### CONSUMER VEHICLE CHOICE MODEL DOCUMENTATION

David L. Greene Changzheng Liu

March 2012

Prepared for U.S. ENVIRONMENTAL PROTECTION AGENCY

Prepared by OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37831-6283

Managed by UT-BATTELLE, LLC for the U.S. DEPARTMENT OF ENERGY under contract DE-AC05-00OR22725iii 

### TABLE OF CONTENTS

LIST OF FIGURES ...................................

................................................... .................................. v LIST OF TABLES ....................................

................................................... ................................... v ACKNOWLEDGEMENT ...................................

................................................... ...................... vii
1. Introduction ..................................

................................................... ........................................... 1
1.1 Project Overview ..................................

................................................... ......................... 1
1.2 Model Usage and Results Interpretation ............

................................................... ........... 2
1.2.1 Model Functionality and Usage .....................

................................................... ........ 2
1.2.2 Prediction Errors .................................

................................................... ................... 3 2. Literature Review on New Vehicle Type Choice Mo deling ............................................ ......... 7 2.1 Aggregate Demand Models .......................

................................................... ........................ 7 2.2 Discrete Choice or Random Utility Models ......

................................................... ................. 9 2.2.1 Multinomial Logit ..........................

................................................... .......................... 10 2.2.2 Probit and Nested Multinomial Logit ........

................................................... .............. 11 2.2.3 Mixed Logit Model (MLM) ....................

................................................... ................. 14 2.3 Summary Observations ..........................

................................................... .......................... 18 3. Methodology ...................................

................................................... ...................................... 21 3.1 Nesting Structure .............................

................................................... ................................ 21 3.2 Equations......................................

................................................... .................................... 24
3.2.1 Prelude .....................................

................................................... ................................. 24 3.2.2 Two-level CVCM Equations ...................

................................................... ................ 25 3.2.3 Full Scale CVCM Equations ..................

................................................... .................. 26 3.3 Value of Fuel Economy .........................

................................................... .......................... 28
3.4 Calibration....................................

................................................... .................................... 29
3.4.1 Generalized Cost Coefficient Determination ..

................................................... .......... 29
3.4.2 Constant Term Calibration ..................

................................................... ..................... 35 4. Implementation and User Guide .................

................................................... .......................... 37
4.1 User Interface ................................

................................................... ................................... 37 4.1.1 Input .......................................

................................................... ................................... 37 4.1.2 Output ......................................

................................................... ................................. 39
4.2 Interaction with OMEGA ........................

................................................... ........................ 40
References ........................................

................................................... .......................................... 41 Appendix A: Derivation of Nested Logit Model Equat ions and Relevant Properties ................. 45iv

Appendix B: Model Sensitivity analysis............

................................................... ....................... 49
B.1 The Distribution of Own Price Elasticities ....

................................................... ................. 49 B.2 Sensitivity Analysis ..........................

................................................... ............................... 52v 

### LIST OF FIGURES

Figure Page

1. Nested Multinomial Logit Structure of Consumer Choi ce Model.................................... 21
2. Distribution of Elasticities ......................

................................................... ....................... 50



### LIST OF TABLES

Tables Page

1. Demand Elasticities of Kleit's Vehicle Class Demand Model (Kleit, 2004) ...................... 7
2. Market Segment and Nameplate Own Price Elasticities Estimated by Bordley (1993) ..... 8
3. Vehicle Class Definition in the CVCM ..............

................................................... ........... 23
4. Own Price Elasticities of New Vehicle Demand in the Literature ................................... 33
5. Generalized Cost Coefficient Calibration ..........

................................................... ............ 34
6. Format of Vehicle Sheet ...........................

................................................... ..................... 38
7. Structure of “GlobalParameter” Sheet ..............

................................................... ............. 39
8. List of Vehicles with Very High Elasticities (in ab solute value) ..................................... . 50
9. Descriptive Statistics of Elasticities ............

................................................... ................... 51
10. Sensitivity Analysis Results ......................

................................................... ..................... 53
11. Market Shares by MPG Decile .......................

................................................... ............... 53
12. Rebound Effect ....................................

................................................... .......................... 54vivii 

### ACKNOWLEDGEMENT

This document was prepared as part of a research pr oject sponsored by the U.S. Environmental Protection Agency (EPA). The authors would like to express their gratitude to Michael Shelby, Sharyn Lie and Gloria Helfand, EPA, for the leaders hip and support in developing the Consumer Vehicle Choice Model (CVCM). The authors are gratef ul to Gloria Helfand and Michael Shelby for valuable comments on an earlier draft of this d ocumentation. The authors also thank Ari Kahan and Richard Rykowski, EPA, for reviewing and testing the CVCM. We are especially grateful to our peer reviewers, Professor David Bun ch, Professor Trudy Cameron, and Dr. Walter McManus, for a very thorough and helpful rev iew of the model and documentation. Any remaining errors or deficiencies are the authors’ r esponsibility.viii1 

### 1. INTRODUCTION

1.1 PROJECT OVERVIEW

In response to the Fuel Economy and Greenhouse Gas (GHG) emissions standards, automobile manufacturers will need to adopt new technologies t o improve the fuel economy of their vehicles and to reduce the overall GHG emissions of their fl eets. The U.S. Environmental Protection Agency (EPA) has developed the Optimization Model f or reducing GHGs from Automobiles (OMEGA) to estimate the costs and benefits of meeti ng GHG emission standards through different technology packages. However, the model d oes not simulate the impact that increased technology costs will have on vehicle sales or on c onsumer surplus. As the model documentation states, “While OMEGA incorporates fun ctions which generally minimize the cost of meeting a specified carbon dioxide (CO 2 ) target, it is not an economic simulation model wh ich adjusts vehicle sales in response to the cost of th e technology added to each vehicle.”

Changes in the mix of vehicles sold, caused by the costs and benefits of added fuel economy technologies, could make it easier or more difficul t for manufacturers to meet fuel economy and emissions standards, and impacts on consumer surplu s could raise the costs or augment the benefits of the standards. Because the OMEGA model does not presently estimate such impacts, the EPA is investigating the feasibility of develop ing an adjunct to the OMEGA model to make such estimates. This project is an effort to devel op and test a candidate model. The project statement of work spells out the key functional req uirements for the new model.

“ORNL shall develop a Nested Multinomial Logit (NMN L) or other appropriate model capable of estimating the consumer surplus impacts and the sal es mix effects of GHG emission standards. The model will use output from the EPA’s Optimization M odel for reducing Emissions of Greenhouse gases from Automobiles (OMEGA), including changes i n retail price equivalents, changes in fuel economy, and changes in emissions, to estimate thes e impacts. ...The model will accept approximately 60 vehicle types, with the flexibilit y to function with fewer or more vehicle types, and will use a 15 year planning horizon, matching the O MEGA parameters. It will be calibrated to baseline sales projection data provided by the EPA and will include a buy/no-buy option to simulate the possibility that consumers will choose to keep their old vehicle or to buy a used vehicle. The fir st version of the model must be completed by the sprin g of 2011. Additional versions may be created in the future, pending further discussion and negotiat ion between the consultant and the EPA.”

Briefly, given changes in each vehicle’s price and fuel economy, the model

(1) calculates impacts of standards on vehicle sale s mix, and (2) calculates cost of standards in terms of consum er surplus.

The initial version of the model, at least, is not intended to project market trends due to other factors, although this might be a fruitful area for future research and development. The goal of this project is to create a simple model to test th e concept of incorporating market share and consumer surplus changes to the OMEGA model and to produce a working initial model.2

A research team at Oak Ridge National Laboratory (O RNL) has designed and implemented a Consumer Vehicle Choice Model (CVCM) for the projec t based on NMNL theory with a representative consumer. This document will detail CVCM design principles, model equations, parameter calibration, implementation and user guid e. Specifically, Section 1.2 further explains CVCM functionality and intended usage and summarize s possible sources of prediction errors. Section 2 reviews relevant new vehicle type choice models in the literature and compares their merits and limitations. Then Section 3 describes NM NL equations and model calibration procedure. Finally, Section 4 gives instructions t o use the model.

1.2 MODEL USAGE AND RESULTS INTERPRETATION

1.2.1 Model Functionality and Usage

The CVCM is intended to perform specific functions as an adjunct to the EPA’s OMEGA model. As such, it has been designed to use the same theor etical basis and premises as the OMEGA model. Specifically, it has been designed to self- calibrate to the baseline vehicle sales distribution used by OMEGA and, given estimates for each individual vehicle of (1) changes in vehicle fuel economy, and (2) changes in vehicle pr ices, it:

1. calculates impacts of those changes on vehicle sale s and the distribution of vehicle sales and the resulting impact on manufactu rers’ abilities to meet fuel economy standards and, 2. calculates changes in consumers’ surplus as a conse quence of the changes in fuel economy and vehicle purchase cost.

The CVCM is not intended to be a tool for forecasti ng the future vehicle fleet. There is no doubt that, over time periods longer than a few years, ve hicle designs will come and go, new vehicle models will be introduced and others retired, new m anufacturers will enter the U.S. market, existing manufacturers will exit, and there will be mergers and divestitures. However, predicting such events is outside the scope of the CVCM. It i s also likely that over future time periods manufacturers will introduce new types of vehicles: plug-in hybrid, battery electric, hydrogen fuel cell vehicles and perhaps vehicles that are no t foreseen at the present time. The CVCM was not designed to predict consumers’ acceptance of th ese advanced technology vehicles. This capacity was left for future research and developme nt.

The CVCM was developed to test the concept of predi cting the differential sales impacts of fuel economy changes together with price changes brought about by fuel economy standards. It is intended to produce credible estimates of such chan ges to determine whether they may have important implications for manufacturers’ abilities to meet the standards and for consumer wellbeing. Given the EPA’s need for periodic and timel y analyses to support its responsibilities for GHG emissions and fuel economy rulemakings, the CVC M should be capable of being readily calibrated to new data sets and updated with new sa les and fuel economy data.

Given the intended purpose and functions of the mod el, it is most appropriately used for estimating changes in the following variables relative to the baselin e values:3

1. Market-wide consumers’ surplus, total sales, total gross revenue, and fleet average miles per gallon (MPG) and GHG emissions, 2. Sales, average MPG and GHG emissions by manufacture r, and 3. Sales by market segment.

The CVCM models vehicle type choice at the most com plete level of detail possible, corresponding to the level of detail at which fuel economy measurements are made by the EPA. Given that the price sensitivity of consumers’ choi ces is greatest at the lowest 1 level of the NMNL nest, i.e., when vehicles are the closest subs titutes, modeling at the greatest feasible level of detail can capture the full range of sales mix s hifts. If vehicle type choice were modeled at a more aggregate level, the modeling process may be o pen to the questions about whether it misses important sales mix changes that would have been ev ident had the model operated at a greater level of detail. However, the CVCM prediction at th e lowest level (i.e., make, model, engine and transmission configuration) is most sensitive to ch anges in input data and model parameters. Reporting results at this level may imply a higher degree of precision than is appropriate. Thus, we recommend reporting CVCM predictions at more agg regate levels.

The model provides highly detailed results. For re asons discussed in Section 1.2.2, the model’s predictions are unlikely to be as precise as is sug gested from the model output. The detail is provided for situations where the CVCM would be use d iteratively with OMEGA, where the detail may provide advantages for model convergence . On the other hand, when final results are presented for consideration, false precision should be avoided. The sensitivity analyses we have done (see Appendix B) suggest that outputs should b e presented to no more than three digits and perhaps only two in the case of consumers’ surplus impacts and impacts on total vehicle sales.

1.2.2 Prediction Errors

The aggregate, or representative consumer, NMNL mod el makes simplifying assumptions about consumer behavior. Since consumer behavior is comp lex, we have focused the modeling initially on the decisions by consumers to trade-of f fuel savings for higher vehicle prices, holding all other vehicle attributes constant. A change in a particular vehicle’s fuel economy is translated into a change in price equivalent (present value do llars) based on a model or theory of how consumers value fuel economy. The change in the pr esent value of future fuel costs perceived by consumers is added to the estimated change in th e vehicle’s price 

### p ∆ . A price sensitivity parameter, B , translates the resulting net change in present va lue into a change in a utility index that determines a vehicle’s market share. The chang e in utility for the i th vehicle in nest j, ij U ,is the following, where PV represents whatever functio n is chosen to transform a change in fuel economy to a change in the present value of fuel sa vings considered in the vehicle purchase decision.


## { }



# ( ) ij j i 

### U B p PV fuel savings ∆ = ∆ − (1)

1 In this document, the higher/lower levels are refe rred to by their relative positions in the nested t ree/nesting structure (Figure 1 in chap. 3) which has a buy/no-buy decisi on at the top/highest level and vehicle configurati ons (combinations of make, model, engine, and transmission) at the bottom/lowe st level. It implies that the lower levels in the t ree are more disaggregated.4

The NMNL model is a tool for estimating changes in market shares as a function of changes in the present value (in dollars) of vehicles. If the changes are small relative to the prices of the vehicles and if the price sensitivity parameters ar e reasonably accurate, the NMNL model should give reasonably accurate predictions. 2 Prediction errors arise from incorrectly estimati ng changes in the utility index, caused either by erro rs in the estimation of the role of a change in fuel economy or inaccurate specification of the pri ce sensitivity parameter, B. Such errors have a specific functional form in logit models.

For illustrative purposes, consider a simple multin omial logit (MNL) model (a derivation of the NMNL model that begins with a specification of the simple MNL model can be found in section 2.2.1 below). 3 The derivative of a vehicle’s market share S i with respect to a change in its utility index is the following:

2

1 ( ) i

j U i i i

N U i i j dS d e S S dU dU e

= = = − 

# ∑ (2)

Since, in general, S i (which is between 0 and 1) will be approximately tw o orders of magnitude larger than 2

( ) i S , the change in market share dS i is approximately the change in utility weighted by the vehicle’s market share, S i dU i . As changes in utility are propagated up the nest ing structure (as inclusive values, or expected utility changes) this simple relationship applies at each step. Since a shock (error) in the utility index o f vehicle i is a change in its utility, the impact of errors in the utility index on the predicted share is proportional to the market share of vehicle i

. Prediction errors will be negatively correlated bet ween alternatives within a nest. At the lowest level of nesting, shocks to the utilities of indivi dual vehicles are independent and identically distributed, in theory. However, the errors in one vehicle’s utility index induce a change in the predicted shares of other vehicles that are negativ ely related to changes for the initial vehicle. The error term of a utility function directly induc es a change in utility so its impact can be described by the derivative of the share of vehicle i with respect to a change in (shock to) the utility of vehicle j

.



## ( ) 2

1 1 1 i j j

i

j U N U U

U i i j

N U j j j j S e e e e S S U U e −

=

=   ∂ ∂

= = − = −   ∂ ∂  



## ∑ ∑ (3)

Thus, a shock to the utility index of vehicle j induces a negative error in the prediction of the share of vehicle i that is proportional to the product of their share s, and prediction errors within a nest are negatively correlated. Because of this, e rrors in utility functions within a nest will tend to cancel, and the sum of the shares within a nest (i.e., the share of that nest) will have a smaller relative error than the relative errors of the indi vidual vehicles within the nest.

2 There is reason to expect the changes in dollar va lue to be small relative to the vehicle’s price in that they will, in general, be comprised of an increase in price (>0) minus a present value of future fuel savings (also >0).

