Does Britain or the United States Have the Right Gasoline Tax?

Transcription

1 Does Briain or he Unied Saes Have he Righ Gasoline Tax? Ian W.H. Parry and Kenneh A. Small March 2002 (rev. Sep. 2004) Discussion Paper rev. Resources for he uure 1616 P Sree, NW Washingon, D.C Telephone: ax: Inerne: hp:// Resources for he uure. All righs reserved. No porion of his paper may be reproduced wihou permission of he auhors. Discussion papers are research maerials circulaed by heir auhors for purposes of informaion and discussion. They have no necessarily undergone formal peer review or ediorial reamen.

2 Does Briain or he Unied Saes Have he Righ Gasoline Tax? Ian W.H. Parry, Resources for he uure and Kenneh A. Small Absrac This paper develops an analyical framework for assessing he second-bes opimal level of gasoline axaion aking ino accoun unpriced polluion, congesion, and acciden exernaliies, and ineracions wih he broader fiscal sysem. We provide calculaions of he opimal axes for he US and he UK under a wide variey of parameer scenarios, wih he gasoline ax subsiuing for a disoring ax on labor income. Under our cenral parameer values, he second-bes opimal gasoline ax is $1.01/gal for he US and $1.34/gal for he UK. These values are moderaely sensiive o alernaive parameer assumpions. The congesion exernaliy is he larges componen in boh naions, and he higher opimal ax for he UK is due mainly o a higher assumed value for marginal congesion cos. Revenue-raising needs, incorporaed in a Ramsey componen, also play a significan role, as do acciden exernaliies and local air polluion. The curren gasoline ax in he UK ($2.80/gal) is more han wice his esimaed opimal level. Poenial welfare gains from reducing i are esimaed a nearly one-fourh he producion cos of gasoline used in he UK. Even larger gains in he UK can be achieved by swiching o a ax on vehicle miles wih equal revenue yield. or he US, he welfare gains from opimizing he gasoline ax are smaller, bu hose from swiching o an opimal ax on vehicle miles are very large. Key Words: gasoline ax, polluion, congesion, accidens, fiscal ineracions JE Classificaion Numbers: H21, H23, R48

3 Conens I. Inroducion Analyical ramework Parameer Values Empirical Resuls Conclusion References Appendix: Analyical Derivaions for Secion

4 Resources for he uure Does Briain or he Unied Saes Have he Righ Gasoline Tax? Ian W.H. Parry and Kenneh A. Small I. INTRODUCTION Recen demonsraions in Europe agains high fuel prices heighened ineres in he appropriae level of gasoline axaion. Excise axes on fuel vary dramaically across counries: Briain has he highes rae among indusrial counries and he Unied Saes he lowes (see igure 1). In Briain he excise ax on gasoline is abou $2.80 per US gallon (50 pence per lier), nearly hree imes he 2001 wholesale price, while in he Unied Saes federal and sae axes ogeher amoun o abou $0.40/gal. 1 The Briish governmen has defended high gasoline axes on hree main grounds. irs, by penalizing gasoline consumpion, such axes reduce he emissions of boh carbon dioxide and local air polluans. Second, gasoline axes raise he cos of driving and herefore indirecly reduce raffic congesion and raffic-relaed accidens. Third, gasoline axes provide significan governmen revenue: in he UK, moor fuel revenue is nearly one-fourh as large as he enire revenue from personal income axes (Chennells e al. 2000). This hird argumen finds an inellecual basis in Ramsey s (1927) insigh ha axes for raising revenue should be higher on goods wih smaller price elasiciies. Gasoline axes have also been defended on oher grounds, such as a user fee for he road nework (is primary role in he US) and as a means o reduce dependence on oil supplies from he Middle Eas. As hese argumens sugges, several imporan exernaliies are associaed wih driving. Each poenially calls for a correcive Pigovian ax, alhough he ideal ax for each would be on somehing oher han fuel. Only for carbon dioxide does a fuel ax closely approximae a direc Pigovian ax. or local air Kenneh Small hanks he Universiy of California Energy Insiue for financial suppor. We are graeful o Howard Gruenspech, Klaus Conrad, arry Goulder, Charles ave, Don Pickrell, Richard Porer, Paul Porney, Mike Toman, and Sarah Wes for helpful commens and suggesions and o Helen Wei for research assisance. 1 Gasoline is also subjec o sales axaion in he Unied Saes and value-added axaion in European counries. However hese oher axes apply o (mos) oher goods, and herefore do no increase he price of gasoline relaive o oher goods (excep insofar as hey are levied on op of he fuel-ax componen of price). 1

5 Resources for he uure polluion, a direc ax on emissions would provide beer incenives o improve polluion abaemen echnologies in vehicles. As for congesion, fuel axes affec i hrough reducing oal vehicle miles raveled (VMT), whereas peak-period congesion fees would also encourage people o consider avoiding peak hours and he mos highly congesed roues. An ideal ax o address acciden exernaliies would charge according o miles driven raher han fuel consumed, and would vary across people wih differen risks of causing accidens. 2 Noneheless, ideal exernaliy axes have no been implemened for poliical, adminisraive, or oher reasons. They raise objecions on equiy grounds, hey require adminisraive sophisicaion, and hey run couner o aemps o reduce geographical differences in axes and insurance raes. The fuel ax, by conras, is adminisraively simple and well acceped in principle, even a very high ax raes in some naions. Therefore i is enirely appropriae o consider how exernaliies ha are no direcly priced should be aken ino accoun in an assessmen of fuel axes. As for revenues, a well-developed public-finance lieraure rigorously compares he efficiency of differen ax insrumens for raising revenues. Recenly, his lieraure has been exended o compare exernaliy axes wih labor-based axes such as he income ax. 3 One of is key insighs is ha by raising he cos of living, exernaliy axes have a disoring effec on labor supply similar o ha of labor-based axes. I is now feasible o bring he insighs of his lieraure o bear on a ax, such as he fuel ax, ha is parially inended as an imperfec insrumen for conrolling exernaliies. A number of previous sudies aemp o quanify he exernal coss of ransporaion. 4 Typically hese sudies esimae exernal coss per disance raveled raher han per volume of fuel consumed. However he implicaions for he opimal fuel ax have rarely been rigorously spelled ou; as our formulaion makes clear, he imporance of disance-based exernaliies in he opimal fuel ax is 2 or furher discussion of he efficiency of gasoline axes a reducing exernaliies, see Walers (1961), UK Minisry of Transpor (1964), De Borger and Proos (2000), Parry (2001) and ulleron and Wes (2001). 3 See for example Bovenberg and van der Ploeg (1994), Bovenberg and Goulder (1996), Parry and Oaes (2000). 4 or example, ee (1993), US OTA (1994), Peirson e al. (1995), Mayeres e al. (1996), Quine (1997), ECMT (1998, ch. 3), Porer (1999), iman (1999), Rohengaer (2000), and various papers in Greene e al. (1997). 2

6 Resources for he uure subsanially diminished o he exen ha people respond o higher fuel axes by purchasing more fuelefficien vehicles raher han driving hem less. 5 I is also imporan o updae prior sudies o ake accoun of changes over ime in vehicle emissions and safey, he value of ravel ime, he value of life, and so on. This paper presens and implemens a formula for he second-bes opimal gasoline ax ha accouns for boh exernaliies and ineracions wih he ax sysem. This formula, exending ha of Bovenberg and Goulder (1996), disaggregaes he opimal fuel ax ino componens wih economic inerpreaions. We furhermore allow for he possibiliy ha gasoline is a relaively weak subsiue for leisure, hereby jusifying a Ramsey ax componen, and we incorporae feedback effecs on labor supply from changes in congesion. We use our formula o esimae opimal gasoline axes in he US and UK, focusing on exernaliies of congesion, air polluion (local and global), and raffic accidens. 6 In his way we illusrae why, and o wha exen, he opimal ax may differ across counries, and under wha circumsances, if any, he low US raes or he high UK raes can be jusified. We summarize he resuls as follows: irs, under our benchmark parameer assumpions he opimal gasoline ax in he US is $1.01/gal (more han wice he curren rae) and in he UK is $1.34/gal (less han half he curren rae). The higher opimal ax for he UK mainly reflecs a higher assumed value for marginal congesion coss. Significanly differen values are obained under reasonable alernaive parameer scenarios, bu a Mone Carlo analysis suggess ha i is highly unlikely for eiher he opimal US ax o be as low as is curren value, or he opimal UK ax o be as high as is curren value. 5 This poin is noed by Newbery (1992, noe 1). By way of conras, De Borger e al. (1997) and Mayeres (2000) model fuel axes in Belgium essenially as axes on vehicle-kilomeers raveled, wih limied scope for improvemens in fuel efficiency. They also consider wo phenomena cross-border refueling and exporing of ax burdens ha we can bypass because he naions we consider have more self-conained economies han Belgium.. 6 Virually all quaniaive esimaes of exernal coss of moor vehicles have placed hese hree a he op of he lis, in magniude far above such oher candidaes as noise, waer polluion, vehicle and ire disposal, policing needs, pavemen damage, and securiy of naional peroleum supplies. See Delucchi (1997), US HWA (1997, pp. III-12 hrough III-23), and US HWA (2000a, secion eniled Oher Highway-Relaed Coss and Table 10). or noise and pavemen damage in comparison o oher coss, see also De Borger e al. (1997, Table 1). 3

7 Resources for he uure Second, he congesion exernaliy is he larges componen of he opimal fuel ax. Thus even hough fuel axes are an imperfec insrumen o conrol congesion, hey sill need o be significan in he absence of congesion pricing. The Ramsey componen is he nex mos imporan, followed closely by accidens and local air polluion. Global warming plays a very minor role ironically since i is he only componen for which he fuel ax is (approximaely) he righ insrumen. Third, he opimal gasoline ax is subsanially diminished by he fac ha only a porion of he ax-induced reducion in gasoline use less han half in our base case is due o reduced driving, he res coming from changes in fuel efficiency. If we had made he misake of assuming ha vehicle miles are proporional o fuel consumpion, we would have compued he opimal gasoline ax in boh naions o be much higher, close o he curren value in he case of he UK. ourh, when considered as par of he broader fiscal sysem, he opimal gasoline ax is only moderaely higher han he marginal exernal cos of gasoline. While i is rue ha gasoline axes should be se above marginal exernal coss because hey raise revenue from a relaively price-inelasic good, he Ramsey componen urns ou o be only abou $0.25 per gallon. urhermore, here is a couneracing influence arising from he inefficiency of using a ax wih a relaively narrow base. inally, we simulae a ax on vehicle miles, which more direcly addresses he disance-relaed exernaliies of congesion, accidens, and local polluion (subjec o regulaions on emissions per mile). The poenial welfare gains from his policy are much larger han hose from opimizing gasoline-ax raes nearly four imes as large in he case of he US. urhermore, he opimal ax rae is much higher, more han wice he opimal fuel ax when convered a he fuel efficiency ha would obain in ha scenario. As a resul, in he UK, mos of he available welfare gains could be obained simply by shifing he curren ax from fuel o VMT, wih a rae chosen o mainain equal revenues once people had adjused heir vehicle socks in response. The Ramsey componen is more imporan wih a VMT ax because ravel, being less elasic han fuel consumpion, is a beer arge for raising revenue. Our analysis absracs from some oher argumens ha have been used o defend high gasoline axes. These include alleged exernal coss in connecion wih road mainenance, parking subsidies, nonopimal urban form, and inernaional poliical and miliary policy o secure peroleum supplies. or he 4

