Description
The purpose of this paper is to deal with the dynamics of a Neo-Keynesian model applied
to a small open economy, in order to show the impact of commercial openness on the choice of the
optimal inflation target.
Journal of Financial Economic Policy
Degree of openness and inflation targeting policy: model of a small open economy
J ihene Bousrih
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To cite this document:
J ihene Bousrih, (2012),"Degree of openness and inflation targeting policy: model of a small open
economy", J ournal of Financial Economic Policy, Vol. 4 Iss 3 pp. 232 - 246
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Degree of openness and in?ation
targeting policy: model of a small
open economy
Jihene Bousrih
University of Rennes 1, Rennes, France
Abstract
Purpose – The purpose of this paper is to deal with the dynamics of a Neo-Keynesian model applied
to a small open economy, in order to show the impact of commercial openness on the choice of the
optimal in?ation target.
Design/methodology/approach – The author uses a neo-Keynesian model with calibration for
Chile.
Findings – The results show that there is a relation between the degree of openness and the type of
in?ation targeting policy.
Originality/value – The originality of the paper is to use a neo-Keynesian model to deal with a small
open economy, which uses in?ation targeting as a monetary rule.
Keywords Chile, National economy, Monetary policy, Prices, In?ation, Consumer price index in?ation,
Producer price index in?ation, Pass-through, Degree of openness
Paper type Research paper
1. Introduction
Since the 1990s, several emerging economies adopt the in?ation targeting as a
monetary policy. The literature trying to explain the different aspects of in?ation
targeting is abundant (Bernanke et al., 1999; Amato and Gerlach, 2002; Truman, 2003;
Giannoni and Woodford, 2003; Martin et al., 2004; Carare and Stone, 2006;
Sanchez-Fung, 2008).
Why the countries choose to target in?ation? Many reasons can be presented: ?rst,
it contain in?ation and make it converge towards a target value. Second, it increases
the credibility of the monetary authorities. Finally, it anchor in?ationary anticipations
of the economic agents and ensure a stable economic environment for a constant
expansion.
For a long time, the emerging markets are characterized by a high degree of openness.
So, the high degree of Pass-Through in these countries has an important effect on
in?ation. Calvo (2001) estimate that the transmission of exchange rate ?uctuations to the
domestic prices is four times more important in the emerging markets than in
the developed ones. Ho and McCauley (2003) compiled a several empirical studies over
the period 1980-2000. They showed that the degree of Pass-Through, related to an
important degree of openness, is higher in the emerging markets.
Nevertheless, an important degree of openness has some ambiguous effects. On one
side, a higher degree of openness means that the economy is strongly in?uenced by
the transmission of exchange rate variations to prices, which brings us to a positive
correlation between the degree of openness and in?ation. But on the other side, for open
economies who adopt in?ation targeting, the central bank try to keep in?ation rate
The current issue and full text archive of this journal is available at
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JFEP
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Journal of Financial Economic Policy
Vol. 4 No. 3, 2012
pp. 232-246
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576381211245962
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at a low level and to minimize the volatility of price level, which limits transmission
of exchange rate variations to consumer good’s prices. Romer (1993) illustrates the
relation between in?ation and the degree of openness. He shows that in the case of
absence of a well de?ned monetary policy, a high degree of openness lead to an
important volatility in the in?ation rate. Whereas in the presence of an explicit
monetary rule with an objective of in?ation, Romer (1993) shows that there exists a
negative relation between the degree of openness and the in?ation.
The impact of exchange rate volatility has a direct or an indirect impact on prices
throughthe change inthe price of the imported consumer goods. Inthe case of small open
economies, dependence towards the rest of the world through the imports plays a very
important rule to sustain domestic economy. In this case we have a consumption basket
largelycomposed of imported goods, implying that the degree of openness in?uences the
price’s variations. Consequently, the central bankface two choice: targeting CPI in?ation
which precisely includes the degree of openness in a complete way through the imported
consumer goods, or targeting PPI in?ation which also includes the variations of
exchange rate but in an incomplete way through the price of the intermediate imported
goods. The aim of this paper is to study the relation between the degree of openness and
the variable that we should target (CPI in?ation or PPI in?ation). So, we try to study the
impact of an important degree of economy’s openness on key variables such as in?ation,
output gap, exchange rate and interest rate when we adopt several in?ation targeting
policies. Then, we check whether the choice of the variable to target is in?uenced by the
nature of the exogenous shocks, or not. The article is organized as follows: in the ?rst
part, we present the model with microeconomic foundations which includes a
representative household, a ?rm, a government and a monetary authority. In a second
part, we calibrate the model with the Chile’s parameters as an example of small open
economy. Finally, the last part presents results and conclusion.
2. The model
Our model presents an adaptation of a neo-Keynesian model applied to a small open
economy. The starting point of our analysis is a model with stochastic growth which
includes monopolistic competition and nominal prices rigidity (Calvo, 1983). The
adoption of price rigidity model allows having more important dynamic effects of the
monetary policy than a model with ?exible prices, commonly used in modeling of a
small open economy. The model describes the worldwide economy as a set of small
open economies of which the number is normalized to 1. Each economy has a negligible
size and thus cannot in?uence the rest of the world, these economies share the same
preferences, technologies and markets structures. First, we focus on study of
consumers and producers behavior in one of these economies considering several
in?ation targeting rules. But before starting our analysis, we make a short remark on
the notation we adopt through this article. Our interest focus on the study of a small
open economy and its interaction with the rest of the world, therefore the not indexed
variables will refer to the modeled economy. The other variables indexed by i [ [0.1]
refer to one of the economies which constitute the rest of the world and ?nally the
variables with an asterisk correspond to the rest of the whole world. The modeled
economy is represented by a central bank, a tax authority which is the government,
a representative consumer and a competitive producer. Time is considered as discrete.
In?ation
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2.1 Households
Our small open economy is inhabited by a representative consumer k whose utility
function is given by:
E
t
½U
s
ðk; jÞ? ¼ E
t
1
s¼t
b
s2t
C
s
ðk; jÞ
12s
1 2s
2
L
s
ðk; jÞ
1þc
1 þc
_ _
_ _
; ð1Þ
with; 0 , b , 1 is the discount rate, C
t
ðk; jÞ consumption of consumer k for good j, c
the Frishienne elasticity and L
t
ðk; jÞ the labor provide by the consumer k to produce a
good j.
The budget constraint of an individual household is given by:
P
t
C
t
þ G
t;tþ1
B
tþ1
¼ ð1 2tÞW
t
L
t
þ B
t
þ TR
t
; ð2Þ
with B
tþ1
is the repayment of the period t þ 1 for debts contracted at the period t, W
t
is
the nominal wage, TR
t
is transfer of the government, G
t;tþ1
¼ ð1 þ i
t
Þ
21
is the factor of
actualization between the period t and the period t þ 1 and t is the wage’s tax imposed
by the government.
In order to maximize his utility the representative consumer chooses to optimize his
consumption C
t
and the quantity of labor L
t
under the budget constraint formulated by
equation (2), we obtain the following ?rst-order conditions:
bE
t
C
tþ1
C
t
_ _
2s
P
t
P
tþ1
_ _ _ _
¼ G
t;tþ1
; ð3Þ
L
c
t
C
s
t
¼ ð1 2tÞ
W
t
P
t
: ð4Þ
The expression (3) represents the Euler equation for consumption whereas expression
(4) corresponds to the Euler equation for labor. The index of total consumption C
t
is
de?ned by:
C
t
¼ ½ð1 2gÞ
1=h
ðC
H;t
Þ
ðh21Þ=h
þg
1=h
ðC
F;t
Þ
ðh21Þ=h
?
h=ðh21Þ
; ð5Þ
with h . 1 is the elasticity of substitution between the domestic goods and the foreign
goods and g corresponds to the proportion of the domestic consumption allocated to
the imported goods.
