Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Household)Vehicle)Bundle)Choice)and)Gasoline)Demand

A)Discrete7Continuous)Approach

E.)Beia Spiller

Resources)for)the)Future

July)2011

01)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Elasticity)of)Demand)for)Gasoline

 Consumer)response)to)changing)gasoline)prices

 Important)in)policy)settings

 Environmental)concerns

 Welfare)outcomes

 Distributional)Concerns

CORRECT&ESTIMATION&IS&CRUCIAL!!

02)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Elasticity)of)Demand)for)Gasoline

 Methods)for)estimating)elasticity:

1. Reduced)Form:)Regress)prices)and)quantities

o Cross7sectional)data;)Panel)data

Schmalensee and)Stoker)(1999)

Structural:)Understand)underlying)parameters

Can)incorporate)many)issues)of)concern)unavailable)to)

reduced)form)methods

Bundle)choices,)substitutability:)West)(2004);)Goldberg)(1998);)

Berkowitz)(1990)

Joint)estimation)of)extensive/intensive)margin:)Feng,)Fullerton)&)

Gan (2005);)Bento,)et.al.)(2008)

03)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Elasticity)of)Demand)for)Gasoline

 Methods)for)estimating)elasticity:

1. Reduced)Form:)Regress)prices)and)quantities

o Cross7sectional)data;)Panel)data

Schmalensee and)Stoker)(1999)

2. Structural:)Understand)underlying)parameters

o Can)incorporate)many)issues)of)concern)unavailable)to)

reduced)form)methods

Bundle)choices,)substitutability:)West)(2004);)Goldberg)(1998);)

Berkowitz)(1990)

Joint)estimation)of)extensive/intensive)margin:)Feng,)Fullerton)&)

Gan (2005);)Bento,)et.al.)(2008)

03)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Proposed)Approach

 Structural,)cross7sectional)analysis)ʹ 2001,)2009)

National)Household)Transportation)Survey

 Revealed)preference

 Can)minimize)number)of)simplifying)

assumptions)that)impact)elasticity

04)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Simplifying)Assumptions)Commonly)Used

1. Model)extensive(and intensive(margin)separately)

(vehicle)purchase)decision)and)VMT)

o Ignores)shared)information)across)margins

Assume)households)do)not)optimize)over)bundle

No)optimal)allocation)of)VMT)between)vehicles

No)substitution)as)relative)operating)costs)change

ŽŶ͛ƚŝŶĐůƵĚĞvehicle(specific(fixed(effects

Ignores)unobserved)vehicle)attributes)affect)purchase)

decision

Aggregate(choice)set)for)easier)estimation

ŽĞƐŶ͛ƚĐĂƉƚƵƌĞƐƵďƚůĞĐŚĂŶŐĞƐŝŶǀĞŚŝĐůĞƉƵƌĐŚĂƐĞ

decision

05)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Simplifying)Assumptions)Commonly)Used

1. Model)extensive(and intensive(margin)separately)

(vehicle)purchase)decision)and)VMT)

o Ignores)shared)information)across)margins

2. Assume)households)do)not)optimize)over)bundle

o No)optimal)allocation)of)VMT)between)vehicles

o No)substitution)as)relative)operating)costs)change

ŽŶ͛ƚŝŶĐůƵĚĞvehicle(specific(fixed(effects

Ignores)unobserved)vehicle)attributes)affect)purchase)

decision

Aggregate(choice)set)for)easier)estimation

ŽĞƐŶ͛ƚĐĂƉƚƵƌĞƐƵďƚůĞĐŚĂŶŐĞƐŝŶǀĞŚŝĐůĞƉƵƌĐŚĂƐĞ

decision

05)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Simplifying)Assumptions)Commonly)Used

1. Model)extensive(and intensive(margin)separately)

(vehicle)purchase)decision)and)VMT)

o Ignores)shared)information)across)margins

2. Assume)households)do)not)optimize)over)bundle

o No)optimal)allocation)of)VMT)between)vehicles

o No)substitution)as)relative)operating)costs)change

3. ŽŶ͛ƚŝŶĐůƵĚĞvehicle(specific(fixed(effects

o Ignores)unobserved)vehicle)attributes)affect)purchase)

decision

Aggregate(choice)set)for)easier)estimation

ŽĞƐŶ͛ƚĐĂƉƚƵƌĞƐƵďƚůĞĐŚĂŶŐĞƐŝŶǀĞŚŝĐůĞƉƵƌĐŚĂƐĞ

decision

05)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Simplifying)Assumptions)Commonly)Used

