Fuel Efficiency and Motor Vehicle Travel: The Declining Rebound Effect
Kenneth A. Small and Kurt Van Dender*
Department of Economics
University of California, Irvine
Irvine, CA 92697-5100
ksmall@uci.edu, kvandend@uci.edu
*Corresponding author. Tel: 949-824-9698; Fax 949-824-2182
UC Irvine Economics Working Paper #05-06-03
This version: April 10, 2006 (corrected July 17, 2006 and August 18, 2007)
Shorter version published, Energy Journal, vol. 28, no. 1 (2007), pp. 25-51.
Note: the published version lacks the corrections to the bottom panel of Tables 5 and B2,
described here in note 26.
Abstract:
We estimate the rebound effect for motor vehicles, by which improved fuel efficiency causes
additional travel, using a pooled cross section of US states for 1966-2001. Our model accounts
for endogenous changes in fuel efficiency, distinguishes between autocorrelation and lagged
effects, includes a measure of the stringency of fuel-economy standards, and allows the rebound
effect to vary with income, urbanization, and the fuel cost of driving. At sample averages of
variables, our simultaneous-equations estimates of the short- and long-run rebound effect are
4.5% and 22.2%. But rising real income caused it to diminish substantially over the period, aided
by falling fuel prices. With variables at 1997-2001 levels, our estimates are only 2.2% and
10.7%, considerably smaller than values typically assumed for policy analysis. With income at
the 1997 – 2001 level and fuel prices at the sample average, the estimates are 3.1% and 15.3%,
respectively.
JEL codes: Q0, D5, R4, C2
Keywords: carbon dioxide, fuel economy, travel demand, motor vehicle use, rebound effect
Acknowledgment:
This paper is partly based on research sponsored by the California Air Resources Board and the
California Energy Commission, and has been revised with support from the University of
California Energy Institute. We would like to thank S. Jun and C.K. Kim for excellent research
assistance. Earlier stages of this work have benefited from comments by David Brownstone,
David Greene, Winston Harrington, Eric Haxthausen, Jun Ishii, Chris Kavalec, Charles Lave,
Lars Lefgren, Reza Mahdavi, Don Pickrell, and Charles Shulock, among others. We also
appreciate comments at colloquia at Brigham Young University, Catholic University of Leuven,
and Resources for the Future. All errors, shortcomings, and interpretations are our responsibility.
Nothing in this paper has been endorsed by or represents the policy of the sponsoring
organizations.
1
1. Introduction
It has long been realized that improving energy efficiency releases an economic reaction
that partially offsets the original energy saving. As the energy efficiency of some process
improves, the process becomes cheaper, thereby providing an incentive to increase its use. Thus
total energy consumption changes less than proportionally to changes in physical energy
efficiency. This “rebound effect” is typically quantified as the extent of the deviation from
proportionality. It has been studied in many contexts, including residential space heating and
cooling, appliances, and transportation (Greening, Greene, and Difiglio, 2000).
For motor vehicles, the process under consideration is use of fuel in producing vehicle-
miles traveled (VMT). When vehicles are made more fuel-efficient, it costs less to drive a mile,
so VMT increases if demand for it is downward-sloping. That in turn causes more fuel to be used
than would be the case if VMT were constant; the difference is the rebound effect. Obtaining
reliable measures of it is important because it helps determine the effectiveness of measures
intended to reduce fuel consumption and because increased driving exacerbates congestion and
air pollution. For example, the rebound effect was an issue in the evaluation of recently adopted
greenhouse-gas regulations for California (CARB, 2004, Sect. 12.3-12.4). It has played a
prominent role in analyses of the Corporate Average Fuel Economy (CAFE) regulations in the
US and of proposals to strengthen them.
