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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
INFLATION TARGETING AND SUDDEN STOPS
Ricardo
J.
Caballero
Arvind Krishnamurthy
Working Paper 03-10
February 19, 2003
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MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
MAY
3
2003
LIBRARIES
Inflation Targeting
Ricardo
J.
and Sudden Stops
Arvind Krishnamurthy*
Caballero
This draft: February
19,
2003
Abstract
Emerging economies experience sudden stops
we have argued
to
in
monetary policy during these sudden stops
for
in capital inflows.
As
Caballero and Krishnamurthy (2002), having access
is
useful,
but mostly
demand reasons. In this
cannot commit to monetary policy
"insurance" rather than for aggregate
environment, a central bank
tliat
choices will ignore the insurance aspect
and foUow a procychcal rather
than the optimal countercychcal monetary pohcy.
will also intervene excessively to
inefficiencies are
The
support the exchange
bank
central
rate.
These
exacerbated by the presence of an expansionary
In order to solve these problems,
bank's objective to
(i)
we propose modifying the
bias.
central
include state-contingent inflation targets,
(ii)
target a measure of inflation that overweights non-tradable inflation,
and
(iii)
weigh reserves holdings.
JEL Codes:
Keywords:
EO, E4, E5, FO, F3, F4,
Gl
External shocks, domestic and international liquidity,
inflation targeting, fear of floating,
commitment, underinsurance.
MIT and NBER; Northwestern University. This paper was prepared
NBER's Conference on Inflation Targeting, January 2.3-26, 200.3, Bal Harbour,
Florida. We are grateful to Ben Bernanke, Andrew Hertzberg and conference participants for their comments. We thank Donna Zerwitz for editorial assistance. Caballero
'Respectively:
for the
thanks the
ity
NSF
for financial
support. Krishnamurthy thanks the
IMF
for their hospital-
while this paper was being written. All errors are our own. E-mails: caball@mit.edu,
a-krishnamurthv@northwestern.edu.
Introduction
1
Underlying weaknesses
in the
domestic financial sector and limited integra-
make emerging market economies vulneraWithout much warning, the capital
boom may come to a halt, exposing the country to an
tion with world financial markets
ble to "sudden stops" of capital inflows.
flows that support a
external
crisis.
Monetary policy
in this
context has often been seen as an additional
source of problems rather than as a remedy.
inflation
problems have limited central bank
Countries with a history of
credibility.
The currency
pres-
sures of the sudden stop test this credibility, so that either the loss of credibility or
the attempt to regain
it
in the
middle of the
crisis
exacerbates the
contraction.
However, there
and unstable
a group of countries for which the problem of high
is
inflation
is
no longer present but the problem of sudden stops
These countries include
persists.
Chile, Mexico,
and many of the Asian
Moreover, looking towards the future, this group
economies.
is
bound
to
grow, as hopefully Brazil, Turkey, and countries of Eastern Europe establish
and
discipline over seignorage
Many
fiscal policies.
of these advanced emerging economies are now
in the
process of
designing their monetary policy framework. Given the success of "inflation
targeting" in a wide range of economies,
framework be contemplated
for
it
seems only natural that
this
these economies as well. In this paper,
we
study how inflation targeting should be adapted to countries whose primary
macroeconomic concern
The
the presence of sudden stops in capital inflows.
starting point of our anah'sis
Krishnamurthy (2002)
its
is
potency.
resources.
that, during a
dubbed
is
the observation from Caballero and
sudden stop, monetary policy
loses
The principal constraint on output is a shortage of external
The main effect of domestic money, on the other hand, is on
agents' domestic borrowing capacity.
central
is
bank to the outflow
"fear of floating"
Thus, the knee-jerk reaction of the
of capital, of raising domestic interest rates
by Calvo and Reinhart (2002)
the natural consequence of a central bank that
and output. Raising
with limited
eff'ects
However, while
interest rates reduces the
is
—
— within our model
concerned with inflation
exchange rate depreciation,
on output beyond the impact of the external constraint.
fear of floating
may seem optimal from
this
contemporaneous
perspective,
it is
The reason
suboptimal ex-ante
.
suboptimality
for this
is
that the anticipation of the central
bank's tight monetary pohcy during the sudden-stop has important effects
on the private
sector's incentives to insure against sudden-stop events. In-
suring against these events
means taking
prior actions that increase the
total dollar assets of the country (decreeise the total dollar liabilities of the
country) in the sudden-stop event. Since a contractionary monetary policy
reduces the domestic scarcity value of dollars,
it
also lowers the returns to
hoarding net dollar assets. Simply put, contracting dollar debt
in
an environment where the peso
of a
costly
is less
expected to be supported
in the event
Thus, the anticipation of a tight monetary policy leaves the
crisis.
economy
is
less insured against the sudden-stop.
In this context, expectations shape policy, not in whether inflation
ticipated or unanticipated, but in
how
the private sector views
its
is
an-
rewards to
insuring against sudden-stops. For incentive reasons, the optimal monetary
rule
is
to
expand during external
contemporaneous
It
effect
crises,
even
if
the expansion has a limited
on output.
should be apparent that time inconsistency
context.
A
central
bank that cannot commit
is
a serious issue in this
will ignore the
insurance as-
pect of monetary policy and follow a procyclical, rather than the optimal
made worse by the presence of an expanBarro and Gordon (1983). The reason is that the central
countercyclical policy. This bias
sionary bias a la
bank only
it
is
sees a benefit from expanding during
normal times. As a
result,
lowers interest rates during these times, leading to higher inflation (as in
Barro and Gordon).
When
the sudden- stop occurs, the central
even more reason to defend the exchange rate as
it
bank has
inherits high inflation.
In our framework, since crises are characterized by dollar shortages, there
is
scope for managing international reserves in order to ease these shortages.
Our model
reserves
provides a natural motivation for both centralized holding of
and holding
reserves in the form of dollars.
