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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].

An EmPiricAl AnAlysis of thE dEtErminAnts of PAssEngEr rAil dEmAnd in mElbournE, AustrAliA

250

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

AlbErt WijEWEErA And michAEl chArlEs

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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).


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.


259

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.


260

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


261

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.


262

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.


263

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.

rEFErEnCES

BITrE(2009).AustralianTransportStatisticsYearbook2009,BureauofInfrastructure,TransportandregionalEconomics,Canberra.

BITrE(2011).Australian TransportStatisticsYearbook2011,BureauofInfrastructure,TransportandregionalEconomics,Canberra.

Breusch,T.S.(1978).TestingforAutocorrelationindynamiclinearModels,Australian Economic Papers.17:334–355.

Brooker,T.andS.Moore(2008).recentdevelopmentsinrailTraveldemandandTransitorienteddevelopment,ATrF2008:31stAustralianTransportresearchForumProceedings.Availableontheweb:http://www.atrf.info/papers/2008/index.aspx,accessed10october,2011.

Chen, n. (2007).Modelling demand for rail Transport with dynamic EconometricApproaches,International Review of Business Research Papers.3:85–96.

doi,M.andW.B.Allen(1986).ATimeSeriesAnalysisofMonthlyridershipforanurbanrailrapidTransitline,Transportation.13:257–269.

douglas,n.andG.Karpouzis(2009).AnExplorativeEconometricModelofSydneyMetropolitanrailPatronage,ATrF2009:32ndAustralianTransportresearchForumProceedings.Availableontheweb:http://www.patrec.org/web_docs/atrf/papers/2009/1799_paper195-douglas.pdf,accessed12december,2011).

Engle,r.F.andC.W.J.Granger(1987).CointegrationandErrorCorrection:representation,EstimationandTesting,Econometrica.55:251–276.


264

Farebrother,r.W.(1980).Thedurbin-WatsonTestforSerialCorrelationWhenThereisnoInterceptintheregression,Econometrica.48:1553–1563.

Fearnley,n.andJ.T.Bekken(2005).long-rundemandEffectsinTransport:Aliteraturereview’,InstituteofTransportEconomics(TØI)ofthenorwegianCentre forTransport research.Availableontheweb:http://www.toi.no/attach/a1274456r371471/Summary_802_05.pdf,accessed2February,2012).

Fowkes,A.S.andC.A.nash(1991).Analysing Demand for Rail Travel.Aldershot:AveburyPress.Fowkes,A.S.andC.A.nash,andA.E.Whiteing(1985).understandingTrendsinInter-cityrailTraffic

inGreatBritain,Transportation Planning and Technology.10:65–80.Gaymer,S.(2010).QuantifyingtheImpactofAttitudesonaShifttowardsPublicTransport,ATrF

2010:33rdAustralasianTransportresearchForumProceedings.Availableontheweb:http://www.atrf.info/papers/2008/index.aspx,accessed10october,2011.

Goodwin,P.B.(1976).HabitandHysteresisinModelChoice,Urban Studies.14:95–98.Granger,C.andP.newbold(1974).SpuriousregressionsinEconometrics,Journal of Econometrics.

2:111–120.Goulias,G.K.,r.M.Pendyala,andr.Kitamura(1990).PracticalMethodfortheEstimationofTrip

GenerationandTripChaining,universityofCaliforniaTransportCentre,reprintno.62,Berkeley,CA.

Jones,I.S.andA.J.nichols(1983).ThedemandforInter-cityrailTravelintheunitedKingdom,Journal of Transport Economics and Policy.17:133–153.

litman,T. (2010).Transport Elasticities:HowPrices andother FactorsAffectTravelBehaviour,VictoriaTransportPolicyInstitute.Availableontheweb:http://www.vtpi.org/elasticities.pdf,accessed20november,2011.

McGeehan,H. (1984). Forecastingdemand for Inter-urbanrailwayTravel in Ireland, Journal of Transport Economics and Policy.18:275–291.

odgers,J.F.andl.A.V.Schijndel(2011).ForecastingAnnualTrainBoardingsinMelbourneusingTimeSeriesdata,34th Australian Transport Research Forum.Availableontheweb:http://www.atrf11.unisa.edu.au/Assets/Papers/ATrF11_0109_final.pdf,accessed02February,2012.

owen,A.d.andG.d.A.Phillips(1987).TheCharacteristicsofrailwayPassengerdemand,Journal of Transport Economics and Policy.21:231–253.

Pindyck,r.andd.rubinfeld(2013).Microeconomics,eighthedition.newJersey:PearsonEducation.Stock,J.H.andM.W.Watson(2001)VectorAutoregressions,Journal of Economic Perspectives.15:

101–115.Voith,r.(1991).Thelong-runElasticityofCommuterraildemand,Journal of Urban Economics.

30:360–372.Wardman,W.(1997).Inter-urbanraildemand,ElasticitiesandCompetitioninGreatBritain:Evidence

fromdirectdemandModels,Logistics and Transportation Review.33:15–28.