The Rebound Effect from Fuel
Efficiency Standards:
Measurement and Projection to 2035
&EPA
United States
Environmental Protection
Agency
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The Rebound Effect from Fuel
Efficiency Standards:
Measurement and Projection to 2035
Assessment and Standards Division
Office of Transportation and Air Quality
U.S. Environmental Protection Agency
Prepared for EPA by
ICF International, L.L.C.
EPA Contract No. EP-W-08-018
Work Assignment No. 4-5
NOTICE:0
This technical report does not necessarily represent final EPA decisions or
positions. It is intended to present technical analysis of issues using data
that are currently available. The purpose in the release of such reports is to
facilitate the exchange of technical information and to inform the public of
technical developments.
&EPA
United States
Environmental Protection
Agency
EPA-420-R-15-012
July 2015
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The Rebound Effect from Fuel Efficiency Standards:
Measurement and Projection to 2035
Kenneth A. Small
Department of Economics
University of California at Irvine
with contributions by
Kent Hymel
Department of Economics
California State University at Northridge
This report discusses empirical values of the "rebound effect" for travel in passenger vehicles in
the United States. The rebound effect refers to effects on the amount of travel that arises from
changes in the fuel efficiency for light-duty motor vehicles (passenger cars and light trucks),
caused in turn by regulations or technological developments. We briefly discuss the literature,
then summarize previous empirical estimates done at University of California at Irvine in
collaboration with Kurt Van Dender and Kent Hymel. Finally we present updated empirical
estimates, which take advantage of newer data through the year 2009, and derive the implications
of the updated estimates for the rebound effect in the time frame 2010-2035.
The literature review and empirical methodology are described more fully in two published
articles (Small and Van Dender 2007a; Hymel, Small, and Van Dender 2010), and even more
fully in the working papers from which the published articles ware derived (Small and Van
Dender 2007b). The empirical estimates have been updated subsequently, by adding five new
years of data, namely 2005-2009. The projections are our own, and use a new methodology
developed for this project which improves on that used for earlier reports by K. Small to EPA
and an older report to the California Air Resources Board (Small and Van Dender 2005).
1. Background and definitions
1.1 Determinants of motor-vehicle travel
The rebound effect is simply a statement of the near-universal economic principle of downward-
sloping demand: when the price of a good or service decreases, people purchase more of it. In
this case the service is passenger transportation, and its price to the user includes the cost of fuel.
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If the amount of service is measured as vehicle-miles traveled (VMT), then the component of
price accounted for by fuel cost, here called "fuel cost per mile" PM, is equal to the price of fuel
Pf(e.g. stated in $/gallon) divided by fuel efficiency E (e.g. stated in vehicle-miles/gallon):
(1)
Thus if fuel efficiency E is increased, fuel cost per mile decreases, and since this is part of the
price paid by consumers to drive, they will increase their VMT. See Greening, Greene and
Difiglio (2000) for a more extended discussion.
The responsiveness of demand to price is often summarized as a ratio of the percent change in
demand, AM/M, to the percent change in price causing it, AP/W//V, where M designates VMT in
mathematical equations and A designates a change in a quantity. A ratio such as this is called an
elasticity., usually defined for the situation when A?M is very small so that the ratio becomes a
derivative. Therefore we define the elasticity of vehicle-miles traveled with respect to cost per
mile as follows:
s --.- (2)
GM,PM , ,, Jr, \^)
M dPM
where the derivative dM/dPMis simply the limit of AM/APM as APM becomes very small. An
equivalent way to write this is in terms of the natural logarithms of M and PM, which we denote
by lower-case letters vma andpm, respectively. (The notation vma stands for vehicle-miles per
adult member of the population, which is how we define Min our empirical work.) Of course the
equation for vma contains other variables besides pm, and these are held constant when
considering the effects ofpm; this makes the derivative in (2) a partial derivative, denoted using
the symbol d. The elasticity written in this form is:
_ d(vma)
^M,PM ~ ~, ^ •> \J )
d(pm)
which could be a single coefficient in the equation for vma or, if pm enters in more than one way,
a combination of several coefficients.
One of the confusing aspects of the literature is that few studies have accounted for the fact that
fuel efficiency E is not simply mandated, but chosen jointly by consumers and motor-vehicle
manufacturers, within certain constraints set by regulation. Therefore one might ask the meaning
of considering a change in E as though it could simply be set by fiat. In our empirical work, Van
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Dender and we meet this challenge by defining a system of three simultaneously determined
travel-related quantities, each applying to a state. The first dependent variable is VMT, written
mathematically asM; it is a function of PM (as already described), the size of the vehicle fleet, V,
and various socio-demographic characteristics including income. The second dependent variable
is V, which is a function of several things reflecting the demand for owning vehicles: a price
index Pv of new vehicles, the amount of travel M (since new vehicles are purchased in large part
to supply desired travel), the price of travel PM, and other characteristics. Note that we do not
distinguish among vehicles of various ages: thus implicitly we ignore possible effects of these
variables on the age composition of the fleet. Finally, the third dependent variable, fuel intensity
l/E (the inverse of fuel efficiency), is presumed to be chosen based on a combination of motives
including the wish to conserve on the cost of traveling M miles, the need to meet various
regulations on fuel efficiency and/or emissions, and tradeoffs with vehicle performance; in our
empirical work E is assumed to be a function ofM, price of fuel PF, a variable measuring the
stringency during any given year of the US federal Corporate Average Fuel Economy (CAFE)
regulations, and other characteristics. This system is summarized in the left panel of Table 1.1.
Table 1.1. Simultaneous Equation Systems
Three-equation system
(without congestion)
Equation (dependent
variable)
VMT per adult
Vehicle stock per adult
Fuel intensity of vehicles
Symbol
Level
M
V
HE
Logarithm
vma
vehstock
fmt
Four-equation system
(with congestion)
Equation (dependent
variable)
VMT per adult
Vehicle stock per adult
Fuel intensity of vehicles
Congestion delay per adult
Symbol
Level
M
V
HE
C
Logarithm
vma
vehstock
fmt
cong
An implicit assumption in the use of aggregate data is that that the response to aggregate changes
in fuel efficiency (or other variables) does not depend significantly on how those changes are
distributed among segments of the population. This could occur, for example, if drivers are
sufficiently homogeneous. In particular, the model assumes that changes in fleet average fuel
economy will have the same impact on behavior whether those changes are caused entirely by
new vehicles entering the fleet, or partly by new vehicles and partly by the retirement of older
ones. This assumption enables us to apply the results of the model to regulations that specifically
impact new vehicles only. It should be adequate insofar as the pattern of mileage driven by
vehicle age is reasonably stable; if it is not, a more fine-tuned analysis tracking elasticities by
vehicle age would reveal additional effects not captured here.
It is worth noting that our system accounts for the effects of a change in regulations through two
potential pathways. We illustrate for an increase in fuel-efficiency standards, with no change in
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vehicle price. First, the regulations increase the average fuel economy of the fleet, and that in
turn reduces the cost per mile of travel, PM, through equation (1); this may directly reduce the
amount of travel because of downward-sloping demand as just discussed. Second, the size of the
vehicle fleet may increase because vehicles are now more useful, in the sense that they can be
driven more cheaply; this change in vehicle fleet size may further affect M since, as already
noted, Mis expected to be a function of Fas well as other things. We estimate a simultaneous-
equations model of M, V, and E that fully accounts for these effects. Empirically, we find that the
first path is by far the dominant one, so that one could ignore the second path as an
approximation; this may simply indicate that vehicle purchases are governed mainly by factors
other than the cost of driving.
Our model, through the influence of fuel cost on fuel efficiency, implicitly incorporates some
changes in the relative prices of vehicles of different sizes and types. (For example, vehicle
manufacturers may respond to a fuel efficiency regulation by offering discounts on their fuel-
efficient vehicle types.) However, the description just given of the effects of regulations assumes
that the average price of new vehicles, Pv, is held fixed. Of course, the full effect of a regulation
would also include any change in this average price on new-vehicle sales. In many cases this
would work in the opposite direction to that arising from a change in fuel cost: if fuel cost
declines due to regulations that force manufacturers to raise vehicle prices, those higher prices
would tend to reduce vehicle sales and thus, ultimately, travel, thereby offsetting some of the
rebound effect. Furthermore, changes in new-vehicle sales would also change scrappage rates
and the price structure of used vehicles of different ages. These effects are not usually considered
part of the "rebound effect", although that is just a matter of definition. Hence they are not
discussed here;1 but they are important to consider as part of the full effects of a regulatory
change.
/*,
In order to distinguish the ultimate effect of both pathways on VMT, we use the symbol M to
designate the combined effect, and designate its elasticity with respect to cost per mile as s^ PM,
reserving the symbol SM PM for the changes operating through the first pathway only. Small and
Van Dender (2007a) show that these quantities are related by:
1 In principle the effect of any specified changes in average new-vehicle price due to regulations could be analyzed
using the results of the vehicle-fleet equation in our model, since that equation includes the variable Pv, which is an
index of nationwide new-car prices. However, the model does not estimate the coefficient of new-vehicle price very
precisely, because there is little variation in that variable (none across states); so we would have less confidence in
using it for that purpose. Probably a better approach for analyzing effects on vehicle purchases would be to consider
the entire range of vehicle sizes and models and how consumers shift between them.
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SM,PM
.
1
where SM, v denotes the direct elasticity of travel with respect to vehicle fleet, SVM denotes the
direct elasticity of vehicle fleet with respect to amount of travel, and SV.PM denotes the elasticity
of vehicle fleet with respect to cost per mile of travel. All the quantities on the right-hand side of
(4) are measured directly as coefficients, or combinations of coefficients, of the three equations
in our model.
In later published work in collaboration with Kent Hymel, the model described above was
extended to account for the interrelationship between travel and congestion, denoted by C and
measured empirically by estimated annual hours of delay due to congestion per adult. To
accomplish this, a fourth equation is added to the model predicting the amount of congestion in a
state, averaged over both its urban and non-urban areas. At the same time, the equation for
vehicle-miles traveled is modified to include an influence from congestion. The expectation is
that more VMT causes congestion to rise, but that rise in congestion also inhibits VMT. The
result of these simultaneous influences is captured by the simultaneous estimation and
application of the VMT and congestion equations.
The result is that in the four-equation model, which includes congestion, equation (4) is modified
by adding an additional term in the denominator:
SM PM
ivi ,rivi
SM,PM
_
M,C
where SM,C is the direct elasticity of VMT with respect to congestion (presumably negative), and
conversely SCM'^ the direct elasticity measuring how congestion is created by VMT (presumably
positive). The combined additional term, -SM,C-SCM is expected to be positive (because the minus
sign cancels the negative sign of SM,C); therefore its presence reduces the magnitude of the
rebound effect. However, Hymel, Small, and Van Dender (2010) find this reduction to be
numerically small, and more than offset by the effects of other changes in the specification of the
model and of including three additional years (2002-2004) in the data used to estimate it.
1.2 Definition of the rebound effect: short-run and long-run
While terminology differs among authors, s^ PM is conceptually what most writers have meant
when discussing the rebound effect. To summarize: it measures the ratio of the responsiveness of
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travelers to the change in fuel efficiency resulting from regulations (with both expressed in
percentage terms), while recognizing that the change in fuel efficiency is not directly set by
regulations but rather results from a complex interactive process. This responsiveness accounts
for both the direct effect of fuel efficiency on the cost of using a given vehicle, and the indirect
effect on travel through changes in the number of vehicles purchased, but all the while holding
average new-vehicle prices constant.
Our analysis, like nearly all in the literature, assumes that this responsiveness to fuel efficiency
arises only through the effect of fuel efficiency on fuel cost per mile. However, this assumption
is debatable and is not inherent in the definition of the rebound effect. Thus, one could posit that
VMT responds to fuel price pp and the exogenous components of fuel efficiency E separately
and not just as a function of their ratio pM^pplE. We explore this question at several points in this
report, but basically are unable to resolve it conclusively.
Because the elasticity s^ PM is expected to be negative, it is convenient to express the rebound
effect bs as a number that is normally positive:
/*,
b" = ~SM,PM (5)
It is also common to express the rebound effect as a percentage rather than a fraction. Thus, if
SM PM =~0-2, we saY the rebound effect is 20%.
The empirical equation systems just discussed also account for the slowness with which changes
can occur, especially changes in the vehicle fleet size and average efficiency, which require
purchases and retirements of vehicles. They are able to do this because we observed a location (a
state or District of Columbia) every year - making the data set a cross-sectional time series,
sometimes also called a panel data set. Slow adjustment is accounted for by assuming that each
of the three behavioral variables explained by the models (M, V, and E) depends not only on the
factors already mentioned, but also on the previous year's value of that same quantity (called a
lagged value of that variable). This is equivalent to assuming that there is a desired level of M, V,
or Fint=l/E, and that any deviation between this desired level and the level attained in the
previous year is diminished in one year by a fraction (1-a), where a is the coefficient of the
lagged value of the variable. We allow a to differ across the three equations and denote its
corresponding values by of", av, and of. Note that congestion formation is an engineering rather
than a behavioral relationship, so no lag is postulated for that equation.
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This slow adjustment process means that the short-run response (that occurring in the same year)
is smaller than the long-run response. Continuing to use the notation s^ PM for the elasticity
determined within this system, it is now a short-run elasticity because the long-run response is
accounted for elsewhere in the equation (through the lagged variables). We represent the
corresponding short-run and long-run rebound effects as bs and 6^, respectively. They are
approximately related by:
(6)
\-am \-am
where d" is the coefficient of the lagged dependent variable in the equation explaining vma. A
more precise relationship accounts for the fact that in the full three-equation and four-equation
systems, the lagged values in more than one equation can affect the long-run response;
specifically, the long-run rebound effect for the three- and four-equation models are:2
-£ = -MfM--
(l-am}-amvavml(l-av)
(\-am-amcacm)-amvavm l(\-av)
where:
• av is the coefficient of the lagged dependent variable in the equation explaining the
logarithm of vehicle stock;
• oTv is the coefficient of vehicle stock in the equation explaining vma;
• avm is the coefficient of vma in the equation explaining vehicle stock;
• (Xmc is the coefficient of congestion in the equation explaining vma;
• acm is the coefficient of vma in the equation explaining congestion; and
• /?2 is the coefficient ofpm in the equation explaining vehicle stock.
In addition to accounting for lagged values within the system determining our dependent
variables, our empirical system accounts for the possibility that the error terms in each equation
are correlated over time. That is, for any given state, the unknown random factors affecting a
dependent variable may have some elements that are the same year after year. Most of these
common factors are accounted for by a "fixed effects" specification, in which a distinct constant
2 See Small and Van Dender (2007a), equation (7); and Hymel, Small, and Van Dender (2010), equation (14a).
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term is estimated for every state instead of just one for the entire system.3 Empirically, the
effects of lagged dependent variables are difficult to distinguish from those of autocorrelation, a
problem plaguing earlier studies investigating changes over time; we are able to distinguish them
because of the long time period covered by our panel data set: 36 years in the 2007 published
paper, 39 years in the 2010 published paper, and 44 years in this report.
There are many ways besides those considered here that regulations on fuel efficiency or related
quantities might affect travel. As already noted, such regulations may raise vehicle prices, which
would affect the vehicle fleet size and thus, indirectly, the amount of travel. Regulations may
affect fuel prices through the impact of aggregate demand for fuel on petroleum markets. They
may influence technological developments, thereby affecting the costs and performance of future
vehicles. A broader analysis of the effects of fuel efficiency on travel might account for such
factors, but they are outside the realm of the "rebound effect" as we define it here and as most
researchers have used the term.4 An advantage of our more restricted definition is that it is a
purely behavioral measure, not depending on supply factors (e.g. the cost to manufacturers of
meeting efficiency standards) or macroeconomic conditions (e.g. the responsiveness of world oil
prices to a particular policy in the US), and thereby more likely to be a stable number applicable
to many situations. However, it is important to be aware that if regulations raise the price of new
vehicles, then the response to that price rise would tend to offset somewhat the rebound effect, as
defined here, by curtailing the number of vehicles available to travelers. Similarly if regulations
curtail U.S. oil demand enough to lower world oil prices and this translates into a lower domestic
gasoline price, some additional travel will be stimulated as a result.
1.3 Dynamic rebound effect
A vehicle owner responds to a change in fuel efficiency not just in the first year or some
hypothetical year in the distant future, but continuously over that lifetime. Thus, the partial
adjustment mechanism postulated here, which is the basis for the distinction between short-run
and long-run responses, implies a continuing gradual change in VMT each year over the
vehicle's life. But at the same time, the driving force itself, i.e. the short-run rebound effect (5),
is changing because the interaction variables that help determine it (income, fuel cost per mile,
urbanization, and possibly congestion) are changing. Thus, the vehicle owner adjusts
3 This is one of two common specifications for panel data, the other being "random effects." A hypothesis test
known as a Hausman test soundly rejects random effects in favor of fixed effects for this data set.
4 Greene (1992) and Gillingham (2011) refer to our definition, combined with any effect due to higher vehicle
prices, as the "direct" rebound effect. This constrast with the "indirect" rebound effect caused by income effects
(people having more money to spend after fuel purchases on other goods that use energy) and the "macroeconomic"
rebound effect (changes in energy use arising from effects of an energy policy on economy-wide prices and growth
rates). See Gillingham (2011, pp. 25-26).
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dynamically to both sources of change simultaneously. The results of tracking this process can
be expressed as the percentage increase in the vehicle's lifetime VMT divided by the percentage
decrease in fuel cost per mile that caused it. That ratio is here called the dynamic rebound effect.
Calculating the dynamic rebound effect requires disaggregating the vehicle fleet by age, even
though that was not done in estimation. Thus, it involves an interpretation of what is happening
within the aggregates in the observed data. Specifically, the calculation relies on the assumption
mentioned earlier that drivers react the same way to a hypothetical difference in fuel cost per
mile whether it occurs at time of purchase or later. It works as follows. Consider the owner of a
vehicle purchased in year t deciding how much to drive in year (t+T). This owner is postulated to
have a target amount of travel based on the average annual mileage for vehicles of age r,
adjusted for the short-run rebound effect as calculated by (5) using values of interacting variables
for year (t+r). Most of these interacting variables (income, urbanization, and congestion) are
simply as projected for that year. The other, fuel cost per mile, is projected based on fuel prices
for year (t+r) but holding fuel efficiency constant at the value that prevailed when the car was
purchased (year r).5
But this target mileage is not achieved immediately, because of the adjustment lags measured by
the coefficient am of the lagged dependent variable in the VMT model. The partial adjustment
mechanism implies that the actual mileage Mt in year t+r will be the weighted average of the
previous year's mileage, Mr-i, adjusted for the natural evolution due to the age-mileage profile
JMT° j, and the target mileage, with weights am and (I -am), respectively:
T-l
where bLt+x is the long-run rebound effect in year M-rfor a vehicle purchased in year t, and MT
is the normal mileage for a car of this age: thus (1 - bLt+r)MT° is the target mileage. The
dynamic rebound effect b° is then the fractional increase in mileage over the car's entire life
that results from a fractional increase 8m fuel efficiency:
5 The underlying hypothesis here is that it is new vehicle owners whose travel changes, and this calculation tracks
how it changes over that and subsequent years. Since the model itself does not distinguish new vehicle owners, the
change in fuel efficiency they experience is diluted by the fuel efficiency of existing used vehicles (assumed
unchanged by the regulations, as discussed earlier). But the resulting change in VMT of new vehicle owners is also
diluted by VMT of existing vehicle owners, so that the ratio which defines the rebound effect still applies to the
aggregates.
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The full calculation is described in somewhat greater detail in Appendix C.
Thus, for example, suppose a regulation in year 2020 results in a fractional increase 8m fuel
efficiency of new vehicles purchased that year. Income is rising and fuel price is falling, starting
in year 2020 and lasting over those vehicles' lifetimes. (Roughly this is what is projected in the
"Low oil price" scenario presented later.) Then the "target" response of VMT to a change in fuel
efficiency for a new vehicle purchased in year 2020 is getting smaller in magnitude as the
vehicle ages, due to the effects of interacting variables. But at the same time the driver is
gradually adjusting to the change that began in that year, meaning the response is shifting
gradually from the short-run response to the long-run response. These two forces work in
opposite directions so the net result could be to either raise or lower the rebound effect; in
practice it usually implies a dynamic rebound effect between the short-run and long-run values.
In effect, this calculation takes account of both the gradual transition from short run to long run
behavior over the life of the vehicle, and the changing values of the rebound effects indicating
changing responsiveness to fuel cost. Iteration of (8) over additional values of r shows that all
the terms in the numerator of (9) are proportional to 8, so the value chosen for £does not affect
the result.
2. Prior Literature
The first part of this section of the report is adapted from the review by Hymel, Small, and Van
Dender (2010), covering literature mostly before 2000—but with the addition of a recent meta-
analysis covering that same literature. The second part updates the review with a discussion of
more recent studies.
2.1 Earlier Literature
Prior research has measured the rebound effect for passenger transport using a variety of data
sources and statistical techniques. Most but not all estimates lie within a range of 10 to 30
percent (expressing the elasticity as an absolute value and as a percentage instead of a fraction).
Greening, Greene, and Difiglio (2000) and Small and Van Dender (2007a) contain more
complete reviews of the earlier literature. A few key contributions are highlighted here.
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The great majority of estimates are based on one of three types of data. The first and probably
least satisfactory is a single time series, either of an entire nation or of a single state within the
U.S. Examples are Greene (1992) and Jones (1993). These studies have difficulty distinguishing
between autocorrelation and lagged effects, and of course suffer from a small number of data
points.
