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Economic AnAlysis & Policy, Vol. 43 no. 3, dEcEmbEr 2013
An Empirical Analysis of the Determinants of Passenger Rail Demand in Melbourne, Australia
Albert Wijeweera1Southern Cross University
Southern Cross Business School – Gold Coast Campus, Southern Cross Drive,
Bilinga, Qld 4225 (Email: [email protected])
and
Michael Charles Southern Cross University,
Southern Cross Business School – Gold Coast Campus, Southern Cross Drive,
Bilinga, Qld 4225 (Email: [email protected])
Abstract: Considerable yet largely unexpected growth in passenger rail demand has occurredrecentlyinAustraliancapitalcities.Thisarticleuseshistoricaldata,togetherwithmoderntimeseriesmethods,toexamineempiricallythefactorsthatmighthavecontributedtogrowthinpassengerraildemandinMelbourne,Australia,andtogaingreaterinsightintotherelationshipsbetweenthevariousexplanatoryvariables.Acointegrationapproachisusedtoestimatethelong-runrailelasticities,whileanerrorcorrectionmodelisusedtoestimateshort-runelasticities.Thestudyfindsthattheshort–runrailelasticityistwiceaslowasthelong-runelasticity,althoughbotharehighlyinelastic.Theinelasticnatureofthedemandsuggeststhatafareincreasewouldnotleadtoasignificantdropinboardings,andhenceresultsinariseintotalrevenue.Inadditiontothefare,citypopulation,petrolpriceandpassengerincomeexertapositiveimpactonpassengerraildemand.
I.InTroduCTIon
unexpected growth in passenger rail demand has occurred recently inAustralian capitalcities.Forexample,Sydney,Australia’slargestcity,experiencedanincreaseof5.1millionannualrailpassengerjourneysfromtheyear2001/02to2006/07(BrookerandMoore2008),whilePerth,thecapitalofWesternAustralia,experiencedanincreaseinpassengerboardingsfrom35.7millionin2007to42.6millionin2008–roughlya20percentincreasewithina
1 Correspondingauthor:[email protected].
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year.Melbourne,thecapitalofVictoriaandthesubjectofthisstudy,experiencedpatronagegrowthof47%between2004/05and2008/09(Gaymer2010).SincestategovernmentsinAustralia,whicharetaskedwithfundingheavilysubsidizedurbanrailservicesandassociatedinfrastructure,arebeingrequiredtodomorewithless,fundingurbanrailprojectswheretheyaremostneeded,andprovidingmoreservicesasrequired,isofcriticalimportance.Hence,itismorecriticalthaneverfortransportplannerstodevelopamoreinformedunderstandingoftheimpactofvariousfactorsonpassengerraildemand.Thisarticleuseshistoricaldata,togetherwithmoderntimeseriesmethods,toexamineempiricallythefactorsthatmighthavecontributedtogrowthinpassengerraildemandinMelbourne,andtogainagreaterinsightintotherelationshipsbetweenthevariousexplanatoryvariables.
Thesequentialfour-steptripgenerationmodel,developedintheunitedStatesinthe1950s,hasregularlybeenusedforcontemporarytransportplanning.Itcomprisesofi)tripgeneration,ii)tripdistribution,iii)modalchoice,andiv)routeassignment(Gouliaset al.1990,Wardman1997).Withburgeoningprivatevehicleusedrivenbyinexpensiveautomobiles,lowaccesspricingandcheapfuel(Mees2000),themodelwassubsequentlyadoptedasthemaintoolforurbantransportplanning.Inrecentyears,however,ithasprovedincreasinglydeficientintermsofpredictingtheurbanraildemandspikesseeninAustraliancapitalcities.Inlightoftheinadequaciesofcurrentdemandestimationmethods,it isimportanttoascertainthefactorsthathavecontributedtotheriseinurbanrailpatronagefromotherapproaches.Here,ademandmodelestimatedbyemployingtimeseriesdatawillbeusedtogaingreaterinsightintothesematters.Thisdoesnotmeanthattraditionaltechniquesshouldbedispensedwith.Instead,thereisaneedtosupplementratherthanreplacethem,especiallysinceanapproachmoredirectlysuitedtoestimatingtherailpassengerdemandfunction,ratherthantransportdemandmoregenerally,isrequired.Sincethetimeseriesmethodisregularlyemployedforforecastinginfinanceandeconomicsfields,itsfunctionalitywillbetested,here,inthecontextofthepassengerraildemandofMelbourne.
This study represents a pilot attempt to develop a time series technique that will beefficaciousfortestingthepassengerdemandfunctionofAustralianurbanrailtravel.ThestudythereforerepresentsanadditiontothemerehandfulofexistingAustralianstudiesemployinga comparable approach (see douglas and Karpouzis 1999, odgers and Schijndel 2011).Moderntimeseriestechniqueswillbeusedtoexaminetherelationshipbetweenpassengerraildemandanditsexplanatoryvariables,especiallysincepreviousstudieshavenotutilisedthesetechniquesintheestimationofpassengerraildemand.Inparticular,thatmosttimeseriesdataisnon-stationaryisnowwellknown.Ifthisisnottakenintoaccount,spuriousresultsandinvalidinferencesmayresult(Grangerandnewbold1974).Fromtheliteraturereview,notimeseriesstudyonurbanpassengerraildemandinAustraliatestedforstationarity,whichcompromisesthevalidityofthetechniquesdevelopedhitherto.Inaddition,cointegrationanderrorcorrectionmodelsallowtheresearchertoseparatebetweentheshort-runandlong-runelasticities(EngleandGranger1987).ThiswasalsolargelyneglectedinpreviousAustralianstudies.Withoutdoingthis,thereisthedangerofconfusingshort-runimpactswiththosethatwilloccurinthelong-runiftherelationshipbetweenkeyvariableschanges.
