1. automotive and vehicles
2. cars

The Significance of the General Equilibrium Effect on Studying
Rebound Effect and the Efficacy of CAFE Standards
A PILOT STUDY
NADHMI ALKHAMIS
9 APRIL 2015
Abstract
In the domain where imposition of fuel tax is socially implausible to correct misallocation of fuel consumption,
imposing corporate average fuel economy standards result from being more reasonable alternative to account
for energy efficiency gap. This paper endeavors to evaluate the impacts of corporate average fuel economy
standards (CAFE) on reducing fuel consumption and the greenhouse gas emissions in the presence rebound
framework. This paper focuses on exploring the rebound effect and energy efficiency gap within general
equilibrium framework, a comparison between CAFE standards and fuel tax as policy instruments, and
assesses on the efficacy of CAFE standards policy. This paper develops a methodology to explore the
expenditure substitution, and auto sector stock effect to better understand their relative stringency. Policy
simulations in this study indicate that the efficacy of the CAFE standards policy relies on the interplay between
the socioeconomic factors and the combination of standard settings and the penalty per unit km/liter
violations.
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1 INTRODUCTION
The Saudi government is adapting policy Intervention measures to unlock the energy efficiency measures in
the economy. Such objectives are to inhibit the potentially adverse increase in domestic fuel consumption in
Saudi Arabia. Promoting efficiency measures are attributed to establish significant scheme for reducing the
consumption of fossil fuel. While some of these measures are designed to promote fuel efficient vehicles,
they can, significantly, help to curb CO2 emissions at the tailpipe.
The main objective of this paper is to aid decision makers in Saudi Arabia via economic perspectives to
understand the implications of deploying Corporate Average Fuel Economy Standards (CAFE) in the presence
of fuel subsidies as, by now, the policy-makers would confront social opposition to removing them. Also, this
paper addresses the significance of the rebound effect as it might intensify in response to a deep reduction
fuel cost when substantial subsidy is applied. This paper endeavors to evaluate the impacts of corporate
average fuel economy standards (CAFE) on reducing both fuel consumption and the greenhouse gas emissions
in the presence rebound effects and energy efficiency gap. At this point, I organize my thesis question around
three areas. First, I examine the rebound effect in the general equilibrium framework. Second, I conduct a
comparison between CAFE standards and fuel tax as substitutive policy instruments. Finally, I assess on the
effectiveness of CAFE standards policy.
Assessing both consumer and producer responses is crucial for understanding the impacts of gasoline
subsidies/taxes and efficiency regulations such as Corporate Average Fuel Economy (CAFE) Standards in auto
transport sector. The paper presents a methodology for studying the effects of automobile fuel efficiency and
emission policies on the long-term design decisions of profit-seeking automobile producers and rational
consumer choice in a dynamic general equilibrium framework through assessing market behaviors and policy
responses. A distinguishing feature of this model is the inclusion a regulatory policy in general equilibrium
through utilizing decomposing technique.
In Saudi Arabia, the regulations of Saudi CAFE are based on how averaging the fuel economy of whole fleet of
an auto company would comply with the proposed legislative standard. For new passenger cars and new light
trucks, the Saudi CAFE follows the U.S. Corporate Average Fuel Economy (CAFE) standard structure with 2012–
2016 and target to be employed in 2016. Though, the used cars have different set of regulations which are not
restricted to vehicle features such as weight or size, sales-weighting [1] [2]. Flexibilities in the legislations, like
accumulation of excess credits with respect to targets, trading between cars and trucks, off-cycle credits, airconditioning credits, and phase-in provisions, offer the manufacturers the opportunity to gain roll-over credits
which can be carried for five enforcement cycles and backward for enforcement cycles[3]. To ease modeling,
this paper will not consider these credits and used cares class.
The direct rebound effect occurs when improved efficiency causes cost reductions, the consumer owes
savings and spends them by increasing the consumption. It is important to consider this behavior when
designing policies, though it should not deter the effort to promote energy efficiency as the increase in
consumption should be low! In the case of fuel consumption, it is inverse propionate with the price of fuel [4]
[5].