8 Resources for he uure mos par, aemps o quanify hese argumens have resuled in smaller coss han hose considered here. or example, Small e al. (1989) show ha he road damage from passenger vehicles is minuscule compared o ha from heavy vehicles (which are mosly diesel), and ha even for heavy vehicles he damage is no closely relaed o fuel consumpion. Delucchi (1998a) has esimaed he US exernal cos of peroleum associaed wih energy securiy, and ges numbers much smaller han hose from congesion, accidens, and air polluion. Neverheless, here remains room for legiimae debae abou he need for high fuel axes for reasons ha are hard o quanify. We hope ha his aricle, by demonsraing wha can and canno be said based on exernaliies and revenue-raising needs, will discipline ha debae. Our model also absracs from equiy consideraions, use of fuel in producion, ax subsidies o peroleum exracion, sraegic rade policy, and ineracions wih he capial marke hese issues are discussed a he end of he paper. The res of he paper is organized as follows. Secion 2 describes our analyical model and a formula for he opimal gasoline ax. Secion 3 discusses parameer values. Secion 4 presens calculaions of he opimal gasoline ax for he US and UK, compares he welfare effecs of axes on gasoline and vehicle miles, and provides an exensive sensiiviy analysis. Secion 5 briefly commens on he poliics of ax reform, and model limiaions. 2. ANAYTICA RAMEWORK A. Model Assumpions Consider a saic, closed economy model wih many agens. The represenaive agen has he following uiliy funcion: (2.1) U = u( ψ ( C, M, T, G), N ) ϕ( P) δ ( A) All variables are expressed in per capia erms. C is he quaniy of a numeraire consumpion good, M is ravel measured in vehicle-miles, T is ime spen driving, G is governmen spending, N is leisure or nonmarke ime, P is he quaniy of (local and global) polluion, and A is severiy-adjused raffic accidens. G, P, and A are characerisics of he individual's environmen, perceived as exogenous. We include T in 5

9 Resources for he uure he uiliy funcion o allow he opporuniy cos of ravel ime o differ from he opporuniy cos of work ime. The funcions u(.) and ψ(.) are quasi-concave, whereas ϕ (.) and δ (.) are weakly convex funcions represening disuiliy from polluion and from acciden risk. 7 Vehicle ravel (VMT) is produced according o he following homogeneous funcion: (2.2) M = M (, H ) where is fuel consumpion and H is money expendiure on driving. This allows for a radeoff beween vehicle cos and fuel efficiency, e.g. via compuer-conrolled combusion or an improved drive rain, while holding qualiy consan. 8 I hereby allows for a non-proporional relaion beween gasoline consumpion and VMT: in response o higher gasoline axes people will buy more fuel-efficien cars (causing an increase in H) in addiion o driving less. 9 Driving ime is deermined as follows: (2.3) T = π M = π ( M ) M where π is he inverse of he average ravel speed and M is aggregae miles driven per capia. We assume π > 0, implying ha an increase in VMT leads o more congesed roads. The noaion disinguishing beween M and M is o remind us ha agens ake M and hence π as fixed hey do no ake accoun of heir own impac on congesion. 7 The separabiliy of polluion and accidens in (2.1) rules ou he possibiliy ha hey could have feedback effecs on labor supply. Williams (2000) finds ha he impacs on labor supply from polluion-induced healh effecs have ambiguous, and probably small, effecs on he opimal polluion ax. The weak separabiliy of leisure is no as srong as i migh appear, as discussed below in connecion wih he Ramsey componen of he opimal ax. 8 In pracice fuel efficiency may ofen be increased by choosing smaller cars ha are less convenien, comforable, or safe. This could be represened by complicaing he producion relaionship, bu a leas for small changes i would make no difference o he welfare evaluaion of fuel-efficiency changes so long as consumers are opimizing heir qualiy choice. urhermore, empirical measures of fuel-price elasiciies should no be affeced by wheher he consumer chooses o use money or qualiy o pay for fuel-efficiency improvemens. 9 We limi our analysis o gasoline-powered passenger vehicles and do no consider possible ineracions beween opimal ax raes for gasoline and diesel fuel. While here are ineresing issues regarding relaive axes on hese wo fuels (Mayeres and Proos 2001a, De Borger 2001), we hink hey would lile affec he quaniaive resuls derived here. 6

10 Resources for he uure We disinguish wo ypes of polluans: hose (denoed P ) like carbon dioxide ha depend direcly on fuel consumpion, and hose (denoed P M ) ha depend only on miles driven. The laer ype includes nirogen oxides, hydrocarbons, and carbon monoxide, for which regulaions force emissions per mile o be uniform across mos new vehicles. 10 P and P M are boh severiy-weighed indices wih unis chosen so we can combine hem as: (2.4) P = P ( ) P ( M ) + M where P, P > 0 M and is aggregae fuel consumpion per capia. Agens ignore he coss of polluion from heir own driving since hese coss are borne by oher agens. The erm δ (A) in (2.1) represens he expeced disuiliy from he exernal cos of raffic accidens. Some acciden coss are inernalized; for example people presumably consider he risk of injury or deah o hemselves when deciding how much o drive. These inernal coss are implicily included eiher in uiliy funcion ψ(.) or money coss H. Bu oher coss are exernal and are couned in δ (.). Many of hese exernal coss are borne by people in heir roles as pedesrians or cycliss, 11 and ohers are funcions of he number of rips raher han heir lengh; so we make he simplifying assumpion ha his disuiliy is independen of he amoun of he individual's own driving (in conras o he cos of congesion as specified in equaion 2.3). The number of severiy-adjused accidens per capia is hus aken o be exogenous o he individual agen, bu dependen on he amoun of aggregae driving per capia: (2.5) A = A( M ) = a( M ) M where a (M ) is he severiy-adjused acciden rae per mile. Noe ha we also ignore any indirec effecs on acciden exernaliies via changes in vehicle size, parly because he direcion of such effecs is 10 See ECMT (2000) for a review of curren and anicipaed emissions sandards in Europe, he US, and Japan. 11 In he US in 1994, 16 percen of faaliies from moor vehicle crashes were o non-mooriss (US HWA 1997, p. III-18). 7

11 Resources for he uure uncerain. 12 The sign of a is ambiguous: heavier raffic causes more frequen bu less severe accidens as people drive closer ogeher bu more slowly. On he producion side, we assume ha firms are compeiive and produce all marke goods using labor (and possibly inermediae goods) wih consan reurns o scale. Therefore all producer prices and he gross wage rae are fixed; since we do no explore policies ha would change hem, we normalize hem all o uniy, aside from he producer price of gasoline which we denoe q. Governmen expendiures are financed by axes a raes on gasoline consumpion and on labor income. Therefore he ne wage rae is 1 and he consumer price of gasoline is q +. The governmen does no direcly ax or regulae any of he hree exernaliies, excep as implicily incorporaed in he funcions δ (.), M(.), π (.), P (.), P (.), and a(.). 13 The agen s budge consrain is herefore: (2.6) C + ( q + ) + H = I = (1 ) where I is disposable income and is labor supply. Agens are also subjec o a ime consrain on labor, leisure, and driving: (2.7) + N + T = M 12 Small cars are more dangerous o heir own occupans bu less dangerous o occupans of oher vehicles and o bicycliss and pedesrians. Curren evidence seems o sugges parially offseing effecs of changes in composiion of he aggregae flee. A shif from very large passenger vehicles (especially ligh rucks, minivans, and spor uiliy vehicles) o moderae sized vehicles decreases he aggregae average severiy of accidens, while a shif from moderae o very small vehicles increases i (Charles ave, personal communicaion; see also Gayer, 2001). 13 or example, requiremens for reformulaed gasoline and bumper effeciveness reduce polluion and acciden coss, bu also increase he money coss of driving and herefore affec M(.) as well as P (.), P M (.), and a(.). We assume ha fuel-efficiency sandards are no binding. This is reasonable because even wih regulaed new-car echnology, people may aler fuel efficiency hrough heir choices of vehicle mix, driving habis, and mainenance pracices ; for example, Rouwendal (1996, Table 3) finds ha he fuel efficiency jus for using a specific given vehicle has a price-elasiciy of In he US, exempions for ligh rucks grealy weaken he effecs of fuel efficiency sandards and a recen aemp o ighen hem found inadequae poliical suppor; if hey are barely effecive now, i seems highly unlikely ha hey would be binding a he opimal ax raes esimaed in his paper. If efficiency sandards are binding a low ax raes, bu no a opimal ones, our welfare calculaions are affeced bu no he opimal ax calculaions. 8

12 Resources for he uure where is he agen s ime endowmen. inally, he governmen budge consrain is: (2.8) + G. = We ake governmen spending as exogenous so ha higher gasoline ax revenues reduce he need o raise revenues from oher sources. 14 B. Opimal Gasoline Tax We now discuss he welfare effec of an incremenal increase in he gasoline ax. This leads o our formula for he opimal gasoline ax, wrien in erms of conceps known from he opimal ax lieraure. We go sraigh o he key equaions, bu provide a rigorous derivaion of hese equaions in he Appendix. (i) Marginal Welfare Effecs. In he Appendix we describe condiions for individual households o maximize uiliy. Differeniaing household uiliy wih respec o he gasoline ax, while aking ino accoun changes in he labor ax required o keep he governmen budge balanced, we obain: 1 P d C A P ( E M ) + ( E + E + E ) dv (2.9) = λ d dm d + d d d where V is indirec uiliy, λ is he marginal uiliy of income and P (2.10) E P = ϕ P / λ ; E M = ϕ P / λ ; E C = vπ M ; E A = δ A / λ ; v u / λ. M 1 T Equaion (2.9) shows he marginal welfare change from increasing he fuel ax, decomposed ino hree effecs. The firs is he welfare change in he gasoline marke. This equals he reducion in gasoline consumpion imes he difference beween he direc marginal polluion damage from fuel combusion, denoed P E, and he ax rae. The second is he welfare gain from he reducion in VMT. This equals he reducion in VMT imes he sum of he (marginal) per-mile exernal coss of congesion (E C ), accidens 14 If insead gasoline-ax revenues financed addiional public spending, he opimal gasoline ax would be higher (lower) han ha calculaed here o he exen ha he social value of addiional public spending were greaer (less) han he social value of using exra revenue o cu disorionary income axes. 9

13 Resources for he uure (E A PM ), and mileage-relaed polluans ( E ). 15 The hird effec, i.e. he las erm in (2.9), is he welfare effec in he labor marke. I equals he change in labor supply (which is negaive) imes he wedge beween he gross and ne wage, ha is, he wedge beween he value of marginal produc of labor and he marginal opporuniy cos of forgone leisure ime. Anoher way o view (2.9) is by grouping he wo erms conaining ax raes. Then he welfare change from an incremenal ax increase is seen as he effec of induced behavioral changes on oal ax revenue less oal exernaliy cos. (ii) Opimal Gasoline Tax. Seing (2.9) o zero yields, afer some manipulaion, he following formula (see Appendix): * (2.11) = Adjused Pigovian ax MEC 1 + MEB ax Ramsey Congesion feedback c (1 η MI ) ε ( q + ) β C c + + E { ε ( 1 ηmi ) ε } η 1 α 1 M where P C A PM (2.12a) MEC E + ( β / α )( E + E + E ) ; M dm / d η (2.12b) β = d / d M η M ; η = η + η ; α M ; M M M / MEB ε 1 ε = =. 1 (1 + ε ) + 1 ε 1 15 All exernal coss are in per capia erms. v denoes he opporuniy cos of ravel ime. 10