3 Each lowest level nest of a NMNL model is a simple multinomial logit model.5

In reality, prediction errors can arise from a numb er of simplifications in the CVCM, errors in parameters and errors in input data.

1. Non-optimizing consumer behavior 2. Aggregate NMNL model applied to heterogeneous consu mers 3. Errors in NMNL model structure 4. Errors in NMNL parameters 5. Omitted variables (including manufacturer pricing d ecisions) 6. Inaccuracies in baseline sales data
7. Inaccuracies in OMEGA model predictions 8. Unanticipated technological innovations over time 9. Changes in consumers’ behavior over time

There is substantial evidence that consumers’ decis ion-making in markets for energy efficiency, and in particular fuel economy, may not correspond to the classical rational economic model (e.g., Jaffe and Stavins, 1994; Greene, 2009). A r eview of the econometric evidence found contradictory and inconclusive results (Greene, 201 0). If, as Greene (2011) proposes, consumers’ decisions about fuel economy are best described by prospect theory of behavioral economics, then the theory of utility maximization that underl ies random utility models like the NMNL model would not be the most appropriate context for evaluating consumers’ surplus impacts. Further theoretical and empirical research is neede d to better understand how consumers' value fuel economy and how fuel economy and emissions sta ndards affect consumers' surplus.

The CVCM is a market or representative consumer NMN L. It does not explicitly represent differences in consumers’ preferences. The only re cognition of differences in consumers’ tastes is in the logit formulation itself which assumes th at each individual perceives a different value for each vehicle (e.g., Train, 1993 ch. 2). Howeve r, this representation of heterogeneity is very limited and, in particular, does not allow for diff erent price sensitivities. The population of consumers is undoubtedly heterogeneous but it is no t known how important that heterogeneity is to the intended purpose of the CVCM. If further re search and development is undertaken, investigating the importance of consumer heterogene ity should be given a high priority. Explicit heterogeneity was not incorporated in the CVCM in o rder to keep the model and its calibration simple.

The nesting structure used in the CVCM is similar t o nesting structures used in empirically estimated models and in constructed models such as Bunch et al. (2011) and NERA (2009). Grouping vehicles by size, functionality and price is intuitive and consistent with the theoretical requirement that vehicles in a nest be similar with respect to unobserved attributes, i.e., be close substitutes. However, there is no guarantee that t he nesting structure chosen is the best possible nesting structure.

Price sensitivities and alternative-specific consta nts are the two classes of parameters of the CVCM. Price sensitivities are the most important b ecause the constants are computed so that the model exactly predicts the baseline market shares, given the assumed price sensitivities. The price sensitivities have been chosen to be consiste nt with the estimates in the published literature6

and to conform to the theoretical requirement that price sensitivities increase in absolute value as one moves down along the nesting tree. However, th e price sensitivity parameters have not been estimated to be consistent with a specific data set and it is always possible that an additional empirical analysis could yield insights missing fro m the existing literature.

Numerous possible explanatory variables have been e xcluded from the CVCM. Indeed, the only variables included are the changes in price and fue l economy supplied by the OMEGA model. Other variables are implicitly held constant in tha t they are included in the baseline constant terms. Including factors such as income and demogr aphic variables may be desirable in a model to be used for estimation over an extended time per iod. However, this would require predicting values for those variables over the same time perio d. A potentially important endogenous variable in the OMEGA/CVCM system might be internal pricing decisions by manufacturers to meet especially stringent (strongly binding) fuel e conomy and emissions standards. This is beyond the scope of the current CVCM project, howev er.

To the extent that the baseline sales data, includi ng the definitions of individual vehicles, differ from the actual market data, errors could be induce d in the CVCM estimates. OMEGA is itself a model and thus its estimates undoubtedly contain so me differences from what will occur, and these will also affect the accuracy of CVCM estimat es.
Over extended time periods, automotive technology w ill change, and may change in ways that cannot be foreseen at the present time. Furthermor e, consumers’ preferences may also change in unpredictable ways. The 2002 National Research Cou ncil report on the CAFE standards and potential for fuel economy improvement did not fore see a successful market for hybrid vehicles (NRC, 2002). The emergence of minivans, SUVs, cros sovers, the near disappearance of station wagons, and more, could not have been predicted wit h any certainty a long time period (e.g. 15 years) in advance. Assessment of technological inn ovation and trends in consumers’ preferences is beyond the state-of-the-art in economic modeling and is probably best handled by scenario analysis.

The CVCM was designed to estimate the impacts of ch anges in vehicle prices and fuel economy provided by the OMEGA model on consumers’ surplus a nd changes in vehicle sales that could impact manufacturers’ abilities to meet fuel econom y and GHG emissions standards. It was developed as a first test of the potential for such estimations to contribute to improved rule making. The goal was to develop a simple model tha t could be readily calibrated and operated in conjunction with the OMEGA model, and that had a so und theoretical and empirical basis.7



### 2. LITERATURE REVIEW ON NEW VEHICLE TYPE CHOICE MODELING

The impacts of changes in vehicle prices and fuel e conomy on vehicle sales and consumer surplus can be estimated by means of systems of dem and equations and discrete choice models, which are reviewed in this section. The emphasis is on two types of discrete choice models – NMNL and Mixed Logit (ML) models.

2.1 AGGREGATE DEMAND MODELS

Automobile demand by type of vehicle can be represe nted by a system of linear or non-linear demand equations. Kleit (2004, 2002a & b, 1990) cr eated a market segment vehicle demand model that he used to evaluate the costs and benefi ts of CAFE standards. Kleit divided the market into eleven vehicle classes and four manufac turers. Demand functions, in the 2002b paper at least, were specified as simple linear fun ctions of vehicle price (i.e ., Q = a + bP ). These equations can be calibrated given an initial set of prices and quantities and own price elasticities. Kleit estimated own price elasticiti es and cross price elasticities by exercising a proprietary model developed by GM (Table 1). Own p rice elasticities for the eleven vehicle classes ranged from -1.5 for large trucks to -4.5 f or large cars. The own price elasticity for luxury cars is -1.7, less than those of standard ca rs (-2.8 to -4.5) but of the same order of magnitude. In general, cross price elasticities ar e small relative to own price elasticities. Cross elasticities are not symmetric because classes with high sales volumes have a greater effect on classes with low sales volumes than vice versa. Ho wever, there are sets of classes for which cross price elasticities are substantial, indicatin g that the vehicle types are relatively close substitutes. The groupings in Kleit’s model sugges t that standard cars are relatively close substitutes, with small cars being better substitut es for medium cars than for large cars. Small and Large SUVs are relatively good substitutes, as are small and large (pickup) trucks. Cars and pickup trucks are not close substitutes, and the on ly vehicle that is even a weak substitute for a full size van is a minivan. In the discussion of discrete choice models below, such grouping become “nests”.

Table 1 Demand Elasticities of Kleit's Vehicle Cla ss Demand Model (Kleit, 2004)

1 2 3 4 5 6 7 8 9 10 11
1 Small Car -2.808 0.423 0.063 0.018 0.000 0.036 0.027 0.009 0.009 0.0 09 0.000
2 Medium Car 0.684 -3.528 1.107 0.027 0.018 0.018 0.018 0.036 0.045 0.054 0.0 09 3 Large Car 0.270 1.926 -4.500 0.027 0.216 0.009 0.054 0.018 0.063 0.054 0.009 4 Sport Car 0.549 0.423 0.324 -2.250 0.009 0.090 0.198 0.045 0.108 0.018 0.000 5 Luxury Car 0.045 0.405 1.062 0.009 -1.737 0.000 0.027 0.045 0.189 0.072 0.009 6 Small Truck 0.162 0.099 0.000 0.009 0.000 -2.988 0.702 0.045 0.054 0.009 0.009 7 Large Truck 0.063 0.072 0.018 0.009 0.000 0.234 -1.548 0.027 0.090 0.018 0.036 8 Small SUV 0.216 0.279 0.099 0.027 0.009 0.090 0.3 51 -3.645 0.747 0.108 0.072 9 Large SUV 0.117 0.243 0.171 0.018 0.018 0.054 0.3 87 0.414 -2.043 0.234 0.108 10 Minivan 0.081 0.171 0.063 0.000 0.009 0.009 0.04 5 0.027 0.135 -2.286 0.180 11 Van 0.027 0.036 0.009 0.009 0.000 0.009 0.054 0. 036 0.072 0.387 -2.3858

Automobile supply was represented by assuming a sho rt-run price elasticity of supply of +2 and a long-run elasticity of +4.

Bordley 4 (1993) estimated own and cross price elasticities for 200 passenger car nameplates using aggregate time-series sales data by market se gment plus survey data on the first and second choices of consumers who had just purchased a new c ar. The aggregate sales data allowed estimation of own price elasticities for seven pass enger car market segments and an overall price elasticity of automobile demand. The survey data w ere used to estimate “diversion fractions” quantifying the propensity of purchasers of one nam eplate to buy any of the others given an increase in its price. Bordley estimated an own pr ice elasticity for passenger car purchases versus all other commodities of -1.0. Car segment elasticities ranged from -1.7 for small cars to -3.4 for sporty cars (Table 2). Elasticities fo r individual nameplates ranged from -1.7 to -8.2; mean values within segments ranged from -2.4 to -4. 7.

Table 2 Market Segment and Nameplate Own Price Elas ticities Estimated by Bordley (1993)

Car Class Class Elasticity Car Nameplate Elasticiti es Minimum Average Maximum

Economy -1.9 -3.3/-3.4 -4.7 -8.2/-8.1 Small -1.7 -1.9/-1.7 -2.4 -3.1/-3.4 Compact -2.0 -2.1/-2.2 -3.1 -4.9/-4.7 Midsize -2.3 -2.3/-2.6 -3.3 -4.6/-4.2 Large -3.0 -3.1/-3.5 -3.8 -4.3/-4.0 Luxury -2.4 -3.2/-3.4 -3.7 -5.3/-4.5 Sporty -3.4 -2.6/-3.4 -4.2 -6.5/-5.3

Bordley’s method could be used to calibrate a syste m of linear nameplate demand equations, as was done by Kleit (1990). More complex systems inc luding cross price elasticities can also be calibrated, as Bordley (1993) points out, but does not explicitly describe calibration of such a model.

Austin and Dinan (2005) used the own- and cross-pri ce elasticity matrix developed by Kleit (2002a) to estimate the impacts of changes in vehic le prices due to fuel economy standards on consumers’ demand for 10 vehicle classes. Consumer demand for a class is a linear function of the difference between vehicle price and the value of future fuel savings induced by the standards. For manufacturer i , demand for its vehicle classes is given by the fo llowing matrix equation,



### ( ) i i i i 

### q A p c = − (4)

in which q i is the vector of quantities for each of the 10 veh icle classes, p i is the vector of prices,

c i is the vector of present value of fuel economy imp rovements and A i is a matrix of own- and cross-price elasticities. Austin and Dinan (2005) do not provide the numerical values for the

4 Bordley was employed by General Motors Research La boratory at the time he conducted and published his study. Thus, there may be a relationship between Kleit’s e lasticity estimates, which are based on a GM model, and Bordley’s.9

elasticities they used in their model, nor does Kle it (2002a), apparently because the model is proprietary.

2.2 DISCRETE CHOICE OR RANDOM UTILITY MODELS

Discrete choice models, sometimes referred to as ra ndom utility (RU) models, are by far the most common methodology used to mathematically mode l automobile demand. Baltas and Doyle (2001) succinctly summarize the methodology.

“In RU models, preferences for such discrete altern atives are determined by the realization of latent indices of attractiveness, called product utilities . Utility maximization is the objective of the decision process and leads to observed choice in th e sense that the consumer chooses the alternative for which the utility is maximal. Individual prefe rences depend on characteristics of the alternative s and the tastes of the consumer....The analyst cannot observe all the factors affecting preferences and the latter are treated as random variables.” (Balt as and Doyle, 2001, pp. 115).

Since the early applications of random utility mode ls in the 1970s (McFadden, 1973), formulations of RU models have proliferated. Balta s and Doyle (2001) identified fourteen different methods which they grouped into three fun damentally different approaches depending on the nature of the random utility:

• Unobserved product heterogeneity,

• Taste Variation (consumer heterogeneity), and

• Choice Set Heterogeneity.

Nearly all applications of random utility models to automobile choice fall into the first two groups because the availability of different types of automobiles is rarely a significant issue. Randomness in the simple multinomial logit model de rives primarily from unobserved attributes. Its error term may also include unobserved variatio ns in taste but the representation of these variations is limited and simplistic. The same app lies to NMNL Models although their ability to represent randomness in unobserved attributes and t astes is much more complex. In these models, heterogeneity in consumers’ preferences is commonly represented by explicit functional relationships between product attributes and consum er characteristics. MNL models allow variations in consumers’ preferences to be represen ted by random coefficients, whose distributions can be inferred either from survey or market shares data.

Which methodology is best for a given application d epends not only on the richness of the modeling approach but on the objectives of the exer cise, as well as practical constraints, including data and resource availability. Baltas a nd Doyle sum up the dilemma well.

“Finally, a general concern relates to overall mode l practicality. As our discussion illustrates, rece nt developments have increased model complexity and ma de estimation, interpretation, and forecasting less straightforward. Some specifications are still rather impractical. The issue can be viewed as the common dilemma between simplicity and flexibility. There is no universal answer to this question as it depends on one’s rate of exchange between the tw o criteria.” (Baltas and Doyle, 2001, p. 123).10

2.2.1 Multinomial Logit

The first application of a multinomial logit model to automobile choice appears to be the seminal paper by Lave and Train (1979) which estimated a mu ltinomial logit model of consumers’ choices among 10 vehicle classes using what was the n a new method for analyzing qualitative choice behavior (McFadden, 1973). The probability of an individual consumer choosing a vehicle class was assumed to be a function of a vec tor of vehicle attributes and household attributes. The model formulation allowed for inte raction of household and vehicle variables in a linear “representative” utility function. Let X ij k be the k th variable, for the j th vehicle class and the i th consumer. The representative utility function is defined as,

1 K

ij k ijk ij k V X β ε

= = + 

## ∑ (5)

in which the β k s are fixed coefficients and the ε ijk s are independent, identically distributed random variables that have extreme value distributi ons. The probability that consumer i will purchase a vehicle from class j is a multinomial logit function of the representat ive utilities of all classes.

1 j

l V

ij L V

l e P

e

= = 

## ∑ (6)

In the Lave and Train model, vehicle price was repr esented by price divided by household income and the same variable squared. The results implied both that sensitivity to price decreased with increasing vehicle price and that pr ice sensitivity decreased with increasing income. The model was calibrated to survey data fr om 541 households collected in seven U.S. cities in 1976.

McCarthy and Tay (1998) estimated a MNL model of co nsumers’ choices among 68 makes and models. Their objective was to test whether buyers of domestic, European and Japanese manufactured vehicles valued vehicle attributes in the same way. Their analysis rejected the hypothesis that vehicle attributes are similarly va lued regardless of country of origin. They also noted certain “anomalies” in their coefficient esti mates. For example, faster acceleration decreased the probability of choosing American and Japanese vehicles, while operating costs were an insignificant variable for makes and models of Japanese manufacture. Similar results have been observed in other studies and may point t o an inherent difficulty in estimating random utility models. A key assumption of such models is that the unobserved attributes are uncorrelated with the observed attributes. If they are not, then biased estimates can result. Given the strong correlations among many observed a ttributes (e.g., size, price, horsepower, fuel economy, weight, interior volume, number of seats, etc.), the assumption that unobserved attributes are uncorrelated with observed attribute s seems unlikely. In addition, the problem of defining and obtaining measures of precisely the ri ght attributes that determine consumers’ choices has also been a persistent issue for random utility models. Is acceleration best measured by the ratio of horsepower to weight, by 0-60 mph t ime, or by the various measures the industry uses to capture the experiences of launch from a st op, intermediate speed range acceleration,11

passing acceleration, and responsiveness? Inaccurac ies in defining and measuring attributes lead to errors in observed variables. Correlated omitte d variables, errors in observed variables and correlated observed variables makes statistical inf erences challenging indeed.

