Vehicle Size Choice and Automobile Externalities: A

Dynamic Analysis

Clifford Winston Jia Yan Brookings Institution Washington State Univ.Cwinston@brookings.edu Jiay@WSU.edu

Broader Implications of Larger Vehicles on the Road

In 2000, 20% of new vehicles sold in the US were SUVs; in 2012, that percentage climbed to 33%

This could increase the risk of a serious accident to occupants of smaller vehicles

Larger vehicles also consume more fuel and thus produce greater emissions

What we do in this paperThe purpose of this study is to provide a

disaggregate analysis of the effects of various factors including price, operating cost and congestion on vehicle size choice and to explore the implications for optimal polices to address automobile externalities

Preliminary results suggest congestion may notably affect vehicle sizes and thus automobile externalities. Optimal policies will then be explored

Why does congestion matter for vehicle size choice?

Consumers are willing to pay a safety premium for larger vehicles.

Vehicle collisions increase with traffic congestion.

Policy implications from our study

Gasoline tax is used to address the externalities, excessive fuel consumption, of large vehicles.

Our study suggests that policies reducing congestion such as congestion pricing have impacts on vehicle size, which in turn affects fuel consumption and safety.

Data On Individuals, 2004-2009A random sample of 475 motorists who lived

and worked in the Seattle, Washington metro area and owned a car as of 2009

Information on:◦ Car ownership, residential and employment location,

and personal profiles such as income, age, and education etc. of the individuals

◦ The route and time of day usually taken by the individuals for their trips to work.

◦ Congestion (travel delay) on the routes used by the individuals—determined as the difference between actual and free flow travel time

About 1/3 of the motorists changed their vehicles between 2004 and 2009.

Commuting in SeattleThe Seattle Metropolitan Area is

adjacent to the Puget Sound and motorists must often travel over a body of water to get to their destinations.

There are many bottlenecks that contribute to congestion that are created by the bridges that people must cross when they drive into Seattle

Defining Choice Set We consider motorists’ choice among 13 combinations

of vehicle class and size: ◦ compact domestic; ◦ compact luxury imported; ◦ compact pickup; ◦ full SUV; ◦ full size domestic; ◦ full size luxury imported; ◦ midsize SUV; ◦ midsize domestic; ◦ midsize luxury imported; ◦ passenger van; ◦ standard pickup; ◦ subcompact domestic; ◦ subcompact luxury imported

Given current vehicle ownership, a motorist chooses a vehicle class and size combination from the most recent 10 model years.

Developing A Dynamic Model of Vehicle Holding and Replacement

Most studies on vehicle choice use data on new vehicle purchase decisions.

Because we have a short panel, we identify motorists’ preferences for vehicle attributes including price, operating cost and vehicle size under different congestion environments from◦motorists’ vehicle purchase decisions to

replace currently owned vehicles AND◦motorists’ decisions to keep currently

owned vehicles.

Why do we need a dynamic model?Motorists do not change their vehicles

frequently and when they do change, they sell their vehicle in the used-vehicle market.

The price of a motorist’s vehicle depreciates and the maintenance costs of the vehicle increases with vehicle age.

Vehicle operating costs, which depend on both mileage-per-gallon (mpg) of vehicles and gasoline price, evolve with time because of the fluctuations in gasoline prices

Vehicle attributes evolve over time because of technological advances in automobiles

Plausible Assumptions to reduce dimensionality

Consumers do not predict the evolution of the automobile industry’s vehicle offerings.

Motorists make reasonable predictions of gasoline prices and base their vehicle replacement decisions on those predictions (Busse, Knittle and Zettelmeyer (2013)).

Motorists monitor the depreciation of their vehicles.

Congestion is persistent and stable.

The Dynamic Vehicle-size Choice Model

t t+1

owns a vehicle has complete information

on owned vehicle and available vehicles in the market

preference shocks realize receives information on

gasoline price and formulates expectation for future gasoline prices

Decision making: to hold current vehicle

or to replace it with another one

Stage 1 Stage 2 Stage 3

Utility realized from driving the vehicle

State space of the dynamic model The information set or the state space of a motorist i , who owns a vehicle j (a combination of class, size and model year) at the beginning of a year t , is

ittjtijt gaj ,,,

where

jta is the age of the owned vehicle;

tg is gasoline price; and tCkiktit , with tC denoting the

choice set, is the set of random shocks on the motorist’s preferences for vehicles.

Transition of the state space

Transition of the uncontrolled states ittjtijt ga , is denoted by ijtijt 1 .

We adopt the conditional independence assumption in Rust (1994) to have

111 itjtjtijtijt SSg

where tjtjt gaS , and the vector-valued transition function jtjt SSg 1 is given

by:

28.0 ,0~,

85.0 implies which ,1

1

*11

1

Ngg

ppaa

tttt

ja

jtjtjtjt

*jp is the manufacturer price of vehicle and the price depreciates with vehicle age

at the rate of 15%, which is consistent with the industry standard. The evolution of gasoline prices follows a normal random-walk process estimated from US city average data from 1981 to 2014. We could not reject the null hypothesis that the dynamics of gasoline prices follows a random-walk process. Anderson et al. (2013) also found that consumers predict gasoline price based on a random-walk process.

