1. Choice Behavior, Asset Integration and Natural Reference Points Steffen Andersen, Glenn W. Harrison & E. Elisabet Rutström

2. Questions Are static lab environments representative? What are the arguments of the utility function? What are the natural reference points for losses and gains?

3. Approach Elicit belief on expected (generic) earnings Simple dynamic choice tasks in the lab No dynamic links between choices other than cumulative income Allow gains and losses … and bankruptcy Write out latent choice processes using EUT and CPT Extend EUT to allow for local asset integration Extend PT to allow for endogenous reference points Estimate with ML, assuming a finite mixture model of EUT and CPT

4. Experimental Design 90 UCF subjects make 17 lottery choices Every choice is played out, in real time Each subject received an initial endowment Random endowment ~ U[$1, $2, … $6] Three “gain frame” lotteries to accumulate income Next 14 lotteries drawn at random from a fixed set of 60 lotteries Replicating Kahneman & Tversky JRU 1992 Subject had a random “overdraft limit” in U[$1, $9] Allowed to bet into that overdraft No further bets if cumulative income negative

5. Typical Choice Task Patterned after log-linear MPL of TK JRU 1992

6. Eliciting Homegrown Reference Point

7. Elicited Beliefs About Earnings

8. Raw Data Average income after choice 17: $89 for survivors (N=65), $50 overall (N=90)

9. Estimation Write out likelihood conditional on EUT or CPT Assume CRRA functional forms for utility Allow for loss aversion and probability weighting in CPT Major extension for EUT: estimate degree of local asset integration Is utility defined over lottery prize or session income? Major extension #2: estimate endogenous reference point under CPT So subjects might frame prospect as a gain or loss even if all prizes are positive Depends on their “homegrown reference point”

10. EUT Assume U(s,x) = (ùs+x) r if (ùs+x) ≥ 0 Assume U(s,x) = -(-ùs+x) r if (ùs+x)< 0 Here s is cumulative session income at that point and ù is a local asset integration parameter Assume probabilities for lottery as induced EU = ∑ k [p k x U k ] Define latent index ∆EU = EU R - EU L Define cumulative probability of observed choice by logistic G(∆EU) Conditional log-likelihood of EUT then defined: ∑ i [(lnG(∆EU)|y i =1)+(ln(1-G(∆EU))|y i =0)] Need to estimate r and ù

11. CPT Assume U(x) = x á if x ≥  Assume U(x) = -λ(-x) â if x<  Assume w(p) = p γ /[ p γ + (1-p) γ ] 1/γ PU = [w(p 1 ) x U 1 ] + [(1-w(p 1 )) x U 2 ] Define latent index ∆PU = PU R - PU L Define cumulative probability of observed choice by logistic G(∆PU) Conditional log-likelihood of PT then defined: ∑ i [(lnG(∆PU)|y i =1)+(ln(1-G(∆PU))|y i =0)] Need to estimate á, â, λ, γ and 

12. Mixture Model Grand-likelihood is just the probability weighted conditional likelihoods of each latent choice process Probability of EUT: π EUT Probability of PT: π PT = 1- π EUT Ln L(r, ù, á, â, λ, γ, , π EUT ; y, X) = ∑ i ln [(π EUT x L i EUT ) +(π PT x L i PT )] Jointly estimate r, ù, á, â, λ, γ,  and π EUT

13. Estimation Standard errors corrected for possible correlation of responses by same subject Covariates and observable heterogeneity: X: {Over 22, Female, Black, Asian, Hispanic, High GPA, Low GPA, High Parental Income} Each parameter estimated as a linear function of X

14. Result #1: asset integration under EUT So we observe local asset integration under EUT within the mixture model

15. Result #2: reference points under CPT So we assume  = $0 for mixture models, but this is checked

16. Result #3: probability of EUT Estimates of π EUT from mixture model: Ln L(r, ù, á, â, λ, γ, π EUT ; y, X) = ∑ i ln [(π EUT x L i EUT ) +(π PT x L i PT )] So support for both EUT and CPT

17. Conclusions EUT does well in a dynamic environment that should breed PT choices EUT choices tend to integrate past income tend to be risk-loving PT choices tend to use the induced choice frame as a reference point consistent with risk aversion over gains and losses, loss aversion, and probability weighting