How to road price in a world with electric vehicles and government budget constraints

Transcription

1 Norwegian University of ife Sienes Shool of Eonois and Business How to road prie in a world with eletri vehiles and governent budget onstraints aal Brevik Wangsness Working apers No. 1/ 2018 ISSN:

2 How to road prie in a world with eletri vehiles and governent budget onstraints aal Brevik Wangsness 1 Institute of Transport Eonois Norwegian Centre for Transport Researh, Gaustadaleen 21, 0349 Oslo, Norway Aknowledgeents: We thank for valuable oents and insights given by Knut Einar Rosendahl, Kenneth øvold Rødseth, Geir Bjertnæs, Kine Josefine Aurland- Bredesen, Bjørn Gjerde Johansen and Stefan Tsharaktshiew. We are also grateful for finanial support by the Norwegian Researh Counil (NRC) and the Industry artners Co-inaning the NRC-projet (Energy Norway, Norwegian Water Resoures and Energy Diretorate, Ringeriks-Kraft AS, Norwegian ubli Roads Adinistration and Statkraft Energi AS). Abstrat The road transport arket has any arket iperfetions suh as loal and global pollution, aidents, noise and road wear. Eletri vehiles (EVs) avoid soe of these by not having any tailpipe CO2 eissions, but they still ontribute to external osts suh as ongestion. Our researh questions are: What haraterizes the set of seondbest road pries for internalizing external osts fro driving EVs and ICEVs when you also have distortionary labor taxes and binding governent budget onstraints? How are these pries affeted by distortions elsewhere in the eonoy? How does this seond-best priing fit with governent set goals of reduing CO2 eissions? This paper further develops an analytial fraework for assessing first- and seondbest road pries on vehile kiloeters, extending it to inlude EVs and externalities that vary geographially and by tie of day. Expressions for the optial road pries are derived analytially, and then solved nuerially. We find that optial road pries largely vary with external ost, giving high pries for driving in ities during peak hours, and relatively low pries for driving in rural areas. We also see that the road pries interations with the rest of the fisal syste have ipliations for deterining the optial set of road pries. However, the optial set of road pries leads to little or no redutions in arbon eissions with the urrently reoended soial ost of arbon estiates. This iplies that any required redution in CO2- eissions will require a shadow prie that exeeds the urrent soial ost estiate. 1 Corresponding author at: Institute of Transport Eonois Norwegian Centre for Transport Researh, Gaustadaleen 21, 0349 Oslo, Norway. Tel.: E-ail address: pbw@toi.no 1

3 1 Introdution The road transport arket is assoiated with any arket iperfetions suh as loal and global pollution, aidents, noise and road wear. Thune-arsen et al (2014) alulate external osts up to 30 billion NOK (Norwegian Kroner; 1 NOK = 0.11 ) per year fro road transport. This figure doesn t even ount the CO2-osts, even though road transport in 2015 ounted for 19% of national GHG-eissions (Ministry of inane, 2017). In addition to externalities fro road transport, ineffiienies in the eonoy also arise fro distortionary taxes elsewhere in the eonoy. Both the issues of externalities and ineffiienies in the tax syste have reently been put under new srutiny by governent assigned expert oittees publishing so-alled Norwegian Offiial Reports (Norges Offentlige Utredinger NOU), with NOU 2014:13 - Capital Taxation in an International Eonoy and NOU 2105:15 Green Tax Coission. ooking for ways to itigate these ineffiienies provide good otivation for this paper. The textbook eonois solution would be to find the set of taxes that provide the optial inentives for the eonoi agents in order to strike the appropriate balane of osts and benefits in the affeted arkets. Several papers derive suh solutions by finding the optial gasoline (or diesel) tax. It has for instane been done for the ases UK and USA (arry & Sall, 2005), and Gerany (Tsharaktshiew, 2014, 2015). However, there are several shortoings to orreting road transport arket failures through fuel taxation. irst of all, the external osts of driving vary a lot aording to where and when the driving takes plae. The fuel tax ould perhaps internalize soe average external ost, but would severely underprie driving in dense ities during peak hour, and overprie driving in rural areas. In addition to this lak of preision, the fuel tax ay inentivize ore energy effiieny, whih ay be benefiial with regards to arbon eissions and oil-reliane, but it ay lead to higher external osts as lower user osts per kiloeter ay indue ore driving. This has been pointed out in arry and Sall (2005) and arry, Evans, and Oates (2014). Seond, the possibility for fuel taxes to (ipreisely) orret for externalities and generate governent revenue is redued when EVs (eletri vehiles) are introdued. EVs have any of the sae externalities as ICEVs (internal obustion engine vehiles), but they annot be aptured by a gas tax, and it sees iplausible that they an tax EVs expliitly fro their eletriity harging. So are there better taxing instruents than the fuel tax, that both internalize external ost with ore preision and allow for the taxation of all ars? We hypothesize that well-designed road priing shee (e.g. through satellite-based road-harging) where the external osts based on tie, distane, plae and vehile harateristis will approxiate a first-best solution. Support for this an be found in the literature. Modelling analysis in the Netherlands fro Meurs, Haaijer, and Geurs (2013) suggested that suh a shee an be revenue neutral and have signifiant environental benefits opared to the urrent tax syste for ar-use and arownership. urtherore, analysis fro arry and Sall (2005) and May and Milne (2004) show that distane-based road priing an generate larger soial benefits than 2

