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Rebound Effect of Efficiency Improvement in Passenger Cars on Gasoline Consumption in
Canada
Saeed Moshiri
Department of Economics, STM College, University of Saskatchewan
1437 College Drive, Saskatoon, SK, Canada S7N 0W6
smoshiri@stmcollege.ca
Kamil Aliyev
Department of Economics, University of Saskatchewan
1437 College Drive, Saskatoon, SK, Canada S7N 0W6
Kta715@mail.usask.ca
Highlights
The rebound effect of fuel efficiency in vehicle transportation is estimated.
The Canadian household spending data and the AIDS model are used.
The average rebound effect is between 82 and 88 percent.
The rebound effect varies in provinces and rises with income and gasoline prices.
1
Rebound Effect of Efficiency Improvement in Passenger Cars on Gasoline Consumption in
Canada
2
Abstract
The fossil fuel-driven transport sector has been one of the major contributors to CO2 emission
across the world, keeping it on the energy policy agenda for the past three decades. Canada ranks
second in gasoline consumption among OECD countries, and Canadian gasoline expenditure share
has been increasing since the 1990s. Fuel efficiency policies aim to decrease gasoline
consumption; however, the effect can be mitigated by changes in consumer behaviour such as
traveling more distances — a rebound effect. Thus, the effectiveness of fuel efficiency policy is
dependent on the magnitude of the rebound effect. In this paper, we estimate rebound effect for
personal transportation in Canada using the data from the Household Spending Survey for the
period 1997-2009. The model includes a system of expenditure share equations for gasoline, other
energy, and non-energy goods specified by AIDS and QUAIDS models and estimated by the
nonlinear SUR method. Our estimation results show a rather high rebound effect of 82-88 percent
on average in Canada, but with a great heterogeneity across income groups and provinces.
Specifically, the rebound effect ranges from 63 to 96 percent across income groups and provinces
and increases with gasoline prices.
Keywords: Gasoline, demand, AIDS, QUAIDS, rebound effect, Canada
JEL Classification: D1, Q41, Q48
3
1. Introduction
The rise in oil prices in the 2000s, along with increasing concerns about the greenhouse
gas (GHG) emissions, spurred policy makers and the auto-manufacturing sector to adopt more
stringent fuel efficiency standards. Fuel efficient cars use less gas per kilometer, resulting in saving
on fuel cost and reduction of GHG emissions. However, the new fuel efficiency standards may
also trigger rebound effect: a tendency to increase distance traveled or to switch to larger vehicles,
offsetting some of the initial gains on fuel costs and emission reduction. High rebound effect
implies that an increase in efficiency itself cannot achieve the desired targets for emission
reduction and should, therefore, be coupled with other policies to dis-incentivize gasoline
consumption. The magnitude of the rebound effect is thus critical for the proper policy design on
reducing gasoline consumption and emissions.
Fuel efficiency can have multiple rebound effects on gasoline consumption.
1
The direct
effect arises from increased energy use induced by the reduction of fuel cost due to higher
efficiency. A secondary effect is associated with an increase in consumption of all other goods and
services whose production requires energy. There is also an economy-wide and international effect
which concerns changes in labour market and international trade and their overall effects on the
aggregate output and energy consumption. Finally, fuel efficiency may bring about changes in
consumer tastes, which may have an impact on energy consumption.
Canada produces about 2% of global greenhouse gas emission, while having only 0.5% of
the world's population. Based on OECD ranking for high-income countries, Canada is second
highest in terms of gasoline consumption per capita, and its CO2 emissions from fuel combustion
have increased by about 24 percent between 1990 and 2010. Emissions from transportation are the
1
See Turner (2013) for a critical view on different classifications of rebound effect.
4
largest contributor to Canada’s GHG emission with about 75 percent of oil-related GHG emission
coming from fuel used by vehicles (Environment Canada, 2013). To curb the GHG emission,
Canada has adopted fuel efficiency standards such as the 2010 Passenger Automobile and Light
Truck Greenhouse Gas Emission Regulation (LDV1), according to which the fuel efficiency of
new passenger light trucks is expected to increase by 37 percent, decreasing gasoline consumption
of new cars from 8.6 l/100 km in 2010 to 6.4 L/100 km in 2020.
Canada is also a geographically large country with a low density population and
heterogeneous provinces in terms of economic activities, energy consumption, and emission
levels. Since natural resources and energy management as well as environmental policies are
primarily under provincial jurisdictions, studies at the provincial level will shed more light on the
dynamics of energy demand and rebound effects in Canada. Energy demand is also heterogeneous
across income groups, leading to different rebound effects in low and high income groups. Low
income households spend more on energy relative to their income than high income households,
but higher income households can better afford to switch to larger cars when gasoline prices fall.
Rebound effects are also expected to increase with energy prices, as fuel efficiency will generate
more savings when prices are higher.
There are many studies on rebound effects in different sectors in OECD countries, but the
number of studies in Canada, particularly at the micro level, is limited. The household spending
data overcomes the shortcomings associated with the small sample size in aggregate level studies
and allows for examining the heterogeneity in income effects and controlling for the impact of
demographical changes. The household spending survey data also allows us to incorporate the
interaction between various energy commodities and non-energy goods in the consumption basket,
an option which is not available in the partial demand models using the transportation survey data.
5
In this paper, we estimate demand for gasoline and direct rebound effect in Canada for three
income groups and nine provinces using the Canadian Survey of Household Spending data for the
period 1997-2009. Our estimation results show that demand for gasoline in Canada is inelastic,
and the rebound effect is significant and higher than the average effect in OECD countries. The
results also indicate great heterogeneities in elasticities and the rebound effects in Canadian
provinces and income groups and at different gasoline price levels. Specifically, the rebound effect
is higher in high income families and provinces than in low income families and provinces, and
increases with gasoline prices.
