gasoline prices in the U.S. Differential demand response to gasoline taxesand Resource and Energy Economics

ContentslistsavailableatScienceDirect

Resource and Energy Economics

jo u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / r e e

Differential demand response to gasoline taxes and gasoline prices in the U.S.

Silvia Tiezzi

, Stefano F. Verde

aDepartmentofEconomicsandStatistics,UniversityofSiena(I),Italy

bFlorenceSchoolofRegulation–Climate,EuropeanUniversityInstitute,Italy

a r t i c l e i n f o

Articlehistory:

Received23February2015

Receivedinrevisedform10February2016 Accepted14February2016

Availableonline22February2016

JELclassification:

C3 D1 H3 Q4 Keywords:

Gasolinetaxation Taxsignaleffect

Differentialdemandresponse

a b s t ra c t

This paper offers new evidence concerning the difference in consumers’ reactions to changes in gasoline taxes relative to market-inducedchangesingasolineprices.Usingmicrodatafrom the2007to2009roundsoftheU.S.ConsumerExpenditureSurvey, weestimateacompletesystemofdemandaugmentedwithinfor- mationongasolineexcisetaxes.Byrelyingonacompletesystem ofdemand,weareabletoestimateelasticitiesthattakebehavioral responsesintoaccount.Crucially,themodelallowsgasolinetaxes toaffectdemandintwodistinctways:throughrelativepricesand aslong-runpolicysignals.Differentincreasesingasolinetaxesare consideredforsimulation.A13.2¢/gallontaxincrease,correspond- ingtoa$15/tCO2carbontax,isfoundtocause,inthelongrun,a reductioningasolinedemandthatisaboutseventimesasbigasthat inducedbyanequalmarket-inducedpriceincrease.Thesamemea- sureofdifferentialdemandresponseisderivedfortaxincreases differentinsizeaswellasbyincomequintileandbyregion.We discusstheimplicationsofourfindingsforthedesignofcorrective taxationintheprivatetransportsector.

©2016ElsevierB.V.Allrightsreserved.

1. Introduction

Agrowingliteraturequestionsthestandardassumptioninpublicfinancethatconsumersrespond tocommoditytaxchangesin thesamewayastheydo topricechangescausedbymarketforces (Chetty,2009;Chettyetal.,2009;Finkelstein,2009;Congdonetal.,2009;GoldinandHomonoff,2013;

∗ Correspondingauthor.Tel.:+390577233029;fax:+390577232661.

E-mailaddresses:[email protected](S.Tiezzi),[email protected](S.F.Verde).

http://dx.doi.org/10.1016/j.reseneeco.2016.02.003 0928-7655/©2016ElsevierB.V.Allrightsreserved.

DavisandKilian,2011;Lietal.,2014;RiversandSchaufele,2015).Thesestudiesvaryinthegoods considered,theapproachesused,butalsointheexplanationsgivenforsuchdifference.Behavioral economicscontributionsfocusonthevisibility,orsalience,oftaxesasadeterminantofconsumer choice.Forexample,Finkelstein(2009)showsthatthedemandcurvefordrivingismoreinelastic whentollsarechargedelectronicallyascomparedtomanualcollection.Inasimilarvein,Chettyetal.

(2009)demonstratethatmakingsalestaxesmoresalientbyincludingtheminpostedpricesincreases demandresponsiveness.¹ Anotherperspectiveisthattaxpaymentsassuchmaybeperceivedasa greaterburdenthanequivalentnon-taxpayments, aphenomenoncalledtaxaversion(McCaffery andBaron,2006).²Butexplanationsmoreconsistentwithrationalbehaviorarealsoprovided.With referencetogasolinedemand,DavisandKilian(2011)andLietal.(2014)suggestthatdifferentdemand responsestochangesingasolinetaxesandtomarket-inducedchangesingasolinepricesmaybedue tothedifferenceinpersistencebetweenthetwotypesofvariations.Astaxchangesarelongerlasting, theyaremorelikelytoinfluencepriceexpectationsand,thereby,long-rundecisionsthathavean impactongasolineconsumption,suchaspurchasingamorefuel-efficientcar,changingtransport modeormovingclosertowork.Thesameauthors,however,allowthateffectsrelatedtosubjective perceptionsoftaxationmayalsoplayarole.Indeed,thesedifferentexplanationsarenotmutually exclusive.Theydescribemechanismsthatinsomemeasuremayallunderliethedifferencesobserved betweendemandresponsestotaxchangesandtomarket-inducedpricechanges.

ThepresentstudyspecificallydealswiththedifferentresponsesofU.S.consumerstochanges ingasolinetaxesandequalchangesingasolinepricescausedbymarketforces.Gasolinetaxesinthe U.S.areverylowcomparedtoothercountries,notablyEuropeanones(OECD,2013).Nonetheless,they generatemorerevenuethananyothercommoditytax,bothatStateandfederallevels.Inrecentyears, growingconcernsrelatedtodecliningfiscalrevenuesandhighCO2emissionsmeantthattheoption ofraisinggasolinetaxeshasreceivedincreasingconsiderationinthepublicpolicydebate.Raising gasolinetaxes,however,isanythingbutapopularmeasure,allthemoresoinaneconomyheavily dependentonprivatetransportation.Thus,thehypothesisthatconsumersmaybemoreresponsive togasolinetaxesthantogasolinepricesisofspecialinterest.Fromanenvironmentalstandpoint,it wouldimplythatataxincreasewouldinducelowergasolineuse–andhenceloweremissions–than standardpriceelasticities(estimatedwithoutdistinguishingbetweenthepricechangesinducedby taxationorbythemarket)wouldindicate.Ofcourse,itwouldalsomeanlessrevenuewouldberaised thanexpected.

Growingempiricalevidence showsthatindeed consumersresponddifferentlytogasolinetax changesascomparedtopricechangesunrelatedtotaxation(DavisandKilian,2011;Lietal.,2014;

RiversandSchaufele,2015).Thepresentpaperofferscorroboratingevidenceofthisphenomenon andcontributestotheliteratureinthreefundamentalrespects.First,theestimatedmodelpositsthat changesingasolinetaxesimpactongasolineconsumptionintwodistinctways.Taxesbeingaprice component,gasolinetaxchangesalterrelativepricesand,consequently,expenditureallocation.At thesametime,astaxesareafiscalpolicyinstrument,gasolinetaxchangesconstitutepolicysignals affectinglong-runconsumerdecisionswhichinturnimpactongasolineconsumption.Therefore,in thelongrun,theeffectivenessofgasolinetaxesinreducinggasolineuseisgivenbythesumofthetwo effects:thepriceeffectandthesignaleffect,respectively.Second,theanalysisiscarriedoutwithin acompletedemandsystemframework.Thismeansthatcomplementaritiesandsubstitutionrela- tionshipsamongthegoodsconsideredareaccountedfor,thusimprovingidentificationoftheeffects understudy.Third,wesimulatedifferentialdemandresponsesfordifferentmagnitudesofthetax- andpricechanges,aswellasacrossdifferentincomelevelsandU.S.regions.Notleast,weprovide newestimatesofdemandelasticitiesforabundleofenergygoods,includinggasoline.Onlyafew studiesongasolinedemandintheU.S.usemicro-foundeddemandsystemswhilealsotakingaccount ofhouseholdheterogeneity(Nicol,2003;Oladosu,2003;WestandWilliams,2004,2007).