4 e.g. fuel taxation and ordon tolling. Sall and Verhoef (2007) and de ala and indsey (2011) argue for the potential for high eonoi effiieny of distane-based road priing, and note that GS tehnology is suitable for suh a shee. de ala and indsey (2011) argue that a satellite-based road priing syste also has advantages over other tehnologies in ters of sale eonoies, potential for value added servies and revenue generation. A satellite based road priing shee is underway in Singapore (Ong & Siong, 2016), whih in tie ay provide experienes that will bring us loser to onfir or rejet our hypothesis. This paper will investigate how to itigate eonoi ineffiienies fro transport externalities and a distorted tax syste elsewhere in the eonoy through road priing: We establish the following researh questions: What haraterizes the set of seond-best road pries for internalizing external osts fro driving EVs and ICEVs when you also have distortionary labor taxes and binding governent budget onstraints? How are these pries affeted by distortions elsewhere in the eonoy? How does this seond-best priing fit with governent set goals of reduing CO2- eissions? We build on analytial fraework introdued in arry and Sall (2005). In arry and Sall (2005) they apply this fraework to derive the optial irst-best igou- Rasey tax for gasoline in the UK and the USA. This odel has also been used in in and rine (2009) and Antón-Sarabia and Hernández-Trillo (2014) to alulate the optial gasoline tax in California and Mexio, respetively. A odified version of the odel is used in arry (2009) and Tsharaktshiew (2015). arry (2009) uses it to alulate optial gasoline and diesel taxes, and Tsharaktshiew (2015) uses it to alulate optial gasoline taxes in the presene of diesel ars and EVs. It is a fairly siple odel that generates insight and intuition. We will to a large degree build on the version fro Tsharaktshiew (2015), as it ontains EV onsiderations. In this paper, we extend these odel exerises in several diensions in order to assess the optial seond-best tax for vehile-ks (hereafter, road pries). irst, we analyze optial road pries for both EVs and ICEVs, and not just a single poliy instruent like the gasoline tax, whih is ost oon in this literature. Seondly, we odel how externalities vary geographially and by tie of day, whih gives us a set of seond-best road pries that will differ aross four different stylized spatioteporal states, large ities during peak hours, large ities off-peak, sall ities and in rural areas. Third, we apply the odel to analyze the shadow prie for reahing a (setorspeifi) GHG eissions redutions target at least ost. The igovian solution of setting the orretive tax equal to arginal external ost (MEC) is well-known (see e.g., eran, Ma, MGlivray, & Coon, 2003). In this paper we plae ourselves in a seond-best world with binding budget onstraints and distortionary labor taxes, so we want to find seond-best road pries. This is related to the debate on how to orretly assess optial environental taxation in the presene of distortionary taxation elsewhere in the eonoy (see e.g., Bovenberg, 1999), and the arginal ost of publi funds (MC). The estiates of MC vary greatly between ountries, and within a ountry the MC will vary depending on whih soure the governent inreases or dereases its revenue fro. arry (2009) disusses how reyling gas tax revenues by lowering inoe taxes would have very large gains and thus inreasing the optial gas tax, but it ould be substantially lower 3

5 if the revenue would be spent on highway aintenane and expansion projets. In Norway, Bjertnæs (2015) find the that the MC is lose to 1.05 fro extrating revenue fro inoe tax and VAT, but lose to 1.2 fro extrating revenue fro apital tax and orporate tax. A review of the reent MC literature an be found in Holtsark and Bjertnæs (2015). A review of ore theoretial disussions about the MC an be found in Jaobs and de Mooij (2015). The authors here lai that the reason for having distorting taxes in the first plae, is for redistributive purposes, stressing the iportane of odelling this issue with heterogeneous agents. Hene, the distortions fro the non-lup-su tax syste are ounterated by the welfare value of the distribution effets, whih in optiu are equal on the argin, thus iplying a MC of one. They further lai that applying a MC higher than one ipliitly reveals a politial preferene for less inoe redistribution, sine the MC is larger than one only if the governent redistributes too uh initially. This paper does not take sides in this debate. Rather, it onstruts a odel that will allow for analysis of optial road pries in an eonoy with distortionary taxes. Any analyst or deision-aker using the odel, ay hoose to disallow arginal osts of publi funds above 1, perhaps as a part of a oral sensitivity analysis (see e.g., Mouter, 2016). The odel an thus serve a purpose as a flexible and pratial tool for analyzing osts and benefits of road pries under varying assuptions. The paper is onstruted as follows. In setion 2 we introdue the analytial fraework and derive expressions for optial road pries. The nuerial odelling, with paraeter values and senarios, is explained in Setion 3. The results fro the odelling exerise is given in Setion 4, while Setion 5 onludes. 2 Analytial fraework As explained above, an iportant goal of this paper is to ephasize the iportane of differentiating between spatioteporal states, as the estiated value of the externalities vary between these states. In order to avoid too ubersoe notation, we intend to solve the odel for a single state that ontains all of the externalities. Suh a state an be thought of as a large ity during peak hours. The nuerial odel will alulate solutions for all of the onsidered states. We will ake the siplifying assuption that agents and their ars are onstrained to stay within one state only. While this onstraint is fairly strit, it should still over the ain purpose eah agent has with her ar. We onsider a stati, losed eonoy odel with any agents. The representative agent has the following utility funtion: (1) U u(, v, X, l, T, E) i All variables are in per household ters. The utility funtion u (.) is quasi-onave and inreasing in arguents, kiloeters driven per vehile i, whih ould be any i i 4