One-Period Utility

One-period utility of motorist i holding a vehicle j in year t : ijtijtijtjijtijt vu Bx ,

:jtx a vector of vehicle attributes including price, operation cost and

vehicle size; :j unobserved vehicle attributes.

One-period utility of vehicle replacement

ikttjik

iktkjtktiikttjik

v

ppu

Bx

jtp is the price of selling the owned vehicle and ktp is the price of buying

another vehicle. Preference heterogeneity in iB and i is explained partly by observed socio-demographic variables denoted by iz . We incorporate random components in some of the coefficients.

We specify the key congestion variable as an interaction Delay is determined as the difference between actual

travel time and free flow travel time. We define it as a dummy of a long commute (>= 1 hour) × dummy for excessive delay (15% or more of total commute time)

We interact the delay faced by a motorist with three vehicle dummies – full size SUV, medium size SUV and standard pickup, and vehicle operating cost. ◦ Motorists are more likely to buy larger vehicles

because of the disutility from traveling in congestion.◦ But motorists are more likely to buy more fuel-

efficient vehicles when congestion is higher.

Identification Issues

Omitted vehicle attributes are correlated with the observed attributes

Endogenous delay: the outcome of location and housing choice. Motorists’ preferences for vehicles are correlated with their preferences for location and housing.

Identification strategy for endogenous vehicle attributes

In baseline models, we use (12) vehicle class and size combination dummies to control for omitted vehicle attributes.

The underlying assumption is that omitted attributes of a vehicle class-size combination do not vary across model years.

This assumption is justified to the extent that vehicle design is stable over time.

Identification strategy for endogenous delay

Possible strategies◦ Modeling location and vehicle choice jointly: infeasible

because of the complications of modeling location as a disaggregate dynamic choice.

◦ Using motorist dummies to control for unobserved preferences for housing and location: infeasible because of the incidental parameter problem caused by nonlinearity in parameters and a short panel.

Our strategy is to follow the assumption of “selection on observables” to use several observed housing and location characteristics as control variables and capture any unobserved influences related to location choice

Let i denote the coefficient of one of the interactions

with delay, which is denoted by id , we formally have

iiiii d πwγz

Where

iz : a vector of socio-demographic variables including age, gender, income, etc.

iw : a vector of housing and location characteristics which we will explain in details later

:i a normal random variable with zero mean to capture heterogeneity from unobserved sources

Observed housing and location characteristics

House square footageZillow home value index of the zip codeMedian household income of the zip codeSchool index of the zip codePersonal crime index of the zip codeProperty crime index of the zip code

Dynamic choice

The present value of motorist i’s maximal attainable life-time utility

of keeping currently owned vehicle

ittitittitijtittit SjSjEVuSjV ,,,,,,~

111

where is the discount rate. If the motorist decides to replace the

current vehicle, the maximization problem becomes:

itittittjikCk

ittit SkEVuMaxSjVt

111 ,,,,ˆ

where tC is the choice set. The valuation function satisfies the

following Bellman equation:

ittitittitittit SjVSjVMaxSjV ,,ˆ,,,~

,,

Expected Value Function

Assuming it to have a multivariate extreme-value

density, we have

itttitijt

ititittittit

ISSjWEv

dSjVSjWit

exp,expln

,,,

11

where

jkCk

jtktittjikijt

t

SjSkWEvI ,,expln 11

A Mixed-Logit Type Choice Probability

The probability that consumer i replaces vehicle type j

with vehicle type k at year t is:

it

tjtkittjki

tjit

itijki

iiijkijki

I

SjSkWEv

SjW

Is

dfssi

exp

,,exp

,exp

exp 11

B

BBBB

The probability that the consumer does not switch is then:

ii

tjit

it

i

dfSjW

I

s

i

BBB

,exp

exp1

0

Dynamic vs. Myopic Choice

If consumers are myopic, there is no forward-looking behavior so the model becomes

itijtjti IvSjW expexpln,

where

jkCk

tjikit

t

vI expln

The choice probability has a standard mixed-logit formula.

Computation: Discretizing state space

13 vehicle class-size combinations

Vehicle Age.

o We assume that when motorists decide to replace their current vehicle, they will choose one from the most recent 10 model years.

o Given a motorist could own an older vehicle, the vehicle age space is

[ 0, 1,…,15 ]

o Vehicle (real) price depreciates 15% annually and stops depreciating after 15 years.

Gasoline price in our sampling period is in the range of [2.00, 3.80]

We take 5 equally divided points for age and 5 equally divided points for gasoline price to evaluate the expected value function ttttit gajgakWE ,,,, 111 , and we then

interpolate the obtained expected valuation at the 325 (13 *5 *5) points to a more finely discretized state space of (13 vehicles * 16 ages * 8 gasoline prices) .

