Beia Spiller Duke University October 2010 Research funded by Resources for the Future’s

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## Beia Spiller Duke University October 2010 Research funded by Resources for the Future’s

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**How Gasoline Prices Impact Household Driving and Auto**Purchasing DecisionsA Revealed Preference Approach BeiaSpiller Duke University October 2010 Research funded by Resources for the Future’s Joseph L. Fisher Doctoral Dissertation Fellowship 10/1001 / 38**Policy Relevance**• Consumer response to changing gasoline prices • Climate change • Air pollution • Congestion • National security concerns 10/1002 / 38**Elasticity of Demand for Gasoline**• Accurately measuring the elasticity of demand for gasoline • Importance in climate policy models • Economic incidence of gasoline tax - burden falls on consumers or producers • Optimal gasoline tax • Prior studies range of elasticities: -0.02 to -1.59 • Espey (1996): data, econometric technique, demand specification, assumptions 10/1003 / 38**VMT Demand/Gasoline Prices**10/1004 / 38**Gasoline Prices/Truck Demand**Graph From Klier and Linn (2008) 10/1005 / 38**Change in SUV/car sales**Taken from US DOE website, 2008 10/1006 / 38**Elasticity of Demand for Gasoline**• Downward bias/Misspecification due to: • Assumptions • Research Methods 10/1007 / 38**Model Objectives and Innovations**Incorporate the following into measurement of gasoline demand elasticity: • Extensive and Intensive Margin (vehicle purchase decision and VMT) • Type of vehicle ↔ Amount of driving • Estimate jointly: • Model choice • Fleet size • Driving demand Household fleet’s VMT decisions jointly determined Allocation of VMT between vehicles Substitution as r elative operating costs a;slkjf;alskjsf’ajkfe;lkjfda;lkjds;lkjf asdflkjas 10/1008 / 38**Model Objectives and Innovations**Incorporate the following into measurement of gasoline demand elasticity: • Extensive and Intensive Margin (vehicle purchase decision and VMT) • Type of vehicle ↔ Amount of driving • Estimate jointly: • Model choice • Fleet size • Driving demand • Household fleet’s VMT decisions jointly determined • Allocation of VMT between vehicles • Substitution as relative operating costs change • Hensher (1985), Berkowitz et.al. (1990): 2 and 3 car households more elastic 10/1008 / 38**Model Objectives and Innovations**• Vehicle Fixed Effects • Unobserved vehicle attributes affect purchase decision • Berry, Levinsohn, and Pakes (1995): no fixed effects biases price coefficient • Unobserved attributes (style) make individuals appear less price sensitive 10/1009 / 38**Model Objectives and Innovations**• Vehicle Fixed Effects • Unobserved vehicle attributes affect purchase decision • Berry, Levinsohn, and Pakes (1995): no fixed effects biases price coefficient • Unobserved attributes (style) make individuals appear less price sensitive • Detailed choice set • To capture subtle changes in vehicle purchase decision • Aggregate choice set won’t capture movement within the aggregation (i.e. Ford Taurus -> Honda Civic) 10/1009 / 38**Methodological Hurdle**• High dimensionality of choice set • 3,751 types of vehicles (model-year) in dataset • If households can choose 2: 7,033,125 possible choices • If households can choose 3: 8,789,061,875 possible choices • Typical logit, probitmodels do not allow for such high dimensionality 10/1010 / 38**Proposed Method**• Revealed preference approach: • Observed household vehicle holdings is equilibrium, provides maximum utility • Any deviation from equilibrium results in lower utility • Thus, can compare the utility levels: Utility(bundle choice) > Utility(deviation from choice) • Allows for unconstrained choice set and fixed effects 10/1011 / 38**Outline**• Literature Review • Model • Method • Unobserved Consumer Heterogeneity • Data • Results • Conclusion 10/1012 / 38**Literature Review**• Extensive/intensive margins estimated independently • West (2007), Klierand Linn (2008), Schmalensee and Stoker (1999) • Two-step sequential estimation of extensive/intensive margins • West (2004), Goldberg (1998) • One step approach • Berkowitz et al. (1990), Feng, Fullerton, and Gan (2005), Bento et al. (2008) • Fleet model • Green and Hu (1985) 10/1013 / 38**Model**Per-vehicle sub-utility (additively separable in total utility): i: household j: vehicle VMTij= Vehicle Miles Travelled per year Xj: observable attributes of vehicle j : unobservable attributes of vehicle j 10/1014 / 38**Model**Marginal utility of driving: Zi : Household i's attributes ni : Number of vehicles in household i’s garage - diminishing marginal returns of use as number of vehicles in garage increases Fixed effects: 10/1015 / 38**Model**Marginal utility of driving: Zi : Household i's attributes ni : Number of vehicles in household i’s garage - diminishing marginal returns of use as number of vehicles in garage increases Fixed effects: Thus: 10/1015 / 38**Model: Utility Maximization**max å r = + U u c i ij i VMT , c j å å = + + d c s . t . y P P VMT P c i j ij ij i j j : household income : vehicle j’sused price (opportunity cost of not selling) : operating cost ($/mile) : price of consumption = 1 10/1016 / 38**Model: Utility Maximization**Interdependence of vehicles in fleet: Indirect Utility 