6 passenger ar ake of any energy soure, be it gasoline, diesel or eletriity ; the vehile stok of ar type i 2, general onsuption X, and leisure l. In ontrast, utility is dereasing in arguents T, aggregate travel tie spent in ars whih, in addition to being an ativity with soe disutility (possibly), it ipliitly also lowers household utility by reduing tie available for work (and thus inoe for onsuption) and leisure. Utility is also dereasing in E, representing an index of environental externalities. or odelling purposes, we will assue that there are two types of vehiles. These are the average fossil-fueled ar and the average eletri ar, with subsripts and, respetively. This gives us a slightly sipler utility funtion: (2) U u(, v,, v, X, l, T, E) Total travel tie for a household depends on aggregate vehile kiloetrage M in a partiular area. We use bar notation to note eonoy wide variables pereived as exogenous by the travelers. Total travel tie for a household per period is (3) T t( M ) M, where t M i is (average) travel tie per kiloeter depending on aggregate vehile t ' 0 kiloetrage ( iplies tie delays due to an inrease in kiloetrage, and in our stylized odel, we assue that suh large traffi volues in one area only ours in the state ities during rush hours) and (4) M M M v v is aggregate distane traveled (vehile kiloetrage) by the representative household. E E E E M E M overs traffi The externality index ( ), ( ), ( ), ( ) i M M externalities steing fro energy onsuption E and E (inreasing in the use of fossil fuels and eletri power, and ) and fro vehile kiloetrage (inreasing in ). The partial derivatives of E then denote the various arginal external daages (in units) related to energy onsuption and vehile kiloetrage. We assue in this paper that there are no externalities assoiated with produing and onsuing eletriity for EVs E ( ) 0. With regards to greenhouse gases (GHGs), this assuption ay hold for ountries like Norway that are within the EU ETS-arket, as disussed in Bjertnæs (2016). However, whether this assuption holds for loal pollution ay deserve soe loser disussion, as highlighted in Holland, Mansur, Muller, and Yates (2016), but that will not take plae in this paper. M i v i E Mi 2 Vehile stok and orresponding vehile hoie per household is taken as a ontinuous variable beause we are averaging over a large nuber of households. 5

7 The assuption of no externalities assoiated with produing and onsuing eletriity will in any ase save spae in this paper 3. The onetary budget onstraint of the household equating expenditures for travel ativities and general onsuption with net inoe an be written as follows: (5) f ( f ) v p ( p) v X (1 ) w X where ( p ) denote the onsuer prie per unit of energy type i. All i i i onsuer pries ontain the pure fixed produer energy supply prie p i and the energy tax i. Energy intensity for ars, expressed in units per kiloeter, is denoted f for ICEVs and p for EVs. The lower the energy intensity, the ore energy effiient is the ar. The ters and denote the other distane dependent osts (repair, servie et.). Tolls are averaged to per-k road pries ( and ). The ters and denote the other osts of owning a ar, independent of distane. This would ainly be an annuity of the pre-tax purhase ost. These osts are assued to depend on energy effiieny, so they apture how inreasing energy effiieny oes at a ost (otherwise everyone would hoose the highest level of energy effiieny). As we will see later, the odel agent has an elastiity of fuel effiieny, and an thus respond to hanges in onsuer fuel osts by hoosing higher or lower fuel intensity. represents the su the annual ownership tax and the annuity of the purhase tax for the vehile type. The onsuer prie of the general onsuption goods basket is. ( f) ( p) i X X Monetary household net (labor) inoe is (1 ) w, where is the labor tax rate. inally, w is the hourly gross wage and is labor supply (hours per year). Total pretax labor inoe is denoted W. The relationship between fuel usage and energy intensity and k driven is given by: (6) f M f v (7) pm pv In addition to the onetary budget onstraint the individual is also subjet to the following tie onstraint (8) l t( M ) M 3 A version of the derivation of optial taxes where ore paraeters are inluded an be obtained fro the author on request. 6

8 This shows that the total tie endowent an be spent on labor, leisure and travel. The following governent budget onstraint equates fixed publi spending GOV with net tax revenue: (9) GOV v v w v v, On the prodution side, it is assued that goods are all produed under onstant returns to sale by opetitive firs using labor as the only priary input. Therefore, there are no pure eonoi profits, and produer pries are fixed. irs pay a gross wage of w equal to the onstant value arginal produt of labor. Optiization The household s optiization progra is to axiize the utility funtion Eq. (1) with respet to the hoie variables, v, f,, v, p, X and l subjet to the onetary budget onstraint Eq. (5) and tie onstraint Eq. (8). The per kiloeter travel tie, externalities, and taxes are treated as given by the household. We for the agrangian denoting as the agrange ultiplier of the household s (full eonoi) budget onstraint (the arginal utility of inoe) and obtain the firstorder onditions (OCs). We then use the OCs to obtain the household s indiret utility funtion, that yields axiized utility given pries, taxes and inoe, but also travel tie and externalities that are deterined by the aggregate level of driving. The governent s optiization progra then is to axiize the household s indiret utility funtion with respet to a set of paraeters,,,,,,, that are exogenous to the household (poliy te variables and tie and environental externalities). (10) V ( ) ax u(, v,, v, X, l, T, E), v, f,, v, p, X, l f ( f ) v p ( ) p v XX (1 ) w( l t( M ) M ) We will show the analytial exerise of deriving the optial tax on EV-k,. All the steps of the analytial derivations are given in the appendix. Here in the ain part of the paper, we only show the ost entral equations before we get to the analytial results. The analytial exerise starts by total differentiation of the household s indiret utility funtion with respet to. After soe algebra, and redefining the externality ters we get the following expression for the arginal welfare effet of the k-tax: 7

9 (11) 1 V d n n e e e e d d d d energy related externalities ongestion externalities kiloetrage related nonongestion externalities d d d d d d D dv d ktax revenue energy tax revenue D dv d diret / indiret tax revenue/os t fro labor tax revenue vehile stok dw d The paraeter e represents the MEC steing fro the onsuption of fossil n n fuel. Siilarly, the paraeters e, e, and e represents the MEC fro driving a k, with regards to ongestion, and k-based environental externalities fro ICEVs and EVs respetively. The paraeters and represent the per vehile annual tax revenue f and f. As we see, the EV-k tax auses a nuber of different hanges in Eq.(11), whih shows that the k-tax affets overall welfare through any different hannels. Derivation of the optial k-tax Setting the arginal welfare hange as displayed in Eq.(11) to zero and solving for yields * d d d n d n e e e e d d d (12) d d dv dv dw 1 D D d d d d d d d D After ore algebra, whih is shown in the Appendix, we finally get the final expression for the optial k-tax (13) D * C I C RR TI C RR ( TI ) C The first ter is the orretive oponent C n n (14) e e ( e e ) e. The paraeters and are paraeters for how onsuption of ICEV-ks and fossil fuel onsuption reat to the EV-k tax. Note that in our seond-best world we have to look at the total effet of the road prie, and not siply equate the orretive tax to MEC. 8

