of 52
Online Appendix for
“Looming Large or Seeming Small?
Attitudes Towards Losses in a Representative Sample”
by Chapman, Snowberg, Wang, and Camerer
Table of Contents
A DOSE Procedure and Survey Implementation
2
A.1 DOSE Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
A.2 Other Survey Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
B Choice Data
6
B.1 Choice Data From DOSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
B.2 Choice Data from MPL Elicitations . . . . . . . . . . . . . . . . . . . . . . .
8
C Additional Results and Robustness
9
C.1 Alternative Utility Specifications . . . . . . . . . . . . . . . . . . . . . . . . .
9
C.2 Additional Correlations with Individual Characteristics . . . . . . . . . . . .
12
C.3 Additional Regressions with Real World Behaviors . . . . . . . . . . . . . . .
21
C.4 Additional Results from Alternative Reference Point Models . . . . . . . . . .
26
C.5 Additional Tests of Survey Fatigue and Inconsistency . . . . . . . . . . . . . .
26
C.6 Tests of Payment Schedule E
ects . . . . . . . . . . . . . . . . . . . . . . . .
31
C.6.1 A Theory of Threshold Response . . . . . . . . . . . . . . . . . . . . .
34
C.6.2 Subgroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
D Principal Components Analysis
38
E Screenshots
39
Online Appendix–1
A DOSE Procedure and Survey Implementation
A.1 DOSE Procedure
This subsection presents further details of the design choices for each of the two DOSE sequences
in our online survey. We start by detailing the information criterion and error specification that
we implement in both the DOSE sequences. We then explain the implementation of the question
selection in our online survey, and specify the particular design choices made for each of the
10-question and 20-question sequences. For full details of the DOSE elicitation method, see
Chapman et al. (2018).
Overview of DOSE procedure
The DOSE procedure selects a personalized sequence of
questions for each participant. Questions are selected sequentially, using a participant’s previous
answers to identify the most informative question at that point in time. In our implementa-
tion, DOSE selects each question to maximize the expected Kullback-Leibler (KL) divergence
between the prior and possible posteriors associated with each answer. That is, the question
that is picked at each point is the one with the highest expected information gain given the
initial prior and previous answers.
Formally, consider a finite set of possible parameter vectors
k
for
k
=1
,...,K
,whereeach
k
=(
k
,
k
k
)isacombinationofpossiblevaluesoftheparametersofinterest. Each
k
has an associated probability
p
k
of being the correct parameters. In the first question, these
probabilities are the priors chosen by the experimenter; they are then updated in each round
according to the participant’s answers. The expected Kullback-Leibler divergence between the
prior and the posterior when asking question
Q
j
is:
KL
(
Q
j
)=
X
k
K
X
a
2
A
log
l
k
(
a
;
Q
j
)
P
j
2
K
p
j
l
j
(
a
;
Q
j
)
!
p
k
l
k
(
a
;
Q
j
)(2)
where
a
2
A
are the possible answers to the question, and
l
k
(
a
;
Q
j
)isthelikelihoodofanswer
a
given
k
—in our implementation this is determined by the logit function in (3). DOSE selects
the question that maximizes
KL
(
Q
), the participant answers it, model posteriors are updated,
the question
Q
j
that now maximizes
KL
(
Q
)(andhasnotalreadybeenasked)isselected.
Mistakes and Choice Consistency
An important feature of DOSE is that it accounts for
the possibility that the participant may make mistakes in their previous choices. In this paper,
we model the mapping between utility and choices using a logit function—Chapman et al.
(2018) show that the procedure is robust to misspecifying the error specification. Specifically,
for any choice between options
o
1
and
o
2
with
V
(
o
1
)
>V
(
o
2
):
Prob[
o
1
]=
1
1+
e
μ
i
(
V
(
o
1
)
V
(
o
2
))
.
(3)
In Specification (3), the probability of making a mistake is 1
Prob[
o
1
], and so
μ
i
represents
greater consistency in choices.
Online Appendix–2
Survey Implementation:
The design of YouGov’s online platform precluded using DOSE
to choose questions in real time and so, instead, simulated responses were used to map out all
possible sets of binary choices in advance. That tree was then used to route participants through
the survey. Mapping such a tree with a refined prior was infeasible given both computational
constraints and the limitations of YouGov’s interface (mapping such a tree over 20 questions
would involve over 500,000 routes through the survey). As such, questions were selected using a
coarser prior and then final individual-level estimates were obtained by performing the Bayesian
updating procedure with a joint 100-point discretized uniform prior.
