1 

Evaluating U.S. Reformed Corporate Average Fuel Economy Standards with 

Endogenous Product Attributes 

Katie Whitefoot 

University of Michigan 

Meredith Fowlie 

University of California, Berkeley 

Steven Skerlos 

University of Michigan 

Working Paper Draft 

August 6, 2010 

Abstract 

In order to reduce greenhouse gas emissions and oil consumption, Congress recently amended 

the Corporate Average Fuel Economy regulation to encourage improvements in the fuel 

efficiency of new vehicles. Automotive firms have multiple strategies available to them to 

respond to this policy intervention, and the responses they choose have potentially significant 

welfare implications. This paper presents one of the first analyses of the reformed CAFE, 

explicitly accounting for medium-term compliance strategies that include both technology 

implementation and tradeoffs between vehicle attributes. We use physics-based simulations to 

identify engineering tradeoffs between fuel economy and other vehicle attributes independent of 

unobservable vehicle attributes. Final estimation of the demand side is still pending, but we 

present preliminary results using a demonstrational demand-side estimation. Preliminary results 

indicate that while firms rely on technology implementation to a significant extent to comply 

with the reformed CAFE, only 50% of the potential reductions in fuel consumption from these 

technologies are realized, with the remainder applied to improving acceleration performance. 

Results also suggest that ignoring tradeoffs between vehicle attributes significantly overestimates 

the social surplus cost of the regulation. The methods presented are generalizable to many other 

consumer product industries with energy-efficiency regulations or incentives. 

1 Introduction 

In an effort to mitigate climate change and reduce dependence on foreign energy sources, 

energy-efficiency standards and incentives are being promoted in many industries. For example, 

proposed federal climate change legislation includes standards for lighting efficiency, an energyefficiency labeling program for buildings, and subsidies for retailers and distributors of highefficiency household appliances and consumer electronics. In 2007, the fuel efficiency standards 

imposed under federal Corporate Average Fuel Economy (CAFE) regulations were significantly 

increased. 
2 

How firms respond to these types of energy-efficiency policies can have significant 

implications for how efficiently energy intensity reductions are achieved and who bears the cost. 

In this paper, we analyze firms’ response to—and implications of—the recently reformed CAFE 

standards. Our approach explicitly accounts for medium-term design changes that firms can use 

to comply with the CAFE regulation by constructing an endogenous product attribute model 

based on engineering vehicle simulations. 

In the automotive sector, industry response to the introduction of mandatory fuel 

economy standards can take many forms. It can manifest immediately as firms adjust prices to 

encourage increased sales of their more efficient models, or more gradually as firms adjust the 

design of the vehicles in order to improve fuel efficiency. Whereas some earlier studies 

emphasized the more immediate response (Goldberg, 1998), more recent analysis suggests that a 

significant share of the fuel efficiency gains (one third to one half) under CAFE can be attributed 

to medium-run changes in vehicle design (Greene, 1997; Klier and Linn, 2008). 

 Ideally, an analysis of the automotive industry response to fuel economy standards 

would account for all of the options firms have to improve fuel efficiency. In the medium-term 

available changes to vehicle design can be classified into two categories: “technology 

implementation”, where firms can choose from a range of technology features (e.g., high 

efficiency alternators) that improve fuel efficiency at some additional cost, and “attribute 

tradeoffs”, which improve fuel efficiency with some loss of another vehicle attribute (e.g., 

acceleration performance) but do not necessarily increase costs, and often decrease costs. Our 

model of endogenous attribute, which is based on engineering vehicle simulations, is the first to 

explicitly model both types of design changes. Consideration of both types of product design 

changes has potentially significant roles in response to the reformed CAFE standards, as well as 

other energy-efficiency policies. 

This paper is germane to literature on endogenous product attributes (e.g., Sweeting 

2007; Fan 2008; Gramlich 2008; Klier and Linn, 2008). Complex products such as automobiles 

present an added challenge to this literature because the process of attribute selection is 

constrained by a complex set of engineering limitations and tradeoffs. We explicitly represent 

these constraints and tradeoffs using methods from engineering literature (e.g., Michalek et al. 

2005; Frischknecht and Papalambros 2008; Shiau et al. 2009). Deriving an endogenous design 

model from a series of engineering simulations confers two advantages: 1) combinations of 
3 

product attributes that are not observed in current data but are possible, and potentially optimal 

under the counterfactual policy instruments we are interested, can be captured, and 2) 

engineering tradeoffs between product attributes can be identified independently of unobserved 

product attributes. This latter advantage is important for industries such as automotive where 

unobserved attributes, such as extra luxury accessories, often coincide with changes in product 

attributes, namely increased acceleration performance. 

This paper also extends the literature that analyzes the social surplus costs of fuel 

economy standards (e.g., Anderson and Sallee, 2009; Jacobsen, 2008; Gramlich, 2008). An 

important challenge in this literature pertains to estimating demand elasticities in the presence of 

correlation of endogenous observed prices and attributes with unobserved attributes. We 

overcome this endogeneity problem by exploiting the structure of the product development 

process, using semi-fixed vehicle attributes as instruments for the endogenous product attributes 

and prices. Our key identifying assumption is that vehicle dimensions are chosen earlier in the 

development process than detailed design variables in the powertrain, which affect both fuel 

efficiency and acceleration performance. We present evidence in support of this assumption in 

Section 2.2. 

Our analysis begins with a model of the medium-term automotive design process, 

incorporating the ability of firms to implement technology features and tradeoff fuel efficiency 

with other attributes of vehicle performance. This model is then incorporated into a partial 

equilibrium, static oligopoly model in which firms choose vehicle attributes and prices. Similar 

to Jacobsen (2010) and Klier and Linn (2008), we distinguish between firms constrained by the 

regulation, firms that violate the regulation and pay a fine, and those that operate above the fuel 

economy standard. A mixed-logit model of consumer demand is estimated using disaggregate 

consumer data. 

Once the parameters of the model have been estimated, we can conduct counterfactual 

simulations of industry response to the reformed CAFE standards. We numerically solve for 

vehicle attributes and prices in equilibrium, examining the changes in technology 

implementation and vehicle attributes induced by the regulation. Final estimation of the demandside is still pending, but for this working paper, we use a simplified demonstrational demand-side 

estimation to perform counterfactual simulations using two model specifications. The first 

specification includes both technology implementation and compromises between fuel efficiency 
4 

and acceleration performance, while the second includes only technology implementation and 

does not allow for firms to tradeoff fuel efficiency with other vehicle attributes. This latter 

specification is particularly relevant to current impact assessments of the reformed CAFE 

regulation conducted by the National Highway Traffic and Safety Administration (NHTSA), 

which account for efficiency-increasing technologies but ignore any tradeoffs between fuel 

efficiency and other vehicle attributes. 

Preliminary results highlight the potentially complex relationship between technology 

implementation and improvements in fuel economy that cannot be captured by models that 

ignore the potential to improve fuel efficiency by trading off performance along another 

dimension. Specifically, our demonstrational results suggest that while the reformed CAFE 

regulation may increase adoption of technology features, the benefit of these features is not 

always applied to improve fuel efficiency. Instead, firms can re-optimize the vehicle with 

additional technology features to improve other vehicle attributes such as acceleration 

performance. 

The remainder of the paper is organized as follows. Section 2 provides an overview of the 

industry, including the CAFE regulation and the vehicle development process. Section 3 details 

the simulations and estimation of engineering tradeoffs between endogenous attributes. Data 

used in the demand- and supply-side estimations are described in Section 4. The basic model is 

presented in Section 5. Section 6 presents and discusses the empirical results and Section 7 

discusses the counterfactual simulations. Conclusions are described in Section 8. 

2 Overview of Industry 

2.1 Fuel Economy Regulation 

Since 1975, the CAFE policy has influenced automotive firms’ decisions by setting a 

standard for the average fuel economy of a manufacturer’s fleet. The principle motivation for 

creating the CAFE regulation was to reduce dependence for oil consumption in the wake of the 

oil embargo. Since that time, interest in maintaining and strengthening the regulation has been 

driven by concerns about global climate change as well as foreign policy. 

The corporate average fuel economy for each manufacturer is calculated as a salesweighted harmonic mean fuel economy across the manufacturer’s fleet of vehicles in a particular 
5 

class (i.e., passenger cars or light trucks). The CAFE standard acts as a floor for this average, 

defining the CAFE requirement as: 

೎,೑ ሻ௝݌ሺ௝ݍ ॅא௝∑

௝ ⁄ ݃݌݉ ሻ௝݌ሺ௝ݍ ೎,೑ॅא௝∑

൒ ݐݏܽ݊݀ ௖ሺ1ሻ

where qj and mpgj are the number of sales and fuel economy vehicle j, and standc is the fuel 

economy standard for vehicle j’s class. If a firm violates this standard, they must pay a fine for 

each vehicle produced of $5.50 per 0.1 mpg below the standard. Historically, there have been 

three categories of firm responses to the CAFE standard: all domestic manufacturers (GM, Ford, 

and Chrysler) have met the standard within allowable deviation, certain Asian manufacturers 

(e.g., Toyota and Honda) have consistently exceeded the standard, and European manufacturers 

have violated the standard and paid the fine (Jacobsen 2010). 

The structure of the CAFE policy from 1975-2008 established a significantly lower 

standard for light trucks than for passenger cars. This distinction allowed minivans and SUVs, 

which composed a very small fraction of sales at the creation of the policy, to meet the lower 

light-truck standard despite their expanding role as a personal vehicle, causing what some called 

the “SUV loophole”. In 2007, Congress passed the Energy Independence and Security Act 

(EISA), phasing out this disparity by setting a target standard for both vehicle classes of 35 mpg 

by model-year (MY) 2020, later moved up to MY2016 by President Obama’s administration. 

In addition, Congress required that the CAFE standard be set dependent on one or more 

vehicle attributes. This decision was based on a National Association of Science report raising 

concerns that the influence of the CAFE regulation to encourage production of smaller vehicles 

was unsafe, and therefore CAFE should be structured to eliminate this incentive (NAS 2002, 24; 

and dissent to this opinion, app. A). NHTSA responded to these concerns by defining the 

reformed CAFE standards as depending on the footprint (track width multiplied by wheelbase) 

of the vehicles in a manufacturer’s fleet. 

The resulting regulation sets an individual fuel economy target, Tj, for each vehicle 

determined from the vehicle’s footprint, where vehicles with larger footprints have lower 

standards. Unlike the unreformed CAFE standards, the reformed standards vary across 

manufacturers. Specifically, the fuel economy standard for firm f and vehicle class c is: 

೎,೑ ሻ௝݌ሺ௝ݍ ॅא௝∑ ൌ௖ ,௙ܽ݊݀ݐݏ

௝ ܶ⁄ ሻ௝݌ሺ௝ݍ ೎,೑ॅא௝∑

 ሺ2ሻ
6 

This change has a number of important implications. With the unreformed CAFE, sales of any 

vehicle that had a higher fuel economy than its class standard (27.5 mpg for passenger cars and 

21.6 mpg for light trucks in MY2006) helped a firm comply with the regulation, and any vehicle 

under the standard hindered a firm’s ability to comply. Under the reformed CAFE, any vehicle 

that has a fuel economy higher than its individual footprint-based target will help a firm comply 

with the regulation. Because the targets are lower for vehicles with larger footprints, this could 

lead to a firm favoring a larger vehicle that can exceed its target over a smaller vehicle that has 

higher fuel economy but does not exceed its target. 

Both the unreformed and the reformed CAFE regulations provide some flexibility to meet 

the fuel economy standards. Specifically, both regulations allow firms to bank and borrow fuel 

economy credits. This allows a firm to meet the standard in a given year by applying any 

available banked credits earned from exceeding the standard in previous years or by borrowing 

credits, which will have to be repaid in future years. In addition to this, the reformed CAFE 

allows a trading program of credits within each firm, between the fuel economy and light truck 

standard, as well as among firms. An upper limit of credit trading was set at 1 mpg through 2013 

and 1.5 mpg through 2017. 

