Lecture 30 Criticisms of Prospect Theory

Sairam

Introduction
- PT around for over 3 decades
- non-conventional and radical nature $\implies$ criticisms
  - both theoretical and empirical
- Distinction between PT and CPT is important
- Theory is contradictory, unclear and contradictory
- Empirically, assumptions are violated and makes incorrect predictions
Theoretical Criticisms
1. Lack of normative status
2. Internal Contradictions
  - Birnbaum #economist
  - Editing rules are 'imprecise, contradictory and conflict with the equations of PT'
  - Can explain most results ex post¹ by applying editing rules selectively (can only explain)
    - $\implies$ Cannot be used for predictions ex ante² (cannot predict)
  - Experiment
    - Urn $A:$ 1 red ($100), 1 blue ($100) and 98 white ($0)
    - Urn $B:$ 1 red ($100), 2 green ($45) and 97 white ($0)
    - Choice 1
      - $A = (0.01,100;0.01,100;0.98,0)$
      - $B = (0.01,100;0.02,45; 0.97,0)$
    - Choice 2 (after combination of choice 1)
      - $A' = (0.02,100;0.98,0)$
      - $B = (0.01,100;0.02,45; 0.97,0)$
    - Choice 3 (after cancellation of choice 1)
      - $A'' = (0.01,100;0.99,0)$
      - $B = (0.02,45; 0.97,0)$
    - $\implies$ May lead to preference reversal. Application of editing rules lead to inconsistent preferences
3. Incompleteness
4. Determination of Reference points
  - Weakness of PT: not determined endogenously
  - determination is necessary:
    - estimate incidence and effects of loss-aversion
    - endowment effect
  - Value of object given for free (gift) $\ll$ earned (efforts) in some way
  - K&T use existing situation as the reference point or an $E[\text{Situation}]$
  - Precision in determination method would be useful e.g.
    - to know if different types of investors have the same reference point?
    - dynamic adjustment of reference points over time etc
Empirical Criticisms
1. Violations of the Combination Principle
2. Violation of Stochastic Dominance
3. Failure to explain Allais Paradox
  - Birnbaum #economist
  - Based on 200 participants' data:
    
    Neither OPT nor CPT with or without editing principles of cancellation and combination can account for the Allais paradoxes
4. Loss aversion
  - Cannot explain why DM find symmetrical bets like lotteries of the form $(0.5, x; 0.5, -x)$ unattractive.
  - A #study by Adam & Kroll #psychologist
    - 50 risk averse subjects
    - choose between $(0.5, y+x; 0.5 y-x)$ vs $(y)$
    - PT predicted $(y)$ because of loss-aversion
    - But 96% of the subjects played at least $\dfrac{1}{25}$ lotteries (average 15.9 played)
  - $\implies$ Evidence for Theory of Attraction to Chance caused by emotional factors
5. Violations of gain loss separability
  - For mixed prospects, CPT evaluates gains and losses separately
  - Assumes Gain-loss separability: Good part of B $\succ$ Good part of A and Bad part of B $\succ$ Bad part of A $\implies$ $B \succ A$
  - Wu and Markle 2008 #psychologist showed evidence for preference reversal: Mixed gamble $A \succ B$ but individual loss and gains portion-wise $B \succ A$
6. Nature of the utility function - Endowment Effects
  - Levy & Levy (LL) #economist 2002
  - Original K&T data didn't provide a reliable indicator to the shape of the utility functions
    - Always asked subjects to choose between prospects both either positive and negative
  - Reality: most prospects are mixed (e.g. stock market, either gain or loss)
  - A #study included asking respondents for mixed prospects
    - Objective:
      - test S-shaped utility function = Markowitz model
      - test reversed S-shaped function
    - Sample - 260 subjects: business students, faculty from institutions (large number of professional practitioners)
    - Experiment
      - Consider investing $10,000 in stock
      - Choose between
        
        $F: (-3000, 0.5; 4500, 0.5)$
        
        $G: (-6000, 0.25; 3000, 0.75)$
      - both mixed, same expected values
        
        Sam gain and loss components: -1500 and 2250
      - According to PT:
        
        risk-averse in gains, so prefer gain of 3000,0.75 $\implies$ $G \succ F$
        
        risk-seeking in losses, so prefer loss of 6000,0.25 $\implies$ $G \succ F$
        
        So, G is dominant
      - However...
        
        LL: $71\%$ preferred $F$ which supported the Markowitz model
        
        $\implies$ strong evidence against PT
7. Discovered preference hypothesis and misconceptions
8. Nature of Framing effects
  - Inconsistency to explain framing effects
  - Types of framing effects
    - Standard risky choice (PT explains this best)
    - Attribute framing
    - Goal framing
  - Doesn't explain the the other two
  - Framing effects depends on
    - task
    - content
    - context, inherent in the choice problem
  - E.g. of Asian Disease
    - Context: 600 citizens' life at threat
    - Positive Frame: choice between
      - saving 200 lives
      - 2/3 chance of killing all
    - Negative Frame
      - 400 dying with certainty
      - 1/3 of nobody dying
  - Several studies argued that this approach confounded the framing and reflection effect
    - Framing effect depends on negation 'not'
    - Reflection effect depends on domain: gain or loss
    - e.g. '200 people will be saved'
      - positive frame
      - positive domain (gain)
    - '400 people will die'
      - negative frame
      - negative domain (loss)
  - $\implies$ In the K&T treatment, it is impossible to disentangle framing and reflection effects
  - But it can be also argued
    - '400 people will not be saved' has...
      - negative frame
      - positive domain
    - '200 people will not be saved' has...
      - positive frame
      - negative domain
  - $\implies$ So we can restate A and C to test PT against other theories.

Once the results are observed then we can selectively apply editing rules to match the result ↩
Before the event is actually observed ↩