Monday, 31 January 2022

The effect of gender matches in the student-advisor relationship

Over the last week, I have posted a series of posts focused mainly on the gender gap in economics (most recently here). Just prior to that, I posted on the impact of student-teacher gender matches on academic performance. However, relationships with teachers are not the only relationships that matter for student performance. In some universities, freshman students are allocated to an academic advisor, and many view this as best practice in ensuring a smooth transition from high school to university. Given the apparent importance of gender matches with teachers, it is worthwhile considering whether gender matches with academic advisors matter for students' academic performance as well.

That is the research question that is addressed by this 2021 article by Takao Kato and| Yang Song (both Colgate University), published in the journal Economic Inquiry (sorry, I don't see an ungated version online). Their data covers all students enrolled from 1996 to 2015 in a selective liberal arts university in the US (which they refer to as LiberalArtsU), which:

...requires every student to take a FYS [first-year seminar] course during their first semester. The instructor of the FYS course automatically becomes their academic adviser and remains the adviser until the student declares their major, which often happens in the second semester of the sophomore year. These FYS courses differ from a standard introductory‐level course in two ways. First, the class size is slightly smaller to limit the advising burden on the instructor, as well as to foster a community‐building environment. Second, the course is required to have a few components to help with high school to college transition, such as teaching students about plagiarism, library resources, and writing skills.

Kato and Song's dataset includes over 14,000 students, with just over half being female. Like many studies of this type, selection bias could be an issue if students could choose their advisor (or their advisor's gender). However, in this case:

...the incoming student makes the course preference list without knowledge of the instructor gender. As such, no student can select the gender of their FYS instructor and therefore the gender of their adviser. Yet, students could influence the odds of having the same‐gender adviser indirectly through FYS course subject choice, as certain subjects have a higher proportion of female professors than others.

So, controlling for the FYS that a student is enrolled in is important, and will deal with residual selection issues. In terms of outcome variables, Kato and Song look at four-year retention in study, GPA, and post-graduation outcomes (that is, whether the student was employed or enrolled in graduate school, rather than unemployed). Looking at retention first, they find that:

The magnitude of the effect on 4‐year retention rate is modest yet meaningful. On average... around 90.5% of all students were retained for 4 years or completed their Bachelor's degrees at LiberalArtsU. Matching female students with female advisers is found to raise it to 93.95%.

You could look at that as a 3.45 percentage point increase in retention, or a 3.8 percent increase. Alternatively, you could recognise that the attrition rate (the proportion of students who are not retained) is 3.45 percentage points lower for female students matched with female advisors, and this is a 36.3 percent decrease in attrition - I wouldn't describe that as modest! Kato and Song then demonstrate that most of the effect is concentrated in retention in the first two years of study (which is not surprising, since most attrition occurs in the first year of study).

Moving onto the effect of gender-matching female students with female advisors on GPA, Kato and Song find that the effect is:

...positive and significant at the 1% level, pointing to the presence of the positive gender match effect on the intensive margin. The size of the gender match effect on cumulative GPA amounts to about 7.8% of a standard deviation...

That's larger than it sounds, and interestingly, Kato and Song demonstrate that it isn't concentrated in first year papers, so it is persistent throughout the students' degree study. Then, looking at post-study outcomes, Kato and Song find that the effect: small and not at all significantly different from zero, pointing to the absence of the gender match effect on the post‐graduation early labor market outcome, or whether students are employed or not within 6 months after graduation...

So, female students matched with female academic advisors are more likely to be retained in study, and perform better in their studies, but are no more likely to be employed or in graduate study after graduation. However, the story doesn't end there. Kato and Song look at whether the effects differ by student academic ability (based on their high school GPA), and find that:

...the gender match effects both on the extensive and intensive margins are mostly larger and more significant for students with below‐median high school GPA than for students with above‐median high school GPA. In particular, the gender match effect on the intensive margin (cumulative GPA) is statistically significant only for students with below‐median high school GPA... This suggests that for relatively more college‐ready students, adviser-student gender match has little impact on their decision to pursue further education in graduate schools. For relatively less college‐ready female students, however, having female advisers is proved to be instrumental in making them pursue graduate education rather than immediate employment.

So, the effects on retention and GPA are concentrated among less college-ready students, and those female students benefit from a higher probability of going on to graduate school when they are matched with a female advisor. Interesting, Kato and Song then extend these results by looking separately at students in STEM FYS courses and non-STEM FYS courses, and find that the effects are concentrated in the non-STEM FYS courses. On this last point, they conclude that:

...students who took a STEM course as an FYS course, indicating interest and commitment to STEM, do not seem to benefit from gender match in advising.

That may be true, but it is possible to disentangle whether that is because the types of students who choose a STEM FYS are less likely to benefit than students who choose a non-STEM FYS, or whether the types of instructors in STEM and non-STEM FYSs are different. This would require some further analysis, which Kato and Song do not undertake.

That points to a more general problem with this research, which Kato and Song acknowledge. While they are able to show that matching female students to female advisors has positive effects, concentrated among less-college-ready female students, they are unable to explain why. And understanding the mechanism is important for knowing whether these results would replicate in other contexts.

Sunday, 30 January 2022

The gender gap in preferences and work aspirations

I've written a number of posts about the gender gap in economics over the last week (see the latest one here), and many more earlier about the gender gap in STEM and in economics. The underlying premise of all the research on the gender gap is that it is something that requires fixing. However, if you reflect on that for more than a moment, the idea that the gender gap is something that can be (or should be) fixed is somewhat disquieting. It involves over-riding the preferences and intentions of young people, encouraging more young women (or fewer young men) to persist in (or change their intentions) towards studying and working in STEM or economics. Such paternalism implies that 'we' (being those of us with the power to enact change) know better than young people do, how and where they should be developing and applying their talents, and that should make us uncomfortable.

Two recent research papers suggest that there is an underlying basis for the gender gap, and that it will take more than simple interventions to address. The first research paper is this NBER Working Paper by Angel Cuevas (Universidad Carlos III de Madrid) and co-authors (ungated version here). Cuevas extract data from the Facebook marketing API (which itself seems to be a fascinating data source and well worth exploring) on the number of Facebook users in each country (and of each gender) that Facebook categorises as having particular interests. In total, Cuevas et al. catalog 45,397 such interests, and then look at the proportions of each gender having each interest. They then:

...differentiate between gender-related and non-gender-related interests. We say that an interest is gender-related if it displays a systematic bias toward the same gender across the globe. More specifically, if in more than 90% of countries an interest is more prevalent among the same gender, then we refer to it as gender-related. For example, "cosmetics" and "motherhood" are universally more common among women, whereas "motorcycles" and "Lionel Messi" are universally more common among men. Conversely, we say that an interest is non-gender-related if its gender bias varies across countries. More specifically, if an interest is more common among men in at least 30% of countries and more common among women in at least another 30% of countries, then we refer to it as non-gender- related. For example, "world heritage site" and "physical fitness" do not display a systematic gender bias across the globe.

They then look at how the difference in interests between men and women relates to a country's level of gender equality (based on the World Economic Forum's Gender Gap Index). They find that there is:

...a sharp distinction between gender-related interests and non-gender-related interests. More gender equality is associated with greater differences between men and women for gender-related interests, whereas the opposite is true for non-gender-related interests.

This is illustrated nicely in Figure 4 from the paper:

The panel on the left shows the relationship between gender equality (on the x-axis) and gender differences in gender-related interests (on the y-axis). The upward-sloping trend line demonstrates a significant positive relationship, so more gender equality is associated with greater gender differences in these interests. The panel on the right shows the opposite for the relationship between gender equality and differences in non-gender-related interests.

What might explain this? Cuevas et al. outline two competing theories for the relationship between gender equality and gender interests, and note that both could simultaneously be true:

The debate on whether greater gender equality should enhance or mitigate preference differences between men and women has often been framed in terms of two competing theories. Evolutionary psychology argues that more gender equality allows men and women to more freely express their innate predispositions, leading to widening preference differences. In contrast, social role theory claims that more gender equality allows breaking down socially constructed barriers between men and women, leading to narrowing preference differences. This suggests that there is no reason why there should be a one-size-fit-all theory. Instead, evolutionary psychology should apply predominantly to innate preferences or interests, whereas social role theory should apply predominantly to socially constructed preferences or interests.