2.2 Vehicle Development Process 

The structure of the vehicle development has implications for understanding how firms 

respond to the CAFE regulation. The automotive development process is a structured sequence 

of interrelated decisions, many of which constrain choices made at later stages (Sörensen 2006). 

The typical design process begins with a concept development, followed by a system-level 

design that defines the geometric layout of the vehicle, followed by a detailed design of all 

subsystems (Sörenson 2006; Weber 2009). 

For a newly designed vehicle model, the development process begins with a target 

catalog specifying the vehicle segment (e.g., compact), powertrain architecture (e.g., hybrid), 

variations (e.g., four door sedan), major dimensions, transmission types (e.g., automatic, torque 

classes) and engine versions (Braess 2005; Weber 2009). Decisions on vehicle dimensions 

progress in a sequence first with definition of the new vehicle’s major target dimensions, then 

definition of remaining interior dimensions, followed by conception of the engine compartment 

and underbody with integration of all planned drivetrain configurations (Braess 2005). 
7 

For a redesigned model, the development process begins with defining how the vehicle 

will differ from its predecessor. The first step involves determination of changes to major 

properties of the vehicle and specifications for subsystems, such as how many drivetrain 

configurations or engine options will be available. Similar to the newly designed vehicle, 

however, early decisions on transmission types, model variations, and other major properties of 

the vehicle will inform updated dimensions for the redesigned vehicle (Braess 2005; Weber 

2009). These specifications for changes to the vehicle design will influence changes to the 

engineering design of vehicle subsystems. These properties of the development processes for 

newly designed and redesigned vehicles causes a structure where certain earlier design decisions 

must be finalized before the detailed engineering design of vehicle subsystems (Braess 2005; 

Sorenson 2006; Weber 2009). 

Figure 1 provides a simple representation of this development process. This figure is 

somewhat misleading insofar as it suggests that the design process proceeds in sequential, clearly 

defined stages. In fact, iteration loops and overlapping tasks may exist between the stages 

presented. However, despite deviations from Figure 1, it is possible to identify a stage in current 

automotive development processes where vehicle segment, powertrain architecture (e.g., 

conventional gasoline, hybrid, diesel), and key dimensions are finalized but “tuning” of 

powertrain variables is still possible. 

The structure of the automotive development process informs our research design in two 

important ways. First, we model medium-term design decisions (Stages B and C1

) separately 

from the longer-term design process. In our model, vehicle segment, powertrain architecture, and 

vehicle dimensions, which are determined in the earlier stages of the design process are taken as 

fixed. Conditional on these attributes, firms can adjust fuel economy and acceleration 

performance by “tuning” various powertrain variables (e.g., engine displacement and final drive 

ratio) and technology features (e.g., a high efficiency alternator). Second, we use the exogenous 

variation in vehicle attributes determined in earlier stages of the design process (i.e. Stage A in 

Figure 1) to instrument for endogenous variables in our demand-side estimation. 

 

1

 Ideally, the supply side should be modeled as a two-stage game to represent the sequence of choosing product 

designs before prices. However, computational complexity prevents us from solving the second-stage using Newtonbased methods and faster fixed-point methods do not exist for the CAFE-constrained case. 
8 

Figure 1: Simplified representation of an automotive development process illustrating short-term 

(Stage C), medium-term (Stage B) and longer-term (Stage A) design decisions

3 Endogenous Attribute Choice 

Credible modeling of endogenous attribute selection in the design of technical products 

such as automobiles requires accurate representation of the engineering and economic tradeoffs. 

We cannot directly observe all of the tradeoffs that firms make as they move through the 

different stages of the vehicle design process. We can, however, generate detailed engineering 

estimates of the tradeoffs that play an important role in determining vehicle fuel efficiency in 

medium-term design decisions. 

In this section, we first introduce the vehicle design choices and tradeoffs that are most 

relevant to our analysis. We then introduce a detailed vehicle simulation model that is used by 

automotive manufacturers to aid in vehicle development and explain how we use this simulation 

model in our analysis. Finally, we conclude with a discussion of how our engineering approach 

to modeling this endogenous attribute choice contrasts with the econometric approaches that are 

more often used in the economics literature. 
9 

3.1Medium-term design decisions affecting fuel efficiency 

Our analysis of firms’ response to the CAFE regulations focuses on medium-term vehicle 

design decisions and short-term vehicle pricing decisions exclusively (Stage B and C in Figure 

1). During this part of the vehicle development process, many major parameters of the vehicle 

have been determined including the segment of vehicle, key internal and external dimensions, 

and the powertrain architecture (e.g., conventional gasoline, hybrid, diesel). The automotive 

manufacturer can still adjust the fuel efficiency and acceleration performance at this point in the 

design process by “tuning” a number of variables in the powertrain. For example, consider a 

given vehicle design such as the Honda Accord. If Honda wants to increase the fuel efficiency of 

the Accord, it could decrease the displacement size of the engine, or it could simply change the 

programming in the powertrain electronic control unit to favor fuel efficiency over acceleration 

performance. Each of these adjustments to improve fuel efficiency will cause some loss in 

acceleration performance. 

Another means of improving fuel efficiency at this stage in the design process involves 

incorporating various extra “technology features” to the vehicle design. Examples include high 

efficiency alternators, low resistance tires, and improved aerodynamic drag of the vehicle body. 

Adding one or more of these features increases the cost of vehicle production. Depending on the 

specific technology features chosen, acceleration performance may increase, or decrease, or not 

be affected at all. For example, cylinder deactivation of the engine can improve fuel efficiency 

by effectively decreasing the size of the engine but because it only is active during coasting, it 

will not affect acceleration. Reducing aerodynamic drag of the vehicle body can improve both 

fuel efficiency and acceleration performance, whereas early shifting logic can improve fuel 

efficiency but will reduce acceleration performance. Note that these technology features only 

affect demand through their influence on fuel efficiency and acceleration performance; they do 

not have intrinsic value to the consumer. 

Figure 2 illustrates a stylized representation of the relationships between vehicle 

attributes of interest and various technology features that can be incorporated at this stage of the 

design process. The vertical axis measures fuel efficiency as the amount of fuel consumed to 

drive a given number of miles (related to the inverse of fuel economy) and the horizontal axis 

measures acceleration performance in terms of the time it takes to accelerate from 0 to 60 miles 

per hour, referred to as the 0-60 acceleration time. The concentric curves in Figure 2 connect all 
10 

of the possible combinations of fuel efficiency and acceleration performance that are possible, 

conditional on a particular set of technology features. We will refer to these curves as Production 

Possibility Frontiers (PPF). 

The choice of technology features determine which PPF a vehicle design belongs to. The 

location of a specific design on a given PPF is determined by choices of powertrain “tuning 

variables” that control fuel efficiency and acceleration performance. These tuning variables 

include the engine displacement (disp), the final drive ratio (the gear ratio between the 

transmission and the wheels). Because the choices of these tuning variables control both fuel 

efficiency and 0-60 acceleration time, the location along a PPF can be uniquely determined by 

the choice of either fuel efficiency or acceleration performance. 

The cost of producing the vehicle is not held constant along these PPFs. Production costs 

are simultaneously determined by the choice of technology features, acceleration performance, 

and fuel efficiency. Increases in fuel efficiency along a PPF will generally reduce the unit cost of 

manufacturing the vehicle, but the value of the vehicle to consumers may also decrease because 

of the loss in acceleration performance. 

Figure 2: Firms can decrease fuel consumption by compromising acceleration performance (a to b) 

or by choosing a different set of technology features (a to c) or some combination (a to d)
11 

3.2Engineering modeling of medium-term design 

Taking a “bottom up” approach, we use detailed engineering simulations to construct the 

baseline PPF, which represents the engineering tradeoffs between fuel consumption and 0-60 

acceleration time for a vehicle with no extra technology features. We then use a combination of 

these engineering simulations and data from NHTSA (2008) to determine how this baseline PPF 

changes with the addition of various technology features. Data generated from these simulations 

are used to define the relationship between fuel consumption, 0-60 acceleration time, and the 

choice of technology features in the medium term (Stage B in Figure 1) conditional on design 

decisions in the longer term (Stage A). 

To assist the engine and drivetrain industry with product design and development, 

detailed simulation models have been developed in the private sector. “AVL Cruise” is an 

integrated simulation platform that is widely used by major automotive manufacturers in 

powertrain development (Mayer, 2008). We use this model to characterize the engineering 

tradeoffs between fuel efficiency and 0-60 acceleration time for each vehicle class2. The fuel 

efficiency of a particular vehicle design is determined in AVL Cruise by simulating the EPA’s 

fuel-economy test procedures (FTP-75 and HWFET schedules). Acceleration performance is 

determined by simulating a shifting program of the vehicle from standstill to 60 mph. 

A total of 29,575 vehicle simulations were conducted. Design input parameters are varied 

at small intervals so that we can observe the influence of each of these parameters and their 

interactions on attributes of interest (i.e. acceleration performance and fuel efficiency). Table 1 

summarizes the range of parameter values we consider in our analysis. These include the 

powertrain variables that can be changed in the medium term (i.e., engine displacement and final 

drive ratio) as well as longer-term design decisions that are continuous (i.e., curb weight), which 

we condition on in the supply-side model. All other vehicle parameters are determined from a 

representative base vehicle for each class. Many of these parameters (e.g., front-wheel drive) are 

determined prior to the medium-term decisions we are interested in, but for some parameters 

(e.g., transmission gear ratios), it is possible that they could be modified in the same time period. 

In these cases, any potential bias in our counterfactual results caused by holding these design 

 

2

 The classes are based on the EPA segment classifications, with some grouping of segments based on similar ranges 

of engine displacement, final drive ratios, and curb weight as well as similar predicted outputs from AVL Cruise. 
12 

parameters fixed will be toward overestimating negative impacts of the CAFE regulations on 

producers and consumers. 

The simulations described above allow us to define the baseline PPF for a vehicle with no 

extra technology features. We then must determine how this baseline PPF is affected by the 

addition of one or more technology feature. The list of technology features we consider in our 

analysis is not comprehensive; we consider a subset of the types of technology features identified 

by NHTSA (2008). The majority of technology features we omit from our analysis are only 

available in longer term planning stages, but some features are eliminated due to the challenges 

in simulating their effects (e.g., variable valve timing) even though it is possible that they could 

be incorporated in the medium term. Similarly, with the powertrain tuning variables, any 

potential affect this would have on our results is to provide an upper bound on any social welfare 

costs of the CAFE regulations. 

NHTSA (2008) estimates the effect of each technology feature on fuel economy, in terms 

of the percentage improvement, based on values reported by automotive manufacturers, 

suppliers, and consultants. We use these estimates to determine how the baseline PPF changes 

with the addition of one or more technology features. However, to do this we also need to know 

the impact of each technology feature on 0-60 acceleration time, which is not reported by 

NHTSA. We determine these impacts by simulating each technology feature in AVL Cruise to a 

level that matches the improvement in fuel economy reported by NHTSA. For example, NHTSA 

reports a 0.5% improvement in fuel economy from using “low friction lubricants” in compact 

vehicles. We simulate this impact by reducing the friction losses in the engine of our 

representative compact vehicle model until we observe fuel economy improving by 0.5% and 

then observe the percentage improvement of 0-60 acceleration time. When NHTSA provides a 

range of fuel economy improvement for a technology feature, the lower bound of this range is 

used, consistent with our other assumptions in creating a conservative endogenous attribute 

model. The results of these simulations are reported in Table 2. 

3.3 Cost of medium-term design decisions 

In addition to representing the impact of medium-term design decisions on vehicle 

attribute performance, we also need to account for the effect of these decisions on vehicle 

production costs. We use two separate sources of data to estimate these costs, one describing 
13 

costs dependent on the powertrain tuning variables we use to construct the baseline PPF, and 

another dataset detailing production costs for each technology feature. The production cost of the 

baseline PPF—representing the cost dependent on choices of engine size and final drive ratio 

without any extra technology features—is taken from Michalek et al. (2004). The authors 

collected cost data from manufacturing, wholesale, and rebuilt engines of varying displacements. 

