Consumer Vehicle Choice Model
            Documentation
&EPA
United States
Environmental Protection
Agency

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          Consumer Vehicle  Choice Model
                         Documentation
                       Assessment and Standards Division
                      Office of Transportation and Air Quality
                      U.S. Environmental Protection Agency
                              Prepared for EPA by
                          Oak Ridge National Laboratory
                       EPA Contract No. DE-AC05-OOOR22725
       NOTICE

       This technical report does not necessarily represent final EPA decisions or
       positions. It is intended to present technical analysis of issues using data
       that are currently available. The purpose in the release of such reports is to
       facilitate the exchange of technical information and to inform the public of
       technical developments.
United States
Environmental Protection
Agency
EPA-420-B-12-052
August 2012

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                            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 Modeling	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 Equations and Relevant Properties	45
                                         iii

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Appendix B: Model Sensitivity analysis	49
  B.I The Distribution of Own Price Elasticities	49
  B.2 The Distribution of Cross Price Elasticities	51
  B.3 Sensitivity Analysis	52
                                             IV

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                               LIST OF FIGURES
Figure                                                                        Page

   1. Nested Multinomial Logit Structure of Consumer Choice 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 absolute value)	50
   9. Descriptive Statistics of Elasticities	51
   10. Sensitivity Analysis Results	53
   11. Market Shares by MPG Decile	53
   12. Rebound Effect	54

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VI

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                            ACKNOWLEDGEMENT

This document was prepared as part of a research project 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 leadership and support in developing the Consumer
Vehicle Choice Model (CVCM). The authors are grateful to Gloria Helfand and Michael Shelby
for valuable comments on an earlier draft of this documentation. 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 Bunch, Professor Trudy Cameron, and Dr.
Walter McManus, for a very thorough and helpful review of the model and documentation. Any
remaining errors or deficiencies are the authors' responsibility.
                                         Vll

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Vlll

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                                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 to improve the fuel economy of their vehicles
and to reduce the overall GHG emissions of their fleets. The U.S.  Environmental Protection
Agency (EPA) has  developed the Optimization Model for reducing  GHGs from Automobiles
(OMEGA) to estimate the costs and benefits of meeting  GHG emission  standards through
different technology packages. However, the model does not simulate the impact that increased
technology costs will have  on  vehicle  sales or  on  consumer  surplus.   As the  model
documentation states, "While  OMEGA incorporates functions which generally minimize the cost
of meeting a specified carbon  dioxide (COi) target, it is not an economic simulation model which
adjusts vehicle sales in response to the cost of the 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 difficult for manufacturers  to meet fuel economy and
emissions  standards, and impacts on consumer surplus 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 developing an adjunct to the OMEGA model to make
such estimates.  This project is  an effort to develop and test a candidate model.  The project
statement of work spells out the key functional requirements for the new model.

    "ORNL shall develop a Nested Multinomial  Logit (NMNL) or other appropriate model  capable  of
    estimating the consumer surplus impacts and the sales mix effects of GHG emission standards. The
    model will use output from the EPA's Optimization Model for reducing Emissions of Greenhouse
    gases from Automobiles (OMEGA), including changes in retail price  equivalents, changes in fuel
    economy,  and  changes  in emissions, to  estimate  these  impacts.  ...The  model will  accept
    approximately 60 vehicle types, with the flexibility to function with fewer or more vehicle types, and
    will use a 15 year planning horizon, matching the OMEGA 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 first
    version of the model must be completed by the spring of 2011. Additional versions may be created in
    the future, pending further discussion and negotiation 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 sales mix, and
       (2)   calculates cost of standards in terms of consumer 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 the concept  of incorporating market  share and
consumer surplus changes to the OMEGA model and to produce a working initial model.

                                            1

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A research team at Oak Ridge National Laboratory  (ORNL) has designed and implemented a
Consumer Vehicle Choice Model (CVCM) for  the project based on NMNL theory with a
representative consumer. This document will detail CVCM design principles, model equations,
parameter calibration, implementation and user guide. Specifically, Section 1.2 further explains
CVCM functionality  and intended usage and summarizes 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  NMNL equations and  model calibration
procedure.  Finally, Section 4 gives instructions to 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 theoretical 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 prices, it:

          1.  -calculates impacts  of those changes  on vehicle sales and  the distribution of
             vehicle sales and the resulting impact on manufacturers'  abilities to meet fuel
             economy standards and,
          2.  -calculates changes in consumers' surplus as a consequence of the changes in fuel
             economy and vehicle purchase cost.

The CVCM is not intended to be a tool for forecasting the future vehicle fleet. There is no doubt
that, over time periods longer than a few years, vehicle designs will come and  go, new vehicle
models will be introduced and others retired, new manufacturers 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 is 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 not foreseen at the present time. The  CVCM was
not designed  to  predict  consumers'  acceptance  of these advanced technology vehicles.  This
capacity was left for future research and development.

The CVCM was developed to test the concept of predicting 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 changes to determine whether they may have
important implications for manufacturers' abilities to meet the standards and for consumer well-
being.  Given the EPA's need for periodic and timely analyses to support its responsibilities for
GHG emissions and fuel economy rulemakings, the CVCM should be capable  of being readily
calibrated to new data sets and updated with new sales and fuel economy data.

Given  the intended  purpose  and functions  of the model, it is  most appropriately used for
estimating changes in the following variables relative to the baseline values:

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    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 manufacturer, and
    3.  Sales by market segment.

The CVCM models  vehicle  type  choice  at  the most  complete  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' choices is  greatest at  the lowest1 level of the
NMNL nest, i.e., when vehicles are the closest substitutes, modeling at the greatest feasible level
of detail  can capture the full range of sales mix shifts. If vehicle type choice were modeled at a
more aggregate level, the modeling process may be open to the questions about whether it misses
important sales mix changes  that would have been evident had the model operated at a greater
level of detail. However, the CVCM prediction at the lowest level (i.e., make, model, engine and
transmission configuration) is  most sensitive to changes 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 aggregate levels.

The model provides highly detailed results.  For reasons discussed in Section 1.2.2,  the model's
predictions are unlikely to be as  precise as is suggested from  the model output. The detail is
provided for situations where the CVCM would be used  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 be 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 model makes simplifying assumptions about
consumer behavior.   Since  consumer  behavior is complex,  we  have focused the  modeling
initially on the decisions by consumers to trade-off 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 dollars) based on a model or  theory of how
consumers value fuel economy. The change in the present value of future fuel costs perceived
by  consumers is added to  the  estimated change in the vehicle's price  Ap . A price sensitivity
parameter, B, translates the resulting net change in present value into a  change  in a utility index
that determines a vehicle's market share. The change in utility  for the ith vehicle in nest j, Utj ,is
the following, where PV represents whatever function is chosen to transform  a change in fuel
economy  to a change in the present  value  of fuel savings considered in the vehicle purchase
decision.
                         AIL = Bj (A;?,. - PV { fuel savings])                       (1)
       1 In this document, the higher/lower levels are referred to by their relative positions in the nested tree/nesting structure
(Figure 1 in chap. 3) which has a buy/no-buy decision at the top/highest level and vehicle configurations (combinations of make,
model, engine, and transmission) at the bottom/lowest level. It implies that the lower levels in the tree are more disaggregated.

                                             3

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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 are reasonably accurate, the NMNL model should
give reasonably  accurate  predictions.2  Prediction  errors arise from  incorrectly estimating
changes in the utility index, caused either by errors in the estimation of the role of a change in
fuel economy or inaccurate specification of the price sensitivity parameter, B.  Such errors have
a specific functional form in logit models.

For illustrative purposes, consider a simple multinomial 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 Si with respect to a change in its utility
index is the following:
                                                                                   (2)
                            dU{    dU{  %
Since, in general, Si (which is between 0 and 1) will be approximately two orders of magnitude
larger than(1S'I.)2 , the change in market share dSi is approximately the change in utility weighted
by  the  vehicle's  market share, SidUi.   As  changes  in utility are  propagated up  the nesting
structure (as inclusive values, or expected utility changes) this simple relationship applies at each
step.  Since a shock (error) in the utility index of 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 between alternatives within a nest.  At the lowest
level  of nesting, shocks to the utilities of individual 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 negatively related to changes for the initial vehicle.
The error  term of a utility function directly induces 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.
                                                                 .S.               (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 shares, and prediction errors within a
nest are negatively correlated. Because of this, errors 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 individual vehicles within the nest.
       2 There is reason to expect the changes in dollar value 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.

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In reality, prediction errors can arise from a number 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 consumers
    3.  Errors in NMNL model structure
    4.  Errors in NMNL parameters
    5.  Omitted variables (including manufacturer pricing decisions)
    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' decision-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 review  of the econometric evidence found
contradictory and inconclusive results (Greene, 2010). 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 underlies 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 needed to better understand how consumers' value
fuel economy and how fuel economy and emissions standards affect consumers' surplus.

The CVCM is a market or representative consumer NMNL.  It does not explicitly represent
differences in consumers' preferences. The only recognition of differences in consumers' tastes
is in the logit formulation itself  which assumes that each individual perceives a different value
for each vehicle (e.g., Train, 1993 ch. 2). However, this representation of heterogeneity is very
limited and, in particular, does  not allow for different price sensitivities.  The population of
consumers  is undoubtedly heterogeneous but it is not known how important that heterogeneity is
to the intended purpose of the  CVCM.  If further research and development is undertaken,
investigating the importance of consumer heterogeneity should be given a high priority.  Explicit
heterogeneity was  not incorporated  in the CVCM in order to  keep the model and its calibration
simple.

The nesting structure used in the  CVCM is similar to 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 the nesting structure chosen is the best possible
nesting structure.

Price  sensitivities  and  alternative-specific constants  are the  two classes of parameters of the
CVCM. Price sensitivities are the most important because 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 consistent with the estimates in the published literature

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and to conform to the theoretical requirement that price sensitivities increase in absolute value as
one moves down along the nesting tree.  However, the 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 from the existing literature.

