Are Women Really More Risk-Averse Than Men Part 2

Results for Cross-Sex Comparisons Table 1 reports on an analysis of 24 published articles. The type of study done varied from analysis of survey questions asking people how they felt about various risks (including financial, environmental, and/or employment risks), to experimental studies in which subjects were offered lotteries of various types, to studies of financial asset allocations among risky or less-risky assets. The generally large sample sizes (often 200 into the tens of thousands) suggest that, if gender differences in mean scores are substantively large—or even, for very large samples, if the differences are substantively small—they will tend to appear as statistically significant. TABLE 1 Magnitudes of Male vs. Female Differences and Similarities Related to Risk Author(s) Arano et al, 2010 Barber and Odean, 2001 Cohen's d NSS Index of Type of Study Similarity Percent of actual retirement assets — held in stock n (approx.) 400 -.09 to .26 — Measures of riskiness of actual common stock holdings 38000 Barsky, Juster, et al., 1997 — .98 Hypothetical question about taking a riskier job 12000 Beckmann and Menkhoff, 2008 NSS to +.46 .67 to .91 Survey questions about investment decisions 200 NSS .87 Percent of actual retirement assets held in stock, and self-report 300 Bernasek and Shwiff, 2001 Booth and Nolen, 2012 NSS to .38 Borghans, Golsteyn, et al., 2009 .32 to .55 Byrnes, Miller, et al., 1999 Dohmen, Falk, et al., 2011 .84 Hypothetical investment, lottery 300 — Lottery experiment 300 -1.23 to +1.45 (Mean = +0.13) — Meta-analysis of 150 studies on risk in many domains -- NSS to .48 .80 to .88 General risk, lottery, and others (e.g., car driving, career) 500 to 22,000 Regression coefficients are not meaningful estimates of effect sizes if a researcher searches for and reports on only those combinations of variables or subsamples that yield statistically significant results, or the results that the researcher finds most plausible. Raw data is less influenced by these potential biasing factors. Note that this approach to reviewing the literature is quite different from the meta-regression analysis advocated by Stanley (2001), which focuses on the outcomes of regression specifications (rather than on raw data) and, in the example given in the article, on the sizes of interferential test statistics (rather than on substantive effect size). Eckel and Grossman, 2008 .55 to 1.13 .60 to .80 Gambling questions 300 Eriksson and Simpson, 2010 .19 to .22 .89 to .91 Lottery experiment 200 Fehr-Duda, De Gennaro, et al., 2006 -.25 to NSS to .49 Finucane, Slovic, et al., 2000 Harris, Jenkins, et al., 2006 Hartog, Ferreri-Carbonell, et al., 2002 Holt and Laury, 2002 .11 to .33 -.34 to NSS to .74 .22 to .29 — Lottery experiments .86 to .93 Risk questions regarding hazards — .85 to .96 Financial Lottery NSS to .37 .83 to .86 Kahan, Braman et al., 2007 .15 to .36 — Lindquist and SaveSoderbergh, 2011 NSS Meier-Pesti and Penz, 2008 NSS to .85 Olsen and Cox, 2001 NSS to .65 — Perceptions of abortion and environmental risks Hypothetical investments and gender risk question .60 to .86 Survey of investment attitudes .06 to .17 .90 to .93 Rivers, Arvai et al, 2010 .25 to .31 Sunden and Surette, 1998 Financial Lottery, hypothetical scenario — Game show wagers Powell and Ansic, 1997 Ronay and Kim, 2006 Survey including health, recreational, gambling risks 100 1200 700 1,500 to 13,000 200 2000 600 150 200 Insurance and market experiments, and survey 100 — Perceptions of health and environmental risks 400 NSS to .44 — Variety of questions and risk scenarios .08 to .16 .95 to .96 Survey on allocation of defined contribution assets 50 6000 Note: Adjusted so that positive d-values indicate relatively lesser risk-aversion (or risk perception) on the part of males, compared to females, on average. N's are approximate sample sizes of groups used for comparisons. NSS=No Statistically Significant difference. (See text for further explanation.) Cohen's d, expressed such that a positive number signifies lesser mean male risk aversion or lesser male mean perception of risk, is reported in Table 1 for differences between means that were reported to be statistically significant (at a 10% level or better). 16 When the data allowed, these were computed for numeric variables and also for qualitative response variables (e.g. Likert scales) that the articles themselves treated as numeric and cardinal. Analysis was generally performed only on the subjects' own direct responses to survey questions, although in a few cases analysis was performed on the authors' univariate transformations of these variables. Because many of the studies presented results for a number of different sampled groups and/or questions, the d-value results are presented as a range. The largest negative and positive (in absolute value) statistically significant numerical values are shown. "NSS" denotes that no statistically significant differences by sex were (also) found for some samples or variables, within a given study. The recording of NSS for an entire study indicates that, when evaluating