Category: Education

The Economics behind the Math Gender Gap

Juan Sebastián Muñoz (the economist, not the golfer) has a new paper on this topic, focusing on Colombia:

The literature that has previously shown that boys outperform girls in math tests has failed to explain the underlying causes of the phenomenon. This math gender gap has been documented to vary across countries, and shown to grow as students advance through school. In this paper I suggest that these patterns may be explained by sample selection caused by gender differences in schooling’s opportunity costs, which lead lower-achieving males to drop out. I present and test the implications of a labor supply model that examines the opportunity cost of school attendance and, thereby, the observed math gender gap. Using an exogenous policy change, the launch of a conditional cash transfers program in Colombia,
I estimate that sample selection explains between 50 percent and 60 percent of the gap. Estimates of non-parametric bounds show that selection in the lower quantiles of the male distribution explains a significant portion of the gap.

More on statistical discrimination

A few of you have raised objections to my recent statistical discrimination hypothesis on the grounds that, if it were true, minority group members who “made it to the top” should be the super-achievers, since they had to pass through so many screens and implicit taxes.  I wrote back the following (edited) in an email:

Maybe, but I think you are assuming fixed quality of talent within each sector.

Let’s say there are two sectors. In the first, the CEO sector, women face statistical discrimination and there are multiple levels. In the second there is no statistical discrimination, let us call it women’s tennis but of course there are other examples too.

It could be that most of the talented women, those who can judge where they really will succeed best and most easily, flock to the latter sectors.  In which case the winners in the CEO sector need not be so special, including in the presence of discrimination.

That also means that employers and intermediaries have no special incentives to hunt for that talent: it has run away to other, less discriminatory sectors (and lowered wages in those sectors, I might add).

By the way, here was one good comment by Willitts on that post:

…if the signal of skill is “years of experience,” then the person filtered at the lower level will always look objectively worse at the higher level filters.

You’re assuming that the higher level decision makers have the opportunity (and desire) to consider walk-on candidates. You’re also assuming that those walk-ons will have adequate means to signal their superiority to those who passed through the filters.

I might be able to be the best CEO who ever lived, but my lack of management experience would never get me in the door for an interview. If (mild) discrimination at several rungs of the ladder kept me from rising to the penultimate rung, I’d have ZERO chance of attaining the top rung, not merely a small chance

And David:

Most elite performers are impressive throughout their lives. But they can stay constantly motivated, by rising through the ranks quickly. A stat-discriminated person might not have that advantage either.

And Jwilli7122:

Well, with the first gatekeeper there’s really no motivation to gamble on the marginalized, because a) there’s not yet a big gap and b) doing so would give up the profit of stereotyping (see the Bayesian analysis referenced in #3 of Dan’s post).

And as you get to the subsequent gatekeepers, a larger actual ability gap starts to form because the discrimination of prior gatekeepers prevented the marginalized group from gaining valuable experience.

I will continue to ponder this problem.

Crowdfunding science, from other scientists

…all qualified scientists would get some guaranteed funding — no grants required. But there should be one added step: everyone must anonymously allocate a fraction of their funds to other researchers of their own choosing.

The goal of this system would be to let scientists devote more of their time to research…

In SOFA [Self-Organizing Funding Allocation], every participant starts with the same allocation of funding every year but must allot a portion to other scientists. Reasons to select someone could range from, ‘That was a great paper’ to ‘I think they will release useful data.’ Those who get the most give the most, because scientists give a percentage of everything received under SOFA. To avoid currying favour, this process will be anonymous…

We can limit collusions and kickback schemes — the financial equivalent of citation cartels — by mandating a minimum number of recipients and restricting people from designating frequent collaborators, or colleagues at the same institution. Counteracting gender, age and prestige biases that plague conventional peer review might even be easier in SOFA because they are measurable.

Here is the Johan Bollen piece in Nature.

My musical self-education

Musick-er requests:

I’ve noticed that you tend to have pretty wide ranging tastes in music, and your recommendation on introduction to classical music was pretty spot-on. I’m wondering what training/expertise you have in music theory/aural skills?…As someone who is obviously very intelligent but not a musician (that I know of), I wonder how you interact with Bach or other master composers – what criteria do you listen for? What makes great works stand out from the merely good?

My history is this:

1. I learned how to play the guitar when I was twelve or so, and also figured out how a piano works.

2. I spent about six years studying jazz chords, American popular song, some classic rock, early acoustic blues and ragtime, Fahey/Kottke, and Bach.  I also learned how to listen with a score, at least for guitar and piano pieces.

