Regulating Automobile Pollution under Certainty, Competition, and Imperfect Information

Ž .JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT 31, 219]239 1996ARTICLE NO. 0042

Regulating Automobile Pollution under Certainty,Competition, and Imperfect Information*

ROBERT INNES

Department of Agricultural and Resource Economics, Uni ersity of Arizona,Tucson, Arizona 85721

Received February 2, 1995; revised September 21, 1995

This paper studies an integrated economic model of automobile emissions that incorpo-rates consumer mileage, automobile feature, and fuel content choices. Subject to informa-tional constraints that bind the government, optimal regulatory policies are shown to includefuel content standards, gasoline taxes, and direct automobile regulation or taxation. Optimalautomobile taxes are tied to the mileage that regulators can anticipate will be driven on agiven car. In dynamic environments, constrained efficiency can be achieved by periodicautomobile taxes or, under some circumstances, a combination of new car regulation andaccelerated vehicle retirement subsidies. Desired properties of vehicle retirement programsare discussed. Q 1996 Academic Press, Inc.

I. INTRODUCTION

Air pollution from automobiles is a major environmental problem in many citiesacross the United States and around the world. In 1990, 140 million U.S. residentslived in 98 areas of the country that did not meet federal standards for photochem-

Ž w x.ical smog EPA 27 . For these ‘‘nonattainment’’ areas, it is estimated thatŽ w x.automobile emissions account for 45% of all volatile organic gases OTA 26 and

Ž w x.90% of all carbon monoxide pollution EPA 28 .Although recent and past research has studied the history, successes and

failures, and costs and benefits of auto emission regulations in the United States,surprisingly little attention has been focused on the characterization of efficientstrategies to limit automobile pollution.1 The objective of this paper is to character-

* Without ascribing blame for any flaws that may remain in this paper, I express my deep thanks toPeter Berck, Glynis Gawn, Jeff LeFrance, Edna Loehman, Rulon Pope, Jonathan Rubin, Rich Sexton,and especially Cathy Kling for invaluable insights, advice, and encouragement on this work. I am alsoindebted to seminar participants at the University of Alberta, University of Arizona, U.C. Davis, and theUniversity of Maryland, and to two anonymous reviewers for meticulous comments. This research hasbeen supported by a grant from the U.S. Environmental Protection Agency. The views expressed in thispaper are those of the author alone.

1 Extant research on automobile regulation has focused on the costs and benefits of auto emissionŽ w x w x w x.control policies in the U.S. e.g., Bresnahan and Yao 6 , Crandall et al. 10 , and Kling 20 , the

Ž w x w x w x.economic effects of fuel economy regulations e.g., Blair et al. 3 , Kwoka 23 , and Greene 13 , theŽ w x. Žeffects of alternative policy measures on carbon dioxide emissions e.g., CRA 8 , alternative fuels e.g.,

w x.NRC 24 , the cost-effectiveness of alternative automobile inspection and maintenance programsŽ w x. Ž w x.Harrington and McConnell 15, 16 , accelerated vehicle retirement policies Alberini et al. 1 , and

Ž w x.benefits of emission banking Kling and Rubin 21 . Useful overviews of U.S. vehicle emission controlw x w x w x w xpolicy can be found in Crandall et al. 10 , OTA 26 , Bryner 7 , and Krupnick 22 . However, none of

this research studies an integrated model of automobile emissions production in order to uncoverimplications of this production process for second-best regulation.

2190095-0696r96 $18.00

Copyright Q 1996 by Academic Press, Inc.All rights of reproduction in any form reserved.

ROBERT INNES220

ize policies that achieve target automobile pollution levels in the most efficientmanner possible subject to constraints on the government’s ability to monitor eachautomobile’s actual emissions, fuel use, and mileage per period.

Recent history suggests that the regulatory issues considered here are of consid-erable importance in practice. In the United States, for example, policymakershave sought to reduce auto pollution in a variety of ways over the past two decades.They have implemented increasingly strict emission-per-mile standards on new

Ž . Žautomobiles, corporate average fuel economy CAFE regulations also on new.cars , fuel content standards for gasoline, state vehicle emission testing programs,

and gasoline taxes on consumers. Although these measures have led to reductionsin U.S. automobile emissions, the extent to which they have done so has beendisappointing. Between 1970 and 1988, U.S. automobile emissions of volatile

Ž .organic gases VOCs , nitrogen oxides, and carbon monoxide declined by 45%, 0%,Žand 48%, respectively; auto emissions of all ozone precursors VOCs and nitrogen

. Ž w x.oxides declined by only 30% Bryner 7 . Over the same period, U.S. standards onper-mile hydrocarbon, carbon monoxide, and nitrogen oxide emissions were re-duced by 90%, 80%, and 70%, respectively. Among the most important explana-tions for the discrepancy between auto emission standards and performance is thedoubling of vehicle miles traveled by U.S. drivers between 1970 and 1988, due inroughly equal measure to increases in the number of drivers and average per-driver

Ž w x.mileage Gately 12 . In addition, increases in the volatility of gasoline have raisedthe evaporative and refueling emissions from automobiles, emissions that have notbeen subject to government regulation and that are now thought to compose about

Ž w x.one third of total U.S. automobile pollution Harrington et al. 17 . Becauseemissions rise with a car’s age, the increased average age of passenger cars in the

Ž .U.S. from 5.7 years in 1974 to 7.6 years in 1989 has also limited pollutionreductions from the U.S. vehicle fleet.

In sum, emissions-reduction objectives have been confounded by changes in fuelcontent, consumer choices of automobile vintages, and driver mileage decisions.This paper studies these and other key problems in mobile source pollution

Ž .regulation by i constructing an integrated model of the emissions productionprocess that incorporates fuel content, automobile feature, and consumer mileage

Ž .choices and ii identifying the implications of these linked choice problems foroptimal regulation.

For simplicity, this paper’s model is first set in a static environment. Sections IIIand IV develop the formal analysis of this case, arguing that a constrained optimalvehicle emission policy entails gasoline taxation, fuel content regulation, and mostimportantly, direct regulation or taxation of the automobile. The analysis isgeneralized to incorporate automobile replacement decisions and other dynamicconsiderations in Section V. First, however, the next section describes someeconomic logic that underpins the paper.

II. THE ECONOMIC ISSUE

The basic economic problem here is that automobile pollution creates anexternal cost to the public that individual automobile ownerrconsumers do notinternalize unless compelled to do so by government policy. If consumers are madeto face the marginal social costs of the actual emissions that they produce,

REGULATING AUTOMOBILE POLLUTION 221

efficiency will be achieved throughout the chain of economic decision making thatdetermines final vehicle pollution levels. Three elements in this chain are of

Ž .particular interest and importance in this paper: 1 consumer mileage choices,choices which, for given levels of emissions-per-mile on a consumer’s automobile,

Ž .determine the total volume of the consumer’s vehicle pollution; 2 consumerdemand for emission abatement devices, fuel economy, and desired vintage, power,and style features, automobile attributes which affect emissions both directly and

Ž .indirectly via impacts on subsequent mileage choices; and 3 consumer demand forfuel attributes that affect emissions levels, including oxygen content and reactivityproperties of gasoline. If automobile users confront the social costs of theiremissions, these costs will be incorporated in their demands for automobile andfuel attributes that affect emissions, which in turn will lead auto manufacturers andfuel producers to internalize these costs in their decisions on automobile designand fuel formulation.

In view of this logic, there are three circumstances under which the problem ofdesigning efficient automobile pollution regulations is rather simple. First, ifemissions could be taxed directly, automobile users could be directly made tointernalize the social costs of their automobile pollution. However, emissionstaxation requires that the government monitor the actual pollution from eachindi idual automobile in each time period. Although government regulators continueto study prospects for tamper-resistant emission-measurement devices on automo-bile tailpipes, the costs of such devices have so far precluded their use. Moreover,

Ž .such devices do not measure the non-tailpipe evaporative and refueling vehiclepollution that is an increasing source of concern to policymakers. For thesereasons, this paper focuses on policy regimes that do not require the directmonitoring of vehicle emissions.

