歐洲央行-喘息沖擊向通貨膨脹的傳遞（英）

EUROPEANCENTRALBANK

EUROSYSTEM

WorkingPaperSeries

LuciaLópez,FlorensOdendahl,SusanaPárraga,EdgarSilgado-Gómez

Thepass-throughtoinflationofgaspriceshocks

No2968

Disclaimer:ThispapershouldnotbereportedasrepresentingtheviewsoftheEuropeanCentralBank(ECB).TheviewsexpressedarethoseoftheauthorsanddonotnecessarilyreflectthoseoftheECB.

ECBWorkingPaperSeriesNo29681

Abstract

ThispaperusesaBayesianStructuralVectorAutoregressive(BSVAR)frameworkto

estimatethepass-throughofunexpectedgaspricesupplyshocksonHICPinflationintheeuroareaanditsfourlargesteconomies.Incomparisontooilpriceshocks,gaspriceshockshaveapproximatelyone-thirdsmallerpass-throughtoheadlineinflation.Country-specificresultsindicategaspriceincreasesmattermoreforGerman,SpanishandItalianinflationthanforFrenchinflation,hingingontherelianceonenergycommoditiesinconsumption,production,anddifferentelectricitypricesregulation.Consistentwithgasbecomingaprominentenergycommodityintheeuroarea,includingtime-variationthroughatime-varyingparameterBVARdemonstratesasubstantiallylargerimpactofgaspriceshocksonHICPinflationinrecentyears.TheempiricalestimatesarethenrationalizedusingaNewKeynesianDynamic

StochasticGeneralEquilibrium(NK-DSGE)modelaugmentedwithenergy.Inthemodel,theelasticityofsubstitutionbetweengasandnon-energyinputsplaysacriticalroleinexplainingtheinflationaryeffectsofgasshocks.Adecompositionoftherecentinflationdynamicsintothemodelstructuralshocksrevealsalargercontributionofgasshockscomparedtooilshocks.

JEL:C11,C32,E31,Q41,

Keywords:Naturalgasandoilshocks;Inflation;BayesianVARs;NewKeynesianDSGE

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Non-technicalsummary

Therecentinflationsurgeintheeuroareawassignificantlyinfluencedbyenergyprices,particularlygasfollowingRussia’sinvasionofUkraineinFebruary2022.Whilepaststudieshavelargelyfocusedontheimpactofoilpricesoninflation,thisresearchshinesalightontheroleofgasprices.

ThroughvariousempiricalmethodsbasedonBayesiantechniques,thispaperestimates

thepass-throughofinternationalgaspricestoconsumerpricesintheeuroarea,includingthelargesteconomiesintheregion:Germany,France,Italy,andSpain.ThesampleperiodgoesfromJanuary1997toDecember2022.Wealsodevelopatheoreticalmodeltogaindeeperinsightsintohowdisturbancestogaspricesinfluenceconsumerpricesdifferentiatingbetweentheirdirectandindirecteffects.Directeffectsincludebasicallyincreasedspendingonhomeheating,whileindirecteffectsinvolvegasusageintheproductionprocesses.

Overall,thepaperenhancesourunderstandingofthecomplexrelationshipbetweengaspricesandinflation,offeringusefulinsightsforpolicymakersandresearchersalike.Findingsindicatethatwhileunexpectedincreasesingaspricesdocontributesignificantlytoinflation,theirimpactissomewhatlesspronouncedcomparedtooilpriceshocks.Thetheoreticalanalysisrevealsthatgasplaysacriticalroleasacomplementaryinputinproduction.Thatis,gasismoreimportantintheproductionsidethanintheconsumptionbasketsothatindirecteffectsdominate.Wealsoprovideanarrativeforthecontributionofseveralstructuralshockstotherecentinflationdynamicsintheeuroarea.Wefindthatthesewereexplainedbyacombinationofgaspriceshocks,withamuchlargercontributionrelativetooilshocks,followedbywagemark-upshocks,demandandproductivityshocks.

