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Pay-at-the-Pump Auto Insurance
J. Daniel Khazzoom
Discussion Paper 98-13-REV
February 1998, Revised February 2000
1616 P Street, NW
Washington, DC 20036
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Pay-at-the-Pump Auto Insurance J. Daniel Khazzoom Abstract PAY-AT-THE-PUMP is a proposal to replace the current insurance system of lump sum payments for automobile insurance by a mechanism whereby motorists pay for their insurance as they buy fuel for their vehicles.
PAY-AT-THE-PUMP has several advantages. It reduces insurance cost and cross subsidies and enhances equity. It also benefits the environment, safety, balance of payments, and security.
In this paper we study limited but very important issues in the theory and implementation of PAY-AT-THE-PUMP insurance. We address issues of efficiency, subsidy, equity, externalities, safety, insurance cost and cost of insuring the uninsured motorist under a PAY-ATTHE-PUMP regime. We use the insurance industry’s criticisms of mandatory auto insurance as a lens through which we view PAY-AT-THE-PUMP insurance and ask how PAY-AT-THEPUMP fares by comparison. Finally we address one aspect of insurance that has been neglected in the current debate -- the human dimension of the problem of uninsured motorist and the contribution PAY-AT-THE-PUMP can make to solve this problem.
Key Words: converting fixed to variable cost; efficient pricing of auto insurance;
environmental benefit of Pay-at-the-Pump; exposure risk; insurance cost;
insurance externalities; mandatory insurance; safety; uninsured motorist;
universal auto insurance JEL Classification Nos.: L2, L9, M2, Q2, Q4, R4 ii Acknowledgments This paper is the second half of a study of PAY-AT-THE-PUMP insurance. I am grateful to Resources for the Future for sponsoring my work on the subject. This work was done during my tenure as Gilbert F. White Fellow with RFF, 1997-1998.
I wish to acknowledge the contribution of Steve Sugarman, UC Berkeley; Winston Harrington, Richard Morgenstern, Matt Cannon, Suzanne Lewis, and Joy Hall, RFF; Steve Carroll, RAND; Robert Lee Maril, Oklahoma State University; Mohammed El Gasseir, Rumla, Inc.; George E. Hoffer, Virginia Commonwealth University; Ben Gentile and Lyn Hunstad, CA Department. of Insurance; Kelly Hill, National Conference of State Legislatures;
Sean Mooney, Insurance Information Institute; Cynthia Knox, Texas Department of Public Safety; Len Marowitz, CA DMV; Mike Miller, Miller, Rapp, Herber and Terry, Inc.; Diana Lee, National Association of Independent Insurers; Eric Nordman, National Association of Insurance Commissioners; Jennifer Gullette, NC Department of Insurance; William van der Meulen, NC Institute for Transportation Research and Education; Jeffrey O'Connell, UVA;
Susan Slivinski, Insurance Information Institute; Steve Robertson, State Farm Insurance, Co.;
Andrew Tobias; Skip Nielsen, Utah DMV; Vana Hunter, Utah Insurance Commission; James Gurney and James Junius, Virginia DMV; Rebecca E. Nichols, Virginia Bureau of Insurance;
Randall Wright, University of Pennsylvania.
Last but not least, I wish to acknowledge the contribution of my wife Mairin.
