Evaluating U.S. Fuel Economy Standards

In a Model with Producer and Household Heterogeneity

Mark R. Jacobsen*

University of California, San Diego

September 2010

Abstract

This paper employs an empirically estimated model to study the equilibrium effects of an increase

in the U.S. corporate average fuel economy (CAFE) standards. The model captures heterogeneity

among producers and among households to describe differences in responses to the regulation. A

distinguishing feature of the model is that it considers the fact that some firms are unconstrained

by CAFE regulation, while others choose either to violate the regulation (pay a fine) or to meet

the standard. By taking this heterogeneity into account, I find that the profit impacts of CAFE

fall almost entirely on domestic producers. In addition, the model develops utility-consistent

welfare analyses that allow direct comparison of the CAFE standard with gasoline taxes,

considering the simultaneous household decision of vehicle and miles traveled. I find that

increased gasoline taxes would reduce gasoline consumption for about one-sixth the welfare cost

of a corresponding increment to the CAFE standard. Finally, the model accounts for the dynamic

effects of CAFE on used vehicle markets – effects that turn out to be important to the welfare

impacts. The consumer surplus changes in used car markets make up nearly half of the gross

welfare costs of an increase in the CAFE standard. These effects fall disproportionately on lowincome households. Contrary to previous findings, the overall welfare costs are regressive.

 

* Department of Economics, 9500 Gilman Drive, La Jolla, CA 92093-0508. Email:

m3jacobs@ucsd.edu. I thank Lawrence Goulder, Timothy Bresnahan, Liran Einav, Frank Wolak,

and seminar participants for their helpful suggestions. Financial support for this work from the 

B.F. Haley and E.S. Shaw Fellowship Fund is gratefully acknowledged.
1

1. Introduction

Gasoline use in the United States is associated with considerable external cost, largely 

associated with environmental and geopolitical concerns. These include economic and 

security risks associated with oil imports as well as the implications of climate change and

local air pollution. Regulation targeted toward the reduction of gasoline consumption was

introduced following the 1973 oil crisis, in the form of the corporate average fuel economy 

(CAFE) standards.

1 These standards impose a limit on the average fuel economy of the

vehicles sold by a particular company in each year, with separate limits for passenger cars and 

light duty trucks.

Substantial increases in the stringency of U.S. fuel economy standards are planned for

the period 2010 to 2020, corresponding to the growing salience of concerns associated with 

gasoline use.

2 This paper contributes an empirical examination of the actions automobile

producers take to meet fuel economy standards and measures the welfare cost associated with 

an increase in the stringency of CAFE. I examine the mechanisms through which the

standards work, and model distributional implications across both producers and consumers.

A number of prior studies have considered fuel economy standards in the context of

comparing alternative policy instruments: Parry et al. (2007) provide a survey and divide

automobile related externalities into those arising from gasoline use and those from miles

driven, showing that gasoline taxes reduce a greater number of important externalities than do

CAFE standards.

3 Furthermore, theory suggests that gasoline taxes are superior to fuel

economy standards even when considering the gasoline externality in isolation. Pricing the

externality directly allows more flexibility in that taxes both reduce miles driven and 

influence vehicle choice while CAFE standards operate only on the latter channel.

4 I offer

 1 Important rationales for CAFE regulation in addition to a reduction in gasoline use include

protectionism and the correction of market failures in demand for fuel economy. Portney et al. (2003)

provide a discussion of the market failure rationale. Goldberg (1998) discusses protection of the

domestic automobile industry.

2 2008 average fuel economy in the U.S. was 27.0 mpg (NHTSA 2009a). The Energy Independence 

and Security Act of 2007 requires an increase to 35.0 mpg by 2020. A 2009 White House 

announcement calls for even stricter regulation to 35.5 mpg by 2016 (EPA 2009).

3 For example fuel economy standards do not directly address automobile accidents or congestion.

4 CAFE standards may increase miles driven since efficient cars are cheaper to operate. Small and

Van Dender (2007) find that this rebound effect can offset 5-10% of the gasoline savings from CAFE.
2

confirmation that this ranking holds in my model, but the focus of my paper lies instead with

the mechanisms and distributional implications of CAFE in particular.

This requires explicitly modeling producer behavior under CAFE, building on a

literature focused on producer response to regulation: Austin and Dinan (2005) consider a

representative car producer that faces a regulatory fuel economy constraint. Using demand

elasticities from the literature, they estimate the changes in vehicle fleet that result and 

consider surplus changes in the market for new cars. Goldberg (1998) develops an oligopoly

model of producer behavior and considers the implications of CAFE for international trade.

5

Kleit (2004) develops a model based on General Motors’ response to CAFE, modeling pricing 

behavior. Similarly, Greene (1991) considers the pricing and fleet mix behavior of U.S.

domestic firms in response to CAFE standards.

6

Anderson and Sallee (2009) also consider producer response, but instead of focusing 

on prices and fleets they examine a loophole in the regulation. They find evidence that firms

have failed to take full advantage of the loophole in spite of its very low cost. This suggests

that the current standard, at least in recent years when gasoline prices are high, may be almost

non-binding.7 In contrast, my work centers around a period of low gasoline prices in the late

1990’s where I find that the regulation substantially influenced firm behavior. The effects

during this period allow insight into how producers and consumers may respond to more

stringent regulation like that currently being adopted.

I address three main challenges unmet in the above literature. First is the treatment of

heterogeneous response across firms, which has been masked by the representative producer

model used in nearly all prior studies. Goldberg (1998) takes an important step, modeling 

certain firms as paying the penalties associated with violation. My model includes this group

of fine-paying firms but also encompasses the behavior of a separate, central group including 

Ford, GM, and Chrysler: I argue that these firms do not violate the standard or pay any fines,

but instead face a shadow cost in meeting the constraint. In contrast to the literature, I model

 5 The producer model is based on demand elasticities estimated in Goldberg (1995).

6 Like Austin and Dinan (2005), Greene develops a model to predict the cost of regulation starting

from an undistorted state but does not examine empirical producer response directly.

7 Agency problems or market failures within the firm might also account for a failure to take full

advantage of the loophole, which involves rewards for the production of flex-fuel vehicles.
3

the heterogeneous behavior of these firms in a single framework and provide empirical

estimates of shadow cost for firms that choose to just meet the constraint.

A second unmet challenge is the simultaneous measurement of welfare effects across

markets for vehicles and gasoline. The literature on CAFE has generally presented measures

of consumer surplus in individual car markets. Studies of gasoline price sensitivity 

necessarily consider utility in gasoline markets as well, but have typically estimated the two 

demand equations separately.

8 In contrast, I make use of recent work in Bento et al. (2009) to

allow consistent equilibrium welfare analysis across markets.

9 I further integrate my model of

producer profits under CAFE, allowing a measure of overall equivalent variation in an

equilibrium setting.

The third main challenge I address concerns the market for used cars. All prior

empirical studies of CAFE to my knowledge have focused on the market for new vehicles, but

regulations influencing new car production necessarily have dynamic effects on used car

markets through time. I model the effects as new cars become used, capturing previously 

overlooked welfare implications of a changing used car fleet.

My main results reflect these innovations. I examine the effects of CAFE at the

manufacturer level and find that almost all profit impacts of the current standard are felt by 

domestic firms. A key mechanism behind this result is substitution in the market for large,

high-horsepower vehicles: When domestic firms cut production of these vehicles in order to 

meet the standard, the unconstrained and fine-paying firms will increase production in their

place. The substitution pattern protects fine-paying firms from profit impacts and also harms

the efficacy of CAFE in reducing gasoline use.

10 Important policy steps toward a harmonized 

standard may be able to mitigate this effect.

At the aggregate level, I find that a 1 mile-per-gallon increment to the stringency of

CAFE reduces long run gasoline use by 3%. Short run effects are much smaller,

 8 For example Goldberg (1995) and West (2004) estimate demand for vehicles and gasoline separately,

correcting for the simultaneity with the technique introduced by Dubin and McFadden.

9 The demand equation for miles is derived using Roy’s identity and the conditional indirect utility

function describing vehicle choice. A single set of utility parameters results that can be used to derive 

a measure of equivalent variation.

10 The degree of imperfect substitution in the luxury vehicle market controls the extent to which gains

in domestic average fuel economy are offset.
4

demonstrating the significance of explicitly modeling the gradual penetration of fuel economy 

standards through the used car fleet. I find that the aggregate welfare costs associated with 

these gasoline savings are about six times larger for a CAFE standard than a comparable

gasoline tax.

11

Finally, one of my more striking conclusions is that the progressivity of a CAFE

standard can be overturned by long run effects in the used car market. The initially 

progressive aspect of the standard is intuitive and confirmed here: wealthier households tend 

to buy more new vehicles, and thus bear much of the initial burden. I find, however, that

changes in used car prices over time and long run shifts in the composition of the used car

fleet eventually overwhelm this, making the total effect regressive. Prior studies of fuel

economy regulation have overlooked this result with their focus on new car markets and a

representative consumer.

The rest of the paper is organized as follows. Section 2 describes the CAFE regulation 

and introduces the model. Section 3 demonstrates the importance of firm heterogeneity and 

categorizes firms empirically. Section 4 describes an estimation procedure using first order

conditions on firm behavior. Section 5 offers an alternative source of evidence for firm

pricing behavior. The welfare and distributional impacts of a change in CAFE policy are

measured in Section 6 using the estimated parameters. Conclusions are offered in Section 7.

2. Regulation and Model of Producer Behavior

a. Fuel Economy Regulation

CAFE standards are enforced at the level of a manufacturer’s fleet of new vehicles in a

given model year. Each manufacturer’s production is divided into two separately regulated 

 11 Austin and Dinan (2005) is the only study to my knowledge to offer comparable estimates. They

approximate consumer surplus changes using new car and gasoline demand elasticities but do not

include used car markets or integrate demands in a utility framework. The find that gasoline taxes

have 60 to 70% less distortionary cost than an equivalent CAFE standard.
5

fleets: passenger cars and light duty trucks.

