NBER WORKING PAPER SERIES
WHEN IS IT OPTIMAL TO ABANDON A FIXED EXCHANGE RATE?
Carlos A. Vegh
Working Paper 12793
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
We thank Linda Goldberg, Pierre-Oliver Gourinchas, Michael Klein, Assaf Razin, seminar participants
at the NBER IFM Program Meeting, Federal Reserve Bank of New York, Princeton, and University
of Pennsylvania for their comments. We are particularly grateful to Bob Flood, Fabrizio Zilibotti, and
two anonymous referees for their suggestions. Financial support from the National Science Foundation
and UCLA Academic Senate is gratefully acknowledged. The views expressed herein are those of
the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.
© 2006 by Sergio Rebelo and Carlos A. Vegh. All rights reserved. Short sections of text, not to exceed
two paragraphs, may be quoted without explicit permission provided that full credit, including © notice,
is given to the source.
When Is It Optimal to Abandon a Fixed Exchange Rate?
Sergio Rebelo and Carlos A. Vegh
NBER Working Paper No. 12793
JEL No. F31
The influential Krugman-Flood-Garber (KFG) model of balance of payment crises assumes that a
fixed exchange rate is abandoned if and only if international reserves reach a critical threshold value.
From a positive standpoint, the KFG rule is at odds with many episodes in which the central bank
has plenty of international reserves at the time of abandonment. We study the optimal exit policy and
show that, from a normative standpoint, the KFG rule is suboptimal. We consider a model in which
the fixed exchange rate regime has become unsustainable due to an unexpected increase in government
spending. We show that, when there are no exit costs, it is optimal to abandon immediately. When
there are exit costs, the optimal abandonment time is a decreasing function of the size of the fiscal
shock. For large fiscal shocks immediate abandonment is optimal. Our model is consistent with the
evidence that many countries exit fixed exchange rate regimes with plenty of international reserves
in the central bank's vault.
Kellogg Graduate School of Management
Evanston, IL 60208-2001
Carlos A. Vegh
Department of Economics
Tydings Hall, Office 4118G
University of Maryland
College Park, MD 20742-7211
Consider an open economy with a fixed exchange rate that suffers an unexpected
fiscal shock. This shock consists of an increase in government expenditures that
has to be financed with seignorage. When, if at all, should the fixed exchange rate
regime be abandoned? Further, suppose that, with some probability, a future fiscal
reform or a financial package from the International Monetary Fund (IMF) can
restore the sustainability of the fixed exchange rate regime. For how long should
policy makers wait for this scenario to materialize?
The decision to exit a fixed exchange rate regime is one of the most important
policy questions in open-economy macroeconomics. This importance was recently
illustrated by Argentina’s abandonment in early 2002 of its 10-year old “Convert-
ibility plan” that had tied the peso to the U.S. dollar at a one-to-one rate since
April 1991. Most analysts agree that fixing the exchange rate was an effective
strategy to eliminate runaway inflation. However, in the mid 1990s, as the fiscal
situation began to deteriorate, the question of whether Argentina should abandon
the fixed exchange rate began to surface with increasing frequency.1The IMF
rescue packages in December 2000 and August 2001 bought Argentina some time.
But, in the end, the fixed exchange rate was abandoned in January 2002.
Economic theory offers surprisingly little guidance as to the optimal time to
exit a fixed exchange rate regime. The dominant paradigm for understanding
this exit is the model proposed by Krugman (1979) and Flood and Garber (1984),
which we refer to as the KFG model.2This model makes two central assumptions.
The first assumption is that the root cause of the eventual abandonment of the
1See Mussa (2002) for a detailed analysis of Argentina’s lax fiscal policy during the mid 1990s.
2The original KFG model does not have microfoundations. However, several authors have
extended the KFG framework to models populated by optimizing representative agents. See,
for example, Obstfeld (1986a), Calvo (1987), Drazen and Helpman (1987), Wijnbergen (1991),
Burnside, Eichenbaum, and Rebelo (2001), and Lahiri and Végh (2003).
fixed exchange rate is an unsustainable fiscal policy. The second assumption is
that the central bank follows an ad-hoc exit rule whereby the fixed exchange rate
regime is abandoned only when the central bank exhausts its foreign exchange
reserves and its ability to borrow.
To study the empirical plausibility of these two hypotheses, we collect in Table
1 data for 51 episodes in which regimes with fixed exchange rates were abandoned.
