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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

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95

*

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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??

KKV

I

I

I

tt

t

t

t

????

?

??

?

?

??

?

?

?

???

?

?

????

?

?

11

1

1

?

, (4)

where? is the depreciationrate andV is an adjustment cost function such that

????

VV

ii

???

?

? 0, and

???

chooses?

V0, where ?iis the growth rate of investment along the balanced growth path. The household

?

C ,L ,M ,D ,B ,B ,u ,K ,I

ttttttttt

to maximize expected lifetime utility (1) subject to con-

ou

straints (3), (4) and initial values for M ,D ,Bo

000, and Bu

0.

The labor used by the intermediate good producers is supplied by a representative competitive firm

that hires labor to each family j.This firm aggregates the differentiated labor of households according

to the production function,

LL dj

t

d

jt

w

w

w

w

?

?

?????

?

?

??????

?

?

?

?

?

?

?

?

1

1

0

1

where?wis the elasticity of substitution betweenthe different types of labor and Lt

dis the aggregate la-

bordemand.This firm maximizesprofits takingasgiventhelaborwageswjtandaggregatelaborwage

wt. Its maximization problem is:

max

L

t t

d

jtjt

jt

w Lw L dj

??0

1

.

The demand for the labor of household j is given by

L

w

w

Lj

jt

jt

t

t

d

w

??

?

???

?

?

????

?

??

,

.

AsreferredabovehouseholdssettheirwagesaccordingtoaCalvo’ssetting,Calvo(1983).Ineachpe-

riod, a fraction1??wof householdscan changetheir wages.All the other householdscan onlypartially

indextheir wagesto past inflationand past productivitygrowth.Indexationto past inflationis controlled

bytheparameter?wandindexationto past productivitygrowthbytheparameter?p. Bothassumeval-

ues in the interval??

01 , . Thus, a household that could not change her wage fors periods has real wage

??

?

1

? ??

?

?

1

? ?

?

?

?

??

t

??

t

?

1

1

1

s

zz

jt

ww

pp

t

w

??

, where ?tis gross inflation of the domestic good in period t, ? is the

steady state domestic inflation, zt is gross productivity growth in period t and z is the steady state

productivity growth.

When setting the wage the relevant part of the objective function for the household is,

??

max

w

t

ws

s

jt

?

s

jts

s

?

t

jt

w

E

L

???

?

?

?

?

?

?

?

?

?

?

?

??

?

1

?

?

?

?

?

0

1

1

1

??

?

?

1

? ?

?

?

?

?

??????

?

????????

?

11

?

??

t

?

w

pp

zz

w L

jt

t

jts

subject to

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L

zz

w

w

jts

s

tt

t

jt

ts

w

w

pp

?

?

?

1

? ?

?

?

?

1

? ?

?

?

?

?

?

????????????

?

??

?

?

??

?

1

11

??

?

???????????????

?

?

?

?

?w

Lj

ts

d

,

.

where?jts

?isthemarginalutilityofconsumptionofthedomesticgoodinperiodts

? ofhousehold j.

In each period a fraction1??wof the households setwt

*as their wage while the remaining fraction in-

dex their wage by past inflation. Thus the real wage evolves according to:

w

zz

w

t

w

tt

t

t

w

w

w

pp

1

1

1

1

1

1

?

?

?

?

?

?

?

?

?

??????

?

?

???

????

?

?

?

?

??

?

??

? ?? ?

??

?

1

?

1

1

?

?

?

w

w

w

t

w*

.

2.2. Final good producer

There is one domestic final good that is produced with intermediate goods:

Yy dj

t

j t

,

d

d

d

d

?

?

?????

?

?

??????

?

?

?

?

?

?

?

?

1

1

0

1

where ?dis the markup in the domestic goods market. The input demand functions of the final pro-

ducer are:

y

p

P

Y

j t

,

j t

,

t

t

d

,

??

?

???

?

?

????

??

where pj,tis the price of intermediate product j and Ptis the price of the final home good. Ptis defined

astheminimumexpenditureinintermediateinputstoproduceoneunitoffinaloutputandisgivenby

Pp dj

t j t

,

d

d

??

?

???

?

?

????

?

1

?

?

.

0

1

1

?

1

?

2.3. Intermediate producers

There is a continuum of intermediate good producers. Each one has the following technology:

y Ak

t

lz

j t

,

j t

,

j t

,

t

,

??

?

?

1

1

??

?

where Atis a total productivity technological shock that follows an autoregressive process:

??

AAz

ttA At

,

??

?1exp,

?

wherezAt A AtAt

,,,

,

? ? ??

~N( , ) 01

and

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zA

t

t

?

?

1

1 ?.

The parameter ? corresponds to the fixed cost of production that guarantees that economic profits are

zero in the steady state. We have:

??

zzz

ttz z t

,

??

?1exp,

?

wherez

z

1 ?and ?

z t

,

At

,

?

?

?

?

z

A

?

1 ?.

Intermediate producers solve two problems. First, given wtand rt, they rent labor and capital in perfect

competitive markets in order to minimize real expenditure.

