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THE MONETARY TRANSMISSION MECHANISM FOR A SMALL

OPEN ECONOMY IN A MONETARY UNION*1

Bernardino Adão**

1. INTRODUCTION

This paper develops a stylized model of a small open economy integrated in a monetary union. As the

small country trades with countries inside and outside of the monetary union, there are three blocks in

the model. The small open country, the block represented by all the remaining countries that belong to

themonetaryunion,andtheonethatincludesallcountriesthatdonotbelongtothemonetaryunion.

As in any monetary dynamic general equilibrium model, in our model too, the behavior of the equilib-

rium variables is described by a system of difference equations, with as many equations as endoge-

nous variables, and some initial and terminal conditions. In general these additional restrictions to the

system are not enough to determine a finite number of solutions.2There is, however, a wayto obtain a

unique locally-bounded equilibrium, that has the property that in its neighbourhood there is no other

equilibrium.3The procedure is relatively simple, the central bank must follow an interest rate rule that

obeys the Taylor principle.4

The Taylorprinciplesaysthat the interest rate rule shouldbe such that the responseof the interest rate

to a unitary change in the appropriate inflation must be larger than unity. The interest rate relevant for

thesmallcountryistheonesetbythecentralbankofthemonetaryunion.The centralbankofthemon-

etary union follows an interest rate rule that is a function of the union’s inflation and output. If the infla-

tion rate in all countries of the union, except the one of the small country, was taken as exogenous the

Taylor principle would be violated. The reason is easy to understand. If those union aggregate vari-

ables were taken as exogenous, a change in the small country’s inflation would imply a negligible

change in the interest rate, since the small country contributes little to the union’s inflation. Thus, to

guarantee local determinacy the variables associated with the countries outside the union can be as-

sumed exogenous, but not the variables associated with the other countries in the union.

To guarantee that the model possesses the local uniqueness property we adopted a straightforward

ad-hoc specification of two blocks of equations, each containing three equations, that specify the be-

havior of some aggregate variables inside and outside the union. One block contains three reduced

Economic Bulletin | Banco de Portugal

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*

I would like to thank Ana Cristina Leal, João Sousa, José Ferreira Machado, Mário Centeno and Nuno Alves for useful comments and Gabriela Castro,

Ricardo Félix, José Maria and Nuno Ribeirofor help with the data. The opinionsexpressed in this article are of the author and do not necessarilycoincide

with those of Banco de Portugal or the Eurosystem.

**

Banco de Portugal, Economics and Research Department.

(1) There is a working paper version of this article, Adão (2009), that has the technical detailed that this version lacks.

1111111111111111111111111111111

(2) J. Cochrane (2007) contains a critical survey of this issue.

2222222222222222222

(3) Besides the local unique equilibrium there are infinitely many explosive equilibria, that cannot be ruled out by transversality conditions.

3333333333333333333333333333333

(4) The Taylor principle is described in Taylor (1999). Unlike in less standard models, the Taylor principle is a necessary and sufficient condition to have local

determinacy in our model.

4444444444444444444444444444444

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form equations, an IS curve, a Phillips curve and an interest rate rule that describe the behavior of out-

put, inflation and the interest rate for the countries outside the union. These three variables are deter-

mined entirelyinside this block. The other block of equationscontains three other similar reduced form

equations, regarding the behavior of inflation, output and the interest rate in the union. This block of

equations contains three equations and five variables. These variables are: the inflation rate and the

output in the small open economy and in the remaining countries of the union, and the interest rate in

the monetaryunion.The arguments in this block of equationsassociatedwiththe small openeconomy

are scaled down in accordance with the dimension of the small country in the union. These five vari-

ables interact with the other variables in the model, and are determined together with them.

Adolfson et al. (2007) developed a model of a small open economy with two blocks only: the small

open economyand all the remainingcountries. In that context, the Taylorprincipleis triviallysatisfied if

foreign inflation, foreign output and the foreign interest rate are taken as exogenously given. This pa-

per can be seen as an extension to their paper, as it considers that the small open economy is inte-

grated in a monetary union. Following their work and the literature, we consider various nominal and

real frictions, such as sticky wages, sticky prices, variable capital utilization, capital adjustment costs,

habit persistence and volume premium on the foreign interest rate.