For an interest to be innate to gender, we claim that it must display a systematic bias toward the same gender across the globe. Viewing this as a necessary condition, we can interpret our gender-related interests as potentially innate. By the same token, interests that do not display such a systematic bias cannot be innate to gender. Hence, non-gender-related interests must be socially constructed. This argument provides us with a mapping from gender-related and non-gender-related interests into innate and socially constructed interests. Using this mapping, the paper's main finding is consistent with both theories: more gender-equal societies display greater differences between men and women in gender-related (innate) interests and smaller differences in non-gender-related (socially constructed) interests.

So, in trying to address the gender gap in STEM or economics by trying to change preferences for STEM or economics, we may simply be pushing against the tide, especially in countries with more gender equality, and even more especially in countries that are becoming more gender-equal.

The research paper is this one by Gijsbert Stoet (University of Essex) and David Geary (University of Missouri, Columbia). Stoet and Geary use data from the 2018 PISA survey of over 470,000 high school students across over 80 countries, focusing on students' answers to a question about their occupational aspirations when they are 30 years old. Stoet and Geary classify:

...these occupations as being "things oriented", "people oriented", or "other"... as well as being STEM or not. Things-oriented occupations are those that involve extensive work with machines, such as computer programming, repairing machines (e.g., cars), or tailoring, whereas people-oriented occupations involve beneficial face-to-face interactions, as in medicine or teaching.

Of course, there are some occupations that are difficult to classify, and some that fit across both classifications. Nevertheless, Stoet and Geary look at the gender ratio of occupational aspirations across countries and its relationship with gender equality (also using the same Gender Gap Index as Cuevas et al.). They find that:

In all 80 countries and economic regions included here, adolescent girls were more likely to aspire to a people-oriented than a things-oriented occupation (and vice versa for boys)... Further, we found that this sex difference is larger in countries with greater empowerment of girls and women, consistent with a so-called gender-equality paradox, which was previously found in university graduation rates and career choices...

Perhaps surprisingly though, these differences are not due to differences in occupational aspirations for girls:

We found that the latter correlations are mostly due to an increase in boys’ aspirations to enter things-oriented blue-collar careers and a decrease in boys' aspirations to enter people-oriented careers in countries with greater women's empowerment. In contrast, the percentages of girls aspiring to things-oriented jobs or people-oriented jobs did not systematically vary with national-levels of girls' and women's empowerment.

When they categorise occupations as 'sex-typical' and 'sex-atypical', Stoet and Geary find that: aspirations were more common in countries with greater levels of women's empowerment.

This is at least as surprising as the results from the Cuevas et al. paper. Stoet and Geary suggest that:

Our interpretation of this result is that increased levels of women's empowerment increases national wealth. The increased levels of national wealth contributes to a situation in which students can aspire to careers that fit their interests rather than being largely based on economic security. We call this the Counter Intuitive Gender Empowerment Model (CIGEM).

I'm not sure that I fully buy that explanation, since it was based on mediation analysis (which I rarely find convincing). Nevertheless, like the Cuevas et al. results, it should give us some pause. Not only may we be pushing against a tide of gender-specific preferences, but we may also be pushing against a tide of gender-specific work aspirations. And both of those tides are pushing in the same direction, and likely against more gender-equal STEM and economics professions. Should we really be pushing against trends that may be themselves being driven by greater gender equality, by trying to override young people's preferences and aspirations?

Now, having given us reason to re-think whether and how we address the gender gap in STEM or economics, we need to recognise one more thing. That is that any discomfort we feel about taking a paternalistic approach to addressing the gender gap assumes that the status quo, wherein there is a persistent gender gap, is somehow the 'natural order' of things. It's unclear how defendable that assumption is. The persistent gender gap that we observe now has arisen from generations of socially constructed gender differences in aspirations, gender norms, and role models. Perhaps there are gender-based comparative advantages (for example, see here or here), but comparative advantages can be changed with determination and sustained investment (for anyone who doubts that, I offer the example of the transformation of South Korea over time). So, it should not only be possible to change the status quo, but it may be desirable to do so.

Another way of considering the moves to address the gender gap in STEM and economics is that it isn't only about changing preferences, but removing or relaxing the constraints that prevent or restrict participation in the field. So, if we consider a constrained optimisation model of occupational choice, relaxing some of the constraints that hamper participation in particular fields would increase the opportunity set of young people. 

Considering interventions that reduce constraints, rather than changing preferences, gives me greater comfort. It means that, in addressing the persistent gender gap, we are not actually doing a disservice to young female economists, but offering them the opportunity to engage and contribute to the discipline now and in the future.

[HT: Marginal Revolution for the two research papers, here and here]

Saturday, 29 January 2022

Where are we at with the gender gap in economics?

I'm been running a bit of a theme in posts over the last week (see here, and here, and here, and here) on the gender gap in economics. It's also something I have written a lot about in the past (see the links at the bottom of this post). The gender gap in economics has been a problem that has been highlighted for many years. So, it is worth asking, after so many years of trying to address the gap, where are we at?

Two articles in the 2021 issue of AEA Papers and Proceedings give us some answer to that question. The first article is this one by Kelly Bedard (University of California, Santa Barbara), Maxine Lee (San Francisco State University), and Heather Royer (University of California, Santa Barbara). They construct a panel dataset of the:

...salaries for all tenure-track faculty in economics departments at public institutions in the United States ranked in the top 50 by the 2017 US News & World Report rankings... The final sample includes 254 women and 1,102 men.

So, really Bedard et al. are looking at the gender pay gap in economics, rather than the gender gap in employment at the extensive margin (which is what most research has been focused on). They find that:

Among economists with nine or fewer years of experience since earning a PhD, we estimate a 4.5 percent salary gender gap using the baseline model. When the model includes controls for the PhD institution and field of specialization, the gap decreases to 2.8 percent. Then, the gap becomes negligible once we include either the institution’s ranking or institution fixed effects.

In other words, the pay gap between male and female economists within nine years of their PhD is entirely explained by where they completed their PhD, their field of specialisation, and at which institution they are employed. However, we can't necessarily take that to mean that the gender gap is not important, because field of specialisation differs strongly between genders (as I noted here), and male economists tend to go into fields where job prospects and pay are higher.

Also, the pay gap is more apparent among economists who are more senior:

The patterns are similar among economists with 10–19 years of experience. The gender pay gap in the first two specifications ranges between 9 and 9.5 percent, and the gap shrinks to 4.3 percent when the model includes the ranking of the current institution...

Lastly, the current institution’s rank does little to change the gender gap among economists with more than 20 years of experience. The gender gap fluctuates between 10.6 and 12.5 percent in this group.

Bedard et al. also include some longitudinal analysis, following cohorts from five years, and eleven years, after their PhD, and show that female economists appear to be less likely to gain tenure, and less likely to be promoted to full Professor. However, I didn't find those analyses as persuasive as they would be if they looked at the changes over time. So, the best we can say is that, among recent PhD graduates, there is no gender pay gap between individuals in the same field of economics, and the situation appears to have improved from earlier cohorts (especially when you factor in the likelihood of survivorship bias in the data on older cohorts).

The second article, by Donna Ginther (University of Kansas) and Shulamit Kahn (Boston University), takes a broader view and asks, "have we made progress?". Using data from Academic Analytics for all faculty who received PhDs from 2005 to 2011 and are employed by one of over 300 academic institutions in the US, they look at rates of promotion to associate professor. Their dataset includes nearly 800 assistant professors, and follows them through until 2018. Based on Cox proportional hazards models, Ginther and Kahn find that in their sample:

...women were 18.5 percent (p < 0.03) less likely to be promoted to associate professor.

