Review of Economic Studies (2024)
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Advance access publication 16 September 2024
Looming Large or Seeming
Small? Attitudes Towards Losses
in a Representative Sample
Jonathan Chapman
University of Bologna, Italy
Erik Snowberg
University of Utah, USA; NBER, USA; and CESifo, Germany
Stephanie W. Wang
University of Pittsburgh, USA
and
Colin Camerer
California Institute of Technology, USA
First version received December
2022
; Editorial decision April
2024
; Accepted September
2024
(Eds.)
We measure individual-level loss aversion using three incentivized, representative surveys of
the U.S. population (combined
N
=
3
,
000). We find that around 50% of the U.S. population is
loss
tolerant
—they are willing to accept negative-expected-value gambles that contain a loss. This is counter
to expert predictions and earlier findings—which mostly come from laboratory/student samples—that
70–90% of participants are loss averse. Consistent with the different findings in our study versus the prior
literature, loss aversion is more prevalent in people with high cognitive ability. Further, our measure of
gain–loss attitudes exhibits similar temporal stability and better predictive power outside our survey than
measures of risk aversion. Loss-tolerant individuals are more likely to report recent gambling, investing
a higher percentage of their assets in stocks, and experiencing financial shocks. These results support
the general hypothesis that individuals value gains and losses differently, and that gain–loss attitudes
are an important economic preference. However, the tendency in a large proportion of the population to
emphasize gains over losses is an overlooked behavioural phenomenon.
Key words
: Loss Aversion, Dynamic Adaptive Design, Risk Preferences, Cognitive Ability, Negative
Shocks, Gambling
JEL codes
: C81, C9, D03, D81, D9
The editor in charge of this paper was Noam Yuchtman.
1
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2
REVIEW OF ECONOMIC STUDIES
1. INTRODUCTION
A central hypothesis in behavioural economics is that people treat losses and gains differently,
resulting in most being
loss averse
: even if they are risk neutral, they tend to shy away from
positive expected value gambles with negative payoffs (losses). Loss aversion is used as an expla-
nation for a number of important economic phenomena, and is an essential ingredient in models
of reference-dependent preferences (
Kahneman and Tversky 1979
;
K
̋
oszegi and Rabin 2006
;
O’Donoghue and Sprenger 2018
).
1
Yet, most evidence of loss aversion comes from economics
and psychology laboratories, usually with university student participants. These participants
often have different preferences than the general population (
Walasek
et al
. 2018
;
Snowberg
and Yariv 2021
).
We find that around 50% of people in the U.S. are
loss tolerant
—even if they are risk neu-
tral, they embrace gambles with negative expected values—and around 50% are loss averse. We
elicit individual estimates of gain–loss attitudes in three representative, incentivized surveys of
the U.S. population (combined
N
=
3
,
000), using Dynamically Optimized Sequential Exper-
imentation (DOSE;
Chapman
et al
. 2010
,
2018
). We implement the same procedure in two
samples of undergraduate students, and find similar levels of loss tolerance as in previous labo-
ratory experiments. Consistent with this finding, loss aversion is more common in people with
high cognitive ability within our representative samples. Loss aversion is also correlated with
behaviour outside of the survey environment: loss-tolerant individuals have more of their assets
invested in stocks, are more likely to have recently gambled, are more likely to have experienced
a recent financial shock, and have fewer financial assets. However, our elicitations of risk aver-
sion are generally not correlated with these real-world behaviours. Together, this suggests that
loss aversion captures an independent, and substantively important, part of risk attitudes.
Although surprising, the prevalence of loss tolerance is further evidence for
Kahneman and
Tversky
’s (
1979
) hypothesis that people treat gains and losses differently. In particular, it is evi-
dence of substantial heterogeneity in the asymmetry, with potentially important consequences
for consumer welfare and reference-dependent theories (
Goette
et al
. 2019
;
Barberis
et al
. 2021
).
Loss aversion can, in theory, reduce the propensity to use financial products that exploit com-
mon characteristics like overoptimism and skew-love (
Kahneman and Lovallo 1993
;
̊
Astebro
et al
. 2015
). Loss tolerance, on the other hand, makes it easier to exploit such characteristics.
Moreover, our evidence suggests that loss tolerance is particularly prevalent in those who tend to
gamble, and among groups that might benefit from more resistance to using problematic finan-
cial products: those with low income, education, and cognitive ability (
Kornotis and Kumar
2010
;
Chang 2016
).
1.1.
Widespread loss tolerance
Our main result can be observed in choices over a simple 50:50 lottery with a negative expected
value, as shown in Figure
1
. All participants face a choice between a sure amount of $0 and
1. Examples of phenomena that have been explained through loss aversion include the equity premium puzzle
(
Mehra and Prescott 1985
;
Benartzi and Thaler 1995
), asymmetric consumer price elasticities (
Hardie
et al
. 1993
),
reference-dependent labour supply (
Dunn 1996
;
Camerer
et al
. 1997
;
Goette
et al
. 2004
;
Fehr and Goette 2007
),
tax avoidance (
Rees-Jones 2018
), opposition to free trade (
Tovar 2009
), performance in athletic contests (
Pope and
Simonsohn 2011
;
Allen
et al
. 2017
), and more.
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Chapman
et al.
LOOMING LARGE OR SEEMING SMALL?
3
F
IGURE
1
Contrary to expert predictions, more than half of respondents accept a simple lottery with negative expected value
Notes:
The left-hand panel displays the proportion of participants in the general population sample and in the undergraduate student
sample choosing a lottery with a 50% probability of gaining $10 and a 50% probability of losing $12, over a sure amount of $0. The
right-hand panel shows results for those in the bottom and top terciles of cognitive ability within the general population sample. Error
bars represent 90% confidence intervals. See Section
2.3
for further details
a lottery over a gain of $10 and a loss of $12, each with 50% probability.
2
As shown in the
left-hand panel, 60% of those in the representative sample (
N
=
1
,
000) choose the lottery,
demonstrating a significant degree of loss tolerance (under the common assumption of local
risk neutrality)—and countering
Kahneman and Tversky
’s (
1979
) assertion that “most people
find symmetric bets of the form
(
x
,.
50
;−
x
,.
50
)
distinctly unattractive” (p. 279). The propor-
tion choosing the lottery is, however, much lower among a sample of University of Pittsburgh
undergraduates (
N
=
437) completing a very similar incentivized online survey—only 28% of
students choose the lottery. Consistent with this finding, in the right-hand panel of Figure
1
,we
see that those in the representative sample with low cognitive ability were more likely to choose
the lottery.
The proportion of loss-tolerant participants in our data is much higher than anticipated by
economists completing a prediction survey (
DellaVigna
et al
. 2019
). The expert respondents
(
N
=
87) accurately predicted the proportion of students that would accept the lottery (an aver-
age prediction of 31% versus the actual 28%), but severely underestimated the proportion in the
representative sample (30% versus 60%).
3
Notably, it appears that respondents overestimated
the similarity between undergraduates and the general population, making very similar guesses
for the two samples. Further, only 10% of the expert respondents reported that they would accept
the same lottery themselves, consistent with academics being unrepresentative of the extent of
loss tolerance across the population.
The patterns in Figure
1
do not reflect a high willingness to gamble in general, due to, for
instance, “house money effects” (
Thaler and Johnson 1990
). Most participants demonstrated
significant risk aversion when no potential loss was involved—for instance, only 39% of the
representative sample preferred a lottery with a 50% chance of $15 and 50% chance of $0 to
a sure amount of $5.90. This proportion is lower than predicted in the expert survey (average
prediction = 56%) and—in contrast to Figure
1
—lower than the proportion of students (49%)
2. We thank Matthew Rabin for suggesting this simple test of loss tolerance.
3. The survey was completed 17–30 November 2020. Recruitment was carried out via social media, research
networks, and
https://socialscienceprediction.org/predict/
.