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

To the extent that the  baseline  sales data, including the definitions  of individual vehicles, differ
from the actual market data, errors could be induced in the CVCM estimates.  OMEGA is itself a
model and thus its estimates undoubtedly contain some  differences from  what  will occur, and
these will also affect the accuracy of CVCM estimates.

Over extended time periods, automotive technology will  change, and may change in ways that
cannot be foreseen at the present time.  Furthermore, consumers' preferences may also change in
unpredictable ways.  The 2002 National Research Council report  on the  CAFE standards and
potential for fuel economy improvement did not foresee a successful market for hybrid vehicles
(NRC, 2002).  The emergence  of minivans, SUVs, crossovers,  the near disappearance of station
wagons, and more, could not have been predicted with any certainty a long time period (e.g.  15
years) in advance. Assessment of technological innovation 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 changes in vehicle prices and fuel economy
provided by the OMEGA model on consumers'  surplus and changes in vehicle  sales that could
impact manufacturers' abilities to meet  fuel economy 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 that could be  readily calibrated and operated in
conjunction with the OMEGA model, and that had a sound theoretical and empirical basis.

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      2. LITERATURE REVIEW ON NEW VEHICLE TYPE CHOICE
                                    MODELING

The  impacts of changes  in vehicle prices and fuel economy on vehicle  sales and consumer
surplus can be estimated by means of systems of demand 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 represented by a system of linear or non-linear
demand equations.  Kleit (2004, 2002a & b, 1990) created a market segment vehicle demand
model that he used to evaluate the costs and benefits of CAFE standards.  Kleit divided the
market into eleven vehicle classes and four manufacturers.  Demand functions, in the 2002b
paper at least, were specified as simple linear functions 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 elasticities and cross price elasticities by exercising a
proprietary model developed by GM (Table 1).  Own price elasticities for the  eleven vehicle
classes ranged from -1.5 for large trucks to -4.5 for large cars.  The own price elasticity for
luxury cars is -1.7, less than those of standard cars (-2.8 to -4.5) but of the  same  order of
magnitude. In general, cross price elasticities are 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.  However, there are sets of classes for which
cross  price elasticities  are substantial, indicating that the vehicle types are relatively close
substitutes.  The groupings in  Kleit's  model  suggest that standard cars are relatively close
substitutes, with small cars being better substitutes 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  only 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 Class Demand Model (Kleit, 2004)

1
2
3
4
5
6
7
8
9
10
11

Small Car
Medium Car
Large Car
Sport Car
Luxury Car
Small Truck
Large Truck
Small SUV
Large SUV
Minivan
Van
1
-2.808
0.684
0.270
0.549
0.045
0.162
0.063
0.216
0.117
0.081
0.027
2
0.423
-3.528
1.926
0.423
0.405
0.099
0.072
0.279
0.243
0.171
0.036
3
0.063
1.107
-4.500
0.324
1.062
0.000
0.018
0.099
0.171
0.063
0.009
4
0.018
0.027
0.027
-2.250
0.009
0.009
0.009
0.027
0.018
0.000
0.009
5
0.000
0.018
0.216
0.009
-1.737
0.000
0.000
0.009
0.018
0.009
0.000
6
0.036
0.018
0.009
0.090
0.000
-2.988
0.234
0.090
0.054
0.009
0.009
7
0.027
0.018
0.054
0.198
0.027
0.702
-1.548
0.351
0.387
0.045
0.054
8
0.009
0.036
0.018
0.045
0.045
0.045
0.027
-3.645
0.414
0.027
0.036
9
0.009
0.045
0.063
0.108
0.189
0.054
0.090
0.747
-2.043
0.135
0.072
10
0.009
0.054
0.054
0.018
0.072
0.009
0.018
0.108
0.234
-2.286
0.387
11
0.000
0.009
0.009
0.000
0.009
0.009
0.036
0.072
0.108
0.180
-2.385

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

Bordley4 (1993) estimated own and cross price  elasticities for 200 passenger car nameplates
using aggregate time-series sales data by market segment plus survey data on the first and second
choices of consumers  who  had just purchased a new car.   The aggregate sales data allowed
estimation of own price elasticities for seven passenger car market segments and an overall price
elasticity of automobile demand.  The survey data were used to estimate "diversion fractions"
quantifying  the propensity of purchasers  of one  nameplate to buy any of the others given an
increase in  its price.   Bordley estimated an own price 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 for 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 Elasticities Estimated by Bordley (1993)
Car Class
Economy
Small
Compact
Midsize
Large
Luxury
Sporty
Class Elasticity
-1.9
-1.7
-2.0
-2.3
-3.0
-2.4
-3.4

Minimum
-3.37-3.4
-1.9/-1.7
-2.1/-2.2
-2.37-2.6
-3.1/-3.5
-3.27-3.4
-2.67-3.4
Car Nameplate Elasticities
Average
-4.7
-2.4
-3.1
-3.3
-3.8
-3.7
-4.2

Maximum
-8.27-8.1
-3.17-3.4
-4.97-4.7
-4.67-4.2
-4.37-4.0
-5.37-4.5
-6.57-5.3
Bordley's method could be used to calibrate a system of linear nameplate demand equations, as
was done by Kleit (1990).  More complex systems including 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-price elasticity matrix developed by Kleit
(2002a) to estimate the impacts of changes in vehicle 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 following matrix
equation,

                                   ^=A.(A-C()                                 (4)

in which qi is the vector of quantities for each of the 10 vehicle classes, pi is the vector of prices,
ci is the vector of present value of fuel economy improvements  and Az- 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 Laboratory at the time he conducted and published his study.
Thus, there may be a relationship between Kleit's elasticity estimates, which are based on a GM model, and Bordley's.

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


2.2 DISCRETE CHOICE OR RANDOM UTILITY MODELS

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

     "In RU models, preferences for such discrete alternatives 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 the sense that the consumer chooses the alternative
     for which the utility is maximal. Individual preferences depend on characteristics of the alternatives
     and the tastes of the consumer... .The analyst cannot observe all the factors affecting  preferences and
     the latter are treated as random variables." (Baltas and Doyle, 2001, pp. 115).

Since  the early applications  of random  utility  models in  the  1970s (McFadden,  1973),
formulations of RU  models have  proliferated.  Baltas  and Doyle (2001) identified fourteen
different methods which they grouped into three fundamentally 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 derives primarily from unobserved attributes.
Its  error term may also include unobserved variations in taste but the representation of these
variations is limited and simplistic.  The  same applies to NMNL Models although  their ability to
represent randomness in unobserved attributes  and tastes is much  more complex.  In these
models, heterogeneity in consumers' preferences is commonly represented by explicit functional
relationships between product  attributes and  consumer characteristics.   MNL  models  allow
variations  in   consumers'  preferences  to  be  represented  by  random  coefficients,  whose
distributions can be inferred either from survey or market shares data.

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

     "Finally, a general concern relates to overall model practicality.  As our discussion illustrates, recent
     developments have increased model complexity and made 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 two criteria." (Baltas and Doyle, 2001, p. 123).

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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 multinomial logit  model  of consumers'
choices among 10 vehicle classes using what was  then 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 vector of vehicle  attributes  and household
attributes. The model formulation allowed for interaction of household and vehicle variables in a
linear "representative" utility function. Let X^ bethel variable, for the/ vehicle class and the
f consumer. The representative utility function is defined as,
in which  the /fe are fixed coefficients and the e^s  are  independent, identically distributed
random variables that have extreme value distributions. The probability that consumer i will
purchase a vehicle from class j is a multinomial logit function of the representative utilities of all
classes.
                                                                               (6)
In the Lave and Train model, vehicle  price was represented 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 price sensitivity decreased with increasing
income.  The model was calibrated to survey data from  541 households collected in seven U.S.
cities in 1976.

McCarthy and Tay (1998) estimated a MNL model of consumers' 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 valued regardless of country of origin.  They also
noted  certain  "anomalies" in their  coefficient estimates.   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 to 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 attributes (e.g., size, price,  horsepower, fuel
economy, weight, interior volume,  number of seats, etc.),  the assumption  that unobserved
attributes are uncorrelated with observed attributes seems unlikely.  In addition, the problem of
defining  and obtaining measures of precisely  the  right 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 time, or by the various measures the industry
uses to capture the experiences  of launch from a stop, intermediate speed range acceleration,


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passing acceleration, and responsiveness? Inaccuracies in defining and measuring attributes lead
to errors in observed variables.  Correlated omitted variables, errors in observed variables and
correlated observed variables makes statistical inferences challenging indeed.

Lave  and Train (1979) noted two key limitations of the MNL model.   First is the so-called
Independence of Irrelevant Alternatives (IIA) property, which makes the ratio of the probabilities
of choice of any two alternatives  independent of  the  presence  or attributes of any  other
alternatives.  A related property is that all alternatives are  assumed to have the same probability
distribution of unobserved utility  (i.e., e has the same  distribution for every alternative) and that
these distributions are independent.  These properties severely restrict the patterns of substitution
the model can represent.  For example, apart from the 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 Lave-
Train 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 across the population of consumers, it is not
possible to estimate a MNL model that includes vehicle attributes and a vehicle specific constant.
In a model estimated using household data, attributes  can only be entered when interacted with
some  household  characteristic.   On one  hand, this allows attribute values  to vary  across
individuals.   On the other, it imposes  specific functional  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, especially its IIA property, led researchers  to
explore alternative formulations that allowed greater flexibility in patterns  of substitution among
vehicles  and  representations of heterogeneous consumer 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 are assumed to  be jointly normally distributed.
Instead of leading to a simple, closed form equation for the choice probabilities (like equation (6)
for the MNL model), the probit model requires numerical integration of a series of integrals. The
probit model's inherent complexity, combined with the ability of a variant of the MNL model to
overcome most of its limitations, is responsible for the very infrequent use of probit models in
modeling automobile choice.

The NMNL Model, a special case of the Generalized  Extreme Value (GEV) model, is based on
the premise that the full  choice set can be portioned  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 their observed utility.  Formally, within a subset
alternatives error terms are independent and identically 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 configuration, m, given that the consumer will
choose a vehicle in nest (class) j, is a simple MNL probability.