1TverskyandKahneman(1974)areprecursorsofthisconceptualstrandinstressingthatconsumers,whenmakingdecisions, heavilyrelyoninformationthatisprominentorreadilyavailable.

2Experimentalevidenceoftaxaversionisgrowing(Kallbekkenetal.,2010,2011;BlaufusandMöhlmann,2014),butthere isnoempiricalevidenceofsuchaframingeffectbasedonchoice,ratherthanexperimental,data.

Therestofthepaperisorganizedasfollows.Section2illustratestheestimatedmodelandthe simulationofdemandresponsestotaxchangesandtoequalmarket-inducedpricechanges.Section 3describesthedata.Section4isdevotedtotheestimationresultsandsimulationresults.Section5 concludes.

2. Methodology

2.1. TheQAIDSmodel

ThefunctionalformchosenforourmodelistheQuadraticAlmostIdealDemandSystem(QAIDS, Banksetal.,1997),whichgeneralizesthepopularAIDS(DeatonandMuellbauer,1980a,b)byaddinga non-linearincometermtothebudgetshareequations.TheQAIDSallowsforflexibleincomeandprice responsesthatdependontheleveloftotalexpenditure,thusprovidingapracticalspecificationfor demandsacrossmanycommodities.Bycontrast,theAIDSimposesthatallgoodshaveEngelcurves varyinglinearlywiththelogoftotalexpenditure.Thismaybeareasonablespecificationfordemand systemswithfewcommodities(e.g.,WestandWilliams,2004,2007,intheliteraturerelevantto thispaper).However,empiricalstudieshaveoftenfoundnonlinearEngelcurves(Banksetal.,1997), especiallywhendealingwithratherdisaggregateddemandsystemsandbundlesofenergygoods,asin ourcase.Moreover,whenusingsurveydata,anadditionaladvantageofrank-threedemandsystems,³ suchastheQAIDS,isthattheyeasilyallowforhouseholdheterogeneity,thusenrichingthedemand modelandleavinglessspaceformisspecification(Nicol,2001;Labandeiraetal.,2006).

TheQAIDSspecificationisobtainedstartingfromthefollowingindirectutilityfunction:

lnV(p,y^h)=



lny^h−lnA(p)+G(p)



(1)

wherey^histhetotalexpenditureofhouseholdh;pisapricevector;thetermB(p)/[lny^h−lnA(p)]

istheinverseoftheindirectutilityfunctionofaPIGLOGdemandsystem;andA,B,andGarethree functionsofprices.

Specifically,lnA(p)hasaTranslogformandislinearhomogeneous;B(p)isaCobb–Douglasprice index,homogeneousofdegreezerointhepricevectorp;andG(p)=



iilnp_iishomogeneousof degreezerointhepricevectorp.ThecorrespondingsystemofMarshalliandemandfunctionsfor householdhandgoodsi=1,...,nexpressedastotalexpendituresharesisgivenby:

w^h_i =˛_i+



k

˛_ikd^h_k+



j

c_ij lnp_j+ˇ_iln





+ i

B(p)



ln





(2)

where˛ikarethecoefficientsofasetofdemographicvariablesenteringthemodelastranslating interceptsd^h=d_i^h,...,d^h_k.

Thetranslatingtechnique(PollakandWales,1992),aspecialcaseofthemodifyingfunctiontech- niqueproposedbyLewbel(1985),consistsinpositinganadditionalsetoflinear,auxiliaryrelationships betweenthe˛iintheshareequations(2)anddemographiccharacteristicsorotherconditioningvari- ables.Thedemandfunctions(2)satisfyintegrability,i.e.areconsistentwithutilitymaximization, ifthefollowingparametricrestrictionshold:



i˛i=1,



iˇi=



ic_ij=



ii=0,



i˛ik=0∀^k(adding up);



jc_ij=0(homogeneity);andc_ij=c_ji∀i,j(symmetry).ComparedtotheAIDS,theQAIDSaddsa quadraticterminthelogoftotalexpenditurewhichallowsfornonlinearchangesinthebudgetshares followingapriceorincomechange.Asimplewaytotestforthepresenceofsuchnonlineareffectsis totestthenullhypothesisthati=0.⁴

3I.e.demandmodelsdependingonthreeindependentpricefunctions.

4Weranalikelihoodratiotesttotestthehypothesisi=0.Thetestrejectedthenullhypothesis(teststatistic²(6)=713.6375, p-value=0.000),thuswechosetheQAIDSspecificationratherthantheAIDSone.

Todealwiththepresenceofzeroesinthedependentvariables,weusethetwo-stepestimator proposedbyShonkwilerandYen(1999).⁵Theprocedureinvolvesaprobitestimationinthefirststep andaselectivity-augmentedequationsysteminthesecondstep.⁶Thesystemofequations(2)isthus estimatedinthefollowingform(subscripthisomittedforeaseofnotation):

si=˚(z^_ii)wi(p,y,)+ıi(z_i^i)+i (3) wheres_iistheobservedexpenditureshareforgoodi;z_iisavectorofexogenousvariables;iisa parametervector;isavectorcontainingallparametersinthedemandsystem(˛i,˛ik,ˇi,iandc_ij);

i=s_i−E(s_i)is theheteroscedasticerrorterm; and˚arethestandardnormal probabilityden- sityfunction(pdf)anditscumulativedistributionfunction(cdf),respectively;andıiistheunknown coefficientofthecorrectionfactoroftheithequationinthesecondstep.

