ABSTRACT
Title of dissertation: ESSAYS ON EXCHANGE-RATE-BASED
STABILIZATION UNDER FISCAL CONSTRAINTS
Nikolay Kirov Gueorguiev, Doctor of Philosophy, 2004
Dissertation directed by: Professor Guillermo A. Calvo
Department of Economics
Exchange-rate-based inflation stabilization programs cause a sizable loss of infla-
tion tax revenue and thus open a fiscal gap. The stabilization literature usually assumes that
this gap can be closed by raising lump-sum (nondistortionary) taxes and/or cutting lump-
sum transfers. As such policies are difficult to implement in practice, these two essays
analyze two alternatives.
The first essay explores the implications of raising a conventional income tax to
make up for the loss of inflation tax revenue in the context of an exchange-rate-based stabi-
lization program in an open economy with sticky prices and monopolistic competition. The
combination of smaller monetary and larger tax distortion in the low-inflation steady state
results in lower consumption and output of nontradable goods than in the high-inflation
equilibrium. In addition, the recession accompanying the transition to the low-inflation
steady state produces welfare losses. Nevertheless, the net welfare result is a gain, as larger
money balances and more leisure time outweigh the cost of lower consumption. The essay
also explores the sensitivity of this welfare trade-off to various structural characteristics of
the economy and exogenous factors.
The second essay assumes that both tax and spending policies are inflexible and
looks instead at the role of monetary policy in closing the emerging fiscal gap. It shows that
in a closed economy a monetary expansion can lower the real interest rate. This benefits the
budget both by generating a money demand boom, which expands the base of the inflation
tax, and by lowering the budget?s interest payments. These effects are, however, dependent
on the credibility of the stabilization program, as the same-size monetary expansion fails
to achieve fiscal sustainability when credibility is lacking.
ESSAYS ON EXCHANGE-RATE-BASED STABILIZATION UNDER FISCAL
CONSTRAINTS
by
Nikolay Kirov Gueorguiev
Dissertations submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfilment
oftherequirementsforthedegreeof
Doctor of Philosophy
2004
Advisory Committee:
Professor Guillermo A. Calvo, Chair
Dr. Michael Kumhof
Professor Enrique G. Mendoza
Professor Carmen M. Reinhart
Professor Susan C. Schwab
cnull Copyright by
Nikolay Kirov Gueorguiev
2004
ACKNOWLEDGMENTS
I owe my gratitude to all who contributed to the completion of this dissertation.
First and foremost I would like to thank my advisor, Professor Guillermo Calvo,
for giving me the invaluable opportunity to draw from his immense expertise. It has been a
pleasure to work with and learn from such an accomplished economist.
I would especially like to thank Dr. Michael Kumhof, a member of my dissertation
committee. This study benefitted a lot from his theoretical ideas and technical expertise.
Thanks are due to Professor Enrique Mendoza, Professor Carmen Reinhart and Professor
Susan Schwab for agreeing to serve on my committee, for sparing their time reviewing the
manuscript, and for providing valuable comments.
Last, but not least, I am enormously indebted to my wife, Roumiana Tiholova, for
her unrelenting support and encouragement in the crucial final years of this journey.
ii
Table of Contents
ListofTables ...................................... v
ListofFigures...................................... vi
1. Introduction ..................................... 1
2. The Trade-Off Inflation?Taxation in Exchange-Rate-Based Stabilization Programs 3
2.1. Introduction . . . . .............................. 3
2.2. The Model . . . . . .............................. 7
2.2.1. Consumers .............................. 7
2.2.2. Producers . .............................. 10
2.2.3. Government Policies and Constraints ................ 15
2.2.4. Equilibrium .............................. 16
2.2.5. Dynamic System . . . . ....................... 19
2.3. Model Solution . . .............................. 21
2.3.1. Calibration .............................. 21
2.3.2. Dynamic Response of the Economy to Stabilization Policies . . . . 23
2.4. Welfare Analysis . .............................. 28
2.4.1. Sensitivity of Welfare to Parameter Specification .......... 29
2.4.2. Sensitivity of Welfare to Speed of Disinflation and Degree of Price/
InflationStickiness.......................... 31
2.5. Sticky Prices Versus Sticky Inflation..................... 33
2.6. Conclusion . . . . .............................. 38
3. Exchange-Rate-Based Stabilization Under Fiscal Constraints and Capital Controls 40
3.1. Introduction . . . . .............................. 40
3.2. The Model . . . . . .............................. 43
3.2.1. Consumers .............................. 43
iii
3.2.2. Government .............................. 45
3.2.3. Equilibrium and Dynamic System . . ................ 45
3.3. Policy Experiments .............................. 47
3.3.1. Permanent Stabilization ....................... 47
3.3.2. Temporary Stabilization ....................... 56
3.4. Conclusion . . . . .............................. 61
References........................................ 63
iv
List of Tables
1 Exchange-Rate-Based Stabilization and Tax Revenue in Central and East-
ernEurope................................... 4
2 ParameterValues ............................... 22
3 Balance Sheet of Government Entities in the High-Inflation Steady State . . 50
4 Balance Sheet of Government Entities Immediately After Start of Stabi-
lizationProgram................................ 51
5 Balance Sheet of Government Entities in the Low-Inflation Steady State . . 52
v
List of Figures
1 Dynamic Paths of the Main Macroeconomic Indicators in the Baseline Case
(inpercent) .................................. 24
2 Selected Macroeconomic Indicators in Exchange-Rate-Based Stabilizations
inCentralandEasternEurope:BulgariaandEstonia ............ 26
3 Selected Macroeconomic Indicators in Exchange-Rate-Based Stabilizations
inCentralandEasternEurope:LatviaandLithuania ............ 27
4 Welfare Gains As a Function of?and? (inpercent) ............ 30
5 Welfare Gains As a Function of? and? (inpercent)............. 33
6 Dynamic Paths of the Main Macroeconomic Indicators in the Sticky-Price-
OnlyCase(inpercent) ............................ 36
7 Welfare Gains as a Function of ? and ? in the Sticky-Price-Only Case (in
percent) .................................... 38
8 PermanentStabilization............................ 53
9 MoneyDynamics............................... 55
10 TemporaryStabilization............................ 59
11 TimePathsofConsumptionandCurrentAccountBalance ......... 60
vi
1. Introduction
The theory and practice of exchange-rate-based stabilization programs has been
the subject of abundant literature explaining the reasons for the success or failure of such
programs by features of their design and implementation.
1
Themaindistilledlessonis
that credibility, generated by a consistent macroeconomic policy mix, is an indispensable
condition for success. As fiscal restraint plays a crucial role in achieving that consistent
policy mix, most authors assume that the government is able to maintain a sustainable fiscal
position after the start of the stabilization program, a necessary condition for permanently
lowering inflation. This assumption is operationalized by endowing the fiscal authority
with either access to lump-sum (i.e., nondistortionary) taxes, or an ability to cut lump-sum
transfers just enough to offset the loss of inflation tax revenue stemming from the lower
inflation without burdening the economy with additional distortions.
Such policies are, however, difficult to implement in the real world. In a high-
inflation economy, a significant fraction of the government?s fiscal revenue comes from the
inflation tax on money holdings. Any credible disinflation program will therefore have to
address the emerging fiscal gap that it has created by lowering inflation tax revenue. This
revenue loss is typically a few percentage points of GDP (see Table 1). In their drive to en-
sure public support for the stabilization program and the overall reform agenda that usually
accompanies it, even rational and nonmyopic governments face considerable constraints in
their ability to achieve spending cuts of that magnitude, and large scale lump-sum taxes are
not widespread. On the other hand, however, a widening fiscal deficit, with the concomitant
rising public debt and (very often) a growing external current account deficit is bound to
erode the credibility of the stabilization program as well. So countries with inflexible fiscal
1
A partial list includes Calvo (1986 and 1987), Drazen and Helpman (1988 and 1990), Kiguel
and Liviatan (1992a and 1992b), Velasco (1993), Calvo and Vegh (1993, 1994, and 1999), Rebelo
and Vegh (1995), Roldos (1993, 1995), Uribe (1995), Agenor and Montiel (1996), Talvi (1996).
1
policy face a dilemma - how to reconcile the loss of inflation tax revenue with the need to
ensure the credibility of their stabilization policies.
This collection of essays explores two ways of addressing this dilemma. Both es-
says assume that fiscal expenditure is untouchable and look for alternative ways to save the
stabilization. In the first essay, the policymaker complements the exchange rate anchor with
a higher distortionary tax to make up for the lost inflation tax revenue in a two-good open
economy with sticky prices and monopolistically competitive producers. In implementing
such a policy mix, the government faces a welfare trade-off: it alleviates the monetary
distortion caused by high inflation, but aggravates the distortion caused by the higher in-
come tax. The combination of lower monetary and higher tax distortion results in lower
consumption (and output) of nontradable goods than in the initial high-inflation equilib-
rium. Moreover, the recession accompanying the transition between the high-inflation and
the low-inflation steady state produces additional welfare losses. Nevertheless, welfare in-
creases on net, as higher money balances and more leisure time outweigh the cost of lower
consumption. The essay also explores the sensitivity of the welfare trade-off to various
structural characteristics of the economy and exogenous factors, such as the interest elas-
ticity of money demand, the wage elasticity of labor supply, the international interest rate,
the size of the government, the speed of disinflation, and the degree of price stickiness.
The second essay assumes that both spending and tax policies are inflexible and
looks instead at the role of monetary policy in closing the emerging fiscal gap. It shows that
in an economy closed to capital flows a monetary expansion can lower the real interest rate.
This benefits the budget in two ways: by generating a consumption and money demand
boom, which expands the base of the inflation tax, and by lowering the budget?s interest
payments. These effects are, however, dependent on the credibility of the stabilization, as
the same-size monetary expansion fails to achieve fiscal sustainability when credibility is
lacking and consumers perceive the stabilization as temporary.
2
2. The Trade-Off Inflation?Taxation in Exchange-Rate-
Based Stabilization Programs
2.1. Introduction
This paper analyzes the consequences of substituting distortionary taxation for in-
flation tax revenue in an exchange-rate-based stabilization program.
2
In a high-inflation
economy, a significant fraction of the government?s fiscal revenue comes from the inflation
tax on money holdings. Any credible disinflation program will therefore have to address
the emerging fiscal gap that it has created by lowering inflation tax revenue. The traditional
stabilization literature assumes that either lump-sum taxes are available, or lump-sum fiscal
transfers are cut just enough to maintain fiscal sustainability.
3
However, in their drive to en-
sure public support for the stabilization program and the overall reform agenda that usually
accompanies it, even rational and nonmyopic governments face considerable constraints
in their ability to cut fiscal transfers, and large scale lump-sum taxes are not widespread.
Therefore, monetary policy is dominated by fiscal policy in its inflation-reducing effort:
given the fiscal stance, the economy needs high inflation to stay in equilibrium. To make
the inflation cut sustainable, the government thus needs to raise conventional distortionary
taxesasneededtooffsetthelostrevenue.
4
For example, Table 1 provides a list of suc-
cessful exchange-rate-based stabilization programs in Central and Eastern Europe, where