The additional production costs resulting from each technology feature is taken from NHTSA 

(2008), which are shown in Table 2. These cost data were estimated by NHTSA based on 

reported values from automotive manufacturers, suppliers, and consultants, and are currently 

used to perform cost-benefit analyses of the CAFE regulations. 

We treat the costs of technology features and the costs of adjusting powertrain tuning 

variables as additively separable. Engines are manufactured separately from other subsystems of 

the vehicle before assembly; with only two exceptions, the specific technology features we 

consider do not require changes in engine design nor affect the assembly of the engine with other 

vehicle subsystems. Two technology features—engine friction reduction and cylinder 

deactivation—do affect the engine subsystem but it is also reasonable to assume their costs are 

additively separable from the baseline production cost of the engine. For example, engine 

friction can be reduced by using higher-performing components of the engine subassembly (e.g., 

piston rings), where the additional production cost depends on longer-term design decisions 

(number of pistons) but not medium term decisions of interest (i.e., the displacement size of each 

piston). 

3.4 Estimating a tractable model of engineering tradeoffs and costs 

Ideally, all of the detailed information about design tradeoffs that are captured by the 

AVL Cruise model would be incorporated directly in our model of supply-side design and 

pricing decisions. However, because of the computational time required to execute the vehicle 

simulations, and because the large number of discrete combinations of technology features, this 

is computationally infeasible. Instead, we approximate these relationships with a flexible 

parametric form. 

Taking all possible combinations of technology features gives automotive firms, 

depending on the vehicle segment, 128 or 256 options to choose from for each vehicle. From this 

set, we consider only those combinations of features that are cost effective—meaning that there 
14 

is no lower cost combination that could achieve the same or better level of acceleration 

performance and fuel efficiency. Although this reduces the set of technology feature 

combinations to 20-76, depending on vehicle segment, it is still computationally infeasible to 

model this number of choices per vehicle per manufacturer in our counterfactual simulations so 

that further simplifications are necessary. 

We approximate the discrete choices of technology features as a continuous variable, 

tech, ranging from zero (the baseline case) to the maximum number of cost-effective 

combinations of technology features for each vehicle class. Note that a particular value for tech

maps to a specific combination of technology features (e.g., low resistance tires and a high 

efficiency alternator) and does not represent the number of technology features. The set of costeffective technology feature combinations is ordered by increasing fuel efficiency (decreasing 

fuel consumption) for the same acceleration performance, which is also increasing in cost. 

Therefore, a higher value of tech corresponds to a higher fuel efficiency and higher cost vehicle 

conditional on 0-60 acceleration time. The impact of the continuous approximation on the results 

is relatively small with the average gap between discrete features less than 1 mpg. Furthermore, 

we provide some evidence in Appendix A that the particular specification we use to estimate the 

relationships of the continuous tech variable to fuel consumption and cost preserve important 

properties of the discrete technology combinations. 

We use the results of the engineering simulations together with data on the technology 

features and technology costs, to estimate the following system of equations: 

 ݂ݑ݈݁ܿ݋݊ݏ௦௝ ൌ ߢ଴௦ ൅ ߢଵ௦݁ି௔௖௖ೞೕ ൅ ߢଶ௦ ݐ݄݁ܿ௦௝൅ߢଷ௦ݐ݄݁ܿ௦௝ · ܽܿܿ௦௝

ଶ ൅ߢସ௦ݐݓ௦௝ ൅ ߢହ௦ݐݓ௦௝ · ܽܿܿ௦௝ ൅ ߝ௦௝ ሺ3ሻ

݁݊݃ܿݐݏ݋௦௝ ൌ ߪଵ௦ ൅ ߪଶ௦݁ି௔௖௖ೞೕ ൅ ߪଷ௝ݐ݄݁ܿ௦௝ ൅ ߪସ௝ݐݓ௦௝ ൅ ߪହ௝ݐݓ௦௝ · ܽܿܿ௦௝ ൅ ߨ௦௝ ሺ4ሻ

where j denotes the vehicle design and s indexes the vehicle class. The fuel consumption of a 

vehicle in gallons per 1,000 miles is measured by fuelcons, acc is the 0-60 acceleration time, wt 

is the curb weight of the vehicle in 1,000 lb, and tech is the scalar measure of technological 

features incorporated. Estimating Eq. 3 and 4 separately for each vehicle segment, and including 

curb weight, conditions the fuel consumption and cost relationships on important vehicle 

parameters that are exogenous in the medium term. Several specifications for each equation were 

tested; the equations above performed the best under the Akaike Information Criterion. The 
15 

similarity of the specifications is due to underlying relationships between the powertrain tuning 

variables and technology features with the attributes of interest (fuelcons, acc, and engcost). 

Figure 3 plots observed and estimated fuel consumption and 0-60 acceleration time for a 

particular vehicle type (a compact vehicle) with no extra technology features. Equation 3 predicts 

observed vehicle performance reasonably well (R2

=0.76). Also, consistent with our earlier 

assumptions, this figure suggests diminishing returns to reducing acceleration performance (in 

terms of gains in fuel efficiency). These diminishing returns can also be intuitively explained by 

recognizing that it is generally easier to decrease fuel consumption of a low-efficiency vehicle 

than a high-efficiency vehicle; increasing fuel economy from 13 to 14 mpg saves 5.5 gal per 

1,000 mi, the same savings realized from increasing fuel economy from 30 to 36 mpg. Appendix 

B discusses comparisons between estimated and observed performance attributes in more detail. 

Figure 3: Comparison of compact-segment model to MY2006 vehicle data 

3.5An engineering approach to endogenous attribute choice modeling 

This is not the first paper to investigate the physical relationships between vehicle 

attributes that constrain vehicle design decisions. In the economics literature, a few recent studies 

have developed econometrically estimated endogenous attribute models for the automotive 

market (Gramlich 2008; Klier and Linn 2008). Although the econometric approach has its 

advantages, we argue that engineering estimates are more appropriate for our purposes. 

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20

Fuel Consumption (gal/1000 mi)

0-60 mph acceleration (s)

Market data Model predictions

Diesels Hybrid
16 

Using physics-based simulations to identify the engineering tradeoffs between vehicle 

attributes allows us to model tradeoffs and attribute combinations that are possible, but are not 

observed in the data. This is an important advantage of our approach because these unobserved 

vehicle designs may be optimal under the policy regimes we are interested in analyzing. In fact, 

fuel economy standards have historically had a significant influence on the types of vehicle 

designs that manufacturer’s produce, indicating that this ability may be particularly important for 

analyzing fuel economy standards. 

Furthermore, the engineering approach we use allows us to isolate the tradeoff between 

fuel efficiency and acceleration performance due to physical powertrain variables—specifically 

engine displacement and the final drive gear ratio—without conflating changes in unobserved 

attributes that affect consumer demand. In contrast, econometric approaches are more limited in 

their ability to account for correlation between endogenous attributes and unobserved attributes. 

In a recent paper, Klier and Linn estimated engineering tradeoffs between attributes using 

observed variations of fuel economy, acceleration performance, and weight based on different 

engine options. For example, the 2010 Chrysler 300 Touring with a 2.7 L engine option has a 

combined fuel economy of 21.6 mpg and a 0-60 acceleration of 10.5 s, whereas the 3.5 L engine 

option has 19.7 mpg and 8.5 s. However, engine options are correlated with unobservable 

attributes; in addition to a larger engine, the 3.5 L Touring also contains a suite of electronic 

accessories including anti-lock brakes, electronic traction control, light-sensing headlamps, and 

an upgraded stereo system. The addition of these extra accessories could increase vehicle weight 

and consume additional energy, further reducing fuel economy on top of the larger engine. 

Therefore, the true feasibility tradeoff between acceleration performance and fuel efficiency will 

not be consistently estimated. 

Using engineering simulations to identify the tradeoffs between vehicle attributes allows 

us to isolate the tradeoff between fuel efficiency and acceleration performance due to physical 

powertrain variables—specifically engine displacement and the final drive gear ratio—without 

conflating changes in unobserved attributes, such as luxury accessories. One concern with this 

approach, however, is that large changes in these powertrain variables have the potential to 

reduce the quality of the driving experience, for example by creating noise and vibrations, that 

may negatively affect consumer demand. However, this is a much weaker assumption than 

treating observed variations of vehicle fuel efficiency as uncorrelated with unobservables. 
17 

Furthermore, we limit violation of this assumption by restricting changes in the powertrain 

variables to ten percent or less, which is a conservative restriction to prevent noticeable noise and 

vibrations. 

4 Data 

We employ a combination of household-level data conducted by Maritz Research and 

vehicle characteristic data available from Chrome Systems Inc. to construct our demand-side 

estimations. The Maritz Research U.S. New Vehicle Customer Study (NVCS) collects data 

quarterly from households that purchased or leased new vehicles. This survey provides 

information on socio-demographic data, household characteristics, and the vehicle identification 

number (VIN) for the purchased vehicle. The survey also asks respondents to list up to three 

other vehicles considered during the purchase decision. Approximately one-third of respondents 

listed at least one considered vehicle. From these data, we sample 6,560 households; because the 

survey oversamples households that purchase vehicles with low market shares, this is a choicebased sample approximating the observed 2006 model-year market shares. Summary data of this 

sample are shown in Table 3. 

We supplement the survey data with information on vehicle characteristics using Chrome 

System Inc.’s New Vehicle Database and VINMatch tool. Vehicle alternatives are identified 

using the reported VIN, distinguishing vehicles by their make, model, and engine option, with a 

few modifications. We eliminate vehicles priced over $100,000, which represent a small portion 

of market sales, and remove seven vehicle alternatives that were not chosen or considered by any 

survey respondent. We further reduce the data set by consolidating pickup truck and full-size van 

models with gross vehicle weight ratings over 8,000 lb to only two engine options each. 

Summary vehicle data are described in Table 4. 

Additionally, data on dealer transactions purchased from JD Power and Associates are used 

to estimate dealer markups in the supply-side model. These data were collected from 

approximately 6,000 dealers from the proprietary Power Information Network data, aggregated 

to quarterly invoice costs and transaction prices for each vehicle model. 
18 

5 Model 

5.1 Demand side 

Demand for new automobiles is modeled using a mixed-logit representation of consumer 

preferences. The indirect utility Unj that consumer n derives from purchasing vehicle model j is 

defined as: 

ሻ5ሺ௡௝ ߳ ൅ ࢐࢔࢝Ԣ࢔ࣆ ൅ ࢐࢔࢞Ԣࢼ ൅ ௝ߜ ൌ௡௝ ܷ

where δj is the portion of utility that is the same across all consumers; xnj are vehicle attributes that 

interact with consumer characteristics and affect utility homogenously across the population; wnj are 

vehicle attributes and attribute-demographic interactions that heterogeneously affect utility, entering 

the equation through draws of assumed distributions, μn, with zero means and standard deviations . 

The disturbance term Ԗnj is the unobserved utility that varies across consumers. Assuming that ߳nj is 

independent and identically distributed (iid) Type I extreme value, the probability that consumer 

n chooses vehicle i takes the form:

ܲ௜௡ ൌ ݁௎೙೔

1 ൅ ∑ ݁௎೙ೕ ௝

 ሺ6ሻ

and the predicted market share of vehicle i is ∑௡ ܲ௜௡.