Thearticleisdividedintofivemainparts.SectionIIprovidesabriefsynopticdiscussionoftherelevanttheoreticalandpertinentempiricalliteratureonthetopic.SectionIIIreflects
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ondatadefinitions,datasources,andthemethodology,whileSectionIVexaminestheshort-runandlong-runpassengerrailelasticitiesobtainedfromtheestimation.ConcludingremarksarepresentedinSectionV.
II.PrEVIouSSTudIESonPASSEnGErrAIldEMAnd
Itisimportanttoreviewthepreviousliteratureontheuseofthetimeseriesapproachtoestimaterailpassengerdemand.Althoughthepresentstudywilllookexclusivelyaturbanrailserviceswithinamajormetropolitancentre,someofthestudiesreviewedestimatethedemandforinter-cityoratleastinter-regionalrailservices.Welookfirstattheinternationalstudies,andthenattwoAustralianstudiesthathaveemployedatimeseriesapproach.
2.1 International Studies
Jonesandnichols(1983)publishedthefirsttimeseriesstudyonpassengerraildemand.Theyemployedfour-weeklyuKdatafromthebeginningof1969tothemiddleof1977.Theauthorsemployedanordinaryleastsquaresmethodtoestimatethepassengerraildemandfunction,withseventeenlondon-basedroutesbeinginvestigated.Asingleequationframeworkwasemployed.Thiswaspreferredoveranostensiblysimultaneousmodelbecausetheauthorscontendedthatpriceisdeterminedbyrailmanagers,andthereforedoesnotchangefrequentlyenoughforittoberegardedasanendogenousvariable.Fortheestimation,adoublelogspecificationwasused.Bydoingthis,theestimatedcoefficientscoulddirectlybeinterpretedaselasticities.Theoutcomewasthatthemeanpriceelasticitywasdeterminedtobe–0.64.Fromthis,onecanextrapolatethat,onaverage,a10percentincreaseinrailfarewouldreducepatronageby6.4percent.demandforpassengerrailservicesisthereforeinelastic.
despitetheground-breakingnatureofJonesandnichols’study,someseriousstatisticalproblemsaffecttheirresults.Fowkesandnash(1991)pointedoutthatthedurbinWatsonstatisticsreportedaresignificantlylow.Thiscouldindicatethepresenceofserialcorrelationandpotentialstatisticalproblems.Theeconometricsliterature(e.g.,Farebrother1980,Breusch1978)makesitveryclearthati)iferrortermsareautocorrelated,theordinaryleastsquaresestimatorcannolongerberegardedasefficient,andii)thatanunbiasedestimatordifferentfromtheolSestimatorhasasmallervarianceandthusgreaterreliability.Jonesandnichols’findingsmustbeusedcautiously.Forexample,thestudyfailstotakeintoaccountpossibleshort-runresponsesfromthemodel.Changesintheexplanatoryvariableswillthereforehavealimitedeffectintheshortrunbecausepassengers,onaccountofshort-termcommitments,willhavedifficultyinrespondingquickly.Indeed,thefulleffectofthesechangesondemandmaytakeseveralmonthstoeventuate.
McGeehan(1984)estimatedtheraildemandfunctionforinter-urbantravelintherepublicofIreland.Todothis,quarterlydatafromthebeginningof1970totheendof1982wasused.FollowingJonesandnichols,McGeehanusedtheordinaryleastsquaresmethodandspecifiedthemodelinasingleequationsetting.YetMcGeehanusedthepassengermilesrunduringtheestimationperiodinsteadofticketsalesdatatorepresentdemand.Therationalebehindhischoiceofexplanatoryvariablesalsodiffered.McGeehancontendedthatrevenueperpassengermile
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travelleddoesnotrepresentasatisfactoryproxyforthefare.Thisisbecausestrongdistancetapersareusedbymostoperators,sothefarechargedpermilefallsastripdistancesbecomelonger.2Ifrailpassengersthereforeswitchedfromlongjourneystocomparativelyshortones,therevenueperpassengermilewouldincrease,yetnoactualchangetothefarewouldhaveoccurred.AformulawasusedbyMcGeehantodetermineaweightedaveragefare.HealsousedtheIndexofIndustrialEarningstocontrolforthepassengerincomevariable,withtherationalebeingthatariseindisposableincomeincreasesthedemandfortravel(includingrail),eventhoughitincreasescompetitionfromothermodes,andprivatevehiclesinparticular.otherimportantexplanatoryvariableswereincluded,suchasprivatevehicleownershipandthreeseasonaldummies.overall,themodel’sresultsaddweighttotheviewthatpassengerraildemandisinelastic.Sincepriceelasticitywasfoundtobe–0.4,a10percentincreaseinrailfarewoulddecreaserailpatronageby4percent.
Fowkes et al. (1985) used annual data (1972–1981) between tenmajor routes in theuKtoputtogetherapooleddatasampleconsistingoftimeseriesaswellascross-sectionaldata.railfareperjourney,carownership,employment,anddummyvariablestocapturetheintroductionofhighspeedrail(HSr)wereusedasexplanatoryvariables.Theresultssuggestthattherailfareexertsasignificantlynegativeeffect,andisalsoinelastic.ConsistentwithJonesandnichols,togetherwithMcGeehan,anyincreaseinpricewillleadtoanincreaseinrevenue.Yettherearesomeproblematicaspects.Asidefromthelimitationimposedbytheassumptionofnochangeinticketcoveragedataovertimebetweenroutes,Fowkeset al.useacombinationofdatafromtendifferentareastoconstructapooleddataset.Thereisstillthepossibilitythatdifferentflowscouldoccurbetweendifferentareasasaresultofroute-specificvariables.Withthatinmind,Fowkeset al.takefirstdifferencesofobservationstomitigatetheeffectsofthis.AsStockandWatson(2001)demonstrate,firstdifferenceshasthepotentialtoaddresssomestatisticalproblems(includingvariablemeanandnon-constantvariance),yetitalsoleadstothelossofusefulinformation.Thisisespeciallythecasewithlong-runrelationships.Fowkeset al.’s findings should thereforebeanalysedaccording towhetherlong–orshort-runrelationshipsareofinterest.
