Digit Ratios (2D:4D) as Predictors of Risky Decision Making for both Sexes Ellen Garbarinoi, Robert Slonimii, Justin Sydnoriii
Abstract: Many important economic decisions involve financial risk, and there is substantial evidence that women tend to be more risk averse than men. We explore a potential biological basis of the variation in risk-taking within and between men and women using an emerging measure of prenatal androgrens, the ratio between the length of the second and fourth digits (2D:4D). A smaller 2D:4D ratio has been linked to higher exposure to prenatal testosterone relative to estradiol, with men having lower ratios than women on average. In an individual decision-making task with financial stakes, we find that both men and women with smaller 2D:4D ratios chose significantly riskier options. We further find that the 2D:4D ratio can partially explain the overall difference in risktaking between men and women. Moreover, for men and women at the extreme ends of the digitratio distribution the difference in risk-taking disappears entirely. Thus, the 2D:4D ratio can at least partially explain variation in financially motivated risk-taking behavior both within and between sexes and offers strong evidence of a biological basis of attitudes toward risk-taking.
Keywords: Risk, Sex Differences, Experiments, Testosterone JEL codes
Acknowledgements: We thank Rachel Croson, John Manning, numerous seminar participants, an anonymous referee and the Journal of Risk and Uncertainty Editorial Board for useful comments on this project. Special thanks to Angelo Benedetti and Jason Cairns for invaluable research assistance. This project was supported by a grant from the Kauffman Foundation.
i
Department of Marketing, Faculty of Economics and Business, University of Sydney, Sydney,
[email protected] ii
Corresponding author: Discipline of Economics, Faculty of Economics and Business, University of Sydney, Sydney,
[email protected] iii
Actuarial Science, Risk Management, and Insurance Department, University of Wisconsin Business School,
[email protected]
1
Digit Ratios (2D:4D) as Predictors of Risky Decision Making for both Sexes 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 is ubiquitous. Despite the importance of risk-taking and the large literature on the subject, relatively little is known about the origins, determinants and sources of heterogeneity in risk attitudes. In this paper, we explore the possibility of a biological origin for one of the most common and consistent findings in the risk-taking literature, namely that men are less risk averse than women. 1 A sex difference in risk-taking preferences is well established. 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 of 16 risk-taking categories (Byrnes, Miller and Schafer 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 in economic experiments. 3,4 Outside of the economics literature, most explanations for the sex difference in risk-
1
The examination of the biological origins of economic behavior has received increasing interest. For instance, Burnham (2007) has looked at the role of testosterone in ultimatum bargaining games and Chen, Katuscak and Ozdenoren (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 of men 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, Eckel, and Heracleous (2010) report that subjects, both men and women, predict that women will make more risk averse choices than men, suggesting that the gender gap is risk attitudes is a stereotype held at least among laboratory participants. Outside the laboratory, Deliere and Levy (2001) report that women are more risk averse than men in terms of the wage premium they accept for risky jobs, and in terms of choosing safer occupations. Leeth and Ruser (2003) further find that for nonfatal risks women receive a risk premium more than three times greater than the risk premium men earn. 4 Harrison and Rutstrom (2008) find that the sex differences in laboratory experiments do not always support the conclusion that women are more risk averse than men. For instance, some of the analyses in the 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 women participate for different reasons, and so the sex difference on risk behavior observed in the laboratory may be the result of selection bias. However, Cleave, Nikifarakis and Slonim (2010) find that there is selection bias in the direction that suggests results from laboratory experiments underestimate the risk attitude difference between women and men in the population subjects were recruited from; they find that women who do not participate are more risk averse than the women who participate while the men who do not participate are less risk averse than the men who participated.