Many policy instruments are available to curb fuel consumption. One of this instruments is taxing the fuel at
the pump. Though this policy is very effective like in United Kingdom (UK) and some other European Union
(EU) countries, nonetheless it faces public dissatisfaction. As a result of this policy, the EU were able to bring
the auto manufacturers voluntarily to agree on the second alternative which is restrictions on the emissions
[6] [7]. Also restrictions can be exerted on the vehicles by Fuel Economy base according to its foot print like
China, Japan, and South Korea [7].
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The policy, in discussion in this paper, is the imposition of the Corporate Average Fuel Economy standards
(CAFE.) The CAFE can be defined as a tax that is enacted on auto manufacturers of new cars that do not meet
required average fuel economy levels of their fleet. The main objective of this policy is to discourage the
production and purchase of fuel-inefficient autos. In order to avoid such a tax, the average fuel economy of an
auto manufacturer fleet should not exceeds the CAFE standards. To achieve this goal, manufacturers targeted
a range of technologies to improve engine and transmission efficiency, reduce weight and aerodynamic drag
and boost fuel economy in other ways [8]. However, tax credits are given, too, like: off-cycle credits, airconditioning credits, and phase-in credits [2]. Other alternative that compliments fuel economy will be
financial incentives, research and development programs, and traffic control measures. In Saudi Arabia, it will
be effective as of January 1, 2016, and will be fully phased in by December 31, 2020. The target is to move
average fuel economy from 12 km/l to 17 km/l for passenger vehicles and to 13.2 for light trucks by the end of
2020 [1].
The research methodology used in this paper is based on the utilizing the economic theory to establish causeeffect nature of relationship between economic variables to quantify the impact and assess on the
effectiveness of the proposed policy. The approach that I am using assumes: maximizing behavior, efficient
markets, and forward-looking behavior. The consumer preferences are treated to capture energy efficiency
gap.
To capture the rebound effect, I present a 2X2 growth model to assess the general equilibrium framework. I
use a decomposition technique, between growth model and auto sector to be able to separate the internal
parameters and calibration of both models to ease analysis and interpretation.
Examples of the main trends in the literature that tackle the fuel economy in the transportation sector are as
follows. The first trend tackles the assumption about the heterogeneity of the household like the Liu paper [9].
The second wave in the literature, which most of the literature lie, is using the panel data to analyze the
impact of standards and fuel prices on new-car fuel economy with the aid of cross-section time series analysis
like the Cleridesa paper [10]. The third wave is utilizing the economic theory in structural form to cause-effect
nature of relationship between economic variables like Wei paper [11]. This paper adapt the third trend of
research.
The rest of this paper is structured as follows: Section 2 establishes the mathematical foundation of the
decomposed model focusing on the auto sector. Section 3 presents the simulation results and some
discussions. In section 4, I present my conclusion and my inputs for the second paper.
2 A MATHEMATICAL MODEL
2.1 OVERVIEW OF THE MODEL
In this section, I present a framework for a stylized intertemporal forward-looking two-sector (auto sector and
others), two-factor growth model (capital and labor) that is integrated with partial equilibrium auto sector.
Sectors in the growth model encounter differential factor proportions and unevenness on the contribution to
the economy in addition to relatively large gap in scale between sectors (others >> auto sector).
2.2 GROWTH MODEL
The economy is initially endowed with an exogenous supply of labor (Lt) units per time which grows at rate 𝑔𝐿
from initial labor L0 at 𝐿𝑡 = 𝐿0 𝑒 𝑔𝐿 𝑡 . The representative agent obtains utility (U) from consumption. An
additively, separable utility in consumption is assumed and households are treated as an infinitely lived-agent
with perfect foresight behavior. I assume a constant inter-temporal elasticity of substitution 1/θ and constant
rate of time preference ρ. The representative agent consumes 𝐶𝑡 with an instantaneous utility
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function 𝑢(𝐶𝑡 ) and savings are determined simultaneously. Then, an agent’s lifetime utility (𝑈) maximizes the
discounted sum of utilities as follows:
∞

U = max  ∫ u ( Ct ) e − ( ρ − g L )t dt 
Ct , Kt
0

 Ct1−θ − 1
if

u ( Ct ) =  1 − θ
 ln C
if
t

(1)
θ ≠ 1, θ ≥ 0
θ =1
The utility is maximized in two steps [12]. In the first step, the household optimize a composite consumption
level, then she/he chooses X, and Y that maximize the discounted present value of utility. To rule out Ponzi
schemes, assume instantaneous logarithmic utility function, the following transversality condition holds
lim K t e −[ ρ − g L ]t = 0
(2)
t →∞
Which means that we should have 𝜌 > 𝑔𝐿 .