The second problem intermediate producers must solve is to choose the price that maximizes ex-

pected discounted real profits. Firms set prices according to a Calvo set-up too. In each period, a frac-

tion1?? of firms can choose optimally their prices. The price chosen in periodt is denoted by pt. We

suppressedthe firm’s indexationbecauseallfirms that havethe opportunityto choosethe priceset the

same price. The remaining ? firms cannot choose the price. In periodt these firms update their price to

pj,t

t

d

d

?

?

?

1

1

1

??

?

?, where pj,t?1is the price firm j was charging in period t?1,?t?1is past inflation of the

domestic good,?is the steady state domestic inflation and ?dis an indexation parameter. The index-

ation parameter, ?dassumes values in the interval??

01 , . Each firm uses the stochastic discount factor

???tto compute the value of its profits.

When a firm can choose its price at date t its problem is:

max

p

()

t

s

ts

s

?

t

t

ts

ts

d

t

d

d

E

p

P

mc

???

?

?

?

?

?

?

1

? ?

?

?

?

?

?x

?????

?

?

1

1

??

?

???????

?

?

?

???

???

?

?

?

???

???

?

?

?

?

s

yj ts

,

0

,

where mct

ddenotes the marginal cost, subject to

y

p

P

j t

, ?

s

s

t

t

ts

d

d

?

?

1

? ?

?

?

?

?

?

??????

?

?

???????

?

x?

?

?

?

1

1

??

d

Yts

?.

2.4. Central bank

The central bank sets the nominal interest rate according to the Taylor rule:

R

R

R

R

ttt

u

u

t

R

??

???

?

???

?

????

?

?

?????

?

?

?

???

?

?

?

?

1

1

?

?

?

?

?

?

???

?

?????

?

?

?

??????

?

?

????

?

?

?????

?

?

?

???

?

1

?

?

?

?

Y

Y

Y

Y

tu

u

t

?

?

???

?

?????

?

?

??????

?

?

????

?

????

?

?

1

?

?

?

Y

R

mt

()

exp()

wheremtisarandomshocktothemonetarypolicythatfollowsmtm m,t

? ? ?

, where?m,t~ ? ?

N 01 , . Variable

?uisthetargetlevelfortheinflationintheunion,whichisequaltothesteadystateinflationintheunion,

?t

uis the inflationin periodtin the unionwithoutincludingthe small open country,Yuis the steady-state

output in the union,Ytuis the output in period t in the union without including the small open country.

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The parameter ? is the weight of the small open country in the union, while ??

R,

?, and ??are the

usual parameters of the Taylor rule.

2.5. Government

The budget constraint of the government in the small open economy is:

P G

t

TMM

tttt

???

?1,

whereGtis government consumption, which includes only domestic produced goods and we take as

exogenous. The other variables are taxes,Ttand money supply, Mt.

2.6. Evolution of net foreign assets

The evolution of net foreign assets at the aggregate level satisfies:

S B

t

B S R

t

z

B

?

R

t

o

t

u

t

o

?

o

t

t

t

o

?

t

u

?

??

?

?

???

?

????

?

?

?

1

1

1

11

?

?

?u

t

t

t

u

?

t

z

B

?

TB

??

?

?

?

???

?

????

?

1

1

1

.

The trade balance isTBP X

t

P X

t

P M P M

tt

u

t

o

tut

u

tot

o

????

.

The total imports from the union are MC

t

u

u,c

P

P

t u,i

P

P

tu

tc

c

tu

ti

?

?

?

???

?

?

???

?

?

?

???

?

?

???

?

??

??i

Itand the total imports from out-

side of the union are MC

t

o

o,c

P

P

t o,i

P

P

to

tc

c

to

ti

?

?

?

???

?

?

???

?

?

?

???

?

?

???

?

??

??i

It. We assume that the demands from the other

countries for the product produced domesticallyhave the same functional form as the demands by the

domestic consumers. Thus, the total exports to the union are XY

t

u

u,u

P

P

tu

t

tu

u,x

?

?

?

???

?

?

???

?

?

?

and the total ex-

ports to outside of the union are XY

t

o

o,o

P

P

to

t

to

o,x

?

?

?

???

?

?

???

?

?

?

, where?u,uand?o,oare shares, and ?u,xand

?o,xare elasticity parameters. The variablesYtuandYtodenote the output of the other countries in the

union and the output of the countries outside of the union, respectively.

2.7. Relative prices

When deciding their consumption and investment baskets agents in the small open economy use the

following relative prices: ?t

c,d

P

P

tc

t

?

and ?t

i,d

P

P

ti

t

?

. To decide imports consumers use two relative prices:

the relative price between imports from the union and the domestically produced good ?t

u,d

P

P

tu

t

?

and

the relative price between imports from outside of the union and the domestically produced good

?t

o,d

P

P

to

t

?

.

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From the definitions of prices we have:

??

??

????

???????

???

t

c d

,

oc

,

u c

,

oc

,

t

od

,

u c

,

t

u d

,

ccc

111

1

???

?????

,

? ?

?

t

??

????

??????

???

i d

,

oi

,

u i

,

oi

,

t

od

,

u i

,

t

u d

,

iii

111

1

???

?????

.

2.8. Aggregation

The aggregate demand in the small open economy is:

YCI a u K

(

GX

tt

h

t

h

tttt

?????

?