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1Introduction

Theenergycomponenthasbeenakeydriveroftherecentinflationsurgeintheeuroarea.Precisely,gastookthecenterstageofenergycommoditymarketsafterRussia’sinvasionofUkraineinFebruary2022triggeredunprecedentedincreasesingasprices.Yet,theinflationaryeffectsofgaspriceshocksremainrelativelyunknownbecausetheliteraturehasfocusedonoilpriceshocks(see,forexample,

BlanchardandGalí,

2007b;

ClarkandTerry,

2010;

Kilianand

Lewis,

2011;

BaumeisterandPeersman,

2013;

Gaoetal.,

2014;

Choietal.,

2018;

K?nzig,

2021;

Caietal.,

2022)ortherelationbetweenoilandgasprices(see,forexample,

Brigida,

2014;

Zhang

andJi,

2018;

SzafranekandRubaszek,

2023

).Thispaperinsteadprovidesacomprehensivestudyofthepass-throughtoconsumerpricesinflationofgaspriceshocks.OurcontributiontotheliteratureistwofoldinthatwemarshalseveralpiecesofempiricalevidencetogetherwithatheoreticalanalysisthatrationalisesourestimatesembeddinggasinastandardNewKeynesianDynamicStochasticGeneralEquilibriummodel(NK-DSGE).

First,webuildaStructuralBayesianVectorAutoregressive(SBVAR)frameworktoestimatethepass-throughofinternationalwholesalegaspricesintotheHarmonisedIndexofConsumerPrices(HICP)inflationintheeuroareaandthefourlargesteconomiesintheregion:Germany,France,ItalyandSpain.ThedatasetofmonthlyobservationsspansfromJanuary1997toDecember2022.Becausenotallcommodityshocksareequal(

Kilian,

2008

),wefocusonunexpectedsupply-sidegaspriceshocksandexploitthenon-linearitiesduetohistoricallyhighgaspricesinthelatestpartofthesampletocomplementtheidentificationofthestructuralBVARwiththenarrativesignrestrictionsmethodologyintroducedby

Antolín-DíazandRubio-Ramírez

(2018)

.MotivatedbythechangesintheinstitutionalsettingovertimebecauseofthedevelopmentoftheEuropeangasmarkets,wealsoestimateatime-varyingparameterBayesianVARwithstochasticvolatilitytoformallyassesthepotentialtimevariationoftheinflationaryeffectsofgassupplyshocks.

Wealsocontributetounderstandingbetterthedynamicsofgaspriceshocksbreakingdowntheestimatedtotalpass-throughintodirectandindirecteffects.Intermsofconsumerprices,Directeffectsstemfromhigherconsumerspendingonhomeheating.Indirecteffectscapturethedownstreamimpactofusinggasasaninputintheproductionprocesses.Theimportanceofthelatterdependsonwhethergasisusedintensivelyduringtheproductionprocessesorwhethergas

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pricesinfluencethepricingofotherinputssuchaselectricityorheatproduction(

Pacceetal.,

2021

).Moreover,theintensityofthetotalpass-throughvariesdependingontheregulationsinplace,thetypesofcontractsusedineachcountry’sretailenergymarketsortheprofitmargindevelopmentsinthefaceofrisingenergyinputcosts.

Wefindthatunexpectedgaspriceshockshavesignificantinflationaryeffects.Agaspriceincreaseof10percentincreasesleadstoagradualpass-throughonheadlineinflationthatpeaksatcloseto0.1aftertwoyears.Comparedtooilpriceshocks,gaspriceshockshaveaboutonethirdsmallerpass-throughtoheadlineinflation.Theresultssuggestthatthetransmissionofunexpectedgaspricesupplyshocksgainedsignificanceonlywhenthepricingofgasmeaningfullydecoupledfromoilprices(apracticeknownasoilindexation).Country-levelestimatesindicatethateconomieswiththehighestinflationaryeffectstendtobemoreintensive

usersofenergycommoditiesintheirproductionstructuresorelectricitygeneration.OurresultssuggestunexpectedgaspricechangesmattermoreforGerman,SpanishandItalianthanforFrenchinflation.

Second,wedevelopaNewKeynesiandynamicstochasticgeneralequilibrium(NK-DSGE)modelaugmentedwithenergy,whichisacomplementaryinputforintermediategoodsfirmsandacomplementarygoodforhouseholds.Inthebaselineframework,theenergycomponentisonlygas,however,intheextendedmodeltheenergybundleiscomposedbygasandoil,whichareassumedtobe(imperfect)substitutes.Inthisway,andsimilartotheempiricalsection,wealsoaccountforoilfluctuationswhenidentifyingthegasshock.