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4
REVIEW OF ECONOMIC STUDIES
accepting the same lottery. Thus, our data suggest that the general population is more loss toler-
ant but—consistent with previous studies (see, for example,
Snowberg and Yariv 2021
)—more
risk averse than undergraduate students.
4
1.2.
Further investigation of heterogeneity in gain–loss attitudes
We confirm and extend the above findings using DOSE to elicit accurate individual-level esti-
mates of loss aversion. A single choice, such as the one used in Figure
1
, cannot distinguish
between loss aversion—a change in behaviour near the reference point (of $0)—from utility
curvature (risk aversion). Disentangling these preferences generally requires a parametric model
and multiple questions—causing standard elicitation methodologies to yield, at best, imprecise
estimates due to measurement error and/or inconsistent choice. Moreover, standard designs offer
a fixed set of questions to all participants, thus likely underestimating heterogeneity in gain–loss
attitudes. DOSE designs around these challenges using a parametric model and Bayesian updat-
ing to dynamically select a personalized sequence of simple binary choices. Our Bayesian prior
assumes considerable loss aversion, and the adaptive design robustly identifies loss tolerance by
offering participants several negative-expected-value gambles. We thus use DOSE to verify the
findings in Figure
1
, and then to investigate the usefulness of gain–loss attitudes—as captured
by predictive power outside of our survey—and their stability over time.
Our DOSE-elicited measure of loss aversion also indicates a much higher level of loss tol-
erance in representative samples of the U.S. population than among students. We compare our
main sample (
N
=
1
,
000)—with two DOSE elicitations—and a supplementary sample (
N
=
2
,
000)—studied twice, six months apart—to two student samples (
N
=
437 and 369) recruited
from the University of Pittsburgh Experimental Laboratory that participated in extremely simi-
lar online studies. In our three representative samples, the proportion of loss-tolerant participants
is 57%, 47%, and 55%; in the corresponding student samples and elicitations, the proportions
are 32%, 22%, and 16%. As a further comparison, across eleven studies that report individual-
level heterogeneity in gain–loss attitudes, the average proportion loss tolerant is 33%.
5
The
similarity between our student samples and these previous studies—largely carried out in the
laboratory using a number of different methodologies—offers further evidence that the degree
of loss tolerance we observe is not an artefact of our approach.
Our study suggests that individual gain–loss attitudes are an important economic preference,
with high predictive power for self-reported economic behaviours and financial outcomes. The
individual loss aversion parameters elicited by DOSE are as stable over time as DOSE-elicited
measures of risk aversion and discounting, and more stable than traditional measures of risk
aversion (
Chapman
et al
. 2023
,
2024
). Moreover, our experimental measure of loss aversion
demonstrates “predictive validity” (
Mata
et al
. 2018
): loss-tolerant participants report a higher
percentage of assets in the stock market, more recent exposure to financial shocks, and lower
total financial assets. Loss tolerance is also associated with a propensity to engage in both casual
(lottos and scratch cards) and serious (casinos or online) gambling. These correlations are strik-
ing given that behavioural measures of risk aversion generally have little predictive power for
real-world outcomes, either in our survey or in the general literature (see
Friedman
et al
. 2014
and
Charness
et al
. 2020
for reviews).
4. Within the subsample of our representative sample that is most like students—those under 35 with a college
education (
N
=
138)—the proportion loss tolerant (31%) is similar to within our student samples.
5.
Delavande
et al
. (2023)
, in a study of uncertainty attitudes released after our initial working paper, report that
43% of participants in a representative sample are loss tolerant.
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Chapman
et al.
LOOMING LARGE OR SEEMING SMALL?
5
Our results are robust to a number of factors, including possible misspecification and remov-
ing participants least likely to be paying attention. Eliciting loss aversion using traditional
methods produces similar estimates of loss tolerance, and identifies similar differences between
the representative and student samples. Allowing for different specifications of the utility func-
tion, or alternative reference point models, still results in much lower estimates of loss aversion
and much higher estimates of loss tolerance than prior studies on student/laboratory popula-
tions. A model accounting for participants’ limited liability within the study—a potential cause
of house money effects—fits the choice data very poorly. Moreover, we show our findings are
not driven by inattention, nor by our parametric specification; they simply reflect a consistent
pattern of many participants accepting negative-expected-value lotteries.
The paper concludes with a discussion of how our findings affect the broader endeavour to
understand gain–loss attitudes. Importantly, our results do not represent a challenge to the key
insights of prospect theory. Our findings instead raise the question of why loss tolerance has
received little attention in the previous literature. The most straightforward explanation, given
our results, is the focus in prior studies on student/laboratory samples. However, methodological
limitations or publication bias may also provide part of the answer (
Walasek
et al
. 2018
;
Yechiam
2019
). Whatever the reason, our findings suggest that loss tolerance, in addition to loss aversion,
is an important behavioural regularity warranting deeper investigation. Indeed, the correlations
we find between loss tolerance and problematic behaviours suggest that loss tolerance may be
particularly harmful.
1.3.
Related literature
This paper expands on and supersedes an earlier working paper that found similar population-
wide estimates of loss tolerance (
Chapman
et al
. 2018
). The current study elicits a wider range
of loss aversion measures from two new samples, and adds a number of new robustness tests to
address concerns raised by various readers and seminar participants.
Our findings differ from the majority of prior studies, which tend to find significant loss
aversion. The loss aversion parameter in Prospect Theory,
λ
, indicates loss aversion when
λ
>
1, and loss tolerance when
λ
<
1(
Kahneman and Tversky 1979
). A recent meta-analysis
reports mean
λ
=
1
.
96 across more than 150 studies in both the laboratory and the field
(
Brown
et al.
2024
)—including an earlier general population study which reported median
λ
=
2
.
38 (
von Gaudecker
et al
. 2011
).
6
The high estimates of loss aversion in these earlier
studies may, at least in part, be explained by their elicitation methods. A series of studies in
social psychology have shown that loss aversion can be inflated by elicitations that offer partic-
ipants choices which are asymmetric in the range of possible gains and losses, or that conflate
loss aversion with the endowment effect or status quo bias (see
Ert and Erev 2013
;
Zeif and
Yechiam 2022
).
von Gaudecker
et al
. (2011)
for instance, offered participants 56 lotteries, but
none involved a negative-expected-value gamble—which is necessary to identify significant loss
tolerance when assuming a reference point of zero.
7
6.
von Gaudecker
et al
. (2011)
estimate a distribution of loss aversion for the population, rather than at the
individual level, and report a median
λ
that ranges from 0.12 to 4.47 depending on parametric assumptions. Similarly, in
a study released after our initial working paper,
Blake
et al
. (2021)
estimate a population-level loss aversion parameter
in the U.K., and report a preferred estimate of 1.21–2.41.
7. Another example is the commonly used elicitation introduced by
Fehr and Goette (2007)
, in which participants
are offered the choice between a safe status quo option and a series of hypothetical lotteries—in which the only option
demonstrating loss tolerance is the worst in the available set of options.
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6
REVIEW OF ECONOMIC STUDIES
Our investigation of the correlates of loss aversion extends the recent literature studying
the relationship between cognitive ability and economic decision-making. Previous studies have
generally concluded that higher cognitive ability is associated with greater normative rationality,
based primarily on investigating either patience or risk aversion (for example,
Frederick 2005
;
Dohmen
et al
. 2010
;
Benjamin
et al
. 2013
).
8
Consistent with most earlier work, we find that
higher cognitive ability individuals are less risk averse over lotteries involving only potential
gains (see
Dohmen
et al
. 2018
, for a detailed review of the literature). However, when confronted
with potential losses, both low- and high-cognitive-ability people tend to depart from normative
rationality, but in different ways—with low-cognitive-ability people being more loss tolerant,
and high-cognitive-ability people being more loss averse.