The two sectors will be referred to as others-sector, X, and auto-sector, Y with two primary factors of
production, labor (L) and capital (K). The goods are produced according to a constant returns to scale
technology. Assume free factor mobility, factor price equalization is imposed which implies that factor prices
are only determined by prices [13]. Then, the price and quantity changes are contingent on the differential
factor intensity. In order to account for infinitely elasticity of capital, multisector framework is used [14].
The economy is initially endowed with initial capital K0. Output is be decomposed of two goods X and Y where
𝛼
1−𝛼𝑥
both sectors use labor, 𝐿𝑥,𝑡 , 𝐿𝑦,𝑡 and capital, 𝐾𝑥,𝑡 , 𝐾𝑦,𝑡 with Cob-Douglas technologies as 𝑋𝑡 = 𝐿𝑥,𝑡𝑥 𝐾𝑥,𝑡
𝑌𝑡 =
𝛼𝑦 1−𝛼𝑦
𝐿𝑦,𝑡
𝐾𝑦,𝑡
and
respectively. Both goods are produced by combinations of two factors of production, labor
and capital, but the assumption of joint products is not exercised. Compared with consumer problem, the
producer optimization problem is intra-temporal [12] where each sector minimize cost and then select the
output to disburse all revenue. No Mobility barriers of both capital and labor between sectors.
The economy can be represented with one final good with CES technology with an elasticity of substitution
𝜇 ∈ (0,1) facilitate factor shifts between sectors [15] as follows:
1
ϑ X tµ + (1 − ϑ ) Yt µ  µ
=
GDP
t
(3)
The consumer derive utility from the consumption of both goods, i.e. ϑ ∈ (0,1). Goods may be either
consumed, C, or added to the capital stock. The representative agent maximizes utility over an infinite horizon
by allocating income to consume good X and Y, and saves by accumulating additional assets and receives
interest income 𝑅𝑘𝑡 per unit of asset. The law of motion of the physical capital stock is thus given by
Ct + I t ≤ F ( K t , Lt ) =
GDPt
(4)
The evolution of the stock of physical capital is thus given by
K =
It − δ Kt
t
(5)
where δ ∈ (0,1) is the rate of depreciation of physical capital, where both sectors depreciates at the same
rate. The aggregate resource constraints are
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Lx ,t + Ly ,t ≤ L0,t e g L t
(6)
K x,t + K y ,t ≤ Kt
(7)
2.3 THE AUTO SECTOR
The consumer encounters two rational decisions: buying a new car and how much to drive every type. Two
types of autos exist in this economy: type A (the fuel economy exceeds CAFE) and B (the fuel economy below
CAFE). With one producer capable of restricting quantities and set prices together with one consumer adept to
peruse his/her preferences to act simultaneously to form an equilibrium in the presence of penalty associated
with CAFE Standard. To ease modeling, this paper will consider the energy efficiency gap indirectly through
consumer trade-off between car type A and B in the sense of cost effectiveness of fuel-efficient technologies,
but not through household buying decisions are considered to be consistent with the costs they face. Also, this
paper will not attempt to internalize externalities from energy consumption and CO2 emissions.
2.3.1 STOCK AND FLOW OF AUTO SECTOR
The main objective of the CAFE standard policy is to augment the car stock in favor of fuel efficient cars to
improve the average fuel economy. Improving the average fuel economy is stock and flow process that
replaces the existing inefficient fuel economy cars with more efficient ones. Then, the success of the policy,
which is a measure of duration of reaching the stabilization and at what average fuel economy, depends on the
initial average fuel economy of stock and the magnitude of replacement rate. The duration at which the
average fuel economy stabilizes depends also on the depreciation of the existing stock (δ), too.