Thesystemofequations(3)isestimatedintwosteps:(i)MaximumLikelihood(ML)probitestimates ˆiofiareobtainedusingbinaryoutcomess_i=0ands_i>0;(ii)˚(z_i^ˆi)and˚(z^_iˆi)arecomputedfor alli,and,ı1,ı2,...,ınareestimatedintheaugmentedsystem(3)byML.Thistwo-stepestimator isconsistent,buttheerrorterms areheteroscedastic.Theestimatedelementsof thesecond-step conventionalcovariancematrixarethereforeinefficient.For thisreason,weempiricallycalculate thestandarderrorsoftheelasticitiesusingnonparametricbootstrapping(with500replications).The dependentvariableinthefirst-stepprobitestimatesisthebinaryoutcomedefinedbytheexpenditure ineachgood.Thepredictedpdfandcdffromthesixprobitequationsareincludedinthesecondstep oftheprocedure(seeYenetal.,2003,p.464).Theexogenousvariablesusedinthefirst-stepprobit estimatesarequarterlydisposableincome(alsoavailableintheCEsurvey)andasetofdemographic andgeographicvariables,whicharedescribedinthenextsection.Asforthesecond-stepestimates,we imposehomogeneityandsymmetrythroughparametricrestrictions,whileadding-upisaccomodated bydroppingoneoftheequations.EconomictheoryalsorequiresthatthematrixofSlutzkysubstitution effectsbenegativesemi-definite,aconditionthatishereimposedusingtheCholeskydecomposition.

Furthermore,toaddressconcernsofendogeneityoftotalexpenditure,weusequarterlydisposable incomeinsteadoftotalexpenditure.

DifferentiationofEq.(3)givesdemandelasticitiesforthefirstn−1goods,whiletheelasticities forthenthgoodarerecoveredexploitingtheCournotandEngelrestrictions(DeatonandMuellbauer, 1980a,b,p.16).Thecorrespondinguncompensated(U),compensated(C)andexpenditureelasticities forgoodiare,respectively:

e^U_ij = ij

wi −ıij (4)

e^C_ij=e^U_ij−eiwi (5)

ei= i

wi+1 (6)

where

ıijistheKroneckerdelta;

i=∂wi/∂lny=ˇi+_B(p)^2i

ln

A(p)

ij=∂wi/∂lnpj=cij−i





k˛ikdk+



jcijlnpj



ln

A(p)

.

5ShonkwilerandYen(1999),Yenetal.(2003),andYenandLin(2006)provideusefulliteraturereviewsonestimation proceduresforcensoreddemandsystems.

6Adifferenttwo-stepprocedure,developedbyHeienandWessells(1990),hasoftenbeenusedinapplieddemandanalysis toaddresstheproblemofestimatingsystemsofequationswithlimiteddependentvariables.WestandWilliams(2004,2007) aretwostudiesadoptingthisprocedure.However,asstatedbyShonkwilerandYen(1999,p.972),“theHeinandWessells procedureisbuiltuponasetofequationswhichdeviatefromtheunconditionalmeanexpressionfortheconventionalcensored dependentvariablespecification”.Instead,theprocedurebyShonkwilerandYen(1999)adoptedinthisstudyprovidesa consistenttwo-stepestimator.

2.2. Incorporatinggasolinetaxesinthedemandsystem

Whiletheliterature offersa few plausibleexplanationsfor observeddifferentialresponsesto changesingasolinetaxesandmarket-inducedchangesingasolineprices,suchargumentsdonot informthemodelspecification.BothLietal.(2014)andRiversandSchaufele(2015)entergasoline taxesandtax-exclusivegasolinepricesseparatelyinsingleequationmodelsforgasolinedemand.

However,noparticularroleoftaxesinrelationtoconsumerchoicesistestedorassumed.Thesameis trueforthestudybyDavisandKilian(2011),whoidentifythetaxeffectbyinstrumentingtax-inclusive gasolinepriceswithgasolinetaxes.Wefundamentallydepartfromtheliteratureinthisrespect,as wepositspecificrolesforgasolinetaxes.

Ourapproachhingesonthepresumptionofadualeffectofchangesingasolinetaxesongasoline demand:thepriceeffectandthesignaleffect.Thefirstisthechangeingasolinedemandcausedby thechangeinrelativepricesfollowingataxchange.Thepriceeffectofataxchangeondemandis perfectlyequivalenttothatofanequalchangeinthefinalprice.Thesecondeffectistheadditional change,oradjustment,ingasolinedemandcausedbylong-runconsumerdecisions,suchasbuyinga morefuel-efficientcarorchangingtransportmode,whichgasolinetaxchangesaspolicysignalsare expectedtoinfluence.Ingeneral,anytaxchangesshouldsignalthewillofthegovernmentconcerning thegivenpolicies.Gasolinetaxchanges,inparticular,areusuallystrongpolicysignals,astheytend tobeinfrequentandalsotoreceivemediaattention(e.g.,Lietal.,2014).Theyarethuslikelytoaffect theexpectationsoffuturegasolineprices.⁷

Accordingly,gasolinetaxesenterourmodelintwodistinctways.First,asapricecomponent,they areembeddedinthegasolinepriceindex.Second,togetherwiththeothertranslatingintercepts(thed’s in(2)),gasolinetaxes(specifiedincentspergallon,¢/gallon)enterthemodelexplicitlyasconditioning variablesadjustinglong-runequilibriumdemands(Pollak,1969).Thesameapproachhasbeenusedin otherdemandsystemstudiestoanalysetheeffectsofnon-price,non-incomevariablessuchasquality information(Jensenetal.,1993;Chernetal.,1995),innovation(Moroetal.,1996)andadvertising (Duffy,1995;BrownandLee,1997).Suchaspecificationimpliesthattaxesasapricecomponent donothaveaspecialrole(i.e.,theyarenodifferentfromotherpricecomponents)indetermining gasolinedemand.Thatis,whenchoosingthequantityofgasolinetoconsume,consumersareassumed toconsiderthelevelofthefinalprice,notitscomposition.Evenifdriverswerewellinformedabout theleveloftaxation,orhadagoodestimationofit,⁸itisdifficulttoimaginetheywouldrefillthe tankdependingonthecompositionofthepricetheypayandnotjustitslevel.Conversely,itseems tousplausiblethatgasolinetaxesaspolicysignalscaninfluencelong-rundecisionswhichinturn determinegasolinedemand.

2.3. Simulatingdemandresponsestotaxincreasesandtomarket-inducedpriceincreases

Themodelin(3),inclusiveofgasolinetaxesamongtheintercepts,canbeusedtoseparatelysimulate demandresponsestochangesingasolinetaxesandtomarket-inducedchangesingasolineprices.In otherterms,definingtax-inclusivegasolineprices(p^G)asthesumoftax-exclusiveprices(^G)and taxes(t^G),p^G=^G+t^G,distinctdemandresponsestot^Gandto^G,respectively,canbesimulated.