These abandonments are often called “currency crises.” Our episodes were selected
from an updated version of Kaminsky and Reinhart’s (1999) list of crisis episodes
according to the criteria outlined in Appendix 7.1. Table 1 reports the change
in the exchange rate in the month in which the fixed exchange rate regime was
abandoned, as well as the change in the exchange rate in the 12 months before and
after the abandonment.3Table 1 also reports the rate of change in real government
spending in the three years prior to the crisis and the reserve losses that occurred
in the 12 months prior to the crisis.
We view the fiscal data in Table 1 as lending empirical support to the first KFG
assumption. There were increases in real government spending in the three years
prior to the abandonment of the peg in 80 percent (37 out of 46) of the episodes
for which we have fiscal data. Therefore, fiscal shocks are plausible suspects as
the root cause of the decision to abandon a fixed exchange rate.
We think that the reserve-loss data in Table 1 implies that the second KFG
assumption is empirically implausible. While the KFG model is not explicit about
the critical lower bound for international reserves (is it zero? is it negative?), it
is clearly in the spirit of the model that the monetary authority holds on to
the peg for as long as it can. So we would expect to see central banks exhaust
their international reserves before the fixed exchange rate is abandoned. Figure
3In some of the episodes included in Table 1 the exchange rate was not literally fixed, but
followed a crawling peg or fluctuated within a narrow band.
1 depicts a histogram of the fraction of initial reserves lost during the 12 months
prior to the crisis. In 12 out of 51 episodes countries have non-positive reserve
losses (i.e., they gained reserves). In 38 out of the 51 episodes (or roughly 75
percent), reserve losses were less than 40 percent of initial reserves. While there
were cases in which the monetary authority was willing to lose a large amount
of reserves before devaluing, in most cases the peg was abandoned with plenty
of ammunition left in the central bank’s coffers. In other words, the monetary
authority chooses to devalue as opposed to being forced to devalue by literally
exhausting its reserves and its ability to borrow. We conclude that the KFG exit
rule, a critical component of the KFG model, is inconsistent with the empirical
behavior of reserves in countries that have abandoned fixed exchange rates. In
addition, and given that it assumes an exogenous exit rule, the KFG model is
unsuitable for understanding the decision to abandon a fixed exchange rate regime.
In this paper, we study the optimal exit from a fixed exchange rate regime.4
Our analysis is in the spirit of the literature on optimal monetary and fiscal
policy pioneered by Lucas and Stokey (1983). We argue that the assumption that
central bankers choose the optimal time to abandon the peg generates empirical
implications that are more plausible than those associated with the KFG exit
Ouranalysis is based on a standard cash-in-advance small-open-economy model,
extended to incorporate rational policy makers. We first consider the case where
4Authors such as Buiter (1987), Flood, Garber, and Kramer (1996), Lahiri and Végh (2003),
and Flood and Jeanne (2005) have studied whether it is feasible and/or optimal to delay the
abandonment of the fixed exchange rate regime (i.e., “defend the peg”) by borrowing or by
raising interest rates. While these models give the central bank a more active role than in the
original KFG model, they continue to assume that abandonment of the peg is governed by the
5Second-generation models of speculative attacks introduce an optimizing central banker
(Obstfeld (1986b, 1996)). However, they assume that currency crises do not have a fiscal origin.
Instead, the crises are caused by the incentive to increase output via unexpected inflation in
Barro-Gordon type formulations.
there are no costs of abandoning the peg. In this case it is optimal to abandon the
peg as soon as the fiscal shock occurs and without incurring any reserve losses.
This policy is optimal independently of the level of international reserves and of
whether the central bank faces a borrowing constraint.
We then consider the case in which there are costs of abandoning the peg.
These exit costs can reflect, for instance, output losses or the cost of bailing out
the banking system.6We choose to abstract from the source of these costs and
simply assume that devaluing entails some fiscal and social cost. In this case
there is a certain threshold value for the fiscal shock beyond which it is optimal
to abandon immediately, incurring no reserve losses. For fiscal shocks lower than
this threshold, the optimal exit time is a decreasing function of the size of the
fiscal shock. In other words, the smaller the fiscal shock, the longer is the optimal
Intuitively, the optimal exit time results from the trade off between two factors.
For a given fiscal shock, delaying the abandonment of the peg reduces the present
discounted value of the cost of abandoning. However, a longer delay requires a
permanently higher level of inflation once the peg is abandoned. This increase
in the post-abandonment rate of inflation produces a larger intertemporal distor-
tion in consumption decisions. For large fiscal shocks, the cost of delaying (i.e.,
the larger intertemporal distortion) dominates because the gain from delaying is
bounded by the economy’s resources.
