IMF-用于综合政策分析的DSGE估计模型（英）

An

Estimated

DSGE

Model

forIntegrated

Policy

AnalysisKailiChen,Marcin

Kolasa,JesperLinde,Hou

Wang,Pawel

Zabczyk,andJianpingZhouWP/23/135IMF

Working

Papers

describe

research

inprogress

by

the

author(s)

and

are

published

toelicit

comments

and

to

encourage

debate.Theviewsexpressed

inIMFWorkingPapersarethoseoftheauthor(s)anddo

notnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.2023JUN©2023InternationalMonetaryFundWP/23/135IMF

Working

PaperMonetaryandCapitalMarketsDepartmentAn

Estimated

DSGE

Model

for

Integrated

Policy

AnalysisPrepared

by

Kaili

Chen,

Marcin

Kolasa,

Jesper

Lindé,

Hou

Wang,

Pawel

Zabczyk,

Jianping

ZhouAuthorizedfordistributionbyJesperLindéJune2023IMF

Working

Papers

describe

research

in

progress

by

the

author(s)

and

are

published

to

elicitcomments

and

to

encourage

debate.

TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,

orIMFmanagement.ABSTRACT:

Weestimatea

NewKeynesiansmallopeneconomymodelwhichallowsforforeignexchange(FX)marketfrictionsandapotentialroleforFXinterventionsforalargesetofemergingmarketeconomies(EMEs)andsomeinflationtargeting(IT)advancedeconomy(AE)countriesservingasacontrolgroup.Next,weusetheestimatedmodeltoexaminetheempiricalsupportfortheviewthatinterestratepolicymaynotbesufficienttostabilizeoutputandinflationfollowingcapitaloutflowshocks,andtheextenttowhichFXinterventions(FXI)canimprovepolicytradeoffs.OurresultsrevealsignificantstructuraldifferencesbetweenAEsandEMEs—inparticularFXmarketdepth—leadingtodifferenttransmissionofcapitaloutflowshockswhichjustifiesoccasionaluseofFXIinsomeEMEsincertainsituations.Ouranalysisalsohighlightsthecriticalimportanceofaccountingfor

theendogeneityofFXIbehaviorwhenassessingFXmarketdepthandpolicytradeoffsassociatedwithvolatilecapitalflowsinpastepisodes.JELClassificationNumbers:Keywords:C6,F4,E5,O5IntegratedPolicyFramework;

EmergingMarkets;

MonetaryPolicy;ForeignExchangeIntervention;

EndogenousRisks;

IncompleteFinancialMarkets;

Bayesian

Estimationkchen4@,mkolasa@,jlinde@,hwang2@,pzabczyk@,jzhou1@Author’sE-MailAddress:*Theauthors

wouldliketo

thankseminarparticipants

at

theIMFfor

veryvaluablediscussions

andcomments.

AspecialthankyoutoAtetWijosenoattheBank

ofIndonesiawhocontributedstronglytoanearlierversionofthemodel.TheviewsexpressedhereinarethoseoftheauthorsandshouldnotbeattributedtotheIMF,itsExecutiveBoard,oritsmanagement.IMF

WORKING

PAPERSAnEstimatedDSGEModelfor

IntegratedAnalysisContentsI.Introduction5II.The

DSGE

Model8II.1.

AggregateDemand

8II.2.

AggregateSupply11II.3.

InternationalFinancialMarkets14II.4.

MonetaryandFiscalPolicy17II.5.

TheForeignEconomy

20III.Model

Estimation21III.1.

CountriesandData22III.2.

Priors

26III.3.

EstimationResults29IV.Posterior

Predictive

Analysis33IV.1.

TransmissionofForeignInvestorsPortfolioOutflowShocks

33IV.2.

TransmissionofInterestRatePolicyShocks36IV.3.

TransmissionofFXInterventions38V.Regime-Switching

Estimation

Results41Conclusion44VI.References46Appendix

A.

