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Julie A. Nelson, Gender and Risk-Taking: Economics, Evidence, and Why the Answer Matters

Cordelia W. Reimers
p. 375-380
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Julie A. Nelson, Gender and Risk-Taking: Economics, Evidence, and Why the Answer Matters, London and New York: Routledge, 2018, 144 pages, ISBN 978-113828401-2

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1As I started to write this review, I happened to read a book review by Hannah Fry in the September 9, 2019 issue of The New Yorker of David Spiegelhalter’s new book, The Art of Statistics. Among other things, Spiegelhalter highlights the pitfalls in the standard practice of using Fisher’s p-test to reject a hypothesis that a result has occurred by chance. The conventional threshold for this “statistical significance” is p < 0.05. This means that in 20 samples, or trials of an experiment, one that rejects the “chance” hypothesis will occur simply by chance! Moreover, this problem is not resolved by setting a lower threshold, say p < 0.01 or even p < 0.0001. If one repeats an experiment enough times (or has a large enough sample), one is bound eventually to find evidence of a “statistically significant” effect, simply by chance. As Fry puts it, “With a threshold of only five per cent, one in twenty studies will inadvertently find evidence for nonexistent phenomena in its data.”

2This problem has raised doubts about published research results, especially in medicine and psychology (perhaps because follow-up studies are more common in those fields). Fry refers to one review that found that 16 percent of the conclusions of the most cited medical publications in 1990-2003 were contradicted by subsequent studies. In psychology, attempts to reproduce “statistically significant” results that were reported in published experiments failed an astonishing 61 percent of the time.

3According to Fry, several remedies have been proposed for this problem. First, scientists should avoid “fishing” for significant results, by declaring their hypothesis in advance. Second, studies designed to replicate others’ results should be valued more highly by publishers and those who determine hiring, promotion, tenure, grants, and salaries. Third, focus should be shifted to the size of the effect from whether the p-value crosses some arbitrary threshold.

4In her book Gender and Risk-Taking: Economics, Evidence, and Why the Answer Matters, Julie Nelson amplifies this critique of current statistical practice as she applies it to economists’ research on gender differences in risk aversion. This book consists of three parts:

  1. A primer on statistical methods and their interpretation for describing differences and similarities between groups;

  2. A comprehensive interdisciplinary review and evaluation of the empirical literature on gender differences in risk aversion;

  3. A critique of the tendency to divide human activities and personality traits into binary categories: masculine/feminine.

5The first part of the book is a must-read for any social scientist who wants to measure differences between groups. It describes the methods used to describe differences and similarities in risk aversion between men and women, but its applications go far beyond gender differences and risk aversion. The methods described are drawn from psychology and economics. They apply to comparisons between any two groups—whether based on race, ethnicity, national origin, nativity, citizenship, age, education level, or region—and on any dimension—income, earnings, labor force status, health, or personality traits.

6Nelson provides an extremely clear explanation of the methods for comparing groups’ characteristics, written at an undergraduate level and thus accessible to anyone with some understanding of statistics. The book is available in paperback and e-book formats, and the short chapters make it ideal for teaching. Part I should be assigned to students in every statistics course.

7Economists have been rather obsessed with finding a gender difference in risk aversion. Nelson provides a thorough-going critique of their common practice of focusing on the difference in group averages and treating a statistically significant difference, no matter how small, as substantively important. (Statistical significance, after all, depends on sample size as well as the threshold chosen for “significance.”) Results are often reported carelessly, in “essentializing” language that implies all members of each group are alike and share that difference. For example, “women are more risk-averse than men,” rather than “we found a statistically significant difference between the means of the male and female distributions of risk aversion.” Nelson calls the former “gender difference at the individual level (GDI)” or “categorical gender difference” and the latter “gender difference at the aggregate level (GDA).” GDA differs from GDI in that there is variation (i.e., a distribution) within each gender as well as between genders; some individuals from each group are similar to each other (i.e., the distributions overlap); and the difference is between distributions, not individuals.