the univariate responses for the sample as a whole, no statistically significant sex differences can be found. In these cases, the authors went on to find some evidence for differences in risk-taking in some subsamples and/or through multivariate analysis. Note that a finding of a d-values exceeding +.50—that is, half a standard deviation, in favor of lesser male risk aversion—occurs in only six of 24 articles, and the finding of a difference of more than one standard deviation of difference occurs in only two. In most cases—and even within the same articles—smaller d-values are found. There are also many cases in which differences found are not statistically significant, and four articles in which differences that are statistically significant in the direction of greater female risk taking (d<0) are among the findings. Table 1 also reports Indexes of Similarity for comparisons reported as statistically significant in the source articles. In some cases, IS values were computed for the same variables for which d-values were also computed, while in other cases they refer to different variables. Since these figures measure similarity but are only reported here for statistically significant differences, the numbers in Table 1 represent the low end of possible IS values that could be found in these data. IS values range from .60 to .98, with most studies yielding no values below .80. Because IS is non-directional, it is worth noting that one instance of IS=.67 (Beckmann and Menkhoff, 2008) is for a case where fewer men than women chose a risky option. Figure 3 visually illustrates, as an example, data taken from one of the studies reviewed in Table 1. Beckmann and Menkhoff (2008) asked financial fund managers in four countries, "In respect of professional investment decisions, I mostly act…" giving 16 A 10% level was chosen, rather than 5% or 1%, to give the existence of "difference" the maximum benefit of the doubt. Numeric values for d (or IS) were not calculated when differences were not statistically significant, because of the rather wild values that occured in some of the small samples. While in very large samples, one can assume that a lack of statistical significance is associated with a small dvalue, in smaller samples, relatively large but highly unreliable d-values can occur, making reporting of their numerical values misleading. them "six response categories ranging from 1=very risk averse to 6=little risk averse" (371). In the one country (Italy) for which the difference in mean response by sex to this question was statistically significant, calculation yields a d which is relatively substantial (≈ .4) for this literature, and IS at the smaller end of the scale (≈ .7). Many of the results in Table 1, therefore, represent cases of less "difference" or more "similarity" than that illustrated in Figure 3 (or even "difference" in the opposite direction). FIGURE 3 d ≈ .4, IS ≈ .7 Are the indicators of difference and similarity in Table 1 small or large? While answering this could depend a great deal on a specific real-world context, the existence of “Men are from Mars, Women are from Venus” differences in risk-taking by sex can clearly be ruled out. To the extent that differences have been shown to exist in the literature—and the evidence is, as one can see, quite mixed—they are of a very much lesser order than, for example, the observable differences in the distributions of heights (d=+2.6) discussed earlier. Instead of difference, similarity seems to be the more prominent pattern, with well over half of men and women "matching up" on risk-related behaviors in every study. As one writer has quipped, perhaps "Men are from North Dakota, Women are From South Dakota" (Dindia 2006)—that is, men and women would seem to be more accurately regarded as being from neighboring states in the same country, with very much in common. It should also be noted that nearly all the studies reviewed were based on men and women from Western industrialized societies. 17 In the cognitive science literature, doubts have been raised about the empirical validity of making generalizations about "human" behavior from such a WEIRD ("Western, Educated, Industrialized, Rich, and 17 The exceptions in Table 1 are Beckmann and Menkoff (2008), who include a sample from Thailand; Eriksson and Simpson (2010), who include subjects from India; and possibly some studies reviewed in Byrnes et al (Byrnes, Miller et al. 1999). Democratic" society) sample (Henrich, Heine et al. 2010). Further checking on behaviors presumed to be characteristic of males and females in cross-cultural context, before generalizing to all men and women, would seem to be warranted. (Essential) Sex Difference, or a Result of Beliefs about Difference? The generic explanation for observed differences in average risk-preference measures by sex (when they occur) is that greater risk aversion is a trait, characteristic, or essence shared by women by virtue of their being women. This, however, is not, as discussed above, the only possible explanation for differences in aggregate patterns by sex (when they occur). Differences that may appear