Lave and Train (1979) noted two key limitations of the MNL model. First is the so-called Independence of Irrelevant Alternatives (IIA) prope rty, which makes the ratio of the probabilities of choice of any two alternatives independent of th e presence or attributes of any other alternatives. A related property is that all alter natives are assumed to have the same probability distribution of unobserved utility (i.e., ε has the same distribution for every alternative) a nd that these distributions are independent. These propert ies severely restrict the patterns of substitution the model can represent. For example, apart from t he measured utility component, Lave and Train’s MNL model implies that a two-seater sports car is just as good a substitute for a luxury sedan as it is for a sporty subcompact. Note that the measured utility component in the LaveTrain model directly accounted for factors such as the number of seats, household size and acceleration performance. Unobserved factors might be such things as styling or image.

Second, because automobile attributes do not vary a cross the population of consumers, it is not possible to estimate a MNL model that includes vehi cle attributes and a vehicle specific constant. In a model estimated using household data, attribut es can only be entered when interacted with some household characteristic. On one hand, this a llows attribute values to vary across individuals. On the other, it imposes specific fun ctional relationships on how attribute values vary that may not be supported by any theory. Thus , heterogeneity of consumers’ preferences is an inherent property of MNL models estimated using household data but is restricted to specific functional relationships chosen by the researcher.
2.2.2 Probit and Nested Multinomial Logit

The shortcomings of the simple MNL model, especiall y its IIA property, led researchers to explore alternative formulations that allowed great er flexibility in patterns of substitution among vehicles and representations of heterogeneous consu mer preferences. The probit model was derived by relaxing the assumptions of independent, identical error distributions (see, e.g., Train, 1993). Instead the error terms in a probit model a re assumed to be jointly normally distributed. Instead of leading to a simple, closed form equatio n for the choice probabilities (like equation (6) for the MNL model), the probit model requires numer ical integration of a series of integrals. The probit model’s inherent complexity, combined with t he ability of a variant of the MNL model to overcome most of its limitations, is responsible fo r the very infrequent use of probit models in modeling automobile choice.

The NMNL Model, a special case of the Generalized E xtreme Value (GEV) model, is based on the premise that the full choice set can be portion ed into subsets (nests) within which the IIA property is appropriate but across which it is not. Put another way, within a nest all vehicles are assumed to be equal substitutes, conditional on the ir observed utility. Formally, within a subset alternatives error terms are independent and identi cally distributed. Across subsets, they are not.

Building on the notation of equations (5) and (6), the probability that a consumer will choose a specific make, model, engine and transmission confi guration, m , given that the consumer will choose a vehicle in nest (class) j , is a simple MNL probability.12 |

1 ijm

ijl

U

im j L U

l e P

e

= = 

# ∑ (7)

The probability that consumer i will choose class j is a function of the utility of attributes common to class j, V j , as well as a function of the composite utility of all vehicles within class j, I ij .

1 ij j ij

il l il V I

ij V I

l L e P

e λ

λ

+

+

= = 

## ∑ (8)

The term I

ij is the “inclusive value” or expected value of the utility of vehicles in set j. It is defined by equation (9).

1

1 K
jk ijmk k M X

ij

m 

### I ln e β

=

= 

###   ∑  

=     

# ∑ (9)

In equation (9) each nest has a different set of co efficients that map vehicle attributes into the utility index. In particular for this model, these coefficients differ across nests. This allows different degrees of substitutability for the choic es within different nests. The unconditional probability of consumer i choosing vehicle m in class j is the following.

| ijm im j ij P P P = (10)

Another feature of the NMNL model that helps overco me the limitations of the MNL model is the ability to define any number of levels of nesti ng. A key advantage of this is that the top nest can represent the choice to buy or not to buy a new automobile. Thus, an NMNL market model can predict the impacts of changes in vehicle attri butes and other factors on total vehicle sales as well as the type of vehicles purchased.

The flexibility and mathematical simplicity of the NMNL model have made it the most widely used tool for modeling automobile choices. Goldber g (1995, 1998) estimated NMNL models of automobile choice in order to evaluate the impacts of fuel economy standards. In the 1995 study, her nests comprised (1) small cars including subcom pacts and compacts, (2) luxury automobiles including sports cars, and (3) all other vehicles. A likelihood ratio test was used to test (and reject) the hypothesis that coefficient values with in the three nests were equal. While such tests can be used to reject a nesting structure, there is no accepted methodology for identifying a correct nesting structure. Goldberg’s 1998 study u sed nine vehicle classes, within which consumers could choose between a foreign or domesti c car. This structure was chosen to allow exploration of differential impacts of standards on foreign and domestic manufacturers.

Stated preference survey data were used by Brownsto ne et al. (1996) to estimate a NMNL model of consumers’ choices among conventional and altern ative fuel vehicles. The 1993 California13

survey asked households to choose among hypothetica l vehicles that included alternative fuel vehicles. Stated preference methods were necessita ted by the fact that very few households purchase or have any experience with vehicles power ed by non-petroleum fuels.

Most often, NMNL models are calibrated via statisti cal inference based on the vehicle choices of individual consumers or households. However, MNL a nd NMNL models can also be interpreted as representing the choice probabilities of a repre sentative consumer or a population of consumers with diverse tastes (Anderson et al., 198 8). In this interpretation, the random error term ( ε ) represents not only unobserved attributes but als o unobserved variations in tastes and errors in perception and optimization by consumers (Madalla, 1992, p. 60). Several modelers have used NMNL models in this way to represent aggr egate market behavior.

Greene (1994) constructed a NMNL choice model for p redicting market shares of alternative fuel vehicles. Rather than estimating a model base d on stated preference survey data, Greene followed a methodology invented by Donndenlinger an d Cook (1997) to infer the values of automobile attributes. The model coefficients were constructed by postulating how vehicle attributes such as range or fuel economy would be v alued by consumers, deriving a coefficient that translates unit changes in each variable to a present dollar value and applying a multiplier to transform that coefficient into one that translates unit changes into the utility index. This multiplier is referred to as generalized cost coeff icient in the remainder of this document. Greene reasoned that since the overwhelming majority of co nsumers had no first-hand experience with alternative fuel vehicles (e.g., battery electric v ehicles, compressed natural gas vehicles, etc.) stated preference surveys data would likely be misl eading. The model did not include a buy/nobuy decision. The first level nest included eight alternative fuel technologies. The second level nest comprised the choice of fuel for bi-fuel or fl ex-fuel vehicles. A similar model also constructed by Greene (2001) contained Conventional Internal Combustion Engine (ICE) vehicles, Dedicated Alternative Fuel vehicles (CNG and LPG), Hydrogen Fuel Cell vehicles and Battery Electric vehicles in the first level nest a nd subcategories of these vehicle technologies in the second. E.g., ICE was divided into conventional liquid fuel vehicles, hybrid vehicles and gaseous-fueled vehicles. Within the conventional l iquid fuel nest, consumers chose among gasoline, diesel, ethanol FFVs and methanol FFVs. Within the FFV nests, consumers chose fuel types, e.g., gasoline or E85. To estimate price co efficients for the nests in his model, Greene (2001) relied on existing studies and the theoretic al requirement that sensitivity to price must increase from the top nest to the bottom (from vehi cle technology choice to fuel choice). Since the overall price elasticity of automobile demand i s generally believed to be approximately -1.0 (Kleit, 1990; McCarthy, 1996; Bordley, 1993) and th e choice of fuel is highly but not infinitely elastic (approximately -10 or more: Greene, 1998, p . 228), this bounds the range of price sensitivity for nests in between. Although this ra nge is an order of magnitude, with three nests between the top and bottom choices it provides usef ul information that can be used in conjunction with estimates from published studies t o greatly reduce the uncertainty about coefficient values.

Greene et al. (2005) and Greene (2009) calibrated c onstructed NMNL models to the market shares of over 800 carline/engine/transmission conf igurations. The data sets included every vehicle in the National Highway Traffic Safety Admi nistration’s (NHTSA) model year 2000 and 2005 fuel economy data sets, respectively, except t hose with annual sales below 25 units per year.14

Generalized cost coefficients were chosen based on the published literature and the relative value rule for nests described above. Vehicle-specific c onstants were used to insure the model exactly fit the base year data. The ability to calibrate t he model to fit any given year’s sales data is an advantage for use in policy analysis where the corr espondence of model estimates to real world experience is of value.

Harrison et al. (2008), like Greene et al. (2005), used a constructed NMNL model to evaluate the benefits and costs of the 2011-2015 CAFE standards. The authors assumed a plausible nesting structure based on their judgments about the substi tutability of different types of vehicles. The guiding principle is that vehicles within a nest ar e closer substitutes for one another than they are for vehicles in other nests. 5 Consumers are assumed to decide to buy or not to buy at the top nest, then choose among three car classes: passenger cars , pickup truck/full-size van, or SUV/minivans. The next level contains 14 vehicle c lasses based on size and price. Within these subclasses are non-intersecting subsets of over 200 vehicle models. Like Greene et al. (2005), Harrison et al. made use of the NMNL requirement th at price sensitivity (price coefficients) must decrease in absolute value (increase in value) as o ne moves up the nesting tree. They began with a price elasticity of -1.0 for the buy/no-buy decis ion, and then assumed the ratios of parameters at each level in order to calculate price coefficie nts for each lower nest. Harrison et al. also calculated a constant term for each model, as Green e et al. did, but then regressed those constant terms against other vehicle attributes in an effort to infer the value of those attributes.
2.2.3 Mixed Logit Model (MLM)

The MLM adds to the NMNL a greater capability to in clude heterogeneous consumer tastes. The utility of vehicle m to consumer i is given by equation (11).

1 1 K H

im m k imk ih imh im

k h U X z δ β μ ε

= = = + + + 

## ∑ ∑ (11)

In equation (11), δ m represents the average utility (intercept term) of vehicle m, the X imk are vehicle attributes interacted with consumer charact eristics, the β k are mean coefficient values for these variables, the μ ih are individual specific random coefficients reflec ting deviations of individual tastes from those β k for which tastes vary, and the z imh are vehicle attributes interacted with consumer characteristics for which tastes vary (Train and Winston, 2007). Assuming that the ε im are independent and identically distributed and ha ve an extreme value distribution, the probability that consumer i chooses vehicle m is given by the mixed logit model (the integral sign represents many integrals over the many probab ility distributions of the random variables).

1 1

1 1 K H m k imk ih imh k h

K H l k ilk ih ilh k h X z

im X z

l 

### e P

e

δ β μ

δ β μ = =

= = + +

+ + 

### ∑ ∑

= ∑ ∑ 

# ∫ ∑ (12)

5 More accurately, the vehicles are more similar wit h respect to their unobserved attributes. Vehicles may differ greatly with respect to the measured attributes that enter the utility index function yet still belong in the same nest.15

Train and Winston (2007) estimated a mixed logit mo del of vehicle choice using a random sample of 458 U.S. consumers who had just purchased a new model year 2000 vehicle in order to investigate reasons for the declining market sha res of U.S. auto manufacturers. Each consumer’s choice set consisted of 200 makes and mo dels. There is no closed form solution for estimating the parameters of the MLM. Instead, sim ulation was used to approximate the integrals for choice probabilities and the resultin g log likelihood function.

The parameters of the MLM are functions of consumer attributes and random variables. For example, the price coefficient in the Train and Win ston model is,



### 1.60 0.86 0.073

i i 

### Y Y ν β 

### − = − − + (13)

The variable ν is a standard normal random variable. This adds r ichness to the model by representing varying tastes across the population. There is even some small probability of finding a consumer who prefers higher prices ( β >0). On the other hand, the functional form is, to a degree, chosen a priori by the researcher, and both estimating the model and predicting with it are substantially more complicated but still qui te feasible. Both require simulations (perhaps only a few hundred) and both require information ab out the distributions of consumer characteristics (available from national surveys).

A comparison of MLM and NMNL models was made by Bro wnstone et al. (2000), combining stated and revealed preference survey data for Cali fornia households. The authors observed that the MLM improves the fit of model to data, and indi cated substantial heterogeneity of preferences across the population. They also noted that revealed preference (RP) data are essential for obtaining realistic predictions of co nsumers’ choices of vehicle types. However, they also commented on the difficulty of statistica l inference using RP data.

“RP data appear to be critical for obtaining realis tic body-type choice and scaling information, but they are plagued by multicollinearity and difficult ies with measuring vehicle attributes. SP data are critical for obtaining information about attributes not available in the marketplace, but pure SP models with these data give implausible forecasts.” (Brownstone et al., 2000)

Bento et al. (2005, 2009) estimated a mixed logit m odel of vehicle choice and a paired model of vehicle use using data from the 2001 National House hold Travel Survey. They divided vehicles into 10 vehicle classes, 5 age categories and 7 man ufacturers. The paired models not only estimate new vehicle choices but vehicle use, as we ll as aging and scrappage. Jacobsen (2010) used the model to assess the impacts of CAFE standa rds on manufacturers but did not include in his model the option they have to use technology to improve the fuel economy of vehicles at increased cost. The mean price elasticity of new v ehicle demand was estimated to be -2.0, substantially more than the unit elasticity found i n models cited above.

Cambridge Econometrics (2008) estimated a mixed log it model of vehicle choice in the UK based on a survey of households who had purchased a new or less than 1-year-old vehicle during the years 2004 to 2007. Households identified the manufacturer, model and engine size of their16

vehicle, which the researchers matched to a separat e data base of vehicle attributes. The survey asked what attributes consumers considered importan t to the purchase of a vehicle. Respondents cited many difficult to measure factors, such as re liability, safety, comfort, warranty and security. Estimated mean price elasticities by vehicle class ranged from -0.96 for multi-passenger vehicles, to -3.51 for luxury vehicles. Relatively elastic m arket segments included Minicars (-2.46), Upper Medium cars (-2.81) and Executive cars (-3.24 ). Less price elastic segments were Superminicars (-1.15), Lower Medium cars (-1.15), S ports cars (-1.79) and 4X4s (-1.75). The observed patterns of own- and cross- price elastici ties led the researchers to comment on the importance of models that allow flexibility in subs titution patterns.

“We observe substitution patterns that represent a significant departure from proportional substitution, i.e. there is a higher level of subst itution between similar models of cars.” (Cambridg e Econometrics, 2008, p. vii)

Mixed logit models can also be estimated using aggr egate market shares, as first shown by Boyd and Mellman (1980) and Cardell and Dunbar (1980) an d later in a seminal paper by Berry, Levinsohn and Pakes (BLP) (1995). BLP provided a p ractical method of estimating a mixed logit model from aggregate sales data. Prices are endogenous in the BLP model, an issue they addressed by means of instrumental variables compri sed of the attributes of other vehicles. Estimates relying on instrumental variables in this context can be unreliable, as Knittel and Metaxoglou (2008) demonstrated using BLP’s data. N oting that the objective function in the BLP model is highly nonlinear and thus prone to mul tiple local optima, they tested 10 different optimization algorithms, using 50 different startin g values for each. Their results call for caution both in interpreting parameter estimates from BLP-t ype models and in their use for forecasting.

