Beia Spiller (Duke University) How Gasoline Prices Impact Household Driving and Auto Purchasing...

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How Gasoline Prices Impact Household Driving and Auto Purchasing Decisions A Revealed Preference Approach
How Gasoline Prices Impact Household Driving and Auto Purchasing Decisions
A Revealed Preference ApproachBeia Spiller
Duke UniversityOctober 2010
Research funded by Resources for the Futures Joseph L. Fisher Doctoral Dissertation Fellowship
10/1001 / 38Beia Spiller (Duke University)Policy RelevanceConsumer response to changing gasoline pricesClimate changeAir pollutionCongestionNational security concerns
10/1002 / 38Beia Spiller (Duke University)Elasticity of Demand for GasolineAccurately measuring the elasticity of demand for gasolineImportance in climate policy modelsEconomic incidence of gasoline tax  burden falls on consumers or producersOptimal gasoline taxPrior studies range of elasticities: 0.02 to 1.59Espey (1996): data, econometric technique, demand specification, assumptions10/1003 / 38Beia Spiller (Duke University)VMT Demand/Gasoline Prices
10/1004 / 38Beia Spiller (Duke University)Gasoline Prices/Truck DemandGraph From Klier and Linn (2008)
10/1005 / 38Beia Spiller (Duke University)
Change in SUV/car sales10/1006 / 38Taken from US DOE website, 2008Beia Spiller (Duke University)Elasticity of Demand for GasolineDownward bias/Misspecification due to:AssumptionsResearch Methods
10/1007 / 38Beia Spiller (Duke University)Model Objectives and InnovationsIncorporate the following into measurement of gasoline demand elasticity:Extensive and Intensive Margin (vehicle purchase decision and VMT)Type of vehicle Amount of drivingEstimate jointly:Model choiceFleet sizeDriving demandHousehold fleets VMT decisions jointly determinedAllocation of VMT between vehiclesSubstitution as relative operating costs a;slkjf;alskjsfajkfe;lkjfda;lkjds;lkjf asdflkjas10/1008 / 38Beia Spiller (Duke University)Model Objectives and InnovationsIncorporate the following into measurement of gasoline demand elasticity:Extensive and Intensive Margin (vehicle purchase decision and VMT)Type of vehicle Amount of drivingEstimate jointly:Model choiceFleet sizeDriving demandHousehold fleets VMT decisions jointly determinedAllocation of VMT between vehiclesSubstitution as relative operating costs changeHensher (1985), Berkowitz et.al. (1990): 2 and 3 car households more elastic10/1008 / 38Beia Spiller (Duke University)Model Objectives and InnovationsVehicle Fixed EffectsUnobserved vehicle attributes affect purchase decisionBerry, Levinsohn, and Pakes (1995): no fixed effects biases price coefficientUnobserved attributes (style) make individuals appear less price sensitive
10/1009 / 38Beia Spiller (Duke University)Model Objectives and InnovationsVehicle Fixed EffectsUnobserved vehicle attributes affect purchase decisionBerry, Levinsohn, and Pakes (1995): no fixed effects biases price coefficientUnobserved attributes (style) make individuals appear less price sensitive
Detailed choice setTo capture subtle changes in vehicle purchase decisionAggregate choice set wont capture movement within the aggregation (i.e. Ford Taurus > Honda Civic)10/1009 / 38Beia Spiller (Duke University)Methodological HurdleHigh dimensionality of choice set3,751 types of vehicles (modelyear) in datasetIf households can choose 2: 7,033,125 possible choicesIf households can choose 3: 8,789,061,875 possible choicesTypical logit, probit models do not allow for such high dimensionality10/1010 / 38Beia Spiller (Duke University)Proposed MethodRevealed preference approach:Observed household vehicle holdings is equilibrium, provides maximum utilityAny 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 effects10/1011 / 38Beia Spiller (Duke University)OutlineLiterature ReviewModel MethodUnobserved Consumer HeterogeneityDataResultsConclusion
10/1012 / 38Beia Spiller (Duke University)Literature ReviewExtensive/intensive margins estimated independentlyWest (2007), Klier and Linn (2008), Schmalensee and Stoker (1999)Twostep sequential estimation of extensive/intensive marginsWest (2004), Goldberg (1998)One step approachBerkowitz et al. (1990), Feng, Fullerton, and Gan (2005), Bento et al. (2008)Fleet modelGreen and Hu (1985)