doi andAllen (1986) analysed two time series regressionmodels in their study of asingleurbanrailrapidtransit lineintheunitedStates.oneofthesemodelswasinlinearform,whiletheotherwaslogarithmic.Bothwereemployedtoestimatemonthlyridership.Variablesrelatingtofare,petrolprice,roadtoll,seasonalcharacteristicsandselecteddummyvariableswereallregressed.Withrespecttotherealfare,doiandAllenfoundthatelasticitiesofmonthlyridershipwere–0.233(usingthelinearmodel),or–0.245(usingthelogarithmicmodel).ElasticitiesaresmallerincomparisonwiththeuKstudies,althoughthefareelasticityofdemandremainsinelastic.Intermsofcross-elasticities,theauthorsfoundthatalternativemodesrepresentsubstitutes.Positiveelasticitieswereobservedfortherealpetrolpriceinboththemodels,with0.113forthelinearmodel,and0.112forthelogarithmic.Anotheroutcomeisthatanyincreaseinbridgeorroadtolls(orindeedcognateoperatingcosts,suchasparkingfees)wouldincreasethedemandforrail.
2 Thiseffectivelymeansthosemakingshortertripseffectivelycross-subsidizethosemakinglongerones.
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overall,theseearlierstudiesonlydealtwithcontemporaneousrelationships,andnolagtermswereincludedinthemodelspecification.Bywayofcontrast,laterstudiesfoundthatinstantaneousadjustmentassumptionisundulyrestrictive.Itwasthereforeclaimedthatthissortofassumptionoversimplifiestheactualresponseofrailusers.Forexample,owenandPhillips(1987),intheiranalysisoftheeffectofvariouseconomicfactorsonthedemandforinter-cityrailpatronageintheuK,developedadynamicrailmodel.Theywereabletoshowthatdemandresponsesarenotinstantaneous,andthatthelong-runresponsescanbequitedifferenttothoseoftheshortrun.owenandPhilipsobservedashort-runelasticityof–0.69andalong-runelasticityof–1.08.Thelong-runresponsestopricechangescouldthereforebehigherthanthoseobservedintheshort-run,wherepassengersarenotabletorespondquicklytochangesintheexplanatoryvariables.So,thereisapotentialforanincreaseinrevenueintheshortrunbyincreasingthefare,butthismightbecounter-productiveinthelong-runbecauseconsumerscanchangetheircircumstances.
InanotheruKstudy,Wardman(1997)pointedoutthattheexistingliteratureallowedonlyaverylimiteddegreeofelasticityvariation.unlikepreviousresearchers,Wardmanquestionedtheconstantelasticityspecificationassumed.Instead,heintroducedarangeoffunctionalformstothedemandmodel,withthebasemodelbeingtheconstantelasticitymodel.Thiswasextendedintothreeotherfunctionalforms:i)aconstantelasticitycompetitionmodel;ii)anexponentialmodel;andiii)anexponentialcompetitionmodel.Theseamendmentsallowedtheelasticitiestovarywiththecompetitiveposition.Yettheestimationmethodemployedisnotpurelytimeseries,sinceannualdatawereavailableforonlythe1985/86–1990/91period.Apooleddatasetof764observationsofdemandchangeson160non-londonflowswasthereforeusedasabasisforanalysis.Theconstantelasticitymodelaside,alltheothermodelswereestimatedbynon-linearleastsquares.Wardman’sresultsconfirmthathisinitialconjecturewascorrect:elasticitiesdovarysignificantly,whichmeansthattheconstantelasticityassumptionmaynotalwaysbeaccurate.
Voith(1991)usedannualdatacovering118of165stationsontheSoutheasternPennsylvaniaTransportationAuthority(SEPTA)commutersystemfrom1978throughto1991pertainingtocommuterrailridership.Theimpactofchangesinfaresandservicelevelswasfoundtooccurwithalag,whilethelong-runeffectswereroughlytwicetheshort-runeffects.ThisaddsgreaterweighttotheworkofowenandPhilips.Asignificantvariationinresultswasalsoobservedacrossstations.Voithconcludedthatthedemographicvariablesexplainverylittleofthestation-specificresidual,withtheimplicationbeingthattheprimarymeasurabledeterminantsofridershiparenotrelatedtotheancillaryeffectsofchangingdemographics,butarerelatedtotransportationpolicy.
Finally,Chen (2007) employed annual data (1995–2002) from46 origin stations tolondon.onaccountoftheshortertimeperiodexploredincomparisonwithotherstudies,thestudyusespaneldatamodelspecifications toestimate the raildemandfunctionandcorrespondingelasticities.Threemainexplanatoryvariableswereusedtospecifythedemandequation:i)averagerevenueperjourney;ii)centrallondonemployment;andiii)regionalgrossvalueaddedperhead.Chendeterminedthatthefareelasticityis–0.767.ThisfigureisveryclosetothatofJonesandnichols(1983).Furthermore,theemploymentelasticityispositive.Thisindicatesthatraildemandwillincreaseifemploymentincreasesincentral
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london,moresogiventhatChenextrapolatedthatemployment in thisarea is themainfactoraffectingdemand.