However, they also find that:

Adding productivity measures to the model... somewhat narrows female disadvantage in tenure receipt to 15 percent and lowers its significance (p = 0.08).

So, there is a small and barely statistically significantly lower rate of female economists being promoted to associate professor. However, Ginther and Kahn then look at the difference between research-intensive institutions and others, and find that:

The gender tenure gap was small and insignificant in very high research activity institutions. However, in less research-intensive universities, it was huge, with women’s rate of receiving tenure (with all controls) 46 percent lower than men’s (p = 0.055).

So the negative effect on female economists' promotion to associate professor is concentrated in less research-intensive universities. Female economists in the most research-intensive universities appear not to be disadvantaged to a significant degree. Those results make the positive effects of mentoring on female economists at lower-ranked institutions (see here) even more important to pay attention to, and even more important to follow up on.

My take on these two papers is that they illustrate that things are improving, albeit slowly. The most recent cohorts of female economists appear to be less disadvantaged than older cohorts were, although this change has happened more quickly at higher-ranked institutions and is less apparent at lower-ranked and less research-intensive institutions. As a discipline, we can do better.

Read more:

Wednesday, 26 January 2022

The positive effect of mentoring for female economists

On Sunday, I posted about the disappointing results from evaluations of simple information interventions to reduce the gender gap in economics, based on several papers from last year's issue of AEA Papers and Proceedings. However, not all of the research in that issue had bad news in dealing with the gender gap. This article by Donna Ginther (University of Kansas) and Rina Na (PRA Health Science) evaluated the impact of the CeMENT workshops, on the co-authorship networks and publication outcomes of female economists. To give you some more context about the workshops, Ginther and Na explain that:

The CeMENT Mentoring Workshop for Faculty in Doctoral Programs was designed to provide role models (senior female economists) and peers in one’s research field. The workshop is held immediately after the ASSA meetings and lasts two days. Between 40 and 50 junior faculty attend and are divided into groups of 4 to 5 women in the same field. Two senior female economists in the same field are assigned to mentor each group. Prior to the conference, each woman circulates a research paper that will be read and discussed by the group. In between group sessions, plenary sessions made up of a panel of senior mentors focused on the topics of research and publishing, getting grants, networking strategies, teaching, the tenure process, and work-life balance.

Ginther and Na essentially compare workshop participants with others who applied for the workshop but were not accepted. Their dataset covers the workshops between 2004 and 2016, and includes 512 female economists. They focus their analysis on pre-tenure publications, and the outcome variables measured in 2018, and find that:

Women who participated in the CeMENT workshop published 1.6 more papers (representing a 26 percent increase at the mean), 0.21 additional top-tier papers (representing a 78 percent increase), and 0.96 additional other refereed papers (representing a 16 percent increase), all statistically significant at p < 0.05...

In addition, the CeMENT workshop significantly expanded a woman’s pre-tenure collaborations, adding three additional coauthors relative to the treatment group (a 51 percent increase)... Finally, the treatment group had 43 more citations to pre- tenure publications than the control group (a 45 percent increase).

That all seems very positive. However, when they split their sample into women at institutions ranked in the top 200 and women at institutions ranked outside the top 200 (or an nonacademic institutions), the effects differed. The increase in total publications was larger for women outside the top institutions (1.6 additional publications, compared with 1.3), but this was concentrated in additional publications outside of the top journals and top field journals. The citation impact was also greater for women outside the top institutions (61 additional citations, compared with 16), although the number of additional co-authors was smaller (2.2 additional co-authors, compared with 3.4).

These are important results. This isn't the first time that the mentoring of emerging female economists by established female economists has been shown to have a positive effect (e.g. see here). I think it's particularly important that the effects seem to be larger at lower-ranked institutions, where (as discussed in this article in the same issue of AEA Papers and Proceedings, which I will discuss in my next post) the gender gap appears to be larger and more persistent. Perhaps the most important aspect of this intervention is that it appears to be quite cost-effective (although, it would be interesting to know how much time the intervention did cost the mentors, and whether it impacted negatively, or perhaps even positively, on their research output or research quality).

Read more:

Tuesday, 25 January 2022

Gendered citations of papers in the 'top five' economics journals

Continuing with this week's theme (see here and here) of research on gender from the 2021 issue of AEA Papers and Proceedings, this article by Marlène Koffi (University of Toronto) looks at the gendered nature of citations. Koffi collected data on all 6431 articles published between 1991 and 2019 at the 'top five' economics journals (American Economic Review, Econometrica, the Journal of Political Economy, the Quarterly Journal of Economics, and the Review of Economic Studies), as well as data on over 800,000 articles that cited those top-journal articles. She then categorises the authoring of each article in the top five journals, and notes that:

5,011 articles (77.92 percent) are written by all-male teams, 268 (4.17 percent) by all-female teams, 1,042 (16.20 percent) by mixed-gender teams, and 110 (1.71 percent) are gender undetermined.

Then, looking at citations, Koffi finds: overall positive citation premium (15.5 log points) for articles written by women when controlling for affiliation, number of authors, seniority, and journal-year fixed effects. However, subfield and style controls reduce the coefficient values substantially to insignificant 6.6 log points and 1.6 log points, respectively.

In other words, articles written by all-female research teams get more citations. This isn't a new finding, as I noted in this 2020 post, and may arise either because female researchers are held to a higher standard during the reviewing process (leading them to have to write higher quality articles to get published), or because the types of empirical research that female economists engage in attracts more citations. Given that female economists are more likely to specialise in health (among other fields, as noted in yesterday's post), and health as a field tends to have more citations, that may explain some of the difference. That interpretation is also supported by Koffi's paper, which goes on to find that:

The share of citing papers belonging to economics is, on average, 2 percentage points less for papers written by women.

So, the citation premiums for female economists is not coming from within economics. The most interesting results in Koffi's research, though, are when she looks at the gender composition of citing papers, and finds that:

...women receive a positive citation premium when considering citations from other women, while they tend to receive a negative premium when considering citations made by everyone else...

...the positive female citation premium in economics is almost entirely driven by females citing other females.

Koffi interprets her results as:

On the one hand, they could represent an overcitation of female papers by lesser-ranked journals or other female authors. On the other hand, they could be interpreted as representing an undercitation of females by top-ranked journals or male authors. However, leaning on previous literature emphasizing the higher standards women face in economics, we can interpret those results as additional evidence for women’s lack of recognition by their peers.

However, there is another interpretation, which as I noted above relates to the subfields that female economists work in. If, in the fields outside of economics (such as health), there are more all-female research teams that are citing these papers, then that could also explain these results. In that case, the 'peers' that Koffi refers to are not all within economics. Moreover, even within subfields, differences in the types of research questions and topics that female economists address might also be those that female researchers in other fields are more likely to be interested in (which, again, relates back to yesterday's post). Unfortunately, Koffi doesn't disaggregate her analysis by subfield, which would be a really interesting next step.

Monday, 24 January 2022

Gender differences in fields of specialisation within economics

Following on from yesterday's post about simple information interventions to close the gender gap in economics, the same AEA Papers and Proceedings issue had a couple of articles on gender differences in the field of specialisation within economics, which are worthwhile considering. The first was this article by Nicole Fortin, Thomas Lemieux, and Marit Rehavi (all University of British Columbia), and looks at:

...the placement outcomes of nearly 5,000 economics PhD graduates from 82 US and Canadian institutions ranked among the top 200 in the RePEc rankings who have sought employment through Econ Job Market... between 2010 and 2017...

Their decomposition analysis first shows differences in the types of jobs that PhD graduates of different genders choose, specifically:

...that the largest and most significant gender differences are for research positions.. the combination of assistant professors and CB/MDB positions, where we find 61.4 percent of men versus 55.3 percent of women. Conversely, 11.8 percent of women versus 9.7 percent of men accept postdoctoral positions, and 24.2 percent of women versus 20.5 percent of men are in other nonacademic positions.