This paper presents estimates of the rebound effect for passenger-vehicle use that are
based on pooled cross-sectional time-series data at the U.S. State level. It adds to a sizeable
econometric literature, contributing four main improvements. First, we use a longer time series
(1966-2001) than was possible in earlier studies. This increases the precision of our estimates,
enabling us (among other things) to determine short- and long-run rebound effects and their
dependence on income. Second, the econometric specifications rest on an explicit model of
simultaneous aggregate demand for VMT, vehicle stock, and fuel efficiency. The model is
estimated directly using two- and three-stage least squares (2SLS and 3SLS); thus we can treat
consistently the fact that the rebound effect is defined starting with a given change in fuel
efficiency, yet fuel efficiency itself is endogenous. Third, we measure the stringency of CAFE
regulation, which was in effect during part of our sample period, in a theoretically motivated
way: as the gap between the standard and drivers’ desired aggregate fuel efficiency, the latter
estimated using pre-CAFE data and a specification consistent with our behavioral model. Fourth,
2
we allow the rebound effect to depend on income and on the fuel cost of driving. The
dependence on income is expected from theory (Greene, 1992), and is suggested by micro-based
estimates across deciles of the income distribution (West, 2004). Just like income changes,
changes in fuel prices affect the share of fuel costs in the total cost of driving, and so we also
expect them to influence the rebound effect.
Our best estimates of the rebound effect for the US as a whole, over the period 1966-
2001, are 4.5% for the short run and 22.2% for the long run. The 2SLS and 3SLS results are
mostly similar to each other but differ from ordinary least squares (OLS) results, which are
unsatisfactory as they strongly depend on details of the specification. While our short-run
estimate is at the lower end of results found in the literature, the long-run estimate is similar to
what is found in most earlier work. Additional estimation results, like the long-run price-
elasticity of fuel demand (-0.43) and the proportion of it that is caused by mileage changes
(52%), are similar to those in the literature.
This agreement is qualified, however, by our finding that the magnitude of the rebound
effect declines with income and, with less certainty, increases with the fuel cost of driving. These
dependences substantially reduce the magnitude that applies to recent years . For example, using
average values of income, urbanization and fuel costs measured over the most recent five-year
period covered in our data set (1997-2001), our results imply short- and long-run rebound effects
of just 2.2% and 10.7%, roughly half the average values over the longer time period. Similarly,
the long-run price elasticity of fuel demand declines in magnitude in recent years and so does the
proportion of it caused by changes in amount of motor-vehicle travel. These changes are largely
the result of real income growth and lower real fuel prices. Future values of the rebound effect
depend on how those factors evolve.
The structure of the paper is as follows. Section 2 introduces the definition of the
rebound effect and reviews some key contributions toward measuring it. Section 3 presents our
theoretical model and the econometric specification, and section 4 presents estimation results.
Section 5 concludes.
2. Background
The rebound effect for motor vehicles is typically defined in terms of an exogenous
change in fuel efficiency, E. Fuel consumption F and motor-vehicle travel M – the latter
measured here as VMT per year – are related through the identity F=M/E. The rebound effect
3
arises because travel M depends (among other things) on the variable cost per mile of driving, a
part of which is the per-mile fuel cost, P
M
≡P
F
/E, where P
F
is the price of fuel. This dependence
can be measured by the elasticity of M with respect to P
M
, which we denote
ε
M,PM
. When E is
viewed as exogenous, it is easy to show that fuel usage responds to it according to the elasticity
equation:
,,
1
FE MPM
ε
ε
=− − . Thus a non-zero value of
ε
M,PM
means that F is not inversely
proportional to
E: it causes the absolute value of
ε
F,E
to be smaller than one. For this
reason, -
ε
M,PM
itself is usually taken as a definition of the rebound effect.
Two of our innovations relate directly to limitations of this standard definition of the
rebound effect. First, the standard definition postulates an exogenous change in fuel efficiency
E.
Yet most empirical measurements of the rebound effect rely heavily on variations in the fuel
price
P
F
,
1
in which case it is implausible that E is exogenous. This can be seen by noting the
substantial differences in empirical estimates of the fuel-price elasticities of fuel consumption,
ε
F,PF
, and of travel,
ε
M,PF
.