We de?ne the total consumption price index (CPI) by:
P
t
¼ ð1 2gÞP
ð12hÞ
H;t
þgP
ð12hÞ
F;t
_ _
1=ð12hÞ
2.2 Firms
We suppose a ?xed number of ?rms with monopolistic competition held by the
households, their number is standardized to 1. Each ?rm produces a differentiated
good and use the same technology. The production requires one factor of production
which is labor:
Y
t
ð jÞ ¼ Z
t
L
t
ð jÞ; ð6Þ
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with Z
t
represent an exogenous factor of technology, and L
t
ð jÞ is the quantity of labor
used to produce a good j.
The model include price rigidity as in Calvo (1983). We suppose that only a fraction
of ?rms is authorized to adjust its prices each period. For this period, each ?rm is face
to the probability (1 2 a) correspondent to the adjustment of his price, independently
of the last period in which the ?rm has adjusted its price.
We note
P
H;t
ð jÞ the ?xed price by the ?rm at the period t, under the assumption of
Calvo (1983), P
H;tþk
ð jÞ ¼
P
H;t
ð jÞ with a probability a
k
pour k ¼ 0; 1; 2; . . .
The producers are a monopolistic competitors, so each ?rm have a demand function
expressed by:
Y
tþk
ð jÞ ¼
P
H;t
ð jÞ
P
H;tþk
_ _
2u
C
H;tþk
þ
_
1
0
C
H;tþk
ði Þdi
_ _
; ð7Þ
The pro?t function of ?rm will be noted:
Max
1
k¼0
a
k
E
t
G
t;tþk
Y
tþk
P
H;t
2MC
n
tþk
_ _ _ ¸ _ _
_ _
; ð8Þ
with a the probability that the producing consumer maintains the same price of the
previous period and MC
n
t
¼ ððð1 2tÞw
t
Þ=Z
t
Þ is the nominal marginal cost[1].
The problem of the producer will be to ?nd the price
P
H;t
ð jÞ which maximizes the
pro?t function under demand constraint.
The ?rst-order condition is given by:
1
k¼0
a
k
E
t
G
t;tþ1
Y
tþk
P
H;t
2
u
u 21
MC
n
tþk
_ _ _ _
¼ 0; ð9Þ
from where we deduce the expression of the optimal price (in log) for a representative
?rm which adjusts his price at the period t:
p
H;t
¼ m þ ð1 2baÞ
1
k¼0
ba
k
E
t
{mc
tþk
þ p
H;t
}; ð10Þ
with
p
H;t
is (log) domestic price, m ¼ logðu=u 21Þ corresponds to (log) of the mark-up
at the stationary state and mc
tþ1
is (log) of the marginal cost at the stationary state.
Equation (10) shows us that the decision of ?xing prices is Forward-Looking. The
reason is that the ?rms at the time when they adjust their prices suppose that this price
will be valid during a given number of period and thus they adjust it like a mark-up of
anticipated marginal cost’s average and not only current marginal cost.
2.3 Government
We suppose that the government adjust its budget each period. The budget constraint
of the government is given by:
tP
H;t
Y
H;t
2TR
t
¼ 0: ð11Þ
In?ation
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This equation shows that the transfer of the government equalizes the domestic income
on which we applies a tax rate t, this latter eliminates the distortions on the market
related to the monopolistic power of the ?rms (?exible prices equilibrium and rigid
prices equilibrium).
2.4 Relation between domestic and foreign prices
2.4.1 Price level and terms of trade. Before beginning our analysis of equilibrium, we
introduce some de?nitions.
We de?ne the term of trade between the domestic economy and country i by
S
i;t
¼ ðP
i;t
=P
H;t
Þ. The effective termof trade will be noted S
t
¼ ðP
F;t
=P
H;t
Þ, the log form
of this equation gives us s
t
¼ log S
t
¼ p
F;t
2p
H;t
. While replacing in the expression of
the price index P
t
, there we obtain a linear expression of the price level CPI:
p
t
¼ ð1 2gÞp
H;t
þgp
F;t
¼ p
H;t
þgs
t
: ð12Þ
Thus, we can de?ne the log of CPI in?ation:
p
t
¼ ð1 2gÞp
H;t
þgp
F;t
: ð13Þ
It follows from this expression:
p
t
¼ p
H;t
þges
t
: ð14Þ
with p
H;t
¼ p
H;t
2p
H;t21
is the domestic in?ation and p
F;t
¼ p
F;t
2p
F;t21
is the
foreign in?ation.
Equation (14) link the two measure of in?ation (domestic and CPI) through the
terms of trade and the coef?cient g which de?ne the degree of economy’s openness.
2.4.2 Uncovered interest parity. Under the assumption of a complete ?nancial
market, the domestic price of a foreign good is given by the uncovered interest parity:
G
t;tþ1
i
t
2i
i
t
E
i;tþ1
E
i;t
_ _ _ _
¼ 0;
with G
t;tþ1
¼ ð1=1 þ i
t
Þ is the factor of actualization for period t þ 1. We take a linear
form of the preceding expression and aggregate it on the whole of small economies i,
we ?nd the expression of uncovered interest parity:
i
t
2i
*
t
¼ E
t
{e
tþ1
} 2e
t
: ð15Þ
3. Aggregation of the model
The modeled economy is de?ned as a sequence of quantities:
{Q
t
}
1
t¼0
¼ Y
t
; C
t
; C
H;t
; C
*
H;t
; C
F;t
; L
t
_ _
1
t¼0
a sequence of price:
{P
t
}
1
t¼0
¼ P
t
; P
F;t
; P
H;t
; P
*
t
; W
t
; Q
t
; S
t
; E
t
_ _
1
t¼0
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and an interest rate rule, i
t
:
.
Equilibrium on goods and services market:
Y
t
ðjÞ ¼ C
H;t
ð jÞ þ
_
1
0
C
H;t
ði; jÞdi ¼ C
H;t
þ C
*
H;t
Y
*
t
¼ C
*
t
.
Equilibrium on labor market:
_
k
L
s
ðkÞdk ¼
_
j
L
d
ð jÞdj
L
t
¼ C
2s
t
ð1 2tÞW
P
_ _
1=c
3.1 Aggregate demand
The equilibrium on goods and services market, requires a level of production for all
j1[0.1], which satis?es the following condition:
Y
t
ð jÞ ¼ C
H;t
ð jÞ þ
_
1
0
C
H;t
ði; jÞdi; ð16Þ
Using the form of the expression (16) at the steady state, we ?nd:
y
t
¼ c
t
þ
gv
s
s
t
; ð17Þ
with v ¼ sz þ ð1 2gÞðsh 21Þ. An analogical condition for country i allows us to
write the following expression: y
i
t
¼ c
i
t
þ ðgv=sÞs
i
t
. Aggregating the latter for the rest
of the world[2], we obtain:
y
*
t
¼
_
1
0
y
i
t
di ¼ c
*
t
; ð18Þ
with y
*
t
is the foreign output and c
*
t
is the foreign consumption of the rest of the world.
Combining equations (14), (17) and (18), we obtain the expression of domestic
demand:
y
t
¼ y
*
t
þ
1
s
g
s
t
; ð19Þ
with s
g
¼ ðs=ð1 2gÞ þgvÞ . 0.
If we replace the equation of output (19) into the Euler equation of consumption, we
obtain the expression of the aggregate demand:
y
t
¼ E
t
{y
tþ1
} 2
1
s
g
i
t
2E
t
{p
H;tþ1
} þgQE
t
{ey
*
tþ1
}
_ _
; ð20Þ
with: Q ¼ ðsz 21Þ þ ð1 2gÞðsh 21Þ, i
t
is the nominal interest rate, p
H;tþ1
is the
domestic in?ation at the period t þ 1 and y
*
tþ1
is the foreign output at the same period.
In?ation
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3.2 Aggregate supply
Taking the price expression obtained by maximization of the pro?t function of ?rm, we
obtain the expression of domestic in?ation which represent a formulation of the
Phillips curve of new Keynesian (NKPC):
p
H;t
¼ bE
t
{p
H;tþ1
} þ k
g
x
t
; ð21Þ
with k
g
¼ lðs
g
þr
z
Þ, l ¼ ððð1 2baÞð1 2aÞÞ=aÞ and x
t
¼ y
t
2y
flex
is the output gap
which is the difference between the domestic output y
t
and the output obtained at
?exible price equilibrium y
?ex
.
