Some reasons not to take an undergraduate degree in economics

In a recent post, Nick Rowe speculated that the President of the Federal Reserve Bank of Minneapolis made basic macro mistakes in part because he has an undergraduate degree in math.

Yet a person wanting to make a career as an academic economist (or a president of a federal reserve bank) should not choose economics as an undergraduate major. Particularly in Canada.

Canadian universities typically offer up to three degrees in economics: BA, MA and PhD. Students are usually required to have a MA before entering a PhD.

An undergraduate major requires, say, between 13 and 18 half term courses in economics. An MA? Another 8 to 10 courses.  PhD programs vary more, but the University of British Columbia's web site tells students to expect to take another 13 courses.

What's wrong with high standards, requiring students to be have a thorough knowledge of economic concepts and methods?

1. It's repetitive and dull.

In the course of an BA/MA/PhD in economics, how many times would a student interested in industrial organization be taught the basic theory of monopoly? Principles, intermediate micro, industrial organization,.... How many times would she be taught basic two-person non-cooperative game theory? The first theorem of welfare economics?

Now there is a theory of education that suggests such repetition is a good thing. Jerome Bruner's spiral curriculum theory says: 'A curriculum as it develops should revisit ... basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them'.

So Ontario's elementary and high schools now use a spiral curriculum, for example.

I relish the thought of WCI commentators, usually skeptical of fancy Ministry of Education pedagogical initiatives, defending a spiral curriculum approach. To me it sounds unbelievably tedious. 

2. The opportunity cost of coursework is high

Let me make two claims about coursework. First, in five years time, 90% of everything except for fundamental concepts (for example, the idea of opportunity cost) and skills and techniques used in everyday life (for example, a wider vocabulary) will be forgotten. Second, anything close to the "frontiers of knowledge" has a 50 percent or better chance of being completely obsolete and irrelevant in ten to 20 years time.

Requiring students to take courses they do not need is simply taking away their time and money. If students forget/don't use material, or if it rapidly becomes obsolete, educators are wasting students time requiring them to learn it.

True, general knowledge and 'learning how to think' are valuable. But history or biology or classics or religion are also valuable in building breadth of knowledge. 

'Free to choose' works for students, too. 

3. Learning other people's models does not teach you to build your own model. Learning other people's ideas does not make you more creative

At some point an economist, whether as a consultant submitting a proposal or a policy analyst writing a briefing note or as an academic writing a research paper has to come up with his or her own research ideas, his own analysis, her own model.

It's tough. Brutally hard. But more course work doesn't necessarily help. My own experience is that the most effective way of learning how to do something is to dig in and do it. Writing this blog, for example, is teaching me to be a better writer, because I know you can and probably will stop reading the second is gets long winded and dull.

My colleagues might disagree with my analysis of the value of course work in general (and their courses in particular). But many would agree that an undergraduate degree in economics is not necessary to succeed in graduate school.

The University of Western Ontario does not require new MA and PhD students to have any background in economics, and indeed actively recruits students with undergraduate degrees in math and physics. Other departments waffle a bit more about their requirements, for example, University of Toronto's MA program requires that applicants have completed, or must be in the final year of an appropriate four-year bachelor's degree program. But I've been involved in graduate admissions for years and am reasonably confident that there isn't a graduate program in the country that would not admit a student with a strong quantitative background and a good grades in a handful of core theory courses (Econ 1000, intermediate micro and macro, advanced micro and macro).

UWO is pursuing a rational strategy. For there are some ugly facts that many people are aware of but few mention in polite company.

Economics departments are usually located in faculties of arts and, at an undergraduate level, draw primarily from the BA student pool, as well as B Com drop outs.

But science and math programs require significantly higher high school grades than arts programs. For example, at Queen's a potential BSc student requires a "competitive average" of 84%+ in university-level grade 12 English, Advanced Functions, Calculus and Vectors, two of: Biology, Chemistry or Physics, plus one other grade 12 courses. A potential BA student requires a "competitive average" of 80%+ in university level grade 12 English plus their best 5 other courses. 

If high school grades, especially grades in math, are a good signal of ability in economics, BSc students will, on average, have higher levels of intrinsic ability in economics than BA students.

Moreover, there is not a super-abundance of job opportunities in the natural sciences. There is a strong market for programs that can translate a degree in math or physics into a good job in government or academia.