at a cursory level to be due to sex "essences" may in fact be due (in part or completely) to a third, confounding variable, such as societal pressures to conform to gender expectations or to locations in a social hierarchy of power, or may no longer be seen when the sampling universe is broadened. What if instead of looking empirically at the effect of sex on risk-taking (which may include both biological and cultural effects), one looks more explicitly at the effect of different socialization patterns or manipulations of cultural gender identifications or expectations? How do these compare? A literature in psychology has, in fact, grown up around this question. One way to go about investigating this is to see if the degree of difference and sameness between the behaviors of men and women varies with cultural effects, either socially-generated or manipulated in a lab. Table 2 reports on the results of three such studies. Booth and Nolen (2012) studied the relationship between single-sex education versus co-education and the experimental lottery and investment behavior of girls and boys. While differences were observed between girls and boys educated in sex-integrated settings, on average, no statistically significant difference was found when both boys and girls received same-sex education. TABLE 2 Magnitudes of Male vs. Female Differences and Similarities Related to Risk, With Confounding Cultural Effects Author(s) Cohen's d Index of Similarity Booth and Nolen, 2012 NSS to .77 within co0.66 to .86 educated: male vs. female Booth and Nolen, 2012 NSS Carr and Steele, 2010 1.3 to 1.7 Subgroup: Contrast Study Type n (approx.) Hypothetical investment, lottery 150 within single-sex — educated: males vs. female Hypothetical investment, lottery 100 within stereotype— threat: male vs. female Experimental gambles 30 Carr and Steele, 2010 NSS Gneezy. Leonard, et al., 2009 NSS within stereotype— irrelevant: male vs. female within Maasai NSS (Khasi) groups: male vs. female Experimental gambles 30 Lottery experiment 50 Note: Adjusted so that positive d-values indicate relatively lesser risk-aversion (or risk perception) on the part of the first group. Approximate N's are for each "within" subgroup. NSS=No Statistically --Significant difference. Carr and Steele (2010) manipulated the gender framing of the experimental situation. They had male and female subjects experience either a "stereotype threat" situation or a "stereotype irrelevant" situation before measuring their risk-taking behavior using lottery games. In the "stereotype threat" situation, subjects were asked to record their gender before they were asked to play lottery games, which were described to them as testing their mathematical abilities. The extensive psychological literature on "stereotype threat" suggests that this may tend to erode women's performance, through causing women to worry about reinforcing a "women aren't good at math" stereotype. In the stereotype-irrelevant situation, subjects were not asked their gender until later, and the (same) experiment was described as being about puzzle-solving. Carr and Steele found very large differences (compared to Table 1—here d is as large as 1.7) when stereotype threat was activated, but no differences between men and women in risk-taking in the stereotype-irrelevant case. While most of the studies in Table 1 were conducted on men and women from Western industrialized societies, Gneezy, Leonard, et al. (2009) studied subjects from a Maasai society in Africa and a Khasi society in South Asia. They found no statistically significant gender difference within either group, in a lottery experiment. 18 Evidence of the disappearance of "sex differences" upon the manipulation of cultural contexts makes the biological explanation appear less plausible, since an "essential" sex characteristic should presumably not vary with social context. Another way of looking at the cultural gender issue is to ask about the degree to which differences within groups of males, or within groups of females, can be evoked through manipulating gender socialization, expectations, or identifications. The results of six such studies are summarized in Table 3. 18 The major reported findings in their article are about competitiveness. On this variable, they found that women from the matrilineal Khasi society were more competitive than Khasi men, on average, while in the patrilineal Maasi society the pattern was reversed. TABLE 3 Magnitudes of Differences of Males from Males, and Females from Females, Related to Risk, with Confounding Variables Author(s) Booth and Nolen, 2012 Index of Cohen's d Similarity Subgroup: Contrast .31 to .71 .68 to .71 within females: single sex vs. coed Study Type Hypothetical investment scenarios, lottery n (approx.) 