At this stage, we notice that the degree of openness of the economy g affects the
dynamics of in?ation through the slope of Phillips curve in other term through its
impact on output gap.
The expression of domestic in?ation combined with equation (14) allows us to ?nd
the expression of a Phillips curve for CPI in?ation:
p
t
¼ bE
t
{p
H;tþ1
} þ k
g
x
t
þgðs
t
2s
t21
Þ: ð22Þ
3.3 Monetary policy
We consider a simple Taylor rule according to which the central bank adjust nominal
interest rate in response to anticipated in?ation and delayed interest rate. Svensson
(1997) considers that the monetary authorities when they target in?ation, they always
have an even implicit target of production. Our choice for a simple policy of Taylor,
which includes in?ation and interest rate, implicitly includes an adjustment of output
through the expression of aggregate supply presented more in details in the previous
part. The monetary policy is given, then, by the following expression:
i
t
¼ ri
t21
þ ð1 2rÞðE
t
½p
tþ1
? 2 pÞ þ1
t
; ð23Þ
with: r
i
is the degree of smoothing of interest rate, i
t21
is delayed nominal interest rate
and p is the in?ation target ?xed by the central bank. The selected monetary rule will
vary according to the variable of in?ation which the central bank seeks to target, then
we have two types of monetary rules:
(1) CPI in?ation targeting policy:
i
t
¼ ri
t21
þ ð1 2rÞ E
t
½p
tþ1
? 2 p
_ _
þ1
t
; ð24Þ
(2) Domestic in?ation targeting policy:
i
t
¼ ri
t21
þ ð1 2rÞ E
t
½p
H;tþ1
? 2 p
_ _
þ1
t
: ð25Þ
For the rest of this paper we take as a reference the framework of Monacelli (2005), we
suppose that the domestic in?ation targeting policy guarantee at the same time a
stabilization of domestic price level and output gap. This result is con?rmed by
Rotemberg and Woodford’s research (1999) which suppose that if there are a transfer
ratio of the government t which is constant, that makes it possible to counterbalance
the distortions associated with the monopolistic power of ?rms on the market and
consequently these ?rms will adjust price by considering the case of equilibrium at
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?exible price. While adopting a domestic in?ation targeting policy, prices of domestic
goods will be consequently constant, which involves that the real marginal costs
equalize the reverse of the mark-up[3]. The intuition is that by ?xing the mark-up and
thus the marginal cost at their ?exible price equilibrium, the ?rm do not may ?nd it
bene?cial any more to adjust their prices and thus the domestic prices remain constant
(Corsetti and Pesenti, 2001; Gali, 2003). With ?exible prices, the relation between the
output gap x
t
and the marginal cost mc
t
is formulated as follows:
mc
t
¼ ðc þs
g
Þx
t
When the marginal cost is stabilized on its equilibrium level, the expression combined
above with equation (21) of the model shows that the output gap will be
consequently constant (Gali, 2003).
4. Calibration
The choice of the variables of calibration for Chile, is based on standard values used
in the literature. The choice for Chile is due to the fact that this small open economy
is considered as one of the emergents economies which succeeded its in?ation
targeting policy in comparison to the other countries. In spite of its in?ationary past,
Chile could reach very low levels of in?ation during very short time by ensuring a
great credibility of its monetary policy. Its dependence on outside did not prevent it to
keep stable its level of in?ation and from thus ensuring the good behavior of its
economy. Table I recapitulates the various parameters used in the calibration of
our model.
The discount factor is b ¼ 0.99. The degree of openness of the economy or the
proportion of the domestic consumption allocated to the imported goods is measured
by the ratio of the imports to the GDP over the period 1998-2000 (Parrado, 2004). This
parameter will be in a ?rst case of reference equal to g
0
¼ 0.29 then we vary it, g
1
¼ 0.2
and g
2
¼ 0.6, in order to see the effect of an increase in the degree of openness on the
choice of the monetary policy.
The economy is open toward outside, so the elasticity of substitution between the
domestic goods and the foreign goods equal h ¼ 1.5.
Parameters of Chile
b 0.99
g
0
0.29
g
1
0.2
g
2
0.6
a 0.75
u 4.33
h 1.5
c 0.63
t 0.25
s 1
r
i
0.8
r
z
0.8
r
yfo
0.8
Table I.
Parameters of calibration
In?ation
targeting policy
239
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The elasticity of substitution between the various varieties of goods in the same
economy is u ¼ 4.33 (Parrado, 2004), which implies a mark-up at the stationary state
m ¼ 26 2 27 percent. According to Moyen and Sahuc (2008), the reverse of Frishienne
elasticity is c ¼ 0.63.
The parameter responsible of the nominal rigidity of the prices is a ¼ 0.75 for Chile,
which corresponds to only one annual adjustment of the prices.
Finally, the parameters of the interest rate rule and the auto regression process of
the exogenous shocks are r
i
¼ 0.8, r
Z
¼ 0.8 and r
yFo
¼ 0.8.
5. Results
The simulation of our model gives us the following results, we start by using the
parameters of Chile without bringing any modi?cation, then we modify the parameter
g which re?ects the degree of openness of the Chilean economy and we study the
impulse response which we will have following the exogenous shocks.
5.1 CPI in?ation targeting
We suppose ?rst, that the Chilean monetary authorities target the CPI in?ation which
includes at the same time domestic in?ation and imported in?ation through the foreign
consumer goods.
5.1.1 Productivity shock. The simulation of our model gives us the following graphs
which illustrate the impulse response of different variables, following a shock of
productivity: CPI in?ation, domestic in?ation, output gap, nominal interest rate, real
exchange rate, terms of exchange, CPI price level and domestic price level.
The ?rst aim of the monetary authorities with a CPI in?ation targeting policy is to
stabilize the CPI price level as well as the level of CPI in?ation.
Following a positive shock of productivity of 1 percent, domestic in?ation varies but
in a small proportion, whereas CPI in?ation remains constant. The improvement of the
productivity involves a persistent reduction in the nominal interest rate which will
in?uence favorably the consumption and the output. Figure 1 shows us that on the one
hand the increase in domestic in?ation involves a real appreciation whereas on the
other hand, the fall of the domestic price level involves an increase in the terms of trade.
By increasing g
1
. g
0
, we notice that the adjustment of the variables is modi?ed.
Although CPI in?ation remained constant when we consider the CPI in?ation
targeting, the other variables became much more volatile in comparison with the
situation of reference g
0
. The variability of the degree of openness in?uences the
aggregate supply, a modi?cation of g affect the slope of the curve through the output
gap, which according to equation (21) of the model implies a fall of the output gap,
which generates consequently a contractionary monetary policy that increase the
interest rate.
A more important openness degree results in an increase in the imports of the
foreign goods what causes an improvement in the demand of imported goods and
consequently a fall in the reciprocal demand for domestic goods, which makes them
less competitive for the consumers. Equation (14) which connects two measurements of
in?ation through the terms of trade, shows us that an increase in the degree of
openness, involves a fall of domestic in?ation. This effect is still con?rmed, the raise in
prices of the domestic goods involves a fall of the terms of trade, which implies a real
appreciation of domestic currency.
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At this stage we can underline, that according to the impulse response of the various
variables, we note that the increase in the degree of economy openness involves a greater
variability translated through nominal interest rate, the terms of trade and real
exchange rate.
5.1.2 Foreign GDP shock. A shock on foreign variables generally have a very
important impact by considering the small open economies, considering in most case
that economies are very dependent on outside. So a variation of the foreign GDP is
quickly transmitted on the national aggregates.
The impulse response of Figure 2 are a little different from those which preceding.
An improvement of the foreign GDP of 1 percent involves a rise in the domestic
in?ation accompanied by a stable level of CPI in?ation and corresponding price level,
this result is foreseeable considering the monetary policy adopted by the central bank
which is the CPI in?ation targeting.
Following an increase in the supply of foreign goods, the monetary
authorities will adopt an expansionary monetary policy by lowering nominal
interest rate in order to support the domestic output, which generates a positive output
gap, which means that the level of production will be higher than the level in
equilibrium state.