List of Figures and Tables
Part One: Efficiency, Cross-Subsidy, Equity, Externalities Due to Accidents and the Role of Vehicle Fuel Efficiency
I. Efficiency, Cross-Subsidy, Equity and Transportation Externalities
1. A System of One-Insured Motorist
2. A System of Two-Insured Motorists
3. A System with One Uninsured Motorist
4. Allowing for Transportation Externalities Due to Accidents
5. Dealing with Unequal and Variable Exposure Risk
i. The Assumption of Equal Marginal Exposure Risk
ii. The Assumption of Constant Marginal Exposure Risk
II. The Role of Vehicle Fuel Efficiency
Part Two: Mandated Auto Insurance versus Pay-at-the-Pump
III. Mandating Auto Insurance As a Way of Eliminating the Uninsured-Motorist Problem
1. Historical Background
2. Insurance Industry’s Arguments against Mandatory Auto Insurance.............. 20 i. Feasibility of Removing the Uninsured Motorist from the Road............. 21 ii. Administrative and Enforcement Costs for the Insurers and for the State... 22 iii. Adverse Effect on the Insurance Cost of Priors
iv. Adverse Effect on Highway Safety
v. Hardship for Low-Wealth Uninsured Motorists
IV. How Does Pay-at-the-Pump as a Medium for Universal Coverage Measure up in Light of the Problems Encountered by Mandated Auto Insurance
1. Removing Uninsured Motorists from the Road
2. Enforcement Made Unnecessary; Costs Reduced
3. Improved Welfare of Low-Wealth Group
4. Enhanced Highway Safety
5. Implications of the Cost of Insuring the No-Priors for Savings Achieved under Pay-at-the-Pump
Part Three: The Forgotten Dimension -- The Human Aspect of the Uninsured Motorist Problem
V. PATP’s Contribution to the Human Aspect of the Uninsured-Motorist Problem.. 36 Part Four: Conclusion
VI. A Concluding Quote
iv List of Figures and Tables
Figure I.1 An Illustration of Pay-at-the-Pump's Pricing Efficiency in a One-InsuredMotorist System
Figure I.2 Pricing Efficiency and Elimination of Cross Subsidy under Pay-at-the-Pump in a Two-Insured-Motorist System
Figure I.3 Pricing Efficiency, Transfers and Welfare under Pay-at-the-Pump in a System with One Uninsured Motorist
Figure I.4 Pay-at-the-Pump Pricing with a Penalty Applied Annually to "Unsafe" Motorist
Figure II.1 An Illustration of the Impact of Gasoline Price on the Demand for Fuel-Efficient Vehicles when CAFE Standards are Binding
Table IV.1 ξ: Ratio of Cost to Revenue (from Insuring the No-Priors) Required to Neutralize the Savings on UM Premium, 1986-1990
PART ONE: EFFICIENCY, CROSS-SUBSIDY, EQUITY, EXTERNALITIES DUE TO
ACCIDENTS AND THE ROLE OF VEHICLE FUEL EFFICIENCYEfficiency, Cross-Subsidy, Equity and Transportation Externalities† I.
I.1 A System of One-Insured Motorist Assume, for simplicity's sake, the marginal cost of driving, MC, is flat. (The results can be generalized in a straightforward manner to the case where the marginal cost rises or falls linearly or nonlinearly.) Consider first the case where the system consists of a single insured motorist, as shown in Figure I.1 (below). With MC = ak, the motorist drives ag miles.
Following Rea (1992), assume for simplicity’s sake a constant exposure risk per mile, ρ (which in the diagram is represented by the segment kd), and an omniscient insurance company, who would charge the motorist the lump sum premium dkfe (= ρ ∗ ag). Under this regime, the consumer surplus is CS (lump sum) = ckf - dkfe = cdh - hfe (I.1.1) where hfe represents the misallocation of resources associated with the motorist's VMT under the current regime of lump-sum payment.
In this section we
from the effect of varying vehicle fuel efficiency, and treat PAY-AT-THE-PUMP insurance as synonymous with VMT insurance -- i.e., insurance based on miles traveled. We discuss the subject of varying vehicle fuel efficiency in Section II.
Under PAY-AT-THE-PUMP, the new marginal cost facing the motorist is ak + ρ = ad.
The motorist now travels ai ag, and pays insurance premium klhd kfed. The consumer surplus is now
which can be seen to exceed CS (lump sum) by hfe. Not surprisingly, the increase in welfare, hfe, is simply the magnitude of resource misallocation eliminated under PAY-AT-THE-PUMP.
* Gilbert White Fellow, Quality of the Environment Division, Resources for the Future, and Professor, Quantitative Studies, San Jose State University.
† This section benefited from extensive discussions with RFF's Matt Cannon. I am indebted to Matt for his insights.
In summary, in a single-motorist system and with an omniscient insurance company, the installation of PAY-AT-THE-PUMP results in (1) reduction in miles traveled, implying increased safety (due to the reduction in exposure risk); it also implies a benefit for the environment; (2) elimination of resource misallocation with an equal increase in welfare; and (3) reduction in the insurance bill due to the reduction in miles traveled (and exposure risk).