3. Later in life, I focused on trying to make sense of early to mid 20th century classical music and Indian classical music, both excellent entry points for many of the other difficult musical genres and styles.  I tried to learn at least something about micro-tonal musics and ragas.

4. Starting in my thirties, I tried to develop a basic familiarity with world musics, not so much the European folkie stuff as those based on different conceptual principles, such as some of the Arab musics, Chinese music, and African musics including the Pygmies.

5. I cultivated “music mentors” to help me understand these musics.  Overall this is not a very book-intensive endeavor, though you will enjoy reading accompanying biographies.

I am not saying that is the right path for everyone, but I found it very rewarding, including for my broader understanding of history.

To address one of the specific questions, I think of Bach-Stravinsky, classic rock, and Indian classical music (live only) as covering some of mankind’s greatest cultural achievements, with only cinema in the running for possible parity.  Most of all just listen plenty, noting that the canonical opinions about what is best are actually pretty much on the mark.

Why statistical discrimination is higher than is either socially optimal or Bayesian rational

Let’s say there is only a mild amount of statistical discrimination in a system.  Not prejudice, just a social judgment that some groups are more likely to succeed at some tasks than others.  Most people, for instance, do not expect women to reach the NBA, but I would not from that conclude they are prejudiced.

But now introduce a further assumption.  There are multiple layers of evaluation, and at each layer people, and institutions, wish to be seen as successful talent spotters, mentors, and coaches.  High schools wish to promote students who will get into good colleges.  Colleges wish to invest in students who will get into best grad schools, or get the best jobs.  Firms wish to hire workers who will rise to CEO, even if elsewhere.  And so on.  Let’s say there are ten levels to this “game.”

Each level will apply its own “statistical discrimination” tax, whether intentionally or not.  Say for instance there is (mild) statistical discrimination against women at the CEO level.  Firms that wish to hire and promote future CEOs will be less likely to seek out women to hire, including at lower levels.  This may or may not be conscious bias; for instance the firms may decide to look for certain personality traits that, for whatever reason, are harder to find in women.  They’ll simply be making decisions that give them plaudits as good talent spotters.

Colleges will then consider similar factors in their decisions.  And so will high schools.  And so on.  In equilibrium, all ten levels of the game will levy a partial “statistical discrimination tax,” with or without conscious bias in thee discriminatory direction.

Does this sound familiar?  It is a bit like the double/multiple marginalization dilemma in microeconomics.  The number of discrimination taxes multiplies, at each level.  Just like the medieval barons put too many tolls on the river.  All of a sudden the initially mild statistical discrimination isn’t so mild any more, due to it being applied at so many veto-relevant levels.  (As you will recall from the double marginalization problem, each supplier does not take into account the effect of his/her mark-up or tax on the gains from trade elsewhere in the system.)

So say the “Bayesian rational” level of statistical discrimination is a five percent discount.  You can get far more than that as the actual effective tax on the disadvantaged group, with everyone in the system behaving in a self-interested manner.

And of course these taxes will discourage effort from the disadvantaged groups, to the detriment of efficiency and also justice.

I am indebted to Anecdotal for a useful query related to this discussion.

My Conversation with Michael Pollan

I was very happy with how this turned out, here is the audio and transcript.  Here is how the CWTeam summarized it:

Michael Pollan has long been fascinated by nature and the ways we connect and clash with it, with decades of writing covering food, farming, cooking, and architecture. Pollan’s latest fascination? Our widespread and ancient desire to use nature to change our consciousness.

He joins Tyler to discuss his research and experience with psychedelics, including what kinds of people most benefit from them, what it can teach us about profundity, how it can change your personality and political views, the importance of culture in shaping the experience, the proper way to integrate it into mainstream practice, and — most importantly of all — whether it’s any fun.

He argues that LSD is underrated, I think it may be good for depression but for casual use it is rapidly becoming overrated.  Here is one exchange of relevance:

COWEN: Let me try a very philosophical question. Let’s say I could take a pill or a substance, and it would make everything seem profound. My receptivity to finding things profound would go up greatly. I could do very small events, and it would seem profound to me.

Is that, in fact, real profundity that I’m experiencing? Doesn’t real profundity somehow require excavating or experiencing things from actual society? Are psychedelics like taking this pill? They don’t give you real profundity. You just feel that many things are profound, but at the end of the experience, you don’t really have . . .

POLLAN: It depends. If you define profundity or the profound as exceptional, you have a point.

One of the things that’s very interesting about psychedelics is that our brains are tuned for novelty, and for good reason. It’s very adaptive to respond to new things in the environment, changes in your environment, threats in your environment. We’re tuned to disregard the familiar or take it for granted, which is indeed what most of us do.