Following Train and Winston (2007), the utility formulation is extended to include 

information about ranked choices when these data are available for a respondent. The ranking is 

specified as U୬୧ ൐ U୬୦భ ... U୬୦ౣ ൐ U୬୨ for all j ് i, hଵ,...,h୫ where i is the chosen vehicle; h1 is 

the second ranked vehicle (the vehicle that would have been chosen if vehicle i was not 

available) and hm is the m ranked vehicle. Therefore, the probability that consumer n chose 

vehicle i and ranked vehicle h1 through hm is defined as: 

ܮ௛௜௡భ...௛೘ ൌ ቆ ݁௎೙೔

1 ൅ ∑ ݁௎೙ೕ ௝

 ቇ ቆ ݁௎೙೓భ

1 ൅ ∑ ݁௎೙ೖ ௞ஷ௜ ቇ ... ቆ ݁௎೙೓೘1 ൅ ∑ ݁௎೙೗ ௟ஷ௜,௛భ,...,௛೘షభ

 ቇ ሺ7ሻ

When no ranking data are available for a consumer, the likelihood consists of only the first term 

in Eq. 7. 

 We define δj as a function of observed vehicle attributes, zj, including all endogenous 

attributes, and the average utility of unobserved attributes, ξj: 

ሻ8ሺ௝ ߦ ൅ ࢐ࢠԢࢻ ൌ௝ ߜ
19 

Berry (1994) showed that, given a set of values for  and , a unique δ exists such that predicted 

market shares match observed market shares. Defining ߜ ௝in this way allows us to address the 

problem of endogenous attributes in zj that are likely correlated with unobserved utility, ξj. Given a 

set of exogenous attributes and instrumental variables for endogenous attributes, y, the condition that 

ॱ൫ݕ௝,ߦ௝൯ൌ0 for all j is sufficient for the instrumental variable estimator of ࢻ to be consistent and 

asymptotically normal conditional on  and . 

 Vehicle attributes in the vector zj include price, fuel consumption, the inverse of 0-60 

acceleration time, vehicle segment, brand, and two parameters representing vehicle size described 

below. Vehicle segments are based on the EPA’s classes (e.g., minivans) and brand is defined as 

vehicle make (e.g., Volvo) with divisions between cars and trucks of some makes. Attributes in the 

vector xnj, which are assumed to have homogeneous effects in the utility specification, include the 

interaction between living in a rural area and the pickup truck segment, and interactions between 

children in the household and SUV and minivan segments. Attributes in the vector wnj, which have 

random effects in the utility specification, are the ratio of vehicle price to income; “cents per mile”, 

cpm, calculated by dividing the price of gas by the vehicle’s fuel economy; the inverse of 0-60 

acceleration time; and the vehicle size terms. The distribution of the price to income ratio and the 

size terms are taken to be normally distributed across the population, and those for inverse 0-60 

acceleration time and cpm are taken as log-normally distributed. 

It is reasonable to assume that, all else constant, consumers would monotonically prefer 

lower price, lower cost to drive, and better acceleration (higher inverse of time to accelerate). 

However, with respect to vehicle size, consumers may monotonically prefer larger vehicles, or 

they may prefer a specific sized vehicle to other vehicles that are larger or smaller than this 

“ideal” size. To account for the latter possibility, we follow Frischknecht et al. (2008), including 

two size parameters in both xnj Eq. 5 and zj in Eq. 8: the footprint (length multiplied by width) of 

the vehicle and the footprint squared. Allowing both of these attributes to enter the equation with 

random coefficients allows consumers to have heterogeneous preferences for the “ideal” size of a 

vehicle. 

Because price, fuel economy, and acceleration performance are correlated with 

unobserved vehicle attributes, estimating Eq. 8 directly will produce biased parameters. We 

address this problem by selecting instruments for the endogenous variables: the moments of 

vehicle dimensions of same-manufacturer vehicles (din, dsqin) and different-manufacturer 
20 

vehicles (dout, dsqout), powertrain architecture (i.e., hybrid, turbocharged, and diesel), and drive 

type (i.e., all wheel drive or 4-wheel drive). The validity of these instruments relies on the 

assumption that the attributes chosen are all determined from longer-term product planning 

schedules than the endogenous variables. Similar moment instruments were used in Berry, 

Levinsohn, and Pakes (1995) and Train and Winston (2007), albeit with a wider attribute set that 

included fuel economy and horsepower. While this wider set of attributes may be appropriate for 

instruments in a model considering the very narrow short term, it is certainly not valid for the 

medium term. In contrast, we limit the set of instruments used in our estimations to only those 

attributes that are exogenous in what we define as the medium term as supported by evidence in 

Section 2.2, and therefore are valid instruments. 

The procedure for calculating the maximum likelihood estimators for all demand-side 

parameters involves solving an iterative equation for δ at each trial estimation value of  and 

such that: 

௝ߜ

௧

ሺ, , ܁ሻ ൌ ߜ௝

௧ିଵሺ, , ܁ሻ ൅ ln൫S୨൯ െ ln S෠୨ ቀ, , ߜ௝௧ିଵሺ, , ܁ሻቁ ሺ9ሻ

Unfortunately, due to the computational complexity of our estimation framework, we are having 

difficulties achieving convergence in this iterative procedure. Note that replacing our mixed-logit 

specification with a nested-logit model of utility could eliminate the need to solve the Eq. 9 

iteratively. However, our data set indicates that consumers considered vehicles from different 

segments in their purchasing decision, leading us to reject the necessary condition that 

consumers are nesting their choice set based on vehicle segments. For the purposes of this 

working paper, we estimate the following equation: 

ሻ10ሺ௡௝ ߳ ൅ ࢐࢔࢝Ԣ࢔ࣆ ൅ ࢐࢔࢞Ԣࢼ ൅ ࢐ࢠԢࢻ ൌ௡௝ ܷ

We use the instrumental variables in a two-stage least squares estimation of Eq. 10 realizing that this 

approach yields inconsistent estimates (Berry, 1994). This estimation approach allows us to present a 

proof of concept of our methods. In future work, we will replace the estimates we obtain here with 

new estimates obtained using the iterative estimation procedure described above. 

5.2 Supply side 

The automotive industry is modeled as an oligopoly of multiproduct firms that maximize 

expected profits with respect to vehicle attributes and prices. Consistent with historical behavior, 

auto firms are characterized into three groups: those that operate at the CAFE standard 
21 

(constrained), those that operate above the standard (unconstrained)3

, and those that violate the 

standard and pay the fine (violators). In our counterfactual simulations, the domestic Big 3 

manufacturers (Chrysler, Ford, and General Motors) are constrained to the standard following 

their historic behavior, and their expected future behavior, of consistently meeting the CAFE 

standards within allowable banking and borrowing credits (Jacobsen 2010). Both Toyota and 

Honda have always voluntarily exceeded the standards and this behavior is supported in our 

counterfactual results. The remaining firms are considered violators in our counterfactuals, 

which indicate that violating the standard is profit-maximizing behavior for these firms rather 

than meeting or exceeding the standards. 

The profit optimization problem solved by an unconstrained firm is: 

 max

ᇱࢗ ࢎࢉࢋ࢚ ,ࢉࢉࢇ

ሺ࢖െࢉሻ ሺ11ሻ

where all quantities are J x 1 vectors with entries for all J vehicles in the firm’s fleet. Similarly, 

for firms paying the CAFE penalty, the profit maximization problem is given by: 

 max

࢖ ,ࢎࢉࢋ࢚,ࢉࢉࢇ

ᇱࢗ 

ሺ࢖െࢉሻ െ ܨ ஼െ ܨ் ሺ12ሻ

where FC and FT are the respective fines for violating the passenger car and light truck standard, 

defined as: 

ሻ௝݌ሺ௝ݍ ෍ 55 ൌ஼ ܨ

಴,೑ॅא௝

಴,೑ ሻ௝݌ሺ௝ݍ ॅא௝∑ െ஼ ܽ݊݀ݐݏቆ

௝ ⁄ ݃݌݉ ሻ௝݌ሺ௝ݍ ಴,೑ॅא௝∑

ቇ

ሻ௝݌ሺ௝ݍ ෍ 55 ൌ ்ܨ

೅,೑ॅא௝

೅,೑ ሻ௝݌ሺ௝ݍ ॅא௝∑ െ ்ܽ݊݀ݐݏቆ

௝ ⁄ ݃݌݉ ሻ௝݌ሺ௝ݍ ೅,೑ॅא௝∑

ቇ

 ሺ13ሻ

For the case of a constrained firm, the profit maximization is identical to Eq. 11 but the 

firm is also subject to meeting the CAFE standards (standC and standT) for their fleet of cars, ॅ௖, 

and their fleet of light trucks, ॅ். Rearranging Eq. 1, these constraints can be written as: 

∑௝אॅ ݍ௝ሺ݌௝ሻ ಴ ൬1 െ ௦௧௔௡ௗ಴

௠௣௚ೕ

൰ ൒ 0

∑௝אॅ ݍ௝ሺ݌௝ሻ ೅ ൬1 െ ௦௧௔௡ௗ೅

௠௣௚ೕ

൰ ൒ 0

 ሺ14ሻ 

 

3

 More precisely, these producers are inactively constrained but we solve for equilibrium by treating them as 

unconstrained and check that their decisions at equilibrium do indeed meet the CAFE standard. 
22 

Therefore, the constrained profit maximization in vector form is: 

max

ᇱࢗ ࢖,ࢎࢉࢋ࢚,ࢉࢉࢇ

ሺ࢖െࢉሻ

ᇱࢗ .ݐ .ݏ

0 ൒ ࡯࢘

ᇱࢗ 

0 ൒ ࢀ࢘

 ሺ15ሻ

where rC is a vector with the jth entry of 1 െ ݐݏܽ݊݀஼⁄݉݌݃ ௝if ݆אॅ ஼and zero otherwise. The 

vector rT is similarly constructed with the jth entry of 1 െ ݐݏ்ܽ݊݀⁄݉݌݃ ௝if ݆אॅ் and zero 

otherwise. 

Note that, for all types of firms, fuel consumption is determined through decisions on 

acceleration performance and technology features from Eq. 3 and therefore is not listed explicitly 

as a decision variable. We could instead have listed mpg and tech as the decision variables and 

implicitly determined acceleration performance; this convention is arbitrary and does not affect 

the formulation. 

For all firms, the marginal cost of producing automobile j is represented as: 

ܿ௝ ൌ ݁݊݃ܿݐݏ݋ ൅ ௝߱ ௝ሺ16ሻ

where ݁݊݃ܿݐݏ݋ ௝is the portion of marginal cost dependent on the endogenous selection of 

attributes as described in Section 3.3. The remaining portion of marginal cost, ߱௝, is determined 

from the first order conditions of Bertrand equilibrium: 

 unconstrained: ࢗሺ࢖ሻ ൅ ൫ܙܘ׏ᇱ

൯ሺ࢖െࢉሻ ൌ ૙ ሺ17aሻ

 fee-paying: ࢗሺ࢖ሻ ൅ ൫ܙܘ׏ᇱ൯ሺ࢖െࢉሻ െ ൫ܨܘ׏஼൯

ᇱ

െ ൫ܨܘ׏்൯

ᇱ

ൌ ૙ ሺ17bሻ

 constrained: ࢗሺ࢖ሻ ൅ ൫ܙܘ׏ᇱ

൯ሺ࢖െࢉെߣ஼࡯࢘ െ ߣ்ࢀ࢘ሻ ൌ ૙ ሺ17cሻ

For the unconstrained and penalty-paying firms, the costs can be directly determined from 

equations 12a and 12b. However because the Lagrange multipliers, ߣ ஼and ߣ், are unknown and 

࢘ ஼and ்࢘ depend on fuel economy, which is correlated with marginal cost, we cannot directly 

solve for marginal cost for the firms constrained to the CAFE standard. The Lagrange 

multipliers, which will be negative, represent the effect on firm profits of incrementally 

increasing the unreformed CAFE constraints in Eq. 14 holding vehicle design fixed. Notice that 

if we assumed that the Lagrange multipliers were zero, then we would overestimate the marginal 

costs of vehicles with fuel economies below the standard and underestimate the costs of vehicles 

that exceed the standard. 
23 

 Following Jacobsen (2010), we estimate these multipliers using the relationship of dealer 

markups to manufacturer markups. However, rather than take the relationship of dealer to 

manufacturer markups as given by Bresnahan and Reiss (1989), which did not incorporate the 

effects of the CAFE regulation, we extend the derivation one-step further by explicitly including 

the CAFE regulation (Appendix C). Using these recovered parameters, we can then solve for the 

equilibrium marginal vehicle costs for the constrained firms. This estimation strategy has the 

limitation of relying on the imposed form of the relationship between dealer and manufacturer 

markups. However, our interest in the estimates of ߣ ஼and ߣ் is limited to their role in picking up 

enough of the correlation between marginal costs and ࢘ ஼and ்࢘. We therefore expect any errors 

in the estimation of ߣ ஼and ߣ் will only have second-order effects on the results of our 

counterfactual simulations. Future work will include performing sensitivity tests on 

counterfactual results to various values of ߣ ஼and ߣ். 

