Dynamic Discrete Choice Models: an application to vehicle holding decisions

Dynamic Discrete Choice Models:an application to vehicle holding decisions

Cinzia CirilloUniversity of Maryland

A. James Clark School of EngineeringDepartment of Civil and Environmental Engineering

Universita’ Roma treJuly 2nd, 2012

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Problem

• What effect will the following factors have on the vehicle marketplace over the next five years:– New vehicle technology– Improvements in existing vehicle technology– Greater availability of different energy sources– Rising fuel prices– Transportation and energy policy

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Objectives

• Collect data on future household vehicle preferences in Maryland in relation to vehicle technology, fuel type, and public policy

• Determine if respondent could make dynamic vehicle purchase decisions in a hypothetical short- to medium-term period

• Determine if results from this hypothetical survey could be modeled using discrete choice methods

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Definitions• BEV – battery electric vehicle, a vehicle which stores electricity in

batteries as its only source of energy• HEV – hybrid electric vehicle, a vehicle which runs on gasoline but

uses larger batteries to aid in the propulsion of the vehicle• PHEV – plug-in hybrid electric vehicle, a vehicle which stores

electricity from the power grid in batteries and includes a gasoline engine

• AFV – alternative fuel vehicle, a vehicle with an internal combustion engine that runs on a liquid fuel that is not gasoline or diesel (e.g. ethanol)

• FFV – flex-fuel vehicle, a vehicle which can run on both gasoline and an alternative fuel

• MPGe – miles per gallon gasoline equivalent, a measure of the average distance traveled per unit of energy in one US gallon of gasoline

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Literature Review• Bunch et al. (1993)

– Conducted Stated Preference (SP) survey in California– Vehicle Choice with two versions

• New Gasoline, Alternative Fuel, Flex-fuel or Electric– Fuel Choice

• Given a flex-fuel vehicle: choose a fuel– MNL and nested logit models

• Kurani, Turrentine, Sperling (1996)– SP with reflexive designs– New Gasoline, CNG, HEV, 2 different highway-capable BEVs, and

Neighborhood BEV– Hybrid Household Hypothesis (Multi-car households more likely

to own BEVs)– Only analyzes with possible hybrid households

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Literature Review

• De Vlieger et al. (2005)– SP survey with MNL and nested logit models– Choice set: Gasoline, Diesel, AFV, BEV, Hydrogen

Fuel Cell Vehicle• Musti and Kockelman (2011)

– Choice set: 12 vehicle alternatives of varying size and technology (Conventional, HEV, PHEV)

– SP survey with MNL Model– Included a simulation over a 25-year period

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Literature Review

• Brownstone and Train (1999)– Used mixed logit and probit models to estimate

preference among gasoline, electric, methanol, and CNG vehicles

– Able to create substitution patterns that more closely resemble real-life expectations

• Bolduc et al. (2008)– Integrated Choice and Latent Variable Model

(Hybrid Choice Model)

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Survey MethodologyTime Frame Summer – Fall 2010Target Population Suburban and Urban Maryland HouseholdsSampling Frame Households with internet access in 5 Maryland countiesSample Design Multi-stage cluster design by county and zipcodeUse of Interviewer Self-administeredMode of Administration

Self-administered via the computer and internet for remaining respondents

Computer Assistance Computer-assisted self interview (CASI) and web-based survey

Reporting Unit One person age 18 or older per household reports for the entire household

Time Dimension Cross-sectional survey with hypothetical longitudinal stated preference experiments

Frequency One two-month phase of collecting responsesLevels of Observation Household, vehicle, person

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Survey Sections

• Household Characteristics• Current Vehicles• Stated Preference Experiments

– Vehicle Technology– Fuel Type– Taxation Policy

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Experiment Directions• Make realistic decisions. Act as if you were actually buying

a vehicle in a real life purchasing situation.• Take into account the situations presented during the

scenarios. If you would not normally consider buying a vehicle, then do not. But if the situation presented would make you reconsider in real life, then take them into account.