Assume the initial stock is S0 which consists of car stock of type A and type B, Sa0 and Sb0 respectively. The total
stock (St) at any time t is
=
S t S a ,t + S b ,t
(0.8)
Where Sa,t and Sb,t are the stock of cars type A and B respectably. The flow variables are the new cars’ sales qa,t
and qb,t. Then, the velocity equations are:
(1 − δ ) Si ,t −1 + qi ,t ,
S i ,t =
In this economy, the objective of the CAFE policy is to maximize
i=
a, b
𝑆𝑎,𝑡
𝑆𝑏,𝑡
(0.9)
at shorter time possible. Considering the
driving habits of the consumer, the objective can be reinstated as to maximize the driving distance of car type
A relative to type B.
5|P a g e
t=0
Consumer Automobile
Buying
Choice
Consumer
Automobile
Buying Choice
t=1
t=T
Consumer Automobile
Buying Choice
Stock
New Automobiles Exceed
New Automobiles Below
theNew
CAFEAutomobiles
Standards Exceed the New
CAFEAutomobiles
Standards Below
Group
Group
the CAFE Standards
the
CAFE Standards
Group
Group
New
Automobiles Exceed
New
Automobiles Below
the CAFE Standards
Group
the CAFE Standards
Group
Old Automobiles Exceed
Old Automobiles Below
the Old
CAFE
Standards Exceed the CAFE
Standards Below
Automobiles
Old Automobiles
Group
Group
the
CAFE Standards
the
CAFE Standards
Group
OldGroup
Automobiles Exceed
Old
Automobiles Below
the CAFE Standards
Group
the CAFE Standards
Group
Scrape
Scrapped Automobiles
Scrapped Automobiles
Exceed
the CAFE
Below
the CAFE
Scrapped
Automobiles
Scrapped
Automobiles
Standards
Standards
Exceed the CAFE
Below the CAFE
Group
Group
Standards
Standards
Scrapped Automobiles
Scrapped Automobiles
Group
Group
Exceed the CAFE
Below the CAFE
Standards
Group
Standards
Group
FIGURE 1: THE STOCK-FLOW REPRESENTATION OF AUTO SECTOR
2.3.2 CONSUMER PROBLEM
It is frequently proclaimed that consumers buying new autos undervalue fuel cost. In this model, I ignore fuel
price reflection in the buying of new cars. The justification for this assumption will be that fuel economy
regulations will improve economic allocation in the presence of market barriers. The consumer maximizes the
utility from buying according to the consumer’s trade-off the two types qa,t and qb,t with prices pa,t and pb,t
according to (capturing the efficiency gap):
1
V = max (ϑ qaρ,dt ( Pt ) + (1 − ϑ ) qb,ρdt ( Pt ) ) ρ
(10)
d
qa ,t , qb ,t
The sales of new cars are constrained by Wt which is determined by the growth model.
∑
i∈{a ,b}
qi ,t ( Pt ) pi ,t ≤ Wt
(11)
To further capture the energy efficiency gap, the consumer obtain another utility (D) from driving type A and
1
Type B, where 𝛼 < such that the consumer obtain more utility from driving type B as:
2
D = arg max d aα,t db1−,tα
(12)
{da ,t , db ,t }
The consumer would drive a total of Dt which is the summation of da,t and db,t or driving of car type A and B
respectively. Later, Dt will be limited to a lower limit depending on economic activities.
d a ,t + d b,t =
Dt
(13)
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Type A is characterized by fuel economy consumption 𝑘𝑝𝑙𝑎 . 𝑘𝑝𝑙𝑎 resamples the amount of distance units that
can be traveled per one unit of fuel. Similarly, 𝑘𝑝𝑙𝑏 represents the fuel economy of type B. Then, the constraint
on fuel consumption can be written as:
d a ,t kpla + d b,t kplb ≤ Wf t
(14)
Where 𝑊𝑓𝑡 is the limit on the fuel consumption budget. Later, 𝑊𝑓𝑡 will be determined in the growth model.
Equation (15) limits the driving by available stock.
d a ,t ≤ dla S a ,t
(15)
db ,t ≤ dlb Sb ,t
Where 𝑑𝑙𝑎 , 𝑑𝑙𝑏 are the driving limit per unit of type A and type B respectfully.