2.2 Australian Studies
TherehavebeenonlytwopublishedstudiesdealingwiththeestimationofthepassengerdemandfunctionusingatimeseriesapproachinAustralia.Thesetwostudiesaresummarizedbelow.
douglasandKarpouzis(2009)used38yearsofrailpatronagedata(1969–2008)toestimatethepassengerraildemandformetropolitanrailinSydney,thestatecapitalofnewSouthWales(nSW).Theauthorsregressedraildemandonfourvariables:i)averagerealfarepertrip;ii)trainkilometresrun;iii)metropolitanofficeemployment;andiv)realgrossstateproductofnSWpercapita.Tocaptureanymajorincidents,dummyvariableswereincluded,suchastrainaccidents,the2000Sydneyolympics,andtheintroductionofautomaticfarecollectionin1989.Incomparisonwiththeinternationalstudies,themodel’soverallgoodnessoffitisnothighlysatisfactory.Indeed,thecoefficientofdeterminationisonly0.35.Thismeansthatamere35percentofthevariationinpassengertripratesisexplainedbytheestimatedmodel.noneoftheparameters,moreover,issignificantat5percentlevel,althoughtheyallhavetheexpectedsigns.onlytheconstanttermissignificant,whichpossiblysuggeststhatthemodelwasnotspecifiedcorrectly.omittedvariablebiasalsoseemstobepresent,sincepreviousstudieshavefoundthatmanyothervariables,suchasseasonalityandthepriceoffuelforprivatevehicles,haveanimpactondemand.unclear,too,iswhetherthestudytestedforunitrootsinthevariables.Sincethisformsanintegralpartofthemoderntimeseriesapproach,thestudyremainshighlyproblematic.
odgersandSchijndel(2011)lookedatpassengerraildemandintheMelbournemetropolitanarea,i.e.,thespecificareaofinteresttothepresentstudy,overatwenty-sevenyearperiod(1983/84–2009/10).Inthisstudy,thedependentvariableistheannualpassengerboardingsperyearonMelbourne’strains.Thisapproachrepresentsacleardeviationfromcomparablestudies,sinceodgersandSchijndelusedpassengerrailmiles(orratherkilometresinthiscase)torepresentoverallraildemand.Themodelsdevelopedinitiallyincludesixexplanatoryvariables. Among the reported multivariate specifications, three of them contain threeindependentvariables,whiletwoofthemcontainonlytwoindependentvariables.Anotherimportantaspectisthatthestudyprovidesdifferentforecastsbasedondifferentspecifications.Forinstance,thefirstregressionmodelforecaststhatthedemandforurbanrailinMelbournewillcontinuetogrow,withthemodelforecastinganaverageannualgrowthof7.7%peryearoverthenextthreeyears.Asignificantissueisthattheauthorsmakenoattempttoidentifynon-lineareffects.Theinternationalstudiesexamineduseddoublelogtransformations,whichenabledsomeof thenon-lineareffects tobecaptured.Problematic, too, is thatvariablesareexpressedinoriginalform.Thismeansthattheestimatedcoefficientsarenotabletobeinterpreteddirectlyaselasticities.Theresultisthatitisharderforthereadertocomparetherailfareelasticitiesobtainedinotherstudies.
The outcomes of the previous time series literature pertaining to passenger rail aresummarisedinTable Ibelow.
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Tabl
e 1:literaturereview:Passengerraild
emandFunction
Study
dataSample
Methodology
Variables
results
Jonesandnichols
(1983).
Weeklydataof17london
routesfrom
beginningof
1969–m
iddleof1977.
olS
insingleequation
setting.
Ticketsales;realincome;
econom
icactivityindicator;rail
fares;serviceindicator;control
foralternativetransportmodes;
seasonaldum
mies.
Meanpriceelasticityof
–0.64.
McG
eehan(1984).
Quarterlydatafrom
republic
ofIrelandover1970–1982.
olS
insingleequation
setting.
Passengerm
iles;nom
inalrail
fare;C
PI;indexofrealindustrial
earnings;dum
myvariablesfor
seasonalvariations.
Priceelasticityof–0.4.
Fowkesetal.
(1985).
uKannualdata(1972–1981)
from
10differentroutes.
Fixedeffectsm
odel.
%changeintraffic;railfare
perjourney;carownership;
employment;dummyvariables
tocaptureintroductionofHSr
.
railfareisinelastic;city
employmentincreases
railtravel;carownership
decreasesraildem
and;
introductionofHSr
has
increasedrailpatronage.
doiandAllen
(1986).
uSmonthlydata1978–1984.
linearandnon-linear
regressionmethods.
num
berofpassengersp
erfiscal
month;realfare;realgasoline
price,realbridgetoll;dum
my
variablestocontrolforsu
mmer
andBroadwayStationclosure.
Fareelasticitieswere
–0.233bylinearm
odel
and–0.245bynon-linear
model.
owenandPhillips
(1987).
4-weekticketsalesdata
recordedbyBritishrail
(1973–mid-1984).
Partialadjustment
model.
railfares;G
dP;introduction
ofHSr
;dum
myvariablesto
captureserviceimprovem
ents
andseasonalvariations
Short-runelasticity
of–0.69andlong-run
elasticityof–1.08(short-
runisinelasticandlong-
runiselastic).
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256
Wardm
an(1997).
datasetof764observations
on160non-london(1985–
1991).
linearandnon-linear
regressionmodels.
raildem
and;railfare;dum
my
variabletocaptureeffectso
frollingstockimprovem
ents;
timetrendvariables;variables
torepresentcom
petitionfrom
coachesandcars.
3functionalforms
torepresentdifferent
competitiveposition;rail
elasticitiesvaryaccording
totheservice’scom
petitive
position.
Voith(1991).
Annualdatacover118of
165stationsonSoutheastern
PennsylvaniaTransportation
Authoritycommuterrail
system
(1978–1991).
reducedformfixed
effectsm
odel.
railtrips;prices;variablesto
controlforattributesofrailm
ode
andcompetingmodes;lagged
dependentvariable.
Impactofchangesinfares
andservicelevelsoccurs
withalag;long-runeffects
areroughlytwicethe
short-runeffects.
Chen(2007).
Annualdatafrom
46origin
stationstolondon(1995–
2002).
Fixedeffectsm
odel.
num
berof2nd-classseason
tickets;averagerevenueper
journey;centrall
ondon
employment;dummyform
ajor
event;regionalgrossvalueadded
perhead;originstationsdum
my
variables.
Fareelasticityis–0.767,
whichisconsistentw
ith
comparablestudies.
douglasand
Karpouzis(2009).