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                                   p   -_
                                    i'ml;    L
                                         1=1
The  probability that consumer i will choose class j is  a function of the utility of attributes
common to class j, Vj, as well as a function of the composite utility of all vehicles within class j,
k-

                                         Vfi +Ajlii
                                          U J 1J
                                                                                (8)
The term ly is the "inclusive value" or expected value of the utility of vehicles in set j.  It is
defined by equation (9).
                                /,, =ln  >'ew                                    (9)
                                 y
                                       m=l
                                      V
In equation (9) each nest has a different set of coefficients 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 choices within different nests.  The unconditional
probability of consumer i choosing vehicle m in class j is the following.

                                    P,m=PM}P,                                (10)

Another feature of the NMNL model that helps overcome the  limitations of the MNL model is
the ability to define any number of levels of nesting. 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 attributes 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. Goldberg (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 subcompacts and compacts, (T) 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 within 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  used nine  vehicle classes, within  which
consumers could choose between a foreign or domestic 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 Brownstone et al. (1996) to estimate a NMNL model
of consumers' choices among conventional and alternative fuel vehicles.  The 1993 California

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survey asked households to choose among hypothetical vehicles that included alternative fuel
vehicles.  Stated preference methods were necessitated by the  fact that very few households
purchase or have any experience with vehicles powered by non-petroleum fuels.

Most often, NMNL models are calibrated via statistical inference  based on the vehicle choices of
individual consumers or households.  However, MNL and NMNL models can also be interpreted
as representing  the  choice probabilities of a  representative  consumer or  a  population  of
consumers with  diverse tastes (Anderson et al., 1988). In  this interpretation, the random error
term (s)  represents not only unobserved attributes but also 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 aggregate  market behavior.

Greene (1994) constructed a NMNL  choice model for predicting market shares of alternative
fuel vehicles.  Rather than estimating a model based  on stated preference survey data, Greene
followed a methodology invented by Donndenlinger and  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 valued 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 coefficient in the remainder of this document. Greene
reasoned that since the overwhelming majority of consumers had no first-hand experience with
alternative fuel vehicles (e.g., battery electric vehicles, compressed natural gas vehicles, etc.)
stated preference surveys data would likely be misleading.  The model did not include a buy/no-
buy decision. The first level nest included eight alternative fuel technologies. The second level
nest  comprised  the choice  of fuel for bi-fuel or  flex-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 and 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 liquid  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 coefficients for  the nests in his model, Greene
(2001) relied on existing studies  and the theoretical requirement that sensitivity to price must
increase from the top nest to the bottom (from vehicle technology choice to fuel choice).  Since
the overall price elasticity of automobile demand  is generally believed to be approximately -1.0
(Kleit, 1990; McCarthy, 1996; Bordley, 1993) and the 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 range is an  order of magnitude, with three nests
between  the  top  and  bottom  choices  it  provides useful information that  can be used  in
conjunction with  estimates from  published  studies to greatly  reduce the uncertainty  about
coefficient values.

Greene et al. (2005) and Greene (2009) calibrated constructed  NMNL models to the market
shares of over  800 carline/engine/transmission configurations.  The data sets included  every
vehicle in the National Highway Traffic Safety Administration's (NHTSA) model year 2000 and
2005 fuel economy data sets, respectively, except those with annual sales below 25 units per year.


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Generalized cost coefficients were chosen based on the published literature and the relative value
rule for nests described above. Vehicle-specific constants were used to insure the model exactly
fit the base year data.  The ability to calibrate the model to fit any given year's sales data is an
advantage for use in policy analysis where the correspondence 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 substitutability of different types of vehicles. The
guiding principle is that vehicles within a nest are 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 classes 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 that price sensitivity (price coefficients) must
decrease in absolute value (increase in value) as one moves up the nesting tree. They began with
a price elasticity of -1.0 for the buy/no-buy decision, and then assumed the ratios of parameters
at each level in order to  calculate price  coefficients for each lower nest.  Harrison et al. also
calculated a constant term for each model, as Greene 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 include heterogeneous consumer tastes.
The utility  of vehicle m to consumer i is given by equation (11).

                                    K          H
                                        ximk + ^ihzimh +eim                      (ii)
                                              h=l

In equation (11),  dm represents the average  utility (intercept term) of vehicle  m, the Ximk are
vehicle attributes interacted with consumer characteristics, the /?# are mean coefficient values for
these  variables, the ju^ are individual  specific  random coefficients reflecting deviations  of
individual tastes from  those /?# for which  tastes vary,  and the zimh are vehicle attributes interacted
with consumer characteristics for which tastes vary (Train and Winston, 2007).  Assuming that
the Sim are independent and identically distributed and have 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 probability distributions of the random variables).
                             4,=j;
        More accurately, the vehicles are more similar with 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.

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Train and Winston (2007) estimated a mixed logit model  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  shares  of U.S. auto manufacturers.  Each
consumer's choice set consisted of 200 makes  and models. There is no closed form solution for
estimating the  parameters of the MLM.  Instead,  simulation  was used  to approximate the
integrals for choice probabilities and the resulting 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 Winston model is,
                                           r,      Y,

The  variable v is  a standard  normal random variable.  This adds  richness to the model by
representing varying tastes  across the population.   There is  even some small probability of
finding a consumer who prefers higher prices (P>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 quite  feasible. Both require simulations (perhaps
only  a  few  hundred) and both  require  information about the distributions  of consumer
characteristics (available from national surveys).

A comparison of MLM and NMNL models was made  by Brownstone et al. (2000), combining
stated and revealed preference survey data for California households.  The authors observed that
the  MLM  improves  the  fit  of  model  to data,  and indicated  substantial heterogeneity of
preferences across  the population.   They also  noted  that revealed preference (RP) data are
essential for obtaining realistic predictions of consumers' choices of vehicle types.  However,
they also commented on the difficulty of statistical inference using RP data.

    "RP data appear to be critical for obtaining realistic body-type choice and scaling information, but
    they are plagued by multicollinearity and difficulties 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 model of vehicle choice and a paired model of
vehicle use using data from the 2001 National Household Travel  Survey.  They divided vehicles
into  10  vehicle  classes, 5  age categories and 7 manufacturers.  The paired models not only
estimate new vehicle choices but vehicle use, as well as aging and scrappage.  Jacobsen (2010)
used the model to assess the impacts of CAFE standards 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  vehicle demand  was estimated to be -2.0,
substantially more than the unit elasticity found in models cited above.

Cambridge Econometrics (2008)  estimated a  mixed logit 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 their


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vehicle, which the researchers matched to a separate data base of vehicle attributes.  The survey
asked what attributes consumers considered important to the purchase of a vehicle. Respondents
cited many difficult to measure factors, such as reliability, 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  market 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), Sports cars (-1.79) and 4X4s (-1.75).  The
observed patterns  of own- and cross- price elasticities led the researchers to comment on the
importance of models that allow flexibility in substitution patterns.

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

Mixed logit models can also be estimated using aggregate market shares, as first  shown by Boyd
and Mellman (1980) and Cardell and Dunbar (1980)  and later in a seminal paper by Berry,
Levinsohn and  Pakes (BLP) (1995).  BLP provided a  practical 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  comprised 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. Noting that the objective function in the
BLP model is highly nonlinear and thus  prone to multiple local optima, they tested 10 different
optimization  algorithms, using 50 different starting values for each.  Their results call for caution
both in interpreting parameter estimates from BLP-type 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 over 100 depending on the set of candidate parameter
    estimates." (Knittel and Metaxoglou, 2008)

On the other hand, other researchers, using variants 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  time-
specific fixed effects with vehicle-specific fixed effects.  The consumer's utility function is,
                                          r=l
in which a' 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 Sjt, represented
by the third hand side term.  The difference between this formulation and that of BLP is the
specific structure imposed on the distribution of product- specific tastes. The final term, %, is the
individual, product and time specific utility component.  Note that if there are on the order of 103

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vehicles and just a few time  periods, this model has thousands of parameters.  In addition,
projecting taste heterogeneity into the future requires  specifying future values for/rt and Sjt or
assuming they remain constant. If these are assumed to be constant at the values of a given year
or at average values, the heterogeneity of tastes is 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 reduces the need for instrumental variables, in
particular,  to  represent price  endogeneity. The  authors find  that, given  their formulation,
coefficient  estimates produced  by methods that assume prices are exogenous versus endogenous
differ little.

The Moon  et al. method also produces price elasticities that are much higher in absolute value
than those  obtained by the standard BLP model estimation 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 prices 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 from -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 MEM 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 registered by private households in 11 regions of
the UK.  They note that their choice set is considerably larger than that of any previous study.
The ability to calibrate a model to such a large choice set is a consequence of the BLP estimation
procedure.  Vehicles were nested into 9 classes  based  on size, body style and price.  Estimated
median price elasticities ranged from -1.3, for vehicles in the SUV class with a range from -2.4
(90th percentile)  to -1.0 (10th percentile), to -5.4  for vehicles in the small-to-medium size  family
car segment with a range from  -7.1 (90th) to -4.5 (10th). Sports cars also had relatively low price
elasticities and subcompact and mini car choices were relatively price elastic.

A number  of recent studies have employed forms of the 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,  2008;  Sawhill, 2008).  These and other
related studies were  reviewed by Greene (2010).  All 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 prices, although most models assumed static
expectations based on the observation that fuel prices appear to follow a random walk.