8Nelson emphasizes that the entire distributions of a characteristic within each gender, not just the averages, should be compared and the amount of overlap as well as difference between the distributions reported. She explains the methods that are used by psychologists to measure similarity as well as difference between groups: the Index of Similarity (IS, the share of women who could be matched with a man with the same score), Cohen’s d (which expresses the cross-group difference between means relative to the within-group variation), and the Common Language Effect Size (CLES, the probability that a randomly chosen man would score higher than a randomly chosen woman).

9In the second part of the book Nelson undertakes a comprehensive interdisciplinary review of the literature on gender differences in risk aversion, from economics, psychology, and other social sciences. She presents the results of 35 studies—Cohen’s d for 34 of them and the Index of Similarity (IS) for 13. Cohen’s d is positive and statistically significant (at a generous 10 percent level, indicating greater female risk aversion) in only 14 (40 percent) of the studies. Cohen’s d is greater than +0.5 (half a standard deviation) in only five (1/7), and greater than +1.0 in only two. The IS values range from 0.60 to 0.98, meaning that at least 60 percent of the women could be paired with a man with an identical degree of risk aversion.

10She also obtained and re-analyzed the data from 37 studies that employed an “investment game” to measure risk preferences. In such a game the measure is the amount chosen to invest in a risky asset vs. a “sure thing.” She was able to compute t-statistics and p-values for the difference between the means for men and women, confidence intervals for Cohen’s d, and the Common Language Effect Size. In only 12 (32 percent) of these studies was there a statistically significant gender difference at all, and only two had a Cohen’s d above 2.0. (By way of comparison, d=2.6 for the gender difference in heights). She concludes that “a hypothesis of GDI (categorical gender difference) was soundly rejected in all cases.”

11Nelson goes on to ask why there nevertheless appears to be a small difference in measured risk aversion between men and women on average. (The average of the eight most precise estimates of d = +0.13.) She attributes this to cultural norms and “framing” effects, and emphasizes context as an important factor that influences the measurement of risk attitudes. In support of this view she cites studies showing that stereotype threat, position in a power hierarchy (white males vs. everyone else), whether respondents are in a single-sex or co-ed school, cultural differences across countries, or priming respondents to think about gender, all had effects on measured risk aversion within gender that are larger than the measured difference between males and females. She suggests that investment portfolios may differ by gender due to men and women receiving different investment advice as a result of stereotyping, not to their own preferences. Nelson criticizes economists for ignoring such factors.

12She presents evidence that stereotypes affect the behavior of analysts as well as respondents. In article titles and conclusions, researchers tend to highlight results showing a gender difference and ignore those showing no significant difference. When reporting results, they often slip into language implying that a difference in the average applies to each individual man and woman. This is the phenomenon known as “confirmation bias,” in which, believing a priori that women and men are fundamentally different, researchers emphasize empirical results that confirm this prior belief and avoid information that conflicts.

13These tendencies are exacerbated by the academic publication system. Articles that find a statistically significant difference are much more likely to be favored by editors and referees. This “publication bias” is revealed by a “funnel” diagram, in which Nelson plotted the results of many published studies, with Cohen’s d on the horizontal axis and the precision (i.e., the reciprocal of the standard error) of the estimate on the vertical axis. Since the best estimates of d are close to zero, sampling variation implies that such a diagram, if it included every analysis of the data, should look like an inverted funnel; i.e., symmetrical about the vertical axis. However, Nelson’s funnel diagram of the published results has few points with both precision and d close to zero, indicating that those non-significant results did not see the light of publication. Beyond that, her diagram is lop-sided; there are many more points with positive d (indicating that men have a higher risk preference) than negative d. Apparently results with the “wrong” sign were usually not published, either.