“We find that convergence may occur at a number of local extreme, at saddles and in regions of the objective function where first-order conditions are not satisfied. We find own- and cross-price elasticity estimates that differ by a factor of ove r 100 depending on the set of candidate parameter estimates.” (Knittel and Metaxoglou, 2008)

On the other hand, other researchers, using variant s of the BLP model and different estimation procedures, have obtained more stable results.

Moon, Shum and Weidner (2010) extend the BLP method by adding interactive fixed effects to the unobserved product characteristics. The specification multiplicatively combines timespecific fixed effects with vehicle-specific fixed effects. The consumer’s utility function is,

1 1 K R

ijt ik kjt rj rt jt ijt k r U X f α λ δ ε

= = = + + + 

## ∑ ∑ (14)

in which α ’s are coefficients measuring the marginal value of each of the K

vehicle attributes X
, whose mean value also includes the R interactive fixed effects of product j , plus δ jt , represented by the third hand side term. The difference betwee n this formulation and that of BLP is the specific structure imposed on the distribution of p roduct-specific tastes. The final term, ε ijt , is the individual, product and time specific utility compo nent. Note that if there are on the order of 10 317

vehicles and just a few time periods, this model ha s thousands of parameters. In addition, projecting taste heterogeneity into the future requ ires specifying future values for f rt and δ jt or assuming they remain constant. If these are assume d to be constant at the values of a given year or at average values, the heterogeneity of tastes i s limited to product-specific heterogeneity.

An advantage of the Moon et al. approach is that it explicitly represents some endogenous factors by means of interactive fixed effects and thereby r educes the need for instrumental variables, in particular, to represent price endogeneity. The aut hors find that, given their formulation, coefficient estimates produced by methods that assu me prices are exogenous versus endogenous differ little.

The Moon et al. method also produces price elastici ties that are much higher in absolute value than those obtained by the standard BLP model estim ation methods. This is apparently due to the inclusion of the fixed effect variables. They applied the method to the same data used by BLP (1995). Own and cross price elasticities were estimated for 23 vehicle classes. Using their interactive fixed effect formulation and assuming p rices to be endogenous produced own price elasticities ranging from -7.0 for Cadillacs to -36 .5 for large Mercurys. Twenty of the 23 estimated elasticities were more price elastic than -25.0. Omitting the interactive fixed effects produced own price elasticity estimates ranging fro m -7.8 (again, for Cadillac) to -17.6 for a “remainder of the market” category. This time, 10 of the 23 elasticity estimates were more elastic than -15.0.

In a study for the UK Department of Transport, the Economics for the Environment Consultancy (EFTEC) estimated a MLM model of consumers’ choices of automobiles in the UK (EFTEC, 2008). The researchers estimated their model using the method of BLP and data on new car market shares for 2,190 different vehicle types reg istered by private households in 11 regions of the UK. They note that their choice set is conside rably larger than that of any previous study. The ability to calibrate a model to such a large ch oice set is a consequence of the BLP estimation procedure. Vehicles were nested into 9 classes bas ed on size, body style and price. Estimated median price elasticities ranged from -1.3, for veh icles in the SUV class with a range from -2.4 (90 th percentile) to -1.0 (10 th percentile), to -5.4 for vehicles in the small-to- medium size family car segment with a range from -7.1 (90 th ) to -4.5 (10 th ). Sports cars also had relatively low price elasticities and subcompact and mini car choices we re relatively price elastic.

A number of recent studies have employed forms of t he Mixed Logit model to estimate the relative effects of vehicle price and fuel economy or fuel costs on vehicle choice (e.g., Allcott and Wozny, 2009; Klier and Linn, 2008; Gramlich, 20 08; Sawhill, 2008). These and other related studies were reviewed by Greene (2010). Al l used extensive, detailed data bases on vehicle purchases in the United States but reached very different conclusions about how consumers trade off vehicle price and fuel economy. Some of the differences can be attributed to how consumers form expectations about future fuel p rices, although most models assumed static expectations based on the observation that fuel pri ces appear to follow a random walk.

Aggregate, mixed logit type models can be used to p redict market shares and estimate changes in consumer surplus. For example, Greene and Liu (198 8) used both a random coefficient MNL model and Lave and Train’s (1979) model to estimate the impacts of changes in vehicle18

attributes related to fuel economy on the consumer surplus associated with automobiles sold in the United States between 1978 and 1985. The rando m coefficient model utilized Monte Carlo simulation to execute repeated draws from the vecto r distribution of random coefficients. Greene and Liu found that the estimated mean consum er surplus values were highly sensitive to the mean values of attributes but they did not test sensitivity of consumer surplus estimates to the variance of attribute values.

2.3 SUMMARY OBSERVATIONS

All three categories of models (aggregate demand mo dels, NMNL, and MLM) can be used to estimate changes in market shares and consumer surp lus due to increases in vehicle prices and fuel economy. Aggregate demand models, like those developed by Kleit (2002a) or Austin and Dinan (2005), could, in principle, produce estimate s for 60 or even 800 vehicle types. Given own- and cross-price elasticities, calibration of s uch models to sales data would be straightforward. Estimating the price elasticity m atrix, however, is a major challenge. An 800 by 800 matrix would require 640,000 elasticity esti mates and even a 60 by 60 matrix would need 3,600 elasticity values. Bordley’s (1993) method o ffers a potential solution to this problem but it requires rarely available data on consumers’ first and second choices. Perhaps this is why it appears not to have been used in subsequent studies

. The ability of mixed logit models to represent cons umer heterogeneity also comes at the price of greater information requirements for model calibrat ion and simulation. Mixed logit models require specification of not only the central tende ncies of key parameters but also their variance, and possibly their correlations. Running a mixed l ogit model requires repeated randomized draws from the distributions of parameters. Fortun ately, software is available for performing the necessary simulations. Calibration and updating of MLMs requires considerable effort. Survey based estimation methods require extensive, detaile d survey data. Aggregate methods have more modest data requirements but the validity of the es timates by the most prevalent algorithms has been called into question by recent research (Knitt el and Metaxoglou, 2008). In either case, there is presently no evidence that MLMs produce mo re accurate predictions than other methods. Should the EPA determine that vehicle choice modeli ng can make an important contribution to its regulatory analyses, it may be worthwhile to de termine whether the potential benefits of using mixed logit models to represent consumer heterogene ity are worth the extra complexity and data requirements of the mixed logit model.

NMNL models have been constructed, calibrated and u sed in policy analyses of fuel economy issues by Greene et al. (2005), Harrison et al. (20 08) and Bunch et al. (2011). All three applications modeled vehicle choices at a fine leve l of detail, ranging from 200 makes and models to over 800 make/model/engine/transmission c ombinations. This high level of detail was considered necessary to adequately represent the ch anges in market shares that might result from fuel economy and emissions standards or fiscal poli cies. Given that the price sensitivity of consumers’ choices is greatest at the lowest level of the NMNL nest, i.e. when vehicles are the closest substitutes, modeling at the greatest feasi ble level of detail should produce a model with the potential to measure the full impacts of price and fuel economy changes on fleet average fuel economy and consumer surplus.19

Given a nesting structure and corresponding price c oefficients, NMNL models can be quickly and precisely calibrated to historical or projected sales data using closed form equations. NMNL models are capable of accommodating the introductio n, termination, or modification of product lines. They are not capable, however, of predictin g when product lines will be introduced or terminated. NMNL models that must be calibrated to sales data are also not able to predict the sales of newly introduced vehicles, since there is no vehicle-specific constant term available for new products. This is a general limitation of mode ls that include fixed effects to accurately predict sales shares and applies to Mixed Logit Mod els and other formulations, as well.

For the purpose of developing an initial model to t est the value of making such estimates, the NMNL method appears to be a good compromise between flexibility and simplicity. It can be readily calibrated with only a small amount of info rmation about price elasticities and base year sales data. It allows for substantial flexibility in representing substitutions among vehicle types. On the other hand, it does not allow great flexibil ity in representing heterogeneous consumer preferences. This may be a fruitful area of future research and development, especially if it can be shown that more detailed representations of cons umer tastes lead to more accurate predictions.2021 

### 3. METHODOLOGY

This project constructs and calibrates a NMNL model along the line of Greene et al. (2005) and Bunch et al. (2011). Generalized cost coefficients are derived from the literature and NMNL properties. Given generalized cost coefficients, co nstant terms of the model are calibrated to baseline sales data such that the model prediction replicates baseline market share.

3.1 NESTING STRUCTURE

Choice alternatives in the CVCM are represented in detail, by make, model, engine and transmission, corresponding to the level of detail at which fuel economy measurements are made by the EPA. There are on the order of 1,000 choice alternatives. Individual vehicles are grouped into nests as in Figure 1 to allow differential sub stitution patterns within and between nests. The structure has 5 levels: Lev0 (Buy a new vehicle/Don ’t buy a new vehicle), Lev1 (Passenger Vehicles, Cargo Vehicles and Ultra Prestige vehicle s), Lev2 (vehicle types: Two Seaters, Prestige Cars, Standard Cars, Prestige SUVs, MiniVa ns, Standard SUVs, Pickup Trucks, Vans, and Ultra Prestige Vehicles), Lev3 (vehicle classes (see Table 3) and Lev4 (vehicle configurations (one configuration is defined as a c ombination of make, model, engine size and transmission type)). Define Lev0 as the highest le vel and Lev4 as the lowest level. Right above Lev0 is root node (not drawn in Figure 1), which is the origin of the nesting structure/tree.

Figure 1 Nested Multinomial Logit Structure of Cons umer Choice Model
Note: “Standard” is synonymous with “Non-Prestige”

The nesting structure in Figure 1 is defined accord ing to general principles that group closer substitutes in a nest and ensure price sensitivity (price coefficient) and substitutability increase a s one goes down to the bottom of the nesting structur e 6 . The inclusion of the buy/no-buy option is necessary to predict impacts on total sales, not ju st the distribution of sales among makes,

6 The requirement that price sensitivity increases a s one goes down to the bottom is explained in Appen dix A.22

models and vehicle classes. Conditioning on buying a new vehicle, vehicle configurations are grouped according to functionality and size of vehi cles and prestige/non-prestige. Thus lev1 distinguishes between passenger vehicles, cargo veh icles, and ultra-prestige vehicles (see its definition in Table 3), which are least substitutab le. Lev2 further divides passenger vehicles into Two Seaters, Prestige Cars, Standard Cars, Prestige SUVs, Standard SUVs, and MiniVans, acknowledging increasing substitutability among the se alternatives (e.g. Standard SUVs and MiniVans, which are both passenger vehicles, are cl oser substitutes than Standard SUVs and Small Pickup Trucks, because Small Pickup Trucks ar e cargo vehicles). Cargo vehicles are divided into Pickup Trucks and Vans. Lev3 continue dividing some nodes in lev2 by vehicle size or prestige/non-prestige.

The literature provides evidence that support our d efinition of nesting structure. A no-buy alternative is often included in previous studies ( e.g., Berkovec, 1985; Berry, 1994; Berry et al., 1995; Goldberg, 1995; NERA, 2009). It is very commo n to segment vehicle market by vehicle size, functionality, and prestige/non-prestige (e.g . Lave and Train, 1979; Berkovec and Rust, 1985; Berkovec, 1985; Goldberg, 1995; Kleit, 2004; NERA, 2009). For example, Kleit (2004) classifies vehicles into small car, midsize car, la rge car, sports car, luxury car, small truck, large truck, small SUV, large SUV, minivan, and van, whic h is consistent with our class definition (Table 3). Moreover, our structure has advantages over other structures in the literature:

(1) It models vehicle market at a high level of det ail, which enables the CVCM to potentially simulate the full range of sales mix shifts. The st ructure includes 5 levels, and choice alternatives are vehicle configurations (on the ord er of 1000), while the literature studies typically include two or three levels, and choice a lternatives are vehicle size classes or makes/models (on the order of 200); (2) The passenger and cargo vehicle distinction in Lev1 is fully compatible with EPA emissions standards’ compliance categories for cars and truck s; (3) Our structure has a more thorough treatment of prestige vehicles in consideration that they have different price sensitivities from non-prestig e vehicles. In addition to grouping prestige two seaters, cars and SUVs into their own nests in Lev2 and Lev3, the structure also groups ultra-prestige vehicles into a nest in Lev1. The sp ecial treatment of ultra-prestige vehicles is to recognize that these vehicles have very distinct consumer demand and thus are hardly ever substitutes for other inexpensive vehicles. T echnically speaking, positioning ultraprestige vehicle nest in Lev1 allows us to assign a small price coefficient to these vehicles.

The structure in Figure 1 is implemented in the CVC M by default. Future versions of the CVCM could support user-defined structure. Alternative s tructures may have impacts on sales predictions. Sales in the level of vehicle configur ations will be most sensitive to the structure change. The degree of sensitivity diminishes as the prediction is targeted at more aggregate levels.23 Table 3 Vehicle Class Definition in the CVCM

CVCM Class No. of Configurations 1 Corresponding EPA Class 1. Prestige 2 Two-Seaters 27 Two Seaters 2. Prestige Subcompact Cars 49 Subcompact Cars, Minicompact Cars 3. Prestige Compact Cars and Small Station Wagons 71 Compact cars, Small Station Wagons 4. Prestige Midsize Cars and Station Wagons 66 Midsize Cars, Midsize Station Wagons 5. Prestige Large Cars 17 Large Cars
6. Two-Seater 26 Two Seaters 7. Subcompact Cars 58 Subcompact Cars, Minicompact Cars 8. Compact Cars and Small Station Wagons 82 Compact Cars, Small Station Wagons 9. Midsize Cars and Station Wagons 100 Midsize Cars, Midsize Station Wagons 10. Large Cars 29 Large Cars 11. Prestige SUVs 109 SUVs
12. Small 3 SUVs 17 SUVs
13. Midsize SUVs 72 SUVs 14. large SUVs 137 SUVs
15. MiniVans 19 MiniVans 16. Cargo/Large Passenger Vans 42 Cargo Vans, Passenger Vans 17. Small Pickup Trucks 49 Small Pickup Trucks 18. Standard Pickup Trucks 67 Standard Pickup Trucks 19. Ultra Prestige Vehicles 3 93 See the definition (note 4) below

Notes: (1) Number of configurations is the number of configura tions which a CVCM class contains. It is not an attribute of the model itself, but specific to t he vehicle data base to which the model is calibrated: a configuration is a record in the data base and a CVCM class consists of multiple records. (2) Prestige and non-prestige classes are defined by ve hicle price: the prestige are vehicles whose prices are higher than or equal to unweighted avera ge price in the corresponding EPA class, and vice versa for non-prestige vehicles; these calcula tions are done after ultra-prestige vehicles (see below) are put in a separate nest. E.g., Prestige Two-Seater class is the set of relatively expensive vehicle configurations in EPA class of two seaters with prices higher than or equal to the unweighted average price of EPA two seaters. (3) Non-prestige SUVs are divided into small, midsize a nd large SUVs by vehicle’s footprint (small: footprint <43; midsize: 43<=footprint<46; large: fo otprint>=46) (4) Ultra Prestige class is defined as the set of vehic les whose prices are higher than or equal to $75,000.24

3.2 EQUATIONS

The CVCM includes a series of equations to define o r calculate vehicle utilities, to calculate market share and sales of each vehicle configuratio n, and to estimate consumer surplus change brought by the installation of fuel economy technol ogies.

