Elsevier Editorial System(tm) for Energy Policy

 Manuscript Draft

Manuscript Number: JEPO-D-09-01151R1

Title: REBOUND 2007: ANALYSIS OF U.S. LIGHT-DUTY VEHICLE TRAVEL STATISTICS

Article Type: Special Issue: Transport Modeling

Keywords: rebound effect; vehicle travel; fuel economy

Corresponding Author: Dr. David Lloyd Greene, Ph.D.

Corresponding Author's Institution: Oak Ridge National Laboratory

First Author: David Lloyd Greene, Ph.D.

Order of Authors: David Lloyd Greene, Ph.D.

Abstract: U.S. national time series data on vehicle travel by passenger cars and light trucks covering the 

period 1966-2007 are used to test for the existence, size and stability of the rebound effect for motor 

vehicle fuel efficiency on vehicle travel. The data show a statistically significant effect of gasoline price 

on vehicle travel but do not support the existence of a direct impact of fuel efficiency on vehicle travel. 

Additional tests indicate that fuel price effects have not been constant over time, although the 

hypothesis of symmetry with respect to price increases and decreases is not rejected. Small and Van 

Dender's (2007) model of a declining rebound effect with income is tested and similar results are 

obtained.

Suggested Reviewers: 
Transportation Policy & Planning Group

National Transportation Research Center

2360 Cherahala Boulevard

Knoxville, TN 37932

Phone: (865) 946-1310

Fax: (865) 946-1314

Email: dlgreene@ornl.gov

February 9, 2010

Energy Policy

Dear Nicky France:

Please find attached the revised manuscript, “Rebound 2007: Analysis of U.S. Light-Duty 

Vehicle Travel Statistics,” that we are submitting for consideration for publication in Energy

Policy. The paper was originally solicited for a special issue by Professor Carol Dahl and this 

submission was requested by Amela Ajanovic. 

None of this research has been previously published nor is it under consideration for publication 

anywhere.

Thank you for your consideration of my manuscript.

Sincerely yours,

David L. Greene

Corporate Fellow

Cover Letter
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REBOUND 2007: ANALYSIS OF U.S. LIGHT-DUTY 

VEHICLE TRAVEL STATISTICS

David L. Greene

Oak Ridge National Laboratory

2360 Cherahala Boulevard

Knoxville, Tennessee, USA

1-865-946-1310 (phone)

1-865-946-1314 (fax)

dlgreene@ornl.gov

*Manuscript

Click here to view linked References
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ABSTRACT

U.S. national time series data on vehicle travel by passenger cars and light trucks 

covering the period 1966-2007 are used to test for the existence, size and stability 

of the rebound effect for motor vehicle fuel efficiency on vehicle travel. The 

data show a statistically significant effect of gasoline price on vehicle travel but 

do not support the existence of a direct impact of fuel efficiency on vehicle 

travel. Additional tests indicate that fuel price effects have not been constant 

over time, although the hypothesis of symmetry with respect to price increases 

and decreases is not rejected. Small and Van Dender’s (2007) model of a 

declining rebound effect with income is tested and similar results are obtained. 

KEYWORDS: rebound effect, vehicle travel, fuel economy
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ACKNOWLEDGMENT

The research presented in this paper was sponsored by the U.S. Environmental 

Protection Agency, Office of Transportation and Air Quality.

1. INTRODUCTION

Increasing energy efficiency is a critical strategy for mitigating greenhouse gas 

emissions and reducing petroleum consumption by motor vehicles. Every major 

automobile manufacturing economy in the world has adopted some form of fuel 

economy or greenhouse gas emissions standards for motor vehicles (An et al., 

2007). Improvements in energy efficiency reduce the variable cost of energy 

services and thereby encourage greater use of energy services (Khazzoom,1980). 

The increased consumption of energy services “takes back” some of the potential 

reduction in energy use and so could be an important determinant of the 

effectiveness of energy efficiency improvements as a means of reducing 

greenhouse gas emissions from transportation (Khazzoom et al., 1990). This 

basic economic response has been termed the “rebound effect” and a substantial

literature has attempted to measure it (Sorrell, 2007). 

The magnitude of the rebound effect for motor vehicles also matters because 

increased vehicle travel may generate external costs: traffic congestion, tailpipe 

emissions and, arguably, some component of the costs of vehicle crashes. If the 

rebound effect is large, these costs can be a significant consideration in the 
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overall costs and benefits of policies to improve energy efficiency (Fischer et al., 

2007).

Three types of rebound effect have been identified (Greening et al., 2000). The 

direct rebound effect occurs when an increase in the energy efficiency of a 

particular service decreases the overall cost of that service, thereby inducing an 

increase in consumption. Indirect rebound effects can result from changes in the 

consumption of other goods and services induced by the change in the price of a 

particular energy service. Economy wide rebound effects occur when a reduction 

in the demand for energy reduces its price, encouraging increased consumption 

in other areas. This paper is concerned only with estimating the direct rebound 

effect of improvements in light-duty vehicle efficiency. 

The most important event in the recent history of passenger car and light truck 

energy efficiency in the United States was undoubtedly the enactment of the 

Corporate Average Fuel Economy (CAFE) standards. The standards were 

enacted in December of 1975 and became effective on model year 1978 vehicles. 

The standards required passenger car fuel economy to almost double and light 

truck fuel economy to increase by approximately 60% over 1975 levels (Figure 

1). Each manufacturer was required to meet the standards individually. Greene 

(1990) showed that in the early years the standards were not binding for many 

foreign manufacturers but were for domestic manufacturers. Thus, in these years 

the industry-wide average tends to exceed the standards. Passage of the CAFE 

law was motivated by the oil price shock and gasoline shortages of 1973-74, 

which also motivated fuel economy improvement between 1974 and 1977. 
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New Light-Duty Vehicle Fuel Economy and CAFE Standards

0

5

10

15

20

25

30

35

1975 1980 1985 1990 1995 2000 2005

Miles per Gallon

Passenger Car

Car CAFE

Light Truck

Truck CAFE

Figure 1. New Passenger Car and Light Truck Fuel Economy and Standards 

The history of light-duty vehicle travel and fuel consumption since 1977 shows a 

clear decoupling of the two brought about by increasing fuel economy (Figure 2). 

U.S. motorists are today consuming on the order of 80 billion gallons less fuel 

than they would have had vehicle use and fuel use continued to increase in direct 

proportion. 
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Miles of Travel and Fuel Use by Light-duty Vehicles: 1965-2007

0

500000

1000000

1500000

2000000

2500000

3000000

1965 1970 1975 1980 1985 1990 1995 2000 2005

Vehicle Miles (millions)

-10000

40000

90000

140000

190000

240000

Gallons (millions)

Vehicle Travel

Fuel USe

Figure 2. Light-duty Vehicle Travel and Fuel Use: 1965-2007

The following section presents the theory of the direct rebound effect and its 

relationship to the elasticity of vehicle travel with respect to the cost of fuel and 

fuel efficiency. Previous empirical estimates of the rebound effect for light-duty 

vehicles are reviewed next, highlighting unresolved issues, including the 

existence of a rebound effect for fuel economy, stability of the effect over time 

and the simultaneity of vehicle travel, fuel economy and vehicle stock. Section 4 

describes the sources of the 1966-2007 national time series data used in this 

analysis, emphasizing that both the fuel economy and vehicle travel data depend 

to an important degree on estimation methods of the Federal Highway 

Administration (FHWA). Model specification, hypothesis tests and results are 

presented in Section 5. 
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2. REBOUND EFFECT OF PASSENGER CAR AND LIGHT TRUCK

FUEL ECONOMY

Travel by passenger cars and light trucks depends on a complex array of factors 

from the structure of the built environment and the supply of highway 

infrastructure to individuals’ incomes and preferences. To move vehicles energy 

must be used and the cost of energy is the chief variable monetary cost of vehicle 

travel.1 Gasoline or gasoline blended with up to 10% ethanol is the predominant 

source of energy to move light-duty motor vehicles in the United States and 

provides 98% of their energy needs, while diesel fuel provides only about 2% 

(Davis et al., 2008, table 2.5).

Motor fuel consumption (F) is related to vehicle travel (V) and fuel 

economy in miles per gallon (E) by the identity: F = V/E. In the long run, both 

the amount of vehicle travel and the fuel economy of vehicles will be affected by 

the price of fuel (P). The price of fuel directly affects the amount of travel 

through the fuel cost per mile of travel (P/E = Pe, where e = 1/E is the rate of fuel 

consumption in gallons per mile). Economically rational consumers will 

consider not only the price of fuel, but the fuel cost per mile of travel in deciding 

how much to use their vehicles. The empirical evidence on whether motorists 

 

1 The other, significant variable cost is the traveler’s time, which in most cases will be 

larger than the cost of fuel. For example, a traveler who values his time at $20/hr. and travels at 

an average speed of 40 mph is spending $0.50/mile in time cost. If his vehicle gets 20 mpg and 

gasoline costs $2.60/gallon, his fuel cost is $0.13/mile.
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consider the fuel cost per mile or only the price of fuel is mixed (Greene et al. 

