garbarino.(2010).digit ratios (2d4d) as predictors of risky decision

Digit ratios (2D:4D) as predictors of risky decisionmaking for both sexes

Ellen Garbarino & Robert Slonim & Justin Sydnor

Published online: 9 December 2010# Springer Science+Business Media, LLC 2010

Abstract Many important decisions involve financial risk, and substantial evidencesuggests that women tend to be more risk averse than men. We explore a potentialbiological basis of risk-taking variation within and between the sexes by studyinghow the ratio between the length of the second and fourth fingers (2D:4D) predictsrisk-taking. A smaller 2D:4D ratio has been linked to higher exposure to prenataltestosterone relative to estradiol, with men having lower ratios than women. Infinancially motivated decision-making tasks, we find that men and women withsmaller 2D:4D ratios chose significantly riskier options. We further find that the ratiopartially explains the variation in risk-taking between the sexes. Moreover, for menand women at the extremes of the digit-ratio distribution the difference in risk-takingdisappears. Thus, the 2D:4D ratio partially explains variation in financial risk-takingbehavior within and between sexes and offers evidence of a biological basis for risk-taking behavior.

Keywords Risk . Sex differences . Experiments . Testosterone

JEL Classification C9 . D81

J Risk Uncertain (2011) 42:1–26DOI 10.1007/s11166-010-9109-6

E. GarbarinoDepartment of Marketing, Faculty of Economics and Business, University of Sydney,Sydney, Australiae-mail: [email protected]

R. Slonim (*)School of Economics, Faculty of Arts and Social Sciences, University of Sydney, Sydney, Australiae-mail: [email protected]

J. SydnorActuarial Science, Risk Management, and Insurance Department, Wisconsin School of Business,University of Wisconsin, Madison, WI, USAe-mail: [email protected]

Many important decisions involve taking financial risks, including career decisions,buying a home or car, investing in the stock market and choosing healthcare plans.The inclusion of risk preferences in economic models of individual utility isubiquitous. Despite the importance of risk-taking and the large literature on thesubject, relatively little is known about the origins, determinants and sources ofheterogeneity in risk attitudes.

In this paper, we explore the possibility of a biological origin for one of the mostcommon and consistent findings in the risk-taking literature, namely that men areless risk averse than women.1 A sex difference in risk-taking preferences is wellestablished. For example, in a meta-analysis of 150 studies of sex differences in risk-taking, men were found to be significantly less risk averse than women on 14 out of16 risk-taking categories (Byrnes et al. 1999).2 Within the financial-risk context,where risk is generally defined over monetary lotteries, Croson and Gneezy’s (2009)review of the evidence finds generally greater risk aversion in women than men ineconomic experiments.3, 4 Outside of the economics literature, most explanations forthe sex difference in risk-taking involve psychological or sociological phenomena,but with the growing research in the neurosciences and neuro-economics inparticular, examination of biological bases for sex differences in risk-taking havebeen receiving increased attention.

One biological factor that has been the focus of recent research is the role ofcirculating testosterone on attitudes toward risk. The expectation of this literature isthat higher testosterone levels will lead to greater risk-taking; however the supporthas so far been mixed. The activational effects of circulating testosterone have beenfound to predict the financial performance of male futures traders (Coates and Hebert2008), with higher testosterone levels associated with higher returns. Apicella et al.(2008) find a positive relationship between testosterone and risk-taking in an

1 The examination of the biological origins of economic behavior has received increasing interest. Forinstance, Burnham (2007) has looked at the role of testosterone in ultimatum bargaining games and Chenet al. (2009) look at the role of the menstrual cycle on bidding in auctions.2 More research is still warranted in the direction of understanding the differences in risk preferences ofmen and women. For instance, as noted by an anonymous referee on this paper, pregnancy is very risky,especially in non-industrialized settings.3 Brooks and Zank (2005) also find that women are more loss averse than men in a laboratory experiment.Moreover, both Daruvala (2007) and Ball et al. (2010) report that subjects, both men and women, predictthat women will make more risk averse choices than men, suggesting that the gender gap in risk attitudesis a stereotype held at least among laboratory participants. Outside the laboratory, DeLeire and Levy(2001) report that women are more risk averse than men in terms of the wage premium they accept forrisky jobs, and in terms of choosing safer occupations. Leeth and Ruser (2003) further find that fornonfatal risks women receive a risk premium more than three times greater than the risk premium menearn.4 Harrison and Rutström (2008) find that the sex differences in laboratory experiments do not alwayssupport the conclusion that women are more risk averse than men. For instance, some of the analyses inthe existing literature may have an omitted variables problem that biases regression analyses. In addition,since subjects in laboratory experiments voluntarily select into experiments, it is possible men and womenparticipate for different reasons, and so the sex difference on risk behavior observed in the laboratory maybe the result of selection bias. However, Cleave et al. (2010) find that there is selection bias in thedirection that suggests results from laboratory experiments underestimate the risk attitude differencebetween women and men in the population subjects were recruited from; they find that women who do notparticipate are more risk averse than the women who participate while the men who do not participate areless risk averse than the men who participated.

2 J Risk Uncertain (2011) 42:1–26

experimental task using male undergraduates. More recently, Sapienza et al. (2009)find no correlation between circulating testosterone and risk-taking for men but dofind a positive correlation for women. However, a medical manipulation ofcirculating testosterone in postmenopausal women found no effect on risk-takingbehavior (Zethraeus et al. 2009). Thus the current evidence on the effects ofcirculating testosterone and risk attitudes is mixed.

While circulating testosterone is thought to have an immediate (or transitory)activational effect on behavior, testosterone has also been proposed to have morepermanent organizational effects on brain development (Arnold and Breedlove1985). One of the increasingly studied markers of the organizational influence oftestosterone is the 2D:4D ratio (the ratio of the length between the second and fourthfingers), which is considered a persistent marker of exposure to prenatal androgens(Manning 2002). Unlike the potentially transitory effects of circulating testosterone,the prenatal androgens that are thought to determine the 2D:4D ratio affect braindevelopment and so may lead to more deterministic influences on human behavior(Goy and McEwen 1980). There is also a clearer causal interpretation of theseorganizational effects; unlike circulating testosterone, the 2D:4D ratio is essentiallyfixed prior to birth (McIntyre et al. 2005) making it clear that the act of makingfinancial choices under risk cannot affect the 2D:4D ratio.5

The 2D:4D ratio has been shown to correlate with a number of biological andpsychological characteristics that show strong sex differentiation. Several traits morecommonly found in men have been found to be negatively correlated with 2D:4D(i.e., more common amongst those with lower 2D:4D ratios) such as good visual andspatial performance (Manning and Taylor 2001; Kempel et al. 2005), autism(Manning et al. 2001), higher levels of immune system dysfunction and myocardialinfarction (Manning and Bundred 2000), athletic achievement (Tester and Campbell2007), dominance and masculinity (Neave et al. 2003), and sensation seeking andpsychoticism (Austin et al. 2002). Conversely, a number of traits more commonlyseen in women are positively correlated with 2D:4D including high verbal fluency(Manning 2002), emotional problems (Williams et al. 2003) and neuroticism (Austinet al. 2002). 2D:4D has also been found to correlate with career interests such that amore masculine hand pattern (i.e., lower 2D:4D) was associated with highertendency toward enterprising and investigative careers (Weiss et al. 2007).

Only a few papers have explored the relationship between the 2D:4D ratio andrisk-taking. Apicella et al. (2008) find no correlation between the 2D:4D ratio andtheir risk-taking measure in a sample of male undergraduates, but they suggest thismay have been due to the small and ethnically heterogeneous sample. Coates et al.(2009) study the performance of a sample of male financial day traders and find thatthose with lower 2D:4D ratios, indicating higher prenatal testosterone levels, earnsignificantly higher returns (Coates et al. 2009). While higher returns may beindicative of greater risk-taking, they are not a direct measure of risk attitudes and

5 The connection between prenatal androgen exposure and the 2D:4D ratio is commonly explained by theshared genetic basis of the distal limbs (e.g., fingers and toes) and the urogenital system controlled by thehomeobox genes, hox-a and hox-d (Kondo et al. 1997; Csatho et al. 2003). In one of the few direct tests ofthe relationship between 2D:4D and prenatal sex hormones in humans, Lutchmaya et al. (2004) found alower 2D:4D ratio was significantly related to higher levels of fetal testosterone relative to fetal estradiol inthe amniotic fluid, within and across sexes (Lutchmaya et al. 2004).

