DISCUSSION PAPER. Is Pay-As-You-Drive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes? Ian W.H. Parry. April 2005 RFF DP 05-15

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1 DISCUSSION PAPER April 25 R DP 5-15 Is Pay-As-You-Drive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes? Ian W.H P St. NW Washington, DC

2 Is Pay-As-You-Drive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes? Ian W.H. Abstract Gasoline taxes are widely perceived as the ost efficient instruent for reducing gasoline consuption because they exploit all behavioral responses for reducing fuel use, including reduced driving and iproved fuel econoy. At present, however, higher fuel taxes are viewed as a political nonstarter. Pay-as-you-drive (PAYD) auto insurance, which involves replacing existing lup-su preius with preius that vary in proportion to iles driven, should be ore practical, since they do not raise driving costs for the average otorist. We show that when ipacts on a broad range of otor vehicle externalities are considered, PAYD also induces significantly higher welfare gains than coparable gasoline tax increases, for fuel reductions below 9%. The reason is that under PAYD, all of the reduction in fuel use, rather than just a fraction, coes fro reduced driving; this produces a substantial additional efficiency gain because ileage-related external costs (especially congestion and accidents) are relatively large in agnitude. Key Words: gasoline tax; pay-as-you-drive insurance; ileage tax; welfare effects; otor vehicle externality JEL Classification Nubers: H21, H23, R48 25 Resources for the uture. All rights reserved. No portion of this paper ay be reproduced without perission of the authors. Discussion papers are research aterials circulated by their authors for purposes of inforation and discussion. They have not necessarily undergone foral peer review.

3 Resources for the uture Contents 1. Introduction Analytical odel... 6 A. Assuptions... 6 B. Welfare Effects fro Reducing uel Paraeters Results Conclusion and Suggestions for uture Work References Appendix

4 Resources for the uture Is Pay-As-You-Drive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes? Ian W.H. 1. Introduction Despite concerns about U.S. dependence on a volatile world oil arket, greenhouse gases fro fuel cobustion, and air quality effects of obile source eissions, substantially higher federal gasoline taxes are currently a political nonstarter. Any fuel conservation easures that ight be ore politically palatable are perceived to be inferior to gasoline taxes on efficiency grounds. 1 This paper challenges the latter assertion: it shows that a policy that could be far ore feasible than a large increase in fuel taxes can also achieve a significant reduction in fuel deand, with a draatically larger welfare gain. The policy is pay-as-you-drive (PAYD) insurance, which is otivated on the grounds of reducing ileage, particularly by high-risk drivers, and reducing the nuber of uninsured drivers by lowering preius for low-ileage vehicles. Under PAYD, auto insurance copanies would switch fro annual lup-su preius to preius levied on annual iles driven, scaled by a driver s rating factor (which would vary with age, crash record, and region). By converting soe of the fixed costs of vehicle ownership into costs that vary with ileage, the policy reduces the distance that vehicles are driven and thereby reduces fuel deand. And unlike under higher fuel taxes, driving costs (fixed plus variable) for the average otorist do not increase; hence political opposition to this policy should be ore uted. To soe extent, we ay see a arket-driven transition to PAYD over the next decade or two, given that technology for onitoring vehicle ileage is iproving rapidly, and that lowileage drivers (who currently subsidize high-ileage drivers) have an incentive to opt for Eail web I a grateful to Richard Arnott, Joel Darstadter, and Ken Sall for helpful coents. A version of this paper will appear in the Aerican Econoic Review Papers and Proceedings One caveat to this has to do with the contentious issue of whether vehicle buyers undervalue lifetie fuel costs; if they do, fuel econoy regulations could be a ore effective way to increase fuel econoy than fuel taxes (e.g., Greene 1998). 4