1999; Small and Van Dender, 2005). 

The price of fuel affects fuel use in the long run through the design of and 

technology embodied in motor vehicles when they are manufactured, as well as 

through the mix of vehicle sold.

2

 Significant fuel economy improvements 

typically require completely redesigning vehicles from engines and transmissions

to body shapes and materials. As a consequence, the full impact of fuel prices on 

the fuel economy of vehicles on the road evolves slowly over a period of about 

15-20 years.3 History confirms this timetable: the fuel economy improvements 

begun after 1975 were fully realized 15 years later in 1991 (Figure 3). Over the 

period of a year or less, the average rate of fuel consumption per mile (e) for the 

stock of vehicles on the road can be influenced to a limited extent by the way 

vehicles are operated and maintained, and by marginal effects on new vehicle 

sales and used vehicle retirement. 

 

2 Over a period as short as one year, the fuel economy of the stock of vehicles on the 

road is approximately constant, determined by their masses and the technology embodied in their 

designs. This is only approximately true because the on-road fuel economy of vehicles can be 

affected by fuel prices via how they are driven and changes in the relative use of more versus less 

efficient vehicles. Empirically, these effects have been found to be very small, however (Greene 

et al., 1999; Greene and Hu, 1984). 

3 The design and tooling of vehicles is fixed two years in advance. Manufacturers 

redesign one-fifth to one-eighth of their product offerings each year in order to spread out capital 

expenditures and make efficient use of engineering resources. Thus, complete redesign of new

vehicle offerings can be accomplished over a period of 5-10 years. These new vehicles gradually 

replace the existing stock of vehicles as older vehicles are retired. Simulations indicate that a 

cycle of fuel economy improvement requires 15-20 years for completion. 
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Fuel Economy Of New Light-Duty Vehicles 

Versus On-Road Fleet MPG, 1975-2005

0

5

10

15

20

25

1975 1980 1985 1990 1995 2000 2005

Miles per Gallon

New Vehicle On-Road MPG

On-Road Fleet MPG

Figure 3. Fuel Economy of New Light-duty Vehicles & On-Road Fleet MPG, 

1975-2007

The impact of a change in fuel economy on fuel use depends on the degree to 

which a reduction in the fuel cost per mile will induce more vehicle travel.4 

Taking the derivative of fuel use with respect to the rate of fuel consumption (e = 

1/E), it can be shown that the elasticity of fuel use with respect to the rate of fuel 

consumption (βF,e) is equal to 1 plus the elasticity of vehicle travel with respect to 

fuel cost per mile (βV,eP). Furthermore, the elasticities of vehicle travel with 

respect to the rate of fuel consumption (gallons per mile) is equal to the elasticity 

with respect to fuel cost per mile, which is equal to the elasticity of vehicle travel 

with respect to the price of fuel. Since fuel consumption is the inverse of fuel 

 

4 As Dimitropoulos and Sorrell (2006, p.7) point out, decreasing the energy costs of 

vehicle travel can also lead to an indirect rebound effect via a shift in sales towards larger or more 

powerful vehicles. This effect would need to be distinguished from changes in preferences due to 

increased income and other factors. When fuel economy increases are mandated by regulation 

sales shifts to larger, more powerful vehicles may be prevented. However, when the fuel 

economy standards differ for different vehicle types, such a substitution effect could be relevant.
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economy, the elasticity of vehicle travel with respect to fuel economy is the 

negative of the elasticity with respect to fuel consumption. 

1

,

( )

,

    

F V eP

eV

V

eP

d eP

dV

F

e

de

dF

F e

 

V e V eP V P

V

P

dP

d eP

d eP

dV

V

P

e

d eP

dV

V

e

P

d eP

dV

V

e

de

d eP

d eP

dV

, , ,

( )

( ) ( ) ( )

( )

( )

        

(1)

Dimitropoulos and Sorrell (2006) have termed βV,e definition 1 of the rebound 

effect and βV,eP definition 2. Most often, fuel cost per mile (eP) is used as a righthand-side variable for empirical estimation. However, the rebound effect is 

concerned with the effect of changes in fuel efficiency, not the price of gasoline. 

Therefore, the more preferred empirical approach should be to test the impacts of 

the rate of fuel consumption (definition 1) and gasoline price separately and then 

to test the restriction on their coefficients implied by definition 2.

The theoretical exposition above assumes that fuel economy or fuel prices

change while other things remain equal. In particular, the capital cost of motor 

vehicles is assumed to remain constant. In effect, the fuel efficiency 

improvement is assumed to be the result of pure technological change. When 

fuel economy increases are required by regulation, this is not likely to be the 

case. Increased fuel economy is likely to come at a cost.

“First, we argue that capital costs form an important part of the total cost 

of providing energy services, and that the higher cost of energy efficiency 
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conversion devices will reduce the magnitude of the rebound effect in

many instances.” (Dimitropoulos and Sorrell, 2006, p. 1)

Consider a vehicle with a fuel economy of 20 miles per gallon (0.05 gallons per 

mile) with an expected lifetime of 150,000 miles.5 Suppose that regulations 

require the vehicle’s fuel consumption to be decreased by 30% (fuel economy to 

be increased by about 40%) and that the technology required to achieve the 

reduction raises the price of the vehicle by $3,000. Assuming a gasoline price of 

$2 per gallon, the fuel cost per mile will fall from $0.10 to $0.07, a reduction in 

the short-run cost per mile of travel of $0.03 or 30%. But if the increased capital 

cost of the vehicle is amortized over its 150,000 mile life, the long-run cost per 

mile will increase by $0.02 per mile to $0.09, a reduction in the long-run cost per 

mile from $0.17 to $0.16, only $0.01 or 10%. Given that the fuel economy of the 

fleet of vehicles on the road improves gradually over a period of about 15 years, 

according to this reasoning the rebound effect observed in the aggregate national 

annual time series data should not reflect the 30% reduction in short-run costs but 

rather the 10% reduction in long-run costs.

Economic trends over the study period (1966-2007) suggest that fuel cost should 

be a less important factor in travel decisions than they were forty years ago. 

Individuals produce vehicle travel by combining their own time, and 

expenditures that include fuel, maintenance, insurance, various fees and tolls, and 

the depreciation of the vehicle itself. During the study period the average 

 

5 More accurately these are discounted lifetime miles, reflecting the fact that future 

variable costs should be discounted to reflect present value.
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transaction price of a new car increased by 25% (in constant dollars, Davis et al., 

2008, table 10.11) while average fuel economy increased by 50%. As a result,

fuel as a share of the long-run financial costs of vehicle travel (excluding time 

costs) decreased substantially (Figure 4). At the same time, real per capita 

income doubled, increasing the value of time as component of the full cost of 

vehicle travel. These changes would be expected to diminish the importance of 

fuel as a determinant of travel demand. 

Light-duty Vehicle Average On-Road Fuel Economy and 

Motor Fuel's Share of Total Costs per Mile

0%

5%

10%

15%

20%

25%

30%

1965 1970 1975 1980 1985 1990 1995 2000 2005

Percent of Cost per MIle

0

5

10

15

20

25

Miles per Gallon

Gasoline Cost Share

Light-duty MPG

Figure 4. Light-duty Vehicle Fuel Economy and Fuel Cost Share of Operating 

Costs 

3. PREVIOUS ESTIMATES OF THE REBOUND EFFECT

A number of studies have estimated the rebound effect for light-duty vehicles. 

Sorrell and Dimitropoulos (2007) provide the most comprehensive survey of the 

literature to date. Most studies base their estimates on the elasticity of vehicle 

travel with respect to fuel cost per mile, thereby constraining the elasticity of fuel 
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price to be equal and opposite in sign to the elasticity of fuel economy. The most 

recently published study indicates that the impact of fuel price and fuel economy 

has been decreasing over time as incomes increase (Small and Van Dender, 

2007). For the time period from 1966-2001, the study found a long-run rebound 

effect consistent with previously published studies, about -0.22. But for the 

period from 1997-2001, the long-run rebound effect had shrunk to -0.12, and the 

estimated short-run elasticity of fuel cost-per-mile was only -0.03. Evidence from 

the latest run-up in gasoline prices lends support to these findings. Considering 

the period from 2001 to 2006, Hughes et al. (2007) found a short-run fuel price 

elasticity of vehicle travel of -0.04. 