)

1

,

whereCt

hand It

hdenotes consumption and investment of the home good. Thus, the demand for each

intermediate good producer is:

? ?

a u K

??

yCIGX

p

P

i

i t

,

t

h

t

h

tttt

i t

,

t

d

,

?????

?

?

???

?

?

????

?

?

?

1

?

.

Using the production function and market clearing we obtain:

?? ? ?

a u KA u K

t

LzCIGX

ttttt

h

t

h

tttt

?

?

1

?

??????

11

?

?

?

.

2.9. Rest of the world

The rest of the world is composed by two regions: the remaining countries in the union and the coun-

tries outside of the union. The output, inflation and the interest rate in the union and outside of the un-

ion are given by two blocks one for each region, each containing three equations: an IS equation, a

Phillips equation and an interest rate equation. More specifically,

??

YfYY

,

tkY

k

tk

?

tkt

k

?

??

111

,?

,

??

???

?

t

kk

t

k

t

k

tk

fY

,

?

???

111

,

,

and

??

RfRY

,

t

k

R

k

t

k

?1,

t

k

tk

??

,

for YY

tk to

?

or

??

YYY

tk tut

???

1

?? , ??

t

k

t

o

?

or

??

???

t

k

t

u

t

???

1

??

, and RR

t

k

t

o

?

or RR

t

k

t

?

.The pa-

rameter ? is the size of the domestic country in the union.

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2.10.Equilibrium

The definition of equilibrium for this economy is standard. It is a vector of prices, policy variables and

quantities that satisfies certain conditions. These conditions are the following:

• The conditions that solve the households problem;

• The conditions that solve the firms problem;

• The government’s budget constraint;

• The budget constraint with the foreign sector,

• The IS, Phillips and interest rate equations for each region,

• The markets clearing conditions.

3. IMPULSE RESPONSE FUNCTIONS

After solving and calibrating the model, which we describe in the appendix, we are ready to study the

impulse response functions of the various variables to a monetarypolicyshock. The shock considered

is a white noise shock to the nominal interest rate rule.

Except for inflation, the nominal interest rate and the interest rate premium, which are reported as an-

nualizedquarterlyrates, the graphsassociatedwiththe impulseresponsefunctionshaveon the y-axis

the percentage deviations of the variables from their steady state values.

There is a feature on the impulse response functions worth noting. As can be seen from Chart 1, with

the exception of the variables associated with trade, most of the variables respond in a hump-shaped

form, peakingafter 3 or 4 quartersandreturningto the preshocklevelsafter aboutthree years.The ex-

ceptions are the nominal exchange rate, some relative prices and the different imports and exports.

The euro area variables: the nominal interest rate, inflation and output replicate closely the path of the

impulse responses of these variables to a monetary shock in the Adolfson et al. (2007) model. On im-

pact the nominal interest rate drops by 40 basis points and returns to the steady state four years later.

Both output and inflation have hump-shaped responses and achieve their peaks after about one year,

around0.3percentofthesteadystateforoutputandaround10basispoints(annualized)forinflation.

The small open economy responses to the monetary policy shock are roughly similar to the ones ob-

tainedin a standardclosedeconomy, eventhoughthe modelpossessesan additionalchannelof mon-

etary policy transmission. We summarize these responses now. Because prices are sticky, the

unexpected decrease in the nominal interest rate implies a decrease in the real interest rate. A lower

real interest rate makes bonds less attractive than investment, which leads to an increase in invest-

ment. As the stock of capital increases the marginal productivity of labor increases also and firms

increase their labor demand.

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The temporarylowerreal interest rate has intertemporal substitution effects on consumption and labor

supply. It makes present consumption and present leisure (since nominal wages are sticky) relatively

less expensive, which lead households to increase consumption and decrease labor supply. The

changes in the labor supply and labor demand lead to an increase in the real wage. Output increases,

since consumption and investment increase, and capital utilization increases because there are costs

in adjusting capital. As consumption and investment increase the demand for imports increases.

The additional channel for the monetary policy transmission associated with an open economy com-

pels firms to increaseproductiontoo. In a closedeconomyhouseholdscan onlysmooth out the path of

consumption by varying the path of investment. But in an open economy households have another al-

ternative to accomplish that, the possibility of changing the path of net exports. The monetary shock

considered leads to an increase in the domestic income. In order to smooth their path of consumption

and leisure households increase their net foreign assets. This behavior of foreign assets implies an in-

crease in net exports and a further increase in the output. After the shock, the stock of net foreign

assets is above its steady state value for about four years.

There is an additional income effect in Portugal that is absent in the Adolfson et al. (2007) calibrated

model of the EMU. They assumed that net foreign assets of the EMU in the steady state werezero, in-

stead we assumed that the ratio between the steady state net foreign debt and GDP for Portugal, and

the ratio between steady state euro denominated and total net foreign debt were equal to those ratios

for Portugal in 2007. Given that most of the net foreign debt of Portugal is denominatedin euro, the im-

pact of a drop in the euro interest rate is more favorable for Portugal than for the EMU. For this reason

alone, it should be expected that investment and output in Portugal would vary more than investment

and output in the EMU.