Second, if automobile emissions are proportional to fuel use and invariant toautomobile design, then fuel use alone determines vehicle pollution levels and aconstant per-gallon fuel tax can make consumers internalize the social costs oftheir own emissions. Such is the case, for example, with automobile emissions ofcarbon dioxide.2 However, such is not the case with the automobile pollutants ofinterest in this paper, including nitrogen oxides, reactive hydrocarbons, and carbonmonoxide. Per-unit fuel emissions of these pollutants vary between automobiles.

w xFor example, in Kling’s 20 sample of new California 1990 model-year automo-Ž . Žbiles, hydrocarbon nitrogen oxide emissions varied from 1.23 to 7.68 0.74 to

.15.08 grams per gallon of gasoline. Cross-automobile variation in emissions ismuch greater when different automobile vintages are considered, not only becausedifferent model years exhibit different emission performance but also becauseautomobile emissions increase with age. Hence, a constant per-gallon gasoline taxcannot make consumers internalize the social costs of their own mileage choicesand attendant fuel use. Nor can it provide consumers with incentives to chooseautomobiles that have desired emission abatement properties. Because the gasolinetax facing a given consumer does not change with a consumer’s choice of

2 Ž . w xCO emissions are the focus of a pioneering study by CRA and David Montgomery 8 . In2Ž .estimating the costs of higher CAFE corporate average fuel economy standards vis-a-vis tax policies

that achieve a given per-unit reduction in carbon dioxide emissions, CRA considers the policies’ effectsŽ .on consumers’ mileage choices, as well as their choice of automobile attributes i.e., vehicle size .

However, because of their focus on CO emissions}and the attendant optimality of per-unit-carbon2taxation}CRA are not concerned with the characterization of optimal regulatory policies.

ROBERT INNES222

emission-decreasing automobile features, the consumer has no incentive to pur-chase such features.3

Third, when automobile-specific gasoline or mileage taxes are possible, then theŽ .government can elicit optimal choices by taxing fuel or mileage at a rate equal to

the marginal social cost of emissions times the automobile-specific emissionsŽ .per-unit-fuel per mile . This point is developed in Section III below. Unfortu-

nately, automobile-specific gasoline andror mileage levies are potentially costly toimplement and subject to abuses that undermine the purpose of the levies. In viewof these difficulties, this paper’s central focus is the problem of auto emissionregulation in the absence of such capabilities.

In such a setting}with hidden mileage decisions and a homogeneous gastax}an optimal gasoline tax serves to make consumers internalize the aërageemission costs of their mileage and attendant fuel use choices, with the averageappropriately defined over the population of drivers. However, because the gaso-line tax is not automobile-specific, an automobile tax}or its regulatory equivalent}is needed to confront consumers with the social costs of emissions when they

Ž .make their ëhicle feature choices. These social costs equal i the marginal socialŽ . Žcost of emissions, times ii the vehicle’s emissions per mile which are a function of

. Ž .vehicle features , times iii the mileage choice which regulators can anticipate willresult from the vehicle’s given features, features which include fuel economy,power, size, ‘‘comfort,’’ and in dynamic generalizations, vehicle age. It is shownbelow that a second-best vehicle tax approximately equals these predicted socialcosts of emissions, less the portion of these costs that are internalized by thegasoline tax.

III. THE MODEL AND FIRST-BEST REGULATION

A. The Model. Consider an economy with a continuum of consumers, each ofwhom purchases and owns one automobile.4 Consumers are distinguished by

� 4preference type, t, and income level, I. The population distribution of t, Iw x w x Ž .parameters has positive support on 0, 1 = I, I and relative frequency q t, I for

w x w x Ž .t g 0, 1 , I g I, I . The total size dimension of the consumer population is NŽ .for the number of consumers .

Each consumer chooses the type of automobile that she will purchase and driveand the number of miles that she will drive with her chosen automobile. Allautomobiles have a common fixed lifespan. Over this lifespan, consumer utility isderived from the joint consumption of miles, m, automobile features, s, and other

Ž .goods, x measured in units of a numeraire . The features s may include theautomobile’s power, size, and any other attributes that yield pleasure in the driving

3 The pollutants of interest in this paper depend crucially upon the extent to which emissions-reducingautomobile features are adopted. Examples of such emission-reducing auto features include higherair]fuel ratios; improved air]fuel ratio controls; refinements in cylinder distribution, choke operation,and combustion chamber design; fuel injection; exhaust gas recirculation; ignition system improve-

Žments; spark and valve timing controls; computer sensors and actuators; and dual catalysts see Johnsonw x.19 .

4 ŽThe analysis does not model decisions on whether or not to own a car and how many cars e.g.,.more than one to own. These decisions and their implications for the analysis are discussed in an

expanded version of this paper that is available upon request.


Ž .experience e.g., transmission type and seating features . Consumer utility takes theform

u s u m , s, x ; E, t , 1Ž . Ž .

where E measures the aggregate emissions to which each person is exposed, t isŽ .the consumer’s preference type, and u is increasing and concave in its first three

arguments.5

ŽAutomobile features other than s are the car’s fuel efficiency miles per unit of.fuel , f , and the car’s emission abatement equipment, a. The abatement parameter

a reflects the nexus of engine design and reliability measures that can affect a car’semissions. The price of an automobile, P c, depends upon all of the automobileattributes, s, f , and a.6

A consumer’s automobile and mileage choices are made to solve the utilitymaximization problem

c g w xmax u m , s, x ; E, t s.t. P s, f , a q P mrf q x F I , 2Ž . Ž . Ž .� 4m , s , f , a , x

where I is the consumer’s income and P g is the price of gasolinerfuel. ProblemŽ .2 maximizes the consumer’s utility subject to a budget constraint which requiresthat the consumer’s expenditures on numeraire good consumption, the automobile,

Žand the gasoline required to drive the automobile the desired number of miles i.e.,g w x.the price of gas, P , times the volume of gas required to drive m miles, mrf be

no greater than the consumer’s available income.The fuel production industry is modeled as a composite firm with constant

returns to scale. The per-unit-fuel production cost depends on a fuel contentŽ . 7parameter vector, z, and is denoted g z . Examples of the fuel content choices, z,

include the following features of gasoline, all of which affect an automobile’semissions of noxious pollutants: content of lead, oxygen, sulfur, and aromatic

5 Ž .Implicit in the specification of the utility function u is the standard public good assumption thatconsumers do not have a ‘‘public ethic’’ concerning automobile emissions. With consumers defined on acontinuum, each individual’s contribution to aggregate emissions E is negligible. Therefore, in theabsence of a financial incentive to do so, consumers will not choose to pay for features of an automo-bile or gasoline that only have the effect of reducing noxious emissions.

6 Throughout this analysis, the following notational conventions will be observed: superscripts willŽ .denote labels; subscripts will denote partial derivatives; and parentheses ? will be used to denote

functions.7 The assumption of constant returns to scale significantly simplifies the analysis, but is not necessary

to the conclusions derived in this paper. Qualitative conclusions extend to the case of decreasing returnsto scale with the per-unit-fuel production cost interpreted as a marginal cost. For simplicity, the analysisalso abstracts from heterogeneous firm costs of achieving fuel content targets, implicitly assuming that agiven average fuel content is achieved in a cost-minimizing fashion. Such cost minimization can beachieved using an appropriate competitive fuel content permit market, the design and efficiencyproperties of which have been exhaustively studied elsewhere. California’s Phase II gasoline programprovides a good ‘‘real world’’ example of fuel content regulation with permit trading. Such permitprograms can give rise to different types of gasoline being made available to consumers on the market,even though the regulatory choice of fuel content is a homogeneous one. As a result, different

Žconsumers may use gasoline with different emission-affecting fuel contents to be distinguished from.octane levels that are considered to have minimal effects on emissions . However, there is no reason to

believe that a systematic relationship exists between such fuel contents and automobile or consumertypes; hence, the law of large numbers permits us to focus on a common average fuel content withoutloss of generality.