Inthefirstcase,theoveralllong-runimpactondemandisgivenbythesumofthepriceeffectand thesignaleffect,aspreviouslydefined.Inthesecond,onlythepriceeffectisinplay.Inparticular,we areinterestedincomparingtheresponsesingasolinedemandtot^Gandto^Gwhenthesetwo variationsarepositiveandequalinmagnitude.Insuchacase,theratioofthetwopredicteddemand variations,,measuresthelong-runeffectivenessofthetaxincreaseinreducinggasolinedemand relativetothatofanequalpriceincreasecausedbymarketforces.Iftheestimatedcoefficientoft^Gin

7Andersonetal.(2013)seemnottosupportthisparticularhypothesis,astheyfindthatconsumers’expectationsofgasoline pricesarerathersimplistic.However,arguablytheirtestwarrantsfurtherinvestigation.Itisnotinconceivablethattherespon- dentstothesurveyusedbytheauthorsexpressedtheirexpectationsongasolinepricesfiveyearsintothefutureconsidering onlymarketforcesandnottaxation.Thismaybethecasesincefuturetaxchangeswithinafive-yearhorizonarevirtually impossibletopredict.

8Postedpricesonbigsignsatgasolinestationsaretax-inclusive.

thegasolineequationisnegative(andstatisticallysignificant),thesignaleffectaddstothepriceeffect (alsonegative)and,ifso,t^Gturnsouttobemoreeffectivethan^Ginreducinggasolinedemand.

Thefirststepforthesimulationofthetax-increasescenarioisderivingthenewgasolinepricep^G_B resultingfromt^G.Atagivenpoint0,

p^G_B,0=p^G_A,0



1+t^G P^G_A,0



(7)

wherep^G_A,0istheinitialpriceindexandp^G_A,0istheinitial(tax-inclusive)priceinlevels.

Similarly,thenewlevelofthegasolinetaxiscomputedbyaddingt^Gtotheinitialtax,

t^G_B,0=t_A,0^G +t^G (8)

Feedingboththenewpriceandthenewtaxtotheestimatedmodel,thenewpredictedbudgetshares areobtained,includingtheoneforgasoline, ˆw^G_B,0.Finally,holdingtotalexpenditurey_A,0asfixed,the percentagechangeingasolinedemandisderivedas

ˆq^G₀ ˆq^G₀ =



wˆ_B,0^G yA,0

p^G_B,0− ˆw_A,0^G yA,0

p^G_A,0



/ ˆw_A,0^G yA,0

p^G_A,0 (9)

Thesameprocedureappliesforthesimulationofthemarket-inducedprice-increasescenario,with thefollowingtwodifferences:(a)t^Gisreplacedby^Gin(7)(althoughp^G_B,0isunchangedsincet^G and^G areequalinsize),and(b)t^G=0in(8),asnopolicysignalisactive.Theaboveisthen computedbycomparingtheresultingpercentagechangeingasolinedemandwiththatobtainedfor thetax-increasescenario,

0= ˆq^G₀/ˆq^G₀(t^G)

ˆq^G₀/ˆq^G₀(^G) (10)

Aresult0=nindicatesthat,inthelongrun,atthegivenpoint0,anincreaseingasolinetaxesis n-timesaseffectiveinreducinggasolinedemandasanequal-in-sizemarket-inducedpriceincrease.

3. Data

3.1. Householdbudgetshares,totalexpenditureanddemographics

TheU.S.ConsumerExpenditureSurvey(CEX)producedbytheBureauofLabourStatistics(BLS) isthemaindatasourceforourapplication.Weusemicrodataof thequarterlyInterviewSurvey (IS)fromthe2007,2008and2009roundsoftheCEX.⁹EachCEXroundhasfiveIScross-sections:

onepercalendarquarter,includingthefirstofthefollowingyear.¹⁰Wedrawon15cross-sections and about90,000observations, as each cross-section hasapproximately6000 observations.The model,however,isestimatedonasubsetof43,457observations,thoseforwhichinformationon theMetropolitanStatisticalArea(MSA)isgiven.Weusesuchasubsetbecausemorepricevariation isobtainedwithpriceindicesthatvarybyMSAthanwithState-levelindices.Theresultingsam- plespans39months,fromJanuary2007toMarch2010,and20MSA(seeTablesA1andA2,inthe Appendix).

In the IS, each household’s expenditures, which refer to thethree monthsbefore the inter- view, are classified into 60 consumption categories. Our system of demand only considers current expenditures (durables and occasional purchases are ignored), corresponding to 40 of the60 categories. Specifically, themodel is estimated for the following shares of total current expenditure:

9SeeChapter16oftheBLSHandbookofMethodsforadescriptionoftheCEX.

10TheISisapanelrotationsurvey.Eachpanelisinterviewedforfiveconsecutivequartersandthendroppedfromthesurvey andreplacedwithanewone.

Table1

Summarystatisticsoftotalcurrentexpenditureshares.

Variable Observations Mean Standarddeviation Coeff.ofvariation Min Max^a Zeros

Foodathome 43,457 22.8% 13.7% 0.60 0.0% 100.0%(15) 0.9%

Electricity 43,457 5.8% 5.3% 0.92 0.0% 100.0%(3) 8.5%

Naturalgas 43,457 2.9% 4.3% 1.50 0.0% 63.4% 38.5%

Otherhomefuels 43,457 0.7% 3.1% 4.59 0.0% 72.8% 91.2%

Motorfuels 43,457 9.1% 7.7% 0.84 0.0% 100.0%(2) 12.9%

Publictransport 43,457 2.0% 5.4% 2.63 0.0% 81.4% 73.4%

Allotherexpend. 43,457 56.7% 17.5% 0.31 0.0% 100.0%(128) 0.1%

aInbracketsisthenumberofobservationswith100%budgetshare.

Table2

Summarystatisticsofdemographicsandtotalcurrentexpenditure.

Variable Obs.(#) Mean Standarddeviation Min Max

Single 43,457 0.28 0.45 0 1

H&W 43,457 0.19 0.40 0 1

H&W,child(ren)<6 43,457 0.05 0.21 0 1

H&W,child(ren)<18 43,457 0.14 0.34 0 1

H&W,child(ren)>17 43,457 0.08 0.27 0 1

Otherhouseholds 43,457 0.26 0.44 0 1

Northeast 43,457 0.31 0.46 0 1

Midwest 43,457 0.20 0.40 0 1

South 43,457 0.24 0.43 0 1

West 43,457 0.26 0.44 0 1

Compositionincomeearners 43,457 0.23 0.42 0 1

Educationreferenceperson^a 43,457 5.44 1.82 1 9

Numberofcars 43,457 0.91 0.89 0 15

Totalcurrentexpenditure,$ 43,457 7178 7298 35 321,316

a1“Neverattendedschool”,2“1stthrough8thgrade”,3“9ththrough12thgrade”,4“Highschoolgraduate”,5“Somecollege, lessthancollegegraduate”,6“Associate’sdegree”,7“Bachelor’sdegree”,8“Master’sdegree”,9“Professional/Doctoratedegree”.