The comparison of the outcome before and after the installation of PAY-AT-THEPUMP has to take into account the fact that the demand curve of the insured motorist does not stay put during the transition. It will shift to the right when PAY-AT-THE-PUMP is introduced because of PAY-AT-THE-PUMP's income-feedback effect, which results from saving the lump-sum insurance premium. Hence VMT under PAY-AT-THE-PUMP will be somewhat greater than ai (but still less than ag). This means the extent by which safety is enhanced (and by which the insurance bill drops) will be smaller than depicted in Figure I.1.
On the other hand, the gain in welfare will exceed the amount of resource misallocation that has been eliminated, due to the shift of the demand curve to the right. But regardless of the magnitude of welfare gain, the important point is that under PAY-AT-THE-PUMP the misallocation of resources will be eliminated.
J. Daniel Khazzoom RFF 98-13-REV I.2 A System of Two-Insured Motorists We continue to make the same assumptions as before, except that we no longer assume the insurer is omniscient.
When more than one motorist are involved, our earlier three results for the one-motorist system will continue to hold. (1) There will be a reduction in miles traveled by every motorist and therefore safety will be enhanced as a result of the reduction in exposure risk, and the environment will benefit as well. (2) Resource misallocation will be eliminated and aggregate welfare will increase by an amount greater than the amount of resource misallocation that has been eliminated. (3) The average insurance bill per motorist will drop.
What is new in the multi-motorist case, however, is that the insurance bill will drop for some motorists and increase for others. This is so because under the current regime, some motorists subsidize others. Insurance companies act as the medium through which these cross subsidies get transferred. The insurance companies themselves may be the beneficiaries or the losers in this system of cross subsidies.1 PAY-AT-THE-PUMP puts an end to all of that.
Additionally one other new factor enters the picture in the multiple-motorist case:
equity. Equity is enhanced, because PAY-AT-THE-PUMP eliminates all cross-subsidization.
We illustrate these results for a system with two insured motorists. We consider the case where the lump-sum premiums charged by the insurance companies are on the average more than sufficient to cover the insurance cost. The case where the insurance companies charge on the average less than what is sufficient to cover the insurance cost can be analyzed analogously.
Suppose the insurer's premium schedule is a step-function of the distance traveled.
For example, a motorist who expects to drive less than 10,000 miles annually is charged $ x;
a motorist who expects to drive between 10,000 miles and 25,000 miles is charged $ (x+k), k0; and so on. The insurer determines the premium for each range based on what the insurer views as the typical or the average number of miles driven within each range of the step function. Thus for the group of motorists who report they will be driving less than 10,000 miles, the insurer may set the premium based on, say, 8,000 miles, on the assumption that the average miles driven by this group will be 8,000 miles; and so on.
Consider now two motorists whose travel demand is given by ff' and gg', as shown in Figure I.2 (next page). Suppose both motorists reported their expected mileage falls within the same step function. The step may be as large as, or larger than Od2 in the diagram. But the insurance company charges each motorist a premium based on OT miles traveled. On the assumption the two motorists have the same constant marginal cost, Op, and the same constant risk exposure ρ, motorist 1 travels Od1 miles, motorist 2 travels Od2 miles, and each motorist pays a lump sum = $ ephi = $ ihk'j'. For motorist 1, the consumer surplus is
1 This can happen in the case of the one-motorist system, as well. Transfers to and from the insurer can occur by design. But they occur primarily because the insurer is omniscient.
(which for the case depicted in Figure I.2 is negative). The triangle abc represents the amount of resource misallocation associated with motorist 1's VMT under the current regime of lumpsum payment, and the rectangle bchi represents the transfer from motorist 1 to the insurer (part of this transfer goes to subsidize motorist 2's travel demand, as we will see). Motorist 2's consumer surplus is CS(2)(lump sum) = fpk - ephi = fem + ihkj - mkj (I.2.2) where ihkj represents the subsidy, transmitted through the insurance company, that motorist 2 receives from motorist 1, and where mkj represents the magnitude of resource misallocation associated with motorist 2's travel under the current regime of lump-sum insurance payment.