Beia Spiller (Duke University) How Gasoline Prices Impact Household Driving and Auto Purchasing Decisions A Revealed Preference Approach Beia Spiller Duke University October 2010 Research funded by Resources for the Future’s Joseph L. Fisher Doctoral Dissertation Fellowship 10/10 01 / 38
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Beia Spiller (Duke University)
How Gasoline Prices Impact Household Driving and Auto Purchasing Decisions
A Revealed Preference Approach
Beia Spiller
Duke UniversityOctober 2010
Research funded by Resources for the Future’s Joseph L. Fisher Doctoral Dissertation Fellowship
10/10 01 / 38
Beia Spiller (Duke University)
Policy Relevance
• Consumer response to changing gasoline priceso Climate changeo Air pollutiono Congestiono National security concerns
10/10 02 / 38
Beia Spiller (Duke University)
Elasticity of Demand for Gasoline
• Accurately measuring the elasticity of demand for gasolineo Importance in climate policy modelso Economic incidence of gasoline tax - burden falls on
consumers or producerso Optimal gasoline tax
• Prior studies range of elasticities: -0.02 to -1.59o Espey (1996): data, econometric technique, demand
specification, assumptions
10/10 03 / 38
Beia Spiller (Duke University)
VMT Demand/Gasoline Prices
10/10 04 / 38
Beia Spiller (Duke University)
Gasoline Prices/Truck Demand
Graph From Klier and Linn (2008)10/10 05 / 38
Beia Spiller (Duke University)
Change in SUV/car sales
10/10 06 / 38
Taken from US DOE website, 2008
Beia Spiller (Duke University)
Elasticity of Demand for Gasoline
• Downward bias/Misspecification due to:o Assumptionso Research Methods
10/10 07 / 38
Beia Spiller (Duke University)
Model Objectives and Innovations
Incorporate the following into measurement of gasoline demand elasticity:• Extensive and Intensive Margin (vehicle purchase decision
and VMT)o Type of vehicle ↔ Amount of drivingo Estimate jointly:
Model choiceFleet sizeDriving demand
Household fleet’s VMT decisions jointly determinedAllocation of VMT between vehiclesSubstitution as relative operating costs a;slkjf;alskjsf’ajkfe;lkjfda;lkjds;lkjf asdflkjas
10/10 08 / 38
Beia Spiller (Duke University)
Model Objectives and Innovations
Incorporate the following into measurement of gasoline demand elasticity:• Extensive and Intensive Margin (vehicle purchase decision
and VMT)o Type of vehicle ↔ Amount of drivingo Estimate jointly:
Model choiceFleet sizeDriving demand
• Household fleet’s VMT decisions jointly determinedo Allocation of VMT between vehicleso Substitution as relative operating costs changeo Hensher (1985), Berkowitz et.al. (1990): 2 and 3 car households
decisiono Berry, Levinsohn, and Pakes (1995): no fixed effects
biases price coefficientUnobserved attributes (style) make individuals appear less
price sensitive
• Detailed choice seto To capture subtle changes in vehicle purchase decisionAggregate choice set won’t capture movement within the
aggregation (i.e. Ford Taurus -> Honda Civic)
10/10 09 / 38
Beia Spiller (Duke University)
Methodological Hurdle
• High dimensionality of choice set• 3,751 types of vehicles (model-year) in dataset
o If households can choose 2: 7,033,125 possible choices
o If households can choose 3: 8,789,061,875 possible choices
• Typical logit, probit models do not allow for such high dimensionality
10/10 10 / 38
Beia Spiller (Duke University)
Proposed Method
• Revealed preference approach:o Observed household vehicle holdings is equilibrium,
provides maximum utilityo Any deviation from equilibrium results in lower
utilityThus, can compare the utility levels:
Utility(bundle choice) > Utility(deviation from choice)
• Allows for unconstrained choice set and fixed effects
10/10 11 / 38
Beia Spiller (Duke University)
Outline
1. Literature Review2. Model 3. Method4. Unobserved Consumer Heterogeneity5. Data6. Results7. Conclusion
10/10 12 / 38
Beia Spiller (Duke University)
Literature Review
• Extensive/intensive margins estimated independentlyo West (2007), Klier and Linn (2008), Schmalensee and
Stoker (1999)• Two-step sequential estimation of