Estimates based on U.S. vehicle travel data published by the U.S. Department of 

Transportation (DOT), FHWA, covering the period from roughly 1950 to 1990,

have found long-run rebound effects on the order of -0.1 to -0.3. These studies 

include national times series analyses (Table 1) and state-level, times series 

cross-sectional data (Table 2). Most analyses use log-linear (i.e., double log) 

lagged adjustment models but some tested linear models and found the fit to the 

data to be equally good. Most models were estimated using ordinary least 

squares (OLS) but models using state level data in particular have used 

simultaneous equation techniques such as two-stage least squares (2SLS) or 

three-stage least squares (3SLS). Results have not varied greatly depending on 

the model formulation or estimation method.
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Table 1. Estimates of the Rebound Effect, U.S. National Vehicle Travel Based 

on Time Series

Author (year) Short-Run Long-Run

Time 

Period

Functional 

Form

Estimation 

Method

Mayo & Mathis 

(1988)

22% 26% 1958-84 Linear and 

Log-linear

3SLS

Gately (1992) 9% 9% 1966-88 Log-linear OLS

Greene (1992) Linear 5-19%

Log-linear 

13%

Linear 5-19%

Log-linear 

13%

1957-89 Linear and 

Log-linear

OLS

Jones (1993) 13% 30% 1957-89 Linear and 

Log-linear

OLS

Schimek (1996) 5-7% 21-29% 1950-94 Log-linear OLS

Source: Dimitropoulos and Sorrell (2007) table 4.6.

Table 2. Estimates of the Rebound Effect, U.S. State Level Data

Author (year) Short-Run Long-Run Time Period

Functional 

Form

Estimation 

Method

Haughton & 

Sarkar (1996)

9-16% 22% 1973-1992 Log-linear 2SLS

Small and Van 

Dender (2007)

4.5% 22% 1961-2001 Log-linear 3SLS

Source: Dimitropoulos and Sorrell (2007) table 4.7.

Studies based on survey data, on the other hand, vary considerably. Greene et al. 

(1999) used individual household survey data from five different years over the 

period 1984-1990 with substantial variation in gasoline prices. His result for the 

long-run elasticity of VMT with respect to fuel cost per mile is very consistent 

with the national time series and state time series, cross-section estimates 

(Table 3). U.S. studies using only a single year of survey data show the widest 

variability and the largest estimates of the rebound effect: 4% to 87%. Sorrell 

(2007) concluded that single year U.S. survey estimates, such as those of Puller 

and Greening (1999) and West (2004) shown below in Table 3, are the least 

reliable since they reflect very little variation in fuel prices and present the 

greatest opportunity for spurious correlations between fuel economy and other 
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determinants of vehicle travel. Pickrell and Schimek (1999) identified one

possible cause of the high elasticity estimates from survey data. Their model 

estimated the elasticity of household vehicle travel to the price of gasoline. Fuel 

economy was not included. When the average of monthly retail prices in the 

state where the survey respondent resided was used as the gasoline price variable, 

a larger rebound effect was estimated (29-34%). When a national average price 

for the month in which the respondent participated in the survey was substituted 

a much lower rebound effect was estimated (4-8%). They found that state 

gasoline prices were correlated with population density in their survey data, 

making it difficult to disentangle their individual effects on vehicle use. States 

with high population density also tended to have the highest gasoline prices, 

chiefly due to higher tax rates. Thus, gasoline price appeared to be acting as a 

surrogate for spatial structure, a key determinant of motor vehicle trip length and 

frequency, creating an upward bias in the estimated price elasticity. On the other 

hand, the national monthly gasoline prices were also correlated with seasonal 

variations in vehicle travel. In the summer months when travel demand is 

highest, gasoline prices are also highest. Thus, the latter approach would be 

expected to underestimate price elasticity due to simultaneous equation bias.
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Table 3. Estimates of the Rebound Effect using U.S. Survey Data

Author (year) Short-Run Long-Run

Time Period & 

Survey Used

Functional 

Form

Estimation 

Method

Goldberg (1966) 0% CES 1984-90 Log-log IV

Greene et al.

(1999)

23% EIA RTECS

1979-1994

Log-log 3SLS

Pickrell & 

Schimek (1999)

4-34% NPTS 1995 

Single year

Log-log OLS

Puller & 

Greening (1999)

49% CES 1980-90

Single year, crosssectional 

Log-log 2SLS

West (2004) 87% CES 1997

Single year

Log-log IV

CES is the U.S. Consumer Expenditure Survey 

EIA is U.S. Energy Information Administration

RTECS is the Residential Transportation Energy Consumption Survey of the U.S. EIA

NPTS is the U.S. Nationwide Personal Transportation Survey

The literature on the effect of fuel prices on vehicle travel and fuel use has 

produced a relatively reliable quantification of the historical relationship between 

vehicle travel or fuel demand and the price of fuel. Reviews of the literature on 

the price elasticity of gasoline demand and its components can be found in Espey 

(1996), Dahl (1995), Dahl and Sterner (1991), and Dahl (1986). In general, the 

more recent the study, the smaller the sensitivity of fuel demand to price. Dahl 

(1995) found that more recent estimates of the long-run price elasticity of 

gasoline demand averaged -0.6, while earlier studies were typically in the range 

of -0.7 to -1.0. Espey (1996) reported an average of -0.5 for studies whose data 

were primarily post-1974. Using state-level data for 1970-1991, Haughton and 

Sarkar (1996) estimated long-run gasoline price elasticities in the range of -0.23 

to -0.35. These results suggest that demand for gasoline has also become less 

sensitive to price over time.
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4. NATIONAL VEHICLE MILES OF TRAVEL (VMT)

AND RELATED DATA

Total U.S. highway vehicle miles of travel by passenger cars and light trucks is

estimated by the U.S. DOT, FHWA and published annually in table VM-1 of 

Highway Statistics (U.S. DOT/FHWA, 2007). The FHWA defines light trucks as 

2-axle, 4-tire vehicles that are not passenger cars, while the CAFE law defines 

trucks as vehicles under 8,500 lbs. gross vehicle weight6that are not passenger 

cars. State departments of transportation are the original source of FHWA’s 

vehicle travel statistics. As the documentation of table VM-1 notes, states’ 

definitions of passenger cars and light trucks vary from state to state (U.S. 

DOT/FHWA, 1996).

Apparently due to these differences, the FHWA first adds the state estimates of

passenger car and light truck VMT together to form a national light-duty vehicle 

total. It then uses data on light truck registrations and average annual miles per 

light truck from surveys conducted approximately every five years and other 

sources to estimate light truck VMT. Because the division of VMT between 

light trucks and passenger cars is based on such estimation methods and because 

the methods have changed over time, total light-duty vehicle VMT is considered 

more reliable than its two components (Figure 5). The FHWA recommends 

aggregating total light-duty vehicle VMT for purposes of comparison over time 

 

6 Gross vehicle weight comprises the empty weight of a vehicle plus the weight of the 

maximum cargo it is rated to carry.
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(U.S. DOT/FHWA, 1996, p. 8) and their advice is followed in the statistical 

analysis below.

U.S. Light-Duty Vehicle VMT: 1965-2007

0

500000

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1965 1970 1975 1980 1985 1990 1995 2000 2005 Millions of Vehicle Miles

Light Trucks

Passenger Cars

Figure 5. Vehicle Travel by U.S. Passenger Cars and Light Trucks: 1965:2007

Fuel use by type of highway vehicle, and fuel economy by vehicle type are 

estimated interdependently by the FHWA (see Schipper et al., 1993, for a 

detailed exploration of the implications of this method), by sharing out total 

highway fuel use, derived chiefly from motor fuel taxation statistics.

“Fuel consumed by all motor vehicles, a shown in VM-1 is a control total. 

It is extracted from Table MF-21 of Highway Statistics (Appendix G). 

The total is distributed among the vehicle types based on the miles per 

gallon for each vehicle type. Average miles traveled per gallon of fuel 

consumed is estimated using the TIUS (Truck Inventory and Use Survey, 

ed.) database. Miles per gallon are projected to the current data year 

using the previous year’s data, TIUS estimates, and CAFE standards.” 

(U.S. DOT/FHWA, 1996, p. 7) 
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Although the FHWA documentation does not explicitly say so, there is 

undoubtedly some iteration that must be done to reconcile VMT, fuel use and 

MPG estimates by vehicle type. Because light-duty vehicles consume 90% or 

more of the gasoline used on roads in the United States, the estimation of MPG 

by the FHWA and the reconciliation of VMT, MPG and fuel use numbers by 

vehicle type is not likely to result in extremely large errors from one year to the 

next. Total fuel use and total VMT (more precisely, traffic counts) are directly 

measured and significant year-to-year changes are not likely to be missed for 

such a large category as light-duty vehicles. Still, it is important to bear in mind 

that VMT and MPG by vehicle type are not directly measured but rather 

estimated interdependently by the FHWA. As we will see below, the FHWA 

methodology can produce anomalies.