There are also substantial differences in the field of specialisation, where Fortin et al. find that:

Women appear to be crowding into a few fields where there are limited positions available. Women are concentrating in the traditionally female fields of health, education, and welfare (I) and labor and demographic economics (J): 28.9 percent of women versus 16.7 percent of men are in these fields...

Women are underrepresented in fields such as macroeconomics, monetary economics, and finance, which have better employment prospects because of more positions outside of academia.  

That isn't too surprising, and accords with earlier research, and also with the second article, by Eva Sierminska and Ronald L. Oaxaca (both University of Arizona), which used data on the fields of nearly 7500 graduate students and nearly 4500 faculty from across 385 universities in the US and overseas. First, looking at students who defended their PhD between 2009 and 2018, they find:

...gender differences in specializations are statistically significant in four fields. Women are more likely to be present in labor/health by 13 percentage points and less likely to be in econometrics, micro, and macro/finance by 2, 3, and 6 percentage points, respectively.

Then, looking at faculty, and separating their results by the year that the academics' PhDs were granted, they find that:

Among those who have completed their PhD prior to 1989, gender differences in specializations are statistically significant in five broadly defined primary fields: econometrics, labor/health, macro/finance, development/growth/international, and other. Women are underrepresented in econometrics and macro/finance (by 2 and 9 percentage points, respectively), and they are overrepresented in labor/health (by 14 percentage points) and other fields (by 3 percentage points). In this earlier period, women were also underrepresented in development/growth/international by 2 percentage points (in later cohorts, they were over represented).

Gender differences in these fields continue to be significant for more recent PhD graduates (except in other). In the group of academic economists who completed their degrees during 1990-2003, an underrepresentation for women occurs in micro by 4 percentage points. The gaps in labor/health and macro/finance slightly diminish (by 1 percentage point).

In the most recent sample of academics, those who completed their degrees between 2004 and 2016, the gaps continue to exist in the same fields and in addition occur in industrial organization (2 percentage points).

So, there are clear gender differences in field of specialisation within economics, and those differences have been persistent over time. What isn't clear from these papers is what contributes to these persistent differences. To what extent is this simply a difference in research preferences (and research topic preferences) between men and women? To what extent is it driven by the fields of specialisation in PhD advisors, and gender matching in advising (more on a related topic in a future post)? Are there differences in the culture of the different sub-fields that make a difference (e.g. see here)? Answering these questions would help us to understand these differences in fields of specialisation better.

Sunday, 23 January 2022

Disappointing results on simple information interventions to close the gender gap in economics

I've written before about simple interventions designed to close the gender gap in economics. For instance, there was this post about an intervention that involved providing students with "information on career prospects, average earnings, and grade distributions", which had reasonably large effects. However, I questioned why providing this information was not routine anyway. Nevertheless, it is worth following up on, and the AEA Papers and Proceedings last year had several papers that described similar simple interventions to reduce the gender gap.

First was this article by Todd Pugatch and Elizabeth Schroeder (both Oregon State University), that tested a variety of information interventions, with students assigned to one of five groups:

(i) Control: no message.

(ii) Basic information: encouragement message based on description of economics major on departmental website.

(iii) Earnings information: basic information, plus information on earnings of economics graduates.

(iv) AEA video: basic information, plus link to AEA career video.

(v) OSU video: basic information, plus link to video testimonials by OSU economics students and alumni.

Their sample is over 2200 students enrolled in introductory economics at Oregon State University, during the 2018-19 academic year. Their main indicators of interest was whether the student was enrolled in an economics major in winter 2020, some two to four semesters after the intervention. Comparing the different treatment groups with controls, they find that:

...basic information increased the likelihood of majoring in economics by 1.9 percentage points, significant at 5 percent... This effect was driven by male students, for whom the magnitude was 2.5 percentage points, also significant at 5 percent... The earnings information increased economics majors by 1.5 percentage points, significant at 10 percent... These magnitudes are similar to the control means...

None of the treatments had a statistically significant effect on majoring in economics for female students... and the point estimate for basic information is near zero.

Yikes! So, these simple information interventions encouraged male students to do an economics major (almost doubling the number of male economics majors), but had no effect at all on female students. This is a worry, and contradicts the study by Li described in the first post I mentioned above. However, it is likely that the type of information you provide to students matters, and it may be that female students might not be as attracted by the career and earnings prospects that majoring in economics provides (more on that point in a future post).

The second article in AEA Papers and Proceedings was by Kelly Bedard (University of California, Santa Barbara), Jacqueline Dodd (Analysis Group), and Shelly Lundberg (University of California Santa Barbara). They also investigated an information intervention, as they describe:

...students earning a C or better in the introductory “principles of microeconomics’’ course (Econ 1) at the University of California, Santa Barbara (UCSB) were sent a letter describing the two majors offered by the department—“economics” and “economics and accounting”—and inviting the student to an informational meeting about the majors and their career prospects. A random sample of students earning a B or better were instead sent a treatment letter that augmented the baseline letter by adding positive feedback about the student’s performance in Econ 1 and encouragement to consider majoring in economics.

They look at the impact of the intervention on attendance at the informational meeting and the probability of enrolling in one of the two majors. Their sample is over 2300 students enrolled between 2015 and 2017, and they find that:

...treatment increases the probability that a student attends the information meeting by 6.1 percentage points for men and 5.8 percentage points for women relative to those who receive the invitation to the meeting without personal encouragement... Treatment increases the probability that men major in economics by 5.8 percentage points... and that women major in economics and accounting by 5.4 percentage points... For neither gender, however, is the effect of treatment on the probability of choosing either major significant.

So, students provided with information are more likely to follow up by attending the informational evening, and there is weak evidence that it increases the chance of majoring in economics. Notice that the effects are similar in size for both male and female students. However, they are not statistically significant. But, even if they were significant effects, I think this might increase the gender gap in economics because, as Bedard et al. note, most 'economics and accounting' majors go on to a job in the accounting profession, not economics. So, it appears that this information intervention might steer female students away from jobs in economics, which is the opposite of the intention of the intervention.

The third article in AEA Papers and Proceedings was by Andrea Chambers (Michigan State University) and co-authors. They investigate two interventions:

The first is a series of videos and infographics that provide information about what economics is, who studies economics, and career options with an economics degree. Each video features diverse MSU undergraduates, alumni, and faculty... The second intervention is a letter from the department chair that provides information on the grade distributions in the introductory courses.

The outcome measure they focus on is self-reported probabilities of taking another economics class, and majoring in economics (based on a survey conducted later). Their sample is over 3500 Michigan State University students enrolled in introductory microeconomics or macroeconomics in 2020, although only 2209 completed the final survey (and the low response was likely due to the pandemic). Chambers et al. find that:

...the primary effects of the treatment are practically small (relative to the mean), with standard errors that include zero.

In other words, the interventions had no statistically significant effect on the self-reported probability that students would take economics, or would major in economics. Chambers et al. also show no significant effect on actual enrolments in economics, from a more limited sample.

Overall, this is not good news for simple information interventions, in terms of their ability to reduce the gender gap in economics. At best, they seem to have no effect, although they may also make the problem worse. Either way, it may not be quite so simple to change preferences, or we need to look more thoroughly at the type of information that is being provided, and tailor it better.

Or perhaps, we discard the simple information interventions and do something else instead. In this 2018 post, I talked about about an intervention that used guest speakers to provide role models, which appeared to have a large and significant effect (and was something I have tried out in my own ECONS101 class). Given that the evaluations I described in this post showed that the earlier research on information interventions may have been overly optimistic, some more replications of simple role modelling interventions would be a good next step.

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Thursday, 20 January 2022

Closing the gender gap in STEM through female student-teacher matches

Back in 2020, I wrote a post about research from the US Air Force Academy, showing that matching female students in STEM (Science, Technology, Engineering and Maths) subjects with female professors improved the students' grades, closing the gender gap in performance, particularly among the best-performing female students. That research suggested that role modelling might be important for female students (as also identified here, here, and here).