2.3.3 PRODUCER PROBLEM
The two types of cars are produced by one producer at prices 𝑝𝑎,𝑡 , 𝑝𝑏,𝑡 and quantities 𝑞𝑎,𝑡 (𝑷), 𝑞𝑏,𝑡 (𝑷)
according to the profit maximization problem [16] to capture fleet mix implications:
max  
∑ (p
{ pi ,t ,i∈{a ,b}} 
  i∈{a ,b}
i ,t
− ci ) qi ,t ( P )  − Pent 
(16)
 pa , t 

 pb ,t 
(17)


Where the Pt is price vector of new cars
Pt = 
The Pent is the penalty that the manufacturer pay if the average fuel economy is above the standard
l ⋅ ( At − CAFEt ) ∑ qi ,t ( Pt ) if
i∈{a , b}
At > CAFEt

At ≤ CAFEt
Pent = 
0
if
(18)
Where 𝑙 is penalty per CAFE standard unit and A the actual average fuel economy of new cars’ sale
At =
∑
i∈{a , b}
∑
i∈{a , b}
qi ,t ( Pt )
(19)
qi ,t ( Pt )
kpli
Income effect will be captured from the economy-wide model.
2.4 THE DECOMPOSITION MODEL
In order to integrate both models, some equations should be modified in market economy formulation. Figure
2 shows the decomposition routine. The representative agent drives above what the economy would require.
The first equation is the labor market resource constraint to be
K y ,t
− K y ,t −1 = ξ ( qa ,t + qb,t ) − δ K y ,t −1
(20)
Then, the income balance block will be
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∞
RA=
d i ,t
∞
∑ Pl L + Rk k + ∑ ∑
t
t
0
0
=t 0
=t 0 i∈{a , b}
pft ⋅
(21)
kpli,t
Now, I impose a lower limit on driving where economy should peruse a minimum of Yt activity
Dt ≥ Yt
(22)
Assume that the price of fuel follows the trend of composite good as:
Pf ,t = Pt
(23)
Wft =Py ,t ⋅ ( d a ,t + db ,t )
(24)
Setting fuel budget constraint is
Then
d 
 d a ,t
+ b ,t  ≤ Wft
 kpla,t kplb,t 
η ⋅ Pf ,t ⋅ 
(25)
Where:
µ is a scale factor to growth model units.
RA is the net present value of the income of the household
Plt is the price of labor
Rk0 is the rent of Capital
pft is the price of the fuel
ξ is a capital scale factor
Contrary to stylized models, applied models account for finite time horizon. In the assumption of a finite
horizon, the household has no motivation invest beyond the imposed final period [17]. Then, certain
adjustment is needed to account for such caveat. Since the utility is assumed to be additive separable, then we
can divide the time horizon into two problems separated at time T. A terminal condition is picked such that the
consumption in period T+1, CT+1, is close to the infinite-horizon optimal value [17]. For complementary
problems, we can restrict the growth rate of investment in the terminal period to the growth of consumption. I
frame this restriction as:
IT +1 CT +1
=
IT
CT
(26)
Decomposition method permits feedback effects between different markets. Growth model can account for
factor price distortions, different markets interactions and income effects [18] [19]. Consequently, the
resulting model can endogenize driving decision with growth model features.
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Start
Growth Model
Calibration
Capital Stock
Driving Distance
Fuel price
Fuel Quantity
Penalty
Calibration
Auto Sector
No
Converge
Yes
End
FIGURE 2: DECOMPOSITION REPRENSTTION OF THE PILOT MODEL
2.5 THE DEFINITION OF BINDING CAFE STANDARDS
It customary to say that in order for CAFE standards to be binding, then the proposed average fuel standard
should higher than the current new cars’ sales fuel average (Actualt) or
CAFEt > Actualt
(27)
Where, 𝑘𝑝𝑙𝑏 < 𝐶𝐴𝐹𝐸 < 𝑘𝑝𝑙𝑎 .
The effectiveness of the policy will be a measure of existence of the policy gap and how fast 𝐴𝑐𝑡𝑢𝑎𝑙𝑡 coverage
to CAFE. This can be attributed to how the policy can deter both producers and consumers from trading
inefficient vehicles or type B. The signals should be sent through prices and availability of new cars through the
imposition of penalty. Furthermore, the penalty should be high enough for producers to restrict produced
quantities of type B cars. Figure 3 depicts theses classifications. In the left graph, the setting of penalty does
not deter the market participants from trading type B and producers tend to pay penalties. The result is a
policy gap. While in the right graph, the imposed penalty causes market participants to trade type A despite
the higher price of this type. No policy gap exists.