On another side, the fall of the domestic price level involves an increase in the terms
of trade combined with an increase in real exchange rate explaining by the raise
Figure 1.
Impulse responses to a
shock of productivity
In?ation
targeting policy
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of domestic in?ation. This increase in exchange rate involves a depreciation of the
domestic currency encouraging exports and dissuading the imports.
This effect is ampli?ed by increasing the degree of openness, the volatility of the
variables increases in a very important way. The output gap, the terms of trade and
the real exchange rate reach a volatility of 5 percent. This important volatility is due to
the increase in the demand of foreign goods which initially affect the price of the
imported goods and considering the increase of g, will modify the composition of CPI
price level in favor of imported goods.
We could conclude at this level that a foreign GDP shock allows to an increase of the
proportion of imported goods in the domestic consumption basket increasing the
degree of Pass-Through towards domestic goods prices, which induces a greater
volatility of economic variables, in spite of CPI in?ation targeting.
5.2 Domestic in?ation targeting
We applies in this part the same model but we suppose this time that the monetary
authorities of Chile adopt a policy of domestic in?ation targeting.
5.2.1 Productivity shock. We start by applying a shock of productivity by
distinguishing between our situation of reference g
0
and the adjusted situation g
1
. g
0
.
Considering a domestic in?ation targeting, Figure 3 shows that the adjustment of
the variables is modi?ed. The goal of monetary authorities, in this case, will be to
stabilize the domestic corresponding in?ation and price level.
Figure 2.
Impulse responses to a
foreign GDP shock
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The level of the output gap is constant by considering the rule of domestic in?ation
targeting, which con?rms the results of Monacelli (2005).
We notices a drop in the level of nominal interest rate, thus it involve implicitly an
increase of consumption and output. This increase in output is not re?ected through
the output gap which remains constant following the shock, that is due to the fact that
by adopting a target of domestic in?ation, the central bank leads an implicit target of
output gap and then tends to bring closer the level of domestic production of the level
of equilibrium of long run (Svensson, 1997).
Following a positive shock of productivity, the parity of interest rate can be
presented as an explanation of the reaction of real exchange rate. The fall of nominal
interest rate involves a depreciation of the national currency and thus increases exports
what explains in its turn the rise of the production.
Monacelli (2005) still underline, that in the event of domestic in?ation targeting,
a depreciation of the national currency, due to a shock of productivity, involves an
increase in CPI in?ation.
By increasing the degree of openness of the economy, we can say that the
adjustment of the variables is made in the same manner but we notice an important
volatility compared to the situation of reference. Nevertheless, this idea is not valid for
real exchange rate, the terms of trades and nominal interest rate. The explanation
Figure 3.
Impulse responses to a
shock of productivity
In?ation
targeting policy
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is simple, when we consider a domestic in?ation targeting policy, a variation of g lead
to a variation of CPI in?ation without in?uencing the level of terms of trade.
We notice that the level of real exchange rate will drop on a level lower than in the
case of g
0
. Finally, the stability of output gap, even with an increase of g makes interest
rate nominal insensitive to this variation of the degree of openness.
We can conclude that when we consider a shock of productivity, we notice that by
comparing the volatility of variables with two different targeting monetary rules, we
can stress that the degree of transmission of the exogenous variations is more
important with a domestic in?ation targeting policy. In addition, with a CPI in?ation
targeting policy, we ?nd that the Pass-Through is less important and thus the reaction
of the variables to an increase of g, is less marked with a volatility on average not
exceeding 0.5 percent (Flamini, 2007).
5.2.2 Foreign GDP shock. We present in this part the impulse response of Chile with
a domestic in?ation targeting policy to a shock of foreign GDP. We compare, as
mentioned above, a ?rst case g
0
to a second case in which we have g
1
. g
0
.
Figure 4 shows that we ?nd a constant level of domestic level of in?ation, of output
gap and domestic price, compatible with the objective of the central bank.
Nevertheless, when we consider the same shock of foreign GDP but under the two
monetary policies, we ?nd different results.
Figure 4.
Impulse responses to a
foreign GDP shock
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The ?rst remark that we can notice by comparing the impulse response for an increase
in the foreign GDP, it is that volatility is much less important with a high degree of
openness, this is valid for a domestic in?ation targeting rule. In fact, when we target
domestic in?ation, the domestic goods price does not vary and thus the variations of
terms of trades are very small. The stability of the output gap is accompanied with a
small variation of interest rate compared to the situation where we have a monetary
rule centered on CPI in?ation.
We can say at this level, that by considering a foreign shock, the domestic in?ation
targeting policy offers more stabilizing characteristics for the domestic price level, the
level of in?ation corresponding and the output gap what, in the event of increase of g,
does not in?uence in an important way the behavior of the economic variables.
While referring to the preceding results, we say that when we consider the case of
reference g
0
, it is more optimal for Chile to adopt a CPI in?ation targeting policy in the
event of domestic or foreign shock. Whereas by increasing the degree of openness, the
choice of monetary policy becomes dependent of the nature of the exogenous shock.
For a domestic shock such as an improvement of the productivity, the optimal rule is
the CPI in?ation targeting, whereas for a foreign shock such as the increase in the
demand of the imported goods the optimal rule would be the domestic in?ation
targeting.
6. Conclusion
We tried through this paper to study the impact of a high degree of openness on the
choice of the in?ation targeting policy which should be adopted by the central bank.
We applied a neo-Keynesian model characterised by nominal rigidities and monopolistic
competition, we take the case of Chile as a reference. We ?nd on the one hand that there is
a signi?cant difference in the impulse response when we consider the two in?ation
targeting policies (domestic and CPI in?ation targeting). And in the other hand, there is a
link between the adopted monetary policy and the nature of the exogenous shocks. By
taking the case of reference g
0
in which we did not modify the Chile’s parameters, we ?nd
that the optimal policy adopted by the monetary authorities would be the CPI in?ation
targeting, which includes at the same time the variations of the domestic prices and the
variations of foreign exchange rate, this result is valid by considering a domestic or a
foreign shock. Now, when we consider the case where we modi?es the degree of
openness of the economy g
1
. g
0
, the choice of the optimal policy becomes dependent on
the nature of the exogenous shock. With a positive shock of productivity, we notice that
the degree of Pass-Through towards the economy is controlled much more with a CPI
in?ation targeting policy than with a domestic in?ation targeting one. Whereas, while
considering a foreign GDP shock, the choice of a rule centered on domestic in?ation
becomes more optimal because it ensures at the same time a stability of the domestic
goods price level, corresponding in?ation and the output gap level.
Notes
1. Monetary Policy and Exchange Rate Volatility in a Small Open Economy, Monacelli (2005).
2. We suppose that
_
1
0
s
i
t
di ¼ 0.
3. We suppose that in ?exible price equilibrium, the marginal cost (log) equalizes the reverse of
the mark-up(log); mc
t
¼ 2m ¼ 2logðu=u 21Þ.
In?ation
targeting policy
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References
Amato, J. and Gerlach, S. (2002), “In?ation targeting in emerging market and transition
economies: lessons after a decade”, European Economic Review, Vol. 46 Nos 4/5, pp. 781-90.
Bernanke, S., Laubach, T., Mishkin, F. and Posen, A. (1999), In?ation Targeting: Lessons from the
International Experience, Princeton University Press, Princeton, NJ.
Calvo, G. (2001), “Capital market and the exchange rate: with special reference to the dollarization
debate in Latin America”, Journal of Money, Credits and Banking, Vol. 33 No. 2, pp. 312-34.
Carare, A. and Stone, M. (2006), “In?ation targeting regimes”, European Economic Review, Vol. 50
No. 5, pp. 1297-315.
Flamini, A. (2007), “In?ation targeting and exchange rate pass-through”, Journal of International
Money and Finance, Vol. 26 No. 7.
Giannoni, M.P. and Woodford, M. (2003), “Optimal in?ation targeting rules”, National Bureau of
Economic Research, NBER Working Papers 9939.
Ho, C. and McCauley, R. (2003), “Living with ?exible exchange rates: issues and recent
experience in in?ation targeting emerging market economies”, Working Paper 130,
available at: www.bis.org/publ/work130.htm
Martin, C., Arghyrou, M. and Milas, C. (2004), “Nonlinear in?ation dynamics: evidence from the
UK”, Money Macro and Finance (MMF) Research Group Conference 2003, Money Macro
and Finance Research Group.