Those results receive further support from this 2020 article by Jaegeum Lim (National Assembly Budget Office, Republic of Korea) and Jonathan Meer (Texas A&M University), published in the Journal of Human Resources (ungated earlier version here). Lim and Meer used data from Korean middle-school students who were followed from seventh grade until the end of high school, and looked at how the effect of teacher gender in seventh grade affected their subsequent outcomes. As with my post from earlier this week, a relevant problem is selection bias, if students (or, their parents) can choose teachers. This isn't a problem in this case, as Lim and Meer explain:

Several features of the South Korean educational system make it well suited to study the impact of teacher–student gender matches. First, elementary school graduates are assigned to a local middle school (spanning Grades 7–9) by lottery... Second, middle school students are randomly assigned to a physical homeroom classroom, through which subject teachers rotate to give lessons.

This randomisation ensures that there is little in the way of selection bias. Many Korean schools do engage in 'ability tracking', sorting students into different classes and teachers by ability, but Lim and Meer account for that with school-by-subject-by-ability-class fixed effects, meaning that they compare students that were assigned female seventh-grade teachers with students that were assigned male seventh-grade teachers, within the same school, subject, and ability grouping. Their data come from between 2000 and 4000 students from 74 schools in Seoul, followed over six years (with the sample size decreasing over time due to attrition). Analysing the effect on standardised seventh-grade test scores, Lim and Meer find that:

Boys with a female teacher rather than a male teacher see a statistically insignificant decrease in performance of 0.06 standard deviations, but a girl with a female teacher relative to a male one has an increase of 0.08 standard deviations.

The negative effect for boys having a female teacher loses statistical significance in the preferred regression specification, leaving a result that suggests that girls' academic outcomes improve significantly when they have a female teacher. And, this effect persists over time:

Somewhat surprisingly, we find that the gender gap effects persist even five years after the initial teacher–student gender match. The effects vary slightly over time, but there are no significant differences between the contemporaneous effect and the effects in the following years...

Specifically, the effect remained statistically significant and sizeable all the way through to 12th grade. The surprising thing is that this is the effect of a female student having a female teacher in seventh grade. We'll come back to that point later.

Turning to high school choices, Lim and Meer find that:

Girls are 15.1 percentage points (SE = 7.5) more likely to choose the math–science track in high school when taught by female versus male math teacher in seventh grade... female students are 15.7 percentage points (SE = 6.6) more likely to take at least one advanced math course when they were taught by a female math teacher in seventh grade versus a male teacher... the male-female gap in attending a STEM-focused high school is substantially reduced when a female student has a female math teacher in seventh grade.

These results clearly demonstrate that the gender gap in STEM can be reduced by having female students have female maths teachers in middle school (specifically, in seventh grade). Now, it is worth noting that there is nothing particularly special about seventh grade compared with other grades. Lim and Meer focus on seventh grade because it is the first year of middle school, so the randomisation is cleanest for students in that grade, and so the causal impact of the results is more defendable. However, given that the results show large and persistent effects, it is reasonable to ask why.

Lim and Meer are able to exclude cumulative exposure to female teachers, as students taught by female teachers in seventh grade are no more likely to have female teachers in later years than students taught by male seventh-grade teachers. They also find no evidence that students with female teachers jump up to higher ability groups in later years, so while their academic performance improves within their ability group, it is not so large that they change groups (and students in higher ability groups will have different aspirations and preferences for high school). Lim and Meer then look at an index of student engagement, and find that:

While female students have a lower engagement score than male students, having a female teacher in a particular subject in seventh grade eliminates this gap, and the effects persist into high school.

So, having a female teacher leads to higher engagement for female students. This is not dissimilar to results from the research I discussed on Sunday. Unfortunately, beyond the effects on high school choices, Lim and Meer aren't able to show any additional statistically significant effects beyond high school. Nevertheless, that seventh-grade teacher-student gender match has effects up to high school is remarkable, and again points to the importance of having more female teachers teaching STEM subjects.

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Sunday, 16 January 2022

The ambiguous, but persistent, effects of teacher gender bias

Past research has shown not only that there is a persistent gender gap in the numbers of students studying in STEM (science, technology, engineering, and maths) subjects (for example, see this post), but that a teacher's gender may make a difference. Moreover, the gender gap may be partially explained by gender bias among students' parents and their peers. But what about gender bias among teachers? That is the question that is addressed in this NBER Working Paper by Victor Lavy (University of Warwick) and Rigissa Megalokonomou (University of Queensland), with a non-technical summary available on The Conversation. They use data from Greek high school teachers and students, and among other things they look at how the gender bias of teachers affects the university enrolment decisions of students. 

Their main analytical sample is based on students and teachers from 21 Greek high schools, over the period from 2003 to 2011. They also distinguish many of their results between core subjects (e.g. modern Greek, history, physics, algebra, and geometry), classics (ancient Greek, Latin, philosophy, etc.), science (maths, physics, chemistry, biology, etc.), and exact science (maths, physics, business administration, computer science, etc.). 

In the first substantive section of the paper, Lavy and Megalokonomou use data from students' high school exams to estimate teachers' gender bias. As they explain:

We measure teachers' bias as the difference between a student's school exam score in 11th and 12th grade (scored by the student's teacher) and his or her external exam score (taken at the end of 11th and 12th grade and scored nationally)... We then define a teachers' bias measure at the class level by the difference between boys' and girls' average gap between the school score and the national score. Positive values indicate that a teacher is biased in favor of boys in a particular subject. We link teachers over time and are therefore able to get a persistent teacher bias measure based on multiple classes (on average 11 classes per teacher)...

So, if teachers systematically give more generous grades to boys than to girls, when each student's performance in the school exam is compared with their performance in the external exam, then the teacher is biased towards boys. The reverse is true for biasedness towards girls. Lavy and Megalokonomou then investigate the gender gap in performance, finding that for 11th grade:

The gender gap varies by subject and type of exam. Boys outperform girls in physics, geometry and algebra (core subjects) in the blind exams. In all other subjects, girls outperform boys in the blind exams.

Nothing surprising there, and pretty much in line with other research. The results are very similar for 12th grade. However, in a surprising result (at least to me), they find that there is (emphasis is mine):

...negative teacher bias throughout, suggesting that on average, teachers are biased in favor of girls across all subjects. The bias in 11th grade is higher in exact science track, highest in computer science (-0.271) and lowest in physics (-0.037). Among 12th grade teachers, the bias is highest in physics in the science track (-0.300) and lowest in economics (-0.085).

Keep that result in mind as we talk about the rest of the paper. Teachers are, on average, biased towards girls in all subjects. That doesn't mean that all teachers are biased towards girls, but it does mean that, in interpreting the results later, 'more biased towards boys' really means 'less biased towards girls'. The framing of this is going to matter, as we will see, and the equivalence of these two framings arises because of the symmetric nature of their measure of bias.

Lavy and Megalokonomou then go on to show that teachers' gender bias is persistent, both across teachers' different classes, and over time. This is a bit of a worry for policy reasons, as we'll see later. But it is a good thing for the analysis, since it means that they can use a single measure of gender bias for each teacher, knowing that it doesn't vary much between their classes or years.

Then, Lavy and Megalokonomou relate this measure of teacher gender bias to students' academic performance, and their university enrolment choices. Importantly, it is worth noting that students are allocated randomly to teachers in Greece, so any effect of selection bias or sorting across classes will be minimal. Looking at scores in the external exams, they find that:

In the core and exact science subjects, the estimated coefficients for boys and girls are almost identical, but with an opposite sign. A one sd increase in 11th grade core subjects' teacher bias increases boys' test score in 12th grade by 0.09 sd and reduces girls' test score by 0.10 sd. In classics, the effect for boys is 0.19 and smaller and not significant. In science, the effects are larger; a 0.21 increase among boys and a 0.11 decrease among girls. In exact science the effect is large and negative for girls at 0.16, while for boys it is 0.15.