1)Foodathome 2)Electricity 3)Naturalgas 4)Otherhomefuels 5)Motorfuels(gasoline) 6)Publictransport 7)Allotherexpenditures

whereFoodathomeisthetotalexpendituresforfoodatgrocerystores(orotherfoodstores)and foodpreparedbytheconsumerunitontrips;Otherhomefuelsisthesumofexpendituresonfueloil, non-pipedgasandotherfuels(heatingfuels);Publictransportisthesumoffarespaidforallformsof publictransport,includingbuses,taxis,coaches,trains,ferriesandairlines.

Table1showsthesummarystatisticsoftheseexpendituresharesastheyappearinthesample.

Onaverage,expenditureonfoodconsumedorpreparedathomeaccountsfor22.8%oftotalcurrent expenditure,followedbymotorfuelsandelectricity,whichrepresent9.1%and5.8%,respectively;the residualcategory,Allotherexpenditures,represents56.7%oftotalcurrentexpenditure.Thecoefficients ofvariationindicatethatvariabilityisgreatestforOtherhomefuels,PublictransportandNaturalgas,in thatorder.Largeproportionsofhouseholdsreportedzeroexpenditurefortheseexpenditureaggre- gates(seethesharesinthelastcolumnofTable1).Consumptionoftherespectivegoodsorservices isindeedconditionaloncertainprerequisites,suchasthepossessionofspecificappliancesandhigh substitutabilitybetweenprivateandpublictransport,whichmaynotholdformanyhouseholds.

DifferenttypesofdemographiccharacteristicsarealsoextractedfromtheISdataset.Descriptive statisticsofthoseandoftotalcurrentexpenditurearereportedinTable2.Thehouseholdprofileis categorizedthroughsixdummyvariablesidentifyingthefollowingtypes:(a)Single;(b)Husband

3540455055

2007 2008 2009 2010

year

GA FL

DC

ME MD MN

NY WA WV

c$/gallon

Federal- plus state gasoline excise taxes

Fig.1. Gasolinetaxesinstates(insample)whererateschangedatleastonce.

andwife;(c)Husbandandwife,witholdestchildunder6;(d)Husbandandwife,witholdestchild under18;(e)Husbandandwife,witholdestchildover17;(f)Otherhouseholds.Geographiclocation isrenderedthroughfourdummyvariables,oneforeachoftheCensus-definedregions:Northeast, Midwest,SouthandWest.Adummyvariablebringsininformationonthecompositionofearnersin thehousehold:ittakesthevalue1ifboththereferencepersonandthespouseareincomeearners;0, otherwise.Acategoricalvariableclassifiestheeducationlevelofthereferencepersoninninelevels.

Moreover,themodelcontrolsforthenumberofcarsownedbythehousehold.

3.2. Priceindicesandgasolinetaxes

Insufficientpricevariationisacommonproblemwhenestimatingdemandmodelswithcross- sectionaldataandpriceindices.WeavoidthisissuebyusingmonthlyindicesvaryingbyMSA,which exhibitsufficienttimeandspatialvariation.¹¹Anotherpotentialproblemissomedegreeofinaccuracy inthecorrespondencebetweendemandandpricedata.Inourapplication,thisissuedoesnotarise becausepriceindices,alsoproducedbytheBLS,followthesameclassificationashouseholdexpen- diture.TheBLSusestheCEXtoperiodicallyrevisetheexpenditureweightsoftheConsumerPrice Index(CPI).Thereis,therefore,perfectcorrespondencebetweenISandCPIstatisticswithrespectto theexpenditureaggregates.IntheAppendix,TableA3showsthesummarystatisticsofpriceindices;

also,Fig.A1showstheevolutionovertimeofpriceindicesaveragedbyregion.

IntheU.S.,threelayersoftaxesapplytotheconsumptionofgasolineandautodiesel,namely, federaltaxes,Statetaxesandlocaltaxes.Thefederaltaxrateongasolineiscurrently18.4¢/gallonand hasnotchangedsince2006.¹²Bycontrast,StatetaxescandiffersignificantlyfromoneStatetoanother andtheyareoccasionallysubjecttorevisions.ThedatausedonthemonthlyratesofStatetaxesare publishedbytheFederationofTaxAdministrators(FTA).¹³Localtaxesarenotconsideredduetoa lackofinformation.InourestimatesgasolinetaxesareadjustedforinflationusingthenationalCPI.¹⁴

11Only,aspriceindicesbyMSAarenotavailableforOtherhomefuelsnorforPublictransport,nationallevelindicesareused inthesecases.

12Source:U.S.EnergyInformationAdministration.

13Tworatesareaddedup:“Statemotorgasolinetaxes”and“OtherStatetaxes”.

14Estimatesobtainedusingtaxesunadjustedforinflationwereverysimilar.

-30-20-1001020304050

2007 2008 2009 2010

year

Taxes Price index

Maine (ME)

-30-20-1001020304050

2007 2008 2009 2010

year

Taxes Price index

Washington (WA)

%

Volatility of gasoline taxes and gasoline prices: distance from mean

Fig.2.Gasolinetaxesandpriceswithinstates:MaineandWashington.

Fig.1showsthesumoffederalandStategasolinetaxesintheStateswherethetaxratechangedat leastonce(9Statesoutof23inthesample)overthemonthscoveredbythesample.Itisapparent thatchangesingasolinetaxesarerelativelyrareeventsandthatvariationbetweenStatesismuch greaterthanvariationwithinStates.Fig.2focusesonthetwoStateswheregasolinetaxesvariedmost intheyearsconsidered,namelyMaine(MA)andWashington(WA).¹⁵Inbothcases,taxesremain withinadistanceof5%fromthemeanoftheperiod,withoneexceptionforWashington,inearly 2007.Bycontrast,pricesroseashighasalmost50%abovethemeanoftheperiodandthenfellto aslowas30%belowthemean.Ingeneral,priceandtaxchangesveryclearlydifferbothinsizeand persistence.

4. Results

In this section, we first discuss estimation results concerning the demand system and its derived parameters (elasticities). We then focus on the simulation results of gasoline demand responsestothegivenincreasesingasolinetaxesandtoequalmarket-inducedincreasesingasoline prices.