14 Resources for he uure In hese formulas, η MI is he expendiure elasiciy of demand for VMT (i.e. he elasiciy wih respec o disposable income), 1/α M is fuel efficiency or miles per gallon, η is he negaive of he gasoline demand elasiciy, η M is he negaive of he elasiciy of VMT wih respec o he consumer fuel price, M η is he elasiciy of fuel efficiency wih respec o he price of fuel (i.e. he negaive of he gasoline c demand elasiciy wih VMT held consan), and ε and are he uncompensaed and compensaed labor supply elasiciies. (We have defined all elasiciies as posiive numbers.) Boh α M and in hese formulas are endogenous. Since α M is a funcion of (see Appendix), ε we approximae his funcion by a consan-elasiciy formula: (2.12c) α M α q = M 0 q M η. inally, is deermined by budge consrain (2.8), which may be rewrien: (2.12d) = α G q α where α = G and α = q are he shares of governmen spending and gasoline producion in G / naional oupu. / Equaion (2.11) expresses he opimal fuel ax as a sum of hree componens. In inerpreing i, le us sar wih he quasi-pigovian ax represened by MEC. We may hink of his as he marginal exernal cos of fuel use. I equals he marginal damage from polluion due direcly o gasoline combusion, plus he marginal congesion, acciden, and disance-relaed polluion coss; he laer are expressed per uni disance raveled and hen muliplied firs by fuel efficiency (1/α M ) and hen by he porion of he gasoline demand elasiciy due o reduced VMT (β). If fuel efficiency were fixed, i.e. if all he response o fuel price worked hrough he amoun of driving, hen we would have ηm = η and β = 1. Bu in fac ηm < η, so β < 1. This poin is imporan because, as we shall see, empirical sudies sugges ha probably β<0.5, i.e. less han half of he long-run price responsiveness of gasoline consumpion is due o 11

15 Resources for he uure changes in he amoun of driving. Therefore he common pracice of muliplying esimaes of he marginal disance-relaed exernal coss by fuel efficiency i.e. seing β=1 in (2.12a) subsanially overesimaes he appropriae conribuion o he opimal fuel ax. 16 This diluion of he exernaliies in calculaing he opimal ax arises because he quasi-pigovian ax MEC addresses mileage-relaed exernaliies only indirecly. The endogeneiy of fuel efficiency inervenes beween he exernal cos and he ax insrumen. To pu i differenly: wha maers for he opimal ax is no he exernal coss generaed while consuming a gallon of fuel, bu raher he exernal coss generaed in he process of increasing fuel consumpion by a gallon as a resul of ax incenives. The former is simply M/ imes he exernal cos per mile, whereas he laer is reduced by he raio η / η. M Even wih MEC correcly compued, he opimal gasoline ax in (2.11) differs from i due o hree effecs arising from ineracions wih he ax sysem. The firs effec is ha MEC is divided by ( 1+ MEB. 17 ) This adjusmen reflecs he fac ha gasoline axes have a narrow base relaive o labor axes, and in his respec are less efficien a raising revenues; i has been discussed elsewhere in he conex of oher exernaliies (e.g., Bovenberg and van der Ploeg 1994, Bovenberg and Goulder 1996). The size of his adjusmen depends on he size of he disorion in he labor marke, which resuls from he ineracion of he labor-ax rae wih he uncompensaed labor-supply elasiciy. 16 or example, Newbery (1995) says of mileage-relaed exernaliies in he UK: If we allow all exernal road coss o be refleced in fuel axes [by muliplying hem by fuel efficiency], hen [heir size] suggess ha doubling he ax would be jusified (p. 1267). He immediaely qualifies his asserion by noing ha fuel axes are a relaively blun insrumen o achieve efficiency in ranspor use. This qualificaion suggess correcly ha raising he fuel ax may be inferior o a more comprehensive ax reform; bu in fac our resuls, as well as ha in Newbery (1992, eq. 7 and noe 1), show ha he suggesed ax is no even second-bes efficien because i ignores he loss of desired impac via changes in he fuel efficiency of vehicles. Noe also ha if he global-warming exernaliy E P increases, he quasi- Pigovian ax MEC rises by even more because fuel efficiency (1/α M ) in (2.12a) responds posiively o any increase * in fuel ax; his is a main poin of Newbery (1992). However, we can see from (2.11) ha does no necessarily rise by more han E P due o he moderaing facor 1/(1+MEB ). 17 MEB equals he welfare cos in he labor marke from an incremenal increase in, divided by he marginal revenue. I is posiive provided ha ε >0 and ha and ε are no so large as o make he marginal revenue negaive. 12

16 Resources for he uure The second effec is he Ramsey ax componen in (2.11). I follows from Deaon (1981) ha when leisure is weakly separable in uiliy, as i is here, ravel is a relaively weak (srong) subsiue for leisure if he expendiure elasiciy for VMT is less (greaer) han one. Thus, leaving aside he oher wo erms in (2.11), gasoline should be axed or subsidized depending on wheher ravel is a relaively weak or srong subsiue for leisure he more so he more inelasic is is demand relaive o he compensaed demand for leisure. This is a familiar resul from he heory of opimal commodiy axes (Sandmo 1976). When we consider sensiiviy analysis, we vary he expendiure elasiciy for VMT and hereby approximae he effecs of relaxing he weak separabiliy assumpion. 18 The hird effec, indicaed by he las erm in (2.11), is he posiive feedback effec of reduced congesion on labor supply in a world where labor supply is disored by he labor ax (cf. Parry and Beno 2000). Reduced congesion reduces he full price of ravel relaive o leisure (see Appendix); hence i leads o a subsiuion ou of leisure ino ravel, which is welfare-improving because labor is axed. This raises he opimal fuel ax, bu only slighly according o our empirical resuls in Secion 4. Equaion (2.11) is no ye a fully compuaional formula for he second-bes opimal ax rae because appears on boh sides of he equaion, being boh explicily in he Ramsey componen and implicily in he oher componens on he righ-hand side via (2.12c-d). However, he sysem of equaions (2.11)-(2.12) can be solved numerically for, given values for he various parameers. A remaining issue is ha he observed values for hese parameers apply o he exising equilibrium (wih non-opimal gasoline axes) whereas (2.11) depends on he values of hese parameers a he social opimum. To infer he appropriae values we simply assume ha elasiciies are consan, and use observed daa direcly in he formulas. 18 The weak separabiliy of leisure in he uiliy funcion (2.1) implies ha labor supply and VMT would increase in he same proporions following an income-compensaed increase in he wage. If all VMT consised of people commuing o work his migh be a reasonable approximaion, as mos of he labor supply elasiciy is due o changes in paricipaion raes raher han changes in hours per day (see below). In pracice less han half of VMT is commuing, and in addiion some of he exra commuing when someone joins he labor force is probably offse by a reducion in ha person s leisure rips. Allowing for his would have he same effec as using a lower value for he expendiure elasiciy of VMT. We will see below ha our resuls are moderaely sensiive o his parameer. 13

17 Resources for he uure (iii) Toal Welfare Effecs and Exernal Coss. We show in he Appendix ha he per capia welfare benefis of an incremenal ax change, as given in (2.9), can be rewrien as: 1 dv d (2.13a) = ( + MEB ) * 1 ( ) λ d d I is convenien o express he welfare change as a proporion of iniial fuel producion coss:. 1 1 dv η * (2.13b) = ( 1 + MEB ) ( ) q 0 λ d q ( q where 0 is iniial per capia fuel consumpion. Saring wih a curren ax rae, we can numerically inegrae (2.13b) o obain he approximae welfare gain from moving o an opimal ax rae, as a fracion of producion coss. 19 As a maer of ineres, we also compue he oal exernal cos, which is jus he sum of fuel- and mileage-relaed exernal cos. Since we will be ineresed only in how i changes over relaively small differences in consumpion, we wrie i as hough he marginal exernaliy parameers (E C, E A, and so forh) were consan; his of course is highly implausible when fuel consumpion and VMT are reduced all he way o zero. Expressed as a facion of iniial fuel producion coss, oal exernal cos calculaed his way is: + ) EC 1 P 1 C A PM (2.14) = + ( + + ) q 0 q 0 E α M E E E 0 (iv) VMT Tax. Wih minor modificaion, our framework can be used o compue he welfare effecs of a VMT ax, i.e. a ax on ravel disance denominaed in cens per vehicle-mile. This requires he observaion ha a VMT ax does no affec fuel efficiency; herefore ravel and fuel change in he same proporions as he ax rae is varied. We show formally in he appendix ha our equaions can simulae a VMT ax 19 In doing so, we ake o depend on fuel price (q + ) wih consan elasiciy -η. We do he same wih α in (2.12d), ignoring any iny difference beween is elasiciy and ha of. Our assumpion ha λ is consan is jusified by he small proporion of fuel in oal expendiures. We sress ha hese assumpions do no affec he opimal fuel-ax raes. 14

18 Resources for he uure simply by making hree changes: (i) se β=1 in compuing MEC ; (ii) replace η by η M in he Ramsey componen (equivalenly, hold η M consan and le η M adjus in reseing β=1); and (iii) divide he resuling value of equaion (2.11), which we now denoe by, by he value of α M ha would prevail wih he VMT ax, namely he value a zero fuel-ax rae. We also show here how he welfare calculaions are modified o evaluae replacing he gasoline ax by any desired VMT ax. The VMT ax has wo advanages over he fuel ax. irs, because mos exernaliies are mileagerelaed, he Pigovian par of he ax ges a he exernaliies more direcly; his is refleced in raising he value of MEC by seing β=1. Second, he revenue-raising funcion of he ax is more efficien because i can be evaded only by reducing mileage, no by adjusing fuel efficiency; ha is, he relevan elasiciy in he denominaor of he Ramsey componen is now η M insead of η. Boh advanages resul in a higher opimal ax rae per vehicle-mile han is he case for he fuel ax. v V 3. PARAMETER VAUES In his secion we choose parameer values for simulaions. Because we are more ineresed in obaining plausible magniudes han definiive resuls, we are free wih approximaions. or mos parameers, we specify a cenral value and a plausible range, inended as roughly a 90% confidence inerval. Table 1 summarizes he parameer assumpions. We would like any parameer differences across naions o reflec differences in condiions raher han in assumpions. Therefore, where possible, we adjus US and UK sudies for cross-naional comparabiliy and sae hem approximaely in US$ a year-2000 price levels; we do his by updaing each naion s figures as appropriae, hen applying he end-2000 exchange raes of UK 1 =US$1.40 and Euro1= US$

19 Resources for he uure 0 Iniial fuel efficiency: 1/ (miles/gal). Daa for he lae 1990s show average fuel efficiency a 20 α M miles/gal for US passenger cars and oher 2-axle 4-ire vehicles. or he UK, he comparable figure is 30 miles/gal. 20 Polluion damages, disance-relaed: PM E (cens/mile). Because mos regulaions specify maximum emissions per mile, we assume local (i.e. ropospheric) air polluion from moor vehicles is proporional o disance raveled. We furher assume he coss are proporional o he amoun of polluion, an assumpion ha is quie good over a wide range of condiions (Small and Kazimi 1995, Burraw e al. 1998), especially considering ha any hresholds would be averaged ou by aggregaing over ime and space. Quine (1997) reviews he European lieraure on polluion coss. McCubbin and Delucchi (1999) describe a comprehensive sudy for he Unied Saes, which for urban areas agrees reasonably well wih Small and Kazimi s (1995) sudy of he os Angeles region. Delucchi (2000) reviews evidence on a wider variey of environmenal coss from moor vehicles, bu finds air polluion o be by far he mos imporan. The US sudies sugges ha coss of local polluion from moor vehicles are roughly cens/mile for auomobiles ypical of he year-2000 flee. 21 In reviewing hese and oher sudies, he auhors of US HWA (2000a) choose a middle value ha comes o 1.9 cens/mile a year-2000 prices, wih low and high values of 1.4 and 16.2, respecively. 22 European sudies give similar if slighly smaller 20 The US figure averages 1998 and 1999 daa from US HWA (2000b, able VM-1). The UK figure is for perolpowered 4-wheeled cars, averaging 1997 and 1999 daa from UK DOE (2000, able 2.4). 21 The cos esimaes are dominaed by healh coss, especially willingness o pay o reduce moraliy risk. or USwide esimaes McCubbin and Delucchi (1999, Table 4, row 1) give a range cens per vehicle-mile for lighduy vehicles in 1990; updaing o 2000 prices gives cens. or he mix of ligh-duy vehicles operaing in he os Angeles region in 1992, Small and Kazimi (1995) provide a cenral esimae of 3.3 cens per vehicle-mile a 1992 prices, or 4 cens per mile in year 2000; however meeorological condiions for polluion formaion are much worse in os Angeles han on average for he US. All hese esimaes are based on vehicles in use in he early 1990s. Small and Kazimi (Table 8) esimae coss from he California ligh-duy vehicle flee projeced for 2000 o be abou half hose from he 1992 flee, due o improved conrols, so we muliply he above esimaes by one-half in quoing hem in he ex. 22 This is calculaed by separaing ou all gasoline vehicles from US HWA (2000a, Table 12), for whom he cenral esimae for year 2000 coss in 1990 prices is 1.42 cens/mile (he VMT-weighed average of he hree classes of 16