9|P a g e
Fuel Economy,
km/liter
Fuel Economy,
km/liter
kpla
kpla
Resulted Fuel Average
Res
Res
Actual
kplb
CAFE
Resulted Fuel Average
CAFE
Improvement Due
to Policy
Policy GAP
Actual Fuel Average
Actual
kplb
Actual Fuel Average
Time
Time
FIGURE 3: BINDING CAFE STANDARDS, (LEFT) TIGHT CAFE STANDARDS, (RIGHT) VERY TIGHT CAFE STANDARDS
2.6 COMPARATIVE STATICS
2.6.1 THE IMPACT OF PENALTY TIGHTNESS ON NEW CARS’ SALE
Definition 1: The policy is effective when
∂qa ,t
∂CAFE
> 0,
∂qb ,t
∂CAFE
<0
(28)
and
∂qa ,t
∂l
> 0,
∂qb ,t
∂l
<0
(29)
Definition 2: The policy is very effective when
lim ( Actualt − CAFEt ) =
0
(30)
t →∞
2.6.2 THE IMPACT OF BUDGET CONSTRAINT ON NEW CARS’ SALE
Proposition 1: Quantities of two types are positively affected and the rate of change is equal.
∂qa ,t
∂Wt
> 0,
∂qb ,t
∂Wt
> 0,
∂qa ,t
∂qb ,t
=
∂Wt
∂Wt
(31)
This is attributed to the assumption of constant return to scale of buying utility function. Proof is provided in
appendix A.
2.6.3 THE IMPACT OF FUEL PRICES ON DRIVING DECISION
Proposition 2: The effect of an increase on the fuel price is positive on the driving of the type A and no change
on the driving of type B.
∂d a ,t
∂db ,t
0,
=
<0
∂Pft
∂Pf t
(32)
10 | P a g e
Proposition 3: The effect of an increase on the fuel budget is negative on the driving of the type A and positive
on the driving of type B.
∂d a ,t
∂Wft
< 0,
∂db ,t
>0
∂Wft
(33)
Proof is provided in appendix A.
2.6.4 THE REBOUND EFFECT
Proposition 4: The effect of an increase in the binding CAFE standard is positive on the driving of the type A
and negative on the driving of type B.
∂d a ,t
∂CAFE
> 0,
∂db ,t
∂CAFE
<0
(34)
Proof is provided in appendix A.
Proposition 5: The effect of an imposition in the binding penalty which is complemented with CAFE standard is
positive on the driving of the type A and negative on the driving of type B.
∂d a ,t
∂l
> 0,
∂db ,t
∂l
<0
(35)
Proof is provided in appendix A.
3 SIMULATION RESULTS
The purpose of this section is to simulate the above model using GAMS code to draw intuition about the
results in the previous section.
3.1 GENERAL EQUILIBRIUM EFFECT
One of benefits of the decomposition model is that we can simulate expenditure substitution. In this exercise, I
apply a binding CAFE standard on year 2015 onwards for policy cycle of five years in ascending manner without
decomposition (left) and with decomposition (right.) To simulate the rebound effect, I left the constraint on
driving non-binding on the decomposed model to allow the constraint on fuel budget to bind through
expenditure substitution and account for more realistic rebound effect.
In the left graph of figure 4, the standalone auto sector does not account for saving budget from utilizing
efficient cars resulted from imposing binding CAFE standards. The results shows an increase in the driving by
about 27% and fuel saving to stabilize around 15%. In the right graph of figure 4, the driving increased only by
2.5% and fuel saving to stabilize around 25% contrast with the left graph. The substitution is minute and can
be in an increase on the capital of sector X and Y. In Y sector, this is reflected on a small increase in the budget
for buying new cars.