• Assume that you maintain your current living situation with moderate increases in income from year to year.

• Each scenario is independent from one another. Do not take into account the decisions you made in former scenarios. For example, if you purchase a vehicle in 2011, then in the next scenario forget about the new vehicle and just assume you have your current real life vehicle.

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Vehicle Technology Experiment

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Fuel Type Experiment

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Taxation Policy Experiment

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Contributions• Dynamic Attributes

– Attribute change from year to year• (e.g. EV price falls then raises, MPG increases annually)

• Time of Purchase– Given two scenarios per year from 2010 -2015

• Choice Set– Includes “Keeping Current Vehicle”– If purchase new vehicle, can keep or sell current vehicle– Does not exclude models

• Respondents– Includes respondents who don’t plan to purchase a

vehicle in next five years

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Results – Descriptive Statistics• Gender: 52% male• Age: 41 years (median), 43 years (mean)• Education: 76% with Bachelor degree or higher• Income: $50k – $75k (median), 22% with incomes

above $150k• Vehicle Ownership: 1.9 (average), 2.0 (median)• Primary Vehicle Age: 6.4 years (average), 6.0 years

(median)• Primary Vehicle Price: $23,763 (average, new),

$11,367 (average, used)• Intend to Purchase Vehicle within Five Years: 62%

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Results - Vehicle Technology

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Results – Fuel Technology

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Results – Taxation Policy

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Model

• Utility Function with Random Parameters and Error Components

• Choice Probability for Mixed Logit with Panel Data

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Results – Vehicle Technology

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Results – Vehicle Technology• Gasoline and hybrid vehicles have a similar inherent

preference• Families influenced by vehicle size• Fuel economy not significant for respondents who did

not know their own vehicle’s fuel economy• Covariance between Vehicle Types

– current vehicle + new gasoline vehicle (largest cov.)– new gasoline or current vehicle + new hybrid vehicle– new gasoline or current vehicle + new electric vehicle– new hybrid vehicle + new electric vehicle (smallest cov.)

• About 65% of respondents preferred smaller vehicles

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Results – Fuel Type

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Results – Fuel Type

• Respondents less sensitive to electricity price – Maybe lack of familiarity, no rule of thumb?

• Charging time has influence on attractiveness of BEVs but not PHEVs

• Error components shows that groups of respondents may have similar propensity towards electric vehicles (BEV and PHEV) and between liquid fuel vehicles

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Results – Taxation Policy

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Results – Taxation Policy

• ASCs similar to Vehicle Technology Experiment

• Toll discount only significant for residents near toll facilities

• Higher VMT tax for gasoline vehicles dissuaded new gasoline vehicle purchases

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Depreciation of new and old vehicles

• Respondent’s vehicle depreciation was obtained by dividing the coefficient of vehicle age (new or used) by the coefficient of purchase price.

• The models found that respondents depreciated their current vehicle at a rate between $1,950 and $1,310 per year for vehicles purchased new.

• For respondents with used vehicles, depreciation was between $1,066 and $710 per year.

• The MNL model placed greater depreciation on both new and used vehicles than the mixed models.

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Survey Redesign

• Eliminate the taxation policy experiment– Incorporate VMT tax into fuel type experiment– Incorporate Rebates into vehicle technology

experiment• Added open-ended questions for purchase

reason of current vehicles– Able to elicit some opinions about vehicle

preferences, attitudes, and concerns• All respondents participate in both choice

experiments

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Survey Redesign• Vehicle Technology Experiment

– Incorporate MPGe into vehicle technology experiment

• Respondents able to compare mpge and mpg in fuel technology experiment well

– Added fees and rebates for different vehicle types– Added Plug-in Hybrid Vehicle (PHEV) alternative