thedropininflation to single digits was accompanied by an increase of conventional tax
revenue in terms of GDP, on account of various income and consumption taxes.
2
The term "distortionary tax" applies to any tax that affects economic agents? incentives to
consume, save or produce. Examples are income, consumption, and payroll taxes. For the sake of
concreteness, our model uses an income tax.
3
See, e.g., Calvo and Vegh (1993 and 1994), Roldos (1993 and 1995) and the survey in Rebelo
and Vegh (1995). An exception is Talvi (1996).
4
See Calvo (1987) and Talvi (1996) for the implications of an exchange-rate-based stabilization
without a fiscal adjustment.
3
Table 1: Exchange-Rate-Based Stabilization and Tax Revenue in Central and Eastern
Europe
Start of Year When Drop in Tax
Exchange- Inflation Inflation Tax Revenue
Country Rate-Based Dropped Below Revenue Increase
Stabilization 10 percent (percent of GDP) (percent of GDP)
1/ 2/ 2/
Bulgaria 1997 1998 -5.9 5.3
Croatia 1993 1994 -4.0 7.6
Estonia 1992 1998 -21.7 8.6
Latvia 1994 1997 -2.4 4.7
Lithuania 1994 1997 -3.8 4.6
Average -7.6 6.1
Sources: IMF, International Financial Statistics; and author?s calculations.
1/ Inflation tax is computed as m*inf/(1+inf),wherem is the monetary base as a ratio to GDP
and inf is the annual average inflation.
2/ Differences are between the year when inflation dropped below 10 percent and the year
preceding the start of the stabilization program, except for Estonia and Latvia, for which the
base year is the year of the program launch.
What does a stabilization package combining an exchange rate anchor with higher
taxation imply for the dynamics of the macroeconomy? The recession in production of
nontradables, brought about by their sticky inflation, is exacerbated by the additional dis-
tortion of higher taxation. The low-inflation steady state involves lower consumption (and
production) of nontradables than in the original high-inflation point of departure. Con-
sumers, however, benefit from a lower tax on money and less time at work. The net welfare
result is a gain, as larger money balances and more leisure time outweigh the cost of lower
consumption. The government runs a transitional deficit, which is financed by its initial
stock of net foreign assets.
5
5
For analytical tractability, we abstract from current account effects by exogenizing the supply
of tradables. This way, in a fully credible stabilization, consumption of tradables does not deviate
from its steady state.
4
In implementing such a policy mix, the government faces a welfare trade-off: it
alleviates the monetary distortion caused by high inflation, but aggravates the distortion
caused by the higher income tax, in addition to the cost of the recession during the tran-
sition between the steady states. Thus, there might be inflation/income tax combinations
that would not be welfare improving compared with the original state. The paper investi-
gates the sensitivity of the welfare gain to changes in the economy?s structural parameters,
specifically the interest elasticity of money demand, the wage elasticity of labor supply,
the international interest rate, the size of the government, the speed of disinflation, and the
degree of price stickiness.
The model employed is an extension of Calvo, Celasun, and Kumhof (2003). They
enhance the standard exchange-rate-based stabilization setup by assuming that, in a stag-
gered price setting, firms choose both a price level and a firm-specificinflation rate when
they get their price-updating signal (which gives rise to "sticky inflation" in addition to
sticky prices). This assumption allows them to generate inflation persistence in a forward-
looking model fully derived from microfoundations.
6
Theyshowthat,eveninafullycred-
ible exchange-rate-based stabilization, inflation does not converge immediately to the rate
of change of the nominal anchor, owing mostly to the existing share of predetermined firm-
specificinflation rates. The slow disinflation leads to sizable real exchange rate apprecia-
tion and a temporary recession. Thus, stabilization involves a welfare trade-off between the
gain of permanently lower inflation and the cost of a transitional recession. In the present
paper, this trade-off is exacerbated by the higher tax rate in the low-inflation steady state.
To reveal the contribution of "sticky inflation" to the welfare results, this paper also recasts
the production side of the model in terms of the traditional sticky prices and finds out that
sticky inflation slightly lowers the welfare gain.
6
Generating endogenous inflation persistence and short-run output loss upon disinflation in
forward-looking dynamic general equilibrium models with nominal rigidities has proved tricky.
See the surveys provided by Clarida, Gali, and Gertler (1999), Lane (2001), and Gali (2002).
5
A few recent papers have also considered the implications of distortionary taxation
for monetary policy conduct in the context of sticky prices (Benigno and Woodford, 2003,
Coreia, Nicolini, and Teles, 2002, Schmitt-Grohe and Uribe, 2004; and Siu, 2002). This
study differs from them in three important aspects. First, these papers are concerned with
the conduct of optimal monetary (and fiscal) policy in the presence of sticky prices, dis-
tortionary taxation, and a flexible exchange rate; in our paper, we analyze the combination
of sticky prices/inflation and distortionary taxation in an exchange-rate-based stabilization
program with an exogenously chosen exchange rate depreciation target, a feature consis-
tently observed in reality. Second, this paper employs the assumption of Calvo, Celasun,
and Kumhof (2003) that, in the context of sticky prices ? la Calvo (1983), firms choose
both a price level and a firm-specificinflation rate when they get the price-updating signal.
This assumption is less restrictive and more intuitively and empirically plausible than the
traditional sticky price approach, employed in the four papers listed above.
7
Third, we
develop a two-goods model, which allows the dynamics of the real exchange rate to be
endogenized.
The paper is organized as follows. Section 2 introduces the basic model (the con-
sumer and producer problems, and government policies and constraints), defines equilib-
rium and specifies the dynamic system that describes the economy?s behavior. Section 3
calibrates and solves numerically the basic model, while Section 4 presents welfare analy-
sis, including welfare sensitivity to parameter configuration, pricing, and policy assump-
tions. Section 5 rewrites the model in terms of the traditional sticky prices, in order to
analyze the contribution of the assumption of a firm-specificinflation rate to the welfare
results. Section 6 concludes.
7
The firms choose only their price and update it thereafter at the steady state inflation rate. See
Calvo (1983) and Yun (1996).
6
2.2. The Model
A small open economy consists of a representative consumer, a continuum, indexed
by j ? 0,1, of monopolistically competitive producers of nontradable goods, and a gov-
ernment. Both the consumer and the producers make their decisions in an infinite horizon,
discounting the future with their respective discount factors. Prices of the tradable goods
obey the purchasing power parity and normalizing the foreign price level to one makes the
price index of tradables equal to the nominal exchange rate, E
t
. The aggregate price level
of nontradable goods is denoted by P
t
, and the associated inflation rate by?
t
=
?
P
t
/P
t
.The
relative price of tradables in terms of nontradables (the real exchange rate) is e
t
= E
t
/P
t
.
Free capital mobility ensures that the uncovered interest parity holds:
i
t
= r +?
t
, (1)
where i
t
is the nominal interest rate on domestic-currency-denominated assets, r is the
exogenous, constant, and positive real international interest rate, and?
t
=
?
E
t
/E
t
is the rate
of exchange rate depreciation, assumed greater than (?r) at all times, so that the nominal
interest rate is always positive.
2.2.1. Consumers
The representative consumer maximizes lifetime utility by choosing her level of
consumption of homogenous tradable goods, c
?
t
, heterogeneous nontradable goods, c
t
(j),
j ? 0,1, nominal money balances, M
t
and labor supply to producers, L
t
. Conventionally,
the rate at which consumers discount the future is assumed equal to the real return, r,on
international bonds, b
t
, measured in units of tradable goods. Consumption of nontradables
is defined as a Dixit-Stiglitz aggregate over the continuum of differentiated goods j:
7
c
t
=
nullnull
1
0
c
t
(j)
??1
?
dj
null
?
??1
, (2)
with elasticity of substitution ?>1. Let P
t
(j) be the price of the individual good c
t
(j).
Then it can be shown through cost minimization of aggregate consumption spending that
c
t
(j)= c
t
null
P
t
(j)
P
t
null
??
, (3)
where the aggregate price index of nontradables P
t
is
P
t
=
nullnull
1
0
P
t
(j)
1??
dj
null
1
1??
. (4)
The representative consumer?s objective function is
Max
null
?
0
?
?
? ln(c
?
t
)+(1 ??)ln(c
t
)+?
m
1?
1
?
t
1 ?
1
?
??
L
1+
1
?
t
1 +
1
?
?
?
e
?rt
dt, (5)
where m
t
= M
t
/E
t
are real money balances. The presence of money in the utility function
is justified by the empirically observable sensitivity of money to the interest rate, which
cannot be obtained under, for example, a cash-in-advance constraint. The separability of
money from the other arguments of utility provides for analytical tractability and does not
materially influence the results. The supply of tradable goods, y
?
, is assumed constant and
exogenous. The consumer also receives lump-sum transfers, g
t
,intermsoftradablesfrom
the government and nominal wages, W
t
L
t
(taxable at a proportional rate ?
t
), as well as
nominal lump-sum profit distributions,
null
1
0
null
t
(j)dj, from the producers. Her flow budget
constraint is thus
8
?
b
t
= rb
t
??m
t
??
t
m
t
+y
?
?c
?
t
+g
t
+
(1 ??
t
)W
t
L
t
E
t
+
null
1
0
null
t
(j)dj
E
t
?
null
1
0
P
t
(j)c
t
(j)dj
E
t
. (6)
After imposing the standard transversality condition, lim
t??
(b
t
+ m
t
)e
?rt
? 0,
we can convert (6) into a lifetime budget constraint:
b
0
+ m
0
+
null
?
0
null
y
?
+ g
t
+
(1 ??
t
)W
t
L
t
E
t
+
null
1
0
null
t
(j)dj
E
t
null
e
?rt
dt (7)
?
null
?
0
null
c
?
t
+
null
1
0
P
t
(j)c
t
(j)dj
E
t
+ i
t
m
t
null
e
?rt
dt .
The consumer maximizes (5) subject to (7). The first-order conditions are (7) hold-
ing with equality, (3), and
?
c
?
t
= ?, (8)
c
t
c
?
t
= e
t
1 ??
?
, (9)
m
t
=
null
?i
t
?c
?
t
null
??
,and (10)
w
t
?
W
t
P
t
=
?c
t
L
1
?
t
(1 ??)(1 ??
t
)
. (11)
These equations are straightforward. According to equation (8), the marginal utility
of consumption of tradables is equal to the marginal utility of wealth (the constant multi-
plier, ?, of the lifetime budget constraint (7)). Equation (9) equates the marginal rate of
substitution between tradables and nontradables to their relative price, the real exchange
rate. Equation (10) is a standard money demand function. Equation (11) provides the la-
bor supply function, expressed as an equation for the real wage demanded by the consumer,
9
which is equal to the marginal rate of substitution between consumption and labor, adjusted
for the distortion coming from the labor income tax.
2.2.2. Producers
Producers in the nontradables sector use only labor as an input and, for simplicity,
have linear production functions:
y
t
(j)= Bl
t
(j), j ? 0,1 , (12)
where B is a constant technology factor. They take the nominal wage as given in the labor
market, but are monopolistically competitive in the goods market and distribute all nominal
profits,null
t
(j), to the consumer in a lump-sum fashion:
null
t
(j)= P
t
(j)y
t
(j)? W
t
l
t
(j), j ? 0,1 . (13)
As in Calvo (1983), producers get only random and exogenous opportunities to
change their prices, which opportunities are drawn from an exponential distribution with
probability density ?e
??t
. The realizations of these opportunities are independent of their
previous occurrences, and across firms. Income uncertainty for the representative consumer
is thus eliminated by the law of large numbers, despite firm-specific revenue uncertainty. At
any given moment, a fraction? of producers update their prices, while the average duration
of a price contract is
1
?
.
Producers maximize the present discounted value of the stream of real future profits
each time they get the price change signal. Their discount rate is the interest rate in terms of
nontradables, r +?
t
??
t
; in addition, they weigh future profits by the probability e
??(s?t)
that today?s price will still be in force at time s. Producers? real marginal cost equals the
10
real wage in terms of nontradables, w
t
= W
t
/P
t
, as determined by equation (11). They
also receive a proportional output subsidy, sub =
1
??1