One of the things that happens on psychedelics, and on cannabis interestingly enough — and there’s some science on it in the case of cannabis; I don’t think we’ve done the science yet with psychedelics — is that the familiar suddenly takes on greater weight, and there’s an appreciation of the familiar. I think a lot of familiar things are profound if looked at in the proper way.

The feelings of love I have for people in my family are profound, but I don’t always feel that profundity. Psychedelics change that balance. I talk in the book about having emotions that could be on Hallmark cards. We don’t think of Hallmark cards as being profound, but in fact, a lot of those sentiments are, properly regarded.

Yes, there are those moments you’ve smoked cannabis, and you’re looking at your hand, and you go, “Man, hands, they’re f — ing incredible.” You’re just taken with this. Is that profound or not? It sounds really goofy, but I think the line between profundity and banality is a lot finer than we think.

And:

COWEN: I’ve never myself tried psychedelics. But I’ve asked the question, if I were to try, how would I think about what is the stopping point?

For my own life, I like, actually, to do the same things over and over again. Read books. Eat food. Spend time with friends. You can just keep on doing them, basically, till you die. I feel I’m in a very good groove on all of those.

If you take it once, and say you find it entrancing or interesting or attractive, what’s the thought process? How do you model what happens next?

POLLAN: That’s one of the really interesting things about them. You have this big experience, often positive, not always though. I had, on balance . . . all the experiences I described in the book, with one notable exception, were very positive experiences.

But I did not have a powerful desire to do it again. It doesn’t have that self-reinforcing quality, the dopamine release, I don’t know what it is, that comes with things that we like doing: eating and sex and sleep, all this kind of stuff. Your first thought after a big psychedelic experience is not “When can I do it again?” It’s like, “Do I ever have to do it again?”

COWEN: It doesn’t sound fun, though. What am I missing?

POLLAN: It’s not fun. For me, it’s not fun. I think there are doses where that might apply — low dose, so-called recreational dose, when people take some mushrooms and go to a concert, and they’re high essentially.

But the kind of experience I’m describing is a lot more — I won’t use the word profound because we’ve charged that one — that is a very internal and difficult journey that has moments of incredible beauty and lucidity, but also has dark moments, moments of contemplating death. Nothing you would describe as recreational except in the actual meaning of the word, which is never used. It’s not addictive, and I think that’s one of the reasons.

I did just talk to someone, though, who came up to me at a book signing, a guy probably in his 70s. He said, “I’ve got to tell you about the time I took LSD 16 days in a row.” That was striking. You can meet plenty of people who have marijuana or a drink 16 days in a row. But that was extraordinary. I don’t know why he did it. I’m curious to find out exactly what he got out of it.

In general, there’s a lot of space that passes. For the Grateful Dead, I don’t know. Maybe it was a nightly thing for them. But for most people, it doesn’t seem to be.

COWEN: Say I tried it, and I found it fascinating but not fun. Shouldn’t I then think there’s something wrong with me that the fascinating is not fun? Shouldn’t I downgrade my curiosity?

POLLAN: [laughs] Aren’t there many fascinating things that aren’t fun?

COWEN: All the ones I know, I find fun. This is what’s striking to me about your answer. It’s very surprising.

W even talk about LSD and sex, and why a writer’s second book is the key book for understanding that writer.  Toward the end we cover the economics of food, and, of course, the Michael Pollan production function:

COWEN: What skill do you tell them to invest in?

POLLAN: I tell them to read a lot. I’m amazed how many writing students don’t read. It’s criminal. Also, read better writers than you are. In other words, read great fiction. Cultivate your ear. Writing is a form of music, and we don’t pay enough attention to that.

When I’m drafting, there’s a period where I’m reading lots of research, and scientific articles, and history, and undistinguished prose, but as soon as I’m done with that and I’ve started drafting a chapter or an article, I stop reading that kind of stuff.

Before I go to bed, I read a novel every night. I read several pages of really good fiction. That’s because you do a lot of work in your sleep, and I want my brain to be in a rhythm of good prose.

Defininitely recommended, as is Michael’s latest book How to Change Your Mind: What the New Science of Psychedelics Teaches Us About Consciousness, Dying, Addiction, Depression, and Transcendence.

10 Things I Learned: Tyler Cowen

That is a short interview with me from Northern Virginia magazine, here is one excerpt:

When did you feel you had “made it”?

Jan. 21, 1962 (his birthday). That was a turning point of sorts for me.