Derivations

of

Linearized

Relationships49A.1

ResourceConstraint

49A.2

UIPandNetForeignAssetDynamics53A.3

WageandPricingSchedules57Appendix

B.

Calibrated

Parameters

and

Full

Estimation

Results

61FIGURES1.FXInterventionsduringRisk-offEpisodes

52.KeyMacroeconomicVariablesIncludedinEstimation

243.U.S.VariablesIncludedin

theEstimation254.

PriorDistributions285.DifferenceinLogMarginalLikelihoodversusCorrelationbetweenFXIandNER

326.Country-SpecificImpulsestoForeigninvestorsPortfolioOutflowShocks

347.AverageImpulsestoForeigninvestorsPortfolioOutflowShocks

358.ImpulsestoanUnexpectedInterestRateTightening

369.MeanImpulsestoanUnexpectedInterestRateTightening

3710.ImpactofFXIsonTransmissionofForeigninvestorsPortfolioOutflowShocks

3911.HowFXIsImpactTransmissionofanUnexpectedInterestRateTightening

40TABLES1.CountriesandSamplePeriodsincludedinEstimation

222.AllObservablesandShocksUsedin

Estimation

23*Theauthors

wouldliketo

thankseminarparticipants

at

theIMFfor

veryvaluablediscussions

andcomments.

AspecialthankyoutoAtetWijosenoattheBank

of

Indonesiawhocontributedstronglyto

anearlierversionof

themodel.IMF

WORKING

PAPERSTitle

of

WP3.PriorandPosterior

294.ComparisonofModelEstimateswithDifferentFXISpecifications

315.Regime-SwitchingEstimation–Time-VaryingFXMarketDepthOnly

426.Regime-SwitchingEstimation–Time-VaryingFXMarketDepthandFXIRule

43APPENDIX

TABLESAppendixB.TableB.1:ParametersCalibratedtoMatch

EMEandAECharacteristics

61AppendixB.TableB.2:ParametersCalibratedtoCountry-SpecificCharacteristics

61AppendixB.TableB.3:Country-SpecificPosteriorandLogMarginalLikelihoodswith

EndogenousFXIRuleinEMEs

62AppendixB.TableB.4:Country-SpecificPosteriorandLogMarginalLikelihoodswith

ExogenousFXIRuleinEMEs

63AppendixB.TableB.5:Country-SpecificPosteriorandLogMarginalLikelihoodsforEndogenousandExogenousFXIRulesinAEs

64INTERNATIONALMONETARYFUND4IMF

WORKING

PAPERSAnEstimatedDSGEModelfor

IntegratedAnalysisI.

IntroductionOverthelasttwodecades,manyemergingmarket

economies(EMEs)

anddevelopingcountrieshavemovedawayfromfixedexchangerateregimesandadopteda

monetarypolicyframeworkbasedoninflationtargeting(IT).

TheIT

framework,first

introducedin

NewZealandin

1990andtheninmanyother

advancedeconomies

(AEs),

was

foundto

beverysuccessfulinstabilizingbothinflationandrealaggregates(Svensson,2010).However,unliketheiradvancedeconomycounterparts,manyEMEcentralbankswithIT

frameworkshavecontinuedto

relyon

foreignexchangeinterventions(FXIs)in

their

monetarypolicy

operations.

This

was

particularlyevidentduringepisodesof

volatilecapital

flows(Hofmannetal.,2019),

liketheTaper

Tantrum

andtheCOVID-19crisis(Kalemli-Ozcanet

al,2022).Weillustratethispoint

in

Figure1,

whichshowsthatFXsalesduringthesetwoepisodesweremuchmoreprevalentin

EMEs

thanin

AEs.Averysimilar

pictureemerges

if

werestrictthesampletoinflationtargetingcountries.Figure

1.

FX

Interventions

during

Risk-off

Episodes35%29%30%25%25%20%15%11%10%6%5%0%TaperTantrumCovid-19AdvancedEconomiesEmergingMarketEconomiesSource:

Own

calculations

based

on

monthly

data

from

Adler

et

al.