12 The regulation defines a firm’s corporate

average fuel economy, for each of the two fleets, as:

CAFEfleet=

qj

j!fleet

"

qj

mpg j!fleet j

"

(1)

where qj is the quantity of model j produced by the firm and mpgj is that model’s fuel

economy measured in miles-per-gallon. The summation is taken over all models in the fleet.

The 2009 limit was 27.5 mpg for passenger cars and 23.1 mpg for light duty trucks.

The passenger car standard has been held constant at 27.5 mpg for every year since 1990.

The light truck standard has increased gradually over time but, convenient for my analysis,

was held fixed at 20.7 mpg in all years between 1996 and 2004. The rules allow for the

banking of “credits,” defined in terms of quantity weighted deviations from the standard, for

up to three years. For example, if the firm’s car fleet has a fuel economy of 28.5 mpg it

accumulates credit that can be used to offset a 26.5 mpg fleet in any of the next three years.

13

Similarly, the firm may borrow against future credits, as long as it repays the debt within three

years. If the firm fails to repay a debt within three years it is found in violation of the

regulation and assessed a fine of $50 for each mile per gallon below the standard multiplied

by the total number of vehicles in the fleet. The fine was increased to $55 after the end of my 

sample period.

The banking and borrowing scheme produces a complex set of dynamic incentives for

the firm. In particular, it can be shown that a decision made in the current period can affect

the firm in all future periods and conversely that a firm’s regulatory compliance status in the

current period can depend on the entire history. This is true in spite of the three year

expiration of credits and is demonstrated in Appendix B. The dynamic features of the

regulation generate effective variation in the stringency of the standard through time. Section

 12 The regulation subdivides the passenger car fleet into those produced more and less than 75%

domestically. While this division may have had some impact initially, firms have since been able to

equalize the fuel economy of the two groups of passenger cars without major structural changes (NRC,

2002). The ease of moving cars above and below the “import” threshold and the lack of complete data 

on the fraction of domestic parts in each vehicle lead me to consider passenger cars as a single group.

13 The example assumes that the overall sales of the firm are the same in the two years, since the

number of credits earned is weighted by quantity.
6

5 expands on the details of this variation and provides a reduced form empirical analysis of

producer pricing response.

b. Model of Producer Behavior

Automobile producers are assumed to be oligopolists in a differentiated products

market and equilibrium is defined as a set of prices such that each firm is maximizing profits

given the actions of all others.

14 Firms are treated consistently in that heterogeneity enters

only through parameters. The maximization problem specified here is written in terms of an 

individual firm conditional on the behavior of its competitors.

Introducing CAFE regulation into the firm’s profit function involves modeling the

cost associated with a violation of the standards. I will assume that this cost comes from two 

sources: The first is the fine levied by the regulator, which varies linearly with the degree of

violation. The second is a fixed cost of violation, encompassing the legal, political, and 

corporate image losses also resulting from infractions.

Avenues for compliance with CAFE regulation will be balanced against the costs of a

violation. Compliance involves selling more high-efficiency vehicles (and fewer lowefficiency ones) as a fraction of the total, which I capture through the firm’s choice of price in 

a Bertrand setting. In the long-run, firms will also invest in new technologies.

15 I do not

estimate a technological frontier directly in the model, but am able to consider the role of

technology in an extension to the overall welfare analysis.

16

With these components I model each firm as maximizing profit net of the costs of

violation, solving:

max

{ pj , j!J }

(pj" cj)qj(P)

j!J

#

$

%

&

'

(

) " I(Qi) Hi + FC (Qi) + FT (Qi ( )) *

+

,

,

-

.

/

/ (2)

 14 The prices of other firms enter through residual demand. All else equal, an increase in the price of a 

car by one firm shifts the residual demand faced by other firms outward.

15 Klier and Linn (2008) consider the question of technology and fuel economy standards, examining a

“medium-run” case where technology enters with an intermediate scope.

16 My extension of the model to include technology follows Austin and Dinan (2005). The extension

relies on the general result that cost-minimizing firms equalize the marginal costs of compliance 

across available channels. For an explanation in the specific context of fuel economy see Anderson

and Sallee (2009).
7

where pj, cj, and qj are respectively the price, cost, and quantity of a particular model j made

by firm i. J is the set of all cars made my firm i. P is the vector of prices of all cars in the

market, and Qi refers to the quantities of all models manufactured by firm i. I is an indicator

function taking the value of 1 if the firm is in violation of the standard and 0 otherwise. The

functions FC and FT represent the fines faced for the car and truck fleets respectively. Hi

represents the firm-specific component of cost that is fixed conditional on violation.

The level of the fines depends on fleet size and deviation from the standard. I use the

functional form directly from the regulation, which is administered by the National Highway 

Traffic Safety Administration (NHTSA):

FC (Qi) = qj(P)

j!carfleet

"#

$

%

&

'

( ) 50 )(dcarfleet

* CAFEcarfleet)

FT (Qi) = qj(P)

j!truckfleet

" #

$

%

&

'

( ) 50 )(dtruckfleet

* CAFEtruckfleet)

(3)

where dcarfleet is the level of the standard for the manufacturer’s car fleet, 27.5 miles per

gallon, and CAFEcarfleet the corporate average fuel economy for the firm’s car fleet as defined

in (1). Note that fleet fuel economy is computed as the harmonic mean in order to match the

NHTSA rule precisely. The expression for the light duty truck fleet, FT, is analogous with the

standard fixed at 20.7 in 2001.

The firm level fixed components of cost, Hi, represent other losses that are incurred 

when violating the regulation.

17 Corporate public image and legal liability for environmental

damage may be important factors. A firm’s political capital, valuable in times of financial

distress or when negotiating stringency of regulation, could also be eroded by violations.

Allowing the magnitude of these costs to vary across firms is important: Foreign companies

may have less exposure to U.S. environmental lawsuits or less need for U.S. political capital.

Similarly, firms that specialize in high performance cars may be less averse to a reputation for

environmental violations than are full-line automakers.

 17 Some of these costs may be argued to vary with the severity of violation. The distinction is

irrelevant for the purposes of estimating the shadow cost of firms never observed to violate the

standard. It could, however, somewhat influence the group of firms observed to violate since they

must weigh the degree to which they fall below the standard.
8

These costs are difficult to measure directly, so in working with the model I must rely 

on two key assumptions to bound Hi: i) For firms that have complied historically the costs in 

Hi are at least large enough to justify their decision. ii) For firms regularly found in violation

of the standard the costs are small enough that the violation is consistent with profit

maximization.

A final important simplification is that the indicator for violations, I, is defined for a

single year in a static version of the problem whereas the regulation in fact allows banking

and borrowing of credits. A dynamic model, as shown in Appendix B, involves optimization 

over all years simultaneously with a state space depending on the firm’s entire history.

18 The

approximation to require compliance in a single year both provides a tractable model and is

consistent with a dynamically optimizing firm’s behavior in a period of stable demand with 

convex costs of compliance.

19

Solving for Firm Behavior

Equation (2) can be divided into three cases, depending on the state of the indicator I.

In the first case, I is equal to 0 at the unconstrained optimum shown below. In other words, if

the firm maximizes profits without regard to I it will already meet or exceed the standard.

The maximization problem in (2) can then be reduced to a standard multi-product profit

maximization problem subject to the residual demand curves given by the qj’s:

max

{ pj , j!J }

(pj" cj)qj(P)

j!J

#

$

%

&

'

(

) (4)

In the second case, the maximum in (2) is reached when I is equal to 1. Profits are

maximized when the firm is violating the standard and paying all associated costs. After

replacing I and eliminating constant terms (2) reduces to:

 18 It may seem that compliance state could be determined via a moving set of seven-year windows, an

already difficult intertemporal problem, but in fact the accounting of credits and debits can lead to

dependence on the entire history.

19 Convexity of compliance costs (which follows from standard assumptions on the multi-product

demand system) causes the cost of repaying borrowed credits to exceed the initial gain. Note also that

this is absent discounting: In a model that permits borrowing, a firm would like to borrow in the early

years of the regulation and pay back late, letting the value of the permits rise with the discount rate. In

the case of CAFE, however, the three-year limit on borrowing mitigates the importance of this effect.
9

max

{ pj , j!J }

(pj" cj)qj(P)

j!J

#

$

%

&

'

(

) " FC (Qi) + FT (Qi) *

+

,

,

-

.

/

/

(5)

In the third case, the maximum in (2) is reached when the firm is just complying with

the standard. In other words, I is equal to 0 but any small reduction in fuel economy would

cause the firm to violate the standard. The solution to (2) for a constrained firm can be

written as the maximization:

max

{ pj , j!J }

(pj" cj)qj(P)

j!J

#

$

%

&

'

(

)

s.t.

qj(P)

j!carfleet

#

qj(P)

j!carfleet mpgj

#

" dcarfleet * 0 and 

qj(P)

j!truckfleet

#

qj(P)

j!truckfleet mpgj

#

" dtruckfleet * 0

(6)

where the constraint above is the definition of

I(Qi) = 0 . For economy of notation I have

omitted the case where a firm may be constrained in one fleet but not the other, although this

possibility is considered in both the estimation and policy simulations.

The first order conditions for each of these three cases are written out explicitly in

Section 4 as estimation equations.

3. Heterogeneous Response to CAFE: Three Types of Firms

I develop a dataset and metric to examine the division of major automakers into the

three categories identified by the theoretical model above. The analysis is based on historical

response to CAFE and my definitions of the groups below are followed by two proposed 

metrics for categorizing firms.

20 In contrast to Goldberg (1998), I not only consider firms that

are affected by the CAFE fines, but also firms that are constrained by the regulation. I will

find that this new group of constrained firms bears much of the burden of policy and 

influences the efficiency of the regulation.

 20 Given enough variation through time, firms may have moved from one category to another, but this

does not appear to have been the case for the major producers in the U.S. market.
10

Groups

I. The first group consists of those firms whose car and truck fleets exceed the standard.

More precisely, given the set of prices and vehicles offered by other makers, the profitmaximizing quantity for each model results in a fleet of new vehicles that is unconstrained by 

the regulation. Toyota and Honda are the two largest firms in this category; their car and 

truck fleets have well surpassed the standard every year since 1978. This group corresponds

to equation (4) above.