, from the government.
8
As in Calvo,
Celasun and Kumhof (2001 and 2003), whenever firms receive a price change signal at time
t, they choose both their current price, V
j
t
, and a firm-specificinflation rate, v
j
t
,atwhich
their price will be updated in every future period until the next opportunity to maximize
profits. We therefore have
P
s
(j)= V
j
t
e
v
j
t
(s?t)
(14)
for every product j and all s > t until the next price update.
Specifically, producers maximize
Max
V
j
t
,v
j
t
null
?
t
e
?
null
s
t
(?+r+?
r
??
r
)dr
null
V
j
t
e
v
j
t
(s?t)
P
s
y
s
(j)(1 + sub)?w
s
l
s
(j)
null
ds , (15)
subject to the production function (12) and goods demand (3), which can, using (14), be
expressed as
y
s
(j)= c
s
null
V
j
t
e
v
j
t
(s?t)
P
s
null
??
(16)
and substituted in (15). As the maximization problem is identical for all firms that receive
a price-changing opportunity, the firm index, j, can be dropped. The first-order condition
for V
t
is
null
?
t
e
?
null
s
t
(?+r+?
r
??
r
)dr
c
s
null
V
t
e
v
t
(s?t)
P
s
null
??
null
V
t
e
v
t
(s?t)
P
s
?
w
s
B
null
ds = 0 .
Let p
t
? V
t
/P
t
be the initial relative price of new price setters. Then, using the fact
that, for s > t, P
s
= P
t
e
null
s
t
?
r
dr
,we can rewrite the last condition as
8
This offsets the steady state price distortion that arises under monopolistic competition (see
Woodford (2002)).
11
null
?
t
e
?
null
s
t
(?+r+?
r
??
r
)dr
c
s
null
p
t
e
?
null
s
t
(?
r
?v
t
)dr
null
??
null
p
t
e
?
null
s
t
(?
r
?v
t
)dr
?
w
s
B
null
ds = 0 . (17)
In the steady state, to which the economy finally converges, we must have ?? =
?v = ?
l
and ?p = 1.
9
From (17), the steady state real wage is thus ?w = B.Thefirst-order
condition forv
t
is
null
?
t
e
?
null
s
t
(?+r+?
r
??
r
)dr
c
s
null
p
t
e
?
null
s
t
(?
r
?v
t
)dr
null
??
(s ? t)
null
p
t
e
?
null
s
t
(?
r
?v
t
)dr
?
w
s
B
null
ds = 0 .
(18)
Our strategy for deriving a dynamic system describing the behavior of the non-
tradable sector of this economy is as follows. The evolution of all other variables in our
economy can be expressed through four endogenous variables: the firm-specificinflation
rate, v
t
, the nontradables inflation rate, ?
t
, the weighted average of historic firm-specific
inflation rates (call it ?
t
), and the producers? marginal cost, the wage rate w
t
. Therefore,
the dynamic behavior of the economy will be fully specified by a system describing the
joint evolution of these four variables. To derive such a system, we use the definitions of
the respective price indices and the producer and consumer first-order (optimal behavior)
conditions, linearized around a stationary steady state.
First, we linearize (17) and (18) around the steady state and obtain the following
expressions:
10
p
t
+
v
t
?+ r
= (?+ r)
null
?
t
e
?(?+r)(s?t)
null
w
s
B
+
null
s
t
?
r
dr
null
ds,and
p
t
?+ r
+
2v
t
(?+ r)
2
= (?+ r)
null
?
t
e
?(?+r)(s?t)
(s ? t)
null
w
s
B
+
null
s
t
?
r
dr
null
ds = 0 .(19)
9
A bar above the respective variable denotes its steady state value.
10
We use the following properties of the exponential distribution: ?
null
?
t
(s ? t)e
??(s?t)
ds =
1
?
,
?
null
?
t
(s ? t)
2
e
??(s?t)
ds =
2
?
2
.
12
Their derivatives with respect to time are
?p
t
+
?v
t
?+ r
= (?+ r)(p
t
?
w
t
B
)+v
t
??
t
,and (20)
?p
t
+
2?v
t
?+ r
= v
t
??
t
. (21)
Combining (20) and (21) yields the following differential equation for the firm-
specificinflation rate,v
t
:
?v
t
=?(?+ r)
2
null
p
t
?
w
t
B
null
. (22)
This is our first dynamic equation. Note thatv
t
is a jump variable, as upon receiving
a price-changing signal it will be optimal for producers to allow discrete changes in both
their current price and their firm-specificinflation rate.
Next we turn to the dynamics of the aggregate price index (4), which can be rewrit-
ten as
P
t
=
null
?
null
t
??
e
??(t?s)
(V
s
e
v
s
(t?s)
)
1??
ds
null
1
1??
, (23)
where ?e
??(t?s)
is the weight of the price V
s
and the firm-specificinflation ratev
s
.Taking
the derivative of (23) with respect to time, we obtain
?
t
=
?
1 ??
(p
1??
t
? 1)+?
null
t
??
e
??(t?s)
null
p
s
e
?
null
t
s
(?
r
?v
s
)dr
null
1??
v
s
ds . (24)
Linearizing this expression around the steady state yields
(?
t
???)=?(p
t
?1)+?
null
t
??
e
??(t?s)
null
(v
s
???)+??(1 ??)(p
s
? 1)?
null
t
s
(?
r
?v
s
)dr
null
ds.
(25)
This expression can be simplified by linearizing the price index (23) around the steady
state:
13
?
null
t
??
e
??(t?s)
(1 ??)
null
(p
s
? 1)?
null
t
s
(?
r
?v
s
)dr
null
ds = 0, (26)
with the last equality following from the linearization of the first-order condition (17)
around the steady state. Substituting (26) into (25), we obtain
(?
t
???)=?(p
t
? 1)+?
null
t
??
e
??(t?s)
(v
s
???)ds . (27)
The weighted average of firm-specificinflation rates currently in force, ?
t
,isde-
fined as
?
t
=?
null
t
??
e
??(t?s)
v
s
ds . (28)
Its time derivative is
?
?
t
=?(v
t
???)??(?
t
???). (29)
Using (28), we can rewrite the expression for aggregate inflation (27) as
(?
t
???)=(?
t
???)+?(p
t
? 1). (30)
The firsttermreflects inertia in the aggregate inflation rate through the historic pric-
ing policies of firms that have not yet received a price-changing opportunity. The second
term, the initial relative price of new price setters, p
t
,isfreetojumpatthestartofthesta-
bilization program (t=0). Therefore, despite the presence of a predetermined component,
aggregate inflation is a "jump" variable. Using (21), (22), (29), and (30), its derivative with
respect to time equals
??
t
=?(3?+2r)(?
t
???)+2?(v
t
???)+(?+2r)(?
t
???)?
2?(?+ r)
B
(w
t
? B).(31)
14
Expression (30) can also be used to rewrite the differential equation for firm-specific
inflation (22) as
?v
t
=
(?+ r)
2
?
(?
t
???)?
(?+ r)
2
?
(?
t
???)+
(?+ r)
2
B
(w
t
? B) . (32)
In order to link the dynamics of the consumer and producer part of this economy,
the system of differential equations (29), (31), and (32) must be completed with an equation
for the evolution of real marginal cost,w
t
, derived from (11). As we will use relations that
hold in equilibrium, we must first describe government policies and define equilibrium.
2.2.3. Government Policies and Constraints
The government owns a stock of net foreign assets, h
t
, issues money, M
t
, collects
labor income tax,?
t
W
t
L
t
, and makes lump-sum transfers, g
t
, as well as subsidy payments,
1
??1
, per unit of output of nontradable goods. Its flow budget constraint in terms of tradables
is
?
h
t
= rh
t
+?m
t
+?
t
m
t
+?
t
W
t
L
t
E
t
? g
t
?
1
? ? 1
c
t
e
t
, (33)
wherewehaveusedtheidentity
null
1
0
null
P
t
(j)y
t
(j)
E
t
null
dj =
c
t
e
t
. By imposing the transversality
condition, lim
t??
(h
t
?m
t
)e
?rt
= 0, we can transform (33) into the government?s lifetime
budget constraint
h
0
? m
0
+
null
?
0
null
i
t
m
t
+?
t
W
t
L
t
E
t
? g
t
?
1
? ? 1
c
t
e
t
null
e
?rt
dt = 0 . (34)
Government policies {?
t
,?
t
,g
t
}
?
t=0
must be such that, given the time paths
{m
t
,c
t
,P
t
,W
t
}
?
t=0
, the government budget constraint (34) holds. As discussed, fiscal ex-
penditure is assumed to be inflexible, so real transfers, {g
t
}
?
t=0
, are constant over time.
Exchange rate policy, {?
t
}
?
t=0
, is the principal disinflation instrument, as the government
15
makes an unexpected announcement at time 0 of a lower rate of exchange rate deprecia-
tion:
?
t
= ?
h
, t ?(??,0), (35)
?
t
= ?
l
, t ? 0,?).
At the same time, the tax rate,?
t
,israisedfromtheexistingrate?
l
to a new constant
rate ?
h
such that in the new steady state the higher income tax revenue offsets the lower
inflation tax revenue in such a way that government net assets, h
t
, are not explosive.
11
In other words, the government flow budget constraint,
?
h = 0, holds at the low-inflation
steady state and thereafter. As the government faces no liquidity constraints, the steady
state level of its reserves,
?
h, is simply determined by the transitional dynamics of (33),
given h
0
.
2.2.4. Equilibrium
Let f
t
= b
t
+ h
t
be the economy?s overall level of net foreign assets. A perfect
foresight equilibrium, given f
0
, the technology factor B, and an endowment of tradables,
y
?
, is a set of time paths
?
?
?
?
?
b
t
,h
t
,m
t
,c
?
t
,L
t
,c
t
,y
t
,l
t
(j),c
t
(j),y
t
(j),P
t
,
W
t
,P
t
(j),V
j
t
,v
j
t
,E
t
,?
t
,g
t
, j ? [0,1]
?
?
?
?
?
?
t=0
such that:
(a) given f
0
,B,y
?
, government policies {?
t
,?
t
,g
t
}
?
t=0
,and the price system
null
P
t
,W
t
,P
t
(j),V
j
t
,v
j
t
null
?
t=0
, the time paths
null
b
t
,m
t
,c
?
t
,y
t
,L
t
,c
t
,c
t
(j)
null
?
t=0
solve the con-
sumer?s problem of maximizing(5) subject to (7);
(b) given f
0
, B, y
?
, government policies {?
t
,?
t
,g
t
}
?
t=0
, and the time paths
{P
t
,W
t
,c
t
}
?
t=0
, the time sequences
null
V
j
t
,v
j
t
,y
t
(j),l
t
(j)
null
?
t=0
solve the producers? problem
of maximizing (15) subject to (12) and (16);
11
We assume that both ?
l
and ?
h
are below the revenue-maximizing tax rate so that revenue
increases when the tax rate is raised.
16
(c) the nontradable goods market clears for all goods and at all times,
y
t
(j)= c
t
(j) ?t,?j ? [0,1]; and (36)
(d) the labor market clears at all times,
L
t
=
null
1
0
l
t
(j)dj ?t . (37)
Combining equations (34) and (7) holding with equality, and using the properties
of equilibrium, we derive the following aggregate budget constraint:
f
0
+
y
?
r
=
null
?
0
c
?
t
e
?rt
dt . (38)
From (8), consumption of tradables is always constant. We therefore have
c
?
t
= y
?
+ rf
0
?t . (39)
From (9), one can see that
c
t
e
t
should also be constant throughout:
c
t
e
t
=(y
?
+ rf
0
)
1 ??
?
?t . (40)
Applying the condition
?
h = 0 to the government budget constraint (33), and using
(9) and the equilibrium condition ?w= B, one can express?
h
as
?
h
=
?
1 ??
(g ? r
?
h
l
)
(y
?
+ rf
0
)
+
1
? ? 1
?
?
?
1 ??
null
?
?y
?
null
1??
?
l
(r +?
l
)
?
, (41)
where
?
h
l
is the amount of government assets in the low-inflation steady state.
12
This ex-
12
This derivation also uses the relation
?
L =
?c
B
.See the next section.
17
pression can be simplified further by assuming, without loss of generality, that the initial
level of the economy?s net foreign assets is f
0
= 0 and also noting that g is implied from
the initial high-inflation equilibrium as
g = rh
0
+
null
?
l
?
1
? ? 1
null
1 ??
?
y
?
+?
h
null
?(r +?
h
)
?y
?
null
??
, (42)
and therefore
?
h
=?
l
+
?
1 ??
r(h
0
?
?
h)
y
?
+
?
?
1 ??
null
?
?y
?
null
1??
null
?
h
(r +?
h
)
?
?
?
l
(r +?
l
)
?
null
. (43)
The tax rate necessary to maintain fiscal sustainability is increasing in the initial
size of the government, ?
l
, in the loss of interest income during the transition between the
steady states, and in the targeted cut in inflation (in a nonlinear way). It is decreasing in the
elasticity of money demand.
13
This equation demonstrates the trade-off the policymaker is
facing: a more ambitious inflation target leads, ceteris paribus, to a larger tax distortion for
a given level of revenue.
As noted in the analysis of the producers? behavior above, ?? =?v = ?
l
, ?p = 1,
and ?w = B. Using the latter in the consumer first-order condition (11), plus the relation
?
L =
?c
B
,one arrives at
?c
h
= B
null
(1 ??)(1 ??
l
)
?
null
?
1+?
;?c
l
= B
null
(1 ??)(1 ??
h
)
?
null
?
1+?
, (44)
where ?c
h
and ?c
l
are the steady state levels of consumption of nontradables in the high- and
13
For inelastic money demand, (?<1), inflation tax revenue declines with inflation and the
last term in (43) is positive. For a sufficiently large ?, however, money demand grows more than
proportionately with the cut in inflation, so that inflation tax revenue in fact increases. As this case
involves no trade-off ? the government can cut both inflation and taxes ? we have ruled it out.
18
low-inflation states, respectively. It follows that
?c
l
?c
h
=
null
1 ??
h
1 ??
l
null
?
1+?
< 1 , (45)
the steady state consumption of nontradables ?c is unambiguously lower in the low-inflation
steady state. The impact on consumer?s welfare is, however, ambiguous in principle, as
lower consumption goes hand in hand with less labor effort. We will come back to this
issue in Section 4.
2.2.5. Dynamic System
To derive a differential equation for real marginal cost, w, we linearize equation
(11) around the steady state, obtaining
14
(w
t
? B)=(ln c
t
? ln ?c)+
1
?
(ln L
t
? ln
?
L)+
1
1 ???
(?
t
???). (46)
Following the steps in Appendix A in Calvo, Celasun, and Kumhof (2003), one can
show that
?
L =
?c
B
and that, around the steady state,
ln L
t
? ln
?
L = ln c
t
? ln ?c . (47)
Therefore (46) becomes
(w
t
? B)=(1 +
1
?
)(ln c
t
? ln ?c)+
1
1 ???
(?
t
???). (48)
From the linearization of equation (9), the first term of equation (48) is
14
It is more convenient to log linearize the right-hand side with respect to c
t
and L
t
.
19
(ln(c
t
)? ln(?c))=(ln(c
?
t
)? ln(?c
?
))+(ln(e
t
)? ln(?e)). (49)