14Another reason to doubt the economists’ conclusion that “women are more risk-averse than men,” even on average, is that “risk” as measured by economists is extremely narrowly defined, in terms of investment decisions, lotteries, and gambles. The excuse for this one-dimensional definition is the desire to measure “risk aversion” precisely, but it leaves out whole areas of human experience. The risks faced by women in marriage, pregnancy, and childbirth are arguably greater than those voluntarily taken by men. To generalize from any of the results in the economics literature to a supposed difference between men and women in overall attitudes toward risk is totally unwarranted.

15In the last part of the book Nelson broadens her scope to ask why the “essentialist” stereotype about a gender difference in risk aversion matters. First, it leads to decisions that are not only unfair to individuals, but they are also inefficient from an economic point of view. The overlap between the distributions is so great that knowing a person’s sex adds very little to a prediction about their degree of risk aversion. “Statistical discrimination” might be efficient if knowing someone’s sex provided information about their attitudes that could not be obtained cheaply in another way. But employers could simply do the same thing researchers do – ask!

16In her final chapters, Nelson attacks the habit in Western culture of “binary” thinking, which divides human activity and personality traits into separate “masculine” and “feminine” spheres. This discussion draws on her earlier work in feminist economics. Business, finance, and the market have been seen as “masculine” and reserved for men; while home, family, and caregiving are “feminine.” Rationality is “masculine”; emotions are “feminine.” Risk-taking is “masculine”; caution is “feminine.”

17The division of knowledge and university departments into separate disciplines has not helped. John Stuart Mill originally defined economics as a separate discipline that would study “economic man” as rational, independent, self-interested and a-social. This has excluded huge areas of human experience from the purview of economics, with those other areas reserved for the other social sciences. Emotions that accompany risk-taking, such as hope and fear (and Keynes’ “animal spirits”), have been excluded from economists’ analyses. This narrow model has made stereotypes about women’s supposed risk aversion seem so obvious to economists that they have largely found what they were looking for.

18Nelson argues that the binary contrast, risk-loving/risk-averse, is too simple. A better comparison, between adventurous and cautious, has both positive and negative dimensions. “Adventurous” (or risk-loving) may be brave or reckless; “cautious” (or risk-averse) may be careful or timid. And being brave does not preclude being careful! She observes that successful business and political leaders need to combine traits from both sides of the false “masculine/ feminine” binary. Fear of the feminine can lead to recklessness among men who buy into the false binary.

19In conclusion, Nelson argues that having more women in leadership positions is important, not because women are “essentially” more risk-averse than men (a false assumption), but because it reflects a breakdown of gender stereotypes, so encourages appropriate caution among all decision-makers, both male and female. And economics would be better able to discover reliable knowledge about the real world if it did not restrict itself to formal, mathematically tractable models of “rational man.”

20I am among the many social scientists who have spent a great deal of time and effort analyzing inter-group differences in means. After reading this book I am convinced that we should be comparing whole distributions, not just group means. But this raises a deeper question: Why do we treat racial, age, education, or gender groups as “real” things, anyway, that have traits and behaviors (beyond those used to classify the group)? If the groups are heterogeneous and the distributions overlap, why is the inter-group difference of interest? Analysis can explain some of the raw difference, but we are still left with an unexplained difference that too easily leads to “essentialist” stereotyping. What do we learn that is useful, other than to practice statistical discrimination (which is unfair to individuals)? That is a subject for another essay.

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Cordelia W. Reimers, « Julie A. Nelson, Gender and Risk-Taking: Economics, Evidence, and Why the Answer Matters »Œconomia, 10-2 | 2020, 375-380.

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Cordelia W. Reimers, « Julie A. Nelson, Gender and Risk-Taking: Economics, Evidence, and Why the Answer Matters »Œconomia [En ligne], 10-2 | 2020, mis en ligne le 01 juin 2020, consulté le 22 avril 2021. URL : http://journals.openedition.org/oeconomia/8123 ; DOI : https://doi.org/10.4000/oeconomia.8123

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Cordelia W. Reimers

Hunter College and the Graduate School of the City University of New York. creimers@hunter.cuny.edu

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