Is Pay-as-You-Drive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes?

Is Pay-as-You-Drive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes? By Ian W.H. Parry Despite concerns about US 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 non-starter. Any fuel conservation easures that ight be ore politically palatable are generally perceived as inferior to gasoline taxes on efficiency grounds. This paper challenges the latter assertion: it shows a policy that should 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. It involves auto insurance copanies switching fro current, annual lup-su preius, to preius levied on annual iles driven, scaled by a driver s rating factor (which varies 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 aount 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 low-ileage drivers have an incentive to opt for PAYD (Todd Litan 21). 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 (Aaron Edlin and Pinar Karaca-andic 24). Gasoline taxes are superior to PAYD on cost-effectiveness grounds as they exploit all behavioral responses for reducing fuel deand. They encourage otorists to drive less, anufacturers to incorporate 1

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 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, as 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. 1 I. 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 Variables are expressed in per capita ters on an annualized basis, a bar denotes an econoy-wide 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 and the optiu tariff fro US onopsony power in the world oil arket (Paul N. Leiby et al. 1997). E is disutility fro ileage-related 2

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. The agent s budget constraint is: (2a) C + v( pv + p) = I + π + G (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 basis and a VT tax respectively; both are initially set at zero. 2 θ is aintenance costs, where θ () >, included to ensure ore than one vehicle is purchased. 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 >, as this requires incorporation of technologies to iprove engine efficiency and transission, etc. 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: (3) G = t, = / f 3

where is total fuel use. Higher/lower fuel tax revenues are reflected in higher/lower household transfers. 3 irs are copetitive, produce 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 x is the expected insurance clai for property daage and edical expenses per ile driven. 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 (all analytical derivations are available on request): dw (5) = dt E t λ d dp E + pa λ dv dp E v λ d dp Price coefficients are assued negative, λ is the arginal utility of incoe, and arginal external ileage costs, inclusive of costs to insurance copanies. E = E + x denotes The first coponent in (5) is the welfare effect in the gasoline arket. It is positive if the arginal external cost of fuel externalities in dollars exceeds 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 if 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. 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 4

η < is the gasoline deand elasticity. This reflects both changes in fuel econoy and in VT; the latter reflects both reduced iles per vehicle and reduced deand for vehicles. 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. ro (5) and (6) and soe anipulation we obtain the welfare effect per gallon of fuel reduction: dw / dt (7) = d / dt E t λ E λ p E fβ (1 β ) + fβ λ a + β (iii) VT tax. or this policy, we convert the VT tax into its equivalent fuel tax at initial fuel econoy t f, and use the sae elasticities, except that, because fuel econoy is unchanged, we assue fuel deand responds only to the ileage coponent of the fuel deand elasticity, β η. The arginal welfare effect, per gallon of fuel reduction, is: dw / dt (8) = d / dt E ( t λ + t f ) E λ p f E (1 β ) + f λ a + β There are two ain differences copared with (7). irst, and ost iportant, efficiency gains fro reducing ileage externalities are not scaled back by β, as all, rather than a fraction, of the reduction in fuel use coes fro reduced driving. Second, the overall tax distortion, converted to its equivalent in the gasoline arket, t + t f, will exceed t in (7) for a given fuel reduction, iplying a higher cost when externalities are ignored; a higher tax is required because only VT, and not fuel econoy, respond to the VT tax. (ii) PAYD. An increase in 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; analogous to (8) the arginal welfare effect is: 5

dw / dpi E (9) = ( t d / dp λ i + p i f ) E + f λ β p i will exceed t for a given reduction in fuel deand, given the vehicle coponent of the change in ileage is absent. Thus, the equivalent tax distortion for a given reduction in fuel is larger than under the VT tax. However, the welfare gain fro reduced VT is larger because all of it coes fro reduced iles per vehicle, for which none of the external costs are offset by initial insurance preius. 4 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). II. Paraeters Table 1 suarizes assued paraeter values and sources. ollowing 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 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. Adittedly, fuel-related externalities are highly contentious; however, it is the ileage-related externalities that deterine the (absolute) differences between the policies studied here. arginal ileage externalities su to 12 cents per ile, or $2.4 per gallon at initial fuel econoy. Thus, ileage externalities are ten-ties as large as fuel externalities; congestion is the ost iportant (6.5 cents per ile), followed by accidents (4.), and then local pollution (1.5). The gasoline deand elasticity is.55, with 6% of it accounted for by long run iproveents in fuel econoy, and 4% fro reduced VT; of the latter, 67% coes 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 ($1.3 per gallon). 6

III. Results If PAYD were fully ipleented gasoline deand would fall by 11.4 billion gallons (9.1%). The equivalent fuel reduction could be achieved by increasing the gasoline tax by 27 cents per gallon, or a VT tax of 3.9 cents per ile. Welfare effects under the three policies are shown in igures 1-3. 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 per vehicle 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 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. We conclude that PAYD appears to ake ore sense on efficiency grounds than higher fuel taxes as a first step towards reducing conventional otor vehicle fuels. A lesson is that ipacts on a broad range of otor vehicle externalities should be considered in evaluating other policy options for transportation, such as subsidies for alternative fuel vehicles and higher fuel econoy standards. 7