2 taking involve psychological or sociological phenomena, but with the growing research in the neurosciences and neuro-economics in particular, examination of biological bases for sex differences in risk-taking have been receiving increased attention. One biological factor that has been the focus of recent research is the role of circulating testosterone on attitudes toward risk. The expectation of this literature is that higher testosterone levels will lead to greater risk-taking, however the support has so far been mixed. The activational effects of circulating testosterone have been found to predict the financial performance of male futures traders (Coates and Herbert 2008), with higher testosterone levels associated with higher returns. Apicella et al. (2008) find a positive relationship between testosterone and risk-taking in an experimental task using male undergraduates. More recently, Sapienza, Zingales and Maestripieri (2009) find no correlation between circulating testosterone and risk-taking for men but do find a positive correlation for women. However, a medical manipulation of circulating testosterone in postmenopausal women found no effect on risk-taking behavior (Zethraeus et al. 2009). Thus the current evidence on the effects of circulating 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 more permanent organizational effects on brain development (Arnold and Breedlove 1985). One of the increasingly studied markers of the organizational influence of testosterone is the 2D:4D ratio (the ratio of the length between the second and fourth fingers), 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 have their effects on brain development and so may lead to more deterministic influences on human behavior (Goy and McEwen 1980). There is also a clearer causal interpretation of these organizational effects; unlike circulating testosterone, the
3 2D:4D ratio is essentially fixed prior to birth (McIntyre et al. 2005) making it clear that the act of making financial choices under risk cannot affect the 2D:4D ratio. 5 The 2D:4D ratio has been shown to correlate with a number of biological and psychological characteristics that show strong sex differentiation. Several traits more commonly 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 and spatial performance (Manning and Taylor 2001; Kempel, Gohlke and Kelmpau 2005), autism (Manning et al. 2001), higher levels of immune system dysfunction and myocardial infarction (Manning and Bundred 2000), athletic achievement (Tester and Campbell 2007), dominance and masculinity (Neave et al. 2003), sensation seeking and psychoticism (Austin et al. 2002). Conversely, a number of traits more commonly seen in women are positively correlated with 2D:4D including high verbal fluency (Manning 2002), emotional problems (Williams, Greenhalgh and Manning 2003) and neuroticism (Austin et al. 2002). 2D:4D has also been found to correlate with career interests such that a more masculine hand pattern (i.e., lower 2D:4D) was associated with higher tendency toward enterprising and investigative careers (Weis, Firker and Hennig 2007). Only a few papers have explored the relationship between the 2D:4D ratio and risk-taking. Apicella et al. (2008) find no correlation between the 2D:4D ratio and their risk-taking measure in a sample of male undergraduates, but they suggest this may 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 that those with lower 2D:4D ratios, indicating higher prenatal testosterone levels, earn significantly higher returns (Coates, Gurnell and Rustichini 2009). While higher returns may be indicative of greater risk-taking, they are not a direct measure of risk attitudes and hence these results 5
The connection between prenatal androgen exposure and the 2D:4D ratio is commonly explained by the shared genetic basis of the distal limbs (e.g., fingers and toes) and the urogenital system controlled by the homeobox genes, hox-a and hox-d, (Kondo et al., 1997; Csatho et al., 2003). In one of the few direct tests of the relationship between 2D:4D and prenatal sex hormones in humans, Lutchmaya et al. (2004) found a lower 2D:4D ratio was significantly related to higher levels of fetal testosterone relative to fetal estradiol in the amniotic fluid, within and across sexes (Lutchmaya, Baron-Cohen and Raggett 2004).
4 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 and women, Sapienza et al. (2009) find no significant correlation between digit ratio and risk-taking for men and a weak positive correlation for women. These results are intriguing since one might well expect that men, with their higher levels and wider variance in testosterone, would show stronger organizational effects (i.e., a higher 2D:4D correlation with risk-taking) than women. Given the limited study of the organizational effects of testosterone on risk-taking and the even more limited study examining both sexes, we will test whether prenatal testosterone exposure can help explain variation in risk-taking decisions both within the sexes as well as risk-taking differences between the sexes. We examine the relationship between prenatal androgen exposure proxied by the 2D:4D ratio and risk-taking using a financially motivated individual decision-making experiment. The experiment was conducted with men and women and included a 2D:4D measurement and a well-established risk-taking instrument involving three financially motivated decisions with varying levels of risk and expected values. The hypotheses are H1: Men and women with lower 2D:4D ratios (suggestive of higher levels of prenatal 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-male gap in risk-taking. Support for these hypotheses suggests that the organizational effects of testosterone exposure affect attitudes toward risk-taking. The remainder of the paper is organized as follows. Section 1 describes the measurement of the 2D:4D ratio and risk attitudes towards financial gambles. For measurement of the 2D:4D ratio and risk attitudes we use well established procedures and for the risk attitudes we include two additional measures. Section 2 presents the results. We first show that the current subject population exhibits the 2D:4D and risk patterns between the sexes documented in past work. We further show that the