Sydneyrailpatronagedata
(1969–2008).
olS
insingleequation
setting
railpatronage;averagereal
farepertrip;trainkmrun;
metropolitanofficeemployment;
realgrossstateproductofn
SW
percapita;dum
myvariables
tocaptureaccidents,and2000
olympics.
noneoftheparameters,is
significantat5%levelof
significance,althoughall
haveexpectedsigns.
odgersand
Schijndel(2011).
Passengerraildem
andinthe
Melbournemetropolitanarea
(1983/84–2009/10).
MultivariateolS
regressionmethod.
realaveragefull-fare;real
averageannualpriceperl
ofpetrol;em
ploymentdata;
housinginterestpaidas%of
householdincome;population.
dem
andforurbanrailwill
continuetogrowovernext
3years.
Tabl
e 1:literaturereview:Passengerraild
emandFunction(contd)
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III.THEModEl
ThisstudyestimatespassengerraildemandelasticitiesofMelbourneusingannualdatafrom1979–2008.Acointegrationapproachisusedtoestimatethelong-runpassengerrailelasticities,whileanerrorcorrectionmodelisemployedtoestimatetheshort-runelasticities.Therearetwomain cointegrationmethods in themodern time series literature.These are: i) singleequationmethods;andii)andsystem-basedmethods.Iftheendogenousrelationshipbetweentheprice(fare)andthedemandisofinterest,thesystemmethodshouldclearlybepreferredoverthesingleequationmethod.Asshownintheliteraturereview,however,thefarevariablecanberegardedasexogenousinanypracticalanalysis,sothelatterisusedinestimatingthecointegrationrelationship.Themostpopularamongthesingleequationmodelsisthetwo-stepprocedureproposedbyEngleandGranger(1987).Itisthereforeusedhere.
TheEngleandGrangermethodconcentratesonvariablesthatareintegratedoforderone.Hence,thefirststepistochecktheorderofintegrationofeachseries,whichcouldbedonebyaunitroottest.Ifaunitrootexistsinlevels,butnotinthefirstdifferences,thatparticularseriesisregardedasbeingnon-stationary.Itcanalsoberegardedasbeingoforderone,I(1).WeuseAugmenteddickeyFuller(AdF)Testinthisanalysis.TherearethreevariationsoftheAdFtestspecification:i)withoutinterceptortrend;ii)withinterceptbutwithouttrends;andiii)withboththeinterceptandtrend.Thesecondspecificationisusedbecauseitismoreconsistentwiththedata-generatingprocess.Thereareeightvariablesinthemodel.unitroottestresultsforeachseriesaregiveninTable 2below.
Table 2:Augmenteddickey-FullerunitrootTestresults
Variablelevels Firstdifferences
t-statistic prob* lag t-statistic prob* laglBoArdInG –0.421 0.890 1 –3.368 0.023 0
lFArE 0.246 0.970 0 –4.529 0.002 0
lFATAlITY –2.239 0.199 0 –4.392 0.003 0
lFuEl 0.215 0.968 0 –5.586 0.000 0
lKMrun –0.639 0.84)4 1 –3.270 0.019 0
lPCI 0.200 0.967 1 –2.919 0.058 0
lPoPulATIon –0.921 0.764 1 –3.058 0.049 0
lVEHIClE –2.124 0.191 1 –4.523 0.003 0
*MacKinnon(1996)one-sidedp-values.
Theresultssuggestthatalltheseriesareintegratedoforderone.Inotherwords,theyhaveaunitrootinlevels,butnounitrootinfirstdifferences.oncetheunitroottestisconductedandtheorderofintegrationestablished,theEngleandGrangercointegrationestimation(1987)involvestwomainsteps.First,thebestpossiblelinearmodelisestimated.Second,theresidualseriesoftheestimatedmodelistestedtoascertainwhetheritisstationary.
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Todecidethebestpossiblelinearform,theexistingliterature(e.g.,Jonesandnichols1983,Chen2007)isfollowed,whileitisassumedthatthefunctionalformgiveninequation(1)representstherelationshipbetweenthepassengerraildemand(Y)anditsfactors(Xi).
Yt = !0X1t!1X2t
!2 ....Xn1t!ne"t ! (1)
Thisnon-linerfunctionisconvertedintoalinearinparametersformusingadouble-logtransformation.Theadvantageofthistransformationisthattheestimatedcoefficientscouldbeinterpreteddirectlyaselasticities.Theestimablefunctionisgivenintheequationbelow.
logYt = logβ0 +β1 logX1t +β2 logX2t + ...+βn logXnt +εt (2)
Inthisparticularcase,Yrepresentsthenumberofboardingsattimet.Therearesevenexplanatoryvariables.TheFArEisthecontrolvariableforthepriceinthedemandfunction.Aseeminglyappropriatevariableforpriceisthecostofaticket.Yetthisturnsouttobeaverycomplexvariable.Therearemanydifferentticketgroups,andthereareseriouscomplicationswithrespecttoaggregatingthemintoonevalue.Jonesandnichols(1983)usedrevenueperkilometer run (totalpassenger rail revenue/totalpassenger railkilometers run)as the farevariable.Thesameprocedureisfollowedinthisstudy,withFArEbeingthelabelappliedtoit.ThecoefficientofFArEistheown-priceelasticityandisexpectedtobenegative,asperthelawofdemand.onemorecomplicationinthecalculationofFArEortherevenueperkilometerwasunavailabilityofrailspecificrevenuedataforthesampleperiodafter1987.dataareavailableforthetotalpassengertransportsector,but,unfortunately,notfortherailsectoralone.Accordingtoourcalculationbasedonhistoricaldata(1970–1986),theproportionofrailrevenuetotalpassengertransportrevenueis46percent.Asaresult,post-1987revenuedataatafactorof0.46wasdiscountedtoobtainrevenueemanatingspecificallyfrompassengerrail.
