DISCUSSION PAPER SERIES
IZA DP No. 16138
Nathan Kettlewell
Jonathan Levy
Agnieszka Tymula
Xueting Wang
The Gender Reference Point Gap
MAY 2023
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DISCUSSION PAPER SERIES
ISSN: 2365-9793
IZA DP No. 16138
The Gender Reference Point Gap
MAY 2023
Nathan Kettlewell
University of Technology Sydney and IZA
Jonathan Levy
University of Sydney
Agnieszka Tymula
University of Sydney
Xueting Wang
Royal Melbourne Institute of Technology
ABSTRACT
IZA DP No. 16138 MAY 2023
The Gender Reference Point Gap
*
Studies have frequently found that women are more risk averse than men. In this paper, we
depart from usual practice in economics that treats risk attitude as a primitive, and instead
adopt a neuroeconomic approach where risk attitude is determined by the reference
point which can be easily estimated using standard econometric methods. We then
evaluate whether there is a gender difference in the reference point, explaining the gender
difference in risk aversion observed using traditional approaches. In our study, women
make riskier choices less frequently than men. Compared to men, we find that women on
average have a significantly lower reference point. By acknowledging the reference point as
a potential source of gender inequality, we can begin a new discussion on how to address
this important issue.
JEL Classification: C90, D87, D91, J16
Keywords: reference point, risk attitude, neuroeconomics, gender,
inequality, experiment
Corresponding author:
Nathan Kettlewell
University of Technology Sydney
Economics Discipline Group
15 Broadway
Ultimo NSW 2007
Australia
E-mail: [email protected]
* We are especially thankful to Australian twins who gave up their time to take part in our study. Participant
recruitment was facilitated by Twins Research Australia, a national resource supported by the National Health &
Medical Research Council (NHMRC) and administered by the University of Melbourne. This work was supported by
the University of Technology Sydney Chancellor’s Post-Doctoral Fellowship for Kettlewell, a UTS Business School small
research grant, and the Australian Research Council’s Centre of Excellence for Children and Families over the Life
Course (Project ID CE200100025). We are grateful for valuable feedback from the participants at the 2022 Society
for Neuroeconomics Annual Meeting, the 2022 Women in Experimental Finance seminar, the 2022 Gender, Norms,
and Economics Workshop, the 2023 Western Economic Association International meeting, and the neuroeconomics
seminar at the University of Zurich.
2
1. Introduction
Studies have frequently found that women are more risk averse than men (Agnew et al., 2008;
Borghans et al., 2009; Charness & Gneezy, 2012; Eckel & Grossman, 2008; Shurchkov &
Eckel, 2018). This gender gap may contribute to numerous gender-based inequities, such as
the underrepresentation of females in entrepreneurship, managerial positions, investing, as well
as the gender pay gap.
Although the gender difference in risk attitude has been replicated in many studies (this is not
always the case, e.g., Filippin & Crosetto, 2016; Nelson, 2015), economists have struggled
with whether and how to use this finding to restore gender balance in economic decision-
making. The main reason for this is that traditional economic models take risk attitudes as static
primitives which makes it impossible to establish the underlying mechanism that leads to
gender differences in risk attitudes. Conceptually, in these models, people maximize their
utility given their preferences and forcing them to change their decisions should result in lower
utility. As such, we are no closer to devising a solution to address this risk attitude-based gender
inequality.
In this paper, we take a different approach to risk attitude. Instead of treating it as a primitive,
we employ a neuroeconomic model in which risk attitude is determined by the payoff
expectation (reference point) (Glimcher & Tymula, 2023). We then evaluate whether there is
a gender difference in the estimated dollar amount that serves as a reference point, explaining
the gender difference in risk aversion observed using traditional approaches. The advantage of
our approach is that it sheds light on the origins of the gender differences in risk attitudes which
in turn enables us to suggest policies that would reduce or eliminate these differences. In the
neuroeconomic model, a person’s reference point is malleable and affected by their financial
history (Glimcher & Tymula, 2023; Rangel & Clithero, 2012; Tymula & Plassmann, 2016).
Different histories of financial outcomes across genders can lead to different reference points
and different risk attitudes. This implies that the existing gender pay gap may be self-
reinforcing—lowering women’s reference points could decrease their tolerance to risk which
in turn reduces their expected financial outcomes.
We use a dataset of 853 participants (18-67 years old; Mean 41.71, Std. Dev. 14.22) to
provide the first evidence on gender differences in reference points estimated from behavior.
3
We use a canonical neuroeconomic model (divisive normalization) in which the reference point
is derived from the neurobiological capacity constraints of the nervous system (Glimcher &
Tymula, 2023; Louie et al., 2013; Webb et al., 2020), and estimate the reference point for men
and women using choices across multiple binary lottery tasks. We find that the reference point
for men is more than double that of women. We estimate models of Expected Utility and
Prospect Theory and show that a model that accounts for a gender difference in the reference
point fits the data better than a model that accounts for gender differences in utility curvature
and probability weighting. Our results suggest that income mediates the gender difference in
the reference point but does not eliminate it. We also replicate the gender gap in reference point
using data from a very similar task (Baillon et al., 2020). As reference points determine risk
tolerance, which arguably could in turn determine financial outcomes (Budria et al., 2013;
Shaw, 1996), the gender difference in reference points can adversely affect women. This
insight is important for guiding both whether and how policymakers should intervene to
eliminate these differences.
We contribute to two strands of literature. First, we contribute to the emerging literature on
gender differences in expectations. Gender differences in expectations have been identified in
a variety of domains, including differences in expectations about inflation (D’Acunto et al.,
2021), labour supply (Grewenig et al., 2020), and salary (Briel et al., 2022; Cortés et al., 2022;
Fernandes et al., 2021; Reuben et al., 2017). In these studies expectations are stated (not
incentivized) and may be influenced by unmeasured differences in the information received by
participants. Our study differs from prior research in this space in two ways. First, the task used
to elicit reference points, conceptually related to payoff expectations, is incentivized. Second,
we elicit reference points in a controlled setting where objective payoffs and probabilities are
identical between subjects and there is no information asymmetry. Heterogeneity in stated
beliefs in areas like wage expectations can be driven by both different satisficing outcomes, as
well as other factors, like private information about ability or beliefs about discrimination. By
holding other factors constant, we provide evidence on whether the gender difference in
expectations is due to a real gap in the reference point.
Second, we contribute to the empirical literature on the estimation of reference points.
Although there has been research prior to ours which has examined reference-dependence
theoretically (e.g., Bell, 1985; Koszegi & Rabin, 2006; Loomes & Sugden, 1986), and
predictions of such models empirically (e.g., Abeler et al., 2011; Allen et al., 2017; Bartling et
4
al., 2015; Baucells et al., 2011; Card & Dahl, 2011; Crawford & Meng, 2011; Gill & Prowse,
2012; Heffetz & List, 2014; Lien & Zheng, 2015; Rosato & Tymula, 2019; Wenner, 2015),
very few studies estimate reference points. To our knowledge the only studies that do so are
Baillon et al. (2020), Rees-Jones & Wang (2022), and Terzi et al. (2016). In each of these
studies a set of reference point rules is proposed and the extent to which participants employ
these reference point rules is estimated. These reference point rules are forward looking
meaning that when a person makes a decision, they evaluate its potential outcomes by
comparing them to some or all of the other possible outcomes that they could have received
had they made a different decision, or their luck changed. The limitation of proposing that
individuals employ such forward-looking reference point rules when making decisions is that
we implicitly assume that reference points are not dependent on historical outcomes. However,
there has been ample research in finance (Andrikogiannopoulou & Papakonstantinou, 2020;
Barberis et al., 2001), behavioral economics (Imas, 2016; Malmendier & Nagel, 2011; Post et
al., 2008), and neuroeconomics (Glimcher & Tymula, 2023; Guo & Tymula, 2021) which
suggests that reference points are at least partially affected by historical outcomes. Unlike the
previous research on reference point estimation (Baillon et al., 2020; Rees-Jones & Wang,
2022; Terzi et al., 2016), we estimate the reference point as a dollar amount rather than a simple
rule. The major difference is that instead of evaluating how the reference point changes from
trial to trial, we propose that the reference point has a more stable component and that risk
attitudes emerge from the reference point rather than being assumed (Rayo & Becker, 2007;
Robson et al., 2022; Woodford, 2012). Using this approach, we estimate that women have a
lower reference point than men, a difference not documented in prior research. In our
framework, the reference point is a continuous latent variable and there is no discontinuity in
the utility function at the reference point. This makes it easy to estimate with the popular risk
elicitation tasks and maximum likelihood estimation routines used widely in behavioral
economics.