However, we show
that a central bank that cannot commit will be too aggressive in injecting
dollar reserves during a crisis. Moreover, this distortion interacts with the
monetary policy problem.
a more severe
crisis,
A more
suboptimal monetary policy
and a greater incentive
for
will lead to
the central bank to inject
reserves.
Given the time inconsistency of the central bank, what should
its
man-
date be? That
that
We
is,
how should the
central bank's objectives be modified so
internahzes the insurance dimension of the sudden-stop problem?
it
propose modifying inflation targeting so that the central bank follows
state-contingent inflation targets, overweights nontradeable inflation in the
measure of
inflation that
is
targeted, and explicitly weighs reserves holdings
in its objectives.
Since the no-commitment central bank loosens during good times and
we suggest that
tightens during bad times,
inflation target countercyclical
(i.e.
mandate should make the
its
low during good times, and high during
In practice, the state contingency
sudden
stops).
making
inflation targets contingent
prices, U.S. interest rates or U.S.
may
be implemented by
on external factors such as commodity
Corporate bond spreads, and the EMBI-I-.
Tradables experience strong inflationary pressures during crises as the ex-
change rate depreciates.
is
more
limited.
On
other hand, the pass-through to non-tradables
Thus targeting a measure of
inflation that overweights
non-
tradables also will reduce the central bank's incentive to raise interest rates
during
crises.
Finally, since the central
crises,
we suggest that
its
bank
injects reserves too aggressively
during
objectives be modified to place weight on the
stock of reserve holdings. Choosing an appropriate weight for reserves will
help the central bank to internalize the effect of
on the private
Our paper
icy in
its
exchange interventions
sector's insurance incentives.
is
most
directly related to the literature
economies with financial
frictions (e.g.,
on monetary pol-
Bernanke and Blinder, 1988;
Bernanke, Gertler and Gilchrist, 1999; Christiano, Roldos, and Gust, 2003;
Diamond and Rajan,
strom and
2001; Gertler, Gilchrist, and Natalucci, 2001;
Tirole, 1998; Kiyotaki
Unlike most of this literature,
we
Holm-
and Moore, 2001; and Lorenzoni, 2001).
are concerned with
monetary policy
in
emerging markets, so we model the presence of two distinct financial constraints:
one between domestic agents and one between domestic agents and
foreign investors.'
The
recent emerging markets literature has identified sudden stops of
international capital flows as an important part of external crises (see, for
'Of the preceding
literature,
Diamond and Rajan
is
the closest to our analysis in the
sense that they also model two distinct constraints: a bank solvency constraint and an
aggregate liquidity constraint,
in their case.
example, Calvo, 1998, and Calvo and Reinhart, 2002).
We
this feature.
financial constraints.
The importance
for
emerging markets was
for
example, Bulow and Rogoff, 1989).
central
bank
that, since so
will recognize
to depreciate during a
In one sense, the
An open
offer
much
the sovereign debt literature (see,
another perspective on fear of floating.
of debt in emerging
too high, and
mechanism
dollar debt
We
as exogenous).
market
is
in dollars,
a
that the output cost of allowing the exchange rate
crisis is
in our
will therefore raise interest rates.
model complements
question in the Calvo and Reinhart model
much
so
of international financial constraints
first identified in
Calvo and Reinhart (2002)
They argue
Our model shares
model the sudden stop as a tightening of international
is
their explanation.
why
firms take on
Calvo and Reinhart take stocks of foreign debt
(i.e.
show that
stabilizing the
exchange rate
will
reduce the
private sector's incentive to insure against sudden stops, and naturally leads
to increasing liability dollarization (see Caballero and Krishnamurthy, 2003).
On
the other hand, our central bank stabilizes the exchange rate because
it
focuses on inflation costs, as opposed to Calvo and Reinhart's output costs.
The emphasis on insurance
closely to
is
central to our analysis,
Dooley (2000), who also emphasizes insurance
Our monetary pohcy
ing framework
(e.g.,
analysis
is
conducted
in
and
links us
more
effects.
a standard inflation target-
I^ing 1994, Svensson, 1999, or
Woodford, 2002). Svens-
son (2000) has extended the inflation targeting framework to open economies
that
fit
the usual small-open-economy assumption, in which countries face
no international
tries
financial constraint. His analysis
such as Australia or Canada, but
less so to
is
most applicable to coun-
the emerging markets that
are the focus of this paper.
The
next two sections develop a model of monetary policy in an en-
vironment of sudden stops.
this environment.
it
Section 4 studies optimal monetary policy in
Section 5 focuses on the central bank's behavior
cannot commit to
its
monetary policy
choices.
when
Section 6 considers two
modifications to the central bank's objectives that result in the optimal
monetary policy being implemented. Section
to the model. Section 8 concludes.
7
adds international reserves
A
2
model of sudden stops
we sketch a model
In this section
to the monetary
is
sudden stops. This serves as a preKide
of
pohcy analysis of the next
section.
The model we
outline
developed more rigorously in Caballero and Krishnamurthy (2002).
Firms have assets at time
t
of
These are domestic assets
y4(.
generate peso revenues), so that their peso value
peso interest rate, and At
We
is
duction. This
is
it
they
is
the
a decreasing function. ^'^
assume that firms need
dollars in order to import
where
At{it)
is
(i.e.
That
dollars for investment.
some investment goods that
is,
they need
are inputs to pro-
by noting that at the margin, firms in developing
justified
countries are borrowers in international markets.
demand, so that firms always have
to
We
are extrapolating this
borrow from abroad.
Moreover, we assume that firms are financially constrained so that the
aggregate
demand
most models of
demand. Firms
for
investment goods can be written as D{At,if). As in
financial constraints, the net
worth of firms influences their
peso assets, worth At, along with any other peso
sell their
funds they are able to borrow, in order to raise dollars for investment goods.
The
dollars are
borrowed at
demand schedule.
