econometric issues in estimating consumer preferences from stated preference data: a case study of...
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Econometric Issues in Estimating Consumer Preferences from Stated Preference Data:
a Case Study of the Value of Automobile Travel Time
The Review of Economics and Statistics (2001), 83(4): 699-707
John Calfee, Clifford Winston, Randolph Stempski**American Enterprise Institute, Brookings Institution, American Enterprise
Institute
Jetpan Wetwitoo, Tao Yu, Le Thi Thuong,
Aung Ko Min, Kyoko Matsui
2BackgroundA stated preference framework is important in marketing.
PurposeEvaluation of the models presenting ordered preference using SP survey on value of congested time
MethodologyComparison in ordered probit, rank-ordered logit, mixed logit and partially ranked model, using data on respondents’ ratings and rankings of alternatives.
Author’s ConclusionMixed logit model is the best, because there are anchoring problem in rating data and spacing problem in ranking data.
Our method: ordered logit
Survey --- ranking & rating stated preference from 1,170 samples 3
1 scenario
13 packages
Make rating & ranking
Rating Ranking
Package 1 1 points 13th
Package 2 9 points 1st
Package 3 8 points 2nd
… … …
Package 13
5 points 3rd
Preference statement
1.Rank-ordered logit with ranking data
2.Ordered probit with rating data3.Mixed logit with ranking data
4.Estimation results
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Rank-ordered logit with ranking data
• Utility function of alternativej for individuali• Ranking: • Probability of the ranking:
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1st: Package 22nd: Package 313th: Package 1
Infinite product of ordinal MNLs!
Ranking
Package 1 13th
Package 2 1st
Package 3 2nd
… …
Package 13
3rd
1.Rank-ordered logit with ranking data
2.Ordered probit with rating data3.Mixed logit with ranking data
4.Estimation results
6
Ordered probit with rating data 1/2 7
Rate (points) for alternative j
Threshold for the rate k
Probability that alternative j is given with rate k :
cumulative normal distribution function
Rating
Package 1 1 points
Package 2 9 points
Package 3 8 points
… …
Package 13
5 points
Ordered probit with rating data 2/2 8
0 𝜇1 𝜇2 𝜇3 𝜇𝐾− 2𝜇𝐾− 1
k=1 k=3k=2 k=K-1k=0
k=K
High utility
Probability distribution of utility for alternativej
Rate (points)
Average:
Low utility
1.Rank-ordered logit with ranking data
2.Ordered probit with rating data3.Mixed logit with ranking data
4.Estimation results
9
Mixed logit with ranking data
• Utility function of alternativej for individuali
• Probability of the ranking:
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:randomly distributed across the population
a certain probability distribution function ex) log-normal
true parameters describing the distribution
Expected probability at a certain
integrate No closed-form
Brownstone & Train, 1999
1.Rank-ordered logit with ranking data
2.Ordered probit with rating data3.Mixed logit with ranking data
4.Estimation results
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Estimation results 1/2 12
… …
Ordered probit Rank-ordered logit
! Positive coefficients on cost & time ! More stable
:Analysis with ranking data is more reliable.
Estimation results 2/2 13
Mixed logit※ should be multiplied by -1
Hyper parameters are distributing
Willingness to Pay for toll=Value of congested time Dollars/hour
might-be causes
Ordered probit“anchoring”
problem
Rank-ordered logit“spacing” problem
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Rating by A
Rating by B
Package 1 1 point 3 points
Package 2 9 points 10 points
Package 3 8 points 9 points
… … …
Package 13
5 points 7 points
Rating Ranking
Package 1 1 points 13th
Package 2 9 points 1st
Package 3 8 points 2nd
… … …
Package 13
5 points 3rd
A & B have same rankingbut different rating:
“5 points” might be different for A & B!
Estimations: unstable
1 rank
1 rank
1 pt
3 pt
Rank-ordered model assumesame intervals among ranks.
Regardless of his degree of preference!
1st
2nd
3rd
13th
1st
2nd
3rd
13th
“anchoring” problem effect on our project?Q. How difficult do you feel it is to find the correct route by using this map?
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3D Japanese map 2D English map
Mr. A Ms. B Mr. A Ms. B
Extremely easy ●
Quite easy ●
Somewhat easy ○
Somewhat difficult
○
Quite difficult
Extremely difficult
Difference of anchoring EXISTS in our problem statement
1st
2nd
1st
2nd
Conclusion & Implications
demerits merits
Ordered probit “anchoring” problem
WITH anchoring problem
Less spacing problemLow calculation cost
Rank-ordered logit “spacing” problem No anchoring problem
Low calculation cost
Mixed logitCalculation costUncertainty in distribution of
No anchoring problemReproducibility
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