A DYNAMIC DISCRETE-CONTINUOUS CHOICE MODEL FOR CAR OWNERSHIP AND USAGE ESTIMATION PROCEDURE

Transcription

1 A DYNAMIC DISCRETE-CONTINUOUS CHOICE MODEL FOR CAR OWNERSHIP AND USAGE ESTIMATION PROCEDURE Aurélie Glerum EPFL Emma Frejinger Université de Montréal Anders Karlström KTH Muriel Beser Hugosson KTH Michel Bierlaire EPFL 14 th Swiss Transport Research Conference 15 th May 2014

2 OUTLINE 2 Introduction Contributions Model specification & estimation Swedish registers Estimation on synthetic & real data Conclusion and future works

3 INTRODUCTION 3 Objective Model households simultaneous choices of car ownership, usage and fuel type, assuming they are forward-looking.

4 INTRODUCTION 4 Objective Model households simultaneous choices of car ownership, usage and fuel type, assuming they are forward-looking. Motivations for a dynamic model Governmental policies to reduce carbon emissions / car usage (e.g. congestion taxes, independence of fossil fuels, ) Technology changes (e.g. increase of alternative-fuel vehicles) Variations in economic factors (e.g. fuel price changes)

5 INTRODUCTION 5 Objective Model households simultaneous choices of car ownership, usage and fuel type, assuming they are forward-looking. Motivations for a dynamic model Governmental policies to reduce carbon emissions / car usage (e.g. congestion taxes, independence of fossil fuels, ) Technology changes (e.g. increase of alternative-fuel vehicles) Variations in economic factors (e.g. fuel price changes) Case study: Swedish registers of vehicles and individuals

6 INTRODUCTION 6 Objective Model households simultaneous choices of car ownership, usage and fuel type, assuming they are forward-looking. # cars Transaction type Annual driving distance Fuel type km

7 INTRODUCTION 7 Transaction type (0-, 1-, 2-car households)

8 INTRODUCTION 8 Objective Model households simultaneous choices of car ownership, usage and fuel type, assuming they are forward-looking. # cars Transaction type Annual driving distance Fuel type km

9 INTRODUCTION 9 Objective Model households simultaneous choices of car ownership, usage and fuel type, assuming they are forward-looking. # cars Transaction type Annual driving distance Fuel type km Discrete variables

10 INTRODUCTION 10 Objective Model households simultaneous choices of car ownership, usage and fuel type, assuming they are forward-looking. # cars Transaction type Annual driving distance Fuel type km Continuous variables

11 CONTRIBUTIONS 11 The method brings together 3 complex aspects of demand modeling Dynamic discrete choice modeling for forward-looking agents Discrete-continuous choice modeling Household decisions for multiple (car) holdings

12 CONTRIBUTIONS 12 The method brings together 3 complex aspects of demand modeling

13 CONTRIBUTIONS 13 The method brings together 3 complex aspects of demand modeling Methodology Address these issues by applying dynamic discrete-continuous choice model (DDCCM) Discrete-continuous choice model Embedded into a dynamic programming framework

14 CONTRIBUTIONS 14 The method brings together 3 complex aspects of demand modeling Methodology Address these issues by applying dynamic discrete-continuous choice model (DDCCM) Discrete-continuous choice model Embedded into a dynamic programming framework Application example Large register data of all individuals and cars in Sweden Approach validated on synthetic data Estimation on real data

15 MODEL SPECIFICATION 15 ASSUMPTIONS 1. Choice at household level: up to 2 cars in household 2. Strategic choice of: Transaction Fuel type(s) Account for forward-looking behavior of households 3. Myopic choice of: Annual driving distance(s)

16 MODEL SPECIFICATION 16 ASSUMPTIONS Myopic choice (static case) Strategic choice (dynamic case)

17 MODEL SPECIFICATION DEFINITION OF THE COMPONENTS 17 Components of the DDCCM Agent Time step State space Action space Transition rule Instantaneous utility function

18 MODEL SPECIFICATION DEFINITION OF THE COMPONENTS 18 Components of the DDCCM Agent Time step State space Action space Fundamental components in a dynamic programming framework Transition rule Instantaneous utility function

19 MODEL SPECIFICATION DEFINITION OF THE COMPONENTS 19 Agent: household Time step t: year State space S Age Age Action space A Transaction type Mileage Mileage Transition rule: deterministic rule: each state s t+1 can be inferred exactly once s t and a t are known.

20 MODEL SPECIFICATION DEFINITION OF THE COMPONENTS 20 Agent: household Time step t: year State space S Age Age Action space A Transaction type Mileage Mileage Transition rule: deterministic rule: each state s t+1 can be inferred exactly once s t and a t are known.

21 MODEL SPECIFICATION DEFINITION OF THE COMPONENTS 21 Agent: household Time step t: year State space S Age Age Action space A Transaction type Mileage Mileage Transition rule: deterministic rule: each state s t+1 can be inferred exactly once s t and a t are known.

22 MODEL SPECIFICATION DEFINITION OF THE COMPONENTS 22 Agent: household Time step t: year State space S Age Age Action space A Transaction type Mileage Mileage Transition rule: deterministic rule: each state s t+1 can be inferred exactly once s t and a t are known.

23 MODEL SPECIFICATION DEFINITION OF THE COMPONENTS 23 Agent: household Time step t: year State space S Age Age Action space A Transaction type Mileage Mileage Transition rule: deterministic rule: each state s t+1 can be inferred exactly once s t and a t are known.