Substituting (49) in (48) and differentiating the result over time while using the fact
that ?c
?
t
=??
t
=??
t
= 0 (at points where they do not jump), as well as
?
(ln e
t
)=?
t
??
t
, (50)
we finally obtain
?w
t
=?B(1 +
1
?
)(?
t
???)+ B(1 +
1
?
)(?
t
???). (51)
This equation says that a real appreciation is associated with a fall in real wages in
the nontradables sector. The reason is that the higher relative price of nontradables lowers
the demand for these goods and, therefore, for labor, depressing the real wage.
We now show that, while w
t
can jump, it is not a free-jumping variable and can
in this sense be considered predetermined. Consider equation (48), with (49) substituted
in and the possibility of jumps at time 0. The real exchange rate is predetermined under a
predetermined nominal exchange rate and sticky prices, while the tradables consumption
path is a function only of the exogenous endowment, y
?
.Jumpsin?
t
and?
t
are also exoge-
nous. Therefore w
t
is a predetermined variable, in the sense that in the four-dimensional
space definedbythevariables?,v,?,and w,it can only jump to specific points exoge-
nously determined by government policies and exogenous variables. The same goes for the
weighted average of existing firm-specificinflation rates, ?
t
. The variables v
t
and ?
t
are
free to jump at time 0 to any point in the four-dimensional space of the system. The full
dynamic system for this economy is represented by equations (29), (31), (32), and (51). In
matrix form it looks as follows:
20
?
?
?
?
?
?
?
?
?
?
?
t
??
t
??
t
?w
t
?
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
?
???00
(?+r)
2
?
0 ?
(?+r)
2
?
(?+r)
2
B
?(3?+ 2r) 2?(?+ 2r)
?2?(?+r)
B
00?Q 0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
(?
t
???)
(v
t
???)
(?
t
???)
(w
t
? B)
?
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
?
0
0
0
Q
?
?
?
?
?
?
?
?
?
(?
t
???).
(52)
where Q = B(1 +
1
?
).
This system has two eigenvalues with positive real parts and two with negative
real parts.
15
Given the number of predetermined variables, this proves that the system
is saddle-path stable. For a broad range of relevant parameter values, all roots are real
and associated with linearly independent eigenvectors, a sufficient condition for a unique
saddle-path solution.
16
The path of the government?s net foreign assets on the economy?s way to the new
steady state is given by (33). Our government can borrow freely at the constant international
interest rate, r, so there is no terminal condition for the steady state value of government
assets
?
h. Given the initial value h
0
(equal to the high-inflation steady state value of h)and
(33),
?
h is completely determined.
2.3. Model Solution
2.3.1. Calibration
The model can only be solved numerically. The chosen parameter values are shown
in Table 2. The time unit is one quarter.
15
The determinant and the trace of the coefficient matrix are positive, establishing that there are
either zero or two eigenvalues with negative real parts. On the other hand, the sum of the four 3x3
principal minors is negative, which implies that exactly two roots have negative real parts.
16
We searched over the range?? 0.05, 1, corresponding to a price contract length between 1 and
20 quarters, and a real interest rate r between 4 percent and 16 percent per annum.
21
Table 2: Parameter Values
Name Value Description
? 13/3 Intratemporal elasticity of substitution
between nontradable goods
?
h
0.20 Initial exchange rate depreciation (per annum)
?
l
0.10 Final exchange rate depreciation (per annum)
?
l
0.246 Tax rate in the high-inflation steady state (per annum)
r 0.05 Real interest rate in terms of tradables (per annum)
? 0.5 Share of tradables in consumption
? 0.7 Interest elasticity of money demand
? 0.013 Weight of money in the utility function
? 5.558 Weight of labor in the utility function
? 0.8 Wage elasticity of labor supply
L 1/3 Proportion of time spent working
in the high-inflation steady state
?y
?
1/3 Output of tradables
? 1/4 Inverse of average contract length in quarters (four)
f
0
0 Initial value of the economy?s net foreign assets
B 1 Technology parameter in the production function
We calibrate?,the weight of money in the utility function, so that money balances
in the high-inflation steady state equal 0.25, the average ratio of cash in circulation to
quarterly GDP in the five emerging markets in Central and Eastern Europe listed in Table 1.
Similarly,?,the weight of labor in the utility function, is calibrated from the high-inflation
steady state. An interest rate elasticity of money demand of 0.7 allows for real money
balances to expand by about 10 percent of GDP in the low-inflation steady state relative
to the high-inflation one, which is again within the range observed in Central and Eastern
Europe. We chose 0.8 for the labor supply elasticity,?,balancing the need to maintain the
empirically observed less-than-unitary elasticity in emerging markets, on the one hand, and,
as low?makes the transitional recession shallow and disinflation less costly, the desire not
to bias the results in favor of disinflation, on the other. The currently low global interest
rates motivate us to set the real interest rate in terms of tradables to 5 percent. Finally,
wesetthetaxrateinthelow-inflation steady state (?
l
) to 0.246, which is the average
22
prestabilization ratio of tax revenue to GDP in the countries in Table 1. For comparability
of results, we take the rest of the parameters from Calvo, Celasun, and Kumhof (2003), and
set the technology factor B to 1.
The numerical procedure of determining ?
h
deserves some elaboration. First, we
solve the government?s flow budget constraint (33) for h
t
as a function of the model?s ex-
ogenous and endogenous variables. Then?
h
is set such that that the amount of government
assets, h
t
in the very long run (1,000 periods after the start of the stabilization program)
is the same as at 900 periods after the start (within a tolerance of 10
?2
). This value of ?
h
satisfies the condition
?
h = 0 in the presumed steady state (50 periods after the start) within
a tolerance of at least 10
?6
.
2.3.2. Dynamic Response of the Economy to Stabilization Policies
The dynamic transition paths of the main variables between the high- and low-
inflation steady states are shown in Figure 1.
17
Inflation of nontradables responds slowly
to the permanently lower depreciation rate for two reasons (see equation (30)). First, the
weighted average of firm-specificinflation rates,?,can only decline only because no more
than a fraction ? of producers can update their pricing policies at any point in time. Sec-
ond, given the undisputed permanency of disinflation, producers choose to put most of the
weight of the price-updating response on the firm-specificinflation rate,v
t
, rather than on
the level of firm prices, p
t
; consequently, p
t
is sluggish as well.
The slow response of nontradables inflation, combined with the immediately lower
exchange rate depreciation, implies that the real exchange rate appreciates sharply, that
is, nontradables become more expensive relative to tradables. This leads to a sharp but
relatively short-lived recession, with a trough of about 3 percent and a duration of three-four
17
Consumption/output series of tradables and nontradables are normalized to one for better visu-
alization of their percentage changes.
23
Figure 1: Dynamic Paths of the Main Macroeconomic Indicators in the Baseline Case (in
percent)
10
20
pi ? Nontradables Inflation Rate
0.96
0.98
1
1.02
Nontradables Output
10
20
v ? Firm?Specific Inflation Rate
0.96
0.98
1
1.02
Real Exchange Rate
10
20
psi ? Lagged Firm Inflation Rate
0.95
1
w ? Real Marginal Cost
0 10 20 30 40 50
10
20
Exchange Rate Depreciation
0 10 20 30 40 50
0.99
1
1.01
Tradables Consumption
quarters. At the nadir, nontradables inflation starts undershooting the speed of exchange
rate depreciation, and the real exchange rate starts depreciating toward its new steady state
level, thereby ending the recession. Still, output rises very gradually and it takes over four
years before the new steady state is reached (which is about 0.5 percent lower than the initial
one under this parameter configuration). The presence of the higher tax rate (which settles
at 29.04 percent) exacerbates and prolongs the recession and dampens the low-inflation
steady state output of nontradables, compared to Calvo, Celasun, and Kumhof (2003). In
24
that paper, the trough in output loss is less than 2 percent below the high-inflation steady
state; the recession has about the same duration, but the recovery is more vigorous, and
the output of nontradables reaches its previous steady state level after five-six quarters and
exceeds it by 1.7 percent in the new steady state. The loss of government assets in our
model during the transition to the new steady state is about 1.7 percent of GDP.
How can we reconcile the model?s predictions with the output booms usually as-
sociated with exchange-rate-based stabilization programs (as documented in, e.g., Kiguel
and Liviatan, 1992a and 1992b, and Calvo and Vegh, 1999)? First, these output booms
are predominantly in the tradables sector; output of nontradables often fell relative to trad-
ables, which is consistent with our model. We chose to model explicitly the production
of nontradables because these goods are subject to the distortion of sticky prices. Prices
of tradables in a small open economy with an exchange rate anchor simply follow inter-
national prices and the exchange rate and are thus determined by exogenous and policy
developments. Second, while we draw our illustration from emerging markets, we have
outlined a general disinflation model, applicable to mature markets as well. In developed
countries, disinflation has been more often associated with recessions than with booms
(see, e.g., Christiano, Eichenbaum and Evans (1996 and 1998)).
Figures 2 and 3 show the evolution of selected macroeconomic indicators, corre-
sponding to the main variables of our model, in four successful exchange-rate-based stabi-
lization programs in Central and Eastern Europe. While these programs accompanied deep
structural transformations in these economies during their transition from central planning
to market ? transformations that may have introduced additional (and different) macro-
economic dynamics ? the main indicators do exhibit many of the features predicted by
our model. The relatively slow disinflation gave rise to appreciating real exchange rates,
the output of nontradables followed a V-shape or an U-shape relative to that of tradables,
and in two of the cases the real wage dropped on impact before recovering later.
25
Figure 2: Selected Macroeconomic Indicators in Exchange-Rate-Based Stabilizations in
Central and Eastern Europe: Bulgaria and Estonia
Bulgaria: Inflation
1
10
100
1000
t-1 t t+1 t+2 t+3 t+4
Estonia: Inflation
1
10
100
1000
t-1 t t+1 t+2 t+3 t+4
Bulgaria: Real Wage
60
80
100
t-1 t t+1 t+2 t+3 t+4
Estonia: Real Wage
60
80
100
t-1 t t+1 t+2 t+3 t+4
Bulgaria: Real Exchange Rate
50
70
90
110
t-1 t t+1 t+2 t+3 t+4
Estonia: Real Exchange Rate
50
70
90
110
t-1 t t+1 t+2 t+3 t+4
Bulgaria: Nontradables Output 
70
85
100
115
t-1 t t+1 t+2 t+3 t+4
Estonia: Nontradables Output 
70
85
100
115
t-1 t t+1 t+2 t+3 t+4
Sources: IMF, International Financial Statistics (IFS) ; and published IMF country reports.
Notes: Inflation is in percentage points on a logarithmic scale. The rest of the indicators are 
indices based on year t-1  or  t , depending on data availability. Real wage is the private sector 
wage for Bulgaria, and the economywide wage for Estonia. The exchange rate is the real effective 
exchange rate from IFS  . Nontradables output is the ratio of gross value added in construction 
and nongovernment services to the rest of the economy.
26
Figure 3: Selected Macroeconomic Indicators in Exchange-Rate-Based Stabilizations in
Central and Eastern Europe: Latvia and Lithuania
Sources: IMF, International Financial Statistics (IFS) ; and published IMF country reports.
Notes: Inflation is in percentage points on a logarithmic scale. The rest of the indicators are indices 
based on year t-1  or  t , depending on data availability. Real wage is the economywide wage for 
Latvia, and the private sector wage for Lithuania. The exchange rate is the real effective exchange 
rate from IFS . Nontradables output is the ratio of gross value added in construction and 
nongovernment services to the rest of the economy.
Latvia: Inflation
1
10
100
1000
t-1 t t+1 t+2 t+3 t+4
Lithuania: Inflation
1
10
100
1000
t-1 t t+1 t+2 t+3 t+4
Latvia: Real Wage
90
110
130
150
170
t-1 t t+1 t+2 t+3 t+4
Lithuania: Real Wage
90
110
130
150
170
t-1 t t+1 t+2 t+3 t+4
Latvia: Real Exchange Rate
70
80
90
100
110
t-1 t t+1 t+2 t+3 t+4