4.1. Estimationresults:QAIDScoefficientsandelasticities

Theestimatedcoefficientsofthefirst-stepprobitmodelsunderShonkwilerandYen’sprocedure arereportedinTableA4,intheAppendix.Incomeissignificantinallprobitequationsandtakeson theexpectedpositivesign.Focusingontheequationforgasoline,comparedtolivingintheMidwest (thereferencelocation),livingintheNortheasthasanegativeimpactontheprobabilityofpurchasing gasoline,whereaslivingintheSouthorintheWesthasapositiveimpactontheprobabilityofbuying gasoline.Havingchildrenhasapositiveimpactontheprobabilityofbuyinggasolinecomparedtoa

15ThegraphsfortheotherStates,whicharesimilar,arenotshownforspacereasons.Theyareavailablefromtheauthors uponrequest.

Table3

EstimatedQAIDScoefficients.

Coefficient i=1 i=2 i=3 i=4 i=5 i=6

Food Electricity Naturalgas Otherfuels Gasoline Pub.transp.

˛i 0.197 0.043 0.046 0.049 0.108 0.090

0.002 0.002 0.002 0.011 0.001 0.010

ˇi −0.038 −0.004 −0.007 −0.008 −0.008 −0.006

0.001 0.001 0.002 0.002 0.001 0.002

i −0.004 −0.001 −0.001 −0.002 −0.001 −0.001

0.001 0.000 0.000 0.000 0.000 0.000

˛i,NE 0.030 −0.000 −0.006 0.045 0.008 −0.003

0.002 0.001 0.001 0.00 0.001 0.004

˛i,SO 0.020 0.034 −0.023 −0.005 0.015 0.005

0.002 0.001 0.001 0.009 0.001 0.004

˛i,WE 0.043 −0.008 −0.039 −0.009 0.019 0.019

0.002 0.001 0.001 0.011 0.001 0.004

˛i,NCAR −0.017 −0.001 0.001 0.009 0.009 −0.008

0.001 0.000 0.000 0.001 0.001 0.001

˛i,TWOE −0.004 −0.000 −0.000 0.015 0.010 0.003

0.001 0.001 0.001 0.004 0.001 0.003

˛i,N1 −0.039 −0.012 0.008 0.048 0.018 −0.011

0.003 0.002 0.001 0.005 0.002 0.004

˛i,N3 0.032 −0.004 −0.003 0.016 0.013 −0.015

0.003 0.001 0.002 0.006 0.001 0.005

˛i,N4 0.043 0.006 −0.002 −0.007 0.012 −0.009

0.002 0.001 0.001 0.004 0.001 0.004

˛i,N5 0.039 0.008 −0.004 −0.008 0.014 −0.014

0.002 0.001 0.001 0.005 0.001 0.004

˛i,N6 0.033 0.002 0.003 0.005 0.020 −0.015

0.002 0.001 0.001 0.004 0.001 0.003

˛i,EDUC −0.009 −0.003 −0.002 −0.004 −0.008 0.005

0.000 0.000 0.000 0.001 0.000 0.001

˛i,TAX −0.053 0.013 −0.013 0.176 −0.062 0.035

0.006 0.003 0.003 0.010 0.004 0.008

Loglikelihood 337.700

R² 0.19 0.13 0.10 0.07 0.12 0.03

Nobs 43,308

Note:Standarderrorsbelowcoefficients.BoldentriesindicaterejectionofH0:e=0atthe5%significancelevelforatwo-tailed test.

childlesscouple(thereferencehouseholdtype).Beingsinglehasinsteadanegativeimpactonthe probabilityofconsuminggasolinerelativetoachildlesscouple.

Table3reportstheresultsofsomeofthesecond-stepQAIDSparameters.¹⁶Heretoowefocus onthecoefficientsofthegasolinebudgetshareequation.Allgeographicdummyvariables(˛NE,˛SO,

˛WE)arestatisticallysignificant.Theirvalues indicatethat,relativetotheMidwest(thereference category),livingintheWesthasapositiveimpactongasolineconsumption,followedbytheSouthand theNortheast(indescendingorder).Asexpected,thenumberofcarsownedbyahousehold(˛NCAR) hasapositiveimpactongasolineconsumption.Thesameistrueforthepresenceoftwoincome earnersinthehousehold(˛TWOE),possiblyduetocumulativelylongerdistancesbetweenhomeand therespectiveworkplaces.Thedummyvariablesforhouseholddemographics(˛N1,˛N3,˛N4,˛N5,

˛N6)areallstatisticallysignificant.Thesizeofthecoefficients,whosevaluesarerelativetothatofthe

“Householdandwife”basecategory,seemstoreflectthenumberofhouseholdmembersoldenough toholdadrivinglicense.¹⁷Ahighereducationleveloftheheadofhousehold(˛EDUC)turnsouttohave anegativeimpactongasolineconsumption.Importantlyforouranalysis,thesameistrueforhigher gasolinetaxes(˛TAX),asonewouldexpect.

16Forspacereasons,pricecoefficientsandcdfcoefficientsarenotreported.Theseparametersareavailablefromtheauthors uponrequest.

17IntheU.S.,theminimumageforobtainingadrivinglicenseis16yearsold.

Table4

Estimatedbudgetshares,income-andcompensatedpriceelasticities.

j=1 j=2 j=3 j=4 j=5 j=6 j=7

Food Electricity Naturalgas Otherfuels Gasoline Pub.transp. Othergoods

wj 0.223 0.057 0.028 0.007 0.090 0.021 0.576

ej 0.860 0.942 0.855 0.919 0.938 0.929 1.080

0.004 0.007 0.009 0.023 0.006 0.021 0.002

e^C_1j −0.445 −0.139 0.076 −0.100 0.081 −0.008 0.535

0.037 0.012 0.009 0.022 0.015 0.027 0.050

e^C_2j −0.443 −0.876 0.058 −0.013 −0.359 −0.500 2.129

0.041 0.026 0.015 0.032 0.027 0.049 0.061

e^C_3j 0.504 0.089 −0.160 0.115 −0.296 −0.167 −0.086

0.045 0.022 0.037 0.034 0.031 0.041 0.072

e^C_4j −0.131 0.028 0.075 −0.477 0.207 0.118 0.180

0.055 0.025 0.019 0.165 0.040 0.038 0.123

e^C_5j 0.214 −0.220 −0.142 0.107 −0.435 −0.447 0.923

0.033 0.016 0.013 0.030 0.027 0.037 0.058

e^C_6j 0.003 −0.382 −0.113 0.087 −0.563 −0.385 1.353

0.080 0.041 0.023 0.038 0.051 0.145 0.134

e^C_7j 0.160 0.183 −0.002 0.021 0.104 0.142 −0.607

0.020 0.007 0.005 0.011 0.010 0.015 0.030

Note:Standarderrorsbelowcoefficients.BoldentriesindicaterejectionofH0:e=0atthe5%significancelevelforatwo-tailed test.