Monacelli, T. (2005), “Monetary policy in a low pass-through environment”, Journal of Money
Credit and Banking, Vol. 37 No. 6, pp. 1047-66.
Moyen, S. and Sahuc, J.-G. (2008), “Le mode´le d’e´quilibre ge´ne´ral de la ‘nouvelle synthe`se’: quelles
hypothe`ses retenir?”, Economie et Pre´vision, Vols 2/3, pp. 15-34.
Parrado, E. (2004), “In?ation targeting and exchange rate rules in an open economy”, IMF
Working Paper 04/21.
Romer, D. (1993), “Openness and in?ation: theory and evidence”, The Quarterly Journal of
Economics, Vol. 108 No. 4, pp. 869-903.
Sanchez-Fung, J.R. (2008), “In?ation targeting and monetary analysis in Chile and Mexico”,
Quantitative and Qualitative Analysis in Social Sciences, Vol. 1, pp. 40-62.
Svensson, L. (1997), “Optimal in?ation targets, ‘conservative’ central banks, and linear in?ation
contracts”, National Bureau of Economic Research 5251.
Truman, E.M. (2003), In?ation Targeting in the World Economy, Peterson Institute for
International Economics, Washington, DC.
Corresponding author
Jihene Bousrih can be contacted at: [email protected]
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The purpose of this paper is to deal with the dynamics of a Neo-Keynesian model applied
to a small open economy, in order to show the impact of commercial openness on the choice of the
optimal inflation target.
Journal of Financial Economic Policy
Degree of openness and inflation targeting policy: model of a small open economy
J ihene Bousrih
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Degree of openness and in?ation
targeting policy: model of a small
open economy
Jihene Bousrih
University of Rennes 1, Rennes, France
Abstract
Purpose – The purpose of this paper is to deal with the dynamics of a Neo-Keynesian model applied
to a small open economy, in order to show the impact of commercial openness on the choice of the
optimal in?ation target.
Design/methodology/approach – The author uses a neo-Keynesian model with calibration for
Chile.
Findings – The results show that there is a relation between the degree of openness and the type of
in?ation targeting policy.
Originality/value – The originality of the paper is to use a neo-Keynesian model to deal with a small
open economy, which uses in?ation targeting as a monetary rule.
Keywords Chile, National economy, Monetary policy, Prices, In?ation, Consumer price index in?ation,
Producer price index in?ation, Pass-through, Degree of openness
Paper type Research paper
1. Introduction
Since the 1990s, several emerging economies adopt the in?ation targeting as a
monetary policy. The literature trying to explain the different aspects of in?ation
targeting is abundant (Bernanke et al., 1999; Amato and Gerlach, 2002; Truman, 2003;
Giannoni and Woodford, 2003; Martin et al., 2004; Carare and Stone, 2006;
Sanchez-Fung, 2008).
Why the countries choose to target in?ation? Many reasons can be presented: ?rst,
it contain in?ation and make it converge towards a target value. Second, it increases
the credibility of the monetary authorities. Finally, it anchor in?ationary anticipations
of the economic agents and ensure a stable economic environment for a constant
expansion.
For a long time, the emerging markets are characterized by a high degree of openness.
So, the high degree of Pass-Through in these countries has an important effect on
in?ation. Calvo (2001) estimate that the transmission of exchange rate ?uctuations to the
domestic prices is four times more important in the emerging markets than in
the developed ones. Ho and McCauley (2003) compiled a several empirical studies over
the period 1980-2000. They showed that the degree of Pass-Through, related to an
important degree of openness, is higher in the emerging markets.
Nevertheless, an important degree of openness has some ambiguous effects. On one
side, a higher degree of openness means that the economy is strongly in?uenced by
the transmission of exchange rate variations to prices, which brings us to a positive
correlation between the degree of openness and in?ation. But on the other side, for open
economies who adopt in?ation targeting, the central bank try to keep in?ation rate
The current issue and full text archive of this journal is available at
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Journal of Financial Economic Policy
Vol. 4 No. 3, 2012
pp. 232-246
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576381211245962
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at a low level and to minimize the volatility of price level, which limits transmission
of exchange rate variations to consumer good’s prices. Romer (1993) illustrates the
relation between in?ation and the degree of openness. He shows that in the case of
absence of a well de?ned monetary policy, a high degree of openness lead to an
important volatility in the in?ation rate. Whereas in the presence of an explicit
monetary rule with an objective of in?ation, Romer (1993) shows that there exists a
negative relation between the degree of openness and the in?ation.
The impact of exchange rate volatility has a direct or an indirect impact on prices
throughthe change inthe price of the imported consumer goods. Inthe case of small open
economies, dependence towards the rest of the world through the imports plays a very
important rule to sustain domestic economy. In this case we have a consumption basket
largelycomposed of imported goods, implying that the degree of openness in?uences the
price’s variations. Consequently, the central bankface two choice: targeting CPI in?ation
which precisely includes the degree of openness in a complete way through the imported
consumer goods, or targeting PPI in?ation which also includes the variations of
exchange rate but in an incomplete way through the price of the intermediate imported
goods. The aim of this paper is to study the relation between the degree of openness and
the variable that we should target (CPI in?ation or PPI in?ation). So, we try to study the
impact of an important degree of economy’s openness on key variables such as in?ation,
output gap, exchange rate and interest rate when we adopt several in?ation targeting
policies. Then, we check whether the choice of the variable to target is in?uenced by the
nature of the exogenous shocks, or not. The article is organized as follows: in the ?rst
part, we present the model with microeconomic foundations which includes a
representative household, a ?rm, a government and a monetary authority. In a second
part, we calibrate the model with the Chile’s parameters as an example of small open
economy. Finally, the last part presents results and conclusion.
2. The model
Our model presents an adaptation of a neo-Keynesian model applied to a small open
economy. The starting point of our analysis is a model with stochastic growth which
includes monopolistic competition and nominal prices rigidity (Calvo, 1983). The
adoption of price rigidity model allows having more important dynamic effects of the
monetary policy than a model with ?exible prices, commonly used in modeling of a
small open economy. The model describes the worldwide economy as a set of small
open economies of which the number is normalized to 1. Each economy has a negligible
size and thus cannot in?uence the rest of the world, these economies share the same
preferences, technologies and markets structures. First, we focus on study of
consumers and producers behavior in one of these economies considering several
in?ation targeting rules. But before starting our analysis, we make a short remark on
the notation we adopt through this article. Our interest focus on the study of a small
open economy and its interaction with the rest of the world, therefore the not indexed
variables will refer to the modeled economy. The other variables indexed by i [ [0.1]
refer to one of the economies which constitute the rest of the world and ?nally the
variables with an asterisk correspond to the rest of the whole world. The modeled
economy is represented by a central bank, a tax authority which is the government,
a representative consumer and a competitive producer. Time is considered as discrete.
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2.1 Households
Our small open economy is inhabited by a representative consumer k whose utility
function is given by:
E
t
½U
s
ðk; jÞ? ¼ E
t
1
s¼t
b
s2t
C
s
ðk; jÞ
12s
1 2s
2
L
s
ðk; jÞ
1þc
1 þc
_ _
_ _
; ð1Þ
with; 0 , b , 1 is the discount rate, C
t
ðk; jÞ consumption of consumer k for good j, c
the Frishienne elasticity and L
t
ðk; jÞ the labor provide by the consumer k to produce a
good j.
The budget constraint of an individual household is given by:
P
t
C
t
þ G
t;tþ1
B
tþ1
¼ ð1 2tÞW
t
L
t
þ B
t
þ TR
t
; ð2Þ
with B
tþ1
is the repayment of the period t þ 1 for debts contracted at the period t, W
t
is
the nominal wage, TR
t
is transfer of the government, G
t;tþ1
¼ ð1 þ i
t
Þ
21
is the factor of
actualization between the period t and the period t þ 1 and t is the wage’s tax imposed
by the government.