How do you define success?

Learning something new all the time, and staying healthy. Getting paid. Interacting with smart people. Having the chance to pass something along to others.

And:

What do you do after a disappointment?

Bid higher next time.

Give us an idea of your work/life balance philosophy.

Do I even try to do balance? For me they are more or less the same. I know that makes me difficult. But I’ve ended up writing about what were once hobbies, and using so-called “leisure” time to prepare for research, writing, speaking and so on. My social life is pretty closely tied to my work life.

And at the end:

Any advice for those who are going into your field?

Listen also to the advice of people who are not in your field. A lot of budding academics listen too much to their advisor and don’t receive enough feedback and mentoring from a broader set of sources.

Self-recommended!

That was then, this is now, a continuing series

This is part of a letter from Miss Howe to Miss Clarissa Harlowe, from Samuel Richardson’s Clarissa [1748].

You and I have often retrospected the faces and minds of grown people; that is to say, have formed images for their present appearances, outside and in, (as far as the manners of the persons would justify us in the latter) what sort of figures they made when boys and girls. And I’ll tell you the lights in which HICKMAN, SOLMES, and LOVELACE, our three heroes, have appeared to me, supposing them boys at school.

Solmes I have imagined to be a little sordid, pilfering rogue, who would purloin from every body, and beg every body’s bread and butter from him; while, as I have heard a reptile brag, he would in a winter-morning spit upon his thumbs, and spread his own with it, that he might keep it all to himself.

Hickman, a great overgrown, lank-haired, chubby boy, who would be hunched and punched by every body; and go home with his finger in his eye, and tell his mother.

While Lovelace I have supposed a curl-pated villain, full of fire, fancy, and mischief; an orchard-robber, a wall-climber, a horse-rider without saddle or bridle, neck or nothing: a sturdy rogue, in short, who would kick and cuff, and do no right, and take no wrong of any body; would get his head broke, then a plaster for it, or let it heal of itself; while he went on to do more mischief, and if not to get, to deserve, broken bones. And the same dispositions have grown up with them, and distinguish them as me, with no very material alteration.

Only that all men are monkeys more or less, or else that you and I should have such baboons as these to choose out of, is a mortifying thing, my dear.

I am enjoying this splendid book for the first time, and yes it is OK to read an abridged edition.

How does your personality correlate with your paycheck?

That is the topic of my latest Bloomberg column, here is one excerpt:

Gensowski revisits a data set from all schools in California, grades 1-8, in 1921-1922, based on the students who scored in the top 0.5 percent of the IQ distribution. At the time that meant scores of 140 or higher. The data then cover how well these students, 856 men and 672 women, did through 1991. The students were rated on their personality traits and behaviors, along lines similar to the “Big Five” personality traits: openness to experience, conscientiousness, extraversion, agreeableness and neuroticism.

One striking result is how much the trait of conscientiousness matters. Men who measure as one standard deviation higher on conscientiousness earn on average an extra $567,000 over their lifetimes, or 16.7 percent of average lifetime earnings.

Measuring as extroverted, again by one standard deviation higher than average, is worth almost as much, $490,100. These returns tend to rise the most for the most highly educated of the men.

For women, the magnitude of these effects is smaller…

It may surprise you to learn that more “agreeable” men earn significantly less. Being one standard deviation higher on agreeableness reduces lifetime earnings by about 8 percent, or $267,600.

There is much more at the link, and no I do not confuse causality with correlation.  See also my remarks on how this data set produces some results at variance with the signaling theory of education.  Here is the original study.

The Pioneer project: finding “the lost Einsteins”

Silicon Valley has created a model for identifying and nurturing high-potential young companies…Pioneer… hopes to do much the same thing for high-potential people.

The group, which is being announced on Thursday, plans to use the internet-era tools of global communication and crowdsourcing to solicit and help select promising candidates in a variety of fields, along with evaluations by experts. Its goal is to put more science and less happenstance into the process of talent discovery — and reach more people, wherever they are in the world.

“We’re trying to build a kind of search engine for finding great people with talent, ambition and potential,” said Daniel Gross, 27, the group’s founder…

Selecting “pioneers” will begin with a monthlong online tournament. Candidates will submit their project ideas. Each week, the projects will be updated. The candidates will vote on each other’s projects, points will be awarded and there will be leader board. Subject experts will also vote, with their votes counting somewhat more than the candidates’.

That is from Steve Lohr at The New York Times, with much more at the link.  Here is the account from Daniel Gross at Pioneer.  I am pleased and honored to be an (informal) advisor to this project.

