IMF-疫情和能源冲击后的欧元区通货膨胀：进口价格、利润和工资（英）

EuroAreaInflationafterthePandemicandEnergyShock:Import

Prices,Profits

andWagesNiels-JakobHansen,FrederikToscani,andJingZhouWP/23/131IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.2023JUN©2023InternationalMonetaryFundWP/23/131IMFWorkingPaperEuropeanDepartmentEuroAreaInflationafterthePandemicandEnergyShock:ImportPrices,ProfitsandWagesPreparedbyNiels-JakobHansen,FrederikToscani,andJingZhouAuthorizedfordistributionby

OyaCelasunJune2023IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate.

TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,or

IMFmanagement.ABSTRACT:

We

document

the

importance

of

import

prices

and

domestic

profits

as

a

counterpart

to

the

recentincrease

in

euro

area

inflation.

Through

a

novel

consumption

deflator

decomposition,

we

show

that

import

pricesaccount

for

40percent

of

the

average

change

in

the

consumption

deflator

over

2022Q1

–

2023Q1,

while

domesticprofits

account

for

45percent.

The

increase

in

nominal

profits

was

largest

in

sectors

benefiting

from

increasinginternational

commodity

prices

and

those

exposed

to

recent

supply-demand

mismatches.

While

the

results

showthat

firms

have

passed

on

more

than

the

nominal

cost

shock,

and

have

fared

relatively

better

than

workers,

thelimited

available

data

does

not

point

to

a

widespread

increase

in

markups.

Looking

ahead,

assuming

nominalwage

growth

of

around

4.5percent

over

2023-24

–

slightly

below

the

level

seen

in

Q1

2023

–

and

broadlyunchanged

productivity,

a

normalization

of

the

profit

share

to

the

average

level

over

2015-19

will

be

necessarytoachieve

aconvergenceof

inflationtotargetoverthenexttwoyears.Monetarypolicy

willthusneedtoremainrestrictive

to

anchor

expectations

and

maintain

subdued

demand

such

that

workers

and

firms

settle

on

relativepricesettingthatisconsistentwithdisinflation.RECOMMENDEDCITATION:

Hansen,Niels-Jakob,FrederikToscani,JingZhou.2023.“TheRoleofImportPrices,ProfitsandWagesintheCurrentInflationEpisodeintheEuroArea”IMFWorkingPaper23/131,InternationalMonetaryFund,Washington,DC.JELClassificationNumbers:Keywords:E31,E24Inflation;

Wages;

Profits;

TermsofTradeNHansen@,

Ftoscani@,Jzhou@Author’sE-MailAddress:WORKINGPAPERSINTERNATIONALMONETARYFUND2EuroAreaInflationafterthePandemicandEnergyShock:ImportPrices,ProfitsandWagesPreparedby

Niels-JakobHansen,FrederikToscani,andJingZhou11We

are

grateful

to

Oya

Celasun

for

her

guidance

and

support.

We

also

thank

Silvia

Albrizio,

Jorge

Alvarez,

Christian

Bogmans,Romain

Duval,

Nir

Klein,

Geoff

Gottlieb,

Rui

Mano,

Pierre-Olivier

Gourinchas,

Mirko

Licchetta,

Andrea

Pescatori,

Jorge

Miranda

Pinto.AlexandreBalduinoSollaci,andseminarparticipantsandreviewersattheIMFfortheirveryhelpfulcommentsandsuggestions.INTERNATIONALMONETARYFUND31.INTRODUCTION

_______________________________________________________________________________

52.DECOMPOSINGTHEGDPDEFLATOR

________________________________________________________

73.DECOMPOSINGTHECONSUMPTIONDEFLATOR

__________________________________________

114.IMPLICATIONSFORPROFITABILITYANDTHEDISTRIBUTIONOFINCOME

______________

135.IMPLICATIONSFORTHEINFLATIONOUTLOOK____________________________________________

166CONCLUSION__________________________________________________________________________________

18REFERENCES_____________________________________________________________________________________

20FIGURES1.DecompositionofChangeintheGDPDeflator

____________________________________________________________

82.SectoralProfit

______________________________________________________________________________________________

83.ComparisonofGDPDeflatorIncreasetoPreviousEnergyPriceShocks

___________________________________

94.ComparisonofEuroAreaGDPDeflatorDecompositionwithOtherMajor

_______________________________105.DecompositionofChangeintheConsumptionDeflator

_________________________________________________126..AccountingfortheContributionofProductivity

toInflation______________________________________________137.IncomeSharesandRealWageandProfit_________________________________________________________________148.ProfitabilityIndicators_____________________________________________________________________________________159.CountryCharacteristicsandIncreaseinUnitProfit________________________________________________________1610.IllustrationofInflation,WageandProfitProjections