In order to maximize his utility the representative consumer chooses to optimize his
consumption C
t
and the quantity of labor L
t
under the budget constraint formulated by
equation (2), we obtain the following ?rst-order conditions:
bE
t
C
tþ1
C
t
_ _
2s
P
t
P
tþ1
_ _ _ _
¼ G
t;tþ1
; ð3Þ
L
c
t
C
s
t
¼ ð1 2tÞ
W
t
P
t
: ð4Þ
The expression (3) represents the Euler equation for consumption whereas expression
(4) corresponds to the Euler equation for labor. The index of total consumption C
t
is
de?ned by:
C
t
¼ ½ð1 2gÞ
1=h
ðC
H;t
Þ
ðh21Þ=h
þg
1=h
ðC
F;t
Þ
ðh21Þ=h
?
h=ðh21Þ
; ð5Þ
with h . 1 is the elasticity of substitution between the domestic goods and the foreign
goods and g corresponds to the proportion of the domestic consumption allocated to
the imported goods.
We de?ne the total consumption price index (CPI) by:
P
t
¼ ð1 2gÞP
ð12hÞ
H;t
þgP
ð12hÞ
F;t
_ _
1=ð12hÞ
2.2 Firms
We suppose a ?xed number of ?rms with monopolistic competition held by the
households, their number is standardized to 1. Each ?rm produces a differentiated
good and use the same technology. The production requires one factor of production
which is labor:
Y
t
ð jÞ ¼ Z
t
L
t
ð jÞ; ð6Þ
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with Z
t
represent an exogenous factor of technology, and L
t
ð jÞ is the quantity of labor
used to produce a good j.
The model include price rigidity as in Calvo (1983). We suppose that only a fraction
of ?rms is authorized to adjust its prices each period. For this period, each ?rm is face
to the probability (1 2 a) correspondent to the adjustment of his price, independently
of the last period in which the ?rm has adjusted its price.
We note
P
H;t
ð jÞ the ?xed price by the ?rm at the period t, under the assumption of
Calvo (1983), P
H;tþk
ð jÞ ¼
P
H;t
ð jÞ with a probability a
k
pour k ¼ 0; 1; 2; . . .
The producers are a monopolistic competitors, so each ?rm have a demand function
expressed by:
Y
tþk
ð jÞ ¼
P
H;t
ð jÞ
P
H;tþk
_ _
2u
C
H;tþk
þ
_
1
0
C
H;tþk
ði Þdi
_ _
; ð7Þ
The pro?t function of ?rm will be noted:
Max
1
k¼0
a
k
E
t
G
t;tþk
Y
tþk
P
H;t
2MC
n
tþk
_ _ _ ¸ _ _
_ _
; ð8Þ
with a the probability that the producing consumer maintains the same price of the
previous period and MC
n
t
¼ ððð1 2tÞw
t
Þ=Z
t
Þ is the nominal marginal cost[1].
The problem of the producer will be to ?nd the price
P
H;t
ð jÞ which maximizes the
pro?t function under demand constraint.
The ?rst-order condition is given by:
1
k¼0
a
k
E
t
G
t;tþ1
Y
tþk
P
H;t
2
u
u 21
MC
n
tþk
_ _ _ _
¼ 0; ð9Þ
from where we deduce the expression of the optimal price (in log) for a representative
?rm which adjusts his price at the period t:
p
H;t
¼ m þ ð1 2baÞ
1
k¼0
ba
k
E
t
{mc
tþk
þ p
H;t
}; ð10Þ
with
p
H;t
is (log) domestic price, m ¼ logðu=u 21Þ corresponds to (log) of the mark-up
at the stationary state and mc
tþ1
is (log) of the marginal cost at the stationary state.
Equation (10) shows us that the decision of ?xing prices is Forward-Looking. The
reason is that the ?rms at the time when they adjust their prices suppose that this price
will be valid during a given number of period and thus they adjust it like a mark-up of
anticipated marginal cost’s average and not only current marginal cost.
2.3 Government
We suppose that the government adjust its budget each period. The budget constraint
of the government is given by:
tP
H;t
Y
H;t
2TR
t
¼ 0: ð11Þ
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This equation shows that the transfer of the government equalizes the domestic income
on which we applies a tax rate t, this latter eliminates the distortions on the market
related to the monopolistic power of the ?rms (?exible prices equilibrium and rigid
prices equilibrium).
2.4 Relation between domestic and foreign prices
2.4.1 Price level and terms of trade. Before beginning our analysis of equilibrium, we
introduce some de?nitions.
We de?ne the term of trade between the domestic economy and country i by
S
i;t
¼ ðP
i;t
=P
H;t
Þ. The effective termof trade will be noted S
t
¼ ðP
F;t
=P
H;t
Þ, the log form
of this equation gives us s
t
¼ log S
t
¼ p
F;t
2p
H;t
. While replacing in the expression of
the price index P
t
, there we obtain a linear expression of the price level CPI:
p
t
¼ ð1 2gÞp
H;t
þgp
F;t
¼ p
H;t
þgs
t
: ð12Þ
Thus, we can de?ne the log of CPI in?ation:
p
t
¼ ð1 2gÞp
H;t
þgp
F;t
: ð13Þ
It follows from this expression:
p
t
¼ p
H;t
þges
t
: ð14Þ
with p
H;t
¼ p
H;t
2p
H;t21
is the domestic in?ation and p
F;t
¼ p
F;t
2p
F;t21
is the
foreign in?ation.
Equation (14) link the two measure of in?ation (domestic and CPI) through the
terms of trade and the coef?cient g which de?ne the degree of economy’s openness.
2.4.2 Uncovered interest parity. Under the assumption of a complete ?nancial
market, the domestic price of a foreign good is given by the uncovered interest parity:
G
t;tþ1
i
t
2i
i
t
E
i;tþ1
E
i;t
_ _ _ _
¼ 0;
with G
t;tþ1
¼ ð1=1 þ i
t
Þ is the factor of actualization for period t þ 1. We take a linear
form of the preceding expression and aggregate it on the whole of small economies i,
we ?nd the expression of uncovered interest parity:
i
t
2i
*
t
¼ E
t
{e
tþ1
} 2e
t
: ð15Þ
3. Aggregation of the model
The modeled economy is de?ned as a sequence of quantities:
{Q
t
}
1
t¼0
¼ Y
t
; C
t
; C
H;t
; C
*
H;t
; C
F;t
; L
t
_ _
1
t¼0
a sequence of price:
{P
t
}
1
t¼0
¼ P
t
; P
F;t
; P
H;t
; P
*
t
; W
t
; Q
t
; S
t
; E
t
_ _
1
t¼0
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and an interest rate rule, i
t
:
.
Equilibrium on goods and services market:
Y
t
ðjÞ ¼ C
H;t
ð jÞ þ
_
1
0
C
H;t
ði; jÞdi ¼ C
H;t
þ C
*
H;t
Y
*
t
¼ C
*
t
.
Equilibrium on labor market:
_
k
L
s
ðkÞdk ¼
_
j
L
d
ð jÞdj
L
t
¼ C
2s
t
ð1 2tÞW
P
_ _
1=c
3.1 Aggregate demand
The equilibrium on goods and services market, requires a level of production for all
j1[0.1], which satis?es the following condition:
Y
t
ð jÞ ¼ C
H;t
ð jÞ þ
_
1
0
C
H;t
ði; jÞdi; ð16Þ
Using the form of the expression (16) at the steady state, we ?nd:
y
t
¼ c
t
þ
gv
s
s
t
; ð17Þ
with v ¼ sz þ ð1 2gÞðsh 21Þ. An analogical condition for country i allows us to
write the following expression: y
i
t
¼ c
i
t
þ ðgv=sÞs
i
t
. Aggregating the latter for the rest
of the world[2], we obtain:
y
*
t
¼
_
1
0
y
i
t
di ¼ c
*
t
; ð18Þ
with y
*
t
is the foreign output and c
*
t
is the foreign consumption of the rest of the world.
Combining equations (14), (17) and (18), we obtain the expression of domestic
demand:
y
t
¼ y
*
t
þ
1
s
g
s
t
; ð19Þ
with s
g
¼ ðs=ð1 2gÞ þgvÞ . 0.