Second, some studies have instead used state-level panel data, most often from the US Federal
Highway Administration (FHWA). Haughton and Sarkar (1996), using such data from 1970-
1991, estimate the rebound effect to be 16% in the short run and 22% in the long run. They
account for endogenous regressors, autocorrelation, and lagged effects. Their study is
comparable in many ways to that of Small and Van Dender (2007), although the latter uses a
longer time period, 1966-2001, and estimates three equations simultaneously explaining VMT,
vehicle stock, and fuel efficiency. Small and Van Dender estimate the rebound effect to be 4.5%
in the short run and 22.2% in the long-run on average, and also find evidence that it has declined
substantially over time due mainly to rising per-capita incomes. Barla et al. (2009), applying the
Small and Van Dender methodology to Canadian data, obtain short- and long-run rebound
effects of around 8% and 20%, respectively. Due to their shorter time series (1990 to 2004) and
more limited cross section (15 provinces), they are not able to investigate changes in these
elasticities over time.
A third type of data is from individual households. Mannering (1986), using a US household
survey, finds that how one controls for endogenous variables in a vehicle utilization equation
strongly influences the estimated rebound effect. He estimates the short- and long-run rebound
effects (constrained to be identical) to be 13-26%. Goldberg (1998) estimates a system of
equations using data from the Consumer Expenditure Survey for years 1984-1990. In a
specification accounting for the simultaneity of the two equations, she cannot reject the
hypothesis of a rebound effect of zero. Greene, Kahn and Gibson (1999) estimate the rebound
effect to be 23% on average using a simultaneous-equation model of individual household
decisions. West (2004), using the Consumer Expenditure Survey for 1997, obtains a somewhat
larger VMT elasticity higher than these other studies, although her focus is mainly on how
behavior differs across income deciles.6
6 West reports an elasticity of VMT with respect to total operating cost (not just fuel cost) of -0.87 in the most fully
controlled specification. Presumably this is a long-run elasticity. If fuel accounted for 50 percent of operating cost,
roughly consistent with Small and Verhoef (2007, p. 97), this would imply an elasticity with respect to fuel cost per
mile of -0.435. As West notes, there are other reasons why this elasticity is not strictly comparable to others in the
literature, one being that it represents a behavior for the entire household with fuel efficiencies (hence fuel cost per
mile) averaged across its vehicle holdings.
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The studies based on individual households in a single cross-section suffer from a limited range
for fuel prices, a key variable for understanding the rebound effect. This disadvantage is partly
overcome by Dargay (2007), who observes repeated cross sections of different individuals in the
UK. She estimates short- and long-run rebound effects of 10% and 14%, respectively, but
suggests that this long-run value may be an underestimate.
Three reviews—Goodwin et al. (2004), Graham and Glaister (2004), and Brons et al. (2008)—
provide systematic statistical analyses of various studies. In the first two, estimated short- and
long-run rebound effects (based on fuel-price elasticities) average about 12 percent and 30
percent, respectively. In the third, which is a meta-analysis of 43 studies containing 176 distinct
elasticity estimates, the implied rebound effects are larger: 17 percent short run and 42 percent
long run for the United States, Canada, and Australia.7 Brons et al. also find that studies using
lagged values have a slightly smaller rebound effect (by about 3 percentage points) than these
values.8 Although the study by Brons et al. separately identifies elasticities of driving per car and
of car ownership, just as we do, they have only three observations of the former and fifteen of the
latter; so in fact their coefficients are mostly identified by variations among studies of total price
elasticity of gasoline consumption, and thus are only an indirect measure of the responsiveness
of driving.
Most of the studies just reviewed agree on long-run elasticities between -0.15 and -0.30 during
the time period of roughly the last third of the twentieth century. In addition, the differences
among the studies point out the importance of model specification. How one deals with
dynamics — by including lagged effects, autoregressive errors, both, or neither — can have a
major impact on results. In particular, omitting such dynamic effects appears to result in over-
estimates of the magnitude of the elasticities in question. In addition, results of US studies are
sensitive to how they account for the influence of the US Corporate Average Fuel Efficiency
(CAFE) standards, which went into effect in 1978.
7 To calculate these numbers we begin with the sums of estimated "baseline" elasticities for kilometers per car and
for car ownership, i.e. columns (3) and (4), as shown in the last two rows of their Table 6, p. 2117. These baseline
estimates are defined as the values predicted by their meta-analysis model with all dummy variables taking their
most common value. This results in is short-and long-run driving elasticities of-0.331 and -0.581 percent,
respectively. The model includes a dummy variable "UCA" for studies in the US, Canada, or Australia, whose most
common value is zero; so we add the sum of columns (3) and (4) for the coefficient of UCA, which is +0.165,
resulting in elasticities of -0.166 and -0.416, respectively. There is considerable uncertainty around these values, as
the standard error of the coefficient of UCA in the equation predicting kilometers per car is very large (0.480).
8 This statement is based on the sum of coefficients of the dummy variable "Dynamic" in columns (3) and (4) of
their Table 6; that sum is 0.027.
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2.2 Recent Literature
More recent literature has extended this work in several directions, especially paying close
attention to the means of identification and controls for bias due to omitted variables. Particularly
relevant to this report are studies seeking to determine whether the determinants of the rebound
effect or of the price-elasticity of gasoline have changed in the decade starting in 2000. (We refer
to such changes as structural change, meaning changes in the manner in which underlying
factors influence the elasticities, as opposed to simply changes in those factors themselves.)
Because that decade is characterized by more closely spaced price fluctuations than has been
typical, observers have sometimes noted substantial changes in behavior.
Brand (2009) summarizes some simple calculations of the VMT- and price-elasticities with
respect to fuel price, based on observations before and after a sharp increase in fuel prices:
specifically, by comparing the first ten months of 2007 and the first ten months of 2008. A
calculation based on U.S. national statistics yields a short-run VMT-elasticity of-0.12. This
involves no controls, and Brand points out that VMT was trending upward at 2.9% per year over
a prior 21-year period of relatively stable prices, which to us suggests a correction to this
elasticity of-0.029, bring it to approximately -0.15.9
Hughes et al. (2008) undertake a more detailed analysis, using models with some control
variables, to compare the price-elasticity of gasoline in the years 1975-80 with that in the years
2001-06. They find a large decline in magnitude, from -0.21 to -0.08 in what appear to be their
favored specification. In the case of the later period, that specification treats fuel price as
endogenous, estimating it with instrumental variables in a standard manner that accounts for
price being determined simultaneously by demand and supply relationships. This finding
suggests that the VMT elasticity declined by a similar amount, since it is a component of the
fuel-price elasticity and no one has suggested that the other main component (the elasticity of
fuel efficiency) has been demonstrated to change significantly.
Hughes et al. also test whether the price-elasticity declines in magnitude with income, as found
by Small and Van Dender (2007) and Hymel et al. (2010). They find instead an effect in the
opposite direction. Thus, they explain the decline in price elasticity as likely due to factors other
than those we suggest here. Specifically, they cite suburbanization and declining public transit
service, both of which lock travelers more firmly into automobile use, and increased fuel
efficiency, which is also consistent with one of the findings of Small and Van Dender (2007) and
9 Brand asserts without explanation a different number, -0.21, for the VMT elasticity accounting for the trend.
Litman (2010, abstract) cites Brand and an unpublished study by Charles Komanoff as supporting an elasticity of
-0.15.
13
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Hymel et al. (2010). Interestingly, Litman (2010) cites these same factors in a heuristic argument
for an opposite argument: Litman suggests these factors were strong during the 1970-2000
period but likely less important during the 2000's. We have not seen any formal argument, either
theoretical or empirical, for why these factors should have a major effect in either direction.
There are some limitations to the Hughes et al. results which make them less than decisive. The
limitation to a single five-year period for each estimation reduces the precision of their estimates
compared to ones that use longer time series. Also, they do not account for a full range of
dynamic effects, as we think is especially necessary to fully capture behavior in the rapidly
changing 2000-2006 period.10
Greene (2012) carries out a number of analyses similar to those of Small and Van Dender
(2007), using national rather than state data but extending the sample to year 2007. Greene
confirms several results of Small and Van Dender: in particular, he finds a similar value for the
price-elasticity of VMT, finds that it has declined over time, and finds that it declines with
income.
Two recent studies make use of odometer readings from California's smog test—arguably the
most accurate available measure of VMT—to provide estimates of the elasticity of VMT with
respect to either fuel price or fuel cost per mile, both using very large samples of individual
vehicles. The first, by Knittel and Sandier (2012), takes advantage of the existence of regions in
which older vehicles must take a smog test every two years. They use test data from 1998
through 2010 and a simple log-log specification, with control variables for demographics and
whether the vehicle is a light truck, and with fixed effects representing year, vintage, and make.
Knittel and Sandier interpret the resulting elasticities as covering a time period of two years,
since that is the time interval over which VMT is measured. The estimates of VMT elasticity
with respect to fuel cost per mile vary between -0.14 and -0.26, depending on whether or not the
make is subdivided further in defining fixed effects.11
The second study using California smog test data is by Gillingham (2013). Gillingham combines
the test data for years 2005-2009 with micro observations of new-vehicle registrations in 2001-
2003, in order to observe VMT over a several-year period, typically six or seven years due to the
10 To be more precise, they do not include lagged endogenous variables or autocorrelation in any of what we would
consider their preferred model results, namely those using instrumental variables to control for simultaneity between
supply and demand factors.
11 These numbers are the range of coefficients of log (dollars per mile) in Table 18.3 for Models 2, 4, and 5. In other
models, the authors find heterogeneity with respect to the size of the dollars per mile variable. They explore
heterogeneity further in a more recent working paper, in which they find the VMT elasticity to vary between -0.11
and -0.18 across quartiles of fuel efficiency (Knittel and Sandier 2013, Table A.2, next to last column).
14
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requirement that vehicles are tested at those ages. (There are also some observations over four to
six years for vehicles that are sold before six years have passed.) He finds an elasticity of VMT
with respect to gasoline price of-0.25, a finding quite robust to various specification checks.
Gillingham interprets this as roughly a two-year elasticity, because it is identified mainly by a
price spike between 2007 and 2009. This means of identification is also a weakness of the study:
during this same time interval the economy entered the most significant recession since the
1930s, accompanied by drastic turmoil in housing markets including foreclosures requiring many
people to move. Despite controlling for macroeconomic conditions through a measure of
unemployment and a consumer confidence index, one must worry that gasoline prices are
correlated with unobserved factors related to tumultuous economic conditions that also influence
the amount of driving.
The two studies just described have the advantage of very large samples of individuals,
permitting greater precision in estimation as well as accounting for heterogeneity across
individuals. Both studies also assume that VMT responds to contemporaneous gasoline prices,
without explicit lags. Yet the suggestive evidence shown by Knittel and Sandier, comparing
graphs of gasoline prices and VMT over time, appears to show a one to two year lag. As already
noted, our analysis of earlier studies suggests that omitting such dynamic effects may cause the
estimated elasticities to be somewhat larger in magnitude than the true short-run (or even two-
year) elasticities, especially when the observations are averaged over periods of more than a year
as is the case in both of these studies.
Molloy and Shan (2010) provide an intriguing look at one possible source of VMT response to
fuel price: changes in household location. They analyze how housing construction within small
areas responded to fuel prices over the period 1981 to 2008.12 Their model includes lags up to
four years, which they found sufficient to account for virtually all the observed responses. Their
results imply that a one percent increase in gasoline price reduces construction over the next four
years by one percent, which is 0.03 percent of the total housing stock (Table 2). This result
suggests one possible explanation for why Small and Van Dender (2007) and Hymel et al. (2010)
find substantial lags in the response of VMT to changes in fuel cost.
Our conclusion from the more recent literature is that it raises the strong possibility that the
rebound effect has become larger during the 2000s. But not enough time has passed to allow
definitive tests, especially because other factors were changing so drastically during that same
time period. Our response to this situation in our own study is twofold. First, we investigate
explicitly whether there is a structural break in the determinants of VMT during the decade
2000-2009. Second, we consider some other explanations for changes in behavior over this time:
12 The areas are "permit-issuing places, which are usually small municipalities" (Molloy and Shan 2010, p. 5).
15
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specifically, asymmetries between response to rising and falling gasoline prices, and possible
behavioral responses to intense media attention to fuel prices.
2.3 Is the rebound effect the same as the responsiveness to price of fuel?
As noted in Section 1.2, one can challenge the assumption that people respond with the same
elasticity to fuel price and to the inverse of fuel efficiency. This assumption is prevalent both
because it is theoretically attractive, based on full consumer rationality, and because it is difficult
to separate the two effects empirically. Nevertheless, only a few studies have tested the
assumption and the evidence for it is not very solid.
Small and Van Dender (2007) and Hymel et al. (2010) both report attempts to estimate models
where fuel pricepp and efficiency E are entered as separate variables. They find that the
measurement of a separate coefficient for E1 is very small but too imprecise to use with
confidence for policy analysis. They interpret their findings as ambiguous, but acknowledge that
they are unable to prove that the rebound effect, defined as the elasticity with respect to E, is not
zero.
Greene (2012, Tables 4-5), using a long time series (1967-2007) of aggregate US data, is
similarly unable to estimate the two elasticities separately with much precision, obtaining a
small, statistically insignificant, and wrong-signed coefficient for fuel consumption per mile (the
inverse of fuel efficiency). Nevertheless, in contrast to the two papers just described, he is able to
statistically reject the hypothesis that the coefficients are equal.
Gillingham (2011, table 3.1) similarly tests whether the two coefficients can be separately
estimated, using his very large disaggregate data set. When model-specific fixed effects are not
included, he is able to separately measure the two elasticities, finding them equal to -0.19 for fuel
price and -0.05 for the inverse of fuel efficiency, both statistically significant. This again
suggests they are not equal, and that the elasticity with respect to inverse fuel efficiency may
actually be considerably smaller in magnitude than the that with respect to fuel price. In some
other specifications, the elasticity with respect to fuel efficiency is small and statistically
insignificant, as in the studies just discussed.13
13 In other work, Gillingham also measures a rebound effect using a much more elaborate model which includes
both vehicle purchase and utilization. He obtains a very small value, equal to 0.06 (i.e. 6 percent) multiplied by the
fraction of people who choose a different vehicle when faced with a hypothetical new set of vehicles offered
following a feebate policy (Gillingham 2011, Section 4.4.3).
16
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While these studies are too few and statistically imprecise to resolve the question definitively,
together they strongly suggest that the effect of fuel efficiency is smaller than that of fuel price,
and possibly very small indeed. Therefore, by adopting the conventional assumption that their
effects are equal and opposite, this study reports rebound effects that may well be larger in
magnitude than those that actually occur when policies are implemented.
3. Data and specification for this report
The data set used here is a cross-sectional time series, with each variable measured for 50 US
states, plus District of Columbia, annually for years 1966-2009. Variables are constructed from
public sources, mainly the US Federal Highway Administration, US Census Bureau, and US
Energy Information Administration. Data sources and a fuller description, including some
weaknesses of the data, are given in Small and Van Dender (2007a,b) and Hymel, Small, and
Van Dender (2010).14 In addition, we have collected variables on media attention to gasoline
prices and on volatility of gasoline prices, as described in Section 3.4.
In the following we list the primary variables used in the statistical estimation. All the dependent
variables, and many others as well, are measured as natural logarithms. Variables starting with
lower case letters are logarithms of the variable described. All monetary variables are real (i.e.
inflation-adjusted).
Dependent Variables
M Vehicle miles traveled (VMT) divided by adult population, by state and year (logarithm:
vma, for "vehicle-miles per adult").
V: Vehicle stock divided by adult population (logarithm: vehstock).
HE: Fuel intensity, F/M, where F is highway use of gasoline15 (logarithm: flnf).
C: Total hours of congestion delay in the state divided by adult population (logarithm: cong).
See Section 3.1 for further details
14 Greene (2012, p. 18) provides an excellent discussion of the VMT data and their weaknesses. He concludes that
the errors that may occur in the FHWA data on VMT and fuel efficiency are unlikely to cause large errors in year-
to-year changes, which are what are used in both this and Greene's study.
15 This term is used by FHWA to mean use by vehicles traveling on public roadways of all types. It excludes use by
not licensed for roadways, such as construction equipment and farm vehicles.
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Independent Variables other than CAFE
PM'. Fuel cost per mile, PplE. Its logarithm is denotedpm = \n(Pp)-\n(E) = pf+fmt. For
convenience in interpreting interaction variables based onpm, we have normalized it by
subtracting its mean over the sample.
Py. Index of real new vehicle prices (1987=100) (logarithm: pv). 16
PF: Price of gasoline, deflated by consumer price index (1987=1.00) (cents per gallon).
Variablepfis its logarithm normalized by subtracting the sample mean.
Other: See Small and Van Dender (2007b), Appendix A; and Small, Hymel, and Van Dender
(2010), Appendices A and B. The first three equations include time trends to proxy for
unmeasured trends such as residential dispersion, other driving costs, lifestyle changes, and
technology. As described below, in equation (8), the set of variables denoted XM includes
the variable (pm)2 and interactions between normalized pm and other normalized variables:
log real per capita income (inc\ and fraction urbanized (Urban - used only in the three-
equation model) and normalized cong (used only in the four-equation model).
Each of these variables is updated to 2009 using the same or similar source as before. However,
in several cases, the responsible agency has revised the numbers for earlier years. We have taken
advantage of these revisions in the updated data series. In order to facilitate comparisons with
earlier years, we also use two other data series in this report, making three in all:
• "Original" data: those used for the earlier published reports, along with 2005-2009 values
that employ as closely as possible to the same methodology as used earlier. (Only values
through 2001 or 2004 are used for estimation; the purpose of the 2005-2009 values in this
data series is only for projection.)
• "Revised" data: those incorporating the data revisions just mentioned, including two
described in Sections 3.1 and 3.2 below, viz.: (a) smoothing of 2000-2010 population,
and (b) substitution of improved congestion data. The term "revised" implies that only
values through 2001 or 2004 are used for estimation.
• "Updated" data: like "Revised," but including data through 2009.
Appendix A shows summary statistics for the data used in our main specification. The next three
sections explain special features of certain important variables.
16 We include new-car prices in the second equation as indicators of the capital cost of owning a car. We exclude
used-car prices because they are likely to be endogenous; also reliable data by state are unavailable.
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3.1 Congestion variables (four-equation model)
This description is adapted from Hymel, Small, and Van Dender (2010). The measure of travel
delay uses data from the annual report on traffic congestion constructed by the Texas
Transportation Institute (TTI) — see e.g. Schrank, Lomax, and Turner (2010). TTI has estimated
congestion annually for 85 large urbanized areas, starting in 1982, using data from the Highway
Performance Monitoring System database of the US Federal Highway Administration.
The TTI measure of congestion used here is annual travel delay, which is simply the aggregate
amount of time lost due to congested driving conditions. TTI has sometimes been criticized for
using this measure as an index of the nation's congestion problem because it includes congestion
that would remain in an optimized system. Irrespective of the validity of this criticism, for our
purposes the TTI measure is appropriate because it describes the experience of the typical driver.
The measure is constructed largely from assumed speed-flow relationships, but supplemented
with speed observations on specific roads. As with other data in this study, it is probably more
reliable in the more recent years.
One criticism of the TTI measures, however, has been addressed in TTI's 2010 edition of its
report. The earlier measure, used in the cited papers by Small and Van Dender and by Hymel,
Small, and Van Dender, estimated speed from observed traffic volumes using volume-delay
relationships. This inevitably introduced some error into the speeds, hence into the estimated
total hours of delay. Recently, however, TTI has collaborated with Inrix®, Inc., to make use of
speed data collected via a nationwide network of mobile devices in vehicles. These measures are
available for a few most recent years, but TTI has back-casted them to 1982 in order to permit
comparisons with its earlier measure. They are also available for an additional 26 urban areas.
All these changes increase the accuracy of the data on congestion, and so are adopted here except
in the "original" data series.
For the collaborative work described earlier and for this report, congestion delays in all covered
urbanized areas are aggregated to the level of a state, then divided by the state's adult population
to create a per-adult delay measure. This procedure implicitly assumes that congestion outside
these 85 urban areas is negligible, a reasonable assumption because congestion in the US is far
more costly to drivers in large than in small urban areas. Furthermore, since data are measured at
the state level, it is appropriate that the congestion in the larger urbanized areas is, for most
states, diluted by the lack of congestion elsewhere in our equations predicting statewide travel
response. A further advantages of the use of total delay, rather than some measure of average
congestion, is that it is relatively unaffected by possible differences in how boundaries are drawn
for urban areas in different states.
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3.2 State population data
Several variables specification, including all but one of the endogenous variables, make use of
data on adult or total state population as a divisor. Such data are published by the U.S. Census
Bureau as midyear population estimates; they use demographic information at the state level to
update the most recent census count, taken in years ending with zero. However, these estimates
do not always match the subsequent census count, and the Census Bureau does not update them
to create a consistent series. As a result, the published series contains many instances of
implausible jumps in the years of the census count. In both of the published papers discussed
above, we applied a correction assuming that the actual census counts taken every ten years are
accurate, and that the error in estimating population between them grows linearly over that ten-
year time interval. This approach is better than using the published estimates because it makes
use of Census year data that were not available at the time the published estimates were
constructed (namely, data from the subsequent census count). See Small and Van Dender
(2007b) for details.
For this report, the same procedure was applied to the 2000-2009 data because the needed
Census counts for 2010 were available in time. This adjustment appears in the "revised" and
"updated" data series, but not in the "original" data series.
3.3 Variable to measure CAFE regulation (RE)
As in the earlier collaborative work, we define here a variable measuring the tightness of CAFE
regulation, starting in 1978, based on the difference between the mandated efficiency of new
passenger vehicles and the efficiency that would be chosen in the absence of regulation. The
variable becomes zero when CAFE is not binding or when it is not in effect. In our system, this
variable helps explain the efficiency of new passenger vehicles, while the lagged dependent
variable in the fuel-intensity equation captures the inertia due to slow turnover of the vehicle
fleet. Because the CAFE standard is a national one, this variable does not vary by state.