The rest of the paper is organized as follows: Section 2 reviews the literature and Section
3 discusses the theoretical background. Sections 4 -6 present and discuss the data the results and
Section 7 draws conclusion.
2. Review of Previous Studies
Studies on rebound effect started in the early 1980s, but only recently has the topic received
growing interest in academic and policy circles. Theoretical and particularly empirical papers on
rebound effects are now numerous with a wide range in reported results. Researchers have used a
variety of models, econometric techniques, data types, and time periods to estimate rebound effect
in different sectors. However, the variation among studies in the empirical results on the rebound
effect of the fuel efficiency can be ascribed mainly to the data types used for estimation, which are
based on either transportation surveys or household budget surveys. Table 1 presents summary of
the selected studies on fuel efficiency rebound effect for OECD countries.
[Table 1 here]
6
There have been also some reviews of the literature summarizing the hugely varying
estimates of the rebound effect in different countries. The earlier studies focus mainly on the price
elasticity of gasoline, which can be used to derive the rebound effect. For instance, Goodwin
(1992) reviews more than 50 studies and reports the price elasticity of fuel consumption in road
traffic within a range of -0.27 to -0.73 in the short-run and long-run, respectively. Espey (1998)
builds on the previous reviews and concludes almost the same ranges for the price elasticities, but
lower values for the long-run. Graham and Glaister (2002), however, report a higher value (-0.8)
for long-run price elasticity. In more recent studies, Goodwin et al. (2004) and Graham and Glaister
(2004) carry out two parallel blind reviews of 69 studies on road traffic and fuel consumption in
OECD countries covering periods from 1929 to 1998. The former reports price elasticities of fuel
consumption within a range of -0.25 to -0.60 and income elasticity within a range of 0.39 and 1.08
in the short-run and long-run, respectively. The reported results are similar in the latter. More
recent studies also report different results on price elasticity of gasoline and rebound effects,
depending on type of the data used. Overall, studies that use aggregate data tend to report a lower
price elasticity and implied rebound effect than those that use household budget survey data. For
instance, the rebound effects obtained from national or state/provincial level data by Matos et al.
(2011) for Portugal (1987-2006), Brännlund et al. (2007) for Sweden (1980-1997), Small and Van
Dender (2007) for US (1966-2001), and Barla et al. (2009) for Canada (1990-2004) are in the
range of 5 to 50 percent. However, the household level studies by West (2004) for US (1997),
Frondel et al. (2008) for Germany (1997-2009), and Chitnis et al. (2014) for UK report rebound
effects in the range of 25 to 87 percent.
7
3. Theoretical Background
A utility maximizer consumer will decide how much to consume of different goods and
services, given a preference structure, disposable income, and the prices. In our context, the
consumer basket includes three goods: gasoline, other energies, and non-energy goods. The total
effect of the improvement in fuel efficiency on gasoline consumption can be divided into two parts:
price or substitution effect and income effect. The former implies that the consumer will purchase
more gasoline as fuel cost is cheaper than other energy and non-energy goods, and the latter means
that the consumer has more income to spend on gasoline and other goods and receives a higher
level of utility. The direct rebound effect refers to changes in gasoline consumption through both
substitution and income effects of fuel efficiency. The indirect (secondary) rebound effect arises
from changes in consumption of other energy and non-energy goods due to the income effect of
fuel efficiency, which may increase total energy consumption. See Appendix A for a more detailed
description of the rebound effect.
Rebound effect of fuel efficiency is defined as a relative change in gasoline consumption
as a result of a relative change in fuel efficiency, or the elasticity of gasoline consumption (G) with
respect to fuel efficiency (:
, (1)
Fuel efficiency is defined as a ratio of energy output, the service produced by energy, to
energy input. In transportation, energy input is gasoline (G) and energy output is vehicle distance
travelled (T). Therefore,
(2)
8
Given the prices, an increase in fuel efficiency will decrease fuel cost per distance traveled,
which may lead to traveling more distances or switching to larger cars—the rebound effect. The
rebound effect can also be defined as a relative change in output (vehicle distance travelled) due
to a relative change in fuel efficiency, or the elasticity of energy output (T) with respect to fuel
efficiency (:
(3)
The rebound effect implies that | or . Substituting for G from (2)
into (1) will yield the relationship between the fuel efficiency elasticities of energy input and
energy output as follows (Khazzoom, 1980):
(4)
Equation (4) suggests that the total changes in gasoline demand (G) come from two sources:
a change in fuel efficiency, which is equal to -1, and a change in demand for energy service
. When is non-zero, will be less than one, indicating that the
expected energy savings from higher efficiency will not be proportional, implying a rebound
effect. However, if demand for energy output does not increase as a result of improving
efficiency, i.e., , the efficiency and the demand for energy input will be proportional,
implying a zero rebound effect.
The rebound effect can be estimated from equation (4), which requires an estimation of the
efficiency elasticity of energy services using a demand model. However, since efficiency is not
observed directly, it can be proxied by the fuel cost, which is assumed to be proportional to
9
efficiency (
). Most studies estimate the vehicle distance travelled to obtain the fuel
efficiency elasticity of energy output as a direct measure of rebound effect. Alternatively, the
demand for gasoline can be used to estimate the price elasticity of energy input as a measure of
rebound effect. Under the assumptions that fuel efficiency is exogenous and energy input and
energy output and their prices are proportional, the two elasticities are the same: .
We use the Almost Ideal Demand System (AIDS) developed by Deaton and Maellbauer
(1980) to estimate demand for gasoline and price elasticity of demand in Canada using the
household spending survey data. The model intends to link consumer behavior theory to the data
by estimating a set of expenditure share equations and is widely used in the empirical literature.