10/1013 / 38Beia Spiller (Duke University)ModelPervehicle subutility (additively separable in total utility):
i: householdj: vehicleVMTij = Vehicle Miles Travelled per yearXj : observable attributes of vehicle j : unobservable attributes of vehicle j
10/1014 / 38Beia Spiller (Duke University)ModelMarginal utility of driving:
Zi : Household i's attributesni : Number of vehicles in household is garage diminishing marginal returns of use as number of vehicles in garage increasesFixed effects:
10/1015 / 38
Beia Spiller (Duke University)ModelMarginal utility of driving:
Zi : Household i's attributesni : Number of vehicles in household is garage diminishing marginal returns of use as number of vehicles in garage increasesFixed effects:
Thus:
10/1015 / 38
Beia Spiller (Duke University)Model: Utility Maximization : household income : vehicle js used price (opportunity cost of not selling): operating cost ($/mile): price of consumption = 1
10/1016 / 38++=+=jjicijdijjijiijicPVMTPPytscuUcVMT..,maxrBeia Spiller (Duke University)19Model: Utility MaximizationInterdependence of vehicles in fleet:
Indirect Utility
10/1017 / 38
Beia Spiller (Duke University)EstimationTwo steps:Difference out fixed effects, estimate , , Recapture fixed effects, estimate
10/1018 / 38Beia Spiller (Duke University)First Stage Estimation: SwappingAssumption 1: Household in equilibrium with vehicle purchase and VMT decision : Fleet chosen by household iTwo households, 1 and 2, have vehicles A, B respectively:
Thus:
10/1019 / 38Beia Spiller (Duke University)First Stage Estimation: SwappingAssumption 1: Household in equilibrium with vehicle purchase and VMT decision : Fleet chosen by household iTwo households, 1 and 2, have vehicles A, B respectively: For Household 1 For Household 2
Thus:
10/1019 / 38Beia Spiller (Duke University)First Stage Estimation: SwappingAssumption 1: Household in equilibrium with vehicle purchase and VMT decision : Fleet chosen by household iTwo households, 1 and 2, have vehicles A, B respectively: For Household 1 For Household 2
Thus:
10/1019 / 38
Beia Spiller (Duke University)First Stage EstimationMaximum Likelihood:
Normalization:
10/1020 / 38Beia 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 utilitiesCalculate objective function (summed log of differences)Find that increases objective functionRepeat until convergence
10/1021 / 38Beia 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 utilitiesCalculate objective function (summed log of differences)Find that increases objective functionRepeat until convergence10/1021 / 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 utilitiesCalculate objective function (summed log of differences)Find that increases objective functionRepeat until convergence10/1021 / 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 utilitiesCalculate objective function (summed log of differences)Find that increases objective functionRepeat until convergence
10/1021 / 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 utilitiesCalculate objective function (summed log of differences)Find that increases objective functionRepeat until convergence
10/1021 / 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 utilitiesCalculate objective function (summed log of differences)Find that increases objective functionRepeat until convergence
10/1021 / 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 utilitiesCalculate objective function (summed log of differences)Find that increases objective functionRepeat until convergence
10/1021 / 38
Beia Spiller (Duke University)Unobserved Consumer HeterogeneityIncorporate observed driving behavior into estimation
Contraction mapping: at each stage of iteration, solve
10/1022 / 38
Beia Spiller (Duke University)Unobserved Consumer HeterogeneityGuess at parameter vectorFind that minimizes distance between observed and optimal Calculate given , Find new parameter vector that maximizes objective function.Repeat steps 24 until convergence.