Aggregate, mixed logit type models can be used to predict market shares and estimate changes in
consumer surplus. For example,  Greene and Liu (1988) used both  a random coefficient MNL
model and  Lave and Train's  (1979)  model to estimate the  impacts of changes  in vehicle


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attributes related to fuel economy on the consumer surplus associated with automobiles sold in
the United States between 1978 and 1985.  The random coefficient model utilized Monte Carlo
simulation  to  execute  repeated  draws from the vector  distribution of  random coefficients.
Greene and Liu found that the estimated mean consumer 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 models, NMNL, and MLM) can be used to
estimate changes in market shares and consumer surplus 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 estimates for 60 or even  800 vehicle types.  Given
own-  and  cross-price  elasticities,  calibration  of such  models to  sales  data  would   be
straightforward.  Estimating the price elasticity matrix, however, is a major challenge.  An 800
by 800 matrix would require 640,000 elasticity estimates and even a 60 by 60 matrix would need
3,600 elasticity values.  Bordley's (1993) method offers 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 consumer heterogeneity also comes at the price of
greater information requirements  for model calibration and simulation.  Mixed logit models
require specification of not only the central tendencies of key parameters but also their variance,
and possibly their correlations.  Running a mixed logit model requires repeated randomized
draws from the distributions of parameters. Fortunately, software is available for performing the
necessary simulations.  Calibration and updating of MLMs requires considerable effort. Survey
based estimation methods require extensive, detailed survey data. Aggregate methods have more
modest data requirements but the validity of the estimates by the most prevalent algorithms has
been called into question by recent research (Knittel and Metaxoglou, 2008).  In either case,
there is presently no evidence that MLMs produce more accurate predictions than other methods.
Should the EPA determine that vehicle choice modeling can make an important contribution to
its regulatory analyses, it may be worthwhile to determine whether the potential benefits of using
mixed logit models to represent consumer heterogeneity are worth the extra complexity and data
requirements of the mixed logit model.

NMNL models have been constructed, calibrated and used in policy analyses of fuel economy
issues by Greene et al. (2005), Harrison et al. (2008) and  Bunch et al. (2011).   All three
applications  modeled vehicle choices at  a fine level of detail, ranging from  200  makes and
models to over 800 make/model/engine/transmission combinations. This high level of detail was
considered necessary to adequately represent the changes in market shares that might result from
fuel economy and emissions  standards or fiscal policies.  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 feasible 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.


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Given a nesting structure and corresponding price coefficients, 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 introduction, termination, or modification of product
lines.  They are not capable, however, of predicting 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 models that include fixed effects to accurately
predict sales shares and applies to Mixed Logit Models and other formulations, as well.

For the purpose of developing an initial model  to test 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 information 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 flexibility 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 consumer tastes lead to more accurate predictions.
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                                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,  constant 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 substitution patterns within and between nests. The
structure has 5 levels: LevO (Buy a  new vehicle/Don't buy a new vehicle), Levl (Passenger
Vehicles, Cargo  Vehicles and  Ultra Prestige vehicles),  Lev2  (vehicle types:  Two Seaters,
Prestige Cars, Standard Cars, Prestige SUVs, MiniVans, 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 combination of make, model, engine size and
transmission type)).  Define LevO as the highest level and Lev4 as the lowest level.  Right above
LevO is root node (not drawn in Figure 1), which is the origin of the nesting structure/tree.
                                            , Don't Buy


Small


Midsize
Large
            Figure 1 Nested Multinomial Logit Structure of Consumer Choice Model

                   Note:  "Standard" is synonymous with "Non-Prestige"

The nesting structure in Figure 1 is defined according to general principles  that group closer
substitutes in a nest and ensure price sensitivity (price coefficient) and substitutability increase as
one goes down to the bottom of the nesting structure6. The inclusion of the buy/no-buy option is
necessary to predict impacts on total sales, not just the distribution of sales among makes,
       ' The requirement that price sensitivity increases as one goes down to the bottom is explained in Appendix A.

                                            21

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models and vehicle classes. Conditioning on buying a new vehicle, vehicle configurations are
grouped according to functionality and size of vehicles and  prestige/non-prestige.  Thus levl
distinguishes between passenger vehicles, cargo vehicles,  and ultra-prestige vehicles (see its
definition in Table 3), which are least substitutable.  Lev2 further divides passenger vehicles into
Two Seaters,  Prestige Cars, Standard Cars, Prestige SUVs, Standard  SUVs,  and MiniVans,
acknowledging increasing substitutability  among these alternatives (e.g.  Standard SUVs and
MiniVans, which  are both passenger vehicles, are closer substitutes than Standard SUVs and
Small  Pickup Trucks, because  Small Pickup Trucks are cargo vehicles). Cargo vehicles are
divided into Pickup Trucks and Vans. Lev3 continue dividing some nodes in Iev2 by vehicle size
or prestige/non-prestige.

The  literature provides evidence that support our definition 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 common 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, large car, sports car, luxury car, small truck, large
truck, small SUV, large SUV, minivan, and van, which 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 detail, which enables the CVCM  to potentially
    simulate the full range  of sales mix shifts. The  structure includes 5  levels,  and choice
    alternatives are  vehicle configurations (on the order of 1000), while  the literature studies
    typically include two or three levels, and choice alternatives are  vehicle size classes or
    makes/models (on the order of 200);
(2) The passenger  and cargo vehicle distinction in Levl is fully compatible with EPA emissions
    standards' compliance categories for cars and trucks;
(3) Our structure has a more thorough treatment of prestige vehicles in consideration that they
    have different price sensitivities from non-prestige 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 Levl. The  special 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.  Technically speaking, positioning ultra-
    prestige vehicle  nest in Levl allows us to assign a small price coefficient to these vehicles.

The structure in Figure 1 is implemented in the CVCM by default. Future versions  of the CVCM
could  support user-defined  structure. Alternative  structures  may  have  impacts  on   sales
predictions. Sales  in the level of vehicle configurations will  be most  sensitive  to the structure
change. The degree  of sensitivity diminishes as the prediction is targeted  at more aggregate
levels.
                                            22

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                         Table 3 Vehicle Class Definition in the CVCM
CVCM Class
    No.  of
Configurations1
Corresponding EPA Class
1. Prestige Two-Seaters
2. Prestige Subcompact Cars
3. Prestige Compact Cars and Small Station
Wagons
4. Prestige Midsize Cars and Station Wagons
5. Prestige Large Cars
6. Two-Seater
7. Subcompact Cars
8. Compact Cars and Small Station Wagons
9. Midsize Cars and Station Wagons
10. Large Cars
11. Prestige SUVs
12. Small3 SUVs
13. Midsize SUVs
14. large SUVs
15. Mini Vans
16. Cargo/Large Passenger Vans
17. Small Pickup Trucks
18. Standard Pickup Trucks
19. Ultra Prestige Vehicles3
      27        Two Sealers
      49        Subcompact Cars, Minicompact Cars

      71        Compact cars, Small Station Wagons
      66        Midsize Cars, Midsize Station Wagons
      17        Large Cars
      26        Two Sealers
      58        Subcompact Cars, Minicompacl Cars
      82        Compacl Cars, Small Slalion Wagons
      100       Midsize Cars, Midsize Slalion Wagons
      29        Large Cars
      109       SUVs
      17        SUVs
      72        SUVs
      137       SUVs
      19        MiniVans
      42        Cargo Vans, Passenger Vans
      49        Small Pickup Trucks
      67        Slandard Pickup Trucks
      93	See Ihe definition (nole 4) below	
Notes:
    (1) Number of configurations is Ihe number of configurations which a CVCM class conlains. II is nol
       an attribute of Ihe model ilself, bul specific to the vehicle dala base to which Ihe  model is
       calibrated: a configuration is a record in Ihe dala base and a CVCM class consisls of multiple
       records.
    (2) Prestige and non-prestige classes are defined by vehicle price: the prestige are vehicles whose
       prices are higher lhan or equal to unweighted average price in Ihe corresponding EPA class,  and
       vice versa for non-prestige vehicles; Ihese calculations are  done after ullra-preslige vehicles (see
       below) are pul in a separate nest E.g., Prestige Two-Sealer class is the sel of relatively expensive
       vehicle  configurations in EPA class of Iwo sealers wilh prices higher lhan or equal to  Ihe
       unweighted average price of EPA Iwo sealers.
    (3) Non-prestige SUVs are divided into small, midsize and large SUVs by vehicle's foolprinl (small:
       foolprinl <43; midsize: 43<=foolprinl<46; large: foolprinl>=46)
    (4) Ullra Prestige class is defined  as Ihe sel of vehicles whose prices are higher lhan or equal to
       $75,000.
                                             23

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3.2 EQUATIONS



The CVCM includes a series of equations to  define or calculate vehicle utilities, to calculate

market share and sales of each vehicle configuration, and to estimate consumer surplus change

brought by the installation of fuel economy technologies.


3.2.1 Prelude


We start from a review of Multinomial Logit (MNL) equations. The representative component of

the utility  expression for an  alternative is defined in  terms of four parts - the attributes^,

attribute coefficients ftk ,  alternative specific  constant aj , and scale parameter /n .  With  the

assumption that the  variance of unobserved factors is  distributed extreme value with variance
   9
 n
- (Train, 2009), the utility  of alternative j for individual n is
                                                                                (16)
where the  sum  G; represents a "generalized cost" (Greene, 2001) for alternative j, ft p is the

coefficient of vehicle price attribute and the scale parameter /n is proportional to the inverse of

the standard deviation of the error term. The choice probability of alternative; is
            p  _

             nl ~
Note that the scale parameter /n and coefficients aj and ft p 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


                                 U}=A}+BG}+e},                             (18)



                                     exp(A.+5G.)
                               P. = - ^- - -                             (19)
                                                     -
with Aj = jUCCj and B = jBpjU. Coefficient B is called generalized cost coefficient since it reflects

the derivative of utility with respect to price or generalized cost. Generalized cost coefficient is
                                            24

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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 the  demand of  a
representative consumer.

3.2.2 Two-level CVCM Equations

The CVCMNMNL equations are first  introduced in  a simplified 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 price 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 vehicle attributes is represented by an alternative-
specific constant term. The constant for each alternative is calibrated to match baseline sales data.
The utility7 for vehicle j in class k is

                   Ujk = Ajk + BkGj + ejk = Ajk + Bk (Cjk - FS jk ) + ejk ,               (20)

where

Ajk'.    constant term for vehicle jin class  k,
Bk:    generalized cost coefficient parameter for vehicles in class k,
Cjk :  incremental cost for improving fuel economy of vehicle j, and
FSjk :  the amount of fuel savings from improved fuel economy, valued  by  consumers when
       making purchase decisions.