10 The seond ter in (13) is the revenue reyling oponent (15) p RR M The ter onsists of the arginal ost of publi funds, is the own- revenue fro arginally inreasing the EV-k tax. The paraeter prie elastiity of EV-ks.., ties the net tax M The third oponent in (13) is the tax interation oponent (not inluding the ongestion feedbak oponent): (16) p ( ) M 1 ( TI ) MI I 1 p D D The fourth oponent is the ongestion feedbak oponent: 1 C (17) 1 (1 ) e 1 I MI The previously unentioned paraeters in these expressions are, MI and MI, the opensated and unopensated inoe elastiities for vehile ks, I, the inoe elastiity of labor supply, and, the opensated elastiity of labor supply. represents the arginal ost of publi funds, whih is defined as (18) w W w 1 (1 ) (1 ) It represents the effiieny ost of raising an extra NOK of revenue through labor taxes (or the effiieny gain of reyling one NOK through uts in labor taxes). 0 is the (unopensated) labor supply elastiity. The nuerator in Eq. (18) reflets the effiieny ost fro an inreental inrease in the labor tax whereas the denoinator is the arginal hange in tax revenue. We have that 0 as a onsequene of 0 and 1 (1 ). The latter iplies that is not so large that we find ourselves beyond the peak of the affer urve, i.e. arginal revenue is positive. The oponents of the optial tax is thoroughly desribed in Tsharaktshiew (2014, 2015), but we will give brief explanation here. The orretive tax oponent aounts for the externalities assoiated with driving an EV-k. It inludes the k-related externalities related to ongestion (sae for all vehiles), and other externalities like pollution, noise and aident risk (differs 9

11 between EVs and ICEVs). Note that the tax on EV-ks ay indue ore driving of ICEVs, whih ontributes to reduing the level of the orretive oponent. The seond oponent is the revenue reyling effet. It represents the effiieny gain fro using additional EV-k tax revenue to ut the distortionary labor tax and so to inrease the effiieny of the tax syste. The effet is equal to the arginal ost of publi funds ties the arginal net EV-k tax revenue to the governent fro raising the EV-k tax. The third oponent is the tax interation effet. It aounts for the effiieny loss in the labor arket fro the higher tax on ks. On one hand, higher taxes redue the real household wage and has a disouraging effet on labor supply. On the other hand, it also inludes the inoe effet fro a higher k-tax on labor supply. The further ters reflet the interation of the EV-k tax with the other (seondary) tax distorted arkets, e.g., the eletriity arket. The fourth oponent is the ongestion feedbak effet. Raising the ost of travel through k-taxes ay redue vehile kiloetrage and ongestion. This indues a feedbak effet on labor supply, leading workers to alloate their tie towards less tie spent on travel and ore spent on labor or leisure. Beause labor is taxed, this feedbak effet is welfare iproving and eteris paribus auses an upward adjustent of the optial k tax. When we present our nuerial results, this oponent will be inluded in the tax interation oponent where relevant, i.e. in the state large ities during peak hours. We solve the odel the exat sae way for * that look like the following:, and obtain analogous expressions (19) * C I C RR TI C RR ( TI ) C With the orretive oponent e e f e e e, C n n (20) ( ) the revenue reyling oponent (21) f RR M the tax interation oponent (not inluding the ongestion feedbak oponent) 4, 4 This expression has a ter that is not present for deterining road pries for EVs, naely d f d M d. This ter is related to indued hanges in fuel effiieny. 10

12 ( TI ) (22) 1 and finally the ongestion feedbak oponent, f ( ) MI I M 1, f D D 1 C (23) 1 (1 ) e 1 The expressions for I MI irror those for, and the applied paraeters are given the sae sybol, but with subsript, and illustrate the ehaniss for the agents responses to a hange in the tax on ICEV-ks. untional relationships araeters like d quantify our assuptions on how households d respond to hanges in tax paraeters. These paraeters an be expressed in ters of M M M elastiities, e.g.,, where is the ross-prie elastiity for ICEV-k, M M M M with respet to prie hange for EV-k. urtherore, the diret response in pervehile-deand for vehile-ks when the EV-k tax hanges an be expressed through * 0 0 M M and * M 0 0,, where we assue onstant elastiity of deand. This is oon pratie in these kinds of analyses of optial priing in the transport setor, see e.g., arry and Sall (2005), arry (2009) and Tsharaktshiew (2014, 2015). We have siilar expressions for responses in vehile stok. The paraeter budget equation, Eq. (5). The paraeters is the pre-tax ost of a k, p 0 and 0 are the per-vehile, as seen in the kiloetrage in the initial equilibriu. The levels in the new equilibriu depends on the road pries in the new equilibriu. If e.g. does not differ fro, then * there will be no hange in the new equilibriu, as would equal 0. As we see fro the equations that oprise the optial taxes, the tax levels are on both the left-hand and the right-hand side of the equation, so we ust solve it nuerially. In addition, we want to solve the odel for road pries for both ICEVs and EVs, and for all the stylized states siultaneously. The next step involves inserting paraeter values into the odel and alulate the optial tax rates. 0 11