Population data was obtained from the U.S. Census Bureau (2008). Personal 

income (Figure 6) was taken from the U.S. Department of Commerce, Bureau of 

Economic Analysis, Regional Information System (2008). The Consumer Price 

Index data are from the Bureau of Labor Statistics, Consumer Price Index, table 

B.17 as reported in Davis et al. (2008). New car prices come from Davis et al.

(2008, table 10.11) and from the BLS quality adjusted vehicle price index.7

 

7 Other variables tested but not statistically significant were the number of licensed 

drivers in each year taken from the FHWA’s Highway Statistics (table DL-1c) and population by 

age group, from the U.S. Census Bureau. 
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$0

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Millions of 2005 $

US Population and Licensed Drivers: 1965-2007

US Population

Licensed Drivers

Real Personal Income

Figure 6. U.S. Population, Licensed Drivers and Personal Income: 1965:2007 

Gasoline price statistics are taken from the U.S. Department of Energy (DOE), 

EIA’s Annual Energy Review 2007, table 5.24 (U.S. DOE/EIA, 2008). The price 

series for “All Grades” in nominal prices is used, deflated by the consumer price 

index (CPI-U series). However, the gasoline price series began in 1978. It was 

extended backward to 1976 by taking a weighted average of EIA’s unleaded and 

leaded regular price series. From the published statistics it can be inferred that 

the 1978 all grades price is a 41%/59% weighted average of the leaded regular 

and unleaded regular prices, respectively. The weights were linearly 

extrapolated to 100% leaded regular in 1975 in order to estimate the 1976 and 

1977 prices. The EIA leaded regular price series were used for 1975 and all 

preceding years. These interpolations are not likely to introduce significant 

errors as can be seen by inspection of the several gasoline price series shown in 

Figure 7.
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EIA Gasoline Price Series: 1965-2007

0

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Nominal Cents per Gallon

Unleaded Premium

All Grades

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Figure 7. Gasoline Price Data Series: 1965:2007 (DOE/EIA, 2008)

4.1 THE EFFECT OF FEDERAL FUEL ECONOMY STANDARDS: 

The U.S. CAFE Standards undoubtedly had a significant effect on the fuel 

economy of new passenger cars and light trucks (see Figure 1) that cannot be 

ignored in any equation that attempts to explain either new vehicle or total onroad fleet average fuel economy. If vehicle travel and fuel consumption are to be 

estimated as simultaneous equations, a variable that effectively represents the 

fuel economy standards is required. Small and Van Dender (2007) used state 

level data from before fuel economy standards went into effect (1966-1977) to 

estimate a lagged adjustment equation to predict what fuel intensity (1/MPG) 

would have been in the absence of fuel economy standards.8 Only three 

 

8 The U.S. CAFE standards were enacted in December of 1975 to take effect in 1978. 

However it is reasonable to use data through 1977 since manufacturers generally “lock in” their 

product plans two years in advance. Thus, even though the manufacturers were aware in 1976 

and 1977 that the standards were coming, there was little they could do to change the designs of 

vehicles sold in those model years.
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variables were statistically significant in the fuel intensity equation, lagged fuel 

intensity, a dummy variable for 1974 and 1975 and a time trend. The time trend 

was interpreted by the authors as representing technological change. Fuel price 

was not statistically significant but had the expected sign. Given that fuel price is 

the only important driving factor for fuel economy in the equation, aside from the 

time trend, its lack of statistical significance creates doubts about the validity of 

the methodology. This equation was then used to predict the (long-run) desired 

fuel intensity for each state. The state fuel intensities were aggregated to national 

fuel intensity by weighting by state vehicle travel. Small and Van Dender 

measured the strength of the CAFE regulation by a variable equal to the ratio of 

the mandated fuel economy9to the desired fuel economy whenever the mandated 

fuel economy was greater, and 1.0 when it was not. However, from Figure 1 in 

the authors’ paper it is clear that the desired fuel economy was equal to or greater 

than the mandated fuel economy only in 1979. 

Apparently considering this result less than satisfactory, Small and Van Dender 

(2007) then developed an alternate version of their CAFE variable by first 

removing the time trend from their initial equation for desired fuel economy and 

using that equation to predict a new variable they called cafe_prelim. However, 

this equation includes only the statistically significant dummy variable and the 

statistically insignificant vehicle price variable. The new variable cafe_prelim

was used to replace the time trend in a newly estimated equation for desired fuel 

 

9 The mandated CAFE levels are based on EPA dynamometer test values. They were 

adjusted downward by multiplying by 0.85 to reflect real-world driving in order to be comparable 

to the FHWA fuel economy data.
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economy based on the entire sample of data. Setting the cafe_prelim variable to 

zero, the new equation is used to predict a new desired efficiency variable. 

For the period 1966-1977 the cafe_prelim variable is equal to the dependent 

variable (FHWA fuel intensity) minus the estimated time trend and the residuals 

from the initial regression. The authors’ interpretation of this variable is that it 

represents pressure from CAFE regulations. Given its construction, another 

interpretation might be that it represents desired fuel economy in the absence of 

technological change. Because the only statistically significant variables in the 

entire methodology are a time trend and a dummy variable, one can only hope 

that it represents what the authors intend it to represent. The authors themselves

express dissatisfaction with both equations.

“On the negative side, we find that with our alternate calculation 

procedure, our estimates of desired fuel efficiency are not robust to 

adding trend variables in the reduced form equation itself. In the end, we 

can offer no judgments about which version of cafe better depicts the 

tightness of regulations as perceived by market participants.” (Small and 

Van Dender, 2007, p. 50).

The method of Small and Van Dender (2007) does not seem to produce an 

adequate representation of the effect of fuel economy standards. A more robust 

approach is needed. The method used here is to directly estimate what the total 

on-road light-duty vehicle fuel economy would have been had all manufacturers 

exactly met the fuel economy standards. The assumption of this method is that

manufacturers used the standards as the basis for planning fuel economy 
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improvements for the period from 1978-2007 but that actual new vehicle fuel 

economy might deviate from those plans, for example, if fuel prices changed 

significantly. The Hausman test will then be used to determine if the data 

support simultaneous determination of on-road vehicle fuel economy and vehicle 

travel.

The CAFE standards apply to new passenger cars and light trucks, not to the 

population of vehicles on the road. Greene (1990) demonstrated that for 

domestic manufacturers, the CAFE standards were a binding constraint 

throughout the decade from 1978 to 1988, but for some foreign manufacturers 

they were not binding. In the years since, there has been substantial progress in 

vehicle technologies enabling higher fuel economy. Over the same period, there 

has been no improvement in fuel economy (0%) but substantial increases in 

horsepower (77%) and weight (25%) (U.S. EPA, 2008, table 2). If the CAFE 

standards had not been a binding constraint on the market during those years, at 

least some of the technology would have been applied to increasing fuel 

economy rather than holding fuel economy constant while increasing horsepower 

and weight. 

The fuel economy of the existing stock of vehicles, however, can be affected to a 

limited extent by driving behavior and maintenance, shifts in the distribution of 

new vehicles sold, and changes in the rate of stock turnover. Thus, on-road fleet 

fuel economy could vary above or below what would be expected assuming a 

normal rate of fleet turnover and typical driving behavior. This suggests 

formulating a CAFE variable that equals what the average fuel economy of the 
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on-road vehicle stock would have been had the standards been met exactly given 

the rate of turnover of the vehicle stock. This is approximated here by assuming 

that new passenger cars exactly met the passenger car standard and new trucks 

exactly met the truck standard. The actual numbers of passenger cars and light 

trucks in operation by model year in each calendar year from 1978 to 2007 are

used as weights for the MPG values to compute a fleet harmonic mean fuel 

economy.10 An on-road adjustment factor of 0.85 is applied in every year. 

Vehicle use is estimated to decline with age at the rate of 4% per year (Pickrell 

and Schimek, 1999). The three resulting CAFE variables are plotted in Figure 8, 

along with the FHWA estimates of passenger car, light truck and combined lightduty vehicle fuel economy. 

Three features of Figure 8 are noteworthy. First, the FHWA on-road fuel 

economy numbers track the predicted CAFE numbers closely.11 (The combined 

light-duty vehicle estimates are considered the most reliable, for reasons given 

above.) Second, there are two distinct periods during which the estimated onroad fuel economy exceeds the predicted CAFE number: 1980-1985 and 1991-

1992. Both are periods of relatively high fuel prices. Third, the FHWA 

 

10 To the extent that rates of vehicle scrappage changed as a function of fuel prices or 

other factors and affected fleet average fuel economy, this will not be reflected in the constructed 

CAFE variable, since the variable reflects the actual numbers of vehicles in operation by model 

year and not what they would have been in the absence of fuel price changes and other factors. 

