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**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

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**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

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**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

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**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

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**Typical Screen Display**

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**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

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**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

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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

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**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

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**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

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**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

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**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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