The utility function for the class k is


                                                                 C,-K<>,)]      (21)
where Ak is constant term representing attributes shared by all alternatives in class k and Broot is

the generalized cost coefficient for vehicle classes. Note that the log-sum  term In^expf/^ is
                                                                                jek
often referred to as the "inclusive value" in the literature (e.g. Train, 2009). Choice probability
for alternative j is


                                     PI = V* '                                 (22)
       7As seen in the appendix A, equation (20) only represents a component of the total utility that is unique to vehicle /
The utility component common to all vehicles in one class is captured by a class specific constant term.

                                             25

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with
                                     exnM. + B, G )
                                              -^4rr                           (23)
and
                           exp[AA + ^l
                     Pk =		~	                  (24)
                         ^ exp[A,, + -^ In 2 exp(A. + 5t,G;.)]
where Pjtk is the conditional probability of choosing alternative j given that an alternative in class
k is chosen, and Pk is the marginal probability of choosing an alternative 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 levels. But a simpler alternative is to define
utilities and calculate choice probabilities recursively 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)), ..., kl t(k) = root}
         Each node c can be considered an "alternative" in its  own right. Nodes in the
          bottom level  are "elemental alternatives", which are vehicle configurations.
          Nodes higher than the bottom level are viewed as "composite alternatives" that
          include all the elementary alternatives below it.
       
Utilities of nodes are then defined by

                                  Uj=Aj+Bt(j)Gj                               (25)
                                                 =Ac+BtcUc                   (26)
                                                        t(c)
                                            26

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with

                                           ~                                    (27)
Equation  (25) defines utilities for elementary alternatives including all vehicle configurations
and  No-Buy  alternative.  Equation (26)  is  recursive, defining the utility of  node  c as the
summation  of constant term Ac and generalized cost coefficient (Bt(c}IBc} weighted log-sum
term. The log- sum term is calculated over all the child nodes of c, where  Ua 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 composite utility for the choice set) is


                                                                   Bu)           (28)
with
                       root  t(a)=root
                                   TJ     -A
                                   u NoBuy   ^
The utility function in equation  (28)  can be used to measure  the  consumer surplus change,
consistent with Small and Rosen (1981):
                              root    t(a)=root           t(a)=root


where the superscripts 0 and 1 refer to before and after the change, and - Bmot is marginal utility
of income.

The choice probability of each alternative is found by solving the following equation for Pc:
                         \nPc=       (Ua~^      expt/J.                      (31)
                                aeALL(c)        t(b)=t(a)

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

                               P = P    P     P                                 (32}
                                 j   1 j^d)1 c\t(c)"  Buy\roof>                            ^ ^ >

with
                                     _   exp Uc
                                 "dt(c)=                                         (33)
                                        t(b)=t(c)
                                             27

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where />cl,(c) 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 product of market size and market share:

                                Nc=MSc=MPc,                             (34)

where Nc is sales for the vehicle segment represented by node c, Sc is corresponding market share
and M is market size, estimated by number of households.

The  key input parameters  for  these  equations include 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 generalized 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 assumption and calculation of consumer value
of fuel economy will be presented in the next section.


3.3 VALUE OF FUEL ECONOMY

How consumers value fuel economy improvements has very 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 of 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 vehicle.  On the other hand, there is evidence that very
few  consumers actually  make such quantitative assessments (Turrentine and Kurani,  2007).
Greene et al. (2009) show that typical consumer loss  aversion combined with the uncertainty of
future fuel savings could  lead to a significant undervaluing of future fuel  savings relative to the
expected present value.   Greene (2010) concludes that 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 fuel 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% discount. In order  to be  consistent with the
OMEGA, the CVCM implemented  the same calculation method by default. However, users can
always change the parameters  (r and  L in equation(35)) in the input file to reflect their own
assumptions on fuel savings calculation.

Denote scenario 0 as the baseline scenario, with fuel economy  at an  initial  value; denote scenario
1 as the policy scenario, where fuel  economy changes 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:
                                           28

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                      t+L    1                     11
                           	-P(T)M(T-t)[	:]           (35)
                           L + r)"              JjMPG(t)  rjMPG}(f)
where

FSi(t):    considered fuel savings of model year t vehicle i relative to its baseline configuration
P(r):      price of fuel in year r
M(T-t ): annual miles traveled for a vehicle with age of T - 1
r:        consumer discount rate
rj :        OnRoad discount factor that discounts fuel economy (MPG) in order to reflect real-
          world driving conditions
L:        assumed payback period, in years.


3.4 CALIBRATION

Generalized cost coefficients and alternative specific constant terms are key input parameters to
the CVCM.  Generalized cost coefficients can be directly assigned, as in NERA (2009), or can be
derived from other measures, e.g. price elasticities,  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 in 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  coefficients can  be  estimated from  price
elasticities according to the following relationship:

                                  77,. =^(1-5,.),                             (36)


                             B  = - ^ -  - ^^                        (37)
where rjj is  the own-price elasticity of demand for  alternative j, pj is the price of j, Sj is / s
conditional  market  share  given nest  c is chosen,  Bc is the  generalized cost  coefficient  for
alternatives  in nest  c, ~pc is average price for alternatives in nest  c , Scis average conditional
market share, and 7/cis a representative value of TfjS . Equation (36) is derived from the definition
of elasticities and logit model equations (for further  details, please refer to Train, 2009). Price
elasticities can be chosen based on an evaluation of values found in the literature.

Secondly, theoretical requirement of NMNL on  generalized cost  coefficients provides  useful
information for determining generalized cost coefficients. The NMNL theory requires that the
absolute value of generalized cost coefficients must  increase as one goes down to the bottom

                                            29

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(vehicle configurations level) for the NMNL model to be consistent with utility maximization
(see Appendix A):
                           \Bc\>\B1(c,)\>\B1(1(c),)\>...>\Brool\,                        (38)
where Bt(c) is the  generalized cost coefficient associated with  the  parent node of c. Thus
generalized cost coefficients  at bottom level provide 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 coefficients 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 inversely proportional to the standard deviation of
unobserved attributes in the nest (Appendix A). Prestige vehicle classes or nests may have large
variance in unobserved  attributes since consumers value these attributes very differently. Thus
generalized cost coefficients of prestige vehicle classes or nests are lower in  absolute value than
those of non-prestige vehicle nests. This is  consistent with the finding of Goldberg (1995) of
lower generalized cost coefficients for higher-price market segments.

We further extend  this relationship with evidence from empirical  studies. Disaggregate vehicle
type choice models (e.g. Train and Winston, 2007) typically include in the utility function the
ratio of vehicle price (p j) and household income (Yn):

                         Ujn=/3^+... + jn=^Pj+... + jn.                      (39)
                                  n            n
So  generalized cost coefficient (filYn  here) is inversely proportional to  income. Assuming that
income elasticity of expenditure is  1  (i.e., expenditure on vehicle purchase is approximately
proportional to income), we conclude that generalized  cost  coefficients  are approximately
                                                                                            o
inversely proportional to vehicle purchase expenditure and, roughly  speaking, vehicle price.
That is,

                                      IT*-^1.                                   (40)
                                       Bc    PC
where c and c' represent two nests, and B and /?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 household level. Equation (40) can act as a proxy to
represent price sensitivity variation due to household income difference.


3.4.1.2 Calculation
The calculation of generalized cost coefficients according to Equation  (37) requires the input of
price elasticities. Table 4 4 has summarized elasticity values from relevant literature that study
new vehicle demand and report elasticities explicitly.  Although these literature elasticities are
valuable, it is difficult  to directly  use them in the  CVCM due to the following reasons: (1)
literature studies and the CVCM have different nesting structures,9 and  (2)  elasticities could be
       8 Our intention is not to derive a definitive relationship, but to obtain a rule of thumb from empirical observations,
which would be useful to generalized cost coefficient calibration.
       9 Thus the categories presented in Table 4 do not correspond to the categories used in the nesting structure of the
CVCM, but instead reflect the categories used in the cited studies.

                                             30

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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 determine 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 corresponding level in Table 5 and is an
intermediate level between level 3 and 4  of Table 5.

The overall price elasticity of automobile demand is set at -0.8 (LevO of Table 5), consistent with
McCarthy (1996)  and  Levinsohn  (1988).  Following equation  (37),  the  generalized cost
coefficient for the buy/no buy decision is calculated and the value (-3.39E-05) serves  as a lower
bound (in absolute value) for all generalized cost coefficients in Table 5.

Not many studies report elasticities at vehicle configuration level (Level 4 of Table 5).  So  we
first look at the make/model level, whose elasticities values are lower bounds   (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). Elasticities 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 make/model level are around -4 for non-luxury cars
(-4 is about the  central  value of the literature estimates) and around -2 for luxury and sport cars
(-2 is about the central estimate). Generalized cost coefficients (usually but not always ranked in
the same way as elasticities) at vehicle configuration 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-prestige11 cars (classes 6,  7, 8, 9, and 10 of Level 4
in Table 5) and -3.5 for prestige cars and two seaters (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 for 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 elasticity is around -1.8  to -2.8 for  small size
       10 Exactly speaking, generalized cost coefficients for choices among makes and models are lower bounds of
generalized cost coefficients for choices among configurations. This relationship is approximately true for elasticities.
                                            i luxi

                                             31
"Prestige cars in Table 3 have the same definition as luxury cars in Table 4.

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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 value 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 according to equation (37). For luxury and sport cars,
elasticities are  around -1.7 to -3.5 in Table 4. Thus the representative value of price elasticities
for choice among  luxury/sport vehicle classes was initially set at -2.5 (Rows "Two Seater" and
"Prestige  Car"  in Level 3 of Table 5), which is about the mean of literature estimates. However,
calculated generalized cost coefficients based on these elasticities are larger in absolute values
than their upper bounds and hence violate the theoretical requirement of NMNL (equation(38)).
So price elasticities are adjusted to be -2.2 for Row "Prestige Car" and -1.3 for Row "Two Seater"
so that12 calculated generalized cost coefficients satisfy the 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 relevant 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 (Level 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 (LevO-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 Ultra Prestige  category, generalized  cost
coefficient of Lev2-Ultra Prestige is copied from Lev4-Ultra Prestige. For Levl, 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 obtained 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 calculated 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) and calculate all generalized cost coefficients
using equation  (37).
       12 A range of elasticities satisfy this constraint. We gradually increase the initial elasticity value of -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 satisfies the constraint.

