Social capital and the spread of coronavirus in Europe

Like many researchers, I've been closely following the emerging research on the coronavirus pandemic, and looking to contribute to it. With some colleagues, I've been looking at how social capital might be related to the success (or otherwise) of lockdown policies, and the effect on coronavirus infections and deaths. The idea was intuitive - reducing infection rates essentially requires that people act in the best interests of society, so (holding other relevant factors constant) countries or regions with higher social capital should be suffering less, with fewer infections and coronavirus-related deaths.

Unfortunately, our data analysis to date hasn't been showing anything of interest, which we have put down to measurement error in the data. However, this new working paper by Alina Kristin Bartscher (University of Bonn) and co-authors offers a sensible explanation for our null results:

From a theoretical perspective, social capital, the spread of Covid-19 and containment policies interact in various ways. First, high-social-capital areas are known to be more vibrant and better connected, economically and socially... Hence, we expect the virus to spread more quickly in those areas in the beginning of the pandemic, when information about the virus and its severity were incomplete. Second, as soon as the importance of behavioral containment norms becomes more salient, we expect the relationship to change... we expect that informal rules of containment are more likely to be (voluntarily) adopted in areas with high social capital, leading to a relative decrease in infections.

In our analysis, we had adopted a cross-sectional approach to try to overcome some of the measurement issues with the high-frequency data. However, in adopting that approach we were conflating the early period, when the relationship between social capital and infections is expected to be positive, with the later period, when the relationship is expect to be negative. It should be no surprise then, that we were finding null results!

Anyway, the Bartscher et al. paper uses data for seven European countries (Austria, Germany, Italy, the Netherlands, Sweden, Switzerland and the UK), and uses electoral turnout in the European elections (or local elections for Switzerland) as a measure of social capital. They also use a number of different measures (both social capital, and outcome measures) for Italy. They found that:

First, the number of Covid-19 cases is initially higher in high-social-capital areas. Second, as information on the virus spreads, high-social- capital areas start to show a slower increase in Covid-19 cases in all seven countries. Third, high-social-capital areas also exhibit a slower growth in excess deaths in Italy. Fourth, individual mobility is reduced more strongly before the lockdown in Italian high-social-capital areas. Fifth, we provide suggestive evidence that the role of social capital is reduced when national lockdowns are enforced, as the differences in mobility between high- and low-social-capital areas vanish after the national lockdown is enacted.

More specifically, the found that high-social capital regions have between 12 percent and 32 percent fewer cumulative coronavirus cases. When they look at Italy in more detail, they found that one standard deviation higher social capital (electoral turnout) is associated with 7 percent lower excess mortality, and a 15 percent reduction is mobility. The latter result demonstrates the likely mechanism through which social capital leads to fewer deaths - people in areas with more social capital adhere more closely to the lockdown rules that people in areas with less social capital.

Overall, Bartscher et al. conclude that:

...the consistent pattern obtained from independent analyses of seven countries as strong evidence in favor of the hypothesis that social capital plays an important role in slowing down the spread of the virus.

This is probably not the last word on this line or research. Bartscher et al.'s approach of simply comparing regions above and below the median level of social capital within the country is rather crude, even though the results are as expected. It would be interesting to see whether the results hold when social capital is treated as a continuous measure rather than simply categorising high/low social capital areas. It would also be interesting to see if similar results are obtained for counties in the U.S. No doubt we will see analysis of U.S. counties sometime in the future.

The effect of studying STEM at high school on employment and wages

Much of the literature on studying STEM (Science, Technology, Engineering, and Maths) at high school focuses on how well it prepares or motivates students to study STEM at university. There is very little consideration of what happens to student studying STEM who don't then go on to university. This 2016 article by Robert Bozick (RAND), Sinduja Srinivasan (Economic Commission for Latin America and the Caribbean), and Michael Gottfried (University of California - Santa Barbara), published in the journal Education Economics (sorry, I don't see an ungated version online) is different. They look explicitly at the employment outcomes of high school STEM studies for non-university-attending students.

Specifically, Bozick et al. use data from the Education Longitudinal Study of 2002 (ELS:2002), which includes a sample of 3473 students who did not go on to attend university-level study. For those students, they have detailed information on their employment outcomes (whereas there is no such data for the university-bound students). What they find is essentially nothing in terms of employment in STEM:

...taking advanced academic STEM courses or applied STEM courses in high school does not improve the likelihood that non-college bound youth will secure jobs in the STEM economy. In fact, there is evidence that some applied STEM courses may serve as a barrier: non-college bound youth who took IT courses in high school were less likely to find employment in the STEM economy than their peers who did not take IT courses in high school...

There is also no statistically significant effect on wages:

In terms of academic STEM courses, all of the effects for above average and advanced math and science courses are positive, but none of them are significantly different from zero. The largest effect among these courses is for advanced math, which includes Calculus and similar classes of that caliber. Relative to students who had taken average math, students who had taken advanced math have a 0.095 wage advantage in their first job and a 0.077 wage advantage in their current job, which translates to approximately $2200 and $2160 per year, respectively. Again, though, these effects are not significantly different from zero.

Looking at wages specifically in STEM jobs, they also find no effect. In other words, studying STEM at high school does not set these students up for jobs in STEM, or as Bozick et al. put it:

Our study indicates that the courses currently offered in America’s high schools are not improving the labor market prospects of non-college bound youth entering the STEM economy after finishing high school.

However, I think the authors may have been a little too negative in their interpretation. Sure, the results are statistically insignificant. That means that the results are not statistically distinguishable from zero. However, if you look at the wage premium in the quote above, the wage premium of maths is also not statistically distinguishable from an advantage of $4000 per year. That is potentially a sizeable effect, given that the average wage in the sample is around $18,000 per year.

