The Effects of New-Vehicle Price Changes
on New- and Used-Vehicle Markets
and Scrappage
United States
Environmental Protection
Lai M »Agency
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The Effects of New-Vehicle Price Changes
on New- and Used-Vehicle Markets
Assessment and Standards Division
Office of Transportation and Air Quality
U.S. Environmental Protection Agency
Prepared for EPA by
RTI International
EPA Contract No. EP-C-16-021
Work Assignment No. 4-28
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.
NOTICE
4>EPA
United States
Environmental Protection
Agency
EPA-420-R-21 -019
August 2021
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CONTENTS
Section Page
Executive Summary ES-1
S ecti on 1. Introducti on 1-1
Section 2. Characterization of the U.S. Passenger Vehicle Inventory 2-1
2.1 Growth of the U.S. Passenger Vehicle Inventory and Contributing Factors 2-1
2.2 Composition of the U.S. Passenger Vehicle Inventory 2-3
Section 3. Theoretical Background 3-1
3.1 Characterizing Vehicle Markets 3-1
3.1.1 Utility and Demand 3-2
3.1.2 Supply and Scrappage 3-6
3.1.3 Equilibrium and Estimation 3-7
3.2 Considerations for Framework Development 3-9
3.2.1 Key Questions 3-9
3.2.2 Overview of Approaches 3-12
Section 4. Description of Studies and Attributes Analyzed 4-1
4.1 Sample Description 4-1
4.2 List of Papers Identified 4-4
Section 5. Literature Synthesis 5-1
5.1 Effect of Changes in New-Vehicle Prices or Costs on New-Vehicle Sales 5-2
5.1.1 Aggregate Own-Price Elasticity of Demand for New Vehicles with
Respect to Price of New Vehicles 5-3
5.1.2 Aggregate Own-Price Elasticity of Demand for New Vehicles with
Respect to Price of New Vehicles, Allowing for Price Effects in
the Used Market 5-6
5.1.3 Summary 5-6
5.2 Effect of Changes in Vehicle Costs or Prices on Prices or Sales of Used
Vehicles 5-7
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5.2.1 Elasticity of Used-Vehicle Price with Respect to New-Vehicle
Price 5-7
5.2.2 Own-Price Elasticity for Used Vehicles with Respect to Price of
Used Vehicles 5-8
5.2.3 Elasticity of Used-Vehicle Quantities with Respect to Price of New
Vehicles 5-8
5.2.4 Summary 5-9
5.3 Effect of Changes in New- or Used-Vehicle Prices or Operating Costs on
Scrappage of Used Vehicles 5-9
5.3.1 Elasticity of Aggregate Scrappage with Respect to Average Price
of Used Vehicles 5-10
5.3.2 Elasticity of Aggregate Scrappage with Respect to Average Price
of New Vehicles 5-12
5.3.3 Summary 5-12
5.4 Effect of the Factors Influencing the Total Size of the (Combined New
and Used) Vehicle Inventory on the Size of the Inventory 5-13
5.4.1 Summary 5-13
5.5 Other Related Parameter Estimates 5-13
Section 6. Long-Run Modeling of the Aggregate U.S. Vehicle Inventory 6-1
6.1 Model Notation 6-1
6.2 Vehicle Demand 6-2
6.3 Vehicle Supply 6-5
6.4 Market Equilibrium 6-7
6.4.1 Asset Values and Ownership Cost 6-8
6.5 Summary of Long-Run Model, Inputs, and Solution 6-9
6.6 Input Values 6-10
Section 7. Long-Run Model Results 7-1
7.1 Effects of Elasticity Parameters on Simulation Results 7-1
7.2 Setting 7-2
7.3 Policy Impact 7-3
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7.4 Calibrated Scenarios Based on Findings of the Literature Review and
Synthesis 7-4
7.5 Effects by Vehicle Age 7-9
7.6 Summary 7-10
Section 8. Dynamic Transition Path Modeling 8-1
8.1 Additional Notation 8-1
8.2 Demand and Supply 8-2
8.3 Asset Values and Ownership Cost 8-2
8.4 Dynamic Market Equilibrium 8-4
8.5 Computation 8-5
Section 9. Results of Dynamic Transition Path Simulations 9-1
9.1 Vehicle Market Dynamics under Rational Expectations 9-1
Section 10. Concluding Observations 10-1
10.1 Model Applicability 10-2
10.2 Linkages to Other Models 10-3
10.3 Limitations and Caveats 10-3
10.4 Priorities for Future Research 10-3
References R-l
Appendixes
Appendix A: Bibliography of Papers Included in our Main Sample A-l
Appendix B: Detailed Specification of Scrap Function B-l
Appendix C: Additional Sensitivity Analyses, Long Run C-l
Appendix D: Additional Sensitivity Analyses, Transition Paths D-l
Appendix E: Application of Policy Elasticities for Analysis of New Vehicle
Sales E-l
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LIST OF FIGURES
Number Page
2-1. Vehicle Growth, Population, and Macroeconomic Indicators Comparison,
1950-2018 2-1
2-2. Number of People per Vehicle, 1950-2017 2-2
2-3. Index of Real Average New- and Used-Vehicle Prices, 1990-2019 2-3
2-4. Composition of the U.S. Passenger Vehicle Inventory, New-Vehicle Share, and
Scrappage Rate, 1970-2017 2-4
2-5. New-Vehicle Share and Scrappage Rate Relative to Percentage Change in Real
GDP, 1970-2017 2-5
3-1. Diagram of Outcomes in New and Used Markets 3-11
4-1. Distribution of the Final Set of Papers Included by Year of Publication 4-3
6-1. Baseline Age Profile of the Vehicle Stock 6-11
6-2. Baseline Vehicle Price Profile by Age 6-12
7-1. Policy Effect on LDV Stocks as a Function of the Scrappage Elasticity for a 1%
Increase in Generalized Cost of New Vehicles, Scenario D 7-9
7-2. Changes in Long-Run Vehicle Inventory by Vehicle Age 7-10
9-1. Dynamics of New-Vehicle Sales under Alternative Policy Implementation
Scenarios 9-3
9-2. Dynamics of New-Vehicle Sales (Levels), Baseline = 100 9-4
9-3. Dynamics of the Used-Vehicle Inventory under Alternative Policy
Implementation Scenarios: Age 10 Vehicles 9-5
9-4. Dynamics in the Used-Vehicle Market with a Preannounced, Phased-In Policy:
Inventory Changes by Vehicle Age Group 9-7
9-5. Dynamics of Vehicle Inventory and Average Age under Alternative Policy
Implementation Scenarios 9-8
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LIST OF TABLES
Number Page
4-1. Literature Summary Statistics Based on our Main Sample 4-3
4-2. List of Papers Included and Parameter Estimates Provided 4-4
5-1. Summary of Aggregate Own-Price Elasticities for New Vehicles 5-3
5-2. Summary of Estimated Effects of Changes in New- or Used-Vehicle Prices on
Used-Vehicle Markets 5-7
5-3. Summary of Scrappage Elasticities from Literature 5-10
5-4. Summary of Estimated Vehicle Inventory Elasticities 5-13
6-1. Inputs Needed to Specify the Simulation Model 6-10
7-1. Demonstration of Channels of Adjustment in Quantities and Prices When
Generalized Cost of New Vehicles Rises by 1% 7-1
7-2. Policy Elasticities Corresponding to Selected Demand and Scrappage
Elasticities 7-5
7-3. Additional Policy Elasticities Corresponding to Selected Demand and
Scrappage Elasticities 7-7
vii
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EXECUTIVE SUMMARY
The U.S. Environmental Protection Agency (EPA) sets emission standards for new light-
duty vehicles (LDVs), with existing vehicles generally not expected to meet the same standards.
Typically, these standards are expected to increase the up-front costs of new vehicles, may affect
vehicle operating costs (e.g., through changes in fuel economy), and are likely to affect new-
vehicle sales because of their effects on new-vehicle prices and characteristics. In addition, given
substitutability between new and used vehicles, changes in new-vehicle prices, sales, and
operating costs are likely to affect the market for used vehicles. Changes in the valuation of used
vehicles are, in turn, likely to affect vehicle scrappage rates. As part of regulatory analyses, EPA
often seeks to characterize these effects and interactions between new- and used-vehicle markets
and scrappage. Consumer response to changes in vehicle prices and characteristics induced by
regulatory policy has important implications for the total size and average age of the U.S. vehicle
inventory, influencing net impacts of regulatory actions on greenhouse gas and criteria pollutant
emissions, vehicle safety, and other outcomes. Improving our understanding of such interactions
at the aggregate level is important for transportation policy analyses.
This study had three major goals. The first was to develop a theoretically sound
methodology for characterizing the aggregate U.S. LDV inventory and the pathways through
which regulatory policy or other scenarios could affect the distribution of the entire vehicle
inventory. The second was to conduct a detailed literature review to identify studies providing
estimates of the values of several elasticities important for modeling U.S. vehicle markets and
vehicle inventory in a manner consistent with the theoretical model and to synthesize available
estimates. The third was to develop and parameterize an aggregate simulation model consistent
with the theoretical framework and the existing data available from the literature and implement
the model to explore the implications of alternative scenarios for U.S. vehicle markets.
We developed a theoretical model of the relationships between new- and used-vehicle
markets, scrappage, and total inventory at an aggregate level for the U.S. LDV market. Key
components of this model include characterization of annual vehicle ownership cost, including
changes in depreciation under different scenarios; utilization of elasticity estimates at an
aggregate market level (i.e., elasticities that reflect changes in cost affecting the entire new
vehicle market simultaneously rather than individual models); reflection of net changes in
"generalized cost" rather than vehicle price only, where generalized costs refer to the change in
vehicle price net of the additional benefits or costs to consumers of changes in vehicle
characteristics, if any; allowing of endogenous scrappage as a function of the used-vehicle price;
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and solving for equilibrium results. Our primary case assumes rational expectations in a dynamic
setting, though we also explore different degrees of myopia on the part of consumers.
We then conducted a detailed review and analysis of the existing literature on the
aggregate effects of changes in new-vehicle prices on new-vehicle sales, used-vehicle sales and
prices, vehicle scrappage, and the factors that affect total vehicle inventory to assess the current
state of knowledge in these areas. Although there have been many studies of vehicle demand, the
majority have estimated elasticities at a disaggregated make/model level as opposed to the
aggregate elasticities we seek for use in national-level inventory analyses. We identified only 20
relevant papers using U.S. data and published since 1995 with enough data to calculate at least
one of the aggregate elasticities on which we are focused, providing a total of 25 elasticity values
(five studies provided more than one estimate). There were 11 estimates of elasticity of demand
for new vehicles from 11 studies, four estimates of the effects of vehicle prices on used vehicles
from three studies (two estimates of the impacts of new-vehicle prices and two focused on the
effects of used-vehicle prices), nine estimates of the impacts of vehicle prices on scrappage from
seven studies, and one estimate of the effect of new-vehicle prices on total vehicle inventory.
Based on the values identified, empirical estimates of new-vehicle demand elasticities were
relatively consistent across studies, but estimates were more variable for scrappage, and very few
values were available for used vehicles or total inventory. Aggregate own-price vehicle
elasticities ranged from -0.37 to -1.27, though the majority of the estimates were inelastic. The
three studies published within the last decade all estimated inelastic response (-0.37 to -0.78). In
addition to these aggregate own-demand elasticities, two of the studies included estimated
aggregate elasticities of-0.18 and -0.36 when accounting for price effects in the used-vehicle
market. Available estimates of the own-price demand elasticity for used vehicles were -0.54 and
-1.23, while estimates of the long-run elasticity of the used-vehicle inventory with respect to
new-vehicle prices were -0.08 and -0.12. Scrappage elasticities estimated from the literature had
a wide range, though the highest and lowest values were derived from simulation models, which
are sensitive to assumptions. Econometrically estimated values of scrappage elasticities with
respect to used-vehicle prices fell within a much narrower range of-0.36 to -0.91. There were
two estimates of scrappage with respect to new-vehicle prices of-0.21 and -0.82, though the
relationship between new-vehicle prices and scrappage is indirect, flowing through equilibrium
effects of changes in new-vehicle prices on used-vehicle prices. The only study identified as
having assessed the responsiveness of the total vehicle inventory with respect to new-vehicle
prices estimated an elasticity of-0.14. Overall, relatively few studies in the literature examined
the aggregate U.S.-level inventory response on which we are focused, and the majority of these
studies relied on data that are from at least 20 years ago.
We then developed and parameterized an aggregate simulation model for the U.S. vehicle
inventory consistent with our theoretical framework and the existing evidence available from the
literature on the magnitudes of key elasticities. This model was applied to simulate both long-run
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steady-state and dynamic transition paths under alternative scenarios, demonstrating its ability to
generate projections of vehicle inventory dynamics consistent with economic theory. To assess
the effect of a policy in the long run, we examined the equilibrium where prices and scrap rates
reached a new stable level (in the presence of a sustained policy change) and demand equaled
supply for vehicles of each vintage between new and 30 years old. In the short and medium runs
and in cases where the policy changes over time, a more complex dynamic transition occurs
where prices and scrappage rates evolve over time during the simulation period. We explored
response of new- and used-vehicle markets, scrappage, and size and composition of the U.S.
vehicle inventory under several different sets of parameter assumptions based on economic
theory and the available literature to assess the range of potential outcomes and the relative
importance of individual parameters. We found that substitution to the outside good is one of the
most important elasticities in determining the effect of a policy or other shocks on new-vehicle
sales, yet this is perhaps the worst identified of the key elasticities estimated in the modern
literature on vehicle demand that we reviewed.
Simulation of the interactions between new- and used-vehicle markets and an outside
good (i.e., substitution of other forms of transportation for a personal passenger vehicle) enabled
us to estimate "policy elasticities" that characterize the net equilibrium response of a change in
generalized cost. Inclusion of interactions with the used-vehicle market, which is much larger in
size than the new-vehicle market, dampens the policy effects of price increases on the new-
vehicle market because higher purchase prices for new vehicles result in substitution toward used
vehicles, raising the equilibrium price of used vehicles. Own-price elasticities for new vehicles
hold other aspects of the system (such as the price of used vehicles) fixed; when used-vehicle
prices also rise, there is less substitution away from purchases of new vehicles than suggested by
own-price elasticities. Dynamic aspects of the system, for example, the fact that lower new-
vehicle sales in the present can be expected to create shortages in the used market in the future,
further contribute to the dampening of the elasticity. We found that policy elasticities are
substantially smaller than the demand elasticities available from the literature, highlighting the
importance of considering interactions between new- and used-vehicle markets when assessing
potential effects of vehicle policy.
Typically, transportation sector regulations are both announced in advance of their date
of implementation and are phased in over time. Our simulations captured key dynamics of the
response to such scenarios. We observed a net increase in new-vehicle purchases between
announcement of the policy and implementation as consumers anticipate higher future prices and
shift new-vehicle purchases forward in time to avoid the anticipated price increases. Then, as the
policy begins to be phased in and new-vehicle prices rise, new-vehicle purchases fall relative to
the no-policy projection. After the policy is fully phased in, new-vehicle sales move toward their
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new long-run equilibrium level. For a policy that increases the generalized cost of new vehicles,
new-vehicle sales will be lower than without a policy, but the long-run equilibrium change in
sales will be a smaller reduction than occurs at the peak. The peak reduction in sales occurs
relatively early on in policy implementation when used-vehicle supply has not yet fallen. Over
time, used-vehicle supply also falls (because fewer new vehicles are entering the system); this
further increases used-vehicle prices, leading some consumers to move back into the new-vehicle
market as the system approaches its new steady state.
Our simulation model built on the existing literature and helped fill a gap in the available
tools for analyzing aggregate impacts on vehicle markets. It offers a method for rapidly
exploring potential impacts under alternative regulatory and other scenarios. Because we
explicitly modeled expectations and forward-looking behavior, the model can be used to explore
market reactions in anticipation of policy implementation and the impacts of phasing in policy
changes over time. In addition, the model was designed to facilitate sensitivity analyses and can
readily be applied to explore the range of outcomes generated using a broad range of inputs.
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SECTION 1.
INTRODUCTION
Standards for vehicle greenhouse gas (GHG) emissions and fuel economy generally
apply to new vehicles while existing vehicles are not required to meet the same standards. As
standards become more stringent, they are expected to increase the up-front costs of new
vehicles, may affect vehicle operating costs (e.g., through changes in fuel economy), and will
likely affect new-vehicle sales because of their effects on new-vehicle prices and characteristics.1
Vehicles are long-lived durable goods, and there is a wide range of model years on the road in
the United States. Because of substitutability between new and used vehicles, changes that affect
new-vehicle prices, sales, and operating costs are likely to also affect the market for used
vehicles. Changes in the valuation of used vehicles are, in turn, likely to affect scrappage rates,
where scrappage refers to the retirement of a vehicle such that it is no longer being driven. The
lower a vehicle's value is, the more likely that the cost of repairing and operating that vehicle
makes its economic value negative, leading the owner to scrap it. Market changes that tend to
raise used-vehicle prices, on the other hand, are expected to reduce scrappage rates.
Because safety features, fuel efficiency, emissions intensity, and other vehicle
characteristics vary systematically at the aggregate level by vehicle vintage, it is important to
consider changes in the composition of the entire U.S. vehicle inventory. Consumer response to
changes in vehicle prices and characteristics induced by regulatory policy has important
implications for the total size and average age of the U.S. vehicle inventory, influencing net
impacts of regulatory actions on GHG and criteria pollutant emissions, vehicle safety, and other
outcomes. Thus, it is helpful to represent expected changes in used-vehicle markets and
scrappage when assessing the costs and benefits of transportation, energy, environmental, or
other policy affecting the transportation sector, even when the policy directly applies only to new
vehicles.
The research presented in this report has three main objectives:
Develop a theoretical framework of the U.S. passenger vehicle inventory to identify
and rigorously characterize the pathways through which a policy directly affecting
only new vehicles affects the entire vehicle inventory over time.
Survey the economic literature on the aggregate effects of changes in new-vehicle
prices on new-vehicle sales, used-vehicle sales and prices, vehicle scrappage, and the
1 While similar market dynamics are expected to apply to heavy-duty vehicles, this report focuses only on the U.S.
inventory of light-duty vehicles (LDVs).
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factors that affect total inventory to assess the current state of knowledge in these
areas.
Develop, parameterize, and implement an aggregate simulation model of the U.S.
vehicle inventory consistent with our theoretical framework and the existing evidence
available from the literature on the magnitudes of key elasticities.
This analysis of the available estimates of aggregate elasticities for vehicle market
responses to changes in new-vehicle prices and other factors influencing consumer behavior is
intended to help provide a better understanding of the extent to which there is consensus in the
literature regarding the parameters necessary to implement our theoretical framework of
consumer response and resulting aggregate-level outcomes. Where the range of estimates in the
literature is broad, we were likewise able to explore a wider range of inputs to the model. We
conducted a detailed review and analysis of the literature and identified only 20 relevant papers
using U.S. data and published since 1995 with enough data to calculate at least one of the
aggregate elasticities on which we are focused, providing a total of 25 elasticity values. There
were 11 estimates of elasticity of demand for new vehicles from 11 studies, four estimates of the
effects of vehicle prices on used vehicles from three studies (two estimates of the impacts of
new-vehicle prices and two focused on the effects of used-vehicle prices), nine estimates of the
impacts of vehicle prices on scrappage from seven studies, and one estimate of the effect of new-
vehicle prices on total inventory. Although there have been many additional studies of vehicle
demand, the majority estimated elasticities at a disaggregated make/model level as opposed to
the aggregate elasticities we seek for use in national inventory-level analyses. Those studies
captured substitution between different makes and models of vehicles, but often did not report
aggregate substitution between purchase of a new vehicle and an outside good of not purchasing
a new vehicle, which is necessary for calculating an own-price elasticity for aggregate new-
vehicle purchases. In fact, one of our findings in this study is that substitution to the outside good
is one of the most important elasticities in determining the effect of a policy or other shocks on
new-vehicle sales. However, it is perhaps the least studied and worst identified of the key
elasticities estimated in the modern literature on vehicle demand that we reviewed.
We limited the scope of our analysis to peer-reviewed and high-quality grey literature on
U.S. studies published between 1995 and the present. We considered only U.S. studies because
our goal is to inform U.S. policy making, and we expected that introducing results from other
countries with different vehicle choices, consumer preferences, and government policies would
require additional analysis of the comparability of elasticities estimated under those differing
conditions. In addition, consumers' preferences can change over time. Focusing on more recent
studies is intended to make our analysis more relevant to current policy making. Within the
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papers identified that met our criteria for inclusion, we focused on the authors' preferred model
for each category of elasticity available within their study. Based on the values identified,
empirical estimates of new-vehicle demand elasticities were relatively consistent across studies,
but estimates were more variable for scrappage, and very few values were available for used
vehicles or total vehicle inventory.
Because our review of the existing literature revealed few studies that provided estimates
of any of the parameters necessary for empirical application of our theoretical model, let alone a
full set of parameters consistent with our theoretical specification, we developed a new dynamic
simulation model of the U.S. passenger vehicle inventory. Existing models that address the used
market are scarce, and many either ignore the dynamics or have difficult-to-interpret reduced
forms and thus can produce inconsistent results. The simulation of the used-vehicle market in
Jacobsen and van Benthem (2015) is most similar to the model structure proposed here.2 In that
model, price expectations are myopic, however, so it presents only one view of the aggregate
implications. Welfare analysis is also prevented or made very difficult when expectations are
myopic (because the nature and degree of mistakes in expectations are not well defined).
Our new model is consistent with economic theory under rational expectations and
reflects substitution between vehicles of different vintages, ranging from new to 30 years old,
and effects on scrappage rates in response to changes in the market for new vehicles. Key
contributions of this study include assessment of the available literature estimating the
parameters necessary for parameterization of an aggregate model of U.S. vehicle markets,
development of a dynamic aggregate model consistent with economic theory, fuller treatment of
expectations in the used-vehicle market, comparison of the net responsiveness of new- and used-
vehicle sales and total vehicle inventory within this model with the elasticities available from the
literature, and analysis of the dynamics of U.S. vehicle markets and inventory response under
alternative scenarios. The lifespan of LDVs is long enough that some of the most important
policy impacts on inventory size and age composition are likely to occur along the transition path
(perhaps over a span of decades). We modeled both the long-run outcomes and the time path
taken to reach those outcomes.
2 As noted by a reviewer, Adda and Cooper (2000) and Schiraldi (2011) also presented dynamic models of the new
and used vehicle markets. Adda and Cooper (2000) used annual time-series data for the United States and France
to estimate vector autoregression and discrete choice models. They did not report price elasticities and focused
largely on the dynamic relationship between shocks to income, price, and taste. Schiraldi (2011) focused on
identifying transactions costs and applied their model to evaluate the impacts of scrappage subsidies on the
Italian vehicle market in 1997 and 1998. We do not include these results in Section 5 because our focus is on
U.S. markets.
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The following section provides background information on the evolution of the U.S.
vehicle inventory over time and key macroeconomic drivers of changes in inventory size and
composition. This is followed by presentation of our theoretical framework for characterizing the
U.S. vehicle inventory at an aggregate level in Section 3. Methods employed for our literature
review and synthesis are described in Section 4. Section 5 presents descriptive statistics and
analysis of the results of our literature review. In Section 6, we present the methodology used for
empirical implementation of our theoretical framework within a long-run steady-state simulation
model of the U.S. vehicle inventory. Section 7 presents results from the long-run steady-state
model. We then present dynamic transition path modeling in Section 8 and results from selected
dynamic scenarios in Section 9. Finally, in Section 10 we conclude by reflecting on the available
evidence from the existing literature and the contributions of our study and discuss model
applicability, potential linkages to other models, and limitations and caveats of this approach.
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SECTION 2.
CHARACTERIZATION OF THE U.S. PASSENGER VEHICLE INVENTORY
This section provides a brief summary of historical changes in the U.S. vehicle inventory
and selected variables that may be important contributors to the evolution of the passenger
vehicle inventory over time.
2.1 Growth of the U.S. Passenger Vehicle Inventory and Contributing Factors
The U.S. LDV inventory grew significantly from 1950 to 2017. In 1950, there were
approximately 43.5 million LDVs in operation. By 2017, there were over 276.1 million. This
represents a 535% increase in the number of LDVs in operation. Figure 2-1 illustrates the change
in the size of the LDV inventory alongside variables expected to influence LDV inventory,
including gross domestic product (GDP), median household income, population, and the number
of households.