The degree of openess is relevant too. The more open an economy is, the less it has to rely on invest-

ment to partially insulate consumption from economic disturbances, as it has access to more foreign

assets, that can be used in addition to investment to smooth out consumption. For that reason, output

in a more open economy tends to be more volatile, as the economy can take advantage of the tempo-

rary shocks it faces, by increasing production when the shock is positive or decreasing production

whenthe shock is negative,withouthavingto changeconsumptiontoo much (i.e. at a lowercost), than

a less openeconomy. Sincethe EMU has a smallerdegreeof opennessthan Portugal,it shouldbe ex-

pected that in reaction to a positive temporary shock, like the monetary policy shock considered, con-

sumption would increase less and output more in Portugal than in the EMU.

The outputincreasesinpercentagedeviationsfrom thesteadystatealittlemoreinPortugalthaninthe

euroarea.The impulseresponsefunctionfortheoutputinPortugalisalmostallthetimeabovetheone

for the EMU. For Portugal the maximum response is just over 0.3 and in the EMU it is just below 0.3.

The investment, employment and real wage in Portugal and in the EMU, as computed by Adolfson et

al. (2007), have similar shapes but in Portugal those variables move more. The impulse response

functionsfor investment, employmentand real wagein Portugalare almost all the time abovethe ones

for the EMU. For Portugal the maximum response for investment is just about 0.6 for employment is

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Page 13

about 0.25, and for the real wage about 0.1, while for the EMU the maximum response for investment

is about 0.5 for employment is about 0.2 and for the real wage is about 0.07.

InflationinPortugalrespondsquickertotheshockthaninflationintheeuroarea,onimpactitincreases

by more and returns faster to the steady state. The maximum increase of inflation in Portugal is 16 ba-

sispointswhilethatmaximumintheEMUisaround10basispoints. This shouldbeassociatedwiththe

fact that we assumed that in Portugal each quarter 20 percent of the firms change their prices opti-

mally, whileAdolfson et al. (2007) took that only 10 percent of the firms in the EMU change their prices

optimally.

The relative price of the euro area’s good is persistently below the steady state in response to the

shock due to the referred differentiated behavior of inflation in Portugal and in the euro area. This fact,

together with the shock having an impact in the output relatively higher in Portugal than in the euro

area, implies that imports from the euro area increase more than exports to the euro area, in response

to the shock.

Even though the effects of the shock are stronger in Portugal than in the euro area, consumption in

Portugal and in the euro area have almost identical paths. This indicates that households in Portugal

are successfully using the available saving instruments to smooth out consumption.

Now we interpret the behavior of the exchange rate. From the first order conditions of the households

weobtain the uncoveredinterest rate parity(UIP) condition, whichsaysthat the expecteddepreciation

of the euro is equal to the current interest rate in the monetary union minus the interest rate outside of

the union minus the change in the volume premium.5The UIP does not restrict the depreciation rate of

the euro in the impact period. Apart from the impact period, the nominal exchange rate behavior is the

one implied by the UIP. The foreign interest rate is unchanged and the volume premium changes little,

astheadjustmentcostsoftheassetstockswereassumedtoberelativelysmall.Thus, justaftertheim-

pact period, from the second to the fifth quarter the euro appreciates as the decrease in the interest

rate is larger in absolute value than the decrease in the volume premium on the foreign debt, and after

the sixth quarter it depreciates, little, as the opposite happens.

In the impact period the currency depreciates because, as we observed before, net exports must in-

crease to smooth out consumption. Net exports to the euro area did not increase due to the evolution,

described above, of the main aggregate variables in Portugal and in the euro area. Thus, in order for

net exports to increase, net exports to outside of the union must increase. That is possible only if the

relative price of the good produced outside of the union increases, given that we assumed that the

main aggregate economic variables outside of the union were constant. The current relative price of

the good produced outside of the union is equal to the price in the previous period plus the current de-

preciation of the euro plus the differential of inflation between the outside of the euro area and Portu-

gal. For the relative price of the good produced outside of the union to be persistently above its steady

state, it is necessarythat on impact the euro depreciatessufficientlyto compensateits subsequentap-

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107

(5) Also known in the literature as risk premium, and denoted in the text by?.

555555555555555555555555

Page 14

preciation, and the persistent domestic inflation. Summing up, in the short run, lowerreal interest rates

in the euro area tend to reduce the foreign exchangevalue of the euro, whichlowersthe relative prices

of the goods produced in Portugal and in the euro area. This leads to higher outside of the union

aggregate spending on goods and services produced in Portugal and in the euro area.

The behavior of the net foreign assets impulse response function, which reflects the evolution of the

net exports, is a result of the households choice to smooth out consumption through time. It has an

hump-shaped pattern, achieves its peak after four quarters at about 0.18 of the steady state, and re-

turns to the steady state after 4 years.

With respect to the impulse response functions of the exports and imports there is a striking difference

betweenthosetoandfrominsidetheeuroareaandthosetoandfromoutsideoftheeuroarea.Exports

and imports to and from the euro area increase but imports increase more, imports achieve a maxi-

mum of 0.42 percent above the steady state while exports achieve a maximum of 0.24 percent above

the steady state. As referred already, this behavior is explained by two facts. First, because output in

Portugal increases more than in the euro area. Secondly, because the relative price of the good pro-

duced in Portugal increaseddue to the fact that inflation in Portugal is slightlyabove the euro area’s in-

flation. As we noted previously too, the trade with the countries outside of the euro area evolves in a

very different way. That is in part explained by the path of the relative price of the good produced out-

side the euro area, which jumps up on impact and returns with some persistence to its steady state 6

quarters after the shock. Both exports and imports to and from countries outside of the euro area

change substantially. Exports on impact are about 0.54 percent above the steady state and imports on

impact are about 0.32 percent below the steady state. Imports from outside of the union achieve its

maximum when investment achieves its maximum, 5 quarters after the shock.