ThesecondexplanatoryvariableisPCI,orthepercapitaincome.Thisisusedtocontrolfortheincomevariableofthedemandfunction.Ifthepassengerrailserviceisassumedtobeanormalgood,apositivecoefficientshouldbeobtained.ThecoefficientofCPIistheincomeelasticityoftheraildemandfunction.AustralianpercapitaincomeishereusedasaproxyforMelbourne’spercapitaincome.
ThethirdvariableisFuEl,whichwillcontrolforthepricesofothergoodsofthedemandfunction.Thisisascertainedfromthefuelpriceindexovertheperiodbeingstudied.Privatevehicletravel,inmostcases,representsasubstitutemodeoftravelforurbanpassengerrail.Thismeansthat,asthepriceofpetrolincreases,thedemandforpassengerrailshouldalsogoup,therebyresultinginapositivecoefficientonFuEl.ThecoefficientonFuElmeasuresthecross-priceelasticity.
ThefourthvariableisthePoPulATIonofMelbourne.Thehigherthepopulation,thelargerthedemandshouldbe.Hence,apositivecoefficientisexpectedonPoPulATIon.
ThefifthvariableistheKMrun,i.e., thenumberofkilometersrunbytheurbanrailserviceduringtheyear.ApositiverelationshipisexpectedbetweenthedemandforpassengerrailandtheKMrun.
Thelastexplanatoryvariable,FATAlITY,isusedtocontrolforthepassengers’perceptionofrail’soverallquality.Thismaynotbethebestvariabletorepresentthisperception,butothervariables,suchasservicequality,aresimplynotavailablefortheentiresampleinvestigated.
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FATAlITYisthusonlyaremoteproxyforpassengerperceptionoftheservice,asperlitman(2010).nevertheless,itwasdeemednecessarytocontrolforservicequalityinsomewaysincethisisregardedasanimportantvariablewithrespecttoencouragingordiscouragingridership.
Finally,thevehiclepriceindexinAustralia(VEHIClE)isincludedasapossiblesubstitutefortheothertransportmodes.ApositiverelationshipbetweentheVEHIClEandBoArdInGishypothesizedbecause,asvehiclepricesincrease,moreandmorepeopleareexpectedtousepublictransportation,therebyincreasingthedemandforpassengerrail.
The data for the researchwere obtained from several sources.Boarding and revenuedatawerecollectedbytheresearchersaspartofafundedresearchproject,populationandfuelindexdatawereobtainedfromtheAustralianBureauofStatistics(ABS)website,andtherestweresourcedfromaBureauofInfrastructure,TransportandregionalEconomicspublication(BITrE,2011).Theexactmodelusedtoestimatethepassengerraildemandisgiveninequation(3)below.
logBORADINGt = β0 +β1 logFAREt +β2 logPCIt +β3 logFUELt .+β4 logPOPULATIONt +β5 logKMRUNt +β6 logFATALITY +β7 logVEHICLE + et
(3)
After initial estimation, itwas noted thatKMrun leads to unexpected estimates onthecoefficients.ThismaybeduetopossiblemulticollinearitybetweenKMrunandotherexplanatory variables, and the FArE variable in particular. As explained above, FArEwascalculatedbydividingthetotalpassengerrailrevenuebythenumberofpassengerrailkilometersrun.Toaccountforthis,arestrictedversionofthedemandmodelwasestimatedbydroppingtheKMrunvariable.Thisresultedinmorerobustoverallestimates.TheresultsareshowninTable 3 below.
Table 3:Cointegrationresults
Variable Coefficient Std.Error t-Statistic Prob.C –7.051 1.441 –4.893 0.000lFArE –0.066 0.023 –2.825 0.010lPCI 0.018 0.011 1.576 0.129lFuEl 0.062 0.020 3.103 0.005lPoPulATIon 0.560 0.098 5.729 0.000lFATAlITY 0.012 0.008 1.428 0.167lVEHIClE –0.064 0.009 –7.209 0.000Adjustedr-squared 0.974 F-statistic 184.347
AnAdFunitroottestwasperformedontheresidualsobtainedfromtheaboveestimation.The results indicated that the residual series is stationary.Thismeans that passenger raildemandanditssixexplanatoryvariablesarecointegrated,andthattheresultsshowninTable 3canthereforebeusedformeaningfulanalysisoftheurbanrailpassengertransportdemand.
Afterestimatingthelong-runelasticities,anerrorcorrectionmodel(ECM)wasemployedtoi)obtainshort-runelasticities,andii)validatethecointegrationresultsreportedinTable 3above.
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ECMmodelsareusefulbecausetheyshowboththeshort-runresponsesandtheadjustmenttothelong-runequilibriuminasinglespecification(EngleandGranger1987).Thisstructureisparticularlyimportantinraildemandmodellingbecausetravellerscannotchangetheirbehaviourinstantaneously,whilelagsdooccurintheirdecisions,aspointedoutintheliterature(see,e.g.,Voith1997).Goodwin(1976)attributesthistohabitpersistence.Commutersarenotparticularlywillingtoaltertheirestablishedroutineatfirst,althoughingrainedhabits,ofcourse,havethepotentialtobeerodedovertime(Chen2007).ThereareseveralmethodstoestimatetheECM.TheEngleandGrangerapproachisusedherebecausetheerrorcorrectiontermcaneasilybeconstructedbyusingthelong-runresultsthathavealreadybeenestimated.
Grangerrepresentationtheoremstatesthat,ifvariablesXandYaregeneratedbyerrorcorrection models, they are cointegrated. It has been shown already that the dependentvariable(BoArdInG),togetherwithitsexplanatoryvariables(FArE,CPI,PoPulATIon,FuEl,KMrun,FATAlITY,VEHIClE)areI(1),whilethefirstdifferenceofthesevariables(ΔBoArdInG, ΔFArE, ΔCPI, ΔPoPulATIon, ΔFuEl, ΔKMrun, ΔFATAlITY,ΔVEHIClE)isI(0).SincevariablesinlevelsareI(1)andcointegrated,theGrangerepresentationTheoremsuggeststhatthemodelgiveninequation(3)canalsobeexpressedinI(0)variables.TheerrorcorrectionmodelintermsofI(0)variablesisgiveninequation(4).ECMcontainsvariablesinfirstdifferencesandanerrorcorrectionterm(ECT).TheECTistheoneperiodlagresidualsobtainedfromthecointegratingmodel.
