The
first
order condition in
CENT
c'{k^'^^^){l
whereas that
is,
+ i*o)A =
(1
-
it)
A + n^{A + a),
for the private sector sets (19) equal to (20).
Aligning the date
private
and consumption-maximizing incentives
ing a tax/transfer policy. Suppose that the central
is
if.
returned to firms in a lump
sum
fashion.
Then
bank
the
a matter of choos-
a tax r per unit of
levies
first
is
k,
which
order condition for the private
sector becomes:
c'{k){l
+ z*)^±l±i =
(1
-
Tr)A
+ 7^11 A +
a^) -
Choosing r to align the private and central-bank incentives
Proposition 4 For any equilibrium
r^ir)
If
there
is
=
I
level
(y^ +
enough domestic
is
c'{k^^^^){l
j
(1
+ zt)).
liquidity during crises so that in the absence of taxes if
date
0.
In other cases, for
example
Up
is
=
small,
result could
be achieved via a contingent liquidity requirement.
solution gives the private sector incentives to choose the efficient k, thus resulting
in the efficient lu
—
f^
.
Alternatively, the central
firm preserve international liquidity for the date
w—
+ zS) (A -
positive.
Note also that the same
The tax
yields:
ofif^, the optimal tax solves,
A — 1, there is no reason for intervention at
the optimal tax
r
f'' is
realized.
22
bank could
1 crisis-state,
directly
mandate that each
so that the efficient level of
In practice, taxes
come with
own
their
deadweight costs of taxation,
sets of distortions:
costs of enforcement, evasion, etc. However, the important point to recognize
vertical framework, the cost of losing
Rather,
it is
Final
Much
is
may be
that, in the
not lack of flexibility at date
underinsurance by the private sector at date
in the
of having to enforce capital controls
6
monetary policy
is
0.
1.
In this sense, the costs
seen as a direct cost of losing monetary policy.
Remarks
monetary policy and exchange rate systems focuses on the
of the discussion of
This
of inflation credibility.
is
largely
an
historical artifact, since inflation stabilization
had been the dominant concern of emerging economies
emerging economies go beyond
This
financial crises.
for
many
many
decades. Today, as
the central concern has shifted to avoiding external
this,
the starting point of our paper.
is
issue
In our analysis, central
bank
actions should be directed toward correcting the chronic tendency of emerging economies
to underinsure against external shocks.
it
monetary
them
we argue
creates a time-consistency problem. Central
policy;
if
policy,
banks should follow coimter-cyclical
they are unable to commit to this policy, inflation concerns will lead
to act in the opposite way.
This change
in perspective also
has relevance for evaluation of other government
Pro-actively managing international reserves
may result
in beneflts in
international reserves are a form of international liquidity
too
that the standard inflation-
be a serious obstacle to implementing optimal monetary
stabilization concern can
because
Moreover,
little
international liquidity into crises, the central
our framework. Since
and the private sector
bank has a
role to play
international financial constraint
Relaxing the constraint
incentives
is
and lowering
crisis
i"^.
beneficial but the effect
is
not, for reasons akin to those
we
carries
by carrying
reserves in place of the private sector. However, the inflation stabilization concern
undercut this policy. Injecting reserves during a
policies.
may
also
has the twin benefits of relaxing the
Hence the exchange rate
is
stabilized.
on the private sector's own insurance
discussed in the context of monetary policy.
Ex-post, the central bank will ignore the incentive effect and inject more reserves than
it
would have chosen ex-ante.
Reserves management and monetary policy are complementary policy tools in this context. If the central
bank
reserves. This raises i^
is
credible,
it
and can fuUy
should expand money at the same time that
offset the incentive effect of
it
injects
the reserves injection. Al-
though few emerging economies have the luxury of following a counter-cyclical monetary
policy, this observation underscores its value.
23
In our environment
device.
A
monetary policy without monetary
,
sector will achieve the
same end.
On
the one hand,
toward distressed firms, then
fiscal
While, in practice,
policy, this interpretation
vertical framework.
it
if
the
would bring to these
i'^
role.
On
exchange rate
is
turned on
may be
firms. In our vertical
i'^,
like ours.
context
still
is
is
At
is
a concern that events
this stage, tightening
can be analyzed
in
is little
impact on the
its
Of
in
course, in
liquidity during crises.
which domestic
in
A
central question for policymakers in this
crisis,
monetary policy
We conjecture that this trade-
need to tighten during the horizontal phase. But
credible or feasible, then the appropriate response
advisable in our simplified model
when
much
is
if
If
the
is
credible,
then
is
not
to tighten during the early phase in
as taxing capital flows at date
extent, comparable in nature to the costs of the ex-ante measures
we
was
In fact, the costs in
terms of the additional financial distress imposed on the domestic private sector
24
commitment
the commitment
there was no commitment.