Figure 2-1. Vehicle Growth, Population, and Macroeconomic Indicators Comparison,
1950-2018
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Number of Vehicles in Operation Real GDP
Resident Population Number of Households
Real Median Family Income
Sources: Oak Ridge National Laboratories (ORNL) (2021a) and Federal Reserve Economic Data (FRED) (2020a,
2020b)
The growth in GDP appears to be a very important driver of the size of the LDV
inventory. GDP and the number of vehicles in operation follow very similar trends from 1950—
1990. GDP growth has outpaced growth in the size of the LDV inventory since 1990, but they
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have continued following similar trajectories. Strong GDP growth is indicative of rising income
and strong market confidence, which are likely key driving factors behind continued growth in
the size of the vehicle inventory (Sivak, 2013).
As the U.S. population has grown, the demand for additional vehicles has increased.
Population growth cannot entirely account for the growth in the number of passenger vehicles,
however. The growth in LDVs has greatly outpaced the growth in the U.S. population, as shown
in Figure 2-2. In 1950, there were approximately 3.5 people per vehicle. By 2017, that number
had shrunk to 1.18. This is also evident when examining the number of vehicles per household.
In 1950, the average household owned a single vehicle. In 2017, the average household owned
2.19 vehicles, even as the average number of people per household declined. The ratios of both
vehicles to people and vehicles to households have strongly increased over time. It appears that
the U.S. passenger vehicle inventory may be approaching market saturation as the change in the
number of people per vehicle has flattened in recent decades.
Figure 2-2. Number of People per Vehicle, 1950-2017
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Source: Authors' calculations using data from ORNL (2021a) and FRED (2020a, 2020b).
Real median family income has remained relatively flat over the past few decades,
suggesting that purchasing power has not drastically increased over this time. While the data for
new- and used-vehicle prices are not available for this full time period, they are available for
more recent years. The Bureau of Transportation Statistics (BTS) used different sources for new
and used average vehicle prices for the time period 1990-2009 and the time period 2010-2019,
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which results in a large shift in the average price level between these two periods. Thus, we
report these two periods as indexes with two separate base years rather than in levels to make
them more comparable (see Figure 2-3). Real vehicle prices are relatively flat over this time
period, though used-vehicle prices have experienced greater percentage changes over time than
for new vehicles. In general, vehicle prices rose more rapidly for used vehicles than new
throughout most of the 1990s before trending downward through the 2000s until 2008, even as
new-vehicle prices continued to rise. This pattern has reversed again since the financial crisis in
2008, with used-vehicle prices trending upward as new-vehicle prices have fallen.
Figure 2-3. Index of Real Average New- and Used-Vehicle Prices, 1990-2019
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2010 2011 2012 2013 2014
-Real new vehicle average price
2015 2016 2017 2018 2019
-Real used vehicle average price
Source: BTS (2020)
Note: BTS switched data sources between 1990-2009 (2-3a) and 2010-2019 (2-3b), resulting in a large upward shift
in the average price of both new and used vehicles between the two periods. Thus, we are presenting these data as
indices with separate base periods to make them more comparable.
2.2 Composition of the U.S. Passenger Vehicle Inventory
The size of the U.S. LDV inventory has grown over time, driven by new-vehicle sales
exceeding scrappage. This relationship is represented using the following formula:
Inventory (Current Year) = Inventory (Previous Year) + New-vehicle sales - Scrapped Vehicles
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Figure 2-4 illustrates changes in the inventory over time with the number of new
vehicles, used vehicles, and scrapped vehicles, as well as changes in the share of new-vehicle
sales and the scrappage rate over time.
Figure 2-4. Composition of the U.S. Passenger Vehicle Inventory, New-Vehicle Share, and
Scrappage Rate, 1970-2017
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New Vehicle Sales
Sources: BTS (2017), BTS (2020), and ORNL (2021a)
On average, for the period 1970-2017, new vehicles made up 7.9% of passenger
vehicles. In the same period, 5.7% of passenger vehicles were scrapped each year. There is some
fluctuation, however, with the share of new vehicles peaking in 1973 at 12.5% and dropping as
low as 4.1% in 2009. The most recent downturns in new-vehicle share and scrappage rates
occurred in or around 1990, 2001, and 2008-2009. It should be noted that these time periods
correspond to the early 1990s recession, the early 2000s recession, and the Great Recession. As
market confidence wanes and people's financial situations worsen, they often opt to continue
driving their used vehicles longer and delay the purchase of a new vehicle. This behavior is
characteristic for durable goods such as vehicles. For example, FRED (2018) found that
expenditures on motor vehicles and parts dropped by as much as 24% during recessions.
While year-to-year fluctuations in the share of new vehicles and the scrappage rate tend
to move with changes in real GDP, there has been a downward trend in the share of new vehicles
in the passenger vehicle inventory and the scrappage rate since 1970 despite overall economic
growth (see Figure 2-4). This trend is likely due at least in part to increased vehicle reliability
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over time. Consumers can continue driving their vehicles for longer, thus reducing the need to
purchase a new vehicle. This fact is reflected in the average age of vehicles. According to data
from ORNL (2021b), in 1970, the average passenger vehicle was 5.6 years old and the average
light truck was 7.3 years old. By 2018, the average age of a passenger vehicle more than doubled
to 11.9 years. The average age of a light truck increased by 60% to 11.7 years.
Figure 2-5. New-Vehicle Share and Scrappage Rate Relative to Percentage Change in Real
GDP, 1970-2017
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Sources: BTS (2017), BTS (2020), and FRED (2020)
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SECTION 3.
THEORETICAL BACKGROUND
U.S. policy directed at the pollution emissions or fuel consumption of LDVs has tended
to concentrate on new vehicles, requiring improvements in technology or changes in attributes to
reduce externalities. However, there are substantial interactions between new- and used-vehicle
markets that have potentially important implications for the net impacts of such policies on the
U.S. vehicle inventory. This section qualitatively discusses important considerations for
developing a framework to adequately identify and rigorously categorize the channels through
which a policy directed only at new vehicles will eventually make its way through the whole
vehicle inventory. Empirical implementation of this framework is presented in Section 6.
3.1 Characterizing Vehicle Markets
As with other goods and services, equilibrium prices and quantities in LDV markets are
determined by supply and demand. However, several characteristics of vehicles make
representation of this important market relatively complex:
Vehicles are quite heterogeneous, with wide variation in model type, comfort, size,
handling, horsepower, handling, fuel economy, and other characteristics. Consumers
have substantial willingness-to-pay values for improved quality of many
characteristics (Greene et al., 2018a, 2018b).
Vehicles are long-lived durable goods such that they are available in many different
vintages simultaneously. There is substantial substitutability between similar vehicles
of different vintages, though presumably declining substitutability among vehicles as
the difference in vintage increases.
When vehicles need repairs, owners evaluate whether it is preferable to repair the
vehicle or to scrap it and shift to an alternative means of transportation (e.g., new
vehicle, used vehicle, or other transportation).
Production of vehicles is very capital intensive with a multiyear planning horizon for
vehicle manufacturers to introduce new models or major changes to existing models.
Nonetheless, in the long run manufacturers build or modify plants and new firms
enter, meaning that the long-run supply of newly manufactured vehicles is likely to be
relatively elastic.3 The supply of used vehicles, however, is expected to be much less
elastic because scrappage is the only channel of adjustment.
Certain vehicle characteristics vary systematically with vintage, including safety, fuel
economy, and emissions. Thus, scenarios that alter the total vehicle inventory or the
distribution of vintages within the inventory can result in substantial national benefits
3 Blonigen et al. (2017) explored long-run competition and entry of vehicle models via redesigns.
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and costs associated with changes in safety, energy markets, and environmental
outcomes.
Because of the extensive substitution between new and used vehicles and between
vintages within the used-vehicle market, it is vital to jointly model the new and used markets
when assessing alternative scenarios affecting the vehicle market. In this study, we focus on
aggregate-level characterization of vehicle markets, capturing substitution between vintages and
scrappage decisions while abstracting from other heterogeneity within the sector to develop a
theoretically consistent model of the aggregate U.S. national vehicle market.
3.1.1 Utility and Demand
Household utility functions determine the choice of vehicles (e.g., number, age, type) and
other goods and services consumed by households for a given set of prices. When the utility
model is of an individual household, the choice may be modeled as discrete (i.e., new vehicle,
used vehicle, or no vehicle). When the function represents all households together (more typical
in the scrappage literature, and the approach we take here), it represents the sum of many
individual, discrete choices that can be approximated as a continuous function. Empirical
estimates of a utility function are often summarized using a matrix of demand elasticities.4 Three
caveats, discussed below, about many of the vehicle demand estimations in the literature deserve
emphasis in this context.
3.1.1.1 Ownership Cost and Durability
When allowing for the possibility of reselling used vehicles, the distinction between the
current market price of a vehicle and the net cost of ownership per unit of time becomes
important and is not always made clear in the literature. One of the largest costs of ownership,
particularly for newer vehicles, is depreciation. Other things being equal, if the price of a new
LDV remained unchanged but the price of used vehicles rose, new vehicle shoppers would view
that increase in the price of used vehicles as evidence that a vehicle "holds its value well," and
would demand more new vehicles because the cost of ownership has declined (i.e., when they
sell or trade in the vehicle in the future, the residual value will be higher, thus lowering the
depreciation their vehicle will experience).
The fundamental difficulty with demand derivatives in this setting comes from the
durable nature of LDVs. The canonical theory of utility and demand assumes that prices
correspond to goods that are consumed within the scope of the utility function. Here, the
4 Elasticities are widely used in economics and are measures of how responsive one variable is to changes in
another. Demand elasticities refer to the percentage change in the quantity demanded of a product for a given
percentage change in the price of that product, all else equal.
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purchase price of a vehicle not only includes the cost of enjoying it in the current time period
(over which utility is being defined), but it also includes a whole series of future ownership costs
(perhaps not even borne by the same individual); an increase in purchase price indicates that
somewhere in a vehicle's future the ownership cost has gone up, but it does not isolate when in
time that ownership cost has increased.
In the literature estimating new-vehicle demand systems (e.g., Berry, Levinson, and
Pakes [BLP] [1995]), the distinction between purchase price and net ownership costs is often not
discussed. That paper, for example, considers only new vehicles and provides estimates of the
responsiveness of the quantity of new vehicles purchased to the price of new vehicles. In a
setting where we want to simultaneously consider decisions about new and used vehicles it is
important to convert new-vehicle price derivatives into ownership cost derivatives. The
conversion requires an estimate of the fraction of the increase in new-vehicle price that is borne
by the new vehicle owner, as compared with the fraction they can pass through to future users of
the vehicle. Consider the effect of a $5,000 increase in the purchase price of a new vehicle on a
buyer who plans to use that vehicle for the first decade of its life and then sell it. If the buyer
believes they will pay almost all that $5,000 themselves (i.e., the residual value of 10-year-old
vehicles in 10 years from now will remain unchanged from what it was prior to the price
increase), then there could be a sharp drop in demand for the new vehicle. On the other hand, if
the purchase price rises by $5,000 but the residual value of 10-year-old vehicles in 10 years is
expected to rise by $3,000, the demand response of the same new vehicle buyer facing the same
purchase price increment becomes much smaller. Data on new and used LDV prices (implying a
sequence of values for depreciation and ownership cost) can be used to construct an estimate of
the proportion of changes in new-vehicle purchase price new-vehicle buyers will be able to pass
through to future users versus the fraction they will bear themselves.
3.1.1.2 Aggregation of Elasticities
For the purposes of many questions in the vehicle literature (e.g., a vehicle
manufacturer's choices about markups), elasticities at a micro level are the relevant unit. A
company can consider raising or lowering the price of one individual model, or even one
individual trim, by itself. In contrast, questions relevant to policy making are typically at a more
aggregate level: suppose a regulation imposes a cost (either an engineering cost or a shadow
cost) on the entire new vehicle market at once. How will consumers respond to this? The
transformation needed to answer this involves adding up the whole "block" of own- and cross-
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price demand derivatives for new vehicles.5 Intuitively, if most of the substitution reflected in a
demand derivative for a new vehicle is just substitution to other new vehicles (as opposed to used
vehicles or public transit), then the aggregate demand derivative may be very small even when
the demand derivative for individual models or trims is quite large.
Much of the literature presents only "average" elasticities, that is, the average own-price
elasticity among individual models of new vehicles. Average elasticities tend to be larger and
may be substantially larger in magnitude than the aggregate own-price elasticity. In Section 5,
we focus on aggregate rather than average elasticities. Sometimes these are presented directly in
the papers reviewed, and in other cases we can compute them if sufficient data are provided in
the paper. Many papers that focus on estimating demand at the level of individual models are not
necessarily structured in such a way as to enable estimation of these aggregate elasticities,
however, because they typically do not include the possibility of substitution to an outside good.
3.1.1.3 Simultaneous Changes in Indirect Utility
The derivatives of demand here reflect a world where (at least from the consumer's
perspective) only the price of new vehicles has increased, with no change in perceived vehicle
quality. This concept is only sufficient in specialized examples where the benefits from a
regulation are fully diffuse (so an imperceptibly small amount of the benefit goes back to an
individual vehicle consumer) and where the technology used to provide this benefit is invisible.
Pure examples like this are hard to find in the space of automobiles, but certain tailpipe
regulations on smog-forming pollutants may come close: suppose an extra $100 is spent using a
more expensive metal in a catalytic converter. If this causes it to work better at reducing smog
but is imperceptible to the consumer (i.e., no changes in maintenance, longevity, power, etc.),
then measuring the price increase by itself is enough to understand the effect of the policy on
demand for new and used vehicles.
More often, however, the price increase creates environmental benefits that are diffuse
but also changes the way the vehicle works (either for the better or worse) such that the
consumer sees a simultaneous change in price and something else about the vehicle. Some
tailpipe requirements on smog-forming pollutants may reduce power, for example, or create fear
of increased "check-engine" faults as the systems grow more complex. This creates a challenge
because the degree to which these things bother consumers is often unknown. The same $100
5 In much of the new-vehicle literature, the derivative presented is with respect to price, implicitly suggesting that
the rental or depreciation price entering utility is a constant fraction of the new-vehicle price. For the literature on
used vehicles, the derivative will tend to be with respect to depreciation or rental price directly. The aggregation
problem applies regardless.
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price increase, when it comes together with some power loss or maintenance fear, might look
more like a much larger price increase in terms of how the consumer reacts. Although it is
theoretically possible to estimate the effects of changes in quality on consumer valuation of
vehicles, there is relatively limited literature for many vehicle attributes and considerable
variability in the available estimates. Greene et al. (2018) summarized the literature on consumer
willingness to pay for vehicle attributes.
Fuel-economy regulations create an even more challenging environment in this sense. By
their very nature, the benefits of improved fuel economy are shared. Part of the benefits from
reduced gasoline use (e.g., improved health and environmental conditions resulting from lower
emissions) are diffuse and go to society, while another part (the money savings at the pump)
goes directly to the vehicle owner. If we do not know how consumers view these savings, we
cannot determine the net change in indirect utility. For example, suppose fuel-economy policy
raises the new-vehicle price by $100 (and power and all other attributes are fixed), while
discounted future fuel expenditures on that vehicle fall by $150. A consumer might mistakenly
think there will only be $100 in gasoline savings and would see this policy as a net zero on
indirect utility. Their demand for new vehicles would not change at all. Another consumer may
think there will only be $60 in fuel savings. They would react to this policy as if it were a $40
increase in cost, reducing their demand by some, but not by as much as they would for a $100
loss in indirect utility (see Greene et al. [2018] and Greene, Evans, and Hiestand [2013] for
discussion of consumers' willingness to pay for fuel economy). In addition to differences in
perceptions of what their discounted savings over time may be for a given driving pattern, there
is also heterogeneity across consumers in the distance they anticipate driving. Consumers who
anticipate driving a greater distance per unit time are expected to place a higher value on fuel
economy than those who drive less.
We will refer to the combined change in perceived cost at the time of purchase as a
"generalized cost." Consumers will be assumed to respond to a $100 increase in generalized cost
the same way they would respond to a $100 price increase when the attributes of the vehicle
remain unchanged. Valuation of changes in vehicle attributes may vary widely across individual
consumers. In our aggregate model characterization, the value of the generalized cost used
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represents the net change in vehicle cost perceived by the average consumer.6
Making use of a demand system in this setting requires three sets of estimates: i) the
demand elasticity as above, ii) the price increase associated with the regulation, and iii) the
perceived utility loss (or gain) associated with the engineering change. We assumed that
combining (ii) and (iii) into generalized cost and then multiplying by (i) leads to the percentage
change in quantity demanded.
3.1.2 Supply and Scrappage
The supply of newly manufactured vehicles is likely to be fairly elastic, especially in the
long run when companies can expand and new entrants can appear. When supply of a product is
elastic, and no used versions are present, a demand system alone (like the one described above)
is enough to accurately predict what will happen when there is a cost increase due to regulation.
The projection for a new equilibrium quantity can be read directly from the cost increase and the
estimated demand elasticity. However, the presence of a used market interacts with the
equilibrium system and the new-vehicle demand elasticity is no longer sufficient to measure the
effect of a policy.
The aggregate supply of used vehicles, in contrast, is far less elastic than that of new
models. When a particular used model's price rises, more of that model become available in total
(e.g., because used-vehicle owners are more likely to trade a valuable used vehicle in than sell it
for scrap metal, and because vehicle dealers, insurance companies, and mechanics decide to
repair and sell a greater fraction of the stream of used vehicles they receive). However, this effect
remains limited by the overall number of vehicles of a certain vintage and model that are
available in the system. Because the elasticity of supply for used models appears to be
intermediate, neither very close to zero nor very close to infinity, the equilibrium outcome for
these vehicles depends importantly on both the elasticity of demand and supply (where used-
vehicle supply is inversely related to scrappage).
The most straightforward scrappage function for used vehicles (which can be inverted to
determine used-vehicle supply) can be derived from an underlying, fixed distribution of repair
cost shocks (e.g., costs from mechanical failures and accidents). A simple model of scrappage
6 As pointed out by a reviewer, one caveat to using generalized cost is that a regulation that changes the attributes of
vehicles may change the substitutability between new and used vehicles. In that case, the relative allocation of
the change in generalized cost between changes in vehicle price and attributes may be something to consider.
This effect may become more important in the future if applying the model to explore the transition to electric or
autonomous vehicles, where major differences in attributes could lead to large changes in substitution between
new and used vehicles.
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states that scrap occurs when these shocks exceed the value of a vehicle.7 In contrast to the issue
identified for demand elasticities whereby demand elasticities vary by level of aggregation (i.e.,
elasticities increase with the level of disaggregation because some or even all of the substitution
may be taking place between the disaggregated vehicle categories), we assumed that vehicle
scrappage depends only on own price of vehicles.8
Empirical estimates will typically be presented as a derivative of the density or elasticity
of this function, rather than of the density of underlying shocks that determines the function. This
is analogous to utility functions, where estimates are typically presented as elasticities or
derivatives rather than as direct utility function parameters.
3.1.3 Equilibrium and Estimation
Evaluating equilibrium effects is the end goal of a policy analysis, but in the context of
estimating the two underlying functions above (demand elasticities and scrappage elasticities)
the presence of equilibrium effects in observational data leads to biased estimates.9 A biased
estimate of the scrap function, for example, might partly reflect the desired underlying scrap-
price relationship, but also partly reflect an equilibrium process in the real-world evolution of
prices and vehicle stocks.
Expanding on the example of a scrap function, notice that in the framework above it is
only a used vehicle's own value (and the comparison of that value to a repair cost shock) that
determines scrappage. The derivative of the scrappage function with respect to a change in the
price of new vehicles is zero. However, even when there is no direct channel for new-vehicle
prices, they will still have an important equilibrium impact on scrappage: increases in new-
vehicle prices tend to increase used-vehicle values, so we might observe that new-vehicle prices
in fact create quite large changes in scrappage. Some of the equilibrium increase in used-vehicle
values could be immediate (via changes in expectations or substitution in the demand system),
7 The presence of transactions costs could lead to a more complicated scrappage function that directly involves the
prices of other, perhaps even new, vehicles. Jacobsen and van Benthem (2015) present a range of arguments why
the prices of other vehicles are unlikely to be important direct determinants of scrap.
8 As pointed out by a reviewer, the vehicle scrappage decision should theoretically also depend on the prices of other
vehicles to the extent that parts needed for certain repairs are interchangeable and supply curves for these parts
slope upwards. This is undoubtably true in the short term and when sourcing repair parts from scrapped used
vehicles, though manufacturers can respond to rising prices by increasing production of these parts, which would
mitigate price increases, or even reverse them to the extent there are economies of scale. In addition, our
aggregate model represents an entire vehicle vintage as a single representative vehicle. Thus, we assumed that
the scrappage decision depends only on the own price of that aggregate vehicle.
9 Equilibrium changes can act as omitted variables (to the extent that not all prices and quantities are included in the
same regression) or as conduits for other omissions (e.g., taste shocks that affect more than one vintage of a
vehicle at once).
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but there will also be changes over time as the currently new portion of the inventory ages and
creates shortages in the used market. The resulting equilibrium increase in used-vehicle value is
what enters the scrap function and determines the scrap rate.
To provide a concrete empirical example, consider running a fixed-effects regression of
scrap rates on new-vehicle prices. We want to learn how much each $1 of increase in new-
vehicle prices lowers the scrap rates of used vehicles. An empirical estimate of this relationship
is a reduced form, in that it reflects the chain of effects that runs first from new prices to used
prices and then through a scrap function and into scrap rates.10 Any unobserved shock that
affects markets for new and used together will confound this regression. As an example, suppose
many fixed effects (e.g., time, vehicle class) are included so that only cross-model variation in
prices and scrap rates remains. Even in this setting the estimates will be confounded: unobserved
shocks that make a single model more popular will both allow the manufacturer to raise the price
of new versions and provide a boost in demand for used versions. Scrap rates may appear to fall
dramatically when new prices rise, but this comes both from the effect we want to measure
(which is an indirect one, coming through the chain of price effects from new to used and then
on to scrappage) and the direct effect from the model-level increase in utility. There is also a
possibility for reverse causality: a downward shock to the scrap rate will create more competition
for new versions of a vehicle (because there are now more used ones remaining in the market),
leading manufacturers to lower prices. Estimating the reduced form successfully would require
good quasi-experimental variation in new-vehicle prices, but the likely confounders and long
time series required have meant that the literature has been unable to find many suitable settings.
Even with a setting providing good variation in new-vehicle prices, it will remain challenging to
identify the appropriate elasticity given the importance of cross-price elasticities with used
vehicle prices, which are reflected in equilibrium.
In contrast, the goal of the underlying parameters approach outlined here is to separate
the two steps between a shock to new-vehicle prices and effects on quantities in the used market.
Credible variation exists to identify demand derivatives (e.g., the approach in BLP and others),
and quasi-experimental variation in used-vehicle prices is also available to identify scrap
elasticities. Separating these two links in the chain makes it easier to demonstrate economic
consistency within each link and, therefore, in the overall estimate.
10 If the variation in the data that creates the change in new-vehicle prices is also connected to other aspects of the
vehicle market or macroeconomy, notice that these other effects will also be wrapped into the observed values of
scrappage. A change in policy would likely create a different outcome. The underlying scrap function, on the
other hand, stays the same regardless of the source of change in used-vehicle value.
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3.2 Considerations for Framework Development
3.2.1 Key Questions
A policy that increases new-vehicle prices (or more generally that decreases indirect
utility associated with new vehicles11) will have a cascade of effects on vehicle quantities
throughout all vintages within the inventory. First, and perhaps most directly, the higher prices
will mean that fewer new vehicles are purchased, with the magnitude of the reduction partially
determined by the aggregate own-price elasticity of demand. Moving forward in time, reductions
in new-vehicle sales will start to produce shortages in the used-vehicle market (e.g., reductions in
sales of new 2020 model-year vehicles mean that there will be fewer used 2020 vehicles
available in all future years). The reduced availability will lead to a higher equilibrium price of
used vehicles than would have been observed in the absence of the policy. Another effect
(present in both the short and long runs) comes via cross-price elasticities of demand for new
vehicles. If the increase in price of new vehicles causes some consumers to purchase in the used
market instead (i.e., a substitution effect), this flow of former new vehicle buyers into the used
market will also tend to drive used-vehicle prices up.
Through both of these channels, used-vehicle prices will increase as a result of the new
vehicle policy. Higher used LDV prices in turn have two key effects. First, higher prices will
force some used-vehicle buyers out of the market—to an "outside option" like public
transportation or carpooling. Second, higher used-vehicle prices will make used vehicles worth
maintaining for longer, reducing scrappage and partially offsetting some of the shortages that
have appeared in the used market.