2
As shown by USDOE (1996: 5-11), they are related by
ε
F,PF
=
PFEPFEPFM ,,,
)1(
ε
ε
ε
−−⋅
, where
ε
E,PF
measures the effect of fuel price on efficiency. Thus the
observed difference between
ε
F,PF
and
ε
M,PF
requires that
ε
E,PF
be considerably different from
zero. Ignoring this dependence of
E on P
F
, as is done in many studies, may cause the rebound
effect to be overestimated if unobserved factors that cause
M to be large (e.g. an unusually long
commute) also cause
E to be large (e.g. the commuter chooses fuel-efficient vehicles to reduce
the cost of that commute).
A second limitation of the standard definition is that fuel cost is just one of several
components of the total cost of using motor vehicles. Another important component is time cost,
which is likely to increase as incomes grow. If consumers’ response to fuel costs is related to the
proportion of total cost accounted for by fuel, then |
ε
M,PM
| should increase with fuel cost itself
and diminish with income (Greene, 1992). Our specification allows for such dependences.
Furthermore, time costs increase with traffic congestion; we account for this indirectly by
allowing the rebound effect to depend on urbanization, although empirically this turns out to be
1
Most studies assume that that travel responds to fuel price P
F
and efficiency E with equal and opposite elasticities,
as implied by the definition of the rebound effect based on the combined variable P
M
=P
F
/E. See for example
Schimek (1996), Table 2 and Greene et al. (1999), fn. 6.
2
See USDOE (1996, pp. 5-14 and 5-83 to 5-87); Graham and Glaister (2002, p. 17); and the review in Parry and
Small (2005).
4
unimportant. An extension, not attempted here, would be to allow congestion to be endogenous
within the system that determines amount of travel.
Some empirical studies of the rebound effect have used aggregate time-series data.
Greene (1992) uses annual U.S. data for 1957-1989 to estimate the rebound effect at 5 to 15%
both in the short and long run, with a best estimate of 12.7%. According to Greene, failing to
account for autocorrelation – which he estimates at 0.74 – results in spurious measurements of
lagged values and to the erroneous conclusion that long-run effects are larger than short-run
effects.
3
Greene also presents evidence that the fuel-cost-per-mile elasticity declines over time,
consistent with the effect of income just discussed; but the evidence has only marginal statistical
significance.
Jones (1993) re-examines Greene’s data, adding observations for 1990 and focusing on
model-selection issues in time-series analysis. He finds that although Greene’s autoregressive
model is statistically valid, so are alternative specifications, notably those including lagged
dependent variables. The latter produce long-run estimates of the rebound effect that
substantially exceed the short-run estimates (roughly 31% vs. 11%).
4
Schimek (1996) uses data
from a still longer time period and finds an even smaller short-run but a similarly large long-run
rebound effect (29%).
5
Schimek accounts for federal CAFE regulations by including a time
trend for years since 1978; he also includes dummy variables for the years 1974 and 1979, when
gasoline-price controls were in effect, resulting in queues and sporadic rationing at service
stations. These controls reduce the extent of autocorrelation in the residuals.
These aggregate studies highlight the possible importance of lagged dependent variables
(inertia) for sorting out short-run and long-run effects. But they do not settle the issue because
they have trouble disentangling the presence of a lagged dependent variable from the presence of
autocorrelation. Their estimates of these dynamic properties are especially sensitive to the time
period considered and to their treatment of the CAFE regulations.
3
Another study that found autocorrelation is that by Blair, Kaserman, and Tepel (1984). They obtain a rebound
effect of 30%, based on monthly data from Florida from 1967 through 1976. They do not estimate models with
lagged variables.
4
These figures are from the linear lagged dependent variable model (model III in Table 1). Estimates for the log-
linear model are nearly identical.
5
These figures are his preferred results, from Schimek (1996), p. 87, Table 3, model (3).