See Caballero and Krishnamurthy (2002).
is
will destroy financially constrained
terms similar to those we have used throughout:
order to protect international hquidity, very
when supply
may lead to a binding international liquidity
to an aggressive coimtercyclical monetary policy in case of a vertical event
there
policy crowds
and external borrowing becomes gradually more expensive, then
projects but save international liquidity for the vertical event.
off
lowers the
in the non-horizontal ingredient
to conduct monetary policy at the early stages of the
horizontal but there
constraint.
and
through a horizontal phase
a sharp vertical sudden stop phase.
how
fiscal
are either vertical or horizontal.
all crises
interestingly, crises build up, going first
falling into
it
One worth mentioning
and the limited substitutability between domestic and international
financial conditions tighten
efficiently
this policy depreciates the
logic of fiscal policy
practice, crises are mostly "diagonal," but our novelty
More
a
its head.^"*
our assumption that
is
fiscal policy in
harmful, because
model, untargeted
There are many caveats about a stylized model
concluding,
less flexible
without the compensating benefit that a selective
The standard Mundell-Fleming
rate.
may be
the other hand, an unselective
out private investment one-for-one. Furthermore, by raising
exchange
policy
instrument can be targeted
fiscal
can play a useful
distressed firms' collateral by raising
fiscal
sheds light on the workings of
expansion designed to boost aggregate demand
fiscal gift
simply a reallocation
that transfers domestic liquidity from consumers to the corporate
fiscal policy
than monetary
frictions is
is,
to a large
already discussed.
References
[1]
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Monetary PoHcy with Credit Constraints, mimeo Harvard 2000.
[2]
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"A
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[3]
Bernanke, B., M. Gertler, and
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Boorman,
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Caballero, R.J.
straints in a
and A. Krishnamurthy, "International and Domestic Collateral Con-
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48,
513-548, 2001a.
[6]
Caballero, R.J.
and A. Krishnamurthy, "Smoothing Sudden Stops," mimeo MIT,
May
2001b.
[7]
Caballero, R.J.
ization
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Pohcy
and A. Krishnamurthy, "International Liquidity Management:
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Caballero, R.J.
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Calvo, G.A., and
CM.
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7740, June 2000a.
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Underinsurance
7792, July 2000b.
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Cespedes, L.F., R. Chang, and A. Velasco, "Balance Sheets and Exchange Rate Policy,"
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J.
Roldos, "Monetary Policy in a Financial Crisis,"
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Diamond,
D.W. and R.G. Rajan,
"Liquidity
Shortages
and Financial
U.Chicago mimeo, June 2001.
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Dornbusch, R. "Fewer Monies, Better Monies,"
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NBER Wp
#8324, June 2001.
Crises,"
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Furman,
J.
and
E. Stiglitz,
J.
Asia," Brookings Papers of
[15]
Gertler, M., S. Gilchrist
Economic
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2,
Evidence and Insights from East
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and F.M.Natalucci, "External Constraints on Monetary Policy
and the Financial Accelerator,"
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"Economic
NYU
working paper, Feb 2001.
Hausmann, Ricardo, Ugo Panizza and Ernesto
Stein,
"Why
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Holmstrom, B. and
Economy
Political
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Kydland,
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Lorenzoni, G., "Interest Rate Stabilization and Monetary Control:
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26
A
Appendix
The
financial frictions of the
Assumption
model are embodied
in
the following two assumptions:
1 (International Collateral)
Foreigners lend to domestic firms only against the backing ofw. Domestic agents lend against both
w
and ak.
Assumption
A
2 (Domestic Collateral)
domestic lender can only be sure that a firm will produce ak units of goods at date
production based on physical reinvestment at date
One
last
assumption
is
Any
excess
neither observable nor verifiable.
insurance arrangments that transfer resources
required to rule out date
from distressed firms to intact
Assumption
1 is
2.
firms.
3 (Non-observability of Production Shock)
The production shock
at date 1 is idiosyncratic.
The
identity of firms receiving the shock is private
information.
In Caballero and Krishnamurthy (2001c),
we
solve the
mechanism design problem associated with
these financing and informational constraints and show that
We
also discuss
how a banking arrangement
constraint, but that
it
will
be very
in principle
it
may
corresponds to the one in
get
around the private information
fragile.
Consider next the technical assumptions on parameters that we have used.
CENT
CENT.
The program
in
is,
CENT:
maxfc J. j6
(1
- w){Ak + w-fs)+ir (tt^ '^ +
f^,f''<w
s-t.
c(fc)<
First,
we
^^)
require that
w =
(7r/^
(^^J(,^,.)
+
(l-^)/^).
/^ in this program, or that the return to investing domestically
exceeds that of investing abroad:
Assumption 4 (High Investment Retin-n)
Second, we require that the solution features some insurance against the 6-state, so that
Assumption 5 (High Return to Insuring)
A+a
''(
)""'''^^"-'-^"-^
(i..;;..;)
27
/*"
<
w.
Finally,
we
no central bank intervention, places us
require that equilibrium, with
in the vertical
region, or,
1+ 2l <
The
first
order condition for the program in
and the smallest value when
condition leads
if
1.
(1
A.
is,
- ^)A +
Then the
this equation as k{if).
= A—
+ Jj <
PRIV
c'im + ro) ^^l^'' =
Denote the solution to
1
Using
this
^1{a +
a^)
largest value of k
in Vertical
Region)
nak{il)
w-(l + iS)(l+2t)c(fc(i*))
Trak{A -
w-
{I
1)
+ i^)(l + il)c{k{A -
28
attained
when
if
=
i*,
knowledge as well as the market clearing
to:
Assumption 6 (Equilibrium
is
.
<
l
>
I))
1
+
ii*
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