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首页 Stock-Watson dynamic OLS (DOLS) and

Stock-Watson dynamic OLS (DOLS) and.pdf

Stock-Watson dynamic OLS (DOLS)…

guanguai
2011-02-14 0人阅读 举报 0 0 暂无简介

简介:本文档为《Stock-Watson dynamic OLS (DOLS) andpdf》,可适用于工程科技领域

ELSEVIEREnergyEconomics()EnergyEconomicsStockWatsondynamicOLS(DOLS)anderrorcorrectionmodellingapproachestoestimatinglongandshortrunelasticitiesinademandfunction:newevidenceandmethodologicalimplicationsfromanapplicationtothedemandforcoalinmainlandChinaRumiMasihd,AbulMMMasihb,*aDepartmentofAppliedEconomics,UniversityofCambridgeCambridgeCBDE,UKbDepartmentofEconomtcsandManagement,UniversityofNewSouthWales,Canberra,ACT,AustraliaAbstractInthispaperrobustelasticityestimatesofcoaldemandforChinaarederivedusingannualdataInsodoing,weillustratetheuseofapowerfulyetpracticallyconvenientandrecentlydevelopedmodellingproceduredevisedbyStockandWatson(knownasDynamicOLS(DOLS)),whoprovideevidence,basedonMonteCarlosimulations,ofthisestimatorbeingsuperiorinsmallsamplescomparedtoanumberofalternativeestimators,aswellasbeingablenotonlytoaccommodatehigherordersofintegrationbutalsotoaccountforpossiblesimultaneitywithinregressorsofapotentialdemandsystemFurthermore,cointegrationanderrorcorrectionmethodsareemployedtoderiveshortrunpriceandincomeelasticitiesEstimatedresultsarequiterobustnotonlyintermsofstatisticalprowessbutalsointermsofeconomicintuitionandindicatethat,overthelongrun,bothpriceandincomeelasticitiesareclosetounityWhileshortrunpriceandincomeelasticitiesareless(inabsolutevalue)thantheirlongruncounterparts,thereseemstobesomedivergenceinshortrunparametersfromasubsampleanalysisOverall,resultsseemtoimplythatforChina,coalconsumptionshouldremainrelativelyconstantasfuturemodernizationstrategiesforeconomicdevelopmentarepursuedInaddition,thestudyhasclearmethodologicalimplicationsforestimatingthelongandshortrunelasticitiesinademandfunctioningeneral,andinawidevarietyoffieldsinfutureappliedresearch*CorrespondingauthorEmail:amasihadfaozau$Cc)ElsevierScienceBVAllrightsreservedPIIS()RMasih,AMMMasihEnergyEconomics()JELclassification:QCKeywords:ChinaCoalenergyconsumptionShortlongrunelasticitiesPriceIncomeDynamicOLSIntroductionTherehavenowbeenseveralstudiesdevotedtotheunderstandingoftherelationshipbetweenmacroeconomicvariablesontheonehandandresourcerelatedvariablesontheother(seeHarvieandHoa,())Somehaveattemptedtostudythemacroeeonomiceffectsarisingfromavarietyofresourcerelatedshocks(examplesincludePindyck()oneffectsofthefirstoilpriceshock,Gregory()fortheAustralianresourceboom,EastwoodandVenables()onreactionfromresourcehikesinopeneconomies)Othershaveconcentratedonthespecificationormodellingapproachofenergydemandinderivingelasticities(seeZilberfarbandAdams()forincomeelasticityestimatesofenergyconsumptionusingcrosscountrydatafordevelopingcountriesDunkerley()onestimatingenergydemandforaselectionofdevelopingcountriesHoa()foramultivariatesimultaneousapproachinmodellingThaienergydemandBentzenandEngsted()inestimatingshortandlongrunDanishenergydemandelasticitiesEngstedandBentzen()onarationalexpectationistapproachtoDanishenergydemand,andBentzen()inanalysisofDanishgasolinedemand)Relatedtothisisawidebodyofliteratureinvestigatingthecausalrelationshipbetweenenergyconsumptionandeconomicgrowth(seeKraftandKraft()ontheseminalstudyfindingevidenceinsupportofunidirectionalcausalityfromincometoenergyfortheUSAkarcaandLong()whocontestedthesefindingsAbosedraandBaghestani()whoreopenedthedebatewithfindingsinsupportofKraft'sandKraft'sinitialstudyStern()whousesanordinaryvectorautoregression(VAR)withvariablesinfirstdifferenceformonUSdata()findingevidenceagainstthehypothesisthatgrossenergyGrangercausesGDP,andMasihandMasih(c)inaninvestigationofbivariatecausalitybetweenenergyconsumptionandeconomicgrowthforsixAsianLDCs)Modellingenergyandeconomicrelatedvariables,however,isoftenassociatedwithproblemsofapracticalnaturewhichhaveseriousconsequencesforinferencemakingbasedontheestimatesFirst,apartfromthestandardproblemsofdeparturesfromclassicalassumptionsoftheregressionframework,reducedformequationstypicallysufferfromendogeneityofregressorsleadingtosimultaneityamongthevariablesinthesystemSecondly,thevariablesusedinsuchstudiesareusuallyveryaggregatedandexhibitnonstationarity(seeNelsonandPlosser()andPerron()onevidenceofnonstationarityinseveralmacroaggregates)butthishasbeenremediedbyapplicationsofcointegrationtechniques(EngleandGranger,)anddevelopmentsinerrorcorrectionmodellingThirdly,thesmallsamplenatureofdatasetsbeingemployedinenergyeconomics(duemainlytoRMasih,AMMMasihEnergyEconomics()availabilityofconsistentdata)begsthequestionoftheadequacyofapplyingstandardcointegrationtechniquesinderivingestimatesofsupposedlylongrunparameters(DeVanyandWalls()isonesuchexamplewhichtestsforbivariatecointegrationbetweenpairsofspotpricesusinghighfrequencydailydata,butonlycoveringasingleyear)Thepurposeofthispaperistoemploytheveryrecentdevelopmentsinmodellinglongrunorcointegratedrelationshipswhichremedy,inpart,someoftheaboveproblems,inanapplicationtoestimatingelasticitiesofpriceandincomeincoaldemandforChinaemployingannualdata()Specifically,weutilizeaproceduredevelopedbyStockandWatson()knownasdynamicOLS(DOLS)whichallowsforvariablesintegratedofalternativeorders(inthissense,ahigherorderofintegration),aswellastacklingtheproblemofsimultaneityamongsttheregressorsFurthermore,basedonMonteCarloevidence,StockandWatson()showthatDOLSismorefavourable,particularlyinsmallsamples,comparedtoanumberofalternativeestimatorsoflongrunparameters,includingthoseproposedbyEngleandGranger(),Johansen()andPhillipsandHansen()Furthermoreshortrunelasticitycounterpartsarealsoderivedviarobustdynamicerrorcorrectionmodels(ECMs)(seeBentzenandEngsted()andBentzen()inanapplicationofECMstoenergyeconomics)Inthisregard,weaimtoprovideaunifiedmethodologicalapproachthatutilizestheserecentadvancesintimeserieseconometricstoexaminetherelationshipgoverningthedemandforavitallyimportantenergyresource,namelycoal,inChinaWechooseChinasinceworkonthiscountryisratherlimitedwithrespecttotheroleplayedbytheenergyorresourcesectorinitsdevelopmentCoalisthefocusofthisstudysinceitdominatesallothersourcesofresourceendowmentinChinaandisalsotheprimarysourceofconsumptionChinais,notsurprisingly,theworld'slargestcoalproducerForouranalysispriceofcoalisalsoreadilyavailableaswiththeothervariablesfromvariousissuesoftheChinaStatisticalYearbookpublishedbythegovernmentofChinaOnlyafewstudies,namelyOwenandNeal(),whoanalyseChina'spotentialforanetexportearner,andSmil()provideviewsforenergyinChina'sdevelopmentRecentlyTangandLaCroix()deriveincomeelasticitiesforenergyconsumptiononaprovinciallevelforChinausingpooledprovincelevel,crosssectiondataWhilethesestudieshavecontributedinimprovingourunderstandingoftheinteractionbetweenenergyconsumptionandtheeconomicdevelopmentprocess,therehavebeennonethatstudythedynamiccharacteristicsoflOneoftheproblemsassociatedwithemployingcointegrationtechniquesisthatitspowerisvitallydependentupontheactuallengthoftimethatthesampleperiodspansThishasbeensupportedinMonteCarlostudiesconductedbyShillerandPerron()andHakkioandRush()Forpurposesofinfcrencemaking,however,standardtestsofhypothesisinregressionmodelsareusuallyassociatedmorefavourablywithdataonahighfrequency,ielargesampleandasymptoticallydistributedHowever,asisoftenthecasewithlongspanningdata,particularlyinaggregatedvariablesusedillenergyanalysis,onlyannualdataofferingasmallnumberofobsevvationscanbereliedupontobeavailableonaconsistentbasisRMasih,AMMMasihEnergyEconomics()thesevariablesoveralongtimehorizontowhichthetechniquesemployedinthispaperadequatelycoverTothisextent,thisstudyhelpstofillthisvoidThepaperisorganizedinthefollowingmannerSectioncontainsabriefoverviewofChina'scoalendowment,consumptionandcontributionineconomicgrowthabriefandintuitiveaccountofthestatisticalmethodologyemployedisprovidedinSectionpriortoapplicationofmethodsandadiscussionofresultsinSectionSomebroadpolicyimplications,conclusionsandasummaryofcontributionsthisstudyhadforfutureresearcharemadeinSectionOverviewofChina'scoalendowmentAmongallthealternativetypesofChina'sresourceendowment,coaldominatesbyfarsomuchsothatin,itaccountedforaboutofitsaggregateenergyproductionThecoalreservesliebothtothenorthandsouthernprovinces(TangandLaCroix,),thoughitsqualityissuperiorinthenorthernreservesAccordingtoTangandLaCroix(),therearethreekeyfeatureswhichdeterminethestructureofChina'stotalenergyandcoalpotential:coalispredominantinChina'senergyconsumption,accountingforalmostall()ofthecountry'sprimaryenergyconsumptionduringthesbeforedecliningoverthenexttwodecadesandrisingagaininthesduetotooheavydependenceonoilwhilecoalendowmentshavehelpedinmakingChinaaselfsufficientenergyconsumer,ithasneverbeenaseriouscandidateforapotentialexportearnereventhoughaggregateenergyconsumptioninChinaishighinworldrankings,itisverylowintermsofpercapitaconsumption(onlyonethirdoftheworldaverage)TheoreticalmodelformulationandeconometricmethodologyTheoreticalmodelanddataThemodelusedinthisanalysisisdictatedbythetypicalformulationpostulatedbyeconomictheoryforaggregateenergydemandfunctions,initsdoublelogformas~logCt=c~(logPt)(logYt)v~()whereCtisaggregatecoalconsumption,PtistherealpriceofcoalandY,representsrealincome(usuallyGDP),u,isanerrortermassumedtobewhitenoiseandnormallyandidenticallydistributedEstimationof()withadequatedatawillprovideapproximatelongrunpriceandincomeelasticitiesAugmentinglaggedtermswilladdstructuretothedynamicsIdeally,inademandfunctionthereoughttobeanadditionalregressor,namelythepriceofasubstituteofcoalHowever,duetolackofappropriatedataorproxiesfortheentirelengthofthesampleperiod,wecouldnotincorporatesuchavariableRMasih,AMMMasihEnergyEconomics()~lO~ECo~Con~mptm~eftScale,,',,',"''~~"~l~o~P~e~lgn(~e),vIIIIII:::l::IIIIIIIIIIIIIIIIIIIIIIFiglAggregatecoalconsumptionandrealcoalpriceinChina:n"~lOOm~~",~'~RealIncome(RightScaJe)!