The supply of
D
is
interest rate of if,
decreasing in
dollars
if,
which
and increasing
comes from two
sources.
Thus
we assume that
The
rest are capital
in equilibrium,
'
A
the price in the
in At-
First,
domestic lenders have a supply of Rt dollars (small).
inflows, CFt-
is
D{At{it),if)
=
Rt
+
CFt.
(1)
supplier of dollars earns a return of
^t+i\t
^In the next section
we
derive a
more
explicit sticky price
mechanism that
justifies
using the nominal interest rate as an argument.
'Note that
if
domestic
liabilities
are extensively doUarized, then Ai also becomes a
decreasing function of the exchange rate. In this case, monetary policy
is less
effective in
influencing the peso value of domestic assets since the expansionary effect of lowering
offset
it
is
by the depreciation such policy causes. See Caballero and Krishnamurthy (2002) for
a discussion of constrained
monetary regimes
in
an environment with sudden stops.
On
the other hand, dollarization of external liabilities can be seen as an endogenous response
to the
mechanism we discuss
Krishnamurthy
(200.3).
in this
paper and
is
described in detail in Caballero and
where
Supplying one dollar yields
the peso/dollar exchange rate.
Et is
pesos today. Invested at the peso interest rate of
dollars
tomorrow
it
£t
and converting back into
at £t+i\t yields the above expression.
Supplying one dollar
profitable as long as this return exceeds the in-
is
ternational interest rate (1 +Zj). Define,
^d
For
if
>
ij
there
_ St{l+it)/St+^t-l.
an excess return on supplying dollars to domestic firms.
is
The spread zf — ij is a liquidity premium.
The usual small-open-economy assumption
is
perfectly elastic at the price of if
of investment
=
i^.
is
that the supply of dollars
In this case, the equilibrium level
simply D{At,it). Fixing the foreign interest
is
rate,
the domestic net worth of firms (say through an increase in
it)
a
fall in
decreases
investment.
The sudden
stop assumption
is
that there are times
when
the country
quantity constrained in borrowing from international markets. That
CFt <
where Lt
is
the
maximum
quantity of funds that foreign investors will supply
D{At,if)
Note here that an increase
is
Defining
in
= Rt+Lt
At has no
if>il
=>
eflPect
is,
is
on
+ Rt-
is
because
Instead the
if.
as the log exchange rate,
et
(2)
on investment. This
determined by the sudden stop supply of Lt
only effect of At
is,
Lt,
to this country. If this constraint binds, equilibrium
investment
is
we can
rewrite the domestic interest
parity condition as,
et+i\t
=
- et^it-
When
if
Ct+i|t,
a decrease in the peso interest rate of
i^
this
is
(3)
if-
the usual interest parity condition. In that case, fixing
rate. In the sudden stop case,
where
if
>
i^,
it
depreciates the exchange
the current exchange rate
is
depreciated relative to the future exchange rate by the size of the liquidity
premium. In
this case, a decrease in
it
has the additional effect of causing
the interest parity condition to shift upward, reinforcing the depreciation in
the exchange rate.
The model we have outhned embeds two principal ideas. First, there
are times when an emerging economy is financially constrained in the inIn this instance, the supply of dollars
ternational market.
inelastic
is
The second
the limited supply determines domestic investment and output.
idea
main
that the
is
capacity of firms.
of monetary policy
effect
The
is
has a potentially very large
It
on the exchange rate but limited contemporaneous
last part of this
effect
on output.
statement follows from the right hand side of
The earlier part
same expression and
fixed.
the
on the domestic borrowing
In particular, decreasing interest rates during a sudden
stop does not attract more capital inflows.
effect
is
and
of the statement follows
from the
the fact that At rises as
it
Thus
falls.
(2),
hand
left
i*^
which
side of
must
rise
to ensure equilibrium; by the interest parity condition, this implies that the
exchange rate depreciates not only to
offset the reduction in
but also the
it
rise in if.
Lt
We denote the sudden-stop state as the V regime. In the V regime,
+ Rt fully determines investment. Let us imagine shifting to date — 1,
t
to a point in
time where private and central bank actions may influence
this
stock.
Suppose that at date
supply of funds
it
faces
is
i
—
1
the
economy
horizontal at i(_j
is
{H
not in a sudden stop.
A
regime).
with some dollars at this date can either lend these funds
investment or can save them
an international bond.
in
the agent will be able to lend the dollar at
if — il. That
is,
the fact that if
>
i*t
will
t
The
domestic agent
By
for
domestic
opting to save,
and earn an excess return of
induce domestic agents to "insure"
against the sudden stop (raising Rt).
We
have shown elsewhere (see Caballero and Krishnamurthy, 2001) that
when domestic
financial markets are underdeveloped, there
- akin to a free-rider problem zf
—
i*,
is
less
than
its social
tor will underinsure against
many
is
an externality
whereby the market value of
value.
this benefit,
In this circumstance, the private sec-
sudden stops. This underinsurance may take
forms: for example, borrowing too much; contracting foreign-currency
denominated debt; choosing short-term debt maturities;
or contracting too
few credit lines (see Caballero and Krishnamurthy, 2003).
Aside from direct (and costly) regulation of capital inflows and the
pri-
vate sector's insurance decisions, there are two instruments at the central
bank's disposal to offset the externality. First,
it
can increase
its
f)wn holding
Our model provides a natural
holding of reserves and holding them in the
We will return to this mechanism before
of foreign reserves and thereby increase Rt-
motivation for both centralized
form of international
liquidity.
concluding the paper. -Second, and most important for the purpose of this
paper, the central bank can
sudden stop. Since lowering
commit
it
monetary policy during the
to expand
during the sudden stop raises
the private sector's incentive to self-insure.
We
this increases
if,
develop this idea fully in the
next sections.
Sudden stops and monetary
3
We now
extend the preceding model to incorporate monetary policy and
Our goal
private-sector price setting.
in
—
t
to study optimal monetary policy
we assume that the economy
1,
the external supply of funds
t,
regime.