extensive/intensive marginso West (2004), Goldberg (1998)
• One step approacho Berkowitz et al. (1990), Feng, Fullerton, and Gan (2005),
Bento et al. (2008) • Fleet model
o Green and Hu (1985)10/10 13 / 38
Beia Spiller (Duke University)
Model
Per-vehicle sub-utility (additively separable in total utility):
i: householdj: vehicleVMTij = Vehicle Miles Travelled per yearXj : observable attributes of vehicle j
: unobservable attributes of vehicle j
ijjjiijijij XVMTu
j
2,0~ Nij
10/10 14 / 38
Beia Spiller (Duke University)
Model
Marginal utility of driving:
Zi : Household i's attributesni : Number of vehicles in household i’s garage
- diminishing marginal returns of use as number of vehicles in garage
increasesFixed effects: ii Zgg 10
jjj Xg 0
10/10 15 / 38
itittiiij nXZaXZaXZa /...exp 222111
Beia Spiller (Duke University)
Model
Marginal utility of driving:
Zi : Household i's attributesni : Number of vehicles in household i’s garage
- diminishing marginal returns of use as number of vehicles in garage
increasesFixed effects:
Thus:
ii Zgg 10
jjj Xg 0
10/10 15 / 38
itittiiij nXZaXZaXZa /...exp 222111
ijjjiij
j
jiij XZgVMT
nXZ
u
1
exp
Beia Spiller (Duke University)
Model: Utility Maximization
: household income : vehicle j’s used price (opportunity cost of not
selling): operating cost ($/mile): price of consumption = 1
iy
jP
dijPcP
10/10 16 / 38
å å
å
j ji
cij
dijji
jiiji
cPVMTPPyts
cuUcVMT
..
,max
Beia Spiller (Duke University)
Model: Utility Maximization
Interdependence of vehicles in fleet:
Indirect Utility
*** , iijii cVMTUV
10/10 17 / 38
å
å
i
i
J
k ik
dik
J
k
uki
ij
dij
ij
P
PyP
VMT1
1
1
11
*
11
Beia Spiller (Duke University)
Estimation
Two steps:1. Difference out fixed effects, estimate , , ρ2. Recapture fixed effects, estimate
ij
1g
0g
10/10 18 / 38
Beia Spiller (Duke University)
First Stage Estimation: Swapping
• Assumption 1: Household in equilibrium with vehicle purchase and VMT decision
: Fleet chosen by household i
Two households, 1 and 2, have vehicles A, B respectively:
Thus:
** iiiFiF
FFVVii
*
iF
10/10 19 / 38
Beia Spiller (Duke University)
First Stage Estimation: Swapping
• Assumption 1: Household in equilibrium with vehicle purchase and VMT decision
: Fleet chosen by household i
• Two households, 1 and 2, have vehicles A, B respectively:
For Household 1 For Household 2
Thus:
** iiiFiF
FFVVii
*
iF
AABB
BBAA
VV
VV
22
11~~
~~
10/10 19 / 38
Beia Spiller (Duke University)
First Stage Estimation: Swapping
• Assumption 1: Household in equilibrium with vehicle purchase and VMT decision
: Fleet chosen by household i
• Two households, 1 and 2, have vehicles A, B respectively:
For Household 1 For Household 2
Thus:
** iiiFiF
FFVVii
*
iF
AABB
BBAA
VV
VV
22
11~~
~~
10/10 19 / 38
0~~~~2211 ABBA VVVV
0~~~~2211 ABABBABA VVVV
Beia Spiller (Duke University)
First Stage Estimation
Maximum Likelihood:
Normalization:
ABBAABABBA VVVVVVVV 2211,122211~Pr0~~~~Pr
~
2211 ABBA VVVV
å
)2,1)(2,1(
12222111
~log
jjiiswaps
jijijiji VVVVLL
1c
10/10 20 / 38
Beia Spiller (Duke University)
First Stage Estimation: Overview
- Guess at parameter vector -For each vehicle in dataset:
Step 1: Randomly choose a vehicle from another householdStep 2: Swap chosen vehicles between householdsStep 3: Calculate optimal VMT for observed fleet and proposed
deviation (given current )Step 4: Calculate indirect utility under each scenario (observed
and proposed)Step 5: Difference indirect utilities
-Calculate objective function (summed log of differences)-Find that increases objective function-Repeat until convergence
1( g
10/10 21 / 38
Beia Spiller (Duke University)
First Stage Estimation: Overview
- Guess at parameter vector -For each vehicle in dataset:
Step 1: Randomly choose a vehicle from another householdStep 2: Swap chosen vehicles between householdsStep 3: Calculate optimal VMT for observed fleet and proposed
deviation (given current )Step 4: Calculate indirect utility under each scenario (observed
and proposed)Step 5: Difference indirect utilities
