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Vehicle Manufacturer Technology Adoption and Pricing Strategies under Fuel Economy/Emissions Standards and Feebates.

1. INTRODUCTION

Corporate Average Fuel Economy (CAFE) Standards, established by the U.S. Energy Policy and Conservation Act of 1975, require automobile manufacturers to meet minimum fleet average fuel economy standards for passenger cars and light trucks. Their effectiveness and impact on social welfare have been extensively studied in the literature (Kleit 1990, 2004; Greene 1991; Austin and Dinan 2005; Goldberg 1998; Parry, Fisher and Harrington 2004). Greene's (1991) work on manufacturer pricing strategies is particularly relevant to this paper. If manufacturers offer multiple vehicle models that vary in fuel economy, they can use price changes to induce sales-mix shifts in order to meet CAFE standards. Specifically, they can increase the price of their less efficient vehicles and/or decrease the price of their more efficient vehicles to increase the average fuel economy of their vehicle sales. Greene (1991) analyzed how short-run pricing strategies could be used to meet a required fuel economy target in this way, and concluded that pricing strategies are cost-effective for very small improvements in fuel economy but are expensive for large improvements. Greene (1991) focused on the short-run response of manufacturers, where the adoption of fuel-economy-improving technologies was not an option.

This paper analyzes manufacturer decision making over a longer planning horizon, and explores the role that both technology adoption and pricing strategies might play in meeting the new post-2010 CAFE and carbon dioxide (C[O.sub.2]) emissions standards, assuming the use of currently available, proven technologies. Pricing is clearly an important tool that manufacturers may use to cope with uncertainties in production, consumer demand, and fuel price fluctuation in the short term; however, the intended purpose of the regulation is to induce technology adoption and spur innovation over time. Pricing might be used to add flexibility, but would only be expected to play a major role if individual manufacturers had difficulty meeting standards using the available technology. Thus an examination of the relative role of technology adoption and pricing strategies helps us understand the functionality of the new standards. We also examine how a feebate program implemented along with CAFE and emissions standards might affect manufacturer decisions and fuel efficiency improvement. A feebate is a market-based policy that levies fees on new vehicles with low fuel efficiency and provides rebates to new vehicles with high fuel efficiency (Greene et al. 2005). Finally, we explore potential benefits and costs to consumers, including average vehicle technology cost, fuel savings, new vehicle sales and sales mix, and the average footprint size of the new vehicle fleet.

The effects of CAFE and emissions standards on manufacturer decisions and vehicle sales mix shifts are estimated using a dynamic multi-period optimization model. Under the assumption of a competitive or monopolistically competitive market, manufacturers maximize social surplus (the sum of consumer and producer surplus) by optimizing their technology adoption and pricing decisions subject to CAFE and emissions standards. Vehicle offerings, including each vehicle's price and fuel economy, are specified for 2010 (the base year). Vehicle offerings remain the same over the planning period, except for fuel economy improvements and price changes made by manufacturers in later years. These changes have an impact on consumer demand for vehicles (and therefore consumer surplus), which is estimated using a nested multinomial logit (NMNL) model. Both manufacturer decisions and consumer demand are modeled at the level of vehicle configuration (a combination of vehicle make/model, engine size and transmission type) corresponding to the level of detail at which fuel economy measurements are made by the U.S. Environmental Protection Agency (EPA) for determining compliance with the standards. Compared with recent CAFE analysis models (Kleit 2004; Austin and Dinan 2005), the advantages of our approach are (1) more realistic modeling of technology adoption by including vehicle redesign cycles, and (2) more detailed simulation of sales mix shifts by representing consumer choices at a higher level of detail.

In the remainder of this paper, we first provide more background on new CAFE and emissions standards. We then describe the dynamic optimization model and define reference and policy cases. Finally, we summarize primary results and present our conclusions.

2. CAFE (2011-2016) AND C[O.sub.2] EMISSIONS (2012-2016) STANDARDS

The new standards have substantially tightened requirements for new light-duty vehicle fuel efficiency, compared with old standards (2010 and earlier). Moreover, in contrast to previous standards, the fuel efficiency target of a vehicle is a function of its footprint (wheelbase X track width). The standards define footprint functions separately for cars and light trucks, and for each model year (U.S. EPA/U.S. DOT 2010).

Manufacturers must meet the standards for cars and light trucks separately: The salesweighted harmonic mean fuel economy for a manufacturer's car or truck fleet is required to equal or exceed its harmonic mean fuel economy target for the case of CAFE standards. For emissions standards, the sales-weighted mean C[O.sub.2] emissions must not exceed the sales-weighted C[O.sub.2] emissions target. For instance, emissions standards for a manufacturer's car fleet can be described by the following equation:

[mathematical expression not reproducible] (1)

where [N.sub.m] denotes the number of car models produced by manufacturer m, Sales(t[).sub.i] represents the sales of car model i for year t, [TotalSales.sub.m] is the total sales of all cars produced by manufacture m, [e.sub.i](t) is the emissions rate of model i, and [e.sub.i]* (t) is its emissions target, calculated using the appropriate footprint function given in the standards.

The new standards also provide compliance flexibility to manufacturers. Manufacturers can earn compliance credits by outperforming the required targets. Credits can be carried forward (i.e. banked) and used toward compliance in future years; credits can also be carried backward (borrowed) to offset a deficit that had accrued in a prior model year. The standards allow credits to be banked and used later for up to five years (1) and borrowed from future years for up to three years.

Manufacturers can also achieve flexible-fuel vehicle (FFV) credits and air conditioning (AC) credits by producing FFVs and improving air conditioning systems. The most prominent new feature is to allow credit transfer between the car and truck compliance categories within a firm, and credit trading (i.e., purchasing or selling credits) among firms. Rubin, Leiby and Greene (2009) estimate that credit transfer and trading can reduce manufacturers' compliance cost by 7% to 16%.