1. Model)extensive(and intensive(margin)separately)

(vehicle)purchase)decision)and)VMT)

o Ignores)shared)information)across)margins

2. Assume)households)do)not)optimize)over)bundle

o No)optimal)allocation)of)VMT)between)vehicles

o No)substitution)as)relative)operating)costs)change

3. ŽŶ͛ƚŝŶĐůƵĚĞvehicle(specific(fixed(effects

o Ignores)unobserved)vehicle)attributes)affect)purchase)

decision

4. Aggregate(choice)set)for)easier)estimation

o ŽĞƐŶ͛ƚĐĂƉƚƵƌĞƐƵďƚůĞĐŚĂŶŐĞƐŝŶǀĞŚŝĐůĞƉƵƌĐŚĂƐĞ

decision

05)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Impacts)on)Elasticity,)Benefits)of)Method

 Allows)me)to)test)impact)of)assumptions)274)on)

elasticity

o Bundles,)disaggregation,)vehicle)fixed)effects

 Not)accounting)for)these)complexities)can)have)

significant)impacts)on)elasticity!

Elasticity&can&be&underestimated&by&66%

06)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Why)This)is)Difficult

1. ƵŶĚůĞƐнĚŝƐĂŐŐƌĞŐĂƚĞĐŚŽŝĐĞƐĞƚуьĐŚŽŝĐĞƐ͊

2. VFE)+)dis.)choice)set)=)too)many)parameters!

Need&a&method&that&allows&for&

very&large&choice&set,

vehicle&specific&fixed&effects

077)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Proposed)Method

 Revealed)preference)approach:

o Observed)household)bundle)is)optimal,)provides)

maximum)utility

o Any)deviation)from)chosen)bundle)results)in)lower)

utility

 Thus,)can)compare)the)utility)levels:

hƚŝůŝƚLJ;ďƵŶĚůĞĐŚŽŝĐĞͿшhƚŝůŝƚLJ;ĚĞǀŝĂƚŝŽŶĨƌŽŵĐŚŽŝĐĞͿ

o Search)for)parameters)that)make)this)inequality)

hold,)use)these)to)calculate)elasticity

 Allows)for)unconstrained)choice)set

08)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Estimation:)Revealed)Preference

 Routine:

o Form)preference)inequality)for)each)household

:)Bundle)chosen)by)household)i

:)One)alternative)bundle)not&

chosen)by)household)i

o Maximize)likelihood)that)chosen)bundle)was)best)

choice)(preference)inequality)holds).

i i

iJ iJ U * tU

*

i J

i J

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Proposed)Method):)Adding)Vehicle)Specific)Fixed)Effects

 Unilateral)comparisons)do(not(allow(inclusion)of)

vehicle)FE!

Household&1 owns vehicle A:)

 Too)many)șj to)estimate)in)this)manner.

To)include)FE:)need)to)do)bilateral comparisons

Additively)separable)FE)fall)away)from)both)sides

Household)1

Household)2

EdKK͞^tWW/E'͟^d/DdKZ͊͊

10)/)16

U1A T A tU1B T B
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Proposed)Method):)Adding)Vehicle)Specific)Fixed)Effects

 Unilateral)comparisons)do(not(allow(inclusion)of)

vehicle)FE!

Household&1 owns vehicle A:

 Too)many)șj to)estimate)in)this)manner.

 To)include)FE:)need)to)do)bilateral comparisons

o Additively)separable)FE)fall)away)from)both)sides

Household)1

Household)2

EdKK͞^tWW/E'͟^d/DdKZ͊͊

10)/)16

U2B T B tU2A T A

U1A T A tU1B T B

U1A T A tU1B T B
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Proposed)Method):)Adding)Vehicle)Specific)Fixed)Effects

 Unilateral)comparisons)do(not(allow(inclusion)of)

vehicle)FE!

Household&1 owns vehicle A:

 Too)many)șj to)estimate)in)this)manner.

 To)include)FE:)need)to)do)bilateral comparisons

o Additively)separable)FE)fall)away)from)both)sides

Household)1

Household)2

EdKK͞^tWW/E'͟^d/DdKZ͊͊

10)/)16

U1A T A tU1B T B

U1A T A tU1B T B

U2B T B tU2A T A

U1A T A U2B T B tU1B T B U2A T A
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Proposed)Method):)Adding)Vehicle)Specific)Fixed)Effects

 Unilateral)comparisons)do(not(allow(inclusion)of)

vehicle)FE!

Household&1 owns vehicle A:

 Too)many)șj to)estimate)in)this)manner.

