Primes and Probability

At the suggestion of a colleague, I recently started reading Charles Wheelan’s Naked Statistics: Stripping the Dread from the Data. So far, it’s a fun, demystifying sort of book, the kind I hope my students will enjoy (watch out Lafayette Economics, I’m coming, and I will make you read). It rests on the twin ideas that statistics can be fun and statistics are incredibly useful to explain, to tell stories.

The book was high in my mind this morning when I read this deliciously accessible Slate piece by Wisconsin professor Jordan Ellenberg about an advance in prime numbers by a University of New Hampshire mathematician. Economists like to make lots of bad jokes about how they are failed physicists, who are in turn failed mathematicians, so while it interests me, I wasn’t expecting to really understand the discovery when someone riffed on twitter about primes.

What’s so wonderful about this really intense mathematical discovery, at least according to the mathematician author of this piece, is that it’s really about statistics, which I can totally get my head around. The theory goes that primes come in infinitely many ‘twin pairs,’ like 3 and 5 or 17 and 19, and the intuition lies in that we can think about primes as random numbers.

And a lot of twin primes is exactly what number theorists expect to find no matter how big the numbers get—not because we think there’s a deep, miraculous structure hidden in the primes, but precisely because we don’t think so. We expect the primes to be tossed around at random like dirt.

Zhang didn’t quite prove the twin pairs theorem, but he made an important step towards proving it, it seems, and understanding probability and statistics is key to getting there.

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Why study social sciences?

Monkey Cage Blog has a great post up in response to criticism of his exhortations to study social sciences. He makes a broad argument about the validity of social science research because it has effects on the way that people live their lives. To be selfish for a moment, he highlights some important questions that I examine every day:

Families.  What makes families more or less successful?   What makes marriages more successful?  What makes them fail?  What are the effects of divorce?  Does it hurt the children of divorce?  How much, in what ways, and for how long?  A medical doctor can treat the effects of family dysfunction and divorce—say, with anti-depressants or therapy and so on—but we can learn and know more about how to prevent some of this dysfunction from doing social science.

The post is really about funding for social science research rather that defending my everyday work. It’s also not really about teaching undergrads social sciences, but clearly, we have train undergrads in social sciences if we eventually want some of them to do research in the social sciences. I think there’s a point to be made about how learning about these wide-reaching social phenomena—families, schools, economies, politics, attitudes, networks and norms—forces students to think about cause and effect in a nuanced way. When it’s not clear how X might affect Y or how Z has effects on X that in turn effect Y, it takes creativity and imagination and critical thinking to sort it out. It’s not that social sciences can do this exclusively, but the nature of the topics student lends itself to varied analysis and the development of skills that are useful in many careers.

Job switching among Baby Boomers

I’m teaching Labor Economics this Fall for the first time, which means I’m constantly in search of interesting ways to get students to think about how we study questions of why people work, why they get hired, how firms decide how much labor to hire, and more. In one of these quests this afternoon, I found a BLS report from July outlining duration and number of jobs held by later period Baby Boomers (born 1957-1964) over their lifetimes.

It’s a short, descriptive report and the numbers come from the NLSY79, which is a fantastic longitudinal study of employment and educational outcomes, families and more. What I found so interesting about the report is that it shows that baby boomers, on average, held 11.3 jobs over their working lives. That number struck me as high. Even though about half of those jobs were held before age 24 (think summer jobs, part-time jobs while in school), there’s still a lot of switching over 30-40 working years. And it runs contrary to the narrative that I’ve both heard and repeated, which says that our parents were likely to take one job and keep it throughout until they retired, while my generation (which is unclear to me–too old to be a Millenial, but feel too young to be Gen X), is more likely to have switch jobs often and have shorter tenures at each job.

Of course, we can’t really compare the lifelong numbers until my generation is much older, but I wonder how much that narrative is perception (because we have the closest experience to more volatile period of the ages of 18-24), or because we actually enjoy less job security.

Back to School

It’s the first day of classes here at Gettysburg College and I am working hard (as I’m sure are many) to get back into the swing of things, to readjust to the humid Pennsylvania weather, and to find my rain jacket and galoshes only to have the sun come out while I’m in class.