____________________________________________________18INTERNATIONALMONETARYFUND41.IntroductionThe

increase

in

firm

profits

in

the

recent

inflation

episode

has

been

catching

the

attention

of

economiccommentatorsand

policy

makersacrossadvancedeconomies.Despitesomecross-countryheterogeneity,therehasbeenapatternof

profitsperunit

ofoutput

(unit

profits)

being

animportantcounterparttotheincreasein

the

GDP

deflator

in

advanced

economies

over

the

past

two

years.

Policy

makers

have

consequently

pivotedin

their

communication

to

highlight

the

role

of

profits

for

inflation

along

with

the

role

of

unit

labor

costs.

Forexample,

ECB

executive

board

member

Philip

Lane

in

an

interview

with

Reuters

pointed

to

“extraordinary

unitprofits”,

and

ECB

executive

board

member

Fabio

Panetta

raised

the

risk

of

a

profit-price

spiral

in

a

New

YorkTimes

interview.2

Former

IMF

chief

economist

Olivier

Blanchard

has

pointed

out

that

distributional

conflict

–

beit

driven

by

strong

aggregate

demand

or

the

initial

desire

of

one

economic

actor

to

increase

relative

prices

relativetoothers–cangenerateinflationaryprocesses.Against

this

background,

our

paper

investigates

the

role

of

profits,

wages,

and

import

prices

in

the

recentepisode

of

high

inflation

in

the

Euro

Area.

We

contribute

to

the

debate

by

disentangling

the

role

of

importprices,profits,andwagesin

inflationintheeuroarea.Focusingontheconsumptiondeflator,

we

addtheroleofimport

prices

to

the

now

well-known

GDP

deflator

decomposition.

To

set

the

scene,

we

confirm

that

unit

profitsin

the

euro

area

have

increased

sharply

and

are

the

main

counterpart

to

the

increase

in

the

GDP

deflator.

Theprofit

increase

was

largest

in

mining

and

utilities

but

was

also

significant

in

agriculture,

construction,manufacturing,

and

contact-intensive

services.

Accounting

explicitly

for

the

import

price

shock

through

aconsumption

deflator

rather

than

GDP

deflator

decomposition,

we

find

that

import

prices

account

directly

for40percentof

inflationonaveragesince2022.

Butthe

role

ofdomestic

profits

remainssignificant,accountingforjust

below

45percent

and

labor

costs

for

25percent

of

inflation.

Net

taxes

were

slightly

disinflationary

over

theperiodandthuscontributednegatively.While

nominal

profits

have

increased,

this

is

not

necessarily

true

for

profitability.

Our

results

imply

thatfirms

have

passed

on

more

than

the

immediate

nominal

import

cost

shock.

Given

the

increasing

profit

share

ofgross

value

added,

firms

have

so

far

also

been

relatively

more

shielded

from

the

adverse

terms

of

trade

shockthan

wage

earners.

But

this

does

not

necessarily

imply

that

profitability

(the

markup

or

profit

margin)

hasincreased.

Analysis

by

economists

at

the

Bank

of

Italy

(Colonna

et

al.,

2023)

carefully

lays

out

the

relationshipbetween

profit

share

and

markup

and

illustrates

the

conditions

under

which

they

can

move

in

opposite

directions.TheyalsoshowthatdataforGermanysuggestsmarkupsinindustryandinmanufacturingremainedconstantin2022,

but

increased

in

construction,

retail,

accommodation,

and

transport.

In

Italy,

markups

in

2022

wereessentially

at

pre-pandemic

levels.

Our

own

reading

of

the

limited

national

accounts-based

data

for

the

euro

areais

consistent

with

this,

pointing

to

broadly

constant

rather

than

increasing

profitability.

How

come

firms

have

beenrelativelymoreshieldedfromtheshockthanworkers?Onereasonisthatpricesare

moreflexiblethanwages—firms

are

able

to

adjust

prices

quickly

to

shield

their

profitability

while

wage

is

subject

to

more

rigidities

such

asbeingsetbypreviouswagenegotiations.The

growing

literature

on

the

role

for

profits

is

generally

aligned

with

our

finding

that

firms

have

faredrelatively

better

than

workers

even

in

the

absence

of

a

large

increase

in

markups.