5 Resources for the uture PAYD. 2 However, even in the absence of externalities discussed here, tax incentives ay still be warranted to hasten such a transition because individual insurance copanies do not consider benefits to other copanies fro reduced accident risks when its own clients convert to PAYD (Edlin and Karaca-andic 24). Ignoring externalities, gasoline taxes are far superior to PAYD on cost-effectiveness grounds because they exploit all behavioral responses for reducing fuel deand. They encourage otorists to drive less, anufacturers to incorporate fuel-saving technologies in new vehicles, and consuers to choose saller, fuel-efficient vehicles. PAYD provides incentives to drive less but not to iprove fuel econoy. However, this arguent does not account for ipacts on a range of otor vehicle externalities. Estiates of cobined ileage-related externalities traffic congestion, accidents, and local eissions (regulated on a gras per ile basis) are an order of agnitude larger than for cobined fuel-related externalities greenhouse gases and oil dependency (see below). or a given reduction in fuel deand, PAYD will reduce ileage-related externalities far ore than fuel taxes, since all (rather than just a portion) of the reduction in fuel deand coes fro reduced driving. We estiate that fully ipleenting PAYD would reduce gasoline deand by 11.4 billion gallons (9.1%) and increase social welfare by $19.3 billion per year. The sae fuel reduction could be achieved by increasing the federal gasoline tax fro 18 to 45 cents per gallon, but resulting welfare gains are $6.2 billion, just 32% of those under PAYD. We also show that PAYD is slightly ore efficient than a siple tax on vehicle iles traveled (VT) for a given fuel reduction and even perfors fairly well relative to a fully optiized VT tax. A VT tax reduces both iles per vehicle and the vehicle stock; the latter 2 Nearly taperproof odoeters and wireless counication systes or global positioning systes (GPS) transponders are increasingly incorporated in new vehicles. Odoeter readings ight be ade (and forwarded to insurance copanies) when vehicles are taken in for eissions inspections or tune-ups, reported by auto owners theselves with rando verification checks, or recorded reotely on an ongoing basis. Experients with PAYD are eerging at the state level. In Oregon, insurance copanies have been offered a state tax credit of $1 per otorist for the first 1, otorists who sign up for PAYD insurance plans. The Texas legislature recently passed legislation authorizing auto insurance copanies to offer per ile insurance, and state governents in aryland and Connecticut also are considering easures to encourage PAYD. Earlier, econoists had advocated pay-at-the-pup (PATP) insurance (e.g., Vickrey 1968, Khazzoo 1999). PATP is inferior to PAYD because charges do not vary with driver characteristics and uch of the response to fuel taxes coes fro iproveents in fuel econoy rather than reduced driving ( 24). 5

6 Resources for the uture effect is neutralized under PAYD, given that overall insurance costs are (approxiately) unchanged. Efficiency gains fro reducing iles per vehicle exceed those fro reducing vehicle deand because in the latter case, fixed insurance costs partly internalize externalities; consequently, a policy that achieves all of a given reduction in fuel deand through reduced iles per vehicle induces a higher welfare gain. 3 Our analysis is highly siplified (e.g., we assue hoogeneous drivers and vehicles) and is eant to provide only a first coparison of the welfare effects of fuel taxes and PAYD, accounting for ipacts on a broad range of externalities. At the end of the paper we discuss caveats and ways the analysis ight be usefully extended in future work. Below we sketch out a siple analytical odel, discuss paraeter values, deonstrate the above results, and discuss liitations. 2. Analytical odel A. Assuptions Consider a static odel with a large nuber of representative agents, each with utility: (1) U = u( C, ) E ( ) E ( ), = v All variables are expressed in per capita ters on an annualized basis, a bar denotes an econoywide variable perceived as exogenous by individual agents, u(.) is quasi-concave in its arguents, and E, E >. C is a (unit price) general consuption good, is fuel consuption, and is VT, equal to the nuber of vehicles purchased, v, ties iles per vehicle, (v is continuously variable in the aggregate). E is disutility fro fuel-related externalities caused by other agents; it represents (future) daages fro cliate change caused by greenhouse gas eissions, the uninternalized risk of acroeconoic disruption costs fro oil price shocks (e.g., due to teporarily idled labor and 3 The flavor of our results ight be anticipated fro Edlin (23), who uses insurance preiu data to estiate welfare gains fro PAYD, and and Sall (24), who estiate welfare effects of gasoline and VT taxes. This paper differs by coparing all three policies for given reductions in fuel deand accounting for all the ajor 6