3. METHODOLOGY

Our approach integrates manufacturer decisions and consumer demand into a multi-period optimization framework. Detailed documentation on the model, its coefficients, calibration, and data are available (Bunch et al. 2011). A brief overview is provided here.

3.1 Manufacturer Decisions

The manufacturer decision problem is formulated as an optimization model that maximizes social surplus subject to the requirements of CAFE and emissions standards over a multi-year planning horizon. In meeting the standards, manufacturers have various options, including

1. adopting fuel economy technologies that increase fuel economy at a cost,

2. employing pricing strategies to shift sales toward fuel-efficient vehicles (or away from fuel-inefficient vehicles) to increase fleet average fuel efficiency,

3. transferring credits among vehicle categories (e.g., cars and trucks),

4. buying credits from other firms,

5. obtaining AC and FFV credits by improving air conditioning systems and producing FFVs, and

6. using banked or borrowed credits.

The first four options are implemented using decision variables in the model. AC and FFV credits are included exogenously. Banking is not included in the main analyses, although this restriction is relaxed in a sensitivity analysis. Borrowing is not included in any of our analyses. (2)

Technology Cost Curves

The technical potential to improve fuel economy is represented by technology cost curves that take into account base year implementation of fuel economy technologies for all vehicle configurations as well as future potential applicability. Technology cost curves (comparable to those curves in U.S. EPA/U.S. DOT 2010) (3) use quadratic functions to specify the incremental retail price equivalent (RPE) for a relative increase in fuel economy (Figure 1). The RPE is intended to represent the long-run average cost of fuel economy technology, including a normal rate of profit. In effect, this implies either competitive or monopolistically competitive market conditions (firms may differentiate products, but on average, products are priced at their long-run average cost). Separate curves are provided for 20 vehicle classes, by engine technology (gasoline, diesel, and hybrid vehicles) and time period (short-, medium- and long-term).

Optimization Model Equations

The optimization model has multiple variants, depending on which assumptions are being used. The basic version of the model is defined as

[mathematical expression not reproducible] (2)

such that

[mathematical expression not reproducible] (3)

[e.sub.i] (t) = [e.sub.i] (t-1), if vehicle i is not redesigned in year t. (4)

The decision variables are fuel efficiency level [e.sub.i] (in fuel consumption or C[O.sub.2] emissions rate), and price adjustment [DELTA][p.sub.i] for each vehicle configuration for each model year. Other vehicle characteristics (e.g., vehicle weight, size and horsepower) are assumed to be unchanged over the planning horizon. The objective function (2) is accumulated total social surplus over the planning horizon, where r is the discount factor, MS is market size represented by the number of households, DCS is consumer surplus change per household relative to the base year, [S.sub.Buy] is the share of the market buying a new vehicle, and [S.sub.i] is conditional market share of vehicle configuration i given the choice to buy a new vehicle. Both [DELTA]CS and [S.sub.Buy] are functions of the decision variables and are calculated using the NMNL model (see the section on Consumer Demand). The second part of the objective function is producer surplus (total profit from pricing). Provision of credit transfer and trading mechanisms by the standards and our assumption of a competitive (or monopolistically competitive) market allows manufacturer-specific CAFE and emissions standards to be replaced by one industry-wide constraint(5), as if there were only one big manufacturer meeting the standards. In constraint (3) the term [e.sub.i]* is the fuel efficiency target of vehicle i, and N is the total number of vehicle configurations in the market. Constraint (4) ensures that a vehicle's fuel efficiency can be improved only in its redesign years. Note that constraints can be formulated either in terms of fuel economy or emissions rates since they are equivalent for regulating manufacturers' fleet fuel efficiency.

Appendix A derives optimality conditions for a simplified version of the optimization model ((2)-(4)), and shows that the total producer surplus from pricing is zero at optimality. Moreover, manufacturers' optimal pricing strategy can be expressed as

[DELTA][p.sub.i] (t) = [lambda](t)([e.sub.i](t)-[e.sub.i]* (t)),[lambda](t) [greater than or equal to]0, [for all]t, (5)

where [lambda] is the pricing rate (in units of $/gram C[O.sub.2] per mile for the case of emissions standards), which is proportional to the Lagrange multiplier (shadow price) for constraint (3). That is, manufacturers will charge more for vehicles whose fuel consumption/emissions rates are above the target levels specified by the standards, and subsidize vehicles whose fuel consumption/emissions rates are below them. The charge or subsidy for a vehicle is proportional to the deviation from its target. Thus, objective function (2) can be equivalently written in the following form:

[mathematical expression not reproducible] (6)

One advantage of this expression is that replacing the pricing variables [DELTA][p.sub.i](t), i = 1,..., N, with the pricing rate [lambda](t) yields many fewer decision variables.

Manufacturers may also convert an existing gasoline internal combustion engine (ICE) vehicle to a hybrid electric vehicle (HEV), which is more fuel-efficient but also incurs a price premium. This option is modeled using binary decision variables that indicate which vehicle configurations will be hybridized and when. The conversion cost (price premium) turns out to be a key parameter impacting the hybridization decision. Prior to 2014, this cost is assumed to be 1.5 times the vehicle's curb weight. Thus, for a 3,000-lb. car, the conversion cost would be $4,500. This drops to 1.0 times the curb weight in 2014 and 0.75 times the curb weight in 2018. These assumptions are consistent with Bandivadekar, et al. (2008), but have been brought forward ten years.