-Calculate objective function (summed log of differences)-Find that increases objective function-Repeat until convergence
10/10 21 / 38
1( g
Beia Spiller (Duke University)
First Stage Estimation: Overview
- Guess at parameter vector -For each vehicle in dataset:
Step 1: Randomly choose a vehicle from another householdStep 2: Swap chosen vehicles between householdsStep 3: Calculate optimal VMT for observed fleet and proposed
deviation (given current )Step 4: Calculate indirect utility under each scenario (observed
and proposed)Step 5: Difference indirect utilities
-Calculate objective function (summed log of differences)-Find that increases objective function-Repeat until convergence
10/10 21 / 38
1( g
Beia Spiller (Duke University)
First Stage Estimation: Overview
- Guess at parameter vector -For each vehicle in dataset:
Step 1: Randomly choose a vehicle from another householdStep 2: Swap chosen vehicles between householdsStep 3: Calculate optimal VMT for observed fleet and proposed
deviation (given current )Step 4: Calculate indirect utility under each scenario (observed
and proposed)Step 5: Difference indirect utilities
-Calculate objective function (summed log of differences)-Find that increases objective function-Repeat until convergence
10/10 21 / 38
1( g
Beia Spiller (Duke University)
First Stage Estimation: Overview
- Guess at parameter vector -For each vehicle in dataset:
Step 1: Randomly choose a vehicle from another householdStep 2: Swap chosen vehicles between householdsStep 3: Calculate optimal VMT for observed fleet and proposed
deviation (given current )Step 4: Calculate indirect utility under each scenario (observed
and proposed)Step 5: Difference indirect utilities
-Calculate objective function (summed log of differences)-Find that increases objective function-Repeat until convergence
10/10 21 / 38
1( g
Beia Spiller (Duke University)
First Stage Estimation: Overview
- Guess at parameter vector -For each vehicle in dataset:
Step 1: Randomly choose a vehicle from another householdStep 2: Swap chosen vehicles between householdsStep 3: Calculate optimal VMT for observed fleet and proposed
deviation (given current )Step 4: Calculate indirect utility under each scenario (observed
and proposed)Step 5: Difference indirect utilities
-Calculate objective function (summed log of differences)-Find that increases objective function-Repeat until convergence
10/10 21 / 38
1( g
Beia Spiller (Duke University)
First Stage Estimation: Overview
- Guess at parameter vector -For each vehicle in dataset:
Step 1: Randomly choose a vehicle from another householdStep 2: Swap chosen vehicles between householdsStep 3: Calculate optimal VMT for observed fleet and proposed
deviation (given current )Step 4: Calculate indirect utility under each scenario (observed
and proposed)Step 5: Difference indirect utilities
-Calculate objective function (summed log of differences)-Find that increases objective function-Repeat until convergence
'
10/10 21 / 38
1( g
Beia Spiller (Duke University)
Unobserved Consumer Heterogeneity
• Incorporate observed driving behavior into estimation
• Contraction mapping: at each stage of iteration, solve
iitittiiij nXZaXZaXZa /...exp 222111
10/10 22 / 38
0112
*
åå
jij
jij VMT
jVMT
j
Beia Spiller (Duke University)
Unobserved Consumer Heterogeneity
1. Guess at parameter vectorFind that minimizes distance between observed
and optimal Calculate given , Find new parameter vector that maximizes
objective function.Repeat steps 2-4 until convergence.
,, 1g
10/10 23 / 38
Beia Spiller (Duke University)
Unobserved Consumer Heterogeneity
1. Guess at parameter vector2. Find that minimizes distance between
observed and optimal Calculate given , Find new parameter vector that maximizes
objective function.Repeat steps 2-4 until convergence.
,, 1g
iijVMT
10/10 23 / 38
Beia Spiller (Duke University)
Unobserved Consumer Heterogeneity
1. Guess at parameter vector2. Find that minimizes distance between
observed and optimal 3. Calculate given , Find new parameter vector that maximizes
objective function.Repeat steps 2-4 until convergence.