(2021).

The

figure

presents

the

share

of

countries

within

eachgroup

that

intervened

during

the

two

considered

episodes.

A

country

isclassified

as

intervening

if

itwas

selling

FX

reserves

(broadmeasure)

in

the

month

following

the

shock

(June

2013

for

Taper

Tantrum,

April

2020

for

Covid-19),

and

the

total

transaction

volumewas

atleast

0.5%ofitsannualGDP.As

exploredindepthbye.g.,

Adrianetal(2020,2021)

andBasuet

al.(2020),onereasonformorefrequentuseofFXIs

in

EMEsisthatthesecountriesfacemoredifficult

stabilizationtradeoffsbecauseofseveral(oftenrelated)

economic

characteristicsthatsetthemapartfromAEs.

EMEstypically

have

relatively

largernetforeignliabilitiesandmorelimitedaccesstointernational

financialmarkets,

whichmakesthemmorevulnerableto

suddenchanges

inglobalfinancialconditions.

Their

FXanddomesticfinancialmarketsare

oftennotasdeepasin

AEs,implyingthatswings

in

internationalcapitalflows

mayleadto

largeundesirablemovementsinINTERNATIONALMONETARYFUND5IMF

WORKING

PAPERSAnEstimatedDSGEModelfor

IntegratedAnalysistheexchangerate.Moreover,exchangeratevolatility

tendsto

havemoreadverseeffectsinEMEsbecauseof

their

limitedabilityto

hedgecurrencymismatchesandlargerandmorepersistent

exchangeratepass-throughto

inflation.This

reasoninghasrecently

foundsupportfromthetheoreticalliterature,

whichidentifiedfrictionswarrantingtheuse

ofFXinterventions

incertaincircumstancesasmorelikely

toemergein

EMEsthaninAEs.Oneof

thekeyfrictionsis

FXmarketshallowness,

whichleads

toinefficientmovementsinuncoveredinterestrateparity(UIP)premiathatcan

beat

least

partiallyoffset

byappropriateuseofFXI(see,

e.g.,GabaixandMaggiori,2015;Cavallino,

2019;

Amadoret

al.,

2019;

FanelliandStraub,2021).Anotherconsiderationisthepresenceofcurrencymismatchesthatmayprecipitateasharprisein

theborrowingspreadswhen

theexchangeratedepreciates,

possiblyleading

toseverefinancialcrises

oftenreferredtoas

‘suddenstops’

(see,e.g.,

JeanneandKorinek,

2010;Mendoza,

2010;Basuetal.,2020).In

arecent

andmorequantitativelyorientedstudy,

Adrianetal.(2021)arguethatthesefrictionsmaycreateaparticularlydifficulttradeofffor

centralbanksineconomies

withstrongprice

andwageindexationmechanisms,fastpass-throughof

exchangeratetoconsumerprices,andhighstickinessof

exportprices

in

foreigncurrency,thelasttwofeaturesstressedbythedominantcurrencyparadigm

literature(Gopinathet

al.,

2020).Thegoalofthispaperisto

testtheempiricalrelevanceofthesemechanismsandquantitativelyverifytheirimplications,includingtheconditionsunder

whichFXI

canbeuseful,

by

embeddingtheminamicrofounded

macroeconomicframeworkthatcanbetakendirectlyto

thedata.Tothisend,wedevelopadynamic

stochastic

generalequilibrium

(DSGE)modelthatcanbeseenasanempiricalformulationofthetwo-countrymodeldescribedin

Adrianet

al.(2021).Themodelis

aNewKeynesiansmallopeneconomysetupwithpotentiallyshallowFXmarkets,

FXmismatchesandarangeofnominalrigiditiesconsideredintheDSGEliterature,

includingstickypricesandwageswithindexationto

past

inflationandpossiblyalsoexchangeratemovements.Pricesareset

in

localcurrency,

whichletsthedata

speaktothedegreeof

exchangeratepass-through.