How do the effects on the composition of the vehicle inventory relate to the initial policy
goals? Longer vehicle lifetimes mean larger used-vehicle inventories and older average vintages,
tending to erode environmental improvements that might have been expected in a world where
inventory turnover, and thus the distribution of the vehicle inventory across vintages, remains at
baseline levels. How large this effect is empirically depends on all the parameters that control the
cascade of effects described above. For example, how easily do LDV consumers substitute from
new vehicles to used vehicles or from personal vehicles generally to public transit or carpooling?
11 We use the term "price increase" throughout, but the concepts apply to any reduction in indirect utility from a new
vehicle purchase. Indirect utility holds income fixed and reflects the maximum utility a consumer can attain. A
vehicle price increase, therefore, reduces indirect utility because it reduces the amount of money left over to buy
other goods. A reduction in weight and horsepower (holding vehicle price constant) also reduces indirect utility:
even though the budget for and consumption of other goods is unaffected, total utility declines to the extent the
vehicle produces less utility when driven. Improvements in other attributes (like fuel economy), on the other
hand, can partially or fully offset price increases in the indirect utility measure; we are interested in the effect of
a price increase net of utility enhancements.
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For the group of consumers that substitutes from new to used, how much does this substitution
drive up equilibrium used-vehicle prices? When buyers substitute between new vehicles and
used vehicles, which vintages are they substituting toward (e.g., likely relatively recent model
used vehicles) and how does this affect the distribution of price changes across vehicles of
different vintages? How does substitution between used vehicles of different vintages work out
in equilibrium?12 Finally, to what extent does the increase in used-vehicle values make repairs
more worthwhile, thereby reducing scrappage and increasing the size of the used inventory?
The chain of effects above can be illustrated in a simplified supply and demand
illustration where there are only two types of vehicles, "new" and "used." The left panel of
Figure 3-1 displays the new-vehicle market. The original impulse is an upward movement in the
(horizontal for convenience) supply curve in the new market: new-vehicle supply moves from Sn
to Sn and produces a corresponding increase in price. If the demand curve for new vehicles
remained at the baseline, Dn, equilibrium quantity would simply fall from point A to point B.
The amount of the decline in quantity from point A to B is given by the demand elasticity for
new vehicles. However, in equilibrium, prices in the used market will also rise. Because new and
used cars are substitutable, this will cause the demand curve for new cars to shift to the right, to a
line like the one labeled Dn. The amount the demand curve shifts to the right is determined by
the elasticity of substitution between new and used vehicles. The final change in new car
quantity is then given by a move from point A to point C. This decline in quantity is what we call
the policy elasticity of new-vehicle sales in the following discussion.
Why do prices rise in the used market? As explained above, there are two main reasons.
The first is the scarcity of new cars feeding into the used market. When quantity drops from A to
C in the new market, the supply of used vehicles shifts to the left by a similar amount (the long-
run maximum number of used vehicles, if all accidents and breakdowns are fully repaired, is
determined by the number of new vehicles coming in). This is shown in the right-hand panel of
Figure 3-1 with the shift from Su to Su. The slope of the Su curves is determined by the scrappage
elasticity. If scrappage responds a lot to vehicle value, then the curves are flatter, or in the
extreme case where scrappage is completely predetermined, these curves would instead be
vertical. The inward shift in the used-vehicle supply curve increases used-vehicle prices (and
reduces quantities) from point i to point ii in the figure. The other force influencing the used
market is substitution. The increase in new-vehicle prices in the left panel increases demand for
12 In the default assumptions within our simulation model, we assumed higher substitutability between vehicles that
are closer in age. We believe this assumption is reasonable, but there is relatively little empirical data on how to
parameterize these substitution patterns, so we examined a wide range of other possibilities, detailed in Appendix
C.
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used substitutes. This substitution appears as a shift out in demand for used vehicles, shown in
the movement from Du to Du. As before, the size of the shift out in demand is determined by
cross-price elasticities between new and used vehicles. The final equilibrium outcome in the used
market is then a shift from point i to point iii. Note that the price of used vehicles always
increases (both forces operate in the same direction), but the direction of the quantity change is
ambiguous. It depends on the relative slopes of Du (determined by the price elasticity of demand
for used vehicles) and Su (determined by the scrappage elasticity).
In the model in Section 6, we parameterized these slopes and allowed for many
interactions among ages, considering 30 overlapping vintages, so that we can calculate
equilibrium results throughout the age profile. It may be interesting in future work to see if an
analytically tractable model with just two ages is feasible in closed form; if so, it could help to
further the intuition for patterns in our quantitative model output below.
Figure 3-1. Diagram of Outcomes in New and Used Markets
New Vehicles
Used Vehicles
Pn
Pu
Sn' S„
Qn
Qu
3-11
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3.2.2 Overvie w of Approaches
Two broad empirical approaches are available to understand effects over time in the new
and used portions of the inventory. One approach is a "quasi-experiment": the analyst would
need to find a shock that changes all new-vehicle prices without also directly affecting used
vehicles or other features of the economy that influence vehicle demand. The short-run effects
from a quasi-experimental increase in all new-vehicle prices could then be studied by examining
the response the shock produces in new and used markets. However, because transportation is
such a fundamental component of the economy, finding a good quasi-experiment has proven
difficult: most factors that increase new-vehicle price have some other connection to the vehicle
market, so the experiment becomes confounded. It is even more challenging to study long-run
equilibrium effects on the used market using a quasi-experiment because the quasi-experimental
increase in new-vehicle prices would need to be very long-lived, lasting at least for the typical
lifetime of a vehicle, to study features of the used market as it transitions to a new steady-state
equilibrium.
A core reason the economics literature has not been able to find good quasi-experimental
variation may be the strong connection between automobile sales (both new and used) and
macroeconomic variables like employment and wages. A quasi-experiment that changes the
price of just one new vehicle model might not have enough connection to the macroeconomy to
confound the estimate, but for the aggregate impacts relevant here one needs a shock that
changes the prices of all new vehicles at once. For example, changes in the prices of inputs to
making vehicles (labor, metals, energy, and so forth), of course, do change new-vehicle prices,
but the effect coming from price alone cannot be disentangled from other effects these changes
would have on vehicle demand. Changes in the overall tax regime for new vehicles may be
related to macroeconomic fluctuations and so forth. Additionally, factors that affect production
of new vehicles are likely to affect components produced for use in repairs, and so confound
elasticities between the new and used markets.
Finally, another difficulty with a quasi-experimental approach is that the price shock
needs to be independent of vehicle attributes valued by consumers. Otherwise, it becomes
difficult to separate out the quality-adjusted price shock. For instance, many historical price
shocks that directly affect new vehicles are associated with regulations that mandate increased
safety (e.g., seat belts, airbags) or fuel economy, either of which provide benefits to consumers
that need to be assessed to evaluate the net change in indirect utility.
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A second empirical approach is to estimate a set of underlying parameters that control the
system and then use those parameters to simulate how vehicle markets evolve over time when
there is an external increase in new-vehicle prices. We explore this approach further in Section 6.
The core idea is that the underlying functions and parameters are static; they determine where the
new equilibrium will end up but are not themselves a function of the equilibrium. Consider
vehicle scrappage as an example: the equilibrium scrap rate of a particular vehicle is dependent
on everything else in the system (e.g., prices and quantities of all new and used vehicles) and
evolves in a dynamic way through time. A scrap function, on the other hand, is defined by an
underlying relationship (here, the tendency to do more repairs on vehicles that are more
valuable) that remains fixed.
The simulation tool we developed translates vehicle demand elasticities and scrappage
elasticities into a time path of policy-relevant outcomes. For example, a new-vehicle own-price
demand elasticity of-1 means that a 1% increase in new-vehicle price will result in a 1%
reduction in the quantity of new vehicles demanded, all else equal. However, in a policy scenario
context, it is not the case that all else remains equal. If a regulation raises new LDV prices by
1%, the effect on purchases of new vehicles is no longer the 1% decline suggested by the own-
price demand elasticity because price expectations for used vehicles and scrappage rates are
adjusting simultaneously with the new-vehicle price shock.
A dynamic model can address relevant questions regarding the impacts of changes in
new-vehicle prices on new- and used-vehicle markets, scrappage rates, and the size and
composition of the U.S. LDV inventory. Assuming the policy shock is long-lived, the effects on
used-vehicle prices and scrappage evolve, likely strengthening as more vintages become directly
affected over time.13 Our simulation model shows the transition path as the vehicle inventory
moves toward its new steady state. The differences between the short- and long-run impacts may
be quite significant, making an aggregate simulation a practical tool for connecting empirical
demand and scrappage elasticities taken from the literature to impacts on policy-relevant
quantities.
The peer-reviewed economics literature has been able to provide empirical estimates of
many of these underlying parameters and functions: these estimates are synthesized in Section 5.
Section 6 then discusses how these elasticities from the literature might be used to inform
parameter selection within the long-run simulation model we developed to assess outcomes in
13 A countervailing effect, which also leads to interesting dynamics, can also be present to the extent compliance
becomes easier as technology advances.
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the new and used components of the inventory resulting from a policy shock. Because there is
often disagreement and, in some cases, very little published work on key elasticities, we have
constructed the simulation model to be very flexible. Sensitivity analyses can be conducted
readily and running multiple simulations with economically plausible combinations of the
underlying elasticities will return a range of outcomes that inherit the economic consistency of
the underlying parameters.
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SECTION 4.
DESCRIPTION OF STUDIES AND ATTRIBUTES ANALYZED
We conducted a systematic literature review for peer-reviewed publications and grey
literature from academic and research institutions that appeared to be relevant based on our
search terms (see text box below). We identified literature using three different search strategies.
We reviewed the results of using these search terms within Google Scholar, JSTOR,14
ResearchGate, and Science Direct search engines directly. In addition to these databases, we
reviewed bibliographies of relevant literature to identify additional potential sources. We also
reviewed the primary set of studies included in a previous review of the literature on willingness
to pay for vehicle attributes conducted for EPA (Greene et al., 2018a) because we anticipated
some overlap with the set of vehicle demand studies identified in that report.
Search parameters:
Types of literature: 1) peer-reviewed publications, 2) grey literature from academic/research institutions
Search engines: Google Scholar, JSTOR, ResearchGate, ScienceDirect
Publication years: 1995-present
Region: primarily U.S.
Search terms: new-vehicle prices, new automobile prices, vehicle replacement demand, used-vehicle price
changes, new-vehicle sales, used vehicle sales, used automobile prices, pricing of new vehicles, pricing of new
automobiles, motor vehicle pricing, vehicle scrappage, new-vehicle demand elasticity, demand for vehicle
ownership, U.S. automobile market dynamics, automobiles secondary market, automobile market equilibrium,
automobile prices, vehicle scrappage in the U.S.
4.1 Sample Description
We used the search parameters above to produce an initial pool of 37 papers. Among this
sample, there were 25 that included information enabling estimation of the elasticity of demand
for new vehicles, 16 that could inform estimates of the impacts of new-vehicle costs or prices on
prices or sales of used vehicles, seven that estimated impacts of new- or used-vehicle prices or
operating costs on scrappage of used vehicles, and four that identified factors influencing the
total size of the combined new- and used-vehicle inventory.15
However, after conducting a more in-depth review and quantifying the estimates
available from these studies, we ended up with only 19 different studies that provided 24 relevant
elasticity estimates that met our search criteria. There were 10 estimates of elasticity of demand
14 We used JSTOR's Text Analyzer to identify relevant literature within their database. This tool allows the user to
upload a document/text for the Analyzer to "find the most significant topics and recommend(s) similar content."
https://guides.istor.org/howto-search/text-analvzer
15 Some studies were identified as falling into multiple categories, so the sum of the individual categories exceeds
the number of studies included.
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for new vehicles from 10 studies, four estimates of the effects of vehicle prices on used vehicles
from three studies (two estimates of the impacts of new-vehicle prices and two focused on the
effects of used-vehicle prices), nine estimates of the impacts of vehicle prices on scrappage from
seven studies, and one estimate of the effect of new-vehicle prices on total inventory size.16
During peer review of the report, a reviewer identified an additional report providing an
elasticity of demand for new vehicles that met our criteria for inclusion, resulting in our final
count of 20 studies providing 25 elasticity values (11 estimates of elasticity of demand for new
vehicles from 11 studies, four estimates of the effects of vehicle prices on used vehicles from
three studies, nine estimates of the impacts of vehicle prices on scrappage from seven studies,
and one estimate of the effect of new-vehicle prices on total inventory).
One of the biggest sources of the differences in number of studies included in the final
quantitative analysis is that many of the studies identified as potentially relevant estimated
demand at a more disaggregated level than our focus for this project. Many studies used vehicle
type, model, or even trim-level data for new vehicles and did not include or did not report
parameters for the outside option (e.g., purchasing a used vehicle or no vehicle rather than a new
vehicle). Thus, they did not generate estimates of the aggregate-level market elasticity that we
are focused on, but rather estimated demand elasticities that reflect substitution between different
new vehicles. Although some of these papers reported "overall" demand elasticities, they are
typically average or median individual elasticities, calculated across vehicle types, models, time,
etc., which means they do not reflect the aggregate elasticities that we want to represent. For the
purposes here, we are interested in the change in new-vehicle demand if many or all new-vehicle
prices increase simultaneously, not what happens to demand for a single model or trim if only its
price increases. As would be expected, the more disaggregated the vehicle sales data used, the
higher the estimated elasticities tend to be. The fact that the elasticities differ in this way is
entirely consistent with economic theory; more disaggregated choice sets (in terms of attributes,
time of purchase, etc.) mean that the best substitutes for any given good within the choice set
will be more similar to it (e.g., more substitution would be expected between sedan models or
between makes of sedan than between new and used vehicles or between a personal passenger
vehicle and alternative means of transportation). Heterogeneous consumers are more likely to be
on the margin between purchasing one vehicle versus another because the way that the vehicle
set is defined becomes more disaggregated and some products are more similar to one another
16 Five studies provided multiple elasticity estimates that we incorporated into our summary, which explains why
there are 25 elasticity estimates drawn from 20 studies.
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for the attributes on which they are focusing their purchase decision. Thus, the own-price
elasticity is higher because an increase in the price of the good will lead to more substitution.
Figure 4-1 shows the distribution of the final set of 20 studies by publication year,
highlighting the relatively low and even distribution of papers in recent years.
Figure 4-1. Distribution of the Final Set of Papers Included by Year of Publication
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As Table 4-1 details, most of the estimates came from peer-reviewed literature (75%);
five papers from the main sample came from grey literature.
Table 4-1. Literature Summary Statistics Based on our Main Sample
Paper count
20
Literature type (out of 20)
Peer reviewed
15
Grey
5
Parameter estimated (sums to more than 20 because some papers estimated multiple parameters)
New-vehicle sales
11
Used-vehicle prices or sales
4
Scrappage
9
Total inventory size
1
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4.2 List of Papers Identified
Table 4-2 lists each paper identified based on our review and summarizes the data used in
each. The type of data used by each study is provided to highlight which studies derived
estimates from stated preference versus collected market data. More than two-thirds of the papers
in our sample implemented actual market data in their models. Market segment further provides
insight into whether the studies used data to represent households or market aggregate. It also
shows the transactions presented in the study (new, used, or both).
Table 4-2. List of Papers Included and Parameter Estimates Provided
Citation
Region
Type of
Data
Market Segment
Alberini, Harrington, and McConnell (1998)
California
Market
Households, used vehicles
Bento, Goulder, Jacobsen, and von Haefen
(2009)
United States
Survey
Households, new and used vehicles
Bento, Jacobsen, Knittel, and van Benthem
(2020)
United States
Market
Households, new and used vehicles
Bento, Roth, and Zuo (2018)
United States
Market
Households, used vehicles
Berry, Levinsohn, and Pakes (2004)
United States
Survey
Households, new vehicles
Berry, Levinsohn, and Pakes (1995)
United States
Market
Market, new vehicles
Chen, Esteban, and Shum (2010)
United States
Market
Households, new and used vehicles
Dou and Linn (2020)
United States
Market
Households, new vehicles
Fischer, Harrington, and Parry (2007)
United States
Market
Market, new vehicles
Goldberg (1996)
United States
Survey
Market, new vehicles
Greenspan and Cohen (1999)
United States
Market
Market, used vehicles
Hahn (1995)
United States
Market
Market, used vehicles
Jacobsen and van Benthem (2015)
United States
Market
Households, used vehicles
Jayarajan, Siddarth, and Silva-Risso, 2018
Indiana and
California
Market
Market, used vehicles
Knittel and Metaxoglou (2014)
United States
Market
Market, new vehicles
Leard (2021)
United States
Survey
Households, new vehicles
McAlinden et al. (2016)
United States
Market
Market, new vehicles
McCarthy (1996)
United States
Survey
Households, new vehicles
Miaou (1995)
United States
Market
Households, used vehicles
Selby and Kockelman (2012)
Texas
Survey
Households, used vehicles
4-4
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SECTION 5.
LITERATURE SYNTHESIS
This section summarizes the findings of our review of the papers identified in Section 4.
We have conducted a review of these papers to identify available estimates that can be used to
predict one or more of the following:
the effect of changes in new-vehicle prices or costs on new-vehicle sales,
the effect of changes in new-vehicle costs or prices on prices or sales of used
vehicles,
the effect of changes in new- or used-vehicle prices or operating costs on scrappage
of used vehicles, and
the effect of the factors influencing the total size of the (combined new and used)
vehicle inventory on the size of the inventory.
We compiled information on each article, including author (s), publication year, journal,
years of data used in the analysis, the kind of data used (e.g., stated preference, revealed
preference, market data), sample size, and methods used for analysis (e.g., nested logit, mixed
logit) (provided in attached spreadsheet).
Despite the importance of the LDVs market to the U.S. economy, the empirical evidence
for the measures of consumer responsiveness necessary for empirical implementation of our
simulation model is quite limited. It is important to note that even in cases where several
estimates are available, these estimates often have remaining shortcomings for the purpose of
evaluating long-run relationships between new-vehicle and used-vehicle markets, scrappage, and
overall U.S. vehicle inventory. For instance, many of the studies are more than a decade old,
often relying on data that are even older. Vehicles are becoming more durable over time, while
embedded vehicle technology is changing rapidly, which may decrease the substitutability
between newer and older vehicles. Thus, older studies may not adequately capture current
consumer behavior. In addition, it is reasonable to expect that the elasticity of demand for new
vehicles may shrink as consumers get richer. In that case, reliance on older studies may tend to
overestimate the new vehicle price elasticity in current vehicle markets. Another consideration is
that many of the available studies from which elasticity parameters can be drawn or calculated
are not primarily focused on the parameters that are of interest for this study. Although we
believe it makes sense to use those parameters for the purposes of this study because they reflect
the range of values implied by the available literature, these papers were not necessarily focused
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on identifying aggregate elasticities and may have chosen a different specification had they been
focused on estimating aggregate market elasticities.
Unfortunately, available information from these papers is generally insufficient to
characterize the distribution of these estimated elasticities. In many cases, the point estimate of
the relevant elasticity is directly stated in the main body of the paper or a footnote. In other cases,
we estimated the elasticity based on available information on parameters combined with
assumptions that make it difficult to formally characterize the uncertainty associated with a given
elasticity estimate. Thus, we focus throughout on reporting the point estimates available from
each study.
The remainder of this section provides descriptions of the set of papers that provided
relevant elasticities or sufficient information to generate elasticity estimates, organized by
elasticity parameter, and summarizes our findings on the state of knowledge and level of
agreement for each.17
5.1 Effect of Changes in New-Vehicle Prices or Costs on New-Vehicle Sales
The aggregate own-price elasticity for new vehicles is the parameter being examined that
has the most estimates available from the literature. These elasticities capture substitution from
new to used vehicles as well as to the outside good, defined here as choosing to travel by means
other than a personal LDV (e.g., switching travel modes to public transit, bicycle, walking, or
other options). Table 5-1 summarizes the studies included and their elasticity estimates,
organized by category of estimate and ordered within those categories by year of publication.18
We then briefly describe each of the studies incorporated and the findings, ordered in the same
way. The elasticities in the first panel hold constant most other aspects of the equilibrium system,
including equilibrium changes in used vehicle prices. They ask how new-vehicle sales change
when new-vehicle prices alone change. The studies in the second panel develop simulation
models that allow prices in the used market to also rise over time. These elasticities are,
therefore, expected to be smaller in magnitude, along the lines of the discussion in Section 3
above and are similar in spirit to the policy elasticities we provide from our modeling. They do
17 For those cases where parameter estimates were calculated by the report authors rather than being obtained
directly from the referenced studies, spreadsheets showing calculations used to obtain elasticity estimates are
available from the report authors upon request.
18 A reviewer suggested adding Stock et al. (2018) to this summary table, but it did not meet our search criteria of
peer-reviewed or high-quality grey literature published by a research institution, so we did not include it in Table
5-1 or in the text summarizing our primary findings on the range of estimates. However, we did add another
sensitivity case to Appendix C with a much lower elasticity value (-0.10) to represent the value implied by Stock
et al. (2018).
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not allow changes in scrappage and other dynamics but are an important reference point for our
estimates.
Table 5-1. Summary of Aggregate Own-Price Elasticities for New Vehicles
Study
Time Frame of Data Used
Elasticity
Aggregate own-price elasticity
BLP (1995)
1971-1990
—1.08a
McCarthy (1996)
1989
-0.87
Goldberg (1998)
1984-1990
-0.90
Berry, Levinson, and Pakes (2004)
1993
-0.40c
Fischer, Harrington, and Parry (2007)
2000
-1.00
Bento et al. (2009)
2001
-1.27b
Knittel and Metaxoglou (2014)
1971-1990
-0.57
McAlinden et al. (2016)
1953-2013
-0.61
Dou and Linn (2020)
1996-2016
-0.78a
Leard (2021)
2014-2015
-0.37
Aggregate own-price elasticity after price effects
in the used vehicle market
Fischer, Harrington, and Parry (2007)
2000; calculated from calibrated model
-0.36
Chen, Esteban, and Shum (2010)
NA; calculated from calibrated model
—0.18a
a Author Calculations. Aggregate elasticity not reported by authors of the cited paper but was calculated using data
from the paper (see text for additional details).
b Author Calculations. Aggregate elasticity not reported by authors of the cited paper, but we were able to access the
model used in this paper and recompute the aggregate elasticity from the logit parameter estimates.
c We note that the authors of the study indicated this estimate relies especially strongly on functional forms and may
not be well identified. In an alternative calculation, they instead considered a market elasticity of -1 (based on
estimates from General Motors).
5.1.1 Aggregate Own-Price Elasticity of Demand for New Vehicles with Respect to Price of
New Vehicles
BLP (1995) estimated disaggregated elasticities, including those to an outside good of not
purchasing a new vehicle. Thus, although they did not report an aggregate elasticity, there was
sufficient information available for us to calculate one. We calculated a simple average of the
model-level price elasticities using the values reported in their Table V (-5.00) and used data
reported in their Table VII to calculate the average substitution to the outside good (i.e., not
purchasing a new vehicle) (21.53%). We then multiplied these values to estimate the aggregate
own-price elasticity for new vehicles as -1.08. There are some important caveats to this
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calculation. We only have the sample of vehicles they reported in their tables and assumed it is
representative of the full set of new vehicles available for sale. In addition, we made a simple
assumption regarding average model-level elasticities and average substitution to the outside
good, whereas we would ideally want to calculate share-weighted averages if sufficient data
were reported. As an additional caveat, the authors noted (p. 881) that "the numbers [on
substitution outside] still seem a bit large to us." This group of authors in a later work (Berry,
Levinson, and Pakes, 2004) considered values of-0.40 and -1.00 for the aggregate elasticity.
McCarthy (1996) reported an estimate of the own-price elasticity for new vehicles, along
with cross-price and income elasticities. They were focused on assessing the effects of
accounting for perceived quality (based on an argument from the literature that the market price
elasticity of demand is substantially biased downward when demand is not corrected for quality
differences), though in the end found relatively little impact on their estimates. The estimate of
the elasticity from their preferred model is -0.87.
Goldberg (1998) focused on assessing the effects of Corporate Average Fuel
Economy (CAFE) standards on new-vehicle sales, prices, and fuel consumption. As part of this
study, a discrete choice model of vehicle demand was estimated using micro data for 1984-1990
from the Consumer Expenditure Survey (CES). They estimated an aggregate elasticity of
demand for new vehicles of-0.9.
Barry, Levinson, and Pakes (2004) estimated an aggregate elasticity of demand of-0.4 in
their preferred model specification, combining micro and macro data, including survey data of
vehicle buyers indicating what their second choice would have been had they not purchased the
new vehicle that they bought. However, they also stated that" [o]n the basis of their experience,
the staff at General Motors suggested that the aggregate (market) price elasticity in the market
for new vehicles was near one," so Barry, Levinson, and Pakes (2004) also present outputs
calibrated to match General Motors' estimate of-1.0.