However, due to its linearity, the model is not capable of capturing the curvature of Engel curve.
We will also use the Quadratic Almost Ideal Demand System (QUAIDS), which includes a
quadratic term in the logarithm of expenditure whose coefficient varies with price and allows
goods to be luxuries or necessities at different levels of expenditures (Banks et al., 1997). The cost
minimization process of the consumers, given the preferences and prices, generates the following
system of expenditure share equations:
2
ϒ
. (5)
where is the expenditure share for good i, is the price of good j (j=1,…, n), and y represents
income. and are positive linearly homogeneous functions, which correspond to the cost
of subsistence and bliss levels, respectively. They have a flexible functional form, so they can
2
See Appendix B for detailed description of the model.
10
reproduce any arbitrary set of the first and second order derivatives of the cost function at any
single point.
ϒ
(6)
The following restrictions apply to ensure the consistency with the consumer theory:
Slutsky symmetry (ϒ ϒ , homogeneity of the Marshallian demand functions of
degree zero in prices and income ( ϒ
), and adding up condition (
ϒ
).
The QUAIDS model is similar to the AIDS model, but leads to an additional quadratic
term for log of real income in the expenditure share equations as follows:
ϒ
(7)
where all variables are the same as defined before and all the restrictions in addition to
apply. The share equations can be used to derive the price and income elasticities of demand
for different goods. The Marshalian uncompensated price elasticity and income elasticity for
AIDS model are as follows (see Appendix C for details):
(8)
. (9)
11
where
ϒ ϒ and is the Kronecker
delta (
.
The uncompensated price elasticities include both substitution and income effects of price
changes. The compensated price elasticity measures the effect of the price changes on demand
when a consumer is compensated for the income effect of price changes. The relationship between
the uncompensated and compensated price elasticities is as follows:
. (10)
where “u” and “c” stand for uncompensated and compensated, and -eisj is the income effect. The
price elasticities above offer different measures of rebound effect. eiic measures the own
substitution (price) effect and -eisi the pure income effect on gasoline demand. We can also
measure the effect of the fuel efficiency on demand for other goods by obtaining the cross-price
elasticities. Specifically, eijc measures the substitution effect of changes in gasoline prices on the
demand for other goods, and -eisj measures the income effect of changes in gasoline prices on other
goods.
4. Data
We use the Canadian Survey of Household Spending published by Statistics Canada and
available for the period 1997-2009. The total sample includes 47,921 observations from 9
federated provinces, which we divide in three income groups nationally and provincially by taking
12
three quantiles (low, mid, high)
3
. The household members in the sample are aged 25 to 64 living
in urban areas.
4
The Summary statistics of the data are presented in Table 2. The expenditure
shares are constructed by dividing corresponding expenditures by the total annual expenditures of
the household. The average gasoline and other energy expenditure shares in Canadian households
are about 3 percent. Price for other energy is constructed as the weighted average of electricity,
natural gas, and other fuels. Weights are obtained by dividing corresponding expenditures by total
expenditures on other energy. The Consumer Price Index, excluding energy prices, is used for
prices of other goods and services. Some demographic variables, such as number of children under
17 and number of vehicles per adult in a household, are also added to the model to control for
household characteristics. Households having more children and a larger number of vehicles per
adult are expected to have higher gasoline expenditure.
[Table 2 here]
Figure 1 shows that gasoline expenditure increases with income and over time, and Figure
2 shows that gasoline expenditure shares decrease with income and have a positive trend for the
low and mid-income households. This suggests that the income elasticity of demand should be
positive and less than one.
[Figures 1 & 2 here]
3
Canada has 10 federated provinces as follows: Alberta (AB), British Columbia (BC), Manitoba (MB), New
Brunswick (NB), Newfoundland and Labrador (NL), Nova Scotia (NS), Ontario (ON), Prince Edward Island (PEI),
Quebec (QC), Saskatchewan (SK). PEI was excluded from the analysis because of the small number of
observations and masked records for urban or rural.
4
The top and bottom 5 percent of observations are cut to avoid outliers. The excluded observations include
extremely low or high gasoline or total expenditures. Extreme high values of gasoline expenditures may be due to
usage of the private car for commercial purposes. The very low values make shares extremely low, generating
unreasonable elasticities.
13
Figure 3 presents the average gasoline price and the gasoline expenditure shares for the
Canadian households, and Figure 4 shows the gasoline price trends in provinces for the period
1997-2009. Overall, gasoline prices and gasoline expenditure shares have been increasing, and
prices vary across provinces, with Newfoundland and Labrador (NL) having the highest prices and
Alberta (AB) the lowest.
[Figures 3 - 4 here]
5. Estimation Results
We estimate a system of expenditures shares equations (5) and (7) for gasoline, other
energy (electricity, natural gas, and others), and non-energy goods using AIDS and QUAIDS
models to obtain the rebound effect of fuel efficiency in the passenger cars in Canada. The models
are estimated by the non-linear Seemingly Unrelated Regression Model (NLSURE), which uses
an iterative feasible generalized least squares (FGNLS) method to estimate a system of non-linear
equations jointly. The standard errors are robust to heteroskedasticity and serial correlation and
the sample weights are applied.
5
We have also added a trend term to the regression equations to
capture the possible changes in tastes during the sample period. Given the prices, income, and
other household characteristics, people may travel by car more or less depending on environmental
concerns, changes in social conditions, and preferences on recreational activities. Using the
estimated elasticities, the rebound effect is calculated from equation (4). Because of the focus of
our study and space limit, we report the results only for gasoline, but the estimation results for
other two equations are also available upon request.
5
We make use of the Stata codes developed by Poi (2010), but modify it according to our data and specification.