3.2.1 Prelude

We start from a review of Multinomial Logit (MNL) e quations. The representative component of the utility expression for an alternative is define d in terms of four parts – the attributes k 

### x , attribute coefficients k



### β , alternative specific constant j α , and scale parameter μ . With the assumption that the variance of unobserved factors is distributed extreme value with variance

2

2 

### 6 

### π μ (Train, 2009), the utility of alternative j for individual n is

, r nj nj nj j r jr nj j p jr nj j p j nj

r r p U V x x G β ε α β ε α β ε α β ε β = + = + + = + + = + +



## ∑ ∑ (15)

2 2
2 Var( ) ,

6 nj π ε σ μ = = (16)

where the sum j

G represents a “generalized cost” (Greene, 2001) for alternative j
, p β is the coefficient of vehicle price attribute and the scal e parameter μ is proportional to the inverse of the standard deviation of the error term. The choi ce probability of alternative j is



### exp ( ) exp exp ( )

. exp exp ( ) exp ( ) j r jr nj j p j r nj ni i r ir i p i i i r i 

### x V G P V x G



### μ α β μ μ α β μ μ α β μ α β

+ +

= = = + + 

# ∑ ∑ ∑ ∑ ∑ (17)

Note that the scale parameter μ and coefficients j α and p β are not separately identified and only the product of them can be estimated (Train, 2009). Thus in the CVCM, utility and choice probabilities have been expressed as

, j j j j U A BG ε = + + (18)



### exp ( )

. exp ( ) j j j i j i 

### A BG P A BG

+

= + 

# ∑ (19)

with j j A μα = and p



### B β μ 

### = . Coefficient B is called generalized cost coefficient since it re flects the derivative of utility with respect to price or generalized cost. Generalized cost coefficient is25

proportional to scale parameter and thus inversely proportional to the standard deviation of error terms. Subscript n for individuals is omitted since the CVCM models th e demand of a representative consumer.
3.2.2 Two-level CVCM Equations

The CVCMNMNL equations are first introduced in a si mplified context with a two-level (vehicle configurations and vehicle classes) nested tree. Then full equations will be detailed in the next section.

The CVCM assumes that fuel economy and vehicle pric e are the only factors changing between model runs, and other attributes (e.g. performance and size) remain constant. This assumption is consistent with the current version of OMEGA which only predicts changes in fuel economy and vehicle prices. Other attributes can be included if the value of the attributes can be accurately quantified. The average value of unmeasured vehicl e attributes is represented by an alternativespecific constant term. The constant for each alter native is calibrated to match baseline sales data. The utility 7 for vehicle j in class k is

( ) , jk jk k j jk jk k jk jk jk U A B G A B C FS

ε ε = + + = + − + (20)

where

A jk : constant term for vehicle j in class k, B k : generalized cost coefficient parameter for vehicl es in class k

,

jk C : incremental cost for improving fuel economy of ve hicle j , and

jk FS : the amount of fuel savings from improved fuel eco nomy, valued by consumers when making purchase decisions.

The utility function for the class k is

ln exp ln exp[ ( )] root root k k jk k jk k jk jk j k j k k k

B B U A U A A B C FS

B B

∈ ∈ = + = + + − 

# ∑ ∑ (21)

where A k is constant term representing attributes shared by all alternatives in class k and root 

### B is

the generalized cost coefficient for vehicle classe s. Note that the log-sum term ln exp jk j k U

∈ 

## ∑ is

often referred to as the “inclusive value” in the l iterature (e.g. Train, 2009). Choice probability for alternative j is

| j j k k P P P = , (22)

7 As seen in the appendix A, equation (20) only repre sents a component of the total utility that is uniq ue to vehicle j

. The utility component common to all vehicles in one class is captured by a class specific constant ter m.26

with

|

' '

' exp( ) exp( ) j k j j k j k j j k A B G P A B G

∈ +

= + 

# ∑ (23)

and

' '

' '

' 

### exp[ ln exp( )]

. exp[ ln exp( )]

root k j k j

j k k k
root

k j k j k j k

k 

### B A A B G B P B

A A B G B ∈

∈ 

### + +

=
+ +



# ∑
∑ ∑ (24)

where |

j k P is the conditional probability of choosing alternat ive j given that an alternative in class

k is chosen, and k



### P is the marginal probability of choosing an alternat ive in class k . Appendix A will show the equivalence of the NMNL specification here to more general formulations in the literature.
3.2.3 Full Scale CVCM Equations

We could list out NMNL equations for all the five l evels. But a simpler alternative is to define utilities and calculate choice probabilities recurs ively based on the notations in Daly (2001). We reproduce the notation here for convenience:

• The tree function t(c) is used to define the nested logit structure: If c is a node in the tree, t(c) denotes the unique parent node at the higher level to which c is attached. For instance, Passenger Vehicle node is the parent of Standard Car node in Figure 1.

• The set ALL(c) denotes the set of nodes consisting of c and all its ancestors: ALL(c) = {c, t(c), t(t(c)), ..., k| t(k) = root}

• Each node c can be considered an “alternative” in i ts own right. Nodes in the bottom level are “elemental alternatives”, which ar e vehicle configurations. Nodes higher than the bottom level are viewed as “c omposite alternatives” that include all the elementary alternatives below it.

• Utilities of nodes are then defined by

( ) j j t j j U A B G = + (25)

( ) ( ) ( ) ln exp t c

c c c a c t c
t a c c B U A U A B U

B

= = + = + 

# ∑ (26)27

with

( ) 1 ln exp . c a

t a c c U U B

= = 

## ∑ (27)

Equation (25) defines utilities for elementary alte rnatives including all vehicle configurations and No-Buy alternative. Equation (26) is recursive, defining the utility of node c as the summation of constant term A c and generalized cost coefficient ( ( ) / t c c B B ) weighted log-sum term. The log-sum term is calculated over all the c hild nodes of c , where U a is the utility of a child node a and again its utility can be expressed by equation (26).

In particular, the utility for root node (overall c omposite utility for the choice set) is

( ) 1 1 ln exp ln(exp exp ) root a Buy NoBuy

t a root root root U U U U B B

= = = + 

## ∑ (28)

with

. NoBuy NoBuy U A = (29)

The utility function in equation (28) can be used t o measure the consumer surplus change, consistent with Small and Rosen (1981):

1 0

( ) ( ) 1 (ln exp ln exp )

a a t a root t a root root CS U U B

= = ∆ = − −



## ∑ ∑ (30)

where the superscripts 0 and 1 refer to before and after the change, and - root 

### B is marginal utility
of income.

The choice probability of each alternative is found by solving the following equation for P c :

( ) ( ) ( ) ln { ln exp }. c a b a ALL c t b t a P U U

∈ = = − 

## ∑ ∑ (31)

Specifically, the choice probabilities of bottom le vel elementary alternatives are calculated as the product of a series of probabilities:

| ( ) | ( ) | ... , j j c j c t c Buy root P P P P = (32)

with

| ( )

( ) ( ) 

### exp

exp c c t c

b

t b t c 

### U P U

= 

### = 

# ∑ , (33)28

where | ( )

c t c P is conditional probability of choosing node c given its parent node t(c) is chosen. In the CVCM, the market share of a vehicle segment is equivalent to the probability of choosing the corresponding node. Vehicle sales then equal the pr oduct of market size and market share:



### , c c c 

### N M S M P = = (34)

where N

c is sales for the vehicle segment represented by nod e c , S c is corresponding market share and M is market size, estimated by number of households.

The key input parameters for these equations includ e constant terms and generalized cost coefficients at each level of the nesting structure , change in vehicle price due to the installation of fuel economy technologies, and the value of fuel economy improvement perceived by consumers. The derivation of constant terms and gen eralized cost coefficients will be described in Section 3.4 on model calibration. Vehicle price change is assumed to be equal to increased vehicle cost, a direct output of the OMEGA. The ass umption and calculation of consumer value of fuel economy will be presented in the next secti on.

3.3 VALUE OF FUEL ECONOMY

How consumers value fuel economy improvements has v ery significant implications for the costs and benefits of fuel economy and emissions policies . The accuracy of consumer choice models depends much on how close the assumption of value o f fuel economy resembles the reality. However the literature has not achieved a consensus on this subject. On one hand, economically rational consumers would measure the value of fuel economy by the expected discounted present value of fuel saved over the full life of the vehic le. On the other hand, there is evidence that very few consumers actually make such quantitative asses sments (Turrentine and Kurani, 2007). Greene et al. (2009) show that typical consumer los s aversion combined with the uncertainty of future fuel savings could lead to a significant und ervaluing of future fuel savings relative to the expected present value. Greene (2010) concludes th at econometric studies are nearly evenly divided about whether car buyers value fuel savings in accord with rational economic principles or significantly undervalue future fuel.

Reflecting this controversy, the National Research Council (2002) fuel economy study considered two alternative methods of estimating fu el savings valued by consumers, full lifetime discounted fuel savings and a 3-year simple payback . The OMEGA has calculated fuel savings as the payback from the first 5 years with 3% disco unt. In order to be consistent with the OMEGA, the CVCM implemented the same calculation me thod by default. However, users can always change the parameters ( r and L in equation(35)) in the input file to reflect thei r own assumptions on fuel savings calculation.

Denote scenario 0 as the baseline scenario, with fu el economy at an initial value; denote scenario 1 as the policy scenario, where fuel economy change s over time in response to fuel economy and emissions policies. Define considered Fuel savings as fuel saved that the consumer takes into account in the vehicle purchase decision in policy scenario relative to baseline scenario:29 0 1 1 1 1 1 ( ) ( ) ( )[ ] (1 ) ( ) ( ) t L

i t

t i i FS t P M t

r MPG t MPG t τ
τ τ τ η η +

− = + = − − + 

## ∑ (35)

where

FS i (t) : considered fuel savings of model year t vehicle i relative to its baseline configuration P( τ ) : price of fuel in year τ M( t τ

− ) : annual miles traveled for a vehicle with age of t τ

−
r: consumer discount rate
η : OnRoad discount factor that discounts fuel econom y (MPG) in order to reflect realworld driving conditions L : assumed payback period, in years.

3.4 CALIBRATION

Generalized cost coefficients and alternative speci fic constant terms are key input parameters to the CVCM. Generalized cost coefficients can be dire ctly assigned, as in NERA (2009), or can be derived from other measures, e.g. price elasticitie s, as in this CVCM. Constant terms represent baseline utilities before any changes to vehicles. It is necessary to calibrate constant terms such that the CVCM prediction replicates market shares i n the baseline scenario.

3.4.1 Generalized Cost Coefficient Determination

3.4.1.1 Methods Generalized cost coefficients in the CVCM have been determined based on multiple relationships and rules. Firstly generalized cost c oefficients can be estimated from price elasticities according to the following relationshi p:

(1 ), j j c j p B S η = − (36)

(1 ) (1 ) j c

c j j c c B p S p S η η

= ≈

− − (37)

where j η is the own-price elasticity of demand for alternati ve j, j p is the price of j, j

S is j ’s conditional market share given nest c is chosen,

c 

### B is the generalized cost coefficient for
alternatives in nest c , c



### p is average price for alternatives in nest c , c S is average conditional market share, and

c



### η is a representative value of s j η . Equation (36) is derived from the definition of elasticities and logit model equations (for furt her details, please refer to Train, 2009). Price elasticities can be chosen based on an evaluation o f values found in the literature.

Secondly, theoretical requirement of NMNL on genera lized cost coefficients provides useful information for determining generalized cost coeffi cients. The NMNL theory requires that the absolute value of generalized cost coefficients mus t increase as one goes down to the bottom30

(vehicle configurations level) for the NMNL model t o be consistent with utility maximization (see Appendix A):

( ) ( ( )) | | | | | | ... | |, c t c t t c root B B B B ≥ ≥ ≥ ≥ (38)
where ( )

t c B is the generalized cost coefficient associated with the parent node of c . Thus generalized cost coefficients at bottom level provi de upper bounds (in terms of absolute value) and generalized cost coefficient at the root node ( choice to buy a new vehicle or not) provides a lower bound for all other generalized cost coeffici ents at intermediate nodes.

Thirdly, generalized cost coefficient of a nest has certain relationship with the price of that nest. We know that generalized cost coefficient is invers ely proportional to the standard deviation of unobserved attributes in the nest (Appendix A). Pre stige vehicle classes or nests may have large variance in unobserved attributes since consumers v alue these attributes very differently. Thus generalized cost coefficients of prestige vehicle c lasses or nests are lower in absolute value than those of non-prestige vehicle nests. This is consis tent with the finding of Goldberg (1995) of lower generalized cost coefficients for higher-pric e market segments.

We further extend this relationship with evidence f rom empirical studies. Disaggregate vehicle type choice models (e.g. Train and Winston, 2007) t ypically include in the utility function the ratio of vehicle price ( j

p ) and household income (

n 

### Y ):

... ... . j jn jn j jn

n n p U p Y Y

β β ε ε = + + = + + (39)

So generalized cost coefficient ( 

### /

n 

### Y 

### β here) is inversely proportional to income. Assuming that income elasticity of expenditure is 1 (i.e., expend iture on vehicle purchase is approximately proportional to income), we conclude that generaliz ed cost coefficients are approximately inversely proportional to vehicle purchase expendit ure and, roughly speaking, vehicle price. 8 That is,

'

' 

### , c c

c c 

### B p B p ≈ (40)

where c and c’ represent two nests, and B and p are generalized cost coefficient and average price respectively. The CVCM models the choice of a representative consumer and cannot directly incorporate income difference at the house hold level. Equation (40) can act as a proxy to represent price sensitivity variation due to househ old income difference.

3.4.1.2 Calculation The calculation of generalized cost coefficients ac cording to Equation (37) requires the input of price elasticities. Table 4 4 has summarized elasti city values from relevant literature that study new vehicle demand and report elasticities explicit ly. Although these literature elasticities are valuable, it is difficult to directly use them in t he CVCM due to the following reasons: (1) literature studies and the CVCM have different nest ing structures, 9 and (2) elasticities could be

8 Our intention is not to derive a definitive relati onship, but to obtain a rule of thumb from empirica l observations, which would be useful to generalized cost coefficie nt calibration.

9 Thus the categories presented in Table 4 do not co rrespond to the categories used in the nesting stru cture of the CVCM, but instead reflect the categories used in th e cited studies.31

quite different from one study to another depending on dataset and model assumptions. In view of these difficulties, one shall cautiously utilize these literature elasticities and also consider other constraints (equations (38) and (40)) to dete rmine generalized cost coefficients. In the following sections, we will detail how generalized cost coefficients are calculated at each level of Table 5 by integrating all available information . Note that the choice levels in Table 4 do not exactly match those in Table 5. Roughly speaking, “ Choice to Buy a New Vehicle or Not” in Table 4 corresponds to Level 0 of Table 5; “Choice of Market Segment” in Table 4 corresponds to Level 3 of Table 5; “Choice of Configurations” in Table 4 corresponds to Level 4 in Table 5. “Choice of Make/Model” in Table 4 has no direct cor responding level in Table 5 and is an intermediate level between level 3 and 4 of Table 5

. The overall price elasticity of automobile demand i s set at -0.8 (Lev0 of Table 5), consistent with McCarthy (1996) and Levinsohn (1988). Following equ ation (37), the generalized cost coefficient for the buy/no buy decision is calculat ed and the value (-3.39E-05) serves as a lower bound (in absolute value) for all generalized cost coeff icients in Table 5.

