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 a nd oil consumption, Congress recently amended the Corporate Average Fuel Economy regulati on to encourage improvements in the fuel efficiency of new vehicles. Automotive firms have multiple strategies available to them to respond to this policy interventi on, and the responses they choos e have potentially significant welfare implications. This paper presents one of the first analyses of the reformed CAFE, explicitly accounting for medium-term complia nce strategies that include both technology implementation and tradeoffs between vehicle a ttributes. We use physics- based simulations to identify engineering tradeoffs between fuel econo my and other vehicle attr ibutes independent of unobservable vehicle attributes. Final estimation of the demand side is still pending, but we present preliminary results using a demonstratio nal 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 potenti al reductions in fuel consumption from these technologies are realized, with the remainder applied to improving accel eration performance. Results also suggest that ignoring tradeoffs betw een vehicle attributes significantly overestimates the social surplus cost of the regulation. The methods presented are generalizable to many other consumer product industries with energy-e fficiency 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 bei ng promoted in many industries. For example, proposed federal climate change legislation include s standards for lighting efficiency, an energyefficiency labeling program for buildings, and su bsidies for retailers a nd distributors of highefficiency household appliances and consumer el ectronics. 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—a nd implications of—the recently reformed CAFE standards. Our approach explic itly accounts for medium-term de sign changes that firms can use to comply with the CAFE regulation by constr ucting an endogenous pr oduct 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 mani fest 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 orde r to improve fuel efficiency. Whereas some earlier studies emphasized the more immediate response (Goldber g, 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 de sign (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, a nd often decrease costs. Our model of endogenous attribute, which is based on engineering vehicle simula tions, is the first to explicitly model both ty pes of design changes. Considera tion of both types of product design changes has potentially significant roles in response to the reform ed CAFE standards, as well as other energy-efficiency policies. This paper is germane to literature on endogenous product attr ibutes (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 limita tions and tradeoffs. We explicitly represent these constraints and tradeoffs using methods fr om engineering literatur e (e.g., Michalek et al. 2005; Frischknecht and Papalambros 2008; Shiau et al. 2009). Deriving an endogenous design model from a series of engin eering simulations confers two a dvantages: 1) combinations of3 product attributes that are not observed in curren t data but are possible, and potentially optimal under the counterfactual policy instruments we are interest ed, can be captured, and 2) engineering tradeoffs between pr oduct attributes can be identifi ed independently of unobserved product attributes. This latter a dvantage is important for industries such as automotive where unobserved attributes, such as extra luxury accessor ies, 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 unobser ved attributes. We overcome this endogeneity problem by exploiti ng the structure of the product development process, using semi-fixed vehicle attributes as instruments for the endog enous product attributes and prices. Our key identifying assumption is that vehicle dimensions are chosen earlier in the development process than detailed design variable s in the powertrain, wh ich affect both fuel efficiency and acceleration performance. We pres ent evidence in support of this assumption in Section 2.2. Our analysis begins with a model of th e medium-term automotive design process, incorporating the ability of firm s to implement technology features and tradeoff fuel efficiency with other attributes of vehicl e performance. This model is then incorporated into a partial equilibrium, static oligopoly model in which fi rms choose vehicle attribut es and prices. Similar to Jacobsen (2010) and Klier a nd Linn (2008), we distinguish be tween firms constrained by the regulation, firms that violate the regulation and pay a fine, and thos e that operate above the fuel economy standard. A mixed-logit model of consum er demand is estimated using disaggregate consumer data. Once the parameters of the model have b een estimated, we can conduct counterfactual simulations of industry response to the reformed CAFE standards. We numerically solve for vehicle attributes and pri ces in equilibrium, examin ing the changes in technology implementation and vehicle attributes induced bythe 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 simulatio ns using two model specifications. The first specification includes both technology implementati on and compromises between fuel efficiency4 and acceleration performance, while the second includes only technology implementation and does not allow for firms to tradeoff fuel efficien cy with other vehicle attributes. This latter specification is particularly relevant to curre nt impact assessments of the reformed CAFE regulation conducted by the National Highway Tr affic and Safety Admi nistration (NHTSA), which account for efficiency-increasing technolog ies but ignore any tradeoffs between fuel efficiency and other vehicle attributes. Preliminary results highlight the potentia lly complex relationship between technology implementation and improvements in fuel econom y that cannot be captured by models that ignore the potential to improve fuel efficien cy by trading off performance along another dimension. Specifically, our demonstrational resu lts suggest that while the reformed CAFE regulation may increase adoption of technology features, the benef it of these features is not always applied to improve fuel efficiency. In stead, firms can re-optimize the vehicle with additional technology features to improve othe r 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 regulat ion and the vehicle developmen t 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. C onclusions are described in Section 8.



### 2 

### Overview of Industry

2.1 Fuel Economy Regulation
Since 1975, the CAFE policy has influenced automotive firms’ d ecisions by setting a standard for the average fuel economy of a manuf acturer’s fleet. The principle motivation for creating the CAFE regulation was to reduce dependence for oil cons umption in the wake of the oil embargo. Since that time, interest in mainta ining and strengthening the regulation has been driven by concerns about global climat e 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 manu facturer’s fleet of vehicles in a particular5 class (i.e., passenger cars or light trucks). The CAFE standard acts as a floor for this average, defining the CAFE requirement as: ∑ ݍ ௝ ݌ሺ ௝ ሻ ॅא௝ ೎,೑ ∑ ݍ ௝ ݌ሺ ௝ ݃݌݉ ሻ ௝ ⁄ ॅא௝ ೎,೑ ൒ ݐݏܽ݊݀ ௖ ሺ1ሻ

where q j and mpg j are the number of sales and fuel economy vehicle j, and stand c is the fuel economy standard for vehicle j’s clas s. If a firm violates this sta ndard, they must pay a fine for each vehicle produced of $5.50 per 0.1 mpg below th e 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 a llowable deviation, certain Asian manufacturers (e.g., Toyota and Honda) have consistently exceede d 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 si gnificantly lower standard for light trucks than for passenger ca rs. This distinction allowed minivans and SUVs, which composed a very small fraction of sales at the creation of the polic y, to meet the lower light-truck standard despite thei r expanding role as a personal ve hicle, causing what some called the “SUV loophole”. In 2007, Congress passed th e Energy Independence and Security Act (EISA), phasing out this disparity by setting a target standard fo r 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 th at the CAFE standard be se t 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 regulat ion to encourage production of smaller vehicles was unsafe, and therefore CAFE should be struct ured 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, T j , for each vehicle determined from the vehicle’s footprint, where vehicles with larger footprints have lower standards. Unlike the unreformed CAFE standa rds, the reformed standards vary across manufacturers. Specifically, the fuel economy standard for firm f and vehicle class c is:

ܽ݊݀ݐݏ ௖ ,௙ ൌ ∑ ݍ ௝ ݌ሺ ௝ ሻ ॅא௝ ೎,೑ ∑ ݍ ௝ ݌ሺ ௝ ܶ ሻ ௝ ⁄ ॅא௝ ೎,೑ ሺ2ሻ6 This change has a number of important implicat ions. With the unreforme d CAFE, sales of any vehicle that had a higher fuel economy than its class standard (27.5 m pg for passenger cars and 21.6 mpg for light trucks in MY2006) helped a firm comply with the regu lation, 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 ta rget will help a firm comply with the regulation. Because the targets are lower fo r 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 re gulations 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 th e 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 trad ing was set at 1 mpg through 2013 and 1.5 mpg through 2017.