14
The sign of the income variable in the expenditure share equation depends on relative
changes in gasoline versus other goods expenditures. Higher income will increase spending on
other goods and gasoline; however, it is expected that expenditures on other goods will be
relatively more than on gasoline, particularly for high-income households. Therefore, the effect of
income on gasoline expenditure share is expected to be negative. Gasoline price is expected to
have a positive impact on the gasoline expenditure share since it is considered a necessity
commodity. Vehicle per adult ratio is expected to have a positive sign as households with more
cars per adult tend to use cars more often and therefore spend more on gasoline. Number of
children is also expected to have a positive sign, since having a child in the family is associated
with more driving for child related activities.
The estimation results for the full sample are presented in Table 3. All coefficients in the
AIDS model have expected signs and are statistically significant. Specifically, the coefficient of
income is negative and gasoline price positive. The former implies that gasoline is a normal and
necessary commodity, and the latter suggests that demand for gasoline is inelastic with respect to
price changes. The coefficients of price of other energy is positive and price of non-energy goods
negative. Number of vehicles per adult and number of children have a positive effect on gasoline
expenditure share and the trend coefficient indicates that Canadians have been spending relatively
more on gasoline in the study period. The coefficients in the QUAIDS model are almost the same
as those in the AIDS model, but all prices have smaller effect and the price of other energy goods
is not significant. λ, which represents the effect of the quadratic term of logarithm of income, is
very small and statistically not significant.
[Table 3 here]
15
Household expenditures may be heterogeneous with respect to income level. Therefore,
we estimate the model for three income groups (low, mid, and high) separately. Table 4 presents
results for AIDS model.
6
The coefficient for income is negative and about the same for all three
income groups. Price coefficients are positive and significant but greater for low and mid income
groups. The coefficient of prices of other energy goods is negative and not significant for low-
income households, but positive and significant for the other income groups. The coefficients of
the price of non-energy goods are negative across all income groups, but smaller for the high-
income households. Vehicle per adult coefficients are positive and statistically significant for all
income groups, but the effect in mid- and high-income households are twice as much as that in
low-income households. The impact of number of children on gasoline expenditure share is also
positive and significant for all income groups, but verey small for high-income households. The
trend effect is positive and significant for mid- and high-income households.
[Table 4 here]
Table 5 presents results for income, own price, and efficiency elasticities of gasoline
demand estimated from AIDS model using equations (8) and (9) and evaluated at the sample mean
for Canada, income groups, and provinces. The nonlinear standard errors are obtained using the
Delta method. Income elasticities are positive, less than one, and significant in Canada and across
income groups and provinces, consistent with our expectation that gasoline is a normal and
necessity good. The average income elasticity in Canada is 0.47 and decreases with income from
0.55 for low income families to 0.33 for high income families, indicating that lower income
families increase their gasoline consumption more relative to high income families as their income
6
Since the results from the QUAIDS model are similar to the AIDS model, we do not report them here, but they are
available upon request.
16
rises. The income elasticities also vary in provinces, with NB having the lowest elasticity (0.40)
and SK and QC the highest (0.50). The price elasticities are all negative, significant, and less than
one, implying an inelastic demand for gasoline. The average price elasticity in Canada is -0.88,
but rises (in absolute value) with income level from -0.86 to -0.94 for low and high income
families, respectively. The provincial price elasticities also vary from -0.63 in NS to -0.96 in BC.
The efficiency elasticities are presented in Column 3. The elasticity is -0.12 on average and
decreases with income. Provincial estimation results also show that BC has the lowest efficiency
elasticity (-0.04) and NS the highest (-0.27). The less than one efficiency elasticities imply that an
increase in efficiency does not lead to a proportional reduction in gasoline consumption by
Canadian households. The difference between the actual response of gasoline demand to an
increase in efficiency and the full response, where efficiency elasticity is equal to 1, is the rebound
effect. Therefore, the lower the efficiency elasticity, the higher the rebound effect. The results
show that the average rebound effect in Canada is 88 percent, which means that a 10 percent
increase in efficiency will decrease gasoline consumption by only 1.2 percent. In other words, 88
percent of the effect of improvement in fuel efficiency is lost by increased driving or a switchto
larger cars. The rebound effect varies with income group and across provinces. Specifically, it
rises with income from 75 percent in low income families to 93 percent in high income families.
The provincial rebound effects range from 73 percent in NS to 96 percent in BC. These results are
consistent with the income group results as lower income provinces have lower rebound effect.
The results of the QUAIDS model, presented in Table 6, are almost the same for income
elasticities, but smaller for price elasticities and greater for efficiency elasticities by 7 percentage
points on average.
[Tables 5 & 6 here]
17
We also estimate elasticities and implied rebound effects for the three income groups
within provinces. As Table 7 shows, the elasticities vary across income groups within provinces
and among provinces. The income elasticities decrease and price elasticities increase with income.
The estimated rebound effects present the same pattern as before; they are smaller for high income
households and provinces. Furthermore, the variation of the rebound effect in income groups is
higher within the lower income provinces than higher income provinces.
[Table 7 here]
Since gasoline prices rose significantly along with the oil prices in the early 2000s, we
further examine the effect of changes in gasoline prices on the rebound effect by re-estimating the
model for the pre and post 2001 periods. The results presented in Table 8 show that income
elasticities remain almost the same on average, but have increased for low-income households and
decreased for the mid- and high-income households. The results also show major differences in
price and efficiency elasticities before and after a hike in gasoline prices. The rebound effects are
markedly greater in the high-price regime comparted to those in the low-price regime in Canada
and across income levels and provinces. The exceptions are the two oil producing provinces (SK
and AB), where the changes in the rebound effects in the two price regimes are small and nil,
respectively.