Such effects will be less important, however, since model year fuel economy is not changed over 

time in constructing the CAFE variable

11 This could also be because the FHWA uses new vehicle fuel economy data along with 

other data to estimate on-road fleet fuel economy, as noted above.
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estimates for 2003 and 2004 for light trucks appear to be anomalies, and they 

affect the combined estimates as expected. As of the time of writing, the FHWA 

had not changed the light truck estimates for 2003 and 2004. The reader is 

reminded that the combined light-duty vehicle CAFE variable (CAFE LDV) in 

Figure 8 is used to represent the effect of the CAFE standards in the regressions 

predicting light-duty vehicle fuel economy presented below, rather than the 

individual passenger car and light truck numbers. Some key inferences depend 

strongly on the validity of the MPG data. In these cases, the hypotheses were 

retested, either including a dummy variable for 2003 and 2004 or replacing the 

suspect 2003 and 2004 MPG numbers with values linearly interpolated between 

2002 and 2005. The conclusions were unaltered by this substitution.

On-Road Light-duty Vehicle MPG and CAFE Variables

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1975 1980 1985 1990 1995 2000 2005 2010

Miles per Gallon

CAFE CAR

FHWA CAR

CAFE LDV

FHWA LDV

CAFE LT

FHWA LT

Figure 8. Constructed CAFELDV Variable and FHWA On-Road Average Fuel 

Economy Data for Passenger Cars and Light Trucks.
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5. MODELS AND HYPOTHESES

The most important question is whether the empirical data support the existence 

of a rebound effect. This was tested by estimating the effects of the price of 

gasoline and the rate of fuel consumption (1/MPG) separately. Using national 

time series data from 1950-1994 Schimek (1996) estimated the elasticities of 

vehicle travel with respect to fuel price and with respect to fuel economy 

individually. He found a short-run elasticity of real gasoline price of -0.06 and of 

miles per gallon of +0.05, almost precisely equal and opposite in sign as theory 

would predict. However, Small and Van Dender (2007) reported that the direct 

effect of fuel economy (miles per gallon) or fuel consumption (gallons per mile)

on vehicle miles traveled was statistically insignificant. Only when fuel cost per 

mile (gasoline price divided by miles per gallon) was used as the right-hand-side 

variable was fuel efficiency statistically significant. However, that formulation 

imposes the hypothesis that fuel price and fuel economy to have equal and 

opposite effects. 

“A second caveat is that our study, like virtually all others, imposes the 

theoretical restriction that people choosing how much to drive care about 

the fuel cost of driving a mile, but not separately about its individual 

components (fuel price and fuel efficiency). Unfortunately, we find that 

this restriction is not supported by a model that relaxes it – in fact, the 

latter model suggests that the amount of driving responds to fuel prices 

but not to changes in fuel efficiency.” (Small and Van Dender, 2007, 

p. 43)
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Greene et al. (1999) concluded that the survey data on which their study was 

based did not reject the hypothesis of equal and opposite effects but, of course, 

this is not the same as confirming it.

A second important question is whether the rebound effect has remained constant 

over time and, if not, why it varies. Greene (1992) argued that the rebound effect 

should be expected to vary over time in proportion to the fuel cost share of total 

vehicle travel costs. His reasoning was that the elasticity of vehicle travel with 

respect to total monetary costs (excluding the costs of time) appeared to be 

approximately constant at about -1. If this were true, then the elasticity of 

vehicle travel with respect to fuel cost per mile would be approximately the 

negative of fuel’s share of total monetary vehicle travel costs. Let C be the nonfuel, long-run costs per mile of travel, let K be a constant term representing other 

factors that affect the amount of travel and let βV be the elasticity of travel with 

respect to total costs per mile. If βV = -1, then the elasticity of travel with 

respect to fuel cost per mile (eP) is just the fuel cost share of total cost per mile. 

 

 

C eP

eP K C eP

V

eP K C eP

d eP

d

V

eP

V

eP

d eP

dV

V K C eP

V V

v

V



     

 



( ) ( 1)

( ) ( )

  1





(2)

Equation (2) implies that the rebound effect will vary with the price of fuel in the 

linear model. For this reason, Greene (1992) suggested that the linear lagged 

adjustment model might be preferred to the log-log formulation. 
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Using time series, cross-sectional data for states, Small and Van Dender (2007) 

developed and tested a model in which the rebound effect varied with the 

logarithm of per capita income. The reasoning behind this formulation was that 

as incomes rise, the time cost of travel becomes more important relative to fuel 

costs. 

6. RESULTS

Linear lagged adjustment models for light-duty vehicle travel were estimated 

using the E-Views6TM software (Quantitative Micro Software, 2007) and the 

1966-2007 national time series data. The dependent variable was total light-duty 

vehicle miles of travel (LDVMT) and right-hand side variables were the real 

price of gasoline (RGASPRICE), the light-duty vehicle fuel consumption in

gallons per mile (FC), real total personal income (RPERSINC), the number of 

light duty vehicles registered (LDVEH), a dummy variable representing the price 

shock years of 1974 and 1979 (DUM7479), and the lagged value of the 

dependent variable (LDVMT(-1)). C and A1 through A6 are coefficients to be 

estimated. The function log() indicates Naperian logarithms of the variables. 

log( ) 7479 log( ( 1))

log( ) log( ) log( ) ( )

4 5 6

1 2 3

  

    

A LDVEH A DUM A LDVMT

LDVMT C A RGASPRICE A F C A RPERSINC

(3)

Results of estimating the linear lagged adjustment model for VMT using ordinary 

least squares is shown in Table 4. Augmented Dickey-Fuller (ADF) unit roots 

tests showed that all variables (except DUM7479) could not reject the null 
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hypothesis of a unit root in levels form. However, the null hypothesis of unit 

roots was rejected for all variables in first differences. The ADF test on the 

residuals from the regression rejected the hypothesis of a unit root at the 0.01 

level, indicating that the variables in equation (3) are co-integrated. All variables 

except fuel consumption are statistically significant and have the expected signs. 

FC is not statistically significant and is expected to have a negative sign 

(increasing fuel consumption per mile should reduce VMT) but does not. Total 

personal income is statistically significant at the 0.06 level. The fit of model to 

data is very close, with an adjusted R2of 0.9996. The Breusch-Godfrey Serial 

Correlation LM test statistics for both first- and second-order autocorrelation do 

not reject the hypothesis of no autocorrelation. The Breusch-Pagan-Godfrey 

Heteroskedasticity test also does not reject constant error variance. At the mean, 

the estimated short-run gasoline price elasticity of vehicle travel is -0.049 = 

-463.5*(193.0/1838201), and the long-run elasticity implied by the lagged 

adjustment formulation is -0.30 at the sample mean values. 

Small and Van Dender (2007) tested the hypothesis that the elasticity of vehicle 

travel with respect to the price of fuel was equal to the elasticity with respect to 

the rate of fuel consumption (gallons per mile) and found, as did Greene (1999), 

that the data did not reject that hypothesis. As a consequence, they estimated the 

rebound effect as the elasticity of vehicle travel with respect to fuel cost per mile, 

which imposes that constraint.
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Table 4. Linear Lagged Adjustment VMT Model 1 (OLS)

Dependent Variable: LDVMT

Method: Least Squares

Sample (adjusted): 1967 2007

Included observations: 41 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 19659.17 67538.15 0.291 0.773

RGASPRICE -463.487 62.770 -7.384 0.000

FC 601170.1 691037.2 0.870 0.390

RPERSINC 2.15E-05 1.13E-05 1.907 0.065

LDVEH 0.001 0.000 3.970 0.000

DUM7479 -65156.72 10447.46 -6.237 0.000

LDVMT(-1) 0.836 0.046 17.970 0.000

R-squared 1.000 F-statistic 14588.41

Adjusted R-squared 1.000 Prob(F-statistic) 0.000

S.E. of regression 12643.13 Mean dependent var 1838201.

Sum squared resid 5.43E+09 S.D. dependent var 591546.3

Log likelihood -441.578

The hypothesis that the elasticities of gasoline price and fuel consumption are 

equal at their sample means was tested for this data set using the Wald Test and 

rejected at the 0.01 level. This is a new finding and indicates that not only is the

direct fuel economy rebound effect not statistically significant in the linear 

lagged adjustment model, but the hypothesis of equal elasticities for gasoline 

price and fuel consumption is rejected at the means of the variables. Accepting 

this hypothesis is necessary in order to justify using fuel cost per mile as a

representation of the rebound effect. This result also holds in the log-log form of 

the vehicle travel equation as will be shown below. 