II. The second group is comprised of firms that violate the standard and pay the

associated fines. BMW and Mercedes (until its merger with Chrysler) are the two largest

firms in this group. They have both violated the standard for each model year since 1987 and 

have paid about $500 million in fines as a result. They correspond to equation (5) above.

III. The third, and arguably most important, category consists of firms that are constrained 

by CAFE as modeled in equation (6). These are firms that, in the absence of regulation,

would choose to produce a fleet that falls below the CAFE standard, but alter their fleet such 

that it just meets the standard when regulation is introduced. Implicitly, this means that total

costs associated with violating the standard are larger than the forgone profits from

compliance. I show below that the traditional “big three” producers, Ford, GM, and Chrysler,

fall into this category.

CAFE compliance status for each firm is calculated annually and available from the

NHTSA.

21 Figure 1 plots the raw data for one firm in each category: The behavior of Toyota

and BMW is clear, with Toyota exceeding and BMW violating the standard in every year.

Ford, while not meeting the standard exactly in any one year, appears constrained in the sense

that through time its deviations from the standard almost precisely cancel. In other words, the

credits that it earns from a year when it is slightly above the standard are offset almost exactly 

by years when it falls below the standard. Figure 2 plots the history of the largest firms in

each category, as divided by the metric below.

 21 National Highway Traffic Safety Administration (2009a) and (2009b).
11

To incorporate the dynamic nature of the regulation, where credits from overcompliance may be used on a one-to-one basis to offset under-compliance, I aggregate firm

deviations from the CAFE standard through time. This is done in Table 1 for the largest

firms. In the left hand (car fleet) panel, the row for Honda, for example, indicates that during 

the period 1990-2001 the firm produced a fleet that exceeded the CAFE standard by an 

average of 3.96 miles per gallon. Mercedes, on the other hand, produced a fleet whose fuel

economy averaged 3.29 miles per gallon below the standard, paying penalties for violating the

regulation in almost every year. Ford, GM, and Chrysler have aggregate deviations very close

to zero – measuring less than 0.2 miles per gallon above the standard. This places them in the

third group, firms that are constrained by the standard but not found in violation.

22

To further emphasize the differences in the three groups, the table also shows the

fraction of years in which the firm had a fleet fuel economy that fell below the standard.

Notice that the firms in the violating group were below the standard in every year, while the

unconstrained firms are above in almost every year. The constrained domestic firms spend 

some years under the standard, and some years over, using credits from the good years to

offset under-compliance in the bad years.

The second panel repeats this exercise for the separately regulated light duty truck 

fleet. The same group of three domestic firms is in the constrained section, with the fleets of

the largest truck makers, GM and Ford, again averaging less than 0.1 miles per gallon above

the standard.23

4. Data and Estimation

In order to develop a more complete understanding of automobile markets in the

context of CAFE regulation, models of both the demand and supply of automobiles are

estimated. Demand follows the model in Bento et al. (2009), while supply is given by the

 22 Since I begin the calculation in 1990 (after the level of the standard was fully stabilized) the slight

over-compliance measured may capture the repayment of credits owed from the late 1980’s.

23 The truck fleets of VW, Isuzu, and Mitsubishi are not differentiated as sharply by the second metric,

so I place these smaller firms according to their average performance, which in all cases coincides

with performance in the central 1997-2001 period I consider. Volkswagen violated the standard in

each year since 1996 and was forced to pay a fine on all of its 1997-2001 truck fleets. Isuzu and

Mitsubishi both had fleets well above the standard in this period, and did not pay fines.
12

model described in Section 2. The pair of models has the advantage of consistency in the

sense that I employ the same data sources and assumptions throughout. In brief, the

household level results from Bento et al., described in the first subsection below, are used to

derive a set of residual demand curves faced by producers and to allow measurement of

welfare effects.

The second subsection describes estimation of the producer model. The computations

for the unconstrained and fine-paying cases follow Goldberg (1998). The constrained case,

for Ford, GM, and Chrysler, provides a new challenge in separately estimating the shadow

costs of the regulation. The first order conditions of the profit-maximization problems above

are employed in estimation. The estimates provide a producer level understanding of

responses to fuel economy regulation.

a. Household Demand

For a more detailed description of the demand estimation, see Bento et al. (2009). The

primary data source is the 2001 National Household Travel Survey (NHTS), which provides,

in addition to demographic indicators, household level survey data on automobiles owned and 

vehicle miles traveled (VMT). The vehicle data for both the demand and supply side are

divided into the following 10 vehicle classes, 5 age categories, and 7 manufacturers:

Classes Age categories Manufacturers

Compact New cars Ford

Luxury compact 1-2 years old Chrysler

Midsize 3-6 years old General Motors

Fullsize 7-11 years old Honda

Luxury mid/fullsize 12-18 years old Toyota

Small SUV Other Asian

Large SUV European

Small truck

Large truck

Minivan

Vehicle characteristics come from Ward’s Automotive Yearbook, and prices from the

National Automobile Dealer’s Association (NADA) Car Guide. An annual measure of

vehicle rental cost based on the change in resale value, registration, and insurance costs is

constructed and given in the model below by 

r

%

hj . Fuel economy and local prices of gasoline

are used to compute a measure of per-mile operating cost for each household and vehicle,
13

p

%

hj

M .

24 (The ~ symbol throughout indicates data and parameters estimated within the

household problem.)

The key advantages of this demand model in application to CAFE standards are i) the

simultaneous estimation of the choice of vehicle and miles driven and ii) the model of

demand for used vehicles. This represents an important improvement over previous work,

much of which has employed a two step procedure and has not considered the used market.

25

The single set of parameter estimates, obtained by using the information in both the vehicle

choice and VMT data, allows the numerical simulation of an integrated set of household 

decisions and consistent measurement of welfare effects under policy scenarios.

Specifically, indirect utility for household h conditional on the discrete choice of

vehicle j is given by:

Vhtj= Vhj

'

+ μh! htj

Vhj

'

=

"1

%

#h

exp "

%

#h

y

%

h / Th

" r

%

hj

p

%

hx

$

%

&

'

(

)

$

%

&

'

(

) "

1

%

*hj

exp +

%

hj +

%

*hj

p

%

hj

M

p

%

hx

$

%

&

'

(

) + ,

%

hj (7)

where

y

%

h

is household h’s income and 

p

%

hx

the price of the outside good. The utility

parameters

%

!h , "

%

hj , 

%

#hj , and $

%

hj

are to be estimated. Subscript t indicates the choice occasion 

for households purchasing multiple vehicles, see full article for an in depth discussion of this

component. The random component of utility, given by μh

! htj , is drawn from the type I

extreme value distribution, with the probability of a given discrete choice j maximizing utility 

therefore taking the logit form:

Pr

ht( j) =

exp(Vhj

' / μh )

exp(Vhk

' / μh )

k!"

#

(8)

where ! represents the set of all new and used vehicles in the market.

 24

p

%

hj

M

also includes a measure of per-mile maintenance costs and the portion of insurance costs that

vary with annual mileage.

25 For example, West (2004), Goldberg (1998) and Train (1986) use a two-step procedure to

sequentially estimate the discrete choice of vehicle and the demand for VMT.
14

The second equation, for the continuous choice, is derived directly from the indirect

utility function in (7) using Roy’s identity, and is given by: M

%

htj

= exp !

%

hj +

%

"hj

p

%

hj

M

p

%

hx

#

$

%

&

'

( +

%

)h

y

%

h / Th

* r

%

hj

p

%

hx

#

$

%

&

'

(

#

$

%

%

&

'

(

( (9)

where

M

%

htj

is miles driven for household h conditional on choosing vehicle j. We assume

M

%

htj

is measured imperfectly, yielding the estimation equation,

M

ˆ

htj

= M

%

htj + !htj , where

M

ˆ

htj

is the observed survey response on miles driven and 

!htj

is i.i.d. Gaussian error.

To compute the estimates, we adopt a Bayesian approach and use a variation of

Allenby and Lenk’s implementation of the Gibbs sampler. Mean values for the elasticities of

miles driven with respect to operating cost and income, respectively, are found to be -0.69 and 

0.62, with the related elasticity of demand for gasoline estimated to be -0.32. The mean 

elasticity of new vehicle demand with respect to price is estimated to be -2.0. The estimated 

utility parameters are allowed to vary by household income, family composition, education,

MSA size, and race. These sources of variation allow a particularly detailed view of the

distributional effects of policy.

b. Producer Costs

Estimation of cost parameters determining producer response to CAFE regulation

represents the final step in using the pair of models for policy analysis. In order to recover the

cost parameters I make use of the firms’ first order conditions drawn from the model of

behavior in Section 2. Where the residual demand functions enter I incorporate estimates

from the household demand system just discussed. We will see that an estimate of costs may 

be computed directly, along the lines of Goldberg (1998), for two of the three groups of firms:

those that are unconstrained or that are paying the fine. For the third class, the constrained 

domestic firms, I introduce an econometric model to separate two components of cost under a

pre-existing CAFE standard: marginal production cost, and the shadow cost of existing 

regulation.
15

i. Computation for Unconstrained and Fine-Paying Firms

First consider the case of the unconstrained firm given in equation (4). This is a

standard multi-product profit maximization problem and the set of first order conditions with

respect to price may be written in matrix notation as:

Qi(P) + Di!(Pi" Ci) = 0

(10)

where Qi is the vector of quantities of each type of vehicle made by firm i, and Pi and Ci the

corresponding price and cost vectors. Di is the j by j matrix of derivatives of demand where

the k, lth element of Di is:

!ql !pk . I compute the matrix Di from the aggregate household 

demand system, and the vectors Qi and Pi are data. An estimate of costs may then be

computed directly from (10).

In the second case, which describes firms observed to be violating the standard and 

paying the fine, the first order conditions may be written as:

Qi + Qi*GiC + Qi*GiT + Di!(Pi" Ci" F

ˆ

iC

" F

ˆ

iT ) = 0

(11)

where F

ˆ

iC

and F

ˆ

iT

are vectors with the elements defined as the per-vehicle fine for each car

and light duty truck. The vectors GiC and GiT are the derivatives of F

ˆ

iC

and F

ˆ

iT

with respect

to vehicle price.

