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LIBRARY
M km [San ,State This is to certify that the
Unlve rsrty dissertation entitled

 

Three Essays on Inflation Stabilization in
a Small Open Economy

presented by

Hyuk-jae Rhee

has been accepted towards fulfillment
of the requirements for the

 

 

 

 

 

/
* Ph.D. _ d/edreeirk 1 Economics
¥\_:;//‘, MAW/IQ. w W
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i 15 October, 2003

Date

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DATE DUE DATE DUE DATE DUE
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6/01 c:/CIRC/DateDue.p65-p. 15

 

ESSAYS ON INFLATION STABILIZATION
IN A SMALL OPEN ECONOMY

By

Hyuk-jae Rhee

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Department of Economics

2003

ABSTRACT

ESSAYS ON INFLATION STABILIZATION
IN A SMALL OPEN ECONOMY

By

Hyuk-jae Rhee

The main objective of this dissertation is to develop models to explain the
stylized facts of various stabilization programs observed in developing countries
in a single unified framework. The basic model is Obstfeld and Rogoff’s dynamic
general equilibrium Mundell-Fleming model with cash-in-advance constraints. I
extend the model to allow for sticky inflation. With this framework I simulate the
disinflation experiments in high inflation environments.

Chapter 1: “Exchange-Rate-Based Stabilization” examines inflation stabiliza-
tion using the rate of devaluation as a nominal anchor under a fixed or pre-
determined exchange rate regime. This study shows that the credible reduction
in the devaluation rate induces initial expansion of non-tradable output and pro-
duces sustained expansion. The inflation rate, however, shows substantial per-
sistence even if the policy is fully credible. This is because of backward-looking
wage contracts. This result is quite consistent with the stylized fact of successful
exchange rate-based stabilization programs. An incredible reduction of the devalu-
ation rate results in a “boom-recession cycle” and inflation inertia, which has been
observed in stabilization programs. Therefore, I conclude that as long as the in-

dexation mechanism has a backward-looking component, credible disinflation can

not reduce the rate of inflation rapidly and inflation shows inertia. I also point
out that the credible disinflation can be welfare-improving regardless of inflation
persistence.

Chapter 2: “Money-based stabilization” analyzes the disinflation attempt in
which the growth rate of the money supply is used as the nominal anchor un-
der the flexible exchange rate regime. This study shows the initial contraction
in the non-tradable sector when the growth rate of the money supply is reduced.
This is because the initial appreciation of the nominal and real exchange rates.
When the supply-side effect, however, dominates, we observe long-run expansion
of the non-tradable sector. In the case of an incredible policy, we can replicate the
“recession-boom cycle” that we observed in money-based stabilization programs.
In both cases, inflation persistence is obtained. This is mainly due to the backward-
looking indexation in wage contracts. This study also suggests that the credible
money-based disinflation can be welfare-enhancing regardless of initial recession
and inflation persistence.

Chapter 3: “Interest rate rule for inflation targeting” analyzes the nominal
interest rate policy for reducing high inflation. I use the same model and same
approach as in the previous chapters. However, I look at the effect of an inflation
targeting interest rate rule. The interest rate policy generates a severe recession
with inflation inertia throughout the inflation stabilization program is observed
even if the policy is fully credible. Therefore I argue that the nominal interest rate

is not the appropriate policy instrument for fighting high inflation.

To My Parents

iv

Acknowledgement

I forever owe a special debt of gratitude to the chair of my dissertation Com-
mittee, Rowena Pecchenino, who taught me macroeconomics, for her suggestions,
encouragements, and comments on this dissertation. The same debt I have towards
Steven Matusz Andrei Shevchenko, Tomas Jeitschko for having offered me support
and advice. I am honored to call myself their student.

Throughout all the hours of work my wife provided an emotional and philo-
sophical support. Of course, I am grateful to my parents for their patience and
love. Without them this work would never have come into existence (literally).

Finally, I wish to thank the following: Hongbak Jung, Yongwon Choi, Jong-
byoug Jun Jungsuk Song (for their friendship); Alina Luca, Iva Petrova (for their
help with comments) ; Ludwig van Beethoven and Led Zeppelin (and they know

WhY);

TABLE OF CONTENTS

LIST OF TABLES viii

LIST OF FIGURES x

1 Exchange rate-based stabilization 1

1.1 Introduction ............................... 1
1.2 Evidence on the real effects of exchange rate-based stabilization in

chronic inflation countries ....................... 7

1.3 Basic model ............................... 11

1.3.1 The aggregate demand side .................. 11

1.3.2 The government ......................... 17

1.3.3 The aggregate supply side ................... 18

1.3.4 A symmetric steady state ................... 20

1.3.5 Staggered wage contract and short-run dynamics ...... 23

1.4 Exchange rate-based stabilization ................... 30

1.4.1 Permanent reduction in the devaluation rate ......... 33

1.4.2 Temporary reduction in the devaluation rate ......... 37

1.5 Concluding remarks ........................... 41

1.6 Appendix ................................ 44

1.6.1 The stability of Equation (1.2.59) ............... 44

1.6.2 The dominant eigenvalue ray .................. 45

1.6.3 Properties of system for temporary stabilization ....... 46

2 Money-based stabilization 55

2.1 Introduction ............................... 55
2.2 Evidence on the real effects of money—based stabilization in chronic

inflation countries ............................ 62

2.3 Basic model ............................... 64

2.3.1 The aggregate demand side .................. 64

2.3.2 The government ......................... 69

2.3.3 The aggregate supply side ................... 70

2.3.4 Equilibrium conditions and a symmetric steady state . . . . 73

2.3.5 Staggered wage contract and short-run dynamics ...... 76

2.4 Money-based stabilization ....................... 82

2.5
2.6

2.4.1 Permanent reduction in the growth rate of money supply . . 86
2.4.2 Temporary reduction in the growth rate of money supply . . 90

Concluding remarks ........................... 95
Appendix ................................ 98
2.6.1 The stability of Equation (2.3.3) ................ 98
2.6.2 The dominant eigenvalue ray .................. 99
2.6.3 Properties of system for temporary stabilization ....... 100

vi

3 Interest rate policy 109

3.1 Introduction ............................... 109
3.2 Basic model ............................... 114
3.2.1 The aggregate demand side .................. 115
3.2.2 The government ......................... 120
3.2.3 The aggregate supply side ................... 121
3.2.4 Equilibrium conditions and a symmetric steady state . . . . 123
3.2.5 Staggered wage contract and short-run dynamics ...... 126
3.3 An interest rate rule with an inflation target ............. 133
3.3.1 Dynamic System ........................ 133
3.3.2 An interest rate rule with an inflation target ......... 137
3.4 Concluding remarks ........................... 142
3.5 Appendix ................................ 145
3.5.1 The stability of Equation (3.3.5) ................ 145
3.5.2 The dominant eigenvalue ray .................. 146

vii

List of Tables

1.1 Major exchange-rate based inflation stabilization plans ....... 8
1.2 Major stabilization plans with crisis .................. 10
2.1 Money-based inflation stabilization plans ............... 63

viii

List of Figures

1.1 Exchange rate—based stabilization ................... 47
1.2 GDP and consumption in exchange-rate based stabilization ..... 47
1.3 Dynamic system of exchange rate-based stabilization ........ 48
1.4 Time path: rate of devaluation .................... 48
1.5 Time path: inflation .......................... 49
1.6 Time path: output of non-tradables .................. 49
1.7 Time path: real exchange rate ..................... 50
1.8 Time path: consumption of tradables ................. 50
1.9 Time path: current account ...................... 51
1.10 Dynamic system of temporary stabilization .............. 51
1.11 Time path: rate of devaluation .................... 52
1.12 Time path: inflation .......................... 52
1.13 Time path: output of non-tradables .................. 53
1.14 Time path: real exchange rate ..................... 53
1.15 Time path: consumption of tradables ................. 54
1.16 Time path: current account ...................... 54
2.1 Money—based stabilization ....................... 101

ix

2.2 Dynamic system of money-based stabilization ............ 101
2.3 Time path: rate of money growth ................... 102
2.4 Time path: inflation .......................... 102
2.5 Time path: output of non-tradable .................. 103
2.6 Time path: real exchange rate ..................... 103
2.7 Time path: nominal exchange rate .................. 104
2.8 Time path: real money balance .................... 104
2.9 Dynamic system of temporary stabilization .............. 105
2.10 Time path: Money growth rate .................... 105
2.11 Time path: inflation .......................... 106
2.12 Time path: output of non-tradables .................. 106
2.13 Time path: real exchange rate ..................... 107
2.14 Time path: consumption of tradables ................. 107
2.15 Time path: current account ...................... 108
3.1 Dynamic system ............................. 147
3.2 Time path: nominal interest rate ................... 147
3.3 Time path: inflation .......................... 148
3.4 Time path: output of non-tradables .................. 148
3.5 Time path: labor supply ........................ 149
3.6 Time path: nominal exchange rate .................. 149
3.7 Time path: real exchange rate ..................... 150

Chapter 1

Exchange rate-based stabilization

1.1 Introduction

Chronic inflation has been one of the distinguishing macroeconomic phenomena
in developing countries since World War II.1 Particularly, some Latin American
countries have suffered from high (relative to developed countries) and persistent
rates of inflation, which in some cases have lasted up to the present day. Those
countries have engaged in repeated inflation stabilization. For example, in the late
1970’s, the Southern-Cone countries, Argentina, Chile and Uruguay, fought infla-
tion by implementing exchange-rate based stabilization programs. Unfortunately,
most of these stabilization attempts have been unsuccessful in eliminating infla-
tion.In the last ten years, however, countries such as Argentina, Israel, and Mexico
have succeeded in reducing inflation close to international levels for substantial
periods.

These episodes of stabilization policy in chronic inflation countries have gained

much attention from macroeconomists. Especially, the stabilization programs of

 

1The term was first coined by Pazos (1972). According to his analysis, in chronic inflation-
ary environment, inflation is relatively high compared to industrial countries and is persistent.
Moreover, inflation does not have an inherent propensity to accelerate.

the Southern-Cone countries gave new challenges to macroeconomic theory. The
common stylized fact we observed in the stabilizations, both exchange rate—based
and money-based programs, is inflation persistence. Contrary to the expectation
of both policy makers and economists, inflation converged slowly to the target rate,
and exhibited considerable inertia. The most intriguing and puzzling phenomena

is the business cycle associated with inflation inertia. In exchange rate—based mo—

 

 

grams, real economic activitieggyghwazs..anfiumpthn.ERAQBPRMcsxuaadedjalhe

earl): stag: Oimeglem-..L.a_t.er.-i.ri..t.he.program, .¢.Y§Q-P§f9¥§ thgprpgraergwwas aban-

; “h” ,:.mr-v.p _~. Ha‘f‘!‘\“

dongsgnaummiqe -ap.d..<;utn1rt. shrankand. thetredc. .bmanccswentintmdeficit.
sparecessjgnysetflin? This boom-recession cycle of exchange-based stabilization
programs was a puzzle to conventional macroeconomists who believed the stabi-
lization should have resulted in an immediate contraction.

A lot of theoretical research has sought to explain these intriguing phenomena
observed in the stabilization programs, especially in exchange-based programs.
Early work by Rodriguez (1982) and Dornbusch (1982) offers a simple description
of the Southern-Cone exchange rate-based programs of the late 19708. They em-
phasized the presence of sticky inflation. Rodriguez assumes adaptive expectations
to point out the backward-looking price and wage behavior. Dornbusch assumes
rational expectations and stickiness of inflation. According to this hypothesis, un-

der perfect capital mobility, if aggregate demand depends negatively on the real

 

2In Argentina, for instance, the stabilization program was launched in 1978. By the 19808,
the annual inflation rate was 88 per cent, but the devaluation rate was 23 per cent. Moreover,
the growth rate of consumption was 1.9 per cent in 1978, but in the first year of program, 1979,
it increased to 12.3 per cent.

interest rate and positively on the real exchange rate (i.e., the relative price of
tradable goods in terms of non-tradable goods), reduction of the devaluation rate
decreases the nominal interest rate, which leads to lower real interest rates because
of sticky inflation. The reduction of the real interest rate induces an initial ex-
pansion of output. After that, the domestic currency begins to appreciate since
domestic inflation shows inertia and remains above the devaluation rate. Eventu-
ally, the real appreciation shrinks domestic consumption and so output falls and
recession sets in.

Those sticky inflation models give a lucid explanation of the phenomena ob-
served in the stabilization programs, especially inflation persistence and boom-
recession cycles. The inflation inertia results from sticky inflation in both models.
However, these early models have critical defect. Both models specify reduced-
form behavioral equations rather than derive them. We find this very ad—hoc. In
the case of Rodriguez(1982), the model relies on non-rational behavior and infla-
tion stickiness is assumed, not derived as in Dornbusch(1982).

An alternative explanation to the major effects of stabilization is the :tempg-
W” by Calvo and Végh (1993, 1994a). This hypothesis considers
the case in which prices or wages are sticky due to staggered contracts, but inflation
is fully flexible because of forward-looking contracts. These models are based on
the optimizing behavior of individuals. Under these circumstances, this hypothesis
argues that slow convergence of inflation and the initial boom in real economic ac-

tivities arise from lack of credibility, not from sticky inflation. Rapid convergence

of inflation, therefore, can be achieved under the fully credible stabilization policy
even if the price level exhibits stickiness.

This hypothesis seems to be successful in capturing the stylized facts associated
with the recent stabilization programs, especially exchange rate based programs.
However, these models are not successful in pointing out the exact cause of in-
flation inertia. In these models, since prices are set in a purely forward-looking
manner, the inflation rate is independent of past inflation and depends only on
future(expected) inflation. Thus, inflation is quite flexible while the price level is
sticky. Therefore, credible disinflation policies can reduce inflation dramatically
without any output cost and no inflation inertia is found, which is not consistent
with reality.3 Therefore, purely forward—looking staggered contract models are not
useful in explaining the inflation dynamics when inflation shows stickiness.

To overcome the flaw, Calvo and Végh (1994b) incorporate backward-looking
indexation into an intertemporal optimizing model and show a fully credible re-
duction in the devaluation rate can result in low inflation convergence. However,
Calvo and Végh start from the Arrow-Debreu style model with sticky prices and
assume that output is demand-determined. Thus, it lacks a solid rationale for the
demand-determined output. And also to obtain the boom-recession cycle of the
stabilization, their model depends on the relative size of the intertemporal and
intratemporal elasticities of substitution.

All the explanations examined so far are based on demand-side considerations:

 

3Agénor and Montiel (1999) pointed out that countries with chronic inflation derived various
indexation mechanisms which are quite backward looking.

This is due to the fact that most literature was inspired by the Southern-Cone
tabilitas of the late 1970s. In the recent programs, such as Mexico’s 1987 and
Argentina’s 1991 convertibility plan, it has been argued that inflation stabilization
may have played an important role in unleashing supply-side responses in labor
and investment. This literature suggests that credible stabilization induces sus-
tained expansion of real economic activities. In Lahiri (2001) and Roldos (1997),
the nominal interest rate introduces a distortion between consumption and leisure.
When inflation falls, labor supply increases. This, in turn, leads to a rise in the
desired capital stock and, hence, in investment. These supply-side considerations
can reproduce the main stylized facts observed in the successful stabilizations (Ar-
gentina (1991-1994) and Mexico (1988-1992) in which the initial boom was not
followed by a recession.

In this paper, we consider the supply-side effects of disinflation with inflation ‘
inertia in exchange rate-based programs within a New-Keynesian framework. To
consider the supply-side response, we introduce imperfect competition in the non-
tradable sector with endogenous labor supply. The reason we adopt imperfect
competition in the model is that imperfect competition is the main characteris-

4 Our model is based on

tic of the industrial structure of developing countries.
Obstfeld and Rogoff’s “Exchange Rate Dynamic Redux” in 1995. We modified

Obstfeld and Rogoff’s model in two ways. First, we assume a small-open economy

with a cash-in-advance constraint in which the change of monetary policy including

 

4See Agénor and Montiel (1999)

the change of money growth rate has a long-run effect on the economy as in the
two-country model in Obstfeld and Rogoff. Second, we adopt a Calvo-type con-
tract model to obtain the inflation dynamics in a way that nominal wage contracts
are staggered. Our model is a modified version of Calvo’s (1983) forward-looking
model including backward-looking components by Ghezzi (2001). We combine the
staggered wage contract with price setting of imperfectly competitive firms to ob-
tain the inflation persistence. Incorporating the backward-looking wage contracts
into the model is quite consistent with the wage indexation of most chronic infla-
tion circumstances.5

We apply this model to investigate the effects of inflation stabilization in a
small open economy. We have two possible experiments, one is exchange—based
stabilization which is perfectly credible and the other is temporary stabilization.
From the first experiment we are able to replicate qualitatively the stylized facts of
the exchange-based stabilization programs in which inflation persistence coexists
with the sustained expansion of domestic sector. Sticky inflation combined with
supply side effects produces inflation persistence and a sustained expansion of the
non—tradable sector. This result is quite consistent with the stylized fact of suc-
cessful stabilization programs, Argentina (1991-1994) and Mexico (19884992), in
which the initial boom was not followed by a recession. In this regard, the model

we present here is quite successful. It should be noticed that the resulting inflation

persistence and associated business cycle have very important policy implications.

 

5For instance, Edwards (1991) pointed out that the primary cause of inflation inertia in the
Chilean stabilization is backward—looking wage indexation.

First, inflation persistence cannot be avoided even if policy is fully credible as long
as there is a backward-looking indexation in price or wage setting. To achieve
rapid stabilization, the indexation mechanism should be considered. The second
implication is that the economy can enjoy a sustained expansion during the sta—
bilization. Therefore slow adjustment of inflation does not weaken the credibility
of policy. The results are not consistent with the arguments of the “temporariness
hypothesis” by Calvo and Végh (1993, 1994a) in which inflation persistence and
associated business cycles are merely due to the lack of credibility. For the tempo-
rary disinflation scenario, we see that the inflation rate accelerates after the initial
decrease, and the “boom-recession again cycle” is observed.

The plan of this paper is as follows. We consider the stylized facts of exchange
rate-based stabilization in Section 1.2. We present the basic model and the equilib-
rium in Section 1.3. The impact effects and transitional dynamics of a fully credible
and temporary disinflation policy are discussed in Section 1.4. In Section 1.5, we

draw the main conclusions. Technical derivations are relegated to Appendices.

1.2 Evidence on the real effects of exchange rate-
based stabilization in chronic inflation coun-
tries

During the past 40 years there have been 13 major exchange rate-based stabiliza-
tion in Argentina, Brazil, Chile, Israel, Mexico, and Uruguay. More often than
not, stabilization attempts have failed and inflation come back. During the 19803,

however, some countries - most notably, Chile, Israel, Mexico, and, more recently,

Table 1.1: Major exchange-rate based inflation stabilization plans

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Program Begin / end date Succeed?
Brazil 1964 March 1964 - August 1968 Yes
Argentina 1967 March 1967 - May 1970 No
Uruguay 1968 June 1968 - December 1971 No
Chilean tablita February 1978 - June 1982 Yes
Uruguayan tablita October 1978 - November 1982 No
Argentine tablita December 1978 - February 1981 No
Israel 1985 July 1985 - December 1991 Yes
Austral (Argentina) June 1985 - September 1986 N0
Crudo (Brazil) February 1986 - November 1986 No
Mexico 1987 December 1987 - November 1986 Yes
Uruguay 1990 December 1990 - present Yes
Convertibility (Argentina) April 1991 - present Yes

 

 

 

Major source: Reinhart and Végh (1995) and Calvo and Végh (1999)

Argentina - have succeeded in drastically reducing their rates of inflation. Ta-
ble 1.1 depicts twelve major exchange-rate based stabilization in chronic inflation
countries in the last 40 years.

Based on these episodes, the literature has identified the following main stylized
facts associated with exchange rate-based stabilizations, which were not successful:

(1) Slow convergence of the inflation rate to the rate of devaluation.

(2) Initial increase in real activities, particulary, real GDP and private con-
sumption, followed by a later contraction.

(3) Real appreciation of the domestic currency.

(4) Deterioration of the trade balance and current account balance.

To take a closer look at the main stylized facts, we need to investigate the time-
series data for inflation stabilization plans. Calvo and Végh (1999) constructed

the panel of annual observations for four countries (Argentina, Chile, Israel, and

Uruguay) for 16 years from 1978 to 1993. Figure 1.1 and 1.2 show the dynamics
of the rate of devaluation and inflation, real exchange rate, real GDP, and real
private consumption observed during the seven exchange rate-based stabilization
plans listed in table 1.1, which includes tablita implemented in Argentina, Chile,
and Uruguay and the Israeli 1985 plan, the Argentine Austral plan, the Uruguayan
1990 plan, and the Argentine 1991 plan.6

Panel A in figure 1.1 illustrates the behavior of the rate of devaluation and
inflation. Even if inflation is highly responsive to the reduction in the rate of de-
valuation, it remains above the rate of devaluation and then lags it as the rate of
devaluation increases. Panel B shows that the real exchange rate appreciates at
the initial stage of the stabilizations.

Calvo and Végh (1999) constructed the panel of annual observations for four coun-
tries (Argentina, Chile, Israel, and Uruguay) for 16 years from 1978 to 1993. Figure
1.1 and 1.2 show the dynamics of the rate of devaluation and inflation, real ex-
change rate, real GDP, and real private consumption observed during the seven
exchange rate-based stabilization plans listed in table 1.1, which includes tablita
implemented in Argentina, Chile, and Uruguay and the Israeli 1985 plan, the Ar-
gentine Austral plan, the Uruguayan 1990 plan, and the Argentine 1991 plan.

Figure 1.2 presents the evidence of the “ boom-recession cycle” in the growth
of per capita GDP, consumption. Panel A shows that real GDP growth increases

in the initial periods of stabilization and decreases sharply thereafter. The same

 

6In the figure 1.1 and 1.2 , time profiles are based on the stabilization time. Stabilization time
is denoted by T + j, where T is the year in which the stabilization program was implemented
and j is the number of years preceding or following the year of stabilization

Table 1.2: Major stabilization plans with crisis

 

 

 

 

 

 

 

 

 

 

Program Main features
Argentina 1967 An 82% decline in reserves
Uruguay 1968 An 81% decline in reserves
Chilean tablita A 65% decline in reserves
Uruguayan tablita A 90% decline in reserves by March 1983
Argentine tablita A 71% decline in reserves by April 1982
Austral (Argentina) A 75% decline in reserves by September 1987
Crudo (Brazil) A 58% decline in reserves by March 1987
Mexico 1987 An 85% decline in reserves between Feb 1994 and Jan 1995

 

 

 

Major source: Reinhart and Végh (1995) and Calvo and Végh (1999)

pattern is observed for private consumption. This stabilization time profiles point
to the presence of a boom-recession cycle associated with exchange rate-based sta—
bilization.

A notable aspect of exchange rate-based stabilization programs is that a vast
majority have ended in balance-of-payments crises. Table 1.2 lists all the major
programs, which were ended in crises with large losses of international reserves.