The rest of the paper is organized as follows. In section 2, we outline the methods used for data
collection and the empirical approach. In section 3 we report results along with several checks
for robustness. Section 4 concludes.
5
2. Methods
2.1. Ethics statement
Our protocols and procedures were approved by the University of Technology Sydney Human
Research Ethics Committee (application number ETH21-6527) and by Twins Research
Australia.
2.2. Participants and procedures
We use data from the second wave of the Australian Twins Economic Preferences Survey.
1
Our sample comprises 853 participants
2
(18-67 years old; Mean 41.71, Std. Dev. 14.22,
708 female) recruited from Twins Research Australia, the largest twin registry in Australia.
Like most datasets that experimentally elicit preferences, our sample is not representative.
However, compared to many related studies, which rely on student samples, our sample has
two notable advantages. First, it includes participants with a range of ages, education levels,
and other socioeconomic and demographic characteristics that are more representative of the
general population. Second, our sample is large, which allows us to precisely estimate gender
differences, even though we have a smaller number of males in our sample.
3
Table 1 presents
the comparison of male and female participants on key demographic and socioeconomic
characteristics. Compared to females, males were significantly less likely to have children,
were significantly more likely to be educated at the university level, had significantly higher
weekly incomes, judged themselves as significantly wealthier, and were significantly less
likely to have a long-term health condition. We control for these differences in our analysis.
1
Kettlewell & Tymula (2021) describe the recruitment and study design for the first wave of the survey in detail.
The second wave included 657 participants from wave 1 as well as an additional 196 new participants.
2
Our sample includes 9 participants who completed the survey but did not provide bank details, so could not be
paid. We retain these participants since they are so few, and we have no reason to think they misrepresented their
preferences (the fact they completed the whole survey indicates a strong intrinsic motivation). Our results do not
change when we exclude these participants from the analysis.
3
This gender difference is largely a feature of the composition of Twins Research Australia’s twin registry (see
Kettlewell & Tymula, 2021).
6
Table 1: Descriptive statistics
Variable
Mean Female
Mean Male
Difference
P-value
Age
41.816
41.172
0.644
0.620
Lives in a city
0.651
0.724
-0.073
0.101
Married/defacto
0.641
0.641
-0.000
1.000
Household size
2.805
2.738
0.067
0.595
Has children
0.487
0.407
0.080
0.083
University degree
0.569
0.683
-0.114
0.012
Employed
0.802
0.828
-0.025
0.564
Retired
0.075
0.097
-0.022
0.396
Income (weekly)
1248.387
1702.427
-454.04
0.000
Wealth (self-reported)
4
4.107
4.269
-0.162
0.019
Long-term health
condition
0.220
0.131
0.089
0.017
Notes: Calculated from non-missing values from a full sample of 145 males and 708 females. See Table A.1 for
variable definitions and observation counts.
The survey was programmed in Qualtrics and conducted online between November 2021 and
April 2022. Participants completed four tasks and a demographic and socioeconomic
questionnaire. One of the four tasks was randomly selected for payment and the payment was
determined by the decision made by participants in this task and chance. To emphasize the
importance of participants’ decisions, they did not receive a fixed payment for participation.
2.3. Lottery choice task
We analyze data from the lottery choice task that included 46 decision scenarios designed to
estimate participants’ reference point (Baillon et al., 2020).
5
Each decision was between two
options: lottery A and lottery B. Each lottery had between one and four possible payoffs at
various probability levels. All payoffs were in Australian dollars and were weakly positive to
make sure that participants would not lose money. Between participants, we randomized the
order of the decision scenarios, and the side on which lotteries appeared. The selection of
decision scenarios ensured the complete coverage of the outcome and probability space and a
balanced pairing of prospects with different numbers of outcomes.
4
Participants reported how prosperous they felt on a scale ranging from 'very poor' (1) to 'prosperous' (5).
5
To reduce the length of the survey, we used 46 decision scenarios instead of the original 70. We also adjusted
the payoffs to Australian dollars. All 46 decision scenarios are listed in Table A.2.
7
Lottery A Lottery B
Figure 1: Presentation of the choices in the survey
Figure 1 shows how the lottery options were displayed. Prospects were presented as vertical
bars with as many parts as there were different payoffs. The size of each part corresponded
with the probability of the payoff. The intensity of the color of each part increased with the size
of the payoff. The payoffs were presented in decreasing order (the lowest at the top and the
highest at the bottom). Participants clicked on a bullet located next to a lottery to indicate their
preference. Decision scenarios 45 and 46 (see Table A.2) had one lottery stochastically
dominating the other.
If the lottery choice task was selected for payment, one of the 46 decisions within this task was
randomly selected for payment. An expected value maximizer would in expectation earn
$19.37 (Std. Dev. 6.09) for this task.
6
2.4. Empirical approach
We estimate the reference point using the recently proposed modeling approach in Expected
Subjective Value Theory (ESVT) (Glimcher & Tymula, 2023). ESVT is based on the
neuroscientific understanding about how value signals are efficiently encoded in the brain. The
6
An expected value maximizer would earn $18.38, $19, and $10.50 for the other three tasks, respectively.
8
main intuition behind ESVT is that the utility function adapts to the payoff expectation to
efficiently encode value (Bucher & Brandenburger, 2022; Steverson et al., 2019). Because the
brain does not have unlimited resources (action potentials) to encode the utility of payoffs, it
adjusts dynamically so that the subjective value function
7
is most sensitive to the payoff ranges
that the brain is expecting to encounter. In this vein, the model is very similar to range
normalization models (Kontek & Lewandowski, 2018; Padoa-Schioppa & Rustichini, 2014).
However, it has a unique advantage over range normalization models, in that it allows for
reference point estimation. ESVT implements behaviors captured by Prospect Theory (PT),
offering new interpretations for risk taking, reflection in risk attitudes, probability weighting,
the endowment effect, and the Allais paradox. For our purposes, the biggest benefit of ESVT
is that it does not assume a discontinuity at the reference point (like PT or other loss-aversion
based reference point models) which allows us to estimate it using the standard maximum
likelihood procedure and is in line with neural evidence that biological systems rarely, if ever,
employ discontinuous functions.
Under ESVT the utility of a payoff
is given by:
where is the payoff expectation (reference point) and is a free parameter called
predisposition.
The utility function takes values between 0 and 1 ( ) consistent with the idea that
decision makers are bounded in the range of subjective values that they can biophysically
assign to payoffs (Rayo & Becker, 2007; Robson et al., 2022; Woodford, 2012).
We assume that the expected utility of a lottery that pays with probability is calculated as:
We therefore diverge from Glimcher & Tymula (2023) by allowing for a probability weighting
function.
7
Neuroeconomists use the term “subjective value” to distinguish it from utility to capture that the former is usually
thought of as cardinal and the latter ordinal. Throughout the paper we use the term utility as is the norm in
economics.
9
Both and determine the shape of the utility function and therefore the risk attitude. As the
reference point () increases, the utility function shifts rightward along the horizontal axis.
This feature prevails in many reference-dependent models. The shift in the utility function is
such that at the reference point the function always takes the same value, .
This property is consistent with mounting evidence that people are indeed reference dependent
when making decisions. Predisposition affects the curvature of the utility function. When
predisposition is low the utility function is concave for all and thus the decision maker is
always risk averse. As increases, the utility function becomes increasingly S-shaped as seen
in PT—for small values of utility is convex (risk seeking) and then as increases changes to
concave (risk averse). Unlike in PT, in ESVT the inflection point does not have to occur at the
reference point. Instead, the inflection point depends on both the reference point () and
predisposition (). If the utility function inflects, then as in PT, for individuals with a higher
reference point (), the utility inflects at a higher meaning that they are risk seeking for a
larger range of values.