20 Resources for he uure resuls, and he differences are very likely due more o differen assumpions han o differen condiions. 23 We herefore use he same values for boh counries, namely a cenral value of 2.0 cens/mile wih range Polluion damages, fuel-relaed: P E (cens/gallon). Global warming coss are much more speculaive due o he long ime period involved, uncerainies abou amospheric dynamics, and inabiliy o forecas adapive echnologies ha may be in place a half-cenury or more from now. Tol e al. (2000) review he esimaes and conclude ha (p. 199): i is quesionable o assume ha he marginal damage coss exceed $50 /C (meric on carbon). In fac, nearly all he evidence reviewed by Tol e al. suggess values considerably lower han his upper bound. ankhauser (1994), using a Mone Carlo echnique o capure uncerainy, suggess an expeced damage in he early 1990s of $20/C, or as high as $33/C if caasrophic evens are given posiive probabiliy. The review by ECMT (1998, p. 70) cies esimaes ranging from $2-$10/C. Nordhaus (1994) and Cline (1990) give mid-range values ha average o $4.2/C in year-2000 prices, while Nordhaus s low esimae is $0.7/C. Nordhaus and Boyer (2000) esimae a shadow value of carbon under a scenario resembling he Kyoo Proocol a $35/C (1990 prices) in year Azar and Serner (1996) arrive a much higher esimaes, $ /C, bu using less convenional vehicles shown); muliplying by 1.31, he 2000-o-1990 raio of he consumer price index for all urban consumers (obained from US Bureau of abor Saisics a hp://sas.bls.gov/cpihome.hm); and applying he raios of low-omiddle and high-o-middle oal air-polluion coss from US HWA (2000a, Table 10). The HWA esimaes are drawn from a sudy by he US Environmenal Proecion Agency (EPA), excep hey are adjused downward o reflec he HWA s preferred 1990 value of saisical life of $2.7 million, which is lower han he value of $4.8 million used by EPA. 23 or he European esimaes, we obain a range of cens/mile from Quine s Table A.1, afer deleing exreme high and low esimaes and muliplying he resuls from he early 1990s by 1.35 o adjus for UK inflaion. A sudy by ECMT (1998, Table 78) esimaes his cos a ECU /km, or 1.2 US cens/mile, for he UK. As for emissions per mile sandards, a definiive comparison is impossible because hey are consanly changing and in he US hey vary by sae; bu a review of Appendices A and B of ECMT (2000) shows ha hey are similar in magniude. 24 Their Table 8.4, column labeled Annex I rade, which permis emissions rading among he developed naions as is allowed by he proocol. The shadow value drops o $11/C if emissions rading is exended globally, which he Clean Developmen Mechanism mimics in a crude way. Nordhaus and Boyer also sae ha all policies ha pass a cos-benefi es have near-erm carbon axes less han $15 per on (p. 175). 17

21 Resources for he uure mehods. 25 A European Union research projec known as QUITS suggess an inermediae range of US$66-170/C (Rohengaer, 2000, p. 108). All hese are esimaed coss o he enire world. Given his evidence and he grea uncerainy, we ake he cenral value o be $25/C wih range P $ This is equivalen o a cenral value for E of 6 cens/gal, wih range These values are small in comparison o local polluion. They do no accoun explicily for he possibiliy ha for poliical or insiuional reasons i may be desirable o adop measures early in order o provide flexibiliy in responding o fuure scienific findings. Exernal congesion cos: E C (cens/mile). Congesion is a nonlinear phenomenon, and highly variable across imes and locaions. Therefore he marginal congesion cos averaged over an enire naion depends on he proporion of is raffic ha occurs in high-densiy areas a peak imes. A number of sudies esimae congesion coss for individual ciies, bu few aemp an average over a naion. One good one is Newbery (1990) for he UK. He esimaes he marginal exernal cos of congesion averaged across 11 road classes a 3.4pence/km, or around US cens/mile afer updaing o By way of comparison, Mayeres (2000, Table 5) and Mayeres and Proos (2001a) obain marginal congesion coss for Belgium equivalen o around 12 cens per mile. 25 or example, hey assume he subjecive rae of ime preference is zero. They also apply disribuional weighs o income losses in rich and poor naions which are equal o one for rich naions and more han one for poor naions, hereby effecively capuring a pure ransfer benefi from spending oday in rich naions in order o help poor naions in he fuure. 26 The conversion rae of 413 gal/c is based on US Naional Research Council (2001), p Scaling up Newbery s esimae by wage inflaion (abou 64% in UK manufacuring beween 2000 and 1990, per Inernaional abour Organizaion 2000, able 5A, p. 894) gives abou 12.5 cens/mile. Wardman (2001) suggess ha he opporuniy cos of ravel ime increases by wage growh o he power 0.5, which insead would yield 9.6 cens per mile. We do no adjus for increased congesion over ime, because some or all of ha increase is offse by people moving o less-congesed regions (Gordon and Richardson, 1994). 18

22 Resources for he uure or he US, Delucchi (1997) esimaes 1990 exernal congesion coss from privae vehicles a cens per vehicle-mile (in 2000 prices), wih a geomeric mean of 2.5 cens. 28 The US ederal Highway Adminisraion (HWA), in is Highway Cos Allocaion Sudy, esimaes marginal exernal congesion coss for auos, pickups, and vans a 5.0 cens/mile, wih range These VMT-weighed averages need o be adjused for our purposes because he congesion cos eners our formula muliplied by he sensiiviy o gasoline price (see equaion 2.14). Tha sensiiviy is less under congesed condiions, boh because more work rips occur during peak periods and because, hrough self-selecion, more rips in congesed condiions are of high value o he user. 30 Wha we require is an average weighed no only by VMT bu also by fuel-price elasiciy. 31 Adjusing he esimaes jus described for his would lower he marginal cos in boh counries, bu more so in he UK han he US; so i also reduces he gap beween heir marginal congesion coss. Anoher facor ha argues for a smaller gap is ha some of he differences among sudies of he wo naions are probably due o differen assumpions. Sill, i is enirely reasonable ha marginal exernal congesion coss are somewha higher in he UK han he US, because he UK has a much higher overall populaion densiy and a higher proporion of is populaion lives in ciies This calculaion is from Delucchi s Table 1-A4 (p. 57), and assumes ha ravel is wo-hirds daily ravel and one-hird long rips, wih average vehicle occupancy 1.3. This yields a range of 0.75 o 3.26 cens per passengermile in We updae by he facor 1.32 for inflaion beween 1990 and Calculaed from US HWA 1997, Table V-23, using VMT weighs 0.73 for auomobiles and 0.27 for pickups and vans (from US HWA 1997, Table ES-1) and updaing from 1994 o 2000 prices by he consumer price index for all urban consumers (facor of 1.16). The low, middle, and high HWA esimaes assume values of congesed ravel ime of $7.18, $14.36, and $21.54 per vehicle-hour in 2000 prices (HWA 1997, Table III-11, updaed by inflaion facor 1.16), and also differ in ha he amoun of delay caused by an average vehicle is halved in he low esimae, and doubled in he high esimae, compared o he middle esimae. 30 or example, Mayeres and Proos (2001b, able 4) repor ha rips on uncongesed roads are hree imes as pricesensiive as peak-period rips. 31 In a richer model disinguishing among many classes of roads and imes of day, each class would conribue a erm like E C (-dm/d ) in (2.9). Adding hese erms ogeher would be equivalen o creaing a weighed average value for he exernal cos, E C, weighing each class of raffic by is fuel-price-sensiiviy. 32 or example, one-sixh of he UK populaion lives in ondon, where sree congesion is nooriously bad. Mohring (1999) esimaes ha he average peak-period marginal exernal cos for roads in he Minneapolis area is 18 cens/mile in 1990 while Newbery s esimae for urban peak-period ravel is 51 cens/mile for 1990, suggesing ha 19

23 Resources for he uure Wih hese facors in mind, we adop cenral values of 3.5 cens/mile and 7 cens/mile for he marginal congesion cos averaged across he US and UK respecively. We consider ranges of cens/mile for he US and 3-15 cens/mile for he UK. 33 Exernal acciden cos: E A (cens/mile). Several researchers have found ha he oal coss of moor vehicle accidens are quie large, comparable o ime coss (Newbery 1988, Small 1992). However, acciden raes have declined significanly since he sudies of he 1980s. urhermore, he majoriy of hese coss are no exernal. Drivers presumably ake ino accoun he uninsured porions of risks o hemselves and probably o oher family members in he car. Traffic laws and graduaed insurance raes creae penalies which drivers may perceive as coss incurred on an expeced basis. And some sudies have suggesed ha he sign of a in equaion (2.15), relaing severiy-adjused acciden raes o oal ravel, is negaive because accidens are so much less severe wih slower raffic. 34 All hese facors end o make he acciden exernaliies much smaller han he average acciden coss esimaed a decade ago. Taking hese consideraions ino accoun, Delucchi (1997) esimaes he marginal exernal cos E A for all moor vehicles for he US in 1991 a cens/mile in 2000 prices. 35 The US ederal Highway Adminisraion esimaes E A for auos, pickups, and vans, which we again updae o 2000 prices o ge 2.3 urban congesion is more severe in he UK han in he US. Moreover, Newbery s able suggess ha abou wohirds of UK ravel was urban, whereas i is abou 60% for he US (US HWA 1991, Table VM-2). 33 Ideally hese values should be considered exogenous o he ax rae, due o nonlineariy of congesion; bu naional daa are barely adequae o esimae a single number, much less a funcional relaionship, so we approximae E C as consan. 34 ridsrøm and Ingebrigsen (1991) and ridsrøm (1999) provide such evidence. or more discussion of hese issues, see Newbery (1990), Delucchi (1998b), and Small and Gomez-Ibanez (1999). Noe ha even if insurance were charged on a per mile basis, he social coss of driving would sill exceed he privae coss. In paricular, insurance companies do no pay he full value of a saisical life for faaliies. 35 We have added he low and high oals in Delucchi s Table 1-8 (moneary exernaliies) o hose in his Table 1-9A (non-moneary exernaliies), and divided by VMT from his Table 1-A5, obaining cens/mile in The US inflaion facor from 1991 o 2000 is