Additionally,to

addressthewell-knownforward-guidancepuzzleimpliedbymodelswithfullyrationalagents(Giannoniet

al.,

2015),weallowforamodestdegreeof

boundedrationalitybyusingtheframeworkdevelopedby

Gabaix(2020)andextendedto

anopeneconomysettingin

Kolasa

etal.(2022).Mostimportantly,andincontrasttopreviouspapersmicrofounding

thedeploymentofFXI,

weestimate

themodel

foraset

of

EMEs

as

wellasasetofsmallopenAEsthat

weuse

asacontrolgroup.WeuseBayesianmethods,drawingonthelargeliteraturedealing

withopeneconomyDSGEmodels(e.g.,Adolfsonet

al.,2007;

JustinianoandPreston,

2010).Acriticalassumptionin

theestimationisthatweadoptthesamepriorsfor

EMEs

and

thecontrolgroupofAEs.

This

implies

that

any

posteriordifferencesin

theparameters,andconsequentlyanydifferencesin

shocktransmission,

aredrivenby

cross-countryvariationinthetimeseriesusedINTERNATIONALMONETARYFUND6IMF

WORKING

PAPERSAnEstimatedDSGEModelfor

IntegratedAnalysisin

estimation.

Takingthe

modeldirectlyto

thedata

allows

ustoassessand

comparethequantitativeimplicationsof

internationaldifferences

in

the

transmissionmechanism

andcouldeasily

becomplemented

byscenarioanalysesassessingcountry-specificpolicy

tradeoffs.Importantly,apartfrom

includingthestandardsetofmacroeconomictimeseriesasobservableswhenestimatingthemodel,

we

usetheAdler

et

al.(2019)estimateofFXinterventions

asanadditionalobservable.

By

doingso,

weovercomeasignificantobstaclein

identifyingFXmarketdepthinmacroeconomicmodels,

whereincountrieswithshallowFXmarketsmayseemto

havedeepmarketssincetheircentralbankshavesystematicallyreliedonFXinterventionstomitigateexchangeratevolatility

duringthesample

period.TheadditionoftheFXIproxy

asobservablein

estimationthusfacilitatesjointidentificationof

FXI

policies

and

FXmarket

depth,especially

in

countrieswherewefindstrongevidencefor

activeFXinterventions.Moreover,

wealsoestimateavariant

of

ourmodelinwhichwerelax

theassumptionthat

FXmarketdepthandthesystematicpart

of

theFXIruleare

constant

and

insteadallowforthepossibility

thattheyvaryovertimeusingregimeswitchingmethodsadvocatedinMaih(2015).Ouranalysisconfirmsthe

empirical

relevanceof

frictions

in

EMEs,whichmaywarranttheuseof

FXIin

certaincircumstances.

The

modelestimatesshowthat

FXmarketsare

shalloweronaveragein

EMEsthanAEs,

implyingthatUIPpremiumshockscanleadto

largermovementsintheexchangerate.Inflationexpectationsare

also

less

well-anchored

in

EMEs,

whichcanposedifficult

output-inflationtradeoffsfollowing

exchangeratedepreciations.The

modelestimatesalsosuggestthat

a

few

EMEshaveusedFXIto

respondto

exchangeratemovementsin

asystematicandrule-basedmanner.By

limitingexchangeratedepreciationduetocapitaloutflows,FXI–intheform

of

FXsales–reducetheneedto

raiseinterest

ratesto

containinflation,

andthereforeimprovepolicytradeoffs.Afinalmodel

extensionfeaturingregimeswitchingprovidesevidencefortime-varyingmarket

depthand,consequently,

greater

impactofFXI

in

periods

whenmarketsareshallow.Therest

of

thepaperis

organizedasfollows.

Section

II

presentstheDSGEmodel.SectionIIIdescribesthemodelestimationprocedureandreportsourestimationresults.