,, 1g
i
i ijVMT
*ijVMT
10/10 23 / 38
Beia Spiller (Duke University)
Unobserved Consumer Heterogeneity
1. Guess at parameter vector2. Find that minimizes distance between
observed and optimal 3. Calculate given , 4. Find new parameter vector that maximizes
objective function.Repeat steps 2-4 until convergence.
,, 1g
i
i ijVMT
*ijVMT
10/10 23 / 38
Beia Spiller (Duke University)
Unobserved Consumer Heterogeneity
1. Guess at parameter vector2. Find that minimizes distance between
observed and optimal 3. Calculate given , 4. Find new parameter vector that maximizes
objective function.5. Repeat steps 2-4 until convergence.
,, 1g
i
i
*ijVMT
*ijVMT
10/10 23 / 38
Beia Spiller (Duke University)
Second Stage Estimation
• Assumption 2: Net sub-utility of jth vehicle > 0• Assumption 3: jth + 1 vehicle decreases total
utilityThus:
Rewriting:
10/10 24 / 38
Beia Spiller (Duke University)
Second Stage Estimation
• Assumption 2: Net sub-utility of jth vehicle > 0• Assumption 3: jth + 1 vehicle decreases total
utility• Thus:
For Household 1
For Household 2
Rewriting:
011 VV A
ABB VV ,22
10/10 24 / 38
Beia Spiller (Duke University)
Second Stage Estimation
• Assumption 2: Net sub-utility of jth vehicle > 0• Assumption 3: jth + 1 vehicle decreases total
utility• Thus:
For Household 1
For Household 2
• Rewriting:
011 VV A
ABB VV ,22
011 AAAV
ABBAABBBB VV 22,222
10/10 24 / 38
Beia Spiller (Duke University)
Second Stage Estimation
• For Household 1:
• For Household 2:
A
AAAAA
VVP
111
A
AAABA
VVVP
2222
10/10 25 / 38
Beia Spiller (Duke University)
Second Stage Estimation
• Maximum Likelihood:
OLS:
å
jj
ji
iij
jiijj
Vy
VyLL
1ln1ln
10/10 26 / 38
Beia Spiller (Duke University)
Second Stage Estimation
• Maximum Likelihood:
• OLS:
å
jj
ji
iij
jiijj
Vy
VyLL
1ln1ln
jjj Xg 0
10/10 26 / 38
Beia Spiller (Duke University)
Second Stage Estimation: Overview
• For each type of vehicle:1) Find all households who own it: positive sub-utility
from owning it.2) Find all households who don’t own it: adding this
vehicle decreases utility.3) Form maximum likelihood over (1) and (2)4) Estimate fixed effect for this vehicle
• Run OLS of all FE on vehicle characteristics
10/10 27 / 38
Beia Spiller (Duke University)
Data
• Household level data: National Household Transportation Survey 2001 and 2009
10/10 28 / 38
NHTS 2001 NHTS 2009
National Sample Full Sample
26,038 households 143,084 households
53,275 observations 309,163 observations
Final Sample Final Sample
11,354 households 11,366 households
18,166 observations 18,305 observations
Beia Spiller (Duke University)
Data: NHTS Summary Statistics
Full Sample Final Sample
% White 87% 85%
% Urban 70% 79%
Average Family Income $55,832 $56,338
Average Household Size 2.82 2.66
Average Workers to Vehicles 0.65 0.72
Average Fleet Size 2.69 2.04
Average MPG 25.72 25.87
Average Vehicle Age (years) 8.49 7.21
Average Yearly VMT 10,995 11,594
10/10 29 / 38
Beia Spiller (Duke University)
Data: Vehicles
• Vehicle characteristic data: Polk, Ward’s Automotive Yearbooko Provides detailed information on 6,594 vehicles
1971-2009• Used vehicle prices: NADA
o Provides used prices of vehicles in 2001 (1982-2002), 2009 (1992 – 2010)
10/10 30 / 38
Beia Spiller (Duke University)
Data: Gasoline Prices
• American Chamber of Commerce Research Association (ACCRA) 2001, 2009 datao provides gas prices at the city levelo yearly averageso aggregate to MSA
MSA Gas Prices 2001 Gas Prices 2009
Oklahoma City, OK 1.23 2.07Houston, TX 1.34 2.34
Raleigh, NC 1.39 2.47
Chicago, IL 1.50 2.73
Philadelphia, PA 1.56 2.53
San Francisco, CA 1.92 2.80
10/10 31 / 38
Beia Spiller (Duke University)
Data: Gasoline Prices
1.15 1.45 1.75 2.05 2.35 2.65 2.95 3.250
10
20
30
40
50
60
70
80
90
100
2009 Gasoline Prices2001 Gasoline Prices
2.44
1.41
10/10 32 / 38
Beia Spiller (Duke University)
Results: First Stage
Interaction Term Parameter Value (Std. Err.)
