DISCUSSION PAPER SERIESIZA DP No. 16138

The Gender Reference Point Gap

Nathan Kettlewell
Jonathan Levy
Agnieszka Tymula
Xueting Wang

MAY 2023

DISCUSSION PAPER SERIESIZA DP No. 16138

The Gender Reference Point Gap

Nathan Kettlewell

Agnieszka Tymula

Jonathan Levy

Xueting Wang

University of Technology Sydney and IZA
University of Sydney

University of Sydney

Royal Melbourne Institute of Technology

MAY 2023

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IZA DP No. 16138

MAY 2023

ABSTRACTThe 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 thenevaluate whether there is a gender difference in the reference point, explaining the genderdifference in risk aversion observed using traditional approaches. In our study, womenmake 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 asa 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: nathan.kettlewell@uts.edu.au* 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.

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 wellas the gender pay gap.
Although the gender difference in risk attitude has been replicated in many studies (this is notalways the case, e.g., Filippin & Crosetto, 2016; Nelson, 2015), economists have struggledwith whether and how to use this finding to restore gender balance in economic decisionmaking. 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 togender differences in risk attitudes. Conceptually, in these models, people maximize theirutility 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 genderinequality.
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 isa 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 theneuroeconomic 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 selfreinforcing—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) toprovide the first evidence on gender differences in reference points estimated from behavior.

2

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 andProspect 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 curvatureand probability weighting. Our results suggest that income mediates the gender difference inthe 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 toeliminate 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 ina 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 (notincentivized) and may be influenced by unmeasured differences in the information received byparticipants. 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 statedbeliefs in areas like wage expectations can be driven by both different satisficing outcomes, aswell 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), andpredictions of such models empirically (e.g., Abeler et al., 2011; Allen et al., 2017; Bartling et3

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 thesestudies 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 bycomparing 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 etal., 2008), and neuroeconomics (Glimcher & Tymula, 2023; Guo & Tymula, 2021) whichsuggests that reference points are at least partially affected by historical outcomes. Unlike theprevious 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 fromtrial 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 alower reference point than men, a difference not documented in prior research. In ourframework, the reference point is a continuous latent variable and there is no discontinuity inthe 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 datacollection and the empirical approach. In section 3 we report results along with several checks
for robustness. Section 4 concludes.

4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 participants2 (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 thegeneral population. Second, our sample is large, which allows us to precisely estimate genderdifferences, 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 lesslikely 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 theirpreferences (the fact they completed the whole survey indicates a strong intrinsic motivation). Our results do notchange when we exclude these participants from the analysis.
3This gender difference is largely a feature of the composition of Twins Research Australia’s twin registry (seeKettlewell & Tymula, 2021).

5

Table 1: Descriptive statistics
Variable
Age
Lives in a city
Married/defacto
Household size
Has children
University degree
Employed
RetiredIncome (weekly)
Wealth (self-reported)4Long-term healthcondition

Mean Female

Mean Male

Difference

P-value

41.816
0.651
0.641
2.805
0.487
0.569
0.802
0.075
1248.387
4.107

41.172
0.724
0.641
2.738
0.407
0.683
0.828
0.097
1702.427
4.269

0.644
-0.073-0.0000.067
0.080-0.114-0.025-0.022-454.04-0.162

0.620
0.101
1.000
0.595
0.083
0.012
0.564
0.396
0.000
0.019

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 forvariable definitions and observation counts.

The survey was programmed in Qualtrics and conducted online between November 2021 andApril 2022. Participants completed four tasks and a demographic and socioeconomic
questionnaire. One of the four tasks was randomly selected for payment and the payment wasdetermined by the decision made by participants in this task and chance. To emphasize theimportance 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 toestimate 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 atvarious 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 theorder of the decision scenarios, and the side on which lotteries appeared. The selection ofdecision scenarios ensured the complete coverage of the outcome and probability space and abalanced 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).
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.
5

6

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 verticalbars with as many parts as there were different payoffs. The size of each part correspondedwith the probability of the payoff. The intensity of the color of each part increased with the sizeof the payoff. The payoffs were presented in decreasing order (the lowest at the top and thehighest at the bottom). Participants clicked on a bullet located next to a lottery to indicate theirpreference. Decision scenarios 45 and 46 (see Table A.2) had one lottery stochasticallydominating 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 theneuroscientific 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.