10/1017 / 38**Estimation**Two steps: • Difference out fixed effects, estimate , ,ρ • Recapture fixed effects, estimate 10/1018 / 38**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: 10/1019 / 38**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, Brespectively: For Household 1 For Household 2 Thus: 10/1019 / 38**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, Brespectively: For Household 1 For Household 2 Thus: 10/1019 / 38**First Stage Estimation**Maximum Likelihood: Normalization: 10/1020 / 38**First Stage Estimation: Overview**- Guess at parameter vector -For each vehicle in dataset: Step 1: Randomly choose a vehicle from another household Step 2: Swap chosen vehicles between households Step 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 10/1021 / 38**First Stage Estimation: Overview**- Guess at parameter vector -For each vehicle in dataset: Step 1: Randomly choose a vehicle from another household Step 2: Swap chosen vehicles between households Step 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 10/1021 / 38**First Stage Estimation: Overview**- Guess at parameter vector -For each vehicle in dataset: Step 1: Randomly choose a vehicle from another household Step 2: Swap chosen vehicles between households Step 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 10/1021 / 38**First Stage Estimation: Overview**- Guess at parameter vector -For each vehicle in dataset: Step 1: Randomly choose a vehicle from another household Step 2: Swap chosen vehicles between households Step 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 10/1021 / 38**First Stage Estimation: Overview**- Guess at parameter vector -For each vehicle in dataset: Step 1: Randomly choose a vehicle from another household Step 2: Swap chosen vehicles between households Step 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 10/1021 / 38**First Stage Estimation: Overview**- Guess at parameter vector -For each vehicle in dataset: Step 1: Randomly choose a vehicle from another household Step 2: Swap chosen vehicles between households Step 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 10/1021 / 38**First Stage Estimation: Overview**- Guess at parameter vector -For each vehicle in dataset: Step 1: Randomly choose a vehicle from another household Step 2: Swap chosen vehicles between households Step 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 10/1021 / 38**Unobserved Consumer Heterogeneity**• Incorporate observed driving behavior into estimation • Contraction mapping: at each stage of iteration, solve 10/1022 / 38**Unobserved Consumer Heterogeneity**• Guess at parameter vector Find that minimizes distance between observed and optimal Calculate given , Find new parameter vector that maximizes objective function. Repeat steps 2-4 until convergence. 10/1023 / 38**Unobserved Consumer Heterogeneity**• Guess at parameter vector • Find that minimizes distance between observed and optimal Calculate given , Find new parameter vector that maximizes objective function. Repeat steps 2-4 until convergence. 10/1023 / 38**Unobserved Consumer Heterogeneity**• Guess at parameter vector • Find that minimizes distance between observed and optimal • Calculate given , Find new parameter vector that maximizes objective function. Repeat steps 2-4 until convergence. 10/1023 / 38**Unobserved Consumer Heterogeneity**• Guess at parameter vector • Find that minimizes distance between observed and optimal • Calculate given , • Find new parameter vector that maximizes objective function. Repeat steps 2-4 until convergence. 10/1023 / 38**Unobserved Consumer Heterogeneity**• Guess at parameter vector • Find that minimizes distance between observed and optimal • Calculate given , • Find new parameter vector that maximizes objective function. • Repeat steps 2-4 until convergence. 10/1023 / 38**Second Stage Estimation**• Assumption 2: Net sub-utility of jth vehicle > 0 • Assumption 3:jth+ 1 vehicle decreases total utility Thus: Rewriting: 10/1024 / 38**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: 10/1024 / 38**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: 10/1024 / 38**Second Stage Estimation**• For Household 1: • For Household 2: 10/1025 / 38**Second Stage Estimation**• Maximum Likelihood: OLS: 10/1026 / 38**Second Stage Estimation**• Maximum Likelihood: • OLS: 10/1026 / 38**Second Stage Estimation: Overview**• For each type of vehicle: • Find all households who own it: positive sub-utility from owning it. • Find all households who don’t own it: adding this vehicle decreases utility. • Form maximum likelihood over (1) and (2) • Estimate fixed effect for this vehicle • Run OLS of all FE on vehicle characteristics 10/1027 / 38**Data**• Household level data: National Household Transportation Survey 2001 and 2009 10/1028 / 38**Data: NHTS Summary Statistics**10/1029 / 38**Data: Vehicles**• Vehicle characteristic data: Polk, Ward’s Automotive Yearbook • Provides detailed information on 6,594 vehicles 1971-2009 • Used vehicle prices: NADA • Provides used prices of vehicles in 2001 (1982-2002), 2009 (1992 – 2010) 10/1030 / 38**Data: Gasoline Prices**• American Chamber of Commerce Research Association (ACCRA) 2001, 2009 data • provides gas prices at the city level • yearly averages • aggregate to MSA 10/1031 / 38**Data: Gasoline Prices**10/1032 / 38