26 As mentioned, this calculation and the one above for unconstrained firms

so far follow the analysis done in Goldberg (1998), with the exception that I model the

average fuel economy calculation using the regulation’s harmonic mean formula rather than a

linear average. The result is that the derivatives in GiC and GiT are no longer linear, but are

given by:

[GiC ]k

!

"F

ˆ

iC

"pk

= 50 #

"qj

j "pk

$

qj

j mpgj

$

%

qj#

j

$ "qj

"pk

1

mpgj

&

'

(

)

*

+

j

$

qj

j mpgj

$

&

'

(

)

*

+

2

,

-

.

.

.

.

.

/

0

1

1

1

1

1

(12)

Despite the complexity of this expression, an estimate of Ci can still be computed directly 

from the data as in the unconstrained case.

 26 The * symbol in (11) indicates element-by-element multiplication.
16

ii. Estimation Procedure for Constrained Firms

The largest domestic automakers fall into neither of the two categories described by 

Goldberg, but instead are constrained by CAFE. The shadow cost of satisfying the regulation 

is unobserved and must be identified separately from production cost in order to understand 

the impacts of policy.

For clarity, first rewrite the maximization problem given in (6) in vector notation:

max

Pi

Qi

'

(P)!(Pi" Ci # ) $ %

&

subject to

Qi

'

(P)! LiC > 0 and Qi

'

(P)! LiT > 0

(13)

where the k-th element of LiC is

1!

27.5

mpgk

"

#

$ %

&

' for passenger cars and 0 otherwise. The k-th 

element of LiT is

1!

20.7

mpgk

"

#

$ %

&

' for light duty trucks and 0 otherwise. We can write the first

order condition with respect to price of the associated Lagrangian as:

Qi(P) + Di!(Pi" Ci + #iC LiC + #iT LiT ) = 0 (14)

where !iCand !iTare the scalar Lagrange multipliers for firm i associated with the passenger

car and light duty truck constraints, respectively. In the previous two cases we saw that an 

estimate of Ci could be computed directly from the first order conditions. This is no longer

possible since the terms representing the shadow cost of CAFE are also unknown. The

remainder of this section describes an econometric approach for estimating !iCand!iT , from

which the remaining parameters needed for the policy simulations may be computed.

Notice that, at the optimum, !iC(and similarly!iT) takes the same value across all

models produced by a given manufacturer. This restriction, that the shadow cost of the

regulation is made equal across products, will be used in identifying the econometric model.

Intuitively, it states that at the optimum firms set the shadow cost of the constraints, given by

the λ terms, equal across models.

A proxy for the price-cost margin is also introduced, constructed using the dealer

markups observed in the data and the ratio of dealer to manufacturer margin suggested in 

Bresnahan and Reiss (1985). They find that this ratio is approximately constant across
17

vehicles – that is, that while markups will differ widely based on attributes of the vehicle and 

the corresponding demand elasticities, the fraction of the total markup kept by the dealer is

roughly constant. I assume that this measure, Bi, includes error and a constant factor, and 

consider the following two forms:

(I) Bi= Pi! Ci +"i + #i

(II) Bi= $ i%(Pi! Ci +"i + #i)

(15)

In specification (I)

!i

is an additive constant, Pi

! Ci

the firm’s price-cost margin, and

!i

is

measurement error independent of the variables entering the producer’s optimization problem.

Specification (II) adds a multiplicative term, ! i , and is preferred since the multiplicative

factor is in keeping with the Bresnahan and Reiss model. I show that the central parameter

estimates of the model are robust across both specifications, but find that model (II), including

the multiplicative factor, fits the data somewhat more closely.

Rearranging the first order condition in (14), we can write the price-cost margin in

terms of the demand system and the shadow costs of CAFE:

Pi! Ci= !D

i

!1

Qi(P) ! "iC LiC! "iT LiT

(16)

Combining (16) with the functional forms considered for Bi in (15) yields the following two 

models:

(I) Bi= !D

i

!1

Qi(P) ! "iC LiC! "iT LiT +#i + $i

(II) Bi= % i&(!D

i

!1

Qi(P) ! "iC LiC! "iT LiT +#i + $i) (17)

The parameters, !iC , !iT , !iand ! i , are estimated by least squares. The results are

presented in Table 2. Model I is estimated first using a scalar value !iand then allowing it to 

vary for each make-fleet combination. Similarly, model II is first estimated with scalar values

for !i and ! i and then more flexibly allowing ! i to vary with make-fleet combination.

While the models are both identified in cross-section, data for the years 1997-2001 is pooled 

due to the limited number of observations available for a single year. Implicitly, this adds the

assumption of a constant shadow cost of CAFE across these five years. Recall, however, that
18

firms can shift the CAFE requirements across time, so that in a period of stable demand it is

not unreasonable to assume that they are able to equalize the shadow costs.

27

The estimates for

!iC

and 

!iT

shown in Table 2 are robust across specifications and 

vary significantly among manufacturers. Perhaps not surprisingly, the models with fixed

effects by make-fleet fit the data considerably better. To attach economic meaning to the

parameters and the differences observed among firms, I compute the marginal effects of a unit

change (one mile per gallon) in the standard on the profits of each firm and fleet in Table 3.28

In this table, and as the central case in the policy simulations, the values from model (IIb) are

used. Appendix A demonstrates the robustness of the results to alternative specifications of

the fixed effects, the inclusion of year fixed effects, and a “placebo” type test on 

unconstrained firms.

The highest shadow costs displayed in Table 3 are for GM’s passenger car fleet.

Intuitively, this fleet is estimated to be the most constrained in the sense that the pricing of

component vehicle models reflects the largest distortions attributable to regulation.

29 At the

other end of the spectrum, Ford’s car fleet shows the smallest effects from CAFE. These

estimates are consistent with casual observation in the domestic auto industry: among 

carmakers, Ford has a reputation for its “practical” car line (Taurus, Escort, Focus) whereas

GM is best known for a lineup of larger, high-horsepower vehicles with correspondingly low

fuel economy. In truck fleets, Ford and GM are similar, while Chrysler, with its dominance in 

the minivan market, has the lowest marginal costs of CAFE. (Minivans have significantly 

better fuel economy than most SUVs.)

 27 The seven-year limit on the window of banking and borrowing and long run changes in market

conditions may mean that firms either can not or do not wish to equalize shadow costs over long time 

horizons. In order to limit the impact of these long run effects, I restrict the time period for estimation

to the five years leading up to 2001 — the year from which the cross-section of household demand

data is drawn. Note also the stability of the CAFE standard through this time period (see Section 2a).

28 The marginal effects are derived by inverting the (nonlinear) transformation performed on the

constraint when writing it in the form of equation (13), and converting to dollar units.

29 The distortions exceed the $50 fine for violation, suggesting that domestic automakers have

substantial profit motives for compliance in addition to the nominal fines imposed for violation. See 

discussion in Section 2b.
19

5. Time Series Model of Prices

The analytical model and parameter estimates above are based on the assumption that

firms react to CAFE by changing prices, thereby affecting demand and the composition of

their fleet. An alternative estimation procedure is also possible, exploiting time series

variation instead and serving as a test of the assumption made in the main model.

The estimation strategy uses a firm’s history of compliance, and therefore information

about how many extra credits it has or obligations it owes, to derive a proxy for how

constrained it is in any given year. Price is regressed on the information about CAFE status to 

assess how firms alter prices based on the regulation. While this model makes a very 

different set of assumptions and uses different data sources, it results in a set of estimates

consistent with the central results just presented in Section 4b.

Recall that the regulation allows both banking credits for three years and borrowing

against three years worth of future credits. If the firm holds credits longer than three years

they expire, and if it fails to repay borrowed credits within three years the firm is found in

violation. The first simple measure of annual “firm state” I construct is simply the number of

credits a firm has that will expire if they go unused minus the number of borrowed credits it

must repay to avoid penalty. A positive value means that a firm may freely produce a fleet

that is less than the standard, so that the firm is less constrained by the regulation. A negative

value means that a firm must exceed the standard in order to avoid a penalty for not paying 

back borrowed credits, and is therefore more constrained by the regulation.

I construct this measure from my dataset as follows. Define the variables:

! 0,t" Credits (debts) expiring (due) in year t

!1,t" Credits (debts) in year t, expiring (due) in year (t + 1)

! 2,t" Credits (debts) in year t, expiring (due) in year (t + 2)

Yt" CAFEt# dt

where as before dt is the standard and CAFEt is the firm’s certified fleet fuel economy in year

t. Positive values of δ indicate credits and negative values indicate debts. I compute the

evolution of the δ parameters through time from the initial state (

! 0,0 = 0 , !1,0 = 0 , and

! 2,0 = 0

) and the complete time series data on Yt beginning with the 1978 inception of CAFE.

For example, in the case that the firm has credits available (so at least one δt is
20

positive) and uses some of them (so Yt is negative) the state variables in the next year (δt+1)

are defined as:

! 0,t +1 =

!1,t

! 0,t + !1,t + Yt

0

 

if " Yt # ! 0,t 

if ! 0,t < "Yt < (! 0,t + !1,t)

otherwise 

$

%

&

'

&

!1,t +1 =

! 2,t

! 0,t + !1,t + ! 2,t + Yt

0

 

if " Yt # (! 0,t + !1,t) 

if (! 0,t + !1,t) < "Yt < (! 0,t + !1,t + ! 2,t)

otherwise 

$

%

&

'

&

! 2,t +1 =

! 0,t + !1,t + ! 2,t + Yt

0

$

%

&

'&

 if " Yt > (! 0,t + !1,t + ! 2,t)

otherwise 

An analogous set of rules applies for computing the stock and flow of debts through time and 

for the remaining cases on Yt. These are provided in Appendix B. With this notation, my first

measure of the firm’s state is given simply by ! 0i,t

" ! 0,t . The effect of a firm’s expiring 

credit surplus or deficit on relative prices proxies for response to changes in the effective

stringency of the constraint and can be estimated as:

(I) ln(Pit) = !t +!i + " # Xit + $i#% 0i,t + &it

(18)

where the left hand side is the log of price of a particular car class for each firm i and year t.