I’m done with my first day and I’m happy to report that my students will be blogging again. This time, there will be two different classes, Quantitative Methods and Labor Economics. I’m really excited to have my Labor students reading BLS jobs reports every month and getting them as addicted to on-the-spot analysis as I am…I mean, well, moving on. Hopefully, we’ll get some good conversations going this semester.

For my part, I’ll be back up and running soon. I owe you all an explanation of what I was doing in Venezuela. It’s forthcoming and will be cross-posted at Caracas Chronicles, so might have a slightly different feel to it than what I usually write here. After that, I should be back to a normal posting schedule. My apologies for a slow August. Good luck to all going back to school with the new semester and talk to you soon!

TCB and student blogging

Though it wasn’t exactly a New Year’s resolution in the traditional sense, I promised myself that when my dissertation was all done, I would stick to a blogging schedule. My dissertation is done in the sense that I’ve graduated, but as all academics know, very little ever actually gets done. So, here it is, almost my bedtime on Monday night, the day I said I would blog, and I haven’t blogged.

I did get a lot done today. I had all of these little errands I’d been putting off and I’m happy to say that many of them are done. TCB, as my old housemate says.

There are a couple of papers I want to read and comment on, but I also really wanted to take today’s post to continue talking about student blogging. I’ve received a lot of support for the idea, from students and other academics, some who are doing something similar in their classes, some who wish they were, some who are just thrilled to watch it unfold.

Despite being the one who is doing it, I’m rather thrilled to watch it unfold. A couple of students have taken initiative and are posting other things–news articles or just general thoughts about school. I know it can be intimidating to think about strangers reading your writing, but I like where it is going. The posts from last week were thoughtful and clearly intended for an audience, which is just fantastic. I haven’t read them all yet, but have great plans for that tomorrow. I’m excited to hear what they have to say, what they’re thinking and learning and how what we do in class affects the way they see their worlds.

In case anyone was wondering, I don’t recommend taking the 8pm train from New York to Harrisburg if you have to teach at 9am in Gettysburg the next morning and are not sure what you’re going to do in class that day.

Tired.

Crowd-sourcing classroom blogging

So, I’ve made some work for myself this semester, I think. In light of the conversation a few weeks ago regarding blogging by academics, and a recent spate of blog posts on LSEImpact on social media, I decided that my students should be blogging.

In reality, I think they should be writing. A lot. And I think they should be reading each other’s writing. It’s amazing to me how many students go through college having had no one read their papers or other written work except their professors. Don’t get me wrong, I have faith in the ability of most professors to present an informed opinion on a work, but those students are missing significant opportunities to improve their skills of crafting an argument if they do not practice and put themselves out there. I can give an opinion on how to write something, but it’s merely one opinion.

It’s a good one, of course, but just one.

So, I have 25 students in two methods classes. They are going to blog about their research projects–still TBD for most, though a few have come to me with interesting ideas. They are going to blog about their reading assignments–mostly from Poor Economics or Freakonomics. Hopefully, they also blog about questions that come up in their textbooks. Hopefully, they blog about interesting things they find in the news. Hopefully, they start reading other blogs and commenting on them as well.

The course blog is here. It has three lists of links. One for each section of my class and one for several economics blogs. Some I read, some were just suggested to me. If your blog is not on there, and you think it should be, let me know. I’m happy to add it. I think the more examples they have, the better.

In addition, I’m totally open to ideas of how to make this work. Assignments that are particularly well-suited to blogging (with an economics or econometrics or research component preferred) are totally welcome. If it worked or if it didn’t, it it was an unmitigated disaster or a resounding success, I’d love to hear about it.

Treating students differently

Education research seems to be teeming lately with the idea of the “threat of stereotype”, whereby women in particular don’t do as well on tests not because they are incapable but because they are faced with prejudice. If people think I’m going to do poorly, why work hard, or so goes the logic.

This article from the Daily Beast, which outlines much of the research on such ideas of late, struck me for its mention of how students are treated differently by their teachers.