                                             32

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Table 4 Own Price Elasticities of New Vehicle Demand in the Literature

Choice of Configuration

Choice of Make/Model







Choice of Market segment







Choice to Buy a Ne w Veh or
Not



Small
Midsize
Large
Luxury
Sport
Average
Small
Midsize
Large
Luxury
Sport
Truck
Van
Small
Midsize
Large
Luxury
Sport
Truck
SUV
Van

Small
Midsize
Large
Luxury
Sport
Own Price Elasticity of Demand

Berry et al. (1995): -6.4 for Mazda 323; Eftec (2008): -4.5
Berry et al. (1995): -4.8 for Nissan Maxima; Eftec (2008): -5.4
Berry et al. (1995): -4.8 for Honda Accord; Eftec (2008): -3.6
Berry et al. (1995): -3.1 for Lexus LS400; Eftec (2008): -4.0
Eftec (2008): -1.6
Bordely (1993):-3.6; Goldberg (1995): -3.3; Goldberg (1998):-3.1;
Bordley (1993): -3.4; Goldberg (1995): -3.5
Bordley (1993): -3.3; Goldberg (1995): -4.6; Goldberg (1996,1998):-4
Bordley (1993): -3.8; Goldberg (1995): -4.7; Goldberg (1996,1998):-4
Bordley (1993): -3.7; Goldberg (1995): -2; Goldberg(1996):-1.2;
Bordley (1993): -4.2; Goldberg (1995): -1.4; Goldberg(1996,1998):-1.2
Goldberg (1995): -3. ID
Goldberg (1995): -4.5D
Bordley (1993):-!. 9; Kleit (2002):-2.8; Cambridge (2008): -1.8
Bordley (1993):-2.3; Kleit (2002):-3.5; Cambridge (2008): -1.3
Bordley (1993):-3; Kleit (2002):-4.5; Cambridge (2008): -2.8
Bordley (1993):-2.4; Kleit (2002):-!. 7; Cambridge (2008): -3.5
Bordley (1993):-3.4; Kleit (2002):-2.3; Cambridge (2008): -1.8
Kleit (2002):-3 for small truck, -1.5 for large truck
Kleit (2002):-3 for small suv, -2 for large suv
Kleit (2002):-2.4
ranged from -0.8 to -1
Levinsohn(1988), Kleit (1990), McCarthy (1996,1998), Goldberg (1998)
Berry et al. (1995): -6.4 for Mazda 323; Eftec (2008): -4.5
Berry et al. (1995): -4.8 for Nissan Maxima; Eftec (2008): -5.4
Berry et al. (1995): -4.8 for Honda Accord; Eftec (2008): -3.6
Berry et al. (1995): -3.1 for Lexus LS400; Eftec (2008): -4.0
Eftec (2008): -1.6
Values Used in Calibration

-5
-5
-5
-3.
-3.

-4
-4
-4
-2
-2


-3
-3
-3
-2.
-1.



-0.
-5
-5
-5
-3.
-3.

5
5 for two sealers





for two sealers





2
3 for two sealers



8
5
5 forlwo sealers
                               33

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                               Table 5 Generalized Cost Coefficient Calibration
LEVEL 4
Class
         1 Prestige Two-Seater
         2 Prestige Subcompact
         3 Prestige Compact and Small Statioi
         4 Prestige Midsize Car and Station Wi
         5 Prestige Large
         6 Two-Seater
         7 Subcompact
         8 Compact and Small Station Wagon
         9 Midsize Car and Station Wagon
        10 Large Car
        11 Prestige SUV
        12 Small SUV
        13 Midsize SUV
        14 Large SUV
        15 Minivan
        16 Cargo / large passenger van
        17 Cargo Pickup Small
        18 Cargo Pickup Standard
        19 Ultra Prestige
ion Configuration within a Class
Price Share No.
79692
276351
536024
727577
113968
112099
1608947
2392457
3180971
752846
1011890
167691
1082846
2485225
801143
84530
353636
984260
214002
$50,888
$41,808
$34,369
$42,988
$47,762
$26,656
$18,869
$17,901
$21,132
$24,217
$46,765
$18,591
$24,133
$29,134
$28,413
$25,002
$20,929
$28,444
$94,930
0.47%
1.63%
3.16%
4.29%
0.67%
0.66%
9.48%
14.10%
18.75%
4.44%
5.96%
0.99%
6.38%
14.65%
4.72%
0.50%
2.08%
5.80%
1.26%
Members Ave. Share1 Elasticity Slope
27
49
71
66
17
26
58
82
100
29
109
17
72
137
19
42
49
67
93
3.7%
2.0%
1.4%
1.5%
5.9%
3.8%
1.7%
1.2%
1.0%
3.4%
0.9%
5.9%
1.4%
0.7%
5.3%
2.4%
2.0%
1.5%
1.1%
-3.5
-3.5
-3.5
-3.5
-3.5
-3.5
-5.0
-5.0
-5.0
-5.0
-3.7
-4.9
-5.1
-5.1
-4.9
-5.1
-5.1
-5.1
-3.7
-7.14E-05
-8.55E-05
-1.03E-04
-8.27E-05
-7.79E-05
-1.37E-04
-2.70E-04
-2.83E-04
-2.39E-04
-2.14E-04
-7.95E-05
-2.79E-04
-2.15E-04
-1.78E-04
-1.82E-04
-2.07E-04
-2.47E-04
-1.82E-04
-3.92E-05
TOTAL2

LEVEL 3
Type
                                     16966155

  Choice Among 19 Vehicle Classes within Vehicle Type
  Name                          Sales
1 Two-Seater
2 Prestige Car
3 Standard Car
4 Prestige SUV
5 Standard SUV
6 Minivan
7 Cargo Van
8 Pickup
9 Ultra Prestige
                                                   $27,227   100.00%
                                                                            1130
TOTAL
s Price3 Share No. Members Ave. Share Elasticity Slope
191791 r
1653920 '
7935221 '
1011890
3735762 '
801143
84530
1337896 r
214002
16966155
$36,725
$40,326
$19,992
$46,765
$27,211
$28,413
$25,002
$26,457
$94,930
$27,227
1.13%
9.75%
46.77%
5.96%
22.02%
4.72%
0.50%
7.89%
1.26%
100. 00% r
2
4
4
1
3
1
1
2
1
18
50.0%
25.0%
25.0%
100.0% na
33.3%
100.0% na
100.0% na
50.0%
100.0% na

-1.3
-2.2
-3.0

-2.7


-2.0


-7.08E-05
-7.27E-05
-2.00E-04
-7.95E-05
-1.47E-04
-1.82E-04
-2.07E-04
-1.51E-04
-3.92E-05

Level 2    Choice of Vehicle Type within Passenger or Cargo Categories
Category   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 Cargo                               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,Cargo 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
           Root Node
                                 US HHs4      price         Buy Share
                                    129973385      $27,227    13.05%
                                                                                                      Elasticity    Slope
                                                                                                            -0.8     -3.38E-05
Note:
l)"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" column, which is sales weighted average price.
3) "Price" here reflects sales weighted average price.
4) "US HHs" is numer of households in the U.S. in base year
                                                             34

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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 within the same vehicle class:
                          P   S   e^k
                         =>Alk-Ajk=\nS?-\nSJ,Vijk
                                                          
where superscript 0 represents  baseline scenario,  F  and  Plk are conditional probabilities of
choosing vehicle i and j given class k has been chosen, and  5 and S are baseline market share
of vehicles i andj. If we normalize one of the constants, e.g., Alk , to be zero, then
                              ^ = In 5  - In Sk , Vi e L                          (42)
Vehicle class level constants can be derived from the following equation:
                    0
                  -   =   - = - -^ - Wenesth               (43)
                                     +^ln(y*)]
                                       "I    Kl
where  Plh and  Pth are conditional probabilities of choosing vehicle class k and / given nest h
has been chosen, 5 and  S are base year market shares of vehicle classes k and / in the nest h,
and Akh and Aih are class -specific constant terms. Normalizing the first class specific constant
to be zero, we get
                                              ) + In 5t - In 5t , Vfc e ne5f A         (44)
                   "\    Kdassl       "k   i^k
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:
                                               - ,Vc, b, such that t(c) = t(b)       (45)
                                 R      *'
                                 -i    r(a)=i
where /^j(c) and Plt(b) are conditional probabilities of choosing alternatives c and b given their
parent has been chosen,  S and S are base year market shares of vehicle segments represented
by c and b, and U  is baseline utility for an alternative a, as described by the recursive equation
(26) with initial condition of
                                    U=Aj,Vj                                (46)
and
                                            35

-------
                                UNoBuy=ANoBuy=Q.                            (47)
Constant terms can be solved from equation (45) given S,  S, and generalized cost coefficients
are known. The constant for the alternative of "not buying a new vehicle" is assumed to be 0.
                                           36

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                  4. IMPLEMENTATION AND USER GUIDE

The CVCM has been implemented in C# at the editor environment of Visual Studio 2010. The
C# code reads input, calibrates the model parameters including constant terms and generalized
cost  coefficients, calculates utilities, choice probabilities, 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 destination  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\output.  The "Open" item selects  input file.
Input files could be located in any  folder.  But by  default,  they are in CVCM installation
folderVinput.  The CVCM installation program has copied 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 correctly read. The gray car button on the upper right
corner will turn green. Users can click on the green 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 characteristics in the baseline scenario (e.g.
price, sales and fuel economy) and  fuel economy improvement and associated incremental
vehicle price in the  policy scenario, where fuel economy changes over time in response to fuel
economy and emissions policies. It then outputs predictions on sales and consumer surplus in the
policy scenario.

All input and output are  in Excel Files. As described 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 engine size), price, baseline sales, and
         baseline fuel economy.
        Predictions on fuel economy and incremental price at vehicle configuration  level: key
         input data, commonly obtained from OMEGA output.
        Generalized cost  coefficients and alternative-specific  constants: model parameters.
         Generalized cost coefficients are  derived from price elasticities and NMNL properties,
       13 The current version of the CVCM does not work on non-windows operations systems (e.g. Mac and UNIX).