6 Empirical Results 

6.1Endogenous attribute model estimation 

The estimation results for Eq. 3, which summarizes the relationship between vehicle 

attributes based on technology features and powertrain parameters for each vehicle class, are 

reported in Table 5. Similarly, results from estimating the cost relationship as in Eq. 4 are 

reported in Table 6. Results from validation tests comparing model predictions to observed 

market data are summarized in Appendix B. Based on these results, the sales-weighted average 

change in 0-60 acceleration time necessary to increase fuel economy by 1 mpg across MY2006 

vehicles is 0.91 seconds. The sales-weighted average cost of increasing fuel economy by 1 mpg 

while maintaining the same acceleration performance is $143. 

6.2Demand-side estimation 

The OLS estimations of the first-stage regressions of price, the inverse of fuel economy, 

and the inverse of 0-60 acceleration time are presented in Table 7. The F-tests for the joint null 

hypothesis that the instruments’ coefficients are zero are 9.52, 26.76, and 8.18, respectively. 

Results of the second-stage IV estimation are shown in Table 8. Significant heterogeneity 

is shown in the ratio of price to income, the cents-per-mile attribute, and both footprint terms. 

The estimated parameters for the footprint terms indicate that preference monotonically increases 

with vehicle size for all individuals in our sample, but the rate of increase varies among 
24 

individuals. SUVs are the only vehicle segment preferred more than sedans, which is used as the 

baseline. As expected, consumers with children have an increased value of both minivans and 

SUVs and consumers living in rural areas have increased value of pickup trucks. 

Based on these estimates, we compute own-price elasticities for the set of 473 MY2006 

vehicles. Table 9 presents the price elasticities for a sample of these vehicles. The sales-weighted 

average price elasticity is -2.64

. Similar to other models of the automotive industry (Berry, 

Levinsohn, and Pakes 1995; Goldberg 1998, Beresteanu and Li 2008) we find that, in general, 

demand is relatively elastic for cheaper “economy” vehicles and relatively inelastic for higher 

priced vehicles, although this relationship is not monotonic. 

6.3Supply-side estimation 

Table 10 shows the estimates of ߣ ஼and ߣ் for domestic firms. These results are in the 

same range as Jacobsen’s (2010) estimates. The estimates indicate that, for passenger cars, 

Chrysler faces a higher cost of compliance than Ford or GM. This result is intuitive given that 

Chrysler neither sells many small vehicles nor has many passenger cars with relatively high fuel 

economy. For light trucks, the estimates indicate that Ford has the lowest cost of compliance and 

GM has the highest. This result can be explained by the fact that, while Ford produces fewer 

models of light trucks than GM, Ford produces a number of high-efficiency light trucks 

including the Escape Hybrid. 

7 Counterfactual Experiments 

Using the structural parameters determined from the demand and supply side, we perform 

counterfactual simulations of the reformed CAFE standards that will be applied to the MY2012 

fleet of vehicles. Twenty firms are represented in these simulations, producing a total of 473 

vehicle models, described by Table 4. The choice of firms represented in these simulations is 

determined following the EPA’s classification of manufacturers as listed on the MY2006 fuel 

economy test data. For example, Saab is considered as part of GM but Land Rover is considered 

a separate firm from Ford. 

 4

 This average price-elasticity is the same as Klier and Linn’s (2008) and similar to Jacobsen’s (2010) estimate 

of -2.0 and Berry, Levinsohn, and Pakes’s (2004) and Train and Winston’s estimates of -2.3, and Goldberg’s (1998) 

estimate of -3.1. 
25 

Our simulations estimate the impact of moving from the unreformed CAFE standards to 

the reformed CAFE standards. A number of structural differences between the two policy 

regimes are of particular interest. First, the reformed standards set individual fuel economy 

targets for each vehicle based on its footprint, so that larger vehicles can meet lower standards. 

Second, the reformed CAFE standards allow trading within a firm between the passenger car 

standard and the light truck standard although they set a floor on the minimum passenger car 

standard of 29.9 mpg. 

While we do account for trading of fuel economy credits within firms in our 

counterfactuals, we do not permit trading between firms or banking and borrowing credits in our 

simulations. Therefore, our results should be interpreted as upper bounds on the producer and 

consumer surplus losses resulting from the regulation. This is consistent with our assumptions in 

the endogenous attribute model, which are constructed to bias producer and consumer losses 

toward the upper bound. For a discussion of banking and borrowing of fuel economy credits, 

interested readers should refer to Jacobsen (2010). 

In all of the scenarios we consider, Chrysler violates its fuel economy standards by 0.01 

mpg. This allowance is made because Chrysler could not meet the 29.9 mpg minimum standard 

for passenger cars. The CAFE standards are enforced up to a tenth of a mile-per-gallon meaning 

that, if Chrysler had an average of 29.85 mpg for its passenger cars, it would be considered in 

compliance with the requirements. However, under our counterfactuals Chrysler could only 

achieve an average of 29.84 mpg. This result is reasonable considering that Chrysler is now 

importing Fiat vehicle models, which have high fuel economy compared to Chrysler’s fleet, in 

anticipation of the reformed CAFE standards. 

 The estimated effects of the reformed CAFE on consumer surplus, producer surplus, and 

fuel consumption are shown in Table 11. Note that this welfare analysis does not account for any 

monetary benefits associated with reduced fuel consumption but only reports the level of 

reductions in millions of gallons of fuel. These values are measured relative to a baseline of Nash 

equilibrium with respect to prices, acceleration performance, and technology implementation in 

the presence of the MY2006 CAFE standards. Details of this baseline can be found in Appendix 

D. Consumer surplus is measured by equivalent variation, or the amount that a consumer would 

need to pay to realize the same amount of utility. Producer surplus is reported for five categories 
26 

of firms. The first three of these categories—the domestic Big 3, Asian Big 4, Euro, and Other 

Asian—currently have manufacturing plants located in the United States. 

7.1 Changes in technology implementation 

The first set of counterfactual simulations allows firms to respond to the CAFE 

regulations using both tradeoffs between acceleration performance and fuel economy and 

technology implementation. Results, shown in Table 11, indicate that firms do adopt technology 

features in response to the reformed CAFE but the benefits conferred by these technology 

features is split between improvements in acceleration performance and fuel efficiency. As Table 

11 indicates, across the market, the total amount of reduced fuel consumption due to 

implementing technology features that increase fuel efficiency is 531 million gallons, but that a 

263 million gallon increase in fuel consumption is due to adjusting powertrain tuning variables to 

improve acceleration performance at some loss of fuel efficiency. This suggests that, across all 

manufacturers considered, only 50% of the potential of implemented technologies to decrease 

fuel consumption is realized and the remaining is applied to improve acceleration performance. 

This behavior illustrates some of the complexity of the relationship between technology 

implementation and improvements to fuel economy. Because the benefit of technology features 

can be applied to improve efficiency or improve other product attributes, incorporating tradeoffs 

between product attributes has added value to assessing the impact of energy-efficiency policies 

on technology adoption. 

Our preliminary results suggest that firms constrained by CAFE, namely the domestic 

Big 3 manufacturers, will improve the fuel economy of their vehicle fleets by an average of 2.6 

mpg. This rise in fuel economy is a result of both changes in technology features and changes in 

prices to shift demand toward vehicles that exceed their fuel economy targets, called mixshifting. Technology implementation increases across these firms’ fleets, but 42% of the 

potential of technology features to decrease fuel consumption are instead used to improve 

acceleration performance. 

Unconstrained firms, most notably Toyota and Honda, actually lower the fuel economy 

of their vehicle fleets by an average of 1.9 mpg. This behavior, also noted by Jacobsen (2010), 

can be explained by the residual demand curve for lower fuel economy vehicles, which are larger 

or have better acceleration, shifting to the right in response to other firms producing higher fuel 
27 

economy vehicles. Technology implementation also increases for these firms, but 100% of it is 

used to improve acceleration performance instead of fuel efficiency. 

7.2 Changes in fuel consumption and social surplus 

These simulation results indicate that a transition from the unreformed CAFE standards 

to the reformed CAFE standards will reduce producer profits by $10 for each gallon of fuel 

saved. However, simulation results suggest that under the reformed CAFE regulations consumer 

surplus increases by an estimated $47 for each gallon of fuel saved compared to the status quo 

fuel economy standards. This increase in consumer surplus can be attributed to the footprintbased fuel economy standards, which our simulation results indicate encourages firms to raise 

prices of vehicles with relatively low price elasticities and lower prices of vehicles with 

relatively high price elasticities as shown in Table 13. For example, the Pontiac G6 is much more 

price-elastic (-1.05) than the Pontiac Solstice (-0.09) and, at equilibrium, the G6 exceeds its fuel 

economy target but, because the Solstice has a smaller footprint, it is 7 mpg below its standard. 

Therefore, it is in GM’s interest to lower the price of the G6 and raise the price of the Solstice so 

that the average fuel economy across its fleet exceeds the average target. Across the fleet of U.S. 

vehicles, the average price-elasticity of vehicles with higher prices under the reformed CAFE 

standards is -0.75 whereas the average price-elasticity of vehicles with lower prices is -5.30. 

However, there are limitations to our current analysis that may affect these results. Most 

notably, the current demand-side parameters are not consistently estimated and our results will 

not necessarily be similar once the demand side is re-estimated. Secondly, sensitivity analyses 

are needed to test the robustness of our results to the assumptions used in our model. Most 

notably, future work will include sensitivity tests to estimates of engine and technology-feature 

costs, the shadow costs of the unreformed standards, and the specification of our consumer utility 

function. Lastly, this approach only considers the medium term, where vehicle size is considered 

fixed. Because the reformed CAFE policy sets lower standards for manufacturers that produce 

vehicles with larger footprints, an incentive may exist for manufacturers to increase the size of 

their vehicles. This potential effect will not be captured in our limited medium-term model. 

7.3 Impact of attribute tradeoffs on social welfare 

In the second specification, shown in Table 12, we shut down the ability of firms to 

tradeoff acceleration performance with fuel economy, considering the determination of 

acceleration performance as exogenous. We do this to investigate the effect of ignoring tradeoffs 
28 

between vehicle attributes on the resulting welfare estimations. Estimated reductions in fuel 

consumption are 26% lower than in the first specification, and increases to social surplus are 

46% lower. These results emphasize the importance of accounting for tradeoffs between vehicle 

attributes when analyzing policies such as the CAFE regulation. 

We also attempted simulations that do not allow firms to make any medium-term design 

changes but instead vehicle design is fixed and firms can only increase their average fuel 

economy by adjusting prices of their vehicles to shift demand toward higher-efficiency vehicles. 

However, firms were unable to meet the reformed CAFE standards. In fact, Chrysler has no 

vehicles that exceed their fuel economy targets, and Ford and GM have very few. This 

demonstrates the value of accounting for medium-term decisions that change vehicle design 

when analyzing policy regimes such as fuel economy standards. 

8 Conclusions 

 This paper presents a model of automotive industry accounting for medium-term firm 

decisions affecting fuel economy and acceleration performance. In addition to accounting for 

technology implementation, our model explicitly accounts for engineering tradeoffs between fuel 

efficiency and acceleration performance—controlled through modification of powertrain 

variables—that provide another mechanism for firms to respond to fuel economy regulations. 