All the major programs, which were unsuccessful to eliminate the chronic in-
flation have ended in full-blown crises with large losses of international reserves
except the Mexico’s plan. This evidence suggests that there is a link between the
dynamics of the exchange rate—based stabilization and the eventual collapse of the

programs.

10

1.3 Basic model

In this section we introduce the aggregate demand side through the household’s
maximization problem and then the aggregate supply side in which the non-
tradable good sector is the locus of the imperfect competition. Next, we solve
for a long-run symmetric steady state where all prices are fully flexible. We, then,
introduce sticky prices through staggered wage contracts. In the last part of this

section, we derive the short-run dynamic system for the next section.

1.3.1 The aggregate demand side

Our model is based on Obstfeld and Rogoff’s (1995) perfect-foresight general equi-
librium Mundell—Fleming model. However, while they specify the models in dis-
crete time, we assume that time is continuous. Instead of a two-country setting,
we consider the small—country model in which non-tradable sector is the locus of
imperfect competition, and also a cash-in-advance economy is assumed.

Consider a two sector small open economy which is perfectly integrated with
the rest of the world in goods and capital markets. The economy is inhabited
by a continuum of identical households which reside on the interval [0,1]. The
representative household derives utility from the consumption of tradable goods,
non-tradable goods and leisure. This economy contains a continuum of differen-
tiated non-tradable goods which are indexed by z and distributed uniformly on

[0,1].

11

The lifetime utility of the representative household is
00
/ U(CZ‘.CIV,1—zt)ezp<—m>dt, (1.1)
0

where U (), the instantaneous utility function, is increasing, twice-continuously dif-
ferentiable, and strictly concave; CE" is consumption of the tradable good and CtN

is a non-tradable consumption index defined by
N 1 N
C. = I [O c. (2)7193, (12)

where CN (2) is the household’s consumption of good 2, and 6 > 1 is the elasticity of
substitution between non-tradable goods. The last term in the the instantaneous
utility function in Eq.(1.2.1) captures the utility from leisure or disutility from
labor supply ( It represents total hours worked by the household), and ,6 is the
positive and constant subjective discount rate.

We employ the convention of letting E represent the nominal exchange rate
in units of domestic currency per unit of foreign currency, while PT denotes the
foreign currency price of the tradable good.7 Here, PN denote the aggregate

domestic currency price index of the non-tradable goods, defined as
N 1 N 1—9 1
P. = {/0 p. <2) in. (1.3)

The real exchange rate (the relative price of tradable goods in terms of non-tradable
_ EPT - - - T _
goods) can be defined as e — W. For Simp11c1ty, we assume that P — 1 and

is constant. By this assumption, we can suppress the unnecessary foreign inflation

 

7We assume that the law of one price holds for the tradable good. Therefore, the domestic
currency price of the tradable good is EtPtT.

12

rate from the model.

To complete the household’s maximization problem, let’s look at the individual
household’s budget constraint. We assume that the representative household can
hold two types of assets as their financial wealth: domestic non-interest bearing
currency and an internationally tradable bond with a constant real interest rate
(in terms of tradable goods). Since the domestic currency and the international

bond are the only two assets held by individual consumers, we have
at =mt+bt, (1.4)

where a, m, b stand for real financial wealth, real money balance and the stock of
real bonds in terms of domestic price of tradable goods, respectively.8

We assume that the household has a constant endowment flow of tradable
goods, yg‘, while it derives human wealth from supplying labor to firm z for the
nominal wage Wt. The household also owns firm .2. Therefore, it can earn the profit
of the firm, Ht(z). Then the household’s dynamic budget constraint is governed
by the following differential equation:

Ht(zl Wtlt T Ct T
+ __ + + 7- .. __ _ (7 , 1.5
Etffl Etffl M t 6t t ( )

 

(it = rat — itmt +

where r is real transfers from the government in terms of tradable goods; 2' is
the instantaneous nominal interest rate in terms of domestic currency; 7" is the
constant real interest rate in terms of tradable goods.9; Wt the is money wage

rate. Notice that in Eq.(1.2.5), household’s expenditure includes the opportunity

 

8If we define nominal financial wealth, money balances and the stock of bonds as A, M and
B, respectively, then real variables can be defined as follows; a = 5%,, m = 73%,, and b = 33%,.

9Since we assume that PT = 1 and is constant, 1' is also the world nominal interest rate.

13

cost of holding real money balances, im.
In order to carry out consumption expenditures, the consumer is required to
hold sufficient domestic money. Following Feenstra (1985), the cash-in-advance

constraint which the consumer faces is thus

CtN

et

a(--—

+ CtT ) < mt, O! > 0, (1.6)

where (1 represents the length of time that money has to be held to finance con-
sumption expenditure.10 Eq.(1.2.6) implies that minimum required money bal-
ances are proportional to the value of consumption expenditures. If the nominal
interest rate, 2', is positive, the consumer will hold the minimum required money
balances. Then the cash-in-advance constraint (1.2.6) will be binding.

Using Equations (1.2.4), (1.2.5) and (1.2.6), and imposing the transversality
conditions, we can derive the household’s intertemporal budget constraint which

is given by

 

a0+/Ooo(l:::/;Dl; +yz+ g:——(Pz—1).+Tt)exp(—rt)dt = fooo (a? + C?)(1 + ait)e:cp(—rt)dt,

(1.7)
where do stands for the initial level of financial wealth. This equation says that the
household’s lifetime expenditure equals the present discounted value of its lifetime
income. At each point in time t, the representative consumer’s expenditure consists

. 0N . .
of the cost of consumpt1on, 7ft— + CtT, plus the opportumty cost of holding real

balances, itmt.

 

loThe cash-in-advance constraint can be written as m¢_ > F(a ).-_-— ft+°(£é: +CT)ds. A Taylor-

series expansion gives F(a) = a(—‘— +CT) + l(12:,(4— +07) + -, so (1.2.6) can be interpreted
as a first-order approximation

14

The decisions the consumer has to make at each point in time are how many
tradable and nontradable goods to consume and how much to work. Therefore,
the consumer’s optimization problem is to choose the paths of CT , CtN and It to
maximize lifetime utility,(1.2.1), subject to initial wealth, a0, and the intertemporal
budget constraint, ( 1 .2.7).

The first-order conditions for this optimization problem are11

 

 

 

UCT(CE",CtN,zt) = NH mi) (1.8)
t
1+ai
(101/(Cf ,0.” .t) = M ‘1 (1.9)
t 3t
UCg‘(C$ngvrlt)
2 et 1.10
UCtIV(CtTrCN1lt) ( )
Wt
U T N r = ,\ 1.1
lt(Ct act a t) (EtPT), ( 1)

where A is the (time-invariant) Lagrange multiplier associated with the house-
hold’s intertemporal budget constraint (1.2.7). As usual, it can be interpreted as
the marginal utility of wealth. Equations (1.2.8) and (1.2.9) indicate that at an
optimum, the consumer equates the marginal utility of consumption of tradable
and non—tradable goods to the marginal utility of wealth times the effective prices
of goods. The effective prices of goods consist of the market prices, unity in the
case of tradables and El; in the case of non-tradables, plus the opportunity cost of

i

holding the a units of money that are needed to purchase both goods, at and a e t’

respectively. Equation (1.2.10) is the familiar condition that at an optimum the

 

11To eliminate inessential dynamics and ensure the existence of a steady state, we assume
that B = r.

15

marginal rate of substitution between tradable and non-tradable goods is equal
to the relative price of tradable goods in terms of home goods which is the real
exchange rate. Equation (1.2.11) is the Euler equation for optimal labor supply.
It ensures that the marginal disutility of labor (due to forgone leisure) equals the
marginal utility from consuming the extra income from another unit of labor sup-
plied. The term (1 + ait) generated by cash-in-advance constraint must be treated
with special attention in this model. This is the usual monetary wedge due to the
fact that any form of wealth has to be liquidated before goods can be purchased.
Even if this monetary wedge increases the eflective price of consumption, it does
not affect the price of leisure.

In order to obtain a closed form solution, we assume the following instantaneous

utility function
U(C?.CIV,1.) = 7109(Cf)+(1- 7)log(C§V) + plogu — It), (112)

where p > 0. Then, first order conditions are

 

 

 

 

'5? =.- 1(1+ ait) (1.13)

10:13 = M1 2“") (1.14)
(”313‘ = 1%,- (1.15)

1 f It = ”(3%) (1.16)

Using (1.2.14) and (1.2.16), we can get

p l—w

__ = 1+az' *1. 1.17
1 _ It Cgv PtN( t) ( )

16

From Eq.(1.2.17) we can see that individual’s optimal labor supply is depen-
dent on the nominal interest rate. Since the nominal interest rate introduces a
distortion between consumption and leisure, a change in the interest rate makes
the consumer substitute leisure for consumption due to the change in the effective
price of consumption. This, in turn, leads to a change in the long-run level of

non-tradable output.

1.3.2 The government

The other participant in this economy is the government. Since Ricardian equiv-
alence holds in this model, we can assume that the government runs a balanced
budget in every period. We also assume no government spending. With these
assumptions, we can simplify government behavior. It is assumed that the govern-
ment holds internationally tradable bonds (international reserves) which pay the
world real interest rate in terms of tradable goods and issues non-interest bearing
debt (domestic currency).

The evolution of the government’s stock of net foreign bonds is governed by
the following differential equation

Mt

h=rh-r+——-—, 1.18
t t t PtTE ( l

where ht is the government’s stock of internationally tradable bonds (international

reserves). Notice that 13%,;— is the government’s seignorage profits. Integrating
t t

2

equation (1.2.18) imposing the transversality condition,1 we can derive the gov-

 

12The appropriate transversality condition is limtqoo htezp(—rt) = O.

17

ernment’s intertemporal budget constraint

(X) 00
/ 'rteccp(—r‘t)dt 2 ho + / (m + ctmt)e:rp(-—rt)dt, (1.19)
0 0

where ct = g: is the nominal rate of depreciation and ho is the initial level of the
government’s stock of foreign bonds.13 The government’s intertemporal budget
constraint indicates that the present value of transfer expenditure has to be equal
to the initial stock of government-held international bonds (i.e., international re—
serves) and revenues from seignorage. By equation (1.2.19), we implicitly assume

that the government returns to the consumer all of its revenues.

1.3.3 The aggregate supply side

We now turn to the supply side of the economy. For simplicity, we assume that
the supply of tradable goods is exogenous and fixed at the constant level yT
(i.e., y? = yT for all t ) and its domestic price will be determined by the law
of one price.

In this model, it is assumed that the non-tradable goods sector is imperfectly
competitive and there is a continuum of imperfectly competitive firms indexed
by z E [0, 1]. Each producer produces a differentiated good and acts as a monop-
olistic competitor, choosing the nominal price and the level of production of the
good.

Given the CES non-tradable consumption index, Eq.(1.2.2), an individual’s

 

13The government’s seignorage revenue 3% is equal to Tilt + ctmt in real term (in terms of
t
tradable goods).

18

demand for non-tradable good z in period t is

ON M”? ’1 90.” . (1.20)

where 6 is the price elasticity of demand.

According to Eq.(1.2.20), a monopolistically competitive firm that produces a

non-tradable good faces the downward—sloping curve

11%) = [91195311909 A, (1.21)

where C’tNAdz = fol Cgv dz -

CtN is aggregate per capita non-tradable goods

consumption.

Labor is the only input into production. The technology available to firms is

identical and is linear in labor:

319(2) = It. (122)
Firm-z’s profit is
we) =m<z>yi<z> — wit. (1.23)

At any time t, a monopolistically competitive firm maximizes profit, Eq.(1.2.23),

subject to the demand function, Eq.(1.2.21), and the production function, Eq.(1.2.22).

Solving the firm’s problem:

0 _ 1
—6—ly , y9(z )PtNC9— _ W. (1.24)

Since the elasticity of demand, 1/6, of all non-tradable goods is identical and

every producer has the same technology, they produce the same level of output

19

and set the same price. Therefore, for any two producers, O < z < z’ < 1
N
y. (z) = give!) = yi"

PM?) = 195(5) = piv- (1.25)

It follows that non-tradable good’s aggregate supply and price index simplify

to
AN 1 N N
yt =_/0 yt (Zld2=yt
PtN = [folpf’n‘BMd/le—if’ =14”. (1.26)
The equilibrium of non-tradable goods can be obtained by Eqs.(1.2.21) and
(1.2.25)
y,” = 0,”. (1.27)
Therefore, from Eq.(1.2.24)
1959) = 6—3—1Wmfz. (1.28)

Equation(1.2.28) shows that producer with market power sets prices above
marginal cost, which is the money wage rate. Thus if it cannot adjust its price it is
willing to produce to satisfy demand in the face of fluctuations in demand. There-

fore, in the short-run, if the price is sticky, output will be demand-determined.

1.3.4 A symmetric steady state
In the model, perfect capital mobility is assumed. It implies that
it = T+€t. (1.29)

20

In the steady state, all prices are fully flexible. Thus the symmetric equilibrium
implies

C,” = y,” = {‘N,Vz. (1.30)

In the steady state where all prices are fully flexible, the supply condition deter-

mines the level of non-tradable output. It means that the long-run level of output

is totally dependent on labor supply. Using Eqs. (1.2.17), (1.2.28) and (1.2.30),

we get the symmetric steady state level of output of non-tradables

p 0 . _
1_,y)(9_1)(1+01933)l 1, (1.31)

 

y§§=ll+(

where 2'33 = r + 633 is the steady state level of nominal interest rate. In the
steady state, all prices are fully flexible and all exogenous variables are constant.
Therefore, the long-run level of non-tradable output is determined by the supply
side. According to Eq.(1.2.31), however, we can see that non-tradable output
depends on the nominal interest rate, which is also a function of the monetary
policy variable, the devaluation rate. The reason is as follows. Since the nominal
interest rate introduces a distortion between consumption and leisure, if there is
a permanent decrease in the nominal interest rate, the household will substitute
leisure for consumption due to a lower effective price of consumption. This, in turn,
leads to a rise in the long—run level of output as in Lahiri(2001) and Roldos(1997).14
This result is consistent with the disinflation scenario of Cooley and Hansen (1989,

1995) in a closed economy model in which variations in the rate of inflation can

 

l"Their models, however, are based on Arrow-Debreu economy. Thus, the welfare implication
of disinflation policy implied our model will be different from their models.

21

affect the steady state labor supply and consumption (or output).

In this model, each producer has monopoly power, so the long-run level of non-
tradable output is lower than the socially optimal level. To see this, let’s look at
the social planner’s problem. The social planner tries to maximizes the utility of

non-tradable consumption considering the disutility from labor supply.15

axle — 7)10gyN — plogu — 19)]. (1.32)

The solution is

N: 1—7 N
313 (1—7+P) > 3133: (1:33)

From Eq.(1.2.33), we can see that the equilibrium output of non-tradables is
inefficiently low under imperfect competition. This fact has important implications
for economic fluctuation as well as monetary policy to stabilize it, as long as prices
are not perfectly flexible because of menu costs or staggered price or wage contracts.
Since the market equilibrium is lower than the socially optimal level, recessions
and booms have asymmetric effects on welfare (Mankiw, 1985). Since equilibrium
output is less than socially optimal level, a boom brings output closer to the social
optimum, whereas a recession in the non-tradable sector pushes it farther away.
In this model, however, the long-run equilibrium level of output is subject to a
monetary policy variable, the devaluation rate. Therefore, a change in monetary
policy can lead the economy closer to the optimum.

In order to investigate the dynamic behavior of the current account triggered

by the policy change, consider the economy’s dynamic resource constraint. To

 

15Remember that by the production condition yN = l.

22

obtain an economy’s dynamic resource constraint, combine the consumer’s dynamic
budget constraint with the profit of the firm and the market clearing condition for

the non-tradable goods sector, then
is, = rkt + yT — 6?, (1.34)

where kt = bt + ht which is the total amount of foreign bonds held by the economy.
Equation (1.2.34) represents the economy’s current account balance. It indicates
that the current account balance is the difference between tradable goods income
and consumption of tradable goods.

Combining Equations (1.2.7), (1.2.22), (1.2.14) and (1.2.24) yields the econ-

omy’s intertemporal constraint

oo 00
k0 + / yTexp(—rt)dt = / ctTezrp(—rt)dt, (1.35)
0 0

where k0 denotes the economy’s initial stock of foreign bonds. Equation (1.2.35)
states that the initial stock of foreign bonds plus the present value of all future
tradable output must equal the present value of tradable consumption. At the
steady state, C? = 037;. Therefore, (:37; = yT + rim and the current account is

balanced at the steady state.

1.3.5 Staggered wage contract and short-run dynamics

So far, we have assumed flexible prices and solved for the long-run equilibrium.
We now introduce the assumption that the price level of the non-tradable good
is sticky because of staggered wage contracts and are ready to consider the short-

run dynamics of the economy. In the short-run, the supply of non-tradable goods

23

will be demand determined and prices will be given by a modified version of the
staggered-price model of Calvo (1983) and Ghezzi (2001), including backward-
looking indexation consistent with our discussion in Section 1.1. We assume nom-
inal wages are sticky as a result of staggered wage contracts.

Following Calvo (1983), we assume that each individual can change wages only
when a wage signal is received. If individuals do not change the wage or is setting
a new wage at time t, the probability (density) that the wage will last for s more

periods is given by the geometric distribution
66:1:p(—6s) (1.36)

and is, therefore, independent of t and of the amount of time the wage has lasted
at t. And it is also stochastically independent across the individual wage set-
ters.The expected length of a wage duration is 1/6. Therefore, nominal wages
specified by the contract will be fixed for the duration of the contract and the
contract itself is staggered.

The aggregate (log of) newly posted wage level is

t
wt = 6/ :rsexp(—6(t — 3))ds, (1.37)

where wage set at time 3, 3:3, is weighted by the probability that it continues in
effect at t, ezp(—6(t — s).16
For analytical simplicity, we assume that at any time t, there are two types of

wage contractors: half of the individual contractors set their nominal wage in a

 

16Since price is a fixed markup over wage, there is no distinction between wage and price in
this model.

24

purely forward -looking manner and half of them set in a backward-looking manner.
By this mechanism we can easily incorporate the backward-looking indexation,
which is proposed by Taylor (1980), into the Calvo model.17

The forward-looking wage contractor will set wages according to the standard

Calvo model
F °° N
961 = 6/1 [ws + «50026? -10gyss)lexp(-5(s - t))ds, (138)

where ()5 reflects sensitivity of contract wages to future excess demand conditions (log of,” —
log yg), where 31% is the steady state level of non-tradable output. According to
Eq.(1.2.38), we can see that when setting a contract, forward-looking agents will
take into account the future average wage level and excess demand during the
length of contract.

For the other half of the contractors, wages are assumed to be set according
to a backward-looking rule. Specifically, we assume that the wage contract at t
indexes money wages to the current aggregate wage level plus a weighted average

of past inflation and current excess demand conditions.

1
$13 = wt + 3771 + M10261” - 10g 119.7). (139)

where cp(> 0) reflects the sensitivity of the current money wage to the current level

of excess demand, and

t
m = (if—00 nsexp(—6(t — 3))ds (1.40)

 

17In original Taylor models, current wage is set according to the past wage level and expected
future wage rate including past and future excess demand condition. Thus, Taylor models can
generate wage level inertia.

25

7'71 = 5(«1— m)- (1.41)

Equation (1.2.40) indicates that backward-looking wage contracts at t index

current nominal wages to the current aggregate wage level, a weighted average

of past inflation m, adjusted by 1 / 6, which is the expected length of the price
(1.18

duration, and the current level of excess deman

Therefore, the log of wage set at time t is
1 F 1 B
(It = Ext + 511% . (1.42)

At any point in time at which every variable is continuous, we can differentiate

Eq.(1.2.37) with respect to time to get19
7ft =wt =5l1‘t-wtl- (1°43)
Combining (1.2.38), (1.2.39), and (1.2.42)

1 1 1 °°
z. = grwt+3m+so<log cii—Iogyéi)1+§[6/t (w.+¢(1ogc§_rogygg))..p(_a(._t))ds).

(1.44)
Differentiating (1.2.44), we obtain the changes in the newly set wage rate
$t = 27ft - 771 - 5(90 + @0084” — 108 3133) + §<P108 C, - (1-45)

In order to obtain non-tradable inflation dynamics, differentiate (1.2.44) with

respect to time and substitute it into (1.2.45)

1r: = 5(7rt — m) - 3(2) + 49001161 -10gyss) + 554mg 0. . (1-46)

 

18In equation (1.2.41), the adjustment parameter is not necessarily equal to 6. It could be c 7E 6
and, therefore 77, = c [:00 7r,e:rp(—6(t - 3))ds. For simplicity, we just assume c = 6. See
Ghezzi(2001) .

19 1r; = log PN = log W,

26

This is the equation for the inflation dynamics. Eq.(1.2.46) indicates that
change in the rate of inflation is dependent on two sources. First, it depends on
the excess demand conditions: the change of inflation is negatively related to ex-
cess demand. The second term of (1.2.46) shows this relation. This is the same
result as Calvo (1983) and Calvo and Végh (1993, 1994a). The intuition for this
higher order inverse Phillips curve is that if there is excess demand at t, individuals
who revise their wages at time t set higher wages. Therefore, the higher excess
demand at time t, the higher the rate of inflation will be. However, since agents
set their nominal wages in a forward-looking manner, wage setters at s > t do not
take excess demand at time t into account. Hence, the higher the excess demand
at t, the greater the reduction in the inflation rate for s > t will be.

In equation (1.2.46), we can see that there is another source for the change of
the rate of inflation. It shows that current inflation depends on a weighted average
of past inflation. Especially, when averaging past inflation, the inflation rate in
the recent past receives more weight which is the same formulation as adaptive
expectations. If current inflation is lower than m, an average of past inflation, the
newly contracted wage has the lower premium over the current price level, which
will be translated into lower inflation. This makes inflation sticky. The first term
on the right-hand side of (1.2.46) represents this relation. The change of aggre-
gate demand in the non-tradable good sector affects inflation positively. This is
the original Phillips curve mechanism. In this regards, equation (1.2.46) can be

interpreted as a traditional Expectations-Augmented Phillips curve.

27

In this model, there is another source for inflation dynamics. In contrast to a
constant steady state level of non-tradable output as in Calvo and Calvo and Végh
models, the long-run level of non-tradable output is subject to nominal variables,
the devaluation rate, since the nominal interest rate introduces a wedge between
consumption and labor supply. Therefore, non-tradable output shows different dy-
namics with respect to the policy change in this model. The wage contract implies
that the nominal wage has its own persistence in addition to the inertia in the
driving term, which is the change in the level of excess demand. By this specifica-
tion, we can overcome the inability of the standard-new Keynesian contract model
to generate significant inflation persistence.