3.2 Consumer Demand

Consumer demand is represented by an aggregate-level NMNL model that assumes a representative consumer. All vehicle attributes except fuel efficiency and price are assumed to remain constant over the period of analysis. There is strong evidence that consumers undervalue fuel savings when making purchase decisions (Greene 2010; 2011; Alcott, Mullainathan and Tabuinsky 2012). This paper assumes that consumers determine the value of future fuel savings using a simple three-year payback rule, implying an undervaluing of the discounted present value of lifetime fuel savings by a factor of two or more. The net change in vehicle cost (incremental technology cost less fuel savings and plus any price adjustment) is the input to the NMNL model. Consumer surplus, vehicle sales, and market shares are calculated as functions of the change.

Choice alternatives are represented in detail at the level of make/model, engine and transmission configuration. Alternatives are grouped into nests as in Figure 2 to allow differential substitution patterns within and across nests. The nesting structure begins with a "buy/no-buy" decision at the top level, followed by the choice between a passenger vehicle and a work truck (pick-up or standard van). Subsequent levels distinguish among vehicle sizes and luxury versus standard vehicles. At the penultimate level, there are 20 different vehicle classes. The bottom level includes over 800 vehicle configurations. The utility expression for each vehicle configuration has two associated parameters: an alternative specific constant, and a price slope (which has a negative sign). For example, the utility for vehicle j in class k is

[U.sub.jk] = [A.sub.jk] + [B.sub.jk] ([C.sub.jk]-F[S.sub.jk] + [DELTA][p.sub.jk]) + [[epsilon].sub.jk] = [A.sub.jk] + [B.sub.jk] ([C.sub.jk]-F[S.sub.jk] + [lambda]([e.sub.jk]-[e.sub.jk]*)) + [[epsilon].sub.jk], (7)

Where

[A.sub.jk]: constant term for vehicle j in class k,

[B.sub.k]: price slope parameter for vehicles in class k,

[C.sub.jk]: incremental cost for improving fuel economy of vehicle j, and

F[S.sub.jk]: the amount of fuel savings from improved fuel economy, valued by consumers when making purchase decisions.

[DELTA][p.sub.jk]: manufacturer price adjustment, which is equal to [lambda]([e.sub.jk]-[e.sub.jk]*) as in equation (7).

The second term in (7) represents the change in utility due to improved fuel economy and/or price adjustments, and is zero by definition for the base year of 2010. The NMNL constant terms were calibrated to match the sales shares for vehicle configurations in 2010. In addition, constants for "buy/no buy" decisions in future model years were calibrated to match new light duty vehicle total sales projections from the Energy Information Administration's Annual Energy Outlook (U.S. DOE/EIA 2012) under the same set of assumptions. The NMNL price slopes were derived (4) from a set of assumed price elasticities based on results found in the literature.

4. RESULTS

4.1 Case Descriptions

The primary purpose of the analysis is to investigate the relative roles of technology adoption and pricing in complying with the standards. This is done by comparing changes in manufacturers' decisions under a policy case to those of a reference case. The reference case for this study assumes there are no CAFE or emissions standards in effect. Under this case, manufacturers make decisions in response to consumer demand with no constraints. They may still want to improve fuel efficiency, but only if the benefit of fuel cost savings to consumers outweighs the technology costs. We also adopt a base case that assumes the 2011-2016 and 2017-2025 CAFE/emissions standards are in place. The analysis period is 2011-2020. For this analysis, all cases use fuel cost projections from the Energy Information Administration's Annual Energy Outlook (U.S. DOE/EIA 2012).

As described previously, manufacturers are allowed to use both technology adoption (including converting vehicles to hybrids) and pricing to comply with the standards. Manufacturers can also employ AC and FFV credits by improving air conditioning systems and producing FFVs. Our model does not formulate these as decisions, but simply assumes they will be used. The credits are directly granted to manufacturers at the industry level according to the amount estimated by the EPA (page 25,409 of U.S. EPA/U.S. DOT, 2010), which essentially relaxes the stringency of the standards.

Cases 3 to 12 are formulated to test the sensitivity of results to changes in various model assumptions. Case 3, No AC and FFV Credits, disables manufacturers' option to obtain AC and FFV credits. Case 4 augments the base case by allowing manufacturers to bank compliance credits. As discussed in the methodology section, hybrid conversion cost is a key parameter for determining if it is cost effective to convert a gasoline vehicle to a hybrid. Case 6 uses base case assumptions, but assumes lower hybridization costs after 2016. Specifically, prior to 2014 this cost is assumed to be 1.5 times the vehicle's curb weight prior, dropping to 1.0 times the curb weight for 2014-2016, and 0.5 times the curb weight after 2016 (versus 0.75 for the base and reference cases). Case 5 is the same as Case 6, except it uses reference case assumptions, providing another basis for comparison.

As discussed in the section on Consumer Demand, assumptions about price elasticities are used to compute price slopes for the NMNL model. Cases 7 to 10 are designed to test the sensitivity of results to changes in the price elasticity assumptions used in the base (and reference) case. Low elasticity cases assume values are 20% lower than in the base case, and high elasticity cases assume values are 20% higher.

Fuel price projection is an important consideration when simulating fuel economy technology adoption. Thus, cases 11 and 12 are devoted to examining the sensitivity of model results to the change in fuel prices using EIA's AEO 2012 high fuel price projection (U.S. DOE/EIA 2012).

Case 13, the Feebate case, evaluates the impact of a feebate program in addition to standards. Feebates are added to vehicle prices, and are calculated according to the following formula: Feebate = feebate rate * (the vehicle's emissions rate-the vehicle's feebate benchmark). The feebate rate (5) is $20 per gram C[O.sub.2] per mile. The feebate benchmark is a policy decision with many possible options. For this study the feebate benchmarks are based on footprint using the same functions as those in the emissions standards. Feebates are assumed to be in effect for the whole analysis period of 2011-2020.

For all cases, we assume that (1) vehicle fuel efficiency and price are the only vehicle attributes that can be changed during the analysis period and that (2) consumers undervalue fuel savings from fuel economy improvement, i.e., they count only the first three years of savings.