The problem here is a lack of statistical power. Studying STEM might have an impact on employment and wages, but this sample is too small to precisely estimate the size of the effect. You might think that a sample of over 3400 is large, but it depends on context. In this case, it limits what the authors can conclude from their results. All that they can say with any reliability is that the wage premium is less than $4000 per year, which isn't saying much.

The other problem with this study is self-selection. Students were not (and cannot be) randomised into whether they went to university or not. This sample also didn't randomise students into who studied STEM. So, it is somewhat limited in terms of what it can say about the causal effect of studying STEM on employment and wages.

Overall, we're going to need a lot more research, probably including studies with some form of randomisation or quasi-randomisation, and larger sample sizes, before we conclude that studying STEM at high school is a waste of time.

Loneliness, income, and unemployment in the time of COVID-19

When your public policy hammer of choice is a universal basic income, every social problem looks like a nail. At least, that's what I thought when I heard this story on Radio New Zealand this morning:

People on low incomes were more likely to suffer high levels of loneliness during lockdown.

The report 'Alone Together', published by the Helen Clark Foundation and consultancy firm WSP reveals the Covid-19 lockdown exacerbated the risks of loneliness, especially for those who had no work.

The report recommends everyone has access to a guaranteed minimum income, high speed internet and mental health support.

You could be forgiven for wondering, if loneliness is the problem, then a first order solution is not a guaranteed minimum income, but guaranteed minimum friends. Yes, the government should start an automatic match-making service to ensure that every person has many high-quality friends and therefore won't be lonely. There is no doubt a missed opportunity there.

On a more serious note, the report itself is available here, and indeed it does show that people on low incomes are lonelier. It finds this using data from the 2018 General Social Survey. However, it also says that:

It is striking how closely loneliness was linked to employment status and household income. The group most likely overall to report feeling lonely in 2018 were people who were unemployed.

If unemployment is a bigger issue than income (and it is: 7.2 percent of unemployed people report being lonely most or all of the time, compared with 6.1 percent of those in the lowest (under $30,000 per year) income bracket). So, based on that alone it would make more sense to advocate for a jobs guarantee, rather than a guaranteed minimum income. However, the report misses that obvious solution and doesn't mention it at all.

There are broader problems with the report though. Essentially the report assumes causal relationships, when all it is showing is correlation. People with low incomes may be lonelier, but that doesn't mean that raising their income will reduce loneliness. Maybe their income is low, and they are lonely, because they are unemployed. Even with a higher income, they would still be unemployed and lonely. Understanding the causal relationships is important in order to identify the appropriate policy (whether that be a guaranteed minimum income, a jobs guarantee, or something else).

Surprisingly, given that the report is subtitled "The risks of loneliness in Aotearoa New Zealand following Covid-19 and how public policy can help", the report mostly uses data from the 2018 General Social Survey. It does have a section where they report some survey data collected by Kate Prickett and others at Victoria University. In that section, they show that the survey data demonstrates higher levels of loneliness for the high-loneliness groups - for example:

...20 percent of those with household incomes under $30,000 reported feeling lonely most or all of the time, compared with 6.1 percent in 2018. Unemployment remained a risk factor, with 19.2 percent of those who lost their job as a result of Covid-19 reporting feeling lonely most or all of the time during the lockdown.

However, they don't report the equivalent changes in loneliness for other groups. So, we have no way of knowing whether the higher lockdown loneliness for the unemployed is greater than or less than that for the employed.

Finally, focusing additional resources on mental health was relegated to the sixth (and last) of the recommendations. I thought that was interesting. That would seem to me to be the most obvious solution, especially based on the data in this report.

Anyway, this report tells us which groups are lonely, but doesn't really help us to understand why. And without knowing why, it is difficult to identify the correct policies. At least with more resources devoted to mental health, you can feel like there will be improvements not just in loneliness, but in mental health and wellbeing more generally.

More on comparative advantage and the gender gap in STEM

Back in 2018, I wrote a post on comparative advantage and the gender gap in STEM, based on two research papers, where I noted:

So, even though female students may be better than male students in STEM subjects at school, we may see fewer of them studying those subjects at university (let alone taking them as a career), because female students are also better in non-STEM subjects at school, and they are better by more in non-STEM than in STEM, compared with male students. Economists refer to this as the students following their comparative advantage. Female students have a comparative advantage in non-STEM, and male students have a comparative advantage in STEM subjects.

In this post, I want to build on that by summarising two other research papers. The first is this article by Thomas Breda (Paris School of Economics) and Clotilde Napp (Paris-Jourdan Sciences-Economiques), published in the journal Proceedings of the National Academy of Sciences in 2018 (open access). Breda and Napp used data from the 2012 wave of PISA, covering some 300,000 15-year-old students across 64 countries. They showed that, in the PISA data:

...boys outperform girls in math by about 10% of a SD... In contrast, girls outperform boys by about a third of a SD in reading. Together, these observations suggest that girls have a comparative advantage in reading, something that appears more strikingly when we look at the gender gap in the difference between math and reading (MR) ability....

Breda and Napp then construct a measure of students' intentions to pursue maths-intensive studies and careers. They found that:

The gender gap in intentions cannot be explained by differences in math ability across genders...

That makes a lot of sense, because simply being good at maths isn't enough to encourage students to follow through on math. That depends on their comparative advantage - that is, is the student good at maths but better at other disciplines? When looking at the relationship between intensions and the difference between maths and reading (MR), Breda and Napp found that:

...the gender gap in intentions to pursue math-intensive studies and careers disappears almost entirely when one controls for individual-level differences in ability between math and reading.

In other words, the intention to study maths is more associated with the difference between maths and reading ability than it is by maths ability alone. On top of that, the difference between maths and reading ability does a better job of explain intentions than self-perceived maths ability.