[Table 8 here]
6. Discussion
Our estimations of rebound effect are higher than those reported by Small and Van Dender
(2007) and Barla et al. (2009). Possible explanations for these differences are that those studies
use aggregate data from the Vehicle Surveys whereas we use micro data from the Household
18
Spending Survey, our models and methods of estimation are different, and we use a longer and
more up-to-date data set. As Goodwin (2004) shows, the price elasticities and the rebound effects
are higher when disaggregated data are used and when gasoline prices are higher, both of which
apply to our data. Our estimated price elasticities of demand for gasoline and the implied rebound
effects are closer to the estimates of long run elasticities using micro data. For instance, the price
elasticities of gasoline demand in Canada reported by Eltony (1993) and Yatchew and No (2001)
are -1, and -0.9, respectively.
The uncompensated price elasticity represents the direct rebound effect, which includes
substitution (price) and income effects as presented by equation (10). As Table (9) shows, the
uncompensated price elasticity of gasoline is -0.88, which is divided into compensated price
elasticity of -0.86 and income effect of -0.01. Since gasoline income elasticity is positive, the
income effect of price change is negative, indicating the rebound effect. Furthermore, cross-price
elasticity of gasoline with respect to other energy goods is negative, indicating that gasoline and
other energy goods are complementary goods. That is, an increase in fuel efficiency increases not
only gasoline consumption, but also other energy goods. The complementarity of energy goods
might be due to a combination of technical factors and income effects; however, the latter will be
more relevant in the case of gasoline and other energy goods. The cross-price elasticity of gasoline
with respect to non-energy goods is positive indicating that they are substitute goods. That is, fuel
efficiency leads to a decline in demand for non-energy goods. This might be explained by the fact
that an increase in fuel efficiency encourages spending on new cars or appliances and, therefore,
given income, consumption of non-durable non-energy goods may decrease.
[Table 9 here]
19
There are not many studies analysing the variations of rebound effect across income groups
and economic activities, but our results seem to be in contrast with the view that the rebound effect
should rise with income, as a higher income makes people less sensitive to fuel costs (Small and
van Dender, 2007). Our findings show that the variations of rebound effect across income groups
depends on the income level of the provinces. In other words, not all high income households are
the same. In general, high income households in low income provinces are more sensitive to fuel
costs and, therefore, rebound more than low-income households in those provinces. The rebound
effect is also higher in provinces with larger population, which may be due to the higher traffic
congestion in the large cities.
7. Conclusion
In this paper, we estimate gasoline demand and rebound effect in Canada using AIDS and
QUAIDS models and data from Canadian Survey of Household Spending from 1997 to 2009. The
results show a rather high rebound effect in the passenger car transport and heterogeneous impacts
of fuel efficiency on gasoline consumption across income groups and provinces. The rebound
effect is on average between 82 to 88 percent, which suggests that doubling vehicle efficiency in
Canada will lead to only 12 to 18 percent decrease in gasoline consumption. The effect decreases
with income in both income group and provincial estimations. Specifically, the rebound effects for
gasoline vary from 75 percent for low-income households to 93 percent for high income
households. That is, high income households on average reduce their gasoline consumption less
relative to low income households as cars become more fuel efficient.
20
Canada has one of the highest gasoline consumption and GHG emission per capita in the
world. Given the fact that passenger transport is one of the major contributors to the Canadian
GHG emission, reducing gasoline consumption should be given a top priority in the environmental
policies. Fuel efficiency regulations and more stringent standards for light-duty vehicles will help
reduce gas consumption; however, they are not applicable to the existing vehicles and their full
potential impacts will not be realized due to high rebound effects in Canada. Alternative ways to
reduce fuel consumption and GHG emission further are promoting public transportation and
increasing gasoline taxes, which are relatively low in Canada. Higher taxes for gasoline will make
driving passenger cars more expensive even with more fuel efficient cars and will likely mitigate
the rebound effect. The gasoline taxes can also be used to fund investments in infrastructures
required for public transport.
Our rebound effect estimates are at the higher end of the range reported in the literature.
As noted earlier, the rebound effects estimated from the aggregate data are generally lower than
those estimated from the micro data. One caveat in our results arises from the assumption that fuel
efficiency is exogenous, whereas the choice of fuel efficient cars may depend on driving long
distances or traffic congestion. The fuel efficiency may also be correlated with other vehicle
attributes, such as power and reliability that affect a consumer’s utility from driving. As Frondel
et al. (2008) point out, the endogeneity problems relating to fuel efficiency are more relevant to
models estimating distance traveled and would not affect our estimates, which are based on fuel
prices. Furthermore, as Mannering (1987) and Klier and Linn (2012) show, failing to control for
endogeneity will generate a downward bias of the rebound effect.
Our study also does not discern between energy prices and energy service prices. If energy
prices are significantly lower than prices for energy services, the estimated rebound effect using
21
energy prices will be biased downward. As Kratena and Wüger (2010) show, although energy
prices have been lower than the prices of energy services in the U.S. from 1972 to 1992, they have
been almost the same since then. Therefore, our estimation of rebound effect using energy prices
is not likely affected by this assumption. Finally, our findings on changes in rebound effect across
income groups seem to be in contrast with the expectations that high-income groups rebound less
as they are less sensitive to price changes. Our conjecture is that population size, income level,
prices, and economic structure may be the important factors driving the rebound effect. However,
a more rigorous analysis is needed to shed more light on the issue.
Acknowledgment: We would like to thank participants at Department of Economics seminar,
University of Saskatchewan, and the Canadian Economic Association conference held at
Ryerson University, Toronto, in May 2013 for their helpful comments.
22
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1709.