 Our modeling approach extends the literature on endogenous product attributes in several 

ways. On the demand side, correlation between endogenous attributes and unobservables is 

addressed by identifying quasi-fixed attributes that can serve as valid instruments in the medium 

term. Additionally, we use physics-based engineering vehicle simulations to generate data on 

fuel economy and acceleration performance based on changes in powertrain tuning variables. 

This allows us to represent the engineering tradeoffs between vehicle attributes on our supply 

side, without conflating effects of unobserved attributes. The methods we develop here are 

generalizable to other technical products such as household appliances and consumer electronics. 

While this specific study uses command-and-control regulation as a case study, an extension to 

market-based instruments is straightforward. 

We use this model to estimate the effects of the model-year 2012 CAFE regulation on 

producer and consumer surplus. Although final estimation of the demand-side is still pending, 

for this working paper, we use a simplified demand-side specification to present our preliminary 
29 

results. Results indicate that domestic firms implement technology features to comply with the 

regulation, but nearly half of the potential benefit of these technologies to reduce fuel 

consumption is instead used to increase acceleration performance. Comparing our model to a 

simpler model that ignores the ability of firms to trade off fuel economy and acceleration 

performance significantly underestimates net welfare benefits of the regulation. These 

demonstrational results suggest that accounting for tradeoffs between vehicle attributes could be 

significantly important for welfare analyses of policy instruments such as fuel economy 

regulations. 

Although we construct our assumptions as much as possible so that estimates of any 

negative impact of CAFE on consumer and producer surplus would represent upper bounds, 

there are limitations of our model that could bias our estimates to underpredict potential negative 

impacts of CAFE. Sensitivity analyses are needed, especially on the production cost estimates, to 

ensure that our estimates are not underpredicting the social surplus cost of the reformed CAFE 

standards. 

Another important caveat of our model and the welfare results presented is that vehicle 

size is considered fixed. Because the reformed CAFE standards are structured to allow 

manufacturers of larger vehicles to meet lower standards, a manufacturer can actually lower their 

fuel economy standard by producing larger vehicles. This property may create the incentive for 

manufacturers to increase the size of their vehicles, which may result in smaller reductions in 

fuel consumption. The potential of this incentive, and its effect on producer and consumer 

surplus, should be considered in future work. 

Table 1: Ranges and intervals of vehicle simulation parameters

Notes: This table lists the min, max, and interval of input parameters used in the “AVL Cruise” vehicle simulations. 

Engine Displacement is in cm3

, Curbweight is in lb, and Final Drive is the final drive gear ratio. All other input 

parameters for the simulations (e.g., front-wheel drive) were taken using data for the “base vehicle”. 

Min Max Int. Min Max Int. Min Max Int.

2seater/Mini Ford Mustang 1,000 8,200 400 1,900 4,300 800 1.0 6.0 0.4

Sub/Compact Honda Civic 1,000 4,200 400 2,200 4,800 800 1.0 6.0 0.4

Midsize Toyota Camry 1,000 4,200 400 2,400 4,800 800 1.0 6.0 0.4

Fullsize Ford Taurus 1,600 6,800 400 3,200 5,400 400 1.0 6.0 0.4

SUV Ford Explorer 2,000 8,400 400 3,200 8,000 800 1.0 6.0 0.4

Small pickup Toyota Tacoma 1,600 8,400 400 2,800 5,200 800 1.0 6.0 0.4

Stand. pickup Ford F150 2,000 8,400 400 3,200 6,600 400 1.0 6.0 0.4

Displacement Curbweight Final Drive Vehicle Class Base Vehicle
30 

Table 2: Technology Costs and Percentage Improvements in Fuel Economy and 0-60 Acceleration Time

Notes: cost represents the unit production cost in $/vehicle produced, % mpg is the percentage increase in combined highwaycity fuel economy, and % acc is the percentage reduction in 0-60 mph acceleration time in seconds. Cost and fuel economy 

figures are taken from NHTSA (2008). The change in acceleration is calculated in the engineering vehicle simulation model 

“AVL Cruise”. 

Table 3: Summary of Sampled Consumer Respondent Demographics 

Technology cost % mpg % acc cost % mpg % acc cost % mpg % acc cost % mpg % acc

Low friction lubricants 3 0.5 0.3 3 0.5 4.1 3 0.5 0.6 3 0.5 0.6

Engine friction reduction 126 1 0.3 84 1 5.6 126 1 1.5 126 1 1.2

Aggressive shift logic 38 1 -0.2 38 1 -5.0 38 1 -0.2 38 1 -0.3

Early torque converter lockup 30 0.5 - 30 0.5 - 30 0.5 - 30 0.5 -

High efficiency alternator 145 1 0.3 145 1 5.6 145 1 1.5 145 1 1.2

Aerodynamic drag reduction 38 3 0.3 38 3 5.1 38 3 0.5 38 3 0.3

Low rolling resistance tires 6 1 0.1 6 1 2.5 6 1 0.2 6 1 0.1

Cylinder deactivation n/a n/a 203 4.5 - 203 4.5 -

Technology cost % mpg % acc cost % mpg % acc cost % mpg % acc

Low friction lubricants 3 0.5 1.6 3 0.5 0.4 3 0.5 0.7

Engine friction reduction 126 1 3.1 126 1 0.7 168 1 1.5

Aggressive shift logic 38 1 0.0 38 1 -0.2 38 1 -2.8

Early torque converter lockup 30 0.5 - 30 0.5 - 30 0.5 -

High efficiency alternator 145 1 3.1 145 1 0.7 145 1 1.5

Aerodynamic drag reduction 38 3 1.4 38 2 0.5 38 2 0.4

Low rolling resistance tires 6 1 0.5 6 1 0.2 0 1 0.1

Cylinder deactivation 203 4.5 - 203 4.5 - 229 4.5 -

SUV Sm Pickup

Two Seater

Lrg Pickup / Van

Compact Midsize / Minivan Fullsize

Attribute Unit Mean Std. Dev Min Max

Income 10,000 2006$ 10.33 8.32 1.75 45.00

Children - 0.27 0.45 0 1

Rural - 0.07 0.26 0 1

Individuals 6,563

Obs. 10,423
31 

Table 4: Summary of Vehicle Characteristic Data

Table 5: Estimation Results for Fuel Consumption in Technology and Design Model

Notes: Standard errors are clustered by vehicle curb weight 

Attribute Unit Mean Std. Dev Min Max

MSRP 1,000 2006$ 32.67 16.73 11.93 97.49

Fuel Economy mpg 21.46 5.14 10.98 56.55

Horsepower hp 241 78 65 520

Curb weight 1,000 lb 3.87 0.85 1.98 6.40

Footprint 1,000 in 2 13.92 2.00 9.52 20.05

Make Grps. 38

Obs. 473

Mean Std. Dev Mean Std. Dev Mean Std. Dev Mean Std. Dev

κ0 20.8484 0.9414 10.7920 0.2158 11.5531 0.5674 10.8515 0.4034

κ1 89.681 31.159 69.524 5.398 733.706 55.371 452.552 23.785

κ2 -0.205 0.025 -0.260 0.013 -0.083 0.002 -0.079 0.004

κ3 0.0016 ** 0.0005 0.0013 *** 0.0003 0.0002 0.0000 0.0002 0.0000

κ4 2.9159 0.3667 12.9897 0.3047 8.6680 0.1119 8.3583 0.1208

κ5 0.0280 * 0.0476 -0.5593 0.0456 -0.2954 0.0223 -0.2539 0.0079

R2 0.443 0.941 0.896 0.976

Obs. 4473 5117 3542 3542

Mean Std. Dev Mean Std. Dev Mean Std. Dev

κ0 14.0535 0.4985 10.5032 0.4049 10.5185 0.4083

κ1 1329.854 115.804 13387.530 1836.191 2979.096 411.241

κ2 -0.154 0.008 -0.093 0.007 -0.089 0.006

κ3 0.0006 0.0001 0.0003 *** 0.0001 0.0003 *** 0.0001

κ4 9.0653 0.1069 8.9932 0.3207 8.6604 0.2813

κ5 -0.2934 0.0148 -0.2224 0.0295 -0.2225 0.0299

R2 0.965 0.952 0.952

Obs. 16863 9450 9450

*p>0.1, **p<0.1, ***p<0.05, all others p<0.01

Two seater Compact Midsize / Minivan Fullsize

SUVs Small Pickup Large Pickup / Van
32 

Table 6: Estimation Results for Cost of Technology and Powertrain Design

Notes: Standard errors are clustered by vehicle curb weight 

Table 7: First Stage Instrumental Variable Results 

*p>0.1, **p<0.05, all others p<0.001 

Notes:The variables din and dout are the distances of vehicle dimensions (length x width 

x height) to the average dimensions of same and different manufacturers, respectively; 

dsqin and dsqout are these values squared. The remaining variables represent powertrain 

architectures— turbo (turbocharged), hybrid, diesel—and the type of drive—all wheel or 

four wheel drive, awd/4wd. 

param std. err. param std. err. param std. err. param std. err.

σ0 0.3669 * 0.0865 0.7800 0.0091 0.5540 0.0355 0.4029 0.0450

σ1 10.669 * 2.231 1.972 0.163 24.384 1.384 24.053 2.727

σ2 0.018 0.000 0.002 0.000 0.005 0.000 0.006 0.000

σ3 0.2579 0.0132 0.2250 0.0051 0.1963 0.0103 0.2339 0.0052

σ4 ‐0.0082 0.0013 -0.0123 0.0005 -0.0071 0.0012 -0.0069 0.0004

R2 0.890 0.898 0.898 0.931

Obs. 4473 5117 3542 3542

param std. err. param std. err. param std. err.

σ0 0.0200** 0.1337 0.3025 * 0.0607 0.3025 * 0.0607

σ1 92.397 16.477 719.579 * 162.643 160.560 * 36.291

σ2 0.004 0.000 0.007 0.000 0.007 0.000

σ3 0.3470 0.0143 0.2621 0.0137 0.2538 0.0117

σ4 ‐0.0108 0.0016 ‐0.0055 * 0.0014 ‐0.0055 * 0.0014

R2 0.887 0.831 0.831

Obs. 16863 9450 9450

*p<0.1, **p<0.05, all others p<0.01

Two seater Compact Midsize / Minivan Fullsize

SUVs Small Pickup Large Pickup / Van

param st. error param st. error param st. error

din 0.0144 (0.0007) 0.0137** -0.0108 (0.0037) (0.0069) 

dout -0.2306 * (0.2360) -0.3165 * (0.2350) -0.6388 0.1231

dsqin 0.0161 * 0.0144 (0.0159) * -0.0011 (0.0158) * (0.0085)

dsqout -1.3409 (0.2767) -1.2976 (0.2740) 0.3644** (0.1506)

turbo -0.2247 * -0.4498 (1.8032) * -0.8157 (1.7849) * (0.9615)

hybrid 16.9815 (3.0274) 16.7553 (2.9951) -12.3003 (1.5621) 

diesel 11.1606 (2.9461) 10.8725 (2.9153) -11.1248 (1.5019) 

awd/4wd 0.8457 * 0.9460 (1.1625) * 3.5495 (0.5951) (1.1491) 

N 473 473 473

R2

0.9645 0.9653 0.9946

Price Fuel Costs Inverse 0-60 acc time
33 

Table 8: Second Stage IV Results 

Notes: The means are the MLEs of 

and , and the standard deviations are 

the MLEs of μ in Eq. 10 

Table 9: Price elasticities for a subset of 2006 vehicles

Notes: The variable MSRP is the manufacturer-suggested 

retail price and dq/dp is the price-elasticity of demand 

price/inc 0.4422

cpm 0.0695

1/acc 0.0177

ftp 10.8191

ftp 2 ‐2.3541

two seater ‐0.1083

minivan ‐0.6661

suv 0.0834

van ‐2.2853

pickup ‐0.8796

minivan‐child 0.9746

suv‐child 0.3445

pickup‐rural 1.1957

price/inc 0.0059

cpm 0.0009 **

1/acc 0.0001 *

ftp 0.0189

ftp 2 0.0332

* p>0.1, ** p<0.05, all others p<0.001

standard deviation

mean

Make Model MSRP dq/dp

Jaguar X-Type 32,330 ‐0.009

Ford F-150 24,405 ‐0.012

General Motors Silverado 1500 23,590 ‐0.038

Chrysler Liberty 21,290 ‐0.084

Ford Escape 23,390 ‐0.181

Toyota Sienna 23,775 ‐0.456

Volkswagen Passat 23,900 ‐1.162

Honda CR-V 20,395 ‐2.910

General Motors Cobalt 12,400 ‐4.313

Nissan Sentra 14,000 ‐11.570

Toyota Corolla 14,905 ‐25.766

Honda Civic Sedan 14,760 ‐43.106
34 

Table 10: Lagrange Multiplier Estimation 

Standard errors are in parentheses. 