In order to analyze the dynamic system of the economy, we will need to obtain
the equilibrium path of consumption of tradables and non-tradables. From Eqs

(1.2.14), (1.2.16) and (1.2.31), we can see that

 

0,1” = }(1+a1.)-1 (1.47)
C,N = 1;7e,C,T, (1.48)

and
_ '7 [000(1 + ait)‘1 exp(—rt)dt
k0 + %yT

is the shadow value of wealth, which is constant as long as there is no policy shocks

1 (1.49)

 

to the economy. From Eqs.(1.2.47) and (1.2.48), we can obtain that

log Cir = C — ait (1.50)

 

+ log (I? + log et, (1.51)

1..
logCtN = log 7 7

28

where C = } is constant.

Differentiating (1.2.51) with (1.2.50) yields
log CtN = log ét — at}. (1.52)
By definition, 6,: = 12561—1. Therefore,
t
10g ét 2 ct —- 7rt. (1.53)
Using the fact that it = rit, we can obtain
log C,” 2 (ct — 7rt) — arit. (1.54)

In the short-run where all prices are sticky, the equilibrium level of employment
is demand-determined. Therefore, non-tradable output is also demand-determined.
It implies

log ytN = log CtN . (1.55)

Combining (1.2.54) and (1.2.46) with the equilibrium condition of non-tradable

goods, we can obtain the differential equation governing the change of rate of

inflation

26 6<p
—2+a6cp(7rt—m)+ 05¢(5t—7Tt)

 

 

_ 520p + ¢)

N N
— O 1.
2 I 06¢ (logyt 1031/33) ( 56)

7ft
Then, the change of non-tradable good can be obtained as

- 206 2 0.6% + <1)
N _ _ _ _ _______
t _ 2+a6<p(7rt 0t) + 2+a6<p<€t 7ft) + 2 +a6<p

 

 

(log 11%" - log 219$)-

(1.57)

29

Therefore, dynamics of the economy consist of three-equation system [Eqs.
(1.2.41), (1.2.56), and (12.57)], in output of non-tradables, ytN, inflation of non-

tradables, rrt, and m, a weighted average of past inflation.
1.4 Exchange rate-based stabilization

This section studies the effects of stabilization policies. We will examine the effects
of an exchange rate—based stabilization. First, we consider the credible stabilization
plan in which the reduction of the devaluation rate is believed to be permanent.
Next, the effect of the temporary reduction in the devaluation rate is considered.

Suppose that, prior to any stabilization (for t < 0), the devaluation rate is 6H ,

and is expected to remain at that level forever. For a given devaluation rate 6H ,

the economy is at a steady state characterized by

i33=T+€H

H
7933 = 7733 = 5

 

cl! = 179.133.»: [1+(,_f,>< )(1+a...)1-1 (1.58)

9—1
C£=yT+rk0

<—’ >959.
1—7 03;

At a steady state, consumption of tradable goods is equal to its permanent

333 =

income level, while consumption of non-tradables equals its full-employment level.
The full employment level of non-tradables is less than the socially efficient level
due to the imperfection in the non-tradable sector. However, this full-employment
level of output is not constant. Monetary policy which affects the nominal interest
rate can change the long-run level of non-tradable output. Nominal variables (the

interest rate and the rate of inflation) are growing at the devaluation rate, CH.

30

The real exchange rate is equal to the ratio of the steady state consumption of
non-tradables to tradables.

To examine the transitional adjustment of the economy, we have to consider the
dynamic system. The system is characterized by the differential equations (1.2.41),
(1.2.56), and (1.2.57) with three variables log y, 7r and 17. Since the system is linear,
we do not need any approximations.

The dynamic system for log y, 7r and 77 is

logy.”

7i.

7i.

' 52(7)» ) 2(1+ 6) 20.5”

a ,. ’p — ”a 7.- logyiV-logyi‘l

= M M _2_5 X 7ft—6t , (1.59)
rt u

p
L 0 —6 6 Vit—ft

 

 

whereu=2+a6cp>0

Now, we need to investigate the stability of the system. It exhibits two con-
vergent (non-positive) roots and one explosive (non-negative) root (see Appendix
A.1.1). At time t, current inflation, m, is given by an average of past inflation,
current excess aggregate demand and future economic conditions, including future
inflation. Therefore, 7rt becomes a jump variable at time t even if it cannot adjust
immediately to a new equilibrium value. The partial forward-looking indexation
(half of households set the new wage in a forward-looking manner) makes inflation
jump initially to the point between the new steady state and the initial steady
state after a shock. And log ytN is also a jump variable (notice that by the equi-
librium condition, log ytN = log cf! ) However, as one can see in (1.2.35), 77¢ is a
predetermined variable. Thus, there is one predetermined variable ( 7)) and two

jump ( 7r and log yN) variables. However, since the jump of log yN is exogenous to

31

the solution of (1.3.2), the system exhibits saddle path stability.20 Also the roots
may be complex conjugates, and the system may show cyclical dynamics.21

Since the system has three variables, it will be difficult to analyze the equilib-
rium paths. However, it is possible to see the exact transitional dynamics of the sys-
tem by resorting to the methods of dominant eigenvalue proposed by Calvo (1987).
The system has two non-positive roots and one non-negative root. Let 11,-,71 = 1, 2,
be the non—positive roots and V3 be the non—negative root, with 111 > V2 ( V1 is the
dominant eigenvalue). Setting to zero the constant corresponding to the unstable

root ( 113),22 the solution to dynamic system (1.3.2) can be expressed as:

10g 311” — 108 yfi, =A1w11 eX13049) + A2w21 6XP(V2t)
7ft - ft =A1w12 eXI)(I/1t) + A2w22 eXP(V2t) (1-60)

771 - ft =A1w13 eXP(V1t) + A2w23 eXP(V2t),

where A232 = 1, 2, and wij, j = 1, 2, 3, denote the constants and the element of the
eigenvector associated with root 12,-.

From the assumption 14 > V2, it follows that (see Appendix A.1.2):

1 N —1 N
lim Ogyt 0“” = 9311- > 0. (1.61)

t—->oo 7ft — ct (1)12

 

This implies that as t becomes large, if the initial value of log yN and 7r are not on

- - . 10 N —l N
the ray correspondmg to solutlon, V2, then the ratio of “tut—6:3 y”

 

will converge

to the slope of the dominant eigenvector ray ( gall-g»), which is positive. It implies

 

”See, Ghezzi (2001).

”For more detail, see Blanchard and Khan (1980) and Turnovsky (1995).

22It is clear from the transversality condition that a necessary condition for convergence of the
system is that 113 = 0.

32

that, graphically, the system will converge asymptotically to the dominant eigen-
vector ray. Figure 1 shows the phase diagram for log y?” and 7rt with the dominant

eigenvector ray.

1.4.1 Permanent reduction in the devaluation rate

Consider the impact of a once—and-for-all reduction in the rate of devaluation. The
case corresponds to the credible disinflation that the public believes the devalua-
tion rate to remain at the lower level for the future.

At the initial steady state, 6 = CH. At t = 0, the authorities announce the

following policy that is unanticipated:

et=cH,fortSO

ct = 6L, for t > 0,

where EH > CL
According to Equation (1.2.29), on impact, the nominal interest rate jumps to

a new level, 1" + EL, falls by the same amount as the rate of devaluation. Since
the reduction in the rate of devaluation is fully credible, the public believes that

nominal interest rate remains at the lower level, 1" + 6L, forever.

From Eq.(1.2.49), if the nominal interest rate is constant over time,
'7 . —1
= ——-—-- 1 + a2 . 1.62
.1 + 31,1 ) ( 1
Hence, Eq.(1.2.47) with (1.3.5) implies

CT = rko + f. (1.63)

33

The consumption of tradable goods is constant over time. By (1.3.6), CT is

equal to its permanent income level. The reason is as follows Even if the nominal
interest rate is reduced, it is constant over time at the lower level, which implies
the constant effective price of tradable consumption at the lower level. Hence, the
consumer does not have any incentives to engage in intertemporal consumption
substitution. This implies that the current account does not change at all during
the transition to the new steady state. As implied by (1.2.48), the consumption of
non-tradables does not change on impact as well because the real exchange rate is
predetermined. However, this result depends on the specific form of utility func-
tion and is not a general case.23

Inflation also falls on impact. The forward-looking contracts make the inflation
rate jump on impact. The inflation rate, however, will jump to a point between 6H
and EL. This is due to the backward-looking indexation of wage contracts.24 The
initial impact effect of the reduction in the rate of devaluation on inflation and
non-tradable output is shown in Fig 1—3. The initial impact implies a movement
from the point of 350 to A.

However, this shows the partial effect of the reduction in the nominal interest

rate on consumption and output. The reduction in the nominal interest rate implies

from (1.2.17) and (1.2.31) that non-tradable output does increase after the initial

 

23If the intertemporal elasticity of substitution is grater than the intratemporal elasticity of
substitution, tradable consumption will increase on impact and there will be the initial jump of
the non-tradable consumption. Therefore, the change of consumption on impact is dependent on
the relative magnitudes of the elasticities of intertemporal and intratemporal substitution. In our
model, both elasticities are equal to 1. Hence, there is no jump of the tradable and non-tradable
consumption; see Calvo and Végh (1994b)

24According to Ghezzi (2001), the size of jump of the inflation rate depends negatively on the
degree of backward-looking indexation

34

impact. The reduction in the nominal interest rate that constitutes reduction in
the monetary wedge generated by the cash-in-advance constraint. This increases
consumer’s labor supply, which induces output expansion in the non-tradable sec-
tor. Hence, by the market-clearing condition of non-tradable goods, consumption
also increases on impact. Since the greater labor supply implies more labor income,
the consumer will increase demand for non-tradables. This permanent increase in
labor supply triggers a positive wealth effect. Therefore, the supply-side effects of
disinflation come in through the change in the labor supply.25

The effect of the reduction in the rate of devaluation on inflation and non-
tradable output is shown in Fig 1-1. The steady state moves from 350 to S 31, the
steady state rate of inflation falls from 6H to EL, and steady state non-tradable
output is higher than it was before the reduction in the devaluation rate. At
point A, inflation starts to fall. Non-tradable output (consumption) also begins to
increase. The economy will move asymptotically to the dominant eigenvector ray,
and proceeds towards the new steady state, S 51.

During the transition, inflation converges to 6L slowly and shows substantial
persistence. This is due to the backward-looking indexation of wage contracts.
This result is broadly consistent with the scenario of inflation inertia described
by Rodriguez (1982), Dornbusch (1982), and Calvo and Végh (1994b). In their
models inflation exhibited considerable inertia even if the disinfiation program was

fully credible. However, these sticky inflation models can not reproduce the styl-

 

25In Argentina (1991-1994) and Mexico (1988-1992), the labor participation rates seems to rise
after the stabilization;see Roldos (1997).

35

ized fact of an initial boom after exchange rate-based stabilization. Specifically, in
Calvo and Végh, the initial consumption expansion depends on the elasticities of
intertemporal and intratemporal substitution. In our model sticky inflation com-
bined with supply side effect can mimic one of most important stylized fact of
stabilizations, the initial boom. After the initial boom, non-tradable output (or
consumption) expands up to the new steady state. The economy experiences a
sustained expansion in the domestic sector through the labor supply effect. These
results are quite consistent with the evidence of the successful stabilizations with
a high degree of credibility in Mexico(1988-1992) and Argentina (1991-1994) [See
Roldos (1997)]. The distinguishing feature of this model compared to the previous
ones is that disinflation produces a sustained expansion even if inflation shows
persistence.

The dynamic adjustment of the main variables is illustrated in Figures 1.4 to
1.9. The first thing we have to notice in this simulation is the movement of the real
exchange rate during adjustment. Due to the sticky inflation, the rate of inflation
remains above the nominal devaluation rate for some time. From (1.2.53), we can
see that the real exchange rate appreciates, which is one of the main stylized facts
in exchange-rate based stabilization. In this model, real appreciation co—exists with
the expansion of the domestic sector. Another interesting result is that inflation is
below the nominal anchor’s growth rate (the rate of devaluation) for some period
of time: inflation shows undershooting. The reason is as follows After disinflation

is implemented, the real exchange rate appreciates due to the sticky inflation. To

36

achieve a high level of non-tradable output (or consumption), however, the real
exchange rate should be higher (real depreciation) in the new steady state than in
the initial steady state since

N
yssl

W. (1.64)

6331 =

For a subsequent real depreciation, some period of inflation below 6 L is required.

This result follows from the fact that
ét = €t(€t — 7ft). (1.65)

The path of the real exchange rate is depicted in Figure 1.7.

It should be noted that in this model inflation stabilization proves to be welfare-
improving, Since the reducing inflation is beneficial in cash-in-advance models with
a labor—leisure choice and imperfect competition in goods market. The lower infla-
tion reduces the transaction cost of holding money. Hence it allows the individuals
more free time for productive activities: more consumption and production. In a
broad sense, disinflation is welfare improving since socially unproductive efforts to

conserve on money balances can be eliminated.

1.4.2 Temporary reduction in the devaluation rate

Consider now the implication of a temporary reduction in the rate of devaluation.
This corresponds to the case of lack of credibility: the authority announces a per-
manent reduction in the rate of devaluation, but the public believes that the rate
of devaluation will go back to its original level after a certain period of time. The

initial steady state corresponds to a rate of devaluation ct = 6H . At t = 0, the

37

devaluation rate is set to a lower level, 6L, but at time T, it is increased back to
its original level.

More specifically, for some T > 0,

ct=eL, OSt<T

ct=cH, t_>_T,

where EH > 6L.

Horn Eq.(1.2.29), we can see that the nominal interest rate will be low from 0
to T, and higher after T. Thus, (1.2.47) implies that consumption of tradables, Cir,
will be high between 0 and T, and low afterwards.26 The reason is as follows. Since
the consumer expects the effective price of tradables (market price and the oppor-
tunity cost of the holding money) to be lower between 0 and T than after T, he or
she will engage in intertemporal consumption substitution. Hence, consumption
will be increased during the interval [0,T) and lowered after T.

The economy’s intertemporal budget constraint implies that before the stabi-
lization policy is reversed, consumption of tradable goods is larger than permanent

income, while consumption of tradables is lower than the initial permanent income

after T. This implies

C£>yT+rk0, OSt<T

C}: < yT + rko, t Z T. (1.66)

 

26By Eq (1.2.49), we can see that A will be constant during the transition.

38

The time path of the current account is given by Eq.( 1.2.34). The increase in
the consumption of tradables the permanent income induces the current account
to jump into deficit. During the transition, the current account deficit will be
larger steadily since the interest rate income on net foreign asset declines. When
the stabilization is abandoned, 0? goes down below permanent income and brings
the current account into balance. The time path of the consumption of tradables
and the current account are illustrated in Figure 1.15, and 1.16 respectively. This
is quite consistent with the deterioration of the current account balance observed
11 the early stage of the Southern-Cone stabilization.

We now turn to examine the behavior of non-tradable output and inflation.
On impact, non-tradable consumption jumps, unlike the case of permanent dis-
inflation. We can see this from Eq.(1.2.48). Since the real exchange rate is pre-
determined, the increase in the consumption of tradable goods induces the non-
tradables to jump on impact. This is consistent with the stylized fact of Southern-
Cone exchange rate-based stabilizations in which consumption and output expand
at the beginning of the programs. Inflation also falls. However, the size of the
initial jump of inflation will be smaller than the permanent case. This is due to
the lack of credibility. The public believes that the money growth rate will revert
to the original level which is higher than it is now. The initial effect will be a move
from $50 to A in Fig.1.8.

After the initial impact, non-tradable output (or consumption) starts to in-

crease. For 0 < t < T, the nominal interest rate will be lower than after t 2 T.

39

The households supply more labor to the non-tradable sector during the transition
than after the policy reverts to the original level. Therefore, non-tradable output
will be higher during the transition. This is due to the intertemporal substitu-
tion effects of labor supply. Since the inflation is above the devaluation rate, the
real exchange rate appreciates. In spite of real appreciation, we observe that con-
sumption and output of non-tradables expand during the transition. This result is
different from the previous literature [Calvo and Végh (1993) and Calvo and Végh
(1994a)]. In their model, there is a long-lived recession after the initial boom in
non-tradable output until the policy is reversed. This is manly due to the fact
that the supply-side effect of disinflation is not considered. Inflation also begins to
increase as the public expects higher inflation in the future. The expected inflation
rate will be incorporated into the wage contracts, especially into forward-looking
contracts. This induces the rate of inflation to keep increasing.

During the transition, for 0 < t < T, the system will be governed by the

dominant divergent path (See Appendix A.1.3).

, 10g 11%” - log 319$, (.13,
11m = —.
t-aoo 7ft - #H 0032

 

(1.67)

In this model, the sign of 5%, the slope of divergent path, is ambiguous [see
(A.1.11)]: it can be positive or negative. However, even if the slope is positive,
it is flatter than the dominant eigenvector ray (in new steady state). Therefore,
the transitional dynamic of the system can not be affected by the indeterminacy.

Figure 1.10 depicts the transitional adjustment of non-tradables and inflation. The

40

direction of motion is indicated by the arrows.27

At T, the rate of devaluation reverts to 6H . The economy now converges to the
dominant eigenvector ray and moves to the original steady state. As the nominal
interest rate goes back to the original level, the households decrease their labor
supply. Thus, non-tradable output (or consumption) also shrinks and the recession
sets in. Since the policy is reversed at T, expectations adjust and inflation starts
to fall, converging to the original level. This result highlights the importance of the
policymaker’s credibility. The credibility of policy will affect people’s expectations,
and produce unpredicted results.

The dynamic path of the main variables is depicted in Figure 1.11 to 1.16.
One of distinguishing features of this policy relative to the credible one is that
the temporary policy induces the current account deterioration. The movement of
tradable consumption and current account dynamics are illustrated in Figure 1.15

and 1.16.
1.5 Concluding remarks

This paper has extended Obstfeld and Rogoff’s dynamic general equilibrium Mundell-
Fleming model to allow for sticky inflation in a way that can be used to analyze
the effect of exchange rate-based stabilization.

The large theoretical literature has provided useful insights into different as-

pects of both failed and successful exchange-rate based stabilizations. The model

 

27In Figure 1.10 we assume that the divergent path is negatively sloped. However, as is
mentioned in the main text, we observe the same transitional path under a positively sloped
divergent path.

41

presented in this paper can replicate the stylized facts observed in both failed and
successful disinflation programs within a single analytical framework. In that re-
spect, this study is quite successful.

This paper also has a very important policy implication for inflation stabi-
lization. As illustrated in the main text, stabilization, even if it is fully credible,
is always accompanied with inflation persistence. Therefore, the inflation inertia
during the program does not necessarily mean the possibility of failure if backward-
looking indexation in price or wage setting exists. Therefore, as long as the policy
maker continues to pursue its goal, he or she can reduce inflation without any
output cost: he can improve welfare. Another piece of advise for the policy maker
implied in this paper is that the economy’s indexation mechanism should be al-
tered to accommodate rapid disinflation before the stabilization is launched.

This paper can be extended in several ways. First, it can be applied to the
money-based stabilization under the flexible exchange rate. And another promis-
ing way would be to adapt the model to analyze the effect of interest rate policy
on the economy including capital flows. For this, the model must explicitly incor-
porate capital accumulation.

In this paper, we assume the degree of backward looking indexation for analyt-
ical simplicity. However, the degree of indexation has a significant implication for
the economic welfare during the stabilization. As the degree of indexation declines,
the model predicts the rapid convergence of inflation. This will enhance the welfare

effects of inflation stabilization. To study the relationship between the the degree

42

of indexation and economic welfare of inflation stabilization is also promising.

43

1.6 Appendix
1.6.1 The stability of Equation (1.2.59)

The stability of the system requires that among the eigenvalues of the matrix
associated with dynamic system (1.2.59), one has a positive real part and two
eigenvalues have negative real parts.

The eigenvalues A;,z’ = 1, 2, 3. of the system

log yg"
1ft.
771
a62(¢+<p) 2(1+a6 2 a
11 — 1. % log 11%" - log 119$
= 62g¢+g) rim-2) _g§ X 7rt — ct (1.68)
n ” p 1it — 61
0 —6 6
have the following properties
63
det(A) = A1A2A3 = 77 > 0 (1.69)
52
/\1/\2 + A2/\3 + A1/\3 = —-;(¢ + 016) < O (1.70)
Tr(A)2 — 4det(A)0. (1.71)

From (A. 1.2), we can see that the three eigenvalues are positive or one is positive
and two are negative. Horn (A.1.3), the case of three positive roots can be ruled
out. As a result, the system has two negative roots. Furthermore, according to
(A.1.4), the eigenvalues may be complex conjugates and the system may exhibit

cyclical behavior.

44

1.6.2 The dominant eigenvalue ray

We assume that 11,-,1' = 1, 2 is the non-positive roots, with 111 > 112. Then, for i =

1, 2, it follows that

a62]¢+<p) _ . _2 1+a6 2911
V w- 0
14 2 11 rt 11
521+ 31:21-). _21 x cur.» = 0 , (1.72)
3 fl 5 . 5 #11 “’93 0
:- - i

where wij, j = 1, 2, 3, are the element of the eigenvector associated with root 11,-.

Therefore,
fl _ [26 — 211,- — 2a611;]/11(6 — 11,-)

“’12 — [a62(¢+.p) _. Viul/u > 0- (1.73)

 

Now, let’s look at the dominant eigenvector ray. Setting to zero constant cor-

responding to the unstable root ( 113), the solution to this system takes the form

log y.” — log yf’f =A1w11 exp(V1t) + 242021 expo/2t)
7ft - 61 =A1w12 eX90119) + 1420122 eKIWI/275) (1-74)

771 - 61 =A1W13 eKIWI/11?) + A2w23 eXP(V2t).

where A;,z’ = 1,2, denote the constants associated with root 11,-. Since 111 > 112, it

follows that:

lim 103 3va -108 gig ___ lim A1&111 eXI)(l/1t) + A2&121 eXP(V2t)
t—»oo 7rt — c t——>oo Alwlg exp(111t) + Agwgg exp(112t)
___ Alain + A201221 e><I>((V2 - Vllt)
t-roo A1w12 + A20122 8XP((V2 - Vllt)

.—_5’—1—1 > 0. (1.75)
“’12

 

 

 

45

1.6.3 Properties of system for temporary stabilization

We assume that 11,-,1' = 1, 2 are non-positive roots and 113 is the non-negative one.

Then, for 0 < t < T, the solution to the system is

108 Eli” - 108 319;, =Blw11 eXI)(1/1t) + 32w21 eXP(V2t) + 330131 eXP(V3t)
7r, — 6H =Blw12 exp(111t) + nggg exp(112t) + B35132 exp(113t) (1.76)

771 - 6H =Blw13 exp(V1t) + B21523 ex100/210 + B3w33 exp(V3t),
and for t Z T

108 ytN — 108 yflo =C'1w11 eXP(Vlt) + 020121 eX13001?)
7r, — 6L =Clw12 exp(111t) + 0211122 exp(112t) (1.77)
Tit - 6L =C1Wl3 eKIWI/11¢) + 020023 eXp(V2t).
where B,- and 0,, z' = 1, 2, 3 are constants associated with root 11,-, and aw, i, j =
1, 2, 3 are the elements of eigenvector for roots 11,-.