The second paper (still a working paper), by Sofoklis Goulas (Stanford University), Silvia Griselda (University of Melbourne), and Rigissa Megalokonomou (University of Queensland), takes the concept of comparative advantage one step further. Their concept of comparative advantage is not just the difference between a high school student's average performance in STEM and non-STEM subjects, compared with the differences for other students in their class. What Breda and Napp refer to as comparative advantage, Goulas et al. refer to as absolute advantage. I think I prefer the Goulas et al. conception, because it more clearly conforms to what we think of as comparative advantage in a trade context - comparing opportunity costs of production between countries is analogous to comparing relative performance in STEM/non-STEM between students. A within-student comparison (like Breda and Napp) is more like a within-country comparison of production costs, i.e. absolute advantage.

Anyway, Goulas et al. have data from over 70,000 Grade 10 Greek students from 123 high schools over the period from 2001 to 2009. One of the interesting aspects of their data is that these students are assigned to classes automatically based on their surname (alphabetically). This means that they are essentially randomly allocated to classroom peers, which is important in overcoming selection bias (as I noted in Sunday's post on peer effects). Their measure of comparative advantage was the in-class ranking for each student, in terms of the difference in their average grades between STEM (algebra, physics, and chemistry) and non-STEM (modern Greek, Greek literature, and ancient Greek). Class ranking is a measure of relative performance in the class, for a group of students that it would be natural for students to compare themselves to (and for whom they probably have good information about).

Using this measure, Goulas et al. found that:

Females perform, on average, significantly higher than males in almost every subject... females' over-performance are even higher in non-STEM (=1.594) compared to STEM (=0.349)... Combining these, females have a lower comparative advantage in STEM subjects compared to males (0.409 for females and 0.487 for males).

Making use of their measures of absolute advantage (difference in average grades) and comparative advantage (within-class rank), they then look at the effects on future applications to STEM programmes in Grade 11. Focusing on the comparative advantage results, they found that:

The estimated coefficient of comparative STEM advantage is not significant for males but it is significant and equal to 0.19 for females (=0.030+0.161). This means that females who are ranked at the top of their classroom distribution in grade 10, are roughly 19% more likely to enroll in a STEM track in grade 11 than females who are ranked at the bottom of their classroom distribution, ceteris paribus...

Our findings suggest that between 4 and 6 percentage points of the 34-percentage-point gender gap (or 12-18%) in initial STEM specialization in high school are attributable to the influence of the comparative STEM advantage.

Looking at longer-term outcomes, Goulas et al. also find that comparative advantage in STEM in Grade 10 leads to a higher probability of applying to a degree-level STEM programme in university. The difference between being at the top and being at the bottom of the classroom distribution leads to a 10 percent higher likelihood of applying to a STEM degree programme. These results all appear to hold when comparing only with classmates of the same gender, when comparing at the school level rather than the class level, when changing the definition of what counts as STEM or non-STEM, and in a number of other robustness checks.

So, why does comparative advantage have such a large effect for female students, but not male students? Goulas et al. pose two mechanisms. First, they suggest lower monetary returns for women in STEM-related fields, which reduces the returns to STEM-related study. However, this is hard to reconcile with the Breda and Napp paper, which notes that the gender wage gap in STEM-related occupations is lower than for non-STEM-related occupations. The second mechanism is different preferences for STEM occupations. STEM occupations tend to be more competitive, and there is a gender gap in competitiveness (see this 2014 post, for example). Societal and environmental influences (including parents), and a lack of role models (which has been suggested as an important factor in female students not studying economics) could also contribute to this.

Coming back to the Breda and Napp article, they have an interesting suggestion on how to close the gender gap in enrolments, given the high contribution of comparative advantage:

As the gender gap in reading performance is much larger than that in math performance, policymakers may want to focus primarily on the reduction of the former. Systematic tutoring for low reading achievers, who are predominantly males, would be a way, for example, to improve boys’ performance in reading.

Redirecting education resources towards boys in order to reduce the gender gap in STEM would no doubt strike many people as counter-intuitive. It also comes with ethical issues. If STEM-related occupations are higher paying, then redirecting (male) students so that they instead study non-STEM-related subjects doesn't necessarily strike me as morally unambiguous solution. Breda and Napp make some noises in that direction but avoid being explicit about the ethical problems, while Goulas et al. more-or-less ignore the policy prescription and associated ethical issues. However, sooner or later, if we are serious about addressing the gender gap, we will have to engage with the ethical implications.

[HT: Marginal Revolution for the Breda and Napp paper; The Conversation for the Goulas et al. paper]

Read more:

• STEM-readiness and the gender gap in STEM at university
• Comparative advantage and the gender gap in STEM

Classroom ethnic diversity and grades

When parents try to get their children into good schools, there are typically two reasons: (1) they hope that the signal provided by the good school will lead to better outcomes for their children; and (2) they hope that their children will benefit from interacting with 'higher quality' peers. Peer effects have been subject to a large research literature (see this 2011 review by Bruce Sacerdote (ungated version here). For instance, there is evidence that being peered with high achieving students leads to higher achievement (although, interestingly, the book I reviewed yesterday suggested that the peer effects literature was less than robust).

The composition of peers may matter other than through their ability. This 2018 article by Angela Dills (Western Carolina University), published in the journal Economic Inquiry (sorry, I don't see an ungated version online) looked at how the ethnic make-up of the classroom affects grades. Specifically, she used data from 4435 non-honours students from 2009 to 2013, who were automatically enrolled into a compulsory course (Development of Western Civilization 101), and randomly allocated to a section. So, the students had no control over who their peer group in the class was, or the racial composition of the section. This randomisation (and the compulsory nature of the course) overcomes any selection bias.