Δ logBORADINGt =α0 +α1Δ logFAREt +α2Δ logPCIt +α3Δ logFUELt .+α4Δ logPOPULATIONt +α5Δ logFATALITY +α6Δ logVEHICLEt ++λECT + et
(4)
Here,theparameterα1istheshort-runelasticityofpassengerraildemandwithrespecttoFArE,α2istheshort-runincomeelasticityofdemand,andα3istheshort-runcross-priceelasticityofdemand.otherparameterscanbeinterpretedinasimilarway.Aftertheown-price,incomeandcross-priceelasticity,themostimportantotherparameteristheλ,whichrepresentsthedisequilibriumerror.Ifthecointegratingrelationshipiscorrect,theestimateontheparameterλhastobebothnegativeandstatisticallysignificant(EngleandGranger1987).Theλiscalledtheadjustmentparameterbecauseitshowshowmuchofthedisequilibriumiscorrectedwithinoneperiod.TheresultsoftheECMaregiveninTable 4below.
Table 4:EngleandGrangerErrorCorrectionModelresults
Variable Coefficient Std.Error t-Statistic Prob.C –0.007 0.003 –2.266 0.034d(lFArE) –0.032 0.016 –2.002 0.058d(lPCI) 0.020 0.010 1.937 0.066d(lFuEl) 0.021 0.014 1.488 0.152d(lPoPulATIon) 1.068 0.219 4.878 0.000d(lFATAlITY) 0.004 0.005 0.793 0.437d(lVEHIClE) –0.024 0.019 –1.252 0.224ECT –0.534 0.186 –2.867 0.009Adjustedr-squared 0.616 F-statistic 18.376
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IV.THErESulTS
Thecointegrationresultssuggestthatthefareexertsanegativeandstatisticallysignificanteffectonpassengerraildemand.Themagnitudeoftheestimate,however,isverysmall.Toillustrate,aonepercentincreaseinfareresultsinonlya0.07percentdecreaseinboardings.Thissuggeststhatafareincreasewillnotleadtoaconsiderabledecreaseinpassengerraildemand.Inotherwords,thepriceelasticityofraildemandisveryinelastic.oneimportantpolicyimplicationisthatanincreaseinfaredoesnotleadtoasignificantdropinboardings,sothatpriceincreasecouldtheoreticallybeusedtogeneratehighertotalrevenue.Thefindingofaninelasticdemandisquiteconsistentwithexistingstudiesonpassengerraildemand,withtheexceptionofowenandPhillips(1987),whoreportedaslightlyelastic(1.08)raildemand.Amongotherstudies,Jonesandnichols(1983)foundthat themeanelasticitywas–0.64,therebysuggestingthat,onaverage,a10percentincreaseinrailfaredecreasesrailpatronageby6.4percent.McGeehan(1984)confirmedtheinelasticnatureofpassengerraildemandandreportedthatthepriceelasticityis–0.4,afiguresmallerthanthatputforwardbyJonesandnichols.doiandAllen(1986),usingdatafromtheunitedStates,observedthatthepriceelasticityis–0.245,asmallerelasticitycomparedtotheuKstudies.TherearenocomparableelasticitiesinthecaseoftheAustralianpassengerrailindustry.
Withrespecttotheothervariables,income(PCI)hastheexpectedpositivesign,butisnotstatisticallysignificantat5percent.Itisinterestingtonote,however,thatthep-valueofthecoefficientis0.129,sothecoefficientwouldbesignificantiftestedatthe13percentlevelofsignificance,insteadofatthe5percentlevel.Hence,thereismoderateevidencetosuggestthatahigherpassengerincomeleadstoanincreaseinurbanraildemandinMelbourne.Yetthemagnitudeofthecoefficientissmall,withaonepercentincreaseinincomeleadingtoanapproximately0.02percentincreaseinboardings.
Asexpected,fuelpriceandpassengerraildemandarepositivelyrelated.Thiscouldbeattributedtotheobservedfact(see,e.g.,Gaymer2010,odgersandSchijndel2011)that,whenthepriceoffuelgoesup,peoplereduceprivatecarusageandincreasetheiruseofpublictransport,includingurbanrailifavailable.Therelationshipishighlystatisticallysignificant,withitsp-valuebeingatalmostzero.AonepercentincreaseinfuelpricethereforeincreasesthepassengerraildemandinMelbourneby0.06percent.Butthisisaverysmallresponse.This suggests that, although the passenger rail demand and othermodes of transport (inparticulartheprivatecaruse)areindeedsubstitutes,theyarenotcloselysubstitutable.Fuelprice,itfollows,maynotbethesolefactorthatcartravellerstakeintoconsiderationwhentheyconsideralternativemodes.Thereareclearlyotherconcernssuchastrafficcongestionandparkingfeesatthedestinationpoint.
Populationandpassengerraildemandarepositivelyrelated,asexpected,withthecoefficientbeingstatisticallysignificantatvirtuallyanylevel.So,anincreaseinthepopulationshouldleadtoahigherdemandforpassengerraildemand.Togetherwiththepriceinelasticbehaviour,thismightbewelcomenews,onthesurfaceatleast,forMelbourne’surbanrailoperator.Thestudysuggeststhataonepercentincreaseinthecitypopulationleadstoaboutahalfofapercentincreaseinthepassengerraildemand.Thepopulationelasticityisthehighestinmagnitudeamongalltheelasticitiesestimatedinthisanalysis.