ROBERT INNES224

hydrocarbon compounds, distillation temperatures, and Reid Vapor Pressure.8

Note that the z choice is common to all automobiles. Thus, with respect to carfuels, this paper focuses on the choice of gasoline properties, rather than on thechoice among alternative fuels for different automobiles.9

An automobile’s emissions per-unit-fuel depend upon the automobile abatementfeatures, a, and the fuel content parameter, z,

e s e a, z 3Ž . Ž .Here, as with other model parameters, emissions are measured over a given timeinterval, namely, the lifespan of the automobile.10

Ž .The parameter z is defined so that higher levels of z or any element of z areassociated with more stringentrless-emissions-producing fuel content choices. Thus,

Ž . Žg G 0 i.e., a higher z implies a higher cost of fuel production and e F 0 i.e., az z.higher z leads to less emissions per unit fuel . The parameter a is similarly defined

Ž .so that higher levels of a are associated with lower emissions e F 0 that areaachieved with a higher automobile cost.

The automobile market is assumed to be sufficiently large relative to theefficient scale of an auto production facilityrplant that there are constant returnsto scale in the production of any given type of car.11 The cost of producing a car

Ž .with the features s, f , a can thus be denoted by

c s c s, f , a, z , c G 0, c G 0, c G 0, c G 0. 4Ž . Ž .s f a z

The incorporation of the z argument in the auto cost function reflects theinteraction between fuel content and various automobile features. For example, anengine’s power can be adversely affected by higher oxygen content in gasoline; at acost, an auto producer can compensate for this lost power by modifying the engine

Ž .design. Similarly, elements of s particularly car power and size and the abatementfeature, a, can adversely affect a car’s fuel efficiency, ceteris paribus. However,auto producers can, within bounds, take measures which offset such fuel efficiencydeclines, and the costs of such measures are captured in the above function ascomponents of marginal s and a attribute costs, c and c .s a

8 Higher levels of Reid Vapor Pressure lead to higher evaporative emissions both from fueldispensation and the automobile itself. Distillation temperature properties of gasoline have rathercomplex effects on the emissions of automobiles. In order to reduce carbon monoxide emissions, theU.S. Clean Air Act Amendments of 1990 now mandate minimal oxygen content in wintertime gasolinefor many areas of the U.S.

9 Recently, it has been argued that reformulated gasoline can achieve emission-reduction objectivesŽ w x w x.at lower cost than alternative fuels e.g., see Harrington et al. 17 , OTA 26 . Nevertheless, an

Ž .expanded version of this paper available upon request argues that implications of the analysis can beextended to the case of alternative fuels. In this extension, the automobile’s fuel type becomes anothervehicle attribute to be chosen by the consumer. A constrained optimal automobile tax then becomescontingent on the car’s fuel type, and regulatory choices of both fuel contents and gasoline taxes alsobecome specific to each fuel type.

10 The emissions function posited here abstracts from hidden consumer-specific effects on emissions,Žincluding the number of hard and cold starts, hard accelerations, and the type of driving e.g., on or off

.highway . Although this analysis does not model regional transportation planning and design policiesthat might alter driving behavior and thereby improve emissions, the model can be interpreted to belocation-specific so that the emissions function reflects average driving behavior in a given area.

11 Recent advances in automotive production practices allow for great flexibility in the production ofdifferent types of cars within a given plant, which makes the constant returns to scale assumption all themore plausible. However, qualitative insights from this analysis are nonetheless extendable to alterna-tive specifications of automotive production technologies.


TABLE IModel Notation

m Miles driven per unit timeŽ .s Automobile features e.g., power, size, style

f Automobile fuel economya Automobile emission abatement featuresx Consumer numeraire good consumptiont Consumer preference type

Ž .I Consumer income in units of the numeraire� 4w s t, I Type-income pair that distinguishes consumers

Ž . Ž . � 4q t, I s q w Relative frequency of t, I consumers in the population, with support onw x w x0, 1 = I, I

Ž .N Dimension of the consumer population number of consumersE Aggregate emissions to which a consumer is exposed

Ž .u s u m, s, x; E, t Consumer utility functionc cŽ .P s P s, f , a Automobile priceg Ž .P Per-unit fuel gasoline pricem gP s P rf Price per mile of driving

Žz Fuel content parameter e.g., content of lead, sulfur, oxygen, Reid.Vapor Pressure

Ž . Ž .e s e z, a Automobile emissions per-unit fuel per unit time , e F 0, e F 0z aŽ . Ž .g z Per-unit cost of fuel gasoline production, g G 0z

Ž . � 4c s c s, f , a, z Cost of producing an automobile with attributes s, f , al Marginal social cost of emissions when achieving the emission target, E s E

g Ž .t Per-unit fuel gasoline taxA A Ž .t s t s, f , a, I Automobile tax function

Ž .W s W m, s, t, I, u Consumer willingness-to-pay functionc gŽ . Ž .m s, P f , w, u Compensated Hicksian mileage demand function for utility level u

m c m« s d ln m rd ln P Price elasticity of mileage demand

Table I summarizes the model notation. While Section V extends this model toallow for automobile replacement choices and other dynamic considerations, two

Ž .crucial assumptions are maintained throughout the analysis: 1 Competition: autoŽ .and fuel producers are competitive; and 2 Certainty: each automobile’s emissions

per-unit-fuel is deterministic and observable. Competitive behavior is necessary toavoid motivating vehicle emissions policy by imperfect competition in automobileand fuel markets, market features which are logically the province of more generaland more direct economic regulation.12 The specification of observable and non-

12 ŽThere is some empirical evidence of imperfect competition in auto and fuel markets e.g., seew x w x .Borenstein et al. 4 on fuel markets and Bresnahan 5 on automobile markets . Imperfect competition

Ž w x.has long been recognized to motivate reduced emission taxes e.g., see Innes et al. 18 , although Oatesw xand Strassman 25 argue, as a general matter, that welfare losses from worsening a monopoly output

market distortion with effluent fees are unlikely to be significant. This literature is developed in thecontext of polluting producers, but the arguments extend to automobile markets in which consumer useof the produced goods yields pollution. For example, imperfect competition in gasoline markets canmotivate a lower emission-deterring gasoline tax because monopolistic behavior is already generatingsome of the desired deterrant. Similarly, imperfect competition in auto markets can motivate an

Ž .automobile regulation or tax that imposes a lower per-car cost on producers or consumers in order toavoid a worsening of monopolistic output restrictions. However, to the extent that there is welfare-depleting imperfect competition in these markets, government action is arguably warranted to directlycorrect the resulting inefficiencies. For example, oligopolistic markups on automobiles can be countered

Žwith per-car subsidies that offset the market distortion perhaps combined with lump-sum company.taxes . This paper begins from the premise that such corrective policies, if needed, are already in place.

ROBERT INNES226

random per-unit-fuel emissions abstracts from some issues associated with vehicleemission monitoring, issues which are important in practice but also, I believe,logically distinct from the automobile and fuel policy issues of interest here.13

B. First-Best Regulation. Assuming the government can freely monitor eachautomobile’s emissions, fuel use, and mileage, how can it regulate competitivemarkets to achieve a given target level of emissions, E, efficiently? While a formaltreatment of this question is available in an expanded version of this paper, theresults and their intuition are quite simple. For a parameter l that is isomorphic tothe target emissions level, E, first-best outcomes can be achieved with regulationsthat have the following three properties:

Ž .a the government sets a fuel content standard z that satisfies the condition

1 I t I t Iz : yg z y le m rf y c q t , I dI dt s 0; 5� 4Ž . Ž . Ž . Ž . Ž .H H z z z0 I

Ž .b there is no regulation of the automobile, so that, given competition in thecŽ . Ž .automobile market, P s, f , a s c s, f , a, z ; and

Ž . Ž .c the government levies either an automobile-specific fuel tax of le a, z perŽ .unit fuel or an auto-specific mileage tax of le a, z rf per mile driven.