11 | P a g e
30.00
30.0
25.00
Rebound Effect
25.0
20.00
Fuel Saving
20.0
15.00
15.0
10.00
10.0
5.00
5.0
Rebound Effect
Fuel Saving
0.0
0.00
2002
2012
2022
2002
2032
2012
2022
2032
FIGURE 4: REBOUND EFFECT AND FUEL SAVING (LEFT) WITHOUT GENERAL EQUILIBRIUM, (RIGHT) WITH GENERAL EQUILIBRIUM
3.2 THE EFFECT OF A 25% TAX ON FUEL PRICE
The effect of imposition of a 25% tax increase on fuel prices is immediate. This effect can be seen only on the
driving behavior of the consumer and not on the decision of buying. In figure 5, it is noticeable that the drop
on type B cars and the increase in driving on type A. This results are attributed to the assumption on the model
that the fuel price is not a factor of the buying decision. The subsequent fuel saving is about 18% with less
driving of about 17%.
Type A Driving
Type B Driving
Total Driving
Type A Driving BAU
Type B Driving BAU
Type A New Sales
Type B New Sales
Type A New Sales BAU
Type B New Sales BAU
2002
2012
2022
2032
2042
2002
30.0
Type A Stock
Type B Stock
Total Stock
Type A Stock BAU
Type B Stock BAU
20.0
2012
2022
2032
2042
Rebound Effect
Fuel Saving
10.0
0.0
2002
-10.0
2012
2022
2032
2042
-20.0
2002
2012
2022
2032
2042
100
Type A Price
BAU Driving Above Needed
Driving Above Needed
Type B Price
Type A Price BAU
Type B Price BAU
50
0
2002
2012
2022
2032
2042
2002
2012
2022
2032
2042
FIGURE 5: THE EFFECT OF 25% TAX ON FUEL, (TOP LEFT) NEW CARS' SALES, (TOP RIGHT) DRIVING DISTANCES, (MIDDLE LEFT) CARS'
STOCKS, (MIDDLE RIGHT) PERCENTAGE CHANGE IN DRIVING AND FUEL SAVING, (BOTTOM LEFT) DRIVING ABOVE WHAT SECTOR X
REQUIRE, (BOTTOME LEFT) PRICES OF CARS
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3.3 ASSESSING THE EFFICACY OF THE POLICY
In order to the CAFE standards policy to be a proxy for fuel saving and emissions reduction, it must be binding
and effective. In this section, I attempt to highlight the efficacy of the proposed policy. I assume that the policy
is binding and I change the value of penalty to study the effectiveness of the policy. In figure 6, the penalty of
CAFE standard is set to be relatively low. The producer is willing to pay for the full amount of the penalty
without restricting quantities of type B. The resultant of this policy is no fuel saving.
Type A New Sales
Type A Driving
Type B Driving
Total Driving
Type A Driving BAU
Type B Driving BAU
Total Driving BAU
Type B New Sales
Type A New Sales
BAU
2002
2012
2022
2032
2042
2002
2012
2022
2032
2042
Type A Stock
Type B Stock
Total Stock
Type A Stock BAU
Type B Stock BAU
Total Stock BAU
CAFE Standard
Average Stock
Average By Driving
By New Cars' Sale
Penalty
2002
2012
2022
2032
2042
2002
2012
2022
2032
2042
FIGURE 6: THE IMPACT OF TIGH CAFE POLICY (TOP LEFT) NEW CARS' SALES, (TOP RIGHT) DRIVING DISTANCES, (BOTTOM LEFT) CARS'
STOCKS, (BOTTOM RIGHT) AVERAGE FUEL ECONOMY
In figure 7, the penalty of CAFE standard is set to be relatively high. The producer is not willing to pay any
amount of penalty and he/she is willing to restrict the quantity of type B. The resultant of this policy fuel
saving stabilized at about 35%. The price of type A increases to exceed the price of type B. Also, the quantity of
new cars’ sales of type A surpasses type B where the producer restrict the quantity. Consequently, the stock of
type A increases with rapid growth and exceeds the stock of type B at year 2045. Moreover, the driving
associated with type B surges and bypass type B at year 2042. The average fuel economy of new cars traces
exactly the CAFE standards after the imposition of the policy. Because of the stock effect, the average fuel
economy of driving and the average fuel economy stock lag the CAFE standards and catch up later, where the
average fuel economy of driving is slightly larger than the average fuel economy of stock. The constraints that
bind is the driving and rebound effect stabilizes at around 2.5%.