In our model the effects over the euro exchange rate are smaller than in Adolfson et al. (2007). In our

model on impact the euro depreciates by about 0.4 percent from the steady state, while in Adolfson et

al. (2007) it depreciates by about 0.5 percent from the steady state. Most likely, if we were to change

some of the parameters in our model in order to get that higher value for the depreciation of the euro,

the effects over many of the real variables like output, investment and real wages, which are already

bigger in Portugal than in the union, would be further augmented.

4. CONCLUSIONS

In this paper we introduce modifications in the benchmark open economy monetary business cycle

model of Adolfson et al. (2007) in order to incorporate a small country that trades with countries inside

and outside of the monetary union to which it belongs. To guarantee local determinacy the variables

associated with the countries outside the union can be assumed exogenous, but not the variables as-

sociated with the other countries in the union. As the interest rate rule for the union depends on the in-

flation and output of the union, if we were to take these variables as exogenous the interest rate would

notobeytheTaylorprincipleandtherewouldnotbea uniquelocalequilibrium.To surpass this difficulty

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Page 15

we assumed that inflation, output and interest rate inside the union change according to a three equa-

tion block, containing an IS curve, a Phillips curve and an interest rate rule. The parameters for these

three equations were chosen so that these equations, together with the remaining conditions of the

model, could deliver the European Union’s inflation, output and interest rate impulse response

functions to a monetary shock, obtained by Adolfson et al. (2007).

We use the model to study the monetary transmission mechanism in Portugal. There are various find-

ings.The shapeandsignof the responsesof the variablesaresimilarto the onesobtainedinthe litera-

ture for the euro area. It seems that real variables in Portugal adjust more. When compared with the

euro area, the output, investment, real wage and employment in Portugal expand more in response to

an unexpected decrease in the interest rate. Inflation in Portugal adjusts quicker and reacts further on

impact. The trade with the two areas responds differently to the referred monetary shock. Trade with

countries insidethe euro area increases, as both exports and imports increase. Imports from countries

outside the euro area decrease in the first two quarters, increasing thereafter, while exports to coun-

tries outside of the euro area increase substantially on impact.

It could be worthwhileto conduct more empirical work in the context of this model. Different behaviors

for the aggregate variables of the countries inside and outside of the euro area can be considered. For

instance, to assume that the equations that determine the evolution of these variables are the ones

given by an estimated VAR. Another dimension that can be explored is the estimation of some of the

parameters of the model using Bayesian methods, as Adolfson et al. (2007) do.6

The model has many frictions, but is simplistic in various dimensions. As such it could be interestingly

extended in various directions. It could incorporate government debt and non-Ricardian households

so that fiscal policy could interact with the monetary policy in a less trivial way. It could incorporate a fi-

nancial sector to study the so called financial accelerator channel of the monetary policy. It could con-

sider the labor market as a more complex market allowing for unemployment. More sectors of

production could be considered, in particular the nontradable good sector.

Economic Bulletin | Banco de Portugal

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109

(6) According to Canova (2007) in general the estimation of this type of models is problematic for many reasons, but specially because it is prone to

identification problems.

666666666666666666666666

Page 16

REFERENCES

Adão, B. (2009), “The Monetary Transmission Mechanism for a Small Open Economy in a Monetary

Union”, Working Paper, Banco de Portugal.

Adolfson, M., S. Laseen, J. Linde, and M. Villani (2007), “Bayesian Estimation of an Open Economy

DSGE Model with Incomplete Pass-through”, Journal of International Economics, Elsevier,

vol. 72(2), pages 481-511, July.

Altig, D., L. J. Christiano, M. Eichenbaum, and J. Linde (2003), The Role of Monetary Policy in the

Propagation of Technology Shocks. Manuscript, Northwestern University.

Backus, D., P. Kehoe, and F. Kydland (1994), “Dynamics of the Trade Balance and the Terms of

Trade: The J-Curve?”, American Economic Review, 84, 84-103.

Calvo, G. (1983), “Staggered Prices in a Utility-Maximizing Framework”, Journal of Monetary

Economics, vol. 12, p. 383-398.

Canova, F. (2007), “Methods for Applied Macroeconomic Research”, Princeton University Press.

Cochrane, J. (2007), “Inflation Determination with Taylor Rules: A Critical Review”, University of

Chicago, mimeo.

Collard, F., and H. Dellas (2002), “Exchange Rate Systems and Macroeconomic Stability”, Journal of

Monetary Economics, 49, p. 571-599.

Christiano, L., M. Eichenbaum, and C. Evans (2005), “Nominal Rigidities and the DynamicEffects of a

Shock to Monetary Policy”, Journal of Political Economy, vol. 113, no. 1.

Christoffel, K., G. Coenen, and A. Warne (2008), “The New Area-Wide Model of the Euro Area: A

Micro-Founded Open-Economy Model for Forecasting and Policy Analysis”, ECB Working

Paper.