• Fuel Technology Experiment– Removed diesel vehicle option, added flex-fuel

vehicle option– Added VMT tax depending on fuel type

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Primary Vehicle Purchase Reasons

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• Preference for:– Fuel Economy– Family Vehicle / Transporting Passengers– Low Maintenance, High Reliability– Personal Appeal– Comfort and Safety

Secondary Vehicle Purchase Reason

• Preference for:– Fuel Economy– Vehicle Cost or Value– Family Vehicle– Cargo Capacity– Low Maintenance, High Reliability

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Dynamic Discrete Choice Models for Transportation

Part II

Background• Discrete choice models are commonly used in transportation

planning and modeling, but their theoretical basis and applications have been mainly developed in a static context.

• With the continuous and rapid changes in modern societies (i.e. introduction of advanced technologies, aggressive marketing strategies and innovative policies) it is more and more recognized by researchers in various disciplines that choice situations take place in a dynamic environment and that strong interdependencies exist among decisions made at different points in time.

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Dynamics models in economics• Dynamic discrete choice models have been firstly developed in

economics and related fields. • In dynamic discrete choice structural models, agents are

forward looking and maximize expected inter-temporal payoffs. • The consumers get to know the rapidly evolving nature of

product attributes within a given period of time and different products are supposed to be available on the market.

• As a result, a consumer can either decide to buy the product or to postpone the purchase at each time period. This dynamic choice behavior has been treated in a series of different research studies.

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Review of economics literature• John Rust (1987) --- bus engine replacement, single agent, two

options, one purchase, homogenous attributes of the products, infinite-horizon. Nested Fixed Point method to estimate.

• Oleg Melnikov (2000) --- printer machine demand one purchase, differentiated durable products, homogenous consumers.

• Szabolcs LŐrincz (2005) --- computer servers demand, persistency effects, choice between using the original product and upgrading its format (operating systems). Dynamic nested logit model.

• Juan Esteban Carranza (2006) --- digital camera demand, heterogeneity over consumers’ preferences and dynamics of quality.

• Gowrisankaran and Rysman (2007) --- digital camcorder, repeat purchases, heterogeneous consumers and differentiated products.

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ijtu

0 if is in the market;0,1

1 otherwise.it

iS

0itStj

itc

Model formulationDynamic, regenerative, optimal stopping problem

Consumer i state at time t

In each time period consumer i in status has two options:(a) to buy one of the products or(b) to postpone

If (a) the consumer i obtains a terminal payoff If (b) is chosen the consumer obtains a one period payoff .

a vector of attributes for i at t, e.g. gender, education, professional status, income. , a vector of characteristics of current vehicle owned by i, e.g. age, mileage, purchase price, etc. , are parameters for and .

( , ; , )it it i ic x q

,itx

itq

,i i itx itq

One period pay off

is a vector of individual attributes (e.g. age, income, education) and is the related parameter; is a vector of vehicle static attributes (e.g. vehicle size) and is the related parameter; is a vector of dynamic attributes (e.g. energy cost per mile, purchase cost, environment incentives) , is the related parameter ; is a random utility component (i.i.d. GEV)

is the mean utility.

jd

jty

ijt

, , , , , ,ijt it j jt i i i ijtu u x d y

i

i

jt

jtjtjtu

Terminal payoff

itxi

Each time period, the consumer decides to buy or postpone

where:

Hypothesis

is the payoff when postponing

is time period when consumer decides to buy (set 1)

expected utility

(Based on Bellman equation):

where:

is time period when consumer decides to buy

itc

tt IEE |

, 1, max ,it it it it i tD v c v c E D v

jtjt uvt

max

1

1 maxmax,,...

tkijJjt

tit

tkitiJtti uEccuuD

The evolution of the industry is represented by a so called random walk; dynamic variable is supposed to follow a normal diffusion process, specified as a random walk with drift