25
Appendix A- Rebound Effect
An improvements in fuel efficiency will lower fuel cost of driving a vehicle. Rebound effect
measures the tendency to take back potential energy savings from efficiency improvements. Consider a
representative consumer who allocates her/his budget between two goods/services: traveling by car (T) and
other goods and services (Z). In Figure A1.a, the consumption bundle (T1, Z1) represents the optimal
allocation given income, prices, and the utility level U1.
Figure A1. The Rebound Effect
A1.a
A1.b A1.c
Other
Goods
Z2
Z1
Z3
T1 T3 T2 Distance Travelled
Ū1
Ū2
G
G1
G3
G2
T1 T3 T2 T G2 G3 G1 Gasoline
a
c
b
a
d
e
f
Price
P
a
d
f
D(E, T1)
D(E’, T1)
D(E’, T3)
E
E’
0<RE<1
RE=1
RE=0
0<RE<1
RE=1
26
As a result of efficiency improvement and lower fuel cost, the consumer will increase traveling
from T1 to T2, which is the new optimal point obtained by rotating the budget line counter clockwise from
a fixed point on vertical axis and a new indifference curve (
. The total change in distance traveled
(T1T2) is divided into two price (substitution) effect (T1T3) and income effect (T3T2). The rebound effect
in gasoline consumption is shown in Figure A1.b. The fuel efficiency improvement will rotate the vehicle
efficiency curve (E ) clockwise to (E’) , which indicates that less gasoline (G1G2) is required to travel the
same distance T1 (point d). The rebound effect is shown by points e and f, where the consumer travels more
distance taking back all or part of the gasoline saving, respectively. The direct rebound effect can also be
shown on the gasoline demand curve in Figure A1.c. An increase in fuel efficiency will shift demand for
gasoline, D (E,T1), leftward to D(E’, T1), moving from point a to d, which reflects the gasoline savings of
G1G2, given the same distance traveled (T1). The full rebound effect occurs when the demand curve shifts
back to its original positon and the partial rebound effect can be shown by positioning the new demand
curve, D(E’, T3), anywhere in the space between a and d, such as f.
The indirect rebound effect is the increase in energy consumption associated with the increase of
consumption of other goods due to income effect of fuel efficiency. This is shown in Figure A1.a by an
moving from Z1 to Z2.
27
Appendix B -AIDS and QUAIDS Models
The quadratic term for expenditure AIDS uses a specific class of preferences (PIGLOG), which
permit exact aggregation over consumers: the representation of market demands as if they were the outcome
of decisions by a rational representative consumer. These preferences are represented by the cost function,
which defines minimum expenditure level to attain a specific utility level (u) at given prices (p).
(1)
u lies between subsistence level 0 and above-subsistence or bliss level 1. and are positive linearly
homogeneous functions, which correspond to the cost of subsistence and bliss levels, respectively. They
have a flexible functional form, so they can reproduce any arbitrary set of the first and second order
derivatives of the cost function (at any single point).
ϒ
(2)
(3)
AIDS cost function is obtained by substituting equation (2) and (3) into (1)
ϒ
. (4)
The following conditions must hold for cost function to be linearly homogeneous in prices
.
Applying the Shepard's lemma to (4) will yield a demand equation (q), which can be written in the
form of expenditure share equations (
) as follows:
ϒ
(5)
where ϒ
ϒ ϒ.
28
For utility maximizing consumer total expenditure is equal to . Indirect utility function is
derived based on this equality and have the following form
. (6)
AIDS demand function in the budget share is obtained by applying Roy's identity to the indirect utility
function (6) or Shepard's lemma to the cost function (4).
ϒ
. (7)
The restrictions on parameters imply the following restrictions of the share equation (7): Slutsky
symmetry (ϒ ϒ , homogeneity of the Marshallian demand functions of degree zero in
prices and income ( ϒ
), and adding up condition (
ϒ
).
Banks et al. (1997) derived QUAIDS by setting expenditure shares of the simplest general form of
demand consistent with the empirical evidence on Engel curves which has the following form:
(8)
for good , is total expenditure,
, where is a vector of prices, is a differentiable,
homogeneous function of degree one in prices, is a differentiable, homogeneous function of degree
zero in prices, are some differentiable functions. The demand systems that are derived from utility
maximization are rank
7
3 quadratic logarithmic budget share system having following indirect utility
functions:
(9)
7
Lewbel (1991) defines the rank of any demand system to be the dimension of the space spanned by its Engel curves.
Gorman (1981) proved that the maximum possible rank of any exactly aggregable demand system (with any number
of terms) is 3.
29
where the extra term is a differentiable, homogeneous function of degree zero of prices
. (10)
Indirect utility from equation (9) reduces to the AIDS indirect utility by setting . The
specifications of and are similar to the specification from AIDS (Deaton and Maellbauer, 1980)
presented above. Solving equation (9) for gives the QUAIDS cost function
. (11)
It is possible to derive QUAIDS share equation by applying the Shepard's lemma to the cost
function (11) or apply Roy's identity to the indirect utility function (9) as follows:
ϒ
(12)
where is the th budget share and ϒ are parameters. All the parameter restrictions in AIDS plus
are required to ensure consistency with the theory.
