Choice Behavior, Asset Integration and Natural Reference Points

1. Choice Behavior,Asset Integration andNatural 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 [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 and ù

11. CPT • Assume U(x) = xá if x ≥  • Assume U(x) = -λ(-x)â if x< • Assume w(p) = pγ/[ pγ + (1-p)γ ]1/γ • PU = [w(p1) x U1] + [(1-w(p1)) x U2] • 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, γ and 

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

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 So support for both EUT and CPT Estimates of πEUT from mixture model: Ln L(r, ù, á, â, λ, γ, πEUT; y, X) = ∑i ln [(πEUT x LiEUT) +(πPT x LiPT)]

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