4.2 Role of Technology Adoption and Pricing

Figure 3 provides a comparison of industry-wide sales weighted average C[O.sub.2] emissions for different cases. The curve ("Standards") plots the average emissions target level required by the standards, i.e., the sales-weighted average of the individual vehicle emissions targets. (6) The base case curve coincides with the (unconstrained) reference curve for years 2011 to 2015, and both exceed the requirements of the standards. The standards first become binding for the base case in 2016, (7) but manufacturers again over-comply in 2017 and 2018. The standards become binding again in 2019 and 2020. This type of pattern is consistent with multi-year planning in the presence of vehicle redesign constraints. Fuel economy technologies can only be added to a vehicle during a redesign period, which occurs once every four to five years. In addition, vehicles vary in their sales levels. The vehicles available for redesign in 2019 and 2020 (if any) may be poor candidates for helping to meet the standards in those years (e.g., due to low sales). Thus, it could be optimal to redesign vehicles to over-comply in an earlier year so that they then help with compliance in later years. This observation of temporary over-compliance illustrates that computer simulations can provide greater understanding of how vehicle markets might respond over time to regulations in terms of both short- and long-run effects. The overall long-run response is the primary concern, but understanding the reasons behind possible short-run deviations provides helpful context for performing policy analysis.

The banking case curve closely follows the reference and base case curves for years 2011-2015, but then diverges. For 2016, the average emissions from new vehicles slightly exceed the target levels. This is possible because credits from earlier years are banked and used to help meet 2016 standards. For 2017-2020 there is notable over-compliance, implying the existence of banked credits that could be used to meet compliance in later years. There is an important aspect of these results that requires additional explanation.

Because this case includes credit banking, the finite planning horizon in this optimization model can yield an end of period effect. Specifically, because any banked credits not used by the end of the planning period lose their value, the model will ensure they are used before the planning period is over. This practical requirement of the model can produce results near the end of the period that differ from what would be seen in the real world. For this reason, the banking results in Figure 3 were computed by extending the planning horizon to 2025. If the nominal planning horizon of 2011-2020 had been used, the end of period effect could have produced misleading results.

We next consider in more detail how technology adoption and pricing are used to improve the average fuel efficiencies of new vehicle sales for the cases in Table 1. Using technology to improve fuel efficiency affects average emissions in two ways: by changing the vehicle emission rates, and by shifting the sales shares. However, pricing can only affect emissions by shifting the sales shares. Table 2 displays the values of the pricing rates (k(t) in equation (5)) for each case, which directly determine the scale of manufacturers' price adjustments in each year. For example, the base case uses pricing in three years (2016, 2019, and 2020) for which the standards are binding (see Figure 3).

We would like to compare the amount of emissions reductions due to pricing versus those from technology adoption. To do this, we decompose the total emissions reductions for each case (relative to the reference case), into those from technology and pricing, respectively, using the following procedure: First solve the model and record the fuel efficiency, price adjustment level, and sales for each vehicle for each year. Calculate the sales-weighted average emissions and emissions reduction relative to the reference case. Second, constrain the fuel efficiencies in the model to equal the levels from the above solution, constrain the price adjustment levels to be zero, and re-run the model solver. Because this version of the model has no decision variables, the solver simply computes values of all model variables and then stops. Calculating sales-weighted average emissions and emissions reduction using this "solution" gives the emissions reduction due to technology alone. These two values are used to compute the proportions in Table 3. These results show that the proportion of emissions reduction due to pricing is relatively small for the base case, in the 4% to 6% range for those years when pricing is used.

If manufacturers are not permitted to obtain AC and FFV credits, meeting emission standards turns out to be more difficult. Pricing is required to meet the standards in 2012, and for every year but one after 2014 (see No AC and FFV credit case in Table 2). The proportion of emissions reduction due to pricing varies from 2% to 10% (Table 3).

The allowance of banking provides manufacturers with greater flexibility in meeting the standards. Under banking, pricing is no longer required in 2016 to achieve compliance. On the other hand, Tables 2 and 3 also demonstrate that, under banking, pricing might be used to accumulate additional credits even when the standards are not binding (e.g., in 2018).

The Low Hybridization Cost case in Tables 2 and 3 shows that a significant reduction in hybrid conversion cost after 2016 can greatly help manufacturers meet the standards and alleviate the need for pricing. The proportion of emissions reduction due to pricing is small, 1% to 4%.

The use of pricing in Low and High Elasticity cases is similar in pattern and scale to the base case. Note that the pricing rate (Table 2) for the high elasticity case is slightly smaller than the base case, and the reverse is true for the low elasticity case, as might be expected. At the same time, the proportion of emissions reductions due to pricing is higher in the high elasticity case, even though the price rate is smaller, which is an indication of how much more sensitive sales shifts are to price adjustments in this case. In the High Gasoline Price scenario, pricing is not used at all until 2020.

4.3 Feebates

A government feebate program can be implemented along with the standards to achieve greater emissions reductions. Feebates not only encourage consumers to buy more fuel-efficient vehicles but also incentivize manufacturers to improve the fuel economy of their vehicles. For comprehensive analyses of feebates, see Bunch et al. (2011) and Liu et al. (2011). Here we specifically focus on how feebates are related to manufacturer pricing strategies in the presence of standards.

Consideration of equation (5) reveals that manufacturers' optimal pricing strategy is equivalent to a self-applied internal feebate system, where the pricing variable [lambda] is the feebate rate and the emissions target [.esub.i]* is the feebate benchmark. Thus the implementation of a government feebate program might reduce the need for manufacturers to use pricing when faced with stringent standards.