We fit decisions of our participants with a logistic choice function, where the probability of
choosing lottery is:
where
, and captures noise. The log-likelihood function is then given by:
where is the number of participants, is the number of trials,
is an indicator
function denoting the choice of lottery for participant in trial , and is the vector of
behavioral parameters to be estimated.
To capture gender effects, we introduce a dummy variable which takes the value 1 if the
participant is male, and 0 otherwise. In our analysis we control for age, and for all descriptive
variables listed in Table 1 in which women and men differ (income, wealth, whether the
participant obtained a university level education, whether the participant has children, and
whether the participant has a long-term health condition).
10
For each parameter
in our model, we specify:
where is a vector of controls and are the associated coefficients. For each parameter , we
report the point estimate for the maximum likelihood estimation. The standard errors are
clustered at the individual level.
8
For comparison and robustness checks we use the one-parameter (
) and
two-parameter (
) probability weighting functions proposed by Prelec
(1998). In these functions, governs the shape of the weighting function, with smaller
corresponding to a more inverse S-shaped function (i.e., greater over (under)-weighting of
low (high) probability outcomes), while determines the level of elevation (where the function
crosses the 45-degree line). The two-parameter probability weighting function is more flexible
and thus we present these results in the main paper and the results using one-parameter
probability weighting in Appendix A.
To allow for easy comparisons with existing literature on risk attitudes, we also estimate a
power utility function (
) with and without Prelec probability weighting. We label
models with probability weighting as PT models and the model without probability weighting
as Expected Utility (EU). Further details on the models estimated are in Appendix C.
3. Results
3.1. Preliminary results
A simple way to determine whether there is a gender difference in risk attitude in our sample
is to compare whether women choose riskier lotteries less or more frequently than men. We
determine which lottery is riskier in each trial using the coefficient of variation (Weber, 2010).
The coefficient of variation for a lottery is its standard deviation divided by its expected value.
Lotteries with higher coefficients of variation are considered riskier. We find that women
choose riskier lotteries less frequently than men (42.7% versus 46.5%, t-test: -value =
0.0087)—see Figure 2A.
9
Their expected earnings, calculated based on their decisions in the
8
The main results do not change when we cluster standard errors at the sibling level.
9
All reported -values are from two-sided tests.
11
lottery choice task, are 0.46 standard deviations lower than men’s ($18.88 versus $18.96, t-test:
-value < 0.001)—see Figure 2B.
10
(A) (B)
Figure 2: Percentage of riskier choices and normalized expected earnings by gender
We confirm that women have a more concave utility function (i.e., are more risk averse) than
men when modeling decisions using EU (Table A.3) and PT with one-parameter (Table A.5)
and two-parameter (Table A.7) Prelec probability weighting functions—see the significant and
positive coefficient estimate on
in all models. As the literature has suggested (Fehr-Duda
et al., 2006; Filippin & Crosetto, 2016), we observe statistically significant differences across
genders in probability weighting (Table A.7). We find that men have significantly lower (no
significant gender difference in ). The coefficient estimates for
are between -0.033 and
-0.029. This gender difference seems small as evidenced by the similarity in the estimated
probability weighting functions drawn separately for each gender based on Table A.7 estimates
in Figure B.1. Such differences in probability weighting could nevertheless have an impact on
earnings if they are paired with substantial payoffs. In our study though, the differences in
probability weighting are not the key driver of differences across the genders. We conducted
an in-sample prediction exercise and found that model predictions are more accurate when
allowing for men and women to differ in utility curvature than when allowing for men and
women to differ in probability weighting. Moreover, the gender difference in utility curvature
persists even when probability weighting is incorporated. To summarize, these findings suggest
10
In Figure 2B, the normalized expected earnings for participant are equal to
where
are the
expected earnings for participant ,
are the average expected earnings in the sample population, and
is the
standard deviation of the expected earnings in the sample population.
0
10
20
30
40
50
% of riskier choices
Male Female
***
-0.2
0
0.2
0.4
0.6
Normalized expected
earnings
Male Female
***
12
that the observed gender differences in risk attitudes are not primarily due to probability
weighting. Our results do not change qualitatively when we employ different probability
weighting functions
11
or exclude participants who violated first-order stochastic dominance
(Table A.8).
3.2. Reference point heterogeneity
We now estimate the ESVT model (Glimcher & Tymula, 2023). This allows us to understand
whether in the neuroeconomic framework the observed differences in willingness to take risk
across genders should be attributed to differences in the reference point or predisposition as
both, in principle, affect risk attitude. We begin by estimating the ESVT model without controls
(first column in Table 2).
Table 2: ESVT model estimates
(1)
(2)
15.119*
34.999***
(8.184)
(13.555)
13.002***
12.620***
(1.524)
(4.743)
Controls
No
Yes
-0.093
-0.246***
(0.087)
(0.068)
1.065***
0.983***
(0.054)
(0.151)
Controls
No
Yes
-0.026***
-0.033***
(0.006)
(0.005)
0.053***
0.052***
(0.004)
(0.004)
Obs.
39238
37352
Clusters
853
812
AIC
50910.979
48337.850
BIC
50962.443
48491.357
Notes:
is the mean difference between males and females in parameter . Controls include age, income,
wealth, whether they obtained a university level education, whether they have children, and whether they have a
long-term health condition. Robust standard errors clustered on individual in parentheses. * 0.1, ** 0.05,
*** 0.01.
11
In addition to estimating PT with as in Prelec (1998) we also estimated prospect theory models with
as in Goldstein & Einhorn (1987) and Tversky & Kahneman (1992). The results from these alternative estimations
were consistent and the model with two-parameter Prelec probability weighting had the lowest BIC score.
13
The coefficient estimate for
is significant and positive, implying women have lower
reference points than men. Using the estimates in the first column of Table 2 we plot the utility
functions for males and females in Figure 3.
Figure 3: Utility functions for males and females plotted using parameter estimates from
column (1) in Table 2
When estimated as a continuous variable, the reference point for women is on average $15
lower than the reference point for men. This is a substantial difference, considering that in our
task, the maximum payoff was $43. This, of course, could happen simply because men and
women in our sample differ on variables that determine the reference point but are not related
to gender. Or it could be that we underestimate the difference in reference points by not
controlling for education or income levels. To ensure that we capture the true gender effect and
compare men and women who are similar in demographic and socioeconomic characteristics,
we introduce controls to the model—age, income, wealth, whether the participant obtained a
university level education, whether the participant has children, and whether the participant has
a long-term health condition (all variables in which we observe gender differences, see Table
1). Not only does the gender difference prevail after adding controls, but it becomes larger
(Table 2 (2)).
In the cross-sectional analysis so far, we assumed that the reference point is fixed within
individuals and estimated it on the aggregate level. Research in neuroscience and
neuroeconomics (Frydman & Jin, 2021; Glimcher & Tymula, 2023; Padoa-Schioppa &
Rustichini, 2014; Rangel & Clithero, 2012; Tymula & Plassmann, 2016) tells us that the
14
reference point is malleable and adaptable and that participants generally adjust their utility
functions to either minimize the number of mistakes or maximize payoffs. In particular, based
on Glimcher & Tymula (2023), we would hypothesize that lower-income individuals adjust to
have lower reference points. While we cannot establish causality, we can check whether such
correlations exist in our data. Furthermore, we can check whether the gender difference in the
reference point exists above and beyond the potential impact of income and wealth on the
reference point. This is particularly important because in our sample women have lower
incomes and are less wealthy than men.
Recall, in the second column of Table 2 the gender difference in the reference point is not only
robust but increases significantly when we include controls. In Table 3 we present the values
of all coefficients of the model presented in the second column of Table 2.
Table 3: Determinants of reference points and predisposition
Reference point
()
Predisposition
()
Male
34.999***
-0.246***
(13.555)
(0.068)
Age
0.057
-0.005***
(0.071)
(0.002)
University degree
-1.246
0.201***
(1.490)
(0.048)
Wealth
-1.074
0.045
(0.965)
(0.028)
Income (weekly)
0.002**
-0.000
(0.001)
(0.000)
Has children
-0.186
0.004
(2.199)
(0.053)
Long-term health
condition
1.077
0.020
(1.551)
(0.068)
Constant
12.620***
0.983***
(4.743)
(0.151)
Obs.