7 Resources for the uture capital), and the optiu tariff fro U.S. onopsony power in the world oil arket. E is disutility fro ileage-related externalities; it represents costs of traffic congestion, local eissions (regulated on a gras per ile basis), and traffic accidents. The latter includes, for exaple, injury risk to pedestrians and other road users but (for now) excludes clais on insurance copanies; own driver injury risks are internalized in agents travel decisions. 4 The agent s budget constraint is as follows: (2a) C + v( p + p = I + G v ) + π (2b) p = p / f + pi + t + θ ( ), p = q + t (2c) p = p p ( f ) v a + P In (2a), p v and p are the (fixed) cost of owning a vehicle and the (variable) per ile driving cost, respectively; I, π, and G are exogenous to individual agents and denote labor incoe, profit incoe, and a cash transfer fro the governent. In (2b), per ile costs consist of four coponents. p /f is fuel costs where p is the consuer price of gasoline, equal to the producer price q plus a specific tax t, and f is fuel econoy, or iles per gallon. p i and t denote insurance preius perceived on a per ile auto externalities. Of course, there are ore efficient policies than PAYD and VT taxes to reduce ileage externalities (e.g., peak-period pricing to reduce congestion), but these policies are beyond our scope. 4 or discussions of otor vehicle externalities, see HWA (2), Litan (23), and Sall (24), and Porter (1999); on accidents and oil dependency in particular, see iller et al. (1998) and Leiby et al. (1997) respectively. 7

8 Resources for the uture basis and a VT tax, respectively; both are initially set at zero. 5 θ is aintenance costs, where θ () >. 6 In (2c), vehicle ownership costs consist of an annual lup-su insurance preiu p a, and (annualized) vehicle purchase costs p P (f). Given other vehicle attributes, consuers pay ore for a ore fuel-efficient vehicle, p P >, since this requires incorporation of technologies to iprove engine efficiency and transission, reduce vehicle drag and rolling resistance, and so forth. Lup-su insurance partly internalizes externalities in the vehicle purchase decision, but not in the decision of how uch vehicles are driven. Agents choose C, v,, and f to axiize (1) subject to (2). The governent budget constraint, equating spending with revenues fro fuel taxes, is as follows: (3) G = t, = / f where is total fuel use. Higher (or lower) fuel tax revenues are reflected in higher (or lower) household transfers. 7 5 Current preius give odest discounts for low-ileage drivers, but because ost drivers are significantly above or below the discount threshold, the per ile preiu is effectively zero. However, the ore people drive, the ore likely they are to be in accidents and face higher preius for the several years; by ignoring this, our results oderately overstate the effectiveness of PAYD. Our analysis also abstracts fro vehicle registration fees, which currently average about $2 per year (Harrington and cconnell 24). Incorporating the would oderately reduce efficiency gains fro introducing a VT tax relative to those fro PAYD. 6 Per ile aintenance costs increase with greater use; this coponent is included siply to ensure that any vehicles (rather than one) are purchased by the representative agent. 7 In practice, revenues ight be used to finance highway projects or reduce other distortionary taxes. However, this possibility ay not greatly strengthen the case for fuel taxes vis-à-vis PAYD. or exaple, Shirley and Winston (24) estiate that the (average) social rate of return on highway projects is around 5%; because this is a typical discount rate used in project evaluation, their estiate suggests that the social value of an additional $1 of highway spending ay be approxiately $1. 8

9 Resources for the uture All firs are copetitive, produce all arket goods using labor with constant returns, and provide the level of fuel econoy deanded by consuers; arket equilibriu equates production costs per vehicle with p P ( f ). Insurance copanies are also copetitive, with expected profits: (4) π = v( p + ( p x) ) a i where x is the expected insurance clai per ile driven (reflecting property daages and a portion of edical services). Profits accrue to households who own firs and are zero in equilibriu. B. Welfare Effects fro Reducing uel (i) Gasoline tax. The welfare change (in dollars), denoted W, fro a arginal increase in t can be expressed (see Appendix) thus: dw (5) = dt E t λ d dp E ~ + pa λ dv dp ~ E v λ d dp where λ is the arginal utility of incoe and ~ E = E + x denotes arginal external ileage costs, inclusive of costs borne by insurance copanies. All of the three price coefficients are assued negative. The first ter on the right in (5) is the welfare effect in the gasoline arket. It is positive if the arginal external cost of fuel externalities, E / λ, exceed the gasoline tax; if not, agents are overcharged for the social costs of fuel use and a reduction in fuel deand reduces efficiency. Second is the welfare effect fro the reduction in vehicle deand; this is positive so Suppose instead we valued extra revenue at its dollar aount plus the efficiency gain that would obtain fro using it to reduce distortionary labor incoe taxes. However, a full assessent of fiscal interactions ust account for the effect of higher driving costs on reducing real household wages and labor supply, and thereby copounding efficiency costs of labor taxes. This efficiency loss ay not offset all of the gains fro recycling additional fuel tax revenues in other tax reductions if driving is a relative leisure copleent ( and Sall 24), though it ay still offset a large portion of the. Although PAYD raises no revenue for recycling, it ay not copound efficiency costs fro prior labor taxes either, as it has no first order effect on overall driving costs. 9