Deardorff, A., and R. Stern (1990), Computational Analysis of Global Trading Arrangements, Ann

Arbor, University of Michigan Press.

Martins, F. (2006), “The Price Setting Behavior of Portuguese Firms Evidence From Survey Data”,

Working Paper 4-06, Banco de Portugal.

Smets, F., and R. Wouters (2003), “An Estimated Stochastic Dynamic General Equilibrium Model of

the Euro Area”, Working Paper 171, ECB.

Stern, R.,J. Francis, and B. Schumacher (1976), Price Elasticities in International Trade: An

Annotated Bibliography, Toronto, Macmillan.

Taylor,J. B. (1999),“AnHistoricalAnalysisofMonetaryPolicyRules”,inMonetaryPolicyRules, ed.by

J. B. Taylor, Chicago, University of Chicago Press, pp. 319-341.

Whalley, J. (1985), Trade Liberalization Among Major World Trading Areas (Cambridge, Mass.: MIT

Press).

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APPENDIX

1.Solving the model

The equilibriumconditions can be described by a set of difference equations, withthe same number of

endogenous variables, see Adão (2009). We want to solve this system of equilibrium equations. How-

ever, therearetwomaindifficultiesindeterminingthesolution.First, sincethereisgrowthinthemodel,

there are variables that are growing while others are stationary. Thus, to solve the model we need to

make all the variables stationary. Second, the equilibrium equations are non-linear difference equa-

tionsandtypicallytheirsolutionis not trivial. The usualprocedureinvolvessimplifyingeachequationof

the system. Each equation of the system is approximated by a linear equation. More specifically, each

equation is replaced by its first order Taylor approximation, and that approximationis taken around the

equilibrium steady state.

To find the steady state it is necessary to give functional forms to

??

a . ,

??

V . and

??

? . . We take

? ?

a u

????

uu

?????

?

1

2

2

11

2

. In the steady state wehave u=1, then ? ?

a 10

?

and

? ?

?

a 1

?

1

? . The invest-

ment adjustment cost function is given by ? ???

V

I

I

k

2

I

I

I

t

t 1

?

t

t 1

?

??

2

?

. Thus, in the steady state,

????

VV

II

???

?

? 0. Finally the volume premium factor is given by ? ??

i

?

??

?i

tt

BBB

???

exp

?

at the

steady state ? ?

?iB ? 1 for i = u,o. To obtain a system in stationary variables we redefine the variables,

see Adão (2009). The transformation of the original system of equations into a system of equations

with stationary variables is involved but trivial.

The next step is to loglinearize the system of equilibrium conditions for the stationarized variables

around the deterministic steady state. Once that is done we obtain a system of various difference

equations. Let statetdenote the vector of endogenous state variables, nstatetdenote the vector of en-

dogenous non-state variables and exotthe vector of exogenous variables. The system obtained has

the format:

AA state

?

BB state

?

CC nstate

?

DD exo

?

tttt

????

?1

0,

E

FF state

?

GG state

?

HH state

?

JJ nstate

??

K

t

ttt

t

??

?

?

?

K nstate

?

?

?

11

1

LL exoMM exo

?

ttt

??

?

?

???

?

?????

?

?1

0,

where the symbols with two equal capital letters denote matrices.

There are a few available algorithms designed to solve this type of difference equations system. We

used the one developed by Uhlig (1995). Uhlig’s algorithm enables us to write all variables as linear

functions of the vectors statet?1, and exot, which are given at date t. More formally, it gives us matrices

P, Q, R and S so that the equilibrium described by the recursive equilibrium law of motion,

state P state

?

Q exo

? ?

ttt

?

?1

,

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Page 18

and

nstate R state

?

S exo

? ?

ttt

?

,

is stable.

6.2. Calibration

Most of the parameters can be related to the steady state values of the variables in the model and

therefore, can be calibrated so as to match the sample mean of these. The remaining weretaken from

Adolfson et al. (2007). Proceeding in this waywe minimized the dimensions in whichPortugal is differ-

ent from the euro area. That makes it easier to identify the causes for the differences between the re-

sults obtained for Portugal and the ones for the euro area obtained by Adolfson et al. (2007).

Manyof the parameterswerecalibratedusingthe “QuarterlySeriesfor the PortugueseEconomy”data

set, which refers to the period 77:Q1-07:Q4. This data set is included in the Economic Bulletin of the

Bank of Portugal, Summer 2008, and is available online. For the period that starts in 1999, the year in

whichPortugalenteredthe EuropeanMonetaryUnion,andendsin 2007,per capita Private Consump-

tion grew at 0.29 percent quarterly, per capita Public Consumption grew at 0.32 percent quarterly, per

capita Investment grew at -0.11 percent quarterly, per capita GDP grew at 0.25 percent quarterly, per

capita Exports grew at 1.05 percent quarterly and per capita Imports grew at 0.79 percent quarterly.

We considered the average growth rate of ztto be 0.25 percent quarterly, which is the growth rate of

real GDP per capita in the period 99:Q1-07:Q4.

The stockofcapitalwascomputedusingtheperpetualinventorymethod.7The quarterlyaggregatede-

preciation rate,?, obtained was 0.011. Adolfson et al. (2007) set it equal to 0.013.