5 risk patterns are robust across the additional risk measures. We then show the critical relationship between the 2D:4D ratio and risk attitudes for both sexes, supporting H1 that both men and women with lower 2D:4D ratios take greater financial risks. 6 We further show that controlling for individual differences in the 2D:4D ratio significantly reduces the sex differences in risk attitudes, supporting H2 that 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 specifications and 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 the 2D4D distribution exhibit insignificant differences in risk attitudes, suggesting that at the extremities of the 2D:4D ratio the gender gap in risk attitudes may disappear entirely. Section 3 provides a brief summary and directions for future work. 1 Methods 7 1.1 Overview A total of 152 (65 female, 87 male) Caucasian students participated in the experiment. Subjects from other ethnic backgrounds were excluded because the average 2D:4D ratio is sensitive to ethnic variation (Manning, Henzi and Venkatramana 2003; Manning et al. 2004). Each subject was asked to make three independent financial decisions. Each decision involved choosing one lottery from a sequence of six lotteries that were ordered from least to most risky. Subjects read the instructions (see appendix) and completed an eleven-item review to verify their understanding of the task (99% accuracy across all subjects and questions). Subjects next made their three financial choices and completed a survey. After completing the survey, subjects were taken to a second room where both
6
In a concurrent studied reported in a working paper, Derber and Hoffman (2007) present evidence showing a qualitatively similar relationship between the 2D:4D ratio and choices over a risky gamble for both male and female university students using an alternative measure of financial risk developed by Gneezy and Potters (1997). 7 The protocols are available at http://research3.bus.wisc.edu/course/view.php?id=245 and include the instructions for all conditions and the survey.
6 their hands were scanned using a flatbed scanner. To complete the study, one of the three financial decisions was randomly chosen for each 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. Each decision required each subject to choose one lottery from a sequence of six ordered lotteries. Harrison and Rutstrom (2008) note that ordered lottery sequences were first used in the 1980’s (Binswanger 1980, 1981), brought into the lab in the late 1980s (Murnighan, Roth and Shoumaker 1987, 1988) and continue to be a popular measure of risk attitudes (Eckel and Grossman 2002, 2008). Table 1 presents the three decisions. Decision 50-50 was first used by Eckel and Grossman (2002, 2008) and Decision 75-25 and Decision 25-75 are modifications to explore behavior across other domains of the probability space. Each decision required 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: the standard 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 the lottery be the expected utility maximizing optimal choice. The lotteries increase in expected value (EV) and both measures of risk from Lottery 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 behavior since Lottery 5 stochastically dominates Lottery 6. If subjects are expected-utility maximizers with CRRA preferences, then they will (weakly) prefer higher ordered lotteries in Decision 75-25 than in Decision 50-50 and likewise (weakly) prefer higher lottery in Decision 50-50 than 25-75. For instance, if a subject has CRRA preferences with r=.45 then he would choose Lottery 3 in Decision 25-75, Lottery 4 in Decision 5050 and Lottery 5 in Decision 75-25. By measuring risk preferences across all three decisions, we are
7 able to better distinguish risk preferences across subjects over a more narrowly defined range than had we measured behavior over just one decision. For instance, three expected utility maximizers with r = .15, r=.25 and r=.35 would be indistinguishable with Decision 50-50 alone (all would choose Lottery 5), yet Decision 25-75 would distinguish them since the more risk averse subject with r=.35 would choose Lottery 3, the subject with r=.25 would choose Lottery 4 and the less risk averse subject with r=.15 would choose Lottery 5. Likewise, three expected utility maximizers with r = 1.05, r=1.55 and r=2.05 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 averse subject with r=2.05 would choose Lottery 2, the subject with r=1.55 would choose Lottery 3 and the relatively less risk averse subject with r=1.05 would choose Lottery 4. Moreover, to the extent that there is noise in the decision process, either in errors made in choice or randomness in risk attitudes (Wilcox 2010), we can reduce some of this noise by measuring three decisions rather than only one. 8 We also examined three framings of the lotteries: Gains, Mixed and Losses. The instructions describing the frames are presented in the appendix and each subject made all their choices in only one of the frames. Subjects in Gains started with a balance of $0 and all lotteries were identical to those presented in Table 1 with each outcome 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 either add to or subtract from the initial $22 balance. Subjects in Losses started with a balance of $60 and all payoffs were equal to those in Gains minus $60 with each outcome 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 (greater risk seeking) behavior when
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>.20) so we collapse across order and do not discuss order any further.