The model is estimated separately for each car class. The first terms on the right hand side are

fixed effects for year and firm, αt and αi. Next is a matrix of vehicle characteristics Xit, with

estimated coefficients γ.

30 !i

is the coefficient on the measure of a firm’s credits or debts,

and is the parameter of interest. It indicates how firm prices are related to CAFE state, after

controlling for car characteristics and make and year fixed effects. Finally, !itcaptures

unobserved heterogeneity in vehicles and is assumed to be uncorrelated with

! 0i,t .

The fixed effects by year are particularly important since they control for changes in 

the popularity of each vehicle class — coming for example from gasoline prices — over time.

 30 The vehicle characteristics controlled for are fuel economy relative to weight and horsepower,

acceleration (horsepower divided by weight), wheelbase, and volume.
21

The availability of CAFE credits is being used here to reflect only differences in prices across

manufacturers within the same year, controlling for fixed brand effects and for the average

price of the vehicle class by year.

A second specification further relaxes the assumption that firms only consider credits

or debts expiring in the current period, and instead uses a measure based on optimal behavior

given the expiration dates for all three vintages of credits or debts it may possess. I again 

assume convexity of compliance costs, causing the firm to repay a debt evenly over three

years, or, analogously, to use a credit evenly over its three year life.

31 This measure of

aggregate firm state (as an optimal deviation from the constraint) is then given by:

St=

max !0,t ,

1

2

!0,t + ! ( 1,t) "

#

$ %

&

' if !0,t + ! ( 1,t) >

2

3

!0,t + !1,t + ! ( 2,t)

max !0,t ,

1

3

!0,t + !1,t + ! ( 2,t) "

#

$ %

&

' otherwise 

(

)

*

*

+

*

*

in the case that a firm has credits. For the case of debts, the sign of St and the inequalities are

reversed. Intuitively, St simply spreads the use of credits or debts evenly over three years,

with the nonlinearities arising because of the constraints imposed by the expiration dates.

Model (II) replaces the firm state in (18) with this aggregate measure:

32

(II) ln(Pit) = !t +!i + " # Xit + $i# St + %it

(19)

The results from estimating models (I) and (II) are presented in Table 4. The point

estimates are the change in vehicle price (for the class given in the column heading) in years

when a firm has an extra one-mile-per-gallon credit that it may use. For example, the top left

estimate indicates that, controlling for make and year fixed effects and car characteristics,

Ford prices compact cars 4.6% higher in years when it can freely deviate one mile per gallon

below the standard.

 31 Note that the assumed foresight here is with respect to the use of credits or payment of debts, and

not to random fluctuations in demand that cause the initial accumulation of such credits or debts. In

other words, the firm now realizes it has three years in which to use a credit, but it still acts according

to a constant expectation over future demands.

32 In principle, a more complex model could be estimated with all of the δ variables entering

separately. The short time series in the case of CAFE (since regulation is on annual averages),

however, presents insufficient variation in the individual state variables to make this approach

feasible.
22

The pattern of estimates across vehicle classes presented in Table 4 strongly supports

the model of firm behavior in Section 4b: the latter model asserts that vehicles with high fuel

economy have a negative shadow cost from regulation, and should therefore be priced higher

in years when the regulation is less binding. The positive coefficients in the first column of

Table 4 bear this out. Similarly, vehicles with the lowest fuel economy (in the right-most

column of Table 4) should have the highest shadow costs, and thus the lowest prices in years

when regulation is less binding. This is also supported. Finally, the price of midsize vehicles

is found to be relatively unaffected by the stringency of regulation, which again fits the

behavioral model since midsize fuel economies tend to be close to the mean and therefore

have near zero shadow costs associated with regulation.

When this same model is repeated for the light duty truck fleet, however, a clear

pattern no longer emerges. Why might this be? While the five classes of cars are well

defined over time and have a stable ranking in terms of fuel economy, the same is not true for

trucks. The rise of two broad classes of light truck — the minivan in the late 80’s and SUV in 

the 90’s — causes the demands and characteristics of vehicles in the truck fleet to change

dramatically. Fuel economy, and in particular the rankings of the various classes by fuel

economy, changes over the sample period. The reduced form model of pricing behavior in

this section assumes a fixed effect of regulation within a class and is not able to adjust for the

shifting demands and fuel economies of the light truck classes.

The estimates in Section 4b, on the other hand, base the shadow costs and implicit

pricing effects on relative fuel economy and demand elasticities. They can therefore capture

the effects as the truck market changes over time. Furthermore, since the full model of firm

behavior also incorporates information from cross-sectional variation, I am able to use the

shorter time period beginning in 1997 after much of the rearrangement in the truck market is

complete.

6. Simulation Model and Results

The simulation model combines household and producer decisions in the automobile

market, using the models and parameters estimated in Section 4. Equilibrium in car markets

is solved numerically at 1 year intervals for 10 years. The results capture the effects of CAFE

standards on both new and used car markets as the fleet turns over. Agents optimize in each 
23

period according to the household utility function and producer problem described above.

33

The quantities and attributes of vehicles available in the used car market are updated through

time, and evolve according to the full history of demands.

a. Structure of the Numerical Model

Aggregate Demand

Aggregate demand for new and used cars comes from the household utility function

described in equations (7) and (9). Households simultaneously make the discrete choice of

vehicle and the continuous choice of miles. Since the estimated utility parameters vary with 

household characteristics, the 20,429 households in the dataset are considered individually.

The resulting household-level demands are combined to arrive at an aggregate demand for

each of the

!

new and used vehicles.

34 There are a total of 225 distinct vehicles in the used 

car market and 59 in the brand-differentiated new car market. Aggregate demand for miles

driven, and therefore gasoline, is calculated directly from the solutions to the household utility 

maximization problems.

Supply of New Cars

The supply of new cars is computed by solving the producer problem given in 

equation (2) for each of the seven firms considered. This requires the use of the cost

estimates described in Section 4b, and the derivatives of the vehicle demand function, Di.

Numerically, the simulation addresses the special cases in (2) by solving the first order

conditions given in (4), (5), and (6) for each of the three cases individually, and then finding

the maximum where all conditions are satisfied.35 This solution procedure must be iterated to 

 33 The period by period solution of the model means that while the fleet evolves endogenously with

policy, the agents are not forward looking in that future demand conditions are not predicted. This

limitation follows from the static models of consumer and producer behavior, and is needed to make 

the model computationally tractable.

34 Each household in the data is assumed to be representative of a group of households proportional to

its sampling weight. The choice probabilities given in (7) are therefore combined using the weights

provided in the NHTS to yield aggregate demands.

35 Subject to the restriction that constrained firms have a sufficiently high value for Hi that they

continue to comply with the standard.
24

find an equilibrium, since the solution for any one firm depends on the prices set by all of the

others.

36

Supply of Used Cars

The supply of used cars available of a particular class, make, and age category

depends on the stock (given endogenously from demand for new cars in previous years) and

the rate at which vehicles of that type are scrapped. At any given time t it is calculated by 

adding the previous year’s production of new cars to the previous supply of used cars, and 

deducting the number of vehicles which are scrapped. Specifically:

ql,t+1

U

= (1! "l )ql,t

U + ql,tN

where

ql,t

U and 

ql,t

N are the quantity of used and new cars of make and class

l

available in year

t, and 

!l

represents the average probability that used cars of type

l

are scrapped. The

computation is performed separately for the transitions between each of the different age

categories.

The probability that a car is scrapped in any given year is determined simultaneously 

with prices where a higher current resale value implies a lower rate of scrap. The relationship 

is captured simply in the model as:

!

" j= bj# ( pj)

$ j

(20)

where

!

bj

is a scale parameter used for calibration and 

!

" j

is an elasticity controlling the

change in scrap probability as the price of the car changes.

37 Baseline scrap rates increase

with car age.

 36 Multi-product oligopoly problems like this one have the potential to exhibit multiple equilibria,

although no alternative equilibria have appeared in my model even under widely varying starting

values. The stability of this particular system is likely due to relatively small cross-price elasticities

and the presence of the much larger, competitive used car market.

37 The elasticity is set to -3 in the central case, see Bento et al. (2009) for discussion of this parameter.
25

Equilibrium

The solution to the numerical model is a set of new car prices, used car prices, and

transfers to the household that simultaneously clear the used car market, solve the producers’

problems subject to CAFE, and balance the government budget. Supply in the used car

market adjusts according to the elasticity given in (20), with aggregate demand derived from

the solution to the households utility maximization problems. The solution to the second 

condition, equilibrium in the oligopoly problem faced by producers, is a set of new car prices

that maximizes profits for each firm conditional on the decisions of the others. The model

solves for the new car market equilibrium, holding used car prices fixed, and then solves the

used car market. Because of the interdependence of demands in the two markets, this

procedure is iterated to convergence.

38

The third condition, balance of the government budget, is reached by adjusting the

level of the transfer to the household. In the simulation, the government receives revenue

from pre-existing gasoline taxes and from the fines levied on violators of the CAFE standard.

It returns the revenue in a flat lump-sum payment to households. Revenue changes resulting 

from the CAFE standard are typically small (the increase in fines and the decrease in gasoline

tax revenue act in opposite directions) so that relatively little adjustment is needed in the

payments.

39 The solution to the system is found using Broyden’s method, a derivative-based 

quasi-Newton search algorithm.

b. Results

My central policy simulation involves an increment of one mile per gallon to the

CAFE standard. I divide the numerical results from this simulation into three parts. First, I

present the effects of the policy on equilibrium gasoline consumption and welfare, with the

latter broken down into effects on consumer and producer surplus. Second, I compare the

 38 Substitution patterns between new and used vehicles have the potential to make this problem very

difficult computationally. In the application here, however, convergence between the two markets is

reached in relatively few steps.

39 This is not true for increments to the gasoline tax, which have substantial revenue implications. The

method in which the revenue is returned is therefore of first-order importance; this issue is considered

in detail in Bento et al. (2009).
26

effects of the policy on fuel economy and profits across the different producers. Third, I

evaluate the distribution of welfare effects across household income groups.

I also perform a secondary simulation where a gasoline tax that reduces gasoline

consumption by the same amount as the CAFE standard is considered. All of the welfare

changes are expressed as gross costs that do not include the benefits associated with the

reduction in gasoline use itself.