Table 11: Counterfactual simulations for MY2012 CAFE, Specification 1 

Passenger Cars Light Trucks

Chrysler 20.71 13.10

 (2.06) (1.58)

Ford 13.57 5.46*

 (3.05) (1.76)

18.18 22.76

 (1.37) (1.39)

*p=0.002. All others, p<0.001

General 

Motors

Big 3 Asian 4 Other Asian Euro 

GM,Ford, Toyota,Honda, Mazda,Kia, MercedesTotal Chrysler Nissan,Hyundai Subaru Benz,BMW All Others Outside 

Consumer Surplus 116.37 41.36 26.54 19.93 -5.06 37.57 -3.95

(billions)

due to

prices 100.92 -0.32 40.56 16.31 -0.66 45.03

attributes 19.41 41.67 -14.02 3.62 -4.40 -7.46

Big 3 Asian 4 Other Asian Euro 

GM,Ford, Toyota,Honda, Mazda,Kia, MercedesTotal Chrysler Nissan,Hyundai Subaru Benz,BMW All Others

Profits -25.5 -5.3 -9.0 -2.5 -2.9 -5.7

(billions)

Big 3 Asian 4 Other Asian Euro 

GM,Ford, Toyota,Honda, Mazda,Kia, MercedesTotal Chrysler Nissan,Hyundai Subaru Benz,BMW All Others Outside 

Fuel Consumption -2,490 -3,342 1,713 -746 -1,081 2,265 -1,300

(million gal.)

due to

tech features -531 -472 15 -94 0 20

acc tradeoffs 263 200 -17 56 5 19

demand shifts from:

price changes -1,113 -5,344 2,508 -716 -776 3,216

attribute changes 43 1,868 -587 -82 -439 -718

rebound effect 143 400 -205 89 129 -271

Producer Welfare

Externalities

(1) Technology and Attribute Tradeoffs

Consumer Welfare

Δ

Δ

Δ
35 

Table 11 Continued: Counterfactual simulations for MY2012 CAFE, Specification 2 

Notes: This table reports demonstrational results of welfare changes due to replacing the unreformed CAFE standards with 

the MY2012 CAFE standards. Fuel consumption figures assume consumers drive 10,000 miles per year and vehicles last 

for 10 years. The rebound effect, caused by increased miles driven in higher fuel economy vehicles, is taken from Small 

and Van Dender (2007) at 10.3%. The change in fuel consumption due to changes in how many consumers choose the 

outside good assumes the outside good is a used vehicle with a fuel economy at the average of on-the-road vehicles, 17.1 

mpg. 

Table 12: Vehicle price-elasticities by changes in prices 

Big 3 Asian 4 Other Asian Euro 

GM,Ford, Toyota,Honda, Mazda,Kia, MercedesTotal Chrysler Nissan,Hyundai Subaru Benz,BMW All Others Outside 

Consumer Surplus 58.09 81.48 -12.39 -4.73 -2.94 -1.98 -1.35

(billions)

due to

price changes 21.34 2.58 8.95 3.81 3.78 2.23

attribute changes 38.10 78.90 -21.34 -8.54 -6.71 -4.21

Big 3 Asian 4 Other Asian Euro 

GM,Ford, Toyota,Honda, Mazda,Kia, MercedesTotal Chrysler Nissan,Hyund Subaru Benz,BMW All Others

Profits 8.77 14.72 -3.01 -1.33 -0.75 -0.86

(billions)

Big 3 Asian 4 Other Asian Euro 

GM,Ford, Toyota,Honda, Mazda,Kia, MercedesTotal Chrysler Nissan,Hyundai Subaru Benz,BMW All Others Outside 

Fuel Consumption -1,839 -808 -373 -214 -257 -187 0

(million gal.)

due to

tech features -570 -569 0 0 0 0

acc tradeoffs - - ----

demand shifts from:

price changes -1,003 -3,297 659 395 784 457

attribute changes -487 2,962 -1,076 -635 -1,071 -667

rebound effect 220 97 45 26 31 22

 Consumer Welfare

Producer Welfare

Externalities

(2) Technology Only

Δ

Δ

Δ

mean s t. dev. min max obs.

-0.75 3.30 -6.0E-07 ‐43.11 256

mean s t. dev. min max obs.

-5.30 35.46 -1.6E-05 ‐333.96 193

Vehicles with lowered prices

Vehicles with raised prices
36 

9 References 

Anderson, S. and J. Sallee. 2009. Using loopholes to reveal the marginal cost of regulation: the case of fueleconomy standards. Michigan State University. Working paper. 

Beresteanu, A. and S. Li. 2008. Gasoline prices, government support, and the demand for hybrid vehicles in 

the U.S. Duke University. Working paper. 

Berry, S. 1994. Estimating discrete-choice models of product differentiation. RAND Journal of Economics

25(2): 242-262. 

Braess, H.-H. and U. Seiffert, ed. 2005 Handbook of automotive engineering. Warrendale, PA: SAE 

International. 

Bresnahan,T. and P. Reiss.1989.Dealer and manufacturer margins.Rand Journal of Economics.16(2): 253-268. 

Fan, Y. 2008. Market structure and product quality in the U.S. daily newspaper industry. Yale University. 

Working paper. 

Frischknecht, B. and P. Papalambros. 2008. A Pareto Approach to Aligning Public and Private Objectives 

in Vehicle Design. ASME IDETC, DETC2008-49143. 

Frischknecht, B., K. Whitefoot and P. Papalambros. 2009. Methods for Evaluating Suitability of 

Econometric Demand Models in Design for Market Systems. ASME IDETC. DETC2009-87165. 

Goldberg, P. K. 1998. The effects of the corporate average fuel efficiency standards in the US. The Journal 

of Industrial Economics 46(1): 1–33. 

Gramlich, J. 2008. Gas Prices and Endogenous Product Selection in the U.S. Automobile Industry. Yale 

University. Job Market Paper. 

Greene, D. and M. Wegener. 1997. Sustainable transport. Journal of Transport Geography 5(3): 177-190.

Jacobsen, M. 2010. Evaluating U.S. Fuel Economy Standards In a Model with Producer Household 

Heterogeneity. Stanford University. Job Market Paper. 

Klier, T. and J. Linn. 2008. New Vehicle Characteristics and the Cost of the Corporate Average Fuel 

Economy Standard. Federal Reserve Bank of Chicago. Working Paper No. 2008-13. 

Mayer, B. 2008. Fuel saving under development. Automotive News Europe. International Supplier Fair, Oct. 

27, 2008. Crain Communications GmbH. 

Michalek, J., Papalambros, P. Y., and Skerlos, S. 2004. A Study of Fuel Efficiency and Emission Policy 

Impact on Optimal Vehicle Design Decisions. Journal of Mechanical Design. 126(6): 1062-1070. 

NHTSA. 2008. Preliminary Regulatory Impact Analysis: Corporate Average Fuel Economy for MY 2011-

2015 Passenger Cars and Light Trucks. U.S. Department of Transportation. 

Small, K. and K. Van Dender. 2007. Fuel Efficiency and Motor Vehicle Travel: The Declining Rebound 

Effect. Energy Journal. 28(1): 25-51. 

Sörenson, D. 2006. The automotive development process:A real options analysis.Frankfurt: Deutscher 

Universitäts-Verlag. 

Sweeting, A. 2007. Dynamic product repositioning in differentiated product markets: The case of format 

switching in the commercial radio industry. NBER Working Paper #13522 

Train, K. and C. Winston. 2007. Vehicle choice behavior and the declining market share of U.S. 

automakers. International Economics Review. 48(4): 1469-1496. 

U.S. Environmental Protection Agency, 2004, “EPA’s Fuel Economy and Emissions Programs” 

http://www.epa.gov/fueleconomy/420f04053.htm. 

Weber, J. 2009. Automotive development processes: Processes for successful customer oriented vehicle 

development. New York: Springer. 
37 

Appendix A Details about the technology combinations and the tech variable 

The specifications for Eq. 3 and 4 were chosen after examining the relationship between the 

discrete technology feature combinations with cost and fuel economy. For example, Figure B1 

below plots production cost against the tech variable assigned to each cost-effective combination 

of technology features conditional on 0-60 mph acceleration time. Each point on the plot 

represents a potential vehicle design with an engine size, final drive ratio, and set of discrete 

technology features. The gaps between vehicle designs achieving the same acceleration time is 

an artifact of the ranges of input variables used in the AVL Cruise vehicle simulations. We 

would expect that as the intervals of these input variables approached zero, the gaps would 

disappear. 

Figure B1 is generated for a specific vehicle segment (an SUV) and a specific curb weight 

(3,200 lb). Similar trends were found for other segments and other curb weights. The figure 

indicates that conditional on vehicle segment, curb weight, and 0-60 acceleration time, moving 

“up the line” of combinations of technology features increases cost linearly. It also indicates that 

the incremental change in cost of changing technology features is roughly constant across the 

various levels of acceleration performance. This structure is preserved in the specification of Eq. 

4 where cost is linear in technology conditional on vehicle segment, curb weight, and 

acceleration time. 

Figure B1: Relationship of ordered technology feature combinations to production cost 

conditional on 0-60 mph acceleration time 

Figure B2 below plots fuel consumption against combinations of technology features for the 

same vehicle segment (SUV) and curb weight (3,200 lb). This figure indicates that conditional 

on vehicle segment, curb weight, and 0-60 acceleration time, the set of combinations of 

technology features linearly decrease fuel consumption. However, unlike cost, the incremental 

change in cost of changing technology features varies across the various levels of 0-60 mph 

y = 0.0074x + 1.5654

y = 0.007x + 1.3708

y = 0.0074x + 1.2074

y = 0.0068x + 1.1381 y = 0.0074x + 1.0151

y = 0.0063x + 1.0123

0

0.5

1

1.5

2

2.5

0 20 40 60 80

Production cost (thousand dollars)

tech variable

4.51 s

4.93 s

5.59 s

8.91 s

10.89

17.53
38 

acceleration time. Figure B2 shows that the incremental decrease in fuel consumption from 

moving to a higher ordered combination of technology features becomes larger as acceleration 

time becomes faster. Also, the rate of this change increases as acceleration time gets faster, with 

the slopes in Figure B2 roughly constant when acceleration time is relatively large but more 

negative for relatively faster acceleration times. Similar trends were found for other segments 

and other curbweights. These properties are represented in the specification of Eq. 3 by including 

a linear tech term as well as an interaction term multiplying tech by acc squared. 