For 0 < t < T, the system will be governed by the unstable root, 113. This

means that the system converges asymptotically to the divergent path, which is

 

 

given by
10 N — lo yN
im 83/1 8 .931 _ lim Blwll exp(111t) + ng21 exp(112t) + B35131 exp(113t)
t—»oo 1r, — 5L t-wo 811.612 exp(r11t) + 3211222 exp(112t) + B30032 exp(113t)
=fl. (1.78)
“’32

From (A.1.11) with 113 > O , we can see that the sign of 5% cannot be determined.
Even if, however, it is positive, the slope is flatter than the dominant eigenvector

ray. For t 2 T, the dominant eigenvector ray is same as (A.1.8).

46

A. Inflation and devaluation 8. Real exchange rate
2000 W WM 120 ‘ (Index W.T-181M)

1500.
1000. \

 

 

110.

 

tn---

 

 

 

 

 

 

 

 

 

 

1.2 M 1" 1+1 Ti: 1+: 7+4
Figure 1.1: Exchange rate-based stabilization
A. Real GDP growth 8. Private consumption growth
6 (percent per year) ,2 (percent per year)

 

 

   

 

 

 

 

 

 

 

 

1.2 '14 r' 11,, r'+2 {.3 7+4 1.2 1.1 1 7+1 r32 1+3 T“

Figure 1.2: GDP and consumption in exchange-rate based stabilization

47

 

 

 

 

 

 

 

log y," 10851” = 0
Dominant
Eigenvcctor ray
10814;,
1°ng SS0
B
3L 71', = a” 71',

Figure 1.3: Dynamic system of exchange rate-based stabilization

8

A

 

 

 

 

 

Time

Figure 1.4: Time path: rate of devaluation

48

 

 

 

 

 

 

 

 

 

 

 

. >
O 1, Tune
Figure 1.5: Time path: inflation
A
N
ySS,
)fsvso
D
O t, Tlme

Figure 1.6: Time path: output of non-tradables

49

 

eSS ‘. /

 

 

 

 

 

 

 

 

 

>
0 t1 Tlme
Figure 1.7: Time path: real exchange rate
0%
rk0 + yT
.
O Tlme

Figure 1.8: Time path: consumption of tradables

50

 

 

 

 

0 Time

Figure 1.9: Time path: current account

log y,” 9

Divergent log y,” = 0
P

 

   
  

N
log ySS'
Dominant
Eigenvector ray

 

 

 

 

 

b
72', = a” 71',

Figure 1.10: Dynamic system of temporary stabilization

51

 

 

 

 

 

 

Figure 1.11: Time path: rate of devaluation

at

 

 

 

 

 

 

O T Time

Figure 1.12: Time path: inflation

52

yss,

N /\

y SS

 

 

 

 

 

 

)
O T Time

Figure 1.13: Time path: output of non-tradables

 

/

 

 

 

 

 

D
0 T Time

Figure 1.14: Time path: real exchange rate

53

 

 

rko + yT

 

 

 

 

 

$
0 T Time

Figure 1.15: Time path: consumption of tradables

 

\—

 

 

 

 

’
0 T Time

Figure 1.16: Time path: current account

54

Chapter 2

Money-based stabilization

2.1 Introduction

Since the end of World War 11, many developing countries have experienced high
and persistent inflation1,which in some cases has lasted until today. Chronic in-
flation is one of the distinguishing macroeconomic characteristics of developing
countries. For the last four decades, countries afflicted by chronic inflation have
engaged in repeated inflation stabilization programs. For example, in the late
1970’s, the Southern-Cone countries, Argentina, Chile and Uruguay, implemented
exchange-rate based inflation stabilization, and Brazil and Peru in the early 1990’s
fought chronic inflation with money growth rates. Unfortunately, most of these
stabilization attempts have failed in the sense that they did not reduce the in-
flation rate to the international level. In the last ten years, however, countries
such as Argentina, Israel, and Mexico have succeeded in reducing inflation close to
international levels for substantial periods.

The stabilization plans implemented in the last four decades, whether they were

 

1Pazos(1972) refers to this phenomenon as “chronic inflation”. According to his analysis,
chronic inflation is relatively high compared to industrial countries and persistent. Moreover,
chronic inflation does not have an inherent propensity to accelerate.

55

successful or not, have provided a lot of issues and puzzles to macroeconomists.
The common stylized fact we observed in the stabilizations, both exchange rate
based and money-based programs, is inflation persistence. Contrary to the ex-
pectation of both policy makers and economists, inflation converged slowly to the
target rate and exhibited considerable inertia. The most intriguing and puzzling
phenomena is the business cycle associated with inflation inertia. In exchange
ratebased programs, real economic activity, such as consumption and output, ex-
pands in the early stage of the program. Later in the program, even before the
program is abandoned, consumption and output shrink and the trade balance goes
into deficit, so recession sets in.2 This boom-recession cycle of exchange-based sta-
bilization programs was a puzzle to conventional macroeconomists who believed
the stabilization should have resulted in an immediate contraction. In the case of
money-based stabilization, the cost of disinflation comes in the early stage of the
program.

A lot of theoretical research has sought to explain these intriguing phenomena
observed in the stabilization programs, especially in exchange-based programs.
Early work by Rodriguez (1982) and Dornbusch (1982) offers a simple description
of the Southern-Cone exchange rate-based programs of the late 1970s. They em-
phasized the presence of sticky inflation. Rodriguez assumes adaptive expectations

to point out the backward-looking price and wage behavior. Dornbusch assumes

 

2In Argentina, for instance, the stabilization program was launched in 1978. By the 19808,
the annual inflation rate was 88 per cent, but the devaluation rate was 23 per cent. Moreover,
the growth rate of consumption was 1.9 per cent in 1978, but in the first year of the program,
1979, it increased to 12.3 per cent.

56

rational expectations and stickiness of inflation. According to this hypothesis, un-
der perfect capital mobility, if aggregate demand depends negatively on the real
interest rate and positively on the real exchange rate (i.e., the relative price of
tradable goods in terms of non-tradable goods), reduction of the devaluation rate
decreases the nominal interest rate, which leads to lower real interest rates because
of sticky inflation. The reduction of the real interest rate induces an initial ex-
pansion of output. After that, the domestic currency begins to appreciate since
domestic inflation shows inertia and remains above the devaluation rate. Eventu-
ally, the real appreciation shrinks domestic consumption and 80 output falls and
recession sets in.

Those sticky inflation models give a lucid explanation of the phenomena ob-
served in the stabilization programs, especially inflation persistence and the boom-
recession cycle. Inflation inertia results from sticky inflation in both models. How-
ever, these early models have a critical defect. Both models specify reduced-form
behavioral equations rather than derive them. We find this very ad-hoc. In the
case of Rodriguez (1982), the model relies on non-rational behavior and inflation
stickiness is assumed, not derived as in Dornbusch(1982).

An alternative explanation to the major effects of stabilization is the “Tempo-
rariness hypothesis” by Calvo and Végh (1993, 1994). This hypothesis considers
the case in which prices or wages are sticky due to staggered contracts, but inflation
is fully flexible because of forward-looking contracts. These models are based on

the optimizing behavior of individuals. Under these circumstances, this hypothe-

57

sis argues that slow convergence of inflation and the initial boom in real economic
activity arise from lack of credibility, not from sticky inflation. Rapid convergence
of inflation, therefore, can be achieved under a fully credible stabilization policy
even if the price level exhibits stickiness. With the same assumptions, Calvo and
Végh (1994, 1999) replicate the recession-boom cycle in a money-based stabiliza-
tion with no inflation inertia.

This hypothesis seems to be successful in capturing the stylized facts associated
with the recent stabilization programs, especially exchange rate based programs.
However, these models are not successful in establishing the exact cause of in-
flation inertia. In these models, since prices are set in a purely forward-looking
manner, the inflation rate is independent of past inflation and depends only on
future (expected) inflation. Thus, inflation is quite flexible while the price level
is sticky. Therefore, credible disinflation policies can reduce inflation dramatically
without any output cost and no inflation inertia is found, which is not consis-
tent with reality.3 Also, this hypothesis cannot replicate both the initial recession
and inflation inertia simultaneously in a money-based program. In Calvo and
Végh (1999), money-based stabilizations replicate the initial contraction without
inflation persistence under the credible policy. Therefore, purely forward-looking
staggered contract models are not useful in explaining inflation dynamics when
inflation shows stickiness.

All the explanations examined so far are based on demand-side considerations.

 

3Agénor and Montiel (1999) point out that countries with chronic inflation derived various
indexation mechanisms which are quite backward looking.

58

This is due to the fact that most literature was inspired by the Southern-Cone
tabilitas of the late 19708. In the recent programs, such as Mexico’s 1987 and
Argentina’s 1991 convertibility plan, it has been argued that inflation stabilization
may have played an important role in unleashing supply-side responses in labor
and investment. This literature suggests that credible stabilization induces sus-
tained expansion of real economic activity. In Lahiri (2001) and Roldos (1997),
the nominal interest rate introduces a distortion between consumption and leisure.
When inflation falls, labor supply increases. This, in turn, leads to a rise in the
desired capital stock and, hence, in investment. These supply-side considerations
can reproduce the main stylized facts observed in the successful stabilizations (Ar-
gentina (1991-1994) and Mexico (1988-1992) in which the initial boom was not
followed by a recession.

Most literature focused on the exchange rate-based stabilizations since money-
based programs in chronic inflation countries have been much less common than
programs based on the exchange rate.4 Several authors provide a number of rea-
sons why policymakers prefer an exchange rate-based program to a money-based
one [Robero and Veg’h (1994), and Calvo and Vegh (1999)]. First, since the ve-
locity of money may be quite unstable during the stabilization, it is difficult for
a policymaker to determine the appropriate growth rate of the money supply in
practice. Second, in the transition from high to low inflation, the economy may

experience a period of deflation. Thus, policymakers will engineer a one time in-

 

4According to Reinhart and Vegh, among 17 stabilization programs from 1964 to early 1990’s,
there are only 5 money-based programs.

59

crease in the money supply to avoid deflation, which weakens the policymaker’s
credibility. Based on arguments mentioned above, it is not surprising to find that
money-based stabilization does not enjoy a high reputation in the academic liter-
ature or in practice. However, there are several reasons to analyze money-based
stabilizations here. First, stabilization programs supported by the use of IMF re-
sources have usually been money-based programs.5 Second, since most exchange
rate—based stabilizations end up in balance-of—payment crises,6 there is a need to
find possible policy instruments to bring down high inflation without triggering
crises. It should be noted that a lot of exchange ratebased stabilization programs
have failed. Therefore, for a country which experienced a series of failed exchange
rate-based programs, it could be wise to switch the anchor. Lastly, there is a pos-
sibility that successful disinflation in a money—based program might lead to the
supply side responses we observed in the exchange-rate programs.

In this paper, we consider the supply-side effects of disinflation with inflation
inertia in money-based programs within a New-Keynesian framework. To consider
the supply-side response, we introduce imperfect competition in the non-tradable
sector with endogenous labor supply. The reason we adopt imperfect competi-
tion in the model is that imperfect competition is the main characteristic of the
industrial structure of developing countries.7 Our model is based on Obstfeld
and Rogoff’s (1995)“Exchange Rate Dynamic Redux”. We modify Obstfeld and

Rogoff’s model in two ways. First, we assume a small-open economy with a cash-

 

5See Agénor and Montiel (1999).
6See Calvo and Veg’h (1999).
7See Agénor and Montiel (1999)

60

in-advance constraint in which a change of monetary policy, including a change
of the money growth rate, has a long-run effect on the economy as in the two-
country model in Obstfeld and Rogoff. Second, we adopt a Calvo-type contracts
model to obtain the inflation dynamics. Our model is a modified version of Calvo’s
(1983) forward-looking, staggered wage contracts model. However, we incorporate
backward—looking indexation into wage contracts. We combine the staggered wage
contract with price setting of imperfectly competitive firms to obtain inflation per-
sistence. Incorporating backward-looking wage contracts into the model is quite
consistent with the wage indexation of most chronic inflation circumstances.8

We apply this model to investigate the effects of inflation stabilization in a
small open economy. We have two possible experiments, one is a money-based
stabilization which is perfectly credible and the other is temporary stabilization.
me the first experiment we are able to replicate qualitatively the stylized facts
of the money-based stabilization programs in which inflation persistence coexists
with the “recession-boom cycle”. Sticky inflation combined with supply side ef-
fects produces inflation persistence and a sustained expansion of the non-tradable
sector. In this regard, the model we present here is quite successful. It should be
noted that the resulting inflation persistence and associated business cycle have
very important policy implications. First, inflation persistence cannot be avoided

even if the policy is fully credible as long as there is backward—looking indexation

in price or wage setting. To achieve rapid stabilization, the indexation mechanism

 

8For instance, Edwards(1991) pointed out that the primary cause of inflation inertia in the
Chilean stabilization is backward-looking wage indexation.

61

should be considered. The second implication is that after the initial cost of dis-
inflation, the economy can enjoy a sustained expansion during the stabilization.
Therefore slow adjustment of inflation does not weaken the credibility of policy.
These results are not consistent with the arguments of Calvo and Végh’s (1993,
1994) “temporariness hypothesis” in which inflation persistence and associated
business cycles are merely due to the lack of credibility. For the temporary disin-
flation scenario, we see that the inflation rate accelerates after an initial decrease,
and the “recession-boom—recession again cycle” is observed.

The plan of this paper is as follows. We consider the stylized facts of exchange
rate-based stabilization in Section 2.2. We present the basic model and the equilib-
rium in Section 2.3. The impact effects and transitional dynamics of a fully credible
and temporary disinfiation policy are discussed in Section 2.4. In Section 2.5, we

draw the main conclusions. Technical derivations are relegated to Appendices.

2.2 Evidence on the real effects of money-based
stabilization in chronic inflation countries

Money-based programs in chronic inflation countries have been much less com-
mon than programs based on the exchange rate. According to Reinhart and Veg’h,
among 17 stabilization programs from 1964 to early 1990’s, there are only 5 money-
based programs. Table 2.1 shows presents the main features of five major money-

based programs undertaken in the last 25 years. The following stylized facts ob-

served in the money-based programs listed above have been identified.

62

Table 2.1: Money-based inflation stabilization plans

 

 

 

 

 

 

 

Program begin/ end date Initial / Lowest inflation
Chile 1975 April 1975 - December 1977 393.4 / 63.4
Bonex (Argentina) December 1989 - February 1991 4923.3 / 287.3
Collar (Brazil) March 1990 - January 1991 5747.3 / 1119.5
Dominican Republic August 1990 - 1999 60.0 / 2.5
Peru 1990 August 1990 - 1999 12377.8 / 10.2

 

 

 

 

Major source: Kiguel and Liviatan (1996), and Calvo and Végh (1999)

(1) Slow convergence of the inflation rate to the rate of growth of the money
supply.

(2) Initial contraction in economic activities. A sharp, though short-lived,
contraction in real GDP, consumption, and investment seems to follow the imple-
mentation of money-based programs.

(3) Real appreciation of the domestic currency.

These stylized facts are less surprising in that they seem to broadly conform with
available evidence for industrial countries. To illustrate some of these stylized
facts, Figure 2.1 shows the panel of annual observations for five countries (Ar-
gentina, Brazil, Chile, Dominican republic, and Peru) for 25 years from 1971 to
1995 constructed by Calvo and Végh (1999).9 Panel A shows that the inflation
rate falls dramatically in the first year after stabilization but begins to rise again
soon afterwards. and inflation rate does remain above the rate of money growth
rate. This evidence shows the existence of inflation persistence. Real GDP growth
falls in the year of stabilization from -3.8 to -7.3 percent, but recover soon after-

ward. The evidence is thus consistent with a short-lived but sharp contraction in

 

91n the figure 1.1 and 1.2 , time profiles are based on the stabilization time. Stabilization time
is denoted by T + j, where T is the year in which the stabilization program was implemented
and j is the number of years preceding or following the year of stabilization

63

economic activity (Panel B). The real exchange rate appreciates throughout the

program (Panel C), while the current account shows no clear pattern (Panel D).

2.3 Basic model

In this section we consider a two sector small open economy, which is perfectly
integrated with the rest of the world in goods and capital markets. First, we
introduce the demand side through the households’ maximization problem and
then the aggregate supply side in which the non—tradable sector is the locus of
imperfect competition. The next step is to solve for a symmetric steady state where
all prices are fully flexible. We, then, introduce sticky prices through staggered
wage contracts. In the last part of this section, we derive the short-run dynamic

system for the next section.

2.3.1 The aggregate demand side

Our model is based on Obstfeld and choff’s (1995) perfect-foresight general equi-
librium Mundell—Fleming model. The economy is inhabited by a continuum of
identical households which reside on the interval [0,1]. The representative house-
hold derives utility from the consumption of tradable and non-tradable goods and
leisure. This economy contains a continuum of differentiated non-tradable goods
which are indexed by z and distributed uniformly on [0,1].

The lifetime utility of typical households is given by
00
.Ut = [0 [1109(Cf)+(1- 7)109(Cfv) +plog(1 - lt)lexp(-fit)dt. (2-1)

64

where Cir is the consumption of the tradable good and CtN is a non-tradable
consumption index, defined by

1 — 0
C.” = [0 Wag—vilfldz. (2.2)

where cN(z) is the household’s consumption of good 2, ,6 is the positive and con-
stant subjective discount rate, and 0 > 1 is the elasticity of substitution between
non-tradable goods. The last term in the lifetime utility function in Eq.(2.2.1)
captures the utility from leisure or disutility from labor supply ( It represents total
hours worked by the household), and we assume p > 0.

We employ the convention of letting E represent the nominal exchange rate in
units of domestic currency per unit of foreign currency, while PT represents the
foreign currency price of the tradable good.10 Here, PN denotes the aggregate

domestic currency price index of the non-tradable goods, defined as
N 1 N 1—0 1
Pt =/0 [Pt (2) ]1:9dz. (2.3)

The real exchange rate (the relative price of tradable goods in terms of non-tradable

T
'EFSV" For simplicity, we assume that PT = 1 and

goods) can be defined as e =
is constant. By this assumption we can suppress the unnecessary foreign inflation
rate from the model.

The typical household can hold two types of assets as their financial wealth:

domestic non-interest bearing currency and an internationally tradable bond with

a constant real interest rate (in terms of tradable goods). Since the domestic

 

10We assume that the law of one price holds for the tradable good. Therefore, the domestic
currency price of the tradable good is E,P,T.

65

currency and the international bond are the only two assets held by individual

consumers, we have
at = mt + (R, (2.4)

where a, m, and b stand for real financial wealth, real money balances and the
stock of real bonds in terms of domestic price of tradable goods, respectively.11
We assume that the household has a constant endowment flow of tradable
goods, 31$, while it derives human wealth from supplying labor to firm 2 for the
nominal wage Wt. Households also own firm 2. Therefore, they can earn the profit
of the firm, Ht(z). Then the household’s dynamic budget constraint is governed

by the following differential equation

111(2) th1 T CtN T
—— -- --— — C , 2.5
EtPT+EtPT+yt +Tt Gt 1 ( )

 

dt = rat -- itmt +

where T is real transfers from the government in terms of tradable goods; 1' is the
instantaneous nominal interest rate in terms of domestic currency; 7‘ is the constant
real interest rate in terms of tradable goods;12 Wt is the money wage rate. Notice
that in Eq.(2.2.5) the household’s expenditure includes the opportunity cost of
holding real money balances, im.

In order to carry out consumption expenditures, the household is required to
hold suflicient domestic money. Following Feenstra(1985), the cash-in-advance

constraint which the household faces is thus

0N
a[—et— + 03"] _<_ rm, (1 > 0, (2.6)
t

 

11If we define nominal financial wealth, money balances and the stock of bonds as A, M and
B, respectively, then real variables can be defined as follows: a = 273%“ m = Big-r, and b = 78%.

12Since we assume that PT = 1 and is constant, 7‘ is also the world nominal interest rate.

66

where 0 represents the length of time that money has to be held to finance con-
sumption expenditure.13 Eq.(2.2.6) implies that the minimum required money
balances are proportional to the value of consumption expenditures. If the nom-
inal interest rate, 2', is positive, the household will hold the minimum required
money. Then the cash-in-advance constraint (2.2.6) will be binding.

Using Equations (2.2.4), (2.2.5) and (2.2.6), and imposing the transversality
conditions, we can derive the household’s intertemporal budget constraint which

is given by

 

a0+/000(Ev:/;:;. +y$+g%+rt)ezp(—rt)dt = /000 (i—{V— + Cf)(1 + ait)ezp(—rt)dt,
(2.7)
where do stands for the initial level of financial wealth. This equation says that the
household’s lifetime expenditure equals the present discounted value of its lifetime
income. At each point in time t, the representative household’s expenditure con-
sists of the cost of consumption, 9:39?- + CT, plus the opportunity cost of holding
real balances, itmt.
The decisions the household has to make at each point in time are how many
tradable and non-tradable goods to consume and how much to work. Therefore,
the household’s optimization problem is to choose the path of QT , CtN and l, to

maximize lifetime utility, (2.2.1), subject to initial wealth, a0, and the intertem-

poral budget constraint, (2.2.7).

 

N
13The cash-in-advance constraint can be written as m, 2 F(a) E tt+°(%— +Cf)ds. A Taylor-
N N
series expansion gives F(a) = a(%— +6?) + %02%(%- +0?) +- - - , 80 (2.2.6) can be interpreted
as a first-order approximation.

67

The first-order conditions for this optimization problem are14

 

 

 

'l’ .
__CtT = /\(1 + an) (2-8)
1— ’7 1 + Olit
= ,\ 2.9
C.” ( e. > ( >
P Wt
= A — , 2.10

where 1\ is the (time-invariant) Lagrange multiplier associated with the house-
hold’s intertemporal budget constraint (2.2.7). As usual, it can be interpreted as
the marginal utility of wealth. Equations (2.2.8) and (2.2.9) indicate that at an
optimum, the household equates the marginal utility of consumption of tradable
and non-tradable goods to the marginal utility of wealth times the effective prices
of goods. The effective prices of goods consist of the market prices, unity in the
case of tradables and i in the case of non-tradables, plus the opportunity cost of

L
et’

holding the 01 units of money that are needed to purchase both goods, at and a
respectively. Equation (2.2.10) is the Euler equation for optimal labor supply. It
ensures that the marginal disutility of labor (due to forgone leisure) equals the
marginal utility from consuming the extra goods from another unit of labor sup-
plied. The term (1 + ait) generated by the cash-in-advance constraint must be
treated with special attention in this model. This is the usual monetary wedge
due to the fact that any form of wealth has to be liquidated before goods can be

purchased. Even if this monetary wedge increases the effective price of consump-

tion, it does not affect the price of leisure.

 

14To eliminate inessential dynamics and ensure the existence of a steady state, we assume
that 6 = r.