Concerningtheelasticities,compensatedown-andcross-priceelasticities(e^c_ij),alongwithincome elasticities(e_i)andthepredictedbudgetshares( ˆwi),areshowninTable4.Alloftheseareevaluated atthesamplemeansofexogenousvariables.Onaverage,18.2%oftotalcurrentoutlayisspenton energyrelatedproducts(thesumofthebudgetsharesofElectricity,Naturalgas,Otherhomefuels andGasoline),withGasolineonitsownmakingup9.0%oftotalcurrentexpenditure.Withregardto incomeelasticities,allthecommoditiesbutOthergoodsturnouttobenecessities.Ingeneral,allown- priceelasticitiesseemplausible,rangingbetween−0.876and−0.160,thesebeingtheelasticitiesfor ElectricityandNaturalgas,respectively.¹⁸ForGasoline,wefindanown-priceelasticityof−0.435,which isinlinewiththeU.S.literatureestimatingcompletesystemsofdemand(e.g.,WestandWilliams, 2004,2007;Nicol,2003;Oladosu,2003).Table5showssomerecentestimatesofown-priceelasticities ofU.S.householddemandforgasoline,distinguishingbetweendemandsystemsandsingleequation models.Singleequationstudiestendtofindlowerpriceelasticities.Thisisprobablyduetosystemsof demandaccountingforbehavioralresponsesafterapricechange,i.e.forhowhouseholdsreallocate theirbudgetafterachangeinoneoftheprices.Thenatureofthedatausedmayalsoplayarole, inasmuchastime-seriesdatatendtoyieldshort-runresponsesandcross-sectionstendtoyieldlong- runresponses,especiallyinthecaseofenergydemand(BaltagiandGriffin,1984;PesaranandSmith, 1995).

Cross-priceelasticitiesmeasurethedegreeofsubstitutionorcomplementaritybetweenthegoods considered.EachentryofTable4shows thepercentage changeinthequantitydemandedofthe goodslistedintherowsfollowinga1%changeinthepriceofthegoodslistedinthecolumns.For Gasoline,relationshipsofcomplementarityarisewithNaturalgas,ElectricityandPublicTransport.Inall thesecases,therelationshipissymmetric,meaninge^c_ijande^C_jihavethesamesign(e^C₃₅=−0.295and e^C₅₃=−0.142;e^C₂₅=−0.359ande^C₅₂=−0.220;e^C₆₅=−0.563ande^C₅₆=−0.447).Apossibleinterpre- tationofthesefindingsisthatsuchcomplementaritiesmaybetheconsequenceofabudgetconstraint tighteningfollowinganincreaseinthepriceofanecessity(gasoline).Thecomplementaritybetween

18Alberinietal.(2011)estimatethepriceandincomeelasticitiesofU.S.householddemandbothforelectricityandgas.For electricity,own-priceelasticitiesrangebetween−0.860and−0.667;forgas,between−0.693and−0.566.

Table5

RecentestimatesofpriceelasticitiesofU.S.householdgasolinedemand.

Study Ownpriceelasticityofgasolinedemand Datatype

Systemofdemandmodels

WestandWilliams(2007) −0.75(largest);−0.27(smallest) Pooledcross-section

WestandWilliams(2004) −0.46 Pooledcross-section

Nicol(2003) −0.59(largest);−0.02(smallest) Pooledcross-section

Oladosu(2003) −0.70(largest);−0.36(smallest) Pooledcross-section

Singleequationmodels

Lietal.(2014) −0.10 Panel

Sentenac-Chemin(2012) −0.30 Time-series

Su(2011) −0.39 Cross-section

DavisandKilian(2011) −0.46(largest);−0.19(smallest) Panel

ManzanandZerom(2010) −0.35 Pooledcross-section

Hughesetal.(2008) −0.07 Time-series

SmallandVanDender(2007) −0.43 Pooledcross-section

GasolineandPublictransport(e^C₆₅=−0.563)isperhapsevenmoresurprising.Onetentativeexplana- tionisthatanincreaseinthepriceofGasolinemakesPublictransportmoreexpensivetoo.¹⁹Wefind insteadsubstitutionbetweenOther(home)fuelsandGasoline(e₄₅=0.207).Noimmediateexplanation presentsitselfforthisresult,butthemeanbudgetshareforOther(home)fuelsisverysmall,0.7%, whichmakessuchsubstitutionnotacriticalfinding.Finally,wefindweaksubstitutionbetweenElec- tricityandNaturalgas(e^C₂₃=0.058).However,theelasticityisactuallyverysmall,implyingthata1%

increaseinthepriceofNaturalGaswouldcauseElectricitydemandtoincreaseby0.058%.

4.2. Simulationresults:demandresponsetotaxchangesandtomarket-inducedpriceschanges

Theestimationresultspresentedintheprevioussectionarehereusedtoquantifyandcompare responsesingasoline demandtogiven increasesin gasoline taxesand toequal market-induced increasesingasolineprices.Pairsoftax-andpriceincreasescenariosarethussimulatedintheway describedinSection2.3.Thecomparisonsoftherespectivepredictedvariationsingasolinedemand provideuswithasmanyvaluesfortheparameterdefinedin(10).Specifically,wederivefordiffer- enttaxincreasesandatdifferentpointsinoursample.Withaviewtoevaluatingthepotentialimpact ofcorrectivetaxation,gasolinetaxincreasesofdifferentmagnitudesareconsideredinrelationto differentlevelsofcarbontaxation.Forexample,a$15/tCO₂carbontaxtranslatesintoa13.2¢/gallon gasolinetax.²⁰SuchalevelofcarbontaxisinlinewiththeratesindicatedinrecentU.S.legislative proposalstoreducenationalCO2emissions.²¹Patternsofarethenderived,foragiven13.2¢/gallon taxincrease,bothacrossincomelevelsandacrossregions.

4.2.1. Differentialdemandresponsebysizeofthetaxincrease

Ourinvestigationofdifferentialdemandresponsesbeginswithexamininghowchangeswiththe sizeofthetaxincrease.Fivetaxincreasesareconsidered,namely5,13.2,25,35,and40¢/gallon,which correspondtocarbontaxlevelsrangingfrom5.7to45.5$/tCO2,approximately.Inallthescenarios, demandresponsesaresimulatedatthesamplemeanvaluesofthemodel’sindependentvariables.