We also contribute to three broader literatures. In finance, there is a large literature that
applies prospect theory to financial market decisions. Similar to us,
Dimmock and Kouwenberg
(2010)
find that loss-averse households invest less in the stock market, consistent with several
theoretical studies suggesting that loss aversion may reduce household investment in equities
(see
Barberis
et al
. 2021
, and citations therein). Our findings also contribute to the study of
gambling by showing that loss tolerance may contribute to individuals’ willingness to gamble,
adding an additional explanation to a literature that has focused on probability misperceptions
(
Snowberg and Wolfers 2010
), skewness of the utility function (
Golec and Tamarkin 1998
),
or non-expected-utility models (
Chark
et al
. 2020
). Finally, our paper contributes to the litera-
ture examining the (generally poor) external validity of laboratory-based measures of economic
preferences.
2. MEASURING LOSS AVERSION
This section introduces the data and methods we use to measure loss aversion and other
behaviours. Our primary measures use DOSE, and we also implement two traditional multi-
ple price list elicitations, as described in Section
2.2
. Section
2.3
introduces our data, which are
drawn from two representative samples and two student samples.
2.1.
Theoretical definition
In line with most empirical studies of loss aversion, we estimate the parameters of a prospect
theory utility function (
Tversky and Kahneman 1992
) with power utility. In this specification,
participants value payments relative to a reference point, which we assume is zero, in line with
the previous experimental literature (
Brown
et al
. 2024
, Table 3). Loss aversion is conceptualized
as distinct from utility curvature, reflecting a kink in the utility function at zero. The standard
S-shaped utility function in prospect theory implies that, for common parameter values, partic-
ipants are risk averse over positive payments (gains), and risk loving over negative payments
(losses). Formally:
v(
x
,ρ
i
,
λ
i
)
=
{
x
ρ
i
for
x
≥
0
−
λ
i
(
−
x
)
ρ
i
for
x
<
0
,
(1)
8. Few studies have investigated the relationship between measures of cognitive skill and loss aversion:
Stango
and Zinman (2023)
report a positive relationship in a large sample in the U.S., while
Andersson
et al
. (2016)
find no
evidence of any relationship in a large sample in Denmark. Consistent with our results,
van Dolder and Vandenbroucke
(2022)
find a positive correlation between education and an individual-level measure of loss aversion in a sample of
financial professionals and investors.
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Chapman
et al.
LOOMING LARGE OR SEEMING SMALL?
7
in which
λ
i
parameterizes loss aversion,
ρ
i
risk aversion, and
x
∈
R
is a monetary outcome
relative to the reference point. If
λ
i
>
1, which is generally assumed, then the participant is loss
averse. If
λ
i
<
1, then the participant is loss tolerant. Our main estimates impose the same utility
curvature in both the gain and loss domain, so that
λ
captures all differences in valuation of gains
and losses. To make tables and figures easier to interpret, we use the
coefficient of relative risk
aversion
,1
−
ρ
i
, so that higher numbers indicate greater risk aversion.
To estimate individual-level risk and loss aversion we use DOSE, which is designed to tackle
the issues associated with estimating multiple preference parameters simultaneously. In the case
of loss aversion, multiple question types are needed: choices over lotteries over gains and losses
separately (risk aversion) and
mixed lotteries
—those including both gains and losses. Incon-
sistent choice across different question types may even prevent the estimation of parameters,
if, for example, some responses violate first-order stochastic dominance.
9
Such issues have
led many previous studies, including those in representative samples, to estimate population-
level statistics rather than elicit individual-level loss aversion parameters. DOSE overcomes
these issues by adapting the question sequences individuals receive to rapidly home in on their
preferences, while accounting for inconsistent choices. As a result, in simulations, the method
measures parameters more accurately than more established elicitation methods, particularly
for participants that are likely to make mistakes (
Chapman
et al
. 2018
). Moreover, DOSE pro-
duces a large quantity of choice data that we use to investigate loss aversion without parametric
assumptions or with alternative parametric forms (see Section
5.2
and
Supplementary Material,
Appendix C.1
).
2.2.
Measurement
Our implementations of DOSE ask participants a personalized sequence of simple questions,
such as those displayed in Figure
2
. The participant is given a simple explanation of the upcom-
ing choices, as in Figure
2
(a). He or she is then given a series of binary choices between a
lottery and a sure amount, similar to those in Figure
2
(b). The sure amounts, and the prizes in
the lotteries, are selected to maximize the informativeness of the choice for the parameters of
interest,
λ
and
ρ
, given a flat prior over those parameters and the participant’s previous choices.
The support of the prior distribution covers individual estimates obtained in laboratory data:
λ
∈[
0
.
1
,
4
.
5
]
and
ρ
∈[
0
.
2
,
1
.
7
]
. Thus, the mean of the prior is both loss averse (
λ
=
2
.
3) and
risk averse (
ρ
=
0
.
95).
10
Our main measure of loss aversion was obtained from a 20-question DOSE sequence, con-
taining three types of binary choices. To help pin down individual risk aversion (
ρ
), some
questions contained lotteries with only gains, while others contained lotteries with only losses.
The third type of question then included both gains and losses, helping to pin down
λ
.Tomake
the choices as simple as possible, all lotteries have 50% probabilities of payoff, and the set of
payoffs always contains one value that is zero.
11
When a lottery contains a gain and a loss,
9. For example, two studies in the Netherlands (
Booij and Van de Kuilen 2009
;
Booij
et al
. 2010
) attempted
to estimate loss aversion in a representative sample, but were only able to obtain estimates for less than 30% of their
participants due to dominated choices.
10. Questions are chosen to maximize the Kullback–Leibler divergence, see
Supplementary Material,
Appendix A
for a technical treatment, and
Chapman
et al
. (2018)
for an exhaustive discussion of the method and its
properties.
11. Our focus is on loss aversion, so we use 50/50 probabilities of two outcomes in lotteries to minimize prob-
ability distortions. Experimental evidence suggests that participants make more consistent choices when lotteries have
this structure (
Olschewski and Rieskamp 2021
).
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8
REVIEW OF ECONOMIC STUDIES
(a)
(b)
F
IGURE
2
DOSE Instructions and Example Question (a) DOSE Instructions. (b) Example DOSE Choice (analysed in Figure
1
)
then the sure amount is always zero. When the choices contain only nonnegative or nonpositive
payoffs, one of the payoffs of the lottery is always zero.
Participants were also asked a 10-question DOSE sequence, for comparison with an ear-
lier survey completed in 2015, as well as two MPL modules eliciting preferences over mixed
lotteries—that is, lotteries with prizes in both the gain and loss domain.
12
The shorter DOSE
sequence did not contain choices with only non-positive payoffs. In the 10-question sequence,
the sure amount appeared first, reversing the order from the longer 20-question sequence. We
find a similar level of loss tolerance across both the DOSE modules (see Section
3
) and the
multiple price list (MPL) modules (see Section
5.1
).
To implement losses in the survey, participants were endowed with a stock of points at the
start of each section containing a potential loss, in line with standard experimental procedure
(see, for example, Figure
2
(a)). This could, in principle, lead to participants not considering any
payoffs as losses, because they are playing with “house money” (
Thaler and Johnson 1990
).
Such effects do not appear to be a concern in our data, see Section
5.3
.
13
12. The order of the modules was randomized. Specifically, the two DOSE modules were randomized to appear
either at the beginning or end of the survey. The MPL modules appeared in a random order between the DOSE modules.
We discuss possible order effects in Section
5.4
.
13.
Etchart-Vincent and l’Haridon (2011)
investigate different methods for implementing experimental losses,
and observe similar behaviour when paying losses out of an endowment or out of a participant’s own pocket.
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Chapman
et al.
LOOMING LARGE OR SEEMING SMALL?
9
2.3.