150 .68 to 1.05 within female: no — stereotype threat vs. threat Kahan, Braman et al. 2007 .20 to .60 white males vs. everyone else Meier-Pesti and Penz, 2008 NSS to 0.91 within males: masculinity-primed — vs. femininityprimed Hypothetical investments and general risk question 30 NSS within females: masculinity-primed — vs. femininityprimed Hypothetical investments and general risk question 30 .58 to 1.16 within males: with — same-sex discussion vs. without Variety of questions and risk scenarios 50 NSS within females: with — same-sex discussion vs. without Variety of questions and risk scenarios 50 within males: — gender threat vs. gender affirmation Gambling experiment 50 Carr and Steele, 2010 Meier-Pesti and Penz, 2008 Ronay and Kim, 2006 Ronay and Kim, 2006 Weaver, Vandello, et al., 2012 .57 to .74 — Experimental gambles Perceptions of gun, abortion, and environmental risks 30 2000 Note: Adjusted so that positive d-values indicate relatively lesser risk-aversion (or risk perception) on the part of the first group. Approximate N's are for each "within" subgroup. NSS=No Statistically Significant difference. Booth and Nolen (2012) found statistically significant differences, on average, between girls who are single-sex educated and girls who are co-educated that tend to be larger than the differences they found between boys and girls taken as groups (reported in Table 1). Carr and Steele (2010) found differences, on average, between women in the stereotype-threat condition and women in the stereotype-irrelevant condition that in some cases exceed d=1.0. Kahan, Braman et al. (2007) have investigated intersections of sex, race, and cultural worldviews following up on a finding that suggested that the most sizeable difference in risk perception tends to be, not between men and women, but between white males and everyone else (Finucane, Slovic et al. 2000). That is, non-white males' risk perceptions may be closer to that of females than to those of their fellow males. The dvalues for white males versus everyone else in Kahan, Braman et al.'s (2007) study (Table 3) tend to be larger than the d-values they found for men versus women (Table 1). While not reviewed in this Table, an article by Flynn, Slovic et al. (1994) focuses more narrowly, and find the lowest perceptions of risk, on average, tend to be among white males who are also well educated, high income, politically conservative, and who trust authorities (1106). They suggest that risk attitudes may in this case be strongly influenced by relative positions in the social, political, and economic hierarchies: "Perhaps white males [on average] see less risk in the world because they create, manage, control, and benefit from so much of it" (1107). Meier-Pesti and Penz (2008) primed subjects to think about gender by asking them to write either about a picture of a man in a business setting or a picture of a woman looking after a baby, while controls looked at a neutral picture. Subjects then completed a questionnaire about actual and hypothetical investment behavior and attitudes towards financial and other risk. While the gender-priming manipulation had little effect on female subjects, for some variables men who received masculinity priming revealed a statistically significantly higher propensity to take risk, on average, than those who were femininity-primed. The substantive magnitude, d=.91, is also quite a bit larger than the most of effects shown in Table 1. Ronay and Kim (2006) found differences by sex, on average, on several exercises related to measuring risk attitudes and behavior (related to areas ranging from surfing to employment) that are in the range of others in the literature, as reported in Table 1. They also, however, had some subjects participate in a small group discussion with same-sex peers, while others answered the questions only individually. Males who participated in the all-male group discussion scored statistically (and substantively, in some cases, d>1.0) significantly higher on average, on risk–taking measures compared to both controls and their own pre-tests, though no effect of all-female group discussion was seen with females. The authors cite "social identity theory," which posits that "a desire to subscribe to [cultural norms of male daring] should be most pronounced when in the presence of one’s own gender group" (Ronay and Kim 2006, 402), to suggest an explanation for these results. The subjects of the study by Weaver, Vandello, et al. (2012) were all heterosexual males. Some were asked to test a feminine, scented hand lotion before doing a gambling experiment, creating a "gender threat" situation after which (some) men may feel a need to reestablish their masculinity. 19 Others were asked to test a power drill before doing the 19 The assertion of bald statements and generalities based (invalidly) on aggregate analysis seems to be endemic to much of the literature, beyond economics. While it may be that only some men find hand lotion to be threatening, statements such as the following —perhaps unconsciously but still unfortunately— suggest that masculine identity is universally fragile: "Specifically, the apprehension that men feel about experiment, creating a "gender affirmation" situation. The average amount bet and the average number of maximum bets was statistically significantly higher for the gender threat group compared to the gender affirmation group. Again, this within-sex substantive magnitude of difference (d>.5) is larger than many of