Table 1. Paraeter Values Paraeter Value Source Coponents of fuel externalities carbon eissions, cents/gal. 12. Nat. Research Council (22) oil dependency, cents/gal. 12. Nat. Research Council (22) su, cents/gal. 24. Coponents of ileage externalities congestion, cents/i. 6.5 Parry et al. (24) accident, cents/i. 4. iller et al. (1998) local pollution, cents/i. 1.5 Parry et al. (24) su, cents/i. 12. uel deand elasticity -.55 Parry/Sall (24) portion due to VT.4 Parry/Sall (24) portion of VT elast. due to i./veh..67 Johansson/Schipper (1997) Initial gasoline tax, cents/gal. 4 Parry/Sall (24) Initial retail gasoline price 15 Parry/Sall (24) Initial (on road) fuel econoy, i./gal. 2 Parry/Sall (24) Initial annual fuel consuption, bn. gals. 13 Energy Info. Adin. (22) Current insurance costs, cents/i. 6.5 Litan (21) 8

igure 1. Welfare Effect under uel Tax 25 2 welfare effect, $bn. 15 1 5 2 4 6 8 1 12-5 -1 gasoline reduction, bn. gals. gasoline vehicles iles/veh. su igure 2. Welfare Effect under VT Tax 25 2 welfare effect, $bn. 15 1 5 2 4 6 8 1 12-5 -1 gasoline reduction, bn. gals. gasoline vehicles iles/veh. su igure 3. Welfare Effect under PAYD 25 2 welfare effect, $bn. 15 1 5 2 4 6 8 1 12-5 -1 gasoline reduction, bn. gals. gasoline iles/veh. su 9

References Edlin, Aaron, S. 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, 23. Edlin, Aaron, S. and Pinar Karaca-andic. The Accident Externality fro Driving. Working paper, University of California, Berkeley, 24. Energy Inforation Adinistration. Annual Energy Review. Washington, DC, 22. 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, 1997, 31, pp. 277-292. Leiby, Paul N., Donald W. Jones, T. Randall Curlee, and Russell Lee. Oil Iports: An Assessent of Benefits and Costs. Oak Ridge, Tennessee: Oak Ridge National Laboratory, 1997. Litan, Todd. Distance-Based Vehicle Insurance easibility, Benefits and Costs: Coprehensive Technical Report. Victoria: Victoria Transport Policy Institute, 21. 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, 1998, 1635, pp. 81-87. National Research Council. Effectiveness and Ipact of Corporate Average uel Econoy (CAE) Standards. Washington, DC: National Acadey Press, 22. Parry, Ian W.H. and Kenneth A. Sall. Does Britain or The United States Have the Right Gasoline Tax? Aerican Econoic Review, 24, forthcoing. Parry, Ian W.H., Carolyn ischer, and Winston Harrington. Should Corporate Average uel Econoy (CAE) Standards be Tightened? Discussion paper, Resources for the uture, Washington, DC, 24. Shirley, Chad and Clifford Winston. ir Inventory behavior and the Returns fro Highway Infrastructure Investents. Journal of Urban Econoics, 24, 55, pp. 398-415. 1

ootnotes Resources for the uture, 1616 P Street NW, Washington DC, 236. Phone (22) 328-5151; fax (22) 939-346; eail parry@rff.org. I a grateful to Richard Arnott, Joel Darstadter and Ken Sall for very helpful coents. 1 The discussion is related to earlier papers, by Edlin (1999) on PAYD and Ian W.H. Parry and Kenneth A. Sall (24) on fuel and VT taxes; this paper differs by coparing welfare effects of all three policies for given fuel reductions. There are ore efficient policies than PAYD to reduce ileage externalities (e.g., peak period pricing to reduce congestion), but these policies are beyond our scope. 2 Current preius give odest discounts for low-ileage, though ost drivers are well above or below the threshold so the per-ile preiu is effectively zero. However the ore people drive, the ore likely they are to crash, and face higher future preius; by ignoring this, we oderately overstate the effectiveness of PAYD. We also abstract fro vehicle registration fees, which average about $2 per year. Incorporating the would oderately reduce efficiency gains fro the VT tax. 3 If instead revenues paid for highways or cuts in other distortionary taxes, this ay not greatly strengthen the case for fuel taxes vis-à-vis PAYD. Chad Shirley and Clifford Winston (24) estiate the (average) social rate of return on highway projects is around 5%; as this is a typical discount rate used in project evaluation, this estiate suggests the social value of an additional $1 of highway spending is approxiately $1. Suppose instead we valued extra revenue at its dollar aount plus the efficiency gain 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 if driving is a relative leisure copleent (Parry and Sall 24), though it ay still offset a large portion of the. Although PAYD raises no revenue for recycling, it ay 11

not copound efficiency costs fro prior labor taxes either, as it has no first order effect on overall driving costs. 4 Welfare gains fro PAYD would be greater with heterogeneous agents because the reduction in driving would be ore concentrated aong those with greater preius and therefore greater accident risk. 12