30
Appendix C –Demand Elasticities
Deriving income elasticity of demand in equation (9)
(C.1)
where
(C.2)
(C.3)
Using (C.2) and (C.3)
(C.4)
Rearranging of (C.4) gives
(C.5)
which yields income elasticity
(C.6)
Deriving uncompensated price elasticity of demand in equation (8)
ϒ
ϒ
(C.7)
where
(C.8)
31
(C.9)
(C.10)
(C.11)
Substituting equation (C.11) into equation (C.10)
(C.12)
Solving equation (C.12) for
yields uncompensated price elasticity
(C.13)
Figure 1. Gasoline Expenditures by Income Groups
Figure 2. Gasoline Expenditure Shares by Income Groups
1000 1500 2000 2500 3000
1995 2000 2005 2010
year
Low Mid
High
.025 .03 .035 .04 .045
1995 2000 2005 2010
year
Low Mid
High
Figure 3. Gasoline Price and Gasoline Expenditure Shares
Figure 4. Gasoline Price across Provinces (cents per litre)
.028 .03 .032 .034
Gasoline Share
40 60 80 100 120
Gasoline Price
1995 2000 2005 2010
year
Gasoline Price Gasoline Share
40 60 80 100 120
1995 2000 2005 2010
year
NL NS NB QC ON
MB SK AB NS
Table 1. A Summary of the Estimates of the Fuel Efficiency Rebound Effect for OCED Countries
Author
Country
Dependent
Variable
Period
Data
Rebound
Effect (%)
Greene (1992)
US
VMT*
1957-1989
National (time series)
5-15
Jones (1993)
US
VMT
1957-1990
National (time series)
11-30
Orasch and Wirl (1997)
UK, France,
Italy
Fuel
consumption
1971-1993
National (time series)
15-30
Matos et al. (2011)
Portugal
VMT
1987-2006
National (time series)
24
Haughton and Sarkar (1996)
US
VMT
1970-1991
State panel
16-22
Small and Van Dender
(2007)
US
VMT
1966-2001
State panel
5-22
Hymel et al. (2010)
US
VMT
1966-2004
State panel
9
Su (2011)
US
VMT
2001-2008
State panel
3-11
Barla et al. (2009)
Canada
VMT
1990-2004
Provincial panel
8-20
Greene et al. (1999)
US
VMT
1979-1994
Residential
Transportation Survey
(pool)
17-28
West (2004)
US
VMT
1997
Consumer Expenditure
Survey (cross section)
87
Brännlund et al. (2007)
Sweden
Expenditure
shares
1980-1997
Household Consumption
Data (pool)
15-42**
Frondel et al. (2008)
Germany
VMT/fuel
consumption
1997-2009
Household Survey
(pool)
57-62
Chitnis et al. (2014)
UK
Expenditure
shares
1964-2013
Household Budget (pool)
25-87
*VMT: Vehicle Mile Traveled. **the total own price elasticity for private and public transports. The range for other energy services
are 5-79.
Table 2. Summary Statistics (1997-2009)
Variable
Mean
Std. Dev.
Min.
Max.
Share of gasoline expenditure
0.031
0.018
0.003
0.19
Share of other energy expenditure
0.031
0.019
0.0002
0.32
Share of all other goods excluding energy
0.94
0.030
0.65
0.99
gasoline price index (1992=100)
138.9
35.1
85.1
232.2
other energy price index (1992=100)
147.2
51.7
91.9
282.8
all other goods excluding energy price index (1992=100)
119.7
9.0
104.9
146.8
Gasoline price (cents per litre)
78.4
18.7
47
123.6
Total annual household expenditure ($)
71,225
29,922
20,572
178,044
No. of Vehicle per adult
0.85
0.356
0.17
4
No. of children in the household
0.81
1.019
0
6
Number of observations
47,921
Source: Survey of Household Spending, Stat Canada, and the authors’ calculations
Table 3. Estimation Results, AIDS and QUAIDS Models (1997-2009)
AIDS
QUAIDS
Variable description
Coef.
Std. Err.
Coef.
Std. Err.
Intercept
-0.297***
0.081
0.002
0.081
Income
-0.016***
0.000
-0.017***
0.002
price
0.009***
0.001
0.006***
0.001
Price of other energy
0.002**
0.001
-0.001
0.001
Price of non-energy
-0.011***
0.002
-0.005***
0.002
No. of vehicle per adult
0.007***
0.000
0.007***
0.000
No. of children
0.001***
0.000
0.001***
0.000
Trend
0.0001***
0.000
0.000***
0.000
Lambda
0.000
0.001
No. of observations
47921
47921
R2
0.79
0.79
Note: Dependent variable is the share of gasoline expenditure. The model is estimated by NLSUR for a system of expenditure
shares for gasoline, other energy, and non-energy goods.
***,**,* indicate that estimates are statistically significant different from zero at 0.10, 0.05, 0.01 level, respectively.
Table 4. Estimation Results for Income Groups, AIDS Model (1997-2009)
Low
Mid
High
Variable description
Coef.
Std. Err.
Coef.
Std. Err.
Coef.
Std. Err.
Intercept
-0.187
0.245
-0.591***
0.137
-0.154*
0.093
Income
-0.018***
0.001
-0.018***
0.001
-0.017***
0.000
price
0.013***
0.003
0.013***
0.002
0.004***
0.001
Price of other energy
-0.003
0.003
0.006***
0.002
0.003***
0.001
Price of non-energy
-0.01
0.006
-0.019***
0.004
-0.007***
0.002
vehicle per adult
0.004***
0.001
0.008***
0.001
0.008***
0.000
No. of children
0.001***
0.000
0.001***
0.000
0.0001**
0.000
Trend
0.0001
0.000
0.0001***
0.000
0.0001**
0.000
No. of observations
9020
18344
20557
R2
0.76
0.79
0.82
Note: Dependent variable is the share of gasoline expenditure. The model is estimated by NLSUR for a system of expenditure
shares for gasoline, other energy, and non-energy goods.
***,**,* indicate that estimates are statistically significant different from zero at 0.10, 0.05, 0.01 level, respectively.