the cross-sex effects seen in Table 1. While sample sizes are relatively small and more replication is needed, taken together, the results shown in Tables 2 and 3 are strongly suggestive of sizeable effects of socialization and cultural beliefs about gender. These effects tend to exceed, in point estimates of quantitative magnitude, the sizes of the effects associated with sex difference per se (shown in Table 1). It may be doubted, then, whether the explanation of empirical sex differences (when they occur) requires hypotheses about metaphysical "essences." In most of the studies summarized in Table 1, no attention was paid to cultural or framing/priming effects. Determining the extent to which the differences found in such studies could be explained by differences in cross-cultural beliefs about gender, rather than sex per se, thus would require new research and/or replication with careful attention to these factors. Digging for Difference? As pointed out earlier, the fact that the hypothesis of different male and female essences is considered plausible (or even as definitively convincing) society-wide, can be expected to possibly lead to instances of confirmation bias. Combined with the fact that academic culture encourages the publication of only statistically significant differences, one may expect to see "differences" in the direction indicated by prior beliefs exaggerated in published studies. This is, in fact, what our review found. The purpose of this essay is to point out profession-wide tendencies to diverge from the goal of objectivity, due in large part to commonly shared cognitive biases. The specific references in the discussion that follows, then, should be considered simply as examples of how a whole literature can drift in a particular direction due to widespread (though possibly erroneous) cultural beliefs, and not as accusations of failure on the part of individual authors. Inaccurate citations of earlier literature In reviewing the literature, one economics article states that "Previous surveys of economics…and psychology (James P. Byrnes, David C. Miller, and William D. Schafer 1999) report the same conclusions: women are more risk averse than men in the vast majority of environments and tasks" (Croson and Gneezy 2009, 449, emphasis added). Another article cites Byrnes, Miller et al. (1999) as demonstrating that "females’ lower risk preferences and less risky behavior is robust across a variety of contexts" (Eriksson and Simpson 2010, 159, emphasis added). In fact, what Byrnes, Miller et al. (1999) actually concluded, after surveying studies of 322 different effects, was that "the majority losing manhood status in other people’s eyes leads them to compensate (or perhaps overcompensate) by taking greater risks and seeking immediate rewards" (Weaver, Vandello et al. 2012, 9). (i.e., 60%) of the effects support the idea of greater risk taking on the part of males" and "a sizable minority (i.e., 40%) were either negative or close to zero" (Byrnes, Miller et al. 1999, 372). Overemphasis on difference within a study's own results In another study (Arano, Parker et al. 2010), a difference between married men and married women in the expected direction was highlighted in the text (Arano, Parker et al. 2010, 153), even though it was statistically insignificant. Meanwhile, differences between single men and single women went in the opposite direction. (That is, the point estimate of d was negative, though also not statistically significant). Regression analysis was then pursued on the married subsample and, with the addition of various covariates, a statistically significant regression coefficient on gender in the expected direction was found. No further investigation of the single subsample was reported. In another study (Beckmann and Menkhoff 2008), the difference between male and female subjects on the most direct measure of risk aversion was statistically significant in only one of the four countries studied, and then only at a 10% significance level. Considering two other less direct questions as well, differences in only 5 out of 12 measures (four countries by three questions) were statistically significant (four at the 10% level and one at the 5% level). In a later section of the paper, it was found that females were statistically significantly more likely than males, on average, to increase investment risk taken on, under certain circumstances (378). Rather than taking this as evidence of possible higher male risk-aversion on average, a convoluted explanation was presented to justify this result as due to a greater presumed preference for conformity on the part of women ("strong ambition to stick close to the benchmark's performance" (Beckmann and Menkhoff 2008, 378)). While the data used in the study would seem to suggest that the evidence for greater female risk aversion is, at best, mixed, the article concludes that the data reveal "a victory for gender difference" and (367) "robust gender differences" (379) in the direction of women being "significantly more risk averse" (379). Another study notes a "striking gender difference" in probability weights