### 2.2 Vehicle Development Process
The structure of the vehicle development ha s implications for unde rstanding how firms respond to the CAFE regulation. The automotive de velopment 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 con cept development, followed by a system-level design that defines the geometric layout of the vehicle, follow ed by a detailed design of all subsystems (Sörenson 2006; Weber 2009). For a newly designed vehicle model, the de velopment process begins with a target catalog specifying the vehicle segment (e.g., comp act), powertrain archite cture (e.g., hybrid), variations (e.g., four door sedan), major dimens ions, 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 th e new vehicle’s major target dimensions, then definition of remaining interior dimensions, fo llowed by conception of the engine compartment and underbody with integration of all planned drivetrain c onfigurations (Braess 2005).7 For a redesigned model, the development pro cess 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 fo r subsystems, such as how many drivetrain configurations or engine options will be available. Similar to the newly designed vehicle, however, early decisions on transm ission types, model variations, and other major properties of the vehicle will inform updated dimensions fo r the redesigned vehicle (Braess 2005; Weber 2009). These specifications for changes to the vehicle design will influence changes to the engineering design of vehicle s ubsystems. These properties of the development processes for newly designed and redesigned vehi cles causes a structure where ce rtain 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 pr oceeds in sequential, clearly defined stages. In fact, iterat ion 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 vehi cle segment, powertrain architecture (e.g., conventional gasoline, hybrid, diesel), and ke y 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 C 1 ) separately from the longer-term design process. In our model, vehicle segment, powertrain architecture, and vehicle dimensions, which are determined in the ear lier 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 vari ables (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 attr ibutes 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 automoti ve 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 sel ection in the design of technical products such as automobiles requires accurate represen tation 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 vehicl e design choices and tradeoffs that are most relevant to our analysis. We then introduce a de tailed vehicle simulation model that is used by automotive manufacturers to aid in vehicle deve lopment 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 cont rasts with the econometric approaches that are more often used in the economics literature.9 

### 3.1 Medium-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 ve hicle, key internal and external dimensions, and the powertrain architecture (e.g., conventio nal gasoline, hybrid, di esel). The automotive manufacturer can still adjust the fuel efficiency and acceleration performanc e 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 im prove fuel efficiency will cause some loss in acceleration performance. Another means of improving fuel efficiency at this stage in the de sign process involves incorporating various extra “tec hnology features” to the vehicl e design. Examples include high efficiency alternators, low re sistance tires, and improved aer odynamic drag of the vehicle body. Adding one or more of these features increase s the cost of vehicle production. Depending on the specific technology features chosen, acceleration pe rformance may increase, or decrease, or not be affected at all. For example, cylinder deactiv ation 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. Re ducing 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 accelera tion performance. Note that these technology features only affect demand through their influence on fuel ef ficiency and acceleration performance; they do not have intrinsic value to the consumer. Figure 2 illustrates a stylized representa tion of the relationships between vehicle attributes of interest and various technology features that can be in corporated 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 th e time it takes to accelerate from 0 to 60 miles per hour, referred to as the 0-60 ac celeration time. The concentric curves in Figure 2 connect all10 of the possible combinations of fuel efficiency and acceleration performance that are possible, conditional on a particular set of technology features. We will refe r to these curves as Production Possibility Frontiers (PPF). The choice of technolog y 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 (t he gear ratio between the transmission and the wheels). Because the choice s of these tuning variables control both fuel efficiency and 0-60 acceleration time, the loca tion along a PPF can be uniquely determined by the choice of either fuel efficiency or acceleration performance. The cost of producing the vehi cle is not held constant al ong these PPFs. Production costs are simultaneously determined by the choice of technology features, accel eration performance, and fuel efficiency. Increases in fuel efficiency along a PPF will generally reduce the unit cost of manufacturing the vehicle, but th e value of the vehicle to cons umers 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 feat ures (a to c) or some combination (a to d)11 

### 3.2 Engineering modeling of medium-term design
Taking a “bottom up” approach, we use detaile d engineering simulati ons to construct the baseline PPF, which represents the engineeri ng 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 f eatures. 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 in dustry with product design and development, detailed simulation models have been develope d in the private sector. “AVL Cruise” is an integrated simulation platform that is wide ly used by major auto motive manufacturers in powertrain development (Mayer, 2008). We use th is model to characterize the engineering tradeoffs between fuel efficiency and 0-60 acceleration time for each vehicle class 2 . The fuel efficiency of a particular vehicle design is de termined in AVL Cruise by simulating the EPA’s fuel-economy test procedures (FTP-75 and HW FET schedules). Acceleration performance is determined by simulating a shifting program of the vehicle from sta ndstill to 60 mph. A total of 29,575 vehicle simulations were c onducted. 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 performa nce and fuel efficiency). Table 1 summarizes the range of parameter values we consider in our analys is. These include the powertrain variables that can be changed in the me dium term (i.e., engine displacement and final drive ratio) as well as longer-ter m design decisions that are conti nuous (i.e., curb weight), which we condition on in the supply-side model. All ot her vehicle parameters are determined from a representative base vehicle for each class. Many of these paramete rs (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 count erfactual 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 overestimati ng 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 determ ine how this baseline PPF is affected by the addition of one or more technology feature. The li st of technology features we consider in our analysis is not comprehensive; we consider a subs et of the types of tech nology features identified by NHTSA (2008). The majority of technology feat ures we omit from our analysis are only available in longer term planning stages, but some features are e liminated due to the challenges in simulating their effects (e.g., variable valve ti ming) even though it is possible that they could be incorporated in the medium term. Similarl y, with the powertrain tu ning 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 va lues reported by automotive manufacturers, suppliers, and consultants. We use these estima tes to determine how the baseline PPF changes with the addition of one or more technology featur es. 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 simulati ng 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 lu bricants” in compact vehicles. We simulate this impact by reduci ng 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 technol ogy feature, the lower bound of this range is used, consistent with our othe r assumptions in creating a cons ervative endogenous attribute model. The results of these simu lations 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 describing13 costs dependent on the powertrain tuning variable s 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 f eatures—is taken from Michalek et al. (2004). The authors collected cost data from manufacturing, wholesal e, 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 co st data were estimated by NHTSA based on reported values from automotive manufacturers, suppliers, and consultant s, and are currently used to perform cost-benefit analyses of the CAFE regulations. We treat the costs of technology features a nd the costs of adjus ting powertrain tuning variables as additively separable. Engines are manufactured separa tely 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 asse mbly of the engine with other vehicle subsystems. Two technology featur es—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 usi ng higher-performing components of the engine subassembly (e.g., piston rings), where the additional production co st depends on longer-term design decisions (number of pistons) but not medium term decision s 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 direct ly in our model of supply-side design and pricing decisions. However, because of the comp utational time required to execute the vehicle simulations, and because the large number of disc rete combinations of technology features, this is computationally infeasible. Instead, we approximate these relationships with a flexible parametric form. Taking all possible combinations of tec hnology 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 feat ures that are cost eff ective—meaning that there14 is no lower cost combination that could achie ve 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 segmen t, it is still computati onally infeasible to model this number of choices per vehicle per ma nufacturer in our counter factual simulations so that further simplifications are necessary. We approximate the discrete choices of t echnology 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 vehi cle class. Note that a particular value for tech maps to a specific combination of technology f eatures (e.g., low resist ance tires and a high efficiency alternator) and does not represent the number of technology features. The set of costeffective technology feature combinations is orde red by increasing fuel efficiency (decreasing fuel consumption) for the same acceleration perf ormance, which is also increasing in cost. Therefore, a higher value of tech corresponds to a higher fuel effi ciency 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 th an 1 mpg. Furthermore, we provide some evidence in A ppendix A that the particular spec ification we use to estimate the relationships of the continuous tech variable to fuel consumpti on and cost preserve important properties of the discrete technology combinations. We use the results of the engineering simula tions together with data on the technology features and technology costs, to estim ate the following system of equations:

݂ݑ݈݁ܿ݋݊ݏ ௦௝ ൌ ߢ ଴௦ ൅ ߢ ଵ௦ ݁ ି௔௖௖ ೞೕ ൅ ߢ ଶ௦ ݐ݄݁ܿ ௦௝ ൅ߢ ଷ௦ ݐ݄݁ܿ ௦௝ · ܽܿܿ ௦௝ ଶ ൅ߢ ସ௦ ݐݓ ௦௝ ൅ ߢ ହ௦ ݐݓ ௦௝ · ܽܿܿ ௦௝ ൅ ߝ ௦௝ ሺ3ሻ
݁݊݃ܿݐݏ݋ ௦௝ ൌ ߪ ଵ௦ ൅ ߪ ଶ௦ ݁ ି௔௖௖ ೞೕ ൅ ߪ ଷ௝ ݐ݄݁ܿ ௦௝ ൅ ߪ ସ௝ ݐݓ ௦௝ ൅ ߪ ହ௝ ݐݓ ௦௝ · ܽܿܿ ௦௝ ൅ ߨ ௦௝ ሺ4ሻ

where j denotes the vehicle design and s indexes the vehicle class. The fuel consumption of a vehicle in gallons per 1,0 00 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 sepa rately 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 specifi cations for each equation were tested; the equations above performed the best under the Akaike Information Criterion. The15 similarity of the specifications is due to underlying relationshi ps between the powertrain tuning variables and technology features w ith 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 technol ogy features. Equation 3 predicts observed vehicle performance reasonably well (R 2 =0.76). Also, consistent with our earlier assumptions, this figure suggests diminishing re turns to reducing acceler ation performance (in terms of gains in fuel efficiency). These dimini shing returns can also be intuitively explained by recognizing that it is generally eas ier to decrease fuel consumption of a low-efficiency vehicle than a high-efficiency vehicle; increasing fu el economy from 13 to 14 mpg saves 5.5 gal per 1,000 mi, the same savings realized from increasi ng fuel economy from 30 to 36 mpg. Appendix B discusses comparisons between estimated and obs erved performance attributes in more detail.

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



### 3.5 An engineering approach to endo genous attribute choice modeling
This is not the first paper to investigat e the physical relations hips between vehicle attributes that constrain vehicle design decisions. In the economics literature, a few recent studies have developed econometrically estimated e ndogenous attribute models for the automotive market (Gramlich 2008; Klier and Linn 2008). Although the econometric approach has its advantages, we argue that engineering estimat es are more appropriate for our purposes. 0 10 20 30 40 50 60 70 80 90 100

0 5 10 15 20Fuel Consumption (gal/1000 mi)

0-60 mph acceleration (s) Market data Model predictions

Diesels Hybrid16 Using physics-based simulations to identify the engineeri ng tradeoffs between vehicle attributes allows us to model tradeoffs and attr ibute combinations that are possible, but are not observed in the data. This is an important adva ntage of our approach because these unobserved vehicle designs may be optimal under the policy regi mes we are interested in analyzing. In fact, fuel economy standards have hist orically had a significant influence on the types of vehicle designs that manufacture r’s produce, indicating that this ability may be particularly important for analyzing fuel economy standards. Furthermore, the engineering approach we us e allows us to isolate the tradeoff between fuel efficiency and acceleration performance due to physical powertrain va riables—specifically engine displacement and the final drive gear ratio—without conflating changes in unobserved attributes that affect consumer demand. In cont rast, econometric approaches are more limited in their ability to account for corr elation between endogenous attri butes and unobserved attributes. In a recent paper, Klier and Linn estimated e ngineering tradeoffs betw een 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 accel eration of 10.5 s, whereas the 3.5 L engine option has 19.7 mpg and 8.5 s. However, engi ne options are correla ted with unobservable attributes; in addition to a larg er 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, fu rther 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 vehicl e attributes allows us to isolate the tradeoff between fuel effici ency and acceleration perf ormance due to physical powertrain variables—specifically engine displacement and the fi nal 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 drivi ng experience, for example by creat ing 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 assu mption by restricting changes in the powertrain variables to ten percent or less, which is a conservative restricti on to prevent noticeable noise and vibrations.



### 4 

### Data
We employ a combination of household-leve l data conducted by Maritz Research and vehicle characteristic data avai lable 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 surv ey 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 vehicl es with low market shar es, 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 informa tion on vehicle characteristics using Chrome System Inc.’s New Vehicle Database and VINMat ch tool. Vehicle alternatives are identified using the reported VIN, distingu ishing vehicles by their make, m odel, and engine option, with a few modifications. We eliminate vehicles pri ced over $100,000, which repr esent a small portion of market sales, and remove seve n vehicle alternatives that were not chosen or considered by any survey respondent. We further re duce the data set by consolidating pickup truck and full-size van models with gross vehicle weight ratings ove r 8,000 lb to only two engine options each. Summary vehicle data are described in Table 4. Additionally, data on dealer tran sactions purchased from JD Po wer and Associates are used to estimate dealer markups in the supply-s ide model. These data were collected from approximately 6,000 dealers from the proprietary Power Information Network data, aggregated to quarterly invoice costs and transac tion prices for each vehicle model.18 