J Risk Uncertain (2011) 42:1–26 33

hence these results could be driven by other factors such as confidence, intelligence,attention, or reaction time. In the only 2D:4D risk study to examine both men andwomen, Sapienza et al. (2009) find no significant correlation between digit ratio andrisk-taking for men and a weak positive correlation for women. These results areintriguing since one might well expect that men, with their higher levels and widervariance in testosterone, would show stronger organizational effects (i.e., a higher2D:4D correlation with risk-taking) than women.

Given the limited study of the organizational effects of testosterone on risk-takingand the even more limited study examining both sexes, we will test whether prenataltestosterone exposure can help explain variation in risk-taking decisions both withinthe sexes as well as risk-taking differences between the sexes. We examine therelationship between prenatal androgen exposure proxied by the 2D:4D ratio andrisk-taking using a financially motivated individual decision-making experiment.The experiment was conducted with men and women and included a 2D:4Dmeasurement and a well-established risk-taking instrument involving three finan-cially motivated decisions with varying levels of risk and expected values. Thehypotheses are

H1: Men and women with lower 2D:4D ratios (suggestive of higher levels ofprenatal testosterone) will take more risks (or equivalently, be less risk-averse)and

H2: The 2D:4D ratio will be a significant predictor of the expected female-malegap in risk-taking.

Support for these hypotheses suggests that the organizational effects oftestosterone exposure affect attitudes toward risk-taking.

The remainder of the paper is organized as follows. Section 1 describes themeasurement of the 2D:4D ratio and risk attitudes towards financial gambles. Formeasurement of the 2D:4D ratio and risk attitudes we use well establishedprocedures and for the risk attitudes we include two additional measures. Section 2presents the results. We first show that the current subject population exhibits the2D:4D and risk patterns between the sexes documented in past work. We furthershow that the risk patterns are robust across the additional risk measures. We thenshow the critical relationship between the 2D:4D ratio and risk attitudes for bothsexes, supporting H1 that both men and women with lower 2D:4D ratios take greaterfinancial risks.6 We further show that controlling for individual differences in the2D:4D ratio significantly reduces the sex differences in risk attitudes, supporting H2that the 2D:4D ratio will be a significant predictor of the gender gap in risk taking.We then show that these results are robust to additional econometric specificationsand omitted variables, and are unlikely to be the result of spurious correlation.Finally, we show that men and women in either the lowest or highest quartiles of the2D:4D distribution exhibit insignificant differences in risk attitudes, suggesting that

6 In a concurrent study reported in a working paper, Dreber and Hoffman (2007) present evidence showinga qualitatively similar relationship between the 2D:4D ratio and choices over a risky gamble for both maleand female university students using an alternative measure of financial risk developed by Gneezy andPotters (1997).


at the extremities of the 2D:4D ratio the gender gap in risk attitudes may disappearentirely. Section 3 provides a brief summary and directions for future work.

1 Methods7

1.1 Overview

A total of 152 (65 female, 87 male) Caucasian students participated in theexperiment. Subjects from other ethnic backgrounds were excluded because theaverage 2D:4D ratio is sensitive to ethnic variation (Manning et al. 2003, 2004).Each subject was asked to make three independent financial decisions. Each decisioninvolved choosing one lottery from a sequence of six lotteries that were orderedfrom least to most risky. Subjects read the instructions (see Appendix) andcompleted an 11-item review to verify their understanding of the task (99%accuracy across all subjects and questions). Subjects next made their three financialchoices and completed a survey. After completing the survey, subjects were taken toa second room where both their hands were scanned using a flatbed scanner. Tocomplete the study, one of the three financial decisions was randomly chosen foreach subject to determine his/her cash payoff.

1.2 Measures

1.2.1 Risk measurement

To assess risk attitudes, we had each subject make three financial decisions. Eachdecision required each subject to choose one lottery from a sequence of six orderedlotteries. Harrison and Rutström (2008) note that ordered lottery sequences were firstused in the early 1980s (Binswanger 1980, 1981), brought into the lab in the late1980s (Murnighan et al. 1987, 1988) and continue to be a popular measure of riskattitudes (Eckel and Grossman 2002, 2008).

Table 1 presents the three decisions. Decision 50–50 was first used by Eckel andGrossman (2002, 2008) and Decision 75–25 and Decision 25–75 are modificationsto explore behavior across other domains of the probability space. Each decisionrequired subjects to choose one of six lotteries each with two possible payoffs.Table 1 also shows the expected value of each lottery and two measures of risk: thestandard deviation and the range of values for r under constant relative risk aversion{CRRA: u(x)=x(1-r)/(1-r) for r>0 and r≠1; u(x)=ln(x) for r=1} that would make thelottery be the expected utility maximizing optimal choice.

The lotteries increase in expected value (EV) and both measures of risk fromLottery 1 to Lottery 5. Lottery 6 is riskier than Lottery 5 but has the same EV.Including Lottery 6 lets us distinguish between risk seeking and risk neutral behaviorsince Lottery 5 stochastically dominates Lottery 6. If subjects are expected-utilitymaximizers with CRRA preferences, then they will (weakly) prefer higher ordered

7 The protocols are available at http://research3.bus.wisc.edu/jsydnor and include the instructions for allconditions and the survey.


http://research3.bus.wisc.edu/jsydnor

lotteries in Decision 75–25 than in Decision 50–50 and likewise (weakly) preferhigher lotteries in Decision 50–50 than 25–75. For instance, if a subject has CRRApreferences with r=0.45 then he would choose Lottery 3 in Decision 25–75, Lottery4 in Decision 50–50 and Lottery 5 in Decision 75–25. By measuring risk preferencesacross all three decisions, we are able to better distinguish risk preferences acrosssubjects over a more narrowly defined range than had we measured behavior overjust one decision. For instance, three expected utility maximizers with r=0.15, r=0.25 and r=0.35 would be indistinguishable with Decision 50–50 alone (all wouldchoose Lottery 5), yet Decision 25–75 would distinguish them since the more riskaverse subject with r=0.35 would choose Lottery 3, the subject with r=0.25 wouldchoose Lottery 4 and the less risk averse subject with r=0.15 would choose Lottery5. Likewise, three expected utility maximizers with r=1.05, r=1.55 and r=2.05

Table 1 The three Lottery decisions that subjects were given

Information Subjects Received Additional Information

Outcome 1 Outcome 2

LotteryChoice

Payoff Prob Payoff Prob EV StandardDeviation

CRRAa

Range

50–50 Decision 1 $22 50% $22 50% 22.00 0.00 r>2.74

2 $30 50% $18 50% 24.00 6.00 0.91<r<2.74

3 $38 50% $14 50% 26.00 12.00 0.55<r<0.91

4 $46 50% $10 50% 28.00 18.00 0.37<r<0.55

5 $54 50% $6 50% 30.00 24.00 0<r<0.37

6 $60 50% $0 50% 30.00 30.00 Risk Seeking

75–25 Decision 1 $22 75% $22 25% 22.00 0.00 r>5.91

2 $26 75% $18 25% 24.00 3.46 1.94<r<5.91

3 $30 75% $14 25% 26.00 6.93 1.11<r<1.94

4 $34 75% $10 25% 28.00 10.39 0.72<r<1.11

5 $38 75% $6 25% 30.00 13.86 0<r<0.72

6 $40 75% $0 25% 30.00 17.32 Risk Seeking

25–75 Decision 1 $22 25% $22 75% 22.00 0.00 r>1.40

2 $30 25% $20 75% 22.50 4.33 0.49<r<1.40

3 $38 25% $18 75% 23.00 8.66 0.31<r<0.49

4 $46 25% $16 75% 23.50 12.99 0.23<r<0.31

5 $54 25% $14 75% 24.00 17.32 0<r<0.23

6 $60 25% $12 75% 24.00 20.78 Risk Seeking

Table 1 presents the three decisions every subject was given. For each decision, subjects were required tochoose one of the six lotteries presented in each row. In each row, we list the monetary payoff andprobability of the two possible outcomes for the lottery. Table 1 also shows, but was not shown to thesubjects, the Expected Value (EV) and Standard Deviation for each lottery, and the Constant Relative RiskAversion (CRRA) parameter range for which the lottery would be the optimal choicea CRRA: U($x)=[x(1-r) ]/(1-r) for r>0 & r≠1; U($x)=LN(x) for r=1


would also be indistinguishable with Decision 50–50 (all would choose Lottery 2),yet Decision 75–25 would distinguish them since the relatively more risk aversesubject with r=2.05 would choose Lottery 2, the subject with r=1.55 would chooseLottery 3 and the relatively less risk averse subject with r=1.05 would chooseLottery 4. Moreover, to the extent that there is noise in the decision process, either inerrors made in choice or randomness in risk attitudes (Wilcox 2009), we can reducesome of this noise by measuring three decisions rather than only one.8

We also examined three framings of the lotteries: Gains, Mixed, and Losses. Theinstructions describing the frames are presented in the Appendix and each subjectmade all their choices in only one of the frames. Subjects in Gains started with abalance of $0 and all lotteries were identical to those presented in Table 1 with eachoutcome adding to the subject’s payoff. Subjects in Mixed started with a balance of$22 and all payoffs were equal to those in Gains minus $22 so payoffs could eitheradd to or subtract from the initial $22 balance. Subjects in Losses started with abalance of $60 and all payoffs were equal to those in Gains minus $60 with eachoutcome thus resulting in subtracting money from their initial balance.