24 Resources for he uure cens/mile wih range cens/mile. 36 or he UK, Newbery (1988) esimaes E A for cars and axis a values ha conver o cens/mile in US currency a 2000 prices. 37 While he US and UK esimaes migh seem raher far apar, hey are really no when wo adjusmens are made: for value of life and for changes in acciden raes since he sudies were performed. Our preferred values for a saisical life are derived from a mea-analysis by Miller (2000) and are $4.8 million for he US and $3.2 million for he UK. 38 or a range, we muliply by 0.5 for he low end and 1.5 for he high end. We adjus he corresponding values of saisical life assumed by he above hree sudies (saed in US$ a 2000 prices) o hese preferred values. When we do his, we find ha he wo US esimaes are adjused only modesly. However, he UK esimae is reduced very subsanially a he low end and slighly a he high end; his is because Newbery used a single value of life ha was US$5.5 million in 2000 prices, subsanially higher han our preferred value for he UK and slighly higher even han our high esimae for he UK US HWA (1997). We have aken he VMT-weighed average of auomobiles and pickups and vans for all highways, from Table V-24, and inflaed by he facor 1.16 o pu in year-2000 prices. The HWA esimaes are derived from calculaions in Urban Insiue (1991). The middle and high esimaes include uncompensaed coss of pain and suffering, bu only he high esimae includes coss paid by insurance companies; see US HWA (1997), p. III Newbery s range, correced for a ranscripion error, is pence/km (1984 coss a 1986 prices). The saed upper range in Newbery s aricle is 4.9 raher han 2.9, bu his is due o an error in copying a column of figures for exernaliy coss from one able o anoher in his working paper, Newbery (1987). We have updaed by he facor 1.74 for inflaion, an approximaion for he UK consumer price index as given by Inernaional Moneary und (2000). We hen muliply by conversion facors 1.4 cens/pence and 1.61 miles/km. rom Newbery s Table 3 i is apparen ha virually all he coss in he low esimae are deahs and injuries o pedesrians, whereas hose in he high esimae also include one-fourh of he coss of faaliies and injuries incurred by mooriss. 38 Miller compiles 68 credible sudies from 13 developed naions and uses regression analysis o relae heir resuls o real gross naional produc (GNP) per capia and o several conrol variables. The resuling values are found o be nearly proporional o GNP per capia, having an elasiciy of urhermore, he regression resuls permi an adjusmen for various differences in sudy mehodologies, and herefore a se of consisen predicions of value of saisical life for any developed naion. In 1995 US$, Miller s prediced values of saisical life are $3.67 million for he US and $2.75 million for he UK. Inflaing o 2000 price levels and adjusing for changes in real GNP per capia (wih 0.96 elasiciy), yields he values saed in he ex. 39 In making he adjusmens, we assume he US esimaes apply o half he coss, bu he UK esimaes apply o all he coss. This procedure is based on he assumpion ha he value of injury prevenion is proporional o value of saisical life, and on he fac ha half he US bu all he UK esimae reflecs deahs and injuries (he res being mainly propery damage). The resuling adjusmen facors are: Delucchi low esimae 0.975, high 1.07; HWA low 1.54, middle 1.26, high 0.95; Newbery low 0.29, high

25 Resources for he uure Nex, we adjus for he dramaic decreases in faaliy and injury raes in boh naions. We assume half of E A is direcly proporional o he faaliy rae and half o he injury rae. In he US, hese wo raes fell on average by 21 percen since 1991 and by 6 percen jus since 1994; in he UK hey fell by 52 percen since Adjusing he sudies by hese facors gives he following ranges, all in year-2000 US cens per vehicle-mile: Delucchi ; HWA (middle 2.7) Newbery (By way of comparison, Mayeres 2000 and Mayeres and Proos 2001a use esimaes of around cens/mile for Belgium.) Based on hese ranges, we ake 3.0 and 2.4 cens/mile as he cenral esimaes for he US and UK, respecively. 40 In each case, we divide he cenral esimae by 2.5 o ge he low esimae, and muliply by 2.5 for he high esimae. Gasoline price elasiciies, η and η M. Reviews of he many ime-series and cross-secional sudies of demand for gasoline conduced before 1990 generally find price elasiciies beween 0.5 and However, more recen sudies ofen find values abou half as large, wih a bes esimae proposed by US DOE (1996) of We adop a compromise value for η ha is somewha closer o he recen esimaes, namely 0.55, wih a range 0.3 o We have deliberaely chosen he raio of hese esimaes o be 0.8 from he following consideraion. The wo main differences beween he US and UK affecing E A are: (a) he UK has abou wo-hirds as high a willingness o pay for reducion in injury and deah, based on Miller's sudy; and (b) he faaliy rae in he UK is abou 79 percen of ha in he US, whereas injury raes are abou he same. (This laer saemen is based on 1998 raes, which are 1.58 and 1.25 per 10 8 vehicle-miles in US and UK, respecively, for faaliies, and 117 and 122 for injuries. Source: Economic Commission for Europe 2000, pp. 18, 122, and US HWA 2000b, Table VM-1.) Assuming ha faaliies accoun for one-fourh of he exernal coss, and injuries anoher one-fourh, and ha oher exernal coss are proporional o injury raes, his suggess ha E A in he UK and he US have he raio 0.25x(2/3)x x(2/3)x x1.0 = Dahl and Serner 1991, Table 2; Goodwin 1992, Table 1; Espey (1996, Table 4); Espey (1998, Table 5); Graham and Glaiser (2002), p The differences occur mainly because he more recen sudies beer conrol for some or all of hree confounding facors: (a) corporae fuel economy sandards ha were binding on some bu no all manufacurers, (b) correlaion among vehicle use, vehicle age, and fuel economy, and (c) geographical correlaion beween fuel price and oher variable coss of driving such as parking fees. See he discussion in US DOE (1996), pp hrough 5-15 and 5-82 hrough The bes esimae quoed is ha in he firs row of numbers in Table 5-2. One recen sudy 22

26 Resources for he uure Sudies of he response of oal vehicle ravel o fuel prices ypically ge much lower long-run elasiciies, mosly ranging from 0.1 o 0.3 bu someimes larger. 43 These numbers would sugges a raio β η M /η around 0.25 o 0.5. When he same sudy is used o measure boh elasiciies, he raio ends o vary beween 0.2 and Based on his informaion, we choose a cenral value for β of 0.4, and a range of 0.2 o 0.6. This cenral value is close o he recommendaions of Johansson and Schipper (1997) and US DOE (1996). 45 Our cenral values for η and β imply ha he elasiciy of VMT wih respec o fuel price, η M, is This quaniy is crucial for he analysis of he VMT ax. Expendiure elasiciy of demand for VMT, η MI. This is for pracical purposes he same hing as an income elasiciy. I is imporan in calculaing he Ramsey componen of he opimal ax rae in (2.11). Esimaes are ypically beween abou 0.35 and 0.8, alhough a few esimaes exceed uniy. 46 We migh expec he income elasiciy o be a lile higher in he UK because here is more room for vehicle ownership o grow, and more room for mode shifs o and from public ranspor. We se he cenral value for income elasiciy a 0.6 for he US and 0.8 for he UK. or a range, we choose plus or minus half he cenral value. producing a higher esimae, albei on Canadian raher han US or Briish daa, is Yachew and No (2001), who sugges he long-run elasiciy is Goodwin (1992), Table 2; Greene e al. (1999), pp. 6-10; US DOE (1996), pp o The VMT-porion of he gasoline demand elasiciy in four sudies reviewed by Schimek (1996), including his own, was 59%, 57%, 24%, and 19%, for an average of 40%. One sudy, Puller and Greening (1999), ges a raio greaer han one, implying a negaive elasiciy of fuel efficiency wih respec o fuel price. This could resul from ravelers selecively reducing rips, such as vacaions, ha are relaively fuel efficien. We are skepical of his resul, and furhermore i would be inappropriae o use in our model because is explanaion implies ha urban VMT, which accoun for mos of he exernaliies, are reduced by much less han oal VMT. Graham and Glaiser (2002, p. 17) conclude from heir review ha he raio is well below one in he long run. 45 The Johansson-Schipper bes value is [1-(0.4/0.7)]=0.43, from heir pp The US DOE bes value is 0.46, calculaed from he op row in US DOE (1996), Table 5-2; ha row decomposes a long-run price elasiciy of ino a fuel efficiency componen (0.200) and a vehicle-ravel componen (0.176). 46 Based on Pickrell and Schimek (1997), and Pickrell (personal communicaion). 23

27 Resources for he uure abor marke and oher parameers. The remaining parameers are less imporan. There is a large lieraure on labor supply elasiciies for he US. 47 Based on his lieraure, we adop he same values for supply elasiciies in boh counries: for he uncompensaed elasiciy ε a cenral value of 0.2 wih range , and for he compensaed elasiciy a cenral value of 0.35 and a range These elasiciies reflec boh paricipaion and hours worked decisions, averaged across males and females. (Since mos of he labor supply-response arises from changes in paricipaion, he relevan labor-ax rae is primarily he average raher han he marginal rae, which provides some jusificaion for our assumpion of a proporional labor ax.) c ε We assume ha he raio of oal governmen spending o GDP (α G ) is 0.35 for he US and 0.45 for he UK, based on summing average labor and consumpion ax raes in Mendoza e al. (1994). or he range we add plus or minus or he producer price of gasoline (q ) we use $0.94/gal and $1.01/gal for he US and UK respecively. 48 or he range, we add plus or minus $0.50/gal, which is 2.7 sandard deviaions of he weekly reail prices for he US (keeping in mind ha some of ha variaion is due o ax changes). Iniial gasoline ax raes are aken from igure 1 (rounding off slighly) a $0.40/gal for he US and $2.80/gal for he UK. inally, we assume producion shares shares of gross domesic produc spen on moor gasoline. 49 α of for he US and for he UK, based on 47 See, for example, Blundell and MacCurdy (1999) for a review of boh US and UK sudies, and also uchs e al. (1998). 48 Boh UK and US prices are provided by he US Energy Informaion Adminisraion weekly from 1996 hrough early June of 2001 (see The reail price for premium gasoline, including ax, averaged over his period was US$1.42/gal in US and US$3.93/gal in UK. We subrac $0.10/gallon, which is abou half he difference beween premium and regular prices in he US, and we subrac he axes shown in igure 1 o obain he producer prices. 49 or he US, he share is based on 1999 consumpion of moor gasoline of 3.06x10 9 barrels (US Energy Informaion Adminisraion 2000, Table 5.11), ne-of-ax gasoline price of $( ) per gallon (average of premium unleaded 95RON and 91RON), and gross domesic produc of $9.30x or UK, i is based on 1998 consumpion of 511,000 barrels per day (source: US Energy Informaion Agency (2001), Table 3.5) a ne price 24

28 Resources for he uure 4. EMPIRICA RESUTS A. Benchmark Calculaions (i) Opimal Tax Raes. Table 2 gives he componens of he second-bes opimal gasoline ax under our cenral parameers. The oal is $1.01/gal for he US, more han wice he curren rae, and $1.34/gal for he UK, less half he curren rae. Thus, according o hese esimaes, he ax rae is jusifiably higher in he UK han in he US bu he curren size of he difference is unjusified. The difference beween he wo counries in he opimal ax rae is due primarily o he higher assumed congesion coss for he UK. These resuls are 9-22 percen above he marginal exernal cos MEC shown in he second row, which would be he opimal ax rae in he absence of labor-marke disorions. The hree ineracions wih he ax sysem ha causes he opimal ax rae o differ from his amoun are relaively modes in size and parially offseing. or he UK, where he marginal excess burden of labor axaion is higher due o he higher average income-ax rae, 50 he narrow base of he gasoline ax relaive o he labor ax shaves $0.19 from MEC in reaching he adjused Pigovian ax; bu he Ramsey componen adds back $0.23 and he congesion-feedback effec anoher $0.07. or he US, he narrow base subracs only $0.09, bu he Ramsey componen adds $0.26. These resuls for Tha value, here denoed * are far below he naïve compuaion ypically proposed in he lieraure. 1 MEC held a is iniial value. Our calculaion of high in he UK because he mileage-relaed exernaliies in, is MEC as compued from (2.12a) bu wih β=1 and wih fuel economy 1 MEC * is shown in he las row of he able. I is especially 1 MEC are muliplied by iniial raher han opimal fuel economy, and in he UK hey are subsanially differen (30 versus 25.6 miles per gallon). ( ) pounds per gallon (average of premium leaded and premium unleaded gasoline) and gross domesic produc of 747x10 9 pounds. Source for prices: Inernaional Energy Agency (2000), pp. 286, In our case he marginal excess burden depends only on uncompensaed labor supply elasiciies, which are fairly small. or oher purposes, for example when he exra revenue is used o finance ransfer spending, he marginal excess burden would be much larger because i would depend in par on he compensaed labor supply elasiciy. See Snow and Warren (1996) for more discussion. 25