7main intuition behind ESVT is that the utility function adapts to the payoff expectation toefficiently encode value (Bucher & Brandenburger, 2022; Steverson et al., 2019). Because thebrain does not have unlimited resources (action potentials) to encode the utility of payoffs, it
adjusts dynamically so that the subjective value function7 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 forreference 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 𝑥 ∈ ℝ+ is given by:𝑢(𝑥) =𝑥𝛼𝑥 𝛼 + 𝑀𝛼(1)where 𝑀 is the payoff expectation (reference point) and 𝛼 > 0 is a free parameter called
predisposition.
The utility function takes values between 0 and 1 (𝑢 ∈ [0, 1]) consistent with the idea thatdecision makers are bounded in the range of subjective values that they can biophysicallyassign to payoffs (Rayo & Becker, 2007; Robson et al., 2022; Woodford, 2012).
We assume that the expected utility of a lottery that pays 𝑥 with probability 𝑝 is calculated as:(2)𝑣(𝑝, 𝑥) = 𝐸[𝑢(𝑥), 𝑝] = 𝑤(𝑝)𝑢(𝑥).

We therefore diverge from Glimcher & Tymula (2023) by allowing for a probability weighting
function.

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 ineconomics.
7

8

Both 𝑀 and 𝛼 determine the shape of the utility function and therefore the risk attitude. As thereference point (𝑀) increases, the utility function shifts rightward along the horizontal axis.
This feature prevails in many reference-dependent models. The shift in the utility function issuch that at the reference point the function always takes the same value, 𝑢(𝑥 = 𝑀) = 0.5.
This property is consistent with mounting evidence that people are indeed reference dependentwhen making decisions. Predisposition (𝛼) affects the curvature of the utility function. When
predisposition is low the utility function is concave for all 𝑥 and thus the decision maker isalways risk averse. As 𝛼 increases, the utility function becomes increasingly S-shaped as seen
in PT—for small values of 𝑥 utility is convex (risk seeking) and then as 𝑥 increases changes toconcave (risk averse). Unlike in PT, in ESVT the inflection point does not have to occur at thereference point. Instead, the inflection point depends on both the reference point (𝑀) andpredisposition (𝛼). If the utility function inflects, then as in PT, for individuals with a higher
reference point (𝑀), the utility inflects at a higher 𝑥 meaning that they are risk seeking for alarger range of 𝑥 values.
We fit decisions of our participants with a logistic choice function, where the probability ofchoosing lottery 𝐴 is:𝑃(𝐴) =
where 𝑍 =1
1 + 𝑒 −𝑍(3)𝑣(𝐴)−𝑣(𝐵)𝜇, and 𝜇 captures noise. The log-likelihood function is then given by:
𝑁

𝐼

𝐿𝐿(𝜽) = ∑ ∑ 𝑦𝑛𝑖 ln(𝑃𝑛𝑖 (𝐴𝑖 )) + (1 − 𝑦𝑛𝑖 ) ln(1 − 𝑃𝑛𝑖 (𝐴𝑖 ))(4)

𝑛=1 𝑖=1

where 𝑁 is the number of participants, 𝐼 is the number of trials, 𝑦𝑛𝑖 = 1(0) is an indicatorfunction denoting the choice of lottery 𝐴(𝐵) for participant 𝑛 in trial 𝑖, and 𝜽 is the vector of
behavioral parameters to be estimated.
To capture gender effects, we introduce a dummy variable 𝑀𝑎𝑙𝑒 which takes the value 1 if theparticipant 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 theparticipant obtained a university level education, whether the participant has children, andwhether the participant has a long-term health condition).

9For each parameter 𝜃𝑛 in our model, we specify:𝜃𝑛 = 𝜃0 + 𝜃𝑀𝑎𝑙𝑒 × 𝑀𝑎𝑙𝑒𝑛 + 𝑋𝑛′ 𝛽(5)where 𝑋 is a vector of controls and 𝛽 are the associated coefficients. For each parameter 𝜃, wereport the point estimate for the maximum likelihood estimation. The standard errors are
clustered at the individual level.8𝛾

For comparison and robustness checks we use the one-parameter (𝑤(𝑝) = 𝑒 −(− ln(𝑝)) ) and𝛾

two-parameter (𝑤(𝑝) = 𝑒 −δ(− ln(𝑝)) ) probability weighting functions proposed by Prelec(1998). In these functions, 𝛾 ∈ [0,1] governs the shape of the weighting function, with smaller
𝛾 corresponding to a more inverse S-shaped function (i.e., greater over (under)-weighting oflow (high) probability outcomes), while 𝛿 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-parameterprobability weighting in Appendix A.
To allow for easy comparisons with existing literature on risk attitudes, we also estimate apower utility function (𝑢(𝑥) = 𝑥 𝑟 ) 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 womenchoose riskier lotteries less frequently than men (42.7% versus 46.5%, t-test: 𝑝-value =0.0087)—see Figure 2A.9 Their expected earnings, calculated based on their decisions in the

8
9

The main results do not change when we cluster standard errors at the sibling level.
All reported 𝑝-values are from two-sided tests.