Not many studies report elasticities at vehicle con figuration level (Level 4 of Table 5). So we first look at the make/model level, whose elasticit ies values are lower bounds 10 (in absolute value) of configuration level elasticities. Table 4 shows the average elasticity for choices among all individual makes and models is in the range of -2.3 to -4 (see ”Choice of Make/Model” Section and Row “Average elasticity” in Table 4). Elasticit ies for choices among makes and models in each market segment vary, with the range of –3.3 to -4.7 for small, medium and large size segments, -1.2 to -3.7 for luxury vehicles and -1.2 to -4.2 for sport vehicles. Based on these estimates, we assume that price elasticities at mak e/model level are around -4 for non-luxury cars (-4 is about the central value of the literature es timates) and around -2 for luxury and sport cars (-2 is about the central estimate). Generalized cos t coefficients (usually but not always ranked in the same way as elasticities) at vehicle configurat ion level (Level 4 of Table 5) shall be larger in absolute value than at make/model level. Therefore the representative value of elasticities is set at -5.0 at vehicle configuration level for non-pres tige 11 cars (classes 6, 7, 8, 9, and 10 of Level 4 in Table 5) and -3.5 for prestige cars and two seat ers (classes 1, 2, 3, 4, and 5 of Level 4 in Table 5. These values are within the range of literature estimates in Table 4 (“Choice of Configuration” section and studies of Berry et al., 1995 and EFTEC , 2008). Generalized cost coefficients for classes 1-10 are calculated according to equation ( 37) given elasticities are known. We don’t have sufficient information to choose elasticities for other classes in Level 4 of Table 5 and will rely on equation (40) to calculate generalized cost coefficients. We select class 10 as the base class for non-prestige vehicles. Generalized cost coefficients of classes 12-18 are derived from class 10 generalized cost coefficient. Similarly fo r prestige vehicles, we select class 5 as the base class. Generalized cost coefficients of classes 11 and 19 are derived from class 5 generalized cost coefficient. Generalized cost coefficients in Level 4 serve as upper bounds (in absolute value) for other generalized cost coefficients in Table 5.

For elasticities at the vehicle class level (Level 3 of Table 5 and “Choice of Market Segment” of Table 4), Table 4 summarizes that own price elastic ity is around -1.8 to -2.8 for small size

10 Exactly speaking, generalized cost coefficients fo r choices among makes and models are lower bounds o f generalized cost coefficients for choices among con figurations. This relationship is approximately tru e for elasticities.

11 Prestige cars in Table 3 have the same definition a s luxury cars in Table 4.32

segment, -1.3 to -3.5 for medium size segment, and -2.8 to -4.5 for large size segment. According to this observation, the representative v alue of price elasticities for choice among vehicle classes within Standard Car type is set at -3 (Row “Standard Car” in Level 3 of Table 5). Generalized cost coefficient is calculated accordin g to equation (37). For luxury and sport cars, elasticities are around -1.7 to -3.5 in Table 4. Th us the representative value of price elasticities for choice among luxury/sport vehicle classes was i nitially set at -2.5 (Rows “Two Seater” and “Prestige Car” in Level 3 of Table 5), which is abo ut the mean of literature estimates. However, calculated generalized cost coefficients based on t hese elasticities are larger in absolute values than their upper bounds and hence violate the theor etical requirement of NMNL (equation(38)). So price elasticities are adjusted to be -2.2 for R ow “Prestige Car” and -1.3 for Row “Two Seater” so that 12 calculated generalized cost coefficients satisfy t he constraint in (38). Again we are not trying to choose elasticity values for Prestige SUV , Standard SUV, and Pickup of Lev3 in Table 5. Instead, we selected Standard Car of Level 3 as the base. Generalized cost coefficients of Standard SUV and Pickup of Level 3 are derived from Standard Car generalized cost coefficient according to equation (40).

For Levels 2 and 1 of Table 5, we don’t find releva nt elasticity estimates in the literature. Thus the calibration of generalized cost coefficients is based on equations (38) and (40). First for choice of vehicle type within passenger category (L evel 2-Passenger in Table 5), generalized cost coefficient is chosen to be -5.23e-5, which is the mean of its upper bound (Lev3-Two Seater: -7.08e-5) and lower bound (Lev0-RootNode: -3.38e-5) . Then applying equation (40), generalized cost coefficient for choice of vehicle type within Cargo category (Lev2-Cargo) is calculated as - 5.23e-5. Since there are no vehicle types within Ul tra Prestige category, generalized cost coefficient of Lev2-Ultra Prestige is copied from L ev4-Ultra Prestige. For Lev1, generalized cost coefficient is simply set as the mean of its upper and lower bounds (-3.92e-5 and -3.38e-5 respectively).

So far all generalized cost coefficients are obtain ed from equation (37) or from equation (40) in the case that elasticities are not available, with equation (38) providing upper and lower bounds. On the other hand, unknown elasticities can be calc ulated once generalized cost coefficients are obtained. For convenience of implementing CVCM in C #, we simply provide C# program with all price elasticities in an input file (with some of the price elasticities back-calculated from the generalized cost coefficients as described above) a nd calculate all generalized cost coefficients using equation (37).

12 A range of elasticities satisfy this constraint. W e gradually increase the initial elasticity value o f -3 by 0.1. The final value of -2.2 (-1.3 for the case of Two Seater) in the table is the first value in this process that s atisfies the constraint.33 Table 4 Own Price Elasticities of New Vehicle Deman d in the Literature

**Own Price Elasticity of Demand Values Used in Calibration**  **Choice of Configuration** Small Berry et al. (1995): -6.4 for Mazda 323; Eftec (2008): -4.5 -5 Midsize Berry et al. (1995): -4.8 for Nissan Maxima; Eftec (2008): -5.4 -5 Large Berry et al. (1995): -4.8 for Honda Accord; Ef tec (2008): -3.6 -5 Luxury Berry et al. (1995): -3.1 for Lexus LS400; Ef tec (2008): -4.0 -3.5 Sport Eftec (2008): -1.6 -3.5 for two seaters

**Choice of Make/Model** Average elasticity Bordely (1993):-3.6; Goldberg (1995): -3.3; Goldber g (1998):-3.1;

Brownstone et al. (2000):-3; Train and Winston (200 7):-2.3; NERA Small Bordley (1993): -3.4; Goldberg (1995): -3.5 -4 Midsize Bordley (1993): -3.3; Goldberg (1995): -4.6; Goldberg (1996,1998):-4 -4 Large Bordley (1993): -3.8; Goldberg (1995): -4.7; G oldberg (1996,1998):-4 -4 Luxury Bordley (1993): -3.7; Goldberg (1995): -2; Go ldberg(1996):-1.2; -2 Sport Bordley (1993): -4.2; Goldberg (1995): -1.4; G oldberg(1996,1998):-1.2 -2 for two seaters Truck Goldberg (1995): -3.16 Van Goldberg (1995): -4.56

**Choice of Market segment** Small Bordley (1993):-1.9; Kleit (2002):-2.8; Cambri dge (2008): -1.8 -3 Midsize Bordley (1993):-2.3; Kleit (2002):-3.5; Camb ridge (2008): -1.3 -3 Large Bordley (1993):-3; Kleit (2002):-4.5; Cambridg e (2008): -2.8 -3 Luxury Bordley (1993):-2.4; Kleit (2002):-1.7; Cambr idge (2008): -3.5 -2.2 Sport Bordley (1993):-3.4; Kleit (2002):-2.3; Cambri dge (2008): -1.8 -1.3 for two seaters Truck Kleit (2002):-3 for small truck, -1.5 for larg e truck SUV Kleit (2002):-3 for small suv, -2 for large suv
Van Kleit (2002):-2.4

**Choice to Buy a New Veh or**
**Not** ranged from -0.8 to -1 Levinsohn(1988), Kleit (1990), McCarthy (1996,1998) , Goldberg (1998) -0.8

Small Berry et al. (1995): -6.4 for Mazda 323; Eftec (2008): -4.5 -5 Midsize Berry et al. (1995): -4.8 for Nissan Maxima; Eftec (2008): -5.4 -5 Large Berry et al. (1995): -4.8 for Honda Accord; Ef tec (2008): -3.6 -5 Luxury Berry et al. (1995): -3.1 for Lexus LS400; Ef tec (2008): -4.0 -3.5 Sport Eftec (2008): -1.6 -3.5 for two seaters34 Table 5 Generalized Cost Coefficient Calibration

LEVEL 4 Choice of Make, Model, Engine Transmission C onfigur ation within a Class
Class Name Sales Price Share No. Members Ave. Share 1 Elasticity Slope

1 Prestige Two-Seater 79692 $50,888 0.47% 27 3.7% -3.5 -7.14E-05 2 Prestige Subcompact 276351 $41,808 1.63% 49 2.0% -3.5 -8.55E-05
3 Prestige C ompact and Small Station Wagon 536024 $34,369 3.16% 71 1.4% -3.5 -1.03E-04
4 Prestige Midsize C ar and Station Wagon 727577 $42,988 4.29% 66 1.5% -3.5 -8.27E-05 5 Prestige Large 113968 $47,762 0.67% 17 5.9% -3.5 -7.79E-05
6 Two-Seater 112099 $26,656 0.66% 26 3.8% -3.5 -1.37E-04 7 Subcompact 1608947 $18,869 9.48% 58 1.7% -5.0 -2.70E-04 8 C ompact and Small Station Wagon 2392457 $17,901 14.10 % 82 1.2% -5.0 -2.83E-04 9 Midsize C ar and Station Wagon 3180971 $21,132 18.75% 100 1.0% -5.0 -2.39E-04 10 Large C ar 752846 $24,217 4.44% 29 3.4% -5.0 -2.14E-04 11 Prestige SUV 1011890 $46,765 5.96% 109 0.9% -3.7 -7.95E-05 12 Small SUV 167691 $18,591 0.99% 17 5.9% -4.9 -2.79E-04 13 Midsize SUV 1082846 $24,133 6.38% 72 1.4% -5.1 -2.15E-04 14 Large SUV 2485225 $29,134 14.65% 137 0.7% -5.1 -1.78E-04
15 Minivan 801143 $28,413 4.72% 19 5.3% -4.9 -1.82E-04 16 C argo / large passenger van 84530 $25,002 0.50% 42 2.4% -5.1 -2.07E-04 17 C argo Pickup Small 353636 $20,929 2.08% 49 2.0% -5.1 -2.47E-04 18 C argo Pickup Standard 984260 $28,444 5.80% 67 1.5% -5.1 -1.82E-04 19 Ultra Prestige 214002 $94,930 1.26% 93 1.1% -3.7 -3.92E-05

TOTAL 2 16966155 $27,227 100.00% 1130

LEVEL 3 Choice Among 19 Vehicle Classes within Vehicle Type Type Name Sales Price 3 Share No. Members Ave. Share Elasticity Slope

1 Two-Seater 191791 $36,725 1.13% 2 50.0% -1.3 -7.08E-05 2 Prestige C ar 1653920 $40,326 9.75% 4 25.0% -2.2 -7.27E-05 3 Standard C ar 7935221 $19,992 46.77% 4 25.0% -3.0 -2.00E-04 4 Prestige SUV 1011890 $46,765 5.96% 1 100.0% na -7.95E-05 5 Standard SUV 3735762 $27,211 22.02% 3 33.3% -2.7 -1.47E-04
6 Minivan 801143 $28,413 4.72% 1 100.0% na -1.82E-04 7 C argo Van 84530 $25,002 0.50% 1 100.0% na -2.07E-04 8 Pickup 1337896 $26,457 7.89% 2 50.0% -2.0 -1.51E-04 9 Ultra Prestige 214002 $94,930 1.26% 1 100.0% na -3.92E-05
TOTAL 16966155 $27,227 100.00% 18

Level 2 Choice of Vehicle Type within Passenger or Cargo C a tegories C ategory Name Sales Price Share No. Members Ave. Share Elasticity Slope

1 Passenger 15329727 $26,362 90.35% 6 16.7% -1.1 -5.23E-05 2 C argo 1422426 $26,371 8.38% 2 50.0% -0.7 -5.23E-05 3 Ultra Prestige 214002 $94,930 1.26% 1 100.0% na -3.92E-05 Level 1 Choice of Passenger,C argo or Ultra Prestige Vehicle

Name Sales Price Share No. Members Ave. Share Elasticity Slope Buy a new vehicle 16966155 $27,227 100.00% 3 33.3% -0.7 -3.65E-05

Level 0 Choice to Buy a New Vehicle or Not US HHs 4 Price Buy Share Elasticity Slope

Root Node 129973385 $27,227 13.05% -0.8 -3.38E-05

Note: 1)"Ave. Share" is the average of conditional shares of members in a nest. It is approximated by 1 over number of members 2)"Total" operation is not applicable to "price" co lumn, which is sales weighted average price. 3) "Price" here reflects sales weighted average pri ce. 4) "US HHs" is numer of households in the U.S. in b ase year35

3.4.2 Constant Term Calibration

Given generalized cost coefficients, constant terms at each level of the nesting structure are calibrated to baseline sales data. Baseline market share and constants have the following relationship for any two vehicle configurations wit hin the same vehicle class:

0 0 |
0 0 |

0 0



### , ,

ln ln , , ik

jk A i k i A j k j

ik jk i j 

### P S e i j k P S e A A S S i j k = = ∀ ∈

=> − = − ∀ ∈ (41)

where superscript 0 represents baseline scenario, 0 | i k 

### P and 0

| j k 

### P are conditional probabilities of choosing vehicle i and j given class k has been chosen, and 0 i S and 0

j 

### S are baseline market share

of vehicles i and j . If we normalize one of the constants, e.g., 1 k 

### A , to be zero, then

0 0

1 ln ln , . ik ik k A S S i k = − ∀ ∈ (42)
Vehicle class level constants can be derived from t he following equation:

0 0 |
0 0 | 

### exp[ ln( )]

, , exp[ ln( )] ik

il A h kh k h i k

k k

A h l h l lh i l l 

### B A e P S B k l nest h

B P S A e

B ∈

∈ 

### + = = ∀ ∈

+ 

# ∑
∑ (43)

where 0

| k h 

### P and 0

| l h 

### P are conditional probabilities of choosing vehicle c lass k and l given nest h
has been chosen, 0 k S and 0

l S are base year market shares of vehicle classes k and l in the nest h

, and A kh and A lh are class-specific constant terms. Normalizing th e first class specific constant A 1h to be zero, we get

1 1 1 1 

### ln( ) ln( ) ln ln , i ik A A h h kh k

i class i k

k 

### B B A e e S S k nest h B B

∈ ∈ 

### = − + − ∀ ∈ 

# ∑ ∑ (44)

Again, we can use Daly (2001) notations to write a general equation. Denote c as a composite alternative and t(c) as its parent. The following equation holds for any two composite alternatives in the same level of the nesting structure:

0

0 ( ) 0 0 | ( ) ( )
0 0 ( ) | ( )

( )

exp[ ln( )] , , ,such that ( ) ( ) exp[ ln( )] a

a t c U

c c t c t a c c c

t b U b t b b b t a b b B A e P B S c b t c t b

B P S A e

B =

= + = = ∀ =

+ 

# ∑
∑ (45)

where 0

| ( ) c t c 

### P and 0

| ( ) b t b 

### P are conditional probabilities of choosing alternati ves c and b given their parent has been chosen, 0

c S and 0

b S are base year market shares of vehicle segments re presented by c and b , and 0

a U is baseline utility for an alternative a , as described by the recursive equation (26) with initial condition of

0



### , j j 

### U A j = ∀ (46)
and36 0 

### 0. NoBuy NoBuy 

### U A = = (47) Constant terms can be solved from equation (45) giv en 0

c S
, 0 b S , and generalized cost coefficients
are known. The constant for the alternative of “not buying a new vehicle” is assumed to be 0.37 

### 4. IMPLEMENTATION AND USER GUIDE

The CVCM has been implemented in C# at the editor e nvironment of Visual Studio 2010. The C# code reads input, calibrates the model parameter s including constant terms and generalized cost coefficients, calculates utilities, choice pro babilities, sales, and consumer surplus, and finally writes output to an Excel file. The C# code is distributed as a Windows installation file and users can install the program on the destinatio n computers with Windows operating systems. 13

4.1 USER INTERFACE

User interface of the CVCM is straightforward. The File menu has mainly two items: “Output Files to...” and “Open”. The “Output Files to...” item specifies the folder of output files. The default output folder is CVCM installation folder\o utput. The “Open” item selects input file. Input files could be located in any folder. But by default, they are in CVCM installation folder\input. The CVCM installation program has co pied example input files in the input folder. Each scenario has one input file, indicated by the file name. Select and open one input file to read in data. Then some of the data content will be displayed in the two tables of the user interface and users can check if the data are corre ctly read. The gray car button on the upper right corner will turn green. Users can click on the gree n button and run the program. After the run is finished, users can then select another input file to start another run.