The foundational research on prospect theory (Kahneman and Tversky 1979;Tversky and Kahneman 1992) predicts and generally finds less risk aversion (greaterrisk seeking) behavior when gambles involve losses rather than gains, ceterisparibus, we thus included a manipulation of frame to investigate whether theexpected differences in risk attitudes of men and women would be consistent acrossframes. Overall, we examined the three Decisions and the three Frames in order totest the robustness of sex differences on risk attitudes across different areas of theprobability distribution (Decisions) and across gains, losses and mixed outcomes(Frames). While we do not a priori anticipate any unique sex differences acrossdecisions and framing, it is nonetheless valuable to include these treatments toexamine the robustness of the results beyond one point in the lottery distributionspace and beyond one framing.

1.2.2 2D:4D measurement

After the three decisions and survey were completed, participants went to anotherroom and had their hands scanned. Subjects removed all rings and placed both handson a flatbed scanner with palms down, fingers together, and light pressure. Figure 1shows a typical male and female hand scan. A second scan was taken if details of thebasal creases were not clear. One subject had to be excluded due to havingpreviously broken her fourth finger. The use of digital images is a commontechnique for 2D:4D measurement (Kemper and Schwerdtfeger 2008). Scanningallows for a record of the outcome that enables test/retest options and precisionmeasurement to minimize error. Lengths of the second and fourth digits weremeasured from the basal crease (i.e., the crease closest to the base of the finger) tothe central point of the finger tip. Measurements were made using the Autometricsoftware developed by DeBruine (2004) for measuring 2D:4D ratios. This form of

8 In the experiment, the order in which subjects were asked to make the three decisions was randomized.All regression analyses indicate that there is no order effects on choice (p>0.20) so we collapse acrossorder and do not discuss order any further.


software-based measurement has been shown to have the highest precision and inter-rater reliability of the common measurement methods (Kemper and Schwerdtfeger2008).

Three research assistants independently coded the length of the second and fourthfingers on both the left and right hands (intra-rater reliability 0.86). To avoid bias,the digit coding was done separately from other data coding and the coders were notinformed of the research questions. To minimize the influence of rater errors, we firstuse the median 2D:4D ratio for each subject’s hand across the three independentcoders’ measures. We then take the mean 2D:4D ratio across the median for eachsubject to use in our analyses.9

2 Results

2.1 Preliminary results

2.1.1 Gender and 2D:4D

Figure 2 shows the distribution of the mean 2D:4D ratios (over both hands) by sex.As observed in the literature, Fig. 2 shows that the difference in the 2D:4D ratiodistribution between men and women is small and there is a large degree of overlap.Nonetheless, the difference between men and women is significant; the mean ratioover both hands for women is 0.969 and for men is 0.959; t-test t=2.232, p=0.027(for the right hand, the ratio for men and women is 0.961 and 0.972, respectively, t=2.133, p=0.035, and for the left hand, the ratio for men and women is 0.957 and0.966, t=2.016, p=0.046). The observed differences are within the range of meanratios in the literature in which female average ratios range from 0.96 to 0.99 while

Fig. 1 Two examples of handscans. The hand on the leftcomes from a subject with alower 2D:4D ratio, indicatingpotentially high levels of in uterotestosterone exposure. Con-versely, the hand on the rightshows a high 2D:4D ratio

9 Our results are qualitatively the same if we use the median measure from either hand alone in theanalyses.


male average ratios range from 0.93 to 0.97 (e.g., Fink et al. 2006; Tester andCampbell 2007).

2.1.2 Decisions and framing on lottery choices

For our primary analysis, we use the lottery choice (from the set of 6 options) as theoutcome measure. As such, our outcome measure is a qualitative 6-point scale.Unlike most qualitative scales, we can be confident that different participantsperceive the scale the same. The reason is that the underlying choices in this scaleare lotteries with well-defined quantitative differences including the mean andvariance. In principle, we could create a structural model that maps these choicesover lotteries into parameter estimates of an underlying utility model. However,because the literature has identified a number of potential drivers of financial riskattitudes—concave wealth utility, loss aversion, probability weighting, and diminishingsensitivity—properly identifying a structural model of utility here would require a largenumber of different gamble choices from each subject. Given that our question ofinterest centers on the direction of risk aversion across gender and digit-ratio markers,rather than the particular drivers of that level of risk aversion, we focus instead on thesimpler qualitative metric of choice, namely which of the 6 rank ordered gambles thesubject chose.

To properly account for the qualitative-scale nature of our outcome measure (thechoice from six lotteries ordered from least to most risky), we use multivariateOrdered Probit regressions. Since we observe three decisions for each subject, onefor each Decision 50–50, 75–25 and 25–75, the regression analyses stack the dataacross the three decisions and include dummy variables for Decision 75–25 andDecision 25–75. We also include dummy variables for the Mixed and Loss Frame.Since we have three observations for each subject, and each subject is nested withina single frame, we estimate and report standard errors clustered at the subject level.

Table 2 presents coefficient estimates from a series of Ordered Probit regressionson lottery choice on different sets of independent variables. The first column showsthe effects of the Decisions and Framings on risk-taking. As anticipated, subjectsmade significantly higher lottery choices in Decision 75–25 reflecting the lower risk

05

1015

kden

sity

rat

io

.9 .95 1 1.05 1.1x

Male Female

Fig. 2 2D:4D distribution bygender. Graph of kernel densityestimates of the distributionof 2D:4D by gender. The 2D:4Dratio is based on average ratioover the left and right hands. Thex-axis is the 2D:4D ratio andthe y-axis is the kernel densityestimate


Tab

le2

Determinantsof

riskychoice.Dependent

variable:Optionchosen

(1=LeastRisky,6=MostRisky

).Ordered

Probitregression

results

Independ

entVariables

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Decision75

–25a

0.397[0.078

]***

0.409[0.080

]***

0.40

3[0.079

]***

0.413[0.080

]***

0.413[0.080

]***

0.43

0[0.114

]***

0.413[0.080

]***

Decision25

–75a

−0.029

[0.095

]−0

.030

[0.098

]−0

.031

[0.097

]−0

.033

[0.099

]−0

.033

[0.099

]0.14

4[0.132

]−0

.033

[0.100

]

Mixed

Frameb

0.075[0.152

]0.104[0.149

]0.08

1[0.150

]0.105[0.148

]0.104[0.148

]0.10

5[0.148

]0.123[0.192

]

LossFrameb

−0.104

[0.171

]−0

.074

[0.170

]−0

.117

[[0.16

9]−0

.088

[0.168

]−0

.090

[0.170

]−0

.090

[0.171

]−0

.078

[0.245

]

Fem

alec

−0.520

[0.130

]***

−0.467

[0.128

]***

−0.466

[0.128

]***

−0.321

[0.156

]**

−0.440

[0.224

]**

Digitratio

(z-score)d

−0.191

[0.059

]***

−0.156

[0.062

]**

−0.150

[0.071

]**

−0.150

[0.072

]**

−0.150

[0.071

]**

Fem

ale*Digitratio

−0.014

[0.131

]−0

.015

[0.132

]−0

.015

[0.131

]

Fem

ale*Decision75

−0.038

[0.157

]

Fem

ale*Decision25

−0.411

[0.196

]**

Fem

ale*Mixed

Frame

−0.047

[0.299

]

Fem

ale*LossFrame

−0.030

[0.366

]

Observatio

ns45

345

345

345

345

345

345

3

Clusters(sub

jects)

