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
0
.01
.02
.03
.04
Den
sity
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 $5Figure 2: Expected Earnings Before The Task
Raw Data
0
50
100
150
200
Cum
ulat
ive
Earn
ings
($)
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
0
.05
.1
.15
.2
Den
sity
-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
0
.5
1
1.5
2
Den
sity
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1Predicted Probability
Figure 7: Probability of EUT Model
0
.1
.2
.3
.4
.5
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.7
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.9
1
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