So, gender bias towards boys (or, less gender bias towards girls) improves outcomes for boys in the external exams, as you would expect, and this effect is statistically significant for all subjects. Importantly, and perhaps surprisingly, there is no difference between teachers of different genders. Pro-boy bias has the same effect for male teachers and female teachers, and pro-girl bias also has the same effect regardless of teacher gender. Lavy and Megalokonomou then explore a potential mechanism that may partially explain the differential performance, being class attendance, and find that: increase in a teacher's bias in favor of boys increases boys' class attendance and reduces girls' class attendance. This effect is largest on unexcused absences. For example, a one sd increase in 11th grade bias in core subjects decreases boys' unexcused absences in 11th grade by 0.6 hours and increases girls' unexcused absences by 0.4 hours. Estimates of girls' unexcused absences are statistically significant for all groups of subjects, except classics. Respective patterns are similar in 12th grade.

So, teachers who are more biased towards boys (or less biased towards girls) have greater attendance among boys, and lower attendance among girls. Since attendance in class is important for academic performance (more on that in future posts), this may explain some of the relationship between teacher gender bias and exam performance.

Next, Lavy and Megalokonomou look at the effect of teacher gender bias on university enrolment, and find that:

Teachers' bias in both grades increase the likelihood of boys' enrollment in any university and they have the opposite effect on girls.

For example, a one sd increase in 11th grade teacher bias in core, classics, science and exact science, increases boys' likelihood of studying in a university by 2, 5, 2, and 2 percentage points. The effects of the same increase in 12th grade is higher and equal to 4, 5, 4, and 3 percentage points. At the same time, the effects for girls are negative. If an 11th grade teacher becomes one standard deviation more pro-boy in core, classics, science and exact science subjects, girls' likelihood of enrolling in any post-secondary program decreases by 5, 1, 3, and 3 percentage points. The effects are similar for females in 12th grade: An increase in teacher bias by one sd decreases their likelihood of enrolling in some post-secondary program by 3, 4, 2, and 3 percentage points.

Here's where the effects are potentially pernicious, but note that, as mentioned earlier, a bias towards boys is the same as a lesser bias towards girls. So, a bias towards boys (or, less bias towards girls) encourages boys to enrol in university, and discourages girls. Then, looking at field of university study, Lavy and Megalokonomou find that:

The absolute size of the estimated effect of 11th grade bias is small and not significant for boys, while for girls the estimates are more precisely measured and are significantly different from zero... The estimated effects for girls with school or class fixed effects suggest that a one sd increase in bias in favor of boys in a given field lowers the probability of girls' choosing that field of study by 4.6 percent. The respective estimate of the 12th grade bias is similar.

Although these results could have been the most important in the paper overall, I find them to be less convincing because of the way that Lavy and Megalokonomou link bias in a small number of high school subjects to university fields of study. Their choices here seem somewhat arbitrary. For example, for social science, the use as a measure of gender bias "11th grade biases in Modern Greek and history and 12th grade bias in economics". Why those particular subjects? As I said, it seems arbitrary. The results are consistent with the overall results for enrolment, but may not be robust.

Then, Lavy and Megalokonomou look at the quality of the university programme that students enrol in (as measured by the average national exam score of students who enrol, or the lowest admission score of any student who enrolled successfully). They find:

...positive estimates for boys... and negative estimates for girls... For example, a one sd increase in 11th grade pro-boys teachers' bias lowers for girls the rank of the department of study in humanities by 6 percentiles in the admissions cutoff distribution... or 7 percentiles in the mean score of the admitted students distribution...

In other words, having teachers who are more biased towards boys improves the quality of the university programme that boys enrol in. Again, that is the same as saying teachers who are less biased towards girls improve the quality of programme that boys enrol in.

Overall, the results so far need to be interpreted quite carefully. It would be tempting to say that teachers are advantaging boys too much, and that some policy should be enacted to reduce the advantage that boys receive. Lavy and Megalokonomou frame their paper in that way, noting all of their results in relation to bias in favour of boys. However, it would be just as valid to reverse the framing and say that teachers are advantaging girls too much, and that some policy should be enacted to reduce the advantage that girls receive. That might be an even more relevant framing, given that on average, teachers are biased in favour of girls.

In fact though, it turns out that both framings are relevant, and both policy prescriptions may be a good idea. In the final (and probably most important) section of the paper, Lavy and Megalokonomou look at how teacher gender bias relates to teacher quality (as measured by teacher value-added (TVA)). They categorise teachers as pro-boys (n = 101), pro-girls (= 259), or neutral (= 58), then compare the quality of teachers with their gender bias. They find that:

...the higher the bias in favor of boys, the lower the teacher quality. Estimates of the pro-girl bias variable are symmetrical, indicating that a higher grading bias in favor of girls also leads to lower TVA.

So, more biased teachers are lower quality teachers. And it doesn't matter if teachers are biased towards boys, or biased towards girls. Teachers who are unbiased (neutral) are the highest quality teachers. The question then becomes, how do we get teachers who are less gender biased (in either direction)? Finding a solution is difficult, because we know from some of the earlier results in the paper that teacher gender bias is highly persistent - it doesn't vary much across classes or over time, for the same teacher. So clearly, nothing that has been done over the period 2003-2011 has had any effect, and we can't rely on general social change. We also don't know why the teachers are biased, or why some teachers are biased towards boys and some are biased towards girls. We also don't know whether these results have any external validity beyond Greece.

Knowing why teachers are biased would certainly help with the next step, which would be to develop an effective intervention. We need further research to investigate interventions that reduce gender bias. And those interventions need to be carefully designed to reduce both pro-boy bias and pro-girl bias.

[HT: The Conversation]

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Saturday, 15 January 2022

Tim Harford on the hidden costs of cost-benefit analysis

Last week I wrote a post about the cost-benefit principle. On the Waikato Economics Discussion Group on Facebook, we had a brief but interesting discussion about how cost-benefit analysis is most valuable in the absence of uncertainty. The algorithm discussed in my post above is overly conservative, since if there is insufficient details on benefits or costs, it suggests that you should not adopt the AI technology. That might be appropriate for a decision-maker who is very risk averse, but for many it would lead to passing up on alternatives where the chances of costs outweighing benefits is very low, simply because the costs or benefits are uncertain.

The cost-benefit principle generally works well as a theoretical framework for rational decision-making. However, cost-benefit analysis, as employed by policy-makers and consultants, can often go wrong, and Tim Harford had a recent post on this topic:

On the surface, cost-benefit analysis is all very rational, and admirably well-suited to decide whether to build a bridge or abolish a regulation. However a new article in the Journal of Benefit-Cost Analysis by Bent Flyvbjerg and Dirk Bester argues that cost-benefit analysis “is broken”. Flyvbjerg and Bester assemble and analyse a data set of more than 2,000 public projects — bridges, buildings, bus transit systems, dams, power plants, railways, roads and tunnels. They conclude that costs have been systematically underestimated. This is broadly true regardless of when or where the project was commissioned, or what type of project it is.

Even allowing for this tendency for projects to run over budget, there are more catastrophic cost overruns than one might expect. There is less data on benefits, but there is some evidence of benefits being overestimated for public transit projects, and no sign that the large cost overruns are in any way compensated for by surprisingly large benefits.

These findings are sobering, if not entirely surprising. As Flyvbjerg and Bester are at pains to point out, “cost overrun” isn’t really the right description of what keeps happening. “Cost underestimate” is better. The problem is not that every project engineer in the world is incapable of delivering to a reasonable budget; it is that the budgets are never reasonable. The infrastructure we see around us is born of rose-tinted spreadsheets and hype.

Yikes! But not surprising, to anyone who pays attention to the costs of large government projects. But it makes projects that fail a benefit-cost test even more important to avoid. Can we do better than cost-benefit analysis? Harford notes that:

So what is the point of cost-benefit analysis if all the costs and benefits being analysed are flights of fantasy? The only answer I can think of, with apologies to Winston Churchill, is that cost-benefit analysis is the worst form of evaluating decisions, except for all those other forms which have been tried from time to time.