151

151

151

151

151

151

151

Log-likelihood

−792

.79

−779

.44

−785

.3−7

74.62

−774

.61

−772

.87

−774

.59

aDecision72–25&

25–75aredummyvariablesequalto

1forthe75–25&

25–75Decisions,respectiv

ely,

andequal0otherw

ise

bMixed

Frameisadu

mmyvariableequalto1fortheDecisions

with

both

positiv

eandnegativ

eou

tcom

es,and

LossFrameisadu


with

negativ

eou

tcom

escFem

aleisadummyvariable

equalto

1forfemalesubjectsandequalto

0formalesubjects

dDigitRatio

isthenorm

alized

2D:4D

ratio

Note:

Robuststandard

errors

clusteredat

thesubjectlevelarein

brackets

**sign

ificantat

5%;**

*sign

ificantat

1%


aversion of the higher lottery choices in Decision 75–25. The estimates inColumn 1 indicate that the lottery choice in Decision 75–25 was significantlyhigher than in Decision 50–50; the estimated coefficient on Decision 75–25 isalso significantly higher than in Decision 25–75 (p<0.01). In addition, subjectsdirectionally chose lower lotteries in Decision 25–75 than in Decision 50–50(again as anticipated), but the difference is not significant (p>0.20). The estimatesin Column 1 also show that there are no significant differences across the frames(p>0.20).10 The effect of decision and framing shown in Column 1 hold across allthe models we investigate.

2.1.3 Gender and risk

Figure 3 shows the lottery choices of women and men by decision. Consistent withthe prevailing evidence on sex differences in risk-aversion, the distribution ofchoices for women shows more risk aversion than men for each of the threedecisions. For instance, for Decision 50–50 men were 17% more likely than womento choose Lotteries 5 and 6 whereas women were 7% more likely than men tochoose Lotteries 1 and 2. The difference is even larger for the other two decisions;for Decision 25–75 men were 32% more likely than women to choose Lotteries 5and 6 and women were 24% more likely than men to choose Lotteries 1 and 2, andfor Decision 75–25 men were 24% more likely than women to choose Lotteries 5and 6 and women were 11% more likely than men to choose Lotteries 1 and 2. Forthe 50–50 Decision, the men’s mean lottery choice was 3.69 and women’s was morerisk averse at 3.11 (t-test; t=2.44, p=0.016). For Decision 75–25, the men’s averagechoice was 4.35 and women’s average choice was 3.72 (t=2.805, p=0.006) and forDecision 25–75 Decision, the men’s average choice was 3.87 and women’s averagechoice was 2.77 (t=3.874, p=0.0002). The female-male gap also holds across allthree frames: Gains: Men 3.94, Women 3.16, t=3.087, p=0.002; Mixed: Men 4.15,Women 3.32, t=3.562, p=0.0005; Loss: Men 3.80, Women 3.11, t=2.44, p=0.016.The Ordered Probit regression in Column 2 of Table 1 also shows that controllingfor Frame and Decision, women chose significantly more risk averse lotteries thanmen (p<0.001).

Table 3 reruns the analyses using an OLS regression model and again clustersstandard errors at the subject level. The results are qualitatively identical. Column2′ shows that women’s choices were on average 0.77 levels lower; in other words,on average women made lottery choices over ¾ of a choice level more risk aversethan men. Thus, consistent with the majority of the literature examining sexdifferences in financial risk taking, we find women made more risk averse choices,and this greater risk aversion holds across decisions and across frames (and wewill show below, this result also holds after addressing potential omittedvariables).

10 We had anticipated that the Loss Frame would lead to less risk averse choices. There are severalpossible reasons the Loss Frame did not significantly affect choices. For instance, the manipulation mayhave been too weak (imagine starting with $60), too transparent so that subjects could easily figure outfinal payments, too subtle and so subjects did not make decisions assuming they had already pocketed theinitial $60 endowment, or framing was not a factor for the current population.

J Risk Uncertain (2011) 42:1–26 1111

2.2 Central results: the influence of the 2D:4D ratio on risk

To examine the effect of the 2D:4D ratio on risk, we first normalized the digit ratiosinto z-scores by subtracting off the population means and dividing by the populationstandard deviation. With this transformation, the 2D:4D coefficient estimates in ourregressions reveal the effect of a one-standard-deviation increase in the 2D:4D ratioon lottery choice.

The primary contribution of this paper is to further our understanding of therelationship between the 2D:4D ratio and risk preferences. Column 3 in Table 2 (and3′ in Table 3) shows the results of regressing the risk scale on the normalized 2D:4Dratio controlling for Frame and Decision. In both the Ordered Probit and the OLSregressions there is a significant (p<0.01) negative relationship between the digitratio and risky choice. The OLS results in Column 3 of Table 3 can be interpreted asshowing that a one standard-deviation decrease in the digit ratio (higher testosteroneexposure) is associated with an increase in risk taking of 0.30 levels. Column 4 in

Fig. 3 Percent of subjects whochose each Lottery by Decisionand Gender


Table 2 (and 4′ in Table 3) includes both controls for sex and the normalized 2D:4Dratio, while Column 5 (5′) further adds the interaction of the 2D:4D ratio and sex.The estimated 2D:4D coefficient estimate in Column 4 indicates that even aftercontrolling for sex subjects with lower 2D:4D ratios made significantly riskierlottery choices (p=0.011). The 2D:4D estimate in Column 4′ in Table 3 (p<0.01)shows that a one standard-deviation lower 2D:4D ratio increased the lottery choiceby 0.235 levels. The non-significant digit ratio by sex interaction estimates inColumn 5 in Table 2 and Column 5′ in Table 3 show that the 2D:4D effect wasstatistically identical for men and women (p>0.90). These results supportHypothesis 1; for both men and women, those with smaller digit ratios (indicatinghigher relative prenatal testosterone levels) made riskier financial choices.

A comparison of the female coefficient in Column 2′ and 4′ in Table 3 shows thatcontrolling for the 2D:4D ratio reduced the risk-taking gap between men andwomen; the gap fell 11% from 0.769 options lower for women without controllingfor 2D:4D to 0.683 lottery levels lower controlling for 2D:4D (χ2=4.02, p<0.045).Thus, the 2D:4D ratio offers a partial explanation for the commonly seen sexdifference in risk-taking, supporting Hypothesis 2.

The estimates of the 2D:4D effect on explaining risk aversion presented inTables 2 and 3 indicate a substantial influence similar in magnitude with the sexeffect. For example, a one standard deviation increase in the 2D:4D ratio lowers thelottery choice level by 0.235 (columns 4′ and 5′ in Table 3), which is equivalent toapproximately one third of the difference in the estimated risk levels chosen between

Table 3 Determinants of risky choice. Dependent variable: Option chosen (1 = Least Risky, 6 = MostRisky). OLS regression results

Independent Variables (2′) (3′) (4′) (5′)

Constant 3.733 [0.197]*** 3.431 [0.181]*** 3.701 [0.192]*** 3.701 [0.193]***

Decision 75–25a 0.642 [0.116]*** 0.642 [0.116]*** 0.643 [0.116]*** 0.642 [0.117]***

Decision 25–75a −0.040 [0.136] −0.040 [0.136] −0.040 [0.136] −0.040 [0.136]

Mixed Frameb 0.189 [0.219] 0.161 [0.225] 0.190 [0.215] 0.191 [0.216]

Loss Frame b −0.097 [0.247] −0.162] [0.249] −0.117 [0.243] −0.117 [0.246]

Femalec −0.769 [0.190]*** −0.683 [0.188]*** −0.683 [0.188]***

Digit ratio (z-score)d −0.296 [0.086]*** −0.235 [0.089]*** −0.235 [0.105]**

Female * Digit ratio 0.000 [0.194]

Observations 453 453 453 453

Clusters (subjects) 151 151 151 151

R-squared 0.101 0.079 0.122 0.122

a Decision 72–25 & 25–75 are dummy variables equal to 1 for the 75–25 & 25–75 Decisions, respectively,and equal 0 otherwisebMixed Frame is a dummy variable equal to 1 for the Decisions with both positive and negative outcomes,and Loss Frame is a dummy variable equal to 1 for the Decisions with negative outcomesc Female is a dummy variable equal to 1 for female subjects and equal to 0 for male subjectsd Digit Ratio is the normalized 2D:4D ratio

Note: Robust standard errors clustered at the subject level are in brackets

** significant at 5%; *** significant at 1%

J Risk Uncertain (2011) 42:1–26 1313

men and women. In other words, the estimates predict that the difference in lotterychoices between a man and a woman is approximately equal to the difference inchoices between two individuals whose 2D:4D ratios are 1.5 standard deviationsbelow and above the mean 2D:4D ratio.