OurbaselineNK-DSGEmodelperformswellmatchingtheIRFsoftheSBVARanalysis.Weobtainthesamequalitativeresultswithsomequantitativedifferences,althoughthemodel-basedIRFsliewellwithintheempiricalcredibilityintervals.Wealsofindakeyroleoftheelasticityofsubstitutionbetweengasandnon-energyinputsintransmittingtheeffectsofgasshocks.Thatis,gasismoreimportantintheproductionsidethanintheconsumptionbasketsothatindirecteffectsdominate.Thelatterresultholdsonlywithsufficientnominal(wage)rigidities.Intuitively,whenwagesareflexible,thesecanadjusttofullyabsorbdisturbancesingasprices.Bycontrast,rigidwagescannotdeclinesufficientlyintheaftermathofashocktocompensatethelargeincreaseinmarginalcosts,leadingtoamorepronouncedpass-throughtoinflation.

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Wealsoprovideanarrativefortherecentcontributionofseveralstructuralshockstoinflationintheeuroarea.Forthisexercise,weemploytheextendedNK-DSGEmodeltobetteraccountforoilshocks.Wefindthattherecentinflationdynamicsareexplainedbyacombinationofgasshocks,withamuchlargercontributionrelativetooilshocks,followedbywagemark-upshocks,demandshocksandproductivityshocks.

Arecentbutstillscantliteratureisbuildingupevidenceaboutthepass-throughofgaspriceshocksinEurope.

Lanetal.

(2022)estimatethedirectpass-throughofinternationalgas

pricesonGermanHICPgasinflation.

Günteretal.

(2024)applytheoilmarketmodelpioneered

by

Kilian

(2008)totheGermangasmarket

.BothpapersthusfocusonasingleEuropeaneconomy.

Casolietal.

(2022)extendtheoilmarketmodelwithadditionalblocksforthegas

marketandinflationinEurope,butthecontemporaneousrelationshipbetweengasandoilpricesintheirmodelmightcastdoubtontheestimatesofthepass-throughofgasprices.

Adolfsenetal.

(2024)useestimatedstructuralgasshocksfromagasmarketmodeltoanalysethepass-through

toeuroareainflationofdemand-driven,supply-drivenandexpectations-drivenstructuralgasshocksusinglocalprojections.Inastepforward,theyalsocontrolforcrudeoilpricesintheestimationofthepass-through.Like

AlessandriandGazzani

(2023),werelyonnarrativemethods

toachieveidentificationoftheeffectsofunexpectedgassupplyshocksonEuropeaninflationinacomplexsampleincludingobservationspost-Covid.However,weextendtheanalysisalongseveraldimensions.First,welookintodifferentHICPitemsandextendthesampletothefourlargestEuropeaneconomies.Second,weconductanevaluationofthepotentialtime-varyingpass-throughofunexpectedgaspriceincreases.Third,andmostimportantly,werationaliseourempiricalfindingswithatheoreticalmodel.Amongthemostcloselyrelatedtheoreticalwork,

GagliardoneandGertler

(2023)developaNewKeynesianmodelaimedataccountingforthe

recentsuddenandpersistentriseininflationintheUSeconomy.Theirmodelplacesparticularemphasisontheroleofoilshocks.Instead,weaccountforbothoilandnaturalgasfluctuationsintheeuroarea.

Theremainingofthepaperisorganisedasfollows.Section

2

summarisesthedevelopmentoftheEuropeangasmarketandthenarrativeepisodesusedtocomplementtheidentificationofthestructuralBVARmodeloutlinedinSection

3.

Section

4

presentstheestimatesofthepass-throughtoHICPinflationofgaspriceshocks,whileSection

5

studiesthetimevariationin

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Figure1:TimelineoftheEuropeanGasMarket

thepass-throughandcomparesitwiththatofoil.Section

6

containsaNK-DSGEmodelwithenergyinputstorationalizetheempiricalresults.Section

7

offersconcludingremarks.

2InstitutionalFramework

2.1ABriefHistoryoftheEuropeanGasMarket

ThecreationoftheEuropeangasmarkettookoffinthelate1990s.Figure

1

presentsatimelinewithkeydatesinitsdevelopment.EuropeanDirectivesin1998and2003setthebenchmarktoexpandtheinternalEUgasmarket.TheDirectivesaimedatbreakingverticalintegrationinthegasindustryandintroducingcompetition.AthirdGasEuropeanDirectivein2009promotedtheintegrationoftheEuropeangasmarketandintroducedincentivesforlaunchingtradinghubs

(Bastianinetal.,

2019

).