Alternatives include decision-making by HIPPO (highest-paid person’s opinion), decision-making by sound bite or decision-making by whatever polls well with people who may not have spent a moment’s thought on the matter. These are not good ways to think through complex, long-term infrastructure projects or wide-reaching regulations.

So, we are stuck with cost-benefit analysis for large projects, even if it is imperfect (and getting more difficult as we understand more about measuring costs and benefits). We probably shouldn't apply the overly conservative say-no-if-you-can't-quantify-something approach, or we would never say yes to any large project (although some may argue that would be an improvement over the current approach). However, we do need to know where the key areas of uncertainty in costs and benefits lie, even if they can't be precisely quantified. And, we definitely need to stop underestimating the costs of these projects. Then, at least, we might avoid the worst public investment outcomes.

Thursday, 13 January 2022

More evidence that Julian Simon was lucky in the Simon-Ehrlich bet

Last October, I wrote a post about the Simon-Ehrlich best:

...the famous bet between University of Maryland professor of business administration Julian Simon and Stanford University biology professor (and author of the influential book The Population Bomb) Paul Ehrlich. Ehrlich had argued that resources were becoming scarcer. Simon pointed out that, if increased scarcity were true, then the price of resources would be increasing. He challenged Ehrlich to choose any raw material, and a date more than a year away, and Simon would bet that the price would decrease over that time rather than increasing.

Ehrlich accepted the bet, choosing copper, chromium, nickel, tin, and tungsten as the raw materials on which the bet would be based. The bet was formalised on 29 September 1980, and was evaluated ten years later. The price of all five materials fell between 1980 and 1990, and Simon won the bet.

The purpose of that post was to highlight this 2010 article that demonstrated that Julian Simon might just have gotten lucky. Now, a new article by Ross Emmett (Arizona State University) and Jesse Grabowski (Université Paris 1 Panthéon-Sorbonne), published in the Journal of Ecological Economics (sorry, I don't see an ungated version online) follows up on the question of whether Simon was lucky, using the tools of financial economics. They argue that financial economics is the appropriate way to analyse the bet, because:

...the Simon-Ehrlich bet [can be] recast as an investment portfolio, specifically a forward contract, with Simon in a short position as an investor and Ehrlich in a long position. 

In other words, Simon's short position makes money if the value of the commodities decreases (which is what happened), while Ehrlich's long position makes money if the value of the commodities increases. Now, recast as an investment, Emmett and Grabowski employ a number of financial economics tools, including portfolio diversification, market beta, the Sharpe ratio, and mean-variance efficiency. I'm not going to go into detail about what each of those methods entails, but in terms of portfolio diversification, Emmett and Grabowski note that:

...Simon should have proposed a wager against a basket of as many resources as possible, to reap the benefits of portfolio diversification.

Simon's offer to bet on any number of resources opened him up to a lot of risk, since a diversified portfolio of resources is more likely to follow the overall price trend (which he believed was downwards), whereas any single (or five) resources could more easily go against that trend, simply due to luck. On the other hand, from Ehrlich's perspective:

A diversified portfolio would still have lost the bet, but it might have saved Ehrlich a few hundred dollars.

So, Emmett and Grabowski believe that Ehrlich was in trouble regardless of portfolio choice. Moving on to their other methods, Emmett and Grabowski find that:

...Ehrlich’s portfolio did not contain as much market trend exposure, as measured by CAPM beta, as it could have, which is surprising given his boisterous confidence in price trends. Luckily for him, however, an explicit strategy of maximizing portfolio beta ended up in failure. When risk profile was held constant at the level he himself chose, however, we found he could have done better given the information available by moving to a mean-variance efficient portfolio.

So, as they suspected, Simon would have lost the bet almost regardless of which resources he chose. However, that doesn't answer the underlying question of whether Simon was simply lucky. If you look at the final value of a $1000 investment in the five resources, for any ten-year period between 1903 and 2015, you get Figure 4 from Emmett and Grabowski's paper:

The red shaded areas show points in time where if the ten-year period ended then, Simon would win the bet, while the green shaded areas show points in time where Ehrlich would win. It is clear that Ehrlich would have won slightly more often over the past 110 years (similar to the findings in the earlier paper). Emmett and Grabowski then go a step further, creating and running a Monte Carlo simulation of the change in resource prices over time, and find that:

From our simulation, we estimate that, were they able to repeatedly make the same bet, Simon would win only 37% of the time, while Ehrlich would win 63%.

So, I guess we can take this as further (and more detailed) evidence that Julian Simon was just a little bit lucky in the Simon-Ehrlich bet.

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Wednesday, 12 January 2022

Price and prejudice

Economists distinguish between two different types of discrimination:

  1. Taste-based discrimination, which involves bias against members of a particular group (this discrimination arises because of people's preferences for or against particular groups); and
  2. Statistical discrimination, which involves treating people differently based on the group they belong to, because of differences in average characteristics between groups (this discrimination arises because of imperfect information about people, leading them to be treated as if all members of a particular identifiable group are the same).

As I noted in my recent review of Thomas Sowell's book Applied Economics, Sowell carefully explained that discrimination often imposes a cost on the person doing the discriminating. For example, if an employer discriminates against employees of a particular type, they may choose to employ others with lower productivity (and lower profitability for the employer) instead. The cost comes in the form of lower profits.

How much of a cost are discriminators willing to bear? That is the research question that is addressed in this 2018 article by Morten Hedegaard (University of Copenhagen) and Jean-Robert Tyran (University of Vienna), published in the American Economic Journal: Applied Economics (appears to be open access, but just in case there is an ungated version here). Hedegaard and Tyran use a field experiment among Danish high school students to estimate the willingness to pay to work with someone of the same ethnicity. Specifically, in the field experiment:

We hire 162 juveniles from secondary schools in Copenhagen, Denmark, with Danish-sounding and Muslim-sounding names to prepare letters for a large mailing and pay a piece rate. Workers are requested to show up for work twice in two consecutive weeks. In the first round, they work by themselves and we measure their individual productivity on the job. Before they come back for the second round, we call randomly selected workers on the phone and inform them that they will again do the same job but now have to work in teams of two. They are informed that they are paid the same piece rate as in round 1 and share earnings from team output in round 2 with the coworker. These randomly selected workers can choose whom to work with. The choice is between a candidate from the ethnic majority group and a candidate from an ethnic minority group. In treatment Info, we provide the decision maker with information about the individual productivity of the two candidates, i.e., the number of letters they prepared in round 1, and their first names as a marker of ethnicity... Rational decision makers who choose the less productive worker of the same ethnic type thus discriminate knowingly and deliberately.

Importantly, because Hedegaard and Tyran know the productivity of the workers from the first round. The sample is essentially split into threes. One person in each group of three is a decision-maker, and chooses which of the other two workers that they will work with in the second round. Hedegaard and Tyran ensure that the choice is between someone of the same ethnicity as the decision-maker, who has lower productivity, and someone of the opposite ethnicity, who has higher productivity. The 'price' of discrimination varies between decision-makers, depending on how more productive the opposite-ethnicity worker is than the same-ethnic worker that each decision-maker is offered. Hedegaard and Tyran can then test how much discrimination varies between decision-makers with higher and lower prices of discrimination. Based on their sample of 140 workers who completed both rounds, they find that:

...discrimination is common even at a substantial cost and that the tendency to discriminate is not different across ethnic types. We estimate that discriminators on average are willing to forego 8 percent of their earnings in round 2 to avoid a coworker of the other ethnic type. Our main result from treatment Info is that discrimination is highly responsive to the price of prejudice. Our best estimate is an elasticity of −0.9, i.e., we find that the probability to discriminate falls by about 9 percent if the price of discrimination goes up by 10 percent.

There is a lot to unpack there. First, people are willing to discriminate even if it costs them (which is consistent with Sowell's argument). Second, and a result that would surprise many people, ethnic majority and ethnic minority workers are equally likely to discriminate. Third, the elasticity is quite high - increasing the cost of discrimination reduces discrimination significantly.

