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

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 0 1 / 38. Policy Relevance.

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

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  1. 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

  2. Policy Relevance • Consumer response to changing gasoline prices • Climate change • Air pollution • Congestion • National security concerns 10/1002 / 38

  3. 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

  4. VMT Demand/Gasoline Prices 10/1004 / 38

  5. Gasoline Prices/Truck Demand Graph From Klier and Linn (2008) 10/1005 / 38

  6. Change in SUV/car sales Taken from US DOE website, 2008 10/1006 / 38

  7. Elasticity of Demand for Gasoline • Downward bias/Misspecification due to: • Assumptions • Research Methods 10/1007 / 38

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. Outline • Literature Review • Model • Method • Unobserved Consumer Heterogeneity • Data • Results • Conclusion 10/1012 / 38

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. Model: Utility Maximization Interdependence of vehicles in fleet:  Indirect Utility 10/1017 / 38

  21. Estimation Two steps: • Difference out fixed effects, estimate , ,ρ • Recapture fixed effects, estimate 10/1018 / 38

  22. 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

  23. 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

  24. 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

  25. First Stage Estimation Maximum Likelihood: Normalization: 10/1020 / 38

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. Unobserved Consumer Heterogeneity • Incorporate observed driving behavior into estimation • Contraction mapping: at each stage of iteration, solve 10/1022 / 38

  34. 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

  35. 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

  36. 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

  37. 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

  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

  39. 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

  40. 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

  41. 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

  42. Second Stage Estimation • For Household 1: • For Household 2: 10/1025 / 38

  43. Second Stage Estimation • Maximum Likelihood: OLS: 10/1026 / 38

  44. Second Stage Estimation • Maximum Likelihood: • OLS: 10/1026 / 38

  45. 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

  46. Data • Household level data: National Household Transportation Survey 2001 and 2009 10/1028 / 38

  47. Data: NHTS Summary Statistics 10/1029 / 38

  48. 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

  49. 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

  50. Data: Gasoline Prices 10/1032 / 38

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