40 Finally, I include an extension that allows for endogenous

technological improvements in fuel efficiency in response to the CAFE standard, allowing a

more direct comparison of my results with those in Austin and Dinan (2005).

Overall Change in Gasoline Consumption and Welfare

The first panel of Table 5 displays the change in gasoline use and fuel economy from a

one mile per gallon increase in the CAFE standard. Notice that gasoline use declines in the

first year by only 0.8 percent since the standard has not yet had time to affect used cars. By 

year 10, however, gasoline use has declined 3.4 percent from the baseline. The gradual effect

of the standard on the used car fleet can be seen in the decomposition of fuel economy 

improvements among new and used cars. Interestingly, the used fleet will never fully reflect

improvements in new car fleet fuel economy due to changing scrap rates. This is because

higher prices for large vehicles, induced by their relative shortage under CAFE, result in

lower scrap rates over time. This creates a used car fleet weighted more heavily toward large

vehicles, and with a correspondingly low average fuel economy relative to new cars.

The second panel of Table 5 displays the overall welfare effect and decomposes it into 

changes in consumer and producer surplus.

41 Notice first that the welfare loss rises through

time, reflecting the increasing incidence of the policy on used car markets in the later years.

Intuitively, much of the welfare loss comes from the shift in composition of the vehicle fleet

toward small vehicles: in the early years households with a strong preference for large

vehicles can shift demand to the used markets and so suffer smaller welfare losses. Over

 40 See for example Parry et al. (2007) for estimates of the environmental and social benefits associated

with reduction in gasoline use.

41 The welfare loss is measured as the weighted sum of equivalent variation for each of the households

in the model. This includes effects on producer profits, since households are assumed to own the 

firms. The decomposition separates the effect on producers from the total welfare costs.
27

time, however, the number of large vehicles in the used market is also diminished, resulting in

the increasing pattern of welfare losses.

This point also appears clearly in the decomposition of welfare effects into producer

and consumer surplus. Loss in producer surplus remains relatively stable over time, declining 

slightly as competition from large vehicles in the used market declines. Loss in consumer

surplus, however, rises sharply over time as the effects of CAFE standards enter the used car

market.

Distribution of Incidence among Producers

Table 6 shows the equilibrium effects on the seven simulated producers and displays

stark contrasts between producers of different types. First consider the effects on fuel

economy: the constrained domestic firms comply with the simulated policy and increase fuel

economy by one mile per gallon. The foreign producers, however, actually reduce average

fuel economy in response to the increased stringency. This reaction is of interest as it points

to an important source of inefficiency in CAFE standards and underscores the need to 

consider heterogeneity among firms in policy decisions. Intuitively, CAFE standards cause

the constrained domestic makers to sell a more fuel efficient — lighter or less powerful —

mix of vehicles.

42 This moves the residual demand curves for vehicles with high horsepower

and weight to the right for all other producers.

Consider the effect of this demand shift on unconstrained firms: they can freely

substitute into a less fuel efficient fleet, up to the amount of slack in the standard, taking over

the demand for larger vehicles.

43 The effect on the fine-paying European producers can be

divided into two competing components: the first effect is the increased marginal cost of the

fine, which acts as an incentive to improve fleet fuel economy. The second is the outward 

movement of residual demand for large vehicles, which acts in the opposite direction. Table 6 

shows that this latter effect dominates: the violating European producers, like the

unconstrained firms, move in the direction of a less fuel efficient fleet.

The distribution of incidence among firms appears in the final two rows of Table 6:

The constrained domestic producers suffer equilibrium profit losses ranging from 4 to 21

 42 Reductions in engine size are captured as shifts from luxury to non-luxury models. Reductions in

weight and wheelbase appear as shifts toward midsize or compact vehicles.

43 The slack in the standard was about 4 miles per gallon for Honda and Toyota in 2001.
28

percent in the first year, while foreign producers realize increased profits.

44 The profit

increases are realized by taking advantage of increased demand for large and luxury vehicles,

with Honda and Toyota seeing the largest gains. I cannot distinguish specific car lines, but

the distribution of models suggests that Honda’s luxury Acura line (and Toyota’s Lexus line)

would be responsible for the majority of the gains.

Distribution of Welfare Effects across Income Groups

Finally, I examine the distribution of welfare effects across households by income

group. My analysis is well suited to addressing the debate over the progressivity of CAFE

standards since it fully models interactions with the used car market and incorporates

consumer heterogeneity. I show that low-income consumers, who tend to purchase used 

vehicles, are affected significantly by CAFE and that this effect varies importantly over time.

The second column of Table 7 displays the total welfare loss as a percentage of

income, with the top and bottom panels respectively representing the first and tenth year of

the simulation. In year 1, the welfare loss is similar in proportion across income groups due

to the larger absolute impact of distortions in new car markets on wealthy households.

45 This

is an argument that is commonly made to support progressivity of CAFE standards, and I

confirm that in the first year of regulation it works as expected. In contrast, the welfare

effects in the tenth year become sharply regressive, with low-income households suffering

welfare losses (as a fraction of income) more than three times as large as those of the highincome group. This result has been overlooked in prior studies since it appears only when 

considering longer run effects of CAFE in used car markets. The intuition is simply that

CAFE will, over time, drive up the price of used vehicles and shift the composition of the

used vehicle fleet toward smaller vehicles. Given the strong preferences for large vehicles

estimated using the household data, the welfare effects in the used market rapidly become

important.

 44 Year 10 losses are moderated for domestic firms, while foreign firms build further on their profit

gains.

45 Producers are assumed to be owned by the households in proportion to income -- meaning a loss in

profits affects high-income households more than low-income households. High income households

also buy a larger share of new vehicles, meaning loss in consumer surplus is similarly distributed.
29

Comparison of the CAFE Standard and Gasoline Taxes

Table 8 offers a comparison of the CAFE standard with a gasoline tax. In the first

year fuel economy standards are a far more costly way to reduce gasoline use since their

effects have not yet entered the used fleet. The year 10 costs of CAFE are correspondingly 

lower, as fuel economy improvements spread through the used fleet, but still more than 6

times as large as those associated with the gasoline tax. It has been established in the

literature that gasoline taxes are typically more efficient than CAFE regulation since they

operate both through changes in miles driven and changes in vehicle choice; CAFE standards

act primarily through the latter channel.

46 The magnitude of the difference in costs I find

therefore reflects the key elasticities estimated in the demand model: consumers adjust driving 

patterns (i.e. miles traveled) far more easily than they alter their choice of vehicle. Not

surprisingly, then, as shown in the second row of the table, the effects of the gasoline tax enter

almost exclusively through the more efficient miles-traveled channel.

Table 8 also offers an extension of the producer model that allows endogenous

technological improvement in fuel economy in response to CAFE. Producers now have two

instruments to comply with CAFE: they may alter the mix of vehicles sold using prices as

before, and they can also improve the fuel economy of individual models. The exogenous

function relating improvement in fuel economy to costs of production is taken from the

National Research Council assessment of CAFE, NRC (2002), as in Austin and Dinan (2005).

The costs per gallon of gasoline saved under CAFE are considerably lower as a result of this

extension, but remain more than twice as large as those of the gasoline tax.

The third row of Table 8 indicates the fraction of the welfare loss borne by producers.

It is generally higher in the case of CAFE, as can be expected given that fuel economy 

regulation constrains firm decisions directly. In the case of endogenous technological change,

however, the cost borne by firms falls considerably. This is in accordance with the cost

estimates made by the NRC (2002), which allow relatively inexpensive improvements in fuel

economy. Finally, I translate the costs per gallon into equivalent costs per ton CO2 avoided 

in the bottom row of the table.

 46 See Parry et al. (2007) and Portney et al. (2003).
30

7. Conclusion

My approach to studying the effects of CAFE standards allows heterogeneous firm

response and considers equilibrium impacts in the interrelated demands for new cars, used 

cars, and gasoline. The parameters are estimated within the producer and household models

and the results can be used to measure overall welfare effects, the distribution of costs among 

groups, and to describe underlying mechanisms that influence efficiency.

I find that heterogeneity among firms causes the profit impacts of an increase in CAFE

to fall almost exclusively on domestic firms. I also find that equilibrium responses, driven by 

firm heterogeneity, reduce the effects of the policy on final gasoline consumption and 

consequently increase the efficiency cost of the regulation. Efforts to harmonize the

regulation across firms, thus reducing the incentive of unconstrained firms to substitute into

the large vehicle market, would improve the efficiency performance of CAFE.

47

I also conclude that the long run effects of increments in fuel economy standards are

not progressively distributed among income groups as might be expected. A common

argument maintains that since CAFE affects new car producers, it will have a greater impact

on wealthier households who purchase a disproportionate share of new vehicles. By 

including used car markets and simulating effects through time, however, I find that increased 

prices and changes in fleet composition for used cars lead to larger proportional welfare losses

for low income households. This suggests that CAFE standards, in much the same way as

gasoline taxes, must be combined with progressive distributional policy if there is a desire to

make the burden proportional across income groups.

In aggregate, and after accounting for competition among car producers and effects in 

the used market, a one mile-per-gallon increment in the standard reduces U.S. gasoline

consumption by about 3 percent. In the first year of this policy 44 percent of welfare costs are

borne by producers, with this share falling to less than 20 percent by the tenth year. The costs

in later years come primarily from losses in consumer surplus as the effects of the policy enter

the used car fleet.

 47 Tradability of credits across firms offers one potential solution. Notice that the firm heterogeneity I 

describe suggests large distributional consequences that could make such a system difficult to

implement.
31

A number of important caveats in the model and points for future research remain.

Principle among them is consideration of induced technological change prompted by fuel

economy regulation. Firm heterogeneity, along the lines described in this paper, may

potentially be used to identify differences in incentives to develop fuel efficiency enhancing 

technology. A deeper understanding of the demand-side tradeoffs between fuel economy and 

vehicle attributes like weight and horsepower is also essential in approaching this issue. My 

findings here provide a starting point for this ongoing research and present a base of empirical

conclusions about firm behavior and efficiency costs under CAFE regulation.
32

References

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CAFE Standards and increased Gasoline Taxes,” Journal of Environmental Economics and 

Management 50:562-582.