As shown in Table 2, manufacturer pricing does not occur under a feebate program with a $20 feebate rate. At the same time, the presence of this feebate program yields additional emissions reductions as shown in Figure 4. Specifically, emissions are reduced by 20-30 grams of C[O.sub.2] per mile, relative to the base case. However, the reduction due to feebates diminishes in the outer years of the analysis period. In the base case, manufacturers start to apply pricing (see Table 2) in the late years when standards are increasingly binding. In the feebate case, feebates replace manufacturers' pricing strategies. As a result, the effective feebate rate is lowered to ($20-[lambda]), where [lambda] is the pricing variable in the base case. Thus the benefits from a feebate program will also depend on the stringency of standards. In scenarios with very stringent standards, government feebates will not produce additional reductions, but would help manufacturers to meet the standards.

4.4 Costs and Benefits of Standards to Consumers

Prior to 2016, the model results for essentially all case coincide with the reference case. However, eventually the standards become binding with average efficiencies higher than the reference case, so theory suggests that consumer surplus is lost in some fashion. The changes in vehicle offerings could make consumers worse off in a variety of ways. For any particular vehicle, the increase in the cost of technology could outweigh the (perceived) value of the increase in fuel savings and consumers could switch to other vehicles that they might not otherwise choose. Other consumers could decide to exit the new vehicle market completely, i.e., new vehicle sales decline.

By comparing results from the reference and base cases we can estimate the private costs and benefits of the standards, including fleet average incremental technology cost, fleet average present discounted value (PDV) of fuel savings over the vehicle' lifetime (at a discount rate of 7%), and fleet average three-year undiscounted fuel savings. Table 4 shows PDV of fuel savings are always larger than incremental technology cost, which suggests that the standards would not be binding if consumers were to value fuel savings over a vehicle's full lifetime. However, we adopt the view that consumers undervalue fuel savings when making purchase decisions, and assume they only value fuel savings from the first three years. Starting in 2016, three-year fuel savings are less than incremental technology cost, suggesting that technology cost exceeds the private benefit of fuel economy improvement. The standards therefore force fuel economy levels to be higher than they would otherwise be, i.e., the standards are binding constraints in the new vehicle market after 2015 as shown in Figure 3.

Table 5 reports the estimated new vehicle sales for the reference and base cases, and the sales reductions due to the standards. Consistent with theory, when the vehicle market is constrained by the standards, new vehicle sales are lower than they would otherwise be. However, the reductions are small, e.g., about 78/14395 = 0.5% of total sales in 2020.

4.5 Impacts of the Standards on Sales Mix

Another area of potential concern is the impact of standards on the sales mix of new vehicles. One conjecture is that a fleet-wide fuel efficiency improvement may make some fuel-inefficient vehicles relatively more attractive (e.g., sports cars are more fuel-efficient than before and may attract new buyers who like performance but also care about fuel cost) and shift sales toward these vehicles. Vehicle sales shifts depend on a number of factors such as the cost of the technology, the redesign decisions for other competing vehicles, and pricing decisions. We don't intend to analyze vehicle sales shifts at the disaggregate market level (e.g. make/model level) but to look at sales mix shifts at the fleet level: will the shifts make fleet average fuel efficiency better or worse? The motivation is to examine whether or not the sales mix shifts would partially offset energy savings and emissions reductions from the standards. As discussed later, our examination is limited.

The examination is done by first calculating the sales-weighted average emissions reduction [bar.[DELTA]]e for each policy case relative to its reference case

[bar.[DELTA]] = [[SIGMA].sub.i] ([S.sub.i.sup.0] [e.sub.i.sup.0] - [S.sub.i] [e.sub.i]), (8)

and then re-computing the emissions reduction number using the sales mix from the reference case

[bar.[DELTA]]e' = [[SIGMA].sub.i] ([S.sub.i.sup.0] [e.sub.i.sup.0] - [S.sub.i.sup.0] [e.sub.i]). (9)

In equations (8) and (9), [S.sub.i.sup.0] and [S.sub.i] are market shares of vehicle i in the reference and policy cases, respectively, [e.sub.i.sup.0] and [e.sub.i] are emissions rates of vehicle i in the reference and policy cases, respectively. If [DELTA]e is less than [DELTA]e', it implies that [[SIGMA].sub.i][S.sub.i][e.sub.i] > [[SIGMA].sub.i][S.sub.i.sup.0][e.sub.i] which in turn means the policy case has a higher mix of lower-MPG or higher-emitting vehicles than the reference case. We say a sales mix rebound effect has occurred in this case. This effect can be quantified by the relative change in the reduction numbers, i.e., ([bar.[DELTA]]e'-[bar.[DELTA]]e)/[bar.[DELTA]]e'. These ratios are reported in Table 6 (as percentages),where a positive ratio indicates the existence of a sales mix rebound effect, and negative ratios indicate that sales have been shifted toward fuel-efficient vehicles. Our results suggest that the sales mix rebound effect is minor (when it exists at all), and that sales tend to shift toward fuel-efficient vehicles in nearly all cases. The rebound effect occurs only in the case of banking, where credits may be used for compliance in lieu of shifting sales toward more fuel-efficient vehicles using pricing.

Table 6 only provides a rough estimate of the impact of sales mix shift on emissions reduction. Calculations in equation (8) and (9) do not consider heterogeneity of VMT (vehicle miles traveled) among vehicles. Fuel inefficient vehicles are presumably driven less than fuel efficient vehicles. If a sales mix rebound effect exists, its impact on total emissions reductions and fuel consumption will be dampened by the lower VMT of fuel inefficient vehicles.

4.6 Impacts of the Standards on Fleet Average Vehicle Footprint

Generally speaking, smaller vehicles have higher fuel efficiency on average, and in the past there have been concerns that manufacturers might choose to comply with standards either by shifting sales to smaller, more fuel efficient vehicles or by "downsizing" existing vehicles. Such shifts can be viewed as another cost in the form of reduced consumer surplus, and also raises concerns among some about safety. At the same time, fuel efficiency can vary among vehicles with the same footprint size. The new footprint-based form of the standards is intended to induce shifts across a range of vehicle sizes, and address the concern that sales mixes might shift to smaller vehicles. An important feature of our model is that it includes the level of detail required to explore this issue.