The calculation proceeds in four steps, described more fully in Small and Van Dender (2007a),
Appendix B. First, we estimated a reduced-form equation explaining log fuel intensity from
1966-1977, prior to CAFE regulations.1? Next, this equation is interpreted as a partial adjustment
model, so that the coefficient of lagged fuel intensity enables us to form a predicted desired fuel
intensity for each state in each year, including years after 1977. Third, for a given year, we
averaged desired fuel intensity (in levels, weighted by vehicle-miles traveled) across states to get
17 This step differs slightly between the three- and four-equation models because they contain slightly different sets
of exogenous variables. Thus, the actual values of the variable cafe differ slightly between the two models.
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a national desired average fuel intensity. Finally, we compared the reciprocal of this desired
nationwide fuel intensity to the minimum efficiency mandated under CAFE in a given year
(averaged between cars and light trucks using VMT weights, and corrected for the difference
between factory tests and real-world driving). The variable cafe is defined as the logarithm of the
ratio between the mandated and desired fuel efficiency, with that ratio truncated below at one.
Thus a value of zero for cafe means the constraint is not binding, since desired fuel efficiency is
as high as or higher than the mandated level.
The resulting variable suggests that the CAFE standard was strongly binding for the first decade
of the CAFE standards; its tightness rose dramatically until 1984 and then gradually diminished
until it was stopped being binding at all, either in 1995 (according to the 4-equation model) or
2005 (according to the 3-equation model).18 This pattern is obviously quite different from a trend
starting at 1978 and from the CAFE standard itself, both of which have been used as a variable in
VMT equations by other researchers.
Implicit in the definition of the regulatory variable is a view of the CAFE regulations as exerting
a force on every state toward greater fuel efficiency of its fleet, regardless of the desired fuel
efficiency in that particular state. Our reason for adopting this view is that the CAFE standard
applies to the nationwide fleet average for each manufacturer; the manufacturer therefore has an
incentive to use pricing or other means to improve fuel efficiency everywhere, not just where it
is low.
3.4 Variables on media coverage and volatility of gasoline prices
Variables measuring media coverage of gasoline price changes are based upon gas-price related
articles appearing in the New York Times newspaper. We queried the Proquest historical database
for years 1960 to 2009, and tallied the annual number of article titles containing the words
gasoline (or gas) and price (or cost). This count was the basis for the variable used in the
econometric analysis: it is formed from the annual number of gas-price-related articles divided
by the annual total number of articles, both in the New York Times. This ratio ranged from
roughly 1 in 4000 during the 1960s to a high of 1 in 500 in 1974. An analogous count of front-
page articles yielded a similar pattern of coverage. Its logarithm, after normalization by
subtracting its mean, is shown in 3.1. In our specifications, we use either the logarithm of the
ratio just defined (called Media in the statistical models) or a dummy variable (called
Media dummy) defined as one in years where the ratio was greater than the 1996-2009 median
: See Small and Van Dender (2007a), Fig. 1, for a graphical depiction.
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value and zero otherwise.
19
Figure 3.1. Media coverage of gas prices
N^
A superior measure of media coverage would include broadcast news, other newspapers, radio,
and the Internet. But such measures are not readily available for the entire the time series from
1960-2009. So the validity of the two variables as a measure of overall coverage of gasoline
prices relies in part on the New York Times' influence on other media outlets. Evidence of so-
called "inter-media agenda setting" suggests that other media outlets follow the New York Times
when choosing their news topics. One study by Golon (2006) found that the topics covered by
the New York Times in the morning were correlated with evening broadcast news coverage
topics, with correlation coefficients between 0.14 and 0.26. In addition, it is reasonable to
assume that national topics such gas-price changes would be similar across news outlets even in
the absence of direct influence of the New York Times.
19This dummy variable was equal to one in years 1973-1981, 1983, 1990-1992, 1994-1997, 2000, 2004-2006, and
2008.
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To measure uncertainty in fuel prices, we constructed a variable whose value in year t is the
logarithm of the variance of fuel prices over the years t-4 through t. (We chose this five-year
interval as the most likely time over which new vehicle purchasers would be aware of volatility.)
This measure varies across States.
For both the media and uncertainty variables, we interact the variable in question with either the
fuel price or the per-mile cost of driving.
4. Results of the Empirical Analysis
A major limitation of the previous literature is its inability to determine whether or not the
rebound effect has changed over time. Theoretical arguments, especially by Greene (1992),
suggest that it should. Basically, the argument is that the responsiveness to the fuel cost of
driving will be larger if that fuel cost is a larger proportion of the total cost of driving. If initial
fuel cost is high, that increases the proportion; but if the perceived value of time spent in the
vehicle is high, either because of congestion (closely related to urbanization) or because of a high
value of time (closely related to income), that decreases the proportion. Thus we expect the
rebound effect to increase with increasing initial fuel cost, and decrease with increasing income
and urbanization. On the few occasions when such factors are even discussed, most analysts have
presumed that income is the dominant one and therefore have hypothesized a decline in the
rebound effect over time, due to rising real incomes. Previously used data sets, however, have
covered too short a time span to test any of these arguments satisfactorily.20
With the longer time span of the data sets compiled for the earlier collaborative papers, and the
even longer data set used here (44 years), there is a much better opportunity to see such changes.
We explore them in three distinct ways. First (Section 4.1), we see whether the basic model,
estimated over different time periods but each with a constant rebound effect, yields different
results. We find a substantial diminution in the rebound effect in the period since 1995; it's
harder to say whether it has risen again since 2000.
Second (Section 4.2), we explore income, fuel costs, urbanization, and congestion as the causes
of these changes. Each of these factors is entered in the model in such a way that the rebound
20 A recent exception is two studies by Wadud, Graham and Noland (2007a, 2007b) using time-series cross sections
of individual households from the US Consumer Expenditure Survey. Cross-sectionally, they find a U-shaped
pattern of the absolute value of the price elasticity of fuel consumption, taking values of 0.35 for the lowest income
quintile, falling to 0.20 for the middle, and rising again to 0.29 for the highest (2007b, Table 2). But when they hold
other variables constant while allowing income to vary both cross-sectionally and over time (1997-2002), they
obtain a nearly steady, though small, decline of the absolute value of elasticity with income, from 0.51 in the lowest
two income quintiles to 0.40 in the highest.
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effect can vary with it rather than varying over time in an unexplained manner, and we do indeed
find substantial variation in exactly the manner predicted by theory: the rebound effect
(measured as a positive number) declines with increasing income (as well as with either
urbanization or congestion), and it increases with increasing fuel cost. By far the most important
of these sources of variation is income, which has a profound effect on projections for the
rebound effect in future years. In Section 4.3, we consider explicitly how the newer data now
available (2002-2009) affect the results from the earlier published studies.
Third (Section 4.4), we consider asymmetry in the response to increases and decreases in fuel
prices, finding a much larger response to increases. We also consider the possible role of media
coverage and price volatility in explaining this asymmetry.
4.1. Variation by Time Period
This section presents the results of estimating a relatively simple version of the three-equation
system described earlier. In this version, the variable/™ (the logarithm of fuel cost per mile) is
simply included in the equation explaining vma (the logarithm of vehicle-miles traveled per
adult). Its coefficient, the "structural elasticity," is the elasticity of VMT with respect to fuel cost
per mile, holding vehicle fleet constant. Accounting for how the vehicle fleet also varies with
fuel cost, and how lagged adjustment creates differences between short-run and long-run
responses, we get the short- and long-run rebound effects from equations (4), (5), and (7).
In order to see whether the rebound effect changes over time, we carry out this estimation on two
subsamples: 1966-1995 and 1996-2009. Table 4.1 shows the estimated structural elasticity
SM PM . As described earlier, these are nearly identical (except for the minus sign) to the short-run
rebound effects, and their values come immediately from the estimated results. The table shows
that the short-run rebound effect falls by 46 percent and 72 percent, without and with
consideration of congestion respectively, between these two time periods.
Table 4.1. Short-run structural elasticity of VMT with respect
to fuel cost per mile, estimated on subsamples
Coefficient of pm
(standard error in
parentheses)
Three-equation model
Four-equation model
1966-1995
-0.0458
(0.0037)
-0.0469
(0.0058)
1996-2009
-0.0246
-0.0071
-0.0131
(0.0075)
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This result of a falling rebound effect is consistent with results noted earlier by Hughes et al.
(2008) and Greene (2012).
4.2. Variation of rebound effect with income, fuel cost, and other variables
4.2.1 Motivation
Before proceeding with the formal estimation, we motivate the approach taken here by
considering what goes into the costs of automobile travel from the traveler's point of view.
Figure 1 shows three categories of the short-run costs of driving and how they are likely to
progress over coming decades, based on compilations of Small and Verhoef (2007) for an urban
commuting trip by automobile.21 The values placed by travelers on travel time and unreliability
22are taken from statistical literature examining how people are willing to trade off those factors
against money. We have then projected fuel costs per mile into the future, using the Energy
Information Administration's projections for fuel prices and fuel efficiency in their 2011
reference scenario (US EIA 2011). We have projected the values of travel time and unreliability
into the future by assuming that the amounts of time and unreliability are unchanged (a
conservative assumption given trends toward increased congestion) while the values of time and
unreliability increase with rising per capita real income according to an elasticity of 0.8, a
recommendation of Mackie et al. (2003) based on many studies of how value of time depends on
income (Small and Verhoef 2007, Section 2.6.5).
21 The initial values are for 2005, taken from Small and Verhoef (2007, Table 3.3) and restated at 2007 prices.
22 In this context, unreliability refers to day-to-day variability in the travel time faced for a given type of trip. It is
typically measured by the standard deviation of travel time across days, although sometimes other measures of
dispersion (such as the difference between the 80th and 50th percentiles) are used instead. Its presence means that
people cannot accurately predict when they will arrive at their destination. There is a substantial literature, reviewed
by Small and Verhoef (2007), showing that travelers are averse to unreliability independently of their aversion to
travel time.
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100
Figure 4.1.
Costs of Driving
Other Costs
I Travel Time and
Unreliability
I Fuel Cost
2005
2015
2025
Thus, it appears that despite the general prognosis for rising fuel prices, the actual fuel costs are
likely to decline, due mainly to increases in fuel efficiency of automobiles; and the prominence
of fuel costs in drivers' decisions is likely to decline even more, due to increases in the value of
time (and, to a lesser extent, to amount of time spent in heavy congestion). Our econometric
model can capture these possibilities by simply specifying it in a way that allows the rebound
effect to vary with income, fuel cost per mile, and other variables that may impinge on travel
time: namely, urbanization and congestion.
4.2.2 Implementation
To see how this can be done, recall from Section 1.1 that the rebound effect is a combination of
elasticities of either three or four distinct equations (known as "structural equations"). Because of
the relative sizes of these elasticities, the rebound effect is approximated by just one of them:
namely SM,PM, giving the effect of fuel cost per mile in the structural equation for vehicle-miles
traveled per adult. In the notation used here, which uses lower-case names for variables that are
expressed in natural logarithms, that elasticity is given by equation (3), i.e. SM,PM =
d(vmd)ld(pm).
In the previous subsection, fuel cost per mile was described as a single variable (pm in
logarithmic terms) included in the equation for vehicle-miles traveled per adult (vma in
logarithmic terms). The elasticity was just its coefficient, which we may call (3pm for
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convenience.23 But it is easy to specify the equation for vma so thatpm appears not only as a
single variable, but also interacted with other variables including itself. We define four such
variables: pm-inc,pm-pm=pm2,pm-Urban., andpm-cong, where inc is the logarithm of per capita
real income, Urban is the fraction of state population that is urbanized, and cong is congestion as
measured by the logarithm of total congestion delay per adult. We denote the coefficients of
these four "interacted variables" by fa, fa, fa, and fa. In practice, fa is set to zero in the three-
equation system (since cong is not measured there), and fa is set to zero in the four-equation
system (since its estimates were small and statistically insignificant).
Then the derivative in (3) consists of four terms:
S
= Ppm + A • inc + 2f32 -pm + fa- Urban + (34 • cong . (8)
M PM =
o(pm)
The factor 2 in this equation is a consequence of properties of the derivative of the quadratic
function (pm)2. Inserting (8) into equations (4) and (7) for the short- and long-run rebound
effects, we see that that those rebound effects also depend on inc,pm, Urban, and cong.
In order to facilitate interpretation of coefficients, we "normalize" the values ofinc,pm, Urban,
and congby subtracting from each variable its mean value over our entire data set. This has no
effect on the coefficients except to change the constant terms in the equations; but it means that
the coefficient (3pm of the variable pm still gives the estimated elasticity SM,PM at the point where
each of the interacting variables is equal to its mean value in our data set - as can be seen by
setting the three normalized variables in (8) to zero. This is especially convenient because the
short-run and long-run rebound effects are approximately -SM,PM and -SM,PM /(l-d"), respectively,
where a™ is coefficient of lagged vma in the vma equation. Thus, one can see the approximate
value of the estimated short- and long-run rebound effects, under average conditions over the
sample period, just by looking at -(3pm and cT.
4.2.3 Estimation results: interaction variables
The models are estimated using the maximum-likelihood simultaneous-equations estimator in
Eviews 5 (Quantitative Micro Software 2004). Technical details are provided in Small and Van
Dender (2007a) and Hymel, Small, and Van Dender (20 10).24 The full results of estimating the
23 This coefficient is named 0™ in Small and Van Dender (2007), eqn. (4) and Hymel et al. (2010), eqn. (9a).
24 For this report, however, we have replaced the multiple imputations for the missing data by a single imputation;
that is, we predict the values of the missing data only once, rather than multiple times using random draws from the
27
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three- and four-equation models on updated data from 1966 through 2009 are presented in
Appendix A; some of the most important coefficients are summarized here in Table 4.2.25
equation estimating them. For this reason, our estimates of standard errors probably understate the true standard
errors.
25 For reasons that will be explained in the next section, these models are named "Model 3.3" and "Model 4.3"
respectively. For simplicity, coefficient estimates and standard errors are shown to three decimal places in these
tables. In some later tables, they are shown to four decimal places.
28
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Table 4.2.
, Selected results of main model with updated data, 1966-2009
Three-equation model
Equation and
Variable
Equation for
vma:
pm
pm*inc
pm2
pm* Urban
pm*cong
inc
lagged vma
Equation for
fint:
pf+vma
cafe
\aggedjint
Coefficient
Symbol
Ppm
fr
fr
fr
A
oT
of
(Model
Coefficient
Estimate
-0.047
0.053
-0.012
0.012
0.078
0.835
-0.005
-0.035
0.904
3.3)
Standard
Error
0.003
0.011
0.006
0.009
0.012
0.010
0.004
0.011
0.010
Four-equation model
(Model
Coefficient
Estimate
-0.046
0.056
-0.022
-0.003
0.083
0.825
-0.007
-0.061
0.889
4.3)
Standard
Error
0.003
0.011
0.006
0.002
0.012
0.010
0.004
0.010
0.010
Notes to Table 4.2:
vma = logarithm of vehicle-miles traveled per adult
pm = logarithm of fuel cost per mile (normalized)
inc = logarithm of income per capita
Urban = fraction of population living in urban areas
cong = logarithm of annual total congestion delay per adult
fint = logarithm of fuel intensity, i.e. log (HE) where E = fuel efficiency
pf= logarithm of fuel price
cafe = variable reflecting how far the CAFE standard is above the desired fuel
efficiency based on other variables (Small and Van Dender 2007a,
Section 3.3.3)
pf+vma is log (price of fuel * vehicle-miles traveled), representing the natural
logarithm of the incremental annual fuel cost of a unit change in fuel
intensity; thus it may be interpreted as the logarithm of the "price" the
user must pay in annual operating costs, per unit of fuel intensity, for
choosing a vehicle with higher fuel intensity.
29
-------
Most coefficients shown in Table 4.2 easily pass the conventional test of statistical significance,
having estimates more than twice the standard deviation of those estimates. Exceptions are (34,
which indicates how the rebound effect varies with congestion, and the coefficient of annual fuel
cost (pf+vma in logarithms) in the equation explaining fuel efficiency. The coefficients of of
lagged vma show that the long-run effect of any variable on VMT is about \K\-d"} or roughly
six times as large as the corresponding short-run effect. Average fleet fuel efficiency responds to
changes with an even longer lag, causing the long-run effects of these variables to be \l(\-cf) or
roughly 9-10 times as large as the corresponding short-run effects.
The coefficient of inc confirms the conventional expectation that vehicle-miles traveled rises
with rising income: the income-elasticity is approximately 0.1 in the short run and 0.5 in the long
run. CAFE standards are shown to be important determinants of average fleet fuel efficiency.
Another way to interpret this is that each year, fleet turnover and/or changes in driving patterns
are able to close (\-cf), or around ten percent, of the gap between the fuel intensity desired this
year (on the basis of variable in the model) and that achieved by the previous year's fleet.
Taking the three-equation model (Model 3.3) for illustration, the short-run rebound effect for
average conditions in this sample (1966-2009) is approximately -/?pm=0.047, i.e. 4.7%, while the
long-run rebound is over six times this value, or about 30%. Furthermore, the coefficients (3\-fh,
for the three interacted variables involving pm show that the magnitude of the rebound effect,
given approximately by the negative of equation (8), declines with increasing income and
urbanization and increases with increasing fuel cost of driving.
To get a better idea of the magnitude of this dependence, we show in Table 4.3 the estimated
rebound effects, computed more precisely using equations (4), (5), and (7), at two different sets
of values for the explanatory variables inc,pm, and Urban. One set consists of the average
values over the sample and the other consists of the average values over the last ten years of the
sample. Under average conditions over the entire sample period, the measured rebound effect is
4.7% short run and 29.5% long run. However, these values are found to fall by nearly half when
we consider conditions in 2000-2009: over those years the rebound effect on average is just 2.8%
short run and 17.8% long run. An examination of the detailed components of the calculation (not
shown in the table) reveals that it is mainly higher incomes that cause the rebound effect to be
lower in the most recent decade than in the entire sample period, although the lower fuel cost per
mile also plays a significant role.
30
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Table 4.3. Estimated Rebound Effects: Model 3.3
Average values (real 2009 $)
Per capita income ($/year)
Fuel price ($/gal)
Fuel cost per mile (cents/mi)
Calculated rebound effect:
Three-equation model (w/ congestion)
Four-equation model (w/o congestion)
1966-2009
$28,452
2.06
11.75
Short run Long run
4.7% 29.5%
4.6% 28.4%
2000-2009
$36,805
2.18
9.77
Short run Long run
2.8% 17.8%
2.5% 15.0%
The decline in the rebound effect portrayed in Table 4.3 is consistent with the overall findings of
Section 4.1. But now we have an explanation for why the rebound effect is lower today than in
the last decades of the previous century. Furthermore, the measured dependence on income, fuel
cost, and other variables permits a calculation of both short-run and long-run rebound effects at
any level of those variables. In Section 5 we take advantage of this to forecast rebound effects
through 2035, based on outside projections of the relevant variables, especially incomes and fuel
costs.
To our disappointment, the additional years of data do not change the fact that, as discussed in
Small and Van Dender (2007), we cannot definitively isolate the separate effect of fuel
efficiency from that of fuel price. In fact, as described there, when we look at fuel efficiency as a
separate variable, it exerts no statistically significant influence on VMT. This could be taken as
evidence that the rebound effect is in fact zero, but we adopt the more conservative approach of
taking it to be the VMT elasticity with respect to fuel price. This is especially conservative (in
the sense of perhaps leading us to overstate the rebound effect) in light of Greene's (2012)
finding of similar magnitudes as we find, but in his case confirming statistically that the effect of
fuel efficiency is in fact smaller than that of fuel price.
4.2.4 Combined interaction variables and structural breaks
The fact that the rebound effect varies with income, fuel cost, and other variables explains some
of the variation in time observed earlier. But does it explain all of it? To find out, we added to
Models 3.3 and 4.3 additional structural breaks at times likely to produce changes in behavior
due to other factors. We considered breaks starting at years 1982, 1995, 2003, or 2005.
-------
Generally, we are unable to find consistent and statistically significant structural breaks at years
starting in 1982, 1995, or 2005. However, we do find evidence of an increase in the rebound
effect, even controlling for the effects of interacting variables, starting in 2003. This is seen by
simply adding a dummy variable for years 2003-2009 to Models 3.3 and 4.3 which is done in the
models labeled 3.18 and 4.13. These estimation results are shown in Table 4.4, along with the
calculation of rebound effect for the most recent five-year period (2005-2009), which falls
entirely within the time after the structural break.
