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Expected Utility Theory and Prospect Theory: One Wedding and A Decent Funeral Glenn W. Harrison & E. Elisabet Rutström Economics, UCF Overview Hypothesis tests assume just one data generating process Whichever DGP explains more of the data is declared “the” DGP, and the others discarded

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expected utility theory and prospect theory one wedding and a decent funeral

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

Glenn W. Harrison & E. Elisabet Rutström

Economics, UCF

overview
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
overview3
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
experimental design
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 [N=63]
    • Loss frame – endowment of $15 and prizes -$15, -$10, -$5 and $0 [N=58]
    • Mixed frame – endowment of $8 and prizes -$8, -$3, $3 and $8 [N=37]
  • Loss frames versus loss domains
the bride eut
The Bride – EUT
  • Assume U(s,x) = (s+x)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)|yi=1)+(ln(1-G(∆EU))|yi=0)]
  • Need to estimate r
the groom pt
The Groom – PT
  • Assume U(x) = xá if x ≥ 0
  • Assume U(x) = -λ(-x)â if x<0
  • Assume w(p) = pγ/[ pγ + (1-p)γ ]1/γ
  • 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)|yi=1)+(ln(1-G(∆PU))|yi=0)]
  • Need to estimate á, â, λ and γ
the nuptial
The Nuptial
  • Grand-likelihood is just the probability weighted conditional likelihoods
  • Probability of EUT: πEUT
  • Probability of PT: πPT = 1-πEUT
  • Ln L(r, á, â, λ, γ, πEUT; y, X) = ∑i ln [(πEUT x LiEUT) +(πPT x LiPT)]
  • Need to jointly estimate r, á, â, λ, γ and πEUT
    • Two DGPs not nested, but could be
    • Easy to extend in principle to 3+ DGPs
consummating the marriage
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
result 1 equal billing for eut pt
Result #1: Equal Billing for EUT & PT
  • Initially only assume heterogeneity of DGP
  • πEUT = 0.55
  • So EUT wins by a (quantum) nose, but we do not declare winners that way
    • H0: πEUT = πPT = ½ has p-value of 0.49
result 2 estimates are better
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
result 3 classifying subjects
Result #3: Classifying Subjects
  • Now move to include covariates X
  • Subjects are either “clearly EUT” or “probably PT,” not two distinct modes
conclusion
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