Computing the Expected Value of Holding a Vehicle

The evaluation is done at a discretized state space by backward induction.

o The discount rate is set at 0.025.

o The expectation with respect to 1tg is approximated by Monte-Carlo integration.

o The number of time-periods is set to be 50 years, which is a plausible length given normal life expectancy.

Results from myopic choiceVariables Estimates Price/Household Income per Capita -0.8829 (0.1321) Operating Cost/Household Income per Capita -0.1085 (0.0246) Horse power -0.3446 (0.1214) Horse Power/Body Weight -1.2364 (0.5002) New Vehicle 0.5803 (0.1723) Vehicle more than 5 years old -0.7127 (0.2366) Household Size × Passenger Van 1.0328 (0.5722) Household Income per Capita × Luxury vehicle -0.0347 (0.7330) Delay × Full-size SUV 0.9709 (0.2933) Delay × Mid-size SUV 0.8580 (0.6866) Delay × Standard pickup 1.7843 (0.7016) Delay × (Operation cost / Household income per capita) 0.0094 (0.1022) Alternative constants included YES Interactions between Full-size SUV/Mid-size SUV/Standard pickup/mpg and demographic variables included 2

YES

Interactions between Full-size SUV/Mid-size SUV/Standard pickup/mpg and housing/residential location characteristics included 3

YES

Notes: 2. Demographic variables include gender, young (age <= 35), household size and household income-per-capita. 3. Housing and residential location characteristics include house square footage, Zillow Home Value Index of the zip code, median house income of the zip code, school index of the zip code, personal crime index of the zip code and property crime index of the zip code.

Results from dynamic choiceVariables Estimates Price/Household Income per Capita -0.2622 (0.0715) Operating Cost/Household Income per Capita -0.0962 (0.0200) Horse power -0.5575 (0.2014) Horse Power/Body Weight -0.7020 (0.2377) New Vehicle 0.1067 (0.0365) Vehicle more than 5 years old -0.2402 (0.1422) Household Size × Passenger Van 1.3310 (0.4865) Household Income per Capita × Luxury vehicle -0.0224 (0.5664) Delay × Full-size SUV 1.3182 (0.4002) Delay × Mid-size SUV 0.3474 (0.4791) Delay × Standard pickup 1.6587 (0.6025) Delay × (Operating cost / Household income per capita) -0.0963 (0.0410) Alternative constants included YES Interactions between Full-size SUV/Mid-size SUV/Standard pickup/mpg and demographic variables included 2

YES

Interactions between Full-size SUV/Mid-size SUV/Standard pickup/mpg and housing/residential location characteristics included 3

YES

Notes: 2. Demographic variables include gender, young (age <= 35), household size and household income-per-capita. 3. Housing and residential location characteristics include house square footage, Zillow Home Value Index of the zip code, median house income of the zip code, school index of the zip code, personal crime index of the zip code and property crime index of the zip code.

Results from dynamic choice without using housing and location characteristics as control variables

Variables Estimates

Delay × Full-size SUV 0.9744 (0.3744)

Delay × Mid-size SUV -0.0321 (0.2748)

Delay × Standard pickup 0.6894 (0.2040)

Delay × (Operation cost / Household income per capita) -0.0659 (0.0252)

Alternative constants included YES

Interactions between Full-size SUV/Mid-size SUV/Standard pickup/mpg and demographic variables included 2

YES

Interactions between Full-size SUV/Mid-size SUV/Standard pickup/mpg and housing/residential location characteristics included 3

NO

Notes: 2. Demographic variables include gender, young (age <= 35), household size and household income-per-capita. 3. Housing and residential location characteristics include house square footage, Zillow Home Value Index of the zip code, median house income of the zip code, school index of the zip code, personal crime index of the zip code and property crime index of the zip code.

Summary of baseline resultsConsumers are more likely to buy full-size

SUV and standard pickups when facing congestion.

Offset effect of congestion: consumers are also more likely to buy fuel-efficient vehicles when facing congestion.

Simulations using the dynamic model show that removing congestion would reduce the market shares of large SUV by 13% and reduce the market shares of standard pickups by 15% respectively.

Additional policy simulations will be performed

Comparison between dynamic and myopic modelCompared with myopic model,

dynamic model fits the data better (log-likelihood values of myopic and dynamic model are

-3083.45 and -3042.78 respectively)

Myopic model overestimates the responsiveness to price and underestimates the effect of congestion on motorists’ willingness-to-pay for more fuel efficient vehicles.

Robustness ChecksCheck1: Split the sample into two subsamples: one contains zip codes with median household income > 50k, and one contains zip codes with median household income <= 50k. Results from the two subsamples are in line with the baseline results.

Check 2: Change the price depreciation from 15% to 25%. Results are still in line with the baseline findings.