### 5 

### Model

5.1 Demand side
Demand for new automobiles is modeled using a mixed-logit represen tation of consumer preferences. The i ndirect utility U nj that consumer n derives from purchasing vehicle model j is defined as:
ܷ ௡௝ ߜ ൌ ௝ ࢞Ԣࢼ ൅ ࢐࢔ ࣆ ൅ ࢔ ࢝Ԣ ࢐࢔ ߳ ൅ ௡௝ ሻ5ሺ

where δ j is the portion of utility that is the same across all consumers; x nj are vehicle attributes that interact with consumer characteristics and affect utility homogenously across the population; w nj are vehicle attributes and attribute-demographic interactions that heterogeneously affect utility, entering the equation through draws of assumed distributions, μ n , with zero means and standard deviations 

. The disturbance term Ԗ nj is the unobserved utility that varies across consumers. Assuming that ߳ nj is independent and identically distri buted (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), t he utility formulation is extended to include information about ranked choices when these da ta are available for a respondent. The ranking is specified as U ୬୧ ൐ U ୬୦ భ ... U ୬୦ ౣ ൐ U ୬୨ for all j ് i, h ଵ ,...,h ୫ where i is the chosen vehicle; h 1 is the second ranked vehicle (the vehicle that w ould have been chosen if vehicle i was not available) and h m is the m ranked vehicle. Therefore, the probability that consumer n chose vehicle i and ranked vehicle h 1 through h m 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 δ j as a function of observed vehicle attributes, z j , including all endogenous attributes, and the average utility of unobserved attributes, ξ j :
ߜ

௝ ࢠԢࢻ ൌ ࢐ ߦ ൅ ௝ ሻ8ሺ19 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 z j that are likely correlated with unobserved utility, ξ j . 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 z j 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 x nj , 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 w nj , 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 di stribution of the price to income ratio and the size terms are taken to be normally distribute d 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, consum ers would monotonically prefer lower price, lower cost to driv e, and better acceleration (higher inverse of time to accelerate). However, with respect to vehicle size, consumer s may monotonically prefer larger vehicles, or they may prefer a specific sized vehicle to other vehicles that ar e larger or smaller than this “ideal” size. To account for the latter possibility, we follow Fris chknecht et al. (2008), including two size parameters in both x nj Eq. 5 and z j 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 hete rogeneous preferences for the “ideal” size of a vehicle. Because price, fuel economy, and acceler ation performance are correlated with unobserved vehicle attributes, es timating 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-manufacturer20 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 th ese instruments relies on the assumption that the attributes chosen are a ll determined from longe r-term product planning schedules than the endogenous va riables. Similar moment inst ruments were used in Berry, Levinsohn, and Pakes (1995) and Train and Winston ( 2007), albeit with a wide r attribute set that included fuel economy and horsepower. While this wi der set of attributes may be appropriate for instruments in a model considering the very narr ow short term, it is certainly not valid for the medium term. In contrast, we limit the set of in struments 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 ar e 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 ௝ ௧ିଵ ሺ  ,  , ܁ ሻ ൅ ln൫S ୨ ൯ െ ln S ෠ ୨ ቀ  ,  , ߜ ௝ ௧ିଵ ሺ  ,  , ܁ ሻ ቁ ሺ9ሻ Unfortunately, due to the computational complex ity 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 consumer s considered vehicles from different segments in their purchasing decision, leadi ng us to reject the n ecessary condition that consumers are nesting their choice set based on vehicle segments. For the purposes of this working paper, we estimate the following equation:

ܷ

௡௝ ࢠԢࢻ ൌ ࢐ ࢞Ԣࢼ ൅ ࢐࢔ ࣆ ൅ ࢔ ࢝Ԣ ࢐࢔ ߳ ൅ ௡௝ ሻ10ሺ
We use the instrumental variables in a two-stage leas t 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. Cons istent with hist orical behavior, auto firms are characterized into three groups : those that operate at the CAFE standard21 (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 constrai ned to the standard following their historic behavior, and thei r expected future behavior, of consistently meeting the CAFE standards within allowable banking and borrowi ng credits (Jacobsen 2010). Both Toyota and Honda have always voluntarily exceeded the sta ndards and this behavior is supported in our counterfactual results. The remaining firms are considered violators in our counterfactuals, which indicate that violating th e standard is profit-maximizing be havior for these firms rather than meeting or exceeding the standards. The profit optimization problem solved by an unconstrained firm is:

max

,ࢉࢉࢇ ࢎࢉࢋ࢚ ࢗ ᇱ ሺ ࢖െࢉ ሻ ሺ11ሻ

where all quantities are J x 1 vector s with entries for all J vehicles in the firm’s fleet. Similarly, for firms paying the CAFE penalty, the pr ofit maximization problem is given by:

max ,ࢎࢉࢋ࢚,ࢉࢉࢇ ࢖ ࢗ ᇱ ሺ ࢖െࢉ ሻ െ ܨ ஼ െ ܨ ் ሺ12ሻ

where F C and F T are the respective fines for violating the passenger car and light truck standard, defined as:

ܨ ஼ ݍ ෍ 55 ൌ ௝ ݌ሺ ௝ ሻ ॅא௝ ಴,೑ ܽ݊݀ݐݏቆ
஼ െ ∑ ݍ ௝ ݌ሺ ௝ ሻ ॅא௝ ಴,೑ ∑ ݍ ௝ ݌ሺ ௝ ݃݌݉ ሻ ௝ ⁄ ॅא௝ ಴,೑ ቇ

ܨ

் ݍ ෍ 55 ൌ ௝ ݌ሺ ௝ ሻ ॅא௝ ೅,೑ ܽ݊݀ݐݏቆ
் െ ∑ ݍ ௝ ݌ሺ ௝ ሻ ॅא௝ ೅,೑ ∑ ݍ ௝ ݌ሺ ௝ ݃݌݉ ሻ ௝ ⁄ ॅ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 ( stand C and stand T ) for their fleet of cars, ॅ ௖ , and their fleet of light trucks, ॅ ் . Rearranging Eq. 1, these constraints can be written as:

∑ ݍ ௝ ሺ݌ ௝ ሻ

௝אॅ ಴ ൬ 1 െ ௦௧௔௡ௗ ಴ ௠௣௚ ೕ ൰ ൒ 0
∑ ݍ ௝ ሺ݌ ௝ ሻ

௝אॅ ೅ ൬ 1 െ ௦௧௔௡ௗ ೅ ௠௣௚ ೕ ൰ ൒ 0 ሺ14ሻ

3 More precisely, these producers are inactively constrai ned 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 ࢖,ࢎࢉࢋ࢚,ࢉࢉࢇ ࢗ ᇱ ሺ ࢖െࢉ ሻ

ࢗ .ݐ .ݏ ᇱ ࢘ ࡯ 0 ൒ ࢗ ᇱ ࢘ ࢀ 0 ൒ ሺ15ሻ

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

vector r T is similarly constructed with the jth entry of 1 െ ݐݏܽ݊݀ ் ݉݌݃ ௝ ⁄ if ݆אॅ ் and zero
otherwise. Note that, for all types of firms, fuel c onsumption is determined through decisions on acceleration performance and technol ogy features from Eq. 3 and ther efore is not lis ted 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 pr oducing automobile j is represented as:

ܿ ௝ ൌ ݁݊݃ܿݐݏ݋ ௝ ൅ ߱ ௝ ሺ16ሻ

where ݁݊݃ܿݐݏ݋ ௝ is the portion of marginal cost de pendent 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 ൅ ൫׏ ܘ ܙ ᇱ ൯ ሺ ࢖െࢉ ሻ ൌ ૙ ሺ17aሻ fee-paying: ࢗ ሺ ࢖ ሻ ൅ ൫׏ ܘ ܙ ᇱ ൯ ሺ ࢖െࢉ ሻ െ ൫׏ ܘ ܨ ஼ ൯ ᇱ െ ൫׏ ܘ ܨ ் ൯ ᇱ ൌ ૙ ሺ17bሻ
constrained: ࢗ ሺ ࢖ ሻ ൅ ൫׏ ܘ ܙ ᇱ ൯ ሺ ࢖െࢉെߣ ஼ ࢘ ࡯ െ ߣ ் ࢘ ࢀ ሻ ൌ ૙ 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 ߣ ் , are unknown and

࢘ ஼ and ࢘ ் depend on fuel economy, which is correlated with marginal cost, we cannot directly solve for marginal cost for the firms constr ained 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 ve hicle 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, rath er than take the rela tionship of dealer to manufacturer markups as given by Bresnahan an d Reiss (1989), which di d not incorporate the effects of the CAFE regulation, we extend the deri vation one-step further by explicitly including the CAFE regulation (Appendix C). Using these r ecovered parameters, we can then solve for the equilibrium marginal vehicle costs for the cons trained firms. This estimation strategy has the limitation of relying on the imposed form of th e relationship between dealer and manufacturer markups. However, our intere st in the estimates of ߣ ஼ and ߣ ் is limited to their role in picking up enough of the correlation be tween marginal costs and ࢘ ஼ and ࢘ ் . We therefore expect any errors
in the estimation of ߣ ஼ and ߣ ் will only have second-order effects on the results of our counterfactual simulations. Future work w ill include performing sensitivity tests on
counterfactual results to various values of ߣ ஼ and ߣ ் .


### 6 

### Empirical Results 6.1 Endogenous attribute model estimation
The estimation results for Eq. 3, which summarizes the relationship between vehicle attributes based on technology features and power train parameters for eac h vehicle class, are reported in Table 5. Similarly, results from esti mating the cost relationship as in Eq. 4 are reported in Table 6. Results from validation te sts comparing model predictions to observed market data are summarized in Appendix B. Ba sed 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 sa les-weighted average cost of increasing fuel economy by 1 mpg while maintaining the same acceleration performance is $143.



### 6.2 Demand-side estimation
The OLS estimations of the first-stage regre ssions of price, the i nverse of fuel economy, and the inverse of 0-60 acceleration time are pres ented in Table 7. The F-tests for the joint null hypothesis that the instrument s’ coefficients are zero ar e 9.52, 26.76, and 8.18, respectively. Results of the second-stage IV estimation ar e shown in Table 8. Si gnificant heterogeneity is shown in the ratio of price to income, the cen ts-per-mile attribute, a nd both footprint terms. The estimated parameters for the footprint terms indica te that preference monotonically increases with vehicle size for all individuals in our sa mple, but the rate of increase varies among24 individuals. SUVs are the only ve hicle 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 fo r a sample of these vehicles. The sales-weighted average price elasticity is -2.6 4 . Similar to other models of the automotive industry (Berry, Levinsohn, and Pakes 1995; Goldberg 1998, Berestea nu 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.



### 6.3 Supply-side estimation

Table 10 shows the estimates of ߣ ஼ and ߣ ் 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 Fo rd or GM. This result is intuitive given that Chrysler neither sells many small vehicles nor ha s many passenger cars with relatively high fuel economy. For light trucks, the estimat es 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-effi ciency 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 represente d 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 sa me 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 movi ng 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 it s footprint, so that larger vehi cles can meet lower standards. Second, the reformed CAFE standards allow trad ing within a firm betw een the passenger car standard and the light truck standard although they set a fl oor 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 betwee n 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 cons istent with our assumptions in the endogenous attribute model, which are cons tructed to bias producer and consumer losses toward the upper bound. For a discussion of ba nking and borrowing of fuel economy credits, interested readers should refer to Jacobsen (2010). In all of the scenarios we consider, Chrysl er 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 enfor ced up to a tenth of a mile-per-gallon meaning that, if Chrysler had an averag e of 29.85 mpg for its passenger car s, 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 reasona ble considering that Chrysler is now importing Fiat vehicle models, which have high fu el economy compared to Chrysler’s fleet, in anticipation of the refo rmed 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, accelerati on performance, and technology implementation in the presence of the MY2006 CAFE standards. Deta ils 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 categories26 of firms. The first three of these categories—the domestic Bi g 3, Asian Big 4, Euro, and Other Asian—currently have manufacturing pl ants 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 accel eration performance and fuel economy and technology implementation. Results, shown in Tabl e 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 accelerat ion 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 fu el 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 fu el efficiency. This suggests that, across all manufacturers considered, only 50% of the potential of implemen ted technologies to decrease fuel consumption is realized and the remaining is applied to improve acceleration performance. This behavior illustrates some of the comp lexity of the relations hip between technology implementation and improvements to fuel econom y. 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 firm s constrained by CAFE, namely the domestic Big 3 manufacturers, will improve the fuel econo my of their vehicle fleets by an average of 2.6 mpg. This rise in fuel economy is a result of both changes in technology f eatures and changes in prices to shift demand toward vehicles th at exceed their fuel economy targets, called mixshifting . Technology implementation increases across these firms’ fleets, but 42% of the potential of technology features to decrease fu el 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 fuel27 economy vehicles. Technology implementation also in creases for these firms, but 100% of it is used to improve acceleration performance in stead of fuel efficiency.