IntheearlystagesoftheEuropeangasmarket,opennessandcompetitivenessweredifficultbecauselong-termcontractslinkedtooilpricespredominated(asystemalsoknownasoilindexation).Oilindexationprovidedthenecessarystabilitytodevelopgasinfrastructures,butpricesdidnotnecessarilyreflectsupplyanddemandfundamentalsofthegasmarket.Overthelasttwodecades,gaspriceshavemovedawayfromoilindexationtospotpricing.InternationalEnergyAgencydatashowsthatoil-indexedcontractswentfromaccountingfor93%oftheEuropeangasimportspricingmechanismin2005to25%in2019.1Thistransitiontospotpricingacceleratedafterthe2008financialcrisisamidloosemarketconditions,theendingofcontracts1SeeIEA,EvolutionofEurope’sgasimportpricingmechanisms:fromoil-tohub-indexation,

https://www.iea.or

g/data-and-statistics/charts/evolution-of-europe-s-gas-import-pricing-mechanisms-from-oil-to-hub-indexation.

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100%90%80%70%60%50%40%30%20%10%0%

199720002003200620092012201520182021RussiaNorwayAlgeriaQatarNigeriaOther

Figure2:EuroAreaGasImportsbyOrigin.1997-2021

ortherenegotiationoftheirtermstoincludespotpricingterms,aswellasanewroundofEUenergymarketlegislationtoimprovetheoperationoftheinternalenergymarket.2

Overtime,liberalisationpromoteddeepandliquidwholesalegastradinghubssuchastheTitleTransferFacility(TTF)gasmarket,operativesince2004.TheTTFhasbecomethemostliquidgasmarketinEurope,overcomingtradedvolumesintheUKNationalBalancePoint(NBP)marketaroundthemid-2010s(see,forexample,

EuropeanComission,

2018)

.Currently,theTTFconstitutesabenchmarkforgaspricesinEuropeandworldwide,togetherwiththeUSHenryHub.

2.2NarrativeEpisodesofSupply-DrivenGasPriceDisruptions

AnotheruniquecharacteristicoftheEuropeangasmarketisitsdependencyonimportsfromRussia.Figure

2

showsthatRussiahasbeenthesolelargestproviderofgastotheeuroarea.Moreover,UkrainehasbeenamajorcorridorforthetransitofRussiangastoEurope.TobypassUkraine’squasi-monopolyinthegastransittoEurope,RussiamadeseveralattemptsofconstructingnewpipelinestraversingeithertothesouthortothenorthofUkraine.Theseeffortsweremarkedbynumerousgasdisputes,themostremarkableforEuropeangasflowsbeingthe2005–2006and2009gascrises,whilein2011theyledtotheopeningofthegaspipelineNordStream.Conversely,followingtheRussianinvasionofUkrainein2022gasflowsfromRussiaplummeted.

2SeeInternationalGasUnionWholesalePriceReportsfordifferentyearsat

.

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%y-o-y

PercentagePoints

200

10

9

150

8

100

7

6

50

5

0

4

3

-50

2

-100

1

-150

0

GasPrices

OilPrices

HighGasPrices(RHS)

HighOilPrices(RHS)

1stGasDispute

2ndGasDispute

Nordstream

RussianinvasionofUkraine

20002005201020152020

Figure3:EpisodesofExogenousGasSupplyShocks

Figure

3

highlightstheepisodesofgaspriceshocksin2005-2006(“1stGasDispute”),in2009(“2ndGasDispute”),in2011(“Nordstream")andin2022(“RussianInvasionofUkraine”).Thefigureshowshighcommoditypricescalculatedfollowing

Hamilton

(2003):

πt=max(1)

,withptthecommoditypriceinmonthtandyrtheaveragepriceduringthemostrecent3

years.Figure

3

alsoshowsthatoilpriceincreasesusedtoleadgaspriceincreasesuntilthe2010s.Next,wegoovereachepisodeinturn.

Stern

(2006)and

Piranietal.

