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

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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://; 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

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