 To)include)FE:)need)to)do)bilateral comparisons

o Additively)separable)FE)fall)away)from)both)sides

Household)1

Household)2

EdKK͞^tWW/E'͟^d/DdKZ͊͊

10)/)16

U1A T A tU1B T B

U1A T A tU1B T B

U2B T B tU2A T A

U1A T A U2B T B tU1B T B U2A T A
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Proposed)Method):)Adding)Vehicle)Specific)Fixed)Effects

 Unilateral)comparisons)do(not(allow(inclusion)of)

vehicle)FE!

Household&1 owns vehicle A:

 Too)many)șj to)estimate)in)this)manner.

 To)include)FE:)need)to)do)bilateral comparisons

o Additively)separable)FE)fall)away)from)both)sides

Household)1

Household)2

Final)Pref.)

Inequality)

EdKK͞^tWW/E'͟^d/DdKZ͊͊

10)/)16

U1A U2B tU1B U2A

U1A T A tU1B T B

U1A T A tU1B T B

U2B T B tU2A T A
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Swapping)Estimation:)Bundles)with)>1)vehicle

 ͞^ǁĂƉ͟сƉƌŽƉŽƐĞĚĚĞǀŝĂƚŝŽŶĨƌŽŵďƵŶĚůĞ͘

o Choose)one)purchased)vehicle)from)two)

ŚŽƵƐĞŚŽůĚƐ͛ŽďƐĞƌǀĞĚďƵŶĚůĞƐ͕ƐǁĂƉƚŚĞŵ

11)/)16
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WƌŽƉŽƐĞĚĞǀŝĂƚŝŽŶ͗͞^ǁĂƉ͟ǁŝƚŚƵŶĚůĞƐ

 Original)Scenario)(Data(Observation)

Household)1))) Household)2

Bundle))))) A))B C))D

 Proposed)Deviation)(Swap)

Household)1))) Household)2

Bundle))))) C))B A))D

Revealed&Preference:&both&HH&better&under&data&

observation!

12)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Estimation)Technique

1. Randomly)swap)two)vehicles)between)two)

households.

2. Run)maximum)likelihood)that)any)random)

swap)makes)both)households)worse)off.

3. Find)parameters)that)maximize)likelihood.

4. Use)these)parameters)to)calculate)elasticity.

13)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Revealed)Preference)7>)Elasticity

 VMT*)=))f((Zi:)HH)characteristics;

Xj:)vehicle)characteristics;

Zi*Xj:)interactions;

:)estimated)parameters;

gasoline&price)

 ůĂƐƚŝĐŝƚLJс;ѐsDdͬѐƉƌŝĐĞͿΎ;ƉƌŝĐĞ0/VMT0)

E

Ö

14)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Results

Baseline 1 2 3 4 5

Fixed&effects No No No Yes Yes Yes

Bundles No Yes No No No Yes

Disaggregation No No Yes No Yes Yes

Elasticity&

estimate&

(std.&err.)

V0.30&

(0.08)

V0.32

(0.09)

V0.43

(0.12)

V0.52

(0.15)

V0.62

(0.17)

V0.89

(0.25)

%&

Underestimated 66% 64% 51% 41% 29% 7

15)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Conclusion

 Elasticity)is)underestimated)if)

o Ignore)bundle)effects

o Aggregate)the)choice)set

o Exclude)vehicle)fixed)effects

 Swapping)Revealed)Preference)method

o Allows)researcher)to)model)more)complex)consumer)

behavior

o Minimizes)distortions)on)elasticity

16)/)16
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16 26)/)28

Thank)you!

Any)Questions?
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Benefits)of)Structural,)Cross)Sectional)Analysis

 Reduced)form:)cannot)predict)impact)of)various)

policy)changes

o Intensive)margin:)Does)not)capture)technological)

change,)substitution)within)household

o WŽůŝĐLJŵĂŬĞƌƐǁŽŶ͛ƚƵŶĚĞƌƐƚĂŶĚŚŽǁŝŶĚŝǀŝĚƵĂůƐ

make)changes)when)faced)with)higher)gas)prices

 Time)series)data:)hard)to)pinpoint)change)in)

demand)due)ONLY)to)gasoline)prices

o Preferences,)demographics,)income,)economy)may)

change)along)with)prices
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Misidentification:)Reduced)Form

Price

P1

P0 D

Q1 Q0 Quantity
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Misidentification:)Reduced)Form

Price

P1

D1

P0

XD0

Q1 Q0 Quantity
Beia Spiller)(Resources)for)the)Future) 7/11 02)/)16

Benefits)of)Structural)Method

 Structural:)Allows)for)the)actual)identification)of)

demand)curve!

 Revealed)Preference:)Want)to)allow)for)more)

complex)consumer)behavior