10 Resources for the uture long as the arginal external cost per vehicle, ~ E / λ, exceeds the per vehicle insurance preiu. Third is the welfare gain fro the reduction in ileage as agents drive vehicles less intensively in response to higher fuel costs; this is an unabiguous welfare gain, since there is no per ile charge to offset external costs. We assue deand for fuel, vehicles, and iles per vehicle respond to fuel prices as follows: (6) p = p η, p = p β β η, v v p = p β (1 β ) η where η < is the gasoline deand elasticity. This reflects changes in fuel econoy and in VT; the latter reflects reduced iles per vehicle (for a given vehicle stock) and reduced deand for vehicles (for a given iles per vehicle). β is the (constant) fraction of reduced gasoline that coes fro reduced VT, and β is the (constant) fraction of reduced VT that coes fro reduced iles per vehicle. reduction: ro (5) and (6) and soe anipulation we obtain the welfare effect per gallon of fuel dw / dt (7) = d / dt E t λ ~ E λ ~ p E fβ (1 β ) + fβ λ a + β Assuing ~ E / λ > p, for a given reduction in fuel deand, the larger the fraction a / of it that coes fro reduced VT, the larger the ancillary welfare gain fro reduced ileage externalities. (iii) VT tax. or this policy, we assue deand functions are as follows: (8) p + t = p f β η, p + t = p f β β η, v v p + t = p f β (1 β ) η That is, we convert the VT tax into its equivalent fuel tax at initial fuel econoy and use the sae elasticities as before, except that because fuel econoy is unchanged, we assue fuel deand responds only to the ileage coponent of the fuel deand elasticity, β η. 1

11 Resources for the uture Appendix): The arginal welfare effect, per gallon of fuel reduction, is the following (see dw / dt (9) = d / dt E ( t λ + t f ) ~ E λ p f ~ E (1 β ) + f λ a + β Note two ain differences fro (7). irst, and ost iportant, efficiency gains fro reducing ileage-related externalities are not scaled back by the fraction β, since all (rather than a fraction) of the reduction in fuel use coes fro reduced driving. Second, the tax distortion, converted to its equivalent in the gasoline arket,, will be greater for a given reduction in fuel; a higher tax is required because only iles driven, and not fuel econoy, falls in response to the tax. (ii) PAYD. An increase in the per ile insurance cost p i is equivalent to an increase in the VT tax t, except that revenues are rebated to consuers in a lower annual fee, p a. We assue no change in vehicle deand 8 ; hence, analogous to (9) and (1), deand functions and the arginal welfare effects are as follows: t + t f (1) p + p i = p f β β η, p + p i = p f β β η dw / dpi (11) d / dp i E ( t + pi f λ ) ~ E + f λ β Note that p i will exceed t for a given reduction in fuel deand because the vehicle coponent of the change in ileage is absent. Thus, the equivalent tax distortion in the fuel arket is larger than under the VT tax. However, the welfare gain fro reduced ileage is 8 This assuption would be exact if iles per vehicle were unchanged, and hence total insurance costs were unchanged (fro Equation 4). ileage and total insurance costs both fall oderately, so it is unclear whether vehicle deand would increase or decrease; however, any effect is likely to be very slight. 11