(j=1,…,J, t = 1,…,T) are i.i.d. multivariate standard normal random vectors. is the Cholesky factor of the variance-covariance matrix

jty

, 1 , 1

, 1

( ) ( )

( )j t jt jt j t

j jt j jt j t

y y L y

y L y

jt

L( ) ( ) ( )T

jt jt jtL y L y y

j

Industry evolution

This is standard optimal stopping problem. The stopping set is given when:

Reservation utility

Here,

, 1 1 , 1, max , [ ( , ) | ]it it it it i t t i t tD v c v c E D v y c y

titititjt yDEcvvyT ||)(

, 1 1 , 1[ ( , ) | ]t it i t t i t tW y c E D v y c y

Equation (1) becomes:

1( ,... )t t Jty y y

Utility formulation

Probability of postponing until next period:

Product adoption rate:

0 | 0, ,it t it t t ti t t P v W y P postpone s y F W yy y

| 0, 1t it t ot th y P buy s y y

1

1

exp( ) ( ,..., )( )

( ,..., )

j jt

j jt

i ijt ikt ijt it

jt jt

jt jty P U U k j u W y

G e eh r

G e e

Demand structure

The parameters estimation can therefore be formulated as a traditional maximum likelihood problem:

Decisions include: buy a car of type j, not buy a car

M

i

T

titithsPhLL

1 10 = ].|decision[ln)(max

0{ , }it i t ijtP

Estimation methodology

Calculate ?

Calculate

Calculate

0i t

( ( ) )0 exp( )t itw y ri t e

tW y

, 1[ ]t it i tW y c E D v

, 1[ ]i tE D v

Calculate

ijt

1

10

exp( ) ( ,..., )(1 )

( ,..., )

j jt

j jt

jt ji t

G e e

G e e

Dynamic estimation process

At t=0 0 0 1[ ]iW y c E D

buy Not buy

1 1 1 2[ ] max , [ ]i iE D E v c E D

t=1

1[ ]E D 1[ ]E D

buy Not buy

t=2

2[ ]E D 2[ ]E D2[ ]E D 2[ ]E D 2 2 2 3[ ] max , [ ]i iE D E v c E D

t=33[ ] 0E D

buy buyNot buy Not buy

Scenario tree

DDCM applied to carownership

• What effect will the following factors have on the vehicle marketplace over the next five years:– New vehicle technology– Improvements in existing vehicle technology– Greater availability of different energy sources– Rising fuel prices– Transportation and energy policy

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Static Model- results

, 1 0.103 2.617 (0,1.78)j t jty y N

Choose electric car price as the dynamic variable

Dynamic model -results

Application – market share forecasting

UNIVERSITY OF MARYLAND DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING

Gas car Hybrid car

Electric car Current car

Market shares - comparison

• New gasoline vehicles, hybrid and electric vehicles occupy smaller market shares (around 10% each) at the end of the five year period;

• All new typologies become more popular after the fifth time period;

• Static models are incapable of recovering peaks in the demand function;

• MNL model underestimates the market share of the "not buy", and dramatically overestimate the share occupied by electric vehicles in the next five years;

• Dynamic model overestimates the market share of the "not buy", but is capable to reproduce the descending trend for this alternative.

Conclusions

• More than one dynamic attributes could be included in the utility specification; this is not trivial since multivariate random walks should be estimated and included in model estimation;

• Individual’s perspective scenarios could be extended to more than two;

• Data collection techniques should be improved to capture the interdependency among successive observations over time, and to incorporate random walks into orthogonal design (for SP data).

• To compare the results from maximum likelihood method with those from the nested fixed point method;

• Apply dynamic framework to other case: dynamic pricing for revenue management, route choice behavior under dynamic tolling, activity scheduling for activity based analysis…

Future work

Acknowledgments

This is joint work with:• Renting Xu;• Michael Maness;• Fabian Bastin.

Thanks to all the students at UMD who participated to the data collection effort.

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Q&A

Thank you

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