10lottery choice task, are 0.46 standard deviations lower than men’s ($18.88 versus $18.96, t-test:
𝑝-value < 0.001)—see Figure 2B.10

(A)

(B)

Normalized expected
earnings% of riskier choices

***
50
40
30
20
10
0

***

0.6
0.4
0.2
0

-0.2
Male

FemaleMale

FemaleFigure 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) thanmen 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 andpositive coefficient estimate on 𝑟𝑀𝑎𝑙𝑒 in all models. As the literature has suggested (Fehr-Duda
et al., 2006; Filippin & Crosetto, 2016), we observe statistically significant differences acrossgenders in probability weighting (Table A.7). We find that men have significantly lower 𝛾 (nosignificant gender difference in 𝛿). The coefficient estimates for 𝛾𝑀𝑎𝑙𝑒 are between -0.033 and-0.029. This gender difference seems small as evidenced by the similarity in the estimatedprobability weighting functions drawn separately for each gender based on Table A.7 estimatesin Figure B.1. Such differences in probability weighting could nevertheless have an impact onearnings if they are paired with substantial payoffs. In our study though, the differences inprobability 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 whenallowing for men and women to differ in utility curvature than when allowing for men andwomen 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 𝑖 are equal to (𝐸𝑖 − 𝐸𝑃 )/𝜎𝑃 where 𝐸𝑖 are theexpected earnings for participant 𝑖, 𝐸𝑃 are the average expected earnings in the sample population, and 𝜎𝑃 is thestandard deviation of the expected earnings in the sample population.

11

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 functions11 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 understandwhether 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
𝑀𝑀𝑎𝑙𝑒
𝑀
Controls𝛼𝑀𝑎𝑙𝑒𝛼Controls
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
15.119*(8.184)13.002***(1.524)No-0.093(0.087)1.065***(0.054)No-0.026***(0.006)
0.053***(0.004)39238
853
50910.979
50962.443(2)
34.999***(13.555)
12.620***(4.743)Yes-0.246***(0.068)0.983***(0.151)
Yes-0.033***(0.005)0.052***(0.004)37352
812
48337.850
48491.357

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Controls include age, income,wealth, whether they obtained a university level education, whether they have children, and whether they have along-term health condition. Robust standard errors clustered on individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05,*** 𝑝 < 0.01.

11

In addition to estimating PT with 𝑤(𝑝) as in Prelec (1998) we also estimated prospect theory models with 𝑤(𝑝)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.

12

The coefficient estimate for 𝑀𝑀𝑎𝑙𝑒 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 fromcolumn (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 ourtask, the maximum payoff was $43. This, of course, could happen simply because men andwomen 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 notcontrolling for education or income levels. To ensure that we capture the true gender effect andcompare men and women who are similar in demographic and socioeconomic characteristics,
we introduce controls to the model—age, income, wealth, whether the participant obtained auniversity 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 andneuroeconomics (Frydman & Jin, 2021; Glimcher & Tymula, 2023; Padoa-Schioppa &Rustichini, 2014; Rangel & Clithero, 2012; Tymula & Plassmann, 2016) tells us that the13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, basedon 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 suchcorrelations exist in our data. Furthermore, we can check whether the gender difference in thereference point exists above and beyond the potential impact of income and wealth on thereference 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 onlyrobust but increases significantly when we include controls. In Table 3 we present the valuesof all coefficients of the model presented in the second column of Table 2.

Table 3: Determinants of reference points and predisposition

Male
Age
University degree
WealthIncome (weekly)
Has children
Long-term healthcondition
Constant

Reference point(𝑀)
34.999***(13.555)
0.057(0.071)-1.246(1.490)-1.074(0.965)0.002**(0.001)-0.186(2.199)1.077

Predisposition(𝛼)-0.246***(0.068)-0.005***(0.002)0.201***(0.048)0.045(0.028)-0.000(0.000)0.004(0.053)0.020(1.551)
12.620***(4.743)(0.068)0.983***(0.151)

Obs.
Clusters
AIC
BIC

37352
812
48337.850
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 (𝑀) and the second column
provides parameter estimates with respect to predisposition (𝛼). Robust standard errors clustered on individual inparentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01.