The log-log form of the lagged adjustment equation has been frequently preferred 

because it produces constant elasticities (Table 5). Unit root tests showed that, in 

levels, only the log of vehicle stock rejected the hypotheses of unit roots. The 
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residuals from the regression, however, did reject the hypothesis of unit roots, 

indicating that the variables are cointegrated. Once again, all variables are 

statistically significant and have the expected signs except for the log of fuel 

consumption. This model too fits the data closely and easily passes the BreuschGodfrey LM test for first-order serial correlation and the BreuschPagan_Godfrey test for heteroskedasticity. The estimated short-run gasoline 

price elasticity of -0.051 is nearly identical to the linear model at its mean. The 

long-run elasticity implied by the lagged adjustment model is -0.23, virtually 

identical to the value of -0.22 obtained by Small and Van Dender (2007) using a 

simultaneous equation formulation applied to state level data. A Wald Test that 

the short-run elasticities of gasoline price and fuel economy (miles per gallon) 

are equal and opposite in sign is likewise rejected for the log-linear model at the 

0.01 level. Thus, neither the linear nor the log-log model provides empirical 

support for a direct rebound effect of fuel economy. 
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Table 5. Log-linear Lagged Adjustment VMT Model 2 (OLS)

Dependent Variable: LOG(LDVMT)

Method: Least Squares

Sample (adjusted): 1967 2007

Included observations: 41 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C -1.607 0.613 -2.624 0.013

LOG(RGASPRICE) -0.051 0.009 -6.032 0.000

LOG(FC) 0.032 0.028 1.139 0.263

LOG(RPERSINC) 0.141 0.050 2.811 0.008

LOG(LDVEH) 0.106 0.035 3.038 0.005

DUM7479 -0.050 0.007 -6.984 0.000

LOG(LDVMT(-1)) 0.777 0.062 12.492 0.000

R-squared 1.000 Prob(F-statistic) 0.000

Adjusted R-squared 0.999 Mean dependent var 14.371

S.E. of regression 0.008 S.D. dependent var 0.338

Sum squared resid 0.002 Breusch-Godfrey

Log likelihood 142.699 F-statistic 0.021

F-statistic 11384.88 Obs x R-squared 0.026

Stability of the log-linear model was tested using the Cusum and Cusumsq 

statistics. The Cusum test showed no evidence of instability. In the Cusumsq 

test, the Cusumsq statistic barely exceeds the 5% bounds during the years 1986-

88, suggesting possible instability in the years following the collapse of world oil 

prices in 1986. Plots of recursive coefficient estimates indicated that the 

coefficients of personal income, DUM7479, and the lagged dependent variable 

remained relatively stable as observations were added. The coefficients of the 

price of gasoline, fuel consumption per vehicle mile and the vehicle stock 

decreased markedly in absolute value over time. The recursive coefficient 

estimate plots for LOG(RGASPRICE) and LOG(FC) are shown in Figure 9a and 

Figure 9b. The trends are generally consistent with Small and Van Dender’s 

(2007) observation that the rebound effect has been decreasing over time.
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Figure 9a. Recursive coefficient estimate of the log of the real price of gasoline.

Figure 9b. Recursive coefficient estimates of the log of fuel consumption per 

mile.

-.6

-.5

-.4

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-.2

-.1

.0

.1

1980 1985 1990 1995 2000 2005

Recursive Estimates

± 2 S.E.

-1.0

-0.8

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-0.4

-0.2

0.0

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0.4

1980 1985 1990 1995 2000 2005

Recursive Estimates

± 2 S.E.
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6.1 TESTING THE ENDOGENEITY OF FUEL ECONOMY AND 

VEHICLE STOCK

Using a time series of state data, Small and Van Dender (2007) formulated

simultaneous equation models of vehicle travel, vehicle stock and fuel economy 

in order to include interdependencies among the variables and to avoid 

simultaneous equations bias in estimating the rebound effect. Using household 

panel data, Greene (1999) also considered a simultaneous equation formulation 

necessary. The estimates presented above are not based on simultaneous 

equation estimation methods because the national time series data do not indicate 

that vehicle travel, vehicle stock and fuel cost per mile are simultaneously 

determined. Schimek (1996) also found that the national time series data from 

1950-94 did not support simultaneity in a three equation model of the number of 

vehicles, vehicle travel and fuel efficiency. The results below are consistent with 

his results although his model formulation is somewhat different.

The Hausman test for simultaneous equation bias first estimates ordinary least 

squares regressions for the suspected endogenous variables using instrumental 

variables. The residuals from the regression are then added to the vehicle miles 

of travel equation as an additional right-hand-side variable. If the coefficient of 

the residual is statistically significant, simultaneous equation bias is indicated. 

The logarithm of fuel consumption was regressed against the following

instrumental variables: logarithm of real gasoline price, log of the constructed 

CAFE variable, log of real personal income, and the dummy variables for 1974 
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and 1979 (fuel shortages) and 2003 and 2004 (data anomalies). The results are 

shown in Table 6. By far the most important variable is the constructed 

CAFELDV variable, whose coefficient is approximately -1, implying that a 1% 

increase in the standards (miles per gallon) would eventually produce a 1% 

reduction in the rate of fuel consumption (gallons per mile) of the vehicle stock. 

The real price of gasoline has the expected negative sign but a relatively small 

elasticity of -0.13, indicating that in the short run a doubling of the price of 

gasoline might cause a 10% or greater decrease in fuel consumption per mile

through such actions as fuel efficient driving behavior, shifting VMT within a 

household to its more fuel efficient vehicles, better maintenance, as well as shifts 

in sales towards more efficient vehicles and increased scrappage of less efficient 

vehicles within the year. Personal income is not significant at the 0.05 level but 

does have a positive sign, possibly indicating that as incomes rise motorists opt 

for acceleration and speed over fuel economy. Of the two dummy variables only 

the data anomalies dummy is significant. 

The residuals from the fuel consumption regression were retained and added to 

the previous list of right-hand side variables in the VMT regression. The result is 

shown in Table 7. 
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Table 6. Regression of Log(FC) on Instrumental Variables

Dependent Variable: LOG(FC)

Method: Least Squares

Sample (adjusted): 1966 2007

Included observations: 42

Variable Coefficient Std. Error t-Statistic Prob.

C -0.471 0.625 -0.754 0.456

LOG(RGASPRICE) -0.127 0.021 -6.002 0.000

LOG(CAFELDV) -1.077 0.067 -16.115 0.000

LOG(RPERSINC) 0.060 0.038 1.582 0.123

DUM7479 0.020 0.016 0.305 0.200

DUM0304 0.039 0.015 2.543 0.015

R-squared 0.988 F-statistic 615.657

Adjusted R-squared 0.987 Prob(F-statistic) 0.000

S.E. of regression 0.020 Mean dependent var -2.809

Sum squared resid 0.015 S.D. dependent var 0.177

Log likelihood 107.274 Durbin-Watson stat 0.448

Table 7. Hausman Test for Endogeneity of Fuel Economy

Dependent Variable: LOG(LDVMT)

Method: Least Squares

Sample (adjusted): 1967 2007

Included observations: 41 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C -1.637 0.631 -2.593 0.014

LOG(RGASPRICE) -0.051 0.009 -5.844 0.000

LOG(FC) 0.034 0.029 1.152 0.258

LOG(RPERSINC) 0.148 0.057 2.609 0.014

LOG(LDVEH) 0.100 0.041 2.424 0.021

DUM7479 -0.050 0.007 -6.887 0.000

LOG(LDVMT(-1)) 0.777 0.063 12.309 0.000

RESIDFC 0.026 0.101 0.261 0.795

R-squared 1.000 Mean dependent var 14.371

Adjusted R-squared 1.000 S.D. dependent var 0.338

S.E. of regression 0.008 Akaike info criterion -6.573

Sum squared resid 0.002 Schwartz criterion -6.238

Log likelihood 142.741 Hannan-Quinn criter. -6.451

F-statistic 9491.093 Durbin-Watson stat 1.929

Prob(F-statistic) 0.000
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The residual is not statistically significant, with a t-statistic of 0.26 and 

significance level of 0.8. Thus, the Hausman endogeneity test does not indicate 

that fuel economy is endogenous in the vehicle travel equation based on national 

time series data. This does not mean that fuel economy is not affected by the 

current values of the exogenous variables (e.g., gasoline price). It does imply 

that the MPG variable is not correlated with the error term of the VMT equation 

and that OLS estimators will not suffer from simultaneous equations bias.

The endogeneity of vehicle stock was tested with a similar result. Instrumental 

variables in the log-log vehicle stock equation were the real price of gasoline, the 

number of licensed drivers, real personal income, the BLS new car price index 

(2005 = 1), and the two dummy variables12. Only the number of licensed drivers 

was statistically significant. When the residuals were added to the vehicle travel 

equation the coefficient of the residuals was again not statistically significant, 

indicating a lack of correlation between vehicle stock and the error term of the

VMT equation.