Lithuania: Real Exchange Rate
70
80
90
100
110
t-1 t t+1 t+2 t+3 t+4
Latvia: Nontradables Output
80
90
100
110
t-1 t t+1 t+2 t+3 t+4
Lithuania: Nontradables Output
80
90
100
110
t-1 t t+1 t+2 t+3 t+4
27
2.4. Welfare Analysis
The combination of lower inflation and higher conventional taxation produces cer-
tain welfare trade-offs. In the low-inflation steady state, the gain from the lower tax on
money has to be evaluated against the cost of the larger income tax distortion. In ad-
dition, the stabilization-induced transitional recession imposes additional welfare losses.
The metric of compensating variation introduced by Lucas (1987) can be used to evaluate
this trade-off. The net welfare gain resulting from the set of stabilization policies {?
l
,?
h
}
compared with the original policy set {?
h
,?
l
} is computed as the fraction by which con-
sumers? original steady state consumption basket would have to be increased to make them
indifferent between their lifetime utility in the high-inflation steady state and the lifetime
utility achieved along the equilibrium path to the new, low-inflationsteadystate.Thus,the
welfare gain,?,is determined from
null
?
0
null
? ln(?c
?
)+(1 ??)ln(?c
h
)+?
(?m
h
)
1?
1
?
1 ?
1
?
??
(
?
L
h
)
1+
1
?
1 +
1
?
+ ln(1 +
?
100
)
null
e
?rt
dt
=
null
?
0
null
? ln(c
?
t
)+(1 ??)ln(c
t
)+?
m
t
1?
1
?
1 ?
1
?
??
L
t
1+
1
?
1 +
1
?
null
e
?rt
dt . (53)
Needless to say, a positive number means that the new set of policies is preferable
to the previous one. For the one-shot permanent disinflation described in the previous
section, this measure produces a welfare gain of 0.751 percent. The benefits of the lower
tax on money and less labor outweigh the loss of consumption resulting from the tax hike
of roughly four percentage points. The difference in one-period utility between the new
andtheoldsteadystateis
28
U
l
? U
h
=(1 ??)ln
?c
l
?c
h
+
?
null
(?m
l
)
1?
1
?
?(?m
h
)
1?
1
?
null
1 ?
1
?
?
?
?
1 +
1
?
?
?
null
?c
l
B
null
1+
1
?
?
null
?c
h
B
null
1+
1
?
?
?
= 0.0076 , (54)
where the superscripts l and h denote the low-inflation and the high-inflation steady states,
respectively. So the steady state welfare gain more than covers the cost of the transitional
recession. We will revisit this issue in Section 5.
2.4.1. Sensitivity of Welfare to Parameter Specification
It is interesting to analyze the welfare response to a varying interest elasticity of
money demand,?,and wage elasticity of labor supply,?. These parameters are important
parts of the tax elasticities of money and labor, respectively. A well-established public
finance result holds that it is optimal to tax more heavily the good with a lower tax elasticity.
A sensitivity analysis with respect to ? and ? will thus reveal to what extent the welfare
gain resulting from the shift in taxation from money to income depends on the chosen
parameter configuration. From (1) and (10), the tax (inflation) elasticity of money is
?ln m
t
?ln?
t
=?
??
t
r +?
t
, (55)
whichisincreasingin? in absolute value. From (11), (12), (36), (37), and the steady state
condition that the wage is equal to the marginal product of labor ( ?w= B), labor supply can
beexpressedinthesteadystateas
?
L =
null
(1 ??)(1 ???)
?
null
?
1+?
, (56)
29
and its income tax elasticity is
?ln
?
L
?ln ??
=?
?
1 +?
?
1 ??
, (57)
whichisincreasingin? in absolute value as well.
18
Figure 4 shows the net utility gain
contours under a permanent and instantaneous stabilization as a function of? and?.
Figure 4: Welfare Gains As a Function of?and? (in percent)
0.2 0.4 0.6 0.8 1 1.2 1.4
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.1
0.3
0.5
0.7
0.9
Wage elasticity of labor supply (mu)
Interest elasticity of money demand (beta)
The welfare gain remains positive for all ? and ? in the analyzed ranges. The
strong sensitivity of the welfare gain to ? is not surprising, as a larger ? elicits larger
money demand response to the sharp and immediate cut in inflation and thus raises welfare
18
Outside the steady state, the tax elasticity of labor cannot be expressed analytically, as the
real wage differs from the marginal product of labor because of the distortion created by the sticky
inflation (see (51)).
30
considerably. The link to ? is much less pronounced, with the welfare gain declining
slightly as more elastic labor supply leads to a larger drop in output (and thus consumption)
in response to the higher tax rate. Clearly, welfare responds much less to variations in ?
than in?,and in this sense labor is a less elastic good than money for a given r,?
l
,and?
l
.
Thus, by shifting the burden of taxation from money holdings to labor income, stabilization
indeed improves welfare for wide ranges of? and?.
It follows from (55) and (57) that the tax elasticities of money and labor also de-
pend on the international interest rate, r, and the initial size of government,?
l
, respectively.
The welfare gains decrease notably in r and less so in ?
l
. A real interest rate higher by 1
percentage point reduces the welfare gain by almost 1 percentage point via two channels: it
lowers the money response to the cut in inflation, as well as discounts the future more heav-
ily, thus giving a larger weight to the bigger short-term output transition losses relative to
the smaller steady state ones. Regarding the initial taxation level, a 5-percentage-point-of-
GDP higher initial government intake reduces welfare by 0.5 percentage point. As higher
?
l
raises the tax elasticity of labor, the output loss is slightly bigger for a given reduction in
inflation.
The welfare results are also positively related to the weight of money in the utility
function, ?. The parameter ? is related to the degree of monetization of the economy,
as explained in Section 3.1. Welfare turns negative only for extremely small values of ?
(below 0.00001), corresponding to a money-to-GDP ratio of below 1/3 of 1 percent.
2.4.2. Sensitivity of Welfare to Speed of Disinflation and Degree of Price/ Inflation
Stickiness
It is natural to ask how welfare comparisons depend on the policy design and/or the
structural features of the economy. To this end, we repeat the sensitivity analysis in Calvo,
Celasun, and Kumhof (2003), varying the speed of disinflation and the degree of price/
31
inflation stickiness. Specifically, the speed of disinflation is operationalized by considering
gradual disinflation policies of the form ??
t
=??until?
t
=?
l
, where the parameter?char-
acterizes the speed of disinflation, while the degree of price/inflation stickiness is given by
the average duration of price contracts 1/?. The results are presented in Figure 5. The fig-
ure shows that, for an empirically relevant average price contract length of about two-four
quarters, halving inflation from 20 percent to 10 percent per annum produces net welfare
gains of 0.71 - 0.75 percent. These gains are decreasing in the degree of price/inflation
stickiness 1/?, because the latter slows the response of the nontradable sector to the lower
depreciation rate, thus deepening and prolonging its recession. They are also decreasing
with a more gradual disinflation, despite the smaller loss of inflation tax revenue, which
requires a lower increase in conventional taxation and thus provides for a shallower reces-
sion. The reason is that money increases by less in response to only a gradual cut in the
interest rate, which effect dominates the gain from higher consumption. In addition, gradu-
alism prolongs the transition to the relatively beneficial low-inflation steady state, an effect
especially pronounced at a low degree of price stickiness as demonstrated by the steeper
contours.
The tax rate necessary to offset the loss of inflation tax revenue comes in at 28.2?
29.4 percent for various values of ? and ?, about 3.5 - 5 percentage points higher than in
the high-inflation steady state. This is at the low end of the range of observed tax revenue
increases listed in Table 1, mainly because these countries needed more revenue to finance
their increased expenditure, while the model assumes constant expenditure. The tax rate is
not very sensitive to either the speed of disinflation or the degree of stickiness, because it
is set such that the government?s assets are stationary in the new steady state, while both?
and? affect primarily the transitional dynamics.
32
Figure 5: Welfare Gains As a Function of? and? (in percent)
1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
5
6
7
8
0.7
0.71
0.72
0.73
0.74
0.75
Length of disinflation period in quarters
Average price contract length in quarters
2.5. Sticky Prices Versus Sticky Inflation
Another interesting dimension of the analysis is what is the impact of the transi-
tional recession generated by sticky inflation (the ability of firms to choose their inflation
rate between price updates in addition to their price). To evaluate this, we recast the pro-
ducer side of the model in terms of the conventional sticky price setting, where firms choose
only their price upon getting the price-changing signal and update that price at the steady
state inflation rate between signals (see Yun (1996)). For the purposes of this analysis,
such sticky prices are analogous to flexible prices, as under a credible stabilization pro-
gram both allow the economy to jump from the high-inflation steady state directly into the
low-inflation one without a transitional recession.
33
Specifically, producers maximize
Max
V
t
null
?
t
e
?
null
s
t
(?+r+?
r
??
r
)dr
null
V
t
e
??(s?t)
P
s
y
s
(1 + sub)?w
s
l
s
null
ds, (58)
subject to the production function (12) and to the goods demand, which can now be ex-
pressed as
y
s
= c
s
null
V
j
t
e
??(s?t)
P
s
null
??
(59)
and substituted in (58).
19
The first-order condition for V
t
is
null
?
t
e
?
null
s
t
(?+r+?
r
??
r
)dr
c
s
null
V
t
e
??(s?t)
P
s
null
??
null
V
t
e
??(s?t)
P
s
?
w
s
B
null
ds = 0 .
Using again p
t
? V
t
/P
t
and P
s
= P
t
e
null
s
t
?
r
dr
for s > t, we can rewrite the last
condition as
null
?
t
e
?
null
s
t
(?+r+?
r
??
r
)dr
c
s
null
p
t
e
?
null
s
t
(?
r
???)dr
null
??
null
p
t
e
?
null
s
t
(?
r
???)dr
?
w
s
B
null
ds = 0 . (60)
Asbefore,inthesteadystatewehave ?? = ?
l
, ?p = 1, and ?w = B. We linearize
(60) around the steady state and obtain the following expression:
p
t
=(?+ r)
null
?
t
e
?(?+r)(s?t)
null
w
s
B
+
null
s
t
(?
r
???)dr
null
ds.
Its derivative with respect to time is
?p
t
=(?+ r)(p
t
?
w
t
B
)?(?
t
???). (61)
The aggregate price index (4) can now be rewritten as
19
The firm index j is dropped, as the maximization problem is identical for all firms.
34
P
t
=
null
?
null
t
??
e
??(t?s)
(V
s
e
??(t?s)
)
1??
ds
null
1
1??
. (62)
Taking its derivative with respect to time, we obtain
?
t
=
?
1 ??
(p
1??
t
? 1). (63)
Linearizing this expression around the steady state yields
(?
t
???)=?(p
t
? 1). (64)
Its derivative with respect to time equals, using (61) and (64) itself,
??
t
= ??p
t
=?(?+ r)(p
t
? 1)?(
w
t
B
? 1)??(?
t
???) (65)
= (?+ r)(?
t
???)??(?+ r)(
w
t
B
? 1)??(?
t
???)
= r(?
t
???)?
?(?+ r)
B
(w
t
? B).
This is the first dynamic equation. As the initial relative price of new price setters,
p
t
, is free to jump at the start of the stabilization program (t=0), aggregate inflation is a
jump variable. The second equation ? for the wage rate ? is equation (51) from above.
Thus, we have the following dynamic system:
?
?
?
??
t
?w
t
?
?
?
=
?
?
?
r
??(?+r)
B
?B(1 +
1
?
) 0
?
?
?
?
?
?
(?
t
???)
(w
t
? B)
?
?
?
+
?
?
?
0
B(1 +
1
?
)
?
?
?
(?
t
???). (66)
This system has one positive and one negative eigenvalue. With one free-jumping
and one predetermined variable (see Section 2.5), it is saddle-path stable.
Figure 6 shows the dynamics of the main macroeconomic indicators. Under a cred-
35
Figure 6: Dynamic Paths of the Main Macroeconomic Indicators in the Sticky-Price-Only
Case (in percent)
0 10 20 30 40 50
5
10
15
20
25
pi ? Nontradables Inflation Rate
0 10 20 30 40 50
0.96
0.97
0.98
0.99
1
1.01
1.02
Nontradables Output
0 10 20 30 40 50
0.96
0.97
0.98
0.99
1
1.01
1.02
Real Exchange Rate
0 10 20 30 40 50
0.96
0.97
0.98
0.99
1
1.01
1.02
w ? Real Marginal Cost
ible, permanent stabilization, the economy jumps directly in the new steady state and there
is no transitional dynamics (see Calvo and Vegh, 1993). Inflation immediately falls to 10
percent, while the wage rate stays at its steady state value. Nevertheless, the economy
contracts by about 0.5 percent again, as the loss of inflation tax revenue forces the fiscal
authority to raise the income tax rate in order to balance the budget, which, in turn, lowers
labor supply, consumption, and output of nontradables, and leads to a one-step real ex-
change rate appreciation. The welfare gain from the utility of larger money balances and
36
less labor outweighs the loss from lower consumption, for a net gain of 0.763 percent, about