The parameter l represents the welfare-preserving tradeoff between a marginalunit of emissions and a marginal unit of the numeraire good; l can thus be

Ž .interpreted as the marginal cost of emissions. Policy a requires optimal fuelcontent choices to equate their marginal cost in fuel and auto production,� Ž .w x Ž .4E g z mrf q c , with their marginal benefit in reduced emissions,z z� Ž . 4 Ž � 4.lE e mrf where E is the expectation operator over t, I .z

Ž . Ž .Policy c has the following interpretation. When making their mileage m , fuelŽ . Ž .economy f , and pollution-abatement a choices, unfettered consumers neglect

the emissions-increasing cost of extra mileage and emissions-reducing benefitsof additional fuel economy and pollution abatement. Moreover, the numeraire-

Ž .w xequivalent social cost of a consumer’s emissions is le a, z mrf , i.e., the nu-meraire value of a unit of emission, l, times emissions per-unit-fuel for the

Ž . w xconsumer, e , times the fuel used by the consumer, mrf . Thus, by taxing eachŽ .unit of fuel at a rate equal to its marginal emissions cost to society, le a, z , the

government will make the consumer internalize the social cost of her emissions andthereby set all relevant decision variables at Pareto optimal levels.

Unfortunately, costly technologies are needed to implement automobile-specificgasoline levies. For example, a tamper-resistant computer code would likely berequired on each automobile; similarly, gasoline pumps would have to be equippedto automatically tack the appropriate tax onto any gasoline that is dispensed to aparticular automobile. Moreover, since a simple siphoning of gas will permitconsumers to bypass taxes on high-emission vehicles, the scope for abuse, particu-larly among those high-emitting consumers who are arguably the most importanttargets of the tax, would be tremendous.

Mileage taxes suffer from similar problems. Although annual odometer readingsmay be used to assess mileage taxes, odometers can be set back. Even if only a

13 For an important set of papers on inspection and maintenance programs, see Harrington andw xMcConnell 15, 16 .


small proportion of consumers cheat in this way, those who cheat are likely to bethose who drive the most, who therefore have the greatest incentive to cheat andwho are arguably the most important targets of mileage taxation.

In sum, automobile-specific gasoline or mileage taxes are costly to implementand subject to undermining abuses, problems which are likely to explain theirabsence in practice and which motivate a characterization of optimal regulationwhen such ‘‘first-best’’ policies cannot be implemented. For these reasons, I nextturn to the choice of auto emissions policy when per-unit-fuel taxes must beconstant across consumers and when consumers have private information abouttheir mileage choices and preference type.

IV. CONSTRAINED OPTIMAL REGULATION

A. The Problem. Without loss of generality, attention will be focused in thissection on auto emission policies that take the form of taxes on gasoline andautomobiles, combined with a government fuel content standard, z. As noted

Ž .above, government taxes will be constrained in two ways: i the gasoline tax is ascalar t g that does not depend on individual automobile or consumer attributes,

Ž .and ii direct mileage taxes are ruled out. Automobile-related taxes on consumersmust therefore take the following form:14

g w x AT s t mrf q t s, f , a, I . 6Ž . Ž .

The government can choose the scalar gas tax parameter t g and the auto taxA Ž .function, t ? . For example, if the government were to adopt fuel economy and

per-mile emission standards that are implemented with a permit program, t A

would take the form of

A e m f ˆt s a e a, z r f y e y a f y f ,Ž . .ˆ

m ˆ ewhere e and f are the per-mile emission and fuel economy standards, and aând a f are the corresponding permit prices.

To characterize efficient choices of these tax policies, it is convenient to focusfirst on choices of mileage and automobile attribute allocations across the popula-

� Ž . Ž . Ž . Ž .4 � 4 Ž .tion of consumers, m w , s w , f w , a w , for w s t, I . The Eq. 6 tax regime,together with the government’s desire to achieve a given overall emissions target,constrain the set of mileage and auto attribute allocations that are possible. Theanalysis proceeds by characterizing allocations that are efficient subject to theseconstraints and then, in turn, developing a t A auto tax function that will elicitconsumer choices of the constrained efficient allocations. Formally, the firstconstraint on consumer choices is that emissions not exceed the governmentpollution target, E:

Emissions Constraint: e a w , z m w rf w q w dw F ErN. 7Ž . Ž . Ž . Ž . Ž .Ž .Hw

14 The government can also levy direct income taxes. However, to avoid dwelling on distributionalissues, I assume that consumer income is post-income-tax. The least appealing feature of the resultingtax structure is the dependence of t A on consumer income. An expanded paper characterizes sufficientconditions for income-invariance of an optimal t A tax function.

ROBERT INNES228

Ž .The second is a consumer mileage choice constraint that is embedded in the eq. 6tax regime. Specifically, consumer mileage choices must satisfy the private firstorder condition

gMileage Choice Constraint: m w solves u ru s g z q t rf w , 8Ž . Ž . Ž . Ž . Ž . Ž .m x

w Ž . g x Ž . Ž .where g z q t is the fuel price, u ru represents the marginalm xnumeraire-equivalent benefit of mileage to the consumer, and the right-hand side

Ž . Ž .of 8 gives the numeraire cost of marginal mileage. Equation 8 departs from itsw Ž . g xfirst-best counterpart in that the consumer cost of mileage, g z q t rf , does

w Ž . Ž .xnot, in general, equal the social cost of mileage, g z q le a, z rf. As noted inthe introduction, this departure prevents consumers from internalizing the truesocial costs of either their mileage decisions or, in the absence of the t A

Ž .automobile tax, their automobile feature selections more on this in a moment .Ž . Ž .Constrained Pareto optimality requires that, subject to constraints 7 and 8

and subject to achieving some given arbitrary utility distribution across consumers� Ž .4 � 4in the economy, u w , w s t, I , total economy-wide surplus available to the

government must be maximized.15 To express this surplus, the following consumer16Ž .willingness-to-pay function, W m, s, t, I, u , is defined:

u m , s, I y W , t s u. 9Ž . Ž .

Ž .W is analogous to a consumer expenditure function, with price parameters� 4replaced by the allocation m, s . Thus, if one thinks of u as an initial utility level

0 0 0 0� 4 Ž .that a consumer obtains with an initial allocation of m , s , u s u m , s , I, t ,Ž .then W is the amount of money that the consumer is willing to give up in

� 4exchange for the alternative allocation, m, s . Using this construct, one canexpress the surplus that would be reaped by the government if it were able to

� 4provide a given consumer both the allocation m, s, f , a and the utility level u,

w xW m , s, t , I , u y g z mrf y c s, f , a, z ,Ž . Ž . Ž .

namely, the consumer’s willingness-to-pay for m and s, less the costs of supplying� 4the gasoline and automobile attributes required for the m, s, f , a allocation.

Using the willingness-to-pay construct, constrained efficient allocations mustsolve the choice problem

max W m w , s w , w , u w y g z m w rf w� Ž . Ž . Ž . Ž . Ž . Ž .Ž .Hg� Ž . Ž . Ž . Ž .4m w , s w , f w , a w , z , t w

yc s w , f w , a w , z q w dw 104Ž . Ž . Ž . Ž . Ž .Ž .