In the first column of Table 3 we can see that in line with our hypothesis the coefficient of

14

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 theexisting 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 ofTable 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 resultschange 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 weadopt.

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 thedominated 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 doobserve a gender difference in decisions in the two trials where one lottery stochasticallydominates the other. Women violate first-order stochastic dominance more frequently than men(25.4% versus 18.6%, Fisher’s exact test: 𝑝-value = 0.089). However, the results pertaining to

12

In column (1) of Table 2, the coefficient of 𝛼𝑀𝑎𝑙𝑒 is not statistically significant, indicating no gender differencein predisposition. As we include controls the coefficient becomes negative and statistically significant. In thesecond column of Table 3 we can see that the coefficients of Age and University degree are significantly negativeand significantly positive, respectively. The noise parameter 𝜇 was significantly different across genders.
Indicating that decisions were noisier for women than men.

15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 featureof 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 theinclusion 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 thatincorporating probability weighting into ESVT may impact our findings. We find that theresults 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 andPT. 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 enhancesmodel 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, weestimate the following PT model where 𝑣(𝑥) = 𝑝𝑢(𝑥) and𝑢(𝑥) = {13(𝑥 − 𝑀)𝑟−(𝑀 − 𝑥)𝑔𝑟𝑙

if 𝑥 ≥ 𝑀(6)otherwise,

The reference point used for males and females was 28.121 and 13.002, respectively.

16and 𝑟 𝑔 and 𝑟 𝑙 represent utility curvature in the gain and loss domains, respectively. To makethe 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 acrossgenders improves the predictive power of the model. Furthermore, the parameter estimatesfrom 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: 𝑝-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 theTechnical 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 ourdataset, 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 thenevaluate whether there is a gender difference in the reference point, explaining the genderdifference in risk aversion observed using traditional approaches. We find that women makeriskier choices less frequently than men. We also find that women on average have asignificantly 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.

17

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 inreference 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 aretreated as the primitives in the economic models of choice, economists would argue that weshould 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 asetting, the interpretation of risk attitudes is different—they are malleable and determined byour 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 willtake less risk and end up making decisions that reinforce the cycle of economic disadvantage.
Policies that address economic inequality by equalizing payoff expectations should beparticularly 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 theplaying field. Indeed, Recalde & Vesterlund (2022) in their literature review conclude thattransparency 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.

18

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 outcomesis 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 weprovided 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 fromneuroeconomics 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 othertopics where reference-dependence plays a role.

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Appendix
A. Tables
Table A.1: Variable definitions
Variable
Age
Lives in a city

Married/defacto
Household size
Has children
University degree

Employed

RetiredIncome (weekly)

WealthDefinition

Female obs.

Male obs.

Age at last birthday= 1 if currently live in a major
city (Sydney, Melbourne,
Brisbane, Adelaide, Perth,Canberra)= 1 if married or in a defacto
relationshipHow many people live in yourhousehold= 1 if they have any children= 1 if highest level of
education obtained is auniversity degree= 1 if worked any time in thelast 7 days or if had a job but
did not work in the last 7 days
due to holidays, sickness or
any other reason= 1 if currently retired fromthe workforce
Average usual weekly own
income in the last monthusing midpoint value for thefollowing 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.
Given your current needs andfinancial responsibility, would
you say that you and yourfamily are: = 1 if Poor, = 2 if
Just getting along, = 3 if
Comfortable, = 4 if Very
comfortable, = 5 if
Prosperous.

707

145

708

145

708

145

707

145

708

145

708

145

708

145

708

145

670

143

708

145

24

= 1 if has a long-term healthcondition, impairment or
disability that has lasted morethan 6 months

Long-term healthcondition

708

145

Table A.2: Lottery decision scenarios
Scenario
number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34

𝑥1𝑎

𝑥2𝑎

𝑥3𝑎

𝑥4𝑎

𝑝1𝑎

𝑝2𝑎

𝑝3𝑎

𝑥1𝑏

𝑥2𝑏

𝑥3𝑏

𝑥4𝑏

𝑝1𝑏

𝑝2𝑏

𝑝3𝑏

17
7
7
16
17
9
17
7
19
17
7
7
15
10
9
17
17
19
14
4
11
19
9
10
7
9
4
8
7
17
21
15
15
29

