An application of cumulative prospect theory to travel time variability

Transcription

1 Katrine Hjorth (DTU) Stefan Flügel, Farideh Ramjerdi (TØI) An application of cumulative prospect theory to travel time variability Sixth workshop on discrete choice models at EPFL August 19-21, 2010 Page 1

2 Travel time variability (TTV) is increasingly acknowledged to be an important concern for both the users and the providers of transport services. The correct measurement of the perception of reliability and its value for the users are important in the design of transport policies It has been the getting more attention in research. The focus of this paper is on the the perception of reliability and its value for the users Page 2

3 Outline Travel time variability (TTV) Risk and TTV Rank Dependent Expected Utility (RDEU) Data Theoretical model Estimation results Summary / further work 26/08/10 Page 3 Institute of Transport Economics

4 Two competing approaches exist on travel time variability TTV Mean-Variance approach Scheduling approach Page 4

5 Risk and TTV Travel time variability is associated with risk Risk and its perception should be reflected in the valuation of reliability Bonsal (2004) de Palma, et al (2008) de Lapport (2009) Page 5

6 Rank Dependent Expected Utility (RDEU) Expected value maximisation (EVM) RDEU v(.) is a probability weighting function is a value function defined with respect to a reference point, typically concave for gains and convex for losses Page 6

7 Rank Dependent Expected Utility (RDEU) Descriptive theories of decision under risk depart from EVM in three essential ways: 1. the transformation of outcomes: Different functional forms to capture concave for gains and convex for losses 2. the transformation of probabilities: Examples: power, Quiggin, Perlec 3. the composition rule that combines the two transformations. Page 7

8 Data The New Norwegian Value of Time Study (2009) Large scale national study Self-administrated web SP survey Modes Long distance: Car, Rail, Bus and Air Short distance: Car and Public transportation (PT) 26/08/10 Page 8 Institute of Transport Economics

9 Presentation of TTV 2 alternative trips that differ in cost and a distinct travel time distribution Alternatives pivoted around a reported reference trip 6 choices for each respondent Page 9

10 Theoretical model Travel time distribution and Cost Relative to the reference travel time: negative values are interpreted as gains and positive values as losses Respondents choose the alternative that generates highest value Alternative 1 is chosen whenever Page 10

11 Following Tversky and Kahneman (1992)

12 Value functions Where :

13 In case of diminishing sensitivity Weights for gains are Weights for losses are If Loss aversion for If Loss aversion for

14 Decision weight Probability weights: Where and are weights, and Weighting functions: Prelec3, Prelec2, TK2, TK1, and No weights

15 PRELEC3, Prelec (1998) 3 parameters (convex, concave S-shaped, or inversely S-shaped) Page 15

16 PRELEC2 2 parameters (convex, concave S-shaped, or inversely S-shaped) Same shape for loss and gain Page 16

17 TK2 (Tvresky and Kahneman,1992) 2 parameters (Inversely S-shaped if and S-shaped if ) Page 17

18 TK1 As TK2, but the same shape for gain and loss Page 18

19 The model where Page 19

20 Assumptions Error term logistic with scale parameter independent across choices, including choices within individual binary logit Normalize cost parameter results from different models) to 1 (to directly compare The full model not identifies or very poorly identified The interactions of and or identification of Hence we imposed the restriction Page 20

21 Summary of statistics of the sample Segment Description Sample size Reference cost Reference time in min (Min,Mean,Max) in NOK (Min,Mean,Max) Car short Car trips less than 100km (10; 26,7;195) (8,4; 49,0; 396) PT short Public transport trips less than 100km 194 (10; 28,5; 90) (10; 33,1; 144) Car long Car trips longer than 100km. 603 (60; 184,9; 1045) (70; 457,1; 4430) Air Plane trips 809 (80; 192,5; 600) (150; 1289,1; 7500) Bus long Bus trips longer than 100km 443 (15; 247,9; 1439) (50; 279,6; 5000) Train long Train trips longer than 100km 551 (40; 252,5; 1319) (62; 336,7; 3598) Page 21

22 Distribution of outcomes on evaluation of w Car long Air Bus long Train long Car short PT short Gains Losses Gains Losses Gains Losses Gains Losses Gains Losses Gains Losses (0.2) - (0) (0.4) - (0) (0.4) - (0.2) (0.6) - (0.4) (0.8) - (0) (0.8) - (0.2) (0.8) - (0.6) (1) - (0.8) Total (gains,losses) Total Page 22

23 Estimation results, Prelec3 Page 23

24 Estimation results, Prelec2 Page 24

25 Estimation results, TK2 Page 25

26 Estimation results, TK1 Page 26

27 Estimation results, No weights Page 27

28 Estimated ration of to The ratio is between Ignoring PT the ratio is (Horowitz & McConnell, 2002) Lowest ratio is for TK2 and highest is for no weight Car short PT short Car long Air Bus long Train long Prelec3 2.2 *** 4.4 ** 1.9 *** 1.5 ** *** Prelec2 2.6 *** 4.4 *** 1.8 *** 1.7 *** 1.9 *** 2.4 *** TK2 1.4 *** *** 1.4 ** TK1 2.9 *** 8.9 *** 2.3 *** 1.6 *** 3.5 *** 4.6 *** No weighting 2.8 *** 10.2 *** 2.6 *** 1.8 *** 4.3 *** 5.9 *** Page 28

29 Value function for time, Perlec3 Page 29

30 Value function for cost, Perlec3 Page 30

31 Value function for time, TK2 Page 31

32 Value function for cost, TK2 Page 32

33 Value function for time, No weight Page 33

34 Value function for cost, No weight Page 34

35 Weight function for time for gains, Prelec3 Page 35

36 Weight function for losses, Prelec3 Page 36

37 Weight function, Prelec2 Page 37

38 Value function for gains, TK2 Page 38

39 Value function for losses, TK2 Page 39

40 Value function, TK Page 40

41 Conclusions is the curvature parameter for value function for time diminishing sensitivity to time changes. is lowest for Prelec3 &2 more convex(concave) functions in the gain (loss) regions and are almost invariant across weighting schemes is always smaller than and similar in size Insufficient data to identify the high end of weigh functions Page 41

42 Conclusions Overall results consistent across the 6 databases Significant loss aversion with respect to travel time ( ) No significant loss aversion with respect to cost The w(.) produce significant behavioral improvements Considerable differences in the shape of probability weighting function. Low probabilities are over-weighted for losses The problem with our data set. Majority of our observations (80%) involve w evaluated at 0.2 and 0.4. Hence the weigh function is estimated based on low probability data Page 42

43 Conclusions It is possible to estimate VTT by this approach. The estimated VTT should capture the value of travel time variability In the first experiment in the Norwegian study time has only one value, i.e., there is no variability of time. The difference between these two VTT should be related to the value of travel time variability. Page 43