8 gambles involve losses rather than gains, ceteris paribus, we thus included a manipulation of frame to investigate whether the expected differences in risk attitudes of men and women would be consistent across frames. Overall, we examined the three Decisions and the three Frames in order to test the robustness of sex differences on risk attitudes across different areas of the probability distribution (Decisions) and across gains, losses and mixed outcomes (Frames). While we do not a prior anticipate any unique sex differences across decisions and framing, it is nonetheless valuable to include these treatments to examine the robustness of the results beyond one point in the lottery distribution space and beyond one framing. 1.2.2 2D:4D Measurement After the three decisions and survey were completed, participants went to another room and had their hands scanned. Subjects removed all rings and placed both hands on a flatbed scanner with palms down, fingers together, and light pressure. Figure 1 shows a typical male and female hand scan. A second scan was taken if details of the basal creases were not clear. One subject had to be excluded due to having previously broken her fourth finger. The use of digital images is a common technique for 2D:4D measurement (Kemper and Schwerdtfeger 2008). Scanning allows for a record of the outcome that enables test/retest options and precision measurement to minimize error. Lengths of the second and fourth digits were measured from the basal crease (i.e., the crease closest to the base of the finger) to the central point of the finger tip. Measurements were made using the Autometric software developed by DeBruine (2004) for measuring 2D:4D ratios. This form of software-based measurement has been shown to have the highest precision and inter-rater reliability of the common measurement methods (Kemper and Schwerdtfeger 2008). Three research assistants independently coded the length of the second and fourth fingers 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 not informed of the research questions. To
9 minimize the influence of rater errors, we first use the median 2D:4D ratio for each subject’s hand across the three independent coders’ measures. We then take the mean 2D:4D ratio across the median for each subject 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, Figure 2 shows that the difference in the 2D:4D ratio distribution 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 ratio over 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=.035, and for the left hand, the ratio for men and women is 0.957 and 0.966, t=2.016, p=.046). The observed differences are within the range of mean ratios in the literature in which female average ratios range from 0.96 to 0.99 while male average ratios range from 0.93 to 0.97 (e.g., Fink et al. 2006; Weis et al. 2006; Tester and Campbell 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 the outcome measure. As such, our outcome measure is a qualitative 6-point scale. Unlike most qualitative scales, we can be confident that different participants perceive the scale the same. The reason is that the underlying choices in this scale are lotteries with well-defined quantitative differences including the mean and variance. In principle, we could create a structural model that maps these choices over lotteries into parameter estimates of an underlying utility model. However, because the literature has identified a number of potential drivers of financial risk attitudes – concave wealth utility, loss 9
Our results are qualitatively the same if we use the median measure from either hand alone in the analyses.
10 aversion, probability weighting, and diminishing sensitivity – properly identifying a structural model of utility here would require a large number of different gamble choices from each subject. Given that our question of interest 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 the simpler qualitative metric of choice, namely which of the 6 rank ordered gambles the subject chose. To properly account for the qualitative-scale nature of our outcome measure (the choice from six lotteries ordered from least to most risky), we use multivariate Ordered Probit regressions. Since we observe three decisions for each subject, one for each Decision 50-50, 75-25 and 25-75, the regression analyses stack the data across the three decisions and include dummy variables for Decision 75-25 and Decision 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 within a single frame, we estimate and report standard errors clustered at the subject level. Table 2 presents coefficient estimates from a series of Ordered Probit regressions on lottery choice on different sets of independent variables. The first column shows the effects of the Decisions and Framings on risk-taking. As anticipated, subjects made significantly higher lottery choices in Decision 75-25 reflecting the lower risk aversion of the higher lottery choices in Decision 75-25. The estimates in Column 1 indicate that the lottery choice in Decision 75-25 was significantly higher than in Decision 50-50; the estimated coefficient on Decision 75-25 is also significantly higher than in Decision 25-75 (p.20). The estimates in Column 1 also show that there are no significant differences across the frames (p>.20). 10 The effect of decision and framing shown in Column 1 hold across all the models we investigate.