(2009)documentthatthedeteriorationinRussian-Ukrainian

relationsduring2005ledtoashort-livedbutsignificantdisputeduring1-3January2006(1stgasdispute).3TheRussiandemandstoupdatethelong-termcontractswithUkrainetochargehigherpriceswerecontinuouslyrejectedbyUkraine,preferringinsteadanextendedtransitionperiodbeforepayinghigherprices.Asaresult,RussiacutoffgassuppliestoUkraineand,inturn,UkrainedivertedvolumesdestinedtotherestofEurope.ByJanuary2,Hungaryreportedtohavelostupto40%ofitsRussiansupplies;Austrian,SlovakianandRomaniasuppliesweresaidtobedownbyonethird,France25-30%andPolandby14%.Italyreportedhavinglostaround25%ofdeliveriesduringJanuary1-3.Germandeliverieswerealsoaffectedbutnofurtherdetailsareknown.On4January2006,apreliminaryagreementwasachieved,andgasflowswere

restored.Atthesametime,relativelymildweatherandthehaltinproductionofgas-intensive

3Seealso“Russiavowstoendgasshortage”,January2,2006,BBCNewsWebsite.

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industrialproducersduringtheNewYearholidayperiodsidewiththeevidencethatthisepisodeofhighgaspriceswassupply-sidedriven.Therefore,weassumethatthe1stRussia-Ukrainegasdisputeconstitutesanegativesupplygasshock.

In2009tookplaceanothersignificantgasdisputebetweenRussiaandUkraine(2ndgasdispute).TheaccumulationandfailuretocleardebtsbyUkraineowedtoRussialedtoanewcrisisduring1-22January2009.ByJanuary6RussiangasdeliveriestoEuropeweredrasticallyreduced,andcutoffonJanuary7.Gaswascutoffcompletelytocountriesinsouth-easternEuropewhichwerefullydependentonRussianimports,andpartiallytoothercountries,for13days.SuppliestoEuropehadneverbeenhaltedbefore,asduringthe2006episodestheshortfallsinsuppliestoEuroperesultednotfromEuropeansuppliesbeinghalted,butfromUkrainebeingcutoffanddivertingaproportionofEuropeanvolumesforitsownuse.On19JanuarytwonewlongtermcontractsforsupplyandtransitbetweenRussiaandUkraineweresignedandgasflowstoEuropewererestoredthefollowingday.Again,weassumethatthe2ndRussia-Ukrainegasdisputeconstitutesanegativesupplygasshock.

In2011,severalnewgasfacilitiesweredeveloped,includingpipelinesfromAlgeriaandRussia(

IEA,

2012

).InNovember2011,theNordStreampipelinewasofficiallyinaugurated.ItsconstructionwaspartofRussia’spoliticallymotivatedstrategytolimittheinfluenceoftransitcountriessuchasUkraine,whileincreasingEurope’senergydependenceonRussia(

SolumWhist,

2008

).TheopeningofNordStreamincreasedgassupplytoEurope,andtherouteranksamongthemostsignificantgascorridorsfromRussia(

McWilliams,

2021

).By2014Russiawasdelivering33bcmofgasviaNordStream,slightlymorethanthe31bcmofgasroutedviaUkraine/Slovakia

(Erbach,

2016

).Therefore,weassumeapositivegassupplyshockinthemonthoftheopeningofNordStream.

Morerecently,Russia’sinvasionofUkraineinFebruary2022resultedinrestrictionstothevolumeofenergyimportsfromRussia,whichgeneratedtensionsintheEuropeanwholesalenaturalgasmarkets.TheconflictputfurtherpressuresonalreadytightEuropeanenergymarkets,asevidencedbydiminishedgasstoragelevelscomparedtohistoricalaveragesandasubstantialdeclineinRussianpipelinegasimports(see,forexample,

IEA,

2022

).Ultimately,RussiaunilaterallydecidedtocutdeliveriesthroughitsmainpipelinetoEurope(NordStream),withanastonishing80%reductioninEuropeanimportsviathemajorRussianrouteincluding

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Figure4:Europe:Russiangasimportsandprices

alsotransitthroughUkraineandBelarus.Thegasshortagesdrovegaspricestorecordhighs,asillustratedinFigure

4.

Again,weassumethisepisodeconstitutesanegativegassupplyshock.