Table 5. Gasoline Demand Elasticities, AIDS Model (1997-2009)
Income Elasticity
Price Elasticity
Efficiency Elasticity
Canada
0.47*
-0.88*
-0.12*
Low income
0.55*
-0.75*
-0.15*
Mid income
0.45*
-0.92**
-0.08*
High income
0.33*
-0.93**
-0.07*
NL
0.41*
-0.72***
-0.18*
NS
0.46*
-0.63***
-0.27*
NB
0.40*
-0.78***
-0.22*
QC
0.50*
-0.92***
-0.08*
ON
0.45*
-0.88***
-0.12*
MB
0.45*
-0.95***
-0.05*
SK
0.50*
-0.83***
-0.17*
AB
0.46*
-0.95***
-0.05*
BC
0.45*
-0.96***
-0.04*
***,**,* indicate that estimates are statistically different from zero for income and statistically different from one for price
elasticity at 0.10, 0.05, 0.01 level, respectively.
Table 6 – Gasoline Demand Elasticitities, QUAIDS Model (1997-2009)
Income Elasticity
Price Elasticity
Efficiency Elasticity
Canada
0.47*
-0.81*
-0.19*
Low income
0.54***
-0.67***
-0.37***
Mid income
0.44***
-0.94***
-0.06***
High income
0.32***
-0.92***
-0.08***
NL
0.42***
-0.73***
-0.27***
NS
0.47***
-0.60***
-0.40***
NB
0.40***
-0.76***
-0.24***
QC
0.50***
-0.94***
-0.06***
ON
0.45***
-0.81***
-0.19***
MB
0.46***
-0.98***
-0.02***
SK
0.51***
-0.87***
-0.13***
AB
0.47***
-0.96***
-0.04***
BC
0.45***
-0.97***
-0.03***
***,**,* indicate that estimates are statistically different from zero for income and statistically different from one for
price elasticity at 0.10, 0.05, 0.01 level, respectively.
Table 7. Elasticity Estimates by provinces and income groups (1997-2009)
Income
Elasticity
Price
Elasticity
Efficiency Elasticity
Low
Mid
High
Low
Mid
High
Low
Mid
High
NL
0.39***
0.46***
0.38***
-0.59*
-0.50**
-0.93***
-0.40*
-0.50***
-0.17***
NS
0.56***
0.37***
0.31***
-0.41***
-0.50***
-0.82***
-0.59***
-0.50***
-0.18***
NB
0.39***
0.37***
0.34***
-0.26***
-1.07***
-0.72***
-0.74***
-0.02***
-0.28***
QC
0.53***
0.44***
0.35***
-0.74***
-1.0***
-0.93***
-0.26***
0.00***
-0.07***
ON
0.53***
0.46***
0.25***
-0.80***
-0.91***
-0.98***
-0.20***
-0.09***
-0.02***
MB
0.54***
0.43***
0.38***
-0. 90***
-0.98***
-0.95***
-0.10***
-0.02***
-0.05***
SK
0.69***
0.49***
0.46***
-0.67***
-0.85***
-0.93***
-0.33***
-0.15***
-0.07***
AB
0.46***
0.48***
0.41***
-0.72***
-1.01***
-1.14***
-0.28***
0.00***
-0.14***
BC
0.60***
0.49***
0.36***
-0.92***
-0.94***
-0.99***
-0.08***
-0.06***
-0.01***
***,**,* indicate that estimates are statistically different from zero for income and statistically different from one for price
elasticity at 0.10, 0.05, 0.01 level, respectively.
Table 8 – Elastiticies in Pre and Post 2001 Periods
Income Elasticity
Price Elasticity
Efficiency Elasticity
1997-2001
2002-2009
1997-2001
2002-2009
1997-2001
2002-2009
Canada
0.48*
0.46*
-0.23*
-0.97*
-0.77*
-0.03*
Low income
0.52*
0.55*
-0.19*
-0.87*
-0.81*
-0.13*
Mid income
0.49*
0.41**
-0.32**
-1.03***
-0.68**
0.03***
High income
0.38*
0.27**
-0.40**
-1.00***
-0.68**
0.00***
NL
0.43*
0.41*
-0.07*
-0.64***
-0.60*
-0.36***
NS
0.45*
0.46*
-0.08*
-0.63***
-0.93*
-0.37***
NB
0.37*
0.44*
-0.13*
-0.97***
-0.92*
-0.03***
QC
0.52*
0.49*
-0.25*
-0.99***
-0.75*
-0.01***
ON
0.44*
0.45*
-0.37*
-0.98***
-0.63*
-0.02***
MB
0.44*
0.46*
-0.93***
-0.65***
-0.07***
SK
0.45*
0.54*
-0.52*
-0.79***
-0.48*
-0.21***
AB
0.48*
0.46*
-0.90***
-0.90***
-0.10***
-0.10***
BC
0.51*
0.41*
-0.27*
-1.16***
-0.73*
0.16***
***,**,* indicate the significance levels at 0.10, 0.05, 0.01 level, respectively.
Table 9 – Uncompensated, Income Effect, and Substitution Effects of Fuel Efficiency
Uncompensated Elasticity
Income Effect
Substitution Effect
Own
Price
Gas-
Other
energy
Gas-
Non
energy
Own
Price
Gas-
Other
energy
Gas-
Non
energy
Own
Price
Gas-
Other
energy
Gas-
Non
energy
Canada
-0.88
-0.03
0.43
-0.01
-0.01
-0.44
-0.86
-0.01
0.88
Low Income
-0.76
-0.04
0.25
-0.02
-0.02
-0.51
-0.74
-0.03
0.77
Mid Income
-0.92
-0.05
0.54
-0.01
-0.42
-0.42
-0.91
-0.04
0.95
High Income
-0.93
0.03
0.58
0
-0.01
-0.3
-0.92
0.04
0.88
All elasticities are significant at 0.05 percent level.