13 3 Nuerial odel desription and paraeter values In this setion, we explain the senario for alulating optial levels of taxes for EVks and ICEV-ks. The thought experient for the baseline alulation an be suarized as: 1) We assue the optial k taxes are ipleented in the tie of writing in ) There is a ediu-run adjustent fro agents towards ) Based on these ediu-run adjustents, we get values for the optial taxes in Our alulations ignore dynais in the adjustents, and we siply alulate the tax rates for 2020 with 2020-values on externalities (i.e. values applied today are realprie adjusted for future years, as is reoended pratie in ost-benefit analysis onduted in Norway, see e.g., NOU 2012:16 (2012)). All onetary values are given in 2015-pries. Applied values for vehile ks and levels of labor and eletriity taxes are also based on 2015 values. Ideally, one would want to have individual tax levels for the hundreds of ar types, based on the ar types individual harateristis. In our odel, we ake the drasti siplifiation of working with two types of ar, an ICEV and an EV. The nuerial values applied to the ICEVs are based on a weighted average of diesel and gasoline powered vehiles, weighted by their estiated aggregate vehile ks in , based on the BIG-odel 6 at the Institute of Transport Eonois. In the theoretial fraework we have taxes on labor, fossil fuel, eletriity, vehile purhase and ownership taxes, ICEV-k and EV-k. In the nuerial odel, the urrent tax on fossil fuels, along with average tolls in the various states, are onverted to a orresponding tax on ICEV-ks. When we optiize road pries, drivers will fae a prie that strikes a balane between osts and benefits fro itigating transport externalities and distortions in the labor arket. That prie will give the drivers inentives to eonoize their kiloetrage appropriately. However, in the orretive oponent of the road pries we find both the distane dependent external osts (e.g., aident risk, loal pollution, noise et.) and the external ost fro fuel usage, whih in this analysis is derived fro the soial ost of CO2. This ost oponent gives not only inentives to eonoize kiloetrage but also fuel use. Changes in the external ost of fuel use would indue hanges to both kiloeters driven and fuel effiieny. It an be thought of as if taxes on fuel have been reoved fro the pup, but inorporated into the road prie. arts of the road prie for a partiular ar would then differ aording to the fuel intensity of that ar, and hene ontain an ipliit fuel tax. This odel tehniality beoes apparently useful when we alulate the shadow prie of reahing a GHG eissions redution target at least ost using this road priing shee. The governent budget onstraint ust hold in equilibriu. The su of hanges fro optiized k-tax revenue (that in the initial ondition ontains urrent fuel taxes and tolls), and subsequent hanges in eletriity, vehile purhase and 5 Gasoline had 59 % of the ICEV ks travelled in 2015 and diesel had 41% 6 The arony is derived fro bilgenerasjonsodell, eaning ar ohort odel 12

14 ownership taxes, ust be offset by hanges in the labor tax. This akes the equilibriu labor tax rate endogenous. The senario an ii a refor where fuel taxes and tolls are shifted over to road pries, whih then are optiized, taking into aount that labor tax rates hange to aintain revenue neutrality. A situation where the optial road pries lead to a redution in labor tax rates, orresponds to a net shift in tax burden fro labor inoe to transport. With regards to transport variables, the representative household in the odel is onsidered as a weighted average of values for the three different geographial areas we onsider. The areas are large ities (larger than inhabitants), sall ities (between and inhabitants) and rural areas (less than inhabitants), whih ontains 28%, 32% and 40% of Norwegian households, respetively. This lassifiation of areas orresponds to the one done for external osts of road transport in Thune-arsen, Veisten, Rødseth, and Klæboe (2014). The applied paraeter values for the odel are given in Table 1. 13

15 Table 1: araeter values for baseline alulations Desription Nae of sybol Value Diension Soures used Transport and other data Initial "fossil" fuel intensity EV el intensity (average of winter and suer) 0 f 0 p l/k Institute of Transport Eonois, BIG-odel 0.25 kwh/k Institute of Transport Eonois, BIG-odel Initial vehile kiloetrage per ar (EV & ICEV), large ities, peak (lp) Initial vehile kiloetrage per ar (EV & ICEV), large ities, off-peak (lo) 0 ilp 0 ilo Initial vehile kiloetrage per ar (EV & ICEV), sall ities (s) 0 is Initial vehile kiloetrage per ar (EV & ICEV), rural (r) 0 ir ICEVs per household, large ities (l) 0 v l ICEVs per household, sall ities (s) 0 v s ICEVs per household, rural (r) 0 v r EVs per household, large ities (l) 0 v l EVs per household, sall ities (s) 0 v s EVs per household, rural (r) 0 v r 940 k Institute of Transport Eonois, Thune-arsen et al. (2014) and Statistis Norway (StatBank) k k k [These ks per ar per area nubers are weighted aording to areas share of households. In su, this results in a national average of k per ar] ars Statistis Norway (StatBank: link) ars ars ars ars ars [These ars per household per area nubers are weighted aording to areas share of households. In su, this results in on average ICEVs per household and EVs per household, iplying on average ars in total per Norwegian household] Car life span 16.5 years ridstrø, Østli, and Johansen (2016) 14