2.3 Robustness checks

Columns 6 and 7 in Table 2 examine the robustness of sex differences across frameand decision, respectively. The main effect of Female on risk in these regressionsindicates the difference in risk choices between women and men in the omittedcategory of Decision 50–50 (Column 6) and of the Gain Frame (Column 7). Theinteraction terms indicate that women are directionally more risk averse in the twoother decisions and two other frames, and significantly more risk averse in theDecision 25–75 than Decision 50–50. Nonetheless, even after these interactions havebeen controlled for, the effect of the 2D:4D ratio on lottery choice remainssignificant (p<0.05).

In Table 4, we take a discrete-choice approach, rather than the ordered-scaleapproach, to the data analysis. We define an indicator variable for whether the personmade a “risky choice,” defined as choosing lottery 4, 5, or 6 (the three riskier lotterychoices). Overall 53.2% of choices fell into this category. We present results for botha linear probability model, i.e., OLS, (Columns 1–3) and a Probit regression(Columns 4–6).11 Column 1 shows that females were 21 percentage points lesslikely (p<0.01) to make a risky choice controlling for Decision and Frame. Column2 shows that a one standard-deviation increase in the 2D:4D ratio (lower testosteroneexposure) is associated with an 8 percentage point drop (p<0.01) in the likelihood ofmaking a risky choice. Consistent with the results from Section 2.2, controlling forthe digit ratio explains some of the gender gap (i.e., the female coefficient falls from21% to 18%), and both sex and the digit ratio have significant independent effects.Column 3 shows that, as in the earlier results, there is no significant interactionbetween sex and the digit ratio. The Probit results in Columns 4–6 are nearlyidentical.

Two additional potential concerns with the interpretation of the estimatedcoefficient of either Female or the 2D:4D ratio on lottery choice are that (1) theestimated effects might be biased due to omitted variables or (2) the 2D:4D effectmight be spurious. To investigate whether omitted variables could explain theresults, Table 5 examines the 2D:4D ratio on lottery choice including other variableswe collected in the survey (age, birth order12), whether the subject was working, andacademic ability (SAT scores13). To investigate whether the 2D:4D results might be

13 Dohmen et al. (2007) find that risk aversion is negatively correlated with cognitive abilities. Ourinclusion of SAT scores could be an important omitted variable if testosterone is correlated with cognitiveability. However, as the estimates in Table 5 indicate, we find no significant relationship between SATscores and lottery choices.

11 To make the results easier to interpret and compare to the OLS case, we report marginal effects at themeans of the independent variables for the Probit regression.12 Sulloway and Zweigenhaft (2010) discuss the potential importance and evidence of birth order on riskattitudes.


Tab

le4

Determinantsof

riskychoice.Dependent

Variable:

Indicatorof

choice

ofLottery

4,5or

6

IndependentVariables

OLS

Probit(M

arginalEffectEstim

ates)

(1)

(2)

(3)

(4)

(5)

(6)

Constant

0.523*

**[0.060

]0.512*

**[0.059

]0.514*

**[0.059

]

Decision75

–25a

0.232*

**[0.042

7]0.232*

**[0.043

]0.232*

**[0.043

]0.23

0***

[0.040

]0.232*

**[0.041

]0.232*

**[0.041

]

Decision25

–75a

−0.046

[0.043

6]−0

.046

[0.044

]−0

.046

[0.044

]−0

.044

[0.041

]−0

.045

[0.041

]−0

.045

[0.041

]

Mixed

Frameb

0.109[0.066

]0.110[0.065

]0.108[0.065

]0.112[0.065

]0.111[0.064

]0.110[0.063

]

LossFrameb

−0.005

[0.075

]−0

.012

[0.073

]−0

.014

[0.073

]−0

.006

[0.073

]−0

.016

[0.070

]−0

.017

[0.071

]

Fem

alec

−0.206

***[0.058

]−0

.177

***[0.058

]−0

.175**

*[0.058

]−0

.202**

*[0.054

]−0

.171

***[0.054

]−0

.171**

*[0.054

]

Digitratio

(z-score)d

−0.081

***[0.030

]−0

.075**

[0.035

]−0

.081

***[0.029

]−0

.076**

[0.035

]

Fem

ale*Digitratio

−0.017

[0.064

]−0

.012

[0.066

]

Observatio

ns45

345

345

345

345

345

3

Clusters(sub

jects)

151

151

151

151

151

151

R-squ

ared

0.112

0.13

80.138

Log-likelihood

−286

.28

−279

.62

−279

.59

aDecision72–25&


1forthe75–25&


ely,

andequal0otherw

ise

bMixed

Frameisadu


with

both

positiv

eandnegativ

eou

tcom

es,and

LossFrameisadu


with

negativ

eou

tcom

escFem

aleisadummyvariable

equalto


0formalesubjects

dDigitRatio

isthenorm

alized

2D:4D

ratio

Note:

Robuststandard

errors

clusteredat


brackets

**sign

ificantat

5%;**

*sign

ificantat

1%

J Risk Uncertain (2011) 42:1–26 1515

spurious, we also include other biological variables (Body Mass Index, height, andindividual finger length).

The results in Table 5 provide further support for the importance of 2D:4Daffecting risk attitudes. Note first that no other biological measure collected

Table 5 Determinants of risky choice. Dependent variable: Option chosen (1 = Least Risky, 6 = MostRisky). Ordered Probit regression results

Independent Variable Parameter Estimate Standard Error p-value

Decision 75–25a 0.032 0.130 .002

Decision 25–75a −0.008 0.173 .964

Mixed Frameb 0.152 0.199 .443

Loss Frameb −0.093 0.213 .662

Femalec −0.450 0.188 .017

Digit ratio (z-score)d −0.152 0.081 .059

Female * Digit ratio 0.005 0.136 .969

Mixed Frame * Decision 75 0.060 0.181 .740

Mixed Frame * Decision 25 −0.157 0.233 .501

Loss Frame * Decision 75 0.018 0.213 .933

Loss Frame * Decision 25 0.090 0.257 .725

4th Digit Length −0.0005 0.0016 .757

Height 0.014 0.026 .603

BMIe 0.014 0.016 .388

LN(age) −0.646 1.599 .686

Only Childf −0.385 0.197 .050

Birth Orderg −0.051 0.058 .379

SAT Mathh −0.082 0.100 .411

SAT Verbalh 0.041 0.070 .561

Worki −0.045 0.140 .746

Observations 453

Clusters (subjects) 151

Log-likelihood −769.31

a Decision 72–25 & 25–75 are dummy variables equal to 1 for the 75–25 & 25–75 Decisions, respectively,and equal 0 otherwisebMixed Frame is a dummy variable equal to 1 for the Decisions with both positive and negative outcomes,and Loss Frame is a dummy variable equal to 1 for the Decisions with negative outcomesc Female is a dummy variable equal to 1 for female subjects and equal to 0 for male subjectsd Digit Ratio is the normalized 2D:4D ratioe BMI = Body Mass Index = (Weight*703)/Height2

f Only Child is a dummy variable equal to 1 for an only child, equals 0 otherwiseg Birth Order = 1 for oldest, 2 for second oldest, 3 for third oldest, etch SAT Math and Verbal equals the self reported scores from student’s High School StandardizedAchievement Testi Work is a dummy variable that equals 1 if the student was currently working, and equals 0 otherwise

Note: Robust standard errors clustered at the subject level are in brackets


significantly predicts lottery choices. The lack of any other biological measure beingcorrelated with lottery choices supports the relationship between the 2D:4D ratio andrisk attitudes not being spurious correlation. Note also that there is little evidencethat omitted variables can explain the relationship between sex and lottery choices orbetween the 2D:4D ratio and lottery choices; the relationship between the 2D:4Dand lottery choice remains significant at the p<0.06 level and likewise therelationship between sex and lottery choice remains significant at the p<0.02 level.

2.4 Nonlinear results of 2D:4D on risk

Recent work on the relationship between testosterone and risk-taking suggests thatthe effect can be nonlinear (Sapienza et al. 2009). To examine the nonlinear effectswe divided men and women into separate quartiles based on their 2D:4D ratios (i.e.,the lowest 25th percentile, 26th–50th percentile, 51st–75th percentile, above 75thpercentile) and then compared the lottery choices for comparable quartiles (e.g.,lowest 25th percentile of women to lowest 25th percentile of men). Figure 4 graphsmean lottery choices against standardized 2D:4D ratios for each sex. Figure 4presents an interesting pattern in which at either extreme of the 2D:4D ratio men andwomen make similar lottery choices to each other.