calculated from a combination of data and a particular theoretical framework, while skipping quickly over the fact that the distribution of men and women in major decisionmaking types was found to be "quite similar." (Bruhin, Fehr-Duda et al. 2010, 1402). While the discussion of the "striking gender difference" goes on for several pages, the practice of showing confidence bands—established in earlier sections of the article—is suddenly dropped. Earlier work on some of the same data (Fehr-Duda, Gennaro et al. 2006) had noted that male and female confidence bands for probability weights overlapped in 3.5 of the 4 treatments studied. Another study reported, based on survey data, that "Women are significantly less willing to take risks than men in all domains." (Dohmen, Falk et al. 2011, 535) (d≈+.40, IS >.80). The same study, however, also included a field experiment with hundreds of subjects. An analysis of that data reveals only a marginally statistically significant difference by sex on one risk question (d=.17, IS = .88, p=.07) and no statistically significant sex difference (d=.05, IS = .90, p=.60) on the other. The published article does not report these weak to non-existent results. In yet another study, findings of sex differences, in the aggregate, on one variable of interest were highlight throughout, while the lack of any statistically significant difference in a risk experiment was relegated to a footnote (Gneezy, Leonard et al. 2009, 1652). Failure to consider confounding variables While a number of studies mention the possibility that social factors may explain some of their results, these were usually not investigated. The experimental studies reviewed here, did not, in general, provide sufficient information about the experimental set-up for a reader to determine whether the sorts of cultural gender factors identified by Carr and Steele (2010)—e.g., asking about gender early on, or describing an exercise as mathematical—could have been important. Future articles could be improved by reporting these details. In addition, considering how many of the studies deal with investment behavior, it is notable that few discuss the role of investment advice. A long tradition of treating "widows and orphans" (de Goede 2004) differently from male investors, as well as stereotypes about the presumed risk-aversion of female investors (Schubert, Brown et al. 1999, 385; Eckel and Grossman 2008, 15) may contribute to differences in average investment patterns, independent of investors' own inclinations. Policy recommendations based on Mars-vs.-Venus stereotypes Some studies base broad policy recommendations for women and men as generic categories on weak evidence about differences in aggregates. Two articles, for example, recommend special treatment for women investors and women investment advisers. In one, it was concluded that due to women's greater risk aversion, "female fund managers may be better suited to female customers who share their pattern in behavior than do men" (Beckmann and Menkhoff 2008, 381). This was in spite of finding mixed directions of the effect, no statistically significant difference larger than d=.5, and many cases of weak-to-no statistical significance. The results from the single statistically significant case (country) in which the difference in the means of the risk variable was statistically significant, in this study, were shown in Figure 3 (above, d ≈ .4, IS ≈ .7). A simulation based on those numbers, however, reveals the following: If we assume that female clients have the same distribution of (presumed) risk preferences as female fund managers (measured on a 6-point scale), the chance of a randomly selected female client being matched on risk aversion with a randomly selected female manager is only 37.5%. Women do not appear to have, as a group, just one “pattern of behavior.” If the randomly selected manager is, instead, male, the chance of a match is not much lower, at 25%. In fact, the chance of a very risk averse female (i.e., one who selected one of the two lowestrisk options) being matched with manager of same risk aversion measure would actually be slightly higher if the manager were randomly taken from male pool than from the female pool (17% vs. 15%). A second article also recommended pairing female investors and advisors, even though IS values on the responses to risk questions can be calculated as exceeding .90 (Olsen and Cox 2001). It would seem that following the authors' recommendations would be a far inferior way of assigning fund managers to clients than simply asking the individuals about their risk preferences. Examination of a narrow range of risks The variety of types of risk studied is also quite limited, with lottery, gambling, and investment scenarios dominating the economic analysis. To what extent do these measure attitudes towards "risk"? Many authors seem to assume the existence of a general sex-identified riskaversion utility parameter applicable to all contexts—in one case, for example, hypothesizing that risk tendencies observed in lottery choices could be extrapolated to preferences concerning marriage and the