Anderson, S. and J. Sallee (2009), "Using Loopholes to Reveal the Marginal Cost of

Regulation: The Case of Fuel-Economy Standards." Working paper, University of Chicago 

and Michigan State University, https://www.msu.edu/~sta/AndersonSallee_ffvcafe.pdf.

Bento, A., L. Goulder, M. Jacobsen, and R. von Haefen (2009), “Distributional and Efficiency 

Impacts of Increased U.S. Gasoline Taxes”, American Economic Review 99(3): 667–99.

Bresnahan, T. and P. Reiss (1985), “Dealer and Manufacturer Margins,” Rand Journal of

Economics 16:253-268.

Environmental Protection Agency (2009), EPA Will Propose Historic Greenhouse Gas

Emissions Standards for Light-Duty Vehicles, Office of Transportation and Air Quality, EPA420-F-09-028.

Goldberg, P.K. (1995), “Product Differentiation and Oligopoly in International Markets: The

Case of the U.S. Automobile Industry,” Econometrica 63:891-951.

Goldberg, P.K. (1998), “The Effects of the Corporate Average Fuel Efficiency Standards in 

the U.S.,” Journal of Industrial Economics 46:1-33.

Greene, D.L. (1991), “Short-Run Pricing Strategies to Increase Corporate Average Fuel

Economy,” Economic Inquiry 29:101-114.

Kleit, A. (2004), “Impacts of Long-Range Increases in the Corporate Average Fuel Economy 

(CAFE) Standard,” Economic Inquiry 42:279-294.

Klier, T. and J. Linn (2008), "New Vehicle Characteristics and the Cost of the Corporate

Average Fuel Economy Standard." Federal Reserve Bank of Chicago Working Paper 2008-

13.

National Highway Traffic Safety Administration (2009a), Summary Of Fuel Economy

Performance, U.S. Department Of Transportation NVS-220.

National Highway Traffic Safety Administration (2009b), Summary Of CAFE Fines

Collected, U.S. Department of Transportation, http://www.nhtsa.dot.gov.

National Research Council (2002), Effectiveness and Impact of Corporate Average Fuel

Economy (CAFE) Standards, National Academy of Sciences, Washington, DC.
33

Parry, I., M. Walls and W. Harrington, (2007), “Automobile Externalities and Policies,”

Journal of Economic Literature, 45:373-399.

Portney, P., I. Parry, H. Gruenspecht and W. Harrington (2003), “The Economics of Fuel

Economy Standards,” Journal of Economic Perspectives 17:203–217.

Small, K.A. and K. Van Dender (2007), "Fuel Efficiency and Motor Vehicle Travel: The

Declining Rebound Effect." The Energy Journal 28(1):25-51.

Train, K.E. (1986), Qualitative Choice Analysis: Theory, Econometrics, and an Application to 

Automobile Demand. MIT Press, Boston, MA.

West, S.E. (2004), “Distributional Effects of Alternative Vehicle Pollution Control Policies,”

Journal of Public Economics 88:735-757.

White House Office of the Press Secretary (2009), President Obama Announces National

Fuel Efficiency Policy, http://www.whitehouse.gov/the_press_office/President-ObamaAnnounces-National-Fuel-Efficiency-Policy/.
Table 1: Average Deviation from CAFE Standard by Firm, 1990-2001

Car Fleet Light Duty Truck Fleet

Firm

Average 

deviation 

(volume 

weighted)

Fraction of 

years under 

standard Firm

Average 

deviation 

(volume 

weighted)

Fraction of 

years under 

standard

Fiat -7.34 1.00 BMW -1.66 1.00

Porsche -4.10 1.00 VW -0.07 0.67

Mercedes -3.30 1.00

BMW -2.48 1.00 GM 0.00 0.50

Volvo -1.84 1.00 Ford 0.08 0.23

Chrysler 0.17 0.42

Ford 0.02 0.33

GM 0.08 0.42 Isuzu 0.47 0.21

Chrysler 0.19 0.25 Mitsubishi 1.45 0.15

Toyota 1.84 0.00

Subaru 0.74 0.00 Nissan 1.86 0.00

Daewoo 1.16 0.00 Kia 2.99 0.00

VW 1.28 0.08 Mazda 3.21 0.00

Nissan 2.09 0.00 Honda 5.00 0.00

Mitsubishi 2.28 0.00 Suzuki 5.86 0.00

Toyota 2.46 0.00 Subaru 9.42 0.00

Kia 3.03 0.00

Mazda 3.45 0.00

Honda 3.96 0.00

Hyundai 4.07 0.00

Isuzu 7.20 0.00

Suzuki 12.07 0.00

Source: NHTSA CAFE compliance records, 1990-2001. Average deviations expressed in milesper-gallon.
Table 2: Estimates of

!iC

and 

!iT

Model Ia Ib IIa IIb

Time Period 1997-2001 1997-2001 1997-2001 1997-2001

Fixed effects None Make by fleet None Make by fleet

Ford

-3.71 0.54 -3.65 4.02

(2.99) (1.80) (4.41) (3.63)

21.16 22.05 26.01 23.48

(4.46) (4.50) (6.28) (5.68)

Chrysler

19.65 20.26 33.76 27.49

(7.39) (6.53) (14.52) (12.04)

2.18 7.93 1.88 10.60

(4.51) (2.85) (5.36) (3.90)

GM

28.87 28.55 36.19 35.50

(2.83) (2.34) (7.03) (8.82)

18.15 19.65 22.86 20.80

(3.93) (3.28) (5.42) (5.01)

N 287 287 287 287

R-squared 0.10 0.93 0.37 0.89

Robust standard errors shown in parentheses. The values are estimated shadow costs for 

constrained firms at the manufacturer and fleet level. Model IIb is based on proportional 

markups and is the preferred specification.

! passenger car

! light truck

! passenger car

! light truck

! passenger car

! light truck

Table 3: Firm and Fleet Marginal Effects

$ (Million) $ Per Vehicle

Ford

Passenger cars 117.59 52

Light duty trucks 693.48 251

Chrysler

Passenger cars 485.01 373

Light duty trucks 283.18 157

GM

Passenger cars 1410.26 438

Light duty trucks 684.78 264

The marginal cost of a one mile per gallon increment to the 

standard is shown. Values are transformed point estimates from 

Table 2, Model IIb. Per vehicle estimates are based on average 

market share and aggregate sales over the period 1997-2001.
Table 4: Vehicle Prices and Quantity of Banked or Borrowed CAFE Credits

Compact Midsize Fullsize Lux-small Lux-large

Model I

! Ford 0.046* 0.001 -0.064* -0.099*

(0.017) (0.013) (0.020) (0.040)

! Chrysler 0.016 -0.007 -0.026 -0.023 -0.091*

(0.016) (0.018) (0.019) (0.065) (0.043)

! GM 0.026 -0.020 -0.062* -0.148 -0.093*

(0.016) (0.013) (0.021) (0.104) (0.045)

Model II

! Ford 0.054* 0.002 -0.060* -0.113*

(0.015) (0.013) (0.030) (0.041)

! Chrysler 0.015 -0.012 -0.014 0.008 -0.053

(0.016) (0.017) (0.019) (0.069) (0.043)

! GM 0.031* -0.015 -0.040 -0.068 -0.098*

(0.015) (0.011) (0.030) (0.086) (0.046)

Observations 140 136 107 81 98

R-squared (I) 0.86 0.89 0.95 0.73 0.89

R-squared (II) 0.86 0.89 0.94 0.73 0.88

Robust standard errors in parentheses, * indicates significance at 5%. Fixed effects by year are included in 

all specifications and each vehicle class (column) represents a separate estimation. Compact vehicles are 

generally priced higher in years when a particular manufacturer has a surplus of CAFE credits, and large 

vehicles offered at a lower price.
Table 5: Effect on Gasoline Consumption and Welfare

of a 1 MPG Increment in the CAFE Standard

Year 1 Year 5 Year 10 

Effect on Gasoline Consumption

Baseline gasoline use (gallons per household) 775.18 801.59 828.89

Change -0.84% -2.62% -3.37%

Baseline fleet fuel economy (mpg) 25.07 25.50 26.60

Change

All 0.19% 0.77% 1.19%

New cars 2.51% 2.41% 2.27%

Used cars 0.00% 0.64% 1.08%

Baseline miles traveled (000's per household) 18.80 19.72 21.23

Change -0.60% -1.73% -2.11%

Welfare Effect

Welfare effect ($billion) -20.04 -28.02 -29.62

Loss in producer surplus -8.83 -7.15 -5.52

Loss in consumer surplus -11.21 -20.87 -24.10

Table 6: Producer Response to a 1 MPG Increment in the CAFE Standard

Manufacturer Ford Chrysler GM Honda Toyota

Other 

Asian European

Year 1 Change in fuel economy (mpg)

Cars 1.00 1.00 1.00 -0.04 -0.07 -0.02 -0.10

Light Trucks 1.00 1.00 1.00 -0.01 -0.01 -0.02 -0.01

Overall 1.22 0.66 0.65 -0.01 -0.04 -0.02 -0.08

Change in sales volume (%)

Cars 2.4% -23.8% -30.2% 3.2% 2.9% 1.5% 2.6%

Light Trucks -10.2% -7.8% -13.8% 1.7% 2.6% 1.5% 2.7%

Overall -3.2% -14.8% -23.3% 2.7% 2.8% 1.5% 2.6%

Change in profit (%) -4.3% -14.7% -21.3% 2.7% 2.8% 1.6% 2.0%

Year 10 Change in profit (%) -0.5% -10.2% -15.4% 4.6% 4.9% 3.0% 3.9%
Table 7: Distribution of Welfare Effects of a 1 MPG Increment in the CAFE Standard

Year 1 Welfare Impact Decomposition

Income EV EV as % of 

income

Producer 

profit

New car 

consumer 

surplus

Used car 

markets

<25 -60 -0.36% -34 -2 -25

25-50 -195 -0.52% -77 -65 -53

50-75 -293 -0.46% -128 -117 -48

>75 -444 -0.45% -205 -184 -55

All -177 -0.46% -78 -54 -45

Year 10 Welfare Impact Decomposition

Income EV EV as % of 

income

Producer 

profit

New car 

consumer 

surplus

Used car 

markets

<25 -187 -1.12% -20 -19 -149

25-50 -270 -0.71% -45 -101 -124

50-75 -329 -0.52% -74 -165 -91

>75 -404 -0.41% -124 -218 -63

All -264 -0.69% -48 -94 -121

Equivalent variation (EV) expressed in 2001 dollars and as a percentage of income.