37352
Clusters
812
AIC
48337.850
BIC
48491.357
Notes: These results are from one estimation. The estimates were split across two columns for display purposes.
The first column provides parameter estimates with respect to the reference point and the second column
provides parameter estimates with respect to predisposition (). Robust standard errors clustered on individual in
parentheses. * 0.1, ** 0.05, *** 0.01.
In the first column of Table 3 we can see that in line with our hypothesis the coefficient of
15
Income is positive and statistically significant. This indicates that a $100 decrease in weekly
income leads to a $0.20 decrease in the reference point. This supports the narrative that the
existing gender pay gap may be self-reinforcing—lowering women’s reference points could
decrease their tolerance to risk which in turn reduces their expected financial outcomes. Income
does seem to be a mitigating factor, however, the gender difference in reference points persists
as indicated by the significantly positive coefficient estimate of Male in the first column of
Table 3.
12
To summarize, our findings suggest that the observed gender differences in risk attitudes could
be due to differences in reference points across genders.
3.3. Robustness checks
In this subsection, we test the robustness of our results. We explore whether our main results
change when we exclude stochastic dominance violators from our sample and incorporate
different probability weighting specifications. We also check whether ESVT better describes
chooser’s behavior than Prospect Theory or Expected Utility Theory. Finally, we try to
replicate our findings using publicly available data from Baillon et al. (2020) whose task we
adopt.
3.3.1 First-order stochastic dominance check
Two trials in our task had one lottery stochastically dominating the other. Out of the 853
participants we recruited, 646 participants (118 males and 528 females) never chose the
dominated lottery, 188 participants (25 males and 163 females) chose the dominated lottery
once, and 19 participants (2 males and 17 females) chose the dominated lottery twice. We do
observe a gender difference in decisions in the two trials where one lottery stochastically
dominates the other. Women violate first-order stochastic dominance more frequently than men
(25.4% versus 18.6%, Fisher’s exact test: -value 0.089). However, the results pertaining to
12
In column (1) of Table 2, the coefficient of
is not statistically significant, indicating no gender difference
in predisposition. As we include controls the coefficient becomes negative and statistically significant. In the
second column of Table 3 we can see that the coefficients of Age and University degree are significantly negative
and significantly positive, respectively. The noise parameter was significantly different across genders.
Indicating that decisions were noisier for women than men.
16
the structural estimations in subsection 3.2 do not change when we exclude participants that
violated stochastic dominance—see Table A.9.
3.3.2 Reference point or probability weighting?
The overweighting of low probabilities and the underweighting of high probabilities is a feature
of human behavior which has been frequently discussed. ESVT (the model we use to estimate
the reference point) does not explicitly employ probability weighting. However, without the
inclusion of probability weighting it can achieve effects captured by probability weighting
much like some other models of behavior which do not include probability weighting (e.g.,
Kontek & Lewandowski, 2018; Schneider & Day, 2018). Yet one might argue that
incorporating probability weighting into ESVT may impact our findings. We find that the
results in subsection 3.2 do not change qualitatively when we incorporate probability
weighting. This is true both when we use a one-parameter probability weighting function
(Table A.10) and a two-parameter probability weighting function (Table A.11).
3.3.3 Predictive power of ESVT versus PT and EU
We compare the BIC scores across the six models listed in Appendix C. ESVT generally
outperforms (has lower BIC scores than) the EU and PT models. This is illustrated in Figure
B.2 where we plot the BIC scores across all models based on the estimates in tables 2, A.3,
A.5, A.7, A.10, and A.11. This implies that ESVT provides a better fit of the data than EU and
PT. ESVT with a two-parameter probability weighting function provides the best fit of the data
across the models.
Next, we determine whether allowing for reference point differences across genders enhances
model fit in a standard Prospect Theory framework. We do so by using the male and female
reference point estimates presented in the first column of Table 2
13
and estimating a standard
behavioral economics model with a reference point and comparing it to EU. To be precise, we
estimate the following PT model where
and
13
The reference point used for males and females was 28.121 and 13.002, respectively.
17
and
and
represent utility curvature in the gain and loss domains, respectively. To make
the comparison fair, this model is without loss aversion and probability weighting but allows
for different utility curvature in the gain and loss domains (relative to the reference point). The
BIC scores for this model are lower than the corresponding BIC scores for EU—see Table A.15
and Figure B.4. Therefore, we conclude that allowing for reference point differences across
genders improves the predictive power of the model. Furthermore, the parameter estimates
from the prospect theory model indicate that both men and women were more risk averse for
payoffs below the reference point than above it (Wald test: -values < 0.01).
3.3.4 Replication study
To check whether the results in this paper extend beyond our dataset, we repeated the structural
estimation process for the models outlined in Appendix C using data from Baillon et al. (2020),
selected due to task similarity.
14
Their sample contains 139 students and employees from the
Technical University of Moldova (17-47 years old; Mean 22.57, Std. Dev. 4.66). Unlike
in our sample, the majority (66%) of participants are male. Consistent with the results from our
dataset, in their dataset the reference point for women is on average 38 Lei (59.3%) lower than
the reference point for men (an expected value maximizer earned approximately 260 Lei in
expectation)—see tables A.12, A.13, and A.14. Furthermore, the BIC scores indicate that
ESVT with a one-parameter Prelec probability weighting function fits the data best. Figure B.3
displays the BIC scores across the six models.
4. Conclusion
In this paper we capture risk attitudes differently. Instead of treating them as primitives, we use
a neuroeconomic approach where risk attitudes are determined by the reference point. We then
evaluate whether there is a gender difference in the reference point, explaining the gender
difference in risk aversion observed using traditional approaches. We find that women make
riskier choices less frequently than men. We also find that women on average have a
significantly lower reference point. We have shown that this result is not only robust to
14
Note, the only demographics included in the Baillon et al. (2020) dataset were age and gender. Hence, we only
controlled for these variables in our analysis.
18
controlling for socioeconomic and demographic variables but that the gender gap in reference
point gets bigger when we control for gender differences in these variables. We have also
replicated our result in an independent sample. Our results suggest that gender differences in
reference points may be the reason why we observe gender differences in risk attitudes.
There have been many studies in behavioral economics that identified the gender gap in risk
attitudes (Borghans et al., 2009; Charness & Gneezy, 2012; Eckel & Grossman, 2008), tested
its limits (Filippin & Crosetto, 2016)
15
, and stressed the importance of its implications (Agnew
et al., 2008; Shurchkov & Eckel, 2018). However, little progress has been made in applying
this finding because of the specific meaning of risk preferences in economics. As they are
treated as the primitives in the economic models of choice, economists would argue that we
should not enforce more or less risk upon expected utility maximizers because this will
decrease their utility. Evolving literature in neuroeconomics (Glimcher & Tymula, 2023;
Rangel & Clithero, 2012; Tymula & Plassmann, 2016) has begun to point out that risk
preferences may not be fixed features of the choosers. Instead, this literature argues that they
emerge from historical payoffs. This happens because the brain efficiently allocates neural
resources to encode payoff values that it expects we are most likely to encounter. In such a
setting, the interpretation of risk attitudes is different—they are malleable and determined by
our payoff history. Under this setting, any economic inequalities that lead to lower payoffs
would decrease the reference point. With a lower reference point, people exhibit greater risk
aversion and thus expect lower payoffs, which in turn begets economic inequality further. To
us, this suggests that as long as there is economic discrimination, the disadvantaged groups will
take less risk and end up making decisions that reinforce the cycle of economic disadvantage.
Policies that address economic inequality by equalizing payoff expectations should be
particularly effective at breaking this self-reinforcing cycle. We find support for this idea in
our paper as we estimate that the reference point increases in income. Policy changes that
equalize pay and improve transparency about salaries could be an effective way to level the
playing field. Indeed, Recalde & Vesterlund (2022) in their literature review conclude that
transparency of pay reduces the gender differences in negotiations.
15
Filippin & Crosetto (2016) argue that women prefer safe options and the gender gap in risk attitudes disappears
if you remove the safe option. Our results provide further evidence of the gender gap in risk attitudes in a lottery
choice task without safe options.
19
In this paper, we focused on gender differences in risk attitudes and reference points.