Bento et al. (2009) did not report an own-price demand elasticity in their paper, but we
were able to access the data and code used for the analysis conducted in that paper and applied it
to estimate an aggregate own-price demand elasticity of-1.27. This is the most elastic estimate
among any of the studies identified for inclusion in this report, perhaps connected to the cross-
sectional nature of the variation and longer-run changes in demand that are implied. The study
used data from the 2001 National Household Travel Survey and is identified from variation
across locations in vehicle ownership costs and gasoline price. Places with high vehicle costs
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tend to have fewer vehicle sales, all else equal, due not only to substitution to the used market
but also to longer run attributes of the location like transit availability and structure of cities.
Knittel and Metaxoglu (2014) employed a broad range of numerical methods, including
many that do not perform especially well in minimizing their objective function. Focusing on the
numerical method that performs best (producing the minimum value for the objective function)
the elasticity estimate is -0.57. They presented a range of-0.41 to -1.74 for this elasticity across
all numerical methods used.
McAlinden et al. (2016) used annual data from 1953-2013 to estimate the change in
consumer spending on new vehicles as a function of income, new-vehicle prices, used-vehicle
prices, consumer credit, interest rates, and total number of households. They found a short-run
own-price elasticity for spending on new motor vehicles of-0.79. Applying a Koyck
transformation, they estimated the long-run own-price elasticity to be -0.61. The authors noted
that their estimate is lower than previous disaggregate, cross-sectional models that they
reviewed, which they attributed to their inclusion of consumer credit and interest rate variables in
their estimation.19
Dou and Linn (2020) estimated a 0.30% decline in new-vehicle sales from the imposition
of a policy that raises the new-vehicle price by $108 ($90 in added cost and $18 in markup).
Using data elsewhere in the paper on average vehicle prices, we calculated a 0.383% increase in
price. The corresponding elasticity is -0.78. The purchase data used in the study are CES
microdata from 1996-2016. They also examined used-vehicle sales but considered changes in
transactions rather than changes in aggregate quantities or scrappage in that component of the
analysis.
Leard (202120) estimated a relatively inelastic response of new vehicle purchases to
changes in new-vehicle prices among the papers included in our study, -0.37. The paper used
second-choice data from a survey of new vehicle buyers. Leard (2021) argued that logit models
such as used in McCarthy (1996) tend to produce unreasonably large substitution toward
alternatives with large market shares (and here, in particular, toward not purchasing a new
vehicle), so they may overstate consumer responsiveness to new-vehicle prices. He noted that in
19 McAlinden et al. (2016) estimated a short-run elasticity of-1.31 when they estimated an alternative version of
their model excluding consumer credit and interest rates as explanatory variables.
20 There are multiple versions of this working paper available. We used the most recent version at the time of
preparing this report, the May 2021 version. This version estimates a more elastic response than the initial version.
It also no longer reported a cross-price elasticity between new and used vehicles that was present in earlier
versions.
5-5
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a given year the market share for not purchasing a vehicle is around 90% and that logit model
specifications implicitly assume little difference between new vehicle buyers and those who do
not purchase a new vehicle, an assumption not supported by data.
5.1.2 Aggregate Own-Price Elasticity of Demand for New Vehicles with Respect to Price of
New Vehicles, Allowing for Price Effects in the Used Market
Fischer, Harrington, and Parry (2007) applied a model of the U.S. vehicle inventory and
simulated changes in the inventory over time and accounted for adjustments in used-vehicle
prices. They estimated a long-run elasticity of-0.36 as their primary case, though also conducted
sensitivity analyses with elasticities of 0 and -0.8.
Chen, Esteban, and Shum (2010) estimated an increase of 3% in new-vehicle sales when
new-vehicle taxes are reduced by 30%. The tax-inclusive price of a new vehicle falls by 17% in
their scenario, implying an aggregate new-vehicle price elasticity of-0.18. Their model allowed
used-vehicle prices to adjust endogenously along the lines of the interactions we explore below,
though it held vehicle lifetimes fixed.
5.1.3 Summary
Even in the category where we have the most empirical estimates available from the
literature, the direct own-price elasticity of demand for new vehicles, relatively few studies
provided aggregate elasticities. The magnitudes estimated are relatively consistent, though.
Demand elasticity estimates range from -0.37 to -1.27, though six out of eight are inelastic
(ranging from -0.37 to -0.90). Studies using second-choice micro data (e.g., Barry, Levinson,
and Pakes [2004], Leard [2021]) tended to have the lowest elasticity estimates.
However, the data used in these studies tend to be quite old, with only two of the studies
identified using data more recent than 2001. To the extent that the responsiveness of vehicle
demand has changed in the last 20 years, most of these studies are not reflective of current
market conditions. In addition, a number of these studies relied on panel data with very short
time series. There may not be enough variation in the panel to identify the choice of an outside
option. It is also the case that many of these studies were not necessarily focused on estimating
the demand elasticity, and authors may not have considered what variation is determining the
estimate of the parameters for the outside option.
As expected given the relationship between the new- and used-vehicle markets, the
available elasticities of new-vehicle demand when used-vehicle prices can adjust (-0.18, -0.36)
indicate less responsiveness. These elasticities reflect medium-term responsiveness, allowing for
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markets to adjust to a new equilibrium. Both available estimates fall below the lower end of the
range for standard demand elasticities measured when the prices of substitutes are fixed. The
model developed here additionally accounts for expectations and allows endogenous changes in
scrappage but is similar in spirit; the two elasticities from the literature support the core intuition
that accounting for market interactions between new and used vehicles leads to substantially
smaller elasticity values.
5.2 Effect of Changes in Vehicle Costs or Prices on Prices or Sales of Used Vehicles
Table 5-2 summarizes the studies identified that provided estimates of the effects of
changes in new- or used-vehicle prices on the used-vehicle market, in terms of either prices or
quantities. A very limited number of such studies are available. The table is organized by
category of estimate and the discussion follows this organization as well. Although our focus
was on the effects of new-vehicle prices on the used-vehicle market, we included a study
examining the relationship between used-vehicle prices and used-vehicle sales.
Table 5-2. Summary of Estimated Effects of Changes in New- or Used-Vehicle Prices on
Used-Vehicle Markets
Study
Time Frame of Data Used
Elasticity
Elasticity of used-vehicle price with respect to
new-vehicle price:
Chen, Esteban, and Shum (2010)
NA; calculated from calibrated model
1.69
Average own-price elasticity, used vehicles:
Jayarajan et al. (2018)
2003-2006
-1.23
Bento et al. (2009)
2001
-0.54
Elasticity of used-vehicle inventory with respect
to new-vehicle price, long run:
Bento et al. (2009)
2001
-0.08
Bento et al. (2020)
NA; calculated from simulation model
-0.12
5.2.1 Elasticity of Used- Vehicle Price with Respect to New- Vehicle Price
Chen, Esteban, and Shum (2010) estimated a 28.8% decline in used-vehicle prices when
the new-vehicle price declines 17%. This estimate is representative of a long-run equilibrium and
corresponds to an elasticity of 1.69. As expected, changes in new-vehicle prices lead to changes
in the same direction in prices in the used-vehicle market. Given the smaller value of used
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vehicles relative to new, the corresponding derivative is smaller than the elasticity and is 0.91 (a
$1 increase in new-vehicle price corresponds to a $0.91 increase in used-vehicle price).
5.2.2 Own-Price Elasticity for Used Vehicles with Respect to Price of Used Vehicles
Jayarajan et al. (2018) reported an average elasticity across estimates at the model level.
We did not include average estimates for individual new vehicles because aggregate elasticities
were more available but provide these because so few studies have examined demand elasticities
of any type in the used market. Their estimate of own-price elasticity for used vehicles ranged
from -0.75 to -1.93 with a mean of-1.23. This is larger than most elasticity estimates for new
vehicles but is not directly comparable to the estimates provided above for new vehicles because
this value represents an average across model-level elasticities rather than an aggregate elasticity
for used vehicles. They find that price changes of new vehicles have a substantially larger effect
on used-vehicle markets than vice versa.
Bento et al. (2009) also reported model-level price elasticities among used vehicles: the
average vehicle-level elasticity among all used vehicles was -0.54. Newer used vehicles appear
more elastic (with a reported average elasticity of-1.01) and are perhaps more comparable with
the sample in Jayarajan et al. (2018). In both papers the demand elasticity reported reflects total
consumer demand for a used vintage at a given price irrespective of how that demand might be
met. The used vehicle quantities we work with are aggregate values and reflect changes in the
total quantity of vehicles in the system rather than numbers of transactions among individuals.21
5.2.3 Elasticity of Used- Vehicle Quantities with Respect to Price of New Vehicles
Bento et al. (2020) took as given that the aggregate elasticity of demand for new vehicles
is -0.21 (from a recent National Highway Traffic Safety Administration rulemaking). They then
constructed bounds on the elasticity of the size of the used inventory (also in long-run
equilibrium) with respect to new-vehicle prices. The most elastic the long-run response of the
used-vehicle inventory can be in their study is the value used for the long-run elasticity of
demand for new vehicles (-0.21) if there is no reaction at all in equilibrium scrappage. This
refers to a long-run equilibrium where the proportionate change in new-vehicle sales year after
year (with no change in scrappage rates) eventually leads to the same percentage change in the
total inventory. It is also possible that scrappage rates decline by so much that all the lost new
vehicles are replaced by extending the life of used ones: this is the upper bound and evaluates to
21 In practice, used vehicle demand can be met by maintaining an existing vehicle (not leading to a transaction) or
buying one from someone else who has maintained it (leading to a transaction). The papers cited, and the model
here, track the total of the two sources together.
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0.016 in the example. The paper then estimated where within these two bounds the true used
inventory elasticity likely falls. For a range of scrappage elasticities between -0.5 and -1.0, the
long-run used inventory elasticity ranged between -0.14 and -0.10. These estimates were all
constructed relative to the new-vehicle demand elasticity and scale directly with it. Because the
new vehicle elasticity used in Bento et al. (2020) is lower than many in the literature (Table 5-1
above) perhaps the most relevant finding here is that the used-vehicle elasticity was estimated to
be roughly one-half (i.e., -0.12 /—0.21 = 0.57) the magnitude of the new-vehicle elasticity.
5.2.4 Summary
Given that we identified very few studies in the three categories of elasticity estimates for
used-vehicle markets (and that the studies examining own-price elasticities for used vehicles
reported average rather than aggregate values), it is not possible to assess the degree of
consensus in the literature. Further exploration of the aggregate response of used-vehicle markets
to changes in new- and used-vehicle prices appears to be an important gap in the literature.
5.3 Effect of Changes in New- or Used-Vehicle Prices or Operating Costs on Scrappage
of Used Vehicles
Table 5-3 lists each paper identified by our review providing a relevant estimate of the
scrappage elasticity, separated into those assessing responsiveness of scrappage to used- versus
new-vehicle prices. We then briefly summarize each of the studies incorporated, following the
same order. There is substantial variation in the methods used to estimate responsiveness of
scrappage to vehicle prices and in the estimates provided. A particularly important distinction is
between those studies that are estimating scrappage econometrically and those that are
conducting simulations of the response to a bounty program encouraging vehicle retirement. An
important caveat of studies looking at a bounty for scrappage lies in the temporary nature of the
program: it may be that a short-lived, salient subsidy will quickly harvest a stock of "almost-
scrapped" vehicles, overstating the elasticity. The elasticities implied by the papers relying on
simulations based on assumed data or a representative base year are very sensitive to the
assumptions we used to calculate them. Based on calculations using what we think are
reasonable central assumptions, these papers generate the highest and lowest elasticities among
our sample. Overall, we question the reliability of these models for our purpose of generating
aggregate scrappage elasticities and emphasize the econometrically estimated values for the
purposes of selecting the range of scrappage elasticities used in our simulations.
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Table 5-3. Summary of Scrappage Elasticities from Literature
Study
Time Frame of Data Used
Elasticity
Scrappage with respect to used-vehicle prices
Hahn (1995)
1993; calculated from simulation
—1.14a
Miaou (1995)
1965-1992
-0.91
Alberini, Harrington, and McConnell (1998)
NA; calculated from simulation
—2.97a
Greenspan and Cohen (1999)
1973-1991
-0.82
Selby and Kockelman (2012)
2009; calculated from simulation
-0.01a
Jacobsen and van Benthem (2015)
1999-2009
-0.69
Bento, Roth, and Zuo (2018)
1981-2014
-0.36
Scrappage with respect to new-vehicle prices
Miaou (1995)
1965-1992
-0.21
Greenspan and Cohen (1999)
1973-1991
-0.82
a Author Calculations. Aggregate elasticity not reported by authors of the cited paper but was calculated using data
from the paper (see text for additional details).
Note: The three papers that generated results using simulation models of bounty programs to encourage retirement
of older vehicles resulted in values that were quite different from the econometrically estimated values in the other
studies. For each of the three, we had to calculate elasticities based on a combination of values presented in the
paper and our assumptions, and we found that elasticities were very sensitive to our assumptions. Therefore, we
have less confidence in the elasticities calculated from those three studies and focus on the econometrically
estimated values in developing the range of values used in our model simulations.
5.3.1 Elasticity of Aggregate Scrappage with Respect to A verage Price of Used Vehicles
In Hahn's (1995) Table 2, he relates an exogenous "bounty" (subsidy to scrappage) to
changes in the absolute number of vehicles scrapped relative to a baseline, reflecting the short-
run response. In a simple theoretical setting, a $1 subsidy to scrapping a vehicle should have the
same effect as reducing the payoff from not scrapping a vehicle (i.e., the price the used vehicle
would bring in the market) by $ 1. The challenge in converting the table to an elasticity is that the
paper does not report the baseline value of scrappage or the baseline price of used vehicles, so
both of those must be inferred to convert the level changes into an elasticity. Based on our
assumptions, the elasticity was estimated to be -1.14, but one can potentially get very different
elasticities by making alternative assumptions.
Miaou (1995) reported estimated elasticities directly, with an estimate of-0.91 for the
elasticity of equilibrium scrappage. This paper looked at correlations in an equilibrium time
series without attempting to separate supply and demand curves.
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As in Hahn (1995), Alberini, Harrington, and McConnell (1998) related an exogenous
bounty to changes in the number of vehicles scrapped (summarized in Figure 3b of their paper)
within a simulation model. In a simple theoretical setting, a $1 subsidy to scrapping a vehicle
should have the same effect as reducing the payoff from not scrapping a vehicle (i.e., the price
the used vehicle would bring in the market) by $1. Based on the average value of used vehicles
that could potentially be scrapped and the change in scrappage between a bounty of $0 and
$1,000, we estimated an elasticity of-2.97.
Greenspan and Cohen (1999) also did not directly provide an elasticity estimate, but one
can be calculated based on the information provided in footnote 22 of their paper, where they
noted that a 1.9% increase in the ratio of the consumer price index (CPI) for repairs to the CPI
for new vehicles reduced scrappage by 150,000 vehicles (1.56%). This led directly to the
elasticity of-0.82. Note that the repair cost elasticity is -1 times the used-vehicle price elasticity
under the (typical) assumption that vehicles are scrapped when the repair cost exceeds the
vehicle's value. A 1% increase in repair cost for vehicles around the margin of scrappage has the
same effect as reducing the value of those used vehicles by 1% (because repair cost and vehicle
value are equal at the scrap margin by definition). In turn, this relationship means that the
functional form imposed in the estimation here (namely that the cost of repairs and new vehicles
enter inversely to one another) implicitly restricts new-price and used-price elasticities to be the
same.
Selby and Kockelman (2012) simulates 5,000 households' vehicle-purchasing decisions
over time based on survey data collected from Austin, Texas, in 2009. The authors conducted a
few different simulations, including one looking at scrappage incentives. They did not report
scrappage (or other) elasticities but did provide some of the information needed to calculate
them. An important qualification in this exercise is that the way scrappage is presented appears
to be unusual: When the scrappage subsidy increases by $2,000, for example, new-vehicle sales
change very little, but the average age of vehicles reported increases. This paper appears to be
defining scrappage (e.g., in Table 6) as vehicles that collect the bounty at the simulated auctions,
while a more typical definition would define scrappage as all vehicles removed from the vehicle
inventory regardless of cause. When we incorporated assumptions to translate the reported
changes into aggregate scrappage, our central estimate of the scrappage elasticity appeared to be
quite small relative to the literature, -0.012. We have less confidence in this calculated value
than other scrappage elasticities presented in this section.
Jacobsen and van Benthem (2015) used data disaggregated at the level of make-model-
age; the -0.69 in the table above is an average that can easily be disaggregated by age, class,
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make, etc. (e.g., columns 2-5 of Table 3 in their paper). Identification used an IV approach and
included a range of fixed effects to remove aggregate shocks (age-year and make-model-age
fixed effects in the main specification). The IV approach is aimed explicitly at tracing out a
supply curve for used vehicles (i.e., the "not-scrapped" vehicles).
Bento, Roth, and Zuo (2018) used annual data on average used-vehicle price and
aggregate scrappage. A structural approach (related to that in Greenspan and Cohen [1999]) is
taken to identify different drivers of scrappage. The structural model included the prices of used
vehicles on the right-hand side (where the -0.36 elasticity we report in the table comes from):
higher used prices led to less scrappage.
5.3.2 Elasticity of Aggregate Scrappage with Respect to Average Price of New Vehicles
Miaou (1995) separately estimated an elasticity of equilibrium scrappage with respect to
the average price of new vehicles. Their estimate was -0.21, less elastic than their estimated
elasticity with respect to the price of used vehicles (-0.91).
As noted above, the functional form imposed by Greenspan and Cohen (1999) implicitly
restricted scrappage elasticities with respect to new- and used-vehicle prices to be the same. The
elasticity from Greenspan and Cohen (1999) is -0.82 and is reported again in this (elasticity with
respect to new-vehicle price) section.
We note that the estimates in Miaou (1995) and Greenspan and Cohen (1999) reflect
correlations in equilibrium time series rather than separate estimation of supply or demand
curves.
5.3.3 Summary
There is a wide range of scrappage elasticity estimates with respect to used-vehicle prices
in the literature, though we have less confidence in some of those that fall at the extremes of our
range. In particular, elasticities calculated from the studies that rely on simulations or bounties
(Hahn, 1995; Alberini, Harrington, and McConnell, 1998; and Selby and Kockelman, 2012) are
more dependent on assumptions and interpretation and can change considerably with changes in
assumptions. For the other four studies examining scrappage with respect to used-vehicle prices,
the range is much tighter, from -0.36 to -0.91. There were only two studies examining
scrappage with respect to new-vehicle prices, which fell in a similar range (-0.21, -0.82) to
those for used-vehicle prices. To the extent there is a strong connection between new and used
prices (as suggested in Table 2 and in the equilibrium simulations in Jacobsen and van Benthem
[2015]) the tight link between the new- and used-price elasticities of scrappage is expected.
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5.4 Effect of the Factors Influencing the Total Size of the (Combined New and Used)
Vehicle Inventory on the Size of the Inventory
Table 5-4 lists the one paper identified as assessing the responsiveness of total inventory
size to new-vehicle price based on our review.
Table 5-4. Summary of Estimated Vehicle Inventory Elasticities
Time Frame
Study
of Data Used
Elasticity
Aggregate elasticity, total inventory with respect to aggregate vehicle
price
Bento et al. (2009)
2001
—0.14a
a Author Calculations. Aggregate elasticity was not reported by authors of the cited paper, but we were able to
access the model used in this paper and recompute the aggregate elasticity from the logit parameter estimates.
Bento et al. (2009) estimated a demand system but did not report the full matrix of own-
and cross-price elasticities. However, we were able to access the logit model code and data used
by Bento et al. (2009) and recompute the aggregate elasticity based on the full matrix using base
parameter estimates. This calculation provided an estimated elasticity value of-0.14, implying
that a 1% increase in the price of new vehicles would result in a reduction in the total U.S. LDV
inventory of 0.14%.
5.4.1 Summary
We found only a single study that met our criteria for providing sufficient information to
calculate an aggregate inventory elasticity. Along with additional focus on the responsiveness of
used-vehicle markets to new-vehicle prices, assessing interactions between new and used
markets and implications for the U.S. vehicle inventory is another area that appears to be an
important area for future research. Because vehicles are durable goods, a key component of the
net impacts of a policy or regulation is these interactions between new and used markets, but
these interactions have been less studied than the demand for new vehicles and scrappage
decisions.
5.5 Other Related Parameter Estimates
As noted above, a number of studies provided estimates of elasticities for new vehicles at
a disaggregated level, typically estimating elasticities in the range of-1.7 to -5.0. However, we
could not directly make use of the majority of these studies because they did not include (or did
not report) an outside good. Thus, their elasticity estimates largely reflect substitution between
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different types or models of new vehicles rather than an aggregate demand response when all
new vehicles become more expensive.
Busse, Knittel, and Zettelmeyer (2013) investigated the effect of gasoline prices on new-
and used-vehicle market shares and prices. There is a unit sales regression (Table 7 in their
paper) that allows us to compute the short-run response of aggregate new-vehicle sales to a $ 1
increase in the price of gasoline. Based on their estimated parameters, we calculated the short-
run elasticity of demand for new-vehicle sales with respect to gasoline price to be -0.13.
Unfortunately, a similar exercise for used vehicles is not possible because the used-vehicle data
reflect changes in vehicles transacted, not changes in the aggregate size of the used inventory.
The response of new-vehicle sales to gasoline prices is related to what we are focused on in this
review but does not directly address the question of elasticity with respect to total operating costs
(given that fuel costs account for only a portion of operating costs). Finally, Dou and Linn (2020)
estimated the elasticity of new-vehicle purchases with respect to CAFE policy stringency to be
-0.3. Like Busse, Knittel, and Zettelmeyer (2013), however, this does not directly allow us to get
at the responsiveness of new vehicle purchases to changes in operating costs.
In addition to estimating an own-price response for new vehicles, Leard (2021) also
estimated responsiveness to own-cost per mile. The new vehicle market cost per mile elasticity is
defined as the percentage change in aggregate new-vehicle sales due to a 1% increase in the cost
per mile of all new vehicles and was estimated as -0.20. The analysis defines cost per mile as the
price of gasoline divided by fuel economy. Direct comparison of this elasticity with the price
elasticities in Section 5.1 would need to consider the fraction of total ownership and operating
cost embedded in vehicle price relative to gasoline expenditure, as well as behavioral effects
related to the timing of the different expenses. Given the lack of data on the former and
uncertainty involved in the latter, this elasticity is likely not directly applicable here.
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SECTION 6.
LONG-RUN MODELING OF THE AGGREGATE U.S. VEHICLE INVENTORY
The longevity of vehicles and the ability to buy and sell them as they age create a
dynamic setting where short-run and long-run impacts from a policy can differ quite significantly
from the impacts of a transient shock to prices. In particular, demand elasticities capture the
impact of shocks to individual prices, but an equilibrium that also considers scrappage and asset
prices is needed to measure the effect of a sustained regulation placed on a durable good. Here
we describe a quantitative long-run steady-state equilibrium that allows us to compute policy
elasticities, accounting for dynamics in the vehicle stock and corresponding to a given set of
demand elasticities and scrappage elasticities. We focus on keeping the setting as parsimonious
and transparent as possible, limiting inputs to those needed to determine equilibrium vehicle
stocks. This model does not address the transition to the long-run equilibrium; that transition is
addressed in Section 8.
We begin with core notation for quantities, prices, and ownership costs and then describe
demand, supply, and equilibrium. Of particular note is the presence of two price vectors: one
describing asset values and the other describing annual depreciation (and other ownership costs).
In the long-run equilibrium discussed in this section, these two vectors are a simple
transformation of one another: If vehicle lifetimes increase, the fraction of the original purchase
price that gets depreciated in any 1 year becomes correspondingly smaller. Keeping the two sets
of prices separate becomes more important for the dynamic problem (Section 8) where
expectations and timing create a more complex relationship.