Looking at how students' grades in the course are affected by the fraction of their classmates who are people of colour, she found nothing much significant in a linear model. However:

The effect of the percent of classmates of color on grades appears strongly nonlinear... Allowing for the quadratic term in percent minority, the estimates show no statistical difference in effects for whites and for nonwhites. At low levels of diversity, the effect of increasing the percent minority is negative; the sign of this effect turns positive with about 18% of classmates being students of color. For a class with 25% students of color, the effect of a 10 percentage point increase is a positive and statistically significant increase of about 0.1 grade points (p value=.003).

There is also some evidence that the effects differ between high-ability students and low-ability students (particularly for black students), but I don't find those results to be as convincing. The range of the proportion non-white students was rather narrow, with sections ranging from 0 percent to 30 percent non-white. It would have also been interesting to see some measures of ethnic diversity (rather than the fairly coarse measure proportion non-white) used in the analysis. Overall, we can consider this paper as providing some suggestive evidence that having diverse peers in the classroom is a good thing.

Book review: Everybody Lies

'Big Data' has become one of the most commonly used buzzwords in both the corporate world and in academia, and 'data science' is not far behind. If you want to understand the increasing relevance of these terms to social science, then Seth Stephens-Davidowitz's book Everybody Lies is a good place to start. Stephens-Davidowitz is a former Google data scientist and has a PhD in economics from Harvard (where Alberto Alesina, who sadly passed away last month, was his PhD advisor).

The subtitle of the book is "Big data, new data, and what the internet can tell us about who we really are", and the content follows on from Stephens-Davidowitz's thesis work using Google Trends search data, but goes much broader - the book also makes use of Pornhub search data, and data scraped from Wikipedia, among other sources. The underlying idea is that:

...people's search for information is, in itself, information. When and where they search for facts, quotes, jokes, places, persons, things, or help, it turns out, can tell us a lot more about what they really think, really desire, really fear, and really do than anyone might have guessed.

Stephens-Davidowitz identifies four 'unique powers' of Big Data: (1) offering up new types of data; (2) providing honest data; (3) allowing us to zoom in on small subsets of people; and (4) allowing us to do many causal experiments. On the first power, among other examples he talks about text-as-data and sentiment analysis (which is a rapidly emerging field, and I have blogged previously about its use - see here), and pictures-as-data and the use of night lights as a proxy for economic activity (I have blogged about several papers that do this - see here and here and here for examples).

On the second power, Stephens-Davidowitz rightly notes that there are a lot of topics where survey data are likely to be seriously flawed due to social desirability bias - people answering survey questions in a way that makes them look better than they actually are. However, it turns out that people are much less worried about social desirability when it comes to what they type into a search engine. Stephens-Davidowitz is able to use these search data to explore questions such as what proportion of men are homosexual (more than most surveys suggest),  how racist Americans really are (much more than surveys reveal, as recent events have demonstrated), and whether Freudian slips are real (probably not).

On the third power, Stephens-Davidowitz provides several examples of where large datasets allow analyses for small areas or small groups, that even large surveys would not be able to tell us much about. Finally, Stephens-Davidowitz devotes a section to experiments and A/B testing to illustrate the fourth power of big data.

Finally, he devotes a chapter to some of the limitations of big data, and in particular, he highlights the ethical issues that may arise. That sets this book apart from, say, Reinventing Capitalism in the Age of Big Data (which I reviewed here), which is much less reflexive in discussing the potential current and future uses of big data.

Overall, I really enjoyed this book, and I highly recommend it to the general reader.

The impact of non-pharmaceutical interventions in the 1918 flu pandemic

The COVID-19 pandemic has many people thinking about the trade-off between public health and the economy (for example, see my post on the optimal coronavirus lockdown period). A reasonable question to ask is how big is the trade-off? After all, a strict lockdown reduces economic activity, and it reduces the spread of the virus, which reduces the public health cost of the pandemic. However, the public health cost in turn has an economic cost, because people who are made sick or die reduce the productive capacity of the economy.

We don't know the answer to the trade-off question in relation to the coronavirus (as I noted in this post), but perhaps looking at past pandemics can help us to infer what the trade-off is likely to be like. As one example, this new (and revised) working paper by Sergio Correia (Federal Reserve Board), Stephan Luck (Federal Reserve Bank of New York), and Emil Verner (MIT) looks at the impact of non-pharmaceutical interventions (NPIs) during the 1918 flu pandemic in the U.S. NPIs include "school, theater, and church closures, public gathering bans, quarantine of suspected cases, and restricted business hours".

Specifically, Correia et al. categorised the speed and intensity of NPIs at the city level for 43 U.S. cities, and look at how differences in the speed and intensity impacted on a measure of business disruptions. The results are a little surprising:

...when we compare cities with strict and lenient NPIs, we find that the increase in business disruptions in the fall and winter of 1918 was quantitatively similar across the two sets of cities. Our findings thus indicate that NPIs did not clearly exacerbate the economic downturn during the pandemic.

Further, we examine the economic impact of NPIs in the medium run. We find no evidence that cities that intervened earlier and more aggressively perform worse in the years after the pandemic, measured by local manufacturing employment and output and the size of the local banking sector.

In other words, there was no difference in business disruption between cities that went 'hard and fast' and those that didn't. That suggests no trade-off between the economy and public health, or as Correia et al. put it:

...our results suggest that it is not a foregone conclusion that there is a trade-off between reducing disease transmission and stabilizing economic activity in a pandemic.

This working paper has already been through at least one set of revisions, in response to some strong critiques such as this one by Andrew Lilley, Matthew Lilley, and Gianluca Rinaldi (all Harvard University). However, let's not get carried away and start believing there is no trade-off between public health and the economy in our current crisis. I still see some fairly major problems with this working paper.