Ž . Ž . Ž .subject to conditions 7 and 8 . For simplicity, problem 10 is assumed to have aŽ .unique interior solution. The maximand in 10 is the net government surplus when

� 4 Ž .each consumer w s t, I pays taxes of W in exchange for the allocation� Ž . Ž . Ž . Ž .4 Ž .m w , s w , f w , a w , and thereby receives the utility level u w . The solution

Ž .to problem 10 will define constrained efficient allocations that can be elicitedŽ .from consumers by a tax regime that takes the equation 6 form. While this

15 Producer utilities can be ignored because of zero-profit conditions implicit in the model set-up.16 Ž .In defining W , the dependence of consumer utility on E is suppressed. This simplification comes

Ž .at no cost in generality so long as constraint 7 binds, which is the only case of interest in this paper.


problem directly chooses the fuel content parameter, z and the gasoline tax, t g, itA � 4chooses the auto tax function, t , indirectly. That is, the s, f , a allocations that

Ž . Asolve problem 10 can be elicited from a t auto tax function that is constructedŽ .to replicate the optimality conditions for problem 10 in each consumer’s auto

attribute choice problem.Ž .A constraint missing from problem 10 is one for incentive compatibility; that is,

the government cannot actually observe t and hence, cannot levy taxes W that areŽ .contingent on t. In the expanded version of this paper available upon request , I

� Ž .4show that, for any income distribution, there is a utility distribution, u w , suchŽ .that the corresponding solution to problem 10 can be supported by a tax regime

Ž . Ž .of the Eq. 6 form. By replicating a solution to problem 10 , the latter tax regimeyields a constrained Pareto optimum. Readers should be alerted that these proofsare crucial to the analytical approach taken here.17

B. Constrained Optimal Automobile Features. The first step toward characteriz-ing a constrained efficient automobile tax is to determine the vehicle attribute

� Ž . Ž . Ž .4choices s w , f w , a w , that we want this tax to elicit from consumers. Fixingfuel content and the gasoline tax for the moment, this task requires a characteriza-tion of the first order optimality conditions for the auto attribute choices in our Eq.Ž .10 welfare maximization problem. This characterization can be simplified with

Ž .the following restatement of the mileage choice constraint in Eq. 8 ,

c gm w s m s w , P , f w , w , u wŽ . Ž . Ž . Ž .Ž .s consumer w compensated mileage demand, 11Ž .

g Ž . g Ž . Ž . Ž .where P s fuel price s g z q t . After substituting 11 into 10 and 7 , oneŽ .can differentiate the resulting Lagrangian for problem 10 with respect to

� Ž . Ž . Ž .4s w , f w , a w and obtain the necessary conditions for an optimum

g cs w : t y le m rf q W y c s 0 12aŽ . Ž . Ž . Ž . Ž . Ž . Ž .s s s

2g c cf w : t y le m rf y m rfŽ . Ž . Ž . Ž . Ž . Ž .½ 5f

2g cq g z q t m rf y c s 0 12bŽ . Ž . Ž . Ž . Ž .½ 5f

a w : yle mc rf y c s 0, 12cŽ . Ž . Ž . Ž . Ž . Ž .a a

17 This approach to incentive compatibility represents the greatest analytical challenge in this paperŽand a fundamental departure from the mechanism design literature springing from Baron and Myerson

w x.2 . In the present problem, there are income effects on automobile purchase decisions which implyconsumer utility functions that are nonlinear in numeraire good consumption. It is well known that suchnonlinearities make it extremely difficult to provide useful characterizations of optimal direct andindirect mechanisms using standard techniques. I therefore develop a different approach to theconstruction and analysis of the government’s choice problem. Readers should note that this approachcharacterizes constrained Pareto optima that correspond to a restricted subset of possible consumerutility distributions. Although the government can use income taxes to redistribute utility acrossdifferent consumer income groups, I implicitly assume that it is not interested in redistributing utilityacross preference types, within an income group, when such redistribution comes at any positive surpluscost. I thus restrict attention to inter-type utility distributions that permit surplus maximization or,equivalently, have zero information-revelation costs.

ROBERT INNES230

Ž .where l is the Lagrange multiplier for constraint 7 . Each of the three conditions,Ž . Ž .12a ] 12c , has two parts. The second part represents the ‘‘private’’ economiceffects of marginal changes in s, f , or a to consumer w in the absence ofautomobile taxation. In the case of s, these effects are the marginal utility benefitsin numeraire equivalent units, W s u ru , less the cost of marginal s in automo-s s xbile production, c . In the case of f , these effects are the consumer’s fuel costssavings from additional fuel economy, P g mcrf 2, less the cost of this economy, c .fFor a, the only private economic effect is the increased automobile cost, c .a

Ž .The first terms in 12 represent additional welfare effects from marginalchanges in s, f , or a that consumer w would not consider in his or heroptimization calculus unless compelled to do so by automobile taxation. For s andf , these welfare effects arise from two sources. First, ignoring emission effects forthe moment, the fuel tax t g leads to a fuel price for the consumer that is higher

Ž .than the social cost of this fuel, g z , thus creating an inefficient deterrent toconsuming fuel and driving miles. Second, the social cost of the emissions produced

Ž .by consumer w’s marginal fuel consumption is le , a cost which is not consideredby consumer w in her mileagerfuel consumption choice and which thus implies aninefficient incentive to use fuel and drive. Together, these two effects lead to a

w Ž . Ž .xdifference between the marginal social cost of fuel use, g z q le , and thew Ž . g x w g xmarginal private cost of fuel use, g z q t , equal to le y t . If this value is

positive, welfare gains can be obtained by adjusting s and f auto features in orderŽ .to elicit less fuel usage lower mileage by the consumer. For example, if mileage is

Ž c .a compliment to a ‘‘fanciness’’ or size attribute of the automobile i.e., m ) 0 ,swelfare gains can be obtained by reducing the level of this fanciness attributebelow its unfettered level in order to elicit less driving. At the margin, the welfaregains from such a reduction will equal the net marginal social gain from mileage

w g x creduction, le y t rf , times the elicited mileage reduction, ym . Similarly in thescase of f , the value of mileage-choice-driven welfare effects equals the net

w g xmarginal social gain from the consumer’s reduction in fuel use, le y t , timesthe marginal reduction in fuel use from increased f ,

cw xd m rfc 2 c c 2 mw xy s m rf y m rf s m rf 1 y « , 13Ž .fdf

where, with P m s P grf , « m s yd ln mcrd ln P m ) 0 is the price elasticity ofmileage demand.

Since the abatement feature a has no direct effects on the consumer mileagechoice, the only welfare effect missed in the consumer’s private optimizationproblem is the net social gain from emissions reductions that attend increases in a,

Ž . cŽ . Ž .namely, yle m rf . This observation is important because it implies that,aeven if the gasoline tax were exactly equal to the non-internalized social costs ofemissions, le, the gasoline tax could not make consumers internalize the socialbenefits of the automobile abatement features, a.

C. Constrained Optimal Automobile Taxation. The objective of automobile taxa-tion is to yield consumer internalization of the welfare effects captured in the first

Ž . A Ž .terms of equation 12 . To characterize t , it is assumed that some subset of theŽ . Ž . � 4automobile attributes which solve problem 10 , s t, I , can be inverted in w s t, I ,


Ž .yielding w s . The characterization of an optimal auto tax then results from thefollowing logic:

For each unit of fuel that is consumed, the non-internalized social cost isw g xle y t . Hence, the total non-internalized social costs of a consumer’s choices

w g xare equal to le y t times the consumer’s fuel usage, mrf. By construction here,it is impossible to compel the consumers’ internalization of these costs in their

� 4mileage choices. However, if the government could observe w s t, I , it couldcompel the internalization of these costs in each consumer’s auto feature selectionsby setting the auto tax equal to the total non-internalized social costs that areelicited by these selections,

A g c gt s le a, z y t m s, P , f , w , u w rf . 14Ž . Ž . Ž .Ž .

Ž .The tax in 14 confronts consumers with the social costs and benefits of themileage choice incentives created by their auto feature choices. For this reason, thetax also compels consumers who tend to drive more}and who therefore creategreater social costs of emissions than others}to internalize these costs in theirauto purchase decisions.