Finally,wehavediscardeddisruptionsintheEuropeangaspricethatcoincidedorseemedtobeledwithdevelopmentsinothercommoditymarkets,suchascoaloroil.Forinstance,risingoilandcoalpricesprovidedsupporttoEuropeanhubpricesinSeptember2018.Wealsodiscardedepisodeswithasizeablecontributionofdemandfactorsorwhenitwasnotpossibletoisolatewhetherdemandorsupplyfactorsdominated.Forexample,earlyin2018acoldwaveinUKandIrelandtriggeredanoutstandingincreaseinseasonaldemand.WediscardedthisepisodeevenifthesevereweatherconditionshadconsequencesoncertainkeyelementsofsupplyinfrastructureinMarch2018.WealsodiscardedthegaspricedisputesaroundtheRussianinvasionofCrimeain2014,astheydidaffectthegassupplytoUkrainebutdidnotaffectthetransitflowofgastotherestofEurope.

3TheBaselineEmpiricalFramework

ConsiderthestandardVectorAutoregressive(VAR)model:

whereytrepresentsthen×1vectorofendogenousvariables,cistheintercept,Ajdenotesthen×nmatricesoflaggedcoefficientsandXtcontainsexogenouscontrolvariables.Theinnovationsut=B?tcorrespondtoalinearcombinationofthestructuralshocks?tundertheassumption

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ofinvertibilityA1=B.Weuse12lagsaccordingtotheAkaikeinformationcriteriaandtheconservativeupperboundsetby

KilianandLütkepohl

(2017)

.TheVARmodelisestimatedusingBayesianmethodsadoptinganon-informativeconjugateuniform-normal-inverseWishartprior(

Antolín-DíazandRubio-Ramírez,

2018

).

Weuseacombinationofsignandnarrativerestrictionstoidentifyeconomicallymeaningfulimpulseresponses.Weimposerestrictionsonthesignthatthedifferentshockshaveonimpactonthevariables.Table

1

illustratesthatanunexpectedgassupplyshockincreasesthegasprice,decreasesactivityandincreasesinflation.Weseparatelyidentifyademandshock,forwhichgasprices,activityandgeneralinflationincrease.Moreover,understandingtheimplicationsofhighgaspricesforinflationduringperiodsliketherecentenergycrisisishighlyrelevantbutchallengesidentification.Thus,wecomplementthetraditionalsignrestrictionswithnarrativeepisodesofexogenousgassupplydisruptions.Wefollowthemethodof“narrativesignrestrictions”developedin

Antolín-DíazandRubio-Ramírez

(2018)

.4Basedonourinstitutionalknowledge(seeagainSection

2

),Table

1

summarisesagainourselectionofepisodeswhenunexpectedandsignificantgassupplychangesoccurred.Themethoddoesnotrequireacompletenarrative,butthekeyidentifyingassumptionthatgassupplyshocksareasignificantcontributortogaspricedynamicsduringthenarrativeepisodes.Weconsiderfourepisodes:i)GasDisputesofJanuary2006;ii)

GasDisputesofJanuary2009;iii)openingofNordStreaminNovember2001;andiv)RussianinvasionofUkraineinMarch2022.Weassumethatthe2006and2009episodesconstituteanegativegassupplyshockandthe2011episodeapositivegassupplyshock;inthe2022episode,thegassupplyshockconstitutesthemaincontributortoexplainingthegaspricedynamicsatthetime.Giventhelackofpublicdataduringtheearliestepisodestocharacterisewellthegasmarketdynamicsatthetime,ourbaselineistousenarrativesignrestrictionsbasedonthe2022episode,whileleavingtotherobustnesschecksexploringalternativerestrictionsbasedontheotherepisodes.

Thedatasetincludesmonthlyobservationsfrom1997m1to2022m12fortheeuroarea,and,respectively,thefourlargesteconomiesintheregion:France(FR),Germany(DE),Italy(IT)andSpain(ES).ytcontainsgaspricesandconsumerpricesinflation,aswellascontrols

forthegenerallevelofeconomicactivityandthestanceofmonetarypolicy.Longseriesof

4Followingtherecommendationsof

Antolín-DíazandRubio-Ramírez

(2018)and

Anetal.

(2021)wesetthe

thenumberofdrawsandresamplingweightstohaveapproximately1000posteriordrawsthatuniquelysatisfyboththesignandnarrativerestrictions.

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