29 Resources for he uure Of he hree exernaliies included in MEC, congesion is easily he larges componen in he UK bu only slighly larger han accidens and air polluion in he US. The global warming componen is small, and is he smalles of he four exernaliies even if we were o riple our cenral esimae of global warming coss. (ii) Welfare Effecs. Table 3 shows he welfare effecs, relaive o he curren siuaion, of several ax raes including he second-bes opimum * and he naïve value jus described. Raising he US ax from is curren rae ($0.40/gal) o * ($1.01/gal) would induce a welfare gain equal o 7.4 percen of pre-ax fuel expendiures. Raising i o he naïve rae ($1.76/gal), by conras, would overshoo he opimal rae so much as o yield very lile ne benefi. or he UK, he welfare gain from reducing he curren ax ($2.80/gal) o he opimal ($1.34/gal) would produce subsanial gains, nearly one-fourh of preax gasoline expendiures, while increasing he ax o he naïve rae of $3.43 would creae a welfare loss of nearly 18 percen of preax expendiures. Table 4 shows resuls for a VMT ax. Resuls are compued a four differen ax raes: (a) he iniial fuel-ax rae convered o a per-mile basis using iniial fuel efficiency; (b) he VMT rae ha raises he same revenue as did he original fuel ax; 51 (c) a pure Pigovian ax equal o he naïve fuel-ax rae described above, convered similarly o a per-mile basis using iniial fuel efficiency; and (d) he opimal VMT ax rae. The welfare change is he ne gain from reducing he gas ax from o zero hen increasing he VMT ax from zero o he rae shown (see Appendix for deails). Table 5 gives some addiional deail for he opimal VMT ax rae for he US, showing ha he mileage-relaed componens of 0 51 Tha rae is 0 α. The revenue from eiher he fuel ax or he VMT ax is in our noaion. Since fuel use M 0 0 under eiher ax is given by = [( q + ) /( q + )] 0 eiher he fuel ax a rae or he VMT ax a rae 0 α. M ε, where 0 is iniial fuel use, is idenical o 0 under 26

30 Resources for he uure he adjused Pigovian ax are approximaely doubled, and he Ramsey componen quadrupled, in comparison o he opimal fuel ax. 52 Comparing he welfare changes in Table 4 wih hose in Table 3, we see ha he VMT ax can achieve much greaer gains han a fuel ax in he US, and moderaely greaer gains in he UK. urhermore, he opimal VMT ax is very high, around 15 cens per vehicle-mile; i brings in 150 percen more revenue han he opimal fuel ax in he US and 70 percen more in he UK (no shown in he able). Several oher observaions abou VMT axes are noeworhy. irs, in he UK, jus convering he curren fuel ax o an equal-revenue VMT ax achieves subsanial benefis more han one-fifh of curren fuel expendiures and more han he welfare gain from cuing he fuel ax from $2.80/gal o is opimal rae of $1.34/gal. (This is less rue in he US, because he fuel-ax rae is already oo low o accomplish much in he way of exernaliy reducion.) Second, i happens ha he curren ax burden on driving in he UK is only seven percen lower han he amoun ha would be opimal if i were levied on VMT insead of fuel. Third, he pure Pigovian ( naïve ) VMT ax achieves mos of he benefis of he opimal VMT ax. ourh, a breakdown of he opimal VMT ax ino he hree componens lised in equaion (2.11) reveals ha he Ramsey componen is quie large: 42 percen of he opimal rae in he US and 31 percen in he UK. This is because he VMT elasiciy wih respec o fuel cos is quie small, 0.22 in our base calculaions, making VMT a more aracive arge han fuel for a Ramsey ax. inally, Table 6 shows how he opimal gasoline ax and he resuling oal exernal coss vary wih governmen revenue requiremens, which effecively means how hey vary wih he labor-ax disorion. In each counry, as governmen revenue requiremen α G is increased, he adjused Pigovian ax decreases bu so does he oal exernaliy damage, calculaed from (2.14). This confirms for our model a 52 The increase in MEC is due o he higher value of β, offse slighly by a lower value of fuel efficiency (1/α M ). The increase in he Ramsey componen is due o he lower value of η and he higher value of afer-ax fuel price v ( q + ). 27

31 Resources for he uure finding of Mecalf (2000) for a simpler model, 53 and reinforces Mecalf s poin ha increasing he laborax disorion does no necessarily make i opimal o pu up wih greaer exernaliy damage. B. Sensiiviy Analysis How sensiive are he resuls in Table 2 o variaions in parameers wihin he ranges we have suggesed are plausible? We explore his quesion in several ways. (i) Varying Parameers Individually. irs, we vary each of he six mos imporan parameers one a a ime, holding all ohers a heir cenral values. The resuls are shown in igure 2. The upper and lower curves in each panel show he calculaed UK and US opimal ax raes, and X denoes he opimal ax in he benchmark case (ha in Table 2). The range covered by each curve is ha shown in Table 1 for ha parameer and naion. In mos cases, opimal ax raes vary by around US$0.50-$1.00/gal as we cover he reasonable range of each parameer. Resuls are more sensiive o congesion coss, due o heir dominance in he opimal ax calculaion. Resuls in he UK are also especially sensiive o he VMT porion of he priceelasiciy of gasoline consumpion, β, because i muliplies all he mileage-relaed exernaliies. Resuls are no very sensiive o he labor ax rae, labor supply elasiciy, fuel-relaed polluion damage, or producer price of gasoline, which when varied individually across heir ranges change he resul by up o only abou plus or minus 5 cens/gal (hese resuls are no shown in he figure). (ii) High and ow Scenarios for he Opimal Tax. Table 7 shows how high exernal coss would have o be in order ha seleced values of he gasoline ax are opimal, assuming specified values for he VMT 53 In Mecalf s model, his occurs because as he labor ax is increased in response o greaer revenue requiremens, he subsiuion of diry for clean goods caused by lowering he adjused Pigovian ax (due o he erm 1+MEB in is denominaor) is more han offse by subsiuion of leisure for consumpion of he diry good. 28

32 Resources for he uure porion of he gasoline demand elasiciy β. In consrucing hese scenarios, all four exernal cos componens of MEC in equaion (2.12) are scaled up or down by he same proporion relaive o heir cenral case values. Each enry in he able is he required value of hese exernal cos componens as a fracion of heir corresponding benchmark values in Table 2. Table 7 shows, for example, ha for he curren US ax rae of $0.40/gal o be opimal, we would have o assume values for all exernal coss ha are only 33% of hose in our cenral case when β = 0.4, or beween 23% and 61% of he cenral case values when β lies beween 0.2 and 0.6. or he UK, wih β = 0.4 he curren ax of $2.80/gal would be opimal if all exernal coss were 1.88 imes heir benchmark values, while a ax of only $1.00/gal would be opimal if all exernal coss were 24% below heir benchmark values. (iii) Mone Carlo Analysis. Clearly, a wide range of oucomes is possible under alernaive parameer scenarios. To give a sense of how likely differen oucomes migh be, given our parameer ranges, we perform some simple Mone Carlo simulaions. We focus on an approximaion for he opimal ax rae (which does no require solving simulaneous equaions) when exernal coss and he VMT porion of he gasoline demand elasiciy are uncerain. or each counry we draw hose parameers randomly and independenly 1000 imes from seleced disribuions and for each draw we calculae he opimal gasoline ax *. This calculaion uses (2.11)-(2.12), bu in (2.12) and on he righ-hand side of (2.11) i uses he values for α M,, and from our benchmark case in Table 2. We hen compue he disribuion of across he 1000 draws. 54 * 54 or all exernal coss we fi gamma disribuions wih means equal o our cenral values and wih 5% and 95% perceniles roughly equal o he minimum and maximum values for hese parameers specified in Table 1. or he VMT fracion of he gasoline price-elasiciy, we assume a uniform disribuion over he parameer range. We experimened wih oher disribuions bu he resuls were only modesly affeced. As discussed above, he opimal gasoline ax is far more sensiive o hese parameers han he oher parameers in he opimal ax formula. Therefore, he resuls would probably be similar if we had done a much more complex Mone Carlo analysis wih all he uncerain parameers in Table 1 drawn from disribuions and wih he opimal ax compued numerically for each draw. 29

33 Resources for he uure Table 8 shows he resuling frequencies wih which he (approximae) opimal ax is less han a given value. Here we see ha for he US, he probabiliy ha he opimal ax is less han he curren ax of $0.40/gal is only 0.01, and he probabiliy ha i is below $1.00 is or he UK, marginal exernal coss are below he curren ax of $2.80/gal wih probabiliy.98, and below $1.50 wih probabiliy CONCUSION Policy oward gasoline axaion can be assessed mos effecively wihin a framework ha explicily incorporaes revenue needs and he exisence of oher disoring axes. Such a framework makes clear, among oher hings, how far from opimal would be a ax calculaed simply by muliplying per-mile exernal coss by average fuel efficiency. A primary reason is ha people can parially evade such an exernaliy ax by increasing fuel efficiency. Our bes assessmen is ha he opimal gasoline ax for he US is more han double is curren rae, while ha for he UK is less han half is curren rae. Paradoxically, he prospecs are remoe for subsanial change in he direcion of opimaliy in eiher naion, given curren poliical facors. In he US, he Clinon Adminisraion achieved an increase in he federal gasoline ax rae of only 4 cens/gal in 1993, despie a major effor. In he UK, he Conservaive Pary s 2001 elecion pledge o cu gasoline axes by 6 pence/lier (32 US cens/gal) failed o resonae wih an elecorae concerned abou global warming and he funding of public services. Boh counries could do a lo beer by addressing he exernal coss of driving, which are subsanial, wih oher insrumens. On ha score here are some limied grounds for opimism, for example he experimens wih value pricing in California and Texas and he plans for cordon pricing in ondon. Bu i will be a long ime before hese ypes of policies could become widespread. However, our resuls also reveal he araciveness of a less drasic change, namely a ax on vehicle-miles. Such a ax is considerably more efficien han a ax on fuel, even hough i falls shor of a rue exernaliy ax. or he US, achieving benefis from such a shif would sill require grealy increasing he ax burden on mooriss, which may be poliically unenable. Bu for he UK, more could be gained in welfare simply from swapping gasoline axes for mileage axes, even wih no change in he overall 30