The CVCM takes input on model parameters, vehicle c haracteristics in the baseline scenario (e.g. price, sales and fuel economy) and fuel economy imp rovement and associated incremental vehicle price in the policy scenario, where fuel ec onomy changes over time in response to fuel economy and emissions policies. It then outputs pre dictions on sales and consumer surplus in the policy scenario.

All input and output are in Excel Files. As describ ed in Section 4.1.2, the user can name the output file via the "GlobalParameter" sheet of the input file.
4.1.1 Input

A list of input data and data sources is as follows

.

• Vehicle database: detailed database at vehicle configuration level. It includes vehicle identification information (e.g. make, model, and e ngine size), price, baseline sales, and baseline fuel economy.

• Predictions on fuel economy and incremental price a t vehicle configuration level: key input data, commonly obtained from OMEGA output.

• Generalized cost coefficients and alternative-speci fic constants: model parameters. Generalized cost coefficients are derived from pric e elasticities and NMNL properties,

13 The current version of the CVCM does not work on non-windows operations systems (e.g. Mac and UNIX)

.38

given elasticities are known from the literature. C onstant terms are calibrated from baseline sales data and generalized cost coefficien ts.

• Market size: size of consumer market, which is typically approxi mated by the number of households. Household number projection for the United States is obtained from U.S. Census and American Community Survey.

• Nesting structure: default nesting structure is built in the model. In the future, users may be able to specify their own structure.

• Fuel prices: used to calculate fuel savings. Source: Annual Ener gy Outlook (AEO) 2010 from Energy Information Administration (EIA).

• Annual and lifetime driving mileage for a typical c ar or truck: used to calculate fuel cost and VMT weighted GHG emissions for manufacture rs. Source: consistent with OMEGA assumptions.

• Emission standards and vehicle footprint : used to check manufacturer compliance with GHG emissions standards. This information is option al and requires linking the CVCM outputs to OMEGA. This linkage may be made availabl e in future releases of the CVCM. At the current time, this field can be left b lank.

Sample input files in the CVCM installation folder contain all the above information. Users should follow the format in these files to prepare their own input. An input file has 7 data sheets, listed as follows. The file also contains a sheet ( “InputValidation”) to validate the input. Click on “Validation Data” button in this sheet and error me ssages will prompt out if the input in the data sheets is not in right data type or within appropri ate range. If the inputs fail the validation test, the implicit meaning is that the model nesting stru cture is not consistent with the parameters. An error message box will pop out and instruct users t o check input files. Users are not able to run the model with invalid inputs.

4.1.1.1 Vehicle Each row in this table contains attributes (see Tab le 6) of a vehicle configuration. CVCM classes are classified based on EPA classes, accord ing to the relationship in Table 3. Users will need to provide data for the columns “predicted mpg ” and “incremental price” based on OMEGA output or other sources.

Table 6 Format of Vehicle Sheet

4.1.1.2 Manufacturer It includes a list of manufacturer names, which mus t be consistent with column “manufacturer” in “vehicle” sheet.
4.1.1.3 Logit This sheet lists price elasticities at each level o f the nesting structure for the purpose of model calibration. Users can change the values of price e lasticities, but not the nesting structure.

4.1.1.4 GlobalParameter The structure of “GlobalParameter” sheet is as foll ows: veh id manufacturer nameplate model CVCM class EPA class fleet type fuel type footprint baseline price baseline mpg baseline sales predicted m pg incremental price39 Table 7 Structure of “GlobalParameter” Sheet

Scenario name defines the name of the output file. Payback period and discount rate are parameters for calculating the value of fuel econom y improvement perceived by consumers. “OnRoad Discount” is used in fuel cost calculation to discounts EPA fuel economy (MPG) test value, which is displayed in fuel economy window st ickers and used in the CVCM, to better reflect fuel economy under real-world driving condi tions. Market Size data are used to calculate sales and calibrate logit model constants at the le vel of Buy/No-Buy.

4.1.1.5 Other Sheets “VehicleUse” and “Fuel” sheets include parameters f or calculating fuel cost. In “VehicleUse” sheet, Annual driving mileage of a car (truck) at c ertain age equals the product of VMT and survival rate. “Fuel” sheet simply records fuel pri ces with year 1 as the 1 st year after redesign
year.
“Target” sheet specifies footprint function paramet ers as in 2012-2016 EPA GHG emissions standards final rule (Table III.B.2–1 and Table III .B.2–2, page 25409 of EPA and NHTSA, 2010). The redesign year in the example input file s is 2016. Thus parameters in this sheet reflect 2016 emissions standard.

4.1.2 Output

Each run will generate an output file, with its name defined by the user (at cell B2 of Global Parameter sheet of the Input file). An output file consists of two sheets: raw output and aggregate output.

“Raw Output” sheet first repeats the input data for the convenience of reading. The model output includes sales, market share, revenue (sales times the sum of vehicle price and incremental price), net price change (incremental price less fuel savin gs), and sales changes relative to the baseline scenario at the level of vehicle configuration.

“Aggregate Output” sheet outputs variables at more aggregate levels, including market-wide consumer surplus change, total sales, industry reve nue, sales weighted average fuel economy and CO 2 emissions; manufacturer level sales, sales weighte d average fuel economy and CO 2 emissions; sales at the level of passenger vehicle, cargo vehicle, or ultra-prestige 14 , and sales at each vehicle class. Note that the fleet average fu el economy is calculated as a harmonic mean: with gpm i as the gallons per mile for vehicle i,



# ∑ =

i i

i gpm Sales TotalSales elEcon FleetAvgFu * Fleet average CO 2 values are calculated two ways: first, sales weig hted:

14 Passenger vehicle, cargo vehicle, and ultra-presti ge distinction corresponds to level 1 of the nested choice structure. **Scenario Name Payback Period Discount rate OnRoad/Test ed MPG Market Size** 40



## ∑ ∑

=

i i i i

i Sales CO Sales SalesWtdCO 2 * 2

Secondly, it is also calculated as VMT-weighted, wit h the VMT based on the full lifetime undiscounted VMT of the vehicle; VMT differs by whethe r a vehicle is classified as a car or a truck for regulatory purposes:

i i i

i i i

i 

### VMT Sales VMT CO Sales dCO VMTSalesWt 

# ∑

∑

= * *

2 * 2

4.2 INTERACTION WITH OMEGA

The CVCM could interact with the OMEGA at different d egree. At this stage of model development, they run as two separate programs and pas s information via excel files. In the future, the CVCM can be fully integrated into the OMEGA as one program. 15 The framework of interaction is as follows:

Step 1: Run OMEGA model. Step 2: Collect data from OMEGA output and prepare inp ut file for the CVCM. Step 3: Run CVCM

3a: Calibrate CVCM using baseline sales data and pric e elasticities 3b: Calculate sales, market share and consumer surplus 3c: Output If the convergence criteria is met (i.e. emissions st andards are complied), STOP here. Otherwise, Go back to step 1

15 One possible way is to program the CVCM as a dynam ic link library (dll) file and call this dll from t he OMEGA.41 

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36. Greene, D.L., P.D. Patterson, M. Singh and J. Li. 20 05. “Feebates, Rebates and Gasguzzler Taxes: A Study of Incentives for Increased Fuel Economy,” Energy Policy , vol. 33, no. 6, pp. 757-776. 37. Harrison, D., A. Nichols and B. Reddy. 2008. “Evalua tion of NHTSA’s Benefit-Cost Analysis of 2011-2015 CAFE Standards,” National Econom ic Research Associates, Boston, Massachusetts, June 30. Available on the in ternet at http://www.nera.com/67_5346.htm

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, Cambridge University Press, Cambridge, UK. 49. McCarthy, P.S. 1996. “Market Price and Income Elastici ties of New Vehicle Demands,” The Review of Economics and Statistics , vol. LXXVII, no. 3, pp. 543-547. 50. McCarthy P.S. and R.S. Tay. 1998. "New Vehicle Con sumption and Fuel Efficiency: A Nested Logit Approach," Transportation Research-E , Vol. 34, No. 1, pp. 39-51. 51. McFadden, D. 1973. “Conditional Logit Analysis of Qu alitative Choice Behavior,” pp. 105-142 in P. Zarembka, ed., Frontiers in Econometrics , Academic Press, New York. 52. Moon, H.R., M. Shum and M. Weidner. 2010. “Estimat ion of Random Coefficients Logit Demand Models with Interactive Fixed Effects,” Department of Economics, University of Southern California, Los Angeles, May 27, 2010.44

53. (NRC) National Research Council. 2002. “Effectiveness and Impact of Corporate Average Fuel Economy (CAFE) Standards,” Report of the Co mmittee, National Academy Press, Washington, D.C. 54. NERA Economic Consulting. 2009. "Evaluation of NHT SA's Benefit-Cost Analysis of 2011-2015 CAFE Standards." 55. Sawhill, J.W. 2008. “Are Capital and Operating Costs Weighed Equally in Durable Goods Purchases? Evidence from the U.S. Automobile Ma rket,” discussion paper, Department of Economics, University of California at Berk eley, Berkeley, California, April. 56. Small, K. A. and H. S. Rosen. 1981. "Applied Welfar e Economics with Discrete Choice Models." Econometrica 46(1): 105-130. 57. Train, K. 2009. Discrete Choice Methods with Simulation , Second Edition, Cambridge University Press, Massachusetts. 58. Train, K. 1993. Qualitative Choice Analysis , MIT Press, Cambridge, Massachusetts. 59. Train, K.E. and C. Winston. 2007. “Vehicle Choice B ehavior and the Declining Market Share of U.S. Automakers,” International Economic Review , vol. 48, no. 4, pp. 1469- 1496. 60. Turrentine, T. and K. Kurani. 2007. “Car buyers and fuel economy?” Energy Policy , vol. 35, pp. 1213-1223. 61. Williams, H. C. W. L. 1977. “On the formation of travel demand models and economic evaluation measures of user benefit.” Environment and Planning , 9A, 285-344.45



### APPENDIX A: DERIVATION OF NESTED LOGIT MODEL EQUAT IONS

AND RELEVANT PROPERTIES

The primary purpose of this appendix is to provide a ge neral form of nested logit model equations and demonstrate CVCM equations as one spec ific instance of the general form. The secondary purpose is to derive conditions on structural parameters in nested logit models.

Without loss of generality, we consider a two-level ne sting structure for the convenience of discussion, which is the most common case in the li terature. Formulations for two-level models can be extended to multi-level cases.

The following formulation framework is consistent with Wi lliam (1977), Daly and Zachary (1978) and Train (2009). Let j denote an elemental alternative in the nested tree an d c the upper level composite alternative (or nest) to which j belongs. The utility of alternative j is

| | | , j c j c j c j c c j c U V V V V

ε ε ε = + + = + + + (A-1)

where the observed component of utility is decomposed into two parts: a part labeled

c 

### V that is constant for all alternatives within the nest c, and a part labeled | j c V that varies over alternatives

within the nest. The error term j ε is also divided into two independent components of

c 

### ε and |

j c ε

. The following assumptions are made. Errors | j c ε are identically and independently distributed (iid) Gumbel with scale parameter

c 

### μ . Errors

c



### ε are distributed such that total errors j ε are distributed Gumbel with scale parameter root 

### μ

.
We first see how the above definition and assumptions imply a relationship of scale parameters

c 

### μ and root 

### μ . The variance of total errors is the sum of variance of tw o error components:

| Var( )=Var( )+Var( )

j c j c ε ε ε , (A-2)

which, because the variance of the Gumbel distribution is 2


### 6 

### π μ with 

### μ as the scale parameter , can
be expressed as

2 2 =Var( )+ . 6 6

c
root c π π

ε μ μ (A-3)

Since 

### Var( )

c 

### ε is non-negative, the above implies the following structural condition (Williams, 1977):



### . root c 

### μ μ 

### ≤ (A-4)46

Then we compare variations of choice probability expres sions. Choice probability for alternative j (Carrasco and Ortuzar, 2002) is

| j j c c P P P = , (A-5)

with

| | '|

' exp( ) exp( ) c j c j c c j c j c V P V

μ
μ

∈ = 

# ∑ (A-6)

and

|

' ' | ' ' '

' ' ' ' ' 

### exp[ ln exp( )] exp[ ]

, exp[ ln exp( )] exp[ ]

root root root c c j c root c c j c c c

c root root

root c c j c root c c c j c c c c 

### V V V I
P V V V I

μ μ μ μ μ μ μ μ μ μ μ μ μ μ

∈

∈ 

### + +

= =

+ + 

# ∑
∑ ∑ ∑ (A-7)

where |

j c P is the conditional probability of choosing alternative j given that an alternative in nest

c is chosen,

c



### P is the marginal probability of choosing an alternativ e in nest c, and I is so called
inclusive value of nest c

. Choice probability form in (A-5) to (A-7) is consistent wit h the one in Train (2009) (equations (4.4) and (4.5) of chapter 4) if the scale parameter root 

### μ is normalized to 1 and

c 

### μ replaced by
1

k λ , the so-called log-sum coefficient. Next we wish to sh ow that CVCM formulation is a

specific instance of this general form. Assume utility fu nction | j c V takes a specific form similar to
the one in CVCM:

| j c j j V p α β = + (A-8)

where j α is alternative specific constant and p is vehicle price or generalized cost. Then choice probability can be expressed as

|

' '

' exp[ ( )] exp[ ( )] c j j j c c j j j c p P p

μ α β μ α β

∈ +

= + 

# ∑ (A-9)

and47 ' ' ' '

' ' ' 

### exp[ ln exp( ( ))]

. exp[ ln exp( ( ))]

root root c c j j

j c c

c root

root c c j j c j c c 

### Y p
P Y p

μ μ μ α β μ μ μ μ α β μ ∈

∈ 

### + +

=
+ +



# ∑
∑ ∑ (A-10)

On the other hand, choice probability in the CVCM is

|

' '

' exp( ) exp( ) j c j j c j c j j c A B G P A B G

∈ +

= + 

# ∑ (A-11)

and

' '

' '

' 

### exp[ ln exp( )]

. exp[ ln exp( )]

root c j c j

j c c

c root

c j c j c j c

c 

### B A A B G B P B

A A B G B ∈

∈ 

### + +

=
+ +



# ∑
∑ ∑ (A-12)

If one defines

j c j A μ α = (A-13)

c root c 

### A Y μ 

### = (A-14)

c c 

### B βμ 

### = (A-15)

root root 

### B βμ 

### = (A-16)

and

, j j p G = (A-18)

then CVCM equations are equivalent to the general form in (A-9) to (A-10). Parameters

c 

### B and

root 

### B are called generalized cost coefficients in the CVCM, s ince they reflect the derivative of utility with respect to price (or generalized cost). Equa tion (A-15) and (A-16) indicate that the absolute value of generalized cost coefficients are prop ortional to scale parameters and thus proportional to the inverse of standard deviation of rand om errors.4849 

### APPENDIX B: MODEL SENSITIVITY ANALYSIS

Among the model’s parameters, the most important ones a re price elasticities and those defining how consumers value fuel savings from fuel economy impro vement. In this section, we examine the sensitivity of model results to variation of price elasticities and consumers’ evaluation of fuel savings.