Nevertheless, our conclusions can be extended to any group that experiences economic
inequality. The insight that risk preferences are not fixed but are shaped by historical outcomes
is perhaps not an entirely new concept (Imas, 2016; Malmendier & Nagel, 2011; Post et al.,
2008) but it has not yet been applied to improve our understanding of economic disadvantage.
Haushofer & Fehr (2014) argued that economic inequality creates a self-perpetuating loop—
poverty increases levels of stress which in turn increases impatience and risk aversion leading
to decisions that result in lower payoffs in expectation. Here, using the example of gender we
provided a new suggestion on how poverty could reinforce itself—through a lower reference
point. We have also provided the first empirical example of how a recent model from
neuroeconomics can be applied to easily estimate reference points from choices. This opens
the door to more research on reference points that relates to economic inequality and other
topics where reference-dependence plays a role.
20
References
Abeler, J., Falk, A., Goette, L., & Huffman, D. (2011). Reference Points and Effort
Provision. American Economic Review, 101(2), 470–492.
https://doi.org/10.1257/aer.101.2.470
Agnew, J. R., Anderson, L. R., Gerlach, J. R., & Szykman, L. R. (2008). Who Chooses
Annuities? An Experimental Investigation of the Role of Gender, Framing, and Defaults.
American Economic Review, 98(2), 418–422. https://doi.org/10.1257/aer.98.2.418
Allen, E. J., Dechow, P. M., Pope, D. G., & Wu, G. (2017). Reference-Dependent
Preferences: Evidence from Marathon Runners. Management Science, 63(6), 1657–
1672. https://doi.org/10.1287/mnsc.2015.2417
Andrikogiannopoulou, A., & Papakonstantinou, F. (2020). History-Dependent Risk
Preferences: Evidence from Individual Choices and Implications for the Disposition
Effect. The Review of Financial Studies, 33(8), 3674–3718.
https://doi.org/10.1093/rfs/hhz127
Baillon, A., Bleichrodt, H., & Spinu, V. (2020). Searching for the Reference Point.
Management Science, 66(1), 93–112. https://doi.org/10.1287/mnsc.2018.3224
Barberis, N., Huang, M., & Santos, T. (2001). Prospect Theory and Asset Prices. The
Quarterly Journal of Economics, 116(1), 1–53.
https://doi.org/10.1162/003355301556310
Bartling, B., Brandes, L., & Schunk, D. (2015). Expectations as Reference Points: Field
Evidence from Professional Soccer. Management Science, 61(11), 2646–2661.
https://doi.org/10.1287/mnsc.2014.2048
Baucells, M., Weber, M., & Welfens, F. (2011). Reference-Point Formation and Updating.
Management Science, 57(3), 506–519. https://doi.org/10.1287/mnsc.1100.1286
Bell, D. E. (1985). Disappointment in Decision Making Under Uncertainty. Operations
Research, 33(1), 1–27. https://doi.org/10.1287/opre.33.1.1
Borghans, L., Golsteyn, B. H. H., Heckman, J. J., & Meijers, H. (2009). Gender Differences
in Risk Aversion and Ambiguity Aversion. Journal of the European Economic
Association, 7(2–3), 649–658. https://doi.org/10.1162/JEEA.2009.7.2-3.649
Briel, S., Osikominu, A., Pfeifer, G., Reutter, M., & Satlukal, S. (2022). Gender differences
in wage expectations: the role of biased beliefs. Empirical Economics, 62(1), 187–212.
https://doi.org/10.1007/s00181-021-02044-0
Bucher, S. F., & Brandenburger, A. M. (2022). Divisive normalization is an efficient code for
multivariate Pareto-distributed environments. Proceedings of the National Academy of
Sciences, 119(40). https://doi.org/10.1073/pnas.2120581119
Budria, S., Diaz-Serrano, L., Ferrer-i-Carbonell, A., & Hartog, J. (2013). Risk attitude and
wage growth: replicating Shaw (1996). Empirical Economics, 44(2), 981–1004.
https://doi.org/10.1007/s00181-012-0549-5
Card, D., & Dahl, G. B. (2011). Family Violence and Football: The Effect of Unexpected
Emotional Cues on Violent Behavior*. The Quarterly Journal of Economics, 126(1),
103–143. https://doi.org/10.1093/qje/qjr001
Charness, G., & Gneezy, U. (2012). Strong Evidence for Gender Differences in Risk Taking.
Journal of Economic Behavior & Organization, 83(1), 50–58.
https://doi.org/10.1016/j.jebo.2011.06.007
Cortés, P., Pan, J., Reuben, E., Pilossoph, L., & Zafar, B. (2022). Gender Differences in Job
Search and the Earnings Gap: Evidence from the Field and Lab. The Quarterly Journal
of Economics.
Crawford, V. P., & Meng, J. (2011). New York City Cab Drivers’ Labor Supply Revisited:
Reference-Dependent Preferences with Rational-Expectations Targets for Hours and
21
Income. American Economic Review, 101(5), 1912–1932.
https://doi.org/10.1257/aer.101.5.1912
D’Acunto, F., Malmendier, U., Ospina, J., & Weber, M. (2021). Exposure to Grocery Prices
and Inflation Expectations. Journal of Political Economy, 129(5), 1615–1639.
https://doi.org/10.1086/713192
Eckel, C. C., & Grossman, P. J. (2008). Chapter 113 Men, Women and Risk Aversion:
Experimental Evidence (pp. 1061–1073). https://doi.org/10.1016/S1574-0722(07)00113-
8
Fehr-Duda, H., de Gennaro, M., & Schubert, R. (2006). Gender, Financial Risk, and
Probability Weights. Theory and Decision, 60(2–3), 283–313.
https://doi.org/10.1007/s11238-005-4590-0
Fernandes, A., Huber, M., & Vaccaro, G. (2021). Gender differences in wage expectations.
PLOS ONE, 16(6), e0250892. https://doi.org/10.1371/journal.pone.0250892
Filippin, A., & Crosetto, P. (2016). A Reconsideration of Gender Differences in Risk
Attitudes. Management Science, 62(11), 3138–3160.
https://doi.org/10.1287/mnsc.2015.2294
Frydman, C., & Jin, L. J. (2021). Efficient Coding and Risky Choice. The Quarterly Journal
of Economics, 137(1), 161–213. https://doi.org/10.1093/qje/qjab031
Gill, D., & Prowse, V. (2012). A Structural Analysis of Disappointment Aversion in a Real
Effort Competition. American Economic Review, 102(1), 469–503.
https://doi.org/10.1257/aer.102.1.469
Glimcher, P. W., & Tymula, A. A. (2023). Expected subjective value theory (ESVT): A
representation of decision under risk and certainty. Journal of Economic Behavior &
Organization, 207, 110–128. https://doi.org/10.1016/j.jebo.2022.12.013
Goldstein, W. M., & Einhorn, H. J. (1987). Expression theory and the preference reversal
phenomena. Psychological Review, 94(2), 236–254. https://doi.org/10.1037/0033-
295X.94.2.236
Grewenig, E., Lergetporer, P., & Werner, K. (2020). Gender Norms and Labor-Supply
Expectations: Experimental Evidence from Adolescents. SSRN Electronic Journal.
https://doi.org/10.2139/ssrn.3711887
Guo, J., & Tymula, A. (2021). Waterfall illusion in risky choice – exposure to outcome-
irrelevant gambles affects subsequent valuation of risky gambles. European Economic
Review, 139, 103889. https://doi.org/10.1016/j.euroecorev.2021.103889
Haushofer, J., & Fehr, E. (2014). On the psychology of poverty. Science, 344(6186), 862–
867. https://doi.org/10.1126/science.1232491
Heffetz, O., & List, J. A. (2014). IS THE ENDOWMENT EFFECT AN EXPECTATIONS
EFFECT? Journal of the European Economic Association, 12(5), 1396–1422.
https://doi.org/10.1111/jeea.12084
Imas, A. (2016). The Realization Effect: Risk-Taking After Realized Versus Paper Losses.
American Economic Review, 106(8), 2086–2109. https://doi.org/10.1257/aer.20140386
Kettlewell, N., & Tymula, A. (2021). The Australian Twins Economic Preferences Survey.