Essentially, Correia et al. want us to believe that they have demonstrated no impact of NPIs on business disruptions. Proving a negative is of course impossible statistically. Proving a positive (e.g. that NPIs do impact business disruptions) is also impossible, but our normal statistical methods are at least geared towards demonstrating the strength (or weakness) of evidence in favour of an impact. As a result, we are generally much more likely to demonstrate that there is no impact when there really is, rather than the other way around.

One of the reasons we are more likely to show no impact where there really is impact is lack of statistical power. To have confidence in the results, and therefore improve the precision of the estimated effects, you need to have lots of data. Smaller datasets are less likely to show statistical significance, not because there is no effect, but because the measured effect is noisy. So, if you want to argue the absence of an effect ('no impact'), you need to argue that your statistical methods have enough statistical power to find an effect if there was one. Correia et al. don't really do this, although I don't have major concerns about the size of their dataset.

The strength (or weakness) of statistical evidence also depends on the quality of the data. Measurement error is typical problem, and when an explanatory variable is measured with error then the statistical estimates are more likely to show up as statistically insignificant. Correia et al.'s measure of NPI speed and intensity might not suffer from much in the way of measurement error - however, their measure does conflate the speed (how soon NPIs were put in place after each city exceeded twice its baseline mortality rate) and intensity (the cumulative sum of the number of days where school closure, public gathering bans, and quarantine/isolation of suspected cases were in place).

More damaging for the paper is the measure of business disruptions, which is based on a coding of city-level qualitative reports of business activity taken from the weekly Bradstreet’s - A Journal of Trade, Finance, and Public Economy. While Correia et al. are clear in how they code this variable in their analysis, it is not at all clear how Bradstreet's constructed this evaluation in the first place. Moreover, some of the Correia et al. coding is likely to induce measurement error, particular how they handle relative descriptors in the data (e.g. "improving" or "slowing down"), and even some of the absolute descriptors (e.g. "below normal" is coded as Bad, while "60 percent" is coded as Fair). The robustness of the analysis to these choices needs to be tested.

Finally, there was one interesting bright spot in the paper, but it surprised me that Correia et al. didn't follow through on it. Early on, they note that:

...cities that experienced outbreaks at later dates tended to implement NPIs sooner within their outbreak, as they learned from the experiences of cities affected earlier... Thus, as the flu moved from east to west, cities located further west were faster in implementing NPIs.

It seems to me that the longitude of each city could be used to instrument for at least the speed measure of NPIs. Using instrumental variables reduces problems of measurement error (at least for the NPI variable - the business disruptions variable still needs some thorough checks on the robustness of results). Perhaps this is an opportunity for some follow-up work, either for these authors or for an enterprising student.

[HT: Marginal Revolution]

A trade-off between grades and future earnings?

As a university student, would you rather have higher grades, or higher earnings in mid-career? It may seem like this isn't a choice you would have to make. After all, it is reasonable to believe that, on average, students with higher grades will end up earning more later in life. So, let me re-frame the question a little bit: Would you rather choose a major that offers higher grades, or a major that offers higher earnings? Now, you may be a little less sure - is there actually a trade-off here?

It turns out that there may be. This 2016 article by Timothy Diette (Washington and Lee University) and Manu Raghav (DePauw University), published in the journal Education Economics (ungated earlier version here) suggests that there is. They used data from students enrolled at a single liberal arts college over the period from 1996 to 2008 (over 120,000 student-course observations), and looked at how students' grades differed by the median mid-career salary of the academic discipline of the course. They also controlled for student demographics, ability (SAT scores), and course characteristics, and found:

...a negative and statistically significant coefficient estimate for the median salary variable. Thus, the results suggest that departments with higher mid-career median salaries on average give lower grades after controlling for observable student characteristics and faculty fixed effects. The coefficient estimate of −0.002 suggests that moving from the lowest to highest paying major, an increase in salary of 46,600 dollars lowers a student’s grade by approximately 0.09 grade points or 12.2% of a standard deviation in grade points, a very small change for a three standard deviation change in median salary.

In other words, there does appear to be a trade-off between grades and earnings, albeit a small one. Students studying in majors that lead to higher later earnings can expect slightly lower grades. The effects were not the same for all students though:

...female students, who far outperform their male counterparts on average, lose some of their advantage in courses associated with higher [mid-career salaries]... those with relatively low SAT math scores are much more likely to get lower grades in courses offered by departments that have higher mid-career salaries.

In other words, the grade penalty for studying in a department leading to a higher mid-career salary is larger for female students, and for students with less mathematical ability. The effect on female students is interesting, and I wonder the extent to which it reflects the robust gender gap in earnings (which I have written about before). This would definitely be interesting to follow up on, because it holds even though student ability is controlled for (which suggests that it isn't necessarily the result of better female students sorting out of majors where grades are lower on average). On the other hand, the effect on less able students is pretty intuitive - it suggests they struggle more in subjects that lead to higher mid-career earnings.

Overall, these results have interesting implications for students. First, if you are using grades as a signal as to what you should major in, look at your grades relative to the rest of your class, not your grade relative to the other classes you are taking. If you are getting an A- in a class where the average is a B-, then that may suggest you are better in that major than you would in a class where you are getting an A but the class average is A-. Second, remember that grades are not the only signal to future employers about your ability. Employers do know the difference between an 'easy' major and a 'hard' major, which is a point I have made before.

The unfortunate thing about this analysis is that it doesn't answer the key question though - would a student be better off changing their major. This applies to students doing well in an 'easy' major (would they be better off changing to a 'harder' major) and to students doing poorly in a 'harder' major (would they be better off changing to an 'easier' major). I guess we will have to wait for an answer to those questions.