Ž .Unfortunately, t is not in fact observable and hence, the tax in 14 is not alwaysfeasible. Instead, the government can only condition the tax on the consumer’s

Ž .t-type indirectly, using the relation t s t s . However, if the government were toA Ž . Ž .set t as in 14 with t s t s , consumer w would choose the s features to

consider not only their effect on non-internalized social costs, but also their effecton the government’s inference of the consumer’s t-type, which in turn affects thetax that is levied. The latter effect would represent an inefficient distortion in the s

w g xchoices. To understand this last point, suppose that le y t is positive forŽconsumer w and that a higher level of t leads to greater demands for mileage i.e.,

c c cŽ . Ž . Ž . . Ž Ž . .dm rdt s m q m u ) 0 and attribute s t s r s ) 0 . Then the taxt u tŽ . Ž .function in 14 , with t s t s , will confront consumer w with three marginal costs

Ž . Ž . Ž .of s: 1 the private cost, c , 2 the otherwise non-internalized social cost,s�w g x 4 c Ž . �w g x 4le y t rf m , and 3 an ‘‘information-revelation’’ cost, le y t rfsw c xw xdm rdt tr s ) 0. This third cost does not reflect any social cost of theattribute s and, thus, inefficiently deters consumer w’s demand for this attribute.

Ž .The Eq. 14 tax can be modified to correct this ‘‘information revelation’’Ž .distortion and thereby replicate the optimality conditions in Equation 12 ,

A g c*t s, f , a, I ; b s le a, z y t m s, f ; b rf q w s, I ; b , 149Ž . Ž . Ž . Ž . Ž .

g c* c gŽ . Ž . Ž Ž . Ž . Ž Ž ... Ž .where b s l, t , z , m s, f ; b s m s, g z q t , f , w s , u w s and w s, I; bsolves

c cw s, I ; b s y m q m u w s rf w s� 4Ž . Ž . Ž . Ž . Ž . Ž .Ž .s w u w s

g= le a w s , z y t . 15Ž . Ž .Ž .Ž .

The w function provides the needed ‘‘information revelation’’ correction.Ž .Several properties of the automobile tax regime in 149 merit mention. First, if

le is larger than t g, so that the adverse welfare effects of mileage-inducedemissions exceed the costs of the gas tax distortion, then t A increases with auto

ROBERT INNES232

attributes s which are compliments to mileage demand. Second}and againassuming that le is larger than t g}the magnitude of t A also decreases with fuel

Ž m .economy, f , so long as fuel consumption decreases with fuel economy « - 1 .The extent to which t A should subsidize f is reduced by the mileage-increasingeffect of fuel economy; that is, higher levels of « m}which the literature refers toas a larger ‘‘rebound effect’’ of fuel economy on fuel consumption}imply loweroptimal fuel economy subsidies. Extant empirical evidence indicates that « m is

Ž w x.between 0.2 and 1 Dahl and Sterner 11 , so that a constrained optimal auto taxwill subsidize fuel economy, but only to a rather limited extent.

Ž . Ž A Ž .Third, the first part of the tax regime in 149 i.e., t without w s, I; b can beŽ .replicated by the following reform of current per-mile emission standards: iŽ .restate the standards in terms of emissions per-unit-fuel, i.e., standards on e

Ž . Ž .rather than per-mile emissions, e rf ; ii allow firms to meet the standards bybuying and selling credits in an emission permit market, where the number of

Ž .credits which a firm can sell or must buy, if this value is negative is the product ofw c*Ž . xm s, f ; b rf and the amount by which the per-unit-fuel standard, e, exceeds itsˆ

Ž . Ž .vehicle’s per-unit-fuel emissions, e z, a ; and iii have the government stand readyto buy and sell credits in this emission permit market at the fixed price l.18 Thesereformed standards will be equivalent to an automobile tax of

c*l m s, f ; b rf e a, z y e , 16Ž . Ž . Ž .ˆ

A Ž . ga tax which replicates the first part of t in 149 when e s t rl.ˆThis reform corrects some potential shortcomings in current policy. Emission-

Ž .per-mile E-M standards give manufacturers of ‘‘over-achieving’’ automobiles,those cars that more than meet the standards, no incentive to further reducenoxious emissions or to further increase fuel economy. This problem can becorrected by putting a permit market in place, thereby attaching a price to per-mileemissions. However, other shortcomings remain. E-M permit regulation yields

e�w x m4 m ean equivalent tax of a erf y e , where e is the per-mile standard and a isˆ ˆthe permit price. Clearly, this tax does not account for fuel consumption differ-ences}and attendant emission differences}between users of different types ofautomobiles. It thereby misses the welfare gains that can be achieved by tyingemission standards to automobile features that are correlated with mileage choices}and hence, emission levels. With respect to fuel economy, E-M standards missthe ‘‘mileage effect’’ of f on emissions. Higher levels of f , by reducing the per-milecosts of driving, lead to mileage increases}and attendant increases in emissions.Speaking rather loosely, E-M permit regulation does not moderate its implicitsubsidy of fuel economy to reflect this emission-creation cost, thus resulting in

18 Notably, this type of reform would not require changes in the government’s emission testprocedures and would not compel manufacturers to make sudden and costly changes in their emissioncontrol technologies. However, because it would be implemented with a tradeable permit program, thereform would replace rigid emission standards with financial incentives that would prompt manufactur-ers to change the emission properties of their vehicles over time in ways that would achieve totalautomotive emission targets with less economic cost.


excessive fuel economy demand incentives.19 Standards on corporate average fuelŽ .economy CAFE implicitly subsidize f and can thereby exacerbate the distor-

tionary effects of E-M policies.Turning this argument around, on the other hand, provides a logical foundation

for E-M permit regulation. Specifically, if consumer mileage levels were fixed andhomogeneous}i.e., invariant to auto attributes, mileage prices, and consumer type}then the non-internalized social costs of a consumer’s emissions-related deci-sions would equal the per-unit social cost of an emission, l, times the fixed

Ž .mileage, say m, times the per-mile emission level, e rf. E-M permit regulationcan confront consumers with this cost by setting the per-mile emission permit priceat lm. This logic may help to explain why we have emission-per-mile standardstoday and also to highlight the central role that mileage choices play in motivatingthe regulatory reforms described above.

This brings us to a fourth set of observations, concerning the economic circum-stances under which the welfare gains from constrained optimal regulation, vis-a-viscurrent forms of auto emission regulation in the U.S., are likely to be large.

Ž .Welfare gains from optimal auto regulation increase with i the marginal socialŽ . m Ž .cost of emissions, l, ii the price elasticity of mileage demand, « , iii the

< c < Ž .auto-feature sensitivity of mileage demand, m , and iv the level and curvature ofson-board automobile emission abatement costs. As the cost of emissions, l, rises,which occurs when emission targets become tighter, the prospective benefits ofimproving the design of emission regulations rises in tandem. The greater thesensitivity of mileage demand to automobile features, the greater the welfare gainsthat can be obtained from linking automobile regulations to these features andthereby confronting consumers with the emission-creating costs of their featureselections. Particularly important among these features is an automobile’s fueleconomy, about which there is abundant evidence for significant mileage increasing

20 Ž .effects. Higher levels and curvature in abatement costs ceteris paribus reducethe cost-effectiveness of targeting abatement features alone when seeking autoemission reductions; hence, the prospective welfare gains from targeting otherdeterminants of emissions, including mileage choices, are greater. Greater curva-ture in abatement costs also implies greater heterogeneity in consumer choices ofabatement features}and hence per-unit-fuel emissions}thus limiting the scopefor gasoline taxes to confront consumers with the emissions costs of their mileagechoices.