Energy economists have observed asymmetric responses of demand to changes 

in the prices of petroleum products (e.g., Dargay and Gately, 1997). Responses 

to price increases greatly exceed responses to price decreases. The asymmetries 

are generally attributed to irreversible technological change and the impacts of 

policies such as energy efficiency standards. The possibility that vehicle travel 

may respond asymmetrically to price or fuel economy was tested using the 

 

12 It can be argued that the BLS new car price index and the on-road vehicle stock may 

be simultaneously determined. Omitting the new car price index does not change the results.
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method of Dargay and Gately (1997). Whether in log or linear form, year-overyear increases are accumulated as a “rise” version of the variable while yearover-year decreases are accumulated as a “fall” version. Let p be the price of 

gasoline in year t. The PRICERISE and PRICEFALL variables are defined as 

follows.

 

  











 

 

T

t

t t t

T

t

t t t

PRICEFALL p p

PRICERISE p p

1

1

1

1

min 0,

max 0,

(4)

If the response to price is symmetrical, the coefficients of PRICERISE and 

PRICEFALL will be equal, and the same as the coefficient of price.

The results of the asymmetry tests are less than entirely decisive but do not reject 

the hypothesis of symmetry. Results for the linear model are shown in Table 8. 

PRICERISE and PRICEFALL (which replace RGASPRICE) both have negative 

coefficients, but PRICEFALL’s is much smaller and not statistically significant. 

Neither of the analogous coefficients of fuel consumption (FCRISE and 

FCFALL) is statistically significant. A Wald test for the simultaneous equality 

of gasoline price coefficients and equality of the fuel efficiency coefficients does 

not reject the hypothesis of symmetry at the 0.2 level. The same test applied to 

the double log form of the model also did not reject symmetry but the 

significance level was smaller: 0.09. 
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Table 8. Test for Asymmetry in Linear Lagged Adjustment Model for Vehicle 

Travel

Dependent Variable: LDVMT

Method: Least Squares

Sample (adjusted): 1967 2007

Included observations: 41 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C -39632.28 45347.61 -0.874 0.389

PRICERISE -704.530 149.701 -4.706 0.000

PRICEFALL -192.236 178.114 -1.079 0.289

FCRISE 6788103. 5758704. 1.075 0.291

FCFALL -2743952. 2097563. -1.308 0.200

RPERSINC 4.64E-05 1.80E-05 2.581 0.015

LDVEH 0.001 0.001 2.049 0.049

DUM7479 -58221.61 11315.19 -5.145 0.000

LDVMT(-1) 0.763 0.063 12.030 0.000

R-squared 1.000 F-statistic 11312.85

Adjusted R-squared 1.000 Prob(F-statistic) 0.000

S.E. of regression 12434.000 Mean dependent var 1838201.

Sum squared resid 4.95E+09 S.D. dependent var 591546.3

Log likelihood -439.652

The above results are quantitatively similar to Small and Van Dender’s (2007)

results with two important differences. First, the 1966-2007 U.S. national time 

series data do not support the existence of a direct rebound effect of fleet average 

light-duty vehicle fuel economy on light-duty vehicle miles of travel. This 

inference is generally consistent with previous studies, including Small and Van 

Dender (2007), but is more definitive in that the hypothesis of equal and opposite 

effects of fuel economy and the price of gasoline is rejected by the data for the 

first time. Second, the 1966-2007 national time series data do not support the 

simultaneity of vehicle travel, fuel economy and vehicle stock. This latter 

difference may be more easily explained. Given an expected vehicle life of 

approximately 15 years (Davis et al., 2008), the size of the vehicle stock and its 

fuel economy is largely predetermined by previous purchase decisions. Changes 
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from year to year in fuel economy may be adequately explained by CAFE 

standards and changes in the price of gasoline, and year-to-year fluctuations in

the stock of vehicles may be explained by changes in income and the prices of 

vehicles. The case for state-to-state, or household level simultaneity of these 

variables appears to be much stronger.

The lack of empirical evidence for a rebound effect of fuel economy on vehicle 

miles of travel requires an explanation. On the one hand, the theory is 

compelling. Why should the response to a change in fuel economy not be 

symmetrical to a change in gasoline price, since the two affect fuel cost per mile 

of travel in equal and opposite ways? A possible explanation that upholds the 

validity of the theory is that the manner in which fuel economy improvements 

were brought about (fuel economy regulations) increases the cost of new 

vehicles, inducing an offsetting effect by increasing the fixed cost of vehicle 

travel. Another explanation may lie in the “experimental design” of the historical 

data, i.e., a gradual change in the level of fuel economy, making its impact more 

difficult to estimate than that of fuel price, whose changes have often been 

sudden and large.

Estimates of the rebound effect published in the economics literature aim to

measure the effect of reduced fuel cost per mile of travel (price per gallon 

divided by miles per gallon) on the amount of travel, other things equal. In 

particular, the stock of motor vehicles is typically included as a right-hand-side 

variable. However, when manufacturers raise fuel economy in response to fuel 

economy standards they do so primarily by adding more expensive fuel economy 
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technology, thereby increasing the cost of the vehicle (NRC, 2002). Whether the 

increased cost of this technology will be less than or greater than the value of fuel 

saved is usually a subject of heated debate, and in any case will depend on how 

high the standards are set. How capital costs and variable energy costs are 

perceived by consumers is yet another unresolved issue. Regardless, in the long 

run the cost of operating a vehicle unquestionably depends on the cost of the 

vehicle as well as the cost of fuel (plus other costs such as insurance, 

maintenance, etc., some of which may increase with vehicle price). A certain 

amount of vehicle depreciation is a function of time, the rest being chiefly a 

function of use. Goodwin et al. (2004) put the average elasticity of vehicle travel 

with respect to vehicle cost at -0.4 based on three studies with a range from -0.2 

to -0.6. Dargay (2007) found a similar effect in an analysis of the effects of fuel 

and car prices on vehicle travel in the UK: other things equal, more expensive 

cars were driven less. She was skeptical of the result, however, and noted the 

dearth of empirical evidence on the relationship between car price and vehicle 

use. Nevertheless, in the long run, the rebound effect of lower fuel costs brought 

about by fuel economy standards should be, in theory, to some degree offset by 

the increased cost of fuel economy technology. 

As an illustration, suppose that fuel economy regulations require a 33% decrease 

in fuel consumption per mile. Evaluated using a rebound elasticity of -0.1, this 

would imply a 3.3% increase in vehicle travel. If the increase in vehicle price for 

technologies to achieve these fuel economy gains is equal to the discounted 

present value of fuel saved, the net decrease in long-run vehicle operating costs 

would be roughly zero. The increased long-run (capital) cost per mile of travel 
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would offset the decreased short run (variable) cost. This would imply that the 

standards had been set above the point at which the marginal cost of increasing 

fuel economy was equal to the marginal private benefit of the resulting fuel 

savings. This could easily be the case if the marginal social value of reduced fuel 

consumption were believed to exceed the taxes on motor fuel. This also assumes 

that motorists perceive that the capital invested in a vehicle is used up with 

vehicle use. Whether or not consumers actually perceive short-run and long-run 

costs in this way is an empirical question, deserving of further study.

6.2 RE-ESTIMATING THE SMALL AND VAN DENDER MODEL WITH 

NATIONAL TIME SERIES DATA

Despite the rejection of equal effects of fuel price and fuel consumption, it is still 

of interest to determine whether the national times series data also support Small 

and Van Dender’s (2007) conclusion that the rebound effect has declined over 

time as per capita income has increased. In these estimations, it is recognized 

that theory is being allowed to overrule the empirical data.

Following the formulation of Small and Van Dender (2007), the logarithm of 

light-duty vehicle miles of travel was regressed against the logarithm of fuel cost 

per mile (CPM) and the product of the logarithms of fuel cost per mile and real 

per capita income. Thus, the rebound effect becomes a linear function of the log 

of per capita income, which is used to represent the value of travelers’ time. The 

hypothesis is that as the value of time increases fuel cost becomes a relatively 

less important determinant of the demand for travel. Other variables included in 
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the regression were the logarithm of vehicle stock, the dummy variable for 1974 

and 1979, and the lagged value of VMT. The log of real personal income was 

dropped due to statistical insignificance. This is problematic because it is unclear 

to what extent the interaction of income and cost per mile is also reflecting the 

effect of income alone. The results are shown in Table 9. The rebound effect 

(the elasticity of fuel cost per mile) is the following function of the logarithm of 

real per capita income.