The
— q.
the
H
regime.
We
t+
the
I,
demand
is
crisis
H
is
in the
H
et
and
H regime, or transits to the V
while that of entering
V
is
episode passes, and the economy
is
in
is g,
f
-I-
1
as
is
what happens
at date
t.
At
this date, ag-
t* is
(4)
the constant foreign interest rate (only
a normalization in this equation). Foreign inflation
it is
inflation
On
is
equal to zero.
real interest rate, rt, is defined by:
= it-
rt
where
and
given by,
the output gap, and
The domestic
e,
et-i-
y^=-b{n-z*).
where yf
That
regime.
elastic at the interest rate of i*
events at the prior dates. At prior dates,
all
are mainly interested in
gregate
is
denote the nominal exchange rate at date
to be independent of
the exchange rates are
We
faces
probability of remaining in
Finally, at date
fix this
it
the economy either remains in the
At date
1
is
an environment of sudden stops.
At date
is,
policy
the (peso) nominal interest rate and
between periods
the supply side,
t
and
(
-I-
1,
(5)
TTj+iit
T^t+i\t is
the expectation of
conditional on information at date
we assume that the economy
is
composed
t.
of two types
of price setters. Slow price-setters set their prices to grow at a constant rate
of
over both periods
fr
this average
from
(i.e.
t
—
1
to
and from
t
t
to
t
+ 1). They
choose
growth rate to be equal to the expected rate of depreciation of
the exchange rate:
-
et
et-i
E;t-1
\
-
ct+i
(
et
(6)
Fast price-setters index their prices to the exchange rate. Putting these two
groups together, and assigning positive weights of a and
and
t
+
an
fast price setters, respectively, yields
—a
1
inflation rate
to the slow
between
t
and
loi,
ait
The expected change
in
+
(1
-
-
a){et+i
et).
the exchange rate between any two dates satisfies
the domestic interest parity condition we derived in
-
et+T.\t
et
=
-
it
(3),
if
(7)
Substituting the interest parity condition into the inflation expression yields,
TTj+i
We now
tion
=
TTt+^t
=
rewrite the aggregate
term we have derived
+
(1
-
a){it
-
demand equation
equation
in
n-i*
avr
(8).
^aiit-i'l-7r)
Substituting this into the aggregate
if).
(8)
to accoiuit for the infla-
First note that,
+
demand
{if-i*).
expression yields,
yf=-b{att+i1),
(9)
where,
it
=
it
—
if
—
7f,
The aggregate demand equation, (9),
aggregate demand in the prior section,
botli the
=
if
is
fj
—
z*.
a simple parameterization of the
(1).
Note that
it
is
decreasing in
domestic (peso) real interest rate and the domestic interest rate on
dollar borrowing.
Equilibrium and policy determine the domestic dollar
rates.
Beginning
witli the former, in the
H
(if)
and peso
(/';)
regime domestic dollar rates
must be equal to international
is
perfectly elastic at
ij.
interest rates because the supply of dollars
Thus:
-d,H
0.
In the
V
regime, the sudden stop implies that
i'^'^
>
i*
(see (2)).
We
impose the sudden stop constraint directly as a constraint on output:
vY
The
first
term
= -% + «rf*£|t-i
term indicates that output
reflects
falls
>
"2/
0-
(10)
below the natural
stop. If the private sector anticipates a high value of
stop,
it
will
level.
be inclined to take precautionary
i^'
steps.
during the sudden
We
that in emerging markets the private value of precautioning
small relative to
for
The second
the private sector's incentives to insure against the sudden
its social
a model showing
concerned with ways
is
typically too
value (see Caballero and Krishnamurthy, 2002,
Thus,
this).
our monetary policy analysis
in
which the central bank
in
argued earlier
we
are
can increase the incentive to
take precautions.
Finally,
we consider the average depreciation
both periods
setters. First
in order to derive
an expression
-
=
et
it
=
-it
+
i"
Next, from the interest parity condition at date
^t\t-\
t
—
the n set by the slow price
for
note that,
et+i\t
We
of the exchange rate over
-
Cf-i
=
it-\
-
t
7ir.
—
\,
i*
need to make an assumption about the central bank's behavior at date
I.
We make
the simplest one, and assume that
it
sets the real
domestic
interest rate equal to the international interest rate (recall that foreign inflation
is
normalized to zero): it-\
—
t^
=
i*
consistent with attaining a zero output gap
in (9) also applied at date
t
—
.
if
Note that
this policy choice
the aggregate
demand
is
relation
1.
Substituting the exchange rates back into the expression for n from (6)
gives,
f
7f
= 2
H
Eiif]
^-^
2
10
+
n
,
which implies that,
=
Eiir]
Relation (11)
what
central to
is
o.
(11)
The
follows.
between the average domestic real interest rate
adjusted international interest rate
rate z"
(i^
—
the deviation
Constraint (11) arises from ra-
(«{''^)-
by the private sector.
tional expectations price setting
is
n) and the liquidity-
It tells
us that
if
the central bank chooses a low real interest rate in one of the states, in
equilibrium, the real interest rate in the other state
We
can rewrite the expression
must be
high.
more concisely using the
for nt+i
tilde
notation as,
TTt
By symmetry
and date
with inflation at
et+i
=
i
+
-
a)2^
(12)
the inflation rate between date
1,
-I-
{1
t
—
1
t is
TTf
=
Since, Cj
== Tf
+l
e)
e
—
and
+
(i'^
e
—
tt
et-i
=
QTT -f (1
-
a){et
-
et-^i).
(from interest parity condition and the assumption
)
=
27r (see
=
Trj
the definition of
7f
-
(1
tt),
we
find that,
- Q)i^
(13)
Optimal policy
4
Maximizing
social welfare for this
economy is achieved by minimizing the
t — I, of the loss function, L:
expected value, given information at
L=Xyf +
where
<
5
<
1 is
a discount
These terms are
first
term
is
fairly
Trf
+ {I-
S)nl,,
(14)
rate.
standard
in the inflation targeting literature.
