1. Glenn W. Harrison & E. Elisabet Rutström Economics, UCF
Expected Utility Theory and Prospect Theory: One 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 [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

5. Typical Screen Display

6. 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

7. The Groom – PT Assume U(x) = xá 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

8. 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

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
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

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

18. 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