For manyreasonsit is difficult to determinethe steadystate real interest rate relevantfor the represen-

tative Portuguese consumer. The average real interest rate measured by the ratio between the 3

month money market interest rate and the realized inflation rate was0.041 percent quarterly in the pe-

riod99:Q1-07:Q4.8The usefulnessofthisrealinterestrateisproblematicasitimpliesadiscountfactor

?, the ratio between the average growth rate and the average real interest rate, larger than one. As

such we discarded it and considered alternatives. The other available nominal interest rate series are

implicit interest rates. They are obtained either by dividing interest received on bank deposits by bank

deposits or by dividing interest received on bank loans by the bank loans. The interest rates on depos-

its we discard as they also imply a discount factor larger than one. Among the interest rates on credit,

the mortgage interest rate is our preferred, as it is the lowest and the most relevant for the representa-

tive consumer. The average real interest rate measured by the difference between the implicit mort-

gage interest rate and the realized inflation rate was0.46 percent quarterlyin the period 99:Q1-07:Q4.

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112

(7) The perpetual inventory method is a method of estimating a country’s total capital stock, using the level of real investment in each year. Investment is

classifiedbytypeof capitalgoods,whichwedenoteby j, suchasbuildings,machinery, andvehicles.Assuminganappropriaterateof depreciation?j t ,for

each type of capital, the law of motion of the different types of capital, Kj t ,, is K

sufficiently long, the initial stock of capital is irrelevant, as it is already completely depreciated,to determine the more recent values of the stock of capital.

The aggregate stock of capital is obtained by aggregating the various types of capital.

KI

j t

,

j t

,

j t

,

j t

,

()

? ??

?

1

1

?

. Notice that if each type the investment series is

77777777777777777777777

(8) This money market interest rate series is the 3-month EURIBOR, and the inflation used was the GDPdeflator growth.

88888888888888888888888

Page 19

This real interest rate together withassumed growthrate of ztimplies a ? equal to 0.998. Adolfson et al.

(2007) consider a similar value of ? for the euro area, 0.999.

Following Adolfson et al. (2007), we set the labor supply elasticity, ?, to 1 and the habit parameter to

0.65. Christiano et al. (2005) consider similar values for these parameters. The constant associated

with labor in the utility function, ? is chosen so that in the steady state agents work 30 percent of their

time. Adolfson et al. (2007) assume agents work 30 percent of their time while Chari et al. (2002) as-

sume agents work 25 percent of their total time in steady state.

We considered labor income to be the sum of Remunerações do Trabalho plus Contribuições para a

Segurança Social and capital income to be all the remaining domestic income.9We took as the value

of?, the sample mean of the ratio between non-labor income and domestic income, which for the pe-

riod 99:07 is 0.27. The value that Adolfson et al. (2007) consider to be the share of capital for EMU is

0.29.

The share of imports in the main components of the domestic expenditure were obtained from the na-

tional input-output matrices of INE. That calculation was done for the period 1996-1999. During that

period the average share of private consumption that was imported was 27 percent and for the same

periodthe averagepercentageof investmentthat wasimportedwas33percent.The samplemean,for

the period 99:1-07:4, of the share of imports from the euro area was 66 percent and the share of im-

ports from countries outside of the euro area was 34 percent. The percentage of imported consump-

tion from the union was assumed to be proportional to the ratio between total imports from the euro

area and aggregate imports. Thus, the share, ?u,c, was calibrated to match the sample mean, 0.18.

Under this assumption, the other parameters,?u,i,?o,cand?o,i, were set to 0.22, 0.09 and 0.11. For

the period, 99:1-07:4, the ratio betweenthe price of investment and the GDPdeflator, and the ratio be-

tween the price of consumption and the GDP deflator, which we denoted by ?i,dand ?c,drespectively,

averaged0.98and0.99.The valuesof theelasticities?cand?icouldbedeterminedif wehadinforma-

tion on the relative prices ?o,dand ?u,d, which we do not have. Studies seem to indicate that for the

United States and Europe the elasticity between home goods and foreign goods is between 1 and 2,

and values in this range are generally used in empirical trade models.10We set ?c? 1.5and ?c? 1.6,

which are the estimates obtained by Adolfson et al. (2007) for the euro area, and set both ?u,xand ?o,x

equal to 1.5.

The evidence from survey data, as described in Martins (2006), indicates that the frequency of price

changesbyPortuguesefirms is 1.9 times per year. And of thosefirms that changepricesonlyabout42

percent use forward looking information to set their price. This implies that in each quarter about 20

percentof thefirms changetheirpricesoptimally. This valueis higherthantheoneestimatedbySmets

and Wouters (2003) and Adolfson et al. (2007) whichis around 10 percent, but lowerthan the one esti-

Economic Bulletin | Banco de Portugal

Articles | Spring 2009

113

(9) As the national accounting data of GDPincludes net indirect taxes, these need to be subtracted from the GDPto obtain the domestic income.

999999999999999999999

(10) For the US see, for example,the survey by Stern et al. (1976). For Europesee, for example,the discussionsof CollardandDellas(2002), Whalley(1985,

Ch. 5) and Deardorff and Stern (1990, Ch. 3). In similar studies, for the United States, Chari et al. (2002) and Backus et al. (1994) set the substitution

elasticity between foreign and domestic investment goods equal to 1.5, and for Europe Christoffel et al. (2008) estimate ?c?19 . and ?i?16 . .