6.1 Model Notation
a indexes vehicle age. Varies between 0 (new) and A (we will set A = 30 in the
quantitative analysis that follows)
qa number of vehicles of age a in equilibrium, so £a qa is the total long-run vehicle
stock
q% aggregate number of vehicles of age a demanded by the representative consumer
aggregate number of vehicles of age a supplied
sa equilibrium probability that vehicle is scrapped between ages a-1 and a. sa = qa~1 qa
Qa-1
ha average repairs needed to keep a vehicle of age a from being scrapped
pa asset value (price if being sold in the market) of a vehicle of age a
6-1
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ra ownership cost of a vehicle of age a, includes depreciation and repairs, ha
6.2 Vehicle Demand
The economics literature estimates elasticities of demand for vehicles using price shocks
that either explicitly or implicitly with the aid of a structural approach, alter one vehicle price at a
time. These price shocks can then be used to trace out the own- and cross-price elasticities of
demand for a given vehicle. However, the elasticities for individual vehicles measured by this
approach do not provide clear signals about an elasticity of demand for new vehicles in the
aggregate. The alternative choice for each individual vehicle includes other new vehicle models
and the outside good (not purchasing a new vehicle, substituting a used vehicle or means of
transportation other than an LDV). Thus, demand for an individual model is likely to be much
more elastic than demand for a generic new vehicle. For our analysis of the age profile and
overall size of the vehicle stock we used a high level of aggregation (considering a representative
vehicle of each age a) and employed a range of demand elasticities from the literature that reflect
the responsiveness of a representative household to price shifts across new and used vehicles.22
The age-level aggregation means we cannot track compositional effects within a given
age; if a new vintage is 10% more fuel efficient than an old vintage, then we assumed it remains
that way as it ages. We address the dynamics of how the new vintage as a whole moves through
the fleet. To the extent a policy has effects on most models within a vintage (e.g., a footprint-
based fuel economy policy that requires simultaneous improvements across models), our
aggregation captures the setting well. If a policy affects only a few models, then we might
instead expect changes in scrappage and age profiles to be more pronounced in those models; our
aggregate model would capture only a more muted average response for the vintage.
Computational costs and lack of availability of detailed elasticities prevent us from writing a
more disaggregate model here, but extensions of the method to account for more vehicle types
may be feasible.
We assumed that the demand system is stable over time such that elasticities and relative
vehicle values in the utility function remain fixed. Elasticities were determined from the
literature and relative vehicle values in utility were implied by observed differences in ownership
cost of vehicles at different ages. In part, the assumption of stable utility is practical; there are no
22 While the demand-elasticity setting maintains generality in many respects, it does require us to abstract from
transaction costs. Any single household might keep a vehicle for several years to reduce transaction costs
(effectively choosing it through a sequence of ages), something we cannot model explicitly with a representative
agent. We note, however, that the policies we consider here tend to increase vehicle lifetimes only slightly,
meaning there are unlikely to be significant changes in overall numbers of transactions. In the short run
(explored in Section 8), transactions costs could potentially enter more importantly as vehicles get reshuffled.
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readily available estimates of how elasticities and relative utility might evolve with policy. We
do note, however, that electrification of the vehicle market could introduce important changes.
Because new electric vehicles will likely come with attractive new gadgets and safety features in
addition to expanded range, this could widen the gulf in utility between new and old vintages,
making new-vehicle buyers less willing to substitute to an old (gasoline-powered) vehicle. On
the other hand, electrification might also narrow the gap in utility between new and old vintages:
to the extent the new technology is not trusted, new-vehicle buyers might instead substitute more
easily to an older gasoline model.
For simplicity the utility structure here also abstracts from a separate choice of miles
driven, holding the number of miles driven by any particular age of vehicle fixed. To the extent
people buy fewer new vehicles or retire more used ones, they would implicitly be choosing to
drive fewer miles. We focus attention on creating a dynamically consistent and parsimonious
translation between demand and scrappage elasticities and outcomes to do with the stock and age
profile of vehicles. This can serve as an input into larger analyses, which could add functional
forms and assumptions to do with the rebound effect to model overall outcomes like gasoline use
and miles driven. A key limitation of the work here is that, to the extent changes in intensity of
vehicle use are large, we do not capture the interaction between intensity of use and increased
depreciation and scrappage.23
We write the demand system over vehicles of different ages and an outside numeraire
good in terms of the ownership costs associated with choosing each vehicle age,
r = [r0, r1(..., rA]. Modeling ownership cost as the variable of interest to the consumer follows
the approach in Bento et al. (2009) and is important when allowing choices to be made between
new and used vehicles. For the literature that examines choice among different new vehicle
models (excluding used vehicles from the choice set), purchase price is the more typical measure
and produces equivalent elasticities.24
To represent the system of demand elasticities as flexibly, yet parsimoniously, as
possible, we followed Deaton and Muellbauer (1980). Their demand system approximates any
utility-consistent setting using a set of n(n — l)/2 free elasticity parameters (the minimum
23 Knittel and Sallee have a working paper (2021) that shows most vehicle depreciation comes from time, not miles,
which suggests that effects on vehicle depreciation and scrappage may be small even if changes in intensity of
vehicle use (i.e., the rebound effect) are relatively large.
24 The equivalence in the case of a new-vehicle-only analysis holds when residual value after a typical holding
period is a constant fraction of the purchase price. Then, a 1% increase in the purchase price equates to a 1%
increase in the ownership cost (i.e., purchase price less residual value), so the relevant demand elasticities are
identical.
6-3
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required for a complete Slutsky matrix) and is fully consistent with utility theory.25 n in our
setting is equal to A + 2, that is: new vehicles, used vehicles of ages 1 through A, and a
numeraire outside good we will label N. Rewriting the Deaton and Muellbauer system in our
notation (and simplifying it to abstract from income effects), we have demand for vehicles given
by:
qS(r) =z-(Pa + Ia=0 °aa ln(ra)) (6-1)
r a
and demand for the numeraire given by:
-------
6jk = 6kj lj 6jk = 0 for all k, and lj (3= 1 (6-4)
This flexible system for imposing demand elasticities laid out in equations (6-3) and (6-4)
has three main advantages. First, it allows for a very intuitive set of inputs (elasticities directly,
as opposed to structural parameters). Second, generating numerous scenarios and experimenting
with bounding or Monte-Carlo type analyses becomes more straightforward. And finally, general
theoretical restrictions on utility are readily satisfied.
6.3 Vehicle Supply
Supply of the numeraire ./Vis competitive and meets demand at the price of one. Supply
functions for vehicles of different ages define the other side of the market and allow us to solve
for long-run equilibrium effects on the vehicle stock.
The price of a new vehicle is taken as given in the model. A change in this price leads to
changes in purchases and retirements and, therefore, to changes in the size and age profile of the
overall vehicle stock. Taken most directly, the effect of an increase in new-vehicle purchase
price could reflect a simple tax. Conceptually, however, the model can also include much richer
policies by using the price increase to represent a net loss in perceived indirect utility coming
from multiple sources. For example, consider a policy that raises the price of vehicles by $10,
reduces horsepower such that the consumer loses $3 worth of utility, and saves the consumer $15
on gasoline. If this consumer is fully rational, they would recognize that this combination of
changes has increased their indirect utility from the new vehicle and would view it as equivalent
to a $2 subsidy for this vehicle. However, suppose the consumer is inattentive to gasoline saving
and only perceives $10 worth of the $15 in savings. $10 + 3 — 10 = $3; the effect on a potential
purchaser of this new vehicle is as if they faced a new-vehicle tax of $3. For a fuel-economy or
electric vehicle policy, these three categories can reflect most of the as-if price increase:
increased production cost (positive), willingness to pay for attribute changes (positive if valuable
attributes are lost), and perceived fuel savings (negative).
We note that changes in the competitiveness of the new-vehicle market would also lead
to changes in new-vehicle prices faced by consumers. To capture this type of change, the
generalized cost faced by new-vehicle buyers (an input to the present model) would need to be
adjusted up or down. We do not have a strong prior on if policy is likely to increase or decrease
market power, so we believe a neutral assumption that markups remain fixed is reasonable. In
this setting, the change in generalized cost from a policy would only need to reflect changes in
production cost (with appropriate markups) and attributes.
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If used versions of vehicles were not an important component of the market and new-
vehicle supply were perfectly elastic as above, then demand elasticity estimates alone are enough
to predict what will happen when there is a cost increase due to policy. The effect of the policy in
that world can just be read directly from the estimated cost increase and the demand elasticity.
The core element that makes the vehicle market unique, however, is the fact that used vehicles
are not perfectly elastically supplied. When a particular used model's price rises, more of that
model becomes available (e.g., because scrap dealers, insurance companies, and mechanics
decide to repair and sell more of them as vehicles instead of as scrap metal). However, this effect
is limited by the overall number of vehicles of a certain vintage and model that are available in
the system. Because the elasticity of supply for used models appears to be intermediate, neither
very close to zero nor very close to infinity, the equilibrium outcome for these vehicles depends
importantly on both the elasticity of demand and supply (where used-vehicle supply is just the
inverse of scrappage).
Jacobsen and van Benthem (2015) showed that a straightforward scrappage function can
be built from an underlying distribution of repair cost shocks (e.g., costs from mechanical
failures and accidents) and the assumption that scrap occurs whenever the realized repair shock
exceeds the value of the vehicle.27 Any underlying distribution of cost shocks with positive
support corresponds to a scrap function sa(pa) that slopes downward as vehicle values increase.
The corresponding scrap elasticity y is also strictly negative, and we followed Jacobsen and van
Benthem (2015) to define it as y =
vPa sa
To keep our equilibrium calculation as straightforward as possible, we considered a
constant elasticity scrappage function taking only two parameters: one parameter that scales
scrappage levels in the baseline and another that directly sets the scrappage elasticity. Following
Jacobsen and van Benthem (2015):
sa = ba ¦ (pa)Y (6-5)
where ba is the baseline scale term and y < 0 is the scrappage elasticity (defined as the
percentage change in scrappage for each 1% increase in vehicle value). Supply of vehicles at any
given age is then just the originally manufactured quantity minus the cumulative effects of
scrappage. In the long run, where manufacturing and scrappage are stable (or growing at a steady
27 More complex scrappage functions could also be introduced, but we believe the repair-cost driven function
captures the essence of the decision. The presence of transactions costs, for example, could lead to a more
complicated scrappage function that directly involves the prices of other, perhaps even new, vehicles. Jacobsen
and van Benthem (2015) presented a range of arguments why the prices of other vehicles are unlikely to be
important direct determinants of scrap.
6-6
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rate) from year to year, we have vehicle supply at any age a > 1 determined by cumulative
survival to that point: = q0 n§=i(l — sa)- Plugging in, suPply any age can be written as a
function of q0 and the vector of asset values p:
<7a(<7o- P) = % ng=i(l - ba ¦ (Pa)7) (6-6)
6.4 Market Equilibrium
To measure the effect of a policy in the long run, we examined the equilibrium where
prices and scrap rates have reached a new stable level (in the presence of a sustained policy) and
where demand for vehicles at each age equals supply. In the short and medium runs and cases
where the policy itself fluctuates, a more complex dynamic transition occurs where prices and
scrappage evolve from 1 year to the next (explored later in Section 8).
To formalize, we want to solve for the long-run effect of a regulation that increases the
price of new vehicles (or equivalently reduces net indirect utility of the purchase) by some
amount A. An equilibrium is characterized by a vector of vehicle asset values p = [p0, p1(..., pA]
and ownership costs r = [r0, r1>..., rA\ such that all markets clear.
To begin, we set new-vehicle price to be the baseline new-vehicle price plus the cost A
associated with the regulation: p0 = Po^aseiine + A. The supplier is assumed to meet demand at
this price.28 New-vehicle demand is a function of the ownership cost vector r, reflecting costs
associated with all possible vehicles in the consumer's choice set. r in turn is a function of the
equilibrium price vector and includes p0 as well as used-vehicle prices (see equation [6-9]
below):
qo = qo(r) = q$ (6-7)
The used-vehicle market for all remaining ages a > 1 clears when:
q%(r) = qS(q0,p) (6-8)
where the expressions for qD and qs are as defined in Sections 6.2 and 6.3 above.
Importantly, supply and demand are written as functions of different, but closely related,
vectors: In the long run, a stable vector of vehicle asset values p will directly determine a
28 This abstracts from potential changes in market power. Extending the quantitative model to allow producers to
choose a profit-maximizing price is feasible, though in the interest of reducing complexity we have abstracted
from that effect here. We believe market power changes are likely to be small relative to the main effects. If large
market power changes are expected under regulation, we note that they could also be approximated by adjusting
A up or down.
6-7
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corresponding vector of vehicle ownership costs r (because changes in p across ages affect
depreciation as well as scrappage and repairs; see next subsection for detail). We are, therefore,
left with a closed system of A equations (one equating supply and demand for each used-vehicle
age) and A unknowns in the vector p. This system of nonlinear equations is readily solved
numerically and leads to the results presented in Section 7 for a small 1% change in purchase
price. Solving the system for large values of A is also straightforward and provides
counterfactuals that can consider how the equilibrium system evolves in regions farther away
from the baseline; for larger values of A, the results necessarily begin to rely more heavily on the
functional forms used to define demand and scrappage.
6.4.1 Asset Values and Ownership Cost
In the long run, when the vehicle stock has reached a new stable path and asset prices
have stopped fluctuating, there is a straightforward relationship between p and r. We describe it
here, building on the setting in Jacobsen and van Benthem (2015). In the short-term transitional
response to a policy, the relationship is more complex, depending on both history and
expectations, and we explore that case in detail in Section 8.
In the long run, ownership cost and asset prices are related as follows:
1
r° ^o-J^Ci-SiXPi-hi)
1
n = Pi - - si)(P2 - hi)
rA = pA (6-9)
where 5 is the discount rate, sa is the scrappage function as above, and ha is average per-vehicle
spending on repairs at age a. Ownership cost at a particular age is the asset value at that age
minus the (discounted) asset value a year later, adjusted downward for repairs and the possibility
of scrap. To the extent some causes of potential scrappage can be insured against, adding the
actuarially fair insurance cost instead of the scrappage possibility would lead to an equivalent
ownership cost.
The role of scrappage is closely connected to the importance of tracking ownership cost r
separately from asset values p. If scrap rates at older ages fall, the ownership cost at younger
ages becomes implicitly smaller. For example, suppose the scrap rates of 6- through 10-year-old
vehicles get smaller but the purchase price of 5-year-old vehicles stays exactly the same. Even
6-8
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though the price is the same, the improved life span of the 5-year-old vehicle should make it
more attractive to potential buyers. The mechanism through which we capture the increased
attractiveness of the vehicle is the ownership cost calculation: lower scrap rates in the future give
the vehicle higher residual value and therefore lower ownership cost. The demand elasticity,
operating on the ownership cost, leads to the expected increase in demand for 5-year-old vehicles
in this scenario.
Because scrappage occurs when repair costs exceed the value of the vehicle, the form of
the scrap function we have chosen (constant elasticity) implies the form of the underlying repair
cost density. Using the implied repair cost density, we can calculate average repair costs paid
(i.e., the average conditional on not scrapping) at each age ha. No new assumptions are needed
to calculate ha; it follows using only the parameters of the scrap function (derivation in
Appendix B):
h i,-n1 + y
K = ° lr v\ (6-10)
(l+y)(l-i>aPa)
A natural feature of this setting is that repairs become an especially important component
of ownership cost for the very old vehicles. Depreciation (conditional on the vehicle being in
working order) becomes small in contrast. This fits with intuition and adds an important degree
of realism to the setup.
6.5 Summary of Long-Run Model, Inputs, and Solution
We solve the system of equilibrium equations defined above with the key goal of
translating demand elasticities and scrappage elasticities into long-run policy elasticities (i.e., the
impact of a policy on equilibrium prices and quantities). The solution to the system of equations
provides answers to questions like: given a regulation that increases new-vehicle cost (net of any
consumer valuation placed on the changes) by an amount A, how much do new-vehicle sales,
used-vehicle stocks, and used-vehicle asset values change once the policy's effect on the vehicle
stock has stabilized?
In a setting where the good is not durable (or equivalently, where used versions are not a
big part of the market), the answers to these policy questions simply echo the demand
elasticities, and the model here is not needed. In the case of vehicles, asset values and scrappage
impacts also enter importantly, and policy elasticities can deviate substantially from demand
elasticities. We demonstrate the core intuition in Section 7.1.
6-9
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All inputs needed are listed in Table 6-1. Each row contains a model parameter, its
definition, and the data needed to calibrate it. The list is ordered such that each parameter can be
determined using only the data described to the right, potentially combined with parameters
appearing higher up in the list.
Table 6-1. Inputs Needed to Specify the Simulation Model
Parameter
Description of parameter and data needed to calibrate
8
Discount rate
K
Baseline growth rate of the vehicle stock
Y
Scrappage elasticity
ba
Scale parameter for scrappage at each age. Calibrated using baseline vehicle prices and survival
probabilities
Pa
Preference parameters determining share of spending on each vehicle age. Calibrated using
baseline vehicle prices and baseline vehicle stock
Qaa
Substitution among vehicles, each corresponds to an own- or cross-price vehicle demand elasticity
as in equation (6-3)
®Na
Substitution between vehicles and the outside good, determined by the overall outside good
elasticity and restrictions in equation (6-4)
Pn
Share of spending on the outside good. Calibrated using GDP. Note: Model output is currently
independent of this parameter because income effects are all assumed to be neutral. The parameter
is included to simplify demand system notation so that income effects could be more easily added.
6.6 Input Values
5: We used a discount rate of 3% for all values presented in the main text. Appendix C
explores alternative discount rates.
k: We used a baseline growth rate of 0.3% per year, meant to reflect expected increases
in population and vehicle demand per capita through time. Nearly all the results we present will
be of policy outcomes relative to a baseline, however, so the growth rates (assumed the same in
both baseline and policy cases) cancel out. Figure 9-2 is the exception, where the growth rate is
visible in the levels.
6-10
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y: The scrappage elasticity is a key parameter of the model. We explored a range of
values for y taken from results in the literature: see Table 5-3 for discussion.
ba\ Equation (6-5) was then solved for ba, and the value of ba calibrated, so that baseline
scrap rates and survival probabilities are exactly reproduced at baseline prices. We drew baseline
vehicle survival probabilities (cumulative survival since new) from the Annual Energy Outlook
(AEO) 2020-NEMS input files with the following two adjustments. First, we extended the
survival rates for 24-year-old vehicles from AEO (the maximum age in that model) to vehicles
age 25 to 30 years old in our model. This conforms with other datasets (e.g., in Leard et al.
[2017]) that show a similar pattern in the oldest segment of the stock. Second, we adjusted
survival of the newest vehicles so that it moves linearly between new and 3 years old (as
opposed to a step function at age 3 as with AEO).29 Figure 6-1 displays the corresponding age
profile of the total inventory of vehicles. To the extent there is growth, sales and quantities at
each age all grow in proportion, preserving this age profile.
Figure 6-1. Baseline Age Profile of the Vehicle Stock
Vehicle age
29 This adjustment has almost no effect in practice (because survival is very close to 100% anyway) but is needed
for numerical reasons (the scrappage elasticity and repair cost densities cannot be applied if baseline scrappage is
exactly 0). We also think it is more realistic: even very new vehicles can be totaled (or nearly totaled) in accidents.
6-11
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Our results are not sensitive to using alternative source data for the age profile, including
those published in Jacobsen and van Benthem (2015) and Leard et al. (2017).
Pa: These scale parameters in the demand system were calibrated to reproduce baseline
expenditure shares at baseline prices; shares can then vary away from this level once policy is
applied. Baseline shares come from combining the age profile above with data on the cost of
vehicles of different ages. For our baseline vehicle costs, we used data from Table 1 of Jacobsen
and van Benthem (2015) adjusted to 2020 dollars (though the units are not relevant for the
elasticities). We extrapolated for prices outside the age range provided in the table.30 This
represents depreciation in typical vehicle values over their assumed 30-year lifetime in the
absence of new policies or other shocks. Alternate data sources for the baseline price path show
similar depreciation patterns and do not substantially affect the results. The price path we
employed is shown in Figure 6-2.
Figure 6-2. Baseline Vehicle Price Profile by Age
Vehicle age
6aa> @Na- Demand elasticities for vehicles and the outside good are key parameters of the model.
We explored a range of values taken from Tables 5-1, 5-2, and 5-4 above. New-vehicle demand
elasticities range from -0.37 to -1.27 in the first panel of Table 5-1, and we explore values of
30 Jacobsen and van Benthem provided data from age 1 to 19. The extrapolation assumed an annual depreciation rate
that is constant past age 20 (at 6.5%) and the same for new vehicles as 1-year-old vehicles (at 14%).
6-12
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-0.4, -0.8, and -1.27 in Section 7 below. We selected these values to span much of the range in
Table 5-1. Stock et al. (2018) considered a value much closer to zero for this elasticity; we
therefore also explore results from a very small new-vehicle demand elasticity (-0.1) in
Appendix C.
6-13
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SECTION 7.
LONG-RUN MODEL RESULTS
In this section, we present results of modeling the long-run steady-state equilibrium in the
U.S. LDV market under alternative combinations of elasticity parameters. We selected
combinations of parameters within ranges of elasticity estimates based on the findings of the
literature synthesis presented in Section 5 to illustrate the implications of alternative
assumptions.
7.1 Effects of Elasticity Parameters on Simulation Results
We first built intuition around the role of key elasticity parameters by presenting a series
of illustrative cases that successively open additional channels of market adjustment.
Table 7-1 is divided into two sections. The left half shows assumptions on the elasticities
of demand for vehicles and our assumption about the scrappage elasticity. The right half of the
table—"Effect of a 1% increase in generalized cost"—displays what we term the "policy
elasticities." We define the policy elasticity as the long-run steady-state change in any quantity
(e.g., the number of new-vehicle sales) that results from a 1% increase in the generalized cost of
new vehicles. The assumed increase in generalized cost is a measure of the magnitude of the
policy, hence the term "policy elasticity" to represent the responsiveness to a given magnitude of
policy change. For example, row 3 in Table 7-1 shows a setting with a new-vehicle price
elasticity of demand set to -1. The effect of policy on new-vehicle sales in the right panel,
however, is only -0.32. This section builds intuition for the much smaller effect that a policy has
on vehicle sales when compared with the raw demand elasticity for new vehicles.
Table 7-1. Demonstration of Channels of Adjustment in Quantities and Prices
When Generalized Cost of New Vehicles Rises by 1%
Setting
Effect of 1% Increase in Generalized Cost
(Policy Elasticities)
Vehicle Demand Elasticities
Quantities (% change)
New-Vehicle
Demand
Cross-Price
New/Used
Outside
Option
Scrappage
Elasticity
New
Used
All
Average Age
-1.00
0.06
0
0
0.00
0.00
0.00
0.00
-1.00
0.06
-0.10
0
-0.18
-0.18
-0.18
0.00
-1.00
0.06
-0.10
-0.70
-0.32
-0.09
-0.10
0.18
7-1
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7.2 Setting
The left panel displays three combinations of parameter settings, all of which have new-
vehicle demand elasticities (column 1) set to -1. The choice of -1 here is for illustration and
easy comparison of the relative magnitude of the demand elasticity versus the policy elasticity.
Section 7.2 calibrates these elasticities to estimates from the literature.
In all three settings in the table, the cross-price elasticity between new and used vehicles
is set to 0.06. That is, if the ownership cost of new vehicles rises by 1%, demand for new
vehicles falls by 1%, and demand for used vehicles (summed over all ages) rises by 0.06%.
Translating to derivatives, if the cost of new vehicles rises by 1%, while the cost of other
vehicles remains fixed, then demand for new vehicles falls by the same number of units as the
demand for used vehicles increases, and total vehicle stock stays constant.31
The third column shows the elasticity between all vehicles and the outside option. In the
first row this is set to zero; the demand system is calibrated so that if the costs of all vehicles
were to simultaneously rise by 1%, there would be no increase in demand for the outside good.
In the second and third rows, this value is set to -0.1; if we were to make all vehicles 1% more
expensive, aggregate demand for vehicles falls by 0.1%. Given the substitution pattern for new
vehicles (all of which flows to used vehicles), it follows that the aggregate substitution to the
outside good is driven by switches from used vehicles to the outside good. This pattern is helpful
for intuition here but need not be the case in other calibrated scenarios.
Finally, the fourth column describing the setting shows the elasticity of scrappage. The
value of 0 in the first two rows means that scrappage is exogenous: a set fraction of vehicles
survive to each age regardless of vehicle values. Following AEO, that fraction is 83% to age 10
and 24% to age 20 (see Section 6.6). The elasticity of-0.7 in the third row means that if vehicle
value increases by 1% at a given age, the number scrapped at that age falls by 0.7%. When the
scrappage elasticity is different from 0, survival probabilities (both one-year survival, which is
one minus the scrap rate, and cumulative survival to a given age) become endogenous to the
policy.