34 Resources for he uure burden of axaion on driving, han from reducing he gasoline ax o is opimal level. The analyical framework described here enhances our abiliy boh o analyze such a shif and o explain is advanages. Our analysis could be criicized for ignoring disribuional issues. I is commonly hough ha gasoline axes are regressive and herefore should be se a lower levels han implied by a pure efficiency maximizing analysis. However he evidence is less convincing when measures of lifeime, as opposed o annual, income are used as proxies for individual well-being. or example, according o Poerba (1991) he porion of lifeime income spen on gasoline is only slighly larger for he lowes income decile han for he op income decile, and is greaes for middle-income households. urhermore, naions ha se higher fuel axes for policy reasons may choose o offse any adverse disribuional aspecs wih oher policies, as arguably is he case hroughou wesern Europe. By ignoring gasoline-powered vehicles used in producion, our model may undersae he disorion caused by axing fuel used as an inermediae good. However, only 3.2 percen of he gasoline used for highway ravel in he US is used for medium or heavy rucks (Davis 2001, Table 2.4), and of he 40 percen used for ligh rucks probably less han half is par of producion. If we were o analyze diesel axaion, we would need o pay more aenion o producion. We do no address he complex indusrial organizaion of he peroleum indusry or he manner in which he ax sysem may favor i. Given he imporance of peroleum impors for he US and expors for he UK, we expec ha such consideraions primarily affec he disribuion of economic rens raher han he resource cos of he marginal source of fuel for consumpion. Similarly, we do no consider how fuel axes migh be used by a large counry o affec is erms of rade; oher aspecs of inernaional poliics are far more significan in deermining he price of impored oil. inally, our model of he ax sysem is grealy simplified and ignores, in paricular, axes on capial. Bovenberg and Goulder (1997) have sudied he ineracions beween gasoline axes and he capial marke, using a highly deailed dynamic model of he US ax sysem. They find ha capial marke ineracions do no grealy aler he welfare coss of gasoline axes ha would be prediced by a purely saic model. This is again because gasoline is primarily a consumpion good, no an invesmen good. 31

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38 Resources for he uure Inernaional Energy Agency, Energy Prices and Taxes: irs Quarer 2000, Paris. Inernaional abour Organizaion, Yearbook of abor Saisics Inernaional abour Organizaion, Geneva. Inernaional Moneary und, Inernaional inancial Saisics Yearbook: IM, Washingon, D.C. Johansson, Olof, and ee Schipper, Measuring he ong-run uel Demand of Cars: Separae Esimaions of Vehicle Sock, Mean uel Inensiy, and Mean Annual Driving Disance. Journal of Transpor Economics and Policy 31(3): ayard, P. Richard G., and Alan A. Walers, Microeconomic Theory. M c Graw-Hill, New York. ee, Douglas B, ull Cos Pricing of Highways. Deparmen of Transporaion, Washingon, D.C. iman, Todd, Socially Opimal Transpor Prices and Markes: Principles, Sraegies and Impacs. Vicoria Transpor Policy Insiue, Vicoria, Briish Columbia, Mayeres, Inge, The Efficiency Effecs of Transpor Policies in he Presence of Exernaliies and Disorionary Taxes. Journal of Transpor Economics and Policy 34: Mayeres, Inge, Sara Ochelen, and Sef Proos, The Marginal Exernal Coss of Urban Transpor. Transporaion Research D 1: Mayeres, Inge, and Sef Proos, 2001a. Should Diesel Cars in Europe be Discouraged? Regional Science and Urban Economics: 31(4): Mayeres, Inge, and Sef Proos, 2001b. Marginal Tax Reform, Exernaliies and Income Disribuion. Journal of Public Economics 79: McCubbin, Donald R., and Mark A. Delucchi, The Healh Coss of Moor-Vehicle-Relaed Air Polluion. Journal of Transpor Economics and Policy 33: Mecalf, Gilber E., Environmenal evies and Disorionary Taxaion: Pigou, Taxaion, and Polluion. Working Paper 7917, Naional Bureau of Economic Research, Cambridge, Mass., Sepember. 35

39 Resources for he uure Miller, Ted, Variaions beween Counries in Values of Saisical ife. Journal of Transpor Economics and Policy 34: Mohring, Herber, Congesion. In Essays in Transporaion Economics and Policy: A Handbook in Honor of John R. Meyer, ed. by José A. Gómez-Ibáñez, William B. Tye, and Clifford Winson (Washingon, D.C.: Brookings Insiuion), pp Newbery, David M., Road User Charges in Briain. Discussion Paper No. 174, Cener for Economic Policy Research, ondon. Newbery, David M., Road User Charges in Briain. Economic Journal 98 (conference 1988): Newbery, David M., Pricing and Congesion: Economic Principles Relevan o Pricing Roads. Oxford Review of Economic Policy 6(2): Newbery, David M., Should Carbon Taxes Be Addiional o Oher Transpor uel Taxes? Energy Journal 13(2): Newbery, David M., Royal Commission Repor on Transpor and he Environmen Economic Effecs of Recommendaions. Economic Journal 105: Nordhaus, William D., Managing he Global Commons: The Economics of Climae Change. Cambridge, MA, MIT Press. Nordhaus, William D., and Joseph Boyer, Warming he World: Economic Models of Global Warming. Cambridge, MA, MIT Press. Parry, Ian W.H., Comparing he Efficiency of Alernaive Policies for Reducing Traffic Congesion. Journal of Public Economics, forhcoming. Parry Ian W.H. and Anonio M. Beno, Revenue Recycling and he Welfare Effecs of Road Pricing. Scandinavian Journal of Economics 103: Parry Ian W.H. and Wallace E. Oaes, Policy Analysis in he Presence of Disoring Taxes. Journal of Policy Analysis and Managemen 19: Peirson, J., I. Skinner, and R. Vickerman, Esimaing he Exernal Coss of UK Passenger Transpor: The irs Sep owards an Efficien Transpor Marke. Environmen and Planning A 27:

40 Resources for he uure Pickrell, Don, and Paul Schimek, Trends in Personal Moor Vehicle Ownership and Use: Evidence from he Naionwide Personal Transporaion Survey. In US ederal Highway Adminisraion, Proceedings from he Naionwide Personal Transporaion Survey Symposium Ocober 29-31, 1997, No. 17 of Searching for Soluions: A Policy Discussion Series, US HWA, Washingon, D.C., pp Porer, Richard C., Economics a he Wheel: The Coss of Cars and Drivers. Academic Press, San Diego, CA. Poerba, James M., Is he Gasoline Tax Regressive? In D. Bradford (ed.), Tax Policy and he Economy 5. MIT Press, Cambridge, MA. Puller, Seven., and orna A. Greening, Household Adjusmen o Gasoline Price Change: An Analysis Using 9 Years of US Survey Daa. Energy Economics 21: Quine, Emile, ull Social Cos of Transporaion in Europe. In: The ull Coss and Benefis of Transporaion, ed. by David. Greene, Donald W. Jones, and Mark A. Delucchi. Springer-Verlag, pp Ramsey, rank P., A Conribuion o he Theory of Taxaion. Economic Journal 37: Rohengaer, Werner, Exernal Effecs of Transpor. In Jacob B. Polak and Arnold Heerje, eds., Analyical Transpor Economics: An Inernaional Perspecive. Chelenham, UK: Edward Elgar, pp Rouwendal, Jan, An Economic Analysis of uel Use per Kilomere by Privae Cars. Journal of Transpor Economics and Policy 30: Sandmo, Agnar, Opimal axaion An Inroducion o he ieraure. Journal of Public Economics 6: Schimek, Paul, Gasoline and Travel Demand Models Using Time Series and Cross-Secion Daa from Unied Saes. Transporaion Research Record 1558: Small, Kenneh, Urban Transporaion Economics. Vol. 51 of undamenal of Pure and Applied Economics. Char, Swizerland: Harwood Academic Publishers. Small, Kenneh A., and Jose A. Gomez-Ibanez (1999). Urban Transporaion. In Paul Cheshire and Edwin S. Mills, eds., Handbook of Regional and Urban Economics, Volume 3: Applied Urban Economics. Amserdam: Norh-Holland, pp

41 Resources for he uure Small, Kenneh A., and Camilla Kazimi, On he Coss of Air Polluion from Moor Vehicles. Journal of Transpor Economics and Policy 29: Small, Kenneh A., Clifford Winson, and Carol A. Evans, Road Work: A New Highway Pricing and Invesmen Policy. Brookings Insiuion, Washingon, D.C. Tol, Richard S.J., Samuel ankhauser, Richard Richels and J. Smih, How Much Damage will Climae Change Do? Recen Esimaes. World Economics 1: U.K. DOE, Transporaion Saisics Grea Briain: 2000 Ediion. UK Deparmen of he Environmen, Transporaion and he Regions, ondon, UK. U.K. Minisry of Transpor, Road Pricing: The Economic and Technical Possibiliies. Her Majesy's Saionery Office, ondon. US DOE, Policies and Measures for Reducing Energy Relaed Greenhouse Gas Emissions: essons from Recen ieraure. Repor No. DOE/PO-0047, US Deparmen of Energy, Office of Policy and Inernaional Affairs, Washingon, D.C., July. US Energy Informaion Agency, Annual Energy Review. US Deparmen of Energy, Washingon, D.C. US Energy Informaion Agency, Inernaional Energy Annual. Inerne address accessed June US HWA, Highway Saisics US ederal Highway Adminisraion, Deparmen of Transporaion, Washingon, D.C. US HWA, ederal Highway Cos Allocaion Sudy. US ederal Highway Adminisraion, Deparmen of Transporaion, Washingon, D.C. US HWA, 2000a. Addendum o he 1997 ederal Highway Cos Allocaion Sudy inal Repor. US ederal Highway Adminisraion, Deparmen of Transporaion, Washingon, D.C. US HWA, 2000b. Highway Saisics US ederal Highway Adminisraion, Deparmen of Transporaion, Washingon, D.C. 38

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43 Resources for he uure APPENDIX: ANAYTICA DERIVATIONS OR SECTION 2 A. Definiions or he analyical derivaions we define he following erms: (A1) I = ( 1 ) M I ; η MI = I M ; I η I = ; I d p η = ; d ( p ) θ I = ; p = q + I ( 1 ) ε = ; dm p η M = ; d M c c ( 1 ) ε = ; M d p η = ; d M = M B. Deriving (2.9) Using (2.1)-(2.3), (2.6) and (2.7), he household s uiliy maximizaion problem can be expressed as: (B1) V (,, P, A, π ) Max = C, M, N,, H u( ψ ( C, M, πm, G), N) ϕ( P) δ ( A) + µ { M (, H ) M } + λ {( 1 )( N πm ) C ( q + ) H} where λ and µ are agrange mulipliers and V(.) is he indirec uiliy funcion. (We have suppressed as argumens of V hose parameers ha are held consan hroughou our simulaion, namely q and G.) The firs-order condiions can be expressed, afer using Euler s heorem ( M u C (B2a) = 1 λ where u = 1 λ u = λ N M ; ; M p = M M H ): + H (B2b) p ( q + ) α + α + νπ ; α M ; α H M ; v u / λ M M HM M / HM / 1 T Households equae he marginal benefi of driving (in dollars), u M / λ, wih p M, he full price of driving. The laer includes fuel used per mile ( α M ), oher marke inpus per mile ( α HM ), and ime per mile (π), all muliplied by heir respecive prices. Noe ha he price of ime, v, is less han he ne wage (1 ) if he marginal uiliy of ravel ime, u T, is posiive. The equaliy of marginal uiliy u M /λ and full price p M holds due o he envelope heorem, even hough p M is endogenous o he individual consumer. 40