Some back-of-the-envelope calculations — based on our model, the fiscal data
in Table 1, and on empirical estimates of the cost of balance of payment crises —
suggest that an immediate abandonment should be at least as common as delayed
abandonment. Hence, unlike the KFG model, our model is capable of explaining
6See Kaminsky and Reinhart (1999) and Gupta, Mishra, and Sahay (2003) for evidence on
output and banking crises during currency crises.
the many episodes illustrated in Table 1 in which pegs were abandoned with still
plenty of international reserves at the Central Banks’ disposal.
To study the theoretical robustness of our results, we then consider four ex-
tensions of the basic model: (i) time-varying exit costs, (ii) social, but non-fiscal,
costs of abandoning the peg, (iii) more general preferences, and (iv) the case in
which the exist cost depends positively on the fiscal shock itself. In every single
case, our main results go through which attests to the theoretical robustness of
the paper’s main message.
We then consider a stochastic version of our model in which the costs of aban-
doning arise endogenously. There are no fiscal or social exit costs but fiscal fun-
damentals are random. These fundamentals are governed by a stochastic process
that captures the idea that a fiscal reform is more likely to occur while the econ-
omy has a fixed exchange rate. In particular we assume that, while the exchange
rate is fixed, there may be a fiscal reform that restores the sustainability of the
fixed exchange rate.7This reform arrives according to a Poisson process. Once
the economy abandons the fixed exchange rate regime, there is no hope of a fis-
cal reform and the initial fiscal shock must be financed with seignorage revenues.
There is thus an option value to maintaining the peg. In this context, the cost of
abandoning the peg consists in giving up this option value. We show that there
is a close connection, both formally and in terms of the properties of the opti-
mal exit time, between this model and our benchmark model. In the stochastic
model there is also a threshold value of the fiscal shock above which it is opti-
mal to abandon as soon as the fiscal shock occurs. For shocks with values below
this threshold, there is a negative relation between the size of the shock and the
optimal exit time.
7See Flood, Bhandari, and Horne (1989) and Rigobon (2002) for analyses that also emphasize
the link between fixed exchange rates and fiscal discipline.
The paper proceeds as follows. In Section 2 we introduce the model. In Section
3 we derive the basic results for the deterministic case. In Section 4 we examine
the theoretical robustness of our results. In Section 5 we develop and solve the
stochastic version of the model. Section 6 concludes.
2. The Basic Model
Consider a standard optimizing small-open-economy model in which money is
introduced via a cash-in-advance constraint on consumption. All agents, including
the government, can borrowand lend in international capital markets at a constant
real interest rate r. There is a single consumption good in the economy and no
barriers to trade, therefore the law of one price holds, Pt= StP∗
t, where Ptand P∗
denote the domestic and foreign price level, respectively. The exchange rate, St, is
defined as units of domestic currency per unit of foreign currency. For convenience
we assume that P∗
t= 1, therefore Pt= St.
Before the fiscal shock occurs at time t = 0−, the exchange rate is fixed at a
level S. For t < 0 the economy has a sustainable fixed exchange rate regime and
the government can satisfy its intertemporal budget constraint without resorting
to seignorage. At t = 0 the economy suffers a ‘fiscal shock’: an increase in
government spending that must be financed with seignorage revenues. Generating
these revenues requires abandoning the fixed exchange rate regime at some point in
time. Denote by T the time at which the fixed exchange rate regime is abandoned.
We wish to solve for the optimal value of T, which we denote by T∗.
The representative household maximizes its lifetime utility, V , which depends on
its consumption path, ct:
The discount factor is denoted by ρ. The household’s flow budget constraint is:
∆bt= −(Mt− Mt−)/St,
˙bt= rbt+ y − ct− ˙ mt− εtmt,
if t ∈ J,
if t / ∈ J.
Throughout the paper a dot over a variable represents the derivative of that
variable with respect to time. Here btdenotes the household’s holdings of foreign
bonds that yield a real rate of return of r, and y is a constant, exogenous, flow of
output. The variable mtrepresents real money balances, defined as mt= Mt/Pt,
where Mtdenotes nominal money holdings. The variable εtdenotes the rate of
devaluation, which coincides with the inflation rate, εt = ˙Pt/Pt =˙St/St. To
simplify, we assume that r = ρ.
