Choice Behavior,Asset Integration and

Natural Reference Points

Steffen Andersen, Glenn W. Harrison & E. Elisabet

Rutström

Questions

Are static lab environments representative?

What are the arguments of the utility function?

What are the natural reference points for losses and gains?

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

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

Typical Choice Task

Patterned after log-linear MPL of TK JRU 1992

Eliciting Homegrown Reference Point

Elicited Beliefs About Earnings

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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Expected Earnings After Show-Up Fee

Kernel density using Epanechnikov kernel function & bandwidth of $5Figure 2: Expected Earnings Before The Task

Raw Data

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Choice

Figure 1: Cumulative Earnings of Each Subject

Average income after choice 17:

$89 for survivors (N=65), $50 overall (N=90)

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”

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

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

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 Li

EUT) +(πPT x LiPT)]

Jointly estimate r, ù, á, â, λ, γ, and πEUT

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

Result #1: asset integration under EUT

Perc

ent

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

ù in Model AssumingThat EUT Explains Every Observation

Perc

ent

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

ù in Mixture ModelAssuming EUT and PT

Figure 11: Asset Integration Parameter for EUT

So we observe local asset integration under EUT within the mixture model

Result #2: reference points under CPT

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-15 -10 -5 0 5 10Reference Point in Dollars

Kernel densityNormal density

Figure 4: Estimated Reference Point for CPT Decision-MakersAllowing Heterogeneous Preferences

So we assume = $0 for mixture models, but this is checked

Result #3: probability of EUT

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0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1Predicted Probability

Figure 7: Probability of EUT Model

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Choice

Point estimate and 95% confidence intervalFigure 8: Probability of EUT Model Over Time

Estimates of πEUT from mixture model:Ln L(r, ù, á, â, λ, γ, πEUT; y, X) = ∑i ln [(πEUT x Li

EUT) +(πPT x LiPT)]

So support for both EUT and CPT

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