Table 6 shows Ordered Probit regression results to test the significance of thispattern. Column 1 shows that there is no significant difference in lottery choicesbetween women and men in the lowest 2D:4D quartile (p>0.82) and Column 4shows that there is no significant difference in lottery choices between women andmen in the highest 2D:4D quartile (p>0.36). These results suggest that for peoplewith the most extreme exposure levels, prenatal androgens are a more criticalpredictor of risk-taking behavior than sex. However, as the estimates in Columns 2and 3 show, the 2D:4D ratio does not explain the female–male gap in risk-taking forsubjects with less extreme prenatal androgen exposure; those in the middle twoquartiles of their sex-specific ratios still show the typical female–male difference inrisk-taking. This pattern suggests that extreme levels of prenatal androgens, asdemonstrated by being in the bottom or top quartile of the 2D:4D ratios,significantly affect risk-taking for both men and women, whereas environmental or

2.5

33.

54

4.5

mea

n Lo

ttery

cho

ice

-2 -1 0 1 2standardized digit ratio

Male Female

Fig. 4 2D:4D ratio and meanLottery choice. The figure showsthe locally weighted regressionestimates for the relationshipbetween the 2D:4D ratio and themean Lottery choice. The x-axisis the 2D:4D ratio standardizedwithin gender and the y-axis isthe mean Lottery choice

J Risk Uncertain (2011) 42:1–26 1717

Tab

le6

Risky

choice

split

bydigitratio

quartiles.Dependent

variable:Optionchosen

(1=LeastRisky,6=MostRisky

).Ordered

Probitregression

results

Independ

entVariables

Quartilesd

(1)

(2)

(3)

(4)

Decision75

–25a

0.355[0.180

]**

0.511[0.149

]***

0.271[0.175

]0.52

2[0.161

]***

Decision25

–75a

0.102[0.218

]0.268[0.192

]−0

.163

[0.209

]−0

.458

[0.212

]**

Mixed

Frameb

0.233[0.286

]−0

.418

[0.317

]0.476[0.314

]0.113[0.290

]

LossFrameb

0.085[0.386

]−0

.268

[0.463

]−0

.288

[0.312

]0.02

8[0.338

]

Fem

alec

−0.115

[0.291

][p=.694]

−1.120

[0.320

]***

[p<.001

]−0

.622

[0.248

]**[p=.012

]−0

.267

[0.252

][p=.290]

Observatio

ns114

114

114

111

Clusters(sub

jects)

3838

3837

Log-likelihood

−189

.42

−186

.04

−190

.73

−182

.48

aDecision72–25&


1forthe75–25&


ely,

andequal0otherw

ise

bMixed

Frameisadu


with

both

positiv

eandnegativ

eou

tcom

es,and

LossFrameisadu


with

negativ

eou

tcom

escFem

aleisadummyvariable

equalto


0formalesubjects

dQuartile

1includes

subjectswho

have

thelowestquarterof

the2D

:4Dratio

sin

thepopulatio

n,…,and

Quartile

4includes

subjectswho

have

thehighestquarterof

the2D

:4D

ratio

sin

thepopulatio

n

Note:

Robuststandard

errors

clusteredat


brackets

*sign

ificantat

5%;**

sign

ificantat

1%


other biological factors may be more important to determine risk attitudes for thosewith 2D:4D ratios within the middle two quartiles of the ratio.

3 Discussion

We show that the 2D:4D ratio, a biological marker linked to in utero androgen exposure,is predictive of choices over financially motivated decisions 20 years after the exposure.Within and between sexes, those who were exposed to higher levels of in uterotestosterone are more willing to take financial risks. Because the 2D:4D ratio isdetermined prenatally and is not situationally sensitive, our evidence supports the theorythat the organizational effects of testosterone exposure affect risk attitudes. Moreover,while the 2D:4D effect leaves substantial room for psychological, sociological and otherbiological explanations for sex differences, it is impressive that a biological eventexperienced many years earlier (on average 20 years earlier for this population) cansignificantly predict choices over financially risky lotteries of both men and women andalso explain 11% of the female–male differences in risk-taking behavior.

The quartile results highlight an interesting aspect of the 2D:4D effects, namely,that for men and women at the more extreme ends of the 2D:4D distribution, in uterotestosterone exposure is more predictive of risk-taking than sex, suggesting thatbiology is having a large impact on risk preferences for these people. Conversely, forthose people in the middle range of the 2D:4D distribution this biological factor doesnot explain the female–male difference in risk-taking, suggesting that the commonlycited psychological and sociological factors are potentially driving differences inbehavior. These results suggest that controlling for the 2D:4D ratio would increasethe explanatory power of the traditional models of the sex difference in risk-taking.

The study of risk-taking is one of the most popular topics in the burgeoning fieldof neuro-economics. Given that the prenatal androgens that determine the 2D:4Dratio affect the structure of the developing brain (Goy and McEwen 1980) it wouldbe worth exploring whether the 2D:4D ratio can help explain brain activationpatterns under risky choices.

Another avenue for continued research would be to further explore the interactionbetween circulating testosterone and prenatal androgens. While one might expectthese two androgen measures to be related, past research suggests they areuncorrelated (Apicella et al. 2008; van Anders and Hampson 2005; Honekoppet al. 2007). However, recent work by Coates et al. (2009) may shed light on theirinterrelationship; they find that the performance of financial traders with lower2D:4D ratios is more responsive to changes in their circulating testosterone. Thisfinding supports the organizational/activational model of steroid action in which theprenatal androgens are thought to affect the organizational development of the brain,which later makes the brain more responsive to the activational effects of circulatingandrogens (McCarthy and Konkle 2005). While Coates et al.’s evidence isintriguing, their sample is small and only includes men, hence it would be usefulto see if a similar pattern of behavior would emerge in a more controlled contextwith a larger and broader sample.

Finally, although this study has provided some evidence of biological forces thathelp explain risk preferences, we still know surprisingly little about the heteroge-

J Risk Uncertain (2011) 42:1–26 1919

neity of risk attitudes. Larger studies that examine gender, race, biological/geneticfactors, cognitive skills and sociological factors across a range of decision-makingtasks could lead to a much richer understanding of the determinants of riskpreferences. For example, Meier-Pesti and Penz (2008) find sex differences infinancial risk-taking decrease once you control for difference in identification withmasculine and feminine gender roles, suggesting a significant sociological influence.However, it might be interesting to see if gender role identification is correlated witha hormone marker such as 2D:4D, which would suggest a more complex interplay ofbiology and socialization. As another example, research on comparisons of behaviorof identical and fraternal twins has revealed that genetics may explain a significantportion of the heterogeneity in preferences in a range of economic domains (seeWallace et al. 2007; Cesarini et al. 2008, 2009). More work in this direction, and inparticular on the interplay between genetic factors and androgen exposure, could beuseful in gaining a better understanding of the variation in attitudes toward risk.

Acknowledgements We thank Rachel Croson, John Manning, numerous seminar participants, ananonymous referee and the Journal of Risk and Uncertainty Editorial Board for useful comments on thisproject. Special thanks to Angelo Benedetti and Jason Cairns for invaluable research assistance. Thisproject was supported by a grant from the Kauffman Foundation.

Appendix: Instructions

(All Subjects)

General Introduction

Thank you for participating in today’s experiment. Please carefully read theinstructions to yourself. The instructions will clearly explain the choices you willbe given and how you will get paid. You may keep these instructions throughout theexperiment, and you may refer back to them at any point.

Please do not communicate in any way with anyone else during the experiment.Further, please do not show anyone the choices you are making during the course ofthe experiment and do not look at what choices anyone else is making. We do notwant you to influence the choices anyone else is making and we do not want anyoneinfluencing the choices you make.

If at any point you have any questions or if anything is not clear in any way,please raise your hand and a monitor will answer your questions privately.

The first part of the experiment will consist of asking you to make three choicesthat will have financial consequences, and the remainder of the experiment will askyou to complete some surveys.

Part 1: Getting Paid

This part of the experiment will ask you to make three decisions. For each decisionyou will make one choice from a number of options. You will be paid for exactlyone decision you make today.