For

the

euro

are,

amongothers,

authors

from

the

European

Central

Bank

(Arce

et

al.,

2023)

and

European

Stability

Mechanism(Capolongo

et

al.,

2023)

as

well

as

the

European

Commission

in

its

Spring

2023

forecast

have

shown

that

unitprofits

rose

significantly

in

2022,

leading

to

an

increase

in

the

profit

share.

Unit

profit

increases

have

been2

https://www.ecb.europa.eu/press/inter/date/2023/html/ecb.in230228~c78d1f2ca5.en.html

andhttps://www.ecb.europa.eu/press/inter/date/2023/html/ecb.in230401~ec65174af7.en.htmlINTERNATIONALMONETARYFUND5concentrated

in

sectors

exposed

to

international

commodity

prices

and

demand-supply

mismatches.

Theanalysis

most

closely

related

to

our

own

is

the

work

presented

in

speeches

by

the

Bank

of

England’s

Dhingra(2023)

and

Haskel

(2023)

which

through

somewhat

different

methodologies

decompose

inflation

into

domesticprofits,

wages,

taxes

and

imported

prices

(splitting

out

energy

costs

and

other

imported

prices

in

Dhingra’sapproach).

While

the

results

differ

somewhat

between

both

approaches,

both

caution

against

an

oversimplisticinterpretation

where

an

increase

in

gross

operating

surplus

is

interpreted

as

corporate

profits

being

the

largestdriverofinflation.

Haskelfindsalargerrolefortermsoftradeforeuroarea

inflationthanintheUKandUS,withmagnitudes

broadly

comparable

to

our

own

work

for

the

euro

area.

On

the

implications

for

profitability

andwhether

a

positive

markup

shock

has

been

a

causal

driver

of

inflation,

work

by

the

IMF

in

the

October

2022

WorldEconomic

Outlook,

does

not

find

a

broad-based

increase

markup

for

advanced

economies

in

2021.

At

the

countrylevel,

in

addition

to

Colonna

et

al.

(2023),

Glover

et

al

(2023a)

find

that

markups

in

2021

increased

3.4percentin

the

US,

contributing

significantly

to

the

increase

in

inflation.

In

a

follow-up

piece,

Glover

et

al.

(2023b)

showthat

the

contribution

of

profits

to

inflation

eased

in

the

US

in

2022,

and

that

the

pattern

has

been

in

line

withpreviouseconomicrecoveries.Werning

and

Lorenzoni

(2023)

present

a

conceptual

framework

which

can

be

used

to

think

about

inflationas

a

manifestation

of

conflict–

disagreement

about

relative

prices

–

between

economic

actors.

In

thecontextofa

largeimportpriceshockastherootcause

ofaninitialincreaseinprices,

forexample,

thiscan

leadto

a

generalized

increase

in

inflation

as

agents

sequentially

(due

to

nominal

rigidities)

adjust

prices

dependingon

their

inflation

expectations.

Blanchard

(1986)

is

an

important

contribution

on

cost

push

inflation,

where

workersattempt

to

maintain

their

purchasing

power

following

an

initial

erosion

leading

to

further

inflation.

This

can

be

auseful

angle

to

interpret

the

consumption

deflator

decomposition

we

present.

It

suggests

that

in

line

with

historicalevidence,

an

acceleration

in

labor

costs

is

likely

ahead.

From

a

more

general

perspective,

our

paper

is

looselylinked

to

the

strand

of

literature

which

analyzes

profitability

and

market

power

using

firm-level

data

(e.g.,

DeLoeckeretal(2020),Davisetal(2022))butwefocusonnationalaccountdata.Illustrative

simulations

show

that

a

compression

in

the

profit

share

to

historic

norms

will

likely

benecessaryto

achievethedisinflationaryprocess

underplausiblewagegrowthassumptions.Westartbyestimating

that

the

terms

of

trade

contribute

negatively

toinflation

in

the

euro

areaover

the

next

two

years

–

onthe

order

of

one

percentage

point

in

2023

based

on

the

assumptions

underlying

the

April

2023

IMF

WorldEconomic

Outlook.

We

also

assume

that

there

will

be

no

contribution

of

net

taxes

to

inflation

and

that

laborproductivity

will

remain

broadly

flat

in

the

next

couple

of

years.