Table 4.4. Models with interacted coefficients and
structural break starting in 2003
Coefficients (standard
errors in parentheses)
pm
pm *Dummy_2003_ 09
pm*inc
pm2
pm*Urban
pm*cong
vma lagged
Calculated rebound
effects:
1966-2009
Short run
Long run
2005-2009
Short run
Long run
Model 3.3
-0.0466
(0.0029)
0.0528
(0.0108)
-0.0124
(0.0059)
0.0119
(0.0094)
0.8346
(0.0102)
4.7%
29.5%
3.1%
19.4%
Model 3. 18
-0.0464
(0.0029)
-0.0251
(0.0076)
0.0699
(0.0121)
-0.0113
(0.0060)
0.0078
(0.0096)
0.8279
(0.0105)
5.0%
30.9%
5.1%
31.1%
Model 4.3
-0.0461
(0.0030)
0.0561
(0.0111)
-0.0224
(0.0060)
-0.0031
(0.0022)
0.8249
(0.0105)
4.6%
28.4%
3.1%
18.6%
Model 4. 13
-0.0460
(0.0030)
-0.0237
(0.0071)
0.0721
(0.0121)
-0.0186
(0.0061)
-0.0032
(0.0022)
0.8189
(0.0107)
5.0%
29.9%
5.0%
29.8%
The estimates show that the elasticity increases sharply in magnitude starting in 2003. In the
models that take this increase into account, the short-run rebound effect computed at average
values of variables over the entire time period is slightly larger, 5.0% instead of 4.6-4.7%. The
long-run effect at this sample average also is slightly higher, though not by much because the
estimated lag parameter (coefficient of vma lagged) is now smaller. Most important, the effect of
32
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income (coefficient ofpm*inc) is measured to be notably larger, and that of fuel cost (coefficient
ofpm2) becomes slightly smaller in magnitude. These latter changes cause the rebound effect to
decline more rapidly over time. This essentially cancels the effect of the dummy variable in
calculating the rebound effect over the last five years of the sample, so the rebound effect is
virtually the same as in the entire sample. However,, the models containing a break at 2003 will
still lead to a sharp decline in the projected rebound effect for years well into the future, as the
effect of income is stronger in these models. This is true even if the conditions causing this
structural break are assumed to continue to hold; if instead they are reversed, the future rebound
effect becomes smaller still.26
Probably the best lesson to take from the measured structural break in 2003 is that the evolution
of the rebound effect is more irregular than is portrayed in the simpler models such 3.3 and 4.3,
but the overall magnitudes those models measure are not affected much by this irregularity. One
can speculate that the irregularity occurs because gasoline price started increasing rather sharply
in 2003, and this was accompanied by a great deal of publicity. Both events may have caused
consumers to become more aware of the significance of fuel prices, and perhaps also to revise
their expectations about what future fuel costs would be. These responses may in turn have
caused them to begin to adjust their living patterns in ways that involve less driving—a process
that can continue gradually as they adapt family structure, household car sharing, and residential
and workplace locations. We explore these potential explanations in Sections 4.4 and 4.5.
26 Projections with Model 4.13, shown in Appendix, show the dynamic rebound effect declining from
approximately 20% in 2010 to 15% in 2020 and 10% in 2030, mainly due to trends in income, all on the assumption
that whatever factors caused the upward shift in 2003 remain in place indefinitely. If instead those factors disappear,
the projected dynamic rebound effect is about 10% in 2010, declining to 5% in 2020 to 1% in 2030.
33
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4.3 Effects of newer data
The results in Section 4.2 portray somewhat larger rebound effects than the studies Small and
Van Dender (2007) and Hymel, Small, and Van Dender (2010), which used these same two
systems of models (the three-equation system without congestion, and the four-equation system
with congestion). As described at the beginning of Section 3, there are two main differences
between those studies and the present study: the data have now been revised, especially data on
congestion, and the data have been extended to 2009. This subsection shows that it is mainly the
latter change, the extension to 2009, which accounts for the differences.
In Table 4.5, we present the primary coefficients of interest and the implied rebound effects in
2000-2009 for three closely related estimates, all using the model without congestion. The first
(Model 3.1) is the original estimate from the published paper, which uses data through 2001. The
second (Model 3.2) is the identical estimate, using identical years, but with the data revised as
described. The third (Model 3.3) is the same as the second except now the sample for estimation
runs through 2009.
34
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Table 4.5. Selected results of model estimated on different versions of data:
three-equation model
Estimation period
Model estimates:
pm
pm*inc
pm2
pm* Urban
vma lagged
Calculated rebound effects
at values for:
1966-2009: short run
1969-2009: long run
2000-2009: short run
2000-2009: long run
Original as
published
(Model 3.1)
1966-2001
Coeff. Std. Err.
-0.045 0.005
0.058 0.014
-0.010 0.007
0.026 0.011
0.791 0.013
4.2%
20.5%
2.2%
10.7%
Estimated with
revised data
(Model 3.2)
1966-2001
Coeff. Std. Err.
-0.046 0.005
0.057 0.015
-0.007 0.007
0.028 0.011
0.800 0.013
4.2%
21.5%
2.4%
12.3%
Estimated with
revised &
updated data
(Model 3.3)
1966-2009
Coeff. Std. Err.
-0.047 0.003
0.053 0.011
-0.012 0.006
0.012 0.009
0.835 0.010
4.7%
29.5%
2.8%
17.8%
Although the coefficients ofpm look almost identical across the three models, the coefficient in
each case has the meaning of the (approximate) short-run elasticity at the sample average21 In
the first two models, the sample average covers a restricted set of years, so when the rebound
effect is calculated for the longer period 1969-2009 it is somewhat lower than that coefficient
(due mainly to the effect of increasing income). Thus, as shown, Model 3.3 produces a higher
short-run rebound effect than the other two. The difference is even greater for the long-run
rebound effect because the estimate of the coefficient for the lagged dependent variable ("vma
lagged") is substantially greater; this means the multiplier l/(l-am~), which converts from short-
run to long-run elasticity, is also greater: 6.1 instead of 4.8 or 5.0.
Table 4.6 carries out the same exercise for the four-equation model. In contrast to the three-
equation model, in this case, adding additional years to the estimation sample reduces the short-
run rebound effect somewhat, for either time period shown. But as before, the multiplier to
convert short-run to long-run elasticities is larger when more recent years are included. In
calculating long-run elasticities, the second effect dominates the first and they are larger when
the full data set is used for estimation.
27 This is due to the way the variables pm, inc, and Urban are normalized: namely, they are created from the
unnormalized versions by subtracting the sample mean.
35
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Table 4.6. Selected results of model estimated on different versions of data:
four-equation model
Estimation period
Model estimates:
pm
pm*inc
pm2
pm*cong
vma lagged
Calculated rebound effects
at values for:
1966-2009: short run
1969-2009: long run
2000-2009: short run
2000-2009: long run
Original as
published
(ModeU.l)
1966-2004
Coeff. Std. Err.
-0.047 0.004
0.064 0.016
-0.025 0.007
-0.012 0.003
0.795 0.013
-5.0%
-25.2%
-2.8%
-14.1%
Estimated with
revised data
(Model 4.2)
1966-2004
Coeff. Std. Err.
-0.051 0.005
0.067 0.015
-0.017 0.007
-0.012 0.003
0.789 0.013
-5.0%
-25.1%
-3.2%
-16.4%
Estimated with
revised & updated
data (Model 4.3)
1966-2009
Coeff. Std. Err.
-0.046 0.003
0.056 0.011
-0.022 0.006
-0.003 0.002
0.825 0.010
-4.6%
-28.4%
-2.5%
-15.0%
Another feature that appears in this set of models is that the data revision alone makes some
difference for estimates for the period 2000-2009, as seen by comparing Models 4.1 and 4.2.
Specifically, the influence of fuel cost on the rebound effect, as given by the coefficient ofpm2,
is smaller; this results in a larger rebound effect in Model 4.2 than in Mode 4.1. The changes due
to extending the sample (Model 4.3) mostly compensate for this.
The finding that adding data for years up to 2009 modestly increases the estimated average
rebound effect, at least in the three-equation model, is consistent with the finding of Section 4.2
that the rebound effect seems to have taken a sharp jump to a larger value starting in 2003. This
observation leads to two further lines of investigation. In Section 4.4, we explore the possibility
that rising fuel prices elicit an inherently larger response than falling prices. In Section 4.5, we
explore specific mechanisms by which that might occur, namely through media attention and/or
changes in how consumer form expectations about future prices.
4.4 Asymmetry in response to price changes
Several researchers have found evidence that for various types of energy purchases, demand is
more responsive in the short run to price rises than to price decreases. In this section, we
investigate whether such asymmetry applies to vehicle-miles traveled as a function of gasoline
price.
36
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4.4.1 Models based on rises versus falls of fue\ price
Our preferred approach is to decompose fuel price into components, following the procedure
used to decompose demand for gasoline use in Dargay and Gately (1997).28 Based on
experimentation, we have simplified the three-way decomposition used by these authors into a
two-way decomposition, measured for each state in our sample.29 In this subsection, we consider
a decomposition ofpf, the logarithm of fuel price, as follows:
Pf=Pfw66 +pf rise +pf cut
where pf rise is the cumulative effects of all annual increases in fuel price since the start of the
sample (here 1966); and pf cut is the cumulative effects of all annual falls in fuel price. In other
words, the value for state /' in year t is defined as:
Pf _risejt =
pf_cutjt =
1967
1967
Because we include state fixed effects in our specification (i.e., there is a constant term for every
state), all coefficient estimates depend on state-specific annual changes in a relevant variable; so
in this specification, the coefficients of pf and variables constructed from it are replaced by two
separate coefficients, one depending on upward annual changes and the other on downward
annual changes.
The two decomposed variables, when added together, fully describe annual changes in variable
pf. Therefore any two of the three variables pf,pf rise, and pf cut can be used in the
specification, with results that are fully equivalent except for the way a t-statistic is used to test a
null hypothesis. The most convenient choice proves to be the two variables,/?/' and pf cut. In that
case, the effect of price rises is given by the coefficient of/?/ while the effect of price falls is
given by the sum of the two coefficients.
28 Nearly identical types of decomposition are also used for other types of energy consumption by Gately and
Huntington (2002) and Dargay (2007).
29 We do this by not distinguishing between increases that occurred before and after the maximum price observed in
the data. In addition, we do not place special importance on the year 1973 as do Dargay and Gately (1997), in part
because we already have a dummy variable for 1977 in our specification to capture special influences on travel
behavior during that year.
37
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These variables are used to replace pfin both the equation explaining the logarithm of vehicle-
miles traveled (vma) and that explaining the logarithm of fuel intensity (fmf). In both cases, fuel
price is also combined with other variables, as in the specifications shown earlier (as well as in
the published articles). Specifically, the main variable giving the rebound effect was previously
the logarithm of fuel cost per mile: pm=pf+ftnt, to which is now added an additional variable,
either pfcut or (pf cut+fint). The variable giving the effect of fuel price was previously given as
the logarithm of annual fuel cost savings per unit change in fuel intensity, (pf+vmd), to which is
now added the additional variable (pf cut+vma).
The results for these two alternative specifications, labeled 3.20b and 3.21b, respectively, are
summarized in Table 4.7, with the base model 3.3 (no asymmetry) shown for comparison. A
more complete listing of coefficients is given in the appendix.
Table 4.7. Selected coefficient estimates: asymmetric specifications
(a) Three-equation models
Model 3.3 Model 3.20b Model 3.21 b
Equation and variable: Coeff. Std. Coeff. Std. Coeff. Std. Error
Error Error
vma equation:
pm=pf+fint -0.0466 0.0029 -0.0520 0.0046 -0.0639 0.0049
pf_cut 0.0124 0.0093
pf_cut+ fint 0.0340 0.0078
pm*inc 0.0528 0.0108 0.0569 0.0110 0.0577 0.0108
pm2 -0.0124 0.0059 -0.0159 0.0061 -0.0207 0.0061
pm* Urban 0.0119 0.0094 0.0124 0.0094 0.0131 0.0093
vma lagged 0.8346 0.0102 0.8256 0.0110 0.8334 0.0105
fint equation:
pf+ vma -0.0050 0.0041 -0.0185 0.0057 -0.0097 0.0060
pf_cut+ vma 0.0316 0.0124 0.0143 0.0123
38
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(b) Four-equation models
Equation and variable:
Model
Coeff.
4.3
Std.
Error
Model 4.20b
Coeff.
Std.
Error
Model 4.21b
Coeff.
Std.
Error
vma equation:
pm= pf+ tint
pf_cut
pf_cut+ fint
pnfinc
pm2
pnfcong
vma lagged
fint equation:
pf+ vma
pf_cut+ vma
-0.0461
0.0561
-0.0224
-0.0031
0.8249
-0.0074
0.0030
0.0111
0.0060
0.0022
0.0105
0.0041
-0.0498
0.0100
0.0548
-0.0225
-0.0013
0.8221
-0.0125
0.0085
0.0046
0.0093
0.0111
0.0061
0.0021
0.0107
0.0055
0.0112
-0.0629
0.0340
0.0573
-0.0275
-0.0016
0.8305
-0.0041
-0.0080
0.0049
0.0079
0.0110
0.0061
0.0021
0.0107
0.0058
0.0112
These results suggest that the rebound VMT elasticity measured previously becomes modestly
stronger (i.e. larger in absolute value) when measured only for price rises. For example,
comparing base model 3.3 to asymmetric model 3.21b, that elasticity rises in magnitude, from
-0.0466 to -0.0639, when changing from the former to the latter. Note that in these models the
rebound effect itself does not depend on whether prices are rising or falling; rather, there is a
direct effect of price on VMT which is asymmetric. In all cases, price cuts have a smaller effect
on driving than price rises, a difference that is strongly statistically significant (t-statistic 4.3 or
4.4) in two of the four specifications (3.21b, 4.21b). Greene (2012) measures similar differences
between the effects of rising and falling prices, although in his case he cannot rule out
statistically that they are identical.
The implications of the two asymmetric specifications for rebound effects are different. In
Models 3.21b and 4.21b, because variable fint (representing the logarithm of inverse of fuel
efficiency) is included with bothpf andpf cut, the rebound effect is assumed equal to the price
elasticity for price cuts. For example, in Model 3.21b that elasticity is approximately -0.0299 (the
sum of coefficients of the two variables containing jint): i.e. a short-run rebound effect of
approximately 3.0%. This is less than half the rebound effect with respect to fuel price rises in
the same model, which is 6.4% (short-run structural elasticity of-0.064). As with other
responses, the short-run response would be multiplied by approximately six in the long run.
In the alternate specification of Models 3.20b and 4.20b, by contrast, the rebound effect is
assumed the same as the price elasticity for price rises. In that case there is no definitive
39
-------
difference between price rises and cuts, because the coefficient ofpfcut is small and statistically
insignificant.
In these models, a change in fuel efficiency, unlike one in fuel price, is the same regardless of
whether fuel efficiency is increased or decreased. In one pair of models (those numbered 20b)
this effect is the same as that of a fuel price rise; in the other (numbered 21b) it is the same as
that of a fuel price cut. The latter seems more likely theoretically because changes in fuel
efficiency are noticed less dramatically than changes in fuel price, and because most of the
changes in fuel efficiency we are interested in are improvements, i.e. they lower the fuel cost per
mile as does a price cut. Furthermore, the asymmetry in behavior is both more notable and more
precisely measured in the second specification, as already noted. For these reasons, we prefer the
two models numbered 21b.
4.4.2. Models based on rises versus falls of fuel cost
We also estimated models that base the asymmetry on the variable measuring fuel cost per mile
(pm), instead of on fuel price (pf). These models assume that people respond differently
depending on whether their fuel cost per mile is rising or falling, regardless of whether this is due
to a change in fuel price or in fuel efficiency.
The variables are formed analogously to the previous subsection. The fuel cost per mi\e,pm (the
price of mileage), is decomposed into pm rise and pm cut. This raises a new problem because
pm rise and pm cut are, like/TO, endogenous; but not in a simple way because their values in a
given year depend on values ofpm in previous years. In the case ofpm, endogeneity is accounted
for as part of the three- or four-equation model.30 A full endogenous treatment would be
impossible, so we have used an approximation instead: the variables are replaced by predicted
values, pm rise hat andpm cut hat, each of which is the value predicted by a regression of the
corresponding variable (pm rise orpmcut) on all the exogenous variables in the system - that
is, on the same set of variables as those used as instruments in the 3SLS estimation routine. This
is basically what instrumental variables does in the case of a simpler endogenous variable, so the
result of this approximation should be reasonably accurate although the standard errors of these
variables may be inaccurately measured.
30 Formally, this is accomplished by entering the variable pm as the sum of two variables, pf+fmt, where fmt is the
logarithm of fuel intensity (see Section 3, "Dependent variables", definition of HE). Since fmt is the dependent
variable of the third equation of our model system, the simultaneous estimation performed by the three-stage least
squares procedure treats it as endogenous where it enters the first equation as part of pm.
40
-------
Table 4.8 shows selected results of a specification, named Model 3.23, analogous to that of
Model 3.21b. The latter is shown for comparison. Each model contains three interaction
variables, whose coefficients are shown just below the second dashed line.
Table 4.8. Selected coefficient estimates: asymmetry in response to
fuel cost per mile
(a) Three-equation models
Equation and variable:
vma equation:
pm= pf+ fint
pm_rise_hat
pm_rise_hat(-1)
pm_rise_hat(-2)
pf_cut+ fint
pm_cut_hat
pm_cut_hat(-1)
pm_cut_hat(-2)
pm_cut_hat(-3)
prrfinc
pm2
pm* Urban
vma lagged
fint equation:
pf+ vma
pfrise
pf_cut+ vma
pf_cut
vma
Model
Coeff.
-0.0639
0.0340
0.0577
-0.0207
0.0131
0.8334
-0.0097
0.0143
3.21b
Std.
Error
0.0049
0.0078
0.0107
0.0061
0.0093
0.0104
0.0060
0.0123
Model
Coeff.
-0.0623
0.0284
0.0535
-0.0180
0.0187
0.8084
-0.0133
0.0042
0.0107
3.23
Std.
Error
0.0055
0.0093
0.0112
0.0062
0.0099
0.0122
0.0062
0.0096
0.0166
Model 3.29
Coeff.
-0.1134
0.0490
0.0210
-0.0037
-0.0486
0.0171
0.0239
0.0281
-0.0276
0.0273
0.8802
-0.0108
-0.0154
-0.0533
Std. Error
0.0153
0.0216
0.0129
0.0105
0.0141
0.0150
0.0108
0.0120
0.0068
0.0103
0.0119
0.0064
0.0097
0.0179
41
-------
(b) Four-equation models
Equation and variable:
vma equation:
pm= pf+ tint
pm_rise_hat
pm_ris8_hat(-1)
pm_rise_hat(-2)
pf_cut+ fint
pm_cut_hat
pm_cut_hat(-1)
pm_cut_hat(-2)
pm_cut_hat(-3)
pm*inc
pm2
pm*cong
vma lagged
fint equation:
pf+ vma
pfrise
pf_cut+ vma
pf_cut
vma
Model
Coeff.
-0.0629
0.0340
0.0573
-0.0275
-0.0016
0.8305
-0.0041
-0.0080
4.21b
Std.
Error
0.0049
0.0079
0.0110
0.0061
0.0021
0.0107
0.0058
0.0112
Model
Coeff.
-0.0615
0.0325
0.0534
-0.0245
-0.0042
0.8229
-0.0122
0.0024
0.0210
4.23
Std.
Error
0.0054
0.0091
0.0115
0.0063
0.0022
0.0112
0.0063
0.0086
0.0152
Model
Coeff.
-0.0629
-0.1068
0.0426
0.0343
-0.0051
-0.0540
0.0161
0.0233
0.0394
-0.0005
-0.0046
0.8655
-0.0144
0.0267
-0.0081
4.29
Std.
Error
0.0049
0.0159
0.0229
0.0137
0.0108
0.0149
0.0163
0.0117
0.0129
0.0002
0.0029
0.0125
0.0063
0.0118
0.0153
The variable pm cut hat, just like the previous variable pf cut, is an increasing function of cost
per mile.31 Given its construction, we expect a negative sign onpm (which is the direct short-run
rebound elasticity if fuel costs are rising) and also on the sum of coefficients ofpm and
pm cut hat (which gives the direct short-run rebound elasticity if fuel costs are falling). The
coefficient onpm cut hat itself tells us the degree of asymmetry: it is positive if the magnitude
of the elasticity is smaller for price cuts than for price rises. Equation (3.23) shows exactly this,
very similarly to (3.21b). The short-run rebound effect is given by elasticity -0.0623 when prices
are rising, and -0.0339 (=-0.0623+0.0284) when prices are falling. The rebound effect is
influenced by pm, income, and Urban much as before. The fact that the coefficient on
pm cut hat is statistically significant (more than twice its standard error) indicates that we can
confidently reject the hypothesis that the magnitude of response to cost rises and cuts are the
same.
31 The actual values ofpm-cut are negative by construction, but become less so aspm increases.
42
-------
Model 3.29 deals with an alternative view of how asymmetry might work. Perhaps the difference
in response between cost rises or cuts is not so much in the magnitude, but in the speed with
which the response occurs. All the models considered in this report already have an "inertia"
built into them, in the form of a lagged dependent variable which governs the speed of response
to all variable changes. But in Model 3.29, we allow also for the possibility that the speed of the
response differs between rises and cuts in cost per mile.
Model 3.29 shows a very plausible and revealing pattern. Adjustment to price rises takes place
quickly; in fact it overshoots and then retreats to a small value after two years. But the
adjustment to price cuts occurs more slowly: it is essentially zero in the year of the price change
(0.0037); takes a modest value after one year (0.0523, from the sum of the first two coefficients
below the first dashed line); remains approximately the same for a second year (sum of three
coefficients); and then retreats to a value of 0.0112 (sum of all four coefficients). These response
patterns are shown in Figure 4.2.
Figure 4.2. Short-run elasticity of VMT with respect to a sustained change in
fuel cost per mile (Model 3.29)
0.06
0.04
0.02
« -0.02
-0.08
-0.1
-0.12
1
Year following change
n Rise in cost per mile D Fall in cost per mile
In these models, unlike those in the previous subsection, the response to a change in fuel
efficiency depends on what's happening to overall fuel costs. If fuel price is rising more rapidly
43
-------
than fuel efficiency, then the variable remains constant; therefore, these models predict that
people would still respond to a small change in fuel efficiency according to the combination of
coefficients of variable/w?. In other words, they respond to any change in fuel efficiency,
including an improvement, as they would to a rise in fuel price. Thus, the effect of a CAFE
tightening could differ depending on whether overall fuel prices are generally rising or not, and if
they are on how fast. The behavioral rationale is as follows: if fuel costs are rising due to
increasing fuel prices and this has heightened people's awareness, then an improvement in fuel
efficiency would have a large effect on their driving decisions because it would help offset that
fuel price rise at a time when they are highly sensitive to it. This is a debatable assumption, as it
implies a degree of rationality in calculating fuel costs that people may not have in reality.