1
10-question Sequence:
The 10-question sequence was selected using the utility function in
Specification 1. Two types of lottery were used. The first had a 50% chance of 0 points, and
a 50% chance of winning a (varying) positive amount of points (of up to 10,000). The second
had a 50% chance of winning an amount up to 10,000 points, and a 50% chance of a loss of up
to 10,000 points. In the latter case, the sure amount was always 0 points.
2
The lottery always
appeared first in both types of question
To account for the survey environment we restricted the question selection procedure in two
ways. First, to focus the procedure on obtaining a precise estimate of
before moving onto
estimates of
,thefirstfourquestionsinthemodulewererestrictedtobelotteriesovergains.
Second, to make it harder for participants to identify the adaptive nature (and hence attempt
to manipulate) the procedure, the maximum prize was restricted to be no more than 7,000
points in each even numbered round.
See Figures E.23–E.25 for module instructions and example questions.
20-question Sequence:
The 20-question sequence was selected using a power utility function
allowing for di
erential curvature over gains and losses—see Specification (4) below. Three
types of lottery were used. The first two types were the same as those in the 10-question
sequence listed above—except that potential prizes ranged from a loss of 15,000 to a gain of
15,000. The third type of question, included to identify curvature over losses, o
ered a choice
between losing a (varying) fixed amount points, or a lottery with a 50% chance of 0 points,
and a 50% chance of losing up to 15,000 points. The sure amount always appeared first in all
questions, reversing the order from the 10-question module.
In order to facilitate comparisons across the sample, the question selection procedure was
restricted so that three questions were fixed for all participants. The first question of the
sequence o
ered a choice between a gain of 5,900 points, or a lottery with a 50% chance of 0
points and a 50% chance of 15,000 points. The fourth question—reported in Figure 1—o
ered
participants a fixed prize of 0 points or a lottery with a 50% chance of gaining 10,000 points,
and a 50% chance of losing 12,000 points. No questions with possible losses were allowed before
1
Specifically, the prior for question selection was constructed using the estimates for laboratory participants
obtained by Sokol-Hessner et al. (2009) and Frydman et al. (2011): 0.2–1.7 for
(12 mass points), and 0–4.6
for
(20 mass points).
2
The set of potential questions allowed for gains ranging between 1,000 and 10,000 points in 500 point incre-
ments, and sure amounts and losses varying ranging from 500 points to 10,000 points in 100 point increments.
Questions were excluded if one choice was first-order stochastically dominated for all values of the prior dis-
tribution. Questions were also selected as if the prize amounts were 3 times the actual amounts o
ered in the
lottery to improve discrimination of the risk and loss aversion parameters.
Online Appendix–3
this question. The twentieth question of the sequence o
ered a similar choice: a 50% chance of
gaining 11,000 points, and a 50% chance of losing 13,000 points.
3
See Figure 2 for the 20-question sequence instructions, and an example of a question involv-
ing a gain and a loss. Figure E.20 presents an example of a question involving only a gain, and
Figure E.21 an example of a question involving only a loss.
A.2 Other Survey Measures
This subsection summarizes the definition of the other measures used in the paper.
MPLs Eliciting Certainty Equivalents
The survey included four MPLs eliciting partic-
ipants’ certainty equivalent for a fixed lottery—see Figures E.28–Figures E.31. Two MPLs
elicited the certainty equivalent for a 50/50 lottery between a loss and a gain, while two elicited
the certainty equivalent for a 50/50 lottery including only gains. The specific lotteries o
ered
were:
1.
50% chance of winning
$
5anda50%chanceoflosing
$
5
2.
50% chance of winning
$
4anda50%chanceoflosing
$
4
3.
50% chance of winning
$
0anda50%chanceofwinning
$
5
4.
50% chance of winning
$
1anda50%chanceofwinning
$
4
MPLs Eliciting Lottery Equivalents
Two MPL o
ered participants a choice between a
fixed prize of
$
0, and a 50/50 lottery with a variable prize—see Figures E.26–Figures E.27.