20
16
18
23
38
20
32
16
32
32
17
14
24
18
15
28
26
27
23
13
28
42
18
16
34
21
19
14
0
0
0
0
0
0

29
29
0
35
0
32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
21
0
0
0
21
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0.4
0.6
0.85
0.35
0.85
0.15
0.55
0.2
0.8
0.45
0.8
0.3
0.75
0.55
0.8
0.4
0.7
0.7
0.6
0.45
0.6
0.75
0.75
0.7
0.3
0.2
0.3
0.1
1
1
1
1
1
1

0.5
0.15
0.15
0.55
0.15
0.8
0.45
0.8
0.2
0.55
0.2
0.7
0.25
0.45
0.2
0.6
0.3
0.3
0.4
0.55
0.4
0.25
0.25
0.05
0.7
0.8
0.7
0.05
0
0
0
0
0
0

0.1
0.25
0
0.1
0
0.05
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.25
0
0
0
0.85
0
0
0
0
0
0

11
3
1
12
6
3
7
4
11
12
1
4
9
2
4
7
12
11
4
1
0
12
6
5
7
9
4
8
1
0
6
8
7
13

14
12
10
19
22
15
27
10
28
22
10
9
18
6
7
12
15
23
18
7
5
27
12
8
25
25
14
24
14
22
28
11
11
34

26
20
15
27
33
26
36
21
37
41
14
12
21
14
13
23
23
31
27
16
28
42
18
21
43
0
25
27
0
0
36
23
18
0

0
24
0
31
0
37
0
0
0
0
20
19
27
27
17
39
29
35
32
19
0
0
0
0
0
0
0
0
0
0
0
0
22
0

0.1
0.3
0.1
0.05
0.05
0.1
0.25
0.2
0.35
0.05
0.1
0.25
0.35
0.05
0.2
0.05
0.3
0.05
0.15
0.4
0.25
0.15
0.15
0.4
0.1
0.45
0.05
0.5
0.45
0.25
0.35
0.45
0.3
0.25

0.4
0.1
0.7
0.55
0.7
0.35
0.7
0.5
0.45
0.7
0.4
0.3
0.05
0.05
0.1
0.1
0.2
0.85
0.7
0.05
0.05
0.7
0.7
0.1
0.8
0.55
0.85
0.3
0.55
0.75
0.45
0.05
0.05
0.75

0.5
0.05
0.2
0.1
0.25
0.45
0.05
0.3
0.2
0.25
0.45
0.05
0.45
0.85
0.6
0.6
0.1
0.05
0.1
0.5
0.7
0.15
0.15
0.5
0.1
0
0.1
0.2
0
0
0.2
0.5
0.5
0

25

35
36
37
38
39
40
41
42
43
44
45
46

22
16
19
27
16
23
19
7
17
10
8
8

31
26
0
0
32
40
27
34
32
18
15
13

0
0
0
0
0
0
0
0
0
0
17
15

0
0
0
0
0
0
0
0
0
0
0
0

0.55
0.45
1
1
0.3
0.6
0.7
0.3
0.45
0.55
0.5
0.1

0.45
0.55
0
0
0.7
0.4
0.3
0.7
0.55
0.45
0.4
0.4

0
0
0
0
0
0
0
0
0
0
0.1
0.5

14
13
13
20
16
12
11
7
12
2
6
6

18
20
26
24
26
17
23
25
22
6
7
12

26
29
0
35
37
40
31
43
41
14
15
14

39
32
0
0
0
0
35
0
0
27
0
0

0.05
0.4
0.45
0.45
0.05
0.25
0.05
0.1
0.05
0.05
0.1
0.25

0.05
0.05
0.55
0.05
0.85
0.05
0.85
0.8
0.7
0.05
0.4
0.25

0.85
0.5
0
0.5
0.1
0.7
0.05
0.1
0.25
0.85
0.5
0.5

Notes: Table A.2 describes the 46 choices between lotteries 𝐴 = (𝑝1𝑎 , 𝑥1𝑎 ; 𝑝2𝑎 , 𝑥2𝑎 ; 𝑝3𝑎 , 𝑥3𝑎 ; 1 − 𝑝1𝑎 − 𝑝2𝑎 − 𝑝3𝑎 , 𝑥4𝑎 )and 𝐵 = (𝑝1𝑏 , 𝑥1𝑏 ; 𝑝2𝑏 , 𝑥2𝑏 ; 𝑝3𝑏 , 𝑥3𝑏 ; 1 − 𝑝1𝑏 − 𝑝2𝑏 − 𝑝3𝑏 , 𝑥4𝑏 ) used in the survey.