The
the cost of output fluctuations around potential output, while
the other terms reflect the cost of inflation.
The parameter A determines
the relative weight on output gap stabilization.
We now
commit
to
derive the optimal monetary policy
its
choices of
The output equation
{i(^ ,i}
in
H
)
when the
central bank can
in advance.
follows directly from (9), with if set to zero:
11
we
In V,
regime,
solve for the equilibrium
must be such that
Zj'
yt
if'
from
external financial constraint (10). That
—
—bif
Since
=
i^'
between
(9) is consistent
= —ay +
baif
is
Z('
we
see that the relation
is:
(15)
+ ad
'
Note that the external constraint
with yY from the
^=7-^.
r/ = ^(ay-hai^),
\
V
0^2^,'
changes in the latter
for anticipated
the
in
(2),
is,
i^i^i under rational expectations,
and i(
i^
Analogous to
.
(10) has yt increasing in
Zj'
Since
.
decreasing in i^ this means that lowering lY has a beneficial effect on
output
,
in
V The
.
effect is
By
through an "insurance" channel.
a lower iY during the sudden stop, the expectation of
i^
anticipating
rises.
'
That
is,
the return to insuring against the sudden stop increases, and this relaxes
On
the aggregate financial constraint.
demand
on y -
the other hand, the usual aggregate
effect of lowering interest rates - the
is
absent in the
V
regime.
positive effect on aggregate
demand
is
rise in i^
state-contingent monetary policy
is
effect of
fixed at date
of a reduction in i\
the negative effect of the corresponding
When
contemporaneous
Ex-post, since lY
is
t,
iY
the
fully offset
by
output
V
.
'
fully anticipated,
in
is,
vY = -^i>(ay +
We
assume throughout that yl <
ocaaiY)-
so that increasing yl lowers the objec-
0,
tive in (14).^
The
objective for the central bank
min
is,
gL^ + (l-g)L^
where,
L^'
=
X{b<i>f{ay
+ aa^Yf +
^This means assuming that
possible to
(Jr
—^> —
i,
(1
.
- a)iYf +
Although,
i,'
is
(1
-
S){Tt
+
- a)iYf
an endogenous variable,
show that the assumption can always be met by choosing Oy
12
{I
it is
large enough.
and,
L" =
X{hc^i^f
+
(tt
-
- a)l^f +
(1
-
(1
5)(7f
+
- 0)1^ f
(1
subject to the rational expectations constraint that,
=
E^t]
Let us start with the
0.
order condition with respect to
first
tt,
which
is
straightforward:
=
-
2(1
+ 2(7(7r -
2tx- 2(1 -
=
2(2 -(5)^
commitment
c
-
no
+
a)i^)
+
2(1
-
2(1
-
2(1
^
=
-
<5)(1
-
q){n
+
(1
-
<5)g(7f
-
(5)(^
=
77^^
(1
-
+
(1
-
ajz^)
a)i^)
cv)E(i^])
0,
stands for the commitment solution. Thus, in the
case, the central
inflation, there is
+
a)lY)
q)£'[z^]
Since
average rate of inflation.
positive average
(1
-
(1
=
where the superscript
full
-
g)(7r
bank chooses policy so
as to achieve a zero
price setters take into account average
all
benefit, only costs, for the central
bank to choose a
inflation.
This does not
mean
that monetary policy
the marginal benefit of increasing
/}',
is
we compute
rates and
we
impotent.
at neutral interest
If
fr'^,
find
ril.
-on
= 2(1 -
\-.H_-V
|.H_-v'_^_o
which implies that the central bank
nWrxn
,n l'^\I(^2 >
q)\aaiay{h^Y
will
choose
i}
<
(since
we
are mini-
mizing the objective).
The exact
solution
is,
''
°^A(6Q)Mg('I'a<i)2+l-'7)
The
central
bank
sets i^
below
i,
sector's incentives to insure against the
is
'
in order to increase
on average
so that policy
is
inflation, the central
tighter in the
H
stop.
regime, and output
13
^^^
the private
The cost of this policy
V regime. To offset the eff'ect of
bank chooses if^ >
(see (11)),
sudden
that the exchange rate depreciates in the
this policy
+ (2-5)(l-a)2-
is
lower.
Note that as a
V
result of its
attempt to increase precautioning against the
regime and hence increase y^, the central bank tolerates some instabihty
and exchange
in inflation
The
5
rates.
bank without commitment
central
Let us now study a central bank that cannot commit to the interest rate
choices of date
commitment.
it will
t,
Two
prior to this date.
First,
if
biases arise from the lack of
the central bank's preferences are as stated in (14)
choose interest rates to completely stabilize the exchange rate ("fear
Second,
of floating").
the central bank's preferences are distorted so as
if
to always prefer to increase output, as in Barro and
the fear of floating problem
the
H
state,
and tightens
rate of inflation. This
commitment
in
is
made
the
V
The
worse.
central
(1983), then
bank loosens
in
state, while inducing a positive average
exactly the opposite of the policy dictated in the
is
solution.
Fear of floating
5.1
Suppose that the central bank chooses
interest rates in each state
to minimize the loss function in (14).
Then
in
H,
-
a)i^)^
+
(1
minL^ =
while in V,
it
Compared
+
(if
-
L^'
is
(1
= {k-{1- a)lYf +
to the loss function in
that there
that there
X{baii^f
it
-
{H
or
V)
solves,
<5)(7f
+
(1
- a)i^f
solves,
min
is
Gordon
is
V
{I
-
5)(n
+
{I
- a)iYf.
of the previous section, the main change
no output term. This follows from our assumption
in (10),
no aggregate demand channel whereby lowering interest rates
increases output.
The
loss function in
H
is
the same as in the previous
section.