The input data (baseline sales and predicted fuel econ omy) are from an OMEGA run which simulates the scenario of light duty vehicles meeting 2016 EPA greenhouse gas emissions standards. The OMEGA results were provided by EPA in N ovember, 2011. Sensitivity analysis results are specific to the data, which is why we use a realistic OMEGA data set. Since OMEGA tends to (but does not precisely) equalize the margin al cost of installing fuel economy technologies across all vehicles, we expect the impa ct of fuel economy improvement on sales mix to be small.

We will start by describing the distribution of price e lasticities and then present sensitivity analysis results.

B.1 THE DISTRIBUTION OF OWN PRICE ELASTICITIES

Generalized cost coefficients are calibrated from assume d price elasticities (see Table 5). The elasticities represent the average elasticities of alte rnatives in a nest. Each vehicle has its own price elasticity depending on its price and market sha re as well as the generalized cost coefficient for its nest. Once the CVCM is calibrated, the actual elasticity of an alternative can be calculated based on equation (36). Alternatively, we can also get actual price elasticities through simulation. For example, the own price elasticity of a vehicle can be obtained by calculating the relative sales change of the vehicle in response to 1% change in its price. We calculated own price elasticities of 1130 vehicle configurations using equa tion (36). 16 The distribution of these individual elasticities is shown in Figure 2.

16 Equation (36) is derived in the case of simple log it models. Thus elasticities calculated using this equation for nested logit models (e.g. CVCM here) are only an approximation t o true values. However the error is very small.50 Figure 2 Distribution of Own Price Elasticities

Most individual vehicle price elasticities are in the range of -6 to -3. Only 10 vehicle configurations have price elasticities less than -8.0, as displayed in Table 8. Those vehicles are either ultra-prestige vehicles with very high prices or re latively expensive cars in their classes.

Table 8 List of Vehicles with Very High Elasticitie s (in absolute value)

manufacturer nameplate model vehicle class generalized cost coefficient elasticity price Daimler MERCEDES-BENZ SLR Ultra Prestige -0.000038 -18.9 497750 BMW ROLLS-ROYCE PHANTOM Ultra Prestige -0.000038 -1 5.6 409000 BMW ROLLS-ROYCE PHANTOM EWB Ultra Prestige -0.00003 8 -15.4 405000

BMW ROLLS-ROYCE PHANTOM DROPHEAD COUPE Ultra Prestige -0.000038 -13.0 342000 VOLKSWAGEN BENTLEY AZURE Ultra Prestige -0.000038 - 12.6 332585 VOLKSWAGEN BENTLEY ARNAGE RL Ultra Prestige -0.0000 38 -10.1 266585 VOLKSWAGEN BENTLEY ARNAGE Ultra Prestige -0.000038 -8.5 224585 Ford FORD MUSTANG Subcompact -0.000264 -8.3 31525 TOYOTA LEXUS IS 250 Subcompact -0.000264 -8.3 31220 TOYOTA LEXUS IS 250 Subcompact -0.000264 -8.2 31220 Mitsubishi MITSUBISHI ECLIPSE SPYDER Subcompact -0. 000264 -8.0 30224 Mitsubishi MITSUBISHI ECLIPSE SPYDER Subcompact -0. 000264 -8.0 30224 Ford VOLVO V50 FWD Compact -0.000289 -8.0 27560 Mazda MAZDA MAZDA RX-8 Subcompact -0.000264 -8.0 30 108

Table 9 provides additional descriptive statistics for elasticities of vehicle configurations within each class. In particular the medians of these elasti cities are comparable to elasticity inputs shown in Table 5.

0 10 20 30 40 50 60 70 80 90 Frequency of Elasticities51 Table 9 Descriptive Statistics of Elasticities

Vehicle Classes No. of vehicles Min 1st

Quartile Median 3rd

Quartile Max Std.

deviation Prestige Two-Seater 27 -5.5 -4.2 -3.6 -3.4 -3.2 0.6 Prestige Subcompact 54 -6.3 -4.6 -3.6 -3.2 -2.8 0.9 Prestige Compact and Small Station Wagon 71 -7.1 -4.3 -3.7 -3.4 -3.0 0.8 Prestige Midsize Car and Station Wagon 58 -6.1 -4.5 -3.9 -3.2 -2.8 0.9 Prestige Large 17 -5.4 -3.6 -3.5 -2.9 -2.7 0.8 Two-Seater 26 -5.9 -5.5 -4.4 -3.8 -2.0 1.1 Subcompact 76 -8.3 -7.0 -6.0 -5.1 -3.0 1.4 Compact and Small Station Wagon 82 -8.0 -6.9 -5.4 -4.6 -3.8 1.3 Midsize Car and Station Wagon 85 -7.8 -6.1 -5.2 -4.6 -3.3 1.2 Large Car 29 -6.6 -5.9 -5.5 -4.9 -4.3 0.6 Prestige SUV 108 -6.1 -4.1 -3.6 -3.2 -2.8 0.7 Small SUV 17 -7.3 -6.1 -5.3 -5.0 -4.5 0.8 Midsize SUV 78 -7.0 -5.7 -5.1 -4.7 -3.4 0.7 Large SUV 132 -6.5 -6.0 -5.4 -4.7 -2.9 0.8 Minivan 19 -6.5 -5.3 -4.6 -4.4 -3.7 0.8 Cargo / large passenger van 42 -6.2 -5.8 -5.7 -5.4 -4.7 0.4 Cargo Pickup Small 49 -6.7 -5.6 -4.9 -4.5 -3.8 0.8 Cargo Pickup Standard 67 -7.8 -5.6 -5.3 -4.6 -3.8 0.9 Ultra Prestige 93 -18.9 -4.8 -3.6 -3.2 -2.9 2.9

B.2 THE DISTRIBUTION OF CROSS PRICE ELASTICITIES

We have also obtained cross price elasticities at veh icle class level through simulation. The demand elasticity of class k with respect to the price of class l is calculated as the relative change in class k sales (total sales for all vehicles in class k ) given 1% price change for all vehicles in class l . The cross elasticities are shown in Table 10, where own price elasticities are in bold text and large cross elasticities are in red. The values re ported in Table 10 are comparable to those in Table 1 in the chapter of literature review.52 Table 10 Price Elasticities at Vehicle Class Level

B.3 SENSITIVITY ANALYSIS

Eight cases are defined for the sensitivity analysis (s ee Table 10). Case 1 Baseline is the case to which other cases are compared. Cases 2-4d assume vehic les are required to improve fuel economy and vehicle prices are increased consequently . The fuel economy improvements and price increases of individual vehicle configurations are the same for all policy cases 2-4d, as provided by the OMEGA output dataset. Case 2 Reference uses default CVCM assumptions. It assumes consumers value the first 5 years of fuel savings using an annual discount rate of 3%. The default elasticities in Table 5 were used to ca librate the model. Varying the length of payback period and the discount rate generates policy cases 3a and 3b, and varying the elasticities generates policy cases 4a-4d. We examin e the impact of these different assumptions on consumer surplus change, fleet average MPG and tota l sales. Class Name 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Prestige Two-Seater 1 -3.47 0.01 0.01 0.01 0.01 0.43 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.0 0 Prestige Subcompact 2 0.02 -2.90 0.16 0.16 0.16 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.00 0.00 0.0 0 0.00 Prestige Compact and Small Station Wagon 3 0.02 0.24 -2.25 0.24 0.24 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.0 1 0.01 Prestige Midsize Car and Station Wagon 4 0.04 0.40 0.40 -2.73 0.40 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.01 0.01 0.0 1 0.01 Prestige Large 5 0.01 0.08 0.08 0.08 -3.33 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.0 0 0.00 Two-Seater 6 0.36 0.00 0.00 0.00 0.00 -1.51 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0 Subcompact 7 0.05 0.05 0.05 0.05 0.05 0.05 -3.10 0.67 0.67 0.67 0.05 0.05 0.05 0.05 0.05 0.01 0.01 0.01 0.01 Compact and Small Station Wagon 8 0.06 0.06 0.06 0.06 0.06 0.06 0.72 -2.72 0.72 0.72 0.06 0.06 0.06 0.06 0.06 0.02 0.02 0.02 0.02 Midsize Car and Station Wagon 9 0.09 0.09 0.09 0.09 0.09 0.09 1.19 1.19 -3.01 1.19 0.09 0.09 0.09 0.09 0.09 0.03 0.03 0.03 0.03 Large Car 10 0.05 0.05 0.05 0.05 0.05 0.05 0.59 0.59 0.59 -4.24 0.05 0.05 0.05 0.05 0.05 0.01 0.01 0.01 0.01 Prestige SUV 11 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0 .06 -2.38 0.06 0.06 0.06 0.06 0.02 0.02 0.02 0.02 Small SUV 12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -2.67 0.09 0.09 0.00 0.00 0.00 0.00 0.00 Midsize SUV 13 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0. 06 0.06 1.15 -2.45 1.15 0.06 0.02 0.02 0.02 0.02 Large SUV 14 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 1.48 1.48 -3.02 0.08 0.02 0.02 0.02 0.02 Minivan 15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0. 03 0.03 0.03 0.03 -1.52 0.01 0.01 0.01 0.01 Cargo / large passenger 16 0.00 0.00 0.00 0.00 0.00 0.00 0 .00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -1.25 0.05 0.05 0.00 Cargo Pickup Small 17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 -2.71 0.39 0.00 Cargo Pickup Standard 18 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.31 2.58 -1.60 0.02 Ultra Prestige 19 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0 .01 0.01 0.01 0.01 0.01 0.01 -3.8453 Table 11 Sensitivity Analysis Results

Case ID Name Payback Period Disc.

Rate Elasticities Avg. Veh. Net Value ($) Consumer

Surplus Change ($/veh.) Fleet

MPG Total Sales (millions)
1 Baseline NA NA NA 0 0 27.35 16.65
2 Reference 5 0.03 default 1284 1227 33.67 17.29

3a Lower value of fuel savings 2 0 default 23 17 33.66 16.66

3b Higher value of fuel savings 15 0.3 default 4054 3591 33.65 18.64
4a 50% lower elasticities 5 0.03 default *0.5 1250 1222 33.7 16.96
4b 25% lower elasticities 5 0.03 default *0.75 1267 1225 33.69 17.12

4c 25% higher elasticities 5 0.03 default *1.25 1301 1230 33.65 17.45

4d 50% higher elasticities 5 0.03 default *1.50 1318 1232 33.64 17.62

The estimated consumer surplus change is highly sens itive to how consumers are assumed to value fuel savings from fuel economy improvements relati ve to the baseline case. The greater the amount of fuel savings that consumers consider when bu ying their vehicles, the larger the column “average vehicle net value” is. The vehicle net value is defined as the value of fuel savings taken into account minus vehicle price increa se. Consumer surplus is largest in case 3b, where consumers are assumed to take into account fuel s avings over the full expected lifetime of a vehicle. Price elasticities have much smaller impac ts on consumer surplus. The higher the price elasticities, the larger the consumer surplus change i s.

The impacts on total sales follow the same pattern as consumer surplus change. Total sales are most sensitive to the value of fuel savings perceived by consumers, with largest sales in case 3b. Total sales also increase when demand is more price el astic because the OMEGA data imply large gains in net values. The assumed price elastic ity of new vehicle demand is -0.8.

Fleet average MPG is robust to all the variables varied in the sensitivity tests. In general, the differences are less than one tenth of a MPG among sensi tivity test cases 2-4d. Fleet average MPG provided by OMEGA, if weighted by baseline sales, is 33.73, which is higher than all sensitivity test case fleet MPGs. This suggests the existence of a very small sales mix rebound effect: In the OMEGA data supplied, the greatest bene fits of improved fuel economy (fuel savings minus vehicle price increase) tend to accrue to lower fuel economy vehicles. Thus, we see a sales mix shift towards lower fuel economy vehicl es, as shown by Table 11. The table displays market shares in the baseline and reference c ases for each baseline MPG decile. The share of lower fuel economy vehicles (decile 1 and 2) inc reases, while the share of higher fuel economy vehicles (decile 9 and 10) decreases.

Table 12 Market Shares by MPG Decile

MPG Decile 1 2 3 4 5 6 7 8 9 10 Baseline 5.1% 20.4% 31.2% 24.3% 13.7% 2.7% 0.6% 0.0 % 0.3% 1.6%54

Reference 5.8% 21.2% 30.4% 24.7% 13.4% 2.4% 0.6% 0. 0% 0.2% 1.3%

The rebound effect can be quantified using the followin g equation

0 '

, ' s

s MPG MPG
MPG MPG φ −
=

− (48)

where S : index for a policy case MPG 0 : fleet MPG in the baseline case MPG s : fleet MPG in the policy case (average OMEGA MPG wei ghted by sales in the policy case) MPG’: fleet average OMEGA MPG weighted by the baseline sale s.

If MPG s is smaller than MPG’, then there is a rebound effect. Table 12 indicates tha t the rebound effect is small, in the range of 1%, and higher price el asticities tend to magnify the rebound effect. Table 13 Rebound Effect

Case ID Name Fleet MPG Rebound Effect
2 Reference 33.67 0.9%

3a Lower value of fuel savings 33.66 1.1%

3b Higher value of fuel savings 33.65 1.3% 4a 50% lower elasticities 33.70 0.5% 4b 25% lower elasticities 33.69 0.6% 4c 25% higher elasticities 33.65 1.3% 4d 50% higher elasticities 33.64 1.4%

In summary, the sensitivity analysis results suggest that fleet MPG is robust to assumptions about price elasticities and the value of fuel economy perceived by consumers. Consumer surplus and total sales are very sensitive to perceived valu e of fuel economy and not very sensitive to variation in price elasticities at lower levels in the nesting structure.