SectionIVpresentsimpulseresponsesto

keyshockstoquantifyshocktransmissionandpolicytradeoffs.InSection

Vweassess

empiricalsupportfortheviewthatFXmarketdepthandthesystematicpartoftheendogenous

FXI

rulearetime-varyingbyestimatingthemodel

usingregime-switchingmethods.Thelast

sectionconcludes.INTERNATIONALMONETARYFUND7IMF

WORKING

PAPERSAnEstimatedDSGEModelfor

IntegratedAnalysisII.

The

DSGE

ModelWestart

bydescribingan

empiricalsmallopeneconomyformulationofthefullyfledgedtwo-country

modelin

Adrianet

al.(2021),whichinturndrawsonthemodelinAdrianetal.(2020).Theframeworkisestimated

usingaset

of

standardmacroeconomictime

seriesfor12emergingmarketcountriesand5smallopenadvancedeconomiesthatallpursueindependentmonetarypolicy

(somevariant

of

inflationtargeting).It

draws

heavily

onthetwo-countrymodel,

butmakesanumber

of

simplifyingassumptions

andintroduces

anumberofdata-drivenadd-onsmeanttoenhanceitsempiricalproperties.Thefirst

of

theseis

thesmallopeneconomyassumption—weposit

thatthesizeof

thedomestic(home)economy(

)

is

arbitrarilysmallrelativeto

theforeigneconomy(

∗),whichmeans

thattheforeigneconomyisessentially

exogenous.

Second,

weattemptto

capturetradein

intermediategoodsbyassumingthatexportingfirmscombinedomesticallyproducedgoods

withimportedgoods

beforesellingthemabroad.

This

waythemodelcanreconcileveryvolatileexportsandimportswitharelativelystabletradebalance(asashareof

GDP).

Third,

and

in

another

importanttwist

onthetwo-countrymodelabove,

weallowforhouseholddiscountingin

thespiritof

Gabaix(2020)

andKolasaetal.(2022),whichhelpsmitigatetheforwardguidancepuzzle(seeDelNegroet

al.,

2008).Fourth,sinceweconsidera(log-)linearizedformulationofthemodel,

wedonot

allowfortheoccassionally

bindingexternaldebt

limit,

andtheLagrangemultiplierΘ

≥

0

onthebank’s

borrowingconstraintis

hencesettoniltobeginwith.Before

turning

to

Bayesian

estimation,

we

next

provide

more

details

on

the

empirical

model

andhighlight

itsrelationshipto

themicrofoundedDSGEmodelof

Adrianetal.(2021).II.1.

Aggregate

DemandThe

home

economy

resource

constraint

can

(under

conditions

discussed

in

Appendix

A.1)

beexpressed

as

a

share-weighted

average

of

home

consumption

,

government

spending

,

and“net

exports”

(the

differencebetween

exports

∗

andimports)weighted

by

the(steady-state)tradeshare∗(1)=++(−).Consumption

demand

is

determined

by

the

consumption

Euler

equation

linking

the

marginal

utilityof

consumptionto

future

marginal

utility

of

consumption

and

short-term

real

interest

rates,facedbyconsumers,,=E+.,(2),,

+1INTERNATIONALMONETARYFUND8IMF

WORKING

PAPERSAnEstimatedDSGEModelfor

IntegratedAnalysisIn

equation

(2),

0

<≤

1

is

the

discounting

parameter

in

the

spirit

of

the

behavioral

NewKeynesian

model

of

Gabaix

(2020)

and

its

open

economy

extension

(Kolasa

et

al.,

2022).1

Themarginal

utility

of

consumption

varies

inversely

with

current

consumption,

but

rises

with

pastconsumption,

withthelatterreflectinghabitpersistenceinconsumption,1=

−

(

−−),,(3),�where=(1−

)

andis

an

exogenous

consumption

demand

shock

which

is

assumed

to,followanAR(1)process:=+.,(4)Taken

together,

these

equations

imply

that

consumption

demand

depends

on

a

long-term

realinterest

rate

,

but

with

an

important

caveat

that

this

borrowing

rate

depends

on

a

discounted,,,sum

of

futureshort-termrates:=

−

E

∑∞(5)−−=

−.,,,The

inclusion

of

discounting

(i.e.,

allowing

for<

1)

implies

that

future

short-term

real

interestrateshavemoremutedeffectsoncurrent

consumptiondemand.2In

addition

to

allowing

for

discounting,

our

model

departs

from

the

standard

New

Keynesian

setupby

assuming

that

the

borrowing

rate

facing

home

consumers

includes

a

time-varying

“privateborrowingspread”