19 To make this statement a little more precise, suppose that for a given marginal social cost ofemissions l and a given individual, an E-M permit policy confronts this individual with the true

e Ž . Ž .marginal social benefits of abatement; that is, suppose a e a, z rf s le a, z mrf. Then the E-Ma ae Ž . 2policy must also present the individual with a marginal subsidy to fuel economy, a e a, z rf s

Ž . 2le a, z mrf , which exceeds the true marginal non-private benefits of this fuel economy; the latterw Ž . 2 xw m xbenefits equal le a, z mrf 1 y « , which are less than the E-M policy benefits to the extent of the

‘‘mileage effect’’ of f , « m. Note, however, that this argument hinges upon a permit market implementa-tion of E-M standards. Without trading in E-M permits, E-M regulation confronts consumers with azero benefit of increased fuel economy for ‘‘over-achieving’’ automobiles, which is lower than the truenon-private marginal benefit of this attribute. These arguments also presume that consumers recognize

w xthe discounted gasoline cost savings that they can reap with a higher level of fuel economy. CRA 8provide evidence in support of this assumption. However, if consumers instead behave myopically whenmaking their fuel economy choices, they will undervalue future gas cost savings from higher fueleconomy, and CAFE-type regulations may be motivated as a counter to the consumer myopia.

20 w x w x w xSee, for example, Walls et al. 29 , Gately 12 , and Dahl and Sterner 11 .

ROBERT INNES234

Ž .An expanded version of this paper available upon request illustrates all ofthese effects in an empirically based numerical analysis. An important ingredient inthis analysis is a mileage demand equation estimated using data on new car usageobtained from the Department of Energy’s Residential Transportation EnergyConsumption Survey; this estimation reveals a statistically significant relationshipbetween mileage demand and a car’s power, weight, import status, and fueleconomy, all of which are directly observable to a regulator. The analysis indicatesthat welfare gains from moving to constrained optimal automobile regulations,

Žfrom current regulations in the U.S., are potentially substantial up to $473 per.car .

Fifth and finally, the analysis has so far ignored spatial concerns in automobileregulation. In fact, damages from automobile emissions vary from location tolocation. For a given car, emissions and fuel economy can also vary from location

Žto location because of different driving conditions including different degrees of.start-and-stop and highway driving . Therefore, an automotive emissions policy

which is spatially homogeneous will not be efficient. For example, the social cost ofemissions, l, is higher in certain urban areas than it is elsewhere, and a given carwill produce higher levels of emissions and experience lower levels of fuel economyin congested regions. Because of these differences, stricter emissions policies arecalled for in urban areas. While this observation is generic to any auto emissionpolicy, it does not alter the qualitative conclusions of this analysis with respect tothe desired structure of emission regulation. Rather, it implies that this analysis is

Ž .properly interpreted as location-specific, with social costs of emissions l , emis-Ž Ž ..sions functions e a, z , and fuel economy measures defined regionally.

D. Fuel Regulation. The last section describes efficient strategies for regulatingthe automobile in order to achieve desired pollution targets, but does so by fixingthe levels of three policy parameters that are not automobile specific. These policyparameters are the gasoline tax, t g, the fuel content parameter, z, and theLagrangian parameter, l, that is isomorphic to the pollution target, E. Turningnow to the choice of these key policy variables, first order optimality conditions are

Ž Ž . .as follows obtained by differentiating the welfare function in Eq. 10 above :

cl: e a w , z m rf w q w dw s ErN 17aŽ . Ž . Ž . Ž . Ž .Ž . Ž .Hw

cz : y g z q le m rf w q c q w dw s 0 17b� 4Ž . Ž . Ž . Ž . Ž . Ž . Ž .H z z zw

g g cgt : t y le a w , z m rf w q w dw s 0. 17c� 4Ž . Ž . Ž . Ž . Ž .Ž .H P

w

Ž . Ž Ž ..Condition 17a simply reproduces the emissions constraint Eq. 7 under theassumption that E is sufficiently small that the constraint binds}and hence, l is

Ž .positive. Condition 17b describes optimal fuel content parameters that equate the� Ž .w x Ž .4parameters’ marginal cost in fuel and auto production, E g z mrf q c , withz z

� Ž . 4 Žtheir marginal benefit in reduced emissions, ylE e mrf where E is thez


. 21 Ž .expectation operator over the consumer population . Finally, condition 17cdefines the optimal gasoline tax. A gas tax t g yields social benefits by reducingautomobile and fuel usage that produce noxious emissions. At the margin, thevalue of this social benefit, for each vehicle, equals the marginal social cost ofemissions, l, times the emissions reduction elicited by a marginal increase in the

w Ž . Ž .x cgfuel price, e rf m - 0. This social benefit comes at the cost of distortingP

consumers’ mileage choices. For a given consumer, the marginal cost of thisdistortion equals the difference between private and true costs of fuel, t g, timesthe reduced fuel consumption that an increased gas tax yields, mc

grf - 0. ThePoptimal gas tax equates its total marginal cost in fuel demand distortion}across allconsumers}with its total marginal benefit in emissions reduction. If the gas taxwere zero, it would have zero marginal costs and strictly positive marginal benefits

Ž .in emission reduction. Thus, an immediate implication of condition 17c is that theoptimal t g will be strictly positive.

V. A DYNAMIC EXTENSION WITH AUTOMOBILE REPLACEMENT

Consumers make auto replacement decisions which can affect emissions becauseof improved emissions abatement properties of newer automobiles, higher fueleconomy of newer cars, and the change in consumer mileage and auto featurechoices that can occur with replacement. For example, the U.S.E.P.A.’s MOBILE4model of automobile emissions predicts that hydrocarbon emissions from thetailpipe rise at a rate of 0.15 grams per mile for every 10,000 additional miles

Žtraveled in a car beyond 50,000 miles compared, for example, to recent hydrocar-.bon standards of 0.41 grams per mile . Hence, when the age of the automobile fleet

rises, as it has in the U.S. over the past 20 years, emissions rise in tandem. Thew ximportance of this phenomenon was first pointed out in Gruenspecht 14 , who

argued that higher emissions standards on new cars will raise their price andthereby lead auto owners to retain their old higher-emitting vehicles for a longer

w xperiod of time. Crandall et al. 10 showed that, in the short run, this deleteriouseffect of new car emission standards on actual mobile source pollution candominate the standards’ direct emission-reduction effect.

In view of these prospects, this section turns to a dynamic setting with consumerŽ .auto replacement choices. Specifically, let us now suppose that i ¨ indexes time,

Ž . Ž . Ž .ii V is an automobile’s age vintage in units of time, iii a car’s fuel economy isdetermined by its vintage and initial fuel economy f 0 according to the relationŽ 0 . Ž . Ž Ž . .f f , V, ¨ , iv e a, V, z ¨ , ¨ represents a car’s time-¨ emissions per-unit-fuel,

Ž . Ž 0 .and v consumers choose their car attributes, s* s s, f , a, V , from a continuumŽ .at each point in time. For this setting, the optimal tax in Eq. 149 has the analog,

now applied at each point in time,

t A s*, I , ¨ ; b ¨Ž .Ž .s l ¨ e ? y t g ¨ mc* s, f ? , V , ¨ ; b ¨ rf ?� 4 � 4Ž . Ž . Ž . Ž . Ž . Ž .Ž .

q w s, V , I , ¨ ; b ¨ , 18Ž . Ž .Ž .

21 Ž .Although identical in form, this condition differs from its first-best counterpart in Eq. 5 becausedifferent mileage and automobile attribute choices enter the calculus.

ROBERT INNES236

Ž . Ž Ž .. Ž Ž ..where b ¨ gives the time ¨ vector of emission prices l ¨ , fuel contents z ¨ ,Ž gŽ .. c*Ž . Ž .and fuel taxes t ¨ , and m and w are generalized versions of the mileage

demand and type-revelation-correction tax functions defined above.A Ž .t in Eq. 18 represents an optimal periodic tax that confronts each consumer

with the otherwise non-internalized social costs of her auto feature choices at eachpoint in time, with features now expanded to include the automobile’s vintage V.

Ž .A corrective w tax is needed for the same reasons as before, namely, to preventdistortions in attribute choices that would result from tax effects of governmentinferences about preference types.

When confronted with this tax, consumers will make constrained optimal vintagechoices, which in turn implies constrained optimal auto replacement decisions. As

Ža car gets older, its emissions and fuel economy deteriorate i.e., e ) 0 andV.f - 0 , leading to higher external costs of its use. The optimal periodic tax reflectsV

these higher external costs, yielding the needed deterrent to continued operationof a high-emitting vehicle.