It is
easy to verify that the solution to these two problems (that
sistent with the rational expectations requirement that E|«|^]
i¥
=
iY
=
0,
with
7f
=
0.
Note that at
14
tt
=
0, inflation
=
is
con-
0) is to set
and the exchange
rate are fully stabilized
gap
H
in
is
While the policy
cost
that output
is
bank
central
by choosing
=
it
—
it
In addition, the output
0.
equal to zero.
both
stabilizes
is
drops too
inflation
much
and the exchange
in the
rate, the
sudden-stop state,
essentially ignores the insurance channel of
and focuses purely on maintaining a stable exchange
V
monetary
.
The
policy,
rate.
Exacerbating the problem: Barro-Gordon
5.2
We now
modify the central bank's objective function to introduce an expan-
sionary bias a la Barro-Gordon (1983):
L=-Ayt+7r2-f(l-5)7r2^i.
The
We
yt
term now
reflects
the central bank's preference to always raise output.
drop the squared-output term since
The
H
choice problem in
minL^ = A6Qzf +
This gives the
Note that a
first
(tt
-
larger value of
choice problem in
- n)i^f +
-
h)(iT
+
(1
- a)i^f.
t,
order condition
A
Since in equilibrium,
for increasing
higher value of
V
remains the same as
is
fixed:
a)l^'f
+
(1
-
offsets this tendency.
ff
<5)(7r
output) leads
in
+
the fear of floating case
(1
- a)iYf.
is,
2
and
(1
A (greater preference
minL^ = {n-{lfirst
(1
order condition;
since output, as of date
The
does not change our message.
it
is,
to a lower interest rate choice.
The
(17)
—
we must have
1
— Q
that
E[z^']
(19) that,
Qba
^^^2(r3^>«15
=
0, it follows
from
(18)
Replacing this expression back into (18) and
ir
>
^"
=
we
z^ <
find that
and
-^^-^)^2(r^<«'
-y
'*
The
central
=
bank preference
qba
^2(l-a)2<5 >
for increasing
bank
sets
rate in
>
0.
H
<
i^
As
0.
in
increases output, the central
raises the private sector's inflation expectations,
is
bank
predetermined by the sudden stop supply. However,
is
now
positive, the central
with an exchange rate that depreciates at date
raises the interest rate in
tighter
and leads to
sees no output benefit to changing interest
since the average rate of inflation
and an even
V^.
t.
To counter
bank
this,
is
crisis is
faced
the central
In equilibrium, this leads to a lower
sudden stop supply. The
Zj'
,
thereby exacerbated.
Implementing optimal policy through
6
eiTect in
Barro-Gordon, the anticipation of the low interest
In V, the central
rates since output
bank
"
output has a perverse
H
our model. Since lowering interest rates in
Tf
(19),
0:
inflation
targets
Given the time inconsistency of the central bank, what should
be? That
it
how should the
is,
its
mandate
central bank's objectives be modified so that
internahzes the insurance dimension of the sudden stop problem?
this section
made
we
highlight
two
possibilities.
state dependent: stringent (low) in
H
First, inflation targets
and loose (high)
in
In
can be
V. Second,
the central bank's mandate can overweight the inflation of non-tradables in
the measure of inflation that
regime, there
bank
is
offsets this
it
targets.
Since output contracts in the
deflation in non-tradables.
The
V
inflation-targeting central
by lowering interest rates and causing the exchange rate
to depreciate (leading to inflation in tradables). This incentive increases by
placing a larger weight on non-tradables.
6.1
We
State contingent inflation targets
continue with the linear-output specification but modify the central
bank's objective function to introduce a state- contingent inflation penalty
16
term of k",
for
w e {H,V}:
L = -Xyt +
A
positive k
means that
(TTf
-
K-)2
inflation
+
(1
-
6)(TTt + i
k'^)2.
(20)
the central bank, while a
less costly for
is
-
negative k penalizes inflation further.
The
choice problem in
minL^^ = Xbai^ +
This gives the
first
{ft
H
is,
- k" -
{I
- a)i^f +
The
L^'
=
(tt
-
K^'
-
order condition
first
V
V
(1
(1
is
- a)iYf +
a)l^)-.
-
a)(5
As
6
"
k^''
+
-
(1
a)tl'f.
—K
1 - Q
we must have that
H_
~
it
is
E[z^]
=
0,
we
obtain:
equal to zero. Imposing
k'^:
^^Q
__
2{l
_
-a)S
1
q
v
g
"
a strong Barro-Gordon inflation bias (high A), then
is
made low
-
(5)(7r
note that in the commitment solution
yields a constraint across
there
-
it
~ 2-5
before, since in equihbrium
We
(1
now,
-y
If
-
is:
^'
it
(1
H
choice problem in
min
—
- k" +
5){tt
that, everything else constant, a larger value of k^' leads to a lower
interest rate in
The
-
order condition:
2-51 -a
Note
(1
k^
can be
in order to offset this bias. Similarly, to the extent that the central
bank has a loose
the net result
is
inflation target in
a
ir
V
of zero.
17
(if
k^
is
high),
k^
can be set low so
Substituting this k expression back into the
order conditions for
first
interest rate choices allows us to solve for the optimal interest rate choices:
-H
If
—
*
1
^
1
-
g
K
r
2-b\-a-
V
q
and
-v
By
kY >
choosing
_
^
Q (and hence
1
n^ <
V
the central bank will follow a
0),
state contingent policy as dictated in the social
iY
<
In equilibrium, this leads to a higher
0.
supply.
The
crisis is
Zj
'
optimum, with i^
,
>
and
and a looser sudden stop
thereby lessened.
Before concluding this section, note that both the state-contingent
tion target
infla-
and the nontradeable-infiation overweight solutions act through
the inflation terms of the central bank objective.
If
we were
to introduce
a contemporaneous output effect of a change in i^ these recommendations
,
We
could
by raising the weight of output
in the
would remain but there would be an additional channel open:
now
also achieve the desirable eiTect
central bank's objective during V-regimes.