0.012 percentage point higher than in the previously analyzed case of sticky inflation. The
bulk of this difference comes from the lack of a transitional recession, while about 1/12 of
it is due to the lower tax rate (28.88 percent now versus 29.04 percent before).
Figure 7 shows the welfare gains with varying speed of disinflation and degree of
price stickiness. While the general shape and direction of the contours are similar to the
ones in the sticky inflation case shown in Figure 5, for each combination of (?,?), the
equilibrium tax rate is now lower, and the welfare gain is larger. Moreover, the contours
are steeper, indicating that the welfare gain declines faster with gradualism than before.
The reason for this is that firms now update their prices by the new steady state inflation
rate ?
l
between price-changing signals, and the more gradual the disinflation, the farther
the exchange rate depreciation ?
t
is from that steady state value, and the more the real
exchange rate appreciates, causing a larger output loss.
Differences in the tax rates between these two exercises (here and in Section 4.2)
are relatively minor, not extending beyond 1/4 of 1 percentage point on an annual basis.
Generally, these differences rise in the degree of price stickiness (as less frequent price
updates exacerbate the recessional effects of sticky inflation and require a higher tax rate
to balance the budget), and decline in the degree of gradualism (as a more gradual decline
in the exchange rate depreciation rate allows for easier adjustment of inflation and thus
reduces the harm of its stickiness).
Inflation stickiness is thus responsible for a small fraction of the necessary tax hike
and the concomitant loss of output. The larger part of the tax increase is simply due to
the need to replace the loss of inflation tax revenue in the steady state caused by disinfla-
tion. Nevertheless, by generating a transitional recession, sticky inflation further lowers the
income tax base and necessitates a higher tax rate than otherwise to maintain fiscal sustain-
ability. Thus, by further raising the tax rate in bad times, inflation stickiness makes fiscal
37
Figure 7: Welfare Gains as a Function of? and? in the Sticky-Price-Only Case (in
percent)
1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
5
6
7
8
0.69
0.7
0.71
0.72
0.73
0.74
0.75
Length of disinflation period in quarters
Average price contract length in quarters
policy procyclical. This is a common feature in emerging markets and other developing
countries, as documented and discussed in Kaminsky, Reinhart and Vegh, (2004).
2.6. Conclusion
This paper explores the implications of substituting conventional distortionary tax-
ation for inflation tax revenue in a model of an exchange-rate-based stabilization with in-
flation inertia and an environment of optimizing agents. The need to raise taxes arises from
the inflexibility of government expenditure, which cannot be cut to offset the loss of in-
flation tax receipts. To ensure the credibility of the stabilization program, the government
38
must find an alternative revenue source. The policy combination of lower inflation and the
resulting higher conventional tax rate has in principle an ambiguous effect on welfare, as
it pits the lower utility during the transition to the new steady state and the efficiency loss
of the higher tax rate against the gains from the permanently smaller monetary distortion
and smaller labor effort. The latter effects seem to dominate with these preferences and
technologies, resulting in a net welfare gain. It therefore seems that, despite its adverse
effect on output, higher conventional taxation is an acceptable substitute for inflation tax
revenue in achieving a lasting and welfare-improving inflation stabilization.
39
3. Exchange-Rate-Based Stabilization Under Fiscal Con-
straints and Capital Controls
3.1. Introduction
The theory and practice of exchange-rate-based stabilization programs has been ex-
tensively analyzed in an effort to explain the reasons for the success or failure of these
programs by features of their design and implementation.
20
The major lessons are that
credibility and fiscal restraint matter most for success. Most models, however, make two
crucial assumptions: (i) perfect capital mobility, which makes the real interest rate ex-
ogenous to the stabilizing economy; (ii) a sustainable fiscal position after the start of the
stabilization program, which is shown to be a necessary, but not always sufficient condition
for permanently lowering inflation.
Recognition of the powerful effects of global capital mobility is a distinctive feature
in open-economy macroeconomics and international finance today. However, situations
where capital mobility is low do still exist. A high-inflation economy in need of stabi-
lization, possibly burdened by inherited debt, could be considered too high a credit risk
and therefore could effectively be shut out of the international capital markets. While a
complete absence of any capital movements is unlikely, especially in the presence of dol-
larization and volatile financial intermediation, domestic real interest rates are nevertheless
endogenous ? influencing and being influenced by the dynamics of consumption, money
and government debt.
On the fiscal side, the obvious policy recommendation for successful stabilization
is to reduce the deficit to a size that can be financed without much recourse to inflation
tax. Most of the time, though, this is easier said than done. On the one hand, governments
20
See footnote 1 for a literature list.
40
face political constraints that could make a cut of the deficit below a certain level not only
politically infeasible, but strategically unwise as well, leading to loss of political support
and jeopardizing the success of the whole program. On the other hand, the burgeoning
debt may break the stabilization on its own if not addressed. So countries with inflexible
budgets face a dilemma ? how to reconcile the loss of inflation tax revenue with the need
to ensure the credibility of their stabilization policies.
Suppose a small open-to-trade economy with high debt burden and a history of
heavyrelianceoninflation-tax budget financing starts an exchange-rate-based stabilization
program. There are sufficient foreign exchange reserves, so this type of stabilization looks
feasible. However, the government cannot lower the primary fiscal deficit (or raise its
primary surplus) beyond the existing level. This level is inconsistent with low inflation:
given the prevailing interest rate, it puts the outstanding government debt on an explosive
trajectory as in Sargent and Wallace (1981). What can this government do to save the
stabilization effort?
Intuitively, lowering inflation at the onset of the stabilization program decreases the
budget?s inflation tax revenue. Other things being equal, the fiscal situation becomes un-
sustainable ? the deficit starts increasing. The policy makers have, however, one more
tool: an expansion of money supply by buying back government debt. The size of this
operation ensures that the resulting dynamics of the real interest rate are consistent with
convergence to the new, lower steady state debt level in a credible stabilization process.
This policy has two desirable effects: (i) it lowers the real interest rate, which by itself
lowers budget expenditures; (ii) it makes consumption and money demand (the inflation
tax base) jump temporarily, raising additional budget revenues. If the stabilization program
lacks credibility for whatever reason (i.e., it is perceived as temporary), the same policies
as in the permanent case have different quantitative effects because consumers anticipate
higher inflation in the foreseeable future and substitute current for future consumption.
41
Now the same monetary operation achieves much lower decline (if any) of the real interest
rate at the start, and the latter quickly overshoots its steady state value. The fiscal ?hon-
eymoon? is much shorter. Since inflation acts as a distortionary tax, consumers? decisions
are affected by inflation variability. The perfectly anticipated jump in inflation at the end
of the stabilization program makes it optimal for the consumers to have a downward jump
in their consumption/money holdings at this point, which results in an upward jump of the
stock of government debt. The favorable temporary effects are completely reversed and the
economy converges to its initial high-inflation equilibrium.
How do the dynamics of the main macroeconomic variables differ from the stan-
dard models of an exchange-rate-based stabilization (e.g., Calvo-Vegh, 1993 and 1994)?
First, policy-induced changes in the real interest rate allow for temporary real effects in a
permanent stabilization: consumption jumps up and then gradually decreases, the current
account deficit does the same, the real interest rate drops and then converges back to its
long-term level. Second, in a temporary stabilization, the effective price of consumption
varies with the interest rate during the stabilization, which makes consumption vary as well
? the smoothing, present in the constant interest rate models is absent. Third, a temporary
stabilization is observationally very close to a permanent one ? the only sign of trouble
is the real interest rate overshooting its steady state level. Moreover, we show that, given
consistency between the target inflation and the level of foreign exchange reserves and
reasonably strict enforcement of capital controls, monetary policy can save an otherwise
unsustainable stabilization program.
Analyses of the fiscal implications of an exchange-rate-based stabilization within
this framework of continuous-time perfect foresight model and endogenous interest rates
are provided in Velasco (1993) and Agenor and Montiel (1996). Velasco considers a sim-
ilar question ? how to use monetary policy to balance the budget if fiscal adjustment is
infeasible ? but only in the context of a permanent, credible stabilization. This paper
42
extends the analysis to temporary stabilization and considers similarities and differences
in the transitional dynamics of the economy between both types of stabilization. Agenor
and Montiel look at the effect of anticipated tax changes on the economy. They are not
explicitly concerned with the dynamics of domestic government debt (in fact, they assume
that it stays constant and normalize it to zero), while it is an important motivator of policy
decision-making in our model.
3.2. The Model
3.2.1. Consumers
An infinitely living representative consumer maximizes utility subject to cash-in-
advance and asset accumulation constraints. The model economy is small and freely trad-
ing, but closed for capital flows. The one consumption good is tradable. International prices
are constant and normalized to one; continuous purchasing power parity (PPP) is assumed,
so the domestic price level is given by the nominal exchange rate, E, and domestic infla-
tion by the exchange rate depreciation. The exchange rate is predetermined, i.e., E cannot
jump, but its rate of change,?,can; however, it is constant between jumps. Output is con-
stant. The assets available to the consumer are money and government bonds. The latter are
inflation-indexed, to eliminate the government?s temptation to inflate the debt away, which
may lead to time inconsistency problems. There are transfers from the government, which
are fixed at their pre-stabilization level. In standard notation, the consumer maximizes
null
?
0
u(c
t
)e
??t
dt,
subject to:
43
m
t
? ?c
t
?a = r
t
a
t
+?y +?g ? c
t
?(r
t
+?
t
)m
t
where a
t
denotes the consumer?s assets, r
t
is the domestic real interest rate, ?y is the (con-
stant) output and ?g is the government?s primary budget deficit, equal to the fiscal transfers
net of any lump-sum taxes. Throughout the paper we assume that the nominal interest rate
is positive, i.e. the cash-in-advance constraint is binding.
The first-order conditions are
u
null
(c
t
) = ?
t
1 +?(r
t
+?
t
), (67)
m
t
= ?c
t
, (68)
?
? = (?? r
t
)?
t
, (69)
?a = r
t
a
t
+?y +?g ? c
t
?(r
t
+?
t
)m
t
, (70)
a
t
e
?
null
t
0
r
s
d
s
? 0, t ??. (71)
Condition (67) says that along the optimal consumption path, marginal utility of
current consumption is equal to its cost ? the foregone utility from wealth accumulation,
which could have been used for future consumption. The term 1+?(r
t
+?
t
)is the effective
price of consumption: the market price (one) plus the opportunity costs of holding money.
Condition (68) establishes the money demand function. The third one gives the law of
motion of the marginal utility of wealth. The fourth one is again the consumer asset-