10
We had anticipated that the Loss Frame would lead to less risk averse choices. There are several possible reasons the Loss Frame did not significantly affect choices. For instance, the manipulation may have been too weak (imagine starting with $60), too transparent so that subjects could easily figure out final payments, too subtle and so subjects did
11 2.1.3 Gender and Risk Figure 3 shows the lottery choices of women and men by decision. Consistent with the prevailing evidence on sex differences in risk-aversion, the distribution of choices for women shows more risk aversion than men for each of the three decisions. For instance, for Decision 50-50 men were 17 percent more likely than women to choose Lotteries 5 and 6 whereas women were seven percent more likely than men to choose Lotteries 1 and 2. The difference is even larger for the other two decisions; For Decision 25-75 men were 32 percent more likely than women to choose Lotteries 5 and 6 and women were 24 percent more likely than men to choose Lotteries 1 and 2, and for Decision 75-25 men were 24 percent more likely than women to choose Lotteries 5 and 6 and women were 11 percent more likely than men to choose Lotteries 1 and 2. For the 50-50 Decision, the men’s mean lottery choice was 3.69 and women’s was more risk averse at 3.11 (t-test; t=2.44, p=.016). For Decision 75-25, the men’s average choice was 4.35 and women’s average choice was 3.72 (t=2.805, p=.006) and for Decision 25-75 Decision, the men’s average choice was 3.87 and women’s average choice was 2.77 (t=3.874, p=.0002). The female-male gap also holds across all three frames: Gains: Men 3.94, Women 3.16, t=3.087, p=.002; Mixed: Men 4.15, Women 3.32, t=3.562, p=.0005; Loss: Men 3.80, Women 3.11, t=2.44, p=.016. The Ordered Probit regression in Column 2 of Table 1 also shows that controlling for Frame and Decision, women chose significantly more risk averse lotteries than men (p 1.40 0.49 < r < 1.40 0.31 < r < 0.49 0.23 < r < 0.31 0 < r < 0.23 Risk Seeking
*CRRA: U($x) = [x(1-r)]/(1-r) for r>0 & r≠1; U($x)= LN(x) for r=1.
27
Table 2. Determinants of risky choice (Ordered Probit regression results) Dependent variable: Option chosen (1=Least Risky, 6=Most Risky) Independent Variables Decision 75-25
(1)
(2)
(3)
(4)
(5)
(6)
(7)
0.397 0.409 0.403 0.413 0.413 0.430 0.413 [0.078]*** [0.080]*** [0.079]*** [0.080]*** [0.080]*** [0.114]*** [0.080]***
Decision 25-75
-0.029 [0.095]
-0.030 [0.098]
-0.031 [0.097]
-0.033 [0.099]
-0.033 [0.099]
0.144 [0.132]
-0.033 [0.100]
Mixed Frame
0.075 [0.152]
0.104 [0.149]
0.081 [0.150]
0.105 [0.148]
0.104 [0.148]
0.105 [0.148]
0.123 [0.192]
Loss Frame
-0.104 [0.171]
-0.074 [0.170]
-0.117 [[0.169]
-0.088 [0.168]
-0.090 [0.170]
-0.090 [0.171]
-0.078 [0.245]
-0.467 -0.466 [0.128]*** [0.128]***
-0.321 [0.156]**
-0.440 [0.224]**
-0.156 [0.062]**
-0.150 [0.071]**
-0.150 [0.072]**
-0.150 [0.071]**
-0.014 [0.131]
-0.015 [0.132]
-0.015 [0.131]
-0.520 [0.130]***
Female Digit ratio (z-score)
-0.191 [0.059]
Female* Digit ratio Female* Decision 75
-0.038 [0.157]
Female* Decision 25
-0.411 [0.196]**
Female* Mixed Frame
-0.047 [0.299]
Female* Loss Frame
-0.030 [0.366]
Observations Clusters (subjects) Log-likelihood
453
453
453
453
453
453
453
151
151
151
151
151
151
151
-792.79
-779.44
-785.3
-774.62
-774.61
-772.87
-774.59
Note: Robust standard errors clustered at the subject level are in brackets. ** significant at 5%; *** significant at 1%
28