Twin Research and Human Genetics, 24(6), 365–370.
https://doi.org/10.1017/thg.2021.49
Kontek, K., & Lewandowski, M. (2018). Range-Dependent Utility. Management Science,
64(6), 2812–2832. https://doi.org/10.1287/mnsc.2017.2744
Koszegi, B., & Rabin, M. (2006). A Model of Reference-Dependent Preferences. The
Quarterly Journal of Economics, 121(4), 1133–1165.
https://doi.org/10.1093/qje/121.4.1133
22
Lien, J. W., & Zheng, J. (2015). Deciding When to Quit: Reference-Dependence over Slot
Machine Outcomes. American Economic Review, 105(5), 366–370.
https://doi.org/10.1257/aer.p20151036
Loomes, G., & Sugden, R. (1986). Disappointment and Dynamic Consistency in Choice
under Uncertainty. The Review of Economic Studies, 53(2), 271.
https://doi.org/10.2307/2297651
Louie, K., Khaw, M. W., & Glimcher, P. W. (2013). Normalization is a general neural
mechanism for context-dependent decision making. Proceedings of the National
Academy of Sciences, 110(15), 6139–6144. https://doi.org/10.1073/pnas.1217854110
Malmendier, U., & Nagel, S. (2011). Depression Babies: Do Macroeconomic Experiences
Affect Risk Taking?*. The Quarterly Journal of Economics, 126(1), 373–416.
https://doi.org/10.1093/qje/qjq004
Nelson, J. A. (2015). ARE WOMEN REALLY MORE RISK-AVERSE THAN MEN? A
RE-ANALYSIS OF THE LITERATURE USING EXPANDED METHODS. Journal of
Economic Surveys, 29(3), 566–585. https://doi.org/10.1111/joes.12069
Padoa-Schioppa, C., & Rustichini, A. (2014). Rational Attention and Adaptive Coding: A
Puzzle and a Solution. American Economic Review, 104(5), 507–513.
https://doi.org/10.1257/aer.104.5.507
Post, T., van den Assem, M. J., Baltussen, G., & Thaler, R. H. (2008). Deal or No Deal?
Decision Making under Risk in a Large-Payoff Game Show. American Economic
Review, 98(1), 38–71. https://doi.org/10.1257/aer.98.1.38
Prelec, D. (1998). The Probability Weighting Function. Econometrica, 66(3), 497.
https://doi.org/10.2307/2998573
Rangel, A., & Clithero, J. A. (2012). Value normalization in decision making: theory and
evidence. Current Opinion in Neurobiology, 22(6), 970–981.
https://doi.org/10.1016/j.conb.2012.07.011
Rayo, L., & Becker, G. S. (2007). Evolutionary Efficiency and Happiness. Journal of
Political Economy, 115(2), 302–337. https://doi.org/10.1086/516737
Recalde, M. P., & Vesterlund, L. (2022). Gender Differences in Negotiation and Policy for
Equalizing Outcomes. In Bargaining (pp. 455–475). Springer International Publishing.
https://doi.org/10.1007/978-3-030-76666-5_21
Rees-Jones, A., & Wang, A. (2022). An Approach to Testing Reference Points.
https://doi.org/10.3386/w30773
Reuben, E., Wiswall, M., & Zafar, B. (2017). Preferences and Biases in Educational Choices
and Labour Market Expectations: Shrinking the Black Box of Gender. The Economic
Journal, 127(604), 2153–2186. https://doi.org/10.1111/ecoj.12350
Robson, A. J., Whitehead, L. A., & Robalino, N. (2022). Adaptive Cardinal Utility. SSRN
Electronic Journal. https://doi.org/10.2139/ssrn.4036252
Rosato, A., & Tymula, A. A. (2019). Loss aversion and competition in Vickrey auctions:
Money ain’t no good. Games and Economic Behavior, 115, 188–208.
https://doi.org/10.1016/j.geb.2019.02.014
Schneider, M., & Day, R. (2018). Target-Adjusted Utility Functions and Expected-Utility
Paradoxes. Management Science, 64(1), 271–287.
https://doi.org/10.1287/mnsc.2016.2588
Shaw, K. L. (1996). An Empirical Analysis of Risk Aversion and Income Growth. Journal of
Labor Economics, 14(4), 626–653. https://doi.org/10.1086/209825
Shurchkov, O., & Eckel, C. C. (2018). Gender differences in behavioral traits and labor
market outcomes. In The Oxford Handbook of Women and the Economy (pp. 480–512).
Oxford University Press.
23
Steverson, K., Brandenburger, A., & Glimcher, P. (2019). Choice-theoretic foundations of the
divisive normalization model. Journal of Economic Behavior & Organization, 164,
148–165. https://doi.org/10.1016/j.jebo.2019.05.026
Terzi, A., Koedijk, K., Noussair, C. N., & Pownall, R. (2016). Reference Point
Heterogeneity. Frontiers in Psychology, 7. https://doi.org/10.3389/fpsyg.2016.01347
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative
representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323.
https://doi.org/10.1007/BF00122574
Tymula, A., & Plassmann, H. (2016). Context-dependency in valuation. Current Opinion in
Neurobiology, 40, 59–65. https://doi.org/10.1016/j.conb.2016.06.015
Webb, R., Glimcher, P. W., & Louie, K. (2020). Divisive normalization does influence
decisions with multiple alternatives. Nature Human Behaviour, 4(11), 1118–1120.
https://doi.org/10.1038/s41562-020-00941-5
Weber, E. U. (2010). On the coefficient of variation as a predictor of risk sensitivity:
Behavioral and neural evidence for the relative encoding of outcome variability. Journal
of Mathematical Psychology, 54(4), 395–399. https://doi.org/10.1016/j.jmp.2010.03.003
Wenner, L. M. (2015). Expected prices as reference points—Theory and experiments.
European Economic Review, 75, 60–79.
https://doi.org/10.1016/j.euroecorev.2015.01.001
Woodford, M. (2012). Prospect Theory as Efficient Perceptual Distortion. American
Economic Review, 102(3), 41–46. https://doi.org/10.1257/aer.102.3.41
24
Appendix
A. Tables
Table A.1: Variable definitions
Variable
Definition
Female obs.
Male obs.
Age
Age at last birthday
707
145
Lives in a city
= 1 if currently live in a major
city (Sydney, Melbourne,
Brisbane, Adelaide, Perth,
Canberra)
708
145
Married/defacto
= 1 if married or in a defacto
relationship
708
145
Household size
How many people live in your
household
707
145
Has children
= 1 if they have any children
708
145
University degree
= 1 if highest level of
education obtained is a
university degree
708
145
Employed
= 1 if worked any time in the
last 7 days or if had a job but
did not work in the last 7 days
due to holidays, sickness or
any other reason
708
145
Retired
= 1 if currently retired from
the workforce
708
145
Income (weekly)
Average usual weekly own
income in the last month
using midpoint value for the
following categories: $1-
$149, $150-$299, $300-$399,
$400-$499, $500-$649, $650
$799, $800-$999, $1,000
$1,249, $1,250-$1,499,
$1,500-$1,749, $1,750-
$1,999, $2,000-$2,999,
$3,000 or more (coded as
$3000). Negative or nil coded
as missing.
670
143
Wealth
Given your current needs and
financial responsibility, would
you say that you and your
family are: = 1 if Poor, = 2 if
Just getting along, = 3 if
Comfortable, = 4 if Very
comfortable, = 5 if
Prosperous.