accumulation equation. The no-Ponzi-game condition in the end is actually a constraint
on both the consumer and the government: it implies that the consumer cannot accumulate
bonds or money without bound; therefore, the government cannot issue bonds forever.
44
3.2.2. Government
The government issues bonds and collects inflation tax to cover its deficit.
21
Its debt
accumulation equation is
?
b = r
t
b
t
+?g ??
t
m
t
.
Note that the primary budget deficit, ?g,can be negative. Here b refers to bonds held
outside the consolidated government. We also assume that real domestic credit growth is
zero, so the fiscal authority gets only?m from money creation:
M = ER?
?
M
E
=?m +
?
R
The fiscal authority gets the first term, while the central bank gets the second one,
the change in reserves.
3.2.3. Equilibrium and Dynamic System
From equation (67), we have c
t
= c(?
t
(?)
, r
t
(?)
,?
t
(?)
), with the signs of the partial
derivatives shown below the variables.
Using the identity that government?s supply of bonds must be equal in equilibrium
to consumer demand, equation (68), and ?m
t
=?a
t
?
?
b
t
, we derive the following equilibrium
asset accumulation equations:
?
b = r
t
b
t
+?g ???
t
c(?
t
,r
t
,?
t
), (72)
?m =?y ? c(?
t
,r
t
,?
t
) or ?c =
1
?
(?y ? c(?
t
,r
t
,?
t
)). (73)
Differentiating equation (67) with respect to time and dividing the differentiated
21
The results easily generalize to an income and/or consumption tax.
45
equation by (67) again, we get (after simplifications)
?r =
1 +?(r
t
+?
t
)
?
null
r
t
??+
u
nullnull
(c
t
)
u
null
(c
t
)
1
?
(?y ? c(?
t
,r
t
,?
t
))
null
. (74)
Let u(c)= log(c);then
u
nullnull
(c)
u
null
(c)
=?
1
c
. Consider the following dynamic system:
?
? = (?? r
t
)?
t
(75)
?r =
1 +?(r
t
+?
t
)
?
null
r
t
???
?y
?c(?
t
,r
t
,?
t
)
+
1
?
null
(76)
?
b = r
t
b
t
+?g ???
t
c(?
t
,r
t
,?
t
) (77)
This system has a steady state at:
?r =?;
?
b =
????y ??g
?
;
?
?=
1
?y(1 +?(?+??))
(78)
Let P = 1 +?(?+??) be the effective price of consumption, evaluated at steady
state. Linearizing the system around the steady state yields the following:
?
?
?
?
?
?
?
?
?r
?
b
?
?
?
?
?
?
=
?
?
?
?
?
?
0 ?
1
?yP
0
?P
2
?y
?
2
P?1
?
0
???y
2
P
?
b ?
?
?
?
?
?
?
?
?
?
?
?
?
?
t
?
?
?
r
t
??
b
t
?
?
b
?
?
?
?
?
?
.
Note that this system is partly recursive: the dynamics of ? and r affect those of
b, but there seems to be no feedback. Nevertheless, the system has to be considered in its
entirety for the following reason. The only free-jumping variable here is r.Because of the
cash-in-advance constraint, consumption cannot jump without money jumping; therefore,
absent money jumps, any jump of the marginal utility of wealth, ?, is supposed to exactly
offset the jump (if any) in r. In the aftermath of a shock, if only one variable is allowed to
46
jump freely, the system may not be able to get on the convergent saddle path. Intuitively,
there is no guarantee that the joint dynamics of r and ? (and thus c(?,r) ) will lead b
towards the steady state, rather than to infinity.
The eigenvalues of the system?s coefficient matrix are given by ?
1
= ?,?
2
=
P
?
, and ?
3
=?
1
?
. Exactly one of these (?
3
) is negative , thus the system has a unique
convergent saddle path. The eigenvector corresponding to ?
3
is(h
1
,h
2
,h
3
), where h
1
has
been normalized to 1, h
2
=
P ?y
?
> 0andh
3
=
?P ?y(?
2
??+
?
b)
1+??
< 0. Thus, along the saddle
path, the endogenous variables are related as follows:
22
?
t
?
?
?
b
t
?
?
b
=
h
1
h
3
< 0,
r
t
??r
b
t
?
?
b
=
h
2
h
3
< 0,
?
t
?
?
?
r
t
??r
=
h
1
h
2
> 0. (79)
In other words, the marginal utility of wealth and the real interest rate move to-
gether along the converging path, while government debt moves in the opposite direction.
Remember that c
t
= c(?
t
(?)
, r
t
(?)
). Thus, lower ?
t
and/or r
t
mean higher consumption and
money, which means more tax revenues, allowing a higher level of steady state debt. Higher
interest rates work, ceteris paribus, in the opposite direction. Finally, higher interest rate
increases the effective price of consumption, and the resulting lower consumption is asso-
ciated with higher marginal utility of wealth.
3.3. Policy Experiments
3.3.1. Permanent Stabilization
This policy experiment consists of two parts:
? An unanticipated decrease of the exchange rate depreciation from ?
h
to ?
l
(which is
considered permanent by the consumers).
22
This follows from creating the ratios of the solution for the endogenous variables from the
linearized system, ruling out the explosive components.
47
? An appropriate supporting policy (if necessary) to put the economy on a stable path
converging to the low-inflation steady state.
Suppose that before the stabilization program starts, the system is in its high-inflation
steady state (see equation 78). What is the reaction of the endogenous variables on impact?
Denote the low-inflation steady state values by ^ and the levels taken immediately after the
start of the stabilization program by
?
Along the convergent saddle path, the variables are
related as follows:
(b
?
?
?
b)+(
?
b ?
?
b) =
h
3
h
1
(?
?
?
?
?)+(
?
??
?
?)=
h
3
h
2
(r
?
??r)+(?r ??r), (80)
(?
?
?
?
?)+(
?
??
?
?) =
h
1
h
2
(r
?
??r)+(?r ??r).
where the eigenvector components are evaluated at the low-inflation steady state.
The new, low-inflation steady state is
?r =?r =?,
?
? =
1
?y(1 +?(?+?
l
))
>
?
?=
1
?y(1 +?(?+?
h
))
,
?c =?c =?y,
?
b =
??
l
?y ??g
?
<
?
b =
??
h
?y ??g
?
.
With the new steady state values, equation (79) simplifies to:
(b
?
?
?
b)+
a(?
h
??
l
)?y
?
=
h
3
h
1
null
(?
?
?
?
?)?
a(?
h
??
l
)
?yP
h
P
l
null
=
h
3
h
2
(r
?
??r), (81)
(?
?
?
?
?)?
a(?
h
??
l
)
?yP
h
P
l
=
h
1
h
2
(r
?
??r).
48
These relationships will be used to determine the jumps at t=0, but first we need
to define which variables can jump and under what circumstances. Since the nominal
exchange rate (and hence the price level) is predetermined, b cannot jump on its own. To
reach the new saddle path, both?and r need to fall, but this would lead to an upward jump
in c, which is precluded by the cash-in-advance constraint. The intuition is clear: since
the targeted lower inflation can be supported only by a lower steady state debt level, the
government needs to run a budget surplus for a while, in order to retire some debt from the
current unsustainable level. However, since the tax rate (inflation) has gone down, there is
a need to increase the tax base (money in this case). Here comes the role of the supporting
policy: a money supply expansion by exchanging money for privately held bonds. Note
that, as explained above, if cutting ? were the only policy change, the economy could
not reach the converging saddle path. The intuition behind this is that the steady state
determined solely by the
?
? = 0and?r = 0 equations does not necessarily involve
?
b = 0
too, given the pre-existing debt level
?
b; in fact, this can happen only by coincidence. So an
additional policy is needed to put the system on the stable path. Aside from adjusting the
primary deficit down or a massive debt retiring (via external assistance, rescheduling etc.,
so that
?
b =
?
b ), both of which we have ruled out, the only other feasible policy is lowering
the real interest rate by adjusting money supply. This can only happen by purchasing
bonds, the sole asset consumers hold, for money. The policy ? purchases of government
bonds by the central bank ? is announced at the beginning of the stabilization program, so
consumers take it into account, as required in a perfect foresight environment.
To illustrate this asset exchange, consider the balance sheets of the central bank, the
fiscal authority, and the consolidated government on the eve of the stabilization program
(Table 3).
49
Table 3: Balance Sheet of Government Entities in the High-Inflation Steady State
Central Bank Fiscal Authority Consolidated Government
Assets Liabilities Assets Liabilities Assets Liabilities
?
R ?mF
?
T b
CB
?
R ?m
b
CB
?
bF
?
T
?
b
Here
?
R is the foreign exchange reserves; ?m base money; b
CB
government bonds in
the central bank portfolio; and
?
b government bonds held by the households.
23
Recall that
the ?bar? values correspond to the high-inflation steady state. Revenues from ?future taxa-
tion? (FT) is an item added to complete the fiscal authority?s balance sheet, as government
bonds are claims on future tax revenues.
Our policy experiment at t=0 can thus be summarized as:
? ?
h
is decreased to?
l
,and
??m is increased to m
?
via the following operation:
1) the central bank begins net repurchases of bonds from the public, issuing new
money for the purpose. This is reflected in its balance sheet as follows:
Central Bank:
?
R + b
CB
+nullb =?m +nullm.
2) The fiscal authority?s balance sheet remains unchanged:
Fiscal Authority: F
?
T = b
CB
+nullb +
?
b ?nullb
3) The consolidated government budget remains the same as well:
Consolidated Government:
?
R+F
?
T =?m+nullm+
?
b?nullb.Note that the composi-
tion of government liabilities has changed: the share of money is up, while that of bonds is
down. By size, m
?
??m =nullm =nullb.The money supply value m
?
can be derived from the
asset exchange relationship m
?
??m =?(b
?
?
?
b)at t=0, where b
?
is among the solutions
of the system:
23
Note that none of the increase in b
CB
t
at t=0 goes to the fiscal authority, and central bank
holdings of bonds stay constant thereafter.
50
?
?
?
?
?
b
?
?
?
b
=
h
1
(?
l
)
h
3
(?
l
)
r
?
??r
b
?
?
?
b
=
h
2
(?
l
)
h
3
(?
l
)
b
?
?
?
b =??(c
?
(?
?
,r
?
)??c)
After the operation, the balance sheets of the government entities look as follows:
Table 4: Balance Sheet of Government Entities Immediately After Start of Stabilization
Program
Central Bank Fiscal Authority Consolidated Government
Assets Liabilities Assets Liabilities Assets Liabilities
?
R m
?
=?m +nullmF
?
T b
CB
+nullb
?
R m
?
b
CB
+nullb b
?
=
?
b ?nullbF
?
T b
?
Now, because money supply has increased, the real interest rate drops, and con-
sumption jumps upward. Moreover, some debt is retired: b
?
?
?
b =?(m
?
??m) =
??(c
?
??c)<0. The debt adjustment to the steady state is a combination of an immediate
stock drop and a slow decline afterwards. The dynamics of the endogenous variables are
shown in Figure 8.
24
We see that ?
t
and r
t
drop down to ?
?
and r
?
, respectively, which
makes c
t
jump upward to c
?
=
m
?
?
, using already provided money. The system gets on
the new saddle path and converges to the new steady state. Government debt decreases ?
?
b < 0 during this transition. The temporary consumption boom leads to a current account
deficit (the top panel of Figure 11), financed out of the central bank reserves, which stay
permanently lower thereafter.
25
Here we assume that the central bank has enough reserves
to sustain the emerged current account deficit, i.e. the new inflation target,?
l
,is consistent
24
The phase diagrams in Figure 1 are projections of a three-dimensional phase dynamics space
onto three two-dimensional phase planes.
25
For simplicity, we abstract from the interest income lost owing to decreased reserves.
51
with the level of reserves: R
0
?
null
SS
0
(?y ? c(?
l
))e
??t
dt where R
0
is the initial level of
foreign exchange reserves and the international real interest rate is assumed to be equal to
?.
The government agencies? balance sheets in the low-inflation steady state is shown
in Table 5. As the money liability is the same in the two steady states, it follows that the
loss of reserves during the transition from the high-inflationtothelow-inflation steady state
is equal to the size of the initial monetary push nullb. Nevertheless, this operation amounts
to more than simply repaying some of he government debt with central bank reserves. It
also lowers the real interest rate on the remaining debt and induces consumers to hold more
money, thus expanding the inflation tax base.
Table 5: Balance Sheet of Government Entities in the Low-Inflation Steady State
Central Bank Fiscal Authority Consolidated Government
Assets Liabilities Assets Liabilities Assets Liabilities
?
R =
?
R ?nullb ?m =?mF
?
T b
CB
+nullb
?
R ?m
b
CB
+nullb
?
bF
?
T
?
b
What is the intuition behind these dynamics? As long as the stabilization is con-
sidered permanent, if the decrease in the devaluation rate were the only policy change, the
consumer would have no incentive to change consumption intertemporally ? the effective
price of consumption stays flat in the future. Technically, with unchanged money supply
the only stable solution of the system (
?
?, ?r )isr
?
=?,?
?
=
?
?; therefore, c
?
=?y,which
leads to
?
b > 0for?
l
<?
h
. However, the budget would become unbalanced ? the rev-
enue decline from lower inflation tax is not matched by a decrease in expenditure. So the
government introduces one more policy action ? a swap of bonds for money.
52
Figure 8: Permanent Stabilization
 