24 MODEL SPECIFICATION DEFINITION OF THE COMPONENTS Instantaneous utility function Deterministic utility 24 Utility for the acquisition Constant elasticity of substitution (CES) utility function Utility of driving Choice probability Expected discounted utility

25 MODEL ESTIMATION 25 Parameters obtained by maximizing likelihood: Optimization algorithm: Rust s nested fixed point algorithm (NFXP) (Rust, 1987): Outer optimization algorithm: search algorithm to obtain parameters maximizing likelihood Inner value iteration algorithm: solves the dynamic programming problem for each parameter trial

26 MODEL ESTIMATION 26 Outer algorithm Standard estimation procedure (as for static discrete choice models) Here: BHHH algorithm Inner algorithm Two steps 1. Finding the optimal value(s) of annual mileage conditional on the discrete choices 2. Finding the expected discounted utility of future choices (= value function) Reasons of step 1.

27 MODEL ESTIMATION Finding the optimal value(s) of mileage (e.g. 2-car households with different fuel types) C Maximization of the continuous utility: max v t m g,t,m d,t Find analytical solutions m g,t and m d,t. Optimal continuous utility v C t (s t, a D t, a C t, x t, θ) s.t. p g,t m g,t + p d,t m d,t = IIc t 2. Finding the expected discounted utility of future choices (= value function) Logsum formula can be applied here given the key assumptions: Choice of mileage(s) is conditional on discrete actions Choice of mileage(s) is myopic V s t, x t, θ = log exp {v t D s t, a t D, x t, θ + v t C s t, a t D, a t C, x t, θ + β V s t+1, x t+1, θ f(s t+1 s t, a t )} a t D s t+1 S Iterate on Bellman equation to find integrated value function V

28 MODEL ESTIMATION Finding the optimal value(s) of mileage (e.g. 2-car households with different fuel types) C Maximization of the continuous utility: max v t m g,t,m d,t Find analytical solutions m g,t and m d,t. Optimal continuous utility v C t (s t, a D t, a C t, x t, θ) s.t. p g,t m g,t + p d,t m d,t = IIc t 2. Finding the expected discounted utility of future choices (= value function) Logsum formula can be applied here given the key assumptions: Choice of mileage(s) is conditional on discrete actions Choice of mileage(s) is myopic V s t, x t, θ = log exp {v t D s t, a t D, x t, θ + v t C s t, a t D, a t C, x t, θ + β V s t+1, x t+1, θ f(s t+1 s t, a t )} a t D s t+1 S Iterate on Bellman equation to find integrated value function V

29 SWEDISH REGISTERS 29 Register data of Swedish population and car fleet Data from 1998 to 2008 All individuals Individual information: socio-economic information on car holder (age, gender, income, home/work location, employment status/sector, etc.) Household information: composition (families with children and married couples) All vehicles Vehicle characteristics (make, model, fuel consumption, fuel type, age) Annual mileage from odometer readings Privately-owned cars, cars from privately-owned company and company cars Car bought new or second-hand

30 ESTIMATION ON SYNTHETIC DATA 30 Approach to validate the model framework Generate 5000 observations (households) based on distributions of variables in the Swedish register data Generate choice (for each observation) based on postulated parameters (10 different samples generated) Estimation of model on 10 samples Approach validated once postulated parameters are retrieved

31 ESTIMATION ON SYNTHETIC DATA 31 Statistics on the Swedish register

32 ESTIMATION ON SYNTHETIC DATA 32 Assumptions for the example Deterministic utility function Transaction costs Transaction-dependant parameters relative to age of oldest car Chose arbitrary values for parameters

33 ESTIMATION ON SYNTHETIC DATA 33

34 ESTIMATION ON SYNTHETIC DATA 34 Outcomes from synthetic data Rho t-test true value Value SD Age 1 car 2 cars Dispose/change Dispose/change oldest car t-test t-test t-test true t-test true 0 value Value SD 0 value Run Value SD t-test 0 Synthetic data True value Initial value Real data Initial value Transaction cost Neg L Increase of 1 Dispose of 1 and change the other / change 1 Run Value SD t-test 0 t-test true value Value SD t-test 0 t-test true value Synthetic data True value -3-4 Initial value -3-4 Real data Initial value Tolerance synthetic data: 0.01 Tolerance real data: 0.8

35 ESTIMATION ON REAL DATA 35 Outcomes from real data Subsample of 446 households from merged registers of individuals and cars in Sweden 3431 observations

36 ESTIMATION ON REAL DATA 36 Outcomes from real data Rho t-test true value Value SD Age 1 car 2 cars Dispose/change Dispose/change oldest car t-test t-test t-test true t-test true 0 value Value SD 0 value Run Value SD t-test 0 Synthetic data True value Initial value Real data Initial value Transaction cost Neg L Increase of 1 Dispose of 1 and change the other / change 1 Run Value SD t-test 0 t-test true value Value SD t-test 0 t-test true value Synthetic data True value -3-4 Initial value -3-4 Real data Initial value Tolerance synthetic data: 0.01 Tolerance real data: 0.8

37 CONCLUSION AND FUTURE WORKS 37 Contributions Integrate three complex aspects of demand Forward-looking decision-makers Discrete-continuous choice: both fixed and operational costs are accounted for. Household decisions for multiple-car fleets Next steps Further specification testing on the subsample of real data from Swedish registers Improvement of the optimization algorithm Scenario testing Validation of policy measures taken during the years available in the data Test policy measures that are planned to be applied in future years

38 Thank you! 38

39 MODEL ESTIMATION 39 Reasons of step 1. Likelihood for the full model L = P D C f C dd D = discrete variables C = continuous variables Back