68

Using (2.2.8) and (2.2.9), we can get

 

 

CtTet 'y
= ___. (2.11)
C,N 1— '7
And combine (2.2.9) and (2.2.10)
’0 — 1'7 Wt (1+ 51,)“1. (2.12)

l-lt_ C,N P,N

Equation (2.2.11) is the familiar condition that at an optimum, the marginal
rate of substitution between tradable and non-tradable goods is equal to the rel-
ative price of tradable goods in terms of non-tradable goods, which is the real
exchange rate. From Eq.(2.2.12) we can see that the individual’s optimal labor
supply is dependent on the nominal interest rate. Since the nominal interest rate
introduces a distortion between consumption and leisure, a change in the interest
rate makes the household substitute leisure for consumption due to the change in
the effective price of consumption. This, in turn, leads to a change in the long-run

level of non-tradable output.

2.3.2 The government

The other participant in this economy is the government. Since Ricardian equiv-
alence holds in this model, we can assume that the government runs a balanced
budget in every period. We also assume no government spending. With these
assumptions, we can simplify government behavior. It is assumed that the govern-
ment holds internationally tradable bonds (international reserves) which pay the

world real interest rate in terms of tradable goods and issues non-interest bearing

69

debt (domestic currency).
The evolution of the government’s stock of net foreign bonds is governed by

the following differential equation:

fit=rht—Tt+

 

t
PtTE.’ (2.13)

where h, is the government’s stock of internationally tradable bonds (international

rese es.Ntc tht 18the oernet’sse 0a ofit.It t
rv) 01e aFtTE gv mn lgnrgepr s negramg

equation (2.2.13) and imposing the transversality condition, we can derive the

government’s intertemporal budget constraint

oo 00
/ Ttesrzp(—rt)dt = ho +/ (m, + ctmt)ea:p(—rt)dt, (2.14)
O 0

where c, = g: is the nominal rate of depreciation and ho is the initial level of the
government’s stock of foreign bondsl‘r’,16 The government’s intertemporal budget
constraint indicates that the present value of transfer expenditure has to be equal
to the initial stock of government-held international bonds (i.e., international re-
serves) and revenues from seignorage. By equation (2.2.14), we implicitly assume

that the government returns to the consumer all of its revenues.

2.3.3 The aggregate supply side

We now turn to the supply side of the economy. For simplicity, we assume that
the supply of tradable goods is exogenous and fixed at the constant level yT

(i.e., y? = yT for all t ) and its domestic price will be determined by the law

 

15The government’s seignorage revenue #1: is equal to m, + ctm, in real term (in terms of

P, E
tradable goods).
16The appropriate transversality condition is lim¢_,,,o htexp(—rt) = 0.

70

of one price.

In this model, it is assumed that the non-tradable good sector is imperfectly
competitive and there is a continuum of imperfectly competitive firms indexed
by z E [0, 1]. Each producer produces a differentiated good and acts as a monop-
olistic competitor, choosing the nominal price and the level of production of the
good.

Given the CES non-tradable consumption index, Eq.(2.2.2), an individual’s

demand for non-tradable good 2 in period t is

6912) = (”V“)

pi"

where 6 is the price elasticity of demand.

 

1‘90.” , (215)

According to Eq.(2.2.15), a monopolistically competitive firm that produces a

non-tradable goods faces the downward-sloping curve

1199(2) = [p—jglé’i’octl“, (2.16)
t

where CtNAdz = fol CtN dz = CtN is aggregate per capita non-tradable good con-
sumption.
Labor is the only input into production. The technology available to firms is

identical and is linear in labor:
119(2) = 1.. (2.17)

Firm z’s profit is

11(2) =pt(2)yi’(2) — W. (2.18)

71

At any time t, a monopolistically competitive firm maximizes profit, Eq.(2.2. 18),
subject to the demand function, Eq.(2.2.16), and the production function, Eq.(2.2. 17).

Solving the firm’s problem:

9-1-71 3
Ty , (2)19,” c, =W,. (2.19)

Since the elasticity of demand, 1 / 6, of all non-tradable goods is identical and
every producer has the same technology, they produce the same level of output

and set the same price. Therefore, for any two producers, O < z < z’ < 1

N N
y. (z) = yivrz’) = y.

PN(Z l: PNZ( )= Pt - (2.20)

It follows that the non-tradable good’s aggregate supply and price index simplify

to
AN 1 N N
211 = /0 yr (Z)dz = 111
P,N = {/O(p,N( ))1 911211—170- — p, . (2.21)
The equilibrium in a non-tradable good’s market can be obtained by Eq.(2.2. 16)
and Eq.(2.2.21)
yi" = 0,”. (2.22)
Therefore, from Eq.(2.2.19)
N 6
p, (z) = fiWt,Vz. (2.23)

Equation (2.2.23) shows that a producer with market power sets prices above

marginal cost, which is the money wage rate. Thus, if it cannot adjust its price, it is

72

willing to produce to satisfy demand in the face of fluctuations in demand. There-

fore, in the short-run, if the price is sticky, output will be demand-determined.

2.3.4 Equilibrium conditions and a symmetric steady state
In this paper, perfect capital mobility is assumed. It implies that
it = 7‘ + 6,. (2.24)
Equilibrium in the non-tradable goods market implied by Eq.(2.2.22) is
y.” = CtN'

In order to investigate the dynamic behavior of the current account triggered by
a policy change, consider the economy’s dynamic resource constraint. Combining
the household’s dynamic budget constraint with the profit of the firm and the
market clearing condition for the non-tradable goods sector yields the economy’s

intertemporal budget constraint:
1. = He. + yT - cf, (2.25)

where k, = bt + ht is the total amount of foreign bonds held by the economy.
Equation (2.2.25) represents the economy’s current account balance. It indicates
that the current account balance is the difference between tradable goods income
and consumption of tradable goods.

Combining Equations (2.2.7), (2.2.22), (2.2.14) and (2.2.24) yields the econ-

omy’s intertemporal constraint

oo 00
k0 + / yTexp(—rt)dt = / CtTezp(—rt)dt, (2.26)
0 0

73

where 190 denotes the economy’s initial stock of foreign bonds. Equation (2.2.26)
states that the initial stock of foreign bonds plus the present value of all future
tradable output must equal the present value of tradable consumption. At the
steady state, CtT = 0,9,. Therefore, 03; = yT + rim and the current account is
balanced at the steady state.
In the steady state, all prices are fully flexible. Thus the symmetric equilibrium
implies
C,” = y,” = ,A”,v2.. (2.27)
In the steady state where all prices are fully flexible, the supply condition deter-
mines the level of non-tradable output. It means that the long-run level of output is
totally dependent on labor supply. Using Equations (2.2.12), (2.2.23) and (2.2.27),

we get the symmetric steady state level of output of non-tradables

p
1-7

 

172. = [1+( 1,? 1)(1+...-.,))-1, (2.28)

where 1'33 = r + 633 is the steady state level of the nominal interest rate. In the
steady state, all prices are fully flexible and all exogenous variables are constant.
Therefore, the long-run level of non-tradable output is determined by the supply
side. According to Eq.(2.2.26), however, we can see that non-tradable output
depends on the nominal interest rate, which is also a function of the monetary
policy variable. The reason is as follows. Since the nominal interest rate introduces
a distortion between consumption and leisure, if there is a permanent decrease in
the nominal interest rate, the household will substitute leisure for consumption

due to a lower effective price of consumption. This, in turn, leads to a rise in the

74

long—run level of non-tradable output. This result is consistent with the disinflation
scenario of Cooley and Hansen (1989, 1995) in a closed economy model in which
variations in the rate of inflation can affect the steady state labor supply and
consumption (or output).

In this model, each producer has monopoly power, so the long-run level of non-
tradable output is lower than the socially optimal level. To see this, let’s look at
the social planner’s problem. The social planner tries to maximizes the utility of

non—tradable consumption considering the disutility from labor supply.17

max[(1 — 7) log y” — plog(1 — y“ ]. (2.29)
The solution is
N 1 — ’7 N
= —— . 2.

From Eq.(2.2.30), we can see that the equilibrium output of non-tradables is
inefficiently low under imperfect competition. This fact has important implications
for economic fluctuations as well as monetary policy to stabilize it, as long as
prices are not perfectly flexible because of menu costs or staggered price or wage
contracts. Since the market equilibrium is lower than the socially optimal level,
recessions and booms have asymmetric effects on welfare (Mankiw, 1985). Since
equilibrium output is less than the socially optimal level, a boom brings output
closer to the social optimum, whereas a recession in the non-tradable sector pushes
it farther away. In this model, however, the long-run equilibrium level of output

is subject to a monetary policy variable. Therefore, a change in monetary policy

 

l'fRiemember that by the production condition y” = l.

75

can lead the economy closer to the optimum level.

2.3.5 Staggered wage contract and short-run dynamics

So far, we have assumed flexible prices and solved for the long-run equilibrium.
We now introduce the assumption that the price level of the non-tradable good
is sticky because of staggered wage contracts, and we are ready to consider the
short-run dynamics of the economy. In the short-run, the supply of non-tradable
goods will be demand determined and prices will be given by a modified ver-
sion of the staggered—price model of Calvo (1983) and Ghezzi (2001), including
backward-looking indexation consistent with our discussion in Section 2.1. We
assume nominal wages are sticky as a result of staggered wage contracts.
Following Calvo (1983), we assume that each individual can change wages only
when a wage signal is received. If individuals do not change the wage or is setting
a new wage at time t, the probability (density) that the wage will last for s more

periods is given by the geometric distribution
6ezp(—6s) (2.31)

and is, therefore, independent of t and of the amount of time the wage has lasted
at t. It is also stochastically independent across the individual wage setters. The
expected length of wage duration is 1 / 6. Therefore, nominal wages specified by
the contract will be fixed for the duration of the contract and the contract itself is

staggered.

76

Then the aggregate (log of ) newly posted wage level follows

t
11), = 6/ :csexp(—6(t — 8))d8, (2.32)

where the wage set at time 8, 2:3, is weighted by the probability that it continues
in effect at t, exp(—6(t — 8).

For analytical simplicity, we assume that at any time t there are two types of
wage contractors: half of the individual contractors set their nominal wage in a
purely forward looking manner and half of them set in a backward-looking manner.
By this mechanism, we can easily incorporate backward-looking indexation, which
is proposed by Taylor (1980), into the Calvo model.18

The forward-looking wage contractor will set wages according to the standard

Calvo model

as? = 6 ftmiw. + 1002 cf — logs/5916211666 — t))ds, (2.33)

where at reflects sensitivity of contract wages to future excess demand conditions (log of” —
log ya), where ya is the steady state level of non-tradable output. According to
Eq.(2.2.33), we can see that when setting a contract, forward-looking agents will
take into account future average wage level and excess demand during the length
of contract.

For the other half of the contractors, wages are assumed to be set according

to a backward-looking rule. Specifically, we assume that the wage contract at t

 

18In the original Taylor models, current wage is set according to the past wage level and the
expected future wage rate including past and future excess demand condition. Thus, Taylor
models can generate wage level inertia.

77

indexes money wages to the current aggregate wage level plus a weighted average

of past inflation and current excess demand conditions
1
$13 = wt + 3771+ 90(108 CtN - 108.71%), (234)

where (,0 > 0 reflects the sensitivity of the current money wages to the current level

of excess demand, and

t
77, = 6]— nsezp(—6(t — 8))ds (2.35)
7'71 = 5(7Tt — 7771 (235)

Equation (2.2.34) indicates that backward-looking wage contracts at t index
current nominal wages to the current aggregate wage level, a weighted average of
past inflation 77,, adjusted by the expected length of the price duration, 1 / 6 , and
the current level of excess demand.19

Therefore, the log of wage set at time t is

l 1
:13, = 5735‘ + 517,3. (2.37)

Since price is a fixed markup over wage, there is no distinction between wage
and price inflation in this model. Therefore, we can differentiate Eq.(2.2.32) with

respect to time to get20

1ft = u), = 6[.’L‘t — 111,]. (2.38)

 

19In equation (2.2.36), the adjustment parameter is not necessarily equal to 6. It could be c aé 6
and, therefore 77, = c fix 7r,e:7:p(—6(t - 3))ds. For simplicity, we just assume c = 6. See Ghezzi
(2001). .

2° 7r, = log P" = log Wt.

78

Combining Equations (2.2.33), (2.2.34) and (2.2.37), we obtain

1 1 °°
$1 = §[w7+3771+(0(1084V-108 y£)l+%l5 ft (ws+¢(108 097-108 yfi)l6$p(—5(s-t))d8l
(2.39)

Differentiating (2.2.39), we obtain the changes in newly set wage rate

. 6 1 '
x1 = 2771 — n7 - 5(«1 + (6)0084V - 108 (15;) + 510108 011N- (2-40)

In order to obtain non-tradable inflation dynamics, differentiate (2.2.39) with

respect to time and substitute it into (2.2.40)

. 62 1 -
7ft = 6(7rt - 771) - 301 + (5)008 CtN - 1081791) + 5590108011V~ (2.41)

This is the equation for the inflation dynamics. Eq.(2.2.41) indicates that a
change in the rate of inflation is dependent on two sources. First, it depends on
excess demand conditions: the change of inflation is negatively related to excess
demand. The second term of (2.2.41) shows this relation. This is the same result
as Calvo and Végh (1993,1994). The intuition for this higher order inverse Phillips
curve is that if there is excess demand at t, individuals who revise their wages at
time t set higher wages. Therefore, the higher excess demand at time t, the higher
the rate of inflation will be. However, since agents set their nominal wages in a
forward—looking manner, wage setters at s > t do not take excess demand at time t
into account. Hence, the higher the excess demand at t, the greater the reduction
in the inflation rate for 8 > t will be.

In equation (2.2.41), we can see that there is another source for the change in

the rate of inflation. It shows that current inflation depends on a weighted average

79

of past inflation. Especially, when averaging past inflation, the inflation rate in
the recent past receives more weight, which is the same formulation as adaptive
expectations. If current inflation is lower than 77,, an average of past inflation, the
newly contracted wage has a lower premium over the current price level, which will
be translated into lower inflation. This makes inflation sticky. The first term on
the right-hand side of (2.2.41) represents this relation. The backward-looking wage
contract mechanism implies that inflation has its own persistence in addition to
the inertia in the driving term, which is the change in the level of excess demand.
By this specification, we can overcome the inability of the standard new-Keynesian
contract model to generate significant persistence of inflation. The change of ag-
gregate demand in the non-tradable good sector affects inflation positively. This
is the original Phillips curve mechanism. In this regard, equation (2.2.41) can be
interpreted as a traditional Expectations-Augmented Phillips curve.

In this model, there is another source for inflation dynamics. In contrast to a
constant steady-state level of non-tradable output as in Calvo and Végh models,
the long-run level of non-tradable output is subject to a nominal variable, since
the nominal interest rate introduces a wedge between consumption and labor sup-
ply. Therefore, non—tradable output shows different dynamics with respect to the
policy change in this model.

In order to analyze the dynamic system of the economy, we will need to ob-

tain the equilibrium path of consumption of tradables and non-tradables. From

80

Equations (2.2.8), (2.2.11) and (2.2.30), we can see that

03' = {41+ 610-1

1..
C',N = 776,031

 

and

/\ __ 7f0°°(1 + (17,)‘1 exp(—rt)dt

 

ko+%yT

(2.42)

(2.43)

(2.44)

is the shadow value of wealth, which is constant as long as there are no policy

shocks to the economy. Rom Equations (2.2.42) and (2.2.43), we can obtain that

log C? = C — 077',

1-7

 

log CtN = log

where C = it is constant.

Differentiating (2.2.45) with (2.2.46) yields
log C',N = log 6, — C12,,
By definition, 6, = 12%;. Therefore,
P t
log ét = Et - 7ft:
Using the fact that 2', = 77,, we can obtain

log CtN = (6, — 7ft) — 07ft.

+ log 03' + log 6,,

(2.45)

(2.46)

(2.47)

(2.48)

(2.49)

In the short-run where all prices are sticky, the equilibrium level of employment

is demand-determined. Therefore, non—tradable output is also demand-determined.

It implies

log y,N = log 0,”, .

81

(2.50)

Combining Equations (2.2.22), (2.2.41) and (2.2.44), we can obtain the differ-
ential equation governing the change of the rate of inflation

26 6(p

_ 52(<p+¢)
_ 2+a6<p<7rt —77t)+ 2+a6(p

N _ N
2+a6(p (logyt logyss)- (2'51)

 

 

(61 - 7ft) —

711
Then, the change of non-tradable good can be obtained as

2016 2 a62((p + 65)

— - — 1 ”—1 ”.
2+05<P(7rt nt)+2+a6<P(€t Wt)”— 2+a6<p (ogy, Ogy”)

 

 

108 y,” =
(2.52)

Therefore, the dynamics of the economy consist of a three-equation system
(Equations. (2.2.36), (2.2.51), and (2.252)), in output of non-tradables, yfv, infla-

tion of non-tradables, 77,, and 77,, a weighted average of past inflation.

2.4 Money-based stabilization

This section studies the effects of stabilization policies. We will examine the effects
of money-based stabilization in which the government lets the exchange rate float
and uses the money supply as the nominal anchor. First, we consider a credible
stabilization plan in which the reduction of the growth rate of money supply is
believed to be permanent. Next, the effect of a temporary reduction in the money
growth rate is considered.

Before we proceed, we need to investigate the relationship between the growth
rate of the money supply and the devaluation rate. According to the definition
of real money balances ( m, = M, / E,PT), the path of real money balances is
governed by

772
—‘ = #t — 6 (2.53)

82

where 7.1,(5 M, /M,) is the growth rate of the money supply. Eq.(2.3.1) is an unsta-
ble differential equation. Unless 11, = 6,, real money balances are ever increasing
or decreasing. To ensure stability, the devaluation rate, Ct, needs to be equal to
the growth rate of the money supply. It implies that under a flexible exchange rate
regime, the devaluation rate, 6,, will adjust instantaneously to its new value when
the growth rate of money supply, 77,, changes.

Now we will introduce a money-based stabilization policy. Suppose that, prior
to any stabilization (for t < 0), the growth rate of the money supply is pH , and is
expected to remain at that level forever. For a given money supply growth rate,

the economy is at a steady state characterized by

i33=r+flH

7fss = 7783 = flH

 

0% = 9.167..» = (1+ (1 5,1,3 ,)(1 + 97..)1‘1 (2.54)

03; = yT + NCO
Cf.

At a steady state, consumption of tradable goods is equal to its permanent

ess =(1—3‘;)

income level, while consumption of non-tradables equals its full-employment level.
The full employment level of non-tradables is less than the socially efficient level
due to the imperfection in the non-tradable sector. However, this full-employment
level of output is not constant. Monetary policy which affects the nominal interest
rate can change the long-run level of non-tradable output. Nominal variables
(the interest rate and the rate of inflation) are growing at the money supply’s
growth rate, 11H . The real exchange rate is equal to the ratio of the steady state
consumption of non-tradables to tradables.

To examine the transitional adjustment of the economy, we have to consider

83

the dynamic system. The system is characterized by the differential equations
(2.2.41), (2.2.51), and (2.2.52), with ,1, = 5,. Since the system is linear, we do not
need any approximations.

The dynamic system for log y, 7r and 77 is

log 94”
7ft
61
- , -
if? 3219:2132 a: 108 y,” - 108 94’;
= J—JX —1—1X —;— X 7T1 " #1 1 (2-55)
L 0 —6 6 _ 7ft _ “t

 

 

where x = 2 + 01690 > 0.

Now, we need to investigate the stability of the system. It exhibits two con-
vergent (non-positive) roots and one explosive (non-negative) root (see Appendix
A.2.1). At time t, current inflation, 7r,, is given by an average of past inflation,
current excess aggregate demand and future economic conditions, including future
inflation. Therefore, 7r, becomes a jump variable at time t even if it cannot ad-
just immediately to a new value. The partial forward-looking indexation (half of
households set the new wage in a forward-looking manner) makes inflation jump
initially to the point between the new steady state and the initial steady state
after a shock. log yfv is also a jump variable (notice that by the equilibrium
condition, log yfv = log cf” ) However, as one can see in (2.2.35), 77, is a prede-
termined variable. Thus, there is one predetermined variable ( 77) and two jump
( 7r and log yN) variables. However, since the jump of log yN is exogenous to the

solution of (2.3.3), the system exhibits saddle path stability.21Also the roots may

 

21see, Ghezzi (2001).

84

be complex conjugates, and the system may show cyclical dynamics.22

Since the system has three variables, it will be difficult to analyze the equilib-
rium paths. However, it is possible to see the exact transitional dynamics of the sys-
tem by resorting to the methods of dominant eigenvalue proposed by Calvo (1987).
The system has two non-positive roots and one non-negative root. Let 11,-,2' = 1, 2,
be the non-positive roots and 113 be the non-negative root, with 111 > 112 ( 111 is the
dominant eigenvalue). Setting to zero the constant corresponding to the unstable

root ( 113),23 the solution to dynamic system (2.3.3) can be expressed as

108 91V - 108 319.; =A1w11 9XP(V1t) + A29121 eKIM/211‘)
7ft - #1 =A1w12 9@040 + A2922 eXP(V2t) (2-55)

771 - #t =A1w13 eX13041) + 1127.123 eXp(V2t).

where A,,7' = 1, 2, and (1),-j, j = 1,2, 3, denote the constants and the element of the
eigenvector associated with root 11,-.

From the assumption 111 > 112, it follows that (see Appendix A22):

1 N —1 N
lim Ogy‘ Ogy” = -——“’n > 0. (2.57)
t->00 7ft - It W12

 

This implies that as t becomes large, if the initial value of log yN and 7r are not

- . . 1 N —1 N
on the ray correspondmg to solution, 112, then the rat10 of 0g y, 0g ”33

711—11 Wlll con-

 

verge to the slope of the dominant eigenvector ray ( 5%), which is positive. It

implies that, graphically, the system will converge asymptotically to the dominant

 

22For more detail, see Blanchard and Khan (1980) and Turnovsky (1995).
23It is clear from the transversality condition that a necessary condition for convergence of the
system is that 113 = 0.

85

eigenvector ray. Figure 2.1 shows the phase diagram for log yfv and 77, with the

dominant eigenvector ray.

2.4.1 Permanent reduction in the growth rate of money
supply

We, now, consider the impact of a once—and-for—all reduction in the growth rate
of the money supply. This case corresponds to the credible disinflation policy.
Suppose that at time t < 0, the economy is at the initial steady state. In terms
of Figure 2.1, the initial steady state is at point 830. At time 0, the policy-
maker announces that he or she will reduce the growth rate of the money supply

permanently, which is unanticipated. Formally, the policy is

11,=71H,fort$0

11,:111’, fort>0.

On impact, the nominal exchange rate adjusts instantaneously to its lower value.24
The nominal appreciation leads to an appreciation of the real exchange rate since
the price level of non-tradables is sticky. The nominal interest rate also jumps to
a new level, ( r + 11L) by the same amount as the money growth rate. Now it is
easy to see the equilibrium path of the main variables. Since the nominal interest

rate remains at the new level, we can see from Eq.(2.2.44) that

_ '7 - —1
A — _rko + yT(l + a7) . (2.58)

2"On impact, real money balances must increase to equilibrate money market. This can only
be achieved with instantaneous appreciation of nominal exchange rate.

