Expected Utility Theory and Prospect Theory: One Wedding and A Decent Funeral

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Expected Utility Theory and Prospect Theory: One Wedding and A Decent Funeral

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Title: Expected Utility Theory and Prospect Theory: One Wedding and A Decent Funeral


1
Expected Utility Theoryand Prospect TheoryOne
Wedding and A Decent Funeral
  • Glenn W. Harrison E. Elisabet Rutström
  • Economics, UCF

2
Overview
  • Hypothesis tests assume just one data generating
    process
  • Whichever DGP explains more of the data is
    declared the DGP, and the others discarded
  • Consider lottery choice behavior
  • Assume EUT Prospect Theory
  • Assume certain functional forms for the models
    generating the data
  • Allow for multiple DGP, united using mixture
    models and a grand likelihood function
  • Solve the model
  • Identify which subjects are better described by
    which DGP

3
Overview
  • Hypothesis tests assume just one data generating
    process
  • Whichever DGP explains more of the data is
    declared the DGP, and the others discarded
  • Consider lottery choice behavior the Chapel in
    Vegas
  • Assume EUT Prospect Theory the Bride Groom
  • Assume certain functional forms for the models
    generating the data the Prenuptual Agreement
  • Allow for multiple DGP, united using mixture
    models and a grand likelihood function the
    Wedding
  • Solve the model Consummating the marriage
  • Identify which subjects are better described by
    which DGP a Decent Funeral for the
    Representative Agent

4
Experimental Design
  • 158 UCF subjects make 60 lottery choices
  • Three selected at random and played out
  • Each subject received an initial endowment
  • Random endowment 1, 2, 10
  • Three frames
  • Gain frame prizes 0, 5, 10 and 15 N63
  • Loss frame endowment of 15 and prizes -15,
    -10, -5 and 0 N58
  • Mixed frame endowment of 8 and prizes -8,
    -3, 3 and 8 N37
  • Loss frames versus loss domains

5
Typical Screen Display
6
The Bride EUT
  • Assume U(s,x) (sx)r
  • Assume probabilities for lottery as induced
  • EU ?k pk x Uk
  • Define latent index ?EU EUR - EUL
  • Define cumulative probability of observed choice
    by logistic G(?EU)
  • Conditional log-likelihood of EUT then defined
    ?i (lnG(?EU)yi1)(ln(1-G(?EU))yi0)
  • Need to estimate r

7
The Groom PT
  • Assume U(x) xá if x 0
  • Assume U(x) -?(-x)â if xlt0
  • Assume w(p) p?/ p? (1-p)? 1/?
  • PU ?k w(pk) x Uk
  • Define latent index ?PU PUR - PUL
  • Define cumulative probability of observed choice
    by logistic G(?PU)
  • Conditional log-likelihood of PT then defined
    ?i (lnG(?PU)yi1)(ln(1-G(?PU))yi0)
  • Need to estimate á, â, ? and ?

8
The Nuptial
  • Grand-likelihood is just the probability weighted
    conditional likelihoods
  • Probability of EUT pEUT
  • Probability of PT pPT 1- pEUT
  • Ln L(r, á, â, ?, ?, pEUT y, X) ?i ln (pEUT
    x LiEUT) (pPT x LiPT)
  • Need to jointly estimate r, á, â, ?, ? and pEUT
  • Two DGPs not nested, but could be
  • Easy to extend in principle to 3 DGPs

9
Consummating the Marriage
  • Standard errors corrected for possible
    correlation of responses by same subject
  • The little pitter-patter of covariates
  • X Female, Black, Hispanic, Age, Business,
    GPAlow
  • Each parameter estimated as a linear function of
    X
  • Numerical issues

10
Result 1 Equal Billing for EUT PT
  • Initially only assume heterogeneity of DGP
  • pEUT 0.55
  • So EUT wins by a (quantum) nose, but we do not
    declare winners that way
  • H0 pEUT pPT ½ has p-value of 0.49

11
Result 2 Estimates Are Better
  • When PT is assumed to characterize every data
    point, estimates are not so hot
  • Very little loss aversion
  • No probability weighting
  • But when estimated in mixture model, and only
    assumed to account for some of the choices, much
    more consistent with a priori beliefs

12
Result 3 Classifying Subjects
  • Now move to include covariates X
  • Subjects are either clearly EUT or probably
    PT, not two distinct modes

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Conclusion
  • Sources of heterogeneity
  • Observable characteristics
  • Unobservable characteristics
  • Unobservable processes
  • Great potential to resolve some long-standing
    disputes
  • EUT versus PT
  • Exponential versus Hyperbolicky discounting
  • Calibrating for hypothetical bias in CVM
  • Serious technical issues to be addressed
  • Data needs just increase N
  • Estimation problems
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