101010101010101010101010101010101010101010

Page 20

mated by Christiano et al. (2005), 40 percent. Following Adolfson et al. (2007) we set the mark-up

equalto 16 percent.11We set the indexationparameter, ?d, equalto 0.22, whichis the value estimated

byAdolfsonetal.(2007)fortheeuroarea.FollowingAdolfsonetal.(2007)andChristianoetal.(2005),

the markup power in wage setting is set to 1.05. Following Adolfson et al. (2007), the indexation of

wages, parameter, ?w, is set to 0.50, and the probability of not being able to change the wage, ?w, is

set equal to 0.69.

The steady state of the model is independent of the adjustment cost functions, but the dynamics de-

pend on them. The estimates in the literature concerning the adjustment costs of investment, capital

utilization and foreign debt differ substantially. Christiano et al. (2005) find estimates of 2.48 and 0.01

for

??

V

and?

?

2

1, respectively. Altig et al. (2003) find a value of 0.049 for?

?

2

1. Adolfson et al. (2007) esti-

mate a value of a 8.67 for

??

V

and estimate a value of 0.252 for ?i.12We took the values reported in

Adolfson et al. (2007).

During the period 99:01-07:04 the share of the exports to countries outside of the euro area was 0.37,

while as referred before, the share of imports from countries outside the euro area was 0.34. The pa-

rameters chosen replicate approximately these ratios as well as the average sample shares in the

GDPof privateconsumption,publicconsumption,investment,totalexports andtotalimports. It is com-

mon in the literature, including Adolfson et al. (2007), to assume that in the steady state exports are

equal to imports, and the net foreign debt is zero. Instead, we assumed that the level and composition

of the steady state net foreign responsabilities were the values for Portugal at the end of 2007. At this

date the net foreign responsibilities were a large fraction of GDP, being 83 per cent denominated in

euros.

The parameters of the IS curve, Phillips curve and Taylor rule were chosen so that the impulse re-

sponse functions of the union’s inflation, output and interest rate to a monetary shock could mimic the

impulseresponsefunctionsof thesevariablesto a monetaryshockinthe modelestimatedbyAdolfson

et al. (2007)for theeuroarea.The parametersof theinterestraterulearesimilarto theonesestimated

fortheeuroareabyAdolfsonetal. (2007)andSmetsandWouters(2003).The parameter?reflectsthe

size of Portugalandis set to 0.05. The parametersin the equationsthat determinethe nominalinterest

rate, output and inflation outside the union do not need to be specified as we assumed that these vari-

ables are not affected by a monetary policy shock in the union.

Banco de Portugal | Economic Bulletin

Spring 2009 | Articles

114

(11) Chari et al. (2005) have a mark-up of 11 per cent.

1111111111111111111111111111111111111111 11

(12) These divergent results in the literature are due to the fact that the data sets are divergent and to the different estimation techniques used. Adolfson et al.

(2007) use Bayesian estimation techniques while Christianoet al. (2005) match the impulse response functions of the identified shocks.

121212121212121212121212121212121212121212

Page 21

Articles | Spring 2009

Economic Bulletin | Banco de Portugal

115

Chart 1(to be continued)

IMPULSE RESPONSES TO THE MONETARY POLICY SHOCK

Nominal Interest Rate

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

12345678 9 10 11 12 13 14 15 16 17

Quarters

Annualized percentage points

Production in Portugal

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Production in the Union

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Investment

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1234567

Quarters

89 10 11 12 13 14 15 16 17

Percentage deviation from SS

Consumption

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Capital Rental Rate

-0.005

0

0.005

0.01

0.015

0.02

123456789 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Real Wage

0

0.02

0.04

0.06

0.08

0.1

0.12

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Inflation in the Union

0

0.02

0.04

0.06

0.08

0.1

0.12

123456789 10 11 12 13 14 15 16 17

Quarters

Annualized percentage points

Inflation in Portugal

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

123456789 10 11 12 13 14 15 16 17

Quarters

Annualized percentage points

Capital Utilization

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Employment

0

0.05

0.1

0.15

0.2

0.25

0.3

1234567

Quarters

8 9 10 11 12 13 14 15 16 17

Percentage deviation from SS

Exchange Rate Depreciation

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

123456789 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Page 22

116

Spring 2009 | Articles

Banco de Portugal | Economic Bulletin

Chart 1(continued)

IMPULSE RESPONSES TO THE MONETARY POLICY SHOCK

Net Foreign Assets

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1234567

Quarters

8 9 10 11 12 13 14 15 16 17

Percentage deviation from SS

Rel. Price Investment

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Real Marg. Cost

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Union Rel. Price

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Outside Union Rel. Price

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Rel. Price Cons

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Imports from Union

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Exports to Outside of the Union

0

0.1

0.2

0.3

0.4

0.5

0.6

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Imports from Outside Union

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Exports to the Union

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

12345678 9 10 11 12 13 14 15 16 17

Quarters

Percentage deviation from SS

Volume Premium on

Foreign Debt

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

123456789 10 11 12 13 14 15 16 17

Quarters

Annualized percentage points