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Type A Driving
Type B Driving
Total Driving
Type A Driving BAU
Type B Driving BAU
Total Driving BAU
Type A New Sales
Type B New Sales
Type A New Sales BAU
Type B New Sales BAU
2002
2012
2022
2032
2042
2002
2012
2022
2032
2042
35.0
Type A Stock
Type B Stock
Total Stock
Type A Stock BAU
Type B Stock BAU
Total Stock BAU
30.0
Rebound Effect
Fuel Saving
25.0
20.0
15.0
10.0
5.0
2002
2012
2022
2032
2042
0.0
2002
2012
2022
2032
2042
CAFE Standard
Average Stock
Average By Driving
By New Cars' Sale
2002
2012
2022
2032
2042
FIGURE 7: THE IMPACT OF VERY TIGHT POLICY (TOP LEFT) NEW CARS' SALES, (TOP RIGHT) DRIVING DISTANCES, (MIDDLE LEFT) CARS'
STOCKS, (MIDDLE RIGHT) PERCENTAGE REBOUND EFFECT AND FUEL SAVING, (BOTTOM) AVERAGE FUEL ECONOMY
4 CONCLUSION
In this paper, I have instigated three main questions. First, how can the rebound effect be studied more
accurately? I found that the expenditure substitution which lessens rebound effect can be studied in general
equilibrium framework. In this model, the expenditure substitution appears in the form of factor substitution,
mainly capital, between sector X and Y. In more realistic models with joint production between sectors, intersectorial allocation will be vibrant. Moreover, the rebound effect relays on the difference between actual fuel
economy and the proposed CAFE in addition to how type A is more efficient compared to actual fuel economy.
Higher difference between actual fuel economy and the proposed CAFE heightens the rebound effect. Higher
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fuel economy rating of type A heightens the rebound effect. Generally, the rebound effect is found to be small
and in this pilot study.
Second, while the restrictions on fuel economy or emissions of every individual type of autos results in about
the same outcomes as CAFE [7], the imposition of fuel tax differs in both the efficacy and economic
predictability of the policy. As the tax on fuel might target the reduction of fuel consumption as the other
methods do, the tax instrument controls for this cause by reduction of driving distances while other methods
through augmentation of stock. Also, while other methods needs adjustment time for the policy to be effective
as the imposition of a tax does not suffer from stock effect. In addition, the administrative cost is lower when
tax is imposed. On the other hand, the imposition of tax can be described as less socially plausible. In addition,
higher fuel taxes increase the rate of the scrappage of older, less-fuel-efficient used vehicles.
Finally, the stringency of the CAFE standards policy relay on the interplay between the socioeconomic factors
and the combination of standard settings and the penalty per unit km/liter violation. In addition, the CAFE
policy encounters stock effect and depends on initial stock and depreciation rates of every type. Moreover, the
effeteness of the policy is so dependent on the elasticity of income of both buying decision and fuel demand.
In this model, I try to capture this through budget constraints on both buying new cars budget and fuel
consumption budget of income balance block, but a more realistic modeling will be to introduce the budgets in
the zero profit and market clearance blocks. To sum up, better policy design will be to assess both the
consumer and producer behaviors to come up with optimal CAFE settings and penalty impositions. It appears
sensible to articulate that tightening CAFE is a welfare improving. One question remains to answer will be how
to define the future technological level of auto energy efficiency.
The novelties of this model are: the introduction of the idea of stock and flow in auto sector to study the
efficacy of the policy and to account for the dynamic effects of CAFE, the attempt to capture energy efficiency
gap through tradeoff in buying new cars and driving, and establishing a decomposition between the auto
sector and 2X2 Growth model to explore expenditure substitution and rebound effect. Besides the high
aggregation and the control of other extraneous factors, one of the drawbacks of this model is the assumption
of one-producer and one-consumer in the presence of a penalty on trading of one of the two goods which
might result on unrealistic prices changes.
The intention of this paper is to complement subsequent paper. The second paper objective will be to obtain
more realistic insight about the effectiveness of the proposed CAFE Standards through implementing a multiproducer version with more representative measures of the Saudi Economy and then to estimate the fuel
saving and GHG emissions reductions and put forward policy recommendations.
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