In a study published last year, psychologist Howard Glasser at Bryn Mawr College examined teacher-student interaction in sex-segregated science classes. As it turned out, teachers behaved differently toward boys and girls in a way that gave boys an advantage in scientific thinking. While boys were encouraged to engage in back-and-forth questioning with the teacher and fellow students, girls had many fewer such experiences. They didn’t learn to argue in the same way as boys, and argument is key to scientific thinking. Glasser suggests that sex-segregated classrooms can construct differences between the sexes by giving them unequal experiences. Ominously, such differences can impact kids’ choices about future courses and careers.

I don’t teach single-sex classes, but in my principles classes, I’ve noticed that the men seem to ask questions–and answer questions–in a way that encourages debate. While women are perfectly willing to raise their hands when they have the right answer, they’re less likely to disagree with me or ask a question that seems to critically engage the subject matter.

Thankfully, this seems to diminish a little in upper division classes, where I see both men and women engaging the ideas and critiquing what is set before them. So at least anecdotally, I’d argue that all is not lost by middle school. But that doesn’t mean we shouldn’t work harder to get women to engage critically at every level.

That is the point

I am in Colorado for what is an admittedly enviably long break from teaching classes. I have been spending time in various cities and this week had the pleasure of spending a day in the mountains with my dear friend from high school and her family.

B’s mom, M, and I were chatting a bit before we headed to breakfast (at the Butterhorn Bakery in Frisco. Love!) and she mentioned Yoram Bauman’s piece in the New York Times two weeks ago on his experiments to uncover the nature of economists’ stinginess. M was curious to hear my opinion on the matter, and so I thought I might share here what I shared with her.

At the heart of the paper is an experiment in which college students are asked whether they want to donate a nominal amount, $3, to one of two charities at the time of their class registration. One is a left-leaning group, WashPIRG, and the other a non-profit with the aim to reduce tuition rates, Affordable Tuition Now (ATN). The take-home message is that economics majors were less likely to contribute to either group and thus are “free-riding.” In addition, those who took economics classes but didn’t become majors were less likely to contribute than those who never took an economics class.

In his NYT piece, and in his paper, Bauman dismisses the type and name of the charities he employs in the experiment as rather meaningless to the outcome. “You may question whether these groups actually serve the common good, but that’s mostly beside the point.” It is my belief that the types and aims of charities are driving a lot the effect he sees, or at least have the potential to drive the effect.

For purely anecdotal purposes, I’ll tell you that I was an economics major, and I’m a little bit cheap, (have been my whole life), but that I also give to charity. Despite five years of impoverished grad student living, I still gave and will continue to give to charities I trust and admire. Now that I have a job and am feeling as though I’ve recuperated much of the year’s moving and dissertation writing losses, I’m also looking to expand that giving. Whether I give more to the charities I know or include new ones is to be determined, but you can bet that it will be a careful decision.

And I think that is where the problem comes in with Bauman’s experiment, carefulness. Research, thought, time, and emotional value all come into play when choosing charities to support. So do politics, often. And while I can’t say for sure that economics students are more careful about those decisions, if Bauman can’t account for that either, I don’t think he has a paper. Snap decisions about giving are likely very different than careful decisions about giving. And just because an economics class makes you less likely to give your money to an unknown organization with an unknown track record (or perhaps a known one that works for something that goes against some part of your belief system), I don’t think that makes us more stingy, it makes us more careful.

From an econometric standpoint, if the students who are more (or even less!) careful are the ones who are choosing not to donate–at least in that moment–then the effect you are attributing to stinginess is in fact not there. It’s what economists call an unobservable. The unobservable effect may be driving the difference in donations.

Even if economics students are not more careful, if there is any unobservable quality that is correlated with unwillingness to contribute, the effect is biased.

It’s also my experience that economics majors are more conservative–politically–than their arts and sciences counterparts. I have a hard time believing that right-leaning students would be inclined to donate to WashPIRG anyway, especially when they have likely spent a good deal of their college career dodging their canvassers in the street. (Maybe that’s just COPIRG.)

Overall, I disagree with the interpretation as much as the method. That taking an economics class leads to “loss of innocence” and thus not contributing is overly dramatic, patriarchal, and just plain silly. Aren’t we supposed to be educators? Since when is it my job to protect the innocence of college students? And why should we conflate giving with innocence?