Which decision you are paid for will be randomly determined at the end of theexperiment. For each person separately and privately we will determine the decisionto pay you for by rolling a normal six sided die, and

If the die roll is a 1 or 2 youwill get paid based on your choice inDecision 1 :If the die roll is a 3 or 4 youwill get paid based on your choice inDecision 2 :If the die roll is a 5 or 6 youwill get paid based on your choice inDecision 3 :

Since you do not know in advance which choice you will be paid for, please paycareful attention to all the instructions and make each choice as if it is the one youwill be paid for.

Please raise your hand if you have any questions about the instructions so far. Ifnot, you may keep reading these instructions.

(Gains Frame)

Task Instructions

You will begin with a starting balance of $0.00. We will add to this amount anyamount you receive as a result of one of the choices you make.

We are going to ask you to make three decisions. For each decision, we are goingto give you six options, labeled (a) through (f), and you must choose one, and onlyone, option. If you do not choose any option, or if you choose more than one option,then we cannot pay you for your participation today.

For each option, we will list two possible outcomes and the probability that eachoutcome will occur. For instance, consider the following two options:

Example Option A: 50% chance to add $1 and 50% chance to add $2Example Option B: 25% chance to add $0 and 75% chance to add $3For all options, there will be either a 50–50% chance each outcome will occur, or

a 25–75% chance the outcomes will occur.If there is a 50–50% situation, then we will place one white and one blue chip in a

container, and then without looking pick one. If the blue chip is picked, then you willadd to your starting balance the first outcome (for instance, the add $1 outcome inExample Option A above). If the white chip is picked, then you will add to your startingbalance the second outcome (for instance, the add $2 outcome in Example Option A).

If there is a 25–75% chance in the option you choose, then we will place threewhite and one blue chip in the container, and without looking pick out one chip. Ifthe blue chip is picked, then you will add to your starting balance the 25% option(for instance, the $0 outcome in Example Option B above), and if any of the whitechips are picked, you will add to your starting balance the 75% option (for instance,the $3 outcome in Example Option B).

To make your choice, you must circle the option you prefer. Be sure to circleexactly one option for each decision.

If you have any questions at this point, please raise your hand.Before we give you the actual decisions, we would like to give you some review

questions to ensure that you fully understand all the procedures. Once you haveanswered the questions, please turn your sheet over and we will come over to seethat you answered all the questions correctly.

J Risk Uncertain (2011) 42:1–26 2121

(Loss Frame)

Task Instructions

In this task you will begin with a starting balance of $60.00. We will subtract fromthis amount any amount you lose as a result of one of the choices you make.

We are going to ask you to make three decisions. For each decision, we are goingto give you five options, labeled (a) through (f), and you must choose one, and onlyone option. If you do not choose any option, or if you choose more than one option,then we cannot pay you for your participation today.

For each option, we will list two possible outcomes and the probability that eachoption will occur. For instance, consider the following two options:

Example Option A: 50% chance to subtract $1 and 50% chance to subtract $2Example Option B: 25% chance to subtract $0 and 75% chance to subtract $3For all options, there will be either a 50–50% chance each outcome will occur, or


container, and then without looking pick one. If the blue chip is picked, then youwill subtract from your starting balance the first outcome (for instance, the subtract$1 outcome in Example Option A above). If the white chip is picked then you willsubtract from your starting balance the second outcome (for instance, the subtract $2outcome in Example Option A).

If there is a 25–75% chance in the option you choose, then we will place threewhite and one blue chip in the container, and without looking pick out one chip. Ifthe blue chip is picked, then you will subtract from your starting balance the 25%option (for instance, the subtract $0 outcome in Example Option B above), and ifany of the white chips are picked, you will subtract from your starting balance the75% option (for instance, the subtract $3 outcome in Example Option B).

To make your choice, you must circle the option you prefer. Be sure to circleexactly one option for each decision.



(Mixed Frame)

Task Instructions

In this task you will begin with a starting balance of $22.00. We may either add orsubtract from this amount any amount you gain or lose as a result of one of thedecisions you make.

We are going to ask you to make three decisions. For each decision, we are goingto give you five options, labeled (a) through (f), and you must choose one, and onlyone option. If you do not choose any option, or if you choose more than one option,then we cannot pay you for your participation today.


For each option, we will list two possible outcomes and the probability that eachoption will occur. For instance, consider the following two options:

Example Option A: 50% chance to add $2 and 50% chance to subtract $4Example Option B: 25% chance to add $0 and 75% chance to subtract $1For all options, there will be either a 50–50% chance each outcome will occur, or


container, and then without looking pick one. If the blue chip is picked, then youwill add to your starting balance the first outcome (for instance, the add $2 outcomein Example Option A above). If the white chip is picked then you will subtract fromyour starting balance the second outcome (for instance, the subtract $4 outcome inExample Option A).

If there is a 25–75% chance in the option you choose, then we will place threewhite and one blue chip in the container, and without looking pick out one chip. Ifthe blue chip is picked, then your starting balance will be affected by the 25% option(for instance, the add $0 outcome in Example Option B above), and if any of thewhite chips are picked, your starting balance will be affected by the 75% option (forinstance, the subtract $1 outcome in Example Option B).

To make your choice, you must circle the choice you prefer. Be sure to circleexactly one option for each decision.



Three of the decisions as presented to subjects (all decisions were on separatepages):

Gains Frame, Decision 50–50

a) 50% to add $22.00 and 50% chance to add $22.00b) 50% to add $30.00 and 50% chance to add $18.00c) 50% to add $38.00 and 50% chance to add $14.00d) 50% to add $46.00 and 50% chance to add $10.00e) 50% to add $54.00 and 50% chance to add $6.00f) 50% to add $60.00 and 50% chance to add $0.00

Loss Frame, Decision 75–25

a) 75% to subtract $38.00 and 25% chance to subtract $38.00b) 75% to subtract $34.00 and 25% chance to subtract $42.00c) 75% to subtract $30.00 and 25% chance to subtract 46.00d) 75% to subtract $26.00 and 25% chance to subtract $50.00e) 75% to subtract $22.00 and 25% chance to subtract $54.00f) 75% to subtract $20.00 and 25% chance to subtract $60.00

Mixed Frame Decision 25–75

a) 25% to add $0.00 and 75% chance to subtract $0.00b) 25% to add $8.00 and 75% chance to subtract $2.00

J Risk Uncertain (2011) 42:1–26 2323

c) 25% to add $16.00 and 75% chance to subtract $4.00d) 25% to add $24.00 and 75% chance to subtract $6.00e) 25% to add $32.00 and 75% chance to subtract $8.00f) 25% to add $38.00 and 75% chance to subtract $10.00

References

Apicella, C. L., Dreber, A., Campbell, B., Gray, P. B., Hoffman, M., & Little, A. C. (2008). Testosteroneand financial risk preferences. Evolution and Human Behavior, 29, 384–390.

Arnold, A. P., & Breedlove, S. M. (1985). Organizational and activational effects of sex steroids on brainand behavior: a reanalysis. Hormones and Behavior, 19(4), 469–498.

Austin, E. J., Manning, J. T., McInroy, K., & Mathews, E. (2002). A preliminary investigation of theassociation between personality, cognitive ability and digit ratio. Personality and IndividualDifferences, 33, 1115.

Ball, S., Eckel, C., & Heracleous, M. (2010). Risk aversion and physical prowess: prediction, choice andbias. Journal of Risk and Uncertainty, 41(3), 167–193.

Binswanger, H. P. (1980). Attitudes toward risk: experimental measurement in rural India. AmericanJournal of Agricultural Economics, 62, 395–407.

Binswanger, H. P. (1981). Attitudes toward risk: theoretical implications of an experiment in rural India.The Economic Journal, 91, 867–890.

Brooks, P., & Zank, H. (2005). Loss averse behavior. Journal of Risk and Uncertainty, 31(3), 301–325.Burnham, T. (2007). High-testosterone men reject low Ultimatum Game offers. Proceedings of the Royal

Society B, 274, 2327–2330.Byrnes, J. P., Miller, D. C., & Schafer, W. D. (1999). Gender difference in risk-taking: a meta-analysis.

Psychological Bulletin, 125(3), 367–383.Cesarini, D., Dawes, C. T., Fowler, J. H., Johannesson, M., Lichtenstein, P., & Wallace, B. (2008).

Heritability of cooperative behavior in the trust game. Proceedings of the National Academy ofSciences USA, 105(10), 3721–3726.