Data
2.3.1. Main Sample.
We measured loss aversion in a large, representative, incentivized sur-
vey of the U.S. population which contained both a 20- and a 10-question DOSE sequence, as well
as the two MPL modules described above. The survey collected a number of behavioural and
demographic measures from 1,000 U.S. adults, and was conducted online by YouGov between
21 February and 24 March 2020.
14
Participants in the survey were drawn from a large panel
maintained by YouGov. Most importantly for our results, this approach allowed us to capture the
preferences of lower-education individuals that are often overlooked in both laboratory exper-
iments and online crowdsourcing platforms such as Prolific.
15
All participants had previous
experience with YouGov’s online survey platform, and had to pass a test showing that they
understood the instructions before starting the survey.
All measures of economic preferences in the survey, such as risk and loss aversion, were
incentivized, with one module randomly selected for payment at the end of the survey.
16
All
outcomes were expressed in YouGov points, an internal YouGov currency used to pay panel
members, which can be converted to U.S. dollars using the approximate rate of $0.001 per point.
For ease of interpretation, we generally convert points to dollars. To enhance the credibility of
these incentives, we took advantage of YouGov’s relationship with its panel, and restricted the
sample to those who had already been paid (in cash or prizes) for their participation in surveys.
The average payment to participants (including the show-up fee) was $10 (10,000 points), which
is approximately four times the average for YouGov surveys of a similar length. The median
completion time was 42 minutes.
The conversion from points to awards can only be done at specific point values, which leads
to a slightly convex payment schedule.
17
In principle, participants’ choices could be influenced
by the opportunity to cross one of these thresholds. We subject this possibility to extensive
checks in
Supplementary Material, Appendix C.6
, and do not observe differences in the extent
of loss tolerance based on the number of points participants began the survey with, or the differ-
ence between their initial point balance and the next threshold. In particular, we find extremely
similar results when we consider only participants who began the survey with 55,000–100,000
points, who are especially likely to treat points as equivalent to cash. Moreover, the payment
schedule does not appear to affect other behavioural regularities, for which we observe behaviour
in line with prior literature (see Table 2 of
Chapman
et al
. 2023
).
18
These findings are perhaps
unsurprising given that panelists tend to accrue points over several years, and that neither par-
ticipants’ points totals nor the exchange thresholds are made salient during recruitment or when
taking the survey.
14. For screenshots of experimental instructions and the questions used in this paper, see
Supplementary
Material, Appendix E
. Full design documents for all our samples can be found at
eriksnowberg.com/wep.html
.
15. YouGov builds representative samples using targeted quota sampling from a large panel and by constructing
sample weights to account for differential nonresponse. This produces better representative samples than other non-
probability sampling procedures, and performs better than traditional probability sampling in eliciting attitudes (
Pew
Research Center 2016
, YouGov is Sample I).
16. Participants did not receive any feedback about their choices until the payment screen. Adaptive methods
such as DOSE are not generally incentive compatible, as in principle participants can make choices strategically to
affect the questions received in future. However, such strategic behaviour does not appear to be a concern in practice:
even very sophisticated participants do not seem to respond strategically after being explicitly informed that a question
sequence is manipulable (
Ray 2015
).
17. Major exchange thresholds exist at 25,000 points (the minimum exchange amount; for a $15 gift card), 30,000
points ($25 gift card), 55,000 points ($50 gift card), and 100,000 points ($100 as a gift card or in cash).
18. For example, we find that most participants in both of our general population samples, and in the sample in
Chapman
et al
. (2023)
, exhibit an endowment effect. However, the endowment effect is uncorrelated with any of our
elicitations of loss aversion, see
Chapman
et al
. (2023)
.
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10
REVIEW OF ECONOMIC STUDIES
F
IGURE
3
The U.S. population is substantially more loss tolerant than student populations
Notes:
Figure displays the kernel density of each parameter, plotted using Epanechnikov kernel with bandwidth chosen by rule-of-thumb
estimator
2.3.2. Supplementary Sample.
The 10-question DOSE module was also included in an
earlier incentivized, representative survey (
N
=
2
,
000) conducted in March–April 2015, and
a follow-up conducted around seven months later. This sample was the subject of our initial
working paper (
Chapman
et al
. 2018
), which also serves as documentation for the modelling
choices and analysis in this paper.
2.3.3. Student Samples.
To provide a comparison to our results in the general population
we elicited loss aversion from a sample of students (
N
=
437) recruited from the University of
Pittsburgh Experimental Laboratory mailing list in November 2021. The implementation of the
study was extremely similar to the one used with YouGov’s panel: the students completed the
survey online, and questions were presented with the same point values as in our representa-
tive sample. The only significant difference was that students received the value of their points
converted into cash within two weeks, via a Visa gift card, rather than deposited into a YouGov
account. The average payment was
≈
$10
.
70, compared to $10 in the representative sample.
The planned comparison between the student and general population sample in Figures
1
and
3
was pre-registered with the Open Science Framework (
Chapman
et al
. 2021
). We also elicited
loss aversion using only a 10-question DOSE module in a Pittsburgh student sample (
N
=
369)
in January 2019, in a study comparable to our supplementary sample.
3. LOSS AVERSION IN A REPRESENTATIVE SAMPLE
The U.S. population is substantially more loss tolerant than participants in student samples.
Consistent with this finding, higher-cognitive-ability participants are more loss averse. Both loss
aversion and loss tolerance are about as stable over six months as risk aversion and discounting.
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Chapman
et al.
LOOMING LARGE OR SEEMING SMALL?
11
3.1.
Widespread loss tolerance in the U.S. Population
Our main finding—that the general population contains a far higher proportion of loss-tolerant
individuals than student samples—is displayed in Figure
3
. Estimating
λ
using the 20-question
DOSE sequence, 57% of participants in the representative sample are loss tolerant, similar to
the proportion observed in Figure
1
. The parametric estimates, however, allow us to investigate
the heterogeneity in gain–loss attitudes in more detail, as they identify the degree of individuals’
loss tolerance or loss aversion.
The distribution of estimates is markedly different in our student sample, where 68% of
individuals are classified as loss averse. Across our two student samples and the two DOSE
sequences, we find that approximately 22% of students are loss tolerant. This proportion is
lower than across eleven previous studies that have investigated individual loss aversion in stu-
dent/laboratory experiments, which classify, on average, 33% of participants as loss tolerant
(combined
N
=
1
,
882).
19
Note that this difference does not simply reflect a greater willing-
ness to accept lotteries in the general population: 90% of the general population sample—and
89% of those classified as loss tolerant—were classified as risk averse, compared to 76% of stu-
dents. This is in line with prior research showing students are less risk averse than the general
population (see
Snowberg and Yariv 2021
, and references therein).
Choices during our survey clearly demonstrate that losses do not “loom larger than gains”
(
Kahneman and Tversky 1979
, p. 279) for a large proportion of the U.S. population. Close to
two-thirds of participants in our main sample preferred at least one 50/50 lottery with negative
expected value—that is, with a potential loss greater than the potential gain—to a sure amount of
zero within the 20-question DOSE module. In many cases, losses appear to have been discounted
substantially, with just short of 40% of participants accepting a lottery with a potential loss of
more than double a possible gain (see
Supplementary Material, Appendix Figures B.2 and B.3
).
We see similar results in the MPL elicitations discussed in Section
5.1
, demonstrating that such
choices are not limited to the DOSE modules. Our data thus provide direct evidence of loss
tolerance, even in the absence of parametric assumptions.
We present a summary of participants’ choices in the DOSE sequences in Figure
4
,drawing
on more than 35,000 individual choices over mixed lotteries.
20
Each panel in this figure displays
the percentage of participants choosing a mixed lottery as a function of the difference between
the lottery’s expected value and a sure amount of $0. The top row of the figure presents the
choice data from the 20-question DOSE sequence, which were used to produce the parameter
estimates in Figure
3
. Each panel presents participants from a different tercile of estimated
λ
.
The bottom panel presents choices from the 10-question DOSE sequence, combining the choices
of participants in both our main and supplementary samples. The width of each line in the figure
captures the proportion of participants within each range of
λ
. For example, there are very few
students classified as highly loss tolerant, so the lines representing student choices in the two
left-hand panels are very thin.