 

86

Combining (2.2.42) and (2.3.6), we obtain
CT = Tko + yT. (2.59)

The consumption of tradable goods is constant over time and equal to its per-
manent income level. The reason is as follows: even if the nominal interest rate
is reduced, it is constant over time at the lower level, which implies a constant
effective price of tradable consumption at the lower level. Hence, the consumer
does not have any incentives to engage in intertemporal consumption substitution.
This implies that the current account does not change at all during the transition
to the new steady state. The path of consumption of non-tradables can be derived
from Eq.(2.2.43) and the path of the real exchange rate. Since the consumption
of the tradable good continues to be equal to permanent income, consumption (or
output) of non-tradable goods falls on impact as the real exchange rate appre-
ciates. Inflation also falls on impact. However, the inflation rate will jump to a
point between 71 H and 71 L- This is due to the backward-looking indexation of wage
contracts even if the forward-looking contracts make it possible that the inflation
rate jumps on impact.25 The impact effects of the reduction in the money growth
rate on inflation and non-tradable output is illustrated as the movement from $30
to A in Fig 2.2.

After the initial impact, the supply-side effects of disinflation come in through
the change in the labor supply. The reduction in the nominal interest rate implies a

reduction in the monetary wedge (or distortion), generated by the cash-in-advance

 

”According to Ghezzi (2001), the size of jump of the inflation rate depends negatively on the
degree of backward-looking indexation.

87

constraint, between consumption and leisure. Thus, the individual household in-
creases labor supply, which leads non-tradable output to expand. Since the greater
labor supply implies more labor income, the household will increase demand for
non-tradables. This permanent increase in labor supply triggers a positive wealth
effect on non-tradable output. At A, non—tradable output starts to increase and in-
flation keeps falling slowly. Finally, they converge to their new steady state ( S SI).

The dynamic path of the main variables we are concerned with is depicted in
Figure 2.3 to 2.8. The first thing we have to notice in this experiment is the move-
ment of inflation. We observe that inflation shows inertia. This result is quite
consistent with a stylized fact in money-based stabilizations described by Agénor
and Montiel (1999), and Calvo and Végh (1999). In this model, however, inflation
persistence can be observed even if the disinflation policy is fully credible. This
result implies that backward-looking indexation is an important factor in explain-
ing inflation inertia in stabilization programs. Another intriguing phenomenon is
that inflation shows undershooting during the transition. Before it reaches the
new level, inflation is below the growth rate of money supply for some period of
time. The reason is as follows: on impact, the real exchange rate appreciates. To
achieve a high level of non-tradable output (or consumption), the real exchange
rate should be higher (real depreciation) in the new steady state than in the initial

steady state as
99$,

= ___, 2.60
63.91 TICO + yT ( )

88

For a subsequent real depreciation, some period of inflation below 11 L is required.

This result follows from the fact that

ét = 61011 - 7R)- (2-61)

The path of the real exchange rate is depicted in Figure 2.5. Inflation undershoot-
ing can be understood more easily if the money market equilibrium condition is in-
vestigated. Let n, = M, / PtN be the real money balance in terms of non—tradables.

Then, the dynamic path of real money balances is
1it = ”1041 - ”0- (2-52)

After the reduction in the money growth rate, real money balances (in terms of
non-tradables) start to decrease as the money growth rate is lower than the in-
flation rate. This result is consistent with the fact of lower non-tradable output.
However, the rise in real money balances is necessary to accommodate the increase
in non-tradable consumption. This is achieved by inflation undershooting. The
time path of real money balances is illustrated in Figure 2.8.

As pointed out in Section 2.2, exchange rate based programs are preferred to
money based programs since a period of deflation may appear in money-based
stabilizations. Thus, policymakers will engineer a one time increase in the money
supply to avoid deflation, which weakens the credibility of the policy maker. The
resulting inflation undershooting effect in this model eliminates the possibility of
an increase in the money supply during the disinflation program.

In this paper, we have succeeded in producing another stylized fact of money-

89

based stabilizations. From the above simulation, non-tradable output (or con-
sumption) shows a sharp and short-lived contraction after the implementation of
a money-based program. This result is broadly consistent with empirical and the-
oretical regularities documented by Calvo and Végh (1999) and Fischer (1986).
It also fares well with the notion that disinflation is contractionary in industrial
countries (Gordon, 1982). The distinguishing feature of this model compared to
the previous literature is that disinflation produces a sustained expansion through
the labor supply effect even if inflation shows persistence. This result is also con-
sistent with the evidence of the successful exchange rate-based stabilizations.

It should be noted that in this model, inflation stabilization proves to be
welfare-improving: the reduction in inflation is beneficial in cash-in—advance models
with a labor-leisure choice and imperfect competition in the goods market. Lower
inflation reduces the transaction cost of holding money. Hence it allows individuals
more free time for productive activities: more consumption and production. In a
broad sense, disinflation is welfare improving since socially unproductive efforts to
conserve on money balances and the inefficiency of the imperfect competition can

be eliminated.

2.4.2 Temporary reduction in the growth rate of money
supply

We now turn to investigate a temporary stabilization experiment. This corresponds
to the case of lack of credibility: the authority announces a permanent reduction

in the growth rate of money supply, but the public believes that the money growth

90

rate will go back to its original level after a certain period of time. The initial
steady state corresponds to a money growth rate 71, = 71”. At t = 0, the money
growth rate is set to a lower level, 711’, but at time T, it is increased back to its

original level. More specifically, for some T > 0,

74:919. 05t<T

741w”, t2T

where pH > 71L.

From Eq.(2.3.1), we can see that during the transition (the interval [0,T)), the
rate of devaluation is lower than after T. Perfect capital mobility implies that the
nominal interest rate is also relatively low during the transition. Therefore, on
impact consumption of the tradable jumps up and remains constant during the
transition. At T, tradable consumption decreases. We can see this from (2.2.42).
The reason is as follows: since the consumer expects that the effective price of non-
tradables (market price and the opportunity cost of holding money) will be lower
between 0 and T than after T, he or she will engage in intertemporal consumption
substitution. Hence, non—tradable consumption will be higher during the interval
[0,T) and lower after T.

The economy’s intertemporal budget constraint implies that before the stabi-
lization policy is reversed, consumption of tradable goods is higher than permanent
income, while consumption of tradables is lower than initial permanent income

after T.

91

This implies

C£>yT+rk0, OSt<T

0,? < yT + rko, t 2 T. (2.63)

The time path of the current account is given by Eq.(2.2.25). The increase in
the consumption of tradables over permanent income induces the current account
to jump into deficit. During the transition, the current account deficit will grow
steadily since the interest income on net foreign asset declines. When the stabi-
lization is abandoned, Cir falls below the permanent income level and brings the
current account into balance.

We now investigate the behavior of non-tradable output and inflation. Since
the real exchange rate appreciates on impact, it is difficult to determine the initial
effect of the temporary disinflation on non-tradable consumption. We can see this
from Eq.(2.2.43): the movement of the real exchange rate and tradable output
(induced by the change in the nominal interest rate) go in opposite directions.
However, by investigating the money market, we can establish that non-tradable
output jumps down on impact. From the definition of real money balances (in

terms of tradables and non-tradables), we can see26

Tl, = 8,771,. (2.64)

On impact, real appreciation reduces real money balances in terms of non-tradable

goods.

 

26From the definition, real money balances in terms of tradable and non-tradable goods can
be expressed as m, = 31%,, n, = %f&. Therefore, 71., = e,m,.

92

Substituting (2.3.10) with (2.2.45) into the cash-in-advance constraint (2.2.6),

we obtain

a

 

n, 0,”. (2.65)

= 1 _ 7
Therefore, initially, non-tradable consumption jumps down as in the permanent
disinflation case. Inflation also falls on impact. However, the size of the initial
jump of inflation will be smaller than the permanent case. This result is due to
the lack of credibility. The public believes that the money growth rate will revert
to the original level which is higher than it is now. The initial effect will be a move
from .350 to A in Fig 2.9.

After the initial impact, non-tradable output (or consumption) starts to in-
crease. For 0 < t < T, the nominal interest rate will be lower than after t 2 T.
Households supply more labor to the non-tradable sector during the transition
than after the policy reverts to the original level. Therefore, non-tradable output
will be higher during the transition. This is due to the intertemporal substitu-
tion effects of labor supply. Inflation also begins to increase as the public expects
higher inflation in the future. The expected inflation rate will be incorporated into
wage contracts, especially into forward-looking contracts. This induces the rate of
inflation to keep increasing.

During the transition, for O < t < T, the system will be governed by the

dominant divergent path (See Appendix A.2.3).

1m 108171” 408951, _ 4131
t—roo 7ft - NH 0132'

 

(2.66)

93

In this model, the sign of 3312-, the slope of the divergent path, is ambiguous [see
(A.2.11)]: it can be positive or negative. However, even if the slope is positive, it is
flatter than the dominant eigenvector ray (in the new steady state). Therefore, the
transitional dynamic of the system will not be affected by the indeterminacy. Fig-
ure 2.11 and 2.12 depict the transitional adjustment of inflation and non-tradables.
The direction of motion is indicated by the arrows.”

At T, the growth rate of the money supply increases back to pH . The economy
now converges to the dominant eigenvector ray and moves to the original steady
state. As the nominal interest rate goes back to the original level, the households
decrea8e their labor supply. Thus, non-tradable output (or consumption) also
shrinks and recession sets in. Since the policy is reversed at T, expectations adjust
and inflation starts to fall, converging to its original rate. This result highlights the
importance of policymaker credibility. The credibility of policy will affect people’s
expectations, and produce unwanted results.

The dynamic path of the main variables is depicted in Figure 2.10 to 2.15. One
of the distinguishing features of this policy relative to the credible one is that the
temporary policy induces a deterioration of the current count. The movement of

tradable consumption and current account dynamics are illustrated in Figures 2.14

and 2.15.28

27In Figure 2.3 we assume that the divergent path is negatively sloped. However, as is men-
tioned in the main text, we observe the same transitional path under a positively sloped divergent
path.

28Figures do not include the transitional adjustment of the nominal exchange rate and real
money balances. However, it is not difficult to see if we consider the behavior of inflation and
the real exchange rate.

 

94

The behavior of non-tradables and inflation are similar to Calvo and Végh’s
(1993) under the incredible policy scenario. In their model, a temporary reduction
in the rate of growth of the money supply induces an initial decrease in consumption
of non-tradable and inflation. After the initial impacts, inflation starts to increase
and converges slowly to its original level. The consumption of non-tradables also
shows a similar dynamic adjustment. The initial recession is followed by an expan-
sion of the non-tradable sector to its original level. In this simulation, however,
the transitional dynamics show a little difference: for non-tradable output, we ob-
serve “boom—recession” cycle after initial recession, and inflation shows overshoot-
ing. This is manly due to the supply-side effect and backward-looking indexation,

which are not considered in Calvo and Végh (1993).

2.5 Concluding remarks

The main objective of this study is to explain the stylized facts of the recent
money-based stabilization programs within a New-Keynesian framework. We ex-
tend Obstfeld and choff’s (1995) dynamic general equilibrium Mundell-Fleming
model to allow for sticky inflation. This is achieved by Ghezzi’s (2001) staggered
contract model including backward-looking wage indexation.

We used the model to study money-based stabilizations. Our model produces
inflation inertia, which is the main stylized fact of inflation stabilization (both

money and exchange rate based). Backward-looking indexation prevents inflation

95

from converging rapidly to the new nominal anchor. This result implies that slow
convergence of the rate of inflation cannot be avoided unless backward-looking in-
dexation is eliminated.

Another important result is that the model successfully replicates the “recession-
boom cycle” in the credible disinflation scenario. We achieve this result by incor-
porating imperfect competition and endogenous labor supply into a small open
economy, high inflation environment. The initial contraction after the stabilize
tion attempt is typical of disinflation programs when the money growth rate is
used as a nominal anchor [Fischer (1986) and Gordon ( 1982)]. In this exercise,
an initial recession is observed after disinflation is implemented. Moreover, the
credible reduction in the money growth rate is capable of replicating the sustained
expansion of the domestic sector, which is observed in the successful exchange rate
based disinfiation. This result is quite consistent with the disinflation scenario in
the closed economy model in Cooley and Hansen (1989,1995). In this respect, our
study is quite successful.

In this paper, the resulting dynamic behavior of inflation and non-tradable out-
put under the permanent disinflation programs provides a counter argument to the
“temporariness hypothesis” of Calvo and Végh (1993, 1994). Our result suggests
that the main causes of inflation inertia and the associated business cycle may not
be an incredible policy, which is claimed by many authors. As long as the index-
ation mechanism has a backward-looking component, credible disinflation cannot

reduce the rate of inflation rapidly. Combined with the supply-side effect, inflation

96

persistence co—exists with sustained expansion of domestic output.

The model has clear welfare implications for disinflation policy. Reducing infla-
tion is beneficial in a cash-in-advance model with labor-leisure choice and imper-
fection in the goods market. Lower inflation reduces transaction costs. Hence it
allows the households more free time for productive activities: more consumption
and production. In a broad sense, permanent disinflation can eliminate existing
inefficiencies in the economy: high inflation and low levels of production. There-
fore, it is definitely welfare enhancing to implement credible disinflation. In
this paper, we assume the degree of backward looking indexation for analytical
simplicity. However, the degree of indexation has a significant implication for the
economic welfare during the stabilization. As the degree of indexation declines,
the model predicts the rapid convergence of inflation.Accoding to the model, rapid
convergence of inflation implies the less severe recession during the early stage of
stabilization. This will enhance the welfare effects of inflation stabilization. To
study the relationship between the the degree of indexation and economic welfare

of inflation stabilization is also promising.

97

2.6 Appendix
2.6.1 The stability of Equation (2.3.3)

The stability of the system requires that among the eigenvalues of the matrix asso-
ciated with dynamic system (2.3.3), one has a positive real part and two eigenvalues
have negative real parts.

The eigenvalues 11,-,7 = 1, 2, 3. of the system

log ,7,”
7ft
lit
052 9+7? 2 1+a6 2 5
+1 ‘Jx— % 10892-108991
= 62(¢+(p) 6((p—2) _2_5 x 7r, — ,1, (2.67)
X X X 7h - Ht
0 —6 6
have the following properties
53
det(A) = 111112113 = T‘- > 0 (2.68)
62
111112 + 112113 + 111113 = —-;(6 + 076) < 0 (2.69)
Tr(A)2 — 4det(A)0. (2.70)

From (A.2.2), we can see that the three eigenvalues are positive or one is pos-
itive and two are negative. From (A.2.3), the case of three positive roots can be
ruled out. As a result, the system has two negative roots. Furthermore, according
to (A.2.4), the eigenvalues may be complex conjugates and the system may exhibit

cyclical behavior.

98

2.6.2 The dominant eigenvalue ray

We assume that 11,,2' = 1, 2 is the non-positive roots, with 111 > 112. Then, for 7' =

1, 2, it follows that

X X 7.
617121 82:21-”, _a x 42.2 = o , (2.71)
6 X-6 6-XV, (11,3 0

where (1),-j, j = 1, 2, 3, are the element of the eigenvector associated with root 11,.

Therefore,
2,, _ [26 - 211,- — 2a611,]/X(6 — 11,)
(#12 [0152615 + 77) — Vin/ X

 

>0 am)

Now, let’s look at the dominant eigenvector ray. Setting to zero the constant

corresponding to the unstable root ( 113), the solution to this system takes the form
1 ”—1 ”=4 7 A t
08 gt 08 yss 19111 eXP(V1 ) + 20121 eXp(V2 )

7ft - #t =A1W12 eXp(l/1t) + A29122 eMAI/275) (2-73)

777 - #1 =A1w13 eMPG/1t) + A2923 eXp(V2t),

where A,,2' = 1, 2, denote the constants associated with root 11,. Since 711 > 112, it

follows that

 

 

lim 10% ygv — 108 11% = lim A19711 eXp(V1t) + A2w21 eXP(V2t)
t—+oo rr, — p. t-—+oo Alwlg exp(111t) + A2w22 eXp(V2t)
= A19111 + A2921 eXP((V2 - Vllt)
t-roo A19112 + A2922 eXP((V2 - Vilt)

=fll>6 an)
“’12

 

99

2.6.3 Properties of system for temporary stabilization

We assume that 11,,7' = 1, 2 are non—positive roots and 113 is the non-negative one.

Then, for 0 < t < T, the solution to the system is

108 91V - 108 77.3.6, =Biw11 exp(V1t) + B29221 exp(Vzt) + B39231 exp(v3t)
7ft - 14H =Blw12 eXP(l/1t) + B29222 exp(Vzt) + B39032 exp(V3t) (2-75)
Tit - 11H =B1w13 exp(l/lt) + 329123 eX13001?) + B39233 exp(V3t),

and for t 2 T

108 MN - 108 31.1960 =ClW11eXP(V1t) + 029121 exp(V2t)
7ft - #L =01W12 eMPG/1’5) + C29122 eX13001) (2-76)
771 — 11L =C1W13 eXP(V1t) + 029123 exp(l/2t),
Where B, and C,, 7' = 1, 2,3 are constants associated with root 11,, and (11,137, j =
1, 2, 3 are the elements of eigenvector for roots 11,.

For 0 < t < T, the system will be governed by the unstable root, 113. This

means that the system converges asymptotically to the divergent path, which is

 

 

given by
1m 108 111v — 108 31.13:, _ lim 310011 exp(111t) + 826121 exp(112t) + 33613, exp(113t)
t—+oo 77, — 77L t—voo 816212 exp(111t) + 8271122 exp(112t) + B36132 exp(113t)
=93—1. (2.77)
“’32

From (A.2.11) with 113 > 0 , we can see that the sign of 3312- cannot be determined.
Even if, however, it is positive, the slope is flatter than the dominant eigenvector

ray. For t 2 T, the dominant eigenvector ray is same as (A28).

100

A. Inflation and money growth 8. Real GDP growth

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3000 WWW” 5 mer)
4.
21 -- ”mean2
0.
'21
'4./
£4 \
.5 v g 1 fl
1-2 T4 7 7+1 T+2 r+3 T+4
C. Real exchange rate 0. Current account
(index number. T-txtOO) (percent ct GDP)
110 -1.9
1054 '1.51
100.
'10..
95.
-2.54
90.,
~10.
85. mean .
I
80. -3.5. V
75 . . . . 4-9 . . . .
1-2 T-1 1 1+1 T+2 T+3 T+4 1-2 1-1 T T+1 T+2 7+3 1+4
Figure 2.1: Money-based stabilization
A .
N - N _
logy, logyr ‘0
Dominant
Eigenvector ray
SS,
N
1081’88,

 

\ .5,
B \A

L _ H
y ”r"/" ”r

Figure 2.2: Dynamic system of money-based stabilization

 

 

 

b

 

101

 

 

 

 

 

+
0 Time

Figure 2.3: Time path: rate of money growth

 

 

 

 

+ >
O 1, Time

 

Figure 2.4: Time path: inflation

102

yss,

J’ss

 

/

 

 

 

_/

 

 

’
1, Time

Figure 2.5: Time path: output of non-tradable

/\

 

eSS,

 

6 SS,

J

 

 

 

0

 

D
1, Time

Figure 2.6: Time path: real exchange rate

103

 

 

 

 

 

E 33,—,
ES,
’
O t , Tlme
Figure 2.7: Time path: nominal exchange rate
"r
n

 

 

 

 

 

’
O 1, Time

Figure 2.8: Time path: real money balance

104

logyf'i

Divergent log 1'1,” = 0
Pat

   
  

 

N
log yss‘
Dominant
Eigenvector ray

 

 

 

 

 

H
71" = fl 7?,
Figure 2.9: Dynamic system of temporary stabilization

 

 

 

 

 

 

,u A
”H
[UL
’
O T Time

Figure 2.10: Time path: Money growth rate

105

 

 

 

 

 

 

 

 

 

 

'uL
0 T Tune
Figure 2.11: Time path: inflation

14’s, ...........-..........,
i

it”... I /\
f\/
‘ +
0 T Time

Figure 2.12: Time path: output of non-tradables

106

 

 

 

 

 

 

 

 

 

 

 

 

 

988,

eSSl
’

0 T T1me
Figure 2.13: Time path: real exchange rate
0%
rkO + yT

. f
O T T1me

Figure 2.14: Time path: consumption of tradables

107

 

\

 

 

 

 

$
0 T Time

Figure 2.15: Time path: current account

108

Chapter 3

Interest rate policy

3.1 Introduction

In industrialized countries, short-term nominal interest rates are the most com-
mon operating instrument for the monetary policy,1 and are most often used to
achieve the target inflation rate. Many industrialized countries have implemented
inflation targeting using the short-term interest rate as a nominal anchor. These
countries include New Zealand, Canada, United Kingdom, Sweden, Finland, Aus-
tralia, Spain, and, of course, United States. In the United States, the Federal
Reserve raises the federal funds rate when the inflation rate is above the its target
level.

Since World War II, developing countries, especially Latin American countries,
have suffered from chronic inflation. Policymakers in those countries have engaged
in repeated inflation stabilization attempts. Monetary policy for inflation stabiliza-
tion in those countries is typically cast as choice between an exchange rate-based

stabilization (using an exchange rate as a nominal anchor under a fixed or prede-

 

1See, for instance, Batten et all (1990), and Bernanke and Mishikin (1992)

109

termined exchange rate), or money-based stabilization (using the growth rate of
the money supply under the flexible exchange rate). Most stabilization plans, how-
ever, have failed. Those which rely on the rate of devaluation have often generated
dramatic balance-of—payment crises. The unsustainable increase in devaluation fi-
nally induces a speculative attack against the domestic currency. The Mexican
crisis of December 1994 and the recent Argentine crisis are perfect examples.

In countries inflicted by chronic inflation, short-term interest rates have also
played a key role in inflation stabilization programs during the 19808. Even in
the exchange rate-based stabilization program, policymakers raise interest rates to
ensure a rapid fall in inflation as well as to prevent a speculative attack against
the domestic currency. In the 1980’s, Argentina, Brazil and Israel supported sta-
bilization efforts by hiking up the interest rate (Calvo and Végh (1995), and Végh
(1998)). In the case of Mexico, analysts blame the monetary authority’s reluctance
to raise interest rates as a main factor in triggering the December 1994 crisis.