TheresultsobtainedareillustratedthroughthefourgraphsinFig.3.

19TheaggregatePublicTransportisthesumofbothintra-cityexpenditureitemsandinter-cityexpenditureitemsassupplied intheCEXsurvey.Specifically,intra-cityexpenditureitemsinclude:intra-citymasstransitfares;taxifaresandlimousine services;schoolbus.Inter-cityexpenditureitemsincludedinouraggregateare:airlinefares;intercitybusfares;localtransport ontrips;taxifaresontrips;intercitytrainfares;shipfares.

20GivenaCO2emissionfactorforgasolineof19.44lbs/gallon.

21Forexample,the2009CongressbillRaiseWages,CutCarbonAct(H.R.2380,111thCongress)setaninitialrateof$15/tCO2, in2010.The2013ClimateProtectionAct(S.332,113thCongress)setaninitialrateof$20/tCO2.

0%

5%

10%

15%

20%

0 5 10 15 20 25 30 35 40 45

Price increase, %

Tax increase, cents per gallon

Increase of sample mean gasoline price by tax increase

0%

2%

4%

6%

8%

10%

0 10 20 30 40 50

Gasoline budget share, %

Tax increase, cents per gallon

Predicted gasoline budget shares by scenario and tax increase

tax-incr.

price-incr.

-50%

-40%

-30%

-20%

-10%

0%

0 10 20 30 40 50

Demand change, %

Tax increase, cents per gallon

Gasoline demand change by scenario and tax increase

tax-incr.

price-incr.

0 2 4 6 8

0 5 10 15 20 25 30 35 40 45

θ

Tax increase, cents per gallon

Differential demand response (θ) by tax increase

Fig.3.Simulationresults:priceincreases,budgetshares,demandchanges,anddifferentialdemandresponses().

ThecurveinthetopgraphofFig.3showsthepercentageincreaseinthesamplemeangasolineprice, whichis$2.7/gallon,asafunctionoftheconsideredgasolinetaxincrease:a13.2¢/gallontaxincrease correspondstoanincreaseinthesamplemeangasolinepriceof4.9%;a25¢taxincreasecorresponds toa9.3%priceincrease;etc.Thefivepairsofgasolinebudgetsharespredictedbythemodel,under thetaxincreasescenarioandunderthepriceincreasescenario,arepicturedinthesecondgraph.Asit canbeseen,thedifferencebetweenthetwobudgetsharesgetslargerwiththesizeofthetaxincrease.

Thecorrespondingvariationsingasolinedemand,derivedasper(9),areshowninthenextgraph.A market-inducedpriceincreaseof13.2¢/gallonisfoundtoreducegasolinedemandby2.5%.However, thesamepriceincreasebroughtinthroughtaxationreducesdemandby18%.Similarly,a25¢/gallon market-inducedpriceincreasereducesgasolinedemandby4.7%,whileanequal-in-sizetaxincrease reducesdemandbyasmuchas30%.Theratiosofeachpairofthesefiguresarethecorresponding, whosevaluesarereportedinthebottomgraphofFig.3.Anegativerelationshipisobservedbetween andthesizeofthetaxincrease.Thismeansthatthesignaleffect,whilestillbeinga(−1)multiple ofthepriceeffect,declinesinrelativetermswithincreasinglylargetaxhikes.Indeed,thisiswhatone wouldexpectassumingsufficientlylargepriceincreasemayalsoaffectlong-runconsumerdecisions suchasinvestmentinmoreefficientcars.Takingthebiggestandthesmallestofthetax-andprice increasesconsidered,isequalto7.3fora5¢/gallonincreaseanditisequalto5.7fora40¢/gallon increase.

Themagnitudeoftheseresultsislargerthanthatoftheresultsfoundintheliterature,which areobtainedusingdifferentdataandeconometricapproaches.Forexample,RiversandSchaufele (2015)findthattheBritishColumbiacarbontaxreducedgasolinedemandbyanamount4.1times greaterthanthatwhichanequalmarket-inducedpriceincreasewouldhavecaused.Thederived byDavisandKilian(2011)rangesbetween2.4and4.6,whileLietal.(2014)find isequalto3, bothinapplicationstoU.S.data.Thereasonforthisdiscrepancybetweenourresultsandthoseof theliteratureliesinthedifferenthorizonofthesimulateddemandresponses:itisthelongrunin ouranalysis,whileitistheshortrunintheotherstudies.Inthiscontext,thedifferencebetween thelong run and the shortrun consists in whetherthe dataand model specification allowfor effectsofgasolinetaxesonrelevantlong-runconsumerchoices,suchasbuyingamorefuel-efficient car,changingtransportmodeormovingclosertowork.Themodelcapturessuchlong-runeffects throughgasoline taxesasconditioningvariablesadjustinglong-runequilibrium demands(Pollak, 1969).

Aformalinvestigationofthemechanismsunderlyingdifferentialresponsestotaxchangesand market-induced price changes is beyond the scope of this study. However, it should be noted that our approach and interpretation are consistent with the findings of Li et al. (2014), who toourknowledgearetheonlyonesdirectlyaddressingthis question.Using U.S.household-level dataon vehicles purchased and miles travelled,the authorsconclude that (a) vehiclepurchase decisions,as reflected in miles per gallon, respond more strongly to tax changes than to price changes,and(b)nodifferentialeffectwithrespecttomilestravelledisfound.Theseresultssup- portourpresumptionthatspecificeffectsofgasolinetaxesunfoldmostly,ifnotentirely,inthelong run.

4.2.2. Differentialdemandresponsebyincomelevel

Incomelevelisalsoexpectedtoaffecthouseholds’demandresponsivenesstochangesingasoline taxes,especiallyinthelongrun.Thus,forthesametwoscenariosof13.2¢/gallontax-andmarket- inducedpriceincreases,wemeasureacrossfiveincomelevelscorrespondingtothequintilesofthe sampleincomedistribution.Toidentifyeffectsthatcanbeattributedonlytoincomedifferences,all independentvariablesotherthanincomeareheldatsamplemeanvalues.Theresultsobtainedare illustratedthroughthegraphsinFig.4.

Theuppergraphcontraststheestimatedelasticitiesofgasolinedemandwithrespecttothetax signal²²andtotheownprice(Eq.(4)),atmeanvaluesofthesampleincomequintiles.Thedifferences betweentheseelasticitiesunderlietheresultsobtainedinthesimulations.Withtheexceptionof

22eit=∂wi/∂lntw⁻¹_i where∂wi/∂lnt=˛it−ˇi



j˛jtlnpj+2i/B(p){ln[y/A(p)]}.