16 ries and taxes "ossil fuel" produer prie Corresponding initial fossil-k produer prie Other private k osts for ICEVs Eletriity onsuer prie (inludes VAT and eletriity tax) Corresponding EV-k prie (inludes VAT and eletriity tax) Other private k osts for EVs Initial fossil fuel tax Corresponding initial fossil-k tax Eletriity tax per kwh p p M p p M NOK/l Statistis Norway (StatBank: link) 0.54 NOK/k 1.32 NOK/k Vegdirektoratet (2015) 0.81 NOK/kWh Statistis Norway (StatBank: link) 0.20 NOK/k 1.13 NOK/k Vegdirektoratet (2015), sartepenger.no 6.58 NOK/l inansdeparteentet (2016) 0.52 NOK/k 0.18 NOK/kWh inansdeparteentet (2016) Corresponding eletriity tax EVs pay per k NOK/k Average toll, large ities 0.47 NOK/k Calulated fro National ubli Road Adinistration s Average toll, sall ities 0.25 NOK/k toll statistis and Statistis Norway s personal transport statistis. Users pay per passing of tolling station, but Average toll, rural 0.11 NOK/k the nubers have been noralized to per k. urhase tax + VAT for ICEV NOK Based on disaggregate ar sales data provided by urhase tax + VAT for EV 0 NOK Norwegian Road federation (OV). Annual ownership tax for ICEV 3565 NOK inansdeparteentet (2016) 15

17 Annual ownership tax for EV 435 NOK Real disount rate for purhase tax annuity 2% Risk-free oponent in real disount rate applied in CBA (NOU 2012:16, 2012). In addition, ar loans are usually given at 4%-5% and Norwegian inflation target is 2.5%. Average arginal labor tax rate (benhark) 40% Bjertnæs (2015) Behavioral responses Own-prie elastiity of fossil intensity Own-prie elastiity of ICEV kiloetrage Own-prie elastiity of EV kiloetrage Own-prie elastiity of ICEV ownership wrt osts per k Own-prie elastiity of EV ownership wrt osts per k Cross-prie elastiity of EV kiloetrage i.e. how ICEV ownership inreases when the ost of EV- k inreases Cross-prie elastiity of ICEV kiloetrage i.e. how EV ownership inreases when the ost of ICEV- k inreases Inoe elastiity of vehile kiloetrage Copensated inoe elastiity of vehile kiloetrage Inoe elastiity of labor supply f M M v M v M v M v M MI MI I Norsk etroleusinstitutt (2011) Steinsland, Østli, and ridstrø (2016) Steinsland et al. (2016) Boug, Dyvi, Johansen, and Naug (2002) Institute of Transport Eonois, BIG-odel Institute of Transport Eonois, BIG-odel Steinsland and Madslien (2007) Weighting estiates fro West and Willias III (2007) on average Norwegian household deographis Correspondene with Thor-Olav Thoresen on OTTEodel at Statistis Norway, douented in Dagsvik, Jia, Kornstad, and Thoresen (2007) 16

18 abor supply elastiity (unopensated) abor supply elastiity (opensated) Dagsvik et al. (2007) I External osts of ars Kiloetrage related external ongestion osts, initially, large ities, peak Calibrated ongestion funtion paraeter arginal ongestion ost per k as a linear funtion of total vehile k driving in peak hours. This an be onsidered a sub-oponent of e Kiloetrage related external non-ongestion osts ICEV, large ities, peak (lp) e n e lp NOK/vk NOK/vk Kiloetrage related external non-ongestion osts EV, large ities, peak (lp) n e lp NOK/vk Kiloetrage related external non-ongestion osts ICEV, large ities, off-peak (lo) e n lo NOK/vk Thune-arsen et al. (2014) Kiloetrage related external non-ongestion osts EV, large ities, offpeak (lo) e n lo NOK/vk Kiloetrage related external non-ongestion osts ICEV, sall ities (s) e n s NOK/vk Kiloetrage related external non-ongestion osts EV, sall ities (s) e n s NOK/vk Kiloetrage related external non-ongestion osts fossil ar, rural (r) e n r NOK/vk Kiloetrage related external non-ongestion osts EV, rural (r) e n r NOK/vk ossil fuel related external osts e NOK/l Based on reoended soial ost of arbon (420 NOK/ton) fro NOU 2015:15 (2016) 17

19 The values for the external osts fro driving are all taken fro Thune-arsen et al. (2014). The external non-ongestion osts onsist of external ost estiates for loal pollution, noise, aident risk, road wear and winter anageent. In Table 1 it is lear to see that the external osts vary signifiantly between the states ity during peak hours, ity in off-peak hours and rural areas. 18

20 4 Model results Here we present the alulations of the seond-best distane-based road pries, differentiated by vehile and spatioteporal state. Main results are given in Table 2. Baseline seond-best road priing The odel alulates road pries that vary signifiantly between states, largely refleting the variation in external osts. This an be seen in Table 2. The highest prie is plaed on driving an ICEV in a large ity during peak hours, ainly beause of the relatively high external ongestion osts. However, the arginal external ongestion osts are lower in the new equilibriu than in the initial situation, as the transport volues during peak hour have been redued signifiantly, both for EVs and ICEVs. It is still worth noting that the tax per k is ore than five tie higher than the urrent su of average toll and fuel tax per k during peak hour. The lowest prie is plaed on driving an ICEV in rural areas. The tax per k is atually 60% lower in the new equilibriu, than the su of average toll and fuel tax per k was initially. It is also worth noting that the optial road prie for ICEVs in rural areas is atually lower than for EVs in the orresponding area. This is the ase for driving in sall ities as well. This brings us over to another iportant observation fro Table 2. In all ases there is a arkup fro the revenue reyling oponent, showing the effiieny gain fro replaing revenue fro labor taxation with revenue fro road priing. We also see that the tax interation oponent lowers the final road pries. This is beause of the negative ipat the total hanges in road pries and labor taxes have on labor supply. The ipat on other tax revenue leads to higher total road prie levels. The exeption is for ICEV driving in rural areas, sall ities and ities off peak, as the negative ipat on other tax revenue beoes quite large. Inentivizing EV driving over ICEV driving in these states will result in lower tax revenues fro e.g. purhase taxes, with inadequate substitution fro EV road pries. This is why the ipat on other tax revenue drives the EV road prie upwards. This shows soe of the endogeneity between the road pries, and how they affet the size of eah other s tax interation oponent whih again will affet the revenue reyling oponent and the total road prie level. or all ases the final road prie is larger than the orretive oponent that targets the internalization of externalities, with the exeption of driving ICEV in rural areas. or this ase the tax interation oponent has a larger ipat on the final prie than the revenue reyling oponent. Table 2: Results fro odel alulations of seond-best road pries in Road pries are given in NOK per k for a given state. Vehile type and state Corretive oponent own vehile Corretive oponent indiret ipat Revenue reyling oponent Tax interation oponent labor arket and ongestion 7 Tax interation oponent other taxes Total Initial (tolls and fuel tax per k) 7 Inluding ongestion feedbak where relevant, i.e. in the state City peak hours 19