Considering the high popularity of interest rate policy in practice, it is sur-
prising to find that it does not enjoy high reputation in the inflation stabilization
literature. Calvo and Végh (1995) analyzed the effectiveness of interest rate policy
in inflation stabilization in the context of the small open economy, flexible price
model. The key assumption of the model is that the representative consumer is
subject to a liquidity-in-advance constraint under which the consumer must hold
money and interest bearing liquid bonds (highly liquid bank deposits). The poli-

cymaker controls the deposit interest rate. In this set-up, a permanent increase in

110

the deposit rate produces an increase in money demand. Therefore, with a con-
stant nominal money supply, the price level and the inflation fall to increase real
money balances. When, an increase in the deposit rate is temporary, the inflation
rate rises continuously after the initial fall in the inflation rate. This result thus
suggests that, in the presence of flexible prices, the increasing interest rate is not
an effective tools for reducing inflation. Calvo and Végh (1995) provided useful
insights into the role of interest rate policy inflation stabilization. However, it
also has some defects. In this model, the nominal interest rate is divided into two
separate rates: a deposit rate and a money rate. Even if policymakers increase
the deposit rate, the money rate is constant by assumption. If the deposit rate is
increased by policy, we would expect that the money rate would also increase. So
the assumption of a constant money rate is quite inapplicable to the real world.
In the real world, if the deposit rate increases the money rate also goes up. When
this is the case, it cannot produce the increase in money demand and the fall in
the price level that they suggest.

In this paper, we analyze the effect of interest rate policy on inflation sta-
bilization. Specifically, we consider the nominal interest rate rule for inflation
stabilization in a small open economy. We depart from Calvo and Végh’s model
by assuming there is only one nominal interest rate, which is common in the lit-
erature. An analytical problem of using the interest rate as a policy instrument
is that interest rate targeting leads to a nominal indeterminacy in equilibrium. In

their famous paper, Sargent and Wallace (1975) pointed out that the price level

111

will be made indeterminate by pure interest rate pegging under a flexible price
model. With sticky prices, nominal interest pegging leads to indeterminate infla-
tion (Calvo, 1983). The indeterminacy problem can be eliminated by designing
appropriate money supply targets (MaCallum (1981), Canzoneri, Henderson, and
Rogoff (1985)), or controlling the interest rate on deposits (Calvo and Végh (1995,
1996)).

To ensure determinacy, we adopt an inflation targeting rule. In this case, the
policymaker announces the inflation target and sets the interest rate according to
the deviation of the actual inflation rate from the target inflation rate. In this
paper, we do not derive the inflation targeting policy rule from the policymaker’s
optimization problem. The policy rule we consider is a variant of the Taylor rule
in which the nominal interest rate responds positively to inflation. We simulate
the model to analyze the effect of the interest rate rule on inflation and other
macro-variables in a small open economy.

Our model is based on Obstfeld and Rogoff’s (1995) “Exchange Rate Dynamic
Redux”. We modify Obstfeld and Rogoff ’8 model in two ways. First, we assume a
small-open economy with a cash-in-advance constraint in which a change of mon-
etary policy, including a change of the money growth rate, has a long-run effect
on the economy as in the two-country model in Obstfeld and Rogoff. Second, we
adopt a Calvo-type contracts model to obtain the inflation dynamics. Our model
is a modified version of Calvo’s (1983) forward-looking, staggered wage contracts

model. However, we incorporate backward-looking indexation into wage contracts.

112

We combine the staggered wage contract with price setting of imperfectly compet-
itive firms to obtain inflation persistence. Incorporating backward-looking wage
contracts into the model is quite consistent with the wage indexation of most
chronic inflation countries.2

We apply this model to investigate the effects of inflation targeting interest rate
policy. In this experiment, we find that interest rate policy triggers a severe reces-
sion during stabilization. The recession arises from both demand and supply side
effects. When policymakers use the growth rate of the money supply for inflation
stabilization (money-based stabilization), only an aggregate demand-oriented re-
cession was observed. In this regard, the model we present here has very important
policy implications in terms of output stabilization. The initial cost of disinflation
is much higher if the nominal interest rate rather than than the growth rate of
money supply is used. Inflation persistence is also implied. Inflation inertia can
not be avoided in disinflation as long as there is backward-looking indexation in
price or wage setting regardless off policy instruments. Hence to achieve rapid
stabilization, the indexation mechanism should be considered. Also the slow con-
vergence of inflation deepens the initial recession through supply side effects. This
result distinguishes the interest rate rule from a money-based stabilization. In case
of money-based stabilizations, backward-looking indexation matters in terms of in-

flation stabilization. Indexation, however, plays a key role in inflation stabilization

as well as output stabilization in interest rate policy.

 

2For instance, Edwards(1991) pointed out that the primary cause of inflation inertia in the
Chilean stabilization is backward-looking wage indexation.

113

Another feature of interest rate policy is that it causes real and nominal appreci-
ation during the initial stabilization period. This result ensures that increasing the
interest rate during the stabilization process prevents the domestic currency from
depreciating. Hence it is possible that a policymaker can avoid a possible specu-
lative attack on the domestic currency, such as those observed in Latin American
exchange rate-based inflation stabilization, when he or she uses the nominal inter-
est rate as an anchor.

This paper proceeds as follows. Section 3.2 develops the basic model and an
interpretation of model is presented. Interest rate policy with inflation targeting

is examined in section 3.3. Section 3.4 closes the paper.
3.2 Basic model

In this section we consider a two sector small open economy, which is perfectly
integrated with the rest of the world in goods and capital markets. First, we
introduce the demand side through the households’ maximization problem and
then the aggregate supply side in which the non-tradable sector is the locus of
imperfect competition. The next step is to solve for a symmetric steady state where
all prices are fully flexible. We, then, introduce sticky prices through staggered
wage contracts. In the last part of this section, we derive the short-run dynamic

system for the next section.

114

3.2.1 The aggregate demand side

Our model is based on Obstfeld and Rogoff’s (1995) perfect-foresight general equi-
librium Mundell-Fleming model. The economy is inhabited by a continuum of
identical households which reside on the interval [0,1]. The representative house-
hold derives utility from the consumption of tradable and non-tradable goods and
leisure. This economy contains a continuum of differentiated non-tradable goods
which are indexed by z and distributed uniformly on [0,1].

The lifetime utility of typical households is given by

U, = (”117041071 + (1 — 717090.”) + 41061 — 411661—9647, (3.1)

where C? is the consumption of the tradable good and C,N is a non-tradable
consumption index, defined by

01” = [116”(2166199—12, (3.2)

where cN(z) is the household’s consumption of good 2, fl is the positive and con-
stant subjective discount rate, and 6 > 1 is the elasticity of substitution between
non-tradable goods. The last term in the lifetime utility function in Eq.(3.2.1)
captures the utility from leisure or disutility from labor supply ( l, represents total
hours worked by the household), and we assume p > 0.

We employ the convention of letting E represent the nominal exchange rate
in units of domestic currency per unit of foreign currency, while PT represents

the foreign currency price of the tradable good.3 Here, PN denotes the aggregate

 

3We assume that the law of one price holds for the tradable good. Therefore, the domestic
currency price of the tradable good is E,P,T .

115

domestic currency price index of the non-tradable goods, defined as
N 1 N 147 1
P1 = [0 19. (2) 1179412. (3.3)

The real exchange rate (the relative price of tradable goods in terms of non-tradable
goods) can be defined as e = @153; For simplicity, we assume that PT = 1 and
is constant. By this assumption, we can suppress the unnecessary foreign inflation
rate from the model.

The typical household can hold two types of assets as their financial wealth:
domestic non-interest bearing currency and an internationally tradable bond with
a constant real interest rate (in terms of tradable goods). Since the domestic
currency and the international bond are the only two assets held by individual

consumers, we have

a, = m, + 6,, (3.4)

where a, m, and b stand for real financial wealth, real money balances and the
stock of real bonds in terms of domestic price of tradable goods, respectively.4
We assume that the household has a constant endowment flow of tradable
goods, 37?, while it derives human wealth from supplying labor to firm 2 for the
nominal wage W,. Households also own firm 2. Therefore, they earn the profit of
the firm, II,(z). Then the household’s dynamic budget constraint is governed by

the following differential equation:

 

 

117(2) th7 T CtN T
dzra —7'm+ +——+ +T————C, 3.5
4If we define nominal financial wealth, money balances and the stock of bonds as A, M and

B, respectively, then real variables can be defined as follows; a = 133%,, m = 1.3—”gr, and b = 327'.

116

where 7' is real transfers from the government in terms of tradable goods; 7 is
the instantaneous nominal interest rate in terms of domestic currency; 7 is the
constant real interest rate in terms of tradable goods;5 W, is the money wage rate.
Notice that in Eq.(3.2.5) household’s expenditure includes the opportunity cost of
holding real money balances, 7m.

In order to carry out consumption expenditures, the household is required to
hold sufficient domestic money. Following Feenstra(1985), the cash-in—advance
constraint which the household faces is thus

03V
a[—— + Ct ] < m,, 01 > 0, (3.6)

where 01 represents the length of time that money has to be held to finance con-
sumption expenditure.6 Eq.(3.2.6) implies that the minimum required money bal-
ances are proportional to the value of consumption expenditures. If the nominal
interest rate, 7', is positive, the household will hold the minimum required money.
Then the cash-in-advance constraint (3.2.6) will be binding.

Using Equations (3.2.4), (3.2.5) and (3.2.6), and imposing the transversality
conditions, we can derive the household’s intertemporal budget constraint which

is given by

 

a0+/Ooo ( tht +y,T-I— IIz,( Z)+T,)e:cp(— rt)dt = fooo (—C—tN +C,T)(1+a7,)e:rp(— rt)dt,

 

E, PT+ +E, PT 6,

(3.7)
5Since we assume that PT = 1 and is constant, 7' is also the world nominal interest rate.
6The cash-in—advance constraint can be written as m, > F(a)= — t+°(-q:- +C'T)ds. A Taylor-

series expansion gives F(a) = 01(9e1—N+C,T)+§la2 “ (“(9L +C,T) + so(3.2.6) can be interpreted

as a first-order approximation

117

where do stands for the initial level of financial wealth. This equation says that the
household’s lifetime expenditure equals the present discounted value of its lifetime
income. At each point in time t, the representative household’s expenditure con-
sists of the cost of consumption, 961,: + CT, plus the opportunity cost of holding
real balances, 7',m,.

The decisions the household has to make at each point in time are how many
tradable and non-tradable goods to consume and how much to work. Therefore,
the household’s optimization problem is to choose the path of C,T , C,N and l, to
maximize lifetime utility, (3.2.1), subject to initial wealth, do, and the intertem-

poral budget constraint, (3.2.7).

 

 

 

 

The first order conditions for this optimization problem are:7
3— : 1(1+ 61,) (3.8)
0%”
10:17 = 4(1 2“”) (3.9)
151, = “BEEN” (3.10)

where A is the (time-invariant) Lagrange multiplier associated with the house-
hold’s intertemporal budget constraint (3.2.7). As usual, it can be interpreted as
the marginal utility of wealth. Equations (3.2.8) and (3.2.9) indicate that at an
optimum, the household equates the marginal utility of consumption of tradable
and non-tradable goods to the marginal utility of wealth times the effective prices

of goods. The effective prices of goods consist of the market prices, unity in the

 

7To eliminate inessential dynamics and ensure the existence of a steady state, we assume that

6=r.

118

case of tradables and i in the case of non-tradables, plus the opportunity cost
of holding the 07 units of money that are needed to purchase both goods, 07'
and (1.7-3?, respectively. Equation (3.2.10) is the Euler equation for optimal labor
supply. It ensures that the marginal disutility of labor (due to forgone leisure)
equals the marginal utility from consuming the extra goods from another unit of
labor supplied. The term (1 + 017,) generated by the cash-in-advance constraint
must be treated with special attention in this model. This is the usual monetary
wedge due to the fact that any form of wealth has to be liquidated before goods
can be purchased. Even if this monetary wedge increases the effective price of
consumption, it does not affect the price of leisure.

Using (3.2.8) and (3.2.9), we can get

 

 

Cge, ’y
= —. 3.11
And combine (3.2.9) and (3.2.10)
70 _ 1-‘7fl - —1
l—lt _ 0N PN(1+077,) . (3.12)

Equation (3.2.11) is the familiar condition that at an optimum the marginal rate
of substitution between tradable and non-tradable goods is equal to the relative
price of tradable goods in terms of non-tradable goods which is the real exchange
rate. From Eq.(3.2.12) we can see that the individual’s optimal labor supply is
dependent on the nominal interest rate. Since the nominal interest rate introduces

a distortion between consumption and leisure, a change in the interest rate makes

119

the household substitute leisure for consumption due to the change in the effective
price of consumption. This, in turn, leads to a change in the long-run level of

non-tradable output.

3.2.2 The government

The other participant in this economy is the government. Since Ricardian equiv-
alence holds in this model, we can assume that the government runs a balanced
budget in every period. We also assume no government spending. With these
assumptions, we can simplify government behavior. It is assumed that the govern-
ment holds internationally tradable bonds (international reserves) which pay the
world real interest rate in terms of tradable goods and issues non-interest bearing
debt(dome8tic currency).

The evolution of the government’s stock of net foreign bonds is governed by
the following differential equation:

Mt

f7=rh —T+ ,
t t t PtTEt

 

(3.13)

where h, is the government’s stock of internationally tradable bonds (international
. M . , . .
reserves). Notice that + 18 the government S se1gnorage profits. Integrating
P, E,
equation (3.2.13) and imposing the transversality condition, we can derive the

government’s intertemporal budget constraint

(X) 00
/ T,e:cp(-—7't)dt = ho + f (in, + c,m,)ea:p(-rt)dt, (3.14)
0 0

120

where e, = g: is the nominal rate of depreciation and ho is the initial level
of the government’s stock of foreign bonds.8,9 The government’s intertemporal
budget constraint indicates that the present value of transfer expenditure has to be
equal to the initial stock of government-held international bonds (i.e., international
reserves) and revenues from seignorage. By equation (3.2.14), we implicitly assume

that the government returns to the consumer all of its revenues.

3.2.3 The aggregate supply side

We now turn to the supply side of the economy. For simplicity, we assume that
the supply of tradable goods is exogenous and fixed at the constant level yT
(i.e., y? = yT for all t ) and its domestic price will be determined by the law
of one price.

In this model, it is assumed that the non—tradable good sector is imperfectly
competitive and there is a continuum of imperfectly competitive firms indexed ‘
by z E [0, 1]. Each producer produces a differentiated good and acts as a monop-
olistic competitor, choosing the nominal price and the level of production of the
good.

Given the CES non—tradable consumption index, Eq.(3.2.2), an individual’s

demand for non-tradable good 2 in period t is

09(2) = (9%?1'901" , (3.15)
t

 

8The ovemment’s sci or e revenue 4’13- is e ual to m, + am, in real term in terms of
P, E,

tradable goods).
9The appropriate transversality condition is lim,_.°o h,e:r:p(—rt) = 0.

121

where 6 is the price elasticity of demand.
According to Eq.(3.2.15), a monopolistically competitive firm that produces a

non-tradable goods faces the downward—sloping curve
N
p (Z) _
429(2) = 1 ‘PN 1 9069, (3.16)
t

where CtNAdz = fol CtN dz = C',N is aggregate per capita non-tradable good con-
sumption.
Labor is the only input into production. The technology available to firms is

identical and is linear in labor
41" (2) =1. (31?)
Firm z’s profit is
11.12) = 2.1221(2) — wtzt. (3.18)

At any time t, a monopolistically competitive firm maximizes profit, Eq. (3.2.18),
subject to the demand function, Eq. (3.2.16), and the production function, Eq.(3.2.17).

Solving the firm’s problem:
_ _ N 1
—y, 9(z)P, 09 = W,. (3.19)

Since the elasticity of demand, 1 / 6, of all non-tradable goods is identical and
every producer has the same technology, they produce the same level of output

and set the same price. Therefore, for any two producers, 0 < z < z' < 1
N N N
317 (Z) = 317 (2') = 97

21V (2) = 21(2) = 21". (3.20)

122

It follows that the non-tradable good’s aggregate supply and price index simplify

to

1
9.9” = [0 11122172221V

1 1
P.” =1/0 (in (2))1—92211—4 = 21". (3.21)

The equilibrium in a non-tradable good’s market can be obtained by Eq.(3.2.16)
and Eq.(3.2.21)

y,” = 0,”. (3.22)

Therefore, from Eq.(3.2.19)

6
pfv(z) = b—_—1W,,Vz. (3.23)

Equation(3.2.23) shows that a producer with market power sets price above
marginal cost, which is the money wage rate. Thus, if it cannot adjust its price, it

is willing to produce to satisfy demand in the face of fluctuations in demand. There-

fore, in the short-run, if the price is sticky, output will be demand-determined.

3.2.4 Equilibrium conditions and a symmetric steady state

In this paper, perfect capital mobility is assumed. It implies that
i, = 7' + 6,. (3.24)
Equilibrium in the non-tradable goods market implied by Eq. (3.2.22) is

yfV=CtN~

123

In order to investigate the dynamic behavior of the current account triggered by
a policy change, consider the economy’s dynamic resource constraint. Combining
the household’s dynamic budget constraint with the profit of the firm and the
market clearing condition for the non-tradable goods sector yields the economy’s

intertemporal budget constraint
7;, = rk, + J — c,T, (3.25)

where k, = b, + h, is the total amount of foreign bonds held by the economy.
Equation (3.2.25) represents the economy’s current account balance. It indicates
that the current account balance is the difference between tradable goods income
and consumption of tradable goods.

Combining Equations (3.2.7), (3.2.22), (3.2.14) and (3.2.24) yields the econ-

omy’s intertemporal constraint

oo 00
k0 +/ yTezp(—rt)dt = / C?e:7:p(—7‘t)dt, (3.26)
0 0

where 160 denotes the economy’s initial stock of foreign bonds. Equation (3.2.26)
states that the initial stock of foreign bonds plus the present value of all future
tradable output must equal the present value of tradable consumption. At the
steady state, C? = 03;. Therefore, 0,7; = yT + Tim and the current account is
balanced at the steady state.

In the steady state, all prices are fully flexible. Thus the symmetric equilibrium
implies

0,” = y,” = 0,9”,v2. (3.27)

124

In the steady state where all prices are fully flexible, the supply condition deter-
mines the level of non-tradable output. It means that the long-run level of output
is totally dependent on labor supply. Using Eqs.(3.2.12), (3.2.23) and (3.3.27), we

get the symmetric steady state level of output of non-tradables

p 6
1—7)(6—-1

 

31.2; = l1+( )(1 + mall—11 (328)

where 733 = 7‘ + 633 is the steady state level of the nominal interest rate. In the
steady state, all prices are fully flexible and all exogenous variables are constant.
Therefore, the long-run level of non-tradable output is determined by the supply
side. According to Eq.(3.2.26), however, we can see that non-tradable output -
depends on the nominal interest rate, which is also a function of the monetary
policy variable. The reason is as follows. Since the nominal interest rate introduces
a distortion between consumption and leisure, if there is a permanent decrease in
the nominal interest rate, the household will substitute leisure for consumption
due to a lower effective price of consumption. This, in turn, leads to a rise in the
long-run level of non-tradable output. This result is consistent with the disinflation
scenario of Cooley and Hansen (1989, 1995) in a closed economy model in which
variations in the rate of inflation can affect the steady state labor supply and
consumption (or output).

In this model, each producer has monopoly power, so the long-run level of non-
tradable output is lower than the socially Optimal level. To see this, let’s look at

the social planner’s problem. The social planner tries to maximizes the utility of

125

non-tradable consumption considering the disutility from labor supply.10
1112340 - 7)1089N - 101080 - le- (3-29)

The solution is

N_ 1—7 N
ys —(1—')+p) >y887 (3°30)

Horn Eq.(3.2.30), we can see that the equilibrium output of non-tradables is
inefficiently low under imperfect competition. This fact has important implications
for economic fluctuations as well as monetary policy to stabilize it, as long as
prices are not perfectly flexible because of menu costs or staggered price or wage
contracts. Since the market equilibrium is lower than the socially optimal level,
recessions and booms have asymmetric effects on welfare (Mankiw, 1985). Since
equilibrium output is less than the socially optimal level, a boom brings output
closer to the social optimum, whereas a recession in the non-tradable sector pushes
it farther away. In this model, however, the long-run equilibrium level of output
is subject to a monetary policy variable. Therefore, a change in monetary policy

can lead the economy closer to the optimum level.

3.2.5 Staggered wage contract and short-run dynamics

So far, we have assumed flexible prices and solved for the long—run equilibrium.
We now introduce the assumption that the price level of the non-tradable good
is sticky because of staggered wage contracts , and we are ready to consider the

short-run dynamics of the economy. In the short-run, the supply of non-tradable

 

10Remember that by the production condition y” = l.

126

goods will be demand determined and prices will be given by a modified ver-
sion of the staggered-price model of Calvo (1983) and Ghezzi (2001), including
backward-looking indexation consistent with our discussion in Section 3.1. We
assume nominal wages are sticky as a result of staggered wage contracts.
Following Calvo (1983), we assume that each individual can change wages only
when a wage signal is received. If individuals do not change the wage or is setting
a new wage at time t, the probability (density) that the wage will last for s more

periods is given by the geometric distribution
6exp(—6s) (3.31)

and is, therefore, independent of t and of the amount of time the wage has lasted
at t. And it is also stochastically independent across the individual wage setters.
The expected length of wage duration is 1/ 6 . Therefore, nominal wages specified
by the contract will be fixed for the duration of the contract and the contract itself
is staggered.

Then the aggregate(log of) newly posted wage level follows

111, = 6 f: zsezp(—6(t — 8))d8, (3.32)

where the wage set at time 8,1133, is weighted by the probability that it continues
in effect at t, erp(—6(t - s).

For analytical simplicity, we assume that at any time t, there are two types
of wage contractors: half of the individual contractors set their nominal wage in

purely forward looking manner and half of them set in a backward-looking manner.

127

By this mechanism, we can easily incorporate backward-looking indexation, which
is proposed by Taylor (1980), into the Calvo model.11
The forward-looking wage contractor will set wages according to the standard

Calvo model

.5=a/t°°[w,+.(1.g.gv_1ogyg)]...(_.(._.)).., ‘ (3.33)

where (75 reflects sensitivity of contract wages to future excess demand conditions
( logcsN — log yg’g), where 3,9,7, is the steady state level of non-tradable output.
According to Eq.(3.2.33), we can see that when setting a contract, forward-looking
agents will take into account the future average wage level and excess demand
during the length of contract.

For the other half of the contractors, wages are assumed to be set according
to a backward—looking rule. Specifically, we assume that the wage contract at t
indexes money wages to the current aggregate wage level plus a weighted average

of past inflation and current excess demand conditions.
1
$78 = wt + 3777 + 72008 CtN - 108115;). (334)

where (p(> 0) reflects the sensitivity of the current money wages to the current

level of excess demand, and

t
77, = 6/— 7rserp(—6(t — 8))ds (3.35)
6t = 5(7Tt — 777). (3-36)

 

11In the original Taylor models, current wage is set according to the past wage level and the
expected future wage rate including past and future excess demand condition. Thus, Taylor
models can generate wage level inertia.