To complete the setting, note that the demand system contains 30 ages, but so far we have
only specified three demand elasticities. The following assumptions define the remaining
31 This motivates the choice of 0.06 as the cross-price elasticity; a value less than 0.06 would mean that not all of the
reduction in new-vehicle demand (in terms of vehicle quantities) moves to used vehicles. Some would flow to
the outside good. Relative substitutability, that is, how much of the flow is to 5- versus 10- versus 20-year-old
vehicles, is a function of age difference, as discussed in more detail in Appendix C.
7-2
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elasticities. Own-price elasticities for used vehicles of a particular age are set the same as the
new-vehicle elasticity.32 Cross-price demand elasticities between individual ages are set to fall at
8% per year of difference in age. For a 15-year-old vehicle, for example, this translates to 47% of
the total substitution going to vehicles plus or minus 3 years (so between 12 and 18) and 85% to
vehicles plus or minus 8 years. Very little evidence exists in the literature on substitution across
ages, so we explore a wide range of alternative assumptions in Appendix C, including cases
where substitution is much more concentrated and cases where it is entirely flat across the age
distribution.
7.3 Policy Impact
The right-hand panel considers the impact of a 1% increase in new-vehicle price (e.g., a
tax of 1% or a regulation that raises vehicle price net of perceived fuel savings by 1%). What
happens to new-vehicle sales? At first glance it might appear that we could simply apply the
new-vehicle demand elasticity of-1 and conclude that the policy would reduce new-vehicle
sales by 1%. However, the policy impact in the first row indicates that new-vehicle sales do not
fall at all: the "policy elasticity" is zero even though the demand elasticity is set to -1.
The intuition for the zero effect in the first row is as follows: new-vehicle buyers might
consider substituting toward used vehicles (or perhaps even do so in the early years of a policy),
but they would soon realize that the fixed survival probabilities and reduction in new vehicles
entering the system create scarcity in the used market, driving up used-vehicle prices. This
spreads out the cost of the regulation across all vehicles, undoing the original motivation to
substitute. The assumption of zero substitution to the outside good in this first row means that
even though all ownership costs have risen, the overall demand for vehicles never falls. There is
no change in either the aggregate vehicle stock or its age profile.
The second row relaxes the assumption of zero substitution to the outside good, creating
a more realistic setting. The continued assumption of fixed survival probabilities (i.e., 0
scrappage elasticity) means that the ratio of new to used vehicles remains fixed. We know that
all vehicle quantities must fall by the same percentage in equilibrium. As in the first row, the
attempted substitution away from newer vehicles creates a price increase across all ages. Note
32 This assumption is mainly for practicality: we know of no estimates of used-vehicle price elasticities at the
individual age level. We would note that used-vehicle demand could be more elastic than new-vehicle demand
because, for example, the substitutability between 10- and 11-year-old vehicles is likely greater than that
between brand-new vehicles and 1-year-old vehicles. However, an argument can also be made for lower own-
price elasticities for older vehicles: a would-be new vehicle buyer can substitute to an almost-new vehicle and
still meet their transportation needs in a very similar way. A would-be used-vehicle buyer, on the other hand,
may be considering substituting out to other modes of travel altogether. We explore both possibilities in
sensitivity analysis.
7-3
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that the policy elasticity (-0.18) for new-vehicle sales is still considerably smaller in magnitude
than -1. This is because it is mainly the (fairly small) elasticity to the outside good that
determines the decline in new-vehicle sales, not the new-vehicle demand elasticity. With fixed
survival probabilities, new-vehicle sales will eventually determine the size of the whole vehicle
stock, so new-vehicle sales can only fall as much as the market is willing to allow the size of the
whole stock to fall.33
Finally, the third row introduces the full version of the model where scrappage is also
allowed to fall when vehicle values rise. Here we use the scrappage elasticity estimate of-0.7
from Jacobsen and van Benthem (2015). New-vehicle sales now fall even more than in the other
two cases, though the policy effect of-0.3 is still much smaller in magnitude than the demand
elasticity of-1. The ability to maintain vehicles for longer, via the scrappage elasticity, means
that quantity changes can now vary between vehicles of different ages. New-vehicle sales fall by
0.3%, but the overall stock only falls by 0.1%. This happens because at each age a few more
vehicles of a given vintage are repaired rather than scrapped. By the time a vintage reaches age
20, the quantity has been restored almost to pre-policy levels. Long-run average vehicle age rises
by 0.18% on a base of 9.6 years (average age implied by the AEO vehicle survival data
discussed in Section 6.6).
7.4 Calibrated Scenarios Based on Findings of the Literature Review and Synthesis
We focused on three key input elasticities: the elasticity of demand for new vehicles, the
overall substitutability between vehicles and the outside good, and the scrappage elasticity. We
show how a range of different inputs along these three dimensions translates to policy elasticities
over key outcomes in the vehicle stock.
The scenarios in Table 7-2 are representative of elasticities presented in the literature
review in Section 5, though they do not span the whole range. (Appendix C explores cases with
elasticities set at more outlying values.) New-vehicle demand elasticities in the table range from
-0.4 (similar to values from Berry, Levinson, and Pakes [2004] and Leard [2021] and at the high
end for long-run elasticities) to -1.3 (following the demand system in Bento et al. [2009]).
Elasticities to the outside good range from 0 (no alternatives to vehicles available) to -0.14
(following the demand system in Bento et al. [2009]). We observe that in the Bento et al. (2009)
demand system substitution away from new vehicles flows almost entirely to used vehicles, with
33 The value is greater than -0.1 in magnitude because substitution to the outside good is greater at older ages than
newer ages (in this stylized setting, but likely also in fact) allowing a chain of substitution that focuses on older
ages.
7-4
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only small effects on the total number of vehicles.34 This is an intuitive result, so we keep it
across scenarios in the table. When new vehicle elasticities are larger, the cross-price elasticity
with used vehicles is also larger. We explore deviations from this in Appendix C.
The first five rows (rows A through E) hold the scrappage elasticity fixed at a value of
-0.7 (Jacobsen and van Benthem [2015] and also close to the median of values in Table 5-3).
The last four rows (rows F through I) explore changes in this elasticity, spanning most of the
range in the literature with values of-0.2 to -1.2 (repeating scenarios B and D in terms of
vehicle demand elasticities).
Table 7-2. Policy Elasticities Corresponding to Selected Demand and Scrappage
Elasticities
Effect of 1% Increase in Generalized Cost
Scenario of New Vehicles (Policy Elasticities)
Vehicle Demand Elasticities Quantities (% changes)
New-Vehicle
Demand
Cross-Price
New/Used
Outside
Option
Scrappage
Elasticity
New
Used
All
Average age
A
-0.40
0.03
0
-0.70
-0.14
0.01
0.00
0.09
B
-0.40
0.03
-0.05
-0.70
-0.17
-0.04
-0.05
0.08
C
-0.40
0.03
-0.14
-0.70
-0.23
-0.10
-0.11
0.08
D
-0.80
0.05
-0.05
-0.70
-0.25
-0.04
-0.05
0.15
E
-1.27
0.09
-0.14
-0.70
-0.39
-0.12
-0.14
0.21
F
-0.40
0.03
-0.05
-0.20
-0.14
-0.06
-0.06
0.07
G
-0.40
0.03
-0.05
-1.20
-0.19
-0.03
-0.04
0.08
H
-0.80
0.05
-0.05
-0.20
-0.19
-0.07
-0.08
0.12
I
-0.80
0.05
-0.05
-1.20
-0.27
-0.03
-0.04
0.15
Scenarios A through C explore an increase in substitution to the outside good. As we saw
in Table 7-1, this is one of the most important elasticities in determining the effect of policy on
new-vehicle sales. When the outside good elasticity ranges from 0 to -0.14, the new-vehicle
demand elasticity of-0.4 (the same for all scenarios A through C) translates to a policy elasticity
between -0.13 and -0.23.
34 Because used vehicles are cheaper than new ones, this means that if measuring in terms of dollars the substitution
is shared between used vehicles and the outside good, also an intuitive pattern.
7-5
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The difference between scenarios C and D provides an interesting comparison. The effect
of policy on new-vehicle sales in these two scenarios is almost the same (-0.23 versus -0.25)
even though the demand elasticity for new vehicles is twice as big in scenario D as it is in
scenario C (-0.8 versus -0.4). This happens because prices and effects in the used stock move
very differently in the two scenarios. In Scenario C, the relatively easy substitution to the outside
good means that used-vehicle prices cannot rise very much; used-vehicle buyers would rather
switch to the outside good than pay higher prices. Much of the cost of the policy, therefore, falls
on new vehicle buyers. In Scenario D, there is less flexibility to go to an outside good, so used-
vehicle values rise more sharply. The higher values in the used market do two things: First, they
mean that residual values are better for new-vehicle buyers, and the cost of the policy does not
fall as much on new-vehicle buyers. Second, higher values in the used market also reduce
scrappage, so the used (and overall) stocks shrink by relatively little in Scenario D. Average age
also increases much more sharply in Scenario D than in Scenario C, rising by 0.15% for a 1%
increase in generalized cost of new vehicles.
The greatest impact on the vehicle stock occurs in Scenario E in the table: in this scenario
new-vehicle demand is set at its most elastic and substitution to the outside good is also set at its
most elastic. The elasticities used in Scenario E follow the demand system estimated in Bento et
al. (2009).
Next, we consider the effect of the scrappage elasticity. First note that in all rows in the
table the used stock shrinks by less (in absolute value) than new-vehicle sales shrink; costlier
new vehicles are leading to longer vehicle lifetimes. This implies some "leakage" of gasoline
savings compared with a world where the whole stock shrinks by the same amount as new-
vehicle sales, as identified in Jacobsen and van Benthem (2015). In theory, the presence of a
scrappage effect could mean that the used stock actually grows larger as the result of policy (as
opposed to just shrinking less). We note, however, that this happens in only a single scenario in
Table 7-2: in Scenario A when there is no substitution available to an outside good. Even very
small elasticities to the outside good (e.g., -0.05) are sufficient to mean the used stock shrinks.
The second panel (Scenarios F through I) of Table 7-2 shows how the policy elasticities
depend on the scrappage elasticity. Between rows F and G, for example, the effect on the stock is
50% larger (-0.06 versus -0.04) when the scrap elasticity is -0.2 versus -1.2. This is intuitive:
when there is less room for a scrappage effect to operate (e.g., elasticity -0.2) used vehicles will
"make up" less of the loss in new-vehicle sales, so the effect on total stock is larger. In rows H
and I, when new-vehicle demand is more elastic, the scrappage elasticity is also somewhat more
important.
7-6
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Table 7-3 displays additional policy elasticities for the same nine scenarios, now focusing
on prices and scrappage. Asset values (in the generalized sense used throughout) are shown in
the first group of columns. For relatively young vehicles, asset values rise substantially (would-
be new-vehicle buyers want to substitute into the used market, for example, by holding onto a
vehicle until it is 5 years old instead of trading it in at 4). The increase in asset value for age-5
vehicles, for example, reduces the scrappage rate for these vehicles shown in the next group of
columns. This "produces" extra used vehicles in the middle of the age range, helping consumers
make up for the new vehicles lost to reduced sales. This could perhaps be the end of the story,
with the market for very old vehicles remaining relatively isolated from the policy. However,
notice that the extra middle-aged vehicles created by the scrappage effect just mentioned could,
if they continue to be maintained, eventually become 25-year-old vehicles. This creates a
potential surplus of 25-year-old vehicles because demand for them has not increased by much.35
Equilibrium asset prices for the oldest vehicles must, therefore, fall to increase scrappage and
prevent the surplus.
Table 7-3. Additional Policy Elasticities Corresponding to Selected Demand and
Scrappage Elasticities
Effect of 1% Increase in Generalized Cost of New Vehicles (Policy Elasticities)
Asset Value (generalized price) Scrappage Rate 5-Year Depreciation
Scenario
Agel
Age 5
Age 25
Age 5
Age 25
New
Age 5
Age 20
A
1.03
1.14
-0.13
-0.79
0.09
0.88
1.05
0.01
B
1.02
1.09
-0.10
-0.76
0.07
0.90
1.00
0.02
C
0.99
1.01
-0.05
-0.70
0.04
0.94
0.93
0.03
D
1.04
1.24
-0.10
-0.86
0.07
0.82
1.05
0.14
E
1.04
1.28
0.04
-0.89
-0.03
0.80
1.04
0.29
F
1.03
1.24
0.31
-0.25
-0.06
0.87
1.19
0.66
G
1.01
1.00
-0.05
-1.19
0.06
0.82
0.77
-0.01
H
1.06
1.38
1.13
-0.27
-0.22
0.79
1.22
1.33
I
1.03
1.17
-0.11
-1.38
0.13
0.75
0.83
0.00
The effect of the policy on 5-year depreciation costs (last group of columns) is generally
to increase them: this must be the case at least on average over the vehicle life because the initial
purchase price has risen, and we assumed the vehicle is fully depreciated by age 30. The pattern
35 The strength of this effect is determined by the demand system in equilibrium: if there is not much substitution
between new vehicles and 25-year-old ones (our baseline assumption), then policy will not increase demand for
25-year-old vehicles very much above the baseline.
7-7
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in asset prices discussed above, however, means that changes in depreciation will not be
uniform; it is not the case that depreciation simply rises by 1% at every age. In particular, the
core substitution pattern (reduced new-vehicle sales increase demand for relatively new
substitutes) increases asset values for 5-year-old vehicles by more than 1%. Depreciation in the
first 5 years, therefore, rises by less than 1%. Asset values fall more quickly going into middle
age (as above, to prevent surplus at the oldest ages), leading to depreciation costs often
exceeding a 1% increase for vehicles aging from 5 to 10 years old. Finally, depreciation for 20-
year-old vehicles tends to rise only a small amount in response to the policy or even fall, again
due to the pattern in asset values. Changes in the scrappage elasticity produce significant changes
in this pattern: for example, when scrappage elasticities are chosen to be small (Scenarios F and
H), then asset values and depreciation for older vehicles rises because the "surplus" effect from
reduced scrappage among middle-aged vehicles is less pronounced. Conversely, when scrappage
elasticities are chosen to be very large, then depreciation for older vehicles changes very little
and can even shrink slightly as in the case of Scenario G.
Figure 7-1 displays the divergence in effects on new-vehicle sales and the used stock for
a continuum of scrappage elasticities between 0 (fixed vehicle survival probabilities) and -1.2
(among the most elastic responses estimated in the literature). In the figure, vehicle demand
elasticities are fixed as in Scenario D of Table 7-2. (Appendix C repeats the figure for Scenarios
B and E.) When the scrap elasticity is -0.7 on the horizontal axis, the values on the vertical axis
reflect the policy elasticities as shown in Table 7-2 for Scenario D. Even for the most elastic
scrappage in the figure, the policy elasticity for new-vehicle sales is still much lower in
magnitude than the new-vehicle demand elasticity of-0.8. Effects on the vehicle stock overall
rise toward zero as scrappage effects grow large. Large scrap elasticities mean that it is cheap to
prolong vehicle life, so substitution to the outside good becomes a less important feature of the
equilibrium.
7-8
-------
Figure 7-1. Policy Effect on LDV Stocks as a Function of the Scrappage Elasticity for a
1% Increase in Generalized Cost of New Vehicles, Scenario D
Scrappage elasticity (absolute value)
Note: The new-vehicle demand elasticity for Scenario D is -0.8. This figure demonstrates that the policy elasticity
(shown on the vertical axis) is much less elastic than the demand elasticity for a plausible range of
scrappage elasticities.
7.5 Effects by Vehicle Age
Figure 7-2 displays changes in the age profile of the vehicle stock as a result of policy.
All changes shown are for a 1% increase in generalized cost, so these values can again be
interpreted as policy elasticities. The left panel shows changes relative to the no-policy case, by
age; the right panel shows the change at each age relative to the aggregate baseline stock.
The policy elasticities for new vehicles can be read off the vertical intercepts of the left
panel of the figure: for example, for Scenario D in Table 7-2 the policy elasticity for new
vehicles is -0.25, so the vertical intercept in the left panel is -0.25.
Quantities of vehicles over 15 years old increase in all the scenarios shown. Because
these vehicles are a relatively small share of the overall stock, the change in used vehicles as a
whole (i.e., age 1 through 30) is negative. This is more easily seen in the right-hand panel, which
shows the changes as a fraction of the stock (rather than as a fraction of the baseline).
7-9
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The right panel is useful for considering the age profile in the broader context. Notice, for
example, that when the scrappage elasticity is large (Scenario G in purple), the bump up in
quantities for middle-aged vehicles is larger and occurs at a younger age relative to Scenario B in
blue because the greater elasticity means relatively more young vehicles can be saved from
scrappage. Once younger vehicles are saved (replacing some of the lost new-vehicle sales),
relatively less saving of the oldest vehicles occurs (the purple line is slightly under the blue line
for age 20, for example). The integral of the right-hand panel reflects the policy elasticity for the
total inventory as reflected in Table 7-2 above; for example, the blue line for Scenario B
integrates to -0.04.
Figure 7-2. Changes in Long-Run Vehicle Inventory by Vehicle Age
7.6 Summary
The long-run results generate policy elasticities for new-vehicle sales that are
substantially smaller than new-vehicle demand elasticities. This effect is strongest when
scrappage is inelastic or when there is little substitution to the outside good. Intuitively, these
two conditions are also the ones where used-vehicle prices will rise the most in equilibrium. If
scrappage is inelastic, shortages in the used market are persistent and cannot be alleviated by
supply, so prices rise. Similarly, if used-vehicle owners are unwilling to substitute away to an
outside good, then there are more serious shortages in the used market, leading to higher prices.
We also observe that the increase In average age of vehicles tends to be small; reductions
in scrappage rates for newer used vehicles increase quantities in the middle of the age
7-10
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distribution. There is not much upward pressure on the prices of the very oldest vehicles
(because they are not very good substitutes for new vehicles), so there is not much increase in
their quantity.
7-11
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SECTION 8.
DYNAMIC TRANSITION PATH MODELING
When new policy is introduced or an existing policy is changed, the vehicle stock will not
instantaneously move to its new long-run steady state described in Section 6. Instead, it will
evolve dynamically, only arriving at the new steady state after a period of years or decades. In
the early years of a policy, for example, unregulated and partially regulated vintages will still
exist within the stock. Prices and scrappage of these older vehicles are driven by expectations,
preferences, and the rate at which newly regulated vehicles are entering the system.
An important advance over existing models of the vehicle stock is our focus on dynamics
and consideration of the way expectations enter the used-vehicle market. Existing models that
address the used market are scarce, and many either ignore the dynamics or have difficult-to-
interpret reduced forms and can produce inconsistent results. The simulation of the used-vehicle
market in Jacobsen and van Benthem (2015) is most like the setup here. In that model, price
expectations are included, though assumed to be myopic: consumers expect the age profile of
vehicle values next year to be the same as the profile this year.36 Here we are able to capture the
decisions of more sophisticated agents who can anticipate changes in vehicle markets caused by
changes in current policy. This provides several advantages, including theoretically consistent
time paths, improved ability to conduct welfare analysis, and greater realism (at least to the
degree real markets tend to evolve rationally). The model here is also capable of simulating
transition paths under many different forms of myopic expectations.
The focus of the setup below is specifically on the dynamics and transition path: some
resolution is given up (e.g., in aggregating across vehicle models and classes), but in exchange
the model provides an intuitive and utility-consistent view of the way the age structure of the
vehicle stock evolves with policy. To the extent that disaggregated outputs are needed for
specific analyses, this model could potentially be linked with more disaggregated models of the
transportation sector to estimate detailed impacts consistent with the aggregate market outcomes.
8.1 Additional Notation
We build on the notation used in Section 6 to evaluate the long-run policy outcome, now
adding a subscript t (for year) throughout. Specifically:
qa t number of vehicles of age a present in year t, so £a qa t is the total vehicle stock in year t
36 For example: "The value of my 5-year-old vehicle next year will equal the value of a 6-year-old vehicle today."
8-1
-------
a,t' h-a,t' Pa,t> ^a,t
time paths of scrappage, repair spending, asset values, and ownership cost analogous to the
steady-state values in Section 6.
8.2 Demand and Supply
The vehicle demand system is the same as that presented in Section 6 and provides a
flexible yet parsimonious structure. It allows us to easily explore arbitrary demand elasticities in
a utility-consistent way. In the dynamic setting, demand in any given time period t is given by
equation (8-1) with preference parameters /?a and 6a& as described above. Subscripts t now
appear on prices, quantities, and income.
Income Mt scales demand equally across ages and increases over time at rate k: Mt+1 =
(1 + K)Mt V t. k is chosen to reflect projected growth in the vehicle stock over time. The age
profile is assumed to remain stable in the baseline. Without a policy change, new-vehicle sales as
well as the entire vehicle inventory, grow steadily at the rate k.37 After a policy is added and the
transition to the new long-run equilibrium is complete, the inventory will again resume steady
growth at rate k. The growth path will be lower to the extent the regulation was costly and
caused switching to the outside good on an aggregate level.
Vehicle supply each year t is a function of the incoming stock from the previous year
adjusted for scrappage (following equations [6-5] and [6-6]). Note that supply now depends on
equilibrium quantities from a year ago and becomes part of the dynamic path:
8.3 Asset Values and Ownership Cost
In considering the connection between asset values and ownership cost, the long-run
version of the model in Section 6 makes use of the steady-state assumption. Specifically, it uses
the feature that the scrappage and depreciation rate of vehicles is stable in the long run. If new
37 Without a policy change, scrap rates and vehicle lifetimes are assumed to be steady so that growth in new-vehicle
sales translates to growth in the whole stock over time. Somewhat more realism could be attained by introducing
technological change that improves vehicle reliability over time. This complicates the model considerably,
however, and we believe it would scale the baseline and policy cases nearly proportionally and not contribute
significantly to the findings.
q%Art) = (Pa + Ea=o °aa
' a,t
(8-1)
tfa.t (l ^a(Pa,t) )9a-l,t-l
(8-2)
8-2
-------
vehicles have tended to lose 40% of their value in the first 3 years, then a new vehicle purchased
this year can be expected to behave the same way.
When a policy is introduced, this is no longer the case. For example, if a policy reduces
new-vehicle sales, then we can reasonably expect that used vehicles will become a little scarcer
and, therefore more valuable, a few years from now. Expected depreciation is, therefore, less
than 40%. A forward-looking, rational agent will correctly anticipate this type of change and can
make an informed decision about a new LDV purchase at any point along the transition path. A
myopic agent, on the other hand, might under- or overcorrect for the effect the policy is having
and make a mistake in their decision. We focus on the forward-looking (and, therefore, utility-
maximizing) case in our main analysis. The model can also apply myopic expectations of any
particular form; we explore a myopic case in Appendix D and show how it converges to the
same steady state, but along a different transition path in the short run.
Rational expectations is a typical assumption in dynamic modeling and provides valuable
insights into how markets may respond to changing expectations even before a policy or other
change takes place. As soon as a policy change is announced, markets will respond to the
anticipated impacts of that policy, even well before the policy goes into effect. For instance,
there is empirical evidence of increased buying in advance of regulatory changes going into
effect, once those changes have been announced (e.g., Ciccone, 2018; Coglianese et al., 2016).
Although individuals may not be well-informed about coming policies and the potential impacts
on new- and used-vehicle prices, sophisticated market actors such as leasing companies and
banks have strong incentives to follow policy developments and analyze potential impacts. These
market actors will adjust the terms of the products they offer consumers to reflect changes such
as updated residual values for vehicles, which is expected to lead to efficient market adjustments
in anticipation of regulatory or other anticipated changes.38
Expectations enter the model where we consider the relationship between asset values
and ownership cost. Equation (9) above expands to:
38 Of course, there are also cases where individual consumers miscalculate the potential costs and benefits of their
own choices, such as potentially underestimating the benefits of fuel economy, and markets do not necessarily
lead to efficient reflection of these costs and benefits.
8-3
-------
Et[r0,t] ~ Po,t ^ ^^t[(l 5i,t+i)(Pi,t+i ^l.t+i)]
^t[rl,t] = Vl,t ~ ^ £t[(l — 52,t+l)(P2,t+l — ^2,t+l)]
£tl>Xt] = rAt = VAX (8-3)
where £"t[-] refers to the expectation held at time t about the object in square brackets. In
equation (8-3), the expected 1-year ownership cost of a new vehicle, for example, is its new
vehicle price less its residual value (the expected value of a 1-year-old vehicle next year, net of
scrap and repair). The agent makes decisions about vehicles in time t based on expected
ownership cost. When agents have rational, forward-looking expectations, we will have that
£t[Pa,t+i] = Pa,t+1 V a, t and the dynamic path produced by the model maximizes utility in any
given time period. It also maximizes present discounted utility across time periods: the agent in
the present makes purchase and repair choices based on the true future residual value, which in
turn reflects future willingness to pay for a used version of the vehicle.