Table 7 reports the percentage change of the industry-wide sales weighted average footprint for each case relative to the average footprint from its corresponding reference case. The results show that there is in fact a small shift in average footprint size; however, the change is minimal in all cases. The average footprint size does in fact show a small decrease in all those years where pricing is used to comply with standards--see Table 2. The footprint-based new standards have removed the incentive for manufacturers to downsize vehicles, but the pricing mechanism used by manufacturers for standards compliance appears to induce small sales shifts toward smaller size vehicles, which are, on average, more fuel efficient.

5. CONCLUSION

Our analysis indicates that technology adoption is likely to play the predominant role in meeting new CAFE and emissions standards, consistent with the intention of the policy. The use of pricing to induce sales shifts is minor for most of the analysis period, but may be employed in outer years if cost-effective technologies are less plentiful. (8) In those instances when pricing is used, the percentage of emissions reduction due to pricing is small, at around 4% to 6%. It suggests that compared with the option to adopt readily available fuel saving technologies, pricing is a relatively costly way to comply with the standards. Policy provisions that increase the flexibility in how standards can be met greatly reduce the use of pricing by manufacturers. Removing AC and FFV credits increases the use of pricing strategies by manufacturers. Allowing banking actually yields average emission rates below base case levels. This is because banking motivates manufacturers to adopt more fuel-efficient technologies, and even employ pricing to accumulate credits so that they can be used to meet compliance requirements in later periods. Other factors could also play an important role. The availability of more cost-effective advanced technologies (hybrids in this study) after 2016 would substantially reduce the need for manufacturers to use pricing to meet the standards. Implementing feebates along with standards can bring additional emissions reductions, but the benefit may diminish over time if feebates act as a replacement for manufacturers' pricing strategies when the standards are increasingly binding, as our results indicate.

Because the standards increase over time, they become binding in essentially all policy cases given the technology assumptions. This necessarily implies a loss of consumer surplus that could come in the form of increased net vehicle cost, switching to less desirable vehicles, or exit from the new vehicle market. The average cost of vehicle technology exceeds the average perceived benefit of fuel savings, and this gap increases over time. However, the gap is relatively small on a per vehicle basis. On the other hand, the full value of fuel savings to society is substantial and exceeds vehicle technology incremental cost. New vehicle sales decline over time, but this effect is also relatively small.

The simulation in this study indicates that the new standards are likely to induce a slight sales shift toward fuel-efficient vehicles. Examining fleet average footprints shows only minor sales shifts toward smaller sized vehicles, and this occurs only in some periods where manufacturers have difficulty meeting standards and need to use pricing.

The analysis has multiple caveats. First, the assumption of full credit trading among cars and trucks and among manufacturers is highly idealized, although it is believed to be close to the real credit market in the long run. If the credit trading market turns out to be inefficient, individual manufacturers may still face binding standards and apply pricing strategies. Second, some technologies that can be used to improve efficiency could instead be used to improve performance. This study does not attempt to address the potential tradeoff between fuel efficiency and performance, and assumes that these technologies are all used to improve fuel efficiency. Although including this feature might be desirable, there is a notable lack of consensus in the literature on how consumers might value, e.g., horsepower versus fuel economy. One specific complication is that vehicle performance and size can produce relative, (9) as well as absolute, utility, implying that they may currently be over-consumed in the market. Third, our technology package includes only proven technologies for conventional vehicles and HEVs. The potential impacts of plug-in hybrid electric vehicles (PHEVs) and other advanced technology vehicles were not addressed in this analysis. Breakthroughs in advanced technologies would further reduce the need for applying pricing strategies. Fourth, although we report model results for 2011-2020, the focus of the paper is on 2011-2016 standards. In view of the limitation of our technology package in representing advanced technologies, the model results for post 2016 years are less reliable. Finally, the representative consumer choice model used in the paper does not explicitly represent heterogeneous consumer preferences. This may be a fruitful area of future research, especially if it can be shown that a more detailed representation of consumer taste leads to more accurate predictions.

ACKNOWLEDGMENTS

The study reported in this paper was sponsored in part by the California Air Resources Board and the U.S. Department of Energy. Opinions and views expressed are those of the authors and do not necessarily reflect those of either agency.

APPENDIX A. OPTIMALITY CONDITIONS OF THE MODEL

Consider the following optimization model, which is a slightly simplified version of equations ((2)-(4)):

[mathematical expression not reproducible] (10)

[mathematical expression not reproducible] (11)

For simplicity and convenience of derivation, we have dropped the coefficient (1 + r[).sup.-1]MS(t) and the redesign constraint (4). We next provide more detailed expressions for [DELTA]CS, [S.sub.Buy], and [S.sub.i], which are functions of vehicle utilities. Again, for simplicity, we assume a two-level nested logit structure for consumer demand (level 1: vehicle configuration, and level 2: Buy or No Buy). The derivation can be extended to cases with additional levels, but the major results derived here are still applicable.

Share of vehicle i, [S.sub.i], is calculated by

[mathematical expression not reproducible] (12)

with utility function for vehicle i, [U.sub.i], expressed as

[U.sub.i] (t) = [A.sub.i] + [B.sub.v] [[g.sub.i.sup.t] ([e.sub.i](t)) + [DELTA][p.sub.i](t)], [for all]i,t, (13)

where [A.sub.i] is a constant term for vehicle i, [B.sub.v] is the price slope or price coefficient for choices among vehicle configurations, and [g.sub.i] is the so-called generalized cost which is the net cost of improving vehicle i's fuel economy from [e.sub.i](0) to [e.sub.i](t). For example, in equation (7), [g.sub.i] is the technology cost less fuel savings from improved fuel economy.