Ψ

:=

E

∑∞

�

�(6)−�+(,−)�=

+Ψ

.,,Hence,is

theeffectivelong-termrealinterestrate

ongovernment

bonds,andtheinterest

ratespread

Ψ

is

a

discounted

sum

of

future

gaps

between

the

nominal

borrowing

rate

and

policy

rate,1i.e.,

Ψ

=

E

∑∞(−)

=

E

∑∞=where

the

last

equality

follows,1−fromthefactthatweassumethattheshort-termborrowingspreadfollowsanAR(1)

process:=+.(7),Fisher

(2015)

shows

that

this

Smets

and

Wouters

(2007)

domestic

risk-premium

shock

can

beinterpreted

as

a

structural

shocktothe

demandfor

safe

andliquid

assets.

In

thetheoretical

two-country

model

by

Adrian

etal.(2021),aspreadbetweeninterest

rates

facedbyhouseholds(),andthecentralbankpolicyrate(

)

only

arises

when

thehomeeconomyhits

theborrowinglimit.Ourspecificationin

eq.(6)allows

thisspreadto

be

positiveeven

when

thehomeeconomyisnot1

Ingeneral,assumingbehavioralexpectationsas

in

Gabaix(2020)mayintroduceadditionaltermsto

theintertemporaloptimalityconditions.Forexample,Kolasaet

al.(2022)showthateq.

(2)

shouldalso

containnetforeignassets.Topreservetractabilityof

themodel,wedisregardtheseadditionalfeatureswhenevertheirquantitativeimplicationsaresmall.2

Accordingly,forwardguidanceaboutfuturemonetarypolicyactionswouldhavemuch

smaller

effectsin

thissetupthaninthestandardworkhorseNewKeynesianmodel.INTERNATIONALMONETARYFUND9IMF

WORKING

PAPERSAnEstimatedDSGEModelfor

IntegratedAnalysisat

the

borrowing

limit,

which

would

arguably

be

the

case

with

a

more

fully

articulated

model

of

thebankingsector,for

example(e.g.,

Gertler

andKaradi,

2011).We

now

turn

to

discuss

the

contribution

of

net

exports

to

aggregate

demandin

eq.

(1).Following

Christiano

et

al.

(2011),

and

as

noted

earlier,

we

allow

exporting

firms

to

combinedomestically

produced

goods

and

imported

goods

in

the

production

of

export

goods.

Thus,exports

involve

a

continuum

of

exporters

with

some

degree

of

monopoly

power

who

combine

ahomogeneous

domestically

produced

good

and

a

homogeneous

good

from

imports.

To

a

first-order

approximation,

demand

for

domestically

produced

(

∗

)

and

imported

(

∗

)

goods

used,,toproduceexports

isthen

givenby∗∗,∗,(8)(9)=−+,,̂̂∗∗,∗(1

−),=−−+,∗,,whereis

the

share

of

imported

goods

directed

towards

the

export

sector

in

the

steady

state,,∗

is

the

relative

price

of

exported

goods

(produced

by

home

exporters)

to

that

of

their

foreigncompetitors,

and

is

the

relative

price

between

imported

and

domestic

goods,

i.e.,,=−.

In

the

export

demand

for

imported

goods,

we

allow

for

a

stationary

exogenous,̂shock

̂=/1,

wherefollows

anAR(1)

process(asdeviationfrom

itsdeterministic∗,∗,∗,meanof

unity):2−

1

=∗�−

1�+,

0

≤<

1,∼

.

.

.