afterlife (Hartog, Ferrer-i-Carbonell et al. 2002, 16). Other studies examine somewhat broader phenomena such as driving behavior or perceptions of environmental hazards. The studies that claim that "women are more risk averse than men," however, do not in general include in consideration areas of life in which women on average take on elevated risks relative to men, for example in pregnancy and childbirth or in relation to domestic violence. The primary focus on lottery-type scenarios tends to draw attention towards situations of Knightian "risk," in which both payoffs and probabilities are known. "Uncertainty" is often narrowly interpreted in the literature as describing a case in which probabilities are not known, though the payoffs still are. Situations concerning the true sort of uncertainty generated simply by the fact that human beings live in a complex world that generates an unknown future, receive less attention. Yet unforeseen events— e.g., new inventions, bursting asset bubbles, or negative environmental consequences— regularly surprise us, and can be of very large economic consequence (Randall 2009; Taleb 2010). It may be argued that lottery experiments have the advantage of being more amendable to study, but if a focus on tractability drives economists to only "look under the lamppost" in studying risks, any generalization to larger-scale real-world concerns should be considered epistemologically suspect. Policy Implications If the economics literature has encouraged—or at least permitted the continuation of—exaggerated beliefs in the existence of greater risk-aversion among women among the public and among policy makers, what difference does this make? One case has already been mentioned: women may end up with inappropriate investment advice, or women fund-managers may end up with an unnecessarily restricted base of clients, if their sex—rather than their actual preference—is taken as a signal of their investment priorities. A perception of greater risk aversion on the part of women may also lead to labor market discrimination, if women are assumed to be uninterested in occupations that involve high levels of risk-taking (Schubert, Brown et al. 1999). The ability of women to combat discrimination may also be compromised if labor market outcomes come to be explained away as a natural consequence of women's (inaccurately presumed) relative timidity, when discrimination is the actual cause. The policy implications are wider than this, however. In the economics literature, having a relatively higher degree of risk aversion is nearly universally interpreted as a defect. Greater risk aversion is associated with an inability to "rationally" play lottery experiments (in an expected utility sense); with inadequate retirement portfolios (Bernasek and Shwiff 2001; Arano, Parker et al. 2010, 147), with neuroticism and a lack of ambition (Borghans, Golsteyn et al. 2009, 655); with an inability to advance in employment or entrepreneurship (Hartog, Ferrer-i-Carbonell et al. 2002, 24; Lindquist and Säve-Söderbergh 2011, 158; Booth and Nolen 2012, F56); and with a general tendency to let outdated, evolved habits get in the way of functioning well in modern societies (Eckel and Grossman 2002, 291). 20 The implication seems to be that men set the norm on risk behavior, to which women would do well to aspire. On the other hand, the psychology, literature tends to examine both behaviors is which risk-taking has positive consequences and in which it has undesirable or dangerous consequences, such as reckless driving, smoking, or risky sexual behavior (Byrnes, Miller et al. 1999). This literature notes that risk-taking may "either be adaptive or maladaptive" (Byrnes, Miller et al. 1999, 368) and that risk-takers may be seen as either "heroes or fools" (Ronay and Kim 2006, 397). Too little risk aversion, it is noted, may be associated with "unrealistic illusions of control" that "suppress the feelings of anxiety that might otherwise serve to warn of danger" (Ronay and Kim 2006, 413). An arguably even greater social harm, then, may come from reinforcing the stereotype of men as relatively more risk seeking. To the extent it is believed that "real men" should ignore risks and charge ahead, and cultures in the top leadership levels of business, finance, and government remain disproportionately masculine, decisions that lead to socially-excessive levels of risk may result (Ronay and Kim 2006, 415). Could the financial crisis that began in 2008 be attributed, at least in part, to issues of sex and gender? In the wake of the crisis, several commentators asked whether women leaders would have prevented it, or whether it would have happened "if Lehman Brothers had been Lehman Sisters" (Kristof 2009; Morris 2009; Lagarde 2010). The evidence reviewed in this essay suggests, however, that the biological sex of the financial decision-makers or regulators is likely not the most important factor. Rather the onesidedly masculine culture of much of the financial world, in which displays of prowess in stereotypically masculine-associated activities such as aggression and risk-taking are the 20 A notable exception to this tendency is Barber and Odean (2001) which looks at a downside of "male" behavior—in this case an empirical tendency of men to trade stock more often, on average, than women, and thus reduce their returns. The authors interpret this as a sex-based difference in "overconfidence." norm, may be more at issue. Such a macho culture has been well-documented in terms of masculine sexual imagery and sexual harassment (Chung 2010; McDowell 2010), and also, more recently, displayed in the increasing prominence of stereotypically masculineassociated technocratic and mathematical activities, such as modeling the values of financial derivatives (de Goede 2004, 207). 