Non-tradable inflation target
6.2
now introduce an infinitesimal (in the sense that it does not feedback
aggregate demand) non-tradable good, whose inflation is determined
Let us
into
by a simple Phillips curve:
-
TV
We
-
modify the measure of inflation that the central bank targets to be
a weighted average of
using so
far.
The
n^ and
the tradable inflation of
central bank's objective function
ttj
that
we have been
is,
L=-Xyt + if3n^ + {l-P)nt-K'^f + {l-6){P7r^^, + {l-p)nt+,-Kn^.
P
is
the weight on non-tradable inflation.
inflation rate
on non-tradables
k" ^ 0).
The choice problem
min
L''
=
{n
+ pyY -
in
(1
-
V
to
be
We
zero.
normalize the
Finally
we
set
(21)
+ 1 (non-crisis)
(leaving
k^' =
t
is:
/3)(1
- a)i]y +
18
{1
~
6){1
- 0f{n +
(1
- a)V(f.
The
order condition
first
zT
is,
= n{l-{l-l3){l-S))+PyY
(1
The
choice problem in
H
-
a){l
- 0){2 -
5)
is,
,H
i
i»
This gives a sohition
and decreasing
As
is,
for
k^
in
z^ that
hnearly increasing in n, decreasing in A,
.
the previous section
in
is
we can always choose k^
when we impose the equilibrium condition that
relation for
Given
ment
<
i^
which
is
By
n in terms of
this
k^
i]
,
-P
is
k^ We
.
proportional to f3yY
by choosing
/?
achieved by setting
> 0. Since
k^ < 0.
£'[j^]
E[i'^]
k^
simply choose
=
0,
so that
Since yY
=
so that
0, this
<
we
tt
0,
n =
0.
That
arrive at a
equals zero.
we can imple-
means that i^ >
0,
increasing the weight on nontradables in the measure of inflation that
the central bank targets, the central bank follows a state contingent policy
as dictated in the social
optimum. Again,
in equilibrium, this leads to
a
Since crises are characterized by dollar shortages (see equation (2)), there
is
higher
7
Zj
,
'
and a looser sudden-stop supply.
Reserves management
for managing international reserves in order to ease these
Our model provides a natural motivation for both centralized
holding of reserves and for holding them in the form of dollars.
We assume that the central bank has a small amount of international
scope in the model
shortages.
reserves at date
beyond date
t
+
t.
These reserves can be injected at date
1,
latter represents the
when they
yield 7
>
utils
t,
or saved for use
per unit of reserves.
opportunity cost of using the reserves
early,
The
and should
be interpreted more broadly as the value of precautioning.
We
contrast
how the
results of section 4
the introduction of international reserves.
modified
and section
The
5.1
loss function in
change upon
both cases
is
to:
L^Xy^ +
7Tf
+ (l-5)nf^,+jRt,
19
(22)
with Rt the amount of reserves injected.
Recall that in section 4,
central
we
5.1,
bank commits to
in
we
solve for the interest rate choices that the
minimizing the
loss function.
While, in section
solve for the sequentially optimal interest rate choices given this loss
function.
There
is
no value
in injecting reserves in
H
Since there
.
is
no dollar
shortage, the action has no effect on either prices or output. Reserves will
be hoarded because
do so has an opportunity cost
failing to
7.
In the
V
regime, the action increases dollar supply and relaxes the vertical constraint:
(10) to:
Vt
One can
=
Rt
-ay + adi^iy
(23)
t\t
see from this expression, that B}[ enters exactly as
—ay
in all the
expressions. In particular,
g = *6(< - % - aarf^HAs we discussed
on
earlier,
(24)
the optimal policy considers the dependence of yY
(which enters through expectations), while the no-commitment case
ij'
does not.
The
introduction of international reserves
management considerations
does not change any of the main qualitative conclusions with respect to
monetary pohcy
commitment
in either the
tions 4 and 5.1, respectively. In particular,
both
and
i
cases; that
<
=
i''^
in the
-i
=
in
commitment
or
no-commitment case of
sec-
=
in
equation (16),
To
i]'
the no-commitment case; and that i^
decreasing in ay. Since
sions, the reserve injection increases the
The most
>
for (countercyclical)
mon-
commitment
solution for iY in
RY
—ay
see this, note that in the
is
tt
case.^
However, reserve injections are a substitute
etary policy.
the case that
it is still
enters as
in all expres-
optimal iY
new result comes from the first order condition
From equations (22) and (24), the solution for RJ in
interesting
with respect to
/?]'
.
the commitment case
is:
Rt'^
= - ^TTTI^TT^ +
2A(6*)2
^These statements assume that Rt <
a.y,
reserves to eliminate the sudden stop shock.
20
«y
+
"«d^'r
so that there
is
(25)
insufficient international
From equations
case
(22)
and
(23), the solution for
is:
^r'"'
Note that
mitment
b'^
case.
have that Rf
only
= jq^ <
will
'"'^
1,
-^ +
=
> Rf
use too
little
(26)
more negative
is
any equilibrium
That
the no-commitment
in
+ aa,z^
so the first term
Also, since for
''^.
a,
RY
level of
R]
in the
<
''^
,
z^
com-
'"''^,
i^
we
the central bank with no commitment not
is,
monetary
policy,
but
it
also will inject reserves too
aggressively.
There are two factors behind this
increases output and decreases
i^'
output benefit, but ignores the
accounts for the second
result.
both
Ex-post, the central bank considers the
.
on
effect
the lower
effect:
First, injecting reserves
Zj'
i^'
.
Ex-ante, the central bank
decreases the private sector's
incentives to insure against the sudden stop shock.
the commitment-central-bank inject
less
The
latter effect
reserves than the
makes
no-commitment
one.
The second
policy.
In the
factor has to
do with the time inconsistency
no-commitment
solution, the central
larger crisis caused by the inadequate
monetary
bank has
policy.