Indeed, as noted elsewhere, our results cannot definitively show that the rebound effect differs
from zero if the responses to fuel price and fuel efficiency are estimated separately. Thus it is
possible that all the rebound results are overstated, and actually are measuring the response to
changes in price rather than in fuel efficiency. For this reason, we prefer the models of Section
4.4.1.
Four-equation results. The same kind of model development was done for four-equation models,
with similar results as shown in Table 4.8(b) and Figure 4.3.
44
-------
Figure 4.3. Short-run elasticity of VMT with respect to a sustained change in
fuel cost per mile (Model 4.29)
OflR -,
n nfi
.04
Ono
•u^
+*
'o
~f n nn
yj U.UU
(B
& -0.02
o n n/i
O. -U.U'l-
1
tJL. r\ r\c
-U.UD
-O.Oo
n -i n
-U.1U
n -10
-U. IZ
0
1
Year folio
n Rise in costper mil
2 3
wing change
e D Fall in cost per mile
45
-------
4.5 Effects of media attention and expectations
Two important findings of previous sections are that the responsiveness of vehicle travel to costs
sharply increased starting around 2003, and that this responsiveness is much larger when fuel
prices or costs are rising than when they are falling. These findings naturally invite the question:
why? In this section, we consider two factors that may help explain the variations in
responsiveness.
The first is variations in media attention to fuel prices and costs. Motor vehicle fuel is a
moderately important part of many people's budgets, and the price of crude oil which tends to
underlie fuel price has even more pervasive effects on consumers. As a result, there is a tendency
for turmoil in gasoline or oil markets to gain much attention in public media. Could it be that this
attention is the underlying cause of some of the variations found in this report?
The second is the uncertainty in future fuel costs. There is evidence that at most times,
consumers' best guess at future prices, i.e. their expectation, is the current price.32 However, we
hypothesize that if prices are viewed as highly uncertain, a recent change in price is more likely
to be viewed as temporary. Therefore, the responsiveness to price changes may be muted during
times when recent history suggests that prices are volatile.
Results for three promising models are presented in Table 4.9. For comparison, we also show the
most comparable base model incorporating asymmetry but not media or uncertainty: namely,
Models 3.21b and 4.21b. Variables Media, Media dummy, and log (fuelprice variance} are as
explained in Section 3, all normalized by subtracting their mean values on the entire sample. (As
with other interacting variables, this normalization is done for convenience: as a result the
coefficients ofpm remains equal to the estimated short-run structural elasticity of VMT with
respect to fuel cost when interacting variables take their mean values in the sample.)
32 Supporting evidence comes from two separate surveys, reported by Anderson et al. (2011) and Allcott (2011),
both of which asked people directly about their price expectations. Technically, the stated result can arise from
consumers assuming a "random walk" in fuel prices: starting at the current level, they are equally likely to go up or
down at each new time period. Anderson et al. (2011) find that this assumption accurately explains their answers
except in late 2008, when they expected (correctly, as it turned out) that the recent fall in prices would prove to be
temporary.
46
-------
Table 4.9. Selected coefficient estimates: asymmetry with media
coverage or fuel-price uncertainty
(a) Three-equation models
Model 3.21b
Equation and variable:
Coeff. Std.
Error
vma equation:
pm=pf+fint -0.0639 0.0049
pf_cut+ fint 0.0340 0.0078
pm* dummy _0309
pf * ( Media_dummy )
pf_ri se* Medi a
pm* \og(fuel price variance)
pm*inc 0.0577 0.0107
pm2 -0.0207 0.0061
pm* Urban 0.0131 0.0093
vma lagged 0.8334 0.0104
fint equation:
pf+ vma
pf cut + vma
-0.0097 0.0060
0.0143 0.0123
Model 3.35
Model 3.37
Model 3.42
Coeff. Std. Coeff. Std. Coeff
Error Error
Std.
Error
-0.0587 0.0052 -0.0641 0.0057* -0.0699 0.0069
0.0286 0.0081 0.0332 0.0083 0.0529 0.0091
-0.0216 0.0079 -0.0265 0.0078
-0.0301 0.0101 -0.0319 0.0101 -0.0316 0.0101
0.0028 0.0007
0.0583 0.0109 0.0711 0.0126 0.0779 0.0124
-0.0053 0.0075 -0.0064 0.0075 -0.0126 0.0070
0.0118 0.0094 0.0100 0.0097 0.0091 0.0095
0.8325 0.0106 0.8276 0.0109 0.8321 0.0108
-0.0124 0.0059 -0.0104 0.0058 -0.0079 0.0058
0.0220 0.0120 0.0129 0.0118 0.0031 0.0115
Model 3.45
Coeff.
-0.0666
0.0210
-0.0347
-0.2680
0.0081
0.0807
-0.0302
0.0118
0.8247
-0.0033
-0.0225
Std.
Error
0.0053
0.0083
0.0084
0.0544
0.0024
0.0136
0.0081
0.0106
0.0117
0.0058
0.0114
(b) Four-equation models
Equation and variable:
vma equation:
pm= pf+ fint
pf_cut + fint
pm* dummy _0309
pf*(Media_dummy)
pf_rise*Media
Model
Coeff.
-0.0629
0.0340
4.21b
Std.
Error
0.0049
0.0079
Model
Coeff.
-0
0
0
.0638
.0352
.0061
4.35
Std.
Error
0.0050
0.0080
0.0058
Model
Coeff.
-0.0729
0.0420
-0.0359
0.0071
4.37
Std.
Error
0.0054
0.0081
0.0071
0.0058
pm* \og(fud price variance)
prrfinc
pm2
pm* Urban
vma lagged
fint equation:
pf + vma
pf_cut+ vma
0.0573
-0.0275
-0.0016
0.8305
-0.0041
-0.0080
0.0110
0.0061
0.0021
0.0107
0.0058
0.0112
0
-0
-0
0
-0
-0
.0575
.0296
.0025
.8314
.0060
.0031
0.0110
0.0065
0.0021
0.0106
0.0057
0.0110
0.0825
-0.0263
-0.0028
0.8314
-0.0059
-0.0022
0.0122
0.0066
0.0021
0.0106
0.0057
0.0110
Model
Coeff.
-0.0706
0.0506
-0.0308
-0.0080
-0.0100
0.0944
0.0037
-0.0044
0.8275
-0.0049
-0.0018
4.42
Std.
Error
0.0054
0.0083
0.0072
0.0063
0.0019
0.0124
0.0085
0.0021
0.0109
0.0057
0.0110
Model
Coeff.
-0.0719
0.0626
-0.0321
-0.3117
-0.0044
0.0905
-0.0114
-0.0057
0.8423
-0.0035
-0.0129
4.45
Std.
Error
0.0053
0.0085
0.0072
0.0490
0.0019
0.0124
0.0074
0.0021
0.0112
0.0057
0.0111
47
-------
The media variable is specified to influence the response to fuel price but not to fuel efficiency,
because the variable involves news about fuel price. Therefore, including this variable does not
affect the rebound effect except insofar as it changes coefficients of pm and its interactions. The
uncertainty variable, by contrast, represents a consumer's own experience with variation in fuel
costs, and therefore is specified so as to influence both responses (i.e., it is interacted with/TO
rather than/?/).
Consider first the four-equation models. The last of these models (4.45) suggests that both media
coverage and fuel-price volatility, taken together, have significant effects in increasing the
magnitude of the elasticity of VMT with respect to fuel price, just as we hypothesized. The effect
of Media is strongest when it is entered as a continuous rather than a dummy variable and when
it is interacted with price rises (pf rise). The effect of these additional variables on coefficients
involving pm is minimal except for one: the coefficient ofpm2 becomes smaller when fuel price
volatility is included. This could mean that the previously observed tendency of the price
elasticity (and rebound effect) to increase with fuel price is explained in part by correlation
between high prices and media coverage. But the results are not consistent enough to draw a firm
conclusion on this point.
In the three-equation models, the media variables alone seem powerful (Models 3.35 and 3.37),
but when fuel price variability is included (Model 3.45), its coefficient has an unexpected sign.
We do not have a good explanation for this. Generally, the sensitivity shown in these models to
the precise form in which variables are entered into the equation is an undesirable property, and
probably indicates that we have reached the limits of our ability to discern these fine-grained
effects using this data set.
Comparing Model 3.35 or 4.35 with the higher-numbered models, which all contain the variable
"dummy 0309", we see there continues to be a structural break toward a larger rebound effect in
years 2003-2009, even with these other variables are accounted for. The amount of this break (an
increase in the short-run rebound effect of roughly 2.0 to 3.5 percentage points) is about the same
size as found previously, in Table 4.4 (Models 3.18 and 4.13). Therefore, it seems these new
variables have not captured whatever factors changed the responsiveness to price and fuel
efficiency starting in 2003. Thus, further research is needed if one wishes to understand the
reason for this change, and in particular the likelihood that it will persist into the future.
Taking into account explanatory power, consistency across three- and four-equation models, and
consistency with theory, our preferred models remain those that omit media and volatility
variables: namely, Models 3.21b and 4.21b. While the exploration of media and volatility elicit
considerable evidence that one or both of these factors helps explain.
48
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5. Implications of the Empirical Analysis: Projections to 2035
By distinguishing the causes of the observed decline in the rebound effect, we are in a position to
consider how the rebound effect is likely to change in the future. By inserting projected values
for real per capita income, real fuel costs of driving, urbanization, and congestion into our model,
we obtain a projection for the rebound effect. Of course, like any projection, the farther into the
future we project, the uncertain are the values of these variables. In addition, in both cases
projections show one or both variables moving outside the range in which they were observed in
our sample; as a result, statistical uncertainty in the estimated model can magnify the uncertainty
in the projected values.
The models estimated here imply the rebound effect is a linear function of the logarithms of per
capita income and fuel cost per mile. This is probably a good approximation within limited
ranges of those variables, but for extreme values the linear function becomes less satisfactory. In
particular, since rising income lowers the rebound effect, linearity implies that the rebound effect
could become negative at high enough incomes. This is unrealistic and so to avoid it, we truncate
the rebound effect for any given state and year at zero. As a result, the aggregate rebound
approaches zero only gradually as incomes rise, because an increasing number of states hit this
limit. In the base projections here, the number of states with zero rebound effects rises from one
in 2008 to either five or seven in 2035, depending on whether the three- or four-equation model
is used.
The first two of the variables needed for projections — per capita income and fuel cost per mile
— are projected in the 2011 Annual Energy Outlook published by the U.S. Energy Information
Administration (US EIA 2011). WWe refer to these input projections as AEO2011. The AEO's
projections are national, whereas the rebound effects calculated here vary by state. Thus for each
state, we use the average of 2008 and 2009 as a starting value, and then change the two variables
(per capita income and fuel cost per mile) by the same proportion that the national projection
changes from those same two starting years.
It is worth noting that these projected values do not take into account any change that might
occur from the regulation itself. Thus, for example, the rebound effect in 2025 is based on fuel
efficiency projections from AEO that do not incorporate the impact of tightened efficiency
regulations in years 2017-2024. Because the effect of fuel costs is to raise the rebound effect, this
means the projections here slightly overestimate the rebound effect compared to one that tracks
the cumulative effects of the regulations on average fuel economy in each year.
For urbanization, we extrapolate from the changes observed in national averages within the data
set from 1999 to 2009. Specifically, the proportion of non-urban population and the number of
49
-------
hours of delay are each assumed to change at the same annual rate as observed over that decade.
That annual rate is -0.4%, resulting in average urbanization (fraction of population in urban
areas) rising from 74.3% in 2010 to 76.7% in 2035.
For congestion, we use a projection by the U.S. Federal Highway Administration that under
current funding for infrastructure, congestion will increase at an average annual rate of 1.26
percent (US FHWA 2011) between 2006 and 2026.33 Applying this same rate to the entire
projection period implies that annual hours of delay per person, averaged over states, rises over
from 8.6 to 11.9. (Congestion affects the projections only for the four-equation model.)
The projection methodology computes the short-run and long-run rebound effects, based on the
formulas already given using values of the "interaction variables" (per capita income, fleet-
average fuel efficiency, urbanization, and congestion) as just described for every state and every
year from 2010-2035. The same methodology is used to "back-cast" the values of rebound effect
that our model implies occurred during years 2000-2009, using the actual values of interacting
variables.
For a given year, the short-run and long-run rebound effects refer to projected changes in VMT
that would occur from a permanent change in the cost per mile beginning in that year, relative to
its baseline projected value, if all the relevant interaction variables (income, fuel price,
urbanization, and congestion) were to remain constant in time following this change. The short-
run rebound describes the change in VMT during the year in question, whereas the long-run
rebound describes the change in VMT in the distant future caused by this same permanent
change. The long-run rebound is larger in magnitude than the short-run rebound because people
adjust slowly to a change, as demonstrated by the coefficients on the lagged dependent variables
in the equations. (Especially, the coefficient of approximately 0.8 on lagged vehicle-miles per
adult indicates that about 80% of the choice about travel in a given year is determined by
"inertia," i.e. by travel the previous year, whereas only 20% is given by the new "target" travel
resulting from new conditions.) These projections provide the best comparison with other values
for the "rebound effect" estimated in the literature, which are based on the same hypothetical
experiment.
For purposes of regulatory analysis, however, a more relevant measure is how much the path of
VMT is shifted by a permanent change in cost per mile in a given year. This measure takes the
interacting variables to be changing over time, as in fact they are projected to be, rather than
being held constant. It tracks how the VMT changes in the years following a regulatory change
33 US FHWA (2008), Exhibit 7-9, column headed "Percent Change in Delay on Roads Modeled in HERS
Congestion Delay per VMT, Funding Mechanism: Fixed Rate User Charges."
50
-------
from two sources simultaneously: (a) the transition from short to long run, as already described;
and (b) the changes in variables that influence the rebound effect. This is what was defined
earlier as the dynamic rebound effect. (See Section 1 and Appendix C for details of its
calculation.)
5.1 Results: Projections using models without media or uncertainty
Tables 5.1 through 5.3 summarize the results of projecting Models 3.3 and 3.21b, our preferred
symmetric and asymmetric models and for the corresponding four-equation models. Year by
year details of these projections are given in the appendix. Table 5.1 compares the two models,
both using the AEO 2011 "Reference Case," while Tables 5.2 and 5.3 give results for each
model if input variables are instead taken from the AEO 2011 "High Oil Price" and Low Oil
Price" cases. Figures 5.1 through 5.3 present some of the same information—specifically, for the
dynamic rebound effect—graphically. Figure 5.1 also shows, for comparison, the results of
Models 3.23 and 4.23 with asymmetry based on fuel cost; this graph illustrates one of the
problems with using such a model to project rebound effects, which is that the effect can
fluctuate wildly from year to year due to the fact that projected cost per mile is relatively flat but
with small variations up or down in various years.
51
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Table 5.1
Projection Results: Rebound Effect (expressed as positive percentage), comparing
symmetric and asymmetric models
(a) Three-equation models: Model 3.3 (symmetric) and 3.21b (asymmetric)
Model 3.3 (symmetric)
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Model 3.21 b (with asymmetry
based on fuel price)
Short Run Rebound
Dynamic Rebound
Long Run Rebound
2000-2009
2.8%
NA
17.8%
0.7%
NA
4.2%
2010
2.8%
1 1 .4%
17.6%
1.0%
4.2%
5.8%
2017
2.4%
8.8%
15.4%
0.8%
2.3%
4.5%
2025
1.6%
5.3%
10.2%
0.2%
0.2%
1.0%
2030
1 .2%
3.8%
7.2%
0.0%
0.0%
0.2%
2035
0.8%
3.2%
4.8%
0.0%
0.0%
0.0%
Regulated
2017-2025
2.0%
6.9%
12.9%
0.4%
1.0%
2.7%
(b) Four-equation models: Model 4.3 (symmetric) and 4.21b (asymmetric)
Model 4.3 (symmetric)
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Model 4.21 b (with asymmetry
based on fuel price)
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Historical
2000-2009
2.5%
NA
15.0%
0.5%
NA
2.4%
D r^ i Q^toH
2010
3.0%
13.2%
18.2%
1.1%
5.4%
6.4%
2017
2.9%
10.7%
17.2%
1.0%
3.3%
5.9%
2025
2.0%
6.6%
1 1 .6%
0.3%
0.3%
1 .4%
2030
1.5%
4.7%
8.3%
0.1%
0.0%
0.2%
2035
1.0%
3.9%
5.6%
0.0%
0.0%
0.0%
Regulated
average
2017-2025
2.4%
8.6%
14.5%
0.6%
1.5%
3.5%
52
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Table 5.2
Projection Results: Rebound Effect (expressed as positive percentage) with symmetric
models, comparing different oil price cases
(a) Three-equation symmetric model (Model 3.3)
Reference Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
High Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Low Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Historical
2000-2009
2.8%
NA
17.8%
2.8%
NA
17.8%
2.8%
NA
17.8%
P r fM o /"*t o H
2010
2.8%
11.4%
17.6%
2.8%
14.4%
17.6%
2.8%
7.8%
17.6%
2017
2.9%
11.1%
18.1%
3.3%
14.5%
20.8%
2.4%
7.1%
14.8%
2025
2.8%
10.8%
17.7%
3.5%
14.4%
22.1%
2.2%
6.5%
13.8%
2030
2.8%
10.5%
17.9%
3.6%
14.1%
22.6%
2.1%
6.0%
12.9%
2035
2.8%
10.1%
17.4%
3.5%
13.7%
22.2%
1.9%
5.5%
11.8%
Regulated
average
2017-2025
2.0%
6.9%
12.9%
2.9%
10.6%
18.3%
0.9%
2.3%
5.8%
(b) Four-equation symmetric model (Model 4.3)
Selected Projection Results: Rebound Effect (expressed as positive percentage)
Four-equation model estimated on 1966-2009 revised & updated data (Model 4.3)
Reference Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
High Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Low Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Historical
2000-2009
2.5%
NA
15.0%
2.5%
NA
15.0%
2.5%
NA
15.0%
2010
3.0%
13.2%
18.2%
3.0%
18.6%
18.1%
3.0%
6.9%
18.1%
Projei
2017
2.9%
10.7%
17.2%
4.4%
17.4%
26.5%
1 .0%
2.4%
5.8%
2025
2.0%
6.6%
1 1 .6%
3.5%
13.0%
21.1%
0.1%
0.1%
0.4%
2030
1 .5%
4.7%
8.3%
2.9%
1 1 .0%
17.5%
0.0%
0.0%
0.1%
2035
1 .0%
3.9%
5.6%
2.5%
9.9%
14.5%
0.0%
0.0%
0.0%
Regulated
average
2017-2025
2.4%
8.6%
14.5%
4.0%
15.1%
24.0%
0.5%
0.8%
2.8%
53
-------
Table 5.3
Projection Results: Rebound Effect (expressed as positive percentage) with asymmetric
models, comparing different oil price cases
(a) Three-equation asymmetric model (Model 3.21b)
Reference Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
High Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Low Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Historical
2000-2009
0.7%
NA
4.2%
0.7%
NA
4.2%
0.7%
NA
4.2%
2010
1.0%
4.2%
5.8%
0.9%
8.5%
5.7%
1.0%
2.0%
5.7%
2017
0.8%
2.3%
4.5%
2.1%
7.5%
12.7%
0.0%
0.0%
0.1%
(b) Four-equation asymmetric model
Reference Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
High Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Low Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Historical
2000-2009
0.5%
NA
2.4%
0.5%
NA
2.4%
0.5%
NA
2.4%
2010
1.1%
5.4%
6.4%
1.1%
11.8%
6.3%
1.1%
2.5%
6.3%
Prnii
2017
1.0%
3.3%
5.9%
2.8%
11.3%
17.4%
0.0%
0.0%
0.0%
•prj
2025
0.2%
0.2%
1.0%
1.2%
3.4%
7.2%
0.0%
0.0%
0.0%
(Model
2025
0.3%
0.3%
1 .4%
1.9%
6.5%
1 1 .6%
0.0%
0.0%
0.0%
2030
0.0%
0.0%
0.2%
0.7%
1 .7%
3.9%
0.0%
0.0%
0.0%
4.21b)
2030
0.1%
0.0%
0.2%
1.3%
4.3%
7.7%
0.0%
0.0%
0.0%
2035
0.0%
0.0%
0.0%
0.3%
1.3%
1.9%
0.0%
0.0%
0.0%
2035
0.0%
0.0%
0.0%
0.8%
3.1%
4.5%
0.0%
0.0%
0.0%
Regulated
average
2017-2025
0.4%
1.0%
2.7%
1.6%
5.3%
10.0%
0.0%
0.0%
0.0%
Regulated
average
2017-2025
0.6%
1.5%
3.5%
2.4%
8.8%
14.7%
0.0%
0.0%
0.0%
54
-------
25.0%
0.0%
Figure 5.1
Selected projection results: Symmetric and two asymmetric models
(a) Three-equation models
Dynamic rebound effects: Comparison of three-
equation models (Reference oil price case)
2000
2010
2020
2030
-Base model (3.3)
-Asymmetry based on
price (Model 3.21 b)
-Asymmetry based on
cost (Model 3.23)
(b) Four-equation models
Dynamic rebound effects: Four-equation models
(Reference oil price case)
-Base model (4.3)
-Asymmetry based on
price (Model 4.21 b)
-Asymmetry based on
cost (Model 4.23)
2000 2005 2010 2015 2020 2025 2030 2035
55
-------
Figure 5.2
Selected Projection Results: Symmetric Models
(a) Three-equation model
15.0%
Dynamic rebound effects: Three-equation base model (3.3)
10.0%
5.0%
0.0% 1
• High oil price case
• Reference case
•Lowoil price case
2000 2005 2010 2015 2020 2025 2030 2035
(b) Four-equation models
Dynamic rebound effects: Four-equation base model (4.3)
25.0%
20
0.0% 4-
-High Oil Price Case
- Reference case
-Low Oil Price Case
2000
2005
2010
2015
2020
2025
2030
2035
56
-------
Figure 5.3
Selected projection results: Preferred asymmetric models
(a) Three-equation model
15.0%
10.0%
5.0%
0.0%
Dynamic rebound effects: Three-equation model with
asymmetry based on price (3.21 b)
•High oil price case
• Reference case
•Low oil price case
2000 2005 2010 2015 2020 2025 2030 2035
(b) Four-equation models
Dynamic rebound effects: Four-equation model with
asymmetry based on price (4.21 b)
15.0%
10.0%
5.0%
0.0% 1
High Oil Price Case
Reference case
Low Oil Price Case
2000
2005
2010
2015
2020
2025
2030
2035
The projections from asymmetric models show more fluctuations than those from symmetric
models, because the sharp break between years of rising and falling fuel costs causes jumps in
the short-run and long-run rebound effects. This occurs each year when the change in fuel price
switches sign, as happened in 2009 (becoming negative) and 2010 (becoming positive again). In
the "low oil price" projections, it happens again in 2011 as the price spike in 2010 is projected to
be reversed, and then again in 2017 when the 2011-2016 downward trend changes to a steady
though very gradual increase. These fluctuations are mainly seen in the short-run and long-run
rebound effects, as illustrated in Figure 5.4.