If we replace the equation of output (19) into the Euler equation of consumption, we
obtain the expression of the aggregate demand:
y
t
¼ E
t
{y
tþ1
} 2
1
s
g
i
t
2E
t
{p
H;tþ1
} þgQE
t
{ey
*
tþ1
}
_ _
; ð20Þ
with: Q ¼ ðsz 21Þ þ ð1 2gÞðsh 21Þ, i
t
is the nominal interest rate, p
H;tþ1
is the
domestic in?ation at the period t þ 1 and y
*
tþ1
is the foreign output at the same period.
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3.2 Aggregate supply
Taking the price expression obtained by maximization of the pro?t function of ?rm, we
obtain the expression of domestic in?ation which represent a formulation of the
Phillips curve of new Keynesian (NKPC):
p
H;t
¼ bE
t
{p
H;tþ1
} þ k
g
x
t
; ð21Þ
with k
g
¼ lðs
g
þr
z
Þ, l ¼ ððð1 2baÞð1 2aÞÞ=aÞ and x
t
¼ y
t
2y
flex
is the output gap
which is the difference between the domestic output y
t
and the output obtained at
?exible price equilibrium y
?ex
.
At this stage, we notice that the degree of openness of the economy g affects the
dynamics of in?ation through the slope of Phillips curve in other term through its
impact on output gap.
The expression of domestic in?ation combined with equation (14) allows us to ?nd
the expression of a Phillips curve for CPI in?ation:
p
t
¼ bE
t
{p
H;tþ1
} þ k
g
x
t
þgðs
t
2s
t21
Þ: ð22Þ
3.3 Monetary policy
We consider a simple Taylor rule according to which the central bank adjust nominal
interest rate in response to anticipated in?ation and delayed interest rate. Svensson
(1997) considers that the monetary authorities when they target in?ation, they always
have an even implicit target of production. Our choice for a simple policy of Taylor,
which includes in?ation and interest rate, implicitly includes an adjustment of output
through the expression of aggregate supply presented more in details in the previous
part. The monetary policy is given, then, by the following expression:
i
t
¼ ri
t21
þ ð1 2rÞðE
t
½p
tþ1
? 2 pÞ þ1
t
; ð23Þ
with: r
i
is the degree of smoothing of interest rate, i
t21
is delayed nominal interest rate
and p is the in?ation target ?xed by the central bank. The selected monetary rule will
vary according to the variable of in?ation which the central bank seeks to target, then
we have two types of monetary rules:
(1) CPI in?ation targeting policy:
i
t
¼ ri
t21
þ ð1 2rÞ E
t
½p
tþ1
? 2 p
_ _
þ1
t
; ð24Þ
(2) Domestic in?ation targeting policy:
i
t
¼ ri
t21
þ ð1 2rÞ E
t
½p
H;tþ1
? 2 p
_ _
þ1
t
: ð25Þ
For the rest of this paper we take as a reference the framework of Monacelli (2005), we
suppose that the domestic in?ation targeting policy guarantee at the same time a
stabilization of domestic price level and output gap. This result is con?rmed by
Rotemberg and Woodford’s research (1999) which suppose that if there are a transfer
ratio of the government t which is constant, that makes it possible to counterbalance
the distortions associated with the monopolistic power of ?rms on the market and
consequently these ?rms will adjust price by considering the case of equilibrium at
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?exible price. While adopting a domestic in?ation targeting policy, prices of domestic
goods will be consequently constant, which involves that the real marginal costs
equalize the reverse of the mark-up[3]. The intuition is that by ?xing the mark-up and
thus the marginal cost at their ?exible price equilibrium, the ?rm do not may ?nd it
bene?cial any more to adjust their prices and thus the domestic prices remain constant
(Corsetti and Pesenti, 2001; Gali, 2003). With ?exible prices, the relation between the
output gap x
t
and the marginal cost mc
t
is formulated as follows:
mc
t
¼ ðc þs
g
Þx
t
When the marginal cost is stabilized on its equilibrium level, the expression combined
above with equation (21) of the model shows that the output gap will be
consequently constant (Gali, 2003).
4. Calibration
The choice of the variables of calibration for Chile, is based on standard values used
in the literature. The choice for Chile is due to the fact that this small open economy
is considered as one of the emergents economies which succeeded its in?ation
targeting policy in comparison to the other countries. In spite of its in?ationary past,
Chile could reach very low levels of in?ation during very short time by ensuring a
great credibility of its monetary policy. Its dependence on outside did not prevent it to
keep stable its level of in?ation and from thus ensuring the good behavior of its
economy. Table I recapitulates the various parameters used in the calibration of
our model.
The discount factor is b ¼ 0.99. The degree of openness of the economy or the
proportion of the domestic consumption allocated to the imported goods is measured
by the ratio of the imports to the GDP over the period 1998-2000 (Parrado, 2004). This
parameter will be in a ?rst case of reference equal to g
0
¼ 0.29 then we vary it, g
1
¼ 0.2
and g
2
¼ 0.6, in order to see the effect of an increase in the degree of openness on the
choice of the monetary policy.
The economy is open toward outside, so the elasticity of substitution between the
domestic goods and the foreign goods equal h ¼ 1.5.
Parameters of Chile
b 0.99
g
0
0.29
g
1
0.2
g
2
0.6
a 0.75
u 4.33
h 1.5
c 0.63
t 0.25
s 1
r
i
0.8
r
z
0.8
r
yfo
0.8
Table I.
Parameters of calibration
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The elasticity of substitution between the various varieties of goods in the same
economy is u ¼ 4.33 (Parrado, 2004), which implies a mark-up at the stationary state
m ¼ 26 2 27 percent. According to Moyen and Sahuc (2008), the reverse of Frishienne
elasticity is c ¼ 0.63.
The parameter responsible of the nominal rigidity of the prices is a ¼ 0.75 for Chile,
which corresponds to only one annual adjustment of the prices.
Finally, the parameters of the interest rate rule and the auto regression process of
the exogenous shocks are r
i
¼ 0.8, r
Z
¼ 0.8 and r
yFo
¼ 0.8.
5. Results
The simulation of our model gives us the following results, we start by using the
parameters of Chile without bringing any modi?cation, then we modify the parameter
g which re?ects the degree of openness of the Chilean economy and we study the
impulse response which we will have following the exogenous shocks.
5.1 CPI in?ation targeting
We suppose ?rst, that the Chilean monetary authorities target the CPI in?ation which
includes at the same time domestic in?ation and imported in?ation through the foreign
consumer goods.
5.1.1 Productivity shock. The simulation of our model gives us the following graphs
which illustrate the impulse response of different variables, following a shock of
productivity: CPI in?ation, domestic in?ation, output gap, nominal interest rate, real
exchange rate, terms of exchange, CPI price level and domestic price level.
The ?rst aim of the monetary authorities with a CPI in?ation targeting policy is to
stabilize the CPI price level as well as the level of CPI in?ation.
Following a positive shock of productivity of 1 percent, domestic in?ation varies but
in a small proportion, whereas CPI in?ation remains constant. The improvement of the
productivity involves a persistent reduction in the nominal interest rate which will
in?uence favorably the consumption and the output. Figure 1 shows us that on the one
hand the increase in domestic in?ation involves a real appreciation whereas on the
other hand, the fall of the domestic price level involves an increase in the terms of trade.
By increasing g
1
. g
0
, we notice that the adjustment of the variables is modi?ed.
Although CPI in?ation remained constant when we consider the CPI in?ation
targeting, the other variables became much more volatile in comparison with the
situation of reference g
0
. The variability of the degree of openness in?uences the
aggregate supply, a modi?cation of g affect the slope of the curve through the output
gap, which according to equation (21) of the model implies a fall of the output gap,
which generates consequently a contractionary monetary policy that increase the
interest rate.
A more important openness degree results in an increase in the imports of the
foreign goods what causes an improvement in the demand of imported goods and
consequently a fall in the reciprocal demand for domestic goods, which makes them
less competitive for the consumers. Equation (14) which connects two measurements of
in?ation through the terms of trade, shows us that an increase in the degree of
openness, involves a fall of domestic in?ation. This effect is still con?rmed, the raise in
prices of the domestic goods involves a fall of the terms of trade, which implies a real
appreciation of domestic currency.