As a
monetary
of
to offset a
result,
it
over-
injects its reserves.
The
latter factor
is
remedied indirectly by solving the monetary policy
time inconsistency problem as we have discussed.
The former
factor,
the other hand, requires further modification to the central bank's
so that
it
increases the value
it
on
mandate
assigns to hoarding reserves during the V-
regime.
8
We
Final remarks
have analyzed monetary policy
den stops are times when a country
in
an environment of sudden stops. Sud-
is
financially constrained in the interna-
tional financial market. In this context, lowering or raising domestic interest
rates has only small effects on the tightness of this financial constraint, but
does have significant
effects
on the domestic borrowing capacity of agents.
Moreover, the anticipation of such actions are important
in
determining
precautionary actions that agents take against sudden stops.
From
this viewpoint,
we have
derived positive and normative results for
21
monetary policy and reserves management.
inconsistency problem and
bias.
Finally,
its
We
have highlighted a new time
interaction with the conventional stabilization
we have suggested how an
inflation targeting
framework can
restore incentives, so that central banks behave optimally.
Our model
is
clearly very stylized.
In particular, our
assumption that
the country faces a vertical supply of funds during sudden stops
But
is
extreme.
important to realize that our main conclusions do not depend on
it is
this extreme.
We
could consider a more general model in which the supply
of funds was not completely inelastic in the
V
regime. In this case, the
V
regime would have both an aggregate demand channel and the insurance
channel
we have
highlighted
(i.e.
lowering iY leads to a contemporaneous
increase in yY). Importantly, relative to the H-iegiuie, the output-inflation
tradeoff will
still
turn steeper (although not vertical) during the V-regime
and hence the central bank
targets
channel
more than
is
in
the
H
will
be prone to favor inflation over output
regime.
Moreover, as long as the insurance
present, this reaction will remain suboptimal.
Insurance against sudden stops affects
many
policy decisions in emerging
markets, from reserve management to liquidity ratio requirements.
It
only natural that optimal monetary policy be analyzed in the same
as in this paper.
Moreover,
it
is
We
light,
important to understand the interaction
of monetary policy with other insurance policies (as
policies).
seems
we have with
hope that our framework provides a starting point
integrated approach.
22
reserve
for such
an
References
[1]
Barro, Robert, and David Gordon,
"A
Positive
Theory of Monetary
Policy in a Natural Rate Model," Journal of Political
Economy, August
1983, Pi (4), pp. 589-610.
[2]
mand," American Economic Review,
[3]
Money and Aggregate De-
Bernanke, Ben and Alan Blinder, "Credit,
Bernanke,
in
B.,
M.
Gertler,
and
May
1988, 75(2), pp. 435-439.
S. Gilchrist,
"The Financial Accelerator
a Quantitative Business Cycle Framework," Handbook of Macroeco-
nomics, Taylor and Woodford, eds., 1999.
[4]
Bulow, Jeremy and Rogoff, Kenneth, "A Constant Recontracting Model
Journal of Political Economy, February 1989,
of Sovereign Debt",
97{1), pp. 155-178.
[5]
Caballero, Ricardo and Arvind Krishnamurthy. "International and Do-
mestic Collateral Constraints in a
Model
of
Emerging Market
Crises,"
Journal of Monetary Economics, December 2001, ^<S(3), pp- 513-548.
[6]
Caballero, Ricardo and Arvind Krishnamurthy.
of
[7]
Monetary Policy
Caballero,
Debt:
in
"A
Vertical Analysis of
Emerging Markets." Mimeo, MIT, 2002.
Ricardo and Arvind Krishnamurthy,
"Excessive Dollar
Financial Development and Underinsurance,"
Journal of Fi-
nance, forthcoming, 2003.
[8]
Calvo, Guillerhio, "Capital Flows and Capital-Market Crises:
ple
[9]
Economics of Sudden Stops," Mimeo, University of Maryland, 1998.
Calvo, Guillermo, and
Journal of Economics.
[10]
Christian©,
cial Crisis,"
[11]
The Sim-
L..I.,
Carmen
May
C. Gust,
Reinhart. "Fear of Floating." Quarterly
2002, 117{2), pp. 379-408
and
.].
Roldos, "Monetary Policy in a Finan-
Journal of Economic Theory, forthcoming, 2003.
Diamond, Douglas and Raghuram Rajan. "Liquidity Shortages and
Banking Crises." Mimeo, University of Chicago, 2001.
[12]
Dooley, Michael, "A model of crises in emerging markets,"
nomic Journal, January 2000, 110{460), pp. 256-272.
23
The Eco-
[13]
Gertler, M., S. Gilchrist
and F.M.Natalucci, "External Constraints on
Monetary Policy and the Financial Accelerator,"
NYU
working paper,
2001.
[14]
Holmstrom, Bengt and Jean
uidity."
[15]
King,
Tirole. "Private
and Public Supply of Liq-
JowTial of Political Economy, February 1998, 106{l), pp. 1-40.
Mervyn
A.,
"Monetary Policy
in the
UK,"
Fiscal Studies 1994,
15(3), pp. 109-128.
[16]
Kiyotaki, Nobuhiro and John Moore. "Liquidity, Business Cycles, and
Monetary
[17]
Mimeo, LSE, 2001.
Lorenzoni, Guido. "Interest Rate Stabilization and Monetary Control:
A
[18]
Policy."
Reconciliation."
Mimeo, Princeton
University, 2001.
Svensson, Lars E. O., "Inflation Targeting as a Monetary Policy Rule,"
Journal of Monetary Economics, 1999, 43, pp. 607-654.
[19]
Svensson, Lars E. 0.,
"Open-Economy
Inflation Targeting," Journal of
International Economics, 2000, 50, pp. 155-183.
[20]
Woodford, Michael,
"Inflation
Stabihzation and Welfare,"
Princeton University, 2002.
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