57
-------
Figure 5.4
Projection results for preferred models with asymmetry
(a) Three-equation model
Projections of Rebound Effect
Model 3.21b: Three-equation model estimated on 1966-2009 data
15.0%
0.0%
2000 2005 2010 2015 2020 2025 2030 2035
(2000-09 are estimates; 2010-35 are projections)
(b) Four-equation model
Projections of Rebound Effect
Model 4.21b: Four-equation model estimated on 1966-2009 data
15.0%
10.0%
5.0%
0.0%
Short run
Dynamic
Long run
2000 2005 2010 2015 2020 2025 2030 2035
(2000-09 are estimates; 2010-35 are projections)
The dynamic rebound effect does not have such large jumps, because it effectively averages the
responses over the lifetime of a vehicle purchased during the year in question. Thus, if over the
next 15 years the impact on VMT is sometimes large and sometimes small, this is diluted first by
the "inertia" in consumer response, which is tracked in the dynamic rebound calculation, and
also by the summation over years in mileage driven. For this reason, it can be larger than the
long-run rebound effect in years when fuel costs have just fallen, because the long-run rebound
effect assumes that all variables, including the indicator for falling prices, will remain unchanged
over the life of the vehicle.
58
-------
The projection results thus far are summarized in Table 5.4, focusing on the regulated average
value of the rebound effect (i.e., average over years 2017-2025). The first two panels present
dynamic rebound effects, the third presents long-run rebound effects.
Table 5.4
Selected summary measures
(a) Dynamic rebound effect: symmetric models
(Average over years 2017-2025)
High Oil Price Case
Reference Case
Low Oil Price Case
Three-equation
model (3.3)
10.6%
6.9%
2.3%
Four-equation
model (4.3)
15.1%
8.6%
0.8%
Average
12.8%
7.8%
1 .5%
Note: Rebound effect is defined as minus the elasticity of VMT with respect to fuel cost
per mile, expressed as positive percentage). Dynamic rebound effect refers to total miles
driven by a vehicle over its life. "Regulated average" over 2017-2015 is weighted by
projected sales of all light duty vehicles.
(b) Dynamic rebound effect: asymmetric models
(Average over years 2017-2025)
High Oil Price Case
Reference Case
Low Oil Price Case
Three-equation
model (3.21 b)
5.3%
1 .0%
0.0%
Four-equation
model (4.21 b)
8.8%
1 .5%
0.0%
Average
7.0%
1.3%
0.0%
(c) Long run rebound effect: asymmetric models
(Average over years 2017-2025)
Three-equation Four-equation
model (3.21 b) model (4.21 b) Average
High Oil Price Case 10.0% 14.7% 12.4%
Reference Case 2.7% 3.5% 3.1%
Low Oil Price Case 0.0% 0.0% 0.0%
Note: Unlike the dynamic rebound effect, which accounts for changes in fuel
prices after a car is purchased, the long-run rebound effect forecasts the result if
fuel prices remained the same throughout the life of the vehicle. This is why it can
sometimes be smaller than the dynamic rebound effect.
Recently, a Reference Case projection has become available using the 2012 version of the
Annual Energy Outlook (AEO2012). In order to see whether this substantially affects the
projections of the rebound effects, a comparison is presented in Figure 5.5. Using our base
models (Models 3.3 and 4.3), the projected dynamic rebound effects are about two percentage
points larger using AEO2012, because of its higher energy prices. In the case of the asymmetric
models, however, this differential disappears by the end of the projection period because the
rebound effect falls essentially to zero due to the strong effect of variable pm cut in reducing the
rebound effect.
59
-------
Figure 5.5
Comparisons of projections using AEO2011 and AEO2012
(a) Three-equation models
Dynamic rebound effects: Three-equation base
model (3.3)
15.0%
10.0%
5.0%
0.0%
2000
2010
2020
2030
- Reference case:
AE02012
- Reference case:
AEO2011
Dynamic rebound effects: Three-equation model
with
asymmetry based on price (3.21b)
15.0%
10.0%
5.0%
0.0%
- Reference case:
AEO2012
- Reference case:
AE02011
2000
2010 2020
2030
60
-------
(b) Four-equation models
20.0%
0.0%
Dynamic rebound effects: Four-equation base model
(4.3)
• Reference case:
AE02012
• Reference case:
AE02011
2000
2010
2020
2030
Dynamic rebound effects: Four-equation model with
asymmetry based on price (4.21 b)
20.0%
15.0%
10.0% -\
5.0%
0.0%
2000
• Reference case:
AE02012
• Reference case:
AE02011
2010
2020
2030
5.2 Results: Projections using models with media variable
Table 5.5 and Figure 5.6 show the results of projecting Model 3.35. Because the media variable
is specified so that it affects the response of VMT to price but not to fuel efficiency, its only
impact on the projections is the way it changes other coefficients. As it happens, the only notable
effect it has is to lessen the impact of future changes in fuel cost per mile, whose effect on
projections is not very large anyhow except in the "high oil price" case. Thus, the projections for
the AEO reference case are little different from those with the corresponding model without
61
-------
media variable (Model 3.21b): they are slightly lower during the early part of the regulatory
period, leading to a "regulated average" dynamic rebound effect of 0.7%.
Table 5.5
Projection results for model with media coverage variable:
Three-equation model
Model 3.21 b
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Model 3.35
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Historical
2000-2009
0.7%
NA
4.2%
0.7%
NA
4.2%
2010
1 .0%
4.2%
5.8%
1.1%
3.3%
6.4%
2017
0.8%
2.3%
4.5%
0.6%
1 .4%
3.7%
2025
0.2%
0.2%
1 .0%
0.2%
0.2%
0.9%
2030
0.0%
0.0%
0.2%
0.0%
0.0%
0.2%
2035
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
Regulated
average
2017-2025
0.4%
1.0%
2.7%
0.4%
0.7%
2.2%
Figure 5.6
Projection results for model with media coverage variable:
Three-equation model
on r\o/_
Z. U . U /O
1 ^ n%
1 n n%
I U . U /O
i
5 no/
.UTO i
0.0% -
20
-^*^*\*±*^
™****-«-^mi
««»»»»» »»«»« T«»^
1 1 1 1 —
00 2005 2010 201
(2000-09 are estimate
"*****
tt**i V^****,
*"y-^.-^ .-- -'*ni »**»tai
5 2020 2025 2030 20
s; 201 0-35 are projections)
— •— Short run
— • — n\/n3mir
-A— Long run
i
35
62
-------
In the four-equation model, the media variable has virtually no effect on results, so the
projections would be essentially the same as in Model 4.21b.
We do not project the rebound effect using the models containing price volatility, because we do
not have an obvious way to forecast volatility. Nor is any significant volatility included in the
AEO forecasts. Nevertheless, one can expect the future to contain some periods of stability and
some of volatility, causing the rebound effect to fluctuate in some unknown manner around the
trends we have projected.
6. Conclusions
The research reported here confirms the findings of previous studies that the long-run rebound
effect, measured over a period of several decades extending back to 1966, is 28-30% (Table
4.3). We also find a short-run (one-year) rebound effect of 4.6-4.7%, which is harder to compare
to previous studies because previous work contains so much variation depending on the
treatment of dynamics and of CAFE regulations.
This research also provides strong evidence that the rebound effect became substantially lower in
more recent years, and that probably this was due to a combination of higher real incomes, lower
real fuel costs, and higher urbanization. Because time spent in travel rises with urbanization and
its attendant congestion, and the value of that time rises with incomes, all three of these
differences tend to make fuel costs a smaller portion of the total cost of traveling. Thus it is not
surprising that people would become less sensitive, on a percentage basis, to changes in those
fuel costs. Our base model implies that the long-run rebound effect was 15-18% on average over
the years 2000-2009 (Table 4.3). Projections suggest that the effect of income is very strong,
reducing the long-run rebound effect from about 11-14% in 2010 to 3-5% in 2035, according to
the base model (Figure 5.1)
There is strong evidence of asymmetry in responsiveness to price increases and decreases. This
makes interpretation of the rebound effect somewhat more difficult, because it accentuates the
unresolved question as to whether travelers respond to a change in fuel efficiency in the same
way as to a change in fuel price. Different assumptions lead to quite different implications for
detailed projections. Still, the overall tendency of the results is to show that the rebound effect is
likely to be moderate, and to decline with income. Furthermore, accounting for asymmetry
greatly reduces the rebound effect when it is identified, as seems plausible, with the observed
response to fuel price declines. For example, using the AEO 2011 reference case, the projected
dynamic rebound effect averaged over the years 2017-2025 and averaged between the three-
equation and four-equation models is 7.8% using a symmetric model, but only 1.3 percent using
the preferred asymmetric model (Table 5.4).
63
-------
There is weaker evidence that media coverage, and perhaps recent fuel-price volatility, also
affect travelers' responsiveness to changes in fuel cost. This evidence tends to confirm
expectations that such variables are important, but it is not conclusive at this point. Furthermore,
it does not undermine the most important finding of this and earlier work, which is that the
rebound effect will decline over time as incomes rise.
64
-------
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Wadud Z., DJ. Graham, and R.B. Noland (2007b). "Modelling fuel demand for different socio-
economic groups," Working paper, Centre for Transport Studies, Imperial College London.West,
67
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Sarah E. (2004), "Distributional effects of alternative vehicle pollution control policies," Journal
of Public Economic, 88: 735-757.
68
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Appendix A. Calculation of Dynamic Rebound Effect
The dynamic rebound takes into account that interacting variables, especially income and fuel
price, are changing over the course of the life of a vehicle—even its life beyond the projection
period which ends in 2035. It is calculated by projecting the dynamic adjustment process that is
implied by the estimated equations but allowing the "target" amount of travel to change each
year according to actual or projected conditions (income, fuel price, and urbanization and/or
congestion) for that year—using actual data from my data sources for 2000-2009 and data from
the AEO projections for 2010-2035. (The projection data are adjusted to match the estimation
data for years 2008-2009, so that projections are consistent with the estimated equations.)
This "target" is based on an adjustment to the typical mileage for a vehicle of a given age, as
derived from the National Personal Travel Survey (NPTS) and reported by the Transportation
Energy Data Book, ed. 29, Table 8.9. The adjustment occurs from two sources: changes in the
interaction variables that determine the long-run rebound effect, and the assumed unit change in
fuel cost per mile resulting from a policy. The adjustment is derived from the equations for the
structural elasticity of mileage with respect to fuel cost per mile (EM. PM in the source papers),
which is influenced directly by the interaction variables according to their estimated coefficients,
and from the equation that converts SM. PM into a long-run rebound effect.34 The actual mileage of
a vehicle purchased in year tin a subsequent year t+r, where ris the age of the vehicle, is
projected as the weighted average of the previous year's mileage, adjusted for the natural
evolution due to the age-mileage profile, and the target mileage, which is based on the age-
mileage profile and the long-term rebound elasticity; the weights in taking this average are am
and (I-O&M), respectively, where am is the coefficient of the lagged dependent variable in the
estimated equation for vehicle-miles per adult. (This notation conforms with the two papers just
cited in the footnote.)
The actual procedure used to compute the dynamic rebound effect has three steps:
• First, the short-run rebound effect is recomputed for each year assuming that all variables
except fuel efficiency change as in the projection being considered.35 This projects the desired
short-run response that would occur for the owner of a vehicle whose fuel efficiency remains
fixed as it ages, but who faces other changes (income, fuel price, urbanization, congestion) that
34 Those equations are equation (7) in Small and Van Dender (2007) and equations (14a) and (15) in Hymel, Small,
andVanDender(2010).
35 Our projections are through year 2035. Vehicles sold in the lateryears of the projection will last beyond 2035, and
for those years we use 2035 values of interacting variables to compute the short-run rebound effect applying to these
vehicles as they age.
Appendix page 1
-------
affect the owner's response. 36 The resulting change over the vehicle's lifetime is denoted by
AD ' t,r = ot+r - bst , where t is the year of purchase and ris the vehicle's age.
• Simultaneously, these changes in short-run rebound as the vehicle ages are converted to the
corresponding change in structural elasticity using equation (1 la) of Hymel et al. (2010), and
that in turn is converted to a change in long-run target response using equation (14a) of the same
paper:
where bLt is the long-run rebound for year t as already calculated, and D and Z^ are quantities
defined in Hymel et al.'s equation which account for effects of the equations for vehicle fleet
size and vehicle fuel efficiency when computing the short- and long-run rebound effects,
respectively. As an approximation, we assume the conversion factors D and Z^ are constant,
although they actually change very slightly over time. The ratio Z)/DL is actually very close to the
simple multiplier, 17(1 -a"*), which converts a short-run to a long-run response.37
• Finally, the baseline age-mileage profile mentioned earlier, denoted by M T ° for ages z=0,l,
. . ., 15, is used as the starting point for changes in mileage over each year of the vehicle's age.38
The computation assumes a unit increase in fuel cost per mile. (The size and sign of the change
in fuel cost per mile is immaterial because the equations are linear so they lead to the same
answer once one divides by that change.) The projected mileage after response to the change in
fuel cost per mile, for a new car purchased in year t, is the weighted average described earlier:
T-l
36 Because of the form of the estimating equations, which are linear in logarithms even accounting for interaction
variables, this calculation depends only very slightly on which year's fuel efficiency is chosen to hold constant:
namely, it depends on it through the truncation that occurs for those few state-year combinations that would
otherwise lead to a positive projected elasticity of VMT with respect to fuel cost (those values are truncated at zero).
Thus for the projections starting in 2010, the computation is simplified by assuming fuel efficiency is held constant
at its projected value for 2020; for the historical computations for 2000-2009, it is held constant at its actual value
for 2005.
37 The equations for D and Ef- in Hymel et al. (2010) are for the four-equation version of the model; they are also
valid for the 3 -equation version, simply by setting the coefficient of"1, which is absent in the latter, equal to zero.
38 The age-mileage profile is derived from the National Personal Travel Survey (NPTS) and reported in the
Transportation Energy Data Book, ed. 29, Table 8.9.
Appendix page 2
-------
This is computed iteratively; for year 0 (the year the vehicle is purchased), the simple short-run
response as already projected is used:
M0=(\-bst)M°t
In these equations, bis a "rebound effect" defined as the negative of the relevant elasticity, so is
normally positive (or zero, if truncated); this is why it appears with a minus sign in the equation.
Appendix page 3
-------
Appendix B. Coefficient estimates
Table Bl. Coefficient estimates: Symmetric and asymmetric models
(a) Three-equation models
Model 3.3
Equation Variable Coeff. Std. Error
vma intercept 1.6261 0.1022
vma income 0.0781 0.0117
vma adults per road mile -0.0149 0.0038
vma popratio 0.0726 0.0322
vma Urban -0.0205 0.0391
vma Railpop -0.0067 0.0043
vma D7479 -0.0439 0.0034
vma Trend -0.0004 0.0002
vma vma(-1) 0.8346 0.0102
vma vehstock 0.0209 0.0067
vma pf+fint -0.0466 0.0029
vma pmA2 -0.0124 0.0059
vma pm*inc 0.0528 0.0108
vma pm'Urban 0.0119 0.0094
vma pm*(dummy 2003-09)
vma pfcut
vma
vma
vma
vma
vma
vma AR(1) -0.1018 0.0204
veh intercept -0.2253 0.1452
veh pnewcar 0.0400 0.0317
veh interest -0.0008 0.0042
veh income 0.0032 0.0146
veh Adults per road mile -0.0136 0.0060
veh licenses/adult 0.0345 0.0184
veh trend 0.0002 0.0007
veh vehstock(-l) 0.9318 0.0104
veh vma 0.0291 0.0147
veh pm 0.0013 0.0058
veh AR(1) -0.1461 0.0230
fint intercept -0.2447 0.0631
fint pf + vma -0.0050 0.0041
fint income -0.0016 0.0144
fint fint(-1) 0.9040 0.0100
fint Population Ratio -0.0168 0.0603
fint Trend66-73 0.0005 0.0011
fint Trend74-79 -0.0068 0.0010
fint Trend80+ -0.0007 0.0003
fint D7479 -0.0070 0.0048
fint Urban -0.0905 0.0467
fint cafe -0.0345 0.0108
fint pfcut
fint
fint AR(1) -0.1773 0.0201
Model 3.18
Coeff. Std. Error
1.6771 0.1035
0.0782 0.0117
-0.0147 0.0038
0.0836 0.0325
-0.0372 0.0395
-0.0053 0.0043
-0.0436 0.0034
-0.0003 0.0002
0.8279 0.0105
0.0238 0.0068
-0.0464 0.0029
-0.0113 0.0060
0.0699 0.0121
0.0078 0.0096
-0.0251 0.0076
-0.2188 0.1451
0.0376 0.0317
-0.001 1 0.0042
0.0033 0.0146
-0.0135 0.0060
0.0344 0.0183
0.0002 0.0007
0.9323 0.0104
0.0285 0.0147
0.0009 0.0058
0.0376 0.0317
-0.2577 0.0631
-0.0052 0.0041
-0.0009 0.0144
0.9036 0.0100
0.0154 0.0602
0.0006 0.001 1
-0.0060 0.0010
-0.0007 0.0003
-0.0082 0.0048
-0.0869 0.0467
-0.0402 0.0108
-0.1756 0.0201
Model 3.20b
Coeff. Std. Error
2.2568 0.4424
0.0814 0.0117
-0.0147 0.0037
0.0804 0.0329
-0.0211 0.0388
-0.0080 0.0043
-0.0432 0.0034
0.0002 0.0004
0.8256 0.0105
0.0202 0.0067
-0.0520 0.0046
-0.0159 0.0061
0.0569 0.0108
0.0124 0.0093
0.0124 0.0093
-0.1038 0.0205
-0.2174 0.1450
0.0432 0.0317
-0.0006 0.0042
0.0037 0.0146
-0.0137 0.0060
0.0345 0.0183
0.0003 0.0007
0.9319 0.0104
0.0281 0.0147
0.0015 0.0058
-0.1464 0.0230
2.4538 1.0475
-0.0185 0.0057
-0.0048 0.0145
0.9140 0.0109
-0.0160 0.0592
0.0005 0.001 1
-0.0058 0.001 1
0.0008 0.0007
-0.0041 0.0048
-0.0778 0.0470
-0.0202 0.0186
0.0316 0.0124
-0.1822 0.0201
Model 3.21 b
Coeff. Std. Error
3.1468 0.3541
0.0770 0.0118
-0.0151 0.0037
0.0630 0.0323
-0.0061 0.0395
-0.0082 0.0042
-0.0445 0.0035
0.0013 0.0004
0.8334 0.0104
0.0161 0.0067
pf+fint -0.0639 0.0049
-0.0207 0.0061
0.0577 0.0107
0.0131 0.0093
pfcut + fint 0.0340 0.0078
-0.1021 0.0204
-0.2188 0.1449
0.0460 0.0317
-0.0004 0.0042
0.0038 0.0146
-0.0137 0.0060
0.0349 0.0183
0.0004 0.0007
0.9316 0.0104
0.0281 0.0146
0.0019 0.0058
-0.1469 0.0230
0.9282 1.0517
pf + vma -0.0097 0.0060
0.0000 0.0146
0.8977 0.0115
-0.0005 0.0586
-0.0005 0.001 1
-0.0061 0.0011
-0.0002 0.0007
-0.0032 0.0048
-0.0890 0.0471
-0.0256 0.0183
pfcut + vma 0.0143 0.0123
-0.1804 0.0202
Model 3.23
Coeff. Std. Error
3.3926 0.5490
0.0792 0.0120
-0.0200 0.0041
0.0732 0.0334
0.0021 0.0407
-0.0061 0.0045
-0.0425 0.0034
0.0013 0.0006
0.8084 0.0122
0.0203 0.0070
pf+fint -0.0623 0.0055
-0.0180 0.0062
0.0535 0.0112
0.0187 0.0099
0.0284 0.0093
-0.0978 0.0215
-0.2232 0.1451
0.0444 0.0317
-0.0003 0.0042
0.0036 0.0146
-0.0138 0.0060
0.0339 0.0184
0.0004 0.0007
0.9316 0.0104
0.0286 0.0147
0.0017 0.0058
-0.1461 0.0230
1.1934 1.2081
pfrise -0.0133 0.0062
-0.0041 0.0151
0.9106 0.0128
-0.0073 0.0594
0.0001 0.0012
-0.0057 0.001 1
0.0001 0.0007
-0.0046 0.0048
-0.0828 0.0463
-0.0312 0.0185
pfcut 0.0042 0.0096
vma 0.0107 0.0166
-0.1807 0.0202
Model 3.29
Coeff. Std. Error
2.8829 0.5547
0.0783 0.0128
-0.0080 0.0043
0.1077 0.0416
0.0492 0.0455
-0.0095 0.0048
-0.0374 0.0043
0.0010 0.0005
0.8802 0.0119
0.0195 0.0074
pmrisejiat -0.1134 0.0153
pmA2 -0.0276 0.0068
pm*lncome 0.0281 0.0120
pm*Urban 0.0273 0.0103
0.0105
pmrise_hat(-1) 0.0490 0.0216
pmrise_hat(-2) 0.0210 0.0129
0.0141
0.0150
0.0108
-0.1203 0.0215
-0.2016 0.1662
0.0716 0.0352
-0.0066 0.0053
-0.0057 0.0163
-0.0149 0.0070
0.0345 0.0220
0.0008 0.0008
0.9233 0.0114
0.0279 0.0167
0.0045 0.0062
-0.1473 0.0244
-0.3690 1 .2382
pfrise -0.0108 0.0064
0.0069 0.0158
0.8577 0.0135
0.0645 0.0664
0.001 1 0.0065
-0.0046 0.0012
-0.0013 0.0007
-0.0077 0.0048
-0.1213 0.0532
-0.0875 0.0188
pfcut -0.0154 0.0097
vma -0.0533 0.0179
-0.1837 0.0216
Appendix page 4
-------
(b) Four-equation models
Model 4.3
Equation Variable Coeff. Std. Err.