708
145
25
Long-term health
condition
= 1 if has a long-term health
condition, impairment or
disability that has lasted more
than 6 months
708
145
Table A.2: Lottery decision scenarios
Scenario
number
1
17
20
29
0
0.4
0.5
0.1
11
14
26
0
0.1
0.4
0.5
2
7
16
29
0
0.6
0.15
0.25
3
12
20
24
0.3
0.1
0.05
3
7
18
0
0
0.85
0.15
0
1
10
15
0
0.1
0.7
0.2
4
16
23
35
0
0.35
0.55
0.1
12
19
27
31
0.05
0.55
0.1
5
17
38
0
0
0.85
0.15
0
6
22
33
0
0.05
0.7
0.25
6
9
20
32
0
0.15
0.8
0.05
3
15
26
37
0.1
0.35
0.45
7
17
32
0
0
0.55
0.45
0
7
27
36
0
0.25
0.7
0.05
8
7
16
0
0
0.2
0.8
0
4
10
21
0
0.2
0.5
0.3
9
19
32
0
0
0.8
0.2
0
11
28
37
0
0.35
0.45
0.2
10
17
32
0
0
0.45
0.55
0
12
22
41
0
0.05
0.7
0.25
11
7
17
0
0
0.8
0.2
0
1
10
14
20
0.1
0.4
0.45
12
7
14
0
0
0.3
0.7
0
4
9
12
19
0.25
0.3
0.05
13
15
24
0
0
0.75
0.25
0
9
18
21
27
0.35
0.05
0.45
14
10
18
0
0
0.55
0.45
0
2
6
14
27
0.05
0.05
0.85
15
9
15
0
0
0.8
0.2
0
4
7
13
17
0.2
0.1
0.6
16
17
28
0
0
0.4
0.6
0
7
12
23
39
0.05
0.1
0.6
17
17
26
0
0
0.7
0.3
0
12
15
23
29
0.3
0.2
0.1
18
19
27
0
0
0.7
0.3
0
11
23
31
35
0.05
0.85
0.05
19
14
23
0
0
0.6
0.4
0
4
18
27
32
0.15
0.7
0.1
20
4
13
0
0
0.45
0.55
0
1
7
16
19
0.4
0.05
0.5
21
11
28
0
0
0.6
0.4
0
0
5
28
0
0.25
0.05
0.7
22
19
42
0
0
0.75
0.25
0
12
27
42
0
0.15
0.7
0.15
23
9
18
0
0
0.75
0.25
0
6
12
18
0
0.15
0.7
0.15
24
10
16
21
0
0.7
0.05
0.25
5
8
21
0
0.4
0.1
0.5
25
7
34
0
0
0.3
0.7
0
7
25
43
0
0.1
0.8
0.1
26
9
21
0
0
0.2
0.8
0
9
25
0
0
0.45
0.55
0
27
4
19
0
0
0.3
0.7
0
4
14
25
0
0.05
0.85
0.1
28
8
14
21
0
0.1
0.05
0.85
8
24
27
0
0.5
0.3
0.2
29
7
0
0
0
1
0
0
1
14
0
0
0.45
0.55
0
30
17
0
0
0
1
0
0
0
22
0
0
0.25
0.75
0
31
21
0
0
0
1
0
0
6
28
36
0
0.35
0.45
0.2
32
15
0
0
0
1
0
0
8
11
23
0
0.45
0.05
0.5
33
15
0
0
0
1
0
0
7
11
18
22
0.3
0.05
0.5
34
29
0
0
0
1
0
0
13
34
0
0
0.25
0.75
0
26
35
22
31
0
0
0.55
0.45
0
14
18
26
39
0.05
0.05
0.85
36
16
26
0
0
0.45
0.55
0
13
20
29
32
0.4
0.05
0.5
37
19
0
0
0
1
0
0
13
26
0
0
0.45
0.55
0
38
27
0
0
0
1
0
0
20
24
35
0
0.45
0.05
0.5
39
16
32
0
0
0.3
0.7
0
16
26
37
0
0.05
0.85
0.1
40
23
40
0
0
0.6
0.4
0
12
17
40
0
0.25
0.05
0.7
41
19
27
0
0
0.7
0.3
0
11
23
31
35
0.05
0.85
0.05
42
7
34
0
0
0.3
0.7
0
7
25
43
0
0.1
0.8
0.1
43
17
32
0
0
0.45
0.55
0
12
22
41
0
0.05
0.7
0.25
44
10
18
0
0
0.55
0.45
0
2
6
14
27
0.05
0.05
0.85
45
8
15
17
0
0.5
0.4
0.1
6
7
15
0
0.1
0.4
0.5
46
8
13
15
0
0.1
0.4
0.5
6
12
14
0
0.25
0.25
0.5
Notes: Table A.2 describes the 46 choices between lotteries
and
used in the survey.
Table A.3: EU model estimates
(1)
(2)
0.124***
0.128***
(0.031)
(0.032)
0.414***
0.359***
(0.014)
(0.044)
Controls
No
Yes
0.040
0.056
(0.036)
(0.037)
0.250***
0.243***
(0.015)
(0.015)
Obs.
39238
37352
Clusters
853
812
AIC
51310.934
48757.487
BIC
51345.244
48842.769
Notes:
is the mean difference between males and females in parameter . Controls include age, income,
wealth, whether they obtained a university level education, whether they have children, and whether they have a
long-term health condition. Robust standard errors clustered on individual in parentheses. * 0.1, ** 0.05,
*** 0.01.
27
Table A.4: EU model estimates for those who did not violate stochastic dominance
(1)
(2)
0.116***
0.119***
(0.033)
(0.034)
0.409***
0.338***
(0.015)
(0.048)
Controls
No
Yes
0.032
0.040
(0.032)
(0.032)
0.213***
0.210***
(0.014)
(0.015)
Obs.
29716
28474
Clusters
646
619
AIC
38255.810
36605.728
BIC
38289.008
36688.296
Notes:
is the mean difference between males and females in parameter . Controls include age, income,
wealth, whether they obtained a university level education, whether they have children, and whether they have a
long-term health condition. Robust standard errors clustered on individual in parentheses. * 0.1, ** 0.05,
*** 0.01.
Table A.5: PT1 model estimates
(1)
(2)
0.117***
0.121***
(0.031)
(0.032)
0.413***
0.368***
(0.013)
(0.042)
Controls
No
Yes
-0.032***
-0.029***
(0.009)
(0.010)
0.990***
1.022***
(0.005)
(0.024)
Controls
No
Yes
0.044
0.056
(0.039)
(0.040)
0.251***
0.244***
(0.015)
(0.015)
Obs.
39238
37352
Clusters
853
812
AIC
51243.926
48684.741
BIC
51295.391
48838.247
Notes:
is the mean difference between males and females in parameter . Controls include age, income,
wealth, whether they obtained a university level education, whether they have children, and whether they have a
long-term health condition. Robust standard errors clustered on individual in parentheses. * 0.1, ** 0.05,
*** 0.01.
28
Table A.6: PT1 model estimates for those who did not violate stochastic dominance
(1)
(2)
0.109***
0.112***
(0.033)
(0.034)
0.407***
0.346***
(0.014)
(0.045)
Controls
No
Yes
-0.033***
-0.029***
(0.010)
(0.010)
0.989***
1.016***
(0.005)
(0.025)
Controls
No
Yes
0.035
0.041
(0.034)
(0.035)
0.214***
0.210***
(0.015)
(0.015)
Obs.
29716
28474
Clusters
646
619
AIC
38173.599
36507.379
BIC
38223.395
36656.000
Notes:
is the mean difference between males and females in parameter . Controls include age, income,
wealth, whether they obtained a university level education, whether they have children, and whether they have a
long-term health condition. Robust standard errors clustered on individual in parentheses. * 0.1, ** 0.05,
*** 0.01.
29
Table A.7: PT2 model estimates
(1)
(2)
0.137***
0.138***
(0.033)
(0.034)
0.441***
0.385***
(0.015)
(0.047)
Controls
No
Yes
0.000
-0.001
(0.008)
(0.009)
1.043***
1.028***
(0.004)
(0.026)
Controls
No
Yes
-0.033***
-0.029***
(0.010)
(0.010)
0.971***
1.010***
(0.005)
(0.025)
Controls
No
Yes
0.067
0.072
(0.047)
(0.049)
0.292***
0.285***
(0.018)
(0.018)
Obs.
39238
37352
Clusters
853
812
AIC
50856.580
48290.993
BIC
50925.199
48512.725
Notes:
is the mean difference between males and females in parameter . Controls include age, income,
wealth, whether they obtained a university level education, whether they have children, and whether they have a
long-term health condition. Robust standard errors clustered on individual in parentheses. * 0.1, ** 0.05,
*** 0.01.
30
Table A.8: PT2 model estimates for those who did not violate stochastic dominance
(1)
(2)
0.125***
0.123***
(0.034)
(0.035)
0.430***
0.354***
(0.015)
(0.049)
Controls
No
Yes
0.002
0.001
(0.008)
(0.008)
1.034***
1.001***
(0.004)
(0.027)
Controls
No
Yes
-0.035***
-0.029***
(0.010)
(0.010)
0.973***
1.014***
(0.005)
(0.025)
Controls
No
Yes
0.050
0.047
(0.038)
(0.039)
0.243***
0.240***
(0.016)
(0.017)
Obs.