The geography of development and the gains from relaxing migration restrictions

I just finished reading this 2018 article by Klaus Desmet (Southern Methodist University), David Nagy (Centre de Recerca en Economia Internacional), and Esteban Rossi-Hansberg (Princeton), published in the Journal of Political Economy (it appears to be open access, but just in case there is an ungated version here). The article is quite daunting because it sets up and calibrates a complex spatial model of development, which is disaggregated down to a 1° x 1° grid across the whole world. The simulation model itself is incredibly mathematical. However, if you can put the maths aside and focus on the results, what you find is interesting and insightful.

Essentially, having calibrated their simulation model, Desmet et al. look at the 'balanced growth path' of the world economy. This is the growth path "in which the geographic distribution of economic activity is constant" - in other words, where every grid cell grows at the same rate. It can take a long time for the world economy to achieve this balanced growth path, so their model runs for 600 years into the future (starting from 2000). They also run the model backwards, and can show that it does a reasonable job of replicating the pattern of population and economic development back to 1870.

Looking forward though, they base their analysis on two main scenarios: (1) holding the current pattern of migration restrictions constant; and (2) an immediate change to the free movement of people between countries and places. Both scenarios have interesting results.

In the status quo scenario, they find that:

...over time the correlation between population and productivity across countries becomes much stronger. As predicted by the theory, in the long run, high-density locations correspond to high-productivity locations...

...the high-productivity, high-density locations 600 years from now correspond to today’s low-productivity, high-density locations, mostly countries located in sub-Saharan Africa, South Asia, and East Asia. In comparison, most of today’s high-productivity, high-density locations in North America, Europe, Japan, and Australia fall behind in terms of both productivity and population.

In case you find those results surprising, Desmet et al. explain:

This productivity reversal can be understood in the following way. The high population density in some of today’s poor countries implies high future rates of innovation in those countries. Low inward migration costs and high outward ones imply that population in those countries increases, leading to greater congestion costs and worse amenities. As a result, today’s high-density, low-productivity countries end up becoming high-density, high-productivity, high-congestion, and low-amenity countries, whereas today’s high-density, high-productivity countries end up becoming medium-density, medium-productivity, low-congestion, and high-amenity countries; the United States is among them. Australia’s case is somewhat different since its low density and high inflow barriers imply that it becomes a low-productivity, high-amenity country. 

You can group New Zealand along with Australia in that paragraph. However, the takeaway message from this scenario is that the current pattern of migration restrictions, that keeps people out of high-income countries, serves to drive population density, innovation, and economic growth in the current lower-income countries to such an extent that they overtake the current high-income countries in income per capita by the end of the simulation period. That can be clearly seen from this picture (part of Figure 3 in the paper, and there are videos of the simulation model here - this is the end of Video 1B), where warmer colours represent higher levels of income per capita:

In contrast, if migration restrictions are ended, the areas that currently have high productivity attract migrants, which boosts their population, innovation, and future economic growth. So, in the free migration scenario, Desmet et al. find that:

Because today’s poor countries lose population through migration, they innovate less. As a result, and in contrast to the previous exercise, no productivity reversal occurs between the United States, India, China, and sub-Saharan Africa... Some countries, such as Venezuela, Brazil, and Mexico, start off with relatively high utility levels but relatively low productivity levels. This means they must have high amenities. Because of migration, they end up becoming some of the world’s densest and most productive countries, together with parts of Australia, Europe, and the United States.

Coastal areas also benefit greatly when migration is free. Here's the corresponding map for the free migration scenario (part of Figure 7 in the paper, and again in the videos online you can see its evolution - this is the end of Video 3B):

You can see the difference in income per capita between the two scenarios by comparing those two maps. Another interesting point is that the effect of lifting migration restrictions is immediate, with 70.3 percent of people moving immediately once the restrictions are lifted. That demonstrates how restrictive current regulations are. There are also substantial welfare gains from free migration:

In present discounted value terms, complete liberalization yields output gains of 126 percent and welfare gains of 306 percent.

While the exact numbers depend on the particular calibration of the model, I think we can safely conclude that there are huge gains in human welfare to be had from lifting migration restrictions. As Michael Clemens noted in this article in the Journal of Economic Perspectives (open access), maintaining migration restrictions leaves trillion dollar bills on the sidewalk.

The results reported in this paper should make high-income country governments seriously reconsider their immigration policies. High immigration restrictions seriously benefit China, India and maritime Asia in the long run, and are detrimental to the future economic growth of the current high-income countries. If high-income countries want to maintain their high-income status, these restrictions need to be reconsidered. However, it would be interesting to see what happens in the simulation model when one country (or a small number of countries; or rather grid cells) lifts restrictions but others do not. Perhaps that is a future exercise, but in terms of providing input to policy decisions, it seems critical.

[HT: Marginal Revolution, last year]

You may be able to buy Coke with Bitcoin, but that still doesn't make Bitcoin money

This story in the New Zealand Herald yesterday caught my eye:

A lot of the narrative on virtual currency revolves around its yo-yo-ing worth.

Will we see geeks buying more Ferraris if bitcoin breaks back toward US$20,000, or crying into their keyboards if it crashes below US$5000 again?

But to become an enduring currency, it will also have to prove its utility on a meat-and-potatoes level - such as buying everyday stuff.

That goal has got a little bit closer today with a deal that means Australians and New Zealanders can now buy a coke from a vending machine with bitcoin.

Interestingly, in our ECONS101 tutorial on the topic of money and inflation, we ask the question of whether Bitcoin is money. The answer is no. To see why though, you have to understand what money is.

As I noted in this post last year:

To an economist, money is something that fulfils three functions, which date back to William Stanley Jevons in 1875...:

1. It is a medium of exchange - you give it up when you buy goods or services, and you can receive it when you sell goods or services.