~FigAggregatecoalconsumptionandrealincomeinChina:Thedatausedinthisanalysisareannualrangingfromto,andwereobtainedfromhistoricalannualstatisticsreportedinrecentissuesoftheChinaStatisticalYearbookPlotsofaggregatecoalconsumptioncomparedtorealpriceofcoalandrealincomearepresentedinFigsandEconometricmethodologyLikeallothermodelsthatutilizetimeseriesdata,itisimportanttorecognizethatunlesstheanalyticaltoolsusedaccountforthedynamicsoftherelationshipRMasih,AMMMasihEnergy'Economics()withinatemporal'causal'framework,thecomplexityoftheinterrelationshipsinvolvedmaynotbefullycapturedHence,thereisarequirementforemployingthelatestadvancesindynamictimeseriesmodellingwithinatemporal'causal'frameworkthatallowsforthecoexistenceofbothshortandlongrunforcesthatdrivetheoftenignoreddeviatingandcyclicalinfluencessoinherentlyinteractivewiththeseaggregatevariablesoversuchatimehorizonThefollowingsequentialprocedureswillbeadoptedaspartasourmethodologyTestsforunivariateintegrationInordertoverifytowhatdegreetheseseriesshareunivariateintegrationproperties,weperformbothunitroottestsandmeanstationaritytestsTheDF(DickeyandFuller,,)typetestsandthenonparametricPhillipsPerron(PP)typetestsdevelopedbyPhillips(),PhillipsandPerron(),andPerron()areconvenienttestingprocedures,bothbasedonthehypothesisthataunitrootexistsintheautoregressiverepresentationofthetimeseriesDFtestsattempttoaccountfortemporallydependentandheterogeneouslydistributederrorsbyincludinglaggedsequencesoffirstdifferencesofthevariableinitssetofregressorsThePPteststrytoaccountfordependentandIIDprocessesthroughadoptinganonparametricadjustmenthenceeliminatinganynuisanceparametersRecentlythesetestshavebeenshown(seeCampbellandPerron()andDeJongetal())tosufferfromlackofpowerastheyoftentendtoaccepttheofaunitroottoofrequentlyagainstastationaryalternativeMoreover,thePhillipsPerronstatisticshavebeenshowntoperformpoorlyoversmallsamplesThesestudieshavealsoimpliedthatitwouldbeworthwhiletoconducttestsofthehypothesisofmeanstationarityinordertodeterminewhethervariablesarestationaryorintegratedMeanstationaritytestsareperformedwithatestrecentlyproposedbyKwiatkowskietal()Thistest(abbreviatedasKPSS)isSeeMasihandMasih(a,b)foraninvestigationofthedynamicsofeconomicactivitywithinamultivariatecointegratedsystemBivariateGrangercausalitytestsusingcointegrationtechniqueshavealsobeenundertakeninMasihandMasih(c)AtreatmentofthesequentialstepsinvolvedinapplyingthePPtestsappearinTaylor()Basically,Perron()showsthatifatimeseriesintrendstationaryandifnoaccountismadeofthisinimplementingthetestingprocedure,thismayleadtohighprobabilitiesofmakingatypeerrorWhilethepreciseformoftheassumptions(withregardtodistributionalpropertiesoferrorterms,etc)iscontainedinPerron(),thefollowingsequenceissuggested:(i)ApplyZ(t~,),Z(~)andZ(~)respectivelyandiftheunitroothypothesisisrejectedweshouldhalttheprocedurehere(ii)IftheunitroothypothesiscannotberejectedthenthegreatestpowermaybeobtainedbyestimatingequationsassociatedwiththePhillipsPerrontransformationsoftherelevanttandFstatistics,Z(t~,)andZ(qb~)Duetothefactthatthesetwotestsarenotinvarianttotheconstantterm,thisisonlyvalidifthedriftterm(x*)usedintestequationsappliedin(i)waszeroInthisrespectthesetwotestsshouldonlybeusedifZ(q~)cannotberejectedRMasih,AMMMasihEnergyEconomics()basedonthestatistic:Ttr(u)=(T)ES~°~whereSt=~,vi,t=Tt=liI()withv,beingtheresidualtermfromaregressionofYtonanintercept,andcrisaconsistentlongrunvarianceestimateofYt,andTrepresentsthesamplesizeKwiatkowskietal()showthatthestatisticr~(u)hasanonstandarddistributionandcriticalvalueshavebeenprovidedthereinIfthecalculatedvalueof~(u)islargethentheofstationarityfortheKPSStestisrejectedSinceweentertainboththePhillipsPerrontestsandtheKPSStestinthisexercise,weconsideravariabletocontainaunitrootorbeunitrootnonstationaryifthehypothesisofnonstationarityisnotrejectedbythePPtestsbutthehypothesisthatthevariableismeanstationaryisrejectedbytheKPSStestsTestsformultivariatecointegrationThecointegrationtechniquepioneeredbyEngleandGranger(),Hendry()andGranger()madeasignificantcontributiontowardsmodellingstationaryrelationshipswhilepreservingthelongrunrelationshiplostthroughdifferencingTwoormorevariablesaresaidtobecointegrated,ietheyexhibitlongrunequilibriumrelationship(s),iftheysharecommontrend(s)(foranapplicationofthistechniqueinrelateddisciplines,seeMasihandMasih,,b)Accordingtothistechnique,iftwovariablesarecointegrated,thefindingofnocausalityineitherdirectionisalsoruledoutAslongasthetwovariableshaveacommontrend,causality(intheGrangersense,notinthestructuralsense),mustexistinatleastonedirectioneitherunidirectionalorbidirectional(Granger,,)Evidenceofcointegrationamongvariablesalsorulesoutthepossibilityoftheestimatedrelationshipbeing'spurious'InthisanalysisweemploytheJohansenandJuselius(JJ)procedureoftestingforthepresenceofmultiplecointegratingvectorsUnlikeitspredecessor,theJJprocedureposesseveraladvantagesoverthepopularresidualbasedEngleGrangertwostepapproachintestingforcointegrationSpecifically,theymaybesummarizedasfollows(i)TheJJproceduredoesnot,apriori,assumetheexistenceofatmostasinglecointegratingvector,ratheritexplicitlytestsforthenumberofcointegratingrelationships(ii)UnliketheEngleGrangerprocedurewhichissensitivetothechoiceofthedependentvariableinthecointegratingregression,theJJprocedureassumesallvariablestobeendogenous(iii)Relatedto(ii),whenitcomestoextractingtheresidualfromthecointegratingvector,theJJprocedureavoidsthearbitrarychoiceofthedependentvariableasintheEngleGrangerapproach,andisinsensitivetothevariablebeingnormalized(iv)TheJJprocedureThisguidelineinconsideringthestochasticpropertiesofunivariatetimeseriesisalsousedinanempiricalanalysiscontainingerrorcorrectionmodellingbyMehra()RMasih,AMMMasihEnergyEconomics()isestablishedonaunifiedframeworkforestimatingandtestingcointegratingrelationswithingtheVECMformulation(v)JJprovidestheappropriatestatisticsandthepointdistributionstotesthypothesisforthenumberofcointegratingvectorsandtestsofrestrictionsuponthecoefficientsofthevectorsItisdemonstratedinJohansen()thattheprocedureinvolvestheidentificationofrankofthembymmatrixHinthespec

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