21 Since social identity theory predicts that exaggerated masculine-associated behavior may be most pronounced in all-male groups, greater prominence of women leaders in fields such as finance could play an important role in stabilizing the economy, for reasons quite other than any presumed innate riskaversion. Were Wall Street firms and regulatory agencies such that they welcomed women and men as equal participants, this might indicate that societal gender stereotypes were breaking down. It might also be likely, then, that certain valuable characteristics and behaviors commonly stereotyped as feminine—such as carefulness—would be encouraged industry-wide, and certain inappropriate, reckless behaviors currently practices would be frowned upon, to the benefit of the industry and society. An additional area in which greater risk-aversion could arguably be socially beneficial is the area of environmental policy, particularly as regards climate change. By assuming high discount rates, continuing steady GPD growth (by simple extrapolation), and infinite substitutability between resources, economists such as Nordhaus (2008), and Tol (2009) have painted a picture of a relatively controllable, rich future, even in the presence of climate change, and thus see rather little present need for ethical concern or mitigation action. Their intellectual framework has been adopted in recent U.S. governmental discussions of the social cost of carbon (U.S. Department of Energy 2010). Sunstein (2002-2003; 2005), the Administrator of the White House Office of Information and Regulatory Affairs, has written very dismissively about the Precautionary Principle advocated by many environmentalists (Randall 2009), advocating only very modest action on climate change. This is in sharp contrast to the emphatic advocacy coming from many scientists (and some economists) that swift and dramatic action is necessary to prevent further environmental and social damage (American Association for the Advancement of Science 2009; Union of Concerned Scientists 2010). Could it be that the continuing close adherence between mainstream economics models and methods and cultural norms of masculinity (Nelson 1992) has served to create "unrealistic illusions of control" (Ronay and Kim 2006, 413; DeMartino 2011, 193; Nelson in press)? As in the financial crisis case, the empirical work reviewed in this essay suggests that it would not be so much the presence of women in policy-making circles that would, through some innate tendency towards anxiety, lead to different sort of policies. Rather, a more accepting attitude towards women in leadership might also signal a breakdown of gender stereotypes that could cause a re-valuation of appropriate precaution and carefulness on the part of all decision-makers. 21 Mathematical abilities is another area in which generic statements such as "Men are more able in math" have created an exaggerated public perception of "difference." Else-Quest, Hyde et al. (2010), in an international meta-analysis, find a range of effect sizes for math achievement of -0.42 to 0.40, with a mean d<0.15. Conclusion The statement "women are more risk averse than men" is fundamentally a metaphysical assertion about unobservable essences or characteristics, and therefore cannot be empirically proven or disproven. A review of the empirical literature, with attention paid to the misleading nature of generic beliefs and statements, the proper interpretation of statistical results, and the quantitative magnitudes of detectable differences and similarities, sheds doubt on whether statements such as these should have any place in an empirical science that aspires to objectivity. The widespread acceptance of such statements appears to perhaps be rooted more in confirmation bias than in reality. In regards to future empirical work, the present essay suggests that more attention to the quantitative sizes of differences and similarities, and a more careful interpretation of aggregate results, could improve economists toolbox, and suggests the expanded use of two such mathematical tools. In regards to issues of risk, it is argued that exaggerated and stereotyped beliefs in the existence of sex-based differences may lead to suboptimal results in economic efficiency and equity. These may arise both through discriminatory treatment and through the encouragement of excessive risk-taking in important economic domains such as finance and the environment.