Under

these

assumptions

we

are

able

to

mapinflation

outcomes

in

the

profit

share-nominal

wage

growth

space

using

our

consumption

deflator

decomposition.This

exercise

shows

that

average

nominal

wage

growth

of

around

4.5percent

over

2023-24

is

consistent

withthe

inflation

projections

in

the

April

2023

World

Economic

Outlook

for

the

euro

area

–

which

show

inflationconverging

to

target

in

early/mid

2025

–

if

profit

shares

return

to

the

average

level

of

2015-19

by

end-2024

andlabor

productivity

remains

broadly

unchanged.

Should

wages

increase

more

significantly

–

for

example,

in

astaticsensewagegrowthofaround5.5

percentwouldensurethatrealwagesreturntotheirpre-pandemiclevelbyend-2024–inflationwouldbenotablyhigherunlesstheprofitsharecompresses

tothelowestlevelsincethemid-1990s.

It

is

then

incumbent

on

policy

makers

to

anchor

expectations

and

support

coordination

amongeconomic

actors

on

a

low

inflation

equilibrium

such

that

the

recovery

in

real

wages

occurs

at

a

measured

paceandfirmsacceptacompressionin

theprofitshare.Thepaperproceedsasfollows.First,itlaysoutthestandardGDPdeflatordecompositionwhichhasreceivedmuchattentionoverrecentmonths.Itcomparesthecontributionofunitprofits,unitlaborcosts,andunittaxestodayintheeuroareawithhistoricalevidencefromthe1970soilpriceshocksaswellaswithothermajoreconomies.Second,theanalysismovesclosertounderstandingthedynamicsofHICPbyproposingadecompositionoftheconsumptiondeflator(whichlikeHICPbutunlikeGDPincludesimportsbutexcludesINTERNATIONALMONETARYFUND6exports).Third,wediscusswhattheresultsimplyforprofitability.Fourth,weanalyzeimplicationsfortheinflationoutlook.Thefinalsectionconcludes.2.DecomposingtheGDP

DeflatorInthissection,weexploitthatGDPfromtheincomesidecanbewrittenasthesumoflaborcompensation,grossoperatingsurplus,andnettaxes.

ItiswellknownthatGDPfromtheincomesidecanbewrittenas퐺퐷푃

=

퐺푉퐴+푁푒푡

푇푎푥푒푠

=

푃푟표푓푖푡푠

+퐶표푚푝푒푛푠푎푡푖표푛

표푓

퐸푚푝푙표푦푒푒푠

+푁푒푡

푇푎푥푒푠(2.1)FromthisitfollowsthattheGDPdeflator(nominalGDPdividedbyrealGDP)

canbeexpressedasthesumofunitlaborcosts,unitprofitsandunitnettaxes.퐺퐷푃=

퐺퐷푃

퐷푒푓푙푎푡표푟

=

푈푛푖푡

푃푟표푓푖푡푠

+푈푛푖푡

퐿푎푏표푟

퐶표푠푡

+푈푛푖푡

푇푎푥푒푠(2.2)퐺퐷푃푅Whilethisaccountingidentifydoesnotallowforanycausalinterpretation,itshowshow(changesin)theGDPdeflatorisreflectedinprofitsperunitofrealGDP(unitprofits),

laborcompensationperunitofrealGDP(unitlaborcost),andtaxeslesssubsidiesper

unitofGDP(unittaxes).ToexploittheGDPdeflator

decompositionidentity,werelyonnationalaccountsdata.

Thenationalaccountsreportprofitsasgrossoperatingsurplusandmixedincome.Operatingsurplusmeasuresthesurplusordeficitaccruingfromproductionbynonfinancialandfinancialcorporations,government,households,andnonprofitinstitutionsservinghouseholds.Mixedincomeisthesurplusordeficitaccruingfromproductionbyunincorporatedenterprisesownedbyhouseholds.Grossoperatingsurplusdiffersfromprofitsshownincompanyaccountsforseveralreasons.Onlyasubsetoftotalcostsaresubtractedfromgrossoutputtocalculatethegrossoperatingsurplus.Essentiallyitisgrossoutputlessthecostofintermediategoodsandservicestogivegrossvalueadded,andlesscompensationofemployeesandtaxesandsubsidiesonproductionandimports.Itisgrossbecauseitmakesnoallowanceforconsumptionoffixedcapital(CFC).Foreaseofnotation,wewillrefertogrossoperatingsurplus

andmixedincomeasnominalprofitsthroughoutthispaper.Profitsperunitofoutputdivergedsharplyfromtheirpre-pandemictrendinrecentquartersandwerethemaincounterpartstotheincreaseintheGDPdeflatorin2022(Figure1).