The logic of this argument is quite general. For example, emissions and fueleconomy levels may depend upon reliability attributes of automobiles androrconsumer maintenance decisions. When reliability is observable to consumers, andits affects on emissions and fuel economy are observable to the government, theautomobile tax can be made to incorporate these effects. Consumers can thus beprompted to choose constrained optimal reliability attributes in their automobiles.Similarly, so long as the emission and fuel economy effects of maintenancedecisions are known to consumers and observable by the government, these effectscan be incorporated in the above tax function, thus eliciting constrained optimalmaintenance decisions. Note, however, that while government observation ofreliability effects need not require any per-period monitoring of individual automo-bile performance, government observation of maintenance effects does requireperiodic monitoring of automobiles, whether via emissions testing or via somedirect maintenance verification. This observation is potentially important whenchoosing between a policy of periodic auto taxation and, for example, a ‘‘two-point’’policy of new car taxes combined with old car retirement subsidies.22 Whileperiodic taxes can potentially elicit emissions-reducing maintenance activities, costsand imperfections in periodic monitoring of individual automobile performancecan favor a two-point regulatory alternative.23

Ž .Accelerated vehicle retirement programs AVRPs have, in fact, become aprominent focus of U.S. air pollution policy.24 In view of this focus, it is instructiveto stretch the present analysis in order to help understand how AVRPs can best be

Ž .structured to enhance economic efficiency. In particular, consider a policy that i

22 Per-period auto taxes are also favored when the emission effects of a given car’s usage vary acrossconsumers, mc / 0. In this case, the allocation of used cars among the consumer public matters fortemissions, and periodic auto taxes are needed in order to confront all consumers with the social costs oftheir used vehicle choices at all points in time.

23 w xSee Harrington and McConnell 15 for an in-depth discussion on costs and pitfalls of emissionmonitoring programs.

24 For example, AVRPs are promoted in the Clean Air Act Amendments of 1990 and have beenŽ w x.implemented in Southern California and Delaware e.g., see Alberini et al. 1 . They have recently been

Žadvanced as promising policy tools in the 1995 Economic Report of the President, which states pp..152]153 : ‘‘Cash for clunkers’ programs, which remove from service older, high-emission vehicles, may

be a cost-effective way of reducing emissions quickly.’’


taxes new cars at a rate equal to the discounted present value of the optimalŽ .periodic tax, over the maximal lifetime of the car, and ii subsidizes old car

retirements at a rate equal to the discounted value of the optimal periodic tax, overthe remaining lifetime of the old car. When maintenance and used car allocationeffects are absent, this policy can be shown to be efficient. In these circumstances,the only emission-related choices that consumers make, beyond mileage, are theautomobile’s initial features and its retirement age. A new-car-tax-cum-AVRPpolicy thus provides consumers with the same emission-related choice incentives asdoes the optimal periodic tax characterized above. While details of this argumentcan be found in my expanded paper, a few qualitative properties of the optimalAVRP merit emphasis here.

First, for a given car, the retirement subsidy declines over time at a rate thatreflects the social costs of the vehicle’s periodic emissions. Retiring an older carnow, as opposed to next year, leads to greater emission reduction benefits becausethe car is off the road an additional year. An efficient retirement subsidy incorpo-rates this benefit by offering a higher reward for retirement today than forretirement next year. This property is important because, so long as an AVRP is

Ž .designed as a continuing rather than one-shot program, the program should notgive owners of old cars an incentive to hold on to their cars in order to qualify forthe program and should give owners of cars that already qualify for the program an

Ž .appropriate social-cost-based incentive not to wait for retirement. For example,the Delaware AVRP offers a given price for cars that are vintage 1980 or earlier.An owner of a vintage 1981 car may hold on to the car longer than he or sheotherwise would in the hope that the car will qualify next year for the AVRP.

Ž .Similarly, an owner of a qualifying pre-1981 car may anticipate that the AVRPoffer price will not decline and may even rise in the future; in this case, theincentive to retire the vehicle now will be less than is needed to elicit a constrainedefficient retirement decision.

Second, the retirement subsidies are linked to the predicted emissions from eachvehicle. Hence, high-emitting vehicles are given the greatest incentive to retire.Of course, the policy must be designed not to give consumers an incentive tomake their cars high-emitting in order to obtain higher retirement subsidies. Forexample, retirement subsidies should not increase with discretionary emissions-increasing choices which consumers make while using the car, such as reducedmaintenance or sabotage of emissions abatement equipment. In addition, retire-ment subsidies should not provide an incentive to choose a high-emitting new car.Here, this objective is achieved by taxing new cars at a rate that reflects theirprospective lifetime emissions.

Third, the AVRP can be implemented entirely through new car producers. ForŽ .every old car that a new car producer retires via purchase from the old car owner ,

this producer can be given the corresponding retirement subsidy as an offset to thenew car taxes that she must pay.

VI. CONCLUSION

Regulating automobile pollution is a complicated business when it is difficult orimpossible for the government to monitor each vehicle’s actual emissions ormileage. For such an environment, this paper has characterized second-best

ROBERT INNES238

emissions policies that entail gasoline taxation, fuel content regulation, and mostimportantly, direct regulation or taxation of the automobile. A second-best auto-mobile tax compels consumers to internalize the social costs of pollution whenmaking vehicle feature selections that will affect emissions, including a car’s fueleconomy and, in a dynamic setting, its age. To achieve this end, an optimal vehicletax approximately equals the social cost of a vehicle’s predicted emissions, less theportion of these costs that are internalized by the gasoline tax.

While these conclusions are intuitive, they are also quite general and provide ananalytical framework that yields insights into the desired structure of regulatorypolicy. For example, in the United States today, two major components of automo-bile emission regulation are standards on emissions-per-mile and corporate aver-

Ž .age fuel economy CAFE . This paper provides an economic backdrop in whichthese types of direct automobile regulations are an efficient component of autoemission policy. However, it also identifies some potential drawbacks of theseregulations. In particular, per-mile-emission standards do not account for mileagechoice differences}and attendant emissions differences}between users of differ-ent types of automobiles. They thereby miss the welfare gains that can be achievedby tying emission standards to automobile features that are correlated with mileagechoices and emissions levels. If implemented with efficiency-enhancing permitsystems, the per-mile standards can exaggerate incentives to increase fuel economyby failing to account for its mileage-increasing cost. Excessive incentives for fueleconomy demand may be worsened by CAFE regulations.

Extending the analysis to a dynamic setting reveals advantages and desirableproperties of periodic vehicle taxes which confront consumers with the periodicsocial costs of the emissions that result from their automobile choices. Constrainedoptimal taxes in this setting are higher on older, higher-emitting cars, thusdeterring their continued use. Periodic taxes can also be made to incorporateeffects of consumers’ maintenance decisions on automobile emissions, providedthese effects can be monitored. When maintenance decisions and used automobiletrades do not affect emissions, constrained optimal taxation can be implementedwith ‘‘two-point’’ regulations that tax new car purchases and subsidize old carretirements. To be efficient, such two-point regulations will tie taxes and subsidiesto a car’s predicted emissions, and specify old car retirement subsidies that declinewith a car’s age in order to enhance retirement incentives.

The importance of structuring automobile regulation to target all determinantsof vehicle emissions, including mileage choices and automobile-specific emissions

Ž w x.per mile, has become widely recognized e.g., see Harrington et al. 17 . Increas-ingly, this recognition is matched by a demand for economic efficiency in thedesign of an integrated auto pollution policy. The complexity of the process bywhich vehicle pollution is produced makes for a rather difficult adaptation ofeconomic theory to the problem of automobile regulation, and a correspondinglydifficult task of characterizing efficient policies. This paper is intended as one ofmany steps in this direction.

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Documents

Regulating Automobile Pollution under Certainty, Competition, and Imperfect Information