Specifically, the lottery consisted of a fixed positive amount
y
(
$
5or
$
4) and a varying negative
amount
c
with equal probabilities. The MPL therefore elicited the participant’s lottery equiv-
alent for
c
such that the participant was indi
erent between gaining
y
and losing
c
with equal
probability, and getting zero for sure.
Cognitive Ability:
We measure cognitive ability using a set of nine questions. Six questions
from the International Cognitive Ability Resource (ICAR; Condon and Revelle, 2014) capture
IQ: three are similar to Raven’s Matrices, and the other three involved rotating a shape in
space. The other three are taken from the Cognitive Reflection Test (CRT; Frederick, 2005):
three arithmetically straightforward questions with an instinctive, but incorrect, answer.
3
The set of potential questions was as follows. For questions with only gains, possible prizes varied between
700 and 14,700 points, in increments of 700. For questions with only losses: possible prizes varied between
100 and 14,800 points, in increments of 700 points. For questions with gains and losses the gain prizes varied
between 300 and 15,000 points, in increments of 700 points; loss prizes varied between 300 and 15,000 points, in
increments of 700 points. Questions were excluded if the highest maximum absolute value of the prize was less
than 8,000 points, or if the lottery was not the optimal choice under any value of the parameters in the prior.
This question set was chosen to provide su
cient flexibility for DOSE to elicit precise estimates, to ensure some
variation in the questions respondents received, and computational constraints due to the need to simulate the
question tree in advance.
Online Appendix–4
Education:
Education is measured on a six point scale, with categories including: No high
school, graduated high school, some college, two-years of college, four-year college degree, and
apostgraduatedegree.
Income:
Participants reported their income in sixteen categories, ranging from “Less than
$
10,000” to “
$
500,000 or more”. 11% of participants chose not to state their income. We
linearize this variable by taking the mid-points of each category (or use
$
500,000 for the top
category), and use random imputation to impute missing values of log income based on age,
sex, education, and employment status. In robustness tests below we include the variable in
quartiles and add a dummy variable capturing missing responses.
Sex:
Sex was measured as a binary choice of “Male” or “Female”.
Age:
Participants were asked to state their birth year, which we convert into age. In robust-
ness tests below we include the variable split into quartiles.
Marital Status:
Participants reported their marital status in six categories: “Married”,
“Separated”, “Divorced”, “Widowed”, “Never married”, or “Domestic / civil partnership”. We
create a binary variable based on these responses.
Gambling Behavior:
Gambling behavior was measured using a battery of questions adapted
from Gonnerman and Lutz (2011) (see Figure E.32). Two principal components were extracted
from this battery of measures—see Appendix D for scree plots.
Household Assets and Stock Investments:
Participants were first asked to specify their
financial assets, by answering: “the value of your bank accounts, brokerage accounts, retirement
savings accounts, investment properties, etc., but NOT the value of the home(s) you live in
or any private business you own.” The following question then asked “What percentage of
your investable financial assets is currently invested in stocks, either directly or through mutual
funds?” These questions were taken from Choi and Robertson (2020).
For the analysis in Table 4, the value of household assets was linearized by taking the
midpoint of each category (or
$
1inthebottomcategory,
$
100,000 for the top category).
Household Shocks:
Household shocks were measured using a battery of six binary questions
adapted from Pew Research Center (2015, p4)—see Figure E.33 for an example. Specifically,
participants were asked whether in the past 12 months,
1.
In the past 12 months, has anyone in your household brought in less income
than expected due to unemployment, a pay cut, or reduced hours?
2.
In the past 12 months, has someone in your household su
ered an illness or
injury requiring a trip to the hospital?
3.
In the past 12 months, has anyone in your household divorced, separated, or
was widowed from a spouse or partner?
Online Appendix–5
4.
In the past 12 months, has anyone in your household needed a major repair or
replacement to their car, truck, or SUV?
5.
In the past 12 months, has the place you live in or any appliances needed major
repair or replacement?
6.
Has your household had some other large, unexpected expense in the past year?
[If yes, add a text box with the question: Can you tell us a bit more about this
expense?]
Two principal components were extracted from this battery of measures—see Appendix D for
scree plots.
Attention Screeners:
The survey included three questions designed to check a participant
was paying attention. See Figures E.34–E.37 for question wording.