                                           37

-------
         given elasticities  are known  from the literature.  Constant terms are calibrated from
         baseline sales data and generalized cost coefficients.
        Market size: size of consumer market, which is typically approximated 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 Energy Outlook (AEO)
         2010 from Energy Information Administration (EIA).
        Annual and lifetime driving mileage for a typical car or truck: used to calculate fuel
         cost and VMT weighted GHG emissions for manufacturers. Source: consistent with
         OMEGA assumptions.
        Emission standards and vehicle footprint: used to check manufacturer compliance with
         GHG emissions standards. This information is optional and requires linking the CVCM
         outputs  to  OMEGA. This  linkage may be  made available in  future releases  of the
         CVCM. At the current time, this field can be left blank.

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 messages will prompt out if the input in the data
sheets is not  in right data type or within appropriate range.  If the inputs fail the validation test,
the implicit meaning is that the model nesting structure is not consistent with the parameters. An
error message box will pop out and instruct users to 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 Table 6) of a vehicle configuration.   CVCM
classes are classified based on EPA classes, according 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
vehid
manufacturer |namepkte
baseline price
baseline mpg
model
CVCM ckss
baseline sales
EPA class
predicted mpg
fleet type
incremental price
fuel type
footprint


4.1.1.2 Manufacturer
It includes a list of manufacturer names, which must be consistent with column "manufacturer"
in "vehicle" sheet.

4.1.1.3 Logit
This sheet lists price elasticities at each level of the nesting structure for the purpose of model
calibration. Users can change the values of price elasticities, but not the nesting structure.

4.1.1.4 GlobalParameter
The structure of "GlobalParameter" sheet is as follows:

                                           38

-------
                        Table 7 Structure of "GlobalParameter" Sheet
Scenario Name
Payback Period
Discount rate |onRoad/Tested MPG
Market Size
Scenario name defines the name of the output file. Payback period and discount rate are
parameters for calculating the value of fuel economy 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 stickers and used  in the CVCM, to better
reflect fuel economy under real-world driving conditions. Market Size data are used to calculate
sales and calibrate logit model constants at the level of Buy/No-Buy.

4.1.1.5 Other Sheets
"VehicleUse"  and "Fuel" sheets include  parameters for calculating fuel cost. In "VehicleUse"
sheet, Annual driving  mileage of a car (truck) at certain age equals the product of VMT and
survival rate. "Fuel" sheet simply records fuel prices with year 1 as the 1st year after redesign
year.

"Target" sheet specifies  footprint function parameters 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 files 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 savings), 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 revenue, sales weighted average fuel economy and
COi emissions; manufacturer  level sales,  sales weighted average  fuel economy and  COi
emissions; sales at the level of passenger vehicle, cargo vehicle, or ultra-prestige14, and sales at
each vehicle class.  Note that the fleet average fuel economy is calculated as a harmonic mean:
with gpnii as the gallons per mile for vehicle i,
         77  777         TotalSales
FleetAvgFuelEcon =
                    2j.Sa.leSi
Fleet average CO2 values are calculated two ways: first, sales weighted:
14 Passenger vehicle, cargo vehicle, and ultra-prestige distinction corresponds to level 1 of the nested choice structure.

                                           39

-------
                   Sales  *C02
SalesWtdCO2 =
Secondly, it is also calculated  as VMT-weighted, with the VMT based on the full lifetime
undiscounted VMT of the vehicle; VMT differs by whether a vehicle is classified as a car or a
truck for regulatory purposes:
                    y  Sales.  *CO2.*VMT
 VMTSalesWtdCO2 = 
4.2 INTERACTION WITH OMEGA

The  CVCM  could  interact  with the  OMEGA at different degree.  At this  stage  of  model
development, they run as  two separate programs  and pass  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 input file for the CVCM.
       Step 3: Run CVCM
              3a: Calibrate CVCM using baseline sales data and price elasticities
              3b: Calculate sales, market share and consumer surplus
              3c: Output
       If the convergence criteria is met (i.e. emissions standards are complied), STOP here.
       Otherwise, Go back to step 1
15 One possible way is to program the CVCM as a dynamic link library (dll) file and call this dll from the OMEGA.

                                           40

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                                      44

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APPENDIX A: DERIVATION OF NESTED LOGIT MODEL EQUATIONS
                        AND RELEVANT PROPERTIES

The  primary  purpose  of this  appendix  is to provide a general form of nested logit  model
equations and demonstrate  CVCM equations as one specific 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 nesting structure for the convenience of
discussion, which is the most common case in the literature.  Formulations for two-level models
can be extended to multi-level cases.

The  following formulation framework is consistent with William (1977),  Daly and Zachary
(1978) and Train (2009). Let j denote an elemental alternative in the nested tree and c the upper
level composite alternative (or nest) to which j belongs. The utility of alternative j is
                       77  =V +V + =V +V
                       Uj   Vc^Vj\c^Cj  Vc T V j\c


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

constant for all alternatives within the nest c, and a part labeled Vjlc that varies over alternatives

within the nest. The error term ej is also divided into two independent components of c and ejlc .

The following assumptions  are made. Errors ejlc are identically and independently distributed

(iid)  Gumbel with scale parameter jUc . Errors  c are  distributed such that total errors ej are

distributed Gumbel with scale parameter fj,root .


We first see how the above definition and assumptions imply a relationship of scale parameters
/Uc and jUroot . The variance of total errors is the sum of variance of two error components:


                            Var(- . )=Var(-c )+Var(- .|c ) ,                       (A-2)
which, because the variance of the Gumbel distribution is  with // as the scale parameter , can
                                                   6fi
be expressed as

                              -^ =Var(c)+.                         (A-3)
Since Var(fc)is non-negative, the above implies the following structural condition (Williams,
1977):

                                   H^Hc-                               (A-4)
                                         45

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

                                     Pi=Vc,                               (A-5)

with
and
                                                                              (A-7)
where /^ is the conditional probability of choosing alternative j given that an alternative in nest
c  is chosen, Pc is the marginal probability of choosing an alternative in nest c, and 7 is so called
inclusive value of nest c.

Choice probability form in (A-5) to (A-7) is consistent with the one in Train (2009) (equations
(4.4) and (4.5) of chapter 4) if the scale  parameter juroot  is normalized to 1  and jUc replaced by
 , the so-called log-sum coefficient. Next  we  wish  to  show that CVCM formulation is a
 4t
specific instance of this general form. Assume utility function Vjlc takes a specific form similar to
the one in CVCM:

                                   Vfe=aj+fipj                              (A-8)

where aj is alternative specific constant and  p is vehicle price or generalized cost. Then choice
probability can be expressed as
                                    exp[// (cr .-,._,
                             P* = ^        /    7  .,                       (A-9)
and
                                            46

-------
                        exp[//roo/c+^^ln
                 P=		^	.           (A-10)
On the other hand, choice probability in the CVCM is
                                     exp(A;+ 5CG;)
                              P, = _  ^  J	c-^                       (A-
                                lc
and
                           exp[4 +l
                     Pc= - -^ - ^ - .               (A-12)
                          exp[Ac, + -^ In  exp(A .
If one defines
                                                                            (A- 14)
and
then CVCM equations are equivalent to the general form in (A-9) to (A- 10). Parameters 5, and
5ro(Mare called generalized cost coefficients in the CVCM, since they reflect the derivative  of
utility with respect to price (or generalized cost). Equation (A-15) and (A-16) indicate that the
absolute  value of generalized cost coefficients are proportional to  scale parameters and  thus
proportional to the inverse of standard deviation of random errors.
                                            47

-------
48

-------
              APPENDIX B:  MODEL SENSITIVITY ANALYSIS
Among the model's parameters, the most important ones are price elasticities and those defining
how consumers value fuel savings from fuel economy improvement. 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 economy) 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 November,  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 marginal  cost  of  installing  fuel economy
technologies  across all vehicles, we expect the impact of fuel economy improvement on sales
mix to be small.

We will start by describing the  distribution of  price elasticities and then present sensitivity
analysis results.
B.I THE DISTRIBUTION OF OWN PRICE ELASTICITIES

Generalized cost coefficients are calibrated from assumed price elasticities (see Table 5). The
elasticities  represent the average elasticities of alternatives in a nest. Each vehicle has its own
price elasticity depending on its price and market share 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 equation  (36).16 The  distribution of these
individual elasticities is shown in Figure 2.
16 Equation (36) is derived in the case of simple logit models. Thus elasticities calculated using this equation for nested logit
models (e.g. CVCM here) are only an approximation to true values. However the error is very small.

                                            49

-------
Frequency of Elasticities
qn
an
vn
fin

Af)


in

&








l.llllll






































































































S>AA>>J)>>5>Sj>>> ?>.>
                         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 relatively expensive cars in their classes.