### 7.2 Changes in fuel consumpt ion and social surplus These simulation results indicate that a tr ansition from the unreformed CAFE standards to the reformed CAFE standards will reduce pr oducer 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 consumersurplus can be attributed to the footprintbased fuel economy standards, which our simulati on results indicate encourages firms to raise prices of vehicles with relati vely low price elasticities and lo wer prices of vehicles with relatively high price elastic ities as shown in Table 13. For exampl e, the Pontiac G6 is much more price-elastic (-1.05) than the Pont iac Solstice (-0.09) and, at equilib rium, the G6 exceeds its fuel economy target but, because the So lstice has a smaller footprint, it is 7 mpg below its standard. Therefore, it is in GM’s interest to lower the pric e of the G6 and raise the price of the Solstice so that the average fuel economy across its fleet exc eeds the average target. Across the fleet of U.S. vehicles, the average price-elasticity of vehicl es with higher prices und er the reformed CAFE standards is -0.75 whereas the av erage price-elasticity of vehicl es with lower prices is -5.30. However, there are limitations to our current an alysis 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 test s 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 onl y considers the medium term, wher e 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 trad eoffs 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 tradeoffs28 between vehicle attributes on the resulting welfare estimations. Estimated reductions in fuel consumption are 26% lower than in the first spec ification, and increases to social surplus are 46% lower. These results emphasize the importan ce of accounting for tradeoffs between vehicle attributes when analyzing policie s such as the CAFE regulation. We also attempted simulations that do not allow firms to make any medium-term design changes but instead vehicle desi gn is fixed and firms can only increase their average fuel economy by adjusting prices of their vehicles to shift demand toward high er-efficiency vehicles. However, firms were unable to meet the reform ed CAFE standards. In fact, Chrysler has no vehicles that exceed their fuel economy target s, 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 acceleratio n performance. In addition to accounting for technology implementation, our model explicitly acc ounts for engineering tradeoffs between fuel efficiency and acceleration performance—c ontrolled 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 pr oduct attributes in several ways. On the demand side, correlation between endogenous attributes and unobservables is addressed by identifying quasi-fixed attributes th at can serve as valid in struments in the medium term. Additionally, we use physics-based engineer ing 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 tr adeoffs between vehicle attributes on our supply side, without conflating effect s of unobserved attributes. The methods we develop here are generalizable to other te chnical products such as household a ppliances and cons umer 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 effect s of the model-year 2012 CAFE regulation on producer and consumer surplus. Although final estimation of th e demand-side is still pending, for this working paper, we use a simplified dema nd-side specification to present our preliminary29 results. Results indicate that domestic firms im plement technology features to comply with the regulation, but nearly half of the potential be nefit of these technologies to reduce fuel consumption is instead used to increase accel eration 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 woul d 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 produc tion 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 manuf acturer can actually lower their fuel economy standard by producing larger vehicl es. This property may create the incentive for manufacturers to increase the size of their vehi cles, which may result in smaller reductions in fuel consumption. The potential of this incen tive, 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 cm 3

, 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 Vehicle30 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 accele ration time in seconds. Cost and fuel economy figures are taken from NHTSA (2008). The change in accelerati on is calculated in the engineer ing 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. 10,42331 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

κ

0 20.8484 0.9414 10.7920 0.2158 11.5531 0.5674 10.8515 0.4034

κ 1 89.681 31.159 69.524 5.398 733.706 55.371 452.552 23.785

κ

2 -0.205 0.025 -0.260 0.013 -0.083 0.002 -0.079 0.004

κ

3 0.0016 * * 0.0005 0.0013 *** 0.0003 0.0002 0.0000 0.0002 0.0000

κ

4 2.9159 0.3667 12.9897 0.3047 8.6680 0.1119 8.3583 0.1208

κ

5 0.0280 * 0.0476 -0.5593 0.0456 -0.2954 0.0223 -0.2539 0.0079 R 2 0.443 0.941 0.896 0.976 Obs. 4473 5117 3542 3542

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

κ

0 14.0535 0.4985 10.5032 0.4049 10.5185 0.4083

κ 1 1329.854 115.804 13387.530 1836.191 2979.096 411.241

κ

2 -0.154 0.008 -0.093 0.007 -0.089 0.006

κ

3 0.0006 0.0001 0.0003 *** 0.0001 0.0003 ** * 0.0001

κ

4 9.0653 0.1069 8.9932 0.3207 8.6604 0.2813

κ

5 -0.2934 0.0148 -0.2224 0.0295 -0.2225 0.0299 R 2 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 / Van32 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 rema ining 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.

σ 0 0.3669 * 0.0865 0.7800 0.0091 0.5540 0.0355 0.4029 0.0450

σ 1 10.669 * 2.231 1.972 0.163 24.384 1.384 24.053 2.727

σ 2 0.018 0.000 0.002 0.000 0.005 0.000 0.006 0.000

σ 3 0.2579 0.0132 0.2250 0.0051 0.1963 0.0103 0.2339 0.0052

σ 4 ‐ 0.0082 0.0013 -0.0123 0.0005 -0.0071 0.0012 -0.0069 0.0004 R 2 0.890 0.89 8 0.898 0.931 Obs. 4473 5117 3542 3542

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

σ 0 0.0200 * * 0.1337 0.3025 * 0.0607 0.3025 * 0.0607

σ 1 92.397 16.477 719.579 * 162.643 160.560 * 36.291

σ 2 0.004 0.000 0.007 0.000 0.007 0.000

σ 3 0.3470 0.0143 0.2621 0.0137 0.2538 0.0117

σ 4 ‐ 0.0108 0.0016

‐ 0.0055 * 0.0014

‐ 0.0055 * 0.0014 R 2 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 / Va n

param st. error param st. error param st. error din 0.0144 (0.0007) 0.0137 * * (0.0069) -0.0108 (0.0037) dout -0.2306 * (0.2360) -0.3165 * (0.2350) -0.6388 0.1231 dsqin 0.0161 * (0.0159) 0.0144 * (0.0158) -0.0011 * (0.0085) dsqout -1.3409 (0.2767) -1.2976 (0.2740) 0.3644 * * (0.1506) turbo -0.2247 * (1.8032) -0.4498 * (1.7849) -0.8157 * (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 * (1.1625) 0.9460 * (1.1491) 3.5495 (0.5951) N 473 473 473 R 2 0.9645 0.9653 0.9946 Price Fuel Costs Inverse 0-60 acc time33 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

‐ 43.10634 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 EuroGM,Ford, Toyota,Honda, Mazda,Kia, MercedesTota l Chrysler Nissan,Hyundai Subaru B enz,BM W All Others Outside Consumer Surplus 116.37 41.36 26.54 19.93 -5.06 37.57 -3.95 (billions) due to p rices 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 EuroGM,Ford, Toyota,Honda, Mazda,Kia, MercedesTota l Chrysler Nissan,Hyundai Subaru B enz,BM W All Others
Profits -25.5 -5.3 -9.0 -2.5 -2.9 -5.7 (billions)

Big 3 Asian 4 Other Asian EuroGM,Ford, Toyota,Honda, Mazda,Kia, MercedesTota l Chrysler Nissan,Hyundai Subaru B enz,BM W 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: p rice 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

Δ35 Table 11 Continued: Counterfactual simulations for MY2012 CAFE, Specification 2

Notes: This table reports demonstrational results of welfare changes due to replacing the un reformed 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, M azda,Kia, MercedesTotal Ch rys l er N issan, H yun d ai S u b aru B enz, BMW All Others Outside Consumer Surplus 58.09 81.48 -12.39 -4.73 -2.94 -1.98 -1.35 (billions) due to p rice 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, M azda,Kia, M ercedesTota l Chrysle r Nissan,Hyund Subaru Benz,BM W 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, M azda,Kia, MercedesTotal Chrysler Nissan,Hyundai Subaru B enz,BM W 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: p rice 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 prices36 