12 Resources for the uture larger. This is because all of it coes fro reduced iles per vehicle, for which none of the externalities are offset by initial insurance preius. 9 We take arginal external costs as constant. Total welfare effects for a given fuel reduction under the three policies are obtained by integrating (7), (9), and (11), using (6), (8), and (1). 3. Paraeters Table 1 suarizes assued paraeter values. We note a few brief points here and refer the reader to the sources listed in the table for ore discussion and justification of chosen values. Based on NRC (22), we adopt values of 12 cents per gallon for carbon daages ($5 per ton of carbon eissions) and 12 cents per gallon for oil dependency externalities ($5 per barrel of oil). Cobined externalities 24 cents per gallon are actually well below the initial (federal and state) fuel tax of 4 cents per gallon, iplying a welfare loss fro the reduction in fuel use itself. Although this result is based on a best assessent of paraeter values, fuelrelated externalities are particularly contentious. 1 However, it is the ileage-related externalities, rather than the fuel-related externalities, that drive the (absolute) differences between the policies studied here. ileage externalities su to 12 cents per ile, or $2.4 per gallon for an initial iles per gallon of 2. Thus, ileage externalities are 1 ties as large as fuel externalities; 9 Welfare gains fro PAYD would be soewhat greater in a heterogeneous agent odel to the extent that rating factors and external accident costs per ile are correlated across drivers, since the reduction in driving would be ore concentrated aong those with highest risk ( 24). 1 Econoic estiates of future cliate change daages are clearly sensitive to assuptions about long-range discount rates and any weights attached to the welfare of rich and poor nations. ost probleatic is the difficulty of allowing for the unknown possibility of abrupt, nonlinear cliate change. Estiates of arginal oil dependency externalities are sensitive to assuptions about future oil prices, and risks of political instability in the Persian Gulf are particularly difficult to gauge. Estiates usually exclude ideast ilitary spending (equivalent to roughly $7 per barrel of oil consuption), since this spending is viewed ore as a fixed cost than as a cost that would vary in response to odest changes in oil iports. They also exclude potentially large global welfare losses fro exercise of arket power by OPEC (e.g., Greene 1991), since this does not in itself drive a wedge between arginal consuer benefit and arginal supply cost in the doestic U.S. oil arket. 12

13 Resources for the uture congestion is the ost iportant (6.5 cents per ile), followed by accidents (4.), and then local pollution (1.5). 11 The gasoline deand elasticity is assued to be.55, with 6% of it accounted for by long-run iproveents in fuel econoy, and 4% due to reduced VT; of the latter, 67% is assued to coe fro reduced ileage per vehicle and 33% fro reduced vehicle ownership. Current lup-su insurance payents are assued equivalent to 6.5 cents per ile (or $1.3 per gallon at initial fuel econoy). 4. Results Welfare effects under the three policies are shown in igures 1 3. If PAYD were fully ipleented, per ile costs would rise by 6.5 cents and gasoline deand would fall by 11.4 billion gallons (9.1%). The equivalent fuel reduction could be achieved by an increase in the gasoline tax of 27 cents per gallon (or an increase in the federal gasoline tax of 147%), or a VT tax of 3.9 cents per ile. Welfare gains fro reducing gasoline are substantially higher under PAYD than under fuel taxes. or the 11.4-billion-gallon decrease in fuel use, welfare gains are $19.3 billion under PAYD, but only 32% of this aount under higher gasoline taxes. This is because welfare gains fro reduced ileage are $27.4 billion under PAYD, copared with $9.7 billion under fuel taxes; this easily outweighs higher losses in the gasoline arket under PAYD ($8.12 billion copared with $3.5 billion under the fuel tax). Overall, axiized welfare gains under PAYD exceed those under the equivalently scaled VT tax by $2.1 billion; again, larger welfare gains fro reduced ileage under PAYD ore than copensate for the larger equivalent fuel tax distortion. We also copute the fully optiized VT tax at 8.9 cents per ile, given the existing fuel tax; this reduces gasoline 11 arginal congestion costs reflect an average across all U.S. cities and rural areas and across peak and off-peak periods, accounting for the saller sensitivity of driving on congested roads to fuel costs. 13