The DOSE parametric estimates are underpinned by a robust pattern of choices, easily
observable by examining the panels of Figure
4
. Participants categorized as having high loss
tolerance accept a large proportion of lotteries with negative expected value (87%)—a much
19. These studies are
Schmidt and Traub (2002)
,
Brooks and Zank (2005)
,
Abdellaoui
et al
.
(
2007
,
2008
,
2011
),
Sokol-Hessner
et al
. (2009)
,
Brooks
et al
. (2014)
,
Goette
et al
. (2019)
,
Koch and Nafziger (2019)
,
L’Haridon
et al
.
(2021)
and
Bocqu
́
eho
et al
. (2023)
.
20.
Supplementary Material, Appendix B.1
presents additional analysis of the choice data, including showing
choices in questions offering lotteries in only the gain or loss domain, and analysing differences in choices according to
cognitive ability tercile.
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12
REVIEW OF ECONOMIC STUDIES
F
IGURE
4
DOSE parametric estimates reflect a clear pattern of choices
Notes:
Each panel displays the kernel density of the percentage of participants choosing a lottery with different expected values rather
than a sure amount of $0, plotted using Epanechnikov kernel with a bandwidth of 1. “High loss tolerance” (
λ
<
0
.
57
), “moderate loss
tolerance/loss aversion” (
0
.
57
<
λ
<
1
.
23
), and “high loss aversion” (
λ
>
1
.
23
) are defined according to the terciles of the
λ
elicited from
the representative sample for the 20-question DOSE module. The top row uses estimates from the 20-question module and our main
samples (1,000 in the general population and 437 students), and the bottom uses estimates from the 10-question module (3,000 in the
general population and 806 students). Line widths are scaled based on the relative proportion of participants in a sample within each of
these categories
larger share than those categorized as having high loss aversion (6%). As expected, most lines
are generally upward sloping, reflecting the fact that participants become more likely to accept
mixed lotteries as the expected value increases.
21
Importantly, the lines for students and the
general population broadly mirror each other, indicating that the major difference between the
samples is the proportion of people falling within each category, rather than different patterns of
choices within categories. Finally, comparing the top and bottom panels demonstrates how the
longer, 20-question sequence allows more refined parameter estimates by offering participants
a broader range of possible choices—and consequently leading to parameter estimates that are
further away from the initial prior. This difference is also reflected in the parametric estimates
from the 10-question sequence that we present in the following subsection.
3.2.
Stability of loss aversion
The loss aversion estimates from our 10-question DOSE sequence show similar levels of loss
tolerance as our main estimates, and also demonstrate that the DOSE-elicited estimates of loss
21. However, the DOSE question selection algorithm means that this is not always the case, particularly when
choices discriminate between possible parameter values far from the mean of the Bayesian prior. In particular, the
flatter parts of lines in the left-hand panels reflect that DOSE only offers lotteries with large negative expected values to
participants that have already revealed loss tolerance through their prior choices.
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Chapman
et al.
LOOMING LARGE OR SEEMING SMALL?
13
F
IGURE
5
DOSE estimates of loss aversion are similar using a 10-question DOSE module, and are stable over time
Notes:
Figure displays the kernel density of each parameter, plotted using Epanechnikov kernel with bandwidth chosen by rule-of-thumb
estimator
aversion are stable over time. As described in Section
2.2
, we used this shorter DOSE sequence
to elicit loss aversion in our main sample, and also in two waves of the supplementary sample.
Consistent with the estimates in Figure
3
, we find that approximately half the U.S. population is
loss tolerant. Further, loss aversion is nearly as stable over time as risk aversion and discounting,
suggesting that all three are similarly useful in describing individual preferences.
The percentage of participants who are loss tolerant—ranging from 47% to 55%—in the
10-question DOSE sequence is similar to our main results, as shown in Figure
5
. This figure
displays the distribution of loss aversion (
λ
) elicited using the 10-question DOSE sequence in our
main sample (left-hand panel) and the multi-wave supplementary sample (right-hand panel). The
slightly smaller proportion of loss-tolerant participants in the 10-question module is consistent
with the fact that the mean of the prior on
λ
(2.3) assumes everyone is loss averse. Loss-tolerant
participants with a true
λ
slightly lower than 1 will require more questions to pull our estimates
away from the prior and below 1. However, the fact that the final estimates of the proportion
loss tolerant are relatively similar across the 10- and 20-question DOSE modules suggests a
relatively small effect of the prior. Moreover, we once again observe a much smaller proportion
of students categorized as loss tolerant; 22% amongst those completing a version of our main
survey, and 16% of those completing a version of the supplementary survey.
The estimates from the 10-question DOSE module are very stable over time, as shown in the
right-hand panel of Figure
5
. The correlation of DOSE estimates of loss aversion across the two
survey waves, collected six months apart, was 0.38 (s.e.
=
0
.
04). This over-time correlation was
similar to that for DOSE elicitations of risk aversion (
ρ
)—0.41 (0.04)—and for time discount-
ing (
δ
)—0.45 (0.05).
22
The within-person stability was lower when using other risk elicitation
techniques—between 0.26 and 0.33 (all with s.e. = 0.04) across two MPLs and a risky project
question (
Gneezy and Potters 1997
)—consistent with lower measurement error in the DOSE
estimates. Moreover, loss tolerance is as stable as loss aversion: of those classified as loss toler-
ant by DOSE on the first survey, 71% were also classified as loss tolerant on the second, whereas
for loss aversion the figure is 67%. The stability of the DOSE-elicited parameters both provides
22. See
Chapman
et al
. (2024)
to compare these figures with the stability of a broad range of preference measures,
including social preferences, overconfidence, and risk and time preferences.
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14
REVIEW OF ECONOMIC STUDIES
F
IGURE
6
A high proportion of participants in every population subgroup accept a negative-expected-value gamble
Notes:
The figure reports choices made by participants in different demographic groups. The left-hand panel displays the proportion of
each group preferring a lottery with a 50% chance of winning $10 and a 50% chance of losing $12 to a sure amount of $0. The right-hand
panel displays the proportion of each group preferring a lottery with a 50% chance of winning $15 and a 50% chance of winning $0 to a
sure amount of $5.90. “Low” and “High” cognitive ability and income refer to the bottom and top terciles within the sample. Error bars
represent 90% confidence intervals
reassurance about the robustness of our results, and suggests that gain–loss attitudes are a useful
descriptor of economic preferences.
3.3.
Economic preferences and cognitive ability
Cognitive ability is the strongest correlate of both loss and risk aversion we examine, even after
controlling for important socio-demographic characteristics. High-cognitive-ability participants
are less risk averse—consistent with most previous studies—but more loss averse. These pat-
terns are robust to controlling for individual characteristics such as income and education, and
reflect both low- and high-cognitive-ability participants consistently making choices that do not
maximize expected value.
We measure cognitive ability using a set of nine questions. Six questions from the Inter-
national Cognitive Ability Resource (ICAR;
Condon and Revelle 2014
) capture IQ: three are
similar to Raven’s Matrices, and the other three involve rotating a shape in space. We also admin-
ister the Cognitive Reflection Test (CRT;
Frederick 2005
): three arithmetically straightforward
questions with an instinctive, but incorrect, answer. Our cognitive ability score is the sum of
correct answers to these nine questions.
23
Participants’ choices in two fixed lottery questions, displayed in Figure
6
, are consistent
with the finding that the general population is less loss averse and more risk averse than
student/laboratory populations. In particular, subgroups of the population that are more similar
23. We combine the IQ and CRT measures because they are highly correlated (0.43, s.e.
=
0
.
03). The pattern
of correlations with each of these two components is similar to the combined measure—see
Supplementary Material,
Appendix Table C.1
. This table also presents correlations with additional socio-demographic measures.