10/1023 / 38Beia Spiller (Duke University)Unobserved Consumer HeterogeneityGuess at parameter vectorFind that minimizes distance between observed and optimal Calculate given , Find new parameter vector that maximizes objective function.Repeat steps 24 until convergence.
10/1023 / 38Beia Spiller (Duke University)Unobserved Consumer HeterogeneityGuess at parameter vectorFind that minimizes distance between observed and optimal Calculate given , Find new parameter vector that maximizes objective function.Repeat steps 24 until convergence.
10/1023 / 38Beia Spiller (Duke University)Unobserved Consumer HeterogeneityGuess at parameter vectorFind that minimizes distance between observed and optimal Calculate given , Find new parameter vector that maximizes objective function.Repeat steps 24 until convergence.
10/1023 / 38Beia Spiller (Duke University)Unobserved Consumer HeterogeneityGuess at parameter vectorFind that minimizes distance between observed and optimal Calculate given , Find new parameter vector that maximizes objective function.Repeat steps 24 until convergence.
10/1023 / 38Beia Spiller (Duke University)Second Stage EstimationAssumption 2: Net subutility of jth vehicle > 0Assumption 3: jth + 1 vehicle decreases total utilityThus:
Rewriting:
10/1024 / 38Beia Spiller (Duke University)Second Stage EstimationAssumption 2: Net subutility of jth vehicle > 0Assumption 3: jth + 1 vehicle decreases total utilityThus:For Household 1For Household 2Rewriting:
10/1024 / 38Beia Spiller (Duke University)Second Stage EstimationAssumption 2: Net subutility of jth vehicle > 0Assumption 3: jth + 1 vehicle decreases total utilityThus:For Household 1For Household 2Rewriting:
10/1024 / 38Beia Spiller (Duke University)Second Stage EstimationFor Household 1:
For Household 2:
10/1025 / 38Beia Spiller (Duke University)Second Stage EstimationMaximum Likelihood:
OLS:
10/1026 / 38Beia Spiller (Duke University)43Second Stage EstimationMaximum Likelihood:
OLS:
10/1026 / 38Beia Spiller (Duke University)Second Stage Estimation: OverviewFor each type of vehicle:Find all households who own it: positive subutility from owning it.Find all households who dont own it: adding this vehicle decreases utility.Form maximum likelihood over (1) and (2)Estimate fixed effect for this vehicleRun OLS of all FE on vehicle characteristics10/1027 / 38Beia Spiller (Duke University)DataHousehold level data: National Household Transportation Survey 2001 and 2009
10/1028 / 38NHTS 2001NHTS 2009National SampleFull Sample26,038 households143,084 households53,275 observations309,163 observationsFinal SampleFinal Sample11,354 households11,366 households18,166 observations18,305 observationsBeia Spiller (Duke University)Data: NHTS Summary StatisticsFull SampleFinal Sample% White 87%85%% Urban70%79%Average Family Income$55,832$56,338Average Household Size2.822.66Average Workers to Vehicles0.650.72Average Fleet Size2.692.04Average MPG25.7225.87Average Vehicle Age (years)8.497.21Average Yearly VMT10,99511,59410/1029 / 38Beia Spiller (Duke University)Data: VehiclesVehicle characteristic data: Polk, Wards Automotive YearbookProvides detailed information on 6,594 vehicles 19712009Used vehicle prices: NADAProvides used prices of vehicles in 2001 (19822002), 2009 (1992 2010)10/1030 / 38Beia Spiller (Duke University)Data: Gasoline PricesAmerican Chamber of Commerce Research Association (ACCRA) 2001, 2009 dataprovides gas prices at the city levelyearly averagesaggregate to MSA