2. It is a unit of account - you can measure the value of something using the amount of money it is worth; and

3. It is a store of value - you can keep it and it will retain its value into the future.

Anything that fulfils those three functions can be considered money. So, coins and banknotes are money because you can exchange them for goods and services, you can use them to measure the value of things, and you can store them and use their value in the future.

Does Bitcoin fulfil those three functions of money? The Herald article only covers the first (medium of exchange) - Bitcoin is used to buy at least some goods and services. However, Bitcoin fails on the last two criteria. It isn't used as a unit of account - no one's quoting you prices in Bitcoin, and I bet the vending machines don't report the Bitcoin price of a can of Coke. And, Bitcoin isn't much of a store of value. It fails on both of those criteria because the value of Bitcoin is far too volatile. Here's the value of Bitcoin over the last twelve months (from Coindesk):

You wouldn't want to store value in an asset that routinely loses a third of its value in a matter of weeks. You're also unlikely to want to quote prices in something that varies widely in value even across a day or two. And on top of that, Bitcoin probably still isn't widely accepted enough to even be considered a medium of exchange.

So, other than creating a bit of media attention for Coke and for their technology partner, this story isn't telling us that Bitcoin is money. You don't need to throw away your dollars just yet.

Book review: Social Economics

I just finished reading Social Economics, by Gary Becker (who sadly passed away in 2014) and Kevin Murphy. Becker and Murphy are known for a lot of research, including the model of rational addiction (based on this 1988 article, ungated here). This book follows a similar trajectory, introducing 'social capital' into the utility maximisation framework. However, this isn't quite social capital as many people would recognise it, but might be better characterised as 'peer effects'. In other words, what Becker and Murphy introduce is an explicit recognition that the utility we derive from consuming a particular good may depend on whether others also consume it (and, in some instances, on who it is who is consuming it).

It has to be said up front that this book is not for the faint of heart. As is the case for a lot of Becker's research, it can be quite mathematical. However, if you are able to look beyond the maths, there are lots of interesting insights to be drawn. For instance, in Chapter 5 they look at the effects of neighbourhoods, where the quality of the neighbours matters. Home buyers are attracted by both the quality of local amenities, and the quality of neighbours. The implication of that model though, is that if local amenities improve in quality (or quantity), that will attract better quality neighbours. If we believe this model, then using hedonic demand models to estimate the value of local amenities must necessarily overestimate their value, because a change in house prices arising from a change in amenity will reflect both the value of the amenity plus the value of the change in the quality of neighbours. I don't believe that I have seen anyone engage with that implication within the hedonic demand literature.

They also demonstrate how a small difference in the quality of art or antiques can lead to a large difference in price. We might think of this as a 'superstar effect' in the art market. They also show how a fashion market with leaders and followers can lead to an upward sloping demand curve in some price ranges, where the price has fallen enough so that some followers can start to purchase the good, but because of its increasing popularity, many of the leaders stop purchasing.

Despite the mathematical foundations, Becker and Murphy write in a style that is reasonably easy to follow and for the most part they explain their reasoning well. The one exception I found is where they argue in Chapter 8 (written with Ivan Werning) that people with higher status have higher marginal utility of consumption (or income). Although this is an important assumption that drives the results in that chapter (and later, in the chapter on leaders and followers), it isn't strongly justified. They do offer this later in the chapter:

...complementarity is necessary to explain the observed positive relation between consumption and status among competing individuals. Without gambles, there would be a compensating differential for higher status, so that persons with higher status would have lower consumption and the same utility as others.

I can see the argument for consumption and status being complementary because it leads to the theoretical results, but I would have liked to have seen more explanation of the authors' reasoning underlying the assumption. This seems too much like working backwards from the conclusion to identify the necessary set of assumptions. 

This book itself should be seen as complementary to George Akerlof and Rachel Kranton's excellent Identity Economics (which I reviewed here), which is less mathematical and admittedly doesn't cover quite the same ground. However, readers of one could not doubt enjoy greater insights by reading both books together. Nevertheless, for readers with a reasonable background in economics looking to understand some utility-based theory on how social relations might affect markets, by itself the book provides a good grounding.

The students' grade scaling dilemma

One of the sad things about teaching online is that I miss out on some of the more interesting conversations with students. I can almost never anticipate some of the truly interesting questions they come up with, and many of them unfortunately cannot be answered with the simple tools of introductory economics. Sometimes though, they can. Consider this example (paraphrased from a real question I was asked recently, but not by a current student of mine): If every paper is going to have its grades scaled to match past semesters, why should anyone do any of the coursework at all?

First, some context. The COVID-19 crisis has caused considerable disruption to university teaching, and the move to teaching and learning online has without doubt disadvantaged many students. There is justifiable concern that students' grades will be negatively affected. Some universities will be automatically scaling up all grades (e.g. University of Auckland). At Waikato, our Vice-Chancellor has announced that there will be no automatic scaling, but individual grades, and grade distributions for papers, will be compared with past trimesters, and adjusted to ensure they compare fairly with those past trimesters.

Now, as a student, if you know that grades will be scaled, then the incentive for you to work hard are lowered somewhat. Now think about the incentives for the class as a whole. If you could coordinate with all of the other students in your class as a 'cooperative', you could all agree to do no coursework at all. At the end of the trimester, you would all have your grades scaled up. And since the grade distribution needs to be similar to past years, most students in the cooperative would pass, without having to do any work at all.

So, why won't this happen? This is essentially an example of the prisoners' dilemma from game theory (see here for another example). The problem for the student cooperative is that the social incentive (to work together, do no coursework, and be scaled into a passing grade) doesn't match the private incentive. The private incentive for each student is to work slightly harder than the students in the cooperative, so that after the scaling you are at the top of the distribution, and get an easy A+ grade.