On the state of economics

I haven’t yet written much about the Nobel Prize this week. There was little discussion of it within my department, likely due to a dearth of macroeconomists and a few days off for “reading days”. I will try to write something more in depth about it, perhaps over the weekend, but I found this piece, by John Kay, rather insightful for several reasons, two of which I’ll highlight here.

The first has to do with teaching. Students often struggle with the concept of a model. It’s something that is so profoundly simple, and even simplistic, that they struggle to see the use of it. I really like Kay’s description of the necessity of simplifying assumptions

All science uses unrealistic simplifying assumptions.  Physicists describe motion on frictionless plains, gravity in a world without air resistance.  Not because anyone believes that the world is frictionless and airless, but because it is too difficult to study everything at once.  A simplifying model eliminates confounding factors and focuses on a particular issue of interest.  To put such models to practical use, you must be willing to bring back the excluded factors.  You will probably find that this modification will be important for some problems, and not others – air resistance makes a big difference to a falling feather but not to a falling cannonball.

At lunch today with my chair, we discussed the decline in female economics majors. Our department, unlike many economics departments, has quite a few female faculty members. I didn’t have a single female economics professor at Duke, though I did in my time abroad. In fact, the female economics faculty with whom I did interact at Duke left a not-fantastic impression. At least anecdotally, I can say that high female-to-male faculty ratios didn’t push me down my current path, or low ones didn’t discourage me, either. Rather, Kay suggests there is something about the nature of our model-making that is profoundly asocial and disconnected, and thus, perhaps, male.

The knowledge that every problem has an answer, even and perhaps especially if that answer may be difficult to find, meets a deeply felt human need.  For that reason, many people become obsessive about artificial worlds, such as computer games, in which they can see the connection between actions and outcomes. Many economists who pursue these approaches are similarly asocial.  It is probably no accident that economics is by far the most male of the social sciences.

The whole piece is incredibly well done and provides a clear, straightforward critique of economics today; it is a bit dense. It addresses much of the debate behind current arguments for and against deficit spending, which, sadly, are likely not well understood by those pushing for either side. I highly recommend reading it.

My favorite oligopoly example just got better!

Though my students are quickly becoming far too young to remember the advent of Netflix, I often start a unit on oligopoly or game theory by posing the question of how much the DVD rental service cost when it started. The answer, you might not remember yourself, is around $20. Now, that seemed like a bargain at the time, when your only real option to rent a movie was to haul your butt over to Blockbuster and pay $4.99 for a single movie, and then face late charges, etc, when you couldn’t get it back the next day. Blockbuster didn’t like the competition of course, and soon got into the online/mail business of renting DVDs itself, leaving us with two big companies sharing the bulk of the market–an oligopoly, or a duopoly, more precisely in this situation.

In principles, and in my intermediate classes, too, I use this example to talk about the options oligopolies face. at least in our simplified, basic model. They can collude, or try to keep prices high and capture as much of the monopoly surplus as possible. Or they can cheat, undercutting their competitor’s prices. In a dichotomous world, we see the two options play out in different ways, allowing our oligopoly to look like a monopoly or to look like perfect competition. That is, high prices mean small quantity, and the consumer gets very little surplus. In the other case, where the companies continue to undercut each other, this drives prices towards the perfectly competitive equilibrium, where each company is charging their marginal cost and capturing very little of the surplus.

In some cases, they’ll even drop below their marginal cost, taking a loss in order to try to drive the other companies out of business. If one company can sustain losses for a long time, he might be able to get rid of the others and then raise prices back up to the monopoly level, thus capturing all the monopoly surplus for himself. Now, he doesn’t have to share with the other guys.

Netflix and Blockbuster have spent the last few years lowering their prices, creating more and more types of plans to have the lowest prices. But lately, Blockbuster has been in trouble. And, just in time for a new school year, Netflix announced today that it was raising prices by 60% come September 1. That makes my example even better! Netflix has a monopoly, Blockbuster enters with a lower price, Netflix responds by lowering their prices, and tit-for-tat until Blockbuster is in trouble, closing stores down all over the place. So, what does Neflix do? They see less competition and raise their prices. Full circle. I love it.