The share of households buying a new vehicle, [S.sub.Buy], is calculated by

[mathematical expression not reproducible] (14)

with utilities for buying a new vehicle, [U.sub.Buy], and not buying a new vehicle, [U.sub.No_Buy], expressed as

[mathematical expression not reproducible] (15)

[U.sub.No_Buy] = 0, (16)

where [A.sub.Buy] is the constant term for the nest of buying a new vehicle and [B.sub.0] is the price slope or price coefficient for the "buy/no buy" choice.

Finally, consumer surplus at year t is given by

[mathematical expression not reproducible] (17)

plus an unknown constant. The optimization is defined using the change in consumer surplus relative to the base year, [DELTA]CS(t), which can be treated as CS(t) minus another constant.

Denote the Lagrangian multiplier associated with the first constraint of the optimization as [lambda](t) and ([e.sub.i](t)-[e.sub.i]* (t)) as [DELTA][e.sub.i](t). The Lagrangian function is

[mathematical expression not reproducible] (18)

The first order conditions are represented by the following equations (suppressing subscript t for simplicity)

[mathematical expression not reproducible] (19)

[mathematical expression not reproducible] (20)

[lambda] [greater than or equal to] 0 (21)

[mathematical expression not reproducible] (22)

[mathematical expression not reproducible] (23)

From equation (19), we get

[mathematical expression not reproducible] (24)

which implies

[S.sub.Buy] [DELTA][p.sub.i]-[lambda][DELTA][e.sub.i] = [S.sub.Buy] [DELTA][p.sub.j]-[lambda][DELTA][e.sub.j], [for all]i,j, (25)

[mathematical expression not reproducible] (26)

and

[DELTA][p.sub.i] = [gamma]/[S.sub.Buy] [DELTA][e.sub.i] = [lambda][DELTA][e.sub.i,]. (27)

Since the last two terms in equation (27) are equal to zero, the following equation holds

[partial derivative][g.sub.i]/[partial derivative][e.sub.i] = - [gamma]/[S.sub.Buy] = - [lambda], [for all]i (28)

Thus, Equation (27) tells us that manufacturers' optimal pricing strategy is to impose an internal feebate system in which the feebate rate ([lambda = [gamma]/[S.sub.Buy]]) is proportional to the marginal value of relaxing the emissions constraint (i.e. the shadow price of the constraint) and the feebate benchmark is the emissions target [e.sub.i]*. Equation (26) states that the producer surplus from pricing is zero, and equation i (28) says that at the optimum, the marginal generalized cost of emission reduction is the same for all vehicles and equal to the pricing rate. Moreover the complementarity condition [mathematical expression not reproducible] implies that the pricing rate is zero if the emission constraint is nonbinding.

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(U.S. EPA/U.S. DOT) U.S. Environmental Protection Agency and U.S. Department of Transportation (2012). "2017 and Later Model Year Light-Duty Vehicle Greenhouse Gas Emissions and Corporate Average Fuel Economy Standards, Final Rule." Federal Register, 77(199), Washington, DC.

Changzheng Liua (*), David L. Greene (a), and David S. Bunch (b)

(a) Oak Ridge National Laboratory, 2360 Cherahala Boulevard, Knoxville, TN 37932, USA.

(b) Graduate School of Management, University of California, Davis, One Shields Avenue, Davis, CA 95616.

(*) Corresponding author. E-mail: liuc2@ornl.gov.

http://dx.doi.org/10.5547/01956574.35.3.4

(1.) EPA emissions standards allow a one-time C[O.sub.2] carry-forward beyond 5 years, i.e., credits generated from model year 2010 through 2016 can be banked up to model year 2021.

(2.) Including banking and borrowing substantially increases the complexity and running time of the model. Substantial testing and experimentation during the model development phase revealed that these features had minimal or no impact on the results, their interpretation, or conclusions.

(3.) The cost estimates are based on a combination of full vehicle simulation modeling of packages of technologies, which estimates synergies directly, and lumped parameter modeling for individual technologies which insures that there is no double counting of benefits.

(4.) The price slopes for a logit model are obtained using the equation: [B.sub.i] = [[eta].sub.i]/[P.sub.i](1-[S.sub.i]), where [[eta].sub.i] is the elasticity of the choice probability or market share of vehicle i with respect to its price, [B.sub.i] is the price slope, [P.sub.i] is vehicle price and [S.sub.i] is market share. Procedures for nested logit are similar: for more details, see Bunch et al. (2011) and Greene et al. (2005).

(5.) The feebate rate can be designed to reflect the size of externalities and market imperfections. For example, the $20 per gram C[O.sub.2] per mile feebate rate roughly corresponds to a carbon price of $50/tC[O.sub.2], plus an oil import premium of $14/bbl and a charge of $1.2/gal to correct consumers' undervaluation of fuel savings (see table 7.2 of Bunch et al., 2011).

(6.) Because of the way the regulations are defined, the average emissions target varies as a function of the actual sales, but sales can shift based on manufacturers' decisions. To simplify matters, we actually plot the average emissions target using the base case sales.

(7.) In general, many different factors can influence whether or not standards are binding in a given year, including: the stringency level of the standards, the specific pattern of when vehicles are available to be redesigned, technology improvement costs, and fuel savings benefits. One particular factor contributing to constraints binding in 2016 is the expiration of FFV credits. The 2016 final rule states "For the GHG program, as proposed, EPA will allow FFV credits in line with EISA limits, but only during the period from MYs 2012 to 2015".

(8.) As an anonymous referee points out, the notion that cost-effective technologies may be less plentiful in outer years presupposes a static supply of fuel-efficient technologies. The standards may spur technology innovation which would resupply the market with cost-effective technologies and reduce the need for pricing.