The Flynn Effect in China??

Data are reported for intelligence of children in China assessed by the Combined Raven’s Test in 1988, 1996 and 2006. The IQ of the samples increased by 15.0 IQ points over 18-year period. The British IQ of China in 1988 and 2006 is estimated as 94.8 and 109.8, respectively.

That is from a new paper by Mingrui Wang and Richard Lynn.  Via a loyal MR reader.  Speculative!

Milton Friedman in *Death Wish*

Dan Klein writes to me:

Yes, a movie character (young woman student) was reading it aloud to her friend in a coma, Bruce Willis’s daughter, who had been attacked and shot. Willis comes in and asks what she’s been reading. The young woman replies that she had to read it anyway, for summer reading in anticipation of NYU, and figured good for coma victim to hear voice. Willis makes a joke about “I don’t think that will wake her up” or “Do you think that will wake her?”

When Willis asks her what she’s reading she says “Essays in Positive Economics, by Milton Friedman”. And then explains that it is on the NYU summer reading list.

The text quoted was: “Normative economics and the art of economics, on the other hand, cannot be independent of positive economics. Any policy conclusion necessarily rests on a prediction about the consequences of doing one thing rather than another…”

Has anyone else seen this movie?

The microfoundations of intersectionality

Here is the introduction to the Wikipedia page on intersectionality:

Intersectionality is an analytic framework which attempts to identify how interlocking systems of power impact those who are most marginalized in society.[ Intersectionality considers that various forms of social stratification, such as class, race, sexual orientation, age, disability and gender, do not exist separately from each other but are interwoven together. While the theory began as an exploration of the oppression of women of color within society, today the analysis is potentially applied to all social categories (including social identities usually seen as dominant when considered independently).

So why might intersectionality matter?  I can think of a few reasons:

1. Perhaps the signal extraction problem becomes more difficult in a non-linear fashion, when you are trying to peer through discrimination and identify underused talent for those with “multiple non-conformities.”  You might have a good sense of what an undervalued black student will look like, but find it harder — indeed much harder — to identify an undervalued Surinamese Haitian trans female student in a wheelchair.

2. Multiple non-conformities are like tolls on a river.  When there are multiple tolls, it doesn’t help commerce much to remove any one of them.  Similarly, you might fix one dent in your car, but it may not be worthwhile to fix fifteen dents or indeed any one of them.  No, I am not saying that individuals with multiple non-conformities are, in a quality sense, like dents in a car.  Rather there is a common logic involving threshold effects.  If you will come across as highly unusual in any case, perhaps you will not spend money to buy a nice suit.  Or perhaps outside parties are more likely to help a person who has only one main “disability” or non-conformity to overcome, perceiving a much higher chance of success with the aid.  Non-linear effects can discourage effort in a wide variety of cases.

3. Marginalized or minority communities may themselves exhibit prejudice against other non-conformities (for instance, some parts of the Jamaican community seem to be especially biased against gay individuals).  That can make it harder for persons with multiple non-conformities to find allies.

4. Note that intersectionality may operate in a favor of a person rather than always operating against a person’s interests.  For instance, black women arguably face less labor marker discrimination than do black men.

Overall, I believe the intersectionality concept is underrated by many people in the mainstream and on the political Right.  It suffers from some of the problems that would be predicted by…the intersectionality concept.

Good advice from Patrick Collison

Here is the whole post, here is one excerpt:

If you’re 10–20: These are prime years!

  • Go deep on things. Become an expert.
  • In particular, try to go deep on multiple things. (To varying degrees, I tried to go deep on languages, programming, writing, physics, math. Some of those stuck more than others.) One of the main things you should try to achieve by age 20 is some sense for which kinds of things you enjoy doing. This probably won’t change a lot throughout your life and so you should try to discover the shape of that space as quickly as you can.
  • Don’t stress out too much about how valuable the things you’re going deep on are… but don’t ignore it either. It should be a factor you weigh but not by itself dispositive.
  • To the extent that you enjoy working hard, do. Subject to that constraint, it’s not clear that the returns to effort ever diminish substantially. If you’re lucky enough to enjoy it a lot, be grateful and take full advantage!
  • Make friends over the internet with people who are great at things you’re interested in. The internet is one of the biggest advantages you have over prior generations. Leverage it.
  • Aim to read a lot.
  • If you think something is important but people older than you don’t hold it in high regard, there’s a decent chance that you’re right and they’re wrong. Status lags by a generation or more.
  • Above all else, don’t make the mistake of judging your success based on your current peer group. By all means make friends but being weird as a teenager is generally good.