14 Resources for the uture deand by 2.6 billion gallons. However, welfare gains fro this fully optiized tax are $22.5 billion, only oderately larger than those under PAYD. 5. Conclusion and Suggestions for uture Work We conclude that PAYD appears to ake ore sense on efficiency grounds than higher fuel taxes as a first step toward addressing concerns about energy security and greenhouse gases, as long as otor vehicles are dependent on conventional fuels. Other easures will be needed to achieve a ore substantial reduction in gasoline use over the long run, and the suite of potential policies includes subsidies for alternative-fuel vehicles, higher fuel econoy standards, and ileage taxes, in addition to higher fuel taxes. A lesson fro the current paper is that ipacts on a broad range of otor vehicle externalities should be factored into any efficiency coparison of these alternative approaches. However, this paper is eant to provide only a first step in coparing the welfare effects of fuel taxes and PAYD. There are any ways in which the analysis ight be usefully extended in future work. One would be to allow for differences in accident risks across drivers. Those with higher risks (e.g., young drivers or those with prior crash records) would face higher per ile charges and would reduce driving ore than those with relatively low risks. This would strengthen the welfare gain fro PAYD relative to gasoline taxes or a unifor VT tax. Allowing for differences in risks across vehicles, or across different regions, would have a siilar effect. It could also be useful to odel the dynaic transition to PAYD. It is unlikely that PAYD will be andated; instead, it will likely be increasingly offered as an option. The first people to buy it will be low-ileage drivers, which in turn will increase the lup-su preius faced by high-risk drivers. In present value ters, the delay in the conversion of high-ileage drivers could significantly reduce the welfare gains fro PAYD relative to those fro an iediate increase in fuel taxes. inally, exploring the epirical iportance for welfare effects of asyetric inforation in auto insurance ay also be iportant. Drivers know ore about their risks than insurance copanies, with the result that their rating factors ay not fully reflect their true driving risks; 14

15 Resources for the uture again, this could liit welfare gains fro the differentiation in per ile charges across drivers with different risks under PAYD. 15

16 Resources for the uture References Edlin, Aaron S. 23. Per-ile Preius for Auto Insurance. In R. Arnott, B. Greenwald, R. Kanbur, and B. Nalebuff, eds., Econoics for an Iperfect World: Essays in Honor of Joseph Stiglitz. Cabridge: IT Press. Edlin, Aaron S., and Pinar Karaca-andic. 24. The Accident Externality fro Driving. Working paper. University of California, Berkeley. EIA. 22. Annual Energy Review. Washington, DC: Energy Inforation Adinistration. HWA. 2. Addendu to the 1997 ederal Highway Cost Allocation Study inal Report. US ederal Highway Adinistration, Washington, DC: Departent of Transportation. Greene, David L A Note on OPEC arket Power and Oil Prices. Energy Econoics13: Why CAE Worked. Energy Policy 26: Harrington, Winston, and Virginia cconnell. 24. otor Vehicles and the Environent. In T. Tietenberg and H. oler, eds., The International Yearbook of Environental and Resource Econoics. Northapton, A: Edward Elgar, Johansson, Olof, and Lee Schipper easuring the Long-Run uel Deand of Cars: Separate Estiations of Vehicle Stock, ean uel Intensity, and ean Annual Driving Distance. Journal of Transport Econoics and Policy 31: Khazzoo, Daniel J Addressing the Criticiss of Pay-at-the-Pup and Exploring What It Takes to ake Pay-at-the-Pup Public- and Industry-riendly. Discussion paper Washington, DC: Resources for the uture. Leiby, Paul N., Donald W. Jones, T. Randall Curlee, and Russell Lee Oil Iports: An Assessent of Benefits and Costs. Oak Ridge, TN: Oak Ridge National Laboratory. Litan, Todd. 21. Distance-Based Vehicle Insurance easibility, Benefits and Costs: Coprehensive Technical Report. Victoria Transport Policy Institute, Victoria, 21. Litan, Todd. 23. Transportation Cost and Benefit Analysis: Techniques, Estiates and Iplications. Victoria, BC: Victoria Transport Policy Institute. iller, Ted R., David T. Levy, Rebecca S. Spicer, and Diane C. Letina Allocating the Costs of otor Vehicle Crashes between Vehicle Types. Transportation Research Record 1635:

17 Resources for the uture NRC. 22. Effectiveness and Ipact of Corporate Average uel Econoy (CAE) Standards. National Research Council. Washington, DC: National Acadey Press., Ian W.H. 24. Coparing Alternative Policies to Reduce Traffic Accidents. Journal of Urban Econoics 56: , Ian W.H., and Kenneth A. Sall. 24. Does Britain or the United States Have the Right Gasoline Tax? Aerican Econoic Review, forthcoing., Ian W.H, Carolyn ischer, and Winston Harrington. 24. Should Corporate Average uel Econoy (CAE) Standards Be Tightened? Discussion paper Washington, DC: Resources for the uture. Porter, Richard C Econoics at the Wheel: The Costs of Cars and Drivers. San Diego, CA: Acadeic Press. Shirley, Chad, and Clifford Winston. 24. ir Inventory Behavior and the Returns fro Highway Infrastructure Investents. Journal of Urban Econoics 55: Vickrey, Willia Autoobile Accidents, Tort Law, Externalities, and Insurance: An Econoist s Critique. Law and Conteporary Probles 33:

18 Resources for the uture Appendix Deriving (5). Using (1) (4) the consuer s optiization proble is defined by: (A1) V ( t, pi, pa, t, G, π, E, E ) = 1 AX 23 u( C, v) E E where V(.) is indirect utility. Partially differentiating (A1) gives: C,, v + λ { I + G + π C v[ p + p ( f ) + t + ( p + θ ) ] ( q t ) } a P i + (A2) Vt = λ, = λ, = λv, = λ, V G = V π = λ, V V = 1 V p i V p a Vt E = E constant, gives: Totally differentiating the indirect utility function in (A1) with respect to t, keeping p i, p a and t (A3) dv dt = V t + V π dπ + V dt G dg dt + V E E d dp + V E E d dp Using (3), (4), (6), with p i = : (A4) dg dt d dπ d = + t, = xv dt dt dt Substituting (A2) and (A4) in (A3), and dividing by λ, and using p a = x, gives (5), where dw dt = ( dv / dt ) / λ. / Deriving (9). Totally differentiating the indirect utility function in (A1) with respect to t, keeping p i, p a and t constant, gives: (A5) dv dt = V t + f V π dπ + V dt G dg dt + V E E d dp + V E E d dp f = f Here assue an increase in the VT tax of dt is equivalent to an increase in the fuel tax of f dt, with fuel econoy fixed at its initial level, f. Thus, analogous expressions to (A4) apply. Substituting these, and (A2) in (A5), and using = / f, and t = t t f gives, after soe anipulation: + 18

19 Resources for the uture 1 dv (A6) = λf dt E t + t f λ d dp f = f E ~ + pa λ dv dp ~ E v λ d dp anipulation. Dividing by d / dt f d / dt f = f, and using (8), we can obtain (9), after soe 19

20 Resources for the uture Table 1. Paraeter Values Paraeter Value Source Coponents of fuel-related externalities carbon eissions, cents/gal. 12. NRC (22) oil dependency, cents/gal. 12. NRC (22) su, cents/gal. 24. Coponents of ileage-related externalities congestion costs, cents/i. 6.5 et al. (24) accident costs, cents/i. 4. iller et al. (1998) local pollution, cents/i. 1.5 et al. (24) su, cents/i. 12. Total fuel deand elasticity -.55 /Sall (24) portion due to reduced VT.4 /Sall (24) portion of VT coponent due to i./veh..67 Johansson and Schipper (1997) Initial gasoline tax, cents/gal. 4 /Sall (24) Initial retail gasoline price 15 /Sall (24) Initial (on road) fuel econoy, i./gal. 2 /Sall (24) Initial annual gasoline consuption, billion gals. 13 EIA (22) Current insurance costs, cents/i. 6.5 Litan (21) 2

21 Resources for the uture igure 1. Welfare Effect under uel Tax igure 2. Welfare Effect under VT tax igure 3. Welfare Effect under PAYD welfare effect, $bn welfare effect, $bn welfare effect, $bn gasoline reduction, bn. gals. gasoline reduction, bn. gals. gasoline reduction, bn. gals. gasoline vehicles iles/veh. su gasoline vehicles iles/veh. su gasoline iles/veh. su 21

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