Table A.3: EU model estimates𝑟𝑀𝑎𝑙𝑒𝑟Controls
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
0.124***(0.031)0.414***(0.014)No
0.040(0.036)0.250***(0.015)39238
853
51310.934
51345.244(2)0.128***(0.032)0.359***(0.044)Yes
0.056(0.037)0.243***(0.015)37352
812
48757.487
48842.769

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Controls include age, income,wealth, whether they obtained a university level education, whether they have children, and whether they have along-term health condition. Robust standard errors clustered on individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05,*** 𝑝 < 0.01.

26

Table A.4: EU model estimates for those who did not violate stochastic dominance𝑟𝑀𝑎𝑙𝑒𝑟Controls
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
0.116***(0.033)0.409***(0.015)No
0.032(0.032)0.213***(0.014)29716
646
38255.810
38289.008(2)
0.119***(0.034)
0.338***(0.048)Yes
0.040(0.032)0.210***(0.015)28474
619
36605.728
36688.296

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Controls include age, income,wealth, whether they obtained a university level education, whether they have children, and whether they have along-term health condition. Robust standard errors clustered on individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05,*** 𝑝 < 0.01.

Table A.5: PT1 model estimates𝑟𝑀𝑎𝑙𝑒𝑟Controls𝛾𝑀𝑎𝑙𝑒𝛾
Controls
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
0.117***(0.031)0.413***(0.013)No-0.032***(0.009)0.990***(0.005)No
0.044(0.039)0.251***(0.015)39238
853
51243.926
51295.391(2)
0.121***(0.032)0.368***(0.042)
Yes-0.029***(0.010)1.022***(0.024)Yes
0.056(0.040)0.244***(0.015)37352
812
48684.741
48838.247

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Controls include age, income,wealth, whether they obtained a university level education, whether they have children, and whether they have along-term health condition. Robust standard errors clustered on individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05,*** 𝑝 < 0.01.

27

Table A.6: PT1 model estimates for those who did not violate stochastic dominance𝑟𝑀𝑎𝑙𝑒𝑟Controls𝛾𝑀𝑎𝑙𝑒𝛾
Controls
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
0.109***(0.033)0.407***(0.014)No-0.033***(0.010)0.989***(0.005)No
0.035(0.034)0.214***(0.015)29716
646
38173.599
38223.395(2)
0.112***(0.034)0.346***(0.045)Yes-0.029***(0.010)1.016***(0.025)Yes
0.041(0.035)0.210***(0.015)28474
619
36507.379
36656.000

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Controls include age, income,wealth, whether they obtained a university level education, whether they have children, and whether they have along-term health condition. Robust standard errors clustered on individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05,*** 𝑝 < 0.01.

28

Table A.7: PT2 model estimates𝑟𝑀𝑎𝑙𝑒𝑟Controls
𝛿𝑀𝑎𝑙𝑒𝛿

Controls𝛾𝑀𝑎𝑙𝑒𝛾
Controls
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
0.137***(0.033)0.441***(0.015)No
0.000(0.008)1.043***(2)
0.138***(0.034)0.385***(0.047)Yes-0.001(0.009)1.028***(0.004)No-0.033***(0.010)0.971***(0.005)No
0.067(0.047)0.292***(0.018)39238
853
50856.580
50925.199(0.026)
Yes-0.029***(0.010)1.010***(0.025)Yes
0.072(0.049)0.285***(0.018)37352
812
48290.993
48512.725

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Controls include age, income,wealth, whether they obtained a university level education, whether they have children, and whether they have along-term health condition. Robust standard errors clustered on individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05,*** 𝑝 < 0.01.

29

Table A.8: PT2 model estimates for those who did not violate stochastic dominance𝑟𝑀𝑎𝑙𝑒𝑟Controls
𝛿𝑀𝑎𝑙𝑒𝛿

Controls𝛾𝑀𝑎𝑙𝑒𝛾
Controls
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
0.125***(0.034)0.430***(0.015)No
0.002(0.008)1.034***(2)
0.123***(0.035)0.354***(0.049)Yes
0.001(0.008)1.001***(0.004)No-0.035***(0.010)0.973***(0.005)No
0.050(0.038)0.243***(0.016)29716
646
37915.212
37981.608(0.027)
Yes-0.029***(0.010)1.014***(0.025)Yes
0.047(0.039)0.240***(0.017)28474
619
36214.049
36428.725

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Controls include age, income,wealth, whether they obtained a university level education, whether they have children, and whether they have along-term health condition. Robust standard errors clustered on individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05,*** 𝑝 < 0.01.