Cesarini, D., Dawes, C. T., Johnnesson, M., Lichtenstein, P., & Wallace, B. (2009). Genetic variation inpreferences for giving and risk-taking. Quarterly Journal of Economics, 124, 809–842.

Chen, Y., Katsucak, P., & Ozdenoren, E. (2009). Why can’t a woman bid like a man? Working paper.Cleave, B., Nikiforakis, N., & Slonim, R. (2010). Is there selection bias in laboratory experiments?

Working paper.Coates, J. M., & Hebert, J. (2008). Endogenous steroids and financial risk-taking on a London trading

floor. Proceedings of the National Academy of Sciences USA, 105(16), 6167–6172.Coates, J. M., Gurnell, M., & Rustichini, A. (2009). Second-to-fourth-digit ratio predicts success among high

frequency financial traders. Proceedings of the National Academy of Sciences USA, 106(2), 623–628.Croson, R., & Gneezy, U. (2009). Gender differences in preferences. Journal of Economic Literature, 47

(2), 448–474.Csatho, A., Osvath, A., Bicsak, E., Karadi, K., Manning, J. T., & Kallai, J. (2003). Sex role identity related

to the ratio of second to fourth digit length in women. Biological Psychology, 62, 147–156.Daruvala, D. (2007). Gender, risk and stereotypes. Journal of Risk and Uncertainty, 35(3), 265–283.DeBruine, L. M. (2004). AutoMetric software for measurement of 2D:4D ratios, from www.facelab.org/

debruine/Programs/autometric.php, accessed June 24, 2008.DeLeire, T., & Levy, H. (2001). Gender, occupation choice and the risk of death at work. National Bureau

of Economic Research, Working Paper 8574.Dohmen, T., Falk, A., Huffman, D., & Sunde, U. (2007). Are risk aversion and impatience related to

cognitive abilities? IZA Discussion Paper 2735.Dreber, A., & Hoffman, M. (2007). Portfolio selection in Utero. Mimeo, Stockholm School of Economics.Eckel, C., & Grossman, P. (2002). Sex differences and statistical stereotyping in attitudes towards financial

risks. Evolution and Human Behavior, 23(4), 281–295.Eckel, C. C., & Grossman, P. J. (2008). Forecasting risk attitudes: an experimental study of actual and forecast

risk attitudes of women and men. Journal of Economic Behavior & Organization, 68(1), 1–17.Fink, B., Neave, N., Laughton, K., & Manning, J. T. (2006). Second and fourth digit ratio and sensation

seeking. Personality and Individual Differences, 41, 1253–1262.


http://www.facelab.org/debruine/Programs/autometric.php

http://www.facelab.org/debruine/Programs/autometric.php

Gneezy, U., & Potters, J. (1997). An experiment on risk taking and evaluation periods. Quarterly Journalof Economics, 112(2), 631–645.

Goy, R., & McEwen, B. (1980). Sexual differentiation of the brain. Cambridge: MIT.Harrison, G., & Rutström, E. E. (2008). Risk Aversion in the Laboratory. In J. C. Cox & G.W. Harrison (Eds.),

Research in experimental economics, 12 (pp. 41–196). Bingley: Emerald Group Publishing Limited.Honekopp, J., Bartholdt, L., Beier, L., & Liebert, A. (2007). Second to fourth digit length ratio (2D:4D)

and adult sex hormone levels: new data and a meta-analytic review. Psychoneuroendocrinology, 32,313–321.

Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica,47, 263–292.

Kempel, P., Gohlke, B., & Kelmpau, J. (2005). Second-to-fourth digit length, testosterone and spatialability. Intelligence, 33, 215.

Kemper, C. J., & Schwerdtfeger, A. (2008). Comparing different methods of digit ratio (2D:4D)measurement. American Journal of Human Biology, 21(2), 188–191.

Kondo, T., Zakany, J., Innis, J. W., & Duboule, D. (1997). Of fingers, toes and penises. Nature, 390(6655),29.

Leeth, J. D., & Ruser, J. (2003). Comparing wage differentials for fatal and nonfatal injury risk by genderand race. Journal of Risk and Uncertainty, 27(3), 257–277.

Lutchmaya, S., Baron-Cohen, S., & Raggett, P. (2004). 2nd to 4th digit ratios, fetal testosterone andestradiol. Early Human Development, 77, 23.

Manning, J. T. (2002). Digit ratio: A pointer to fertility, behavior and health. New Jersey: RutgersUniversity Press.

Manning, J. T., & Bundred, P. E. (2000). The ratio of 2nd to 4th digit length. Medical Hypotheses, 54,855.

Manning, J. T., & Taylor, R. P. (2001). Second to fourth digit ratio and male ability in sport: implicationsfor sexual selection in humans. Evolution and Human Behavior, 22, 61–69.

Manning, J. T., Baron-Cohen, S., Whellwright, S., & Sanders, G. (2001). The 2nd to 4th digit ratio andautism. Developmental Medicine and Child Neurology, 143, 160–164.

Manning, J. T., Henzi, P., & Venkatramana, P. (2003). 2nd to 4th digit ratio: ethnic differences and familysize in English, Indian and South African populations. Annals of Human Biology, 30, 579–588.

Manning, J. T., Stewart, A., Bundred, P. E., & Trivers, R. L. (2004). Sex and ethnic differences in 2nd to4th digit ratio of children. Early Human Development, 80, 161–168.

McCarthy, M. M., & Konkle, A. T. M. (2005). When is a sex difference not a sex difference? Frontiers inNeuroendocrinology, 26(2), 85–102.

McIntyre, M. H., Ellison, P. T., Lieberman, D. E., Demerath, E., & Towne, B. (2005). The development ofsex differences in digital formula from infancy to the Fels Longitudinal Study. Proceedings of theRoyal Society B, 272(157), 1473–1479.

Meier-Pesti, K., & Penz, E. (2008). Sex or gender? Expanding the sex-based view by introducingmasculinity and femininity as predictors of financial risk-taking. Journal of Economic Psychology, 29,180–196.

Murnighan, J. K., Roth, A. E., & Shoumaker, F. (1987). Risk aversion and bargaining: some preliminaryresults. European Economic Review, 31, 265–271.

Murnighan, J. K., Roth, A. E., & Shoumaker, F. (1988). Risk aversion in bargaining: an experimentalstudy. Journal of Risk and Uncertainty, 1(1), 101–124.

Neave, N., Laing, S., Fink, B., & Manning, J. T. (2003). Second to fourth digit ratio. Proceedings of theRoyal Society of London. Series B, 270, 2167.

Sapienza, P., Zingales, L., & Maestripieri, D. (2009). Gender differences in financial risk aversion andcareer choices are affected by testosterone. Proceedings of the National Academy of Sciences USA,106(36), 15268–15273.

Sulloway, F., & Zweigenhaft, R. (2010). Birth order and risk taking in athletics: a meta-analysis and studyof Major League Baseball. Personality and Social Psychology Review, Online April 30, 2010.

Tester, N., & Campbell, A. (2007). Sporting achievement: what is the contribution of digit ratio? Journalof Personality, 75(4), 663–677.

Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: cumulative representation ofuncertainty. Journal of Risk and Uncertainty, 5(4), 297–323.

van Anders, S. M., & Hampson, E. (2005). Testing the prenatal androgen hypothesis: measuring digitratios, sexual orientation, and spatial abilities in adults. Hormones and Behavior, 47, 92–98.

Wallace, B., Cesarini, D., Lichtenstein, P., & Johannesson, M. (2007). Heritability of ultimatum gameresponder behavior. Proceedings of the National Academy of Sciences USA, 104, 15631–15634.

J Risk Uncertain (2011) 42:1–26 2525

Weiss, S., Firker, A., & Hennig, J. (2007). Associations between the second to fourth digit ratio and careerinterests. Personality and Individual Differences, 43, 485–493.

Wilcox, N. (2009). ‘Stochastically more risk-averse:’ a contextual theory of stochastic discrete choiceunder risk. Journal of Econometrics. doi:10.1016/j.jeconom.2009.10.012.

Williams, J. H. G., Greenhalgh, K. D., & Manning, J. T. (2003). Second to fourth digit ratio and possibleprecursors of developmental psychopathology in preschool children.Early Human Development, 72, 57–65.

Zethraeus, N., Kocoska-Maras, L., Ellingsen, T., von Schoultz, B., Linden Hirschberg, A., & Johannesson,M. (2009). A randomized trial of the effects of estrogen and testosterone on economic behavior.Proceedings of the National Academy of Sciences USA, 106(16), 6535–6538.


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