Between2000and2019,unitprofitscontributedslightlylesstotheGDPdeflatorthanunitlaborcosts,withaminorrolefor

increasingtaxes.2020and2021sawhighvolatilityincomponents,inpartduetothetemporarypandemictaxcuts,evenastheGDPdeflatorincreasedbyasteady3percentinbothyears.In2022,theGDPdeflatoracceleratedsharply,withbothunitlaborcostsandunitprofitsrisingsignificantlyaboveaveragesinrecentyears.Unitprofitscontributedthelargestshareoftheincrease.Thelatestavailabledata

atthetimeofwritingwasQ12023,showingafurtherincreaseinboththecontributionofunit

profitsandunitlaborcostsrelativetothe2022average.INTERNATIONALMONETARYFUND7Figure1.EuroArea:DecompositionofChangeintheGDPDeflatorUnitprofitsincreasedinagriculture,construction,miningandutilities,manufacturingandcontact-intensiveservices.Theminingandutilitiessectorsawthelargestincrease,whilesomesectorssuchasprofessionalsandpublicadministrationremainedbelowpre-COVIDlevels(Figure2).LookingintermsofcontributionstototalGDPdeflatorinflationsince2022,trade,travel,accommodationandfood—withasignificantincreaseinunitprofitandasizableshareintotalgrossvalueadded—sawthelargestincreaseintheirshare.Similarchangealsoappliestominingandutilities,whopreviously

contributedanegligiblesharetoGDPdeflatorinflation,now

wasresponsiblefortwotenthsoftheaverageinflationbetween2022Q1and2023Q1.Onthecontrary,manufacturing,whichusedtocontributeaquartertotheGDPdeflatorinflationinthelastdecade,onlyaccountedforaroundonetenthoftheinflation.Figure2.EuroArea:SectoralProfitINTERNATIONALMONETARYFUND8TheincreaseintheGDPdeflatorfollowingthecurrentenergyshockhasbeencomparableinmagnitudetothefirstoilpriceshockofthe1970s,butthecompositionhasbeendifferent.Followingthefirstoilpriceshockin1973

–spurredbytheOrganizationofthePetroleumExportingCountriesoilembargo–thegrowthintheGDPdeflatorrosemarkedly,drivenalmostexclusivelybyacceleratinglaborcostswhileprofitsfell(Figure

3,leftpanel).

3

Laborcostsalsoplayedmoreofaroleduringthesecondoilpriceshockin1979

–triggeredEuroArea:GDPDeflator(Percent,

year-on-year)1614121086420-2Unit

TaxUnit

ProfitUnit

Labor

CostTotal-4bythetemporaryreductioninoilsupplyamidtheIranianrevolution–althoughtheoverallincreaseintheGDPdeflatorgrowthwassmallerinthatepisode(Figure

3,middlepanel).ThemagnitudeofthecurrentincreaseintheGDPdeflatorinflationrateiscomparabletothefirstoilpriceshock(Figure

3,rightpanel),albeitfromamuchlowerstartinglevelofinflation(textchart).Profitshaveplayedalargerrolethanlaborcostssofarinthecurrentepisode(Figure3,rightpanel).However,duringallthreeepisodestherelativecontributionfromlaborcostsgrewovertime.Thisisconsistentwiththenotionthatfirmscanpassonhigherinputscostmorepromptly,whileittakesalongertimeforwagestoadjust(the

wageadjustmentswerelargeafterthefirstoilpriceshockoncetheykickerinafteraboutthree-fourquarters,likelyduetoexplicitindexationarrangementsandlessanchoredexpectations).Theresultinginitiallylowerrealwageswouldincentivizemorehiring,eventuallyalsopushingupwages.Thus,anincreaseintherelativecontributionfromwagesduring2023wouldbeconsistentwiththehistoricalevidenceandtheory.Figure3.EuroArea:ComparisonofGDPDeflatorIncreasetoPreviousEnergyPriceShocksSources:OECD;Eurostat;theAreawideDatabase;IMFstaffcalculations.RelativetotheUSandCanada,theincreaseintheGDPdeflatorintheeuroareahasrecentlybeenmoretiltedtowardsprofits.InCanadaandtheUnitedStates,theaccelerationintheGDPdeflatorstartedearlierandwasmorebiasedtowardshigherlaborcosts(Figure