8.4 Dynamic Market Equilibrium
For ease of notation, we first observe that demand at time t, expressed in equation (8-1)
as a function of rt, can be rewritten as a function of pt and Et[pt+1] by using equation (8-3).
Bold type indicates the vector across ages as before.
An equilibrium over a finite horizon T is defined as a set of vectors pt, for t between 1
and T, such that the following conditions hold:
i) New-vehicle quantity in each time period is given by demand (assuming elastic
supply as before):
Ro,t = Ro,t(PfEt\Pt+i]) (M
ii) Used-vehicle quantities for all a > 1 are such that demand and supply are equated at
each time t:
qa,t(Pt'Et[Pt+1]) = qa,t(qa-i,t-i'Pt) (8-5)
where qa 0 (the incoming vehicle stock from the before the policy is implemented) is given by
the long-run equilibrium from Section 6 when A=0, that is, the steady state is in place before the
8-4
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policy change. The model is, therefore, constructed such that time t = 1 is defined as the
announcement date of the policy. The implementation of the policy on new vehicles could also
begin immediately in time 1, but this is not necessary. To the extent implementation (or
additional phase-in) occurs when t > 1, another advantage of a dynamic model is that
anticipation effects (e.g., "prebuying") can be measured.
iii) Expectations are such that:
Et\Pt+1] = Vt+1 ^ t 6 [0,71 — 1]
Et\Pt+i] = V (8-6)
where p without subscript is the long-run policy outcome computed in Section 6. Expectations in
all time periods 1 through T — 1 are rational. The assumption on expectations at T is made for
computational convenience and discussed below.
8.5 Computation
We use the following algorithm to find a series of price vectors that satisfy all of
equations (8-4) through (8-6) above.39 The equilibrium quantities and scrap rates follow from the
price vectors:
1) Set the starting value of expectations for time periods 1 through T — 1 equal to the
baseline price vector (or the policy price vector, either appears to converge about equally
quickly).
2) Solve for the individual time period equilibria from t = 1 to T sequentially (because
supply at time t depends on quantities from t — 1).
3) Use the results from Step (2) to assign a new set of expectations for time periods 1
through T — l.40
4) Iterate Steps (2) and (3) to a fixed point.
Step (2) ensures that equations (14) and (15) hold given expectations. Step (4) ensures
that equation (16) holds.41 In all reported runs, we selected a value of T sufficiently large that the
39 Although we cannot completely rule out the possibility that multiple time paths might satisfy all the conditions,
we have also never encountered multiple equilibria over (very) many different model runs and starting values.
We would also note that the dynamic solutions we report evolve smoothly from the baseline steady state to the
policy steady state, both of which are uniquely determined.
40 Convergence is faster in some cases if using a scaling factor (i.e., moving 0.9 times the distance between the
values for expectations and the outcome price vectors from the last iteration). The final solution is unaffected.
41 We use the Python SciPy "optimize" library for numerical solution.
8-5
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price vector at time T — 1 has already converged nearly (to a machine epsilon) to the long-run
steady state. 100 years is (much) more than sufficient for this in all scenarios explored; the
majority of transition dynamics are complete by t = 20.
8-6
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SECTION 9.
RESULTS OF DYNAMIC TRANSITION PATH SIMULATIONS
We computed the results of a dynamic transition following the setup above. The paths
explored below all reflect the results of computations done under Scenario D from Table 7-2
above. This scenario is used as an example to show how the vehicle stock evolves through time.
The same figures under the assumptions of Scenario B are produced in Appendix D. The scale of
effects differs, but the patterns and intuition for the transition path are very similar.
9.1 Vehicle Market Dynamics under Rational Expectations
Figure 9-1 displays the time path of the effect of policy (a 1% increase in generalized cost
as before) on new-vehicle sales. The horizontal dashed line shows the long-run effect: -0.25% as
reported in Table 7-2 for Scenario D. The goal here is to study the path that new-vehicle sales
take through time. The top-left panel shows an "immediate" policy: in time 0, the policy is
announced and fully implemented. There is no change leading up to time 0 (because the policy is
not announced yet) and then a drop in sales at time 0 of about 0.4%. Sales then recover and after
about 5 years settle in at their long-run steady state value of 0.25% less than baseline. The reason
for the larger sales drop at the beginning is that shortages have not yet appeared in the used
market: would-be new-vehicle buyers can simply hold on to their existing used vehicle. We note
that the demand elasticity is -0.8, yet the sales drop at time 0 is only 0.4% because price effects
in the used market, unlike quantity effects, happen immediately. Consumers expect that future
used prices will be higher, making current used prices higher in anticipation, leading to an effect
on sales that is smaller than the demand elasticity. Although we do not model dealerships
separately from the representative agent, in more practical terms, the likely channel is that
dealers will understand the changes coming in the used market and offer higher trade-in values to
new-vehicle buyers. From the perspective of a new-vehicle buyer, the 1% policy effect is then
muted because they are also receiving a better trade-in price for their used vehicle.
The top-right panel considers the same policy, going into effect all at once at time 0, but
now it is preannounced. Even though nothing has changed in the new-vehicle market at time -5
(that is, 5 years before the policy goes into effect), there are already some visible effects. In
particular, the announcement of the policy is a windfall gain to used-vehicle owners: asset values
rise in anticipation of shortages that will occur several years in the future. This is a small-scale
version of changes in real estate prices that can occur even when the announced change is
decades away. As pointed out by a reviewer, Holland, Mansur, and Yates (forthcoming) also
found substantial responses in vehicle markets in anticipation of policy changes when using a
9-1
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dynamic model. In one of their scenarios, they assessed a scenario incorporating a future ban on
gasoline vehicle production, which leads to a spike in production of these vehicles before the ban
goes into effect (leading the authors to explore alternative policies that could increase economic
efficiency relative to a production ban). The expected lifetime of the asset is what determines
how far out policy can matter. For vehicles in this model, this seems to be a little over 5 years.
The higher used-vehicle values (and anticipation of even better trade-in values coming later,
when a current new-vehicle buyer might be thinking about trading in) make new-vehicle
purchases ever more attractive leading up to time 0. At time 0, the impact of the policy on new-
vehicle sales is now even greater than in the top-left case: when there is preannouncement, the
market prepares by building up the vehicle stock ahead, allowing it to avoid even more purchases
once the policy enters. Preannouncement has no effect on the long-run outcome: new vehicle
sales converge to the 0.25% decline in a little over 5 years.
The lower left panel considers a policy that is phased in over 5 years, with the policy
announced in time 0 together with the first piece of the phase-in. The time 0 effect consists of
two countervailing forces. First, there is the impact of the policy that will tend to reduce new-
vehicle sales. Second is the impact of the announced trajectory, encouraging new-vehicle buyers
to purchase now (i.e., in time 0) before the policy becomes stronger. In this particular case, the
positive effect on sales slightly outweighs the negative, so, on net, sales increase in time 0. In
years 1 through 5, sales decline steadily as the policy phases in. In year 6 and beyond, once the
policy is fully in place, sales recover toward the same long-run outcome as before. The phase-in
delays convergence to the long-run steady state, which now occurs around time period 10.
Finally, the lower right panel combines phase-in with preannouncement, likely the most
realistic setting. Some prebuying occurs (though relatively little, because the phase-in dilutes the
benefits over time), and convergence to the steady state occurs after about 10 years. To the extent
the phase-in of a policy is made smoother (e.g., by placing only a slight change in year 0 and
then accelerating in the later years of phase-in), the transition effect will be correspondingly
smoother.
9-2
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Figure 9-1. Dynamics of New-Vehicle Sales under Alternative Policy Implementation
Scenarios
Immediate Pre-announced
Figure 9-2 presents the same data from the top-left and bottom-right panels in Figure 9-1,
but now in levels, with the no-policy baseline equal to 100. The background trend upward in
new-vehicle sales dominates in the case of the preannounced phase-in: the policy does not
initially reduce vehicle sales in an absolute sense but instead slows the growth in vehicle sales
during the phase-in period. A stronger policy, even if phased in, could reduce vehicle sales in an
absolute sense while it phases in. In either case, once the new steady state is reached growth in
the new vehicle market will resume (driven here by an assumed exogenous, steady increase in
the population, or per capita demand for vehicle travel).
9-3
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Figure 9-2. Dynamics of New-Vehicle Sales (Levels), Baseline = 100
Immediate Pre-announced phase in
Figure 9-3 explores effects in the used-vehicle stock, picking out a single age to provide
intuition. The figure follows the stocks and prices of 10-year-old vehicles through time. In the
top left, we see three distinct phases of the impact on the stock of 10-year-old vehicles. Because
there is no preannouncement in the top left, Phase (i) is flat, reflecting the baseline. At time
period 0, the policy starts to raise used-vehicle prices, slowing scrappage of all vintages. As
Phase (ii) continues, the effect from reduced scrappage compounds: in time period 1, the
scrappage effect has only operated for 1 year, but by time period 9, there have been 9 years'
worth of scrappage effects accumulated into the vintage that is 10 years old in year 9. Time
period 9, therefore, sees the maximum quantity of age-10 vehicles.
In time period 10, the first vintage that was directly affected by the policy (vehicles that
were brand new in time period 0 of Figure 9-1) turns 10 years old. The original shock to new-
vehicle sales shows up in the big drop in Figure 9-3 for time period 10. The shock to new-vehicle
sales in year 0 was -0.4%, but the shock visible in Figure 9-3 is only a little over -0.2%. The
reason the shock has gotten smaller over time is again the reduced scrappage. Roughly half of
the decline in sales when the vehicles were new has been made up by the time they reach age 10.
Finally, Phase (iii) in the top-left graph just mirrors the recovery in new-vehicle sales that we
saw in Figure 9-1.
9-4
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Figure 9-3. Dynamics of the Used-Vehicle Inventory under Alternative Policy
Implementation Scenarios: Age 10 Vehicles
-0.2 ¦
Stock (Immediate)
Long run
0.2 H Policy
¦£ 1.0
Oi
J? 0.8
U
- 0.6
CT
§ 0.8
-C
u
g 0.6
a;
£ 0.4
a.
0.2
-5 0 5 10 15 20
Years from Policy Effective Date
-5 0 5 10 15 20
Years from Policy Effective Date
Price (Immediate)
o.i-
o.o
-o.i -
-0.2-
Price (Pre-announced phase in)
The top right of Figure 9-3 follows prices. Note that the price jumps up discontinuously
in time period 0: this reflects the capitalization of the policy announcement. The continued
increase in price during Phase (ii) marked on the price graph comes from ever-increasing
shortages as the policy continues. Not only do the shortages increase, the vintages of vehicles
experiencing those shortages also get "closer" to age 10. By time period 9, for example, there is a
shortage of 9-year-old vehicles (caused by the initial drop in sales 9 years earlier), and because
10-year-old vehicles could be quite good substitutes for 9-year-old ones, the price effects grow
stronger. At time period 10, the discontinuity from sales is visible in prices. Now, not only are
close substitutes in short supply, 10-year-old vehicles themselves are in short supply. From there,
prices move downward toward the steady state as new-vehicle sales (10 years ago) recover.
The bottom two graphics show the same effects, but now with the effects of
preannouncement and phase-in. Preannouncement appears as a slight drop in prices and
9-5
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quantities of 10-year-old vehicles at the time of preannouncement (they are driven out of the
stock by the surplus of vehicles coming in as new). The 5-year phase-in period replaces the sharp
jumps between Phases (ii) and (iii) in the top panels. Finally, the recovery toward steady state in
Phase (iii) is very similar to the top panels.
Applying the intuition from a single age of vehicle, we now examine the stock of vehicles
as a whole in response to a policy announced 5 years before its effective date and then phased in
over five years. Figure 9-4 divides the stock into three parts with roughly equal stocks in the
baseline: new through 5-year-old vehicles, 6- through 11-year-old vehicles, and 12 through 30-
year-old vehicles. The changes in these stocks are followed through time, as well as the change
in the total vehicle inventory labeled "All" in the blue dashed line.
The inventory as a whole moves smoothly, increasing slightly in the years leading up to
the policy (prebuying effects) and then declining smoothly to its steady state reduction of 0.05%
(as in Table 7-2). The three components move much more dynamically, following the patterns
described above. Newer vehicle stocks, in purple, decline fairly sharply as the policy phases in
and then recover to their steady state once the preexisting used stock can no longer buffer the
initial decline in sales. Middle-aged vehicles in orange follow the pattern for 10-year-old
vehicles described just above. There is an initial surge because scrappage is reduced and the
initial stocks of the middle-aged vehicles were sold before the policy was put in place. Then,
once enough time has passed that the policy affected the original sales of middle-aged vehicles,
their quantities decline and settle at the steady state. The oldest vehicles follow the same general
pattern, with two notable differences. First, the "increasing" phase can last much longer because
the oldest vehicles were originally sold a long time before policy came into effect. Second, these
vehicles can settle at a steady state above the baseline because the scrappage effects get to
compound over a long horizon. Twenty years of compounded reductions in scrappage amount to
a long-run increase in quantities of 0.24% for the oldest vehicles, even though the original sales
of those vintages are about 0.25% smaller than the baseline.
9-6
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Figure 9-4. Dynamics in the Used-Vehicle Market with a Preannounced, Phased-In Policy:
Inventory Changes by Vehicle Age Group
Years from Policy Effective Date
Figure 9-5 compares the patterns in overall inventory and average age for the four policy
approaches in terms of preannouncement and phase-in. The gray line in the left panel is the same
as the dashed blue line in Figure 9-4 above (the scale on the vertical axis is expanded).
The right-hand panel of the figure shows average age through time. For the most part,
average age moves inversely to the total inventory: when there is prebuying, we see average age
fall for a brief period, for example. Average age increases by a relatively small amount in the
long run, by 0.15% for a 1% generalized cost increase, and converges to the steady state
relatively quickly.
9-7
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Figure 9-5. Dynamics of Vehicle Inventory and Average Age under Alternative Policy
Implementation Scenarios
Immediate
Pre-announced
Phase in
Pre-announced phase in
Long run
5 0 5 10 15 20
Years from Policy Effective Date
0.02 -
0 5 10 15 20
Years from Policy Effective Date
0.150
0.125
{? 0.100
ra
| 0 075
S 0.050
in
I 0.025
ai
•2 0.000
-0.025
-0.050
-0.04 -
-0.02 -
9-8
-------
SECTION 10.
CONCLUDING OBSERVATIONS
This study had three major goals. The first was to develop a theoretically sound
methodology for characterizing the aggregate U.S. LDV inventory and the pathways through
which regulatory policy or other scenarios could affect the distribution of the entire vehicle
inventory. The second was to conduct a detailed literature review to identify studies providing
estimates of the values of several elasticities important for modeling U.S. vehicle markets and
vehicle inventory in a manner consistent with the theoretical model and to synthesize available
estimates. The third was to develop and parameterize an aggregate simulation model consistent
with the theoretical framework and the existing data available from the literature and implement
the model to explore the implications of alternative scenarios for U.S. vehicle markets.
Based on our review of the available literature, we found that despite the large number of
studies assessing vehicle markets, relatively few quantified our elasticities of interest at an
aggregate market level. We found the most robust evidence to be around the aggregate own-price
elasticity of demand for new vehicles, with most elasticity estimates falling within a range from
-0.37 to -0.90. Estimates accounting for changes in used-vehicle prices were smaller in
magnitude, -0.18 and -0.36. Scrappage elasticities had a fairly wide range, but we had less
confidence in the values estimated for those that fall at the extremes of our range. Elasticities
calculated from studies relying on simulations with varying bounties for scrappage are generally
not reported within the studies themselves and are dependent on assumptions and interpretation.
We found that the estimated values change considerably with changes in assumptions. If we limit
the range to the four studies examining scrappage with respect to used-vehicle prices using other
techniques, the range is considerably smaller, from -0.36 to -0.91. Only two studies examined
scrappage with respect to new-vehicle prices and those fell in a similar range to the subset of
elasticities with respect to used-vehicle prices reflected in the previous sentence (-0.21 and
-0.82). Given the lack of studies quantifying aggregate responses in used-vehicle markets or
characterizing changes in the total inventory size, determining the extent to which there is
consensus was not possible.
In an effort to help fill in the gaps identified from this review, we considered methods to
estimate elasticities of used vehicles and inventory size. However, endogeneity caused by the
long horizons and equilibrium effects led us to redirect our focus toward development of a
broader model framework that would encompass new- and used-vehicle markets within an
integrated model with a goal of improving consistency of estimates of the evolution of the U.S.
vehicle inventory over time under alternative scenarios. As described in Section 6, we developed
10-1
-------
an integrated framework that provides insights at an aggregate level and that can be used to
conduct rapid scenario analyses. To implement this model, we selected elasticity parameters
based on the ranges identified from the literature as our starting points for model
parameterization. However, recognizing the considerable uncertainty surrounding these values,
particularly in the case of used-vehicle markets and total inventory, we designed the model to be
easy to apply with alternative assumptions such that it can be readily used for analyses of
alternative transportation policies and scenarios.
10.1 Model Applicability
One of the key insights of this assessment of the literature is that very few existing
models in the literature attempted to capture interactions between household demand for new and
used vehicles and nonpersonal vehicle transportation. The elasticity values available from the
literature are not generally suitable for direct use in policy analysis because they do not capture
these interactions. For instance, a study using an estimate of the own-price demand elasticity for
new vehicles to estimate the new-vehicle market response to a price shock may substantially
overstate the actual change in new-vehicle sales that would result because own-price demand
elasticities do not reflect the interactions between new- and used-vehicle markets. Because used-
vehicle prices will rise in response to a positive price shock that directly affects the new vehicle
market (affecting the degree of substitution between new and used vehicles) and substitution to
the outside good is relatively small, the net reduction in new-vehicle sales will be smaller than
implied by the own-price elasticity.
Thus, our simulation model aimed to build on the existing literature and fill a gap in the
available tools for analyzing aggregate impacts on vehicle markets. Our simulation model can be
used to generate policy elasticities that reflect the interactions between these key markets and to
estimate net impacts of many different scenarios affecting vehicle markets. It can also be applied
directly to simulate aggregate outcomes under specific scenarios, such as regulatory policies that
increase the purchase price of new vehicles (and may also simultaneously result in changes in
fuel economy or other vehicle characteristics). Because it includes rational expectations, the
model can be used to explore market reactions in anticipation of policy implementation as well
as the impacts of phasing in policy changes over time. In addition, the model was designed to
facilitate sensitivity analyses and can readily be applied to explore the range of outcomes
generated using a range of inputs.
10-2
-------
10.2 Linkages to Other Models
Although our simulation model makes a valuable contribution to enabling assessment of
the aggregate impacts of alternative policies and other scenarios within a theoretically consistent
framework, there are many applications where policy analysts may wish to explore impacts at a
more disaggregated level. This model could potentially be linked to more disaggregated models
in a manner ranging from soft linkages passing policy elasticities or other aggregate outcomes to
other models to more formal hard linkages with iteration between the models.
10.3 Limitations and Caveats
As with any model, a number of assumptions underlie our model specification. We drew
on relevant elasticities available from the literature, but this literature is limited and there is a fair
amount of uncertainty regarding individual elasticity values. We explored a number of different
combinations of parameters to assess the relative importance of different parameters and
generate a plausible range of responses. However, it is possible that consumer responsiveness to
vehicle price changes and substitutability between new and used vehicles and an outside good is
changing with the increase in ride-sharing, projected electrification of the vehicle sector in
coming decades, potential for widespread adoption of autonomous vehicles, and other major
developments that may transform the transportation sector. There are additional gaps in
knowledge regarding substitutability between used vehicles of different vintages, relative price
responsiveness for new versus used vehicles, and other specific parameters.
In addition, our simulation model is specified at an aggregate level, which may be a
limitation for certain applications, though it may be feasible to link to other more disaggregated
models as noted above. Although this approach provides an advance in simulating aggregate
changes in the vehicle inventory, additional work would be needed to address the stated
limitations.
10.4 Priorities for Future Research
One of the findings of this report is that there is considerable uncertainty regarding the
key elasticity parameters needed to define the relationship between changes in new-vehicle costs
and responses in the new- and used-vehicle markets. Subsequent research that focuses on
specification of the relevant elasticities and provides updated estimates of key parameters would
be valuable for future scenario analyses. In particular, uncertainty in the aggregate demand
elasticity for new vehicles and in the degree of substitution to the outside good appears
particularly influential in the overall policy elasticities in Table 7-2. Scrappage elasticities are
also important, but less so: the wide range of-0.2 to -1.2 explored in Table 7-2 has a more
10-3
-------
modest impact on policy elasticities. Our results are less sensitive to the structure of substitution
among used vehicles (explored in Appendix C), though increased understanding of consumer
preferences in this dimension would also be useful in further narrowing the range of results.
In future work, it may also be possible to expand on the current version of the model to
differentiate between market segments; disaggregate alternative-fuel vehicles, especially battery
electric vehicles given their expected growth in market share, and otherwise expand on the level
of disaggregation incorporated within the model.
Distinguishing between U.S. vehicles being exported from the United States or fully
decommissioned when they are scrapped and removed from the U.S. inventory was not a priority
for this study, which focused on the U.S. market and vehicle inventory. However, this distinction
is potentially an important component of calculating the net global emissions impacts of U.S.
policy. Future work could incorporate trade and more fully characterize scrappage to better
inform calculations of changes in emissions.
The current model also abstracts from transactions costs, though they may be substantial
and could have important effects in the short run. We believe they are much less important for
the long-run policy elasticities described in Section 7: as long as the overall lifetime of vehicles
does not change too dramatically, the typical number of owners over a vehicle lifespan (and so
frequency of transactions) is also unlikely to change by very much. In the short run, high
transactions costs could slow down the transition toward the new equilibrium, but we think the
effect is small. In the cases we studied, the desired transition is toward slightly older vehicles—
perhaps a few months older for a large generalized cost increase. Because this age change is
relatively small from the perspective of one individual, it is likely that a person who finds
themselves with the "wrong" vehicle after the policy change would simply wait (i.e., letting their
current vehicle age a few months) rather than making an extra transaction. The time scales are
such that this transaction delay would likely be small relative to the time it will take the overall
system to adjust, which is more on the order of decades.
Another limitation is that we abstract from the choice of annual vehicle miles traveled,
holding the number of miles driven by any particular vehicle vintage fixed. Further exploration
of the decision regarding how much to drive each household vehicle in a year in addition to the
decision regarding vehicle ownership may be valuable, though complex. It would additionally
rely on estimates of elasticities of demand across vehicles with different odometer readings,
separate from age. Here we combine these, effectively looking at demand conditional on a
typical odometer reading for a given age.
10-4
-------
Although this model could be expanded in a number of ways, it is also important to
balance expansion against the ability to conduct rapid analyses. It may be useful to maintain a
streamlined aggregate version of the model, in addition to a version that incorporates additional
disaggregation and features.
10-5
-------
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Bento, A. M., Goulder, L. H., Jacobsen, M. R., & von Haefen, R. H. (2009). Distributional and
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Combination of Micro and Macro Data: The New Car Market. Journal of Political
Economy, 112(1), 68-105. https://doi.org/10.1086/379939
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Greenspan, A., & Cohen, D. (1999). Motor Vehicle Stocks, Scrappage, and Sales. Review of
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Hahn, R. W. (1995). An Economic Analysis of Scrappage. The RAND Journal of Economics,
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Jacobsen, M. R., & van Benthem, A. A. (2015). Vehicle Scrappage and Gasoline Policy.
American Economic Review, 105(3), 1312-1338. https://doi.org/10.1257/aer.2013Q935
Jayarajan, D., Siddarth, S., & Silva-Risso, J. (2018). Cannibalization vs. Competition: An
Empirical Study of the Impact of Product Durability on Automobile Demand.
International Journal of Research in Marketing, 35(A), 641-660.
https://doi.Org/10.1016/i.iiresmar.2018.09.001
Knittel, C. R., & Metaxoglou, K. (2014). Estimation of Random-Coefficient Demand Models:
Two Empiricists' Perspective. Review of Economics and Statistics, 96(1), 34-59.