44 Resources for he uure Because of he homogeneiy propery of M(.), he inpu raios for producing ravel are funcions only of prices, which are all consan excep for he fuel ax rae. Therefore we can wrie he inpu raios as α M ( ) and α HM ( ). In pracice, we simplify by specifying α M ( ) as a simple empirical funcion raher han deriving i from he full model. Using (B2a) and (2.6)-(2.7), we can hen obain he demand funcions in a convenional manner, wriing hem as (B3a) C = C p M, ) ; M = M p, ) M ; = p, ) ; M ( ( ( = π, ) = α ( ) M ( p, ) ; H = H, π, ) = α ( ) M ( p, ) (, M M ( HM M The full price of driving depends on all he exogenous variables: (B3b) p = p, π, ). M M ( Parially differeniaing (B1), we can eliminae erms using (B2), he firs-order condiions for and H, and he Euler equaion for M(.); we hen obain: (B4) V V V V V = λ ; = λ ; = ϕ (P) ; = δ (A) ; = λvm P A π Toally differeniaing (2.8) while holding G consan gives: (B5) d d + = d + d d d This is he balanced budge reducion in he labor ax from an incremenal increase in he gasoline ax. The welfare effec of an incremenal increase in he gasoline ax is found by using (B4) o wrie he oal derivaive dv/d, while aking ino accoun he budge consrain via (B5) and he exernaliies via (2.3)- (2.5). Because his is a normaive analysis, he aggregaes and M are variables in his calculaion, and are se equal o and M. The resul is (2.9). C. Deriving (2.11) and (2.12) To deermine he opimal ax * erms of empirically measurable elasiciies., we will se (2.9) o zero. Bu before ha, we wrie is componens in irs, consider he las erm in (2.9). Subsiuing (B3b) ino (B3a), we can wrie as a funcion of, π, and. Differeniaing oally as changes: 41

45 Resources for he uure (C1) d d d d d d + + = π π Subsiuing (C1) ino (B5) and solving for d /d yields an alernaive expression for he balanced-budge change in labor ax rae: (C2) d d d d d d = π π Subsiuing (C2) ino (C1) and muliplying by yields: (C3) + = d d MEB d d MEB d d π π / where MEB is defined in (2.12b). We now consider he erm in brackes in (C3). Using (B2b) and (B3a), and he chain rule for differeniaing π(m): (C4) M p M α = ; q p M = π ; d dm d d π π = rom he Slusky equaions applied o he demand funcions in (B3a): (C5) M I p p M c M = ; I c = where superscrip c denoes a compensaed coefficien. rom he Slusky symmery propery for goods in he uiliy funcion: (C6) c M c M p = eisure is weakly separable in our uiliy funcion. Therefore when is price changes due o a change in, he resuling changes in he demands for consumpion and for ravel occur only hrough a change in disposable income (ayard and Walers 1978, p. 166). Therefore: (C7) c c I M M = ) 1 ( 42

46 Resources for he uure where (1 c ) / is he change in disposable income following a compensaed increase in he labor ax. Using (C4)-(C7) and he definiions of I, η MI and E C from (A1) and (2.10): c (C8) = ( η MI 1) ; dπ = η π d MI c E I C dm d c Subsiuing (C8) in (C3), using he definiions of ε, ε and η I in (A1), and using he Slusky c equaion ε = ε + η I gives: d d MEB c C dm c (C9) = MEB ε ( η 1) + E { ε (1 η ) ε } d d Using (C9) we can now equae (2.9) o zero. Dividing hrough by η in (A1) and MEB in (2.12b), we obain (2.11). inally, using (B1): ε MI d d / d MI, and using he definiion of (C10) d d = M dm d + Mα M Muliplying hrough by ( q + ), and using α = ( d / d ) M / M / M, we obain he decomposiion for η in (2.12b). D. Deriving (2.13) irs, use he definiions of η, η M, and MEC o wrie (2.9) as: 1 dv λ d (D1) = ( MEC ) η p + d d where p q +. Nex, subsiue (C9) for he las erm, regroup erms, and facor ou (η /p ) o ge 1 dv λ d (D2) = [ MEC (1 + MEB )] η p 43

47 Resources for he uure η p τ 1 τ ε C (1 ηmi ) ε τ p η β α C { ε (1 η ) ε } τ C + MI M where τ /( 1 ). rom (2.12b) we can see ha ( 1 + MEB ) = 1/(1 τ ε ). Subsiuing his in he second erm, facoring ou (1+MEB )(η /p ) from boh erms, and using (2.11) yields (2.13b). E E. VMT Tax Suppose we replace he fuel ax by a VMT ax, i.e. a ax on M. To keep noaion as similar as possible, v v v denoe he ax rae by α, where is he inverse of fuel economy wih no fuel ax, deermined M α M from (2.12c) wih =0. Because he producion funcion M(,H) is homogeneous and we no longer vary v he price of eiher or H, he inpu raio α is now consan a. Therefore he ax paymens can be M v v wrien as α M, in analogy o he ax paymens in he case of he fuel ax. M = As a resul, he above derivaions all apply wih replaced by. This includes replacing any v derivaive wih respec o by he corresponding derivaive wih respec o. As already noed, α M v α M is consan wih respec o where M v v. Equivalenly, η = 0, so we see from (2.12b) ha η = η and β=1, v M (E1) q + dm q + d η. v v v v η M ; v v M d d The quesion remains: Wha is he empirical counerpar of? Recall ha he raveler is opimizing inpus and H o produce M a leas cos. Therefore he price of ravel p M changes in eiher v case by imes he change in ax rae ( d or d ). To show his more formally, we decompose he changes in M boh in he VMT-ax case and he fuel-ax case. Recall ha M=M(p M, ) from (B3a), wih p M given by (B2b). Ignoring he small feedback from changes in via balanced-budge consideraions (which is also ignored in our empirical measuremen of he elasiciies), we can use he chain rule as follows: v η M (E2) (E3) dm d v dm d M = α p M M p M M =. M dp d 44

48 Resources for he uure The cos funcion for producing M is jus yields C( M ; ) = ( p νπ M. Applying Shephard s emma M ) (E5) dpm M = d v which implies ha he righ-hand sides of (E2) and (E3) are equal. Equivalenly, η = η M M. This means ha for purposes of calculaing he VMT ax, η M is held a he same value as in he fuel-ax calculaion, while η η / β is reduced o he value η as β is changed o one. v rae α v M M In order o compue he welfare effecs of replacing he fuel ax by a VMT ax a some arbirary M, we proceed as follows. irs, we gradually reduce he fuel-ax rae o zero, using (2.12c) o calculae he value of fuel efficiency and inegraing (2.13b) o calculae he welfare change. Second, we use (2.11) o calculae he opimal fuel-equivalen VMT ax rae, equal o is previous value, η =η M, and α M o is zero-fuel-ax value, v*. In his calculaion we se β=1, η M v α M. Third, using his value of v* * v o replace in (2.13b), we inegrae (2.13b) (wih η replaced by η M ) while raising from 0 o. The oal welfare change is he sum of he wo inegraion seps. 45

49 Resources for he uure igure 1. Gasoline Excise Taxes in Differen Counries Gasoline Tax (US cens/gallon) UK rance Germany Ialy Japan Spain Ausralia New Zealand Canada USA Source: Inernaional Energy Associaion, Energy Prices and Taxes, irs Quarer

50 Resources for he uure igure 2. Sensiiviy of Opimal Gasoline Tax o Parameer Variaion US UK opimal ax, ce n s/gal opimal ax, cens/gal opimal ax, cens/gal polluion (disance), cens/mile congesion coss, cens/mile acciden coss, cens/mile opimal ax, cens/gal opimal ax, cens/gal opimal ax, cens/gal gasoline price elasiciy VMT porion of gas elasiciy VMT expendiure elasiciy 47

51 Resources for he uure Table 1. Parameer Assumpions (US unis) Parameer Iniial fuel efficiency: (miles/gal) 0 1/ M Polluion damages, disancerelaed: E PM (cens/mile) Polluion damages, fuel-relaed: P M E (cens/gal) Exernal congesion coss: E C (cens/mile) Exernal acciden cos: E A (cens/mile) US UK Cenral value range Cenral value range α Gasoline price elasiciy: η VMT porion of gas price elasiciy, β VMT expendiure elasiciy: Uncompensaed labor supply elasiciy: ε Compensaed labor supply elasiciy: c ε η MI Governmen spending/gdp: α G Gasoline producion share: Producer price of gasoline: q (cens/gal) Iniial ax rae on gasoline: 0 (cens/gal) α

52 Resources for he uure Table 2. Benchmark Calculaions of he Opimal Gasoline Tax Rae (All moneary figures in cens/gal a US 2000 prices) Elemens in Equaion (2.11): uel efficiency, M/ (miles/gal) Marginal exernal cos, MEC Polluion fuel componen, US UK P E 6 6 PM Polluion disance componen, ( β / α ) E M C Congesion componen, ( β / α ) E M A Acciden componen, ( β / α ) E M Marginal excess burden, MEB Adjusmen o MEC for excess burden, MEC [(1+MEB ) -1-1] Componens of opimal gasoline ax rae: Adjused Pigovian ax: Polluion, fuel-relaed 5 5 Polluion, disance-relaed Congesion Accidens Ramsey ax Congesion feedback 1 7 * Opimal gasoline ax rae ( ) Naïve gasoline ax rae, a MEC a The naïve rae is MEC compued from (2.12a) wih 0 α M = α M and β=1. 49

53 Resources for he uure Table 3. Welfare Effecs of Gasoline Tax Raes Using Benchmark Parameers (Relaive o curren rae, expressed as percen of iniial preax fuel expendiures) uel ax rae US UK Rae (cens/gal) Welfare change a (% of preax expen.) Rae (cens/gal) Welfare change (% of preax expen.) * * * Opimal rae ( ) * * 1 Naïve rae ( MEC )

54 Resources for he uure Table 4. VMT Tax: Benchmark Parameers US UK VMT ax rae v ( α ) M VMT ax rae (cens/mile) Equiv. fuel ax rae (cens/gal) v ( ) Welfare change a (% of preax expen.) VMT ax rae (cens/mile) v ( α ) M Equiv. fuel ax rae (cens/gal) v ( ) Welfare change a (% of preax expen.) (a) Equiv. iniial rae 0 0 ( α ) M (b) Equal-revenue ( 0 α ) M 1 0 (c) Naïve ( MEC α ) M v (d) Opimal ( * α ) M Componens b v* of : Adjused. Pigov. ax Ramsey ax Congesion feedback 2 13 a Welfare effec of replacing he iniial fuel ax by a VMT ax a he rae shown. Calculaed using (2.11)-(2.13) wih 0 β=1 and η =. M η M b v* v The componens of are he hree idenified erms in equaion (2.11), wih replaced by.and wih β=1, α M held a is value when =0, and η se equal o η M. 51

55 Resources for he uure Table 5. Comparison of uel Tax wih VMT Tax: US Componens of opimal gasoline ax rae: Adjused Pigovian ax: uel Tax ( /gal) Gasolineequivalen rae ( /gal) VMT Tax Acual Rae ( /mile) Global warming Polluion Congesion Accidens Ramsey componen Congesion feedback * v* Opimal ax rae ( or ) uel efficiency (miles/gal)

56 Resources for he uure Table 6. Effecs of Governmen Revenue Requiremen on Opimal Tax Rae and Toal Exernal Cos (Exernal cos is relaive o zero revenue requiremen, as percen of iniial preax fuel expendiures) α G * * US Adj. Pigov. Tax Toal Exern. Cos * * UK Adj. Pigov. Tax Toal Exern Cos Table 7. Values for Exernal Coss ha Yield High and ow Values for he Opimal Gasoline Tax (expressed relaive o he exernal coss for he benchmark case) VMT porion of gasoline demand elasiciy, β low value: =$0.40/gal US high value: =$1.50/gal low value: =$1.00/gal UK high value: =$2.80/gal

57 Resources for he uure Table 8. Mone Carlo Resuls for Approximae Opimal Gasoline Tax Amoun in US cens/gal (X) US Probabiliy ha * < X Amoun in US cens/gal (X) UK Probabiliy ha * < X 54