So for these two reasons - a desire to attract students with a high level of intrinsic ability, and a desire to access a large potential student pool - it is rational for graduate programs to target people with undergraduate degrees in subjects other than economics.

But where does this leave students who choose economics as an undergraduate major? As graduate programs increasingly recruit people with undergraduate degrees in subjects other than economics, graduate programs will spend more time repeating basic economic concepts. How can a student who has already learned these concepts sustain his or her interest? And when students are evaluated on the basis of their mathematical modeling and problem-solving ability, how can a student with an undergraduate degree in economics compete with a physicist? 

I see two solutions.

The first is truth in advertising: honestly advise our most talented undergraduate students to switch to a math major/econ minor. But given the sheer joy that my most talented undergraduates give me, it's hard to take that route - plus a student's aptitude for graduate level economics may not be readily apparent until their undergraduate choices are largely determined.

The second is to accept design separate graduate programs for economics majors, ones that skip the unnecessary repetition of undergraduate economics. But I'm having trouble imagining what that program would look like, or who would take it.

This is getting personal for me right now because I have university-age children. I have tried to convince them (and their friends, and my first cousin once removed, and hundreds of students) to study economics. An undergraduate economics degree is an excellent background for a career in law or policy analysis, and is a sound choice for someone looking for a general arts degree. But neither one of my children is interested in taking a BA. Both are applying for/taking degrees with more restricted enrollment and thus a higher prestige value. As a firm believer that the value of education is in large part the signal it provides of your ability, who am I to argue with their choices?

I'm just hoping one of them will stumble into ECON 1000 with a good prof, fall in love with the subject, and think about it for a graduate degree.

Comments

[Stephen Gordon]

I started out in political science, and got hooked on economics as my degree progressed. I took principles and liked it, so I decided to take a couple of second-year courses for a minor. By fourth year, I ended up with a double specialist degree (as it was known at U of T back then). While I was never really a math-o-phobe, the task of picking up enough math to get through grad school was very much a catch-up operation.

In Quebec, things are structured differently. Students have to decide what programs they want to specialise in BEFORE they get to university. In order to attract a student, we have to hope - often vainly - that she had a decent economics instructor at CEGEP. That's a problem.

On the other hand, once they're here, we know they've made the commitment. So we do what we can to make sure our students have the required math background.

[Just visiting from Macleans]

In undergraduate engineering, in my day, each semester sudents were req'd to take a 1/2 yr course from the arts faculty. I can't recall if I took an economics elective (or whether it was taught as part of another engineering related course in their faculty), but I do certainly recall my intro Psych 101 course(hey is the use of 1000 as in Economics 1000 like grade inflation or some sort of marketing ploy?) and my third yr Liking and Loving psych course.

But, I have to say, wherever I studied economics - I hated those two line supply and demand "curves" (are they really stright lines?)- Like Pavlov's dog (thanks Psych 101) my eyes immediately gloss over - boring, boring, boring. Add some coloured lines - marginally less boring.

So, from my perspective, promoting interest in the field of economics and a better understanding is best accomplished as you are collectively doing on this site - a healthy mixture of practical everyday situations, policy related discussions with a dose of politics, and some really high level stuff for thre heavyweights (it's still entertaining to watch some battle it out in the comments even though generally I haven't a clue of what they are talking about, and do't want to).

So, carry on carrying on. Good post.

[Stephen Gordon]

I just checked: Laval requires *25* half-year courses!

[JKH]

I have no recent experience regarding this subject, but it seems analogous to what I thought was a standard attitude in that MBA programs don't look for commerce undergraduates. As I recall, UWO used to be particularly sticky on this.

"The second is to accept design separate graduate programs for economics majors, ones that skip the unnecessary repetition of undergraduate economics. But I'm having trouble imagining what that program would look like, or who would take it."

If you want to salvage young minds, I think you have to do this as a matter of principle. Give course credits liberally, and in doing so make it tougher and more challenging to make the full grade in the graduate program.

[Frances Woolley]

Stephen: you wouldn't be able to reproduce your U of T experience at Carleton today, because students have *six* required courses that they must take in second year, and if they delay taking those courses they most likely won't have the prerequisites they need to complete their program in four years. As an undergrad, I would never have been organized enough to work it out. If I'd been at Carleton, I would have ended up either staying in business (less likely) or majoring in philosophy (more likely).