MSAGas Prices 2001Gas Prices 2009Oklahoma City, OK1.232.07Houston, TX1.342.34Raleigh, NC1.392.47Chicago, IL1.502.73Philadelphia, PA1.562.53San Francisco, CA1.922.8010/1031 / 38Beia Spiller (Duke University)Data: Gasoline Prices10/1032 / 38Beia Spiller (Duke University)Results: First StageInteraction TermParameter Value (Std. Err.)Marginal Utility of Driving Parameters(HP/weight) * urban2.341*** (0.055)Vehicle Size * household size0.252* (0.147)Wheelbase* urban 0.051 (1.531)Household size/# vehicles 0.166 (0.353)***: significant at 99% level, *: significant at 90%10/1033 / 38Beia Spiller (Duke University)Results: First StageInteraction TermParameter Value (Std. Err.)Indirect Utility of Driving Parameters
Green* income0.063 (0.268)Green* Pacific0.124 (1.147)Green*New England0.731** (0.347)Size* Income0.547*** (0.146)Size* Pacific1.703*** (0.220)Size* Mountain2.085*** (0.204)Domestic* Income0.101 (0.439)Domestic*Midwest (WNC)2.147*** (0.142)Domestic*Midwest (ENC)1.118*** (0.168)European* Income0.989*** (0.137)Japanese* Income0.495*** (0.149)Japanese* Pacific1.170*** (0.161)Vehicle Age* Income0.037 (0.144)Size* Urban2.021*** (0.154)(***: statistically significant at 99%, **: statistically significant at 95%, *: statistically significant at 90%)
10/1034 / 38Beia Spiller (Duke University)Results: First Stage
CoefficientParameter Value (Std. Err.)CES Parameter0.456*** (0.084)Std. Dev. Of Error Term1.539*** (0.517)Elasticity of Demand for Gasoline, Price = 1%1.277*** (0.219)(***: statistically significant at 99%)
10/1035 / 38Beia Spiller (Duke University)Results: Second Stage EstimationOLS Regression
Parameter Value (Std. Err.)Constant 16.086*** (1.231)Green0.869** (0.321)Vehicle Size1.081*** (0.435)Domestic2.941*** (1.012) European1.181* (0.876)Japanese7.777*** (1.452)Vehicle Age0.512*** (0.035)R20.675 (***: statistically significant at 99%, **: statistically significant at 95%, *: statistically significant at 90%)10/1036 / 38Beia Spiller (Duke University)Measuring the BiasUnobserved heterogeneity:Elasticity = 1.108, 15.3% bias (+)Independence assumption:Elasticity = 1.123, 12.1% bias ()Aggregation assumption:Elasticity = 1.003, 21.5% bias ()Independence and aggregation:Elasticity = 0.992, 22.3% bias. ()10/1037 / 38Beia Spiller (Duke University)ConclusionDemand for gasoline is elasticBias due to assuming independence and aggregating the choice setHousehold choices are better representedDiscretecontinuous household portfolio modelEstimation method does not artificially restrict choice set
10/1038 / 38Beia Spiller (Duke University)10/1026 / 28Thank you!Any Questions?Beia Spiller (Duke University)57Starting Values for First StageMinimize distance given observed and optimal VMT, calculate that solves:
2. Hold fixed, calculate to solve likelihood function3. Use and as the full set of starting values.
Beia Spiller (Duke University)Indirect Utility FunctionAssumptions:Constant MRS between vehicles =1 due to static nature of modelAdditive separability in and Nonlinear in Nonseparable in Composite error term
Beia Spiller (Duke University)McFadden et.al. (1978)Subsampling of AlternativesIIA property > parameter estimates off random sample of choices statistically equal to whole choice set estimatesRed bus/blue bus problem in logit errors/IIAIn bundle application: errors are bundle specificSwapping: prior to swaps, errors are iid. Han (1987) : cross sectional error terms iid, then consistency in pairwise estimation
Beia Spiller (Duke University)