  

   

 

Long Run pcinc

pcinc Short Run

LR

SR

1 0.83

0.27 0.7 log

0.27 0.7 log



 



  





(5)

Table 9. Rebound Effect as a Function of Log of Per Capita Income

Dependent Variable: LOG(LDVMT)

Method: Least Squares

Sample (adjusted): 1967 2007

Included observations: 41 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 1.859 0.528 3.518 0.001

LOG(CPM) -0.272 0.072 -3.797 0.000

LCPMINC 0.071 0.021 3.368 0.002

LOG(LDVEH) 0.039 0.036 1.092 0.283

DUM7479 -0.047 0.007 -6.958 0.000

LOG(LDVMT(-1)) 0.828 0.037 22.416 0.000

R-squared 0.999 F-statistic 11909.71

Adjusted R-squared 0.999 Prob(F-statistic) 0.000

S.E. of regression 0.009 Mean dependent var 14.371

Sum squared resid 0.003 S.D. dependent var 0.338

Log likelihood 139.293
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Both coefficients are statistically significant at the 0.01 level. The implied 

pattern of the long-run elasticity of light-duty vehicle travel with respect to fuel 

cost per mile is shown in Figure 10. 

Small and Van Dender noted that while their formulation fitted the historical data 

well, it could not be extrapolated far into the future without running the risk of 

predicting a rebound elasticity greater than zero. This would imply that reducing 

the fuel cost per mile of vehicle travel would decrease the quantity of travel, a 

decidedly counterintuitive effect. The authors recognized that an alternative 

functional form might be needed. If income is assumed to have its effect via the 

total cost (time plus monetary) of vehicle travel, then the rebound effect should 

probably decrease with the inverse of income. For simplicity, assume that the 

total cost of vehicle travel can be represented as a(pcinc) + X, where X is the 

total monetary cost of travel per mile and includes fuel costs (eP). In equation 

(2) above, C = X – eP. The coefficient “a” translates per capita income (Y) into a 

time cost per mile (and so depends on average speed).13

   

aY X

eP K aY X

V

eP K aY X

d eP

d

V

eP

V

eP

d eP

dV



    

 ( )

( ) ( )

1 



 

(6)

 

13 In reality, the value of time spent traveling varies enormously not only across 

individuals but depending on a variety of circumstances. This simple assumption is used to 

suggest that an inverse function of income may be a reasonable alternative to the logarithm of 

income.
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Two alternative formulations of the elasticity of fuel cost per mile as a function 

of the inverse of income were tested. The first assumes that βV,eP = b0 + b1/pcinc, 

while the other eliminates the constant term, βV,eP = b/pcinc . The first 

formulation resulted in insignificant coefficients for the constant term of the 

income elasticity, as well as for the logarithms of personal income and vehicle 

stock. The second formulation was more satisfactory; however, vehicle stock 

was not statistically significant (Table 10).

Table 10. Rebound Effect as a Function of the Inverse of Personal Income

Dependent Variable: LOG(LDVMT)

Method: Least Squares

Sample (adjusted): 1967 2007

Included observations: 41 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 0.144 0.576 0.249 0.805

LCPMOVRINC -1.035 0.190 -5.464 0.000

LOG(RPERSINC) 0.112 0.048 2.326 0.026

LOG(LDVEH) 0.042 0.032 1.332 0.191

DUM7479 -0.045 0.007 -6.634 0.000

LOG(LDVMT(-1)) 0.766 0.157 13.395 0.000

R-squared 0.999 F-statistic 12514.56

Adjusted R-squared 0.999 Prob(F-statistic) 0.000

S.E. of regression 0.085 Mean dependent var 14.371

Sum squared resid 0.003 S.D. dependent var 0.338

Log likelihood 140.308

Empirically, the results are similar to those found by Small and Van Dender 

(2007). The authors reported an estimated short-run rebound effect of 2.2% and 

long-run rebound effect of 10.7% for 2001. The inverse income model estimated 

here implies a short-run rebound effect of 3.1% and a long-run effect of 13.1% 

for the same year (Figure 10). This is notable given the differences in data 

(national time series in this study, state cross-sectional times series in Small and 
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Van Dender) and the differences in method of estimation and equation 

formulation. The inverse income formulation generally shows a slower rate of 

change in the rebound elasticity over time, as might be expected. 

Both models indicate that the rebound effect from 1966 to 1983 was about two to 

three times larger than at present. Both models indicate that using time constant 

elasticities would overstate the rebound effect at present and even more so in the 

future when incomes will presumably be higher. 

Estimates of the Rebound Effect as Functions of Per Capita Income, 

1966-2007

-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

1965 1970 1975 1980 1985 1990 1995 2000 2005

Elasticity

Constant Short-Run

Short Run Inverse Income

Short-Run Small+VanDender

Constant Long-Run

Long Run Inverse Income

Long-Run Small+VanDender

Figure 10. Estimates of the Rebound Effect as a Functions of Per Capita Income, 

1966-2007

7. DISCUSSION AND INFERENCES

Several studies have estimated the rebound effect of motor vehicle fuel efficiency 

on vehicle travel in the United States. With few exceptions, these studies find a 
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relatively small rebound effect, on the order of -0.2 in the long run. These 

conclusions may have to be revised. Using national time series data for 1966 to 

2007, this study finds a statistically significant elasticity of vehicle travel with 

respect to fuel price, but no statistically significant elasticity of vehicle travel 

with respect to fuel economy. This result is not new, having been previously 

reported by Small and Van Dender (2007). What is new is the finding that the 

hypothesis that the elasticities of vehicle travel with respect to fuel price and fuel 

efficiency (gallons per mile) are equal, as predicted by theory, is now rejected by 

the national time series data. 

The rejection of equal effects of gasoline price and fuel efficiency may not 

contradict rational economic behavior if it is due to the countervailing effect of 

increased vehicle purchase costs due to fuel economy improvements required by 

the CAFE standards. Higher vehicle costs would increase the long-run cost per 

mile of driving and there is some evidence that higher vehicle prices lead to 

lower levels of vehicle travel but more definitive research is needed. In 

particular, it would be useful to know whether vehicle travel responds to changes 

in long-run capital costs in the same way it responds to changes in short-run 

variable costs. There is also the possibility that data shortcomings and a 

relatively poor “experimental design” in the historical data also contributed. 

Additional investigation of this result is warranted.

Two studies have suggested that the rebound effect may have decreased over 

time, and may be much smaller today than it was in the 1970s and 1980s. 

Greene (1992) hypothesized that the rebound effect varied with the fuel cost 
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share of total vehicle operating costs. Small and Van Dender (2007) 

acknowledged that this hypothesis was reasonable but found a stronger 

relationship between per capita income and the rebound effect, based on state 

level data for the period 1966 to 2002. Recursive coefficient tests on the linear 

and log-linear models support this inference, showing a decline in the absolute 

values of coefficients for gasoline price and fuel efficiency after 1980. 

Although the hypothesis that fuel cost per mile could be used as a right hand side 

variable in place of separate gasoline price and fuel efficiency variables was 

rejected by the data, the possibility of a decreasing rebound effect as a function 

of income was explored using Small and Van Dender’s (2007) formulation of the 

rebound effect as a function of income. The results obtained here with national 

time series data are quite consistent with Small and Van Dender’s estimates 

using state level time series, cross sectional data. An alternative formulation of 

rebound elasticity as an inverse function of income produced a similar but less 

dramatic decline. The inverse function should be more consistent with the 

hypothesis that the causal factor in the declining rebound effect is the value of 

time, and has the advantage that it will not lead to an eventual reversal in the sign 

of the rebound effect as income grows. The results imply that if there has been a 

direct rebound effect of fuel efficiency on light-duty vehicle travel in the United 

States over the period of this study, it is by now on the order of 10%. Still, these 

results must be interpreted with great caution in light of the rejection of fuel cost 

per mile as the appropriate variable for estimating the rebound effect.
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45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

61 

62 

63 

64 

65 

54

APPENDIX A:

FUTURE EXTRAPOLATION OF THE REBOUND EFFECT

Assuming a per capita income growth rate of 1.5%, the estimated rebound 

effect shown in Figure 10 can be projected for future years. 

Table A-1 Projected Rebound Effect

Projected Rebound 

Effect, Assuming 1.5% 

Per Capita Income 

Growth

2008 -12.0%

2009 -11.8%

2010 -11.6%

2011 -11.5%

2012 -11.3%

2013 -11.1%

2014 -11.0%

2015 -10.8%

2016 -10.7%

2017 -10.5%

2018 -10.3%

2019 -10.2%

2020 -10.0%

2021 -9.9%

2022 -9.7%

2023 -9.6%

2024 -9.5%

2025 -9.3%

2026 -9.2%

2027 -9.0%

2028 -8.9%

2029 -8.8%

2030 -8.6%