As in Drazen and Helpman (1987), equation (2.2) takes into account the pos-
sibility of discrete changes in btand Mtat a finite set of points in time, J. Below
we see that this set contains t = 0 and the time at which the peg is abandoned,
T. These jumps are defined as ∆bt≡ bt−bt−, where bt− represents the limit from
the left. Since at any point in time after t = 0, the total level of real financial
assets cannot change discretely, bt− +mt− = bt+mt.8At time t = 0−, just before
the household’s time zero decisions are made, agents hold an amount b0− in real
bonds. Their holdings of nominal money balances are M0− and their real money
balances are therefore m0− = M0−/S.
Consumption is subject to a cash-in-advance constraint:
Since we only consider environments in which the nominal interest rate is positive,
equation (2.3) always holds with equality.
8At t = 0 the total level of real financial assets may change discretely due to an unanticipated
jump in the exchange rate, which changes the value of real money balances from M0−/S to
The flow budget constraint, (2.2), together with (2.3) and the transversality
t→∞e−rtbt= 0, implies the following intertemporal budget constraint:
This budget constraint can be further simplified by using the cash-in-advance
b0− +y/r =
( ˙ mt+εtmt)e−rtdt+
constraint and imposing the condition that lim
+ y/r =
ct(1 + r + εt)e−rtdt. (2.5)
This expression makes clear that, as is typical of cash-in-advance models, the
effective price of consumption is given by 1 + r + εt.
The first-order condition for the household’s problem is:
1/ct= λ(1 + r + εt),(2.6)
where λ is the Lagrange multiplier associated with (2.5).
The government collects seignorage revenues and carries out expenditures, gt. To
simplify, we assume that government spending yields no utility to the representa-
tive household. The government’s flow budget constraint is given by:
∆ft= (Mt− Mt−)/St,
˙ft= rft− gt+ ˙ mt+ εtmt,
if t ∈ J,
if t / ∈ J,
where ftdenotes the government’s net foreign assets. This flow budget constraint,
together with the condition lim
t→∞e−rtft = 0, implies the following intertemporal
budget constraint for the government:
( ˙ mt+ εtmt)e−rtdt +
e−rj(Mj− Mj−)/Sj= Γ0−,(2.7)
9This condition is always satisfied in equilibrium since (2.3) holds as an equality.
where, by definition, Γ0− is the present value of government spending:
If the peg is abandoned at time zero the jump in the money supply (M0−M0−)
is controlled by the central bank through its choice of M0. In contrast, if the peg is
abandoned at T > 0, the jump in the money supply (MT−MT−) is endogenously
determined. Under perfect foresight the path for the exchange rate has to be
continuous for all t > 0 to rule out arbitrage opportunities. This requirement
implies that in equilibrium the household reduce its money holdings at time T in
anticipation of the higher inflation rate for t ≥ T.
2.3. Equilibrium Consumption
Combining the household’s and government’s intertemporal constraints (equa-
tions (2.5) and (2.7), respectively), we obtain the economy’s aggregate resource
b0− + f0− + y/r =
cte−rtdt + Γ0−.(2.8)
This constraint implies that the present value of output plus the total net foreign
assets in the economy must equal the present value of consumption and govern-
2.4. A Sustainable Fixed Exchange Rate Regime
Before time zero, the economy is in a sustainable fixed exchange rate regime, so
agents expect ε to be permanently zero. Sustainability of the peg requires that
the government’s net foreign assets be sufficient to finance the present value of
government expenditures. This requirement condition for t = 0−is:
f0− = Γ0−.
In the fixed exchange rate regime, equations (2.3) and (2.8) imply that consump-
tion and real balances are given by:
= y + rb0−,(2.9)
Using the household’s intertemporal constraint we can write consumption before
time zero as:
c0− =ra0− + y
1 + r
where a0− ≡ b0− + M0_/S0−.
2.5. Optimal Monetary Policy
Suppose that at time zero there is an unanticipated increase in the present value
of government expenditures from Γ0− to Γ0and that this increase in expenditure
must be financed with seignorage. Clearly, the peg has to be abandoned at some
point because Γ0cannot be intertemporally financed with ε = 0. When is the
optimal exit time? Throughout the paper we focus on the perfect commitment
solution to this question.
After the fiscal shock takes place the aggregate constraint for the economy is:
where ∆Γ = Γ0− Γ0− represents the increase in the present value of government
expenditures. Suppose that the government could finance this extra expenditure
b0− + y/r =
cte−rtdt + ∆Γ, (2.11)
with lump sum taxes. Consumption would be constant over time at a level:
c0= c0− − r∆Γ.