21 EV ities peak hours ICEV ities peak hours EV ities off-peak ICEV ities off-peak EV sall ities ICEV sall ities EV rural areas ICEV rural areas In all the states, the optial k-taxes are higher than their urrent levels for EVs. However, for ICEVs the optial k-taxes are lower than urrent levels of fuel taxes and tolls, with the exeption of large ities. It sees that ICEVs are taxed higher than optial in ost parts of the ountry. Hene, the optial ar travel volues are higher than urrent volues in these areas. This results in total 0.2% ore vehile k travelled per household, fro to k per year, in spite of a large redution in ity driving. The odel also finds 0.5% lower rates of average vehile ownership, fro to ars per household. The ipats differ greatly between states. In large ities, EV ownership rates inrease by 36% as the ross-prie effet fro the road prie on ICEVs doinates the own-prie effet for EVs. At the sae tie ownership rates of ICEVs drop by 8% in large ities. or the rest of the ountry, the effets go in the opposite diretion. On average, EV ownership rates inrease by about 11%, but the orresponding rates for ICEVs fall by 0.8%. Beause the odel results indiate over taxation of ICEVs in ost parts of the ountry in the initial situation, the net revenue fro the road priing shee is lower than the initial revenue. This indiates that in optiu, it is better with a slightly higher labor tax burden than a higher tax burden fro road priing. The total inrease in labor taxes orresponds to an inrease in the average arginal tax rate fro 40% to 40.1%. In order to alulate the welfare effet of this road priing shee, we nuerially integrate the arginal welfare ipat, shown in eq. (11) and rewritten in eq. (84). When nuerially integrating the arginal welfare effet for all the road pries, we end up with an annual welfare gain of 255 NOK (or about 32 per household). or oparison, Tsharaktshiew (2014) finds a welfare gain of 13 per household when optiizing gasoline taxation. What are the GHG eission ipliations when suh values are applied in the odel and seond-best road pries are alulated? As ephasized in Setion 3, the applied soial ost of arbon (SCC) of 420 NOK per ton is a paraeter in the orretive 20

22 oponent in Eq. (20), that gives a diret inentive to eonoize fuel, while the road prie as a whole gives inentive to eonoize kiloetrage. It is equivalent to oving the fuel tax fro the pup, but inorporating it into the road priing that would differ with the vehile s fuel intensity. The SCC is lower than the urrent tax on fuel, so fuel effiieny inentives beoe weaker in the new optiized equilibriu. This leads to agents hoosing about 5% lower average fuel effiieny. With alost unhanged travel deand in the nation as a whole, the annual GHG eissions fro transport inreases by 5.1% in optiu. It is lear that reduing GHG eissions through an optial road priing shee, iplies that the arbon prie would have to be higher than the reoended values. Optial road pries and a shadow prie on CO 2 The Norwegian governent has a goal to redue GHG-eissions fro 1990-levels by 40% within By 2016, annual eissions were about 3% higher than in or the road transport setor, it was even worse, where the eissions were about 28% higher 8. In our next odelling exerise, we onsider a binding eission redution requireent for personal road transport fro 2015 levels (the initial situation in the odel) to 2020, about when the new equilibriu following the poliy hange would be reahed. We onsider a 15% redution to be roughly in line with the neessary trajetory in order to fulfill the eission redution requireent. or this exerise, we set a onstraint on equilibriu eissions, and we allow the arbon prie oponent in the road prie (in effet, the fuel tax) to vary freely, and not be set equal to the reoended SCC. The odel will solve for the optial road priing shee given onstraints, where the arbon prie oponent will serve as a shadow prie for the eission onstraint. We then have the ase of ahieving the eission redutions in the ost effiient priing shee available, i.e. reduing eissions at least ost. The results are given in Table 3. Table 3: Results fro odel alulations of seond-best road pries in 2020 under a GHG eission onstraint of 15% redution fro 2015 levels. Road pries are given in 2015-NOK per k for a given state. Vehile type and state Revenue reyling oponent Total Corretive oponent own vehile Corretive oponent indiret ipat Tax interation oponent labor arket and ongestion Tax interation oponent other taxes EV ities peak hours ICEV ities peak hours EV ities off-peak ICEV ities off-peak EV sall ities Statistis Norway: StatBank: Table: 08940: Greenhouse gases, by soure, energy produt and pollutant (retrieved Noveber 2017). 21