128

Equation (3.2.34) indicates that backward-looking wage contracts at t index
current nominal wages to the current aggregate wage level, a weighted average of
past inflation 77,, adjusted by the expected length of the price duration, 1 / 6 , and
the current level of excess demand.12

Therefore, the log of wage set at time t is

1 1
r, = 52:? + 557,8. (3.37)

Since price is a fixed markup over wage, there is no distinction between wage
and price inflation in this model. Therefore, we can differentiate Eq.(3.3.32) with
1313

respect to time to ge

77, = u), = 6[:c, — 711,]. (3.38)

Combining Equations (3.2.33), (3.2.34) and (3.2.37), we obtain

1 1 1 0°
2. = 512233632004c.”—1c>gy§§)1+-,—16 /. (w,+.(1og cé’ —1og yfi))ezp<—6(s—t))ds1

(3.39)
Differentiating (3.2.39), we obtain the changes in newly set wage rate
. 6 1 '
.2. = 2771- — ,(2 + 60042.” —1ogygg)+ 5121040.”. (3.40)

In order to obtain non-tradable inflation dynamics, differentiate (3.2.39) with

respect to time and substitute it into (3.2.40)

. 62 N N 1 '
7r. = 6(777 —. 77.) - 30p + (2)0086. -108 31..) + 5697103 C.”- (3-41)
12In equation(3.2.36), the adjustment parameter is not necessarily equal to 6. It could be c 76 6
and, therefore 77, = c fix 7r,e:rp(—6(t — 3))ds. For simplicity, we just assume c = 6. See
Ghezzi(2001) .
13 71', = log P” = log W,

 

129

This is the equation for the inflation dynamics. Eq.(3.2.41) indicates that a
change in the rate of inflation is dependent on two sources. First, it depends on
excess demand conditions: the change of inflation is negatively related to excess
demand. The second term of (3.2.41) shows this relation. This is the same result
as Calvo and Végh (1993, 1994). The intuition for this higher order inverse Phillips
curve is that if there is excess demand at t, individuals who revise their wages at
time t set higher wages. Therefore, the higher excess demand at time t, the higher
the rate of inflation will be. However, since agents set their nominal wages in a
forward-looking manner, wage setters at s > t do not take excess demand at time t
into account. Hence, the higher the excess demand at t, the greater the reduction
in the inflation rate for s > t will be.

In equation (3.2.41), we can see that there is another source for the change in
the rate of inflation. It shows that current inflation depends on a weighted average
of past inflation. Especially, when averaging past inflation, the inflation rate in
the recent past receives more weight which is the same formulation as adaptive
expectations. If current inflation is lower than 77,, an average of past inflation, the
newly contracted wage has a lower premium over the current price level, which will
be translated into lower inflation. This makes inflation sticky. The first term on
the right-hand side of (3.2.41) represents this relation. The backward-looking wage
contract mechanism implies that inflation has its own persistence in addition to
the inertia in the driving term, which is the change in the level of excess demand.

By this specification, we can overcome the inability of the standard new-Keynesian

130

contract model to generate significant persistence of inflation. The change of ag-
gregate demand in the non-tradable good sector affects inflation positively. This
is the original Phillips curve mechanism. In this regard, equation (3.2.41) can be
interpreted as a traditional Expectations-Augmented Phillips curve.

In this model, there is another source for inflation dynamics. In contrast to a
constant steady-state level of non-tradable output as in Calvo and Végh models,
the long-run level of non-tradable output is subject to a nominal variable, since
the nominal interest rate introduces a wedge between consumption and labor sup-
ply. Therefore, non—tradable output shows different dynamics with respect to the
policy change in this model.

In order to analyze the dynamic system of the economy, we will need to obtain
the equilibrium path of consumption of tradables and non-tradables. From Eqs

(3.2.8), (3.2.11) and (3.2.30), we can see that

 

0,3" = }(1+ 570—1 (3.42)
0,” = 1:720,” (3.43)

and
_ ’7 f0°°(1 + 077',)-1 exp(—7‘t)dt

A
[to + -,1:yT

 

(3.44)

is the shadow value of wealth, which is constant as long as there are no policy

shocks to the economy. From Eqs.(3.2.42) and (3.2.43), we can obtain that

log C,T = C — cm, (3.45)

+ log (I? + log 6,, (3.46)

 

1..
logCtN = log 7 7

131

where C = } is constant.

Differentiating (3.2.45) with (3.2.46) yields
log 0,” = log 6, — 0.1,. (3.47)
By definition 6, = 1:21-5:77; Therefore
1 Pt 3
log 6, = c, — 77,. (3.48)
Then, we can obtain
. N _ ..
log C, — (c, — 7r,) — C17,. (3.49)

This is the equation for the aggregate demand dynamics of non-tradables.
Equation (3.2.49) indicates that a change in demand for non-tradable goods arises
from two sources: real appreciation and the change in the nominal interest rate.
The increase in the nominal interest rate reduces the demand for non-tradables by
increasing the effective price of non-tradable goods. Real appreciation induces the
intratemporal substitution between non-tradable and tradable goods.

In the short-run where all prices are sticky, the equilibrium level of employment
is demand—determined. Therefore, non-tradable output is also demand-determined.
It implies

log yfv = log CtN . (3.50)

Combining equations (3.2.49) and (3.2.50), we can obtain the differential equa-

tion governing the change of the aggregate demands for non—tradable outputs
l N=(c —7r)—077’. (3.51)
0% y, t t t

132

3.3 An interest rate rule with an inflation target

This section studies the effects of inflation stabilization policy. We consider the
case that policymakers announce an inflation target, and let the nominal interest

rate vary according to the change in inflation rate.

3.3.1 Dynamic System

Suppose that policy makers have an inflation target and adjust the nominal interest

rate gradually to achieve the target rate. Formally
ft =X(7It —7_T). (3-52)

where x > O. This policy regime implies that the nominal interest rate is increased
when the inflation rate is above its target ( 7'7).

From equation (3.2.51), it follows that
103 y,” = (6. — 777) - axm — 7‘7) (3-53)

Combining Equations (3.2.41), (3.2.50), (3.2.51) and (3.3.1),we are able to ob-
tain

2

7‘7. = 5(771-772) - -(52-((0+95)(108.yfv -1081/§’§)+ $61016. — 77.) -ax(7rt —7'r)l- (3.54)

Equations (3.2.36), (3.3.1), (3.3.2), and (3.3.3) constitute a four-equation dif-
ferential equations system in 7,41,17,77,, and 77,.
Now we will introduce a stabilization policy. Suppose that, prior to any stabi-

H

lization (for t < 0), the target rate of inflation is 7r , and is expected to remain

133

at that level forever. For a given inflation rate, the economy is at a steady state

characterized by

5.98 =7TH
2'83 = 7' + 7TH

_ _ H
7rsaw-7733—7r

 

. 6 . _
02:229.»):11+<,_",)<,_,)(1+az..)1 1 (3.55)
C£=yT+rk0

_ 7 9232’.
ess—(l_7)Cg;.

At a steady state, consumption of tradable goods is equal to its permanent
income level, while consumption of non-tradables equals its full-employment level.
The full employment level of non-tradables is less than the socially efficient level
due to the imperfec competition in the non-tradable sector. However, this full-
employment level of output is not constant. Monetary policy which affects the
nominal interest rate can change the long-run level of non-tradable output. Nom—
inal variables (the interest rate and the rate of depreciation) are growing at the
inflation rate, 77H . The real exchange rate is equal to the ratio of the steady state
consumption of non-tradables to tradables.

To examine the transitional adjustment of the economy, we have to consider the

dynamic system. The linear approximation of the system around the steady-state

134

is given by

7',

 

 

logy;V
7ft
717
X 0 0 0 1 it — 7:58
_ 1 62 6 1_ 6 7r —7'r .
—QC¥¢<.0X —‘2'(90+¢) — (TX) — t H

Now, we need to investigate the stability of the system. It exhibits two con—
vergent (non-positive) roots and two explosive (non-negative) roots (see Appendix
A.3.1). At time t, current inflation, 7r,, is given by an average of past inflation,
current excess aggregate demand and future economic conditions, including future
inflation. Therefore, 77, becomes a jump variable at time t even if it cannot ad-
just immediately to a new value. The partial forward—looking indexation (half of
households set the new wage in a forward-looking manner) makes inflation jump
initially to the point between the new steady state and the initial steady state
after a shock. log yfv is also a jump variable (notice that by the equilibrium
condition, log ytN = log of”). However, as one can see in (3.2.35), 77, is a prede-
termined variable. Also since the interest rate rule is specified in terms of rates
of change, the nominal interest rate is a predetermined variable at each instant in
time. Thus, there are two predetermined variables ( 7' and 77) and two jump ( 7r
and log 77””) variables. Therefore, the system exhibits saddle path stability. Also
the roots may be complex conjugates, and the system may show cyclical dynam-

ics.14

 

1"For more detail, see Blanchard and Khan (1980) and Turnovsky (1995).

135

Since the system has four variables, it will be difficult to analyze the equilibrium
paths. However, it is possible to see the exact transitional dynamics of the system
by resorting to the methods of dominant eigenvalue proposed by Calvo (1987). The
system has two non-positive roots and two non-negative roots. Let 11,,7' = 1, 2, be
the non-positive roots and 11,, j = 3,4 be the non-negative roots, with 111 > 112
( 111 is the dominant eigenvalue). Setting to zero the constant corresponding to
the unstable root ( 113 and 114),15 the solution to dynamic system (3.3.5) can be

expressed as

it - iss =A1w11 eX17041?) + A297121 eX13001)
1 ”—1 ”—A A
08 y. 0811.. — 1w12 eXp(V1t) + 29022 eXI>(I/2t)
7ft - ”H =A1W13 e><P(V1t) + A2723 eXP(l/2t) (3-57)
777 - W H =A1w14 eX13041) + A2924 exp(V2t).
where A,,7' = 1, 2, and 61,, j = 1, 2, 3, 4, denote the constants and the element of

the eigenvector associated with root 11,.

From the assumption 111 > 112, it follows that (see Appendix A32)

1 N—1 N
lim 033” 0’5”” = $3 > 0. (3.58)

t—->oo 7r, — 71H (.1113

 

This implies that as t becomes large, if the initial value of log yN and 77 are not

 

f log 11%” —log 11.96

”r7111 will con-

on the ray corresponding to solution, 112, then the ratio 0

verge to the slope of the dominant eigenvector ray ( 5%), which is positive. It

implies that, graphically, the system will converge asymptotically to the dominant

 

15It is clear from the transversality condition that a necessary condition for convergence of the
system is that 113 = 114 = 0.

136

eigenvector ray. Figure 3.1 shows the phase diagram for log yfv and 77, with the

dominant eigenvector ray.

3.3.2 An interest rate rule with an inflation target

We, now, consider the impact of an inflation targeting policy which is a once—and-
for-all reduction in the target rate of inflation. Suppose that at time t < 0, the
economy is at the initial steady state. In terms of Figure 3.1, the initial steady
state is at point 380. At time 0, the policymaker announces that he or she will
reduce the target rate of inflation permanently, which is unanticipated. Formally,

the policy is

7r,=7rH,fortSO

7r, =7rL, fort>0.

On impact, inflation jumps down as the policy maker reduces the target rate of in-
flation. However, the inflation rate will jump to a point between 77 H and 77L. This
is due to the backward-looking indexation of wage contracts even if the forward-
looking contracts make it possible that the inflation rate jumps on impact. Thus
the inflation rate is higher than the target rate on impact. After initial impact, the
inflation rate declines to the target rate slowly. The backward-looking indexation
of wage contracts also play a key role in slow convergence of inflation rate to the
target rate, inflation inertia.

From Eq(3.3.1), we can see that on impact the nominal interest rate begins to

137

increase as current inflation is higher than the target rate. The increase in interest
rate continues until inflation reaches the target rate. During this transition, the
economy experiences a higher nominal interest rate. A higher nominal interest
rate induces gradual nominal appreciation. And the nominal appreciation leads to
an appreciation of the real exchange rate since the domestic inflation is sticky.

Now consider the supply-side effects of disinflation.The increase in the nominal
interest rate implies a higher monetary wedge (or distortion), generated by the
cash-in-advance constraint, between consumption and leisure. Thus, the individ-
ual household decreases labor supply, which leads non-tradable output to contract.
Since the lower labor supply implies less labor income, the household will reduce
demand for consumption of non-tradables. This decrease in labor supply triggers
a negative wealth effect on non-tradable output.

Now look at the policy effect on consumption. It is not obvious whether con-
sumers would reduce their consumption of the tradable good. First, consumer
would reduce the consumption of the tradable as the nominal interest rate in-

creases. From Eq(3.2.45), we can see
log C? = —o.7'°,. (3.59)

The reason is as follows. Since the consumer finds that the effective price of trad-
ables (market price and the opportunity cost of holding money) will be higher, he
or she will engage in intertemporal consumption substitution. Hence, tradable con-
sumption will be reduced after impact. However, the real appreciation triggered

by the increase in the nominal interest rate reduces the relative price of tradable

138

goods in terms of non-tradables. Thus consumers will increase consumption of
tradables. The total effect depends on the size of intertemporal and intratemporal
elasticities of substitution. In this paper, we assume the both elasticities of sub-
stitutions are equal to 1, which implies that those effects cancel each other out.
As a result consumption of tradable goods remains unchanged. Consumption of
non-tradables, however, jumps down on impact after the target rate is lowered.
The initial increase in the nominal interest rate sparks the nominal appreciation.
The nominal appreciation leads to an appreciation of the real exchange rate which
in turn reduces consumption of non-tradables. The initial jump of non-tradables
is induced by intratemporal substitution. After initial impact, due to the increase
in the nominal interest rate, the consumer finds that the effective price of trad-
ables (market price and the opportunity cost of holding money) will be higher,
he or she reduces consumption of non-tradable goods. This is the intertemporal
consumption substitution effect. Also supply-side effects play a key role in reduc-
ing non-tradable consumption. Hence, tradable consumption will be reduced after
impact. The overall effect means that the economy jumps to the point A in Figure
3.1 and converges to the point B. So initial disinflation policy triggers a severe
recession.

After initial impact, the nominal interest rate is still increasing as the inflation
rate is higher than the target rate. So consumption and output of non-tradables de-
creases until inflation converges to the target rate. The recession observed under

the interest rate rule is more severe and longer than in the money—based stabi-

139

lization case. In the money-based stabilization, the initial recession results from
decreases in demand. After the initial recession, the economy starts to recover
immediately. However, interest rate policy induces a long-lived, severe recession
since it is triggered by a decrease in demand as well as in supply (decrease in labor
supply). After initial impact, the economy moves to the point B in Figure 3.1.

An intriguing phenomenon observed in this exercise is that inflation shows un-
dershooting during the transition. Before it reaches the new level, inflation remains
below the target rate for substantial periods. The intuition behind the inflation
undershooting result just discussed is as follows. The permanent reduction in the
target inflation rate implies that, in the new steady state, inflation, and thus the
nominal interest rate, will be lower, and output higher. Hence real money balances
in the new steady state will be higher. How will the increase in real money bal-
ances come about? Since nominal money balances do not change at all, the only
way for the economy to generate higher real money balances is for the inflation to
undershoot. Thus tight monetary policy forces the economy to undergo a defla-
tionary period.

As inflation undershoots its long run value, the target rate (or new steady state
value), the nominal interest rate starts decreasing. Therefore, the supply-side ef-
fects of disinflation come in through the change in the labor supply. The reduction
in the nominal interest rate implies a reduction in the monetary wedge (or dis-
tortion), generated by the cash—in-advance constraint, between consumption and

leisure. Thus, the individual household increases labor supply, which leads non-

140

tradable output to expand. Since the greater labor supply implies more labor
income, the household will increase demand for non-tradables. This permanent
increase in labor supply triggers a positive wealth effect on non-tradable output.
At B, non-tradable output starts to increase and inflation keeps increasing slowly.
The economy begins to recover from recession. Inflation also converges to the new
steady state level. Finally, they converge to their new steady state ( $31). The
dynamic path of non-tradable goods and inflation is depicted in Figure 3.1.

The dynamic paths of the other main variables we are concerned with are de-
picted in Figure 3.2 to 3.7. The first thing we have to notice in this experiment
is the movement of inflation. We observe that inflation shows inertia. This result
is mainly due to backward-looking indexation in wage the contract. As long as
the indexation mechanism has a backward-looking component, the policymaker
can not expect rapid disinflation. Inflation persistence in this model also is the
main cause for the disinflationary recession. The slow convergence of inflation
triggers a higher nominal interest rate, which significantly reduces consumption
and output of non-tradables. If inflation converges to the target rate rapidly, the
economy avoids a recession during the transition period. This result assures a well
established notion that disinflation is contractionary. The contractionary effect
of disinflation, however, usually arises from contraction in aggregate demand. In
this paper, the demand side as well as the supply side contracted during disinfla—
tion, which makes the recession more severe. In a high inflation environment, high

nominal interest rates significantly reduce labor supply since the public tries to

141

reduce the high opportunity cost of money. Hence it allows individuals less time
for productive activities: less consumption and production. Therefore, increasing
the nominal interest rate for disinflation results in a recession.

The movement of real and nominal exchange rates are presented in Figure 3.6
and 3.7. We can see that for substantial periods of time, both real and nominal

exchange rates appreciate due to the high nominal interest rate.
3.4 Concluding remarks

This paper examines the inflation stabilization when policymakers use the nominal
interest rate as main anchor. Recently, policymakers increasingly view short-term
nominal interest rates as the main instruments of monetary policy, often in con-
junction with an inflation target. Inflation targeting has been implemented in
many industrial countries. Short-term interest rates have also played a key role in
the exchange rate-based inflation stabilization programs in chronic inflation coun-
tries to ensure a rapid fall in inflation as well as to prevent a speculative attack
against the domestic currency.

Policymakers prefer a higher interest rate for two reasons: first, exchange-rate
based stabilizations often end up with balance of payment crises. Therefore, inter-
est rate policy if it is used under the exchange rate-based stabilization has better
chance to bring down inflation without crisis. Second, under interest rate policy, it
is much easier for the public to identify the government’s disinflation policy than

under money based stabilization in which the growth rate of money supply is used.

142

This paper has simulated an inflation targeting rule in the context of a sticky-
inflation, small-open economy model. Especially, we focus on the inflation stabi-
lization effect of nominal interest rate policy in high inflation environment. In this
case, the nominal interest rate is the main anchor.

The main lesson from the analysis is that using the nominal interest rate may
be not a good policy option to fight high inflation. A high interest rate succeeds
in reducing inflation in the long-run, but results in severe recession during the
transition period. This recession arises from both demand and supply sides ef-
fects. In the present paper, the individual’s optimal labor supply is dependent on
the nominal interest rate. Since the nominal interest rate introduces a distortion
between consumption and leisure, a change in the interest rate makes the house-
hold substitute leisure for consumption due to the change in the effective price of
consumption. Hence high and increasing interest rates substantially reduce labor
supply. From this perspective, an inflation targeting rule is not appropriate in high
inflation environment under which the cost of holding money is high even if the
high interest rate due to the inflation inertia prevents speculative attacks against
the domestic currency during the stabilization. The speed of convergence of in-
flation we observed in this experiment is not significantly different from exchange
rate and money-based stabilizations with a backward-looking wage contract.

In this paper, however, we do not consider the case that the policymaker raises
the nominal interest rate under the exchange-rate based policy. Applying interest

policy to the exchange rate-based stabilization would be an promising extension.

143

Another possible extension is to incorporate the target inflation rate into a
backward-looking indexation. In that case, we can expect that inflation converges

to the target rate rapidly, and no recession results.

144

3.5 Appendix
3.5.1 The stability of Equation (3.3.5)

The stability of the system requires that among the eigenvalues of the matrix
associated with dynamic system (3.3.5), two eigenvalues have positive real parts
and the other two eigenvalues have negative real parts.

The eigenvalues A,,7 = 1, 2, 3, 4. of the system

7',

 

 

log 31,”,
7ft
717
x 0 0 0 2', — 1.3
—a O —1 0 N _ N
= 1 X 62 1_ X log y, _ log 983 (3.60)
12.72). 71.2 + 2) «5111) —6 772 7H
L 0 0 6 —6_ 777 — 7TH
have the following properties
63X
det(A) = A1A2A3A4 = 7(X + Q5) > 0 (3.61)
62
A1212 + A1A3 + A1214 + A21\3 + A2214 + A3214 = —;(¢ + 06) < 0 (3.62)
Tr(A)2 — 44.1mm. (3.63)

From (A.3.2), we can see that the four eigenvalues are positive or two are
positive and two are negative. From (A.3.3), the case of four positive roots can be
ruled out. As a result, the system has two negative roots. Furthermore, according
to (A.3.4), the eigenvalues may be complex conjugates and the system may exhibit

cyclical behavior.

145

3.5.2 The dominant eigenvalue ray

We assume that 11,,7' = 1, 2 is the non-positive roots, with 111 > 112. Then, for 7' =

1, 2, it follows that

 

 

f X — V, 0 O 0 9 (11,1 0
_ax 0 — V, —1 0 W72 0

2 — x = , (3.64)
’2‘1‘6‘PX —‘-’7(<p + 95) —5(1—52‘) — 11, -—6 (11,3 0
L 0 O 5 -6 - 71,; L974 0

where w,,, j = 1, 2, 3, 4, are the element of the eigenvector associated with root 11,.
Therefore,
(11,2 1

— = —— > 0. (3.65)
“’73 ”7'

Now, let’s look at the dominant eigenvector ray. Setting to zero constant cor—

responding to the unstable roots ( 113,114), the solution to this system takes the

form

it - iss =A1W11 eX11041) + A29121 eX17001)
1 N — 1 N =A t A t
08 311 081/33 19012 exp(Vi )+ 29722 exp(Vz )
7r, — 7rH =A1w13 exp(111t) + A2w23 exp(112t) (3.66)
771 - 7? H =A1W14 exp(l/lt) + A29124 exp(Vfl),
where A,,7' = 1, 2, denote the constants associated with root 11,. Since 111 > 112, it

follows that:

log y.” - log 719$

 

 

1' _ . «419012 exp(Vlt) + A2922 8Xp(V2t)
1m H — 11m
t—mo 7r, — 7r t—700 A1w13 exp(111t) + 14271123 exp(112t)
____ A19112 + A29122 ex13((1/2 - V1)t)
t-+oo A19713 + A2923 exp((V2 - V1)t)

=“—’2 > 0. (3.67)
“’13

 

146

logy,” logij=0' ~ 10855.” =0

SS, / Dominant
Eigenvector my

log J’gs.

 

 

EVA

75" 7t” 72',

Figure 3.1: Dynamic system

 

 

 

 

 

 

 

 

 

,- A
r+x”
r+nL
A
0 t1 Time

Figure 3.2: Time path: nominal interest rate

147

 

 

 

 

 

 

 

 

 

 

 

 

72'
7:” I
”L
. >
O 11 Tune
Figure 3.3: Time path: inflation
N
yssl
N
. b
0 t1 T1me

Figure 3.4: Time path: output of non-tradables

148

 

 

 

 

 

 

 

 

 

 

 

 

S
[85" _
/
. D
o t, T1me
Figure 3.5: Time path: labor supply
A
E!
E ss :
q i
1 . ,
O t 1 Tune

Figure 3.6: Time path: nominal exchange rate

149

 

 

 

 

 

 

 

eSSo \/
_>

0 t, Time

Figure 3.7: Time path: real exchange rate

150

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