In fact, working slightly harder is a dominant strategy - it makes you better off if all of the other students do no coursework (since you get an easy A+), and it makes you better off if all the other students work slightly harder as well (since otherwise you fall behind and drop down the grade distribution, and are at risk of failing even after the grades are scaled). [*]

So, no student would agree to join the 'no-coursework cooperative', unless they could be sure that every other student would join as well. And no student could trust the other students to follow through on the cooperative, since every one of them could get an easy A+ by working slightly harder.

Cooperation is hard. As I note in my ECONS101 class, it requires trust between the players. And trust usually requires developing a reputation for being trustworthy. Unless you know the other students in your class really well, you probably have no reason to trust that they will follow through on a no-coursework agreement.

And so, that's why students should continue to do some coursework.

*****

[*] This doesn't quite extend to a strategy of 'working crazy hard' being a dominant strategy, because at some point the costs of increasing how hard you work on a paper begin to outweigh the benefits of doing so. We could easily make this much more complicated than necessary, so let's stick to two strategies - 'doing no coursework', and 'working slightly harder'.

Rioting as a coordination game

There are many situations that require decision-makers to coordinate their decisions. These include situations where we are better off doing the same as everyone else, or better off doing something different to everyone else. Economists refer to these situations as coordination games (such as in this post about the panic buying of toilet paper). Earlier this week, the Scholar's Stage blog had a post about rioting that demonstrates a coordination game at work:

Let us say you are a man inclined towards a riot...

Yet you and all those like you have a problem. The man inclined towards a riot cannot simply wake up one day and begin one. The lone rioter is not a rioter at all. He is simply a common vandal. The system can handle that problem with ease. This is the sorrow of the would-be rioter: he cannot begin his riot until he is sure all the other would-be rioters will pound the streets besides him.

Up front I want to point out that people may have good reason to be angry (and in the case of recent events, justifiably so), and have good cause to have their voices heard. However, there is a difference between protest and rioting (which as the Scholar's Stage blog post notes, explains why riots have also occurred after good news like sports team victories). So, the analysis of rioting need not rely on consideration of any underlying anger.

Now, let's consider this situation using some simple game theory. To keep things simple, let's assume that there are just two potential rioters, Person A and Person B. There are two strategies: riot, and not riot. Assuming that this is a simultaneous game (both players' decisions about strategy are revealed at the same time), then we can lay out the game as a payoff table, like this:

The payoffs are measured in utility (satisfaction, or happiness), for the two players. If both players riot, they get to release their angry and smash some stuff up, and both players receive positive utility (utility = +5). If one player riots and the other doesn't, then the rioter is easily singled out by police as a vandal and subject to punishment (utility = -5), but the player not rioting is no better or worse off than before (utility = 0). If neither player riots, then both are no better or worse off than before (utility = 0).

Now, to find the Nash equilibriums in our game, we can use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the textbook definition of Nash equilibrium). In this game, the best responses are:

1. If Person B chooses to riot, Person A's best response is to riot (since +5 is a better payoff than 0) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If Person B chooses not to riot, Person A's best response is not to riot (since 0 is a better payoff than -5);
3. If Person A chooses to riot, Person B's best response is to riot (since +5 is a better payoff than 0); and
4. If Person A chooses not to riot, Person B's best response is not to riot (since 0 is a better payoff than -5).

Notice that there are two Nash equilibriums in this game: (1) where both players choose to riot; and (2) where both players choose not to riot. Which of these two equilibriums will obtain depends on what each player thinks the other player will do. So, if there is good reason to believe that the other player is not going to riot, your best response is also not to riot (and vice versa for the other player). But, if there is good reason to believe that the other player is going to riot, your best response is to riot too (and vice versa for the other player).

How does each player work out what to do? Notice that both players in this game prefer to riot (they are better off both rioting, than both not rioting). However, you wouldn't riot if you couldn't be sure that the other player was going to as well. If one of the players can send a credible signal about their strategy to riot, then everyone knows that rioting is on the cards, and a riot develops. So, what makes a credible signal? The Scholar's Stage blog quotes David Haddock and Daniel Posby (Understanding Riots):

Certain kinds of high-profile events have become traditional “starting signals” for civil disorders. In fact, incidents can become signals simply because they have been signals before. What ignited the first English soccer riot has been lost in the mists of history; but they had become a troublesome problem sometime during the nineteenth century, as Bill Buford (1991) makes clear in quoting old newspaper accounts in his Among the Thugs. Today, there is a century’s weight of tradition behind soccer violence. People near a football ground on game day know that a certain amount of mischief, possibly of a quite violent kind, is apt to occur. Those who dislike that sort of thing had best take themselves elsewhere. Certain people, though, thrive on the action —relish getting drunk, fighting, smoking dope; enjoy the whiff of anarchy, harassing and beating respectable people and vandalizing their property. Such people—hooligans—make a point of being where the trouble is likely to start....  In Detroit in recent years, “Devils Night” (the night before Halloween) has become a springboard for multiple, independent, almost simultaneous acts of arson. These are examples, baleful ones, of how culture, habit, and tradition can overcome major organizational barriers to cooperative social endeavors and lower the cost of transacting business.

A credible signal has to be costly, and other players have to be sure that the signalling player will follow through on the strategy choice (in this case, rioting). Throwing the first stone (literally and figuratively) is a costly action, and demonstrates the willingness to riot. However, players need to know that it is 'safe' to be the person throwing that stone. Coordinating around certain 'trigger events', where rioting is 'expected' behaviour (or at least, not unexpected) provides the appearance of safety and therefore provides a way of overcoming the uncertainty inherent in this coordination game.

Based on this simple analysis, it is obvious that even something as chaotic as a riot requires some coordination.

[HT: Marginal Revolution]