Marginal Utility of Driving Parameters
(HP/weight) * urban 2.341*** (0.055)
Vehicle Size * household size -0.252* (0.147)
Wheelbase* urban 0.051 (1.531)
Household size/# vehicles -0.166 (0.353)
***: significant at 99% level, *: significant at 90%
10/10 33 / 38
Beia Spiller (Duke University)
Results: First StageInteraction Term Parameter Value (Std. Err.)
Indirect Utility of Driving Parameters
Green* income -0.063 (0.268)
Green* Pacific 0.124 (1.147)
Green*New England 0.731** (0.347)
Size* Income 0.547*** (0.146)
Size* Pacific -1.703*** (0.220)
Size* Mountain 2.085*** (0.204)
Domestic* Income 0.101 (0.439)
Domestic*Midwest (WNC) 2.147*** (0.142)
Domestic*Midwest (ENC) 1.118*** (0.168)
European* Income 0.989*** (0.137)
Japanese* Income 0.495*** (0.149)
Japanese* Pacific 1.170*** (0.161)
Vehicle Age* Income -0.037 (0.144)
Size* Urban -2.021*** (0.154)
(***: statistically significant at 99%, **: statistically significant at 95%, *: statistically significant at 90%)
10/10 34 / 38
Beia Spiller (Duke University)
Results: First Stage
~
Coefficient Parameter Value (Std. Err.)
CES Parameter 0.456*** (0.084)
Std. Dev. Of Error Term 1.539*** (0.517)
Elasticity of Demand for Gasoline, ΔPrice = 1%
-1.277*** (0.219)
(***: statistically significant at 99%)
10/10 35 / 38
Beia Spiller (Duke University)
Results: Second Stage Estimation
• OLS Regression
jjj Xg 0
Parameter Value (Std. Err.)
Constant 16.086*** (1.231)
Green 0.869** (0.321)
Vehicle Size 1.081*** (0.435)
Domestic 2.941*** (1.012)
European 1.181* (0.876)
Japanese 7.777*** (1.452)
Vehicle Age -0.512*** (0.035)
R2 0.675
(***: statistically significant at 99%, **: statistically significant at 95%, *: statistically significant at 90%)
• Independence and aggregation:o Elasticity = -0.992, 22.3% bias. (-)
10/10 37 / 38
Beia Spiller (Duke University)
Conclusion
• Demand for gasoline is elastic• Bias due to assuming independence and
aggregating the choice set• Household choices are better represented
o Discrete-continuous household portfolio modelo Estimation method does not artificially restrict
choice set
10/10 38 / 38
Beia Spiller (Duke University) 10/10 26 / 28
Thank you!Any Questions?
Beia Spiller (Duke University)
Starting Values for First Stage
1. Minimize distance given observed and optimal VMT, calculate that solves:
2. Hold fixed, calculate to solve likelihood function
3. Use and as the full set of starting values.
0112
åå
jij
jij VMT
jVMT
j
ij 1g
ij
ij 1g
Beia Spiller (Duke University)
Indirect Utility Function
• Assumptions:o Constant MRS between vehicles =1 due to static
nature of modelo Additive separability in and o Non-linear in o Non-separable in o Composite error term
j
ij
*ijVMT
*ijVMT
åj
ijij N 2~,0~~
Beia Spiller (Duke University)
McFadden et.al. (1978)
• Subsampling of Alternativeso IIA property -> parameter estimates off random sample of
choices statistically equal to whole choice set estimateso Red bus/blue bus problem in logit errors/IIAo In bundle application: errors are bundle specific
• Swapping: prior to swaps, errors are iid. o Han (1987) : cross sectional error terms iid, then consistency