Since ∆Γ > 0, the new level of consumption is lower than before. The economy has
the same resources as before the fiscal shock, so the rise in government spending
has to be accommodated by a fall in private consumption. The corresponding
fall in real money balances occurs through a fall in the nominal money supply at
t = 0.
The government can replicate the lump sum taxes outcome by either expanding
the money supply at a constant rate from t = 0 on, by printing money at t = 0,
or by combining these two strategies. Suppose that the government abandons the
fixed exchange rate regime at time zero, keeps M0= M0−, and expands the money
supply at a constant rate ε such that the government budget constraint is satisfied:
Since the central bank abandons the fixed exchange rate regime as soon as news
( ˙ mt+ εtmt)e−rtdt = ∆Γ.
about the fiscal shock arrives, there are no losses of reserves. Private agents are
not given a chance to trade their money balances for foreign reserves at the fixed
exchange rate S before the devaluation occurs. The adjustment in the level of
real balances occurs through a jump in the exchange rate, rather than through a
discrete fall in the nominal money supply at time zero. The aggregate resource
constraint (2.11) implies that consumption is equal to c0. The cash-in-advance
constraint implies that the new level of real balances is m0= c0. This monetary
policy is optimal since it replicates the outcome that can be achieved under lump
The fall in real balances fromc0− to c0is associated with a jump in the exchange
rate from S to:
S0= Sc0−/c0. (2.12)
The constant level of money growth is given by: ε = r∆Γ/c0> 0. So from time
zero on the currency depreciates at rate ε.
There is another optimal policy which consists of abandoning the peg at time
zero and printing enough money to finance the new government spending. In this
case the resource constraint of the government is given by: (M0−M0−)/S0= ∆Γ.
Printing money at time zero amounts to taxing existing real balances and is there-
fore equivalent to lump sum taxes. Since all the seignorage revenue is collected at
time zero, this policy implies a higher rate of instantaneous depreciation at time
zero than that given by (2.12):
c0− − (1 + r)∆Γ.
Any combination of the two policies discussed above, expanding the money
supply at a constant rate from time zero on and printing money at time zero, is
also optimal. Thus, there are multiple ways for monetary policy to achieve the
optimal outcome but all these policies require that the fixed exchange rate be
abandoned at time zero.
Abandoning the peg at time T > 0 yields a lower level of welfare than the
policies just discussed. To show this result we use the following proposition.10
Proposition 2.1. Once the fixed exchange rate regime is abandoned at time
T > 0, it is optimal to expand the money supply at a constant rate, ε. So the
optimal path for money growth, conditional on abandonment at time T, is:
εt= 0, for 0 ≤ t < T ,
εt= ε, for t ≥ T .
We now show that any positive ε generates an intertemporal distortion on
consumption. The value of ε has to satisfy the government’s intertemporal budget
constraint, (2.7), which can be written as:
= ∆Γ +M0− − M0
10To prove this proposition solve the planner’s problem for an economy with no cash-in-
advance constraint. Then it is possible to show that the cash-in-advance economy with constant
ε can replicate the solution to the planner’s problem. See Rebelo and Xie (1999) for details of
a closed economy version of this result.
The term (M0− − M0)/S + [(M0− MT)/S]e−rTrepresents the net reserve losses Download full-text
incurred by the government as the household rearranges its money balances while
the exchange rate is fixed in response to the changes in the path for inflation.
The first-order condition for the household’s problem, (2.6), implies that con-
sumption is constant within the subperiods 0 < t < T and t ≥ T. Let us denote
by c1and c2the level of consumption in the periods 0 < t < T and t ≥ T, respec-
tively. Using equations (2.9), (2.11), and the cash-in-advance constraint, (2.3), we
can show that independently of the form of the momentary utility function and
the value of T, the net reserve loss incurred by the government is given by:
(M0− − M0)/S + [(M0− MT)/S]e−rT= r∆Γ. (2.15)
Using this result, we can rewrite the government budget constraint (2.14) as:
= ∆Γ(1 + r). (2.16)
This equation implies that ε > 0. The first-order condition for the household’s
problem, (2.6), implies that c2< c1. Since the present value of resources that are
available for consumption is independent of T, this non-flat path of consumption
results in lower welfare compared to the case where the peg is abandoned at time
The net reserve loss described in (2.15) is a cost that the government incurs
when the abandonment of the fixed exchange rate regime is delayed. However,
since this cost represents a transfer from the government to households it is not a
cost to the economy as a whole. As a result this cost does not affect the optimal
exit time. The next section considers the case in which there are social costs
associated with the abandonment of the peg.