29716
28474
Clusters
646
619
AIC
37915.212
36214.049
BIC
37981.608
36428.725
Notes:
is the mean difference between males and females in parameter . Controls include age, income,
wealth, whether they obtained a university level education, whether they have children, and whether they have a
long-term health condition. Robust standard errors clustered on individual in parentheses. * 0.1, ** 0.05,
*** 0.01.
31
Table A.9: ESVT for those who did not violate stochastic dominance
(1)
(2)
16.715*
32.555*
(9.806)
(16.870)
12.827***
13.334***
(1.637)
(4.567)
Controls
No
Yes
-0.132
-0.286***
(0.094)
(0.081)
1.069***
0.957***
(0.060)
(0.159)
Controls
No
Yes
-0.023***
-0.030***
(0.006)
(0.005)
0.046***
0.047***
(0.004)
(0.004)
Obs.
29716
28474
Clusters
646
619
AIC
37895.297
36189.271
BIC
37945.094
36337.892
Notes:
is the mean difference between males and females in parameter . Controls include age, income,
wealth, whether they obtained a university level education, whether they have children, and whether they have a
long-term health condition. Robust standard errors clustered on individual in parentheses. * 0.1, ** 0.05,
*** 0.01.
32
Table A.10: ESVT1 model estimates
(1)
(2)
9.381*
27.870**
(5.307)
(11.946)
11.358***
10.649***
(1.050)
(3.613)
Controls
No
Yes
-0.088
-0.320***
(0.100)
(0.078)
1.157***
1.108***
(0.055)
(0.161)
Controls
No
Yes
-0.028***
-0.010
(0.011)
(0.011)
0.969***
1.005***
(0.006)
(0.030)
Controls
No
Yes
-0.025***
-0.037***
(0.007)
(0.005)
0.059***
0.060***
(0.004)
(0.004)
Obs.
39238
37352
Clusters
853
812
AIC
50774.148
48195.634
BIC
50842.767
48417.366
Notes:
is the mean difference between males and females in parameter . Controls include age, income,
wealth, whether they obtained a university level education, whether they have children, and whether they have a
long-term health condition. Robust standard errors clustered on individual in parentheses. * 0.1, ** 0.05,
*** 0.01.
33
Table A.11: ESVT2 model estimates
(1)
(2)
22.976
45.055**
(16.926)
(19.571)
14.986***
14.183***
(2.102)
(5.364)
Controls
No
Yes
-0.083
-0.197***
(0.101)
(0.072)
0.991***
0.905***
(0.055)
(0.158)
Controls
No
Yes
0.005
0.004
(0.009)
(0.010)
1.025***
1.002***
(0.005)
(0.027)
Controls
No
Yes
-0.030***
-0.018
(0.011)
(0.012)
0.964***
1.010***
(0.006)
(0.030)
Controls
No
Yes
-0.026***
-0.033***
(0.008)
(0.005)
0.051***
0.051***
(0.004)
(0.005)
Obs.
39238
37352
Clusters
853
812
AIC
50699.228
48081.644
BIC
50785.002
48371.601
Notes:
is the mean difference between males and females in parameter . Controls include age, income,
wealth, whether they obtained a university level education, whether they have children, and whether they have a
long-term health condition. Robust standard errors clustered on individual in parentheses. * 0.1, ** 0.05,
*** 0.01.
34
Table A.12: ESVT model estimates with Baillon et al. (2020) data
(1)
(2)
37.515***
36.523***
(12.231)
(11.023)
25.755**
-94.911*
(11.805)
(48.889)
Age
No
Yes
1.004**
0.839*
(0.404)
(0.433)
1.087***
2.121***
(0.264)
(0.519)
Age
No
Yes
-0.010
0.006
(0.024)
(0.021)
0.110***
0.092***
(0.021)
(0.016)
Obs.
9587
9587
Clusters
137
137
AIC
12584.720
12567.378
BIC
12627.729
12624.724
Notes:
is the mean difference between males and females in parameter . Robust standard errors clustered
on individual in parentheses. * 0.1, ** 0.05, *** 0.01.
35
Table A.13: ESVT1 model estimates with Baillon et al. (2020) data
(1)
(2)
29.342**
30.752**
(14.737)
(12.674)
31.417**
-105.329**
(14.205)
(52.742)
Age
No
Yes
0.978**
0.789*
(0.464)
(0.470)
1.120***
2.154***
(0.320)
(0.512)
Age
No
Yes
0.101**
0.087**
(0.040)
(0.034)
0.961***
1.056***
(0.033)
(0.104)
Age
No
Yes
-0.008
0.008
(0.025)
(0.021)
0.111***
0.092***
(0.022)
(0.015)
Obs.
9587
9587
Clusters
137
137
AIC
12556.317
12538.245
BIC
12613.663
12617.095
Notes:
is the mean difference between males and females in parameter . Robust standard errors clustered
on individual in parentheses. * 0.1, ** 0.05, *** 0.01.
36
Table A.14: ESVT2 model estimates with Baillon et al. (2020) data
(1)
(2)
32.852**
29.486*
(13.996)
(15.509)
1.020***
0.989***
(0.027)
(0.091)
Age
No
Yes
1.155**
0.910
(0.517)
(0.563)
1.099***
2.260***
(0.280)
(0.547)
Age
No
Yes
0.019
0.026
(0.032)
(0.029)
1.025***
0.978***
(0.005)
(0.013)
Age
No
Yes
0.100***
0.084***
(0.038)
(0.032)
0.953***
1.067***
(0.029)
(0.101)
Age
No
Yes
0.001
0.015
(0.024)
(0.022)
0.112***
0.094***
(0.020)
(0.015)
Obs.
9587
9587
Clusters
137
137
AIC
12544.800
12529.091
BIC
12616.481
12629.445
Notes:
is the mean difference between males and females in parameter . Robust standard errors clustered
on individual in parentheses. * 0.1, ** 0.05, *** 0.01.
37
Table A.15: EU and PT model estimates with gender dependent reference points
EU
PT
0.124***
0.553***
(0.031)
(0.109)
0.414***
0.840***
(0.014)
(0.015)
0.169
(0.113)
1.316***
(0.021)
0.040
6.542
(0.036)
(4.217)
0.250***
3.534***
(0.015)
(0.200)
Obs.
39238
39238
Clusters
853
853
AIC
51310.934
51246.883
BIC
51345.244
51298.347
Notes:
is the mean difference between males and females in parameter . Robust standard errors clustered
on individual in parentheses. * 0.1, ** 0.05, *** 0.01.
38
B. Figures
Figure B.1: Utility and probability weighting functions by participant gender
39
Figure B.2: BIC scores across models
Figure B.3: BIC scores across models with Baillon et al. (2020) data
48100
48200
48300
48400
48500
48600
48700
48800
48900
EU PT1 PT2 ESVT ESVT1 ESVT2
BIC score
12400
12500
12600
12700
12800
12900
EU PT1 PT2 ESVT ESVT1 ESVT2
BIC score
40
Figure B.4: BIC scores across models
51250
51275
51300
51325
51350
EU PT
BIC score
41
C. Models used for estimation
Assume, the expected utility function of receiving with probability is given by:
where is the probability weighting function and is the utility function.
We employed the following six specifications for the above equation:
1. EU: expected utility
2. PT1: prospect theory with one parameter probability weighting as in Prelec (1998)
3. PT2: prospect theory with two parameter probability weighting as in Prelec (1998)
4. ESVT: expected subjective value theory as in Glimcher & Tymula (2023)
5. ESVT1: expected subjective value theory as in Glimcher & Tymula (2023) with one
parameter probability weighting as in Prelec (1998)
6. ESVT2: expected subjective value theory as in Glimcher & Tymula (2023) with two
parameter probability weighting as in Prelec (1998)