Figure B2: Relationship of ordered technology feature combinations to fuel consumption 

conditional on 0-60 mph acceleration time 

y = ‐0.1128x + 82.052

y = ‐0.1242x + 60.503

y = ‐0.0675x + 50.551 y = ‐0.0642x + 48.081

y = ‐0.0594x + 45.547

y = ‐0.0529x + 39.569

y = ‐0.0552x + 36.564

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80

Fuel Consumption (gal/1,000 mi)

tech variable

3.95 s

4.49 s

5.10 s

5.46 s

6.04 s

10.31 s

13.61 s
39 

Appendix B Endogenous Attribute Model 

We compare the results of our approximated endogenous attribute model, fit using 

simulation data, to market vehicle data as a validation test. Figure A1 and A2 show this 

comparison for the compact and SUV segments, respectively. Similar comparisons were done for 

all other segments. The midsize, fullsize, small pickup, and large pickup/van segment 

comparisons are comparable to those shown in the figures. The two-seater model, however, does 

not predict the market data as well as the other segments, but because this segment represents 

less than 1% of sales, this is unlikely to affect our counterfactual results. 

Figure A1: Comparison of compact-segment model to MY2006 compact vehicle data 

Figure A2: Comparison of SUV-segment model to MY2006 SUV data

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20

Fuel Consumption (gal/1000 mi)

0-60 mph acceleration (s)

Market data Model predictions

Diesels Hybrid

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15

Fuel Consumption (gal/1000 mi)

0-60 mph acceleration (s)

Market data Model predictions

Hybrids
40 

Appendix C Derivation of Lagrange Multiplier Estimation Model 

The first-order conditions of the constrained firm’s profit maximization are: 

૙ ൌ ሻࢀ்࢘ߣ ൅ ࡯࢘஼ߣ൅ࢉെ࢖൯ሺ܂ܙܘ׏൫ ൅ ሻ࢖ሺࢗ

where ܂ܙܘ׏ is the gradient of ࢀࢗ with an i x jth entry of ߲ݍ௝⁄߲݌௜. Therefore, in order to solve for 

the marginal costs at equilibrium, we must first solve for the Lagrange multipliers, ߣ ஼and ߣ். 

Following Bresnahan and Reiss (1989), the dealer’s problem is defined by 

max ΠD

೑ॅא௝׊ ೕ௤

௝ݍ෍ൌ

೑ॅא௝

൫݌௝ሺݍሻ െ ݓ ௝െ ݏ௝൯

where ݓ ௝and ݏ ௝are the wholesale price and marginal selling costs of vehicle j, respectively, and 

݌ ௝depends on all ݍ‘௝s. It is assumed that the dealer has constant marginal selling costs for all 

products. Note that I am slightly changing the notation from Bresnahan and Reiss to conform to 

the notation used above. 

The manufacturer’s problem is defined by: 

max ΠM

೑ॅא௝׊ ೕ௤

௝ݍ෍ൌ

೑ॅא௝

൫ݓ௝ሺݍሻ െ ܿ௝൯

subject to 

௝ݍ ෍

಴೑ॅא௝

ቆ1 െ ݉݌݃஺஼ிா,஼

௝݃݌݉

ቇ൒0

௝ݍ ෍

೅೑ॅא௝

ቆ1 െ ݉݌݃஺஼ிா,்

௝݃݌݉

ቇ ൒ 0.

The first order conditions of the dealer’s problem are: 

௜ݍ෍൅ ௝݌ ൌ ሻݍሺ௝ܴܯ

ሻݍሺ௜݌߲

೑ॅא௜ ௝ݍ߲

ሻ1ܣሺ௝ ݏ ൅ ௝ݓ ൌ

where ܯܴ௝ሺݍሻ is the retail marginal revenue of the jth product. Substituting the dealer’s solution 

into the manufacturer’s first order condition gives: 
41 

௜ݍ෍൅ ௝ܿ െ ሻݍሺ௝ݓ

ሻݍሺ௜ݓ߲

೑ॅא௜ ௝ݍ߲

൅ ߣ ஼ቆ1 െ ݉݌݃஺஼ிா,஼

௝݃݌݉

ቇ ൅ߣ் ቆ1 െ ݉݌݃஺஼ிா,்

௝݃݌݉

ቇൌ0

Substituting in ݓ௝ሺݍሻ ൌ ܯܴ௝ሺݍሻ െ ݏ ௝from Eq. A1, noting that CAFE does not affect the 

dealer’s decisions directly, the first order conditions become: 

௜ݍ ∑ ൅ ௝ݏ െ ሻݍሺ௝ܴܯ ൌ ሻݍሺ௝ܴܯܯ

డெோ೔ሺ௤ሻ

డ௤ೕ ௜אॅ ೑ൌ ܿ௝ െ ߣ ஼൬1 െ ௠௣௚಴ಲಷಶ,಴

௠௣௚ೕ

൰ െߣ் ൬1 െ ௠௣௚಴ಲಷಶ,೅

௠௣௚ೕ

൰

Using this relationship, the ratio of dealer to manufacturer markups is: 

൯௝ݏ ൅ ௝ݓ൫ െ௝ ݌

௝ܿ െ௝ ݓ

ൌ ݌ ௝െ ܯܴ௝ሺݍሻ

ݓ ௝െ ܯܯܴ௝ሺݍሻെߣ ஼൬1 െ ݉݌݃஺஼ிா,஼

݉݌݃ ௝൰ െߣ் ൬1 െ ݉݌݃஺஼ிா,்

൰௝ ݃݌݉

Substituting in for ܯܴ௝ሺݍሻ and ܯܯܴ௝ሺݍሻ, this ratio can be written as: 

௜ݍ ∑

ሻ௜ݍሺ௜݌߲

೑ॅא௜ ௝ݍ߲

௜ݍ ∑ 2

ሻݍሺ௜݌߲

௞ݍ௜ݍ ∑ ∑ ൅ ೑ॅא௜ ௝ݍ߲

߲ଶ݌௜ሺݍሻ

஼,ிா஼஺݃݌݉ െ 1൬஼ ߣെ೑ ॅא௞ ೑ॅא௜ ௞ݍ߲௝ݍ߲

݉݌݃ ௝൰ െߣ் ൬1 െ ݉݌݃஺஼ிா,்

൰௝ ݃݌݉

 ሺܣ2ሻ

To simplify this equation, let: 

ൌ௝ ߟ

௞ݍ௜ݍ ∑ ∑

߲ଶ݌௜ሺݍሻ

೑ॅא௞ ೑ॅא௜ ௞ݍ߲௝ݍ߲

௜ݍ ∑

ሻݍሺ௜݌߲

೑ॅא௜ ௝ݍ߲

which, following Bresnahan and Reiss, is constant across all products, and therefore we will drop 

the subscript. Substituting in to Eq. A2 gives: 

൯௝ݏ ൅ ௝ݓ൫ െ௝ ݌

௝ܿ െ௝ ݓ

ൌ 1

െߟ൅2

ߣ ஼൬1 െ ݉݌݃஺஼ிா,஼

݉݌݃ ௝൰ ൅ߣ் ൬1 െ ݉݌݃஺஼ிா,்

൰௝ ݃݌݉

௜ݍ ∑

ሻݍሺ௜݌߲

೑ॅא௜ ௝ݍ߲

 ሺܣ3ሻ

Note that because the additional term representing the impact of CAFE is not constant across 

products, the ratio of dealer to manufacturer markups will not be constant as in Jacobsen (2010). 

However, I will propose another method of estimating ߣ ஼and ߣ் using dealer markups. 

Substituting in ܾ௝ ൌ ݌ ௝െ ൫ݓ ൅ ௝ݏ௝൯ into Eq. A3 and rearranging gives: 
42 

൮2൅ߟെ

ߣ ஼൬1 െ ݉݌݃஺஼ிா,஼

݉݌݃ ௝൰ ൅ߣ் ൬1 െ ݉݌݃஺஼ிா,்

൰௝ ݃݌݉

௜ݍ ∑

ሻݍሺ௜݌߲

೑ॅא௜ ௝ݍ߲

൲ ܾ௝ ൌ ݓ ௝െ ܿ௝

Rewriting this equation in terms of the entire markup ݌ ௝െ ܿ௝: 

൮2൅ߟെ

ߣ ஼൬1 െ ݉݌݃஺஼ிா,஼

݉݌݃ ௝൰ ൅ߣ் ൬1 െ ݉݌݃஺஼ிா,்

൰௝ ݃݌݉

௜ݍ ∑

ሻݍሺ௜݌߲

೑ॅא௜ ௝ݍ߲

൲ ܾ௝ ൌ ݌ ௝െ ܿ௝ െ ܾ௝ െ ݏ

Or 

൮3൅ߟെ

ߣ ஼൬1 െ ݉݌݃஺஼ிா,஼

݉݌݃ ௝൰ ൅ߣ் ൬1 െ ݉݌݃஺஼ிா,்

൰௝ ݃݌݉

௜ݍ ∑

ሻݍሺ௜݌߲

೑ॅא௜ ௝ݍ߲

൲ ܾ௝ ൌ ݌ ௝െ ܿ௝ െ ݏ

In vector formation, this relationship can be represented as: 

൯܂ܙܘ׏െ൫ ൌ ࢈ ሻቁ૚ࢀ்࢘ߣ൅૚࡯࢘஼ߣሺ૚ିࡲ െ ߟ ൅ 3ቀ

ି૚

ݏ െ ࢀ்࢘ߣ െ ࡯࢘஼ߣ െ ሻ࢖ሺࢗ

where b is a vector of markups for all products, ࡲ is a diagonal matrix with the j x jth entry of 

௜ݍ ∑

డ௣೔ሺ௤ሻ

డ௤ೕ ௜אॅ ೑and 1 is a row vector of ones. Distributing ࢈ to separate ߣ ஼and ߣ் gives: 

൯܂ܙܘ׏െ൫ ൌ ࢀ்࢘ߣ ൅ ࡯࢘஼ߣ ൅ ࢈૚ࢀ࢘૚ିࡲ்ߣ െ ࢈૚࡯࢘૚ିࡲ஼ߣെ࢈ሻߟ൅3ሺ

ି૚

ݏ െ ሻ࢖ሺࢗ

Finally, we rearrange this equation to extract the Lagrange multipliers: 

൯܂ܙܘ׏െ൫ ൌ ሻࢀ࢘ െ ࢈૚ࢀ࢘૚ିࡲሺ்ߣ െ ሻ࡯࢘ െ ࢈૚࡯࢘૚ିࡲሺ஼ߣെ࢈ሻߟ൅3ሺ

ି૚

ݏ െ ሻ࢖ሺࢗ

Given data on dealer markups and an estimation of demand, we could estimate ߣ ஼and ߣ் from 

the following: 

൫܂ܙܘ׏൯

ି૚

ࣕ൅ݏെ࢈̂ߟ ൅ ሻࢀ࢘ െ ࢈૚ࢀ࢘૚ିࡲሺ்ߣ ൅ ሻ࡯࢘ െ ࢈૚࡯࢘૚ିࡲሺ஼ߣ ൌ ሻ࢖ሺࢗ

where ߟ̂ൌ െሺ3൅ߟሻ. 
43 

Appendix D Counterfactual baseline 

Because our endogenous attribute model is derived from engineering simulations and cost 

data, observed attributes are not necessarily restricted to be in equilibrium. We therefore perform 

simulations of the CAFE regulations that were applied to the MY2006 automotive market. The 

simulation results are in Nash equilibrium with respect to firm decisions on 0-60 acceleration 

time, and technology implementation—which implicitly determines fuel economy—as well as 

price for each of their vehicles. All other counterfactual results are measured from this baseline. 

Our results shown in Table C1 indicate that fuel economy and 0-60 acceleration time for 

MY2006 vehicles are very close to equilibrium. 

Due to a lack of data on adoption of each technology feature, we cannot compare the 

results of adopted technology features to those in the MY2006 vehicles. But, the simulations 

results appear to match general information about technology. For instance, very few vehicles in 

MY2006 included cylinder deactivation, which is supported by the simulations. 

Table C1: Comparison of observed attributes and baseline simulation

Avg mpg Avg. acc Avg. tech

Observed 21.46 7.11 ‐

Baseline 

Simulation 21.91 7.42 0.72