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Chapman
et al.
LOOMING LARGE OR SEEMING SMALL?
15
TABLE 1
Loss aversion is positively correlated with cognitive ability
(
N
=
1
,
000
)
DV = Loss Aversion (
λ
)DV
=
Risk Aversion (1-
ρ
)
Univariate
Multivariate
Univariate
Multivariate
Correlations
Regression
Correlations
Regression
Cognitive Ability
0
.
20***
0
.
17***
−
0
.
30***
−
0
.
29***
(
0
.
044
)(
0
.
049
)(
0
.
044
)(
0
.
045
)
Income (Log)
0
.
10**
0
.
06
−
0
.
03
0
.
02
(
0
.
050
)(
0
.
053
)(
0
.
066
)(
0
.
068
)
Education
0
.
16***
0
.
10*
−
0
.
12**
−
0
.
06
(
0
.
045
)(
0
.
051
)(
0
.
051
)(
0
.
048
)
Male
−
0
.
06
−
0
.
09*
−
0
.
05
−
0
.
01
(
0
.
049
)(
0
.
049
)(
0
.
048
)(
0
.
044
)
Age
−
0
.
05
−
0
.
04
0
.
14***
0
.
10**
(
0
.
054
)(
0
.
052
)(
0
.
053
)(
0
.
046
)
Married
0
.
01
−
0
.
03
0
.
07
0
.
09**
(
0
.
050
)(
0
.
049
)(
0
.
049
)(
0
.
045
)
Notes:
***, **, * denote statistical significance at the 1%, 5%, and 10% level, respectively. Robust standard errors, in
parentheses, come from a standardized regression. The first and third columns report univariate correlations, and the sec-
ond and fourth columns report the coefficient from a multivariate regression. See
Supplementary Material, Appendix C.2
for additional specifications with alternative definitions of loss aversion, control variables, and cognitive ability.
to college students are generally less likely to accept the negative-expected-value gamble dis-
cussed in the introduction—and are therefore more likely to be loss averse—but are more likely
to accept a similar lottery where only gains are involved—suggesting they are less risk averse.
The left-hand-panel of Figure
6
investigates the willingness to accept a negative-expected-value
lottery—between gaining $10 and losing $12—across subgroups of our general population sam-
ple. As we have seen in Figure
1
, 60% of the representative sample preferred this lottery to a
sure amount of $0, whereas only 28% of our student sample did. Here we can see that the pro-
portion choosing the lottery is above 40% in each demographic group within the representative
sample, suggesting that loss tolerance is prevalent across different population categories—and
that undergraduate students are an unusually loss averse demographic. Further, individuals with
high cognitive ability—a characteristic that is typical of undergraduates (
Snowberg and Yariv
2021
)—or a college education, are less likely to accept the lottery. However, as shown in the
right-hand panel, these groups are more willing to accept a $0/$15 lottery over a sure amount of
$5.90—suggesting that they are also less risk averse.
Correlations between the DOSE-elicited estimates of loss aversion and other individual char-
acteristics, reported in Table
1
, confirm the most important visual patterns of Figure
6
. The first
column in the table reports univariate correlations between loss aversion and each characteris-
tic, while the second column reports the results of a multivariate regression. The correlations
we observe are very similar to the patterns of choices displayed in Figure
6
. In particular, more
educated and more cognitively able individuals tend to be more loss averse and also less risk
averse. In line with previous studies, younger individuals also tend to be less risk averse, and
perhaps also more loss averse—although the latter finding is not robust across samples and
specifications.
24
24. We find a statistically significant negative correlation between age and loss aversion elicited with the 10-
question DOSE sequence. Age is also associated with being less risk averse over losses when allowing for differential
utility curvature across the gain and loss domains. See
Supplementary Material, Appendix C.2
for more details.
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16
REVIEW OF ECONOMIC STUDIES
Both high- and low-cognitive-ability participants consistently deviate from expected-value
maximization in our data—but in very different ways. Less than 2% of participants made an EV-
maximizing choice in more than 18 out of 20 questions. Consistent with some previous studies
(for example,
Burks
et al
. 2009
;
Benjamin
et al
. 2013
), participants in the highest tercile of
cognitive ability were slightly more likely to make an expected-value maximizing choice (doing
so in 66% of questions versus 56% for those in the lowest tercile of cognitive ability). Low-
cognitive-ability participants were more likely than high-cognitive-ability participants to choose
mixed lotteries, whether or not those lotteries had a positive (74% versus 65%) or negative (60%
versus 35%) expected value. The correlation between loss aversion and cognitive ability is thus
underpinned by a clear pattern of individual choices.
One notable feature of Table
1
is that the groups that tend to be more loss tolerant—the
less educated, lower income, and less cognitively able—are also those we might expect to
have encountered more losses in life. This raises the intriguing possibility that loss tolerance
either shapes or is shaped by everyday experiences. While our survey cannot test this hypoth-
esis directly, in the next section, we investigate the relationship between loss aversion and
individuals’ exposure to losses outside of the survey environment.
4. LOSS AVERSION AND EXPOSURE TO REAL WORLD LOSSES
Our measure of loss attitudes is correlated with important real-world behaviours and outcomes.
Loss-tolerant participants in our survey are more likely to risk potential losses through gambling
or investing in stocks. Loss-tolerant individuals also appear to experience more losses: they are
more likely to report a recent financial shock and also hold fewer financial assets. Our data do not
allow us to distinguish the direction of causality in these relationships: individuals may be more
likely to spend and invest in a way that leads to real-world losses because they are loss tolerant,
or they may become loss tolerant due to experiencing losses. However, these results demonstrate
that our measure of loss aversion reflects individuals’ exposure to real-world losses.
4.1.
Measures of behaviour outside of the survey
To understand the relationship between loss aversion and behaviour outside of the study, we
asked participants about their equity investments, recent gambling, and household shocks. Par-
ticipants were asked to specify their total investable financial assets (excluding the value of their
home), and the percentage of those assets invested in the stock market (directly or through mutual
funds).
25
There is likely some noise in these measures, which will tend to bias the correlations
with estimated preference parameters towards zero (
Gillen
et al
. 2019
).
Gambling behaviour and the experience of household shocks were each measured using a
battery of questions that we summarize using principal components analyses. Table
2
provides
a brief description of each question, and shows that two principal components emerge for each
module.
26
Most types of gambling behaviour load on the first component, which we term
Serious
gambling. The second component captures
Casual
gambling—lottos and scratch cards—which
involve smaller stakes, and can often be done at supermarkets and convenience stores.
25. Specifically, participants were asked to include, “the value of your bank accounts, brokerage accounts, retire-
ment savings accounts, investment properties, etc., but NOT the value of the home(s) you live in or any private business
you own.”
26. Questions on household shocks were taken from
Pew Research Center
(
2015
, p 4); questions on gambling
were adapted from
Gonnerman and Lutz (2011)
.
Supplementary Material, Appendix D
details the principal components
analyses.
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Chapman
et al.
LOOMING LARGE OR SEEMING SMALL?
17
TABLE 2
Principal components analysis
Gambling
Household Shocks
(Last Time Gambled)
(Experienced in Last 12 Months)
Components
Components
Serious
Casual
Financial
Personal
Sports Bets
0
.
45
−
0
.
05
Unemployment
0
.
37
0
.
08
Online
0
.
40
0
.
00
Injury
0
.
38
0
.
33
Slots
0
.
26
0
.
26
Auto Accident
0
.
51
−
0
.
37
Casino
0
.
43
0
.
04
Housing Related
0
.
44
0
.
03
Friends /Family
0
.
43
−
0
.
03
Divorce
−
0
.
01
0
.
86
Lotteries/Lottos
−
0
.
03
0
.
68
Other
0
.
51
0
.
04
Scratch Cards
−
0
.
00
0
.
67
–
–
–
Other
0
.
45
−
0
.