Table 8: Comparison of Increase in CAFE and Increase in Gasoline Tax

Year 1 Year 10

Gasoline 

tax

CAFE 

standard

Gasoline 

tax

CAFE 

standard

CAFE standard 

w/ technology

EV per gallon of avoided 

gasoline consumption 0.82 22.85 0.82 5.47 1.97

Fraction of gasoline savings 

from improved fuel economy 

(fleet composition changes) 0.02 0.66 0.02 0.84 1.02

Fraction of welfare loss 

falling on producers 0.37 0.62 0.35 0.47 0.15

EV per ton CO2 avoided1 92 2572 92 616 222

1

Calculated as line 1 divided by 0.008887, the typical amount of CO2 released per gallon of

gasoline burned.
Figure 1: Toyota, Ford, and BMW: Fleet Fuel Economies
Figure 2: Fleet Fuel Economies by Firm Type
A-1

Appendix A: Alternative Specifications and Tests

This appendix extends the econometric model of Section 4 to consider different

forms, fixed effects, and conduct a “placebo” type test on unconstrained firms.

Year fixed effects

My estimation of the shadow costs using a pooled sample rests on the assumption 

of relatively stable demand conditions over the period 1997–2001. The second column of

Table A1 shows that the estimates of

!

are nearly unchanged when including fixed

effects by year. The estimated coefficients on year are also relevant as they signal

changes in average markups over time: None of the coefficients are significantly

different from zero or one another and their magnitudes are all less than 0.05 in absolute

value.

1 This lends some support to the assertion that average markups, and by association 

demand conditions, were stable over the years considered.

Structure of fixed effects

The ratio of markups, ! i , is the focus of the literature and also the parameter I

allow to vary by make and fleet in the central case. Column 3 of Table A1 considers the

alternative, where

!i

is instead allowed to vary and 

!

is estimated as a scalar. The

coefficients of interest are slightly reduced in magnitude, although all that are significant

in the central specification remain so.

Placebo test

An instructive placebo test is to imagine that the other 4 manufacturers (Honda,

Toyota, Other Asian, and European) are in fact constrained by CAFE around their

average fuel economy. This allows the construction of the LiC and LiT variables, and 

estimation together with the constrained domestic firms. The results appear in column 4

of Table A1. While the coefficients are more often positive than negative none is

significant at the 5% level. The coefficient on European cars is positive and has the

largest t-statistic (1.63), perhaps picking up the effects of the CAFE fines that alter the

pricing of European imports. Note that these vehicles tend to have high base prices and 

are part of an aggregate that includes complying companies, so we shouldn’t expect the

difference in markups to be very large.

 1 Change in ! i by model year:

Year 1997 1998 1999 2000 2001

Coefficient omitted -0.002 -0.001 -0.029 -0.042

(SE) (0.024) (0.026) (0.025) (0.026)
A-2

Table A1: Alternative Specifications

Case Central 

(Model IIb)

Year Fixed 

Effects

Fixed Effects 

in !

Unconstrained 

Makes

Fixed effects (") Make by fleet Make by fleet, 

year - Make by fleet

Fixed effects (!) - - Make by fleet -

Ford

4.02 3.75 1.40 3.00

(3.63) (3.87) (2.53) (3.27)

23.48 23.56 23.59 22.15

(5.68) (5.36) (5.41) (5.33)

Chrysler

27.49 27.70 24.98 24.34

(12.04) (11.43) (11.20) (11.28)

10.60 10.18 8.22 10.36

(3.90) (3.51) (3.05) (3.81)

GM

35.50 35.40 31.90 32.59

(8.82) (8.87) (6.33) (7.98)

20.80 21.11 20.93 19.61

(5.01) (5.18) (4.14) (4.70)

Honda

2.88

(7.05)

-3.14

(4.55)

Toyota

11.57

(7.70)

5.75

(3.94)

Other asian

-4.44

(11.47)

5.65

(6.10)

European

5.84

(3.57)

9.90

(11.01)

N 287 287 287 287

R-squared 0.89 0.90 0.89 0.90

Robust standard errors shown in parentheses. The model is column IIb of Table 2, with the indicated

modifications and additions. Findings from the main text are robust to the alternative forms considered.

# passenger car

# light truck

# passenger car

# light truck

# passenger car

# light truck

"#" passenger car

"#" light truck

"#" passenger car

"#" light truck

"#" passenger car

"#" light truck

"#" passenger car

"#" light truck
B-1

Appendix B: Dynamics of Banking and Borrowing in U.S. CAFE Regulation

This appendix provides an outline of the dynamic decisions made by firms in the

context of CAFE banking and borrowing.

Banking and borrowing rules

Under the rules established for the CAFE program, a set of certified fleet fuel

economies is produced for each firm on an annual basis. Deviations from the standard 

are first used to offset the firm’s stock of credits or debts, beginning with the oldest.

When no existing credits or debts remain, deviations from the standard are “banked” for

three years into the future. If a firm has debts owed from three years in the past and has

failed to repay them, the firm is found to be in violation and a fine is assessed in the

amount of $50 per vehicle per mile per gallon. Notice that no violation occurs and no 

penalties are assessed if the firm repays its debts within three years.

The following example illustrates the accounting method used: the “deviation” in 

year t, Yt, takes a positive value if the firm has a fleet fuel economy above the standard,

and a negative value if it is below. The values for

!

take a positive value if the firm has

credits that it may use to offset a negative deviation, and a negative value if it has debts it

must repay. As in the main text, the three subscripts on 

!

distinguish credits or debts

according to years remaining until expiry: ! 0 , for example, indicates credits or debts that

expire in the current year. The following example considers ten years, starting with the

inception of the regulation when the firm has no credits or debts:

Deviation from 

standard Credits (+) or debts (-) Fine payment if violation

Year Yt !0 !1 !2 Ft

1 -2 0 0 0 -

2 0 0 0 -2 -

3 3 0 -2 0 -

4 0 0 0 1 -

5 0 0 1 0 -

6 -3 1 0 0 -

7 0 0 0 -2 -

8 0 0 -2 0 -

9 1 -2 0 0 50·Q

10 0 0 0 0 -

In the first year of the regulation, the firm’s fleet is 2 miles per gallon below the

standard, and so it carries a debt into the second year. This is indicated by ! 2 = "2 in 

row 2. It complies exactly in the second year, and so the debt continues into year three,

now indicated by 

!1 = "2 . The firm’s fleet is 3 miles per gallon over the standard in year

3, so it repays the debt and accumulates a credit of 1 mile per gallon to be used in the

future. The values of ! are computed in this way through year 10. Notice that in year 9 

the firm has an expiring debt that it fails to repay, and so it is fined $50 per vehicle.
B-2

An interesting feature of this accounting system is that a firm’s action has the

potential to affect violation in any future year, not just three years into the future. For

example, if the firm had deviated by -1 instead of -2 miles per gallon in the first year of

regulation, it could have avoided violation altogether in the 9th year. This result is

somewhat counter-intuitive, since one might expect the three-year limit on banking and 

borrowing to limit the dependence of current violations on actions long in the past.

The set of necessary and sufficient conditions for compliance can be written after

defining the evolution of the

!

parameters through time. There are four cases that must

be considered. The case of positive

!

and negative Y is provided as an example in the

main text; the accounting definitions in the remaining cases are provided below. Notice

that the accounting method means that a firm can not carry both credits and debts at the

same time, so if any 

!

is positive (negative) all of the others are weakly positive

(negative).

For (

!

≥ 0 and Y ≥ 0) or (

!

< 0 and Y < 0):

! 0,t +1 = !1,t

!1,t +1 = ! 2,t

! 2,t +1 = Yt

For

!

< 0 and Y ≥ 0:

! 0,t +1 =

!1,t

! 0,t + !1,t + Yt

0

 

if Yt " #! 0,t 

if # ! 0,t < Yt < #(! 0,t + !1,t)

otherwise 

$

%

&

'

&

!1,t +1 =

! 2,t

! 0,t + !1,t + ! 2,t + Yt

0

 

if Yt " #(! 0,t + !1,t) 

if # (! 0,t + !1,t) < Yt < #(! 0,t + !1,t + ! 2,t)

otherwise 

$

%

&

'

&

! 2,t +1 =

! 0,t + !1,t + ! 2,t + Yt

0

$

%

' if Yt > #(! 0,t + !1,t + ! 2,t)

otherwise 

After computing the evolution of credits and debts as above, the compliance condition

itself can be defined easily. A firm is in compliance with regulation in all years t if and

only if:

! 0,t > 0 or Yt > "! 0,t for all t
B-3

The firm’s full maximization problem over time (without discounting) can then be

written as:

max

{ pj,t }

(pj,t! cj,t)qj,t(Pt)

j

"

t

"

#

$

%

&

'

( ! I(Q) H + FC,t(Q)

t

" + FT ,t(Q)

t

" #

$

% &

'

(

)

*

+

+

,

-

.

.

where

I(Q) = 0 iff (! 0,t > 0 or Yt > "! 0,t for all t) .

The problem for the unconstrained firm reduces to period-by-period profit

maximization since the right hand term drops out. For constrained firms, however, the

constraint includes multiple discontinuities and the complete history of a firm’s actions

(since I depends on the entire time series of

! 0 , !1 , and! 2

). In order to simplify the

problem for estimation I define compliance in a single year as Yt ≥ 0. This is a sufficient

condition for compliance in the dynamic model, but abstracts from banking and 

borrowing. If demands are certain and stable over time and assuming convex profits with 

respect to fleet fuel economy, however, the period-by-period solution to the static

problem coincides with the solution to the full dynamic problem above.