B Choice Data
The analysis in the main text has primarily estimated loss aversion using parametric specifi-
cations. The parametric approach allows us to disentangle loss aversion from the curvature
of the utility function, but could lead to concerns that the results are driven by our choice of
utility function. In this Appendix we use the survey data to show that there is a clear pattern
of choices underpinning our parametric estimates. First we demonstrate that the classification
of loss tolerant by DOSE reflects participants accepting a number of negative-expected-value
lotteries. The second subsection shows a similar pattern in the MPL choice data.
B.1 Choice Data From DOSE
The DOSE parameter estimates reflect clear patterns in choice, as shown in Figure B.1. In each
panel we split participants according to their classification in the 20-question DOSE module.
The x-axis is the di
erence between the expected value of a lottery and the sure amount in a
given choice. The left-hand panel shows that loss-tolerant participants (
<
1) are clearly more
likely to choose lotteries with losses than those who are loss averse (
>
1). Similar patterns
exist for risk aversion over gains (middle panel) and losses (right hand panel): individuals
classified as risk loving are more likely to choose gambles in the relevant domain at every
expected value di
erence. For all six groups of participants, the probability of choosing the
lottery generally increases with the di
erence between the expected value of the lottery and the
sure amount. However, portions of the lines in each panel are flat, reflecting the fact that the
questions participants receive are determined by their previous answers. For instance, in the
left-hand panel, DOSE will only o
er a question with expected value far below the sure amount
to participants that have already revealed loss tolerance through prior choices of lotteries with
large negative expected values. Selection into receiving questions with large expected value
di
erences is thus not random.
Figure B.2 shows that our finding of widespread loss tolerance in the representative sample
reflects a common tendency to accept negative-expected-value gambles. In both panels, we order
participants according to the smallest expected value of a mixed lottery (o
ering both gains
and losses) that they accepted in the 20-question (left-hand panel) and 10-question (right-hand
Online Appendix–6
Figure B.1: A clear pattern of choices underpins the DOSE-elicited parameters.
0%
20%
40%
60%
80%
100%
Probability Chose Lottery
$8
$4
$0
$4
$8
Expected Value
Sure Amount
Loss Tolerant
Loss Averse
Lotteries with Gains and Losses
0%
20%
40%
60%
80%
100%
Probability Chose Lottery
$2
$0
$2
$4
$6
$8
Expected Value
Sure Amount
Risk Loving
Risk Averse
Lotteries with Only Gains
0%
20%
40%
60%
80%
100%
Probability Chose Lottery
$8
$6
$4
$2
$0
$2
Expected Value
Sure Amount
Risk Loving
Risk Averse
Lotteries with Only Losses
Notes:
The figure displays choices from the 20-question DOSE sequence using local mean regressions with
Epanechnikov kernel and bandwidth 1. Loss Tolerant (Averse) refers to participants for who
<
1(
>
1)
according to the DOSE 20-question estimates. Similarly, Risk Averse (Loving) refers to participants for who
<
1(
>
1) according to the DOSE 20-question estimates for lotteries with only gains, and
>
1(
<
1) for
lotteries with only losses.
panel) DOSE modules. More than 64% of participants in the representative sample accepted at
least one lottery with negative expected value in the 20-question module (left-hand panel) and
48% did so in the 10-question module (right-hand panel). These proportions are much higher
than among students, of whom 35% and 12% accepted a negative-expected-value lottery in the
respective modules.
Figure B.3 shows that the classification of participants as loss tolerant by DOSE reflects
participants’ willingness to accept lotteries with negative expected value, and is not an artefact
of our parametric assumptions. Here, we investigate choices by examining the ratio between
the possible gain (
g
)andthepossibleloss(
l
) for a mixed lottery accepted by participants (over
asureamountof
$
0). This ratio o
ers a simple measure of the loss aversion coe
cient: with
linear utility, a participant should accept a mixed lottery if
g
l
.
4
The figure shows that
the DOSE-elicited parameters capture such choices: more than three-quarters of participants
with estimated
>
2(bottom-rightpanel)acceptedonlylotterieswith
g
l
>
2, while almost
all participants with estimated
0
.
5(top-leftpanel)acceptedalotterywith
g
l
0
.
5.
These results o
er further evidence that the DOSE parameter estimates reflect a widespread
willingness to accept negative-expected-value lotteries.
There are clear di
erences in choices according to cognitive ability, as shown in Figure B.4.