06
–
–
–
% of Variation
41
21
% of Variation
29
18
Notes:
Only first two principal components are shown, rotated using varimax rotation.
The two components of household shocks correspond to shocks that are primarily
Financial
, and
to shocks which are more
Personal
in nature, including divorce and (to a lesser extent) injury.
4.2.
Gambling and equity investing
Loss-tolerant individuals are more willing to expose themselves to losses through gambling
activity and financial markets. Gambling is the most natural real world analogue to the simple
lotteries offered by DOSE, and so provides a test of whether our findings are an artefact of the
stylized survey environment. Moreover, a large literature in finance has suggested that loss aver-
sion may inhibit equity investments (see
van Bilsen
et al
. 2020
. Consistent with that literature,
we find that loss-averse individuals are less willing to invest in stocks, conditional on their asset
holdings.
Loss aversion is negatively correlated with both of the principal components of gambling
activity, as shown in Figure
7
. Moreover, Table
3
shows that these relationships are robust
to controlling for other individual characteristics, including risk aversion and cognitive abil-
ity. Loss-tolerant individuals not only accept negative-expected-value bets in our study; they
participate in such gambles in their day-to-day lives.
Loss-tolerant individuals also hold a greater proportion of their investable assets in the stock
market, as shown in Figure
8
. That figure plots the results from regressing the percentage of all
financial assets held in the stock market against our measures of risk aversion and loss aversion,
controlling for demographic characteristics, cognitive ability, and total asset ownership. The
left-most point includes the whole sample. Each point further to the right progressively limits
the sample to those with greater assets. The coefficient is consistently negative, and becomes
statistically significant at conventional levels once the sample is restricted to those with at least
$1,000 of financial assets.
27
Combined with the results regarding gambling behaviour, these
findings suggest that loss-tolerant individuals might be more likely to spend and invest in a way
that leads to real-world losses.
27. These results do not conflict with previous studies finding that low IQ inhibits stock market participation
(
Grinblatt
et al
. 2012
, see, for instance): our data also show a negative correlation between cognitive ability and whether
an individual has any stock market investment.
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18
REVIEW OF ECONOMIC STUDIES
F
IGURE
7
Loss tolerance is associated with more recent gambling
Notes:
Each panel refers to a principal component of our gambling measures—see Section
4.1
for details. The figure displays local mean
regressions, plotted using Epanechnikov kernel with bandwidth of 0.8. Grey dotted lines represent 90% confidence intervals
TABLE 3
Correlations between loss aversion and gambling are robust to controlling for risk aversion and other individual
characteristics
(
N
=
1
,
000
)
Serious Gambling
Casual Gambling
Loss Aversion (
λ
)
−
0
.
12**
−
0
.
11**
−
0
.
10**
−
0
.
13***
−
0
.
12***
−
0
.
09**
(
0
.
052
)(
0
.
051
)(
0
.
049
)(
0
.
045
)(
0
.
046
)(
0
.
043
)
Risk Aversion (1 -
ρ
)– 0
.
03
0
.
04
–
0
.
05
−
0
.
03
–
(
0
.
051
)(
0
.
051
)
–
(
0
.
052
)(
0
.
046
)
Cognitive Ability
–
–
−
0
.
13***
–
–
−
0
.
14***
––
(
0
.
050
)
––
(
0
.
045
)
Education
–
–
0
.
03
–
–
−
0
.
06
––
(
0
.
050
)
––
(
0
.
048
)
Income (Log)
–
–
0
.
11*
–
–
0
.
03
––
(
0
.
061
)
––
(
0
.
051
)
Age
–
–
−
0
.
20***
–
–
0
.
22***
––
(
0
.
065
)
––
(
0
.
049
)
Male
–
–
0
.
45***
–
–
0
.
18**
––
(
0
.
097
)
––
(
0
.
086
)
Married
–
–
−
0
.
18*
–
–
0
.
01
––
(
0
.
107
)
––
(
0
.
088
)
Owns Home
–
–
0
.
22*
–
–
0
.
24**
––
(
0
.
118
)
––
(
0
.
093
)
Notes:
***, **, * denote statistical significance at the 1%, 5%, and 10% level, respectively. All continuous variables
are standardized. Robust standard errors are displayed in parentheses. The magnitude and statistical significance of the
coefficients for loss and risk aversion are similar when including controls as categorical variables—see
Supplementary
Material, Appendix Table C.8
. There is no statistically significant relationship between risk aversion and any of the
dependent variables when loss aversion is excluded—see
Supplementary Material, Appendix Table C.9
.
Loss aversion is a much stronger predictor of both gambling and investment behaviour
than small-stakes risk aversion. The regressions in Table
3
show little evidence that risk aver-
sion predicts either component of gambling behaviour: the results are similar even when loss
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Chapman
et al.
LOOMING LARGE OR SEEMING SMALL?
19
F
IGURE
8
Loss aversion is negatively correlated with stock market investments, conditional on total financial assets
Notes:
Figures display coefficients from regressing the percentage of an individual’s assets invested in the stock market on loss aversion
and risk aversion, controlling for log household financial assets, cognitive ability, home ownership, and the socio-demographic variables
in Table
1
. Loss and risk aversion are standardized, and so the coefficients represent a one standard deviation change in the relevant
variable. Error bars represent 90% confidence intervals. See
Supplementary Material, Appendix Table C.12
for full regression results,
and
Supplementary Material, Appendix Figure C.8
for results with alternative sets of control variables
aversion is excluded (see
Supplementary Material, Appendix Tables C.9 and C.13
). We do
find some evidence that risk aversion is associated with smaller investments in the stock
market—see the right-hand panel of Figure
8
—but only amongst those with very high financial
assets.
4.3.
Shocks and total assets
A plausible explanation for the existence of loss tolerance is that individuals become habituated
to repeated losses. The correlations in Table
1
are consistent with this explanation: loss toler-
ance is more common among groups that we would expect to experience more losses—those
with lower cognitive ability, education, and income. This subsection shows that loss tolerance is
associated with both being more likely to have experienced a recent financial shock, and holding
fewer financial assets, even after controlling for other characteristics.
Loss aversion is negatively correlated with having experienced a recent financial shock, but
not a personal shock, as shown in Figure
9
and in Table
4
. There is a clear negative relationship
between loss aversion and financial shocks—unemployment, housing, automotive, and other
losses—the first principal component of household shocks (see Table
2
). However, there is no
relationship with personal shocks (the second principal component), which loads heavily on
divorce and personal injury. As might be expected, given that we measure loss aversion in the
domain of monetary gambles, our measure of loss aversion is associated with losses which are
likely of a financial, rather than personal, nature.
Loss-tolerant individuals also hold fewer total financial assets, as shown in Table
4
. There is
a strong positive relationship between loss aversion and the amount of financial assets owned,
even after controlling for income, cognitive ability, and other demographics. The final column
of the table shows that the relationship is also robust to controlling for home ownership, which
could capture either familial wealth or other major asset holdings. Moreover, the rate of home
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20
REVIEW OF ECONOMIC STUDIES
F
IGURE
9
Loss aversion is associated with less exposure to financial shocks
Notes:
Each panel refers to a principal component of our household shocks measures—see Section
4.1
for details. The figure displays
local mean regressions, plotted using Epanechnikov kernel with bandwidth of 0.8. Grey dotted lines represent 90% confidence intervals
TABLE 4
Loss-tolerant individuals experience more financial shocks and have fewer financial assets
(
N
=
1
,
000
)
Financial Shocks
Personal Shocks
Financial Assets (Log)
Loss Aversion (
λ
)
−
0
.
12***
−
0
.
13***
−
0
.
01
−
0
.
00
0
.
14***
0
.
07*
(
0
.
044
)(
0
.
043
)(
0
.
051
)(
0
.
047
)(
0
.
048
)(
0
.
038
)
Risk Aversion (1-
ρ
)
−
0
.
09*
−
0
.
04
0
.
03
0
.