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McAlinden, S. P., Chen, Y., Schultz, M., & Andrea, D. J. (2016). The Potential Effects of the
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Automotive Research Report, https://www.cargroup.org/wp-
content/uploads/2017/02/The-Potential-Effects-of-the-2017 2025-EPANHTSA-
GHGFuel-Economv-Mandates-on-the-US-Economy.pdf
McCarthy, P. S. (1996). Market Price and Income Elasticities of New Vehicle Demands. The
Review of Economics and Statistics. 78(3), 543-547. https://doi.org/10.2307/2109802
Miaou, S.-P. (1995). Factors Associated with Aggregate Car Scrappage Rate in the United
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nt SAFE Rule.pdf
R-4
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APPENDIX A:
BIBLIOGRAPHY OF PAPERS INCLUDED IN OUR MAIN SAMPLE
Alberini, A., Harrington, W., & McConnell, V. (1998). Fleet Turnover and Old Car Scrap
Policies. RFF Discussion Paper 98-23. Retrieved from
https://www.rff.org/Dublications/working-DaDers/fleet-turnover-and-old-car-scraD-
policies/
Bento, A. M., Goulder, L. H., Jacobsen, M. R., & von Haefen, R. H. (2009). Distributional and
Efficiency Impacts of Increased US Gasoline Taxes. American Economic Review, 99(3),
667-699. https://doi.Org/10.1257/aer.99.3.667
Bento, A. M., Jacobsen, M. R., Knittel, C. R., & van Benthem, A. A. (2020). Estimating the
Costs and Benefits of Fuel-Economy Standards. Chapter in Kotchen, M.J., J.H. Stock,
and C.D. Wolfram (eds.), Environmental and Energy Policy and the Economy, Volume 1,
pp. 129-157. University of Chicago Press: Chicago, IL.
Bento, A., Roth, K., & Zuo, Y. (2018). Vehicle Lifetime Trends and Scrappage Behavior in the
U.S. Used Car Market. The Energy Journal, 39(1).
https://doi.org/10.5547/01956574.39.Laben
Berry, S., Levinsohn, J., & Pakes, A. (1995). Automobile Prices in Market Equilibrium.
Econometrica, 63(4) ,841. https://doi.org/10.2307/21718Q2
Berry, S., Levinsohn, J., & Pakes, A. (2004). Differentiated Products Demand Systems from a
Combination of Micro and Macro Data: The New Car Market. Journal of Political
Economy, 112(1), 68-105. https://doi.org/10.1086/379939
Chen, J., Esteban, S., & Shum, M. (2010). Do Sales Tax Credits Stimulate the Automobile
Market? International Journal of Industrial Organization, 28(4), 397-402.
https://doi.Org/10.1016/i.iiindorg.2010.02.011
Dou, X. & Linn, J. (2020). How Do US Passenger Vehicle Fuel Economy Standards Affect New
Vehicle Purchases? Journal of Environmental Economics and Management 102: 102332.
https://doi.Org/10.1016/i.ieem.2020.102332
Fischer, C., Harrington, W., & Parry, I.W.H. (2007). Should Automobile Fuel Economy
Standards be Tightened? The Energy Journal, 28(4). https://doi.org/10.5547/ISSNQ195-
6574-ET-Vol28-No4-l
Goldberg, P. K. (1998). The Effects of the Corporate Average Fuel Efficiency Standards. The
Journal of Industrial Economics, 46(1), 1-33.
Greenspan, A., & Cohen, D. (1999). Motor Vehicle Stocks, Scrappage, and Sales. Review of
Economics and Statistics, 81(3), 369-383. https://doi.org/l0.1162/003465399558300
Hahn, R. W. (1995). An Economic Analysis of Scrappage. The RAND Journal of Economics,
26(2). 222. https://doi.org/10.2307/2555914
A-l
-------
Jacobsen, M. R., & van Benthem, A. A. (2015). Vehicle Scrappage and Gasoline Policy.
American Economic Review, 105(3), 1312-1338. https://doi.org/10.1257/aer.2013Q935
Jayarajan, D., Siddarth, S., & Silva-Risso, J. (2018). Cannibalization vs. Competition: An
Empirical Study of the Impact of Product Durability on Automobile Demand.
International Journal of Research in Marketing, 35(A), 641-660.
https://doi.Org/10.1016/i.iiresmar.2018.09.001
Knittel, C. R., & Metaxoglou, K. (2014). Estimation of Random-Coefficient Demand Models:
Two Empiricists' Perspective. Review of Economics and Statistics, 96(1), 34-59.
https://doi.org/10.1162/REST a 00394
Leard, B. (2021). Estimating Consumer Substitution Between New and Used Passenger Vehicles.
RFF Working Paper 19-01 (latest update May 2021). Retrieved from
https://media.rff.org/documents/WP 19-01 rev 2021.pdf
McAlinden, S.P., Chen, Y., Schultz, M. & Andrea, D.J. (2016). The Potential Effects of the
2017-2025 EPA/NHTSA GHG/Fuel Economy Mandates on the U.S. Economy. Center
for Automotive Research Report. Retrieved from https://www.cargroup.org/wp-
content/uploads/2017/02/The-Potential-Effects-of-the-2017 2025-EPANHTSA-
GHGFuel-Economv-Mandates-on-the-US-Economy.pdf
McCarthy, P. S. (1996). Market Price and Income Elasticities of New Vehicle Demands. The
Review of Economics and Statistics, 78(3), 543. https://doi.org/10.2307/2109802
Miaou, S.-P. (1995). Factors Associated with Aggregate Car Scrappage Rate in the United
States: 1966-1992. Transportation Research Record, 1475. Retrieved from
http://onlinepubs.trb.org/Qnlinepubs/tiT/1995/1475/1475-001.pdf
Selby, B., & Kockelman, K. M. (2012). Microsimulating Automobile Markets: Evolution of
Vehicle Holdings and Vehicle Pricing Dynamics. Journal of the Transportation Research
Forum. 51(2). https://doi.Org/10.5399/osu/itrf.51.2.2916
A-2
-------
APPENDIX B:
DETAILED SPECIFICATION OF SCRAP FUNCTION
Following Jacobsen and van Benthem (2015), the scrap rate for vehicles of a given age is
given by sa = ba- (pa)7. More elastic scrappage implies that repair cost shocks are relatively
dense around the vehicle value: small increases in value therefore make a relatively large number
of repairs become worthwhile, reducing scrappage more sharply.
To formalize this define the realization of any given repair cost shock as Ha. The
cumulative density function of Ha follows directly from the scrappage function:
p(Ha (— 1 . We can then integrate to evaluate the expected repair cost
(conditional on the vehicle being repaired, i.e., conditional on ha < pa) as:
b y — b vv^+^
i _ n/r. |r \ ua Y uaYtJa
(' al' a
-------
APPENDIX C:
ADDITIONAL SENSITIVITY ANALYSES, LONG RUN
This appendix contains additional model runs to highlight other scenarios and
relationships and perform sensitivity analyses.
Figure C-l replicates Figure 7-1 for alternative elasticity scenarios. The general patterns
are the same, with the higher demand elasticities in Scenario E shifting the curves downward,
implying greater policy effects throughout the stock.
Figure C-l. Policy Effect on LDV Stocks as a Function of the Scrappage Elasticity for a
1% Increase in Generalized Cost of New Vehicles
Table C-l explores sensitivity of the policy elasticities to a range of other assumptions
and input parameters. Row (1) reproduces Scenario D from Table 7-2, and the remaining rows
explore changes relative to this scenario.
C-l
-------
Table C-2. Policy Effect on LDV Stocks, Sensitivity to Additional Parameters
Effect of 1% Increase in Generalized Cost
Scenario of New Vehicles
Vehicle Demand Elasticities
Quantities (% changes)
New-Vehicle
Demand
Cross-Price
New/Used
Outside
Option
Scrappage
Elasticity
New
Used
All
Average
Age
(1) Scenario D
-0.80
0.05
-0.05
-0.70
-0.25
-0.04
-0.05
0.15
(2) New-outside substitution
-0.80
0.04
-0.05
-0.70
-0.26
-0.04
-0.05
0.16
(3) Double used-vehicle elasticity
-0.80
0.05
-0.05
-0.70
-0.26
-0.03
-0.05
0.18
(4) Half used-vehicle elasticity
-0.80
0.05
-0.05
-0.70
-0.25
-0.05
-0.06
0.14
(5) Zero decline over age difference
-0.80
0.05
-0.05
-0.70
-0.32
-0.04
-0.06
0.23
(6) Double decline with age difference
-0.80
0.05
-0.05
-0.70
-0.20
-0.04
-0.05
0.10
(7) Four times decline with age difference
-0.80
0.05
-0.05
-0.70
-0.14
-0.03
-0.04
0.05
(8) Faster decline for newer vehicles
-0.80
0.05
-0.05
-0.70
-0.27
-0.05
-0.06
0.17
(9) 10% discount rate
-0.80
0.05
-0.05
-0.70
-0.27
-0.04
-0.06
0.17
(10) Baseline survival based on Jacobsen
and van Benthem (2015)
-0.80
0.05
-0.05
-0.70
-0.29
-0.04
-0.06
0.17
(11) Baseline survival based on Leard et
al. (2017)
-0.80
0.05
-0.05
-0.70
-0.26
-0.04
-0.05
0.15
(12) Baseline depreciation based on
caredge.com
-0.80
0.05
-0.05
-0.70
-0.23
-0.03
-0.04
0.14
(13) Small new-vehicle demand elasticity
-0.10
0.01
-0.00
-0.70
-0.06
0.00
0.00
0.02
-------
Row (2) allows part of the substitution away from new vehicles to go to the outside good.
In the main text, all of the new-vehicle demand elasticity of-0.8 went to used vehicles; here
25% of it goes to the outside good. The key policy elasticities are not much affected by the
source of substitution to the outside good (which is fixed at 0.05).
Row (3) explores an elasticity for older vehicles that rises to double that of new vehicles
(i.e. -1.6 rather than -0.8) by age 30. Because new vehicles may be owned by wealthier
consumers, who are often shown to be less price sensitive, this case represents a plausible
possibility. Policy elasticities are not much affected, though we note that average age increases
somewhat more when substitutability among used vehicles is increased. Row (4) explores the
opposite case: perhaps older vehicles are more likely to be necessities or the only vehicle a
household owns, making their price elasticities smaller. Here, elasticities fall to half (i.e., -0.4
rather than -0.8) for the oldest vehicles. Policy elasticities are not much affected in this scenario.
Rows (5) through (8) explore the way that substitutability relates to the age difference. In
Scenario D, the substitution elasticity is set to fall 8% per year of age difference, resulting in a
demand system where 49% of substitution away from new vehicles stays within 5 years of age.42
Very little evidence exists in the literature on substitution across ages, so we explore a wide
range of alternative assumptions here. In row (5), all ages are set to be equally good substitutes
for new vehicles: the same substitution fraction falls to 32%. This case may still be somewhat
realistic because would-be new-vehicle buyers often consider holding on to their, potentially
very old, used vehicle instead of buying new. Some degree of substitution across wide age
ranges is therefore possible, though we might argue this case is less likely than our main
assumption in row (1). In row (6), the rate of drop-off with each year of age difference is
doubled. Now, 65% of substitution away from new vehicles stays within 5 years of age. Row (7)
quadruples the rate of drop-off such that very high fractions of substitution stay close by in age.
Finally, row (8) makes the drop-off fast for newer vehicles (where we think buyers may be
sensitive to slight differences across model years) and slow for older vehicles (where we think a
few years' age difference may not matter much from the buyer's perspective). In this case, the
drop-off rate ranges from 16% (newer vehicles) to 4% (older vehicles) per year of age difference.
42 Specifically, the demand elasticity matrix is constructed starting with the diagonal—own-price elasticities for
different ages—as specified in the input, -0.8 in Scenario D. Cross-price elasticities to other ages are given by
the formula £ ¦ (1 — falloff)age-dl^erence where falloff is the amount by which the elasticity falls off for each
year of age difference, 8% in Scenario D, and £ is a scalar chosen so that the aggregate cross-price elasticity
between new and used vehicles matches the input, 0.05 in Scenario D.
C-3
-------
We find that the model results are not overly sensitive to even this very wide range of
possibilities for the role of age differences. In row (5), buyers are willing to switch easily to very
old vehicles (which have the most potential for long-run reductions in scrappage). This increases
the magnitude of the overall policy elasticity for new vehicles somewhat from -0.25 to -0.31.
We note that this is a bounding case (in row [5], consumers do not favor low age differences at
all), so it represents the maximum policy elasticity along this dimension.
Conversely, in rows (6) and (7) when new-vehicle buyers are unwilling to consider
vehicles with big age differences, the policy elasticity falls because the potential for long-run
changes in scrappage among relatively new vehicles is small. Because the vehicles that can be
saved from scrappage are not great substitutes for new vehicles, new vehicle sales do not fall by
as much in equilibrium. The policy elasticity in the quadrupled case in row (7) falls to as low as
-0.14 because of this effect. Finally, row (8), with variable degrees of substitutability, is quite
close to the original case in row (1).
Row (9) explores a discount rate of 10% instead of 3%. The demand system is
recalibrated so that it continues to reproduce baseline vehicle choices even though depreciation is
now felt more strongly (because more of residual values are discounted away). Effects on the
policy elasticities are small; relative, not absolute, differences in levels of depreciation drive the
substitution patterns.
Rows (10) through (12) explore alternative data sources for baseline survival
probabilities and rates of depreciation. Effects on the policy elasticities are small.
Finally, row (13) explores a very small demand elasticity for new vehicles. Interestingly,
even with this elasticity set very close to zero, the policy elasticity is still much smaller than the
demand elasticity at -0.06 versus -0.10. The main effects on quantities and scrappage appear to
scale mostly proportionately as the new-vehicle demand effect scales toward zero.
C-4
-------
APPENDIX D:
ADDITIONAL SENSITIVITY ANALYSES, TRANSITION PATHS
This appendix contains additional model runs and output to highlight the way myopia
influences the dynamic transition and to provide additional cases and sensitivity analysis.
Figure D-l reproduces Figure 9-1 in the main text, now without allowing consumers to
anticipate the changes policy will produce. The blue lines are rational agents, as before, while the
orange lines reflect the choices of consumers who believe that the profile of asset values will not
change in the future. In the context of new-vehicle purchasers, this would be a consumer who
assumes that the trade-in value of a current purchase in 5 years is the present price of 5-year-old
vehicles. This results in a large shock to purchases in time period 0: new-vehicle sales fall by
1.5%, exceeding the demand elasticity of 0.8. The reason the decline exceeds the demand
elasticity is that new-vehicle buyers believe they will bear a more than 1% ownership cost
increase when new-vehicle price rises by 1%. These fully myopic new-vehicle buyers do not
allow for any increase in residual value as a result of policy; they think that the lifetime policy
cost will fall entirely on the first owner, as opposed to being shared with future owners of the
vehicle. This large shock to sales creates, in subsequent time periods, an even greater shortage of
inventory in the used-vehicle market. Used prices then overcorrect, rising well above long-run
levels and swinging the pendulum the other way. New-vehicle buyers now believe trade-in
values will remain very high. This cycle of over- and undershooting continues, with the
oscillation still visible many years after the policy is implemented.
The myopic response in the top-right panel is identical to the top-left panel: myopic
agents are unaffected by a policy announcement because they only respond to changes in
current-period vehicle values.
The response to a phased-in policy with myopia is somewhat gentler because the
overshoot in time period 1 is dampened by the fact that the policy is only partly phased in. The
myopic time path in this case exhibits the same overshoot and oscillation, but with a lower
frequency oscillation than in the top panels. The phase-in spreads the overresponse from the
myopic agent over 5 years as opposed to concentrating it in a single year.
In all four cases, the myopic path converges to the same long-run outcome from Table 7-
2: the steady state is not affected by this form of myopia because agents do, eventually, assign
correct expectations to asset prices.
D-l
-------
Figure D-l. Dynamics of New-Vehicle Sales with Myopic Agents
Note: The figure displays the results of two distinct model runs in each panel: blue displays a model run (as in
Section 9 of the report) where expectations about used vehicle price responses to policy are correct. In
orange, the model is re-run in a world where consumers only expect the part of the change in prices that
they can see through immediate equilibrium impacts.
Figure D-2 compares aggregate patterns in the stock when agents are myopic versus
forward looking. The heavy lines reproduce the results shown in Figure 9-4, dividing vehicles
into three age groups and showing the path taken as the system transitions to its new steady state.
The thin lines in the figure show how the system transitions when agents are myopic. With
myopia there is a more substantial decline in newer vehicle quantities early on: this reflects the
overshooting that happens with myopia and new-vehicle sales. Shortages created by the decline
in sales lead to a more dramatic response in the used stock: used-vehicle prices rise very quickly,
scrappage falls, and quantity (in green) rises. The myopic system also produces periodic sharp
adjustments as agents correct for mistakes in prior periods. In contrast, the forward-looking
agents take a smoother trajectory toward the eventual steady state.
D-2
-------
One additional point of interest in Figure D-2 is that myopic agents arrive at the
aggregate steady state (shown in the blue dashed lines) somewhat more quickly than forward-
looking agents do. This is because forward-looking agents build up the vehicle stock early on in
preparation for the more stringent phases of the policy and can slightly prolong their arrival at
the long-run change.
Figure D-2. Dynamics in the Overall Vehicle Market with Myopic Agents
Years from Policy Effective Date
Figure D-3 shows the trajectory of new vehicle sales over time under a range of
alternative scenarios. The line for Scenario D reproduces the upper left panel of Figure 9-1,
looking at new vehicle sales with immediate policy implementation. The strength of initial
impact across scenarios is largely controlled by the demand elasticity (largest for Scenario E).
The speed of convergence to the steady-state sales level is similar across scenarios, with
somewhat longer time needed to stabilize when the initial impact is larger.
D-3
-------
Figure D-3. Dynamics of New-Vehicle Sales with Immediate Policy Implementation Under
a Range of Elasticity Scenarios
Years from Policy Effective Date
Figure D-4 compares the dynamics of vehicles in different age groups for a
preannounced, phased-in policy. The solid lines reproduce the results for Scenario D as
presented in Figure 9-4. The dashed lines show results from using the elasticities in Scenario B
instead. The long run effects on the entire inventory (in blue) are very similar for scenarios B and
D: this reflects the feature that the two scenarios share the same overall elasticity to the outside
good (-0.05). The transition paths for individual age categories, however, differ between the two
scenarios. In Scenario B, new vehicle demand elasticities are smaller, so less substitution from
new to used occurs. New-vehicle inventories (in purple) fall by less and inventories for the oldest
vehicles (in green) rise by less in Scenario B.
D-4
-------
Figure D-4. Dynamics in the Used-Vehicle Market Under Alternative Elasticity Scenarios
(Scenarios B and D)
0.3 -
Seen D, New-5
Seen D, 6-11
Seen D, 12-30
Seen D, All
Seen B, New-5
Seen B, 6-11
Seen B, 12-30
Seen B, All
-0.3-
-5
0
5
10
15
20
25
Years from Policy Effective Date
Note: Implementation of the policy is preannounced and phased-in, as in Figure 9-4.
Figure D-5 again reproduces results for Scenario D as shown in Figure 9-4, now
comparing Scenario D with Scenario C (dashed lines). Scenario C involves a lower new-vehicle
demand elasticity and a higher outside-good elasticity relative to Scenario D. The overall effect
on the inventory (shown in blue) is larger in Scenario C because of the more elastic substitution
to the outside good. The larger overall effect on the stock in Scenario C competes with the lower
new-vehicle demand elasticity in Scenario C to determine the effect on new-vehicle sales (shown
in purple). They approximately offset one another, leading to similar long-run effects. The short-
run effect on new-vehicle sales is more importantly influenced by the new-vehicle demand
elasticity and shows a somewhat larger pre-buying effects, and larger dip afterward, in Scenario
D relative to Scenario C.
D-5
-------
Figure D-5. Dynamics of the Used-Vehicle Inventory under Alternative Policy
Implementation Scenarios: Age 10 Vehicles
so 0.0
0s
1-0.!
-0.2
Seen
D,
New-5
Seen
D,
6-11
Seen
D,
12-30
Seen
D,
All
—
Seen
C,
New-5
—
Seen
C,
6-11
—
Seen
C,
12-30
Seen
C,
All
Years from Policy Effective Date
-0.3
-5
Note: Implementation of the policy is preannounced and phased-in, as in Figure 9-4.
D-6
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APPENDIX E:
APPLICATION OF POLICY ELASTICITIES FOR ANALYSIS OF NEW VEHICLE SALES
This appendix describes the applicability of the policy elasticities of new vehicle sales, for
example, as reported in Table 7-2, to settings with large changes in generalized cost or where the short-
run path of vehicle sales is of interest.
When the generalized cost of a new vehicle rises, the demand for that vehicle falls, all else equal.
This demand change is measured by the demand elasticity. In equilibrium, however, not all else is equal,
because a generalized cost increase for new vehicles also increases prices in the used market. New
vehicle sales fall less than would be assumed if only looking at the demand elasticity. As explained in
the main text, we capture the overall effect on sales in what we term the policy elasticity. It is the
percentage change in new vehicle sales, after allowing for changes in the used market, coming from a
1% increase in generalized cost.
The policy elasticities in the main text are the long-run, steady state change in sales associated
with an incremental increase in generalized cost. This document addresses the possibility of applying
these long-run, marginal elasticities in two alternative settings: when the generalized cost change is large
and in the short run. All values reported below are based on the assumptions of Scenario D in the main
text, which assumes a new-vehicle demand elasticity of-0.8 and a scrappage elasticity of-0.7.
E.l Large Generalized Cost Changes
Figure E-l shows the average, long-run policy elasticity of new-vehicle sales (vertical axis) for
various levels of generalized cost increase (horizontal axis). Note that the vertical axis shows the
elasticity (change in sales relative to change in price). The assumed starting new-vehicle cost is $30,000.
The policy elasticity (shown in blue) becomes slightly more negative with large policies but is
generally quite stable, going from -0.249 to -0.257 over the range shown. The reason it is so stable
likely relates to the underlying constant-elasticity demand and constant-elasticity scrappage equations
driving the model. The results in the figure suggest that using a simple policy elasticity calculated at the
margin (i.e., based on an incremental change in generalized cost as in the main text) provides a good
approximation for the change in sales under a wide range of policies. This is subject to the constant
elasticity assumptions that appear elsewhere in the model. The demand elasticity for this model run
(-0.8) is shown with the dashed red line for comparison.
E-l
-------
Figure E-l. Policy Elasticity of New-Vehicle Sales and the Scale of Generalized Cost
-0.3 -
03
U
Average Policy Elasticity
Demand Elasticity
in
to
-0.8-
0
1000 2000 3000 4000 5000
Generalized Cost Increase ($)
E.2 Short-Run Effect on Sales
Figure E-l addresses only long-run changes in sales. In the short run, the dynamic effect on sales
from a generalized cost increase will generally be different than in the steady state. Figure E-2 displays
the policy elasticities produced by the full, dynamic version of the model. Used-vehicle prices do not
adjust immediately to their steady state but instead are governed by expectations about asset values and
the way the policy works through the fleet (affecting one additional used vintage every year it is in
place). We display the dynamic policy elasticity in each year using different assumptions for how the
policy is phased in. "Immediate" means that the generalized cost increase is immediate in time 0 and
then stays fixed throughout. New-vehicle sales drop more in the short run than in the long run, because
in the short run there is a greater "buffer" available in the used fleet. After the policy has been in place
for several years, the sales declines in these years mean there are no longer as many used vehicles
around to absorb the loss in new-vehicle sales. Prices, and new-vehicle sales, rebound toward the steady
state. When the policy is phased in, there are two competing effects in the short run. The buffer of used
vehicles is still present as above, tending to produce a sharper drop in sales in the short run. There is
now also a competing effect from the announcement of the phase-in. The knowledge that generalized
cost will be rising in coming years means that additional sales are encouraged in the early years of the
policy, a "pre-buying" effect coming from the increasing stringency in the future. Under a linear phase-
in (shown in orange and green), the pre-buying effect outweighs the buffer effect to the point of creating
a positive short-run elasticity. With a policy that is phased in but starts more quickly, the two effects
could cancel each other more evenly, or the buffer effect could dominate.
E-2
-------
In general, it is ambiguous if the short-run policy elasticity will be larger or smaller than the
long-run one because of the competing effects. Approximating the policy elasticity in all years with the
long-run policy elasticity (in blue dashes) appears to be a reasonable approximation to the dynamics in
the first 2 to 3 years and a good approximation once the policy has been in place for 5 years or more. In
all cases and all years in the figure, the long-run policy elasticity is a better approximation to the true
dynamic effect than the demand elasticity (red dashes).
Figure E-2. Variation in Policy Elasticity of New-Vehicle Sales with Time
0.2
Policy Elasticity (Immediate)
Policy Elasticity (3-yr phase-in)
Policy Elasticity (10-yr phase-in)
Policy Elasticity (Long Run)
Demand Elasticity
u
1/1
re
-0.6
LU
—0.8
0
5
10
15
20
Years from Policy Effective Date
E-3
------- |