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Asstatedpreviously,thefatalityvariablewasusedasaproxyforasafetyandreliabilityindicator,despitesomemisgivingsaboutitsabilitytorepresenttheservicequalitydimensionofurbanrail.Theestimateonthefatalitycoefficientisneitherstatisticallysignificant,norhastheexpectedsign.Thisinsignificancecouldbeattributedtothefactthatthereisnotransportmodesaferthanpassengerrail.Indeed,privatevehiculartransport,whichislikelytobeurbanrail’smaincompetitor,hasahistoricallyappallingsafetyrecordrelativetothenumberoftripsmade(BITrE2009).However,sincethecoefficientisnotstatisticallysignificant,inferencescannotbemadebasedontheestimateperformed.
Thelastexplanatoryvariableincludedintheestimationisthevehiclepriceindex.Thiswasexpectedtocapturethesubstitutioneffectofothermodes,andprivatevehicleusageinparticular,andthereforeenablethecross-priceelasticitytobecalculated.Thecoefficientisstatisticallysignificant,buthastheunexpectedsign.Thisfindingcanbeattributedtoapossiblelinearrelationshipbetweenthevehiclepriceandotherexplanatoryvariables,inparticularthefuelpriceindex.Itwasdecidedtoretainboththefuelpriceandthevehiclepricebecausei)bothofthemarehighlystatisticallysignificant,andii)becausedroppingeitherofthemwouldhavenegativelyaffectedthemodel’soverallperformance.
Itisnowpossibletoinvestigatetheshort-runelasticitiesofthepassengerraildemandandcomparethemwiththelong-runelasticitiesdiscussedabove.Short-runelasticitieshavebeenestimatedviaanEngleandGrangererrorcorrectionmodel,withtheresultsshowninTable4above.Thefareelasticityofdemandhastheexpectedsignandisstatisticallysignificantatthe10percentlevel.Inpracticalterms,thismeansthata1percentcutinthepriceleadstoa–0.032percentincreaseinthedemandforpassengerrailintheshortrun.Thisistwiceaslowasthatseenforthelong-runestimation.
In the short run, consumersmight be constrained by contracts or obligations (such asunemploymentoreducationandthelike).Acompleteresponsetoapricechangewillthereforenotberealizeduntilthelongrun.So,ingeneral,long-runpriceelasticitiesarelargerthantheshort-runelasticities.ThisisanoutcomesupportedbyFearnleyandBekken(2005),whosuggestthattheshort-rundemandresponseisonlyafractionofthetotallong-rundemandresponse.Accordingtothem,thereasonforthisisthat,intheshortrun,passengershavefeweroptionscomparedtothelongrun,wherepassengersareabletorespondmorecomprehensivelybychangingtheirjoblocation,dwellinglocation,orvehicleownershipstatus.Inasimilarstudy,owenandPhillips(1987)developedadynamicrailmodelforanalysingthedemandforinter-cityrailpatronageintheunitedKingdom.Theyobservedthattheshort-runelasticityof–0.69andthelong-runelasticityof–1.08meansthatthelong-runresponsestopricechangescouldbehigher.
Alltheothershort-runelasticities,suchasincomeelasticityandcrosspriceelasticities,arealsosmallerthanthelong-runelasticities,withtheexceptionofpopulationelasticity.Itwouldbeusefultoinvestigatewhyanincreaseinthepopulationleadstolargerresponseinthepassengerraildemandintheshortruncomparedtothelongrun.noteworthy,too,isthattheestimatefortheadjustmentparameterisnegativeandstatisticallysignificant.Thisconfirmsthelong-runrelationshipobtainedviatheEngleandGrangertwo-stepapproach.Themagnitudeoftheestimateisparticularlyinteresting,foritsuggeststhatlittlemorethan50percentofanydisequilibriumiscorrectedwithinayear.Whenitisrecalledthatlow-frequencyyearlydatawereused,thishighadjustmentemergesasnotparticularlysurprising.
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V.ConCludInGrEMArKS
TheEngleandGrangerTwo-Stepmethodwasusedtoestimatethelong-runelasticitiesofpassengerraildemandinMelbourne,whileanerrorcorrectionmodelwasemployedtoestimatetheshort-runelasticities.Fromthefindings,itcanbeconcludedthatpassengerraildemandishighlypriceinelastic.Indeed,thepassengerresponsetoafareincreaseisalmostnon-existent.Asisclearfromthemicroeconomicsliterature,thepriceelasticityofdemandismoreorlessinelasticwhenthepriceisalreadyperceivedaslow(Pindyckandrubinfeld2013).Ahigherelasticitymighthavebeenobservediffareincreaseshadbeenmorepronounced.Althoughexistingstudiesgenerallyagreewiththenotionofinelasticpassengerraildemand,themagnitudeofelasticityobservedinMelbourneisconsiderablysmallerthantheelasticityobservedinmostotherstudies(e.g.,Jonesandnichols1983,doiandAllen1986).So,ifitisassumedthatallothervariablesremainconstant,areductioninfarewouldnotleadtoariseintotalrevenue.onthecontrary,anincreaseinthefarewouldpotentiallyleadtoariseinthetotalrevenue.Itisquestionable,ofcourse,whethersuchapricerisewouldbepalatableatapoliticallevel.
Inadditiontothefare,thereareothersignificantvariablesthataffectthepassengerraildemand.City population (and that of the surrounding region) is themost significant andinfluentialoftheexplanatoryvariablesexamined.GiventhatMelbourne’spopulationissteadilyrising,onewouldthereforeexpect toseethaturbanraildemandwillcontinueto increaseinthecomingyears.Thecross-priceelasticityofthepassengerraildemandispositiveandstatisticallysignificant.Hence,thestudypresentsstatisticalevidencetosupportthepropositionthat, inMelbourne,passengerrailandprivatevehiclesaresubstitutes,at least toacertaindegree.likewise,thestudyfindsstatisticalsupporttosuggestthatahigherincomeleadstomorepassengerboardingsinMelbourne.
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