Table 3. Determinants of risky choice (OLS regression results) Dependent variable: Option chosen (1=Least Risky, 6=Most Risky) Independent Variables
(2’)
(3’)
(4’)
(5’)
Constant
3.733 3.431 3.701 3.701 [0.197]*** [0.181]*** [0.192]*** [0.193]***
Decision 75-25
0.642 0.642 0.643 0.642 [0.116]*** [0.116]*** [0.116]*** [0.117]***
Decision 25-75
-0.040 [0.136]
-0.040 [0.136]
-0.040 [0.136]
-0.040 [0.136]
Mixed Frame
0.189 [0.219]
0.161 [0.225]
0.190 [0.215]
0.191 [0.216]
Loss Frame
-0.097 [0.247]
-0.162] [0.249]
-0.117 [0.243]
-0.117 [0.246]
Female
-0.769 [0.190]***
-0.683 -0.683 [0.188]*** [0.188]*** -0.296 -0.235 [0.086]*** [0.089]***
Digit ratio (z-score)
0.000 [0.194]
Female*Digit ratio Observations Clusters (subjects) R-squared
-0.235 [0.105]**
453 151 0.101
453 151 0.079
453 151 0.122
Note: Robust standard errors clustered at the subject level are in brackets. ** significant at 5%; *** significant at 1%
453 151 0.122
29
Table 4. Determinants of risky choice (OLS and Probit Regressions) Dependent Variable: Indicator of c choice of Lottery 4, 5 or 6 Probit OLS (Marginal Effect Estimates) Independent Variables
(1)
(2)
(3)
(4)
(5)
(6)
Constant
0.523*** [0.060]
0.512*** [0.059]
0.514*** [0.059]
Decision 75-25
0.232*** [0.0427]
0.232*** [0.043]
0.232*** [0.043]
0.230*** [0.040]
0.232*** [0.041]
0.232*** [0.041]
Decision 25-75
-0.046 [0.0436]
-0.046 [0.044]
-0.046 [0.044]
-0.044 [0.041]
-0.045 [0.041]
-0.045 [0.041]
Mixed Frame
0.109 [0.066]
0.110 [0.065]
0.108 [0.065]
0.112 [0.065]
0.111 [0.064]
0.110 [0.063]
Loss Frame
-0.005 [0.075]
-0.012 [0.073]
-0.014 [0.073]
-0.006 [0.073]
-0.016 [0.070]
-0.017 [0.071]
Female
-0.206*** [0.058]
-0.177*** [0.058]
-0.175*** [0.058]
-0.202*** [0.054]
-0.171*** [0.054]
-0.171*** [0.054]
-0.081*** [0.030]
-0.075** [0.035]
-0.081*** [0.029]
-0.076** [0.035]
Digit ratio (z-score) Female* Digit ratio Observations Clusters (subjects) R-squared Loglikelihood
-0.017 [0.064]
-0.012 [0.066]
453
453
453
453
453
453
151
151
151
151
151
151
0.112
0.138
0.138 -286.28
-279.62
-279.59
Note: Robust standard errors clustered at the subject level are in brackets. ** significant at 5%; *** significant at 1%
30
Table 5. Determinants of risky choice (Ordered Probit regression results) Dependent variable: Option chosen (1=Least Risky, 6=Most Risky) Independent Parameter Standard p-value Variable Estimate Error Decision 75-25 0.032 0.130 .002 Decision 25-75 -0.008 0.173 .964 Mixed Frame 0.152 0.199 .443 Loss Frame -0.093 0.213 .662 Female -0.450 0.188 .017 Digit ratio (z-score) -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 th 4 Digit Length -0.0005 0.0016 .757 Height 0.014 0.026 .603 BMI 0.014 0.016 .388 LN(age) -0.646 1.599 .686 Only Child -0.385 0.197 .050 Birth Order -0.051 0.058 .379 SAT Math -0.082 0.100 .411 SAT Verbal 0.041 0.070 .561 Work -0.045 0.140 .746 Observations 453 Clusters (subjects) 151 Log-likelihood -769.31 Note: Robust standard errors clustered at the subject level are in brackets.
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Table 6. Risky choice spilt by digit ratio quartiles (Probit regression results) Dependent variable: Option chosen (1=Least Risky, 6=Most Risky) Quartiles Independent Variables
(1)
(2)
(3)
(4)
Decision 75-25
0.355 [0.180]**
0.511 [0.149]***
0.271 [0.175]
0.522 [0.161]***
Decision 25-75
0.102 [0.218]
0.268 [0.192]
-0.163 [0.209]
-0.458 [0.212]**
Mixed Frame
0.233 [0.286]
-0.418 [0.317]
0.476 [0.314]
0.113 [0.290]
Loss Frame
0.085 [0.386]
-0.268 [0.463]
-0.288 [0.312]
0.028 [0.338]
Female
-0.115 [0.291] [p=.694]
-1.120 [0.320]*** [p