### 9 

### References Anderson, S. and J. Sallee. 2009. Using loopholes to rev eal the marginal cost of regulation: the case of fueleconomy standards. Michigan State University. Working paper. Beresteanu, A. and S. Li. 2008. Gasoline prices, gover nment support, and the demand for hybrid vehicles in the U.S. Duke University. Working paper. Berry, S. 1994. Estimating discrete-choi ce 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. Papalamb ros. 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 corporat e average fuel efficiency standards in the US. The Journal of Industrial Economics 46(1): 1–33. Gramlich, J. 2008. Gas Prices and Endogenous Product Se lection 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 St andards In a Model with Producer Household Heterogeneity. Stanford University. Job Market Paper. Klier, T. and J. Linn. 2008. New Vehicle Character istics 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. Jour nal of Mechanical Design. 126(6): 1062-1070. NHTSA. 2008. Preliminary Regulatory Impact Analys is: 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 Efficien cy and Motor Vehicle Travel: The Declining Rebound Effect. Energy Journal. 28(1): 25-51. Sörenson, D. 2006. The automotive development pr ocess: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 i ndustry. NBER Working Paper #13522 Train, K. and C. Winston. 2007. Vehicle choice be havior 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 fo r 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 combin ations 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 de sign with an engine size, final drive ratio, and set of discrete technology features. The gaps between vehicle de signs 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 i nput variables approached zero, the gaps would disappear. Figure B1 is generated for a sp ecific vehicle segment (an SUV) and a specific curb weight (3,200 lb). Similar trends were found for other se gments 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 li nearly. It also indicates that the incremental change in cost of changing tech nology features is roughly constant across the various levels of accelera tion performance. This structure is pr eserved in the specification of Eq. 4 where cost is linear in technology conditiona l 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 agains t combinations of tec hnology features for the same vehicle segment (SUV) and curb weight ( 3,200 lb). This figure indi cates that conditional on vehicle segment, curb weight, and 0-60 acce leration time, the set of combinations of technology features linearly decr ease fuel consumption. However, unlike cost, the incremental change in cost of changing t echnology 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 80Production cost (thousand dollars)

tech variable 4.51 s

4.93 s 5.59 s 8.91 s 10.89 17.5338 acceleration time. Figure B2 show s that the incremental decreas e in fuel consumption from moving to a higher ordered combination of techno logy 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 rela tively large but more negative for relatively faster a cceleration times. Similar trends were found for other segments and other curbweights. These properties are repres ented 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 80Fuel 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 s39 

### Appendix B Endogenous Attribute Model We compare the results of our approxima ted 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-seat er model, however, does not predict the market data as well as the othe r segments, but because this segment represents less than 1% of sales, this is unlikel y to affect our count erfactual 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 20Fuel 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 15Fuel Consumption (gal/1000 mi)

0-60 mph acceleration (s) Market data Model predictions

Hybrids40 

### Appendix C Derivation of Lagrange Multiplier Estimation Model

The first-order conditions of the constr ained firm’s profit maximization are:
ࢗ ሺ ࢖ ሻ ׏൫ ൅ ܘ ܙ ܂ ൯ ሺ ߣ൅ࢉെ࢖ ஼ ࢘ ࡯ ߣ ൅ ் ࢘ ࢀ ሻ ૙ ൌ
where ׏ ܘ ܙ ܂ is the gradient of ࢗ ࢀ 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 ߣ ் . Following Bresnahan and Reiss (1989), th e dealer’s problem is defined by

max Π D ௤ ೕ ॅא௝׊ ೑ ݍ෍ൌ ௝ ॅא௝ ೑ ൫݌ ௝ ሺ ݍ ሻ െ ݓ ௝ െ ݏ ௝ ൯

where ݓ ௝ and ݏ ௝ are the wholesale price and marginal selling costs of ve hicle 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 no tation from Bresnahan and Reiss to conform to the notation used above.

The manufacturer’s problem is defined by:

max Π M ௤ ೕ ॅא௝׊ ೑ ݍ෍ൌ ௝ ॅא௝ ೑ ൫ݓ ௝ ሺ ݍ ሻ െ ܿ ௝ ൯

subject to ݍ ෍ ௝ ॅא௝ ಴೑ ቆ1 െ ݉݌݃ ஺஼ிா,஼ ݃݌݉ ௝ ቇ൒0 ݍ ෍ ௝ ॅא௝ ೅೑ ቆ1 െ ݉݌݃ ஺஼ிா,் ݃݌݉ ௝ ቇ ൒ 0.

The first order conditions of the dealer’s problem are:

ܴܯ ௝ ሺ ݍ ሻ ݌ ൌ ௝ ݍ෍൅ ௜ ݌߲ ௜ ሺ ݍ ሻ ݍ߲ ௝ ॅא௜ ೑ ݓ ൌ ௝ ݏ ൅ ௝ ሻ1ܣሺ

where ܯܴ ௝ ሺݍሻ is the retail marginal revenue of the jth product. Substituting the dealer’s solution
into the manufacturer’s fi rst order condition gives:41 ݓ

௝ ሺ ݍ ሻ ܿ െ ௝ ݍ෍൅ ௜ ݓ߲ ௜ ሺ ݍ ሻ ݍ߲ ௝ ॅא௜ ೑ ൅ ߣ ஼ ቆ1 െ ݉݌݃ ஺஼ிா,஼ ݃݌݉ ௝ ቇ ൅ߣ
் ቆ1 െ ݉݌݃ ஺஼ிா,் ݃݌݉ ௝ ቇൌ0

Substituting in ݓ ௝ ሺ ݍ ሻ ൌ ܯܴ ௝ ሺ ݍ ሻ െ ݏ ௝ from Eq. A1, noting that CAFE does not affect the dealer’s decisions directly, the first order conditions become:

ܴܯܯ ௝ ሺ ݍ ሻ ܴܯ ൌ ௝ ሺ ݍ ሻ ݏ െ ௝ ൅ ∑ ݍ ௜ డெோ ೔ ሺ௤ሻ డ௤ ೕ ௜אॅ ೑ ൌ ܿ ௝ െ ߣ ஼ ൬ 1 െ ௠௣௚ ಴ಲಷಶ,಴ ௠௣௚ ೕ ൰ െߣ ் ൬ 1 െ ௠௣௚ ಴ಲಷಶ,೅ ௠௣௚ ೕ ൰

Using this relationship, the ratio of dealer to manufacturer markups is:

݌ ௝ ݓ൫ െ ௝ ݏ ൅ ௝ ൯

ݓ

௝ ܿ െ ௝ ൌ ݌ ௝ െ ܯܴ ௝ ሺݍሻ

ݓ

௝ െ ܯܯܴ ௝ ሺ ݍ ሻ െߣ ஼ ൬ 1 െ ݉݌݃ ஺஼ிா,஼ ݉݌݃ ௝ ൰ െߣ ் ൬ 1 െ ݉݌݃ ஺஼ிா,் ݃݌݉ ௝ ൰

Substituting in for ܯܴ ௝ ሺݍሻ and ܯܯܴ ௝ ሺ ݍ ሻ , this ratio can be written as:

∑ ݍ ௜ ݌߲ ௜ ሺ ݍ ௜ ሻ ݍ߲ ௝ ॅא௜ ೑
2 ∑ ݍ ௜ ݌߲ ௜ ሺ ݍ ሻ ݍ߲ ௝ ॅא௜ ೑ ൅ ∑ ∑ ݍ ௜ ݍ ௞ ߲ ଶ ݌ ௜ ሺݍሻ ݍ߲ ௝ ݍ߲ ௞ ॅא௞ ೑ ॅא௜ ೑ ߣെ ஼ ൬ െ 1 ݃݌݉ ஼,ிா஼஺ ݉݌݃ ௝ ൰ െߣ ் ൬ 1 െ ݉݌݃ ஺஼ிா,் ݃݌݉ ௝ ൰ ሺܣ2ሻ

To simplify this equation, let:

ߟ ௝ ൌ ∑ ∑ ݍ ௜ ݍ ௞ ߲ ଶ ݌ ௜ ሺ ݍ ሻ ݍ߲ ௝ ݍ߲ ௞ ॅא௞ ೑ ॅא௜ ೑ ∑ ݍ ௜ ݌߲ ௜ ሺ ݍ ሻ ݍ߲ ௝ ॅא௜ ೑

which, following Bresnahan and Reiss, is constant across all products, and therefore we will drop the subscript. Substituting in to Eq. A2 gives:

݌ ௝ ݓ൫ െ ௝ ݏ ൅ ௝ ൯

ݓ

௝ ܿ െ ௝ ൌ 1

െߟ൅2 ߣ ஼ ൬ 1 െ ݉݌݃ ஺஼ிா,஼ ݉݌݃ ௝ ൰ ൅ߣ ் ൬ 1 െ ݉݌݃ ஺஼ிா,் ݃݌݉ ௝ ൰

∑ ݍ ௜ ݌߲ ௜ ሺ ݍ ሻ ݍ߲ ௝ ॅא௜ ೑ 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 ߣ ் using dealer markups.

Substituting in ܾ ௝ ൌ ݌ ௝ െ ൫ݓ ௝ ൅ ݏ ௝ ൯ into Eq. A3 and rearranging gives:42 ൮ 2൅ߟെ ߣ ஼ ൬ 1 െ ݉݌݃ ஺஼ிா,஼ ݉݌݃ ௝ ൰ ൅ߣ ் ൬ 1 െ ݉݌݃ ஺஼ிா,் ݃݌݉ ௝ ൰

∑ ݍ ௜ ݌߲ ௜ ሺ ݍ ሻ ݍ߲ ௝ ॅא௜ ೑ ൲
ܾ ௝ ൌ ݓ ௝ െ ܿ ௝

Rewriting this equation in te rms of the entire markup ݌ ௝ െ ܿ ௝ : ൮ 2൅ߟെ ߣ ஼ ൬ 1 െ ݉݌݃ ஺஼ிா,஼ ݉݌݃ ௝ ൰ ൅ߣ ் ൬ 1 െ ݉݌݃ ஺஼ிா,் ݃݌݉ ௝ ൰

∑ ݍ ௜ ݌߲ ௜ ሺ ݍ ሻ ݍ߲ ௝ ॅא௜ ೑ ൲
ܾ ௝ ൌ ݌ ௝ െ ܿ ௝ െ ܾ ௝ െ ݏ

Or ൮ 3൅ߟെ ߣ ஼ ൬ 1 െ ݉݌݃ ஺஼ிா,஼ ݉݌݃ ௝ ൰ ൅ߣ ் ൬ 1 െ ݉݌݃ ஺஼ிா,் ݃݌݉ ௝ ൰

∑ ݍ ௜ ݌߲ ௜ ሺ ݍ ሻ ݍ߲ ௝ ॅא௜ ೑ ൲
ܾ ௝ ൌ ݌ ௝ െ ܿ ௝ െ ݏ

In vector formation, this rela tionship can be represented as: ࡲ െ ߟ ൅ 3ቀ ૚ି ሺ ߣ ஼ ࢘ ࡯ ߣ൅૚ ் ࢘ ࢀ ૚ ሻ ׏െ൫ ൌ ࢈ ቁ ܘ ܙ ܂ ൯ ି૚ ࢗ ሺ ࢖ ሻ ߣ െ ஼ ࢘ ࡯ ߣ െ ் ࢘ ࢀ ݏ െ
where b is a vector of markups for all products, ࡲ is a diagonal matrix w ith 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 ߣ ் gives:
ሺ ߟ൅3 ሻ ߣെ࢈ ஼ ࡲ ૚ି ࢘ ࡯ ߣ െ ࢈૚ ் ࡲ ૚ି ࢘ ࢀ ߣ ൅ ࢈૚ ஼ ࢘ ࡯ ߣ ൅ ் ࢘ ࢀ ׏െ൫ ൌ ܘ ܙ ܂ ൯ ି૚ ࢗ ሺ ࢖ ሻ ݏ െ
Finally, we rearrange this equation to extract the Lagrange multipliers: ሺ ߟ൅3 ሻ ߣെ࢈ ஼ ሺ ࡲ ૚ି ࢘ ࡯ ࢘ െ ࢈૚ ࡯ ሻ ߣ െ ் ሺ ࡲ ૚ି ࢘ ࢀ ࢘ െ ࢈૚ ࢀ ሻ ׏െ൫ ൌ ܘ ܙ ܂ ൯ ି૚ ࢗ ሺ ࢖ ሻ ݏ െ Given data on dealer markups and an estimation of demand, we could estimate ߣ ஼ and ߣ ் from the following: ൫׏ ܘ ܙ ܂ ൯ ି૚ ࢗ ሺ ࢖ ሻ ߣ ൌ ஼ ሺ ࡲ ૚ି ࢘ ࡯ ࢘ െ ࢈૚ ࡯ ሻ ߣ ൅ ் ሺ ࡲ ૚ି ࢘ ࢀ ࢘ െ ࢈૚ ࢀ ሻ ߟ ൅ ̂ ࣕ൅ݏെ࢈
where ߟ ̂ ൌ െ ሺ 3൅ߟ ሻ

.43 

### Appendix D Counterfactual baseline Because our endogenous attribute model is deri ved from engineering simulations and cost data, observed attributes are not n ecessarily restricted to be in e quilibrium. We therefore perform simulations of the CAFE regula tions 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 implic itly determines fuel economy—as well as price for each of their vehicles. All other counte rfactual results are measured from this baseline. Our results shown in Table C1 indicate th at 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 thos e 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, whic h 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