              Table 8 List of Vehicles with Very High Elasticities (in absolute value)
manufacturer
Daimler
BMW
BMW


BMW
VOLKSWAGEN
VOLKSWAGEN
VOLKSWAGEN
Ford
TOYOTA
TOYOTA
Mitsubishi
Mitsubishi
Ford
Mazda
nameplate
MERCEDES-BENZ
ROLLS-ROYCE
ROLLS-ROYCE


ROLLS-ROYCE
BENTLEY
BENTLEY
BENTLEY
FORD
LEXUS
LEXUS
MITSUBISHI
MITSUBISHI
VOLVO
MAZDA
model
SLR
PHANTOM
PHANTOM EWB
PHANTOM
DROPHEAD
COUPE
AZURE
ARNAGE RL
ARNAGE
MUSTANG
IS 250
IS 250
ECLIPSE SPYDER
ECLIPSE SPYDER
V50FWD
MAZDA RX-8
vehicle class
Ultra Prestige
Ultra Prestige
Ultra Prestige


Ultra Prestige
Ultra Prestige
Ultra Prestige
Ultra Prestige
Subcompact
Subcompact
Subcompact
Subcompact
Subcompact
Compact
Subcompact
generalized
cost
coefficient
-0.000038
-0.000038
-0.000038


-0.000038
-0.000038
-0.000038
-0.000038
-0.000264
-0.000264
-0.000264
-0.000264
-0.000264
-0.000289
-0.000264
elasticity
-18.9
-15.6
-15.4


-13.0
-12.6
-10.1
-8.5
-8.3
-8.3
-8.2
-8.0
-8.0
-8.0
-8.0
price
497750
409000
405000


342000
332585
266585
224585
31525
31220
31220
30224
30224
27560
30108
Table 9 provides additional descriptive statistics for elasticities of vehicle configurations within
each class. In particular the medians of these elasticities  are  comparable to elasticity inputs
shown in Table 5.
                                              50

-------
                         Table 9 Descriptive Statistics of Elasticities
Vehicle Classes
Prestige Two-Seater
Prestige Subcompact
Prestige Compact and Small Station
Wagon
Prestige Midsize Car and Station Wagon
Prestige Large
Two-Seater
Subcompact
Compact and Small Station Wagon
Midsize Car and Station Wagon
Large Car
Prestige SUV
Small SUV
Midsize SUV
Large SUV
Minivan
Cargo / large passenger van
Cargo Pickup Small
Cargo Pickup Standard
Ultra Prestige
No. of
vehicles
27
54

71
58
17
26
76
82
85
29
108
17
78
132
19
42
49
67
93
1st 3rd
Min Quartile Median Quartile
-5.5
-6.3

-7.1
-6.1
-5.4
-5.9
-8.3
-8.0
-7.8
-6.6
-6.1
-7.3
-7.0
-6.5
-6.5
-6.2
-6.7
-7.8
-18.9
-4.2
-4.6

-4.3
-4.5
-3.6
-5.5
-7.0
-6.9
-6.1
-5.9
-4.1
-6.1
-5.7
-6.0
-5.3
-5.8
-5.6
-5.6
-4.8
-3.6
-3.6

-3.7
-3.9
-3.5
-4.4
-6.0
-5.4
-5.2
-5.5
-3.6
-5.3
-5.1
-5.4
-4.6
-5.7
-4.9
-5.3
-3.6
-3.4
-3.2

-3.4
-3.2
-2.9
-3.8
-5.1
-4.6
-4.6
-4.9
-3.2
-5.0
-4.7
-4.7
-4.4
-5.4
-4.5
-4.6
-3.2
Std.
Max deviation
-3.2
-2.8

-3.0
-2.8
-2.7
-2.0
-3.0
-3.8
-3.3
-4.3
-2.8
-4.5
-3.4
-2.9
-3.7
-4.7
-3.8
-3.8
-2.9
0.6
0.9

0.8
0.9
0.8
1.1
1.4
1.3
1.2
0.6
0.7
0.8
0.7
0.8
0.8
0.4
0.8
0.9
2.9
B.2 THE DISTRIBUTION OF CROSS PRICE ELASTICITIES

We have also obtained cross  price elasticities  at vehicle class level  through  simulation.  The
demand elasticity of class k with respect to the price of class / 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 /. 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 reported in Table  10 are comparable to those in
Table 1 in the chapter of literature review.
                                           51

-------
                       Table 10 Price Elasticities at Vehicle Class Level
| Class Name
Prestige Two-Seater
Prestige Subcompact
Prestige Compact and
Small Station Wagon
Prestige Midsize Car
and Station Wagon
Prestige Large
Two-Seater
Subcompact
Compact and Small
Station Wagon
Midsize Car and Station
Wagon
Large Car
Prestige SUV
Small SUV
Midsize SUV
Large SUV
Minivan
Cargo / large passenger
Cargo Pickup Small
Cargo Pickup Standard
Ultra Prestige

1
2

3

4
5
6
7

8

9
10
11
12
13
14
15
16
17
18
19
1
-3.47
0.02

0.02

0.04
0.01
0.36
0.05

0.06

0.09
0.05
0.06
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
2
0.01
-2.90

0.24

0.40
0.08
0.00
0.05

0.06

0.09
0.05
0.06
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
3
0.01
0.16

-2.25

0.40
0.08
0.00
0.05

0.06

0.09
0.05
0.06
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
4
0.01
0.16

0.24

-2.73
0.08
0.00
0.05

0.06

0.09
0.05
0.06
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
5
0.01
0.16

0.24

0.40
-3.33
0.00
0.05

0.06

0.09
0.05
0.06
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
6
0.43
0.02

0.02

0.04
0.01
-1.51
0.05

0.06

0.09
0.05
0.06
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
7
0.01
0.02

0.02

0.04
0.01
0.00
-3.10

0.72

1.19
0.59
0.06
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
8
0.01
0.02

0.02

0.04
0.01
0.00
0.67

-2.72

1.19
0.59
0.06
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
9
0.01
0.02

0.02

0.04
0.01
0.00
0.67

0.72

-3.01
0.59
0.06
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
10
0.01
0.02

0.02

0.04
0.01
0.00
0.67

0.72

1.19
-4.24
0.06
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
11
0.01
0.02

0.02

0.04
0.01
0.00
0.05

0.06

0.09
0.05
-2.38
0.00
0.06
0.08
0.03
0.00
0.00
0.02
0.01
12
0.01
0.02

0.02

0.04
0.01
0.00
0.05

0.06

0.09
0.05
0.06
-2.67
1.15
1.48
0.03
0.00
0.00
0.02
0.01
13
0.01
0.02

0.02

0.04
0.01
0.00
0.05

0.06

0.09
0.05
0.06
0.09
-2.45
1.48
0.03
0.00
0.00
0.02
0.01
14
0.01
0.02

0.02

0.04
0.01
0.00
0.05

0.06

0.09
0.05
0.06
0.09
1.15
-3.02
0.03
0.00
0.00
0.02
0.01
15
0.01
0.02

0.02

0.04
0.01
0.00
0.05

0.06

0.09
0.05
0.06
0.00
0.06
0.08
-1.52
0.00
0.00
0.02
0.01
16
0.00
0.00

0.01

0.01
0.00
0.00
0.01

0.02

0.03
0.01
0.02
0.00
0.02
0.02
0.01
-1.25
0.05
0.31
0.01
17
0.00
0.00

0.01

0.01
0.00
0.00
0.01

0.02

0.03
0.01
0.02
0.00
0.02
0.02
0.01
0.05
-2.71
2.58
0.01
18
0.00
0.00

0.01

0.01
0.00
0.00
0.01

0.02

0.03
0.01
0.02
0.00
0.02
0.02
0.01
0.05
0.39
-1.60
0.01

0.00
0.00

0.01

0.01
0.00
0.00
0.01

0.02

0.03
0.01
0.02
0.00
0.02
0.02
0.01
0.00
0.00
0.02
-3.84
B.3 SENSITIVITY ANALYSIS

Eight cases are defined for the sensitivity analysis (see Table 10). Case 1 Baseline is the case to
which  other cases are compared. Cases 2-4d assume  vehicles 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  calibrate 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 examine the impact of these different assumptions
on consumer surplus change, fleet average MPG and total sales.
                                           52

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                            Table 11 Sensitivity Analysis Results

Case
ID
1
2

3a
3b
4a
4b
4c
4d

Name
Baseline
Reference
Lower value of fuel
savings
Higher value of fuel
savings
50% lower elasticities
25% lower elasticities
25% higher
elasticities
50% higher
elasticities

Payback
Period
NA
5

2
15
5
5
5
5

Disc.
Rate
NA
0.03

0
0.3
0.03
0.03
0.03
0.03

Elasticities
NA
default

default
default
default *0.5
default *0.75
default *1.25
default *1.50

Avg. Veh.
Net Value
($)
0
1284

23
4054
1250
1267
1301
1318
Consumer
Surplus
Change
($/veh.)
0
1227

17
3591
1222
1225
1230
1232

Fleet
MPG
27.35
33.67

33.66
33.65
33.7
33.69
33.65
33.64

Total
Sales
(millions)
16.65
17.29

16.66
18.64
16.96
17.12
17.45
17.62
The estimated consumer surplus change is highly sensitive to how consumers are assumed to
value fuel savings from fuel economy improvements relative to the baseline case. The greater the
amount of fuel  savings  that consumers  consider when buying 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 increase. Consumer  surplus is largest in case 3b,
where consumers are assumed to take into account fuel savings over the full expected lifetime of
a vehicle. Price elasticities have much smaller impacts on consumer  surplus. The higher the price
elasticities, the larger the consumer surplus change is.

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 elastic  because the OMEGA data imply
large gains in net values.  The assumed price elasticity 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 sensitivity 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 benefits  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 vehicles, as shown by Table  11. The table
displays market  shares in the baseline and reference cases for each baseline MPG decile. The
share of lower fuel  economy vehicles  (decile 1 and 2) increases, while the share  of higher fuel
economy vehicles (decile 9 and 10) decreases.

                           Table 12 Market Shares by MPG Decile
 MPG Decile
   1
3
5
10
 Baseline
5.1%  20.4%  31.2%  24.3%   13.7%   2.7%  0.6%  0.0%  0.3%   1.6%
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 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 following equation
                                 s   MPG'-MPGS
                               9=	jr.                            (48)
                                    MPG'-MPG
where
S: index for a policy case
MPG: fleet MPG in the baseline case
MPGS: fleet MPG in the policy case (average OMEGA MPG weighted by sales in the policy
case)
MPG': fleet average OMEGA MPG weighted by the baseline sales.

If MPGsh smaller than MPG', then there is a rebound effect. Table 12 indicates that the rebound
effect is  small, in the range of 1%, and higher price elasticities tend to magnify the rebound
effect.
                                 Table 13 Rebound Effect
Case
ID
2

3a

3b
4a
4b
4c
4d
Name
Reference
Lower value of fuel
savings
Higher value of fuel
savings
50% lower elasticities
25% lower elasticities
25% higher elasticities
50% higher elasticities
Fleet MPG
33.67

33.66

33.65
33.70
33.69
33.65
33.64
Rebound Effect
0.9%

1.1%

1.3%
0.5%
0.6%
1.3%
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 value of fuel economy and not very sensitive to
variation in price elasticities at lower levels in the nesting structure.
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