(9.) If a part of the value of horsepower is derived from having a more powerful vehicle than others, increasing the horsepower of all vehicles will not produce as great a gain in utility as it would have if all of the value of horsepower were absolute. Thus, the consumer opting for a vehicle with higher horsepower will gain less utility than expected if others do the same.
Table 1: Cases Analyzed in the Study

    Case Name                    Case Description

1   Reference                    No Standards
2   Base                         Standards in place; manufacturers use
                                 both technology adoption and pricing in
                                 response to standards
3   No AC and FFV Credits        Base case assumptions and manufacturers
                                 are not permitted to obtain AC and FFV
                                 credits
4   Banking                      Base case assumptions and manufacturers
                                 can bank compliance credits for future
                                 use.
5   Reference-Low Hybridization  Reference case assumptions and lower
    Cost                         hybridization cost
6   Low Hybridization Cost       Base case assumptions and lower
                                 hybridization cost
7   Reference-Low Elasticity     Reference case assumptions and lower
                                 price elasticities
8   Low Elasticity               Base case assumptions and lower price
                                 elasticities
9   Reference-High Elasticity    Reference case assumptions and higher
                                 price elasticities
10  High Elasticity              Base case assumptions and higher price
                                 elasticities
11  Reference-High Oil Price     Reference case assumptions and high oil
                                 price
12  High Oil Price               Base case assumptions and high oil
                                 price
13  Feebates                     Base case assumptions and a feebate
                                 program in place

Table 2: Value of Manufacture Pricing Rate ([lambda] in equation (5),
unit: $/gram C[O.sub.2]/mile) in Each Case (Blank cells indicate zero
values)

Case Name               2011  2012  2013  2014  2015  2016  2017  2018

Base                                                   8.1
No AC and FFV Credits         3.1               9.1   14.0         8.7
Banking                                                           13.3
Low Hybridization Cost                                 4.9
Low Elasticity                                         9.2
High Elasticity                                        7.2
High Gasoline Price
Feebate

Case Name               2019  2020

Base                    12.6  19.2
No AC and FFV Credits   29.4  34.0
Banking                 20.0  20.3
Low Hybridization Cost   4.3  13.1
Low Elasticity          12.9  20.2
High Elasticity         12.3  18.3
High Gasoline Price            8.8
Feebate

Table 3: Proportion of Emissions Reduction versus Reference Case Due to
Pricing (Percentage; Blank cells indicate zero values)

Case Name               2011  2012  2013  2014  2015  2016  2017  2018

Base                                                  6.3
No AC and FFV Credits         9.9               7.1   8.8         2.3
Banking                                                           4.7
Low Hybridization Cost                                3.9
Low Elasticity                                        5.6
High Elasticity                                       6.7
High Gasoline Price

Case Name               2019  2020

Base                    4.0   5.0
No AC and FFV Credits   6.5   6.3
Banking                 5.8   5.2
Low Hybridization Cost  1.4   3.6
Low Elasticity          3.2   4.1
High Elasticity         4.8   5.9
High Gasoline Price           2.2

Table 4: Technology Cost vs. Fuel Savings

$/veh                    2011  2012  2013  2014  2015  2016  2017  2018

Technology Cost           4     8    25    42     52   122   246   295
PDV of Fuel Savings      15    23    52    91    139   284   537   635
(7% discount rate)
Three Year Fuel Savings   6     9    21    37     56   114   216   256

$/veh                    2019  2020

Technology Cost          398    582
PDV of Fuel Savings      772   1046
(7% discount rate)
Three Year Fuel Savings  311  422

Table 5: Impact on Total Sales (thousands)

Case Name   2011   2012   2013   2014   2015   2016   2017   2018

Reference   11338  11686  13132  13855  14346  14734  14678  14320
Base        11338  11686  13130  13853  14346  14728  14665  14303
Difference      0      0     -2     -3      0     -6    -13    -17

Case Name   2019   2020

Reference   14417  14395
Base        14378  14318
Difference    -39    -78

Table 6: Sales Mix Rebound Effect of the Standards (Percentage, see text
for the definition of this measure; Blank cells indicate zero values)

Case Name               2011  2012   2013  2014  2015  2016  2017  2018

Base                                                   -6.6  -0.1  -0.1
No AC and FFV Credits         -10.8  -0.1  0.1   -7.5  -9.4  -0.3  -2.6
Banking                                           0.8   2.1   1.6  -4.1
Low Hybridization Cost                                 -4.0
Low Elasticity                                         -5.9  -0.1  -0.1
High Elasticity                                        -7.2  -0.1  -0.1
High Gasoline Price

Case Name               2019  2020

Base                    -4.3  -5.6
No AC and FFV Credits   -7.3  -6.8
Banking                 -5.6  -4.7
Low Hybridization Cost  -1.5  -3.9
Low Elasticity          -3.4  -4.5
High Elasticity         -5.2  -6.6
High Gasoline Price           -2.0

Table 7: Impact of Standards on Fleet Average Footprint (Percentage
change; Blank cells indicate zero values)

Case Name               2011  2012  2013  2014  2015  2016  2017  2018

Base                                                  -0.3
No AC and FFV Credits         -0.1              -0.2  -0.4  -0.1  -0.2
Banking                                          0.1   0.1   0.1  -0.3
Low Hybridization Cost                                -0.2
Low Elasticity                                        -0.2
High Elasticity                                       -0.3
High Gasoline Price

Case Name               2019  2020

Base                    -0.3  -0.4
No AC and FFV Credits   -0.5  -0.6
Banking                 -0.4  -0.4
Low Hybridization Cost  -0.1  -0.3
Low Elasticity          -0.2  -0.3
High Elasticity         -0.3  -0.5
High Gasoline Price           -0.2
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Author:Liua, Changzheng; Greene, David L.; Bunch, David S.
Publication:The Energy Journal
Date:Jul 1, 2014
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