05
0
.
05
0
.
06
(
0
.
051
)(
0
.
048
)(
0
.
056
)(
0
.
050
)(
0
.
070
)(
0
.
041
)
Cognitive Ability
–
0
.
08*
–
0
.
01
–
0
.
06
–
(
0
.
045
)
–
(
0
.
046
)
–
(
0
.
041
)
Education
–
0
.
07
–
−
0
.
09*
–
0
.
08**
–
(
0
.
049
)
–
(
0
.
052
)
–
(
0
.
038
)
Income (Log)
–
−
0
.
14**
–
0
.
13*
–
0
.
40***
–
(
0
.
062
)
–
(
0
.
067
)
–
(
0
.
053
)
Age
–
−
0
.
17***
–
−
0
.
01
–
0
.
09*
–
(
0
.
052
)
–
(
0
.
058
)
–
(
0
.
045
)
Male
–
0
.
11
–
0
.
06
–
−
0
.
05
–
(
0
.
090
)
–
(
0
.
102
)
–
(
0
.
074
)
Married
–
0
.
23**
–
−
0
.
16
–
−
0
.
00
–
(
0
.
097
)
–
(
0
.
112
)
–
(
0
.
090
)
Owns Home
–
−
0
.
15
–
−
0
.
35**
–
0
.
35***
–
(
0
.
102
)
–
(
0
.
138
)
–
(
0
.
091
)
Notes:
***, **, * denote statistical significance at the 1%, 5%, and 10% level, respectively. All continuous variables
are standardized. Robust standard errors are displayed in parentheses. The magnitude and statistical significance of the
coefficients for loss and risk aversion are similar when including controls as categorical variables—see
Supplementary
Material, Appendix Table C.10
. There is no statistically significant relationship between risk aversion and any of the
dependent variables when loss aversion is excluded—see
Supplementary Material, Appendix Table C.11
.
ownership is, if anything, slightly lower among participants classified as loss tolerant (55% ver-
sus 59%), suggesting that the results are not due to loss-tolerant individuals investing more into
alternative assets.
The findings in this section provide suggestive evidence that loss tolerance is a harmful
behavioural bias. Loss-tolerant individuals are more likely to gamble, and they also experience
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Chapman
et al.
LOOMING LARGE OR SEEMING SMALL?
21
more financial shocks—consistent with making life choices that carry a more substantial risk of
potential losses. The fact that loss tolerance is associated with greater stock market investment
could, in principle, help overcome the general tendency of individuals to have too little of their
portfolio in equities (
Benartzi and Thaler 1995
) and hence lead to positive financial outcomes. In
practice, however, loss-tolerant individuals end up with fewer financial assets, even conditional
on other individual characteristics. Pinning down whether loss tolerance causes these outcomes
is beyond the scope of this study, but the results point to a need for further research into the
causes and consequences of loss aversion.
5. ROBUSTNESS
The widespread willingness to accept negative-expected-value gambles, displayed in Figures
1
,
4
, and
6
, demonstrates that our central finding—that a large proportion of the U.S. population is
loss tolerant—is not driven by the DOSE elicitation method or by our parametric assumptions.
However, our data present the opportunity to further reduce concerns about the robustness of our
results, while learning more about participants’ behaviour. First, we find a similar level of loss
tolerance when preferences are elicited using the more traditional multiple price list (MPLs;
Holt
and Laury 2002
) procedure. Second, we analyse alternative parametric specifications, allowing
for differences in risk aversion across the gain and loss domain (second subsection), and then for
heterogeneity in participants’ reference points (third subsection). Finally, the fourth subsection
shows that inattention and fatigue seem to be relatively unimportant in our study, and do not
confound our results. Across all these robustness tests, the estimated proportion of the population
that is loss tolerant is consistently around 50%.
5.1.
Traditional elicitations of loss aversion
Our results are similar when using MPLs (
Holt and Laury 2002
), rather than DOSE, to elicit
loss aversion. An MPL offers participants a table with two columns of outcomes. In each row,
the participant is asked to make a choice between the outcomes in the columns. One column
contains the same outcome in all rows, while outcomes in the other column vary, becoming more
attractive as one moves down the table.
28
Each MPL then provides a set of binary choices which
we use to estimate risk and loss aversion using the same parametric form, priors, and Bayesian
procedure as the DOSE method.
The survey elicited loss attitudes using two different MPL elicitation methods. First, partic-
ipants answered two MPLs eliciting
Lottery Equivalents
for a fixed amount of $0. Specifically,
the lottery consisted of a fixed positive amount
y
and a varying negative amount
c
with equal
probabilities. The MPL therefore elicited the amount
c
, such that the participant was indifferent
between gaining
y
and losing
c
with equal probability, and getting zero for sure. The second set
of MPLs then elicited
Certainty Equivalents
for two mixed lotteries. Participants were asked two
questions eliciting their certainty equivalent for a 50/50 lottery between a loss and a gain—for
example a lottery with a 50% chance of winning $5 and a 50% chance of losing $5. To estimate
risk and loss aversion, the answers to these MPLs were combined with the responses to two
28. Participants who understand the question should choose the former option for early rows, and at some point
switch to choosing the latter (varying) option for all remaining rows. In our survey participants were not allowed to
proceed if there were multiple switches in their choices. Participants had to complete an MPL training module at the
start of the survey, and were able to return to the instructions if they made an error. See
Supplementary Material,
Appendix Figures E.26–E.31
for screenshots of the MPL elicitations.
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REVIEW OF ECONOMIC STUDIES
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IGURE
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The finding of widespread loss tolerance is robust to allowing for utility curvature to differ between losses and gains
Notes:
The figure displays the results from estimating alternative utility specifications using choice data from the 20-question DOSE
sequence presented to our representative sample (
N
=
1
,
000
). “CRRA with
1
ρ
”—our preferred specification—imposes the same utility
curvature over gains and losses. “CRRA with
2
ρ
” allows for differential curvature across gains and losses. Distributions are plotted using
an Epanechnikov kernel with bandwidth chosen by rule-of-thumb estimator
additional MPLs which elicited participants’ certainty equivalents for two lotteries involving
only positive prizes.
Consistent with the DOSE estimates, the estimated proportion of loss-tolerant participants
is much higher in the general population than amongst the student sample. Using the
Lottery
Equivalent
elicitation technique, 54% of participants in the general population are classified as
loss tolerant (compared to 57% using DOSE), whereas only 35% of students are (compared to
32% using DOSE). The
Certainty Equivalent
method also finds a higher degree of loss tolerance
in the representative sample than the student sample (42% versus 23%).
The Bayesian estimates account for individual heterogeneity in risk aversion, and so provide
a direct comparison to DOSE, but we can observe widespread loss tolerance simply by exam-
ining choices in the MPLs—as we discuss in detail in
Supplementary Material, Appendix B.2
.
Specifically, we can simply assume equal utility curvature in both the gain and loss domains, and
classify choices in the four mixed-risk MPLs as demonstrating loss aversion or loss tolerance.
Doing so, we find the range of loss-tolerant responses is 41–63% across the four mixed-risk
MPLs. Further, a significant proportion of participants demonstrated strong loss tolerance; for
example, 22% of participants preferred a lottery between -$10 and $4 to a sure amount of $0.
Choices in the MPLs thus provide further reassurance that loss tolerance is not an artefact of our
parametric assumptions, or of the DOSE question format.
5.2.
Allowing for differential utility curvature over losses
The choice data elicited by DOSE allows us to investigate the robustness of our results to alter-
native utility specifications. In this subsection, we use the choice data from the 20-question
DOSE module to show that our results about the prevalence of loss tolerance are robust to re-
estimating individual preference parameters allowing for the curvature of the utility function to
differ between gains and losses. That is, we re-estimate our main specification (
1
), but allow for
separate risk parameters for gains (
ρ
+
) and for losses (
ρ
−
)(
Tversky and Kahneman 1992
).
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