4).Onayear-on-yearbasistheGDPdeflatorhasdeceleratedinbothcountriesinthesecondhalfof2022.IntheeuroareaandtheUK,ontheotherhand,theGDPdeflatoracceleratedpreciselyinthesecondhalfof2022,withalargeroleplayedbyprofits.Thiscouldpartlyreflectthedifferentnatureofshocks,withtheshockinNorthAmericabeingrelativelymore

drivenbydemand(andapositivetermsoftradeshockin2022)whiletheadverseenergyshockplayedanimportantroleintheeuroareaandUK.TakingalongerperspectivetounderstandthecumulativeGDPdeflatorchangeover3

Nominal(unit)profitsincreasedsharplyintheyearsjustbeforetheoilpriceshock(1971-1973).Theoutsizedroleoflaborcosts'followingtheoilshockmightthushavepartlybeenareactiontothisincrease.INTERNATIONALMONETARYFUND9boththepandemicandenergyshockperiod(Q42019toQ42022),showsthatprofitsplayedthelargestroleintheEuroAreainrelativeterms(Figure4).4Figure4.EuroArea:ComparisonofEuroAreaGDPDeflatorDecompositionwithOtherMajorEconomiesUnitedStates:GDPDeflator(Percent,

year-on-year)151050-5-10-15UnitprofitsUnitlaborcostUnittaxTotalSources:OECD;Eurostat;theAreawideDatabase;IMFstaffcalculations.Notes:FortheUnitedStates,thebarsdonotsumuptothefulldeflatorgrowthineachquarter,asprofits,nettaxes,and

laborcostheresumtogrossdomestic

income.4

IMF(2022)hadaboxwithasimilarexerciseoncontributionstocumulativeGDPdeflatorchanges,however,the

periodcoveredwas2019q4-2021q4.INTERNATIONALMONETARYFUND103.DecomposingtheConsumptionDeflatorConceptually,theGDPdeflatordoesnotprovideafullpictureoftherecentepisodeofsurging

consumerpriceinflationsinceitincludesexportpricesandexcludesimportprices.Onaverage,differentmeasuresofpricechangesintheeconomysuchastheGDPdeflator,thetotalconsumptiondeflatorandHICP/CPIinflationtendtoco-moveclosely(textchart).However,attimesoflargeterms-of-tradeswingstheycandecouple,andthishasbeenthecaseovertherecentyears.ThelinkbetweentheconsumptiondeflatorandHICPdevelopmentsistighter,sincetheybothincludeimportpricesofconsumergoodsandunliketheGDPdeflatorexcludeexportprices.Usingasetofsimplifyingassumptions,consumerpriceinflationcan

bedecomposedintocontributionsfrom

domesticprofits,labor,foreign,and

nettaxes.AssumethattheproductionfunctiontoproducetotalconsumptionisCobb-Douglas,withweight휆

forvalueaddedfromcountry푗

sector푠

(∑푗,푠

휆푗푠=푗푠1).Thecostminimizationproblemforproduceris:min

∑

푝

푞푞푠.

푡.

∏(푞

)휆푗푠

=

1푗푠

푗푠푗푠푗푠푗,푠푗,푠Theresultingproducercostforoneunitoftotalconsumptionisequalto휆푗푠푝∏

(

푗푠)휆푗푠푗,푠andtheshareofthecostofgoodsfromcountry푗

sector푠

inthetotalcostamountsto휆

.Assumingthatretailer푗푠takesaconstantmarkup(correspondingtoaconstantelasticityofsubstitutionbetweengoodsinconsumer’sutilityfunction),thenthedynamicsofconsumptiondeflatorinflationmimicthoseofproducerpricescombinedwithasalestax휏.휆푗푠푝푝

=

(1+휏)

∏

(

푗푠)휆푗푠푗,푠Consumptiondeflatorinflationcanbewrittenas:ln

푝

−ln

푝̃

=

∑푗,푠

휆

(ln

푝

−ln

푝̃

)+ln(1+휏)−ln(1+휏̃)(3.1)푗푠푗푠푗푠̃where

denotesvalueofagivenvariableinthelastperiod.Essentially,(ln

푝푗푠

−ln

푝̃

)

canbecalculatedfrom푗푠theGVAdeflatorinflationofcountry푗

sector푠,whichcanbedecomposedintolaborcompensation(퐿)andprofit(퐹)usingrealGVA(푦)andgroupedintodomesticprofit,domesticla