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Expected Utility Theoryand Prospect TheoryOne

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 - 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

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

- 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

Typical Screen Display

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

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 ?

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

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

- 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

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

- 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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