vma intercept 1.6801 0.1066
vma inc 0.0835 0.0117
vma congestion 0.0014 0.0027
vma cong'inc -0.0156 0.0032
vma cong*pm -0.0031 0.0022
vma D7479 -0.0430 0.0034
vma Trend -0.0003 0.0002
vma vma(-1) 0.8249 0.0105
vma vehstock 0.0276 0.0065
vma pm -0.0461 0.0030
vma pmA2 -0.0224 0.0060
vma pm'inc 0.0561 0.0111
vma popratio 0.1201 0.0384
vma urban -0.0842 0.0413
vma road miles/land area 0.0180 0.0065
vma pm*(dummy for 2003-09)
vma pfcut
vma
vma
vma
vma
vma
vma AR(1) -0.0900 0.0207
vehstock intercept -0.3535 0.1422
vehstock pnewcar 0.0418 0.0317
vehstock interest -0.0033 0.0040
vehstock income 0.0044 0.0146
vehstock urban -0.0420 0.0465
vehstock licenses/adult 0.0441 0.0178
vehstock trend 0.0000 0.0007
vehstock vehstock(-l) 0.9354 0.0102
vehstock vma 0.0384 0.0143
vehstock pm 0.0028 0.0057
vehstock rho -0.1468 0.0230
fint intercept -0.3202 0.0618
fint pf + vma -0.0074 0.0041
fint inc -0.0002 0.0143
fint fint(-1) 0.8894 0.0102
fint Trend66-73 0.0013 0.0009
fint Trend74-79 -0.0038 0.0008
fint Trend80+ -0.0010 0.0003
fint 7479 dummy -0.0118 0.0047
fint Urban -0.0847 0.0468
fint cafe -0.0607 0.0103
fint popratio 0.1096 0.0556
fint pfcut+vma
fint
fint rho -0.1694 0.0201
cong intercept -3.8401 0.9940
cong urban-lane-miles/adult -0.6926 0.1316
cong (vehicle miles/adult)+log(ui 0.2258 0.0885
cong population / state land aree 0.6121 0.0520
cong percent trucks 0.4597 0.2062
cong urban -4.3113 0.3550
Model 4.13
Model 4.20b Model 4.21 b Model 4.23
Coeff. Std. Err. Coefficient Std. Error
1.7249 0.1078
0.0839 0.0117
0.0014 0.0027
-0.0146 0.0032
-0.0032 0.0022
-0.0429 0.0034
-0.0002 0.0002
0.8189 0.0107
0.0308 0.0066
-0.0460 0.0030
-0.0186 0.0061
0.0721 0.0121
0.1289 0.0386
-0.0980 0.0416
0.0173 0.0066
-0.0237 0.0071
-0.0856 0.0208
-0.3516 0.1422
0.0392 0.0317
-0.0036 0.0040
0.0043 0.0146
-0.0424 0.0465
0.0440 0.0178
-0.0001 0.0007
0.9357 0.0102
0.0384 0.0143
0.0025 0.0057
-0.1471 0.0230
-0.3191 0.0619
-0.0075 0.0041
-0.0002 0.0143
0.8900 0.0102
0.0013 0.0010
-0.0037 0.0008
-0.0010 0.0003
-0.0119 0.0047
-0.0839 0.0468
-0.0601 0.0103
0.1130 0.0557
-0.1691 0.0201
-3.8457 0.9940
-0.6931 0.1316
0.2263 0.0885
0.6119 0.0520
0.4594 0.2062
-4.3124 0.3550
2.1693 0.4400
0.0847 0.0117
0.0032 0.0026
-0.0134 0.0031
-0.0013 0.0021
-0.0430 0.0034
0.0000 0.0005
0.8221 0.0107
0.0282 0.0066
-0.0498 0.0046
-0.0225 0.0061
0.0548 0.0111
0.1006 0.0419
-0.0694 0.0409
0.0181 0.0065
0.0100 0.0093
Coefficient Std. Error
3.1388 0.3529
0.0807 0.0119
0.0016 0.0026
-0.0131 0.0031
-0.0016 0.0021
-0.0441 0.0035
0.0013 0.0005
0.8305 0.0107
0.0242 0.0066
-0.0629 0.0049
-0.0275 0.0061
0.0573 0.0110
0.1010 0.0410
-0.0589 0.0415
0.0155 0.0066
pfcut+fint 0.0340 0.0079
-0.0901 0.0207 -0.0888 0.0206
-0.3569 0.1421
0.0430 0.0317
-0.0032 0.0040
0.0043 0.0146
-0.0418 0.0465
0.0442 0.01 78
0.0000 0.0007
0.9353 0.0102
0.0387 0.0143
0.0030 0.0057
-0.1468 0.0230
0.4210 0.9482
-0.0125 0.0055
0.0021 0.0144
0.8950 0.0106
0.0011 0.0010
-0.0028 0.0009
-0.0005 0.0006
-0.0088 0.0047
-0.0801 0.0470
-0.0678 0.0158
0.1293 0.0562
0.0085 0.0112
-0.1702 0.0201
-4.1046 0.9274
-0.6057 0.1102
0.2825 0.0860
0.5900 0.0490
0.4622 0.1983
-4.0385 0.3434
-0.3554 0.1421
0.0445 0.0317
-0.0030 0.0040
0.0044 0.0146
-0.0416 0.0465
0.0445 0.01 78
0.0000 0.0007
0.9351 0.0102
0.0384 0.0143
0.0032 0.0057
-0.1471 0.0230
-1 .0263 0.9488
-0.0041 0.0058
0.0064 0.0144
0.8805 0.0111
0.0001 0.0010
-0.0034 0.0009
-0.0014 0.0006
-0.0078 0.0047
-0.0919 0.0471
-0.0714 0.0155
0.1302 0.0556
pfcut+vma -0.0080 0.0112
-0.1691 0.0202
-4.0860 0.9273
-0.6058 0.1102
0.2799 0.0860
0.5908 0.0490
0.4634 0.1983
-4.0331 0.3434
Coeff icien Std. Error
3.4021 0.4991
0.0781 0.0120
-0.0001 0.0028
-0.0166 0.0033
-0.0042 0.0022
-0.0441 0.0035
0.0014 0.0005
0.8229 0.0112
0.0274 0.0067
-0.0615 0.0054
-0.0245 0.0063
0.0534 0.0115
0.1437 0.0394
-0.0763 0.0419
0.0181 0.0067
pmcut_hat 0.0325 0.0091
-0.0932 0.0212
-0.3653 0.1422
0.0412 0.0318
-0.0030 0.0040
0.0041 0.0146
-0.0424 0.0466
0.0438 0.0178
-0.0001 0.0007
0.9348 0.0102
0.0396 0.0143
0.0028 0.0058
-0.1458 0.0230
0.7587 1 .0646
prfise -0.0122 0.0063
0.0005 0.0149
0.9108 0.0117
0.0010 0.0010
-0.0048 0.0010
0.0004 0.0006
-0.0033 0.0046
-0.0724 0.0462
0.0064 0.0158
0.1744 0.0542
pfcut 0.0024 0.0086
vma 0.0210 0.0152
-0.1753 0.0198
-4.6094 0.9904
-0.7682 0.1296
0.2914 0.0900
0.6424 0.0521
0.4061 0.2093
-4.6372 0.3616
Model 4.29
Coefficient Std. Error
1.8244 0.5610
0.0827 0.0127
0.0076 0.0031
-0.0234 0.0042
pmrise hat*cong -0.0046 0.0029
-0.0401 0.0044
0.0003 0.0006
0.8656 0.0125
0.0146 0.0079
pmrisejiat -0.1068 0.0159
pmrise_hat*pm -0.0005 0.0002
pmrise+hafinc 0.0394 0.0129
0.1763 0.0487
-0.0499 0.0500
0.0234 0.0086
-0.0051 0.0108
pmrise_hat(-1) 0.0426 0.0229
pmrise_hat(-2) 0.0343 0.0137
-0.0540 0.0149
0.0161 0.0163
0.0233 0.0117
-0.1106 0.0227
-0.3608 0.1419
0.0416 0.0317
-0.0031 0.0040
0.0043 0.0146
-0.0423 0.0465
0.0441 0.0178
0.0000 0.0007
0.9347 0.0102
0.0391 0.0143
0.0030 0.0057
-0.1464 0.0230
2.0808 1.0989
prfise -0.0144 0.0063
0.0087 0.0149
0.8904 0.0123
0.0016 0.0012
-0.0045 0.0010
0.0007 0.0006
-0.0027 0.0046
-0.0775 0.0459
-0.0171 0.0172
0.1555 0.0575
pfcut 0.0267 0.0118
vma -0.0081 0.0153
-0.1795 0.0209
-4.3021 0.9677
-0.7034 0.1233
0.2886 0.0896
0.6517 0.0516
0.3840 0.2081
-4.6468 0.3604
Appendix page 5
-------
Table B2. Coefficient estimates: models with media and uncertainty variables
(a) Three-equation models
Model 3.21 b
Equation Variable Coeff. Std. Error
vma intercept 3.1468 0.3541
vma inc 0.0770 0.0118
vma Adults /road mile -0.0151 0.0037
vma popratio 0.0630 0.0323
vma Urban -0.0061 0.0395
vma Railpop -0.0082 0.0042
vma D7479 -0.0445 0.0035
vma Trend 0.0013 0.0004
vma vma(-1) 0.8334 0.0104
vma vehstock 0.0161 0.0067
vma pf+fint -0.0639 0.0049
vma pm"2 -0.0207 0.0061
vma pmlnc 0.0577 0.0107
vma pm*Urban 0.0131 0.0093
vma pfcut + fint 0.0340 0.0078
vma Media variable
vma pm*(dummy2003-09)a
vma Fuel price variance
vma AR(1) -0.1021 0.0204
veh intercept -0.2188 0.1449
veh pnewcar 0.0460 0.0317
veh interest -0.0004 0.0042
veh income 0.0038 0.0146
veh adults /road mile -0.0137 0.0060
veh licenses/adult 0.0349 0.0183
veh trend 0.0004 0.0007
veh vehstock(-l) 0.9316 0.0104
veh vma 0.0281 0.0146
veh pm 0.0019 0.0058
veh AR(1) -0.1469 0.0230
fint intercept 0.9282 1.0517
fint pf + vma -0.0097 0.0060
fint inc 0.0000 0.0146
fint fint(-1) 0.8977 0.0115
fint popratio -0.0005 0.0586
fint Trend66-73 -0.0005 0.0011
fint Trend74-79 -0.0061 0.0011
fint Trend80+ -0.0002 0.0007
fint D7479 -0.0032 0.0048
fint Urban -0.0890 0.0471
fint cafe -0.0256 0.0183
fint pfcut 0.0143 0.0123
fint AR(1) -0.1804 0.0202
'dummy is normalized
Model 3.35
Coeff. Std. Error
2.9103 0.3668
0.0830 0.0121
-0.0142 0.0038
0.0725 0.0328
-0.0114 0.0400
-0.0084 0.0043
-0.0440 0.0035
0.0011 0.0005
0.8325 0.0106
0.0162 0.0068
pf +fint -0.0587 0.0052
-0.0053 0.0075
0.0583 0.0109
0.0118 0.0094
pfcut + fint 0.0286 0.0081
pf *Media_dummy -0.0301 0.0101
-0.0969 0.0206
-0.2117 0.1449
0.0449 0.0317
-0.0002 0.0042
0.0039 0.0146
-0.0139 0.0060
0.0348 0.0183
0.0004 0.0007
0.9316 0.0104
0.0274 0.0146
0.0016 0.0058
-0.1469 0.0230
1.6171 1.0241
pf + vma -0.0124 0.0059
-0.0031 0.0145
0.9070 0.0115
-0.0391 0.0590
0.0000 0.0011
-0.0075 0.0011
0.0005 0.0007
-0.0015 0.0048
-0.0872 0.0470
-0.0023 0.0172
pfCut + vma 0.0220 0.0120
-0.1851 0.0202
Model 3.37
Coeff. Std. Error
3.1487 0.3810
0.0828 0.0123
-0.0145 0.0039
0.0786 0.0334
-0.0231 0.0407
-0.0076 0.0044
-0.0436 0.0035
0.0014 0.0005
0.8276 0.0109
0.0181 0.0070
pf +fint -0.0641 0.0057
-0.0064 0.0075
0.0711 0.0126
0.0100 0.0097
pfcut + fint 0.0332 0.0083
pf *Media_dummy -0.0319 0.0101
-0.0216 0.0079
-0.0894 0.0209
-0.1996 0.1445
0.0434 0.0317
-0.0004 0.0042
0.0043 0.0146
-0.0139 0.0060
0.0346 0.0183
0.0003 0.0007
0.9319 0.0104
0.0262 0.0146
0.0012 0.0058
-0.1475 0.0230
0.8319 1.0025
pf + vma -0.0104 0.0058
-0.0003 0.0145
0.9009 0.0115
0.0020 0.0585
-0.0002 0.0011
-0.0063 0.0011
-0.0001 0.0007
-0.0031 0.0048
-0.0876 0.0468
-0.0210 0.0169
pfCut + vma 0.0129 0.0118
-0.1810 0.0202
Model 3.42 [ Model 3.45
Coeff. Std. Error Coeff. Std. Error
3.9416 0.402o| 2.6376 0.3750
0.0746 0.0121 0.0912 0.0127
-0.0140 0.0038 -0.0155 0.0042
0.1462 0.0376
-0.0132 0.0401
-0.0065 0.0043
-0.0429 0.0035
0.0024 0.0005
0.8321 0.0108
0.0185 0.0069
pf +fint 3.9959 0.0069
-0.0126 0.0070
0.0779 0.0124
0.0091 0.0095
pfcut + fint 0.0529 0.0091
pf*Media_dummy -0.0316 0.0101
-0.0265 0.0078
pm*log(pf_var) 0.0028 0.0007
-0.0960 0.0207
-0.2249 0.1443
0.0423 0.0317
-0.0004 0.0042
0.0033 0.0146
-0.0136 0.0060
0.0355 0.0183
0.0003 0.0007
0.9314 0.0104
0.0289 0.0146
0.0014 0.0058
-0.1466 0.0230
0.0017 0.9813
pf + vma -0.0079 0.0058
0.0050 0.0144
0.8930 0.0112
0.0070 0.0583
-0.0017 0.0011
-0.0045 0.0010
-0.0009 0.0006
-0.0049 0.0047
-0.0920 0.0467
-0.0592 0.0166
PFCut + VMA 0.0031 0.0115
-0.1786 0.0202
0.1205 0.0368
-0.0333 0.0407
-0.0052 0.0048
-0.0278 0.0043
0.0006 0.0005
0.8247 0.0117
0.0253 0.0075
pf +fint -0.0666 0.0053
-0.0302 0.0081
0.0807 0.0136
0.0118 0.0106
pfcut + fint 0.0210 0.0083
pf_rise * Articles -0.2680 0.0544
-0.0347 0.0084
pm*log(pf_var) 0.0081 0.0024
-0.0780 0.0221
-0.1865 0.1380
0.0400 0.0316
-0.0006 0.0042
0.0045 0.0145
-0.0137 0.0060
0.0350 0.0183
0.0003 0.0007
0.9324 0.0104
0.0250 0.0139
0.0000 0.0058
-0.1469 0.0230
-2.1591 0.9725
pf+vma -0.0033 0.0058
0.0038 0.0144
0.8881 0.0116
0.0813 0.0615
0.0010 0.0012
-0.0037 0.0011
-0.0019 0.0006
-0.0097 0.0047
-0.0921 0.0466
-0.0879 0.0165
PFCut + VMA -0.0225 0.0114
-0.167898 0.021329
Appendix page 6
-------
(b) Four-equation models
Model 4.21 b
Equation Variable Coeff. Std. Error
vma intercept 3.1388 0.3529
vma inc 0.0807 0.0119
vma cong 0.0016 0.0026
vma conglncome -0.0131 0.0031
vma cong*pm -0.0016 0.0021
vma 7479 dummy -0.0441 0.0035
vma trend 0.0013 0.0005
vma vma(-1) 0.8305 0.0107
vma vehstock 0.0242 0.0066
vma pm -0.0629 0.0049
vma pm"2 -0.0275 0.0061
vma pm*inc 0.0573 0.0110
vma popratio 0.1010 0.0410
vma urban -0.0589 0.0415
vma road miles/state land area 0.0155 0.0066
vma pfcut + fint 0.0340 0.0079
vma Media variable
vma pm*(dummy2003-09)a
vma Fuel price variance
vehstock intercept -0.3554 0.1421
vehstock pnewcar 0.0445 0.0317
vehstock interest -0.0030 0.0040
vehstock income 0.0044 0.0146
vehstock urban -0.0416 0.0465
vehstock licenses/adult 0.0445 0.0178
vehstock trend 0.0000 0.0007
vehstock vehstock(-l) 0.9351 0.0102
vehstock vma 0.0384 0.0143
vehstock pm 0.0032 0.0057
vehstock rho -0.1471 0.0230
fint intercept -1.0263 0.9488
fint pf + vma -0.0041 0.0058
fint inc 0.0064 0.0144
fint fint(-1) 0.8805 0.0111
fint Trend66-73 0.0001 0.0010
fint Trend74-79 -0.0034 0.0009
fint Trend80+ -0.0014 0.0006
fint 7479 dummy -0.0078 0.0047
fint urban -0.0919 0.0471
fint cafep -0.0714 0.0155
fint popratio 0.1302 0.0556
fint pfcut+vma -0.0080 0.0112
fint rho -0.1691 0.0202
cong intercept -4.0860 0.9273
cong urban-lane-miles/adult -0.6058 0.1102
cong (vehicle miles/adult)+log(ui 0.2799 0.0860
cong population / state land aree 0.5908 0.0490
cong percent trucks 0.4634 0.1983
cong urban -4.0331 0.3434
Model 4.35
Coeff. Std. Error
3.1737 0.3555
0.0791 0.0119
0.0011 0.0027
-0.0144 0.0032
-0.0025 0.0021
-0.0445 0.0035
0.0014 0.0005
0.8314 0.0106
0.0236 0.0065
PM -0.0638 0.0050
-0.0296 0.0065
0.0575 0.0110
0.1093 0.0397
-0.0639 0.0415
0.0148 0.0065
pfcut+fint 0.0352 0.0080
pf *Media_dummy 0.0061 0.0058
-0.3577 0.1421
0.0443 0.0317
-0.0030 0.0040
0.0043 0.0146
-0.0417 0.0465
0.0446 0.0178
0.0000 0.0007
0.9350 0.0102
0.0387 0.0143
0.0031 0.0057
-0.1469 0.0230
-0.6026 0.9380
pf + vma -0.0060 0.0057
0.0064 0.0144
0.8833 0.0110
0.0002 0.0010
-0.0037 0.0009
-0.0010 0.0006
-0.0069 0.0047
-0.0896 0.0470
-0.0585 0.0148
0.1330 0.0553
pfcut+vma -0.0031 0.0110
-0.1706 0.0202
-3.9180 0.9530
-0.6394 0.1176
0.2546 0.0872
0.6062 0.0502
0.4554 0.2016
-4.2241 0.3484
Model 4.37
Coeff. Std. Error
3.5432 0.3653
0.0794 0.0119
0.0006 0.0027
-0.0128 0.0032
-0.0028 0.0021
-0.0444 0.0035
0.0019 0.0005
0.8221 0.0109
0.0277 0.0066
PM -0.0729 0.0054
-0.0263 0.0066
0.0825 0.0122
0.1248 0.0399
-0.0828 0.0419
0.0133 0.0066
pfcut+fint 0.0420 0.0081
pf *Media_dummy 0.0071 0.0058
-0.0359 0.0071