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At this stage we can underline, that according to the impulse response of the various
variables, we note that the increase in the degree of economy openness involves a greater
variability translated through nominal interest rate, the terms of trade and real
exchange rate.
5.1.2 Foreign GDP shock. A shock on foreign variables generally have a very
important impact by considering the small open economies, considering in most case
that economies are very dependent on outside. So a variation of the foreign GDP is
quickly transmitted on the national aggregates.
The impulse response of Figure 2 are a little different from those which preceding.
An improvement of the foreign GDP of 1 percent involves a rise in the domestic
in?ation accompanied by a stable level of CPI in?ation and corresponding price level,
this result is foreseeable considering the monetary policy adopted by the central bank
which is the CPI in?ation targeting.
Following an increase in the supply of foreign goods, the monetary
authorities will adopt an expansionary monetary policy by lowering nominal
interest rate in order to support the domestic output, which generates a positive output
gap, which means that the level of production will be higher than the level in
equilibrium state.
On another side, the fall of the domestic price level involves an increase in the terms
of trade combined with an increase in real exchange rate explaining by the raise
Figure 1.
Impulse responses to a
shock of productivity
In?ation
targeting policy
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of domestic in?ation. This increase in exchange rate involves a depreciation of the
domestic currency encouraging exports and dissuading the imports.
This effect is ampli?ed by increasing the degree of openness, the volatility of the
variables increases in a very important way. The output gap, the terms of trade and
the real exchange rate reach a volatility of 5 percent. This important volatility is due to
the increase in the demand of foreign goods which initially affect the price of the
imported goods and considering the increase of g, will modify the composition of CPI
price level in favor of imported goods.
We could conclude at this level that a foreign GDP shock allows to an increase of the
proportion of imported goods in the domestic consumption basket increasing the
degree of Pass-Through towards domestic goods prices, which induces a greater
volatility of economic variables, in spite of CPI in?ation targeting.
5.2 Domestic in?ation targeting
We applies in this part the same model but we suppose this time that the monetary
authorities of Chile adopt a policy of domestic in?ation targeting.
5.2.1 Productivity shock. We start by applying a shock of productivity by
distinguishing between our situation of reference g
0
and the adjusted situation g
1
. g
0
.
Considering a domestic in?ation targeting, Figure 3 shows that the adjustment of
the variables is modi?ed. The goal of monetary authorities, in this case, will be to
stabilize the domestic corresponding in?ation and price level.
Figure 2.
Impulse responses to a
foreign GDP shock
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The level of the output gap is constant by considering the rule of domestic in?ation
targeting, which con?rms the results of Monacelli (2005).
We notices a drop in the level of nominal interest rate, thus it involve implicitly an
increase of consumption and output. This increase in output is not re?ected through
the output gap which remains constant following the shock, that is due to the fact that
by adopting a target of domestic in?ation, the central bank leads an implicit target of
output gap and then tends to bring closer the level of domestic production of the level
of equilibrium of long run (Svensson, 1997).
Following a positive shock of productivity, the parity of interest rate can be
presented as an explanation of the reaction of real exchange rate. The fall of nominal
interest rate involves a depreciation of the national currency and thus increases exports
what explains in its turn the rise of the production.
Monacelli (2005) still underline, that in the event of domestic in?ation targeting,
a depreciation of the national currency, due to a shock of productivity, involves an
increase in CPI in?ation.
By increasing the degree of openness of the economy, we can say that the
adjustment of the variables is made in the same manner but we notice an important
volatility compared to the situation of reference. Nevertheless, this idea is not valid for
real exchange rate, the terms of trades and nominal interest rate. The explanation
Figure 3.
Impulse responses to a
shock of productivity
In?ation
targeting policy
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is simple, when we consider a domestic in?ation targeting policy, a variation of g lead
to a variation of CPI in?ation without in?uencing the level of terms of trade.
We notice that the level of real exchange rate will drop on a level lower than in the
case of g
0
. Finally, the stability of output gap, even with an increase of g makes interest
rate nominal insensitive to this variation of the degree of openness.
We can conclude that when we consider a shock of productivity, we notice that by
comparing the volatility of variables with two different targeting monetary rules, we
can stress that the degree of transmission of the exogenous variations is more
important with a domestic in?ation targeting policy. In addition, with a CPI in?ation
targeting policy, we ?nd that the Pass-Through is less important and thus the reaction
of the variables to an increase of g, is less marked with a volatility on average not
exceeding 0.5 percent (Flamini, 2007).
5.2.2 Foreign GDP shock. We present in this part the impulse response of Chile with
a domestic in?ation targeting policy to a shock of foreign GDP. We compare, as
mentioned above, a ?rst case g
0
to a second case in which we have g
1
. g
0
.
Figure 4 shows that we ?nd a constant level of domestic level of in?ation, of output
gap and domestic price, compatible with the objective of the central bank.
Nevertheless, when we consider the same shock of foreign GDP but under the two
monetary policies, we ?nd different results.
Figure 4.
Impulse responses to a
foreign GDP shock
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The ?rst remark that we can notice by comparing the impulse response for an increase
in the foreign GDP, it is that volatility is much less important with a high degree of
openness, this is valid for a domestic in?ation targeting rule. In fact, when we target
domestic in?ation, the domestic goods price does not vary and thus the variations of
terms of trades are very small. The stability of the output gap is accompanied with a
small variation of interest rate compared to the situation where we have a monetary
rule centered on CPI in?ation.
We can say at this level, that by considering a foreign shock, the domestic in?ation
targeting policy offers more stabilizing characteristics for the domestic price level, the
level of in?ation corresponding and the output gap what, in the event of increase of g,
does not in?uence in an important way the behavior of the economic variables.
While referring to the preceding results, we say that when we consider the case of
reference g
0
, it is more optimal for Chile to adopt a CPI in?ation targeting policy in the
event of domestic or foreign shock. Whereas by increasing the degree of openness, the
choice of monetary policy becomes dependent of the nature of the exogenous shock.
For a domestic shock such as an improvement of the productivity, the optimal rule is
the CPI in?ation targeting, whereas for a foreign shock such as the increase in the
demand of the imported goods the optimal rule would be the domestic in?ation
targeting.
6. Conclusion
We tried through this paper to study the impact of a high degree of openness on the
choice of the in?ation targeting policy which should be adopted by the central bank.
We applied a neo-Keynesian model characterised by nominal rigidities and monopolistic
competition, we take the case of Chile as a reference. We ?nd on the one hand that there is
a signi?cant difference in the impulse response when we consider the two in?ation
targeting policies (domestic and CPI in?ation targeting). And in the other hand, there is a
link between the adopted monetary policy and the nature of the exogenous shocks. By
taking the case of reference g
0
in which we did not modify the Chile’s parameters, we ?nd
that the optimal policy adopted by the monetary authorities would be the CPI in?ation
targeting, which includes at the same time the variations of the domestic prices and the
variations of foreign exchange rate, this result is valid by considering a domestic or a
foreign shock. Now, when we consider the case where we modi?es the degree of
openness of the economy g
1
. g
0
, the choice of the optimal policy becomes dependent on
the nature of the exogenous shock. With a positive shock of productivity, we notice that
the degree of Pass-Through towards the economy is controlled much more with a CPI
in?ation targeting policy than with a domestic in?ation targeting one. Whereas, while
considering a foreign GDP shock, the choice of a rule centered on domestic in?ation
becomes more optimal because it ensures at the same time a stability of the domestic
goods price level, corresponding in?ation and the output gap level.
Notes
1. Monetary Policy and Exchange Rate Volatility in a Small Open Economy, Monacelli (2005).
2. We suppose that
_
1
0
s
i
t
di ¼ 0.
3. We suppose that in ?exible price equilibrium, the marginal cost (log) equalizes the reverse of
the mark-up(log); mc
t
¼ 2m ¼ 2logðu=u 21Þ.
In?ation
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Corresponding author
Jihene Bousrih can be contacted at: [email protected]
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