Adolfson et al. (2007) calibrated and estimated their model using the euro area data. This paper pres-

ents a model designed to assess the transmission of monetary policy shocks in a small country inte-

grated in a monetary union. As Portugal can be thought as such an economy, weused the Portuguese

data to calibrate several of the parameters of our model. We assume that after the monetary shock, in-

flation, output and the interest rate outside of the union are unchanged and that inflation, output and

the interest rate inside the union change according to the referred three equation block, containing an

IS curve, a Phillips curve and an interest rate rule. More specifically, in the quantitative exercise per-

formed we consider parameters for the IS curve, Phillips curve and the interest rate rule that, together

withtheremainingcalibratedequations,generateresponsesof thesevariablesto thetypicaleuroarea

monetary shock that mimic the paths of the responses of these variables in the general equilibrium

model of Adolfson et al. (2007) to the same shock.

Some of the model parameters are calibrated to the steady state values of the Portuguese economy

variables, for others wedo not have information and theycorrespondto the estimates obtained(or val-

ues assumed) by Adolfson et al. (2007) for the euro area. The shape and sign of the impulse re-

sponses of the main macro variables to an unanticipated temporary decrease in the nominal interest

rate are wellin line withthe literature. When compared withthe euro area, output, employment,invest-

ment and real wagein Portugal increase more and inflation adjusts quicker and reacts slightlymore on

impact. On the other hand, consumption in Portugal has a behavior almost identical to the one of the

euro area. In general, economies where inflation adjusts faster in response to a given monetary policy

shock, have smaller responses of the real variables to that shock. That is not the case here, since Por-

tugal was assumed to have a higher net foreign debt level and a higher degree of openness than the

EMU.

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The trade with the two areas responds differently. Due to the change in the exchange rate, the trade

with countries outside the euro area changes substantially more than the trade with countries inside

the euro area. Both exports and imports to and from the euro area increase, with exports changing

less. Imports from outside the euro area decrease initially and exports to outside the euro area

increase.

The paper is organized as follows. In Section 2 the model is explained. Section 3 studies the effects of

a monetary shock on the Portuguese economy. Section 4 provides some conclusions. The appendix

describes how the model is solved and calibrated.

2. MODEL

The model has 3 economic blocks: the small open country, the other countries inside the monetary un-

ionandthe countriesoutsidethe monetaryunion.We are concernedwiththe smallopeneconomyand

assume the developments in the small openeconomyhavesmall effects over the remainingeconomic

areas. As such, in the model the small open economy is described in detail, but the other economic

areas are not.

2.1. Households

There is a representative household in the small open economy, whose preferences over stochastic

sequences of consumptionCtreal money

M

P

t

t, and labor Ltare represented by the utility function:

??

EC bC

M

P

L

1

0

t

t 0

?

t t 1

?

t

t

t

?

1

???

?

?

?

?

?

??

?

?

???

?

?

?????

log log

?

????

?

?

?????

?

(1)

where E0is the conditional expectation operator, ? ? (0,1) is the discount factor, and b is a parameter

that controls the habit persistence. This utility function is similar to the one used by Christiano et al.

(2005) and Adolfson et al. (2007). The aggregateconsumptionis a bundlegiven bya CES indexof do-

mestically produced and imported foreign goods:

?

?

?

? ?

C

?? ? ?

C

??

C1

t o,cu,ct

h

o,ct

o

u,c

1

c

c 1

?

?

?

c

1

c

c 1

?

?

?

c

1

??????????

??

? ?

Ct

?

?

?

?

c 1

?

?

c

c 1

?

c

c

u

?

??

?

??

?

, (2)

whereCt

hdenotesconsumptionofthehomegood,Ct

odenotesconsumptionofthegoodproducedout-

side of the union,Ct

udenotes consumption of the good produced inside of the union,?o,cis the share

of imported consumption from outside of the union in total consumption,?u,cis the share of imported

consumption from inside of the union in total consumption and ?cis the elasticity of substitution be-

tween the three consumption goods. Thus, consumers derive utility from the consumption of domesti-

cally produced goods as well as from the consumption of goods produced outside and inside of the

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union. The price of aggregate consumption (defined as the minimum expenditure required to buy one

unit ofCt) is given by:

?

??

?? ?

P

? ?

P

o,c

? ?

P

u,c

P1

tc o,c u,ct

1

to1

tu1

c

cc

?????

?

?

?

?

??

????

?

??

?

?

1

1

c

?,

where Ptis the price of the domestically produced good, Ptois the price of the outside of the union im-

ported good and Ptuis the price of the inside of the union imported good. All these prices are in units of

the domestic currency. Consumers choose quantities of each of these three goods that for a given ex-

penditure maximize aggregate consumption. The individual demands for each good that maximize (2)

subject to PCP CP C P C

tt

h

tot

o

tut

u

tct

???

, are:

??

C1

P

P

C

t

h

o,cu,c

t

tc

t

c

???

?

????

?

?

????

?

?

??

?

,

C

P

P

C

t

o

o,c

to

tc

t

c

?

?

????

?

?

?????

?

?

?

?