30

Table A.9: ESVT for those who did not violate stochastic dominance
𝑀𝑀𝑎𝑙𝑒
𝑀
Controls𝛼𝑀𝑎𝑙𝑒𝛼Controls
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
16.715*(9.806)12.827***(1.637)
No-0.132(0.094)1.069***(0.060)No-0.023***(0.006)
0.046***(0.004)29716
646
37895.297
37945.094(2)
32.555*(16.870)
13.334***(4.567)Yes-0.286***(0.081)
0.957***(0.159)Yes-0.030***(0.005)0.047***(0.004)28474
619
36189.271
36337.892

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Controls include age, income,wealth, whether they obtained a university level education, whether they have children, and whether they have along-term health condition. Robust standard errors clustered on individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05,*** 𝑝 < 0.01.

31

Table A.10: ESVT1 model estimates
𝑀𝑀𝑎𝑙𝑒
𝑀
Controls𝛼𝑀𝑎𝑙𝑒𝛼Controls𝛾𝑀𝑎𝑙𝑒𝛾
Controls
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
9.381*(5.307)
11.358***(1.050)No-0.088(0.100)1.157***(0.055)No-0.028***(0.011)
0.969***(0.006)
No-0.025***(0.007)0.059***(0.004)39238
853
50774.148
50842.767(2)
27.870**(11.946)
10.649***(3.613)
Yes-0.320***(0.078)1.108***(0.161)
Yes-0.010(0.011)1.005***(0.030)Yes-0.037***(0.005)0.060***(0.004)37352
812
48195.634
48417.366

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Controls include age, income,wealth, whether they obtained a university level education, whether they have children, and whether they have along-term health condition. Robust standard errors clustered on individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05,*** 𝑝 < 0.01.

32

Table A.11: ESVT2 model estimates
𝑀𝑀𝑎𝑙𝑒
𝑀
Controls𝛼𝑀𝑎𝑙𝑒𝛼Controls
𝛿𝑀𝑎𝑙𝑒𝛿

Controls𝛾𝑀𝑎𝑙𝑒𝛾
Controls
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
22.976(16.926)
14.986***(2.102)No-0.083(0.101)
0.991***(0.055)No
0.005(0.009)1.025***(2)
45.055**(19.571)
14.183***(5.364)Yes-0.197***(0.072)0.905***(0.158)Yes
0.004(0.010)1.002***(0.005)No-0.030***(0.011)
0.964***(0.006)
No-0.026***(0.008)0.051***(0.004)39238
853
50699.228
50785.002(0.027)
Yes-0.018(0.012)1.010***(0.030)Yes-0.033***(0.005)0.051***(0.005)37352
812
48081.644
48371.601

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Controls include age, income,wealth, whether they obtained a university level education, whether they have children, and whether they have along-term health condition. Robust standard errors clustered on individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05,*** 𝑝 < 0.01.

33

Table A.12: ESVT model estimates with Baillon et al. (2020) data
𝑀𝑀𝑎𝑙𝑒
𝑀
Age
𝛼𝑀𝑎𝑙𝑒
𝛼
Age
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
37.515***(12.231)25.755**(11.805)
No
1.004**(0.404)1.087***(0.264)No-0.010(0.024)0.110***(0.021)9587
137
12584.720
12627.729(2)
36.523***(11.023)-94.911*(48.889)
Yes
0.839*(0.433)2.121***(0.519)Yes
0.006(0.021)
0.092***(0.016)9587
13712567.378
12624.724

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Robust standard errors clusteredon individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01.

34

Table A.13: ESVT1 model estimates with Baillon et al. (2020) data
𝑀𝑀𝑎𝑙𝑒
𝑀
Age
𝛼𝑀𝑎𝑙𝑒
𝛼
Age
𝛾𝑀𝑎𝑙𝑒
𝛾
Age
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
29.342**(14.737)
31.417**(14.205)
No
0.978**(0.464)1.120***(0.320)No
0.101**(0.040)0.961***(0.033)No-0.008(0.025)0.111***(0.022)9587
13712556.317
12613.663(2)
30.752**(12.674)-105.329**(52.742)Yes
0.789*(0.470)2.154***(0.512)
Yes
0.087**(0.034)
1.056***(0.104)Yes
0.008(0.021)
0.092***(0.015)9587
13712538.245
12617.095

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Robust standard errors clusteredon individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01.