Similarly to Figure B.1, each panel displays the likelihood of accepting a lottery for each cat-
egory of question. Now we compare the choices of participants according to their level of
cognitive ability. Low-cognitive-ability participants consistently accept lotteries with negative
expected value (left-hand-panel). High-cognitive-ability participants, in contrast, choose such
lotteries less frequently. When lotteries contain only gains (middle panel) low-cognitive-ability
participants are less likely to accept lotteries where the expected value exceeds the sure amount
than participants with high cognitive ability—consistent with the negative correlation between
risk aversion and cognitive ability reported in Table 1.
4
We can also construct individual-level loss-aversion measures based on the range of
g
l
values accepted by
participants—doing so leads to an estimate of 53% of participants as loss tolerant.
Online Appendix–7
Figure B.2: There is greater willingness to accept negative-expected-value gambles among the
general population than among students.
0
20%
40%
60%
80%
100%
Cumulative % of Participants
$8
$4
$0
$4
$8
Lowest EV of Lottery Accepted
Population
Students
DOSE 20
Question Module
0
20%
40%
60%
80%
100%
Cumulative % of Participants
$8
$4
$0
$4
$8
Lowest EV of Lottery Accepted
Population
Students
DOSE 10
Question Module
Notes:
Each panel presents the cumulative density of participants, ranked according to the smallest
expected value of a mixed lottery (i.e., o
ering both gains and losses) that they chose to accept.
Densities are plotted using a local cubic polynomial, with a bandwidth of 0.5. The left-hand panel
includes participants in the main survey sample, the right-hand panel includes participants in both
the main and supplementary samples. Participants that never accepted a mixed lottery are excluded
from the figure.
B.2 Choice Data from MPL Elicitations
Figure B.5 displays the choices made in the six MPL elicitations discussed in Section 5.1.
The first two rows relate to the MPLs used to identify loss aversion, through eliciting lottery
equivalents or certainty equivalents. The final row displays the two MPLs over only gains, which
identify the curvature of the utility function. Choices in all six MPLs clump around salient
rows, including at end-points of the distribution, and some choices are first-order stochastically
dominated.
In the main text we use the MPL choice data to estimate Bayesian parameters. Alterna-
tively, we can estimate loss aversion parameters using a double MPL method (Andersen et al.,
2008; Andreoni and Sprenger, 2012), in which risk aversion is estimated separately by eliciting
the certainty equivalent for a lottery over gains. This method is problematic because many
participants select the (highly salient) top or bottom rows of the MPL leading to extreme
parameter estimates (for example,
>
100) or choices that are first-order stochastically dom-
inated. Consequently, the method is unable to estimate
for a significant proportion of the
population: ranging from 10% to 42% of the sample across the four MPLs. However, we observe
ahighdegreeoflosstoleranceamongthesubsampleforwhichweobtainparameterestimates:
between 39% and 62% of these participants are classified as loss tolerant.
Online Appendix–8
Figure B.3: DOSE estimates of
reflect participants’ willingness to accept mixed lotteries.
0
25
50
75
100
<=0.5
(0.5,1]
(1,2]
>2
λ
(0,0.5]
0
25
50
75
100
<=0.5
(0.5,1]
(1,2]
>2
λ
(0.5,1]
0
25
50
75
100
<=0.5
(0.5,1]
(1,2]
>2
λ
(1,2]
0
25
50
75
100
<=0.5
(0.5,1]
(1,2]
>2
λ
(2,4.5]
Percentage of Participants
Minimum Gain:Loss Ratio Accepted
Notes:
Each panel of the figure represents di
erent groups of participants, grouped according to the
estimated
elicited by the 20-question DOSE sequence. The bars in each panel represent the smallest
gain-loss ratio in a mixed lottery accepted by the participant. Eight participants never accepted a
mixed lottery and are excluded from the figure.
C Additional Results and Robustness
C.1 Alternative Utility Specifications
This Appendix presents the estimates, discussed in Section 5.2, obtained when allowing for the
curvature of the utility function to di
er between gains and losses, as suggested by Prospect
Theory (Kahneman and Tversky, 1979). Specifically, we estimate the following unrestricted
power utility function:
u
(
x,
+
i
,
i
,
i
)=
(
u
(
x
)=
x
+
i
for
x
0
u
(
x
)=
i
(
x
)
i
for
x<
0
(4)
We also re-estimate the loss aversion parameter using the exponential utility function sug-
gested by K ̈obberling and Wakker (2005):
Online Appendix–9
Figure B.4: Low-cognitive-ability participants make di
erent choices to participants with high
cognitive ability, supporting the correlations reported in Table 1.