23 ICEV sall ities EV rural areas ICEV rural areas The ost notable hange in Table 3 opared to Table 2 is that the road prie for ICEVs inreases for driving in all states. The inrease is between 20%, for driving in large ities during peak hours, and 550%, for driving in rural areas. The sae oparison for EVs results in redutions for all states. The redution is between 7%, for driving in large ities in off-peak hours, and 24%, for driving in sall ities. These road prie hanges in disfavor of the ICEV arise fro a substantial inrease in the arbon prie oponent, now the shadow prie of the eission onstraint. This shadow prie is shown in Table 4, alongside the SCC and the initial fuel tax (59% gasoline, 41% diesel), easured in NOK per liter. Table 4: uel taxes/ arbon ost oponent in road prie NOK per liter. Initial fuel tax (inluding VAT) Soial ost of arbon (SCC) Shadow prie of eission onstraint NOK per liter fossil fuel We see fro Table 4 that the shadow prie of the eission onstraint is about 16 ties the SCC. This orresponds to a arbon prie of 7057 NOK/ton. We also see that arbon ost oponent surpasses the initial fuel tax, by about 150%. This eans that in order to ahieve the eissions redutions target at least ost alongside an optiized road priing shee it would not be a question of shifting fro fuel tax and tolls to road prie. It would require inreasing the tax burden both on fossil fuel and on kiloeters. So how do the agents redue their eissions at least ost? The agents an drive ICEVs less and/or drive the ore effiiently (or replaing the with ore effiient ICEVs). The results show an about 10.3% drop in total household driving with ICEVs, and average fuel intensity drops by about 5.3%. Soe of the redution in ICEV-kiloeters aterialize in a shift fro ICEV ownership to EV ownership. The results show that they drive about 9.6% fewer k in total, when EVs are inluded. EV ownership has inreased by about 33% nationwide (and even higher in ities). On the ICEV side, ownership rates have dropped by about 5.5% nationwide. The inrease in road priing in this senario opens up for larger uts in labor taxation. The total redution in labor taxes orresponds to a drop in the average arginal tax rate fro 40% to 37%. However, this is not enough to save the senario fro substantially less welfare, opared to the initial situation. In this senario eah household gets a welfare derease of 219 NOK per year. This welfare alulation assues that the atual welfare ost of a ton of GHG is 420 NOK, the SCC, even 22

24 though a higher shadow prie has been fored upon the transport setor. The high shadow prie for the eission onstraint reflets high welfare osts fro large-sale CO2-abateent within the transport setor. or the Norwegian eonoy as a whole, the shadow prie of suh a CO2-onstraint would probably be lower. This is beause the existing eissions taxation is generally lower than in the transport setor (see e.g., NOU 2015:15, 2016), so heaper abateent opportunities would be exploited. Sensitivity analysis and alternative senarios The odel results rely on the paraeter values, whih in soe ases are derived fro fairly noisy and unertain estiates (see e.g., Thune-arsen et al., 2014). We therefore provide sensitivity analysis to show how the unertainty in the underlying paraeters reflet the unertainty in the results. This applies for both estiates of external osts and behavioral relationships, i.e. elastiities. We will ainly fous on testing the sensitivity of the elastiity values. The ipliations for road prie levels of higher/lower external ost values are easier to iagine, and we have already shown the ipliations of higher arbon osts. It will also save spae in the artile. There are any ways to do sensitivity analysis. A oon pratie is to vary the entral paraeters one-by-one to show how hanging one paraeter affets the result. We often find it ore rewarding to vary a set of variables siultaneously in a onsistent senario. This is often ore suitable to show the range of outoes, and it helps the reader see the unertainty in ters of different stories. Two of our fous on the unertainty on how the agents will respond in the transport arket, i.e. unertainty in transport related elastiity paraeters. In one of the senarios, the agents turn out to be less responsive to transport poliies, and vie versa for the other. The paraeters we vary in the two senarios are given in Table 5. Table 5: Diretion and relative hange of paraeter values in two senarios for sensitivity analysis on responsiveness in transport arkets Elastiity paraeter More responsive transport arket (MRTM) ess responsive transport arket (RTM) Own-prie elastiity of fossil intensity + 30% - 30% Own-prie elastiity of ICEV kiloetrage + 30% - 30% Own-prie elastiity of EV kiloetrage + 30% - 30% Own-prie elastiity of ICEV purhase wrt ICEV k-ost Own-prie elastiity of EV purhase wrt. EV k-ost Cross-prie elastiity of ICEV purhase wrt. EV k-ost Cross-prie elastiity of EV purhase wrt. ICEV k-ost + 30% - 30% + 30% - 30% + 30% - 30% + 30% - 30% 23

25 The next two senarios fous on the unertainty on how the agents will respond in the labor arket. In one of the senarios, we look at the ase where agents behavior in the labor arket are less responsive to hanges, and vie versa in the other senario. The paraeters we vary in the two senarios are given in Table 6. Table 6: Diretion and relative hange of paraeter values in two senarios for sensitivity analysis on responsiveness in labor arkets Elastiity paraeter More responsive labor arket (MRM) ess responsive labor arket (RM) abor supply elastiity (unopensated) + 30% - 30% Inoe elastiity of labor + 30% - 30% We further add two ore senarios. These senarios test the ipliations of different developents for EV purhases and EV purhase taxes. The first of these senarios onsiders the ase where the stok of EVs has doubled at the expense of ICEVs, i.e. a doubling of the EV-share under the sae ar fleet size. This is partiularly relevant sine the growth of EV s has been quite large sine the 2015, the base year of the analysis. This senario is denoted 2X EV. The last senario onsiders the ase where the governent relaxes the largest inentive for purhasing EVs, naely the exeption fro VAT. A 25% VAT on the average EV sold in Norway would orrespond to a NOK addition to the sales prie. This is ipleented in the odel as an inrease in the purhase tax annuity for EVs. In addition, EVs will pay the sae annual ownership tax as ICEVs, whih orresponds to an inrease fro 455 NOK to NOK per year. This senario is denoted EV VAT. The resulting seond-best road prie levels in these senarios are given in Table 7. Table 7: Results fro odel alulations of seond-best road pries in 2020 under various senarios. Road pries are given in 2015-NOK per k for a given state. Vehile type and state Baseline MR- TM R- TM MR- M R- M 2X EV EV VAT EV ities peak hours ICEV ities peak hours EV ities off-peak ICEV ities off-peak EV sall ities ICEV sall ities EV rural areas ICEV rural areas