A Quantitative Measurement of Regret Theory

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A Quantitative Measurement of Regret Theory
Alessandra Cillo
Joint work with Han Bleichrodt
Enrico Diecidue Erasmus University
INSEAD
FUR XII, Rome, June 23, 2006
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Presentation Outline

• Background on Regret Theory
• Methodology
• Experiment
• Results Discussion

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Background on Regret Theory

• Regret Theory (RT)
• - Mathematically (Bell 1982, Loomes Sugden
  1982, 1987) and psychologically (Larrick 1993,
  Zeelenberg 1996, 1999) sound
• - Important theory consistent with
  violations of transitivity

• Empirical studies to support RT
• - Many but event splitting effects
  confounded results (Starmer Sugden 1993)

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Regret Theory

• Under RT (Bell 1982, Loomes Sugden 1982)
• About
• Intuition net advantage of choosing f rather
  than g if state of nature j occurs
• Properties of Q() increasing, skew-symmetric,
  convex

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Contribution

• First quantitative measurement of RT
• - New methodology to test the convexity
  assumption

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Presentation Outline

• Background on Regret Theory
• Methodology
• Experiment
• Results Discussion

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Methodology

• Two stages

First stage elicitation of u() Tradeoff method
(Wakker Deneffe 1996) to determine a sequence
of outcomes equally spaced in terms of utility
Second stage elicitation of Q() Use the
standard sequence of outcomes to elicit Q
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Elicitation Procedure

• First Stage u() s.t. f g
• Second Stage Q() with chained procedure
  s.t. f g

f
g

f
g
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Presentation Outline

• Background on Regret Theory
• Methodology
• Experiment
• Results Discussion

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Experiment

• Subjects and Stimuli
• - 82 undergraduate students from Erasmus
  University
• - Flat fee of 10 plus 10 chance to play
  one of the choices for real
• Procedure
• - Computer based, 2 experimenters for max 4
  subjects, 30 minutes on average
• - Choice task, 5 iterations, zooming in
  process

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Experiment First Stage
Example of a screen in the first stage

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Experiment Second Stage

• Example of a screen in the second stage

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Presentation Outline

• Background on Regret Theory
• Methodology
• Experiment
• Results Discussion

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Results for u()

• Power coefficient based on median data is 0.96
  (p0.106)
• 
  

• Median of individual estimates of the power
  coefficient is 0.94
• 
  

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Results for Q()

• Median of individual exponential estimates is
  0.19
• 
  

• Exponential coefficient based on median data is
  0.45 with (p0.043)
• 
  

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Q() on 0,2/5 and 1/5,1
Subdomain 1/5,1
Subdomain 0,2/5

• Exponential coefficient based on median data is
  1.01

• Exponential coefficient based on median data is
  -1.28

• Median of individual exponential estimates is
  -1.28
• 
  

• Median of individual exponential estimates is
  1.13
• 
  

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Robustness of Results
Normal Procedure Consistency Checks




Asymp. Sig. (2-tailed) 0.01 0.205 0.767
Wilcoxon signed ranks tests. Upper row indicates
alternative hypotheses

• When exclusion of 16 most risk seeking subjects
  no major changes
• Effect of response error small for both u() and
  Q()

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Conclusions

• Linearity of u()
• - Not surprising for a nonexpected utility
  model (Tversky Kahneman 1992, Abdellaoui
  2000, Abdellaoui et al. 2005)
• Concavity on 0,2/5
• - Anchoring might be a plausible
  explanation
• Convexity on 1/5,1

• Take home contributions
• - First to make RT quantitatively observable
• - We do not believe that utility and
  regret are the only factors that influence
  behaviour under uncertainty, but just that these
  factors seem particularly significant. (Loomes
  Sugden 1982, p. 819)
  

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Thank you!
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First Stage Elicitation of u()

• Applying RT and because Q() is increasing
• By eliciting indifferences between
  
• Setting

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Second Stage Elicitation of Q()

• By eliciting indifferences between
  and applying RT
• Disadvantages
• - Highly sensitive to response error when
  is close to zero
• - Small indifference probabilities lead to
  skewed error distributions

Direct Procedure for Q(j/k), j2,..,k
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Second Stage Elicitation of Q()

• By eliciting indifferences between
  and applying RT
• Disadvantage
• - Sensitive to error propagation but we can
  control for this

Chained Procedure for Q(j/k), j2,..,k
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First Stage Randomization
1st It. Filler 2nd It. 3rd It. Filler 4th It. 5th It. Filler 1st It. Rep.
1 2 3 4 5 6 7 8 9
If 1st It. Rep. 1st It. then stop, otherwise
Filler 2nd It. 3rd It. Filler 4th It. 5th It. Filler 1st It. Repeated
10 11 12 13 14 15 16 17
If 1st It. Repeated 1st It. Rep. then stop,
otherwise
Filler 2nd It. 3rd It. Filler 4th It. 5th It. Filler 1st It. Rep.
18 19 20 21 22 23 24 25
Then stop and take the elicited value. This is
true for every with j1,..5
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Second Stage Randomization

1st Iteration 4 2 1 3
2nd Iteration 6 5 7 8
3rd Iteration 9 11 12 10
4th Iteration 15 13 14 16
5th Iteration 20 19 18 17
1st Iteration Rep. 21 24 23 22
If 1st Iteration Rep. 1st Iteration then stop,
otherwise

2nd Iteration 25
3rd Iteration 26
4th Iteration 27
5th Iteration 28
1st Iteration Repeated 29

2nd Iteration 30
3rd Iteration 31
4th Iteration 32
5th Iteration 33
1st Iteration Repeated 34
If 1st Iteration Repeated 1st Iteration Rep.
then stop, otherwise
Then stop and take the elicited with
j2,..,5
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Three Consistency Checks
Normal Procedure Consistency Checks



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Elimination of Subjects

• 16 for extreme risk-aversion
• 2 for violation of monotonicity
• 8 for violation of stochastic dominance, i.e.
• 
  

33 67
f 100
g 40
67 33
f 400 200
g 200 300
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Analyses for u()

• Curvature of u() at individual level
• Specific parametric assumptions about u()
• 
  

Concavity if for at least 12 out of 20 values
Linearity if for at least 12 out of 20 values
Convexity if for at least 12 out of 20 values
Power coefficient r
Concave If r sign. lt 1
Linear If r sign. 1
Convex If r sign. gt 1
Power coefficient r
Concave r lt 0.95
Linear 0.95 r 1.05
Convex r gt 1.05
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Analyses for Q()

• Curvature of Q() at individual level
• Specific Parametric Assumptions about Q()
• 
  

0,1 1/5,1
Concave lt0 for at least 12 out of 20 values for at least 6 out of 10 values
Linear 0 for at least 12 out of 20 values for at least 6 out of 10 values
Convex gt0 for at least 12 out of 20 values for at least 6 out of 10 values
Power coefficient r
Concave r lt -0.05
Linear -0.05 r 0.05
Convex r gt 0.05
Power coefficient r
Concave If r sign. lt 0
Linear If r sign. 0
Convex If r sign. gt 0
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Consistency Checks
Normal Procedure
Consistency Check

f 610 200
g 200 390

f 810 610
g 1000 200
Median Values


0.595
0.74

• Reference-dependence can explain high values of
• 
  

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Error Propagation

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Elicited Probabilities

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Experiment
Example of the elicitation of

Example of the elicitation of