0%
20%
40%
60%
80%
100%
Probability Chose Lottery
$8
$4
$0
$4
$8
Expected Value
Sure Amount
Lotteries with Gains and Losses
0%
20%
40%
60%
80%
100%
Probability Chose Lottery
$2
$0
$2
$4
$6
$8
Expected Value
Sure Amount
Lotteries with Only Gains
0%
20%
40%
60%
80%
100%
Probability Chose Lottery
$8
$6
$4
$2
$0
$2
Expected Value
Sure Amount
Lotteries with Only Losses
Low Cognitive Ability
High Cognitive Ability
Notes:
The figure displays choices from the 20-question DOSE sequence using local mean regressions with
Epanechnikov kernel and bandwidth 1. “Low” and “High” cognitive ability refer to the bottom and top
terciles within the sample.
u
(
x,
i
,
i
)=
(
1
e
i
x
i
for
x
0
i
e
i
x
1
i
for
x<
0
(5)
where
i
represents loss aversion (as in our main estimates) and
i
captures risk aversion. This
utility specification exhibits Constant Average Risk Aversion, and so we refer to the associated
estimates as “CARA” in the following.
Our finding of widespread loss tolerance is robust to these alternative specifications as
shown in Figure C.6. The left-hand panel presents results from re-estimating the data from the
20-question DOSE sequence using unrestricted CRRA utility curvature (specification (4) and
CARA utility (specification 5). The right-hand panel presents the results from the 10-question
DOSE sequence—the unrestricted CRRA model is not presented here, since the sequence did
not include any questions involving only losses, and so we cannot identify utility curvature over
losses. We can see that the CARA estimates are extremely similar to our main estimates. We
observe more di
erence from our preferred estimates when allowing for di
erential curvature
over gains and losses—more than two-thirds of the U.S. population are classified as loss tolerant
by this specification.
In Figure C.7 we investigate the estimates of risk aversion over gains and losses, obtained
by estimating Specification 4. The left-hand panel shows that our risk aversion parameter in
the main specification is closely correlated to the risk aversion over gains when allowing for
di
erential curvature (r=0.59; s.e.=0.04). The restricted parameter is more weakly correlated
with risk aversion over losses (r=-0.41; s.e.=0.04). The right-hand panel of the figure shows
that the average risk aversion parameter is similar across the two domains, providing some
support for our assumption that utility curvature is the same over gains and over losses. The
mean di
erence in the two parameters is small, although statistically distinguishable from zero
(-0.11; s.e.=0.03). These results are consistent with previous findings that utility over losses
is closer to linearity (Booij et al., 2010). However, it is clear from the figure that there is
considerable individual heterogeneity that is not captured by the average estimate.
Online Appendix–10
Figure B.5: Choices in MPLs also show widespread loss tolerance.
0
5
10
15
20
25
More loss tolerant
More loss averse
$10
$5
$0
$0 or Lottery Over $5/$
l
0
5
10
15
20
More loss tolerant
More loss averse
$10
$5
$0
$0 or Lottery Over $4/$
l
Lottery Equivalent ($
l
)
MPLs Eliciting Lottery Equivalents for $0
0
5
10
15
More loss averse
More loss tolerant
$5
$0
$5
$
c
or Lottery Over
$5/$5
0
5
10
15
More loss averse
More loss tolerant
$4
$0
$4
$
c
or Lottery Over
$4/$4
Certainty Equivalent ($
c
)
MPLs Eliciting Certainty Equivalents in Mixed Domain
0
5
10
15
More risk averse
More risk loving
$0
$2.50
$5
$
c
or Lottery Over $5/$0
0
5
10
15
More risk averse
More risk loving
$1
$2.50
$4
$
c
or Lottery Over $4/$1
Certainty Equivalent ($
c
)
MPLs Eliciting Certainty Equivalents in Gain Domain
Frequency (%)
Notes:
All lotteries involved 50% probabilities of each outcome. Red bars at extremes of the MPL reflect
choices that are first-order stochastically dominated.
Online Appendix–11