 
 
Phase Plane Dynamics 
 
 
            
        ? ? r  r r          r 
 
 
SS                    A                                       A  
                                      b                                      b       ? 
                                                    SS                                A  SS 
                 B B   
                                                                                        B       
Temporal Dynamics 
 
 
 
b           ?                r 
  
 
   
A            A       A   
            B                                     B                  B 
 0     SS           0     SS                 0     SS  
53
Look at the money market (the top panel of Figure 9). Most of the time, money
supply passively follows money demand. At t=0, there is an exchange of asset stocks:
bonds for money. Without this exchange, demand for money would not shift on its own at
t=0: since the effective price of consumption appears flat, the forward-looking consumers
would not change their consumption (and money demand) without an additional stimulus.
This stimulus comes from the asset exchange: money supply shifts right. The equilibrium
interest rate drops down, dragging the effective price of consumption with it; this causes an
upward jump in consumption, financed by the already provided jump in money. Over time,
the endogenous interest rate increases as the economy overheats, increasing the effective
price of consumption. Hence, after the initial jump, consumption declines to its steady
state.
Compare the permanent-stabilization solution of this model to the perfect capital
mobility model (e.g., Calvo and Vegh, 1993 and 1994, Talvi, 1996). Because of the perfect
capital mobility there, r cannot deviate from the international interest rate and c is constant
? there is no room for additional discretionary policy. Here, policy can influence (tem-
porarily) interest rates and thus consumption. The temporary current account deficit caused
by this intervention does not jeopardize the sustainability of the stabilization, as long as it
can be financed out of the monetary authorities? reserves.
Admittedly, the practical implementation of the above-described operation is not
easy. If money demand is unstable, a given increase in money supply may not result in
the desired real interest rate. This can be remedied if the monetary authority sets the real
interest rate and adjusts money supply in response to demand. In addition, capital controls
usually leak, so part of the increased money supply may get immediately transformed in
foreign exchange and thus not contribute to lowering the real interest rate. However, as long
as domestic-currency assets yield more than foreign-exchange ones, this tendency should
not persist in an otherwise credible stabilization program.
54
Figure 9: Money Dynamics
 
 
 
Permanent Stabilization 
 
  r  
 
 
                          A  
       
   
     B 
                      r* m=?c 
 m 
                                               ?y                                        m* 
Temporary Stabilization 
                          r 
 
D     C 
     B 
                                             A 
                r (TS) 
 
r*  
                                                           m=?c 
                                                                   m 
?y m*
55
3.3.2. Temporary Stabilization
So far, we have been looking at the sustainable (permanent, credible) stabilization
outcome; we showed that with the right policy package a permanent stabilization is fea-
sible, despite the temporary boom in domestic demand. Now suppose that the public is
skeptical about the government?s long-term commitment to stabilization. They expect the
government to revert to high-inflation policies at some point in the future. In perfect fore-
sight, this point is known from the beginning of the stabilization attempt.
At the launch of the stabilization program, the policymakers cannot tell if the public
expects it to be permanent or temporary. So they act as in the permanent case and send the
same policy signals at t=0:
? ?
h
is decreased to?
l
,and
? the same open-market operation is repeated: ?m is increased to m
?
,
?
b drops to b
?
.
As, however, consumers believe the decrease in inflation will be only temporary,
the signals they receive are
? ?
h
is decreased to ?
l
for a period (0,T ), after which it is restored to?
h
. The end-date
T is exogenously given and known to the consumer;
26
??m is increased to m
?
,
?
b is decreased to b
?
.
For expositional simplicity, let us split the effects of the above policies. First, con-
sider the movements of the depreciation rate. Now, even without any other policy change,
26
Endogenizing T by making the stabilization crash when b
T
reaches certain level (say, its origi-
nal level
?
b ) leads to non-uniqueness. The shorter the expected T , the higher is consumption in [0,T ]
(as the life-time budget constraint of the consumer is unchanged), as well as the real interest rate.
These two developments result in opposing effects on debt dynamics, but it can be shown under
reasonable assumptions that the interest rate effect dominates. Thus, debt grows faster if expected
T is shorter, so the crisis level b
T
is hit earlier. Therefore, expected shorter T leads to actual shorter
T ; since expectations are exogenous, non-uniqueness follows.
56
the effective price of consumption jumps with inflation at T . So the consumers have a rea-
son to substitute consumption intertemporally, which reason alone is sufficient to trigger a
jump in consumption up at t=0anddownatt=T . Now look at the money market again (the
bottom panel of Figure 9). Since consumption jumps up at t=0 and down at t=T ,money
demand does the same (from point A to B at t=0, and from C to D at t=T ). Note the
difference from the permanent stabilization case, where this effect is not present.
Second, money supply goes up at t=0 by policy design and down at t=T as un-
wanted money balances are converted to bonds. The net effect on the interest rate at t=0
is ambiguous: it depends both on the intertemporal elasticity of consumption substitution
(IES) and the expected duration of the stabilization effort, T , via the consumer?s life-time
budget constraint. Empirical evidence points to low IES (Reinhart and Vegh, 1995); more-
over, if a stabilization program is being discussed at all, its credibility has to be consid-
erable at least in the eyes of the policymakers, which is proxied by long T . Suppose,
therefore, that the IES is relatively low and T is expected to be long enough, so money
demand jumps by less than money supply and r drops down a bit (still, it always stays
above r
?
in the permanent stabilization case, because money supply shifts by the same
amount as before, while money demand shifts up autonomously now). On impact, con-
sumption jumps to the same point c
?
as in the permanent case because money jumps again
to m
?
and the cash-in-advance constraint is binding. We also find that
?
b|
TS
>
?
b|
PS
?debt
grows faster under a temporary stabilization (TS) than under a permanent one (PS). (
?
b|
TS
= r
TS
b
?
+?g ???
l
c
?
>
?
b|
PS
= r
?
b
?
+?g ???
l
c
?
;sinceinTSr increases faster and c
decreases faster than in PS, the relationship stays the same thereafter.) Actually, debt still
decreases in the beginning, but much more slowly than what is needed to put the economy
on a sustainable path.
Figure 10 shows the dynamics of the model variables. At t=0, bonds drop to b
?
again and r drops slightly to r
TS
. At T+ inflationshootsbackupto?
h
and the system
57
has to be on the saddle path leading to the high-inflation steady state. Since consumers
can exchange money for bonds on demand and the price level is predetermined, the real
interest rate is continuous at T ; otherwise, there would have been intertemporal arbitrage
opportunities. Also, because the crash has been anticipated, the real consumer wealth does
not jump; therefore, the marginal utility of wealth, ?, is continuous at T . The jump of the
economy between T -andT+ isgivenbythefollowingsystem:
u(c
T+
)+?
T
r
T
a
T
+?y +?g ? c
T+
?(r
T+
+?
h
)m
T+
= u(?y) (82)
?
T
?
?
?
r
T
??
=
h
1
(?
h
)
h
2
(?
h
)
=
?
?yP
h
(83)
b
T+
?
?
b
?
T
?
?
?
=
h
3
(?
h
)
h
1
(?
h
)
=?
1 +??
?yP
h
(?
2
?
h
+
?
b)
(84)
b
T+
? b
T?
=??(c
T+
? c
T?
) =?
?
2
(?
l
??
h
)
?
T
P
h
P
l
(85)
Equation (82) follows from the constancy of the Hamiltonian between T+ and
the steady state. Equations (83) and (84) are the saddle-path relationships between the
endogenous variables, derived in (79) ? since the system has to be on the convergent
trajectory to the high-inflation steady state at T+. Equation (85) follows from the asset-
exchange requirement ? unwanted money is exchanged for bonds at T ? and the cash-
in-advance constraint. The prices P
h
= 1 +?(?+?
h
)and P
l
= 1 +?(?+?
l
).
This system involves four unknowns: ?
T,
r
T
,b
T+
,b
T?
.
27
The end-date T and ?
h
are exogenous, c
T?
and c
T+
can be derived from the first-order condition (67) at T?
and T+. Consumption jumps down, dragging money demand with it; because of that,
government debt jumps up ? unwanted money is exchanged for bonds. As can be seen in
the bottom panel of Figure 11, the current account shifts from a deficit to a surplus.
27
Note that, using the cash-in-advance constraint, equation (67), and a
t
= m
t
+ b
t
, (82) can be
written in terms of the four unknowns.
58
Figure 10: Temporary Stabilization
 
 
 
Phase Plane Dynamics 
 
 
            
        ? ? r  r r          r 
 
 
 
            C   D    A                           C   D   A                 A   C   D   
                                      b                                      b      ? 
                                                    
                 B B               
                                                                                        B       
Temporal Dynamics 
 
 
 
 
b           ?                r 
            C D                    C D 
                                        
    A B                                     A                                         A 
               D                     B    B     
             C                  
       0       T     SS                     0           T     SS             0         T       SS    
  
59
Figure 11: Time Paths of Consumption and Current Account Balance
 
 
 
 
Permanent Stabilization 
 
 
          Consumption                                      Current Account Balance 
 0   SS  0 SS 
Temporary Stabilization 
           Consumption                                                  Current Account Balance  
 
                        0       T       SS 0        T         SS 
60
To summarize the intuition, a temporary stabilization program looks sustainable
for a while ? the dynamics are almost like those in the permanent case: consumption
jumps up and then gradually decreases, the interest rate does the opposite, and government
debt decreases. This is the so-called Talvi effect in play ? the temporary increase in the
tax base provides a revenue boost, which masks the need for a genuine fiscal adjustment
(Talvi, 1996). Even the current account deficit decreases with the declining consumption
after the initial overshooting. But then, at some tnull < T , the interest rate dynamics deviate
from those in the permanent case ? r goes above ? and continues increasing; it becomes
clear that the public do not expect the good times to last. The stabilization program ends
at T with a consumption and money demand collapse (and then slow recovery), the real
interest rate starts declining, debt still rises for a while, until reaching its stable (albeit high)
equilibrium level.
So, with the help of the same-size one-time expansion in money supply, a temporary
real boom is generated again. However, lack of credibility leads to different dynamics. The
most marked difference is in the trajectory of the real interest rate, which overshoots its
steady state level before the collapse.
3.4. Conclusion
In this paper, we have derived the following results. First, not surprisingly, in an
economy where capital flows are restricted, economic policymakers have a degree of con-
trol over domestic interest rates. They can change the initial conditions of the economy by
a one-time open-market operation, which lowers the real interest rate at the beginning of
the stabilization program and thus ensures fiscal sustainability.
Second, the ability to influence interest rates does not substitute for credibility. If
the program is not sufficiently credible at the start, monetary policy is only temporarily suc-
61
cessful in bringing the real interest rate and the fiscal deficit down. The initial interest rate
push is quickly overturned, and the real interest rate overshoots its steady state value before
the crash of the program. Thus, it can serve as a early warning signal that stabilization is in
peril.
Third, owing to the real interest rate variability that affects the effective price of
consumption, the economy experiences a temporary consumption boom, accompanied by
a current account deficit in both the permanent and the temporary stabilization cases. This
emphasizes the need for a sufficient amount of reserves (or a guaranteed access to low-
interest loans, for example from the multilateral financial institutions) at the start, for the
government to be able to afford the described set of policies.
62
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