,

and

C

P

P

C

t

u

u,c

tu

tc

t

c

?

?

????

?

?

?????

?

?

?

?

.

Also, the aggregate investment is a bundle given by a CES index of domestically produced and im-

ported foreign goods:

?

?

? ? ?

?? ? ?

??

III

t o,iu,it

h

o,it

o

u,i

i

i

?

?

i

i

i

?

?

i

?????

1

1

?

1

1

?

1

1

?? ?

It

????

??

i

i

?

i

i

i

u

?

?

?

?

?

?

??

?

??

?

1

1

,

where It

hdenotes the home good investment, It

odenotes outside of the union investment good, It

ude-

notes inside of the union investment good,?o,iis the share of outside of the union investment good in

total investment,?u,iis the share of inside of the union investment good in total investment and ?iis

the elasticityof substitution betweenthe three investment goods. The price of aggregate investment is

equal to:

?

??

?? ?

P

? ?

P

o,i

? ?

P

u,i

P

tio,i u,it totu

i

ii

?????

??

?

?

??

1

1

11

????

?

??

?

?

1 ?i.

1

The individual demands for each investment good are

??

I

P

P

I

t

h

o,iu,i

t

ti

t

i

???

?

????

?

?

????

?

?

1 ??

?

,

I

P

P

I

t

o

o,i

to

ti

t

i

?

?

????

?

?

?????

?

?

?

?

,

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and

I

P

P

I

t

u

u,i

tu

ti

t

i

?

?

????

?

?

?????

?

?

?

?

.

Each household is a monopoly supplier of its own labor and can set its wage according to the mecha-

nism describedin Calvo (1983), to whichwewillcome back later. In order to guaranteethat this friction

does not cause households to become heterogeneous we assume complete domestic financial mar-

ketsagainsttheoutcomesofthisfriction.Asaresultallhouseholdshavethesamebudgetconstraint:

? ?

a u

??

P CP IMD S B

t

B Pw L

t

P ru

t

K

tct tit

?

?

ttt

o

t

u

t tt ttt

?????

?

?

?

?

?

???

?1

MDR

S R

t

B

z

BR

t 1

?

tt

t

o

?

o

t

t

t

o

?

t

??

?

?

?

?

???

?

?

????

?

11

1

1

1

1

?

?

?

t 1

B

z

?

t 1

?

???

????

??

11

u

u

t

u

tt

BT F .

?

(3)

The terms on the left hand side of the equality show how the households use their income and the

terms on the right hand side the various sources of that income. Here, Mtare money holdings, Dtare

deposits that pay nominal gross interest rate Rt, Bt

oare holdings of foreign bonds denominated in for-

eigncurrencythatpayanominalgrossinterestrateRt

o

o

? , Stisthenominalexchangerate, Bt

uarehold-

ings of foreign bonds denominated in domestic currency that pay a nominal gross interest rate Rt

u

u

?

andwtis therealwage.The term Pru

t t trepresents thehousehold’s earningsfrom supplyingcapitalser-

vices. The function ? ?

a u K

tt?1denotes the cost of setting the utilization rate of capital to ut. We assume

? ?

a utis increasing and convex. These assumptions capture the idea that the more intensely the stock

of capital is utilized, the higher are maintenance costs. We assume that ut? 1 in steady state and that

?

?

? ?

1aa 0,0

?

?? ,and ???

a0.The expressionR

B

z

t

o

?

u

t

t

?

?

???

?

?

????

1

1

1

?

isthelevel-adjustedgrossinterestrateonfor-

eign bonds denominated in foreign currency, Bt

S B

t

B

P

totu

t

?

?

.The term ztis a unit root technology shock

to be describedlater. The function ? ?

?i

B

z

t

t

for i o,u,

?

is assumedto be strictlydecreasingin Btandto

satisfy ? ?

?iB ? 1, where Bis thesteadystatevalueof

B

z

t

t. This functiondependsontherealholdingsof

the aggregate foreign assets. This means that domestic households take the functions

??

?i. as given

when deciding on the individual optimal holdings of the foreign bonds.

Functions ?itry to capture imperfect integration in the international financial markets. If the domestic

economyas a wholeis borrowingabove its steadystate, domestic householdsare chargeda premium

on the foreign interest rates, if borrowingbelowits steadystate, domestic householdspayless. The in-

troduction of this premium is needed in order to ensure a well-defined steady-state in the model (see

Schmitt-Grohë and Uribe, 2003, for further details). Without this premium, the stock of bonds and con-

sumption would not be stationary. The remaining variables areTtwhich is a lump-sum transfer, and Ft

that stands for the profits of the firms in the economy.

Investment Itinduces a law of motion for capital:

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