�0,

∗�.∗,∗,

−1∗,∗∗,This

shock

will

tend

to

shift

both

exports

and

imports

in

parallel,

without

affecting

the

tradebalance.

The

demand

equations

above

imply

that

total

export

demand

∗

=

(1−canbebeexpressedas:)∗+,∗,̂̂∗∗,∗(10)=−+.∗,Hence,

total

export

demand

∗

rises

with

foreign

output

∗

and

falls

with

the

relative

price

ofgoods

exported

to

the

foreign

economy,

i.e.,

∗.

So,

allowing

for

imported

goods

to,∗

=−,be

used

in

the

export

sector

does

not

affect

the

final

export

demand

equation,

but

relative

pricechangesbetweenimportedanddomesticallyproducedgoods

wouldchangethe

relativeshareofthosetwotypesof

goodsusedin

producingexports.Finally,

noticethat

inthespecialcasewhenforeign

currency

prices

of

home

products

move

inversely

one-to-one

with

the

nominal

exchangerate,

wehave

,∗

equalto

thenegativeoftheproductrealexchangerate,

which

is

givenby,∗(11)=+−.,Similarly,

total

imports

equal=

(1

−)+∗where

import

demand

for

domestic,,consumption

purposes

expands

as

domestic

consumption

rises

and

falls

in

response

to

anincreaseintheirrelativeprice,INTERNATIONALMONETARYFUND10IMF

WORKING

PAPERSAnEstimatedDSGEModelfor

IntegratedAnalysis,̂(12)=−+,,,where,

=−is

the

price

of

a

bundle

of

imported

goods

relative

to

that

of

a

consumption,,basket

comprising

both

domestically-produced

and

imported

goods

and

̂=/1.

The,,specificationwithprivate

consumptionrather

than

governmentspending

meansthatwemaintaintheassumptionthat

government

spendinghasanegligibleimport

content.Importantly,domesticimport

demand

is

also

subject

to

an

exogenous

transient

preference

shifter,AR(1)

process(asadeviationfromitsdeterministicmeanofunity):which

follows

an,−

1

=�−

1�+Furthermore

and

finally,

note

that

the

relative

pricefrom

exchangeratesto

import

pricesreducesto

theconsumption-basedrealexchangerate,

0

≤<

1,∼

.

.

.

(0,

2

).,,,,,

under

the

assumption

of

full

pass-through∗(13)=+−.,,II.2.

Aggregate

SupplyTurning

to

the

supply

side,

the

price-setting

equation

for

domestically

produced

goods

takes

theform

of

amodifiedNewKeynesianPhillips

Curve:−=E

(This

specification

is

based

on

Calvo-style

price

setting,

with

the

sensitivity

of

domestic

producerpriceinflation

to

marginalcost

determinedbytheslopecoefficient−)++.(14),(1−

)(1−)=,(15)which

varies

inversely

with

the

mean

duration

of

price

contracts.

The

Phillips

Curvespecificationin(14)

allows

forthepossibilityof

somestructuralpersistencethatis

determinedbythe

indexation

parameter

0

≤

≤

1.

This

persistence

may

be

interpreted

as

reflecting

dynamicindexation

as

in

Christiano

et

al.

(2005),

so

that

non-optimizing

firms

index

theirnew

price

to

pastinflation

and

the

inflation

target

according

to=

(1+

)1−

(1

+),

which

impliesthat

the

steady-state

embeds

no

price

distortions.

But

it

is

also

empirically

consistent

with

theviewthat

inflationexpectations

featureanadaptivecomponent,asin

Claridaet

al.

(1999).Eitherway,

when

>

0

i.i.d.

cost-push

shocks

likemay

exert

persistent

“second

round”

effects

on,inflation.Marginal

costrises

with

an

increase

in

the

producer

real

wage

,

and

falls

with

a

decline

inthemarginalproductoflabor=−,(16)INTERNATIONALMONETARYFUND11IMF

WORKING

PAPERSAnEstimatedDSGEModelfor

IntegratedAnalysisand

with

our

Cobb-Douglas

production

function