Could it be that Hedegaard and Tyran are picking up statistical discrimination? That is, are the workers basing their decision on the average expected productivity of the workers of different ethnic groups? This seems unlikely, since both ethnicities are engaging in discrimination, and by definition both groups can't be less productive than each other (in fact, the Danish group is statistically significantly more productive). However, Hedegaard and Tyran explicitly test how important taste-based discrimination using a different treatment group, where the decision-makers were not provided with information about the round 1 productivity of the workers they could choose between (Hedegaard and Tyran refer to this as the 'NoInfo' treatment). They find that:

...statistical discrimination does not explain observed outcomes in NoInfo well. We find a large gap between observed earnings and earnings predicted by statistical discrimination (about 4 percent of total output). To account for taste-based discrimination, we use our estimate from treatment Info and find that it predicts well out of sample; about 40 percent of that gap is explained by animus-driven prejudice. Thus, our results suggest that prejudice is an important cause of ethnic discrimination in the workplace, and that it needs to be taken into account above and beyond the theory of statistical discrimination.

So, clearly there is a substantial amount of taste-based discrimination in this sample. To see just how much, consider that in the NoInfo experiment, 78 percent of decision-makers chose the same-ethnic worker, compared with just 38 percent in the Info experiment. Simply providing information about the price of discrimination was enough to reduce discrimination substantially.

Other than an interesting test of the relative important of the two types of discrimination, does this research provide some policy implications? It clearly demonstrates the existence of substantial ethnic bias or prejudice between workers. However, in terms of addressing the problem of discrimination this research suggests that, if there is some way to explicitly estimate the costs of discrimination, and make those explicit to decision-makers, discrimination could be reduced. Unfortunately, it is not clear how that would work as a solution in other real-world contexts.

Tuesday, 11 January 2022

Contract cheating, blackmail, and the end of game problem

When we designed the new ECONS101 paper some years ago, I tried desperately to include two weeks of game theory. Ultimately, it proved unworkable, but my rationale for trying to include it was that it would allow more time to explore repeated games. One aspect of that is the end of game problem. In a repeated game, the outcome may differ from the Nash equilibrium, because the players may realise that some other outcome benefits them more over many plays of the game. For example, in the repeated prisoners' dilemma, the dominant strategy equilibrium is for both prisoners to confess, but the best outcome is obtained if both prisoners remain silent (for an example of this, see this post on the drug dealers' dilemma). In a repeated game, players may be more likely to cooperate (and both prisoners stay silent) in the hopes of future cooperation. The American political scientist Robert Axelrod noted that players cooperate because of "the shadow of the future".

However, there is a difference between what happens when a game is infinitely repeated (it is played many times without end), and when a game is finitely repeated (played many times, but the players know when it will end). In a finitely repeated game, both players have an incentive to cheat in the last play of the game. Knowing that the other player will cheat in the last round, then both players realise that there is little point in cooperating in the second-to-last round of the game, so both players will cheat in that round. And knowing that, there is an incentive to cheat in the third-to-last round, and then the same logic applies to the fourth-to-last round, the fifth-to-last round, and so on all the way back to the first round of the repeated game. In a finitely repeated game, any cooperation breaks down, and neither player should be able to trust the other player to cooperate. Notice that this wouldn't be the case for an infinitely repeated game, because since neither player knows when the game will end, they never know when they should start cheating.

That brings me to the example of contract cheating, which involves a student outsourcing their assessment work to someone else to complete, usually for payment. Contract cheating has become a big issue at universities (see for example this 2017 article in The Conversation), and has been exacerbated by the shift to online teaching and assessment during the pandemic. Estimates suggest that around 8 percent of students may engage in contract cheating during their university studies. That might not sound like a lot, but that equates to hundreds of students at even a relatively small university like Waikato.

However, the up-front monetary payment that students face, and the chance that their cheating is detected and they are sanctioned, are not the only costs that students may face when they use contract cheating services. As this recent article in The Conversation notes, students may later be blackmailed by the contract cheating service, which threatens to reveal their cheating to the university unless further payments are made. In this new study by Jonathan Yorke, Lesley Sefcik, and Terisha Veeran-Colton (all Curtin University), published in the journal Studies in Higher Education (sorry, I don't see an ungated version online), 14 out of 587 students surveyed:

...stated that they directly or indirectly knew students who had been blackmailed by contract cheating services.

That's a disturbingly high incidence of blackmail, and something that students who engage these services should be concerned about. And if students were better advised of the risk of blackmail, contract cheating would probably decline. To see why, we can use some game theory and the end of game problem.

Consider a simple sequential game for a single assessment, as laid out in the decision tree (which we refer to as extensive form) below. The student makes a decision first, whether to engage in contract cheating or not. If they choose not to engage in contract cheating, the game ends, and their payoff (measured in utility) is based on the chances that they pass the assessment. If the student chooses to engage in contract cheating, then the cheating service chooses whether to blackmail the student or not. The payoff to the cheating service is profits from the fees or blackmail payment that the student pays.

There are three important aspects to this game. First, the Nash equilibrium of this game is for the student not to engage in contract cheating. To see why, we can use backward induction - essentially we start at the end of the game and work our way backwards, eliminating strategy choices that would not be chosen by each player. If the student chooses to engage in contract cheating, then the cheating service will choose to blackmail the student (because the payoff of 100 is greater than the payoff of 60). A rational student would then know that if they engage in contract cheating, they will get blackmailed, and their payoff will be -50. They won't get the payoff of 50, because the cheating service is going to blackmail them. Knowing this, the student is choosing between not engaging in contract cheating (and receiving a payoff of 15), and engaging in contract cheating (and receiving a payoff of -50). They are better off not engaging in contract cheating. That outcome is the subgame perfect Nash equilibrium in this game.

Second, many students are naïve. They don't realise that the cheating service can blackmail them. They think they are playing a different game, where they get to choose between the payoff of 50 (from engaging in contract cheating) and the payoff of 15 (from not engaging in contract cheating). The grey strategy and outcome are hidden from them. These naïve students think they are better off cheating, and will do so.

Third, this is actually a repeated game, because it is played over and over for each assessment that a student completes. That changes the incentives for the cheating service. Once a cheating service blackmails a student, the student probably isn't going to go back to that service. That means that the cheating service will receive a one-off payoff of 100. However, if the cheating service can encourage the student to return for more assessments, the cheating service will receive a payoff of 60 from every play of the game. Using the (made up) numbers from the game above, the cheating service only needs the student to pay twice in order to make them better off than they would be by blackmailing automatically. Strategically, the cheating service would therefore be better off overall by not blackmailing the student in each play of the game.

The repeated nature of the game affects naïve and rational students differently. The naïve students didn't realise that blackmail was an option at all, so from their perspective nothing has changed. The rational students may be tempted to engage in some contract cheating, even though they realise that the cheating service could engage in blackmail.

Of course, you can probably see where all this is going. The repeated game where the cheating service avoids engaging in blackmail only exists in an infinitely repeated game. However, this game is not infinitely repeated, because eventually the student is going to graduate, after which they won't need the contract cheating service any more. The contract cheating service has a strong incentive to string the student along, extracting fees from each assessment, and collecting evidence of the student's cheating, before blackmailing them in the last play of the game (which might even be after the student has graduated!).

In this finitely repeated game, the naïve students are hurt tremendously. At least if the game was not repeated, they get blackmailed in the first play. However, this finitely repeated game maximises the profits of the cheating service, by keeping the naïve student in the game until the very end. For the rational students, hopefully they are rational enough not only to recognise the possibility of blackmail, but also the end of game problem.

How can universities help students and mitigate the problem of blackmail from contract cheating services? Most universities now require students to complete an academic integrity module at the start of their studies, which impresses upon them that cheating (of various forms) is not allowed. One component of those programmes should certainly be (as discussed by Yorke et al.) to discuss with students the possibility of blackmail by contract cheating services, and how widespread (and growing) the practice is. At the very least, that will convert naïve students into more rational students by making them realise the full game that they are playing with the contract cheating services.