-0.3557 0.1420
0.0412 0.0317
-0.0035 0.0040
0.0042 0.0146
-0.0421 0.0465
0.0445 0.0178
-0.0001 0.0007
0.9354 0.0102
0.0387 0.0143
0.0028 0.0057
-0.1474 0.0230
-0.5382 0.9373
pf + vma -0.0059 0.0057
0.0066 0.0144
0.8823 0.0110
0.0000 0.0010
-0.0035 0.0009
-0.0010 0.0006
-0.0068 0.0047
-0.0894 0.0470
-0.0583 0.0148
0.1360 0.0553
pfcut+vma -0.0022 0.0110
-0.1704 0.0202
-3.8896 0.9664
-0.6352 0.1217
0.2533 0.0872
0.6088 0.0504
0.4506 0.2020
-4.2191 0.3485
Model 4.42 Model 4.45
Coeff. Std. Error Coeff. Std. Error
3.8758 0.3711 4.2917 0.3752
0.0652 0.0122
-0.0004 0.0027
-0.0117 0.0032
-0.0044 0.0021
-0.0467 0.0035
0.0024 0.0005
0.8275 0.0109
0.0268 0.0066
PM -0.0706 0.0054
0.0037 0.0085
0.0944 0.0124
0.0669 0.0414
-0.0967 0.0420
0.0111 0.0066
pfcut+fint 0.0506 0.0083
pf*Media_dummy -0.0080 0.0063
-0.0308 0.0072
pm*log(pf var) -0.0100 0.0019
-0.3592 0.1420
0.0403 0.0318
-0.0038 0.0040
0.0041 0.0146
-0.0425 0.0465
0.0444 0.0178
-0.0001 0.0007
0.9354 0.0102
0.0391 0.0143
0.0028 0.0057
-0.1467 0.0230
-0.5531 0.9355
pf + vma -0.0049 0.0057
0.0046 0.0144
0.8749 0.0112
0.0009 0.0010
-0.0036 0.0009
-0.0010 0.0006
-0.0071 0.0046
-0.0898 0.0470
-0.0554 0.0148
0.1700 0.0556
pfcut+vma -0.0018 0.0110
-0.1697 0.0203
-3.8874 0.9650
-0.6311 0.1209
0.2552 0.0871
0.6103 0.0503
0.4493 0.2018
-4.2251 0.3483
0.0683 0.0123
0.0019 0.0027
-0.0137 0.0032
-0.0057 0.0021
-0.0320 0.0042
0.0027 0.0005
0.8423 0.0112
0.0299 0.0066
PM -0.0719 0.0053
-0.0114 0.0074
0.0905 0.0124
0.0581 0.0410
-0.0801 0.0422
0.0103 0.0066
pfcut+fint 0.0626 0.0085
PF_rise* Articles -0.3117 0.0490
-0.0321 0.0072
PM*log(pf var) -0.0044 0.0019
-0.3689 0.1420
0.0400 0.0318
-0.0039 0.0040
0.0037 0.0146
-0.0427 0.0465
0.0443 0.0178
-0.0001 0.0007
0.9355 0.0102
0.0402 0.0143
0.0029 0.0057
-0.1468 0.023C
-1.4809 0.9456
pf + vma -0.0035 0.0057
0.0029 0.0144
0.8686 0.0112
0.0016 0.0010
-0.0035 0.0009
-0.0015 0.0006
-0.0087 0.0046
-0.0952 0.0471
-0.0747 0.0145
0.1640 0.0554
pfcut+vma -0.0129 0.0111
-0.1681 0.0204
-4.3568 0.9984
-0.7236 0.1269
0.2682 0.0882
0.6056 0.0509
0.4685 0.2037
-4.3221 0.3514
dummy is normalized
Appendix page 7
-------
Appendix C. Detailed yearly projections
Model 3.3:
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025
Short Run Rebound
Dynamic Rebound
Long Run Rebound
2.3% 2.1%
11.1% 11.3%
14.7% 13.1%
2.1% 2.4% 2.6%
11.5% 11.8% 12.0%
13.0% 14.9% 16.4%
2.9% 3.0% 3.0% 3.3% 2.5% 2.8% 2.9% 2.8% 2.8% 2.8% 2.7% 2.5% 2.4% 2.4% 2.3% 2.2% 2.0% 2.0% 1.8% 1.8% 1.6%
12.0% 12.0% 11.8% 11.7% 11.4% 11.4% 11.1% 10.8% 10.5% 10.1% 9.6% 9.2% 8.8% 8.3% 7.9% 7.4% 6.9% 6.5% 6.1% 5.7% 5.3%
18.4% 18.8% 19.0% 20.7% 15.9% 17.6% 18.1% 17.7% 17.9% 17.4% 16.7% 15.9% 15.4% 14.9% 14.4% 13.7% 12.9% 12.3% 11.5% 11.0% 10.2%
2026
1.5%
4.9%
9.6%
2027
1.5%
4.6%
9.1%
2028
1 .4%
4.3%
8.5%
2029
1 .3%
4.0%
8.0%
2030
1.2%
3.8%
7.2%
2031
1.1%
3.6%
6.7%
2032
1 .0%
3.5%
6.2%
2033
0.9%
3.4%
5.7%
2034
0.9%
3.3%
5.3%
2035
0.8%
3.2%
4.8%
High Oil Price Case
Short Run Rebound 2.3% 2.1% 2.1% 2.4% 2.6% 2.9% 3.0% 3.0% 3.3% 2.5% 2.8% 3.3% 3.5% 3.6% 3.5% 3.4% 3.3% 3.3% 3.2% 3.2% 3.1% 2.9% 2.8% 2.7% 2.6% 2.5% 2.4°/i
Dynamic Rebound 11.5% 11.8% 12.3% 12.8% 13.2% 13.5% 13.7% 13.9% 14.0% 14.1% 14.4% 14.5% 14.4% 14.1% 13.7% 13.3% 12.9% 12.5% 12.0% 11.6% 11.1% 10.6% 10.1% 9.6% 9.3% 8.8% 8.4°/i
Long Run Rebound 14.7% 13.1% 13.0% 14.9% 16.4% 18.4% 18.8% 19.0% 20.7% 15.9% 17.6% 20.8% 22.1% 22.6% 22.2% 21.7% 21.0% 20.8% 20.4% 19.9% 19.3% 18.6% 17.6% 17.0% 16.3% 15.7% 14.9°/i
2.3% 2.2% 2.1% 2.0% 1.9% 1.8% 1.7% 1.6% 1.5%
8.1% 7.8% 7.5% 7.2% 7.0% 6.8% 6.6% 6.5% 6.4%
14.2% 13.6% 13.1% 12.4% 11.9% 11.3% 10.8% 10.2% 9.6%
Low Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
2.3% 2.1% 2.1% 2.4% 2.6% 2.9% 3.0% 3.0% 3.3% 2.5% 2.8% 2.4% 2.2% 2.1% 1.9% 1.7%
10.6% 10.6% 10.7% 10.7% 10.6% 10.4% 10.0% 9.5% 8.9% 8.2% 7.8% 7.1% 6.5% 6.0% 5.5% 4.9%
14.7% 13.1% 13.0% 14.9% 16.4% 18.4% 18.8% 19.0% 20.7% 15.9% 17.6% 14.8% 13.8% 12.9% 11.8% 10.6%
1 .5%
4.5%
9.6%
1 .4%
4.0%
8.7%
1.3%
3.5%
8.1%
1.2%
3.0%
7.4%
1 .2%
2.6%
7.4%
0.9%
2.1%
5.5%
0.8%
1.8%
4.7%
0.7%
1.4%
4.0%
0.6%
1.2%
3.7%
0.5%
1.0%
3.1%
0.4%
0.8%
2.7%
0.4%
0.6%
2.4%
0.4%
0.5%
2.2%
0.3%
0.3%
1.8%
0.3%
0.1%
1 .6%
0.2%
0.1%
0.9%
0.2% 0.1%
-0.1% 0.1%
1.0% 0.4%
0.1%
0.1%
0.3%
0.0%
0.2%
0.3%
Model 3.21b:
.
2000 2001 2002 2003 2004 2005 2006 2007
Reference Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
High Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Low Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
0.4%
3.1%
2.2%
0.4%
3.7%
2.2%
0.4%
2.5%
2.2%
0.1%
3.4%
0.1% 0.2%
3.7% 4
1%
0.8% 0.6% 1.4%
0.1%
4.3%
0.8%
0.1%
2.6%
0.8%
0.1% 0.2%
4.9% 5
0.6% 1
6%
4%
0.1% 0.2%
2.8% 2
0.6% 1
9%
4%
0.5%
4.4%
3.2%
0.5%
6.3%
3.2%
0.5%
2.9%
3.2%
1.0% 1.2%
4.6% 4.6%
6.2% 7.3%
1.0% 1.2%
6.9% 7.4%
6.2% 7.3%
1.0% 1.2%
2.8% 2.5%
6.2% 7.3%
1 .3%
4.6%
8.0%
1 .3%
7.8%
8.0%
1 .3%
2.1%
8.0%
2008
1 .7%
4.4%
10.5%
1 .7%
8.1%
10.5%
1 .7%
1 .6%
10.5%
2009 2010 2011 2012 2013 2014 2015
0.6% 1 .0%
4.2% 4.2%
3.3% 5.8%
0.6% 0.9%
8.4% 8.5%
3.3% 5.7%
0.6% 1 .0%
1.0% 2.0%
3.3% 5.7%
1.1%
4.2%
6.5%
1 .7%
9.3%
10.6%
0.4%
1 .2%
2.5%
1.0%
4.0%
6.1%
2.1%
9.4%
12.9%
0.3%
0.8%
1.6%
1.1%
3.8%
6.6%
2.3%
9.2%
14.0%
0.2%
0.5%
1.1%
1.0%
3.5%
6.2%
2.2%
8.8%
13.7%
0.1%
0.3%
0.6%
0.9%
3.0%
5.6%
2.2%
8.4%
13.4%
0.1%
0.1%
0.3%
2016
0.8%
2.7%
4.9%
2.1%
8.0%
12.6%
0.0%
0.1%
0.2%
2017
0.8%
2.3%
4.5%
2.1%
7.5%
12.7%
0.0%
0.0%
0.1%
2018
0.7%
1 .9%
4.0%
2.0%
7.0%
12.2%
0.0%
0.0%
0.1%
2019 2020
0.6% 0.5%
1.6% 1.2%
3.7% 3.2%
1.9% 1.8%
6.4% 5.9%
11.8% 11.1%
0.0% 0.0%
0.0% 0.0%
0.0% 0.1%
2021
0.4%
0.9%
2.6%
1 .7%
5.3%
10.4%
0.0%
0.0%
0.0%
2022
0.4%
0.7%
2.2%
1.5%
4.7%
9.2%
0.0%
0.0%
0.0%
.
2023 2024 2025 2026 2027 2028 2029
0.3%
0.5%
1.7%
1.4%
4.2%
8.6%
0.0%
0.0%
0.0%
0.2%
0.3%
1 .4%
1 .3%
3.8%
7.8%
0.0%
0.0%
0.0%
0.2%
0.2%
1.0%
1.2%
3.4%
7.2%
0.0%
0.0%
0.0%
0.1%
0.1%
0.7%
1.1%
2.9%
6.3%
0.0%
0.0%
0.0%
0.1%
0.1%
0.6%
0.9%
2.5%
5.7%
0.0%
0.0%
0.0%
0.1%
0.0%
0.4%
0.8%
2.2%
5.0%
0.0%
0.0%
0.0%
0.1%
0.0%
0.3%
0.8%
1 .9%
4.5%
0.0%
0.0%
0.0%
2030
0.0%
0.0%
0.2%
0.7%
1.7%
3.9%
0.0%
0.0%
0.0%
2031 2032
0.0% 0.0%
0.0% 0.0%
0.1% 0.1%
0.6% 0.5%
1.5% 1.4%
3.5% 3.1%
0.0% 0.0%
0.0% 0.0%
0.0% 0.0%
2033
0.0%
0.0%
0.1%
0.5%
1.3%
2.8%
0.0%
0.0%
0.0%
2034
0.0%
0.0%
0.1%
0.4%
1 .3%
2.3%
0.0%
0.0%
0.0%
2035
0.0%
0.0%
0.0%
0.3%
1 .3%
1 .9%
0.0%
0.0%
0.0%
Model 3.35 (Reference case):
— Calculated using values of variables from historical data —
Short Run Rebound
Dynamic Rebound
Long Run Rebound
2000
1.1%
4.5%
6.6%
2001
1.0%
4.5%
6.1%
2002
1.0%
4.4%
6.3%
2003
1.1%
4.4%
6.9%
2004
1 .2%
4.3%
7.0%
2005
1 .3%
4.2%
7.6%
2006
1 .2%
4.0%
7.3%
2007
Calculated using values of variables from AEO
2008
1 .2% 1 .2%
3.8% 3.6%
7.0% 7.5%
2009
1.0%
3.4%
5.9%
2010
1.1%
3.3%
6.4%
2011
1.1%
3.0%
6.5%
2012
1 .0%
2.8%
6.3%
2013
1 .0%
2.5%
6.0%
2014
0.9%
2.2%
5.4%
2015
0.8%
1 .9%
4.7%
2016
0.7%
1.6%
4.1%
2017
0.6%
1.4%
3.7%
2018
0.6%
1 .2%
3.3%
2019
0.5%
1 .0%
3.0%
2020
0.4%
0.8%
2.6%
2021
0.4%
0.6%
2.2%
2022
0.3%
0.5%
1 .8%
2023
0.3%
0.3%
1 .5%
2024
0.2%
0.2%
1.2%
2025
0.2%
0.2%
0.9%
2026
0.1%
0.1%
0.7%
2027
0.1%
0.1%
0.5%
2028
0.1%
0.0%
0.4%
2029
0.1%
0.0%
0.3%
2030
0.0%
0.0%
0.2%
2031
0.0%
0.0%
0.2%
2032
0.0%
0.0%
0.1%
2033
0.0%
0.0%
0.1%
2034
0.0%
0.0%
0.0%
2035
0.0%
0.0%
0.0%
Appendix page 8
-------
Model 4.3:
— Calculated using values of variables from historical data —
2000 2001 2002 2003 2004 2005 2006 2007
Reference Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
High Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Low Oil Price Case
Short Run Rebound
Dynamic Rebound
Lonq Run Rebound
2.0% 1.6% 1.4%
11.7% 12.0% 12.2%
12.1% 9.2% 8.0%
2.0% 1.6% 1.4%
12.8% 13.5% 14.1%
12.1% 9.2% 8.0%
2.0% 1.6% 1.4%
10.4% 10.3% 10.1%
12.1% 9.2% 8.0%
1.9% 2.5% 3.1%
12.5% 12.7% 12.9%
11.4% 14.7% 18.6%
1.9% 2.5% 3.1%
14.9% 15.6% 16.3%
11.4% 14.7% 18.6%
1.9% 2.5% 3.1%
9.8% 9.5% 9.1%
11.4% 14.7% 18.6%
3.3% 3.4%
12.8% 13.1%
20.0% 20.8%
3.3% 3.4%
16.7% 17.7%
20.0% 20.8%
3.3% 3.4%
8.2% 7.9%
20.0% 20.8%
2008
3.9%
13.5%
23.5%
3.9%
17.7%
23.5%
3.9%
8.6%
23.5%
2009 2010 2011 2012
2.5%
13.2%
14.9%
2.5%
18.1%
14.9%
2.5%
7.6%
14.9%
3.0% 3.2% 3.1%
13.2% 13.1% 12.9%
18.2% 19.0% 18.7%
3.0% 3.9% 4.3%
18.6% 19.1% 19.2%
18.1% 23.8% 26.2%
3.0% 2.2% 2.0%
6.9% 6.0% 5.3%
18.1% 13.3% 11.7%
2013
3.2%
12.5%
19.3%
4.5%
19.0%
27.5%
1 .8%
4.7%
10.6%
2014
3.2%
12.2%
19.0%
4.5%
18.6%
27.3%
1.6%
4.1%
9.4%
2015
3.1%
11.7%
18.4%
4.5%
18.3%
27.1%
1.4%
3.4%
7.9%
Calculated usin values of variables from AEO
2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034
2.9% 2.9% 2.8% 2.7% 2.6% 2.4% 2.3% 2.2% 2.1% 2.0% 1.9% 1.8% 1.7% 1.6% 1.5% 1.3% 1.3% 1.2% 1.1%
11.2% 10.7% 10.2% 9.7% 9.1% 8.6% 8.1% 7.6% 7.1% 6.6% 6.2% 5.8% 5.4% 5.0% 4.7% 4.5% 4.3% 4.1% 4.0%
17.6% 17.2% 16.6% 16.2% 15.4% 14.4% 13.9% 13.0% 12.5% 11.6% 11.0% 10.6% 9.8% 9.4% 8.3% 7.7% 7.1% 6.5% 6.2%
4.3% 4.4% 4.3% 4.2% 4.1% 4.0% 3.8% 3.7% 3.6% 3.5% 3.4% 3.3% 3.1% 3.1% 2.9% 2.9% 2.8% 2.7% 2.6%
17.8% 17.4% 16.8% 16.3% 15.7% 15.1% 14.5% 14.0% 13.5% 13.0% 12.5% 12.1% 11.7% 11.4% 11.0% 10.8% 10.5% 10.3% 10.1%
26.3% 26.5% 26.1% 25.7% 25.1% 24.3% 23.1% 22.5% 21.7% 21.1% 20.2% 19.5% 18.8% 18.3% 17.5% 17.0% 16.3% 15.8% 15.1%
1.2% 1.0% 0.9% 0.8% 0.9% 0.4% 0.3% 0.2% 0.2% 0.1% 0.1% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
2.9% 2.4% 1.8% 1.3% 0.8% 0.4% 0.3% 0.2% 0.1% 0.1% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
6.8% 5.8% 5.1% 4.2% 4.7% 2.0% 1.4% 1.0% 0.9% 0.4% 0.3% 0.2% 0.2% 0.1% 0.1% 0.0% 0.0% 0.0% 0.0%
2035
1.0%
3.9%
5.6%
2.5%
9.9%
14.5%
0.0%
0.0%
0.0%
Model 4.21b:
Reference Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
High Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
Low Oil Price Case
Short Run Rebound
Dynamic Rebound
Long Run Rebound
— Calculated using valu
2000 2001 2002
0.2% 0.0% 0.0%
4.1% 4.7% 5.1%
0.9% 0.1% 0.0%
0.2% 0.0% 0.0%
5.5% 6.5% 7.4%
0.9% 0.1% 0.0%
0.2% 0.0% 0.0%
2.9% 3.1% 3.1%
0.9% 0.1% 0.0%
ss of variables from historical data —
2003 2004 2005 2006 2007
0.1%
5.2%
0.4%
0.1%
8.1%
0.4%
0.1%
2.8%
0.4%
0.4%
5.2%
2.2%
0.4%
8.7%
2.2%
0.4%
2.3%
2.2%
1.1% 1.4% 1.6%
5.3% 5.1% 5.5%
6.5% 8.4% 9.5%
1.1% 1.4% 1.6%
9.4% 9.9% 11.1%
6.5% 8.4% 9.5%
1.1% 1.4% 1.6%
2.0% 1.3% 1.2%
6.5% 8.4% 9.5%
2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035
2.1% 0.5% 1.1% 1.3% 1.2% 1.3% 1.3% 1.2% 1.1% 1.0% 0.9% 0.9% 0.7% 0.6% 0.5% 0.4% 0.4% 0.3% 0.2% 0.2% 0.1% 0.1% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0%
5.6% 5.4% 5.4% 5.5% 5.3% 5.1% 4.8% 4.3% 3.8% 3.3% 2.8% 2.3% 1.8% 1.4% 1.0% 0.7% 0.5% 0.3% 0.2% 0.1% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
13.0% 3.0% 6.4% 7.4% 7.1% 7.9% 7.7% 7.1% 6.3% 5.9% 5.4% 4.9% 4.2% 3.3% 2.9% 2.2% 1.9% 1.4% 1.0% 0.9% 0.6% 0.5% 0.2% 0.1% 0.1% 0.1% 0.1% 0.0%
2.1% 0.5% 1.1% 2.2% 2.7% 2.9% 2.9% 2.9% 2.8% 2.8% 2.8% 2.7% 2.6% 2.5% 2.3% 2.2% 2.0% 1.9% 1.8% 1.6% 1.5% 1.4% 1.3% 1.2% 1.1% 1.0% 0.9% 0.8%
10.7% 11.3% 11.8% 12.9% 13.1% 12.9% 12.5% 12.2% 11.7% 11.3% 10.6% 10.0% 9.4% 8.8% 8.1% 7.5% 7.0% 6.5% 5.9% 5.4% 5.0% 4.6% 4.3% 4.0% 3.7% 3.4% 3.3% 3.1%
13.0% 3.0% 6.3% 13.3% 16.4% 18.1% 18.0% 17.8% 17.0% 17.4% 16.9% 16.5% 15.9% 15.1% 13.8% 13.1% 12.2% 11.6% 10.6% 9.8% 9.0% 8.5% 7.7% 7.1% 6.5% 5.9% 5.2% 4.5%
2.1% 0.5% 1.1% 0.3% 0.2% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
1.6% 0.8% 2.5% 0.9% 0.4% 0.2% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
13.0% 3.0% 6.3% 1.6% 0.7% 0.4% 0.2% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
Appendix page 9
-------
Appendix D. Projections from model with structural break in 2003
35.0%
Projections of Rebound Effect:
Four-equation model estimated on 1966-2009 data with structural break
in 2003: projections assume break remains through 2035
2005 2010 2015 2020
2025
2030
2035
• Short run
•Dynamic
• Long run
Projections of Rebound Effect:
Four-equation model estimated on 1966-2009 data with structural break
in 2003: projections assume break is "turned off" starting 2010
oc no/, _
on no/
oU.Uvo
oc no/
ZD.U /o
on no/
ZU.U /o
1 O.Uvo
A n no/.
5 no/.
Ono/,
\
I
V-±~L. L_A
•-.tn*******
4, ^**^*****»^*^^
^^^^^^^^^v^
—*— Short run
— •— Dynamic
—A— Long run
2005 2010 2015 2020 2025 2030 2035
Appendix page 10
------- |