35

Table A.14: ESVT2 model estimates with Baillon et al. (2020) data
𝑀𝑀𝑎𝑙𝑒
𝑀
Age
𝛼𝑀𝑎𝑙𝑒
𝛼
Age
𝛿𝑀𝑎𝑙𝑒
𝛿

Age
𝛾𝑀𝑎𝑙𝑒
𝛾
Age
𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

(1)
32.852**(13.996)1.020***(0.027)No
1.155**(0.517)1.099***(0.280)No
0.019(0.032)
1.025***(2)
29.486*(15.509)
0.989***(0.091)Yes
0.910(0.563)2.260***(0.547)Yes
0.026(0.029)0.978***(0.005)No0.100***(0.038)0.953***(0.029)No
0.001(0.024)0.112***(0.020)9587
13712544.800
12616.481(0.013)Yes
0.084***(0.032)
1.067***(0.101)
Yes
0.015(0.022)
0.094***(0.015)9587
13712529.091
12629.445

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Robust standard errors clusteredon individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01.

36

Table A.15: EU and PT model estimates with gender dependent reference points
𝑔
𝑟𝑀𝑎𝑙𝑒

𝑟

𝑔

EU
0.124***

PT
0.553***(0.031)0.414***(0.014)(0.109)0.840***(0.015)
0.169

𝑙
𝑟𝑀𝑎𝑙𝑒

𝑟

(0.113)
1.316***

𝑙

𝜇𝑀𝑎𝑙𝑒
𝜇
Obs.
Clusters
AIC
BIC

0.040
(0.036)0.250***(0.015)39238
853
51310.934
51345.244(0.021)
6.542(4.217)3.534***(0.200)39238
853
51246.883
51298.347

Notes: 𝜃𝑀𝑎𝑙𝑒 is the mean difference between males and females in parameter 𝜃. Robust standard errors clusteredon individual in parentheses. * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01.

37

B. Figures

Figure B.1: Utility and probability weighting functions by participant gender38

4890048800

BIC score

48700
48600
48500
48400
48300

48200
48100
EU

PT1

PT2

ESVT

ESVT1

ESVT2

ESVT1

ESVT2

Figure B.2: BIC scores across models

12900

BIC score

12800

12700

12600

12500

12400
EU

PT1

PT2

ESVT

Figure B.3: BIC scores across models with Baillon et al. (2020) data39

51350

BIC score

51325

51300

51275

51250
EU

PT

Figure B.4: BIC scores across models

40

C. Models used for estimation
Assume, the expected utility function 𝑣 of receiving $𝑥 with probability 𝑝 is given by:𝑣(𝑝, 𝑥) = 𝑤(𝑝)𝑢(𝑥)where 𝑤 is the probability weighting function and 𝑢 is the utility function.
We employed the following six specifications for the above equation:
1. EU: expected utility𝑣(𝑝, 𝑥) = 𝑝𝑥 𝑟
2. PT1: prospect theory with one parameter probability weighting 𝑤(𝑝) as in Prelec (1998)
𝛾𝑣(𝑝, 𝑥) = 𝑒 −(− ln(𝑝)) 𝑥 𝑟
3. PT2: prospect theory with two parameter probability weighting 𝑤(𝑝) as in Prelec (1998)
𝛾𝑣(𝑝, 𝑥) = 𝑒 −δ(− ln(𝑝)) 𝑥 𝑟
4. ESVT: expected subjective value theory as in Glimcher & Tymula (2023)𝑥𝛼𝑣(𝑝, 𝑥) = 𝑝 𝑥 𝛼+𝑀𝛼
5. ESVT1: expected subjective value theory as in Glimcher & Tymula (2023) with one
parameter probability weighting 𝑤(𝑝) as in Prelec (1998)
𝑣(𝑝, 𝑥) = 𝑒 −(− ln(𝑝))𝑥𝛼𝛾𝑥 𝛼 +𝑀𝛼

6. ESVT2: expected subjective value theory as in Glimcher & Tymula (2023) with twoparameter probability weighting 𝑤(𝑝) as in Prelec (1998)𝛾𝑥𝛼𝑣(𝑝, 𝑥) = 𝑒 −𝛿(− ln(𝑝)) 𝑥 𝛼+𝑀𝛼41