JKH: I think a student taking a B Com or BBA and then an MBA faces many of the same problems as I've identified here. Honestly, a student wanting a career in business might be as well advised to take a program such as Carleton's Bachelor of the Humanities and learn how to write well and think clearly and then go on and do an MBA.

Yes, perhaps course credits is the answer - if someone has a strong undergrad background in econ, we should allow him or her advanced credit for fourth year undergraduate level field courses and instead allow the student to replace those courses with courses in the math department. There just aren't that many students with Canadian undergraduate degrees in economics going on to Canadian PhD programs, so the issue doesn't arise often enough for graduate advisers to devise standard solutions and alternative types of degree programs.

[Evan Harper]

I dropped out of high school and got a GED, in large part because of that "spiral curriculum" bullshit. I'm sure it's good for many of the students, but for a quick learner who retains information well, it is crushingly boring indeed.

[Tim Worstall]

"Writing this blog, for example, is teaching me to be a better writer, because I know you can and probably will stop reading the second is gets long winded and dull. "

Aha! A new corollary (or perhaps extension) to Muphry's Law: that any complaint about spelling, grammar or typos will contain one such at least as bad as the original being complained about.

Our extension being that any writing about how writing a lot makes you a better writer will contain the evidence that one needs to write (or at least proof) more in order to become a better writer.

A minor example with "is" and "it" but a score all the same!

[Frances Woolley]

Tim - oops! - I won't fix it so it can continue to give you and others pleasure.

[Jim Rootham]

Was Muphry's deliberate?

Or is self referencing spiraling out of control?

[Ian Lippert]

I just competed my undergrad in economics and I think one of the problems is that my program seemed to lack focus. For my micro, 2nd and 4th year where were I learned most of the core theory, with 1st and 3rd being a mish-mash of optimization, edgeworth boxes and game theory. Macro was 1st year intro, second year Keynsianism, 3rd year Barro's models which seemed to add very little to the Keynsianism, and 4th year a mish mash of theory focusing on growth models. You learn econometrics and stats pretty thoroughly and it one of the more useful skills you acquire in an undergrad degree. But other than that you are free to pursue your interests. I focused on finance, and even my finance courses werent really focused, a little balance sheet stuff, interest rate calculation, an intro to options and futures and a bit if international finance. A student that isnt focused could take a bunch of intro courses and easily forget it or not see how it all fits together. For example I didnt touch industrial organization nor the public policy courses and have very little knowledge of what they are about. What would have happened if I had dropped a few of the finance courses for one of these? I'd be a jack of all trades, master of none, and all that would be soon forgotten.

I can only speak for the program I was in, but I often felt that economics fell right in between being in the hard degrees like math, engineering, and science, and the typical soft arts degrees like history, psychology, and sociology. You get a lot of students that wouldnt be able to successfully complete a math degree but dont want to waste their time with what they perceive to be a worthless arts degree. I think this leads the econ programs to be designed to cater to this core of students while giving the opportunity for the more academically inclined students to pursue a more focused degree in with master's and PhD programs. If you wanted econ to get serious you could ratchet up the math requirement and move a lot of the stuff learned in the masters program back down to undergrad level. I'm not sure what effect this would have on econ as an overall program as I think you would lose a lot of the more casual students.

[Greg Ransom]

Guild members are not suppose to tell the truth about this.

You've broken the Ivory Tower code of silence, and must be punished.

[Jim Sentance]

I'll start by agreeing that an undergrad degree in economics can be irrelevant. I settled on economics as a major after first year and more or less just did what I had to while taking as many history courses as possible and writing history papers in my economics courses. Useless electives and only a basic coverage of theory didn't really prepare me for the MA (not sure how, but I believe I managed to get through an entire honours BA in economics without seeing calculus applied to theory even once). Needless to say the MA was a shock, but I survived.

That being said, I would argue for making students take a variety of courses, and even contradict you when you say that "Learning other people's models does not teach you to build your own model. Learning other people's ideas does not make you more creative". First off, you have to know what a model looks like to build one yourself. Secondly, I've found, in my own work and in what I see from others, that often the spark of creativity comes from seeing a variety of approaches to modeling in a variety of fields, and taking an approach that's useful in one area and applying it in another.

Finally for now, I'd be cautious about assuming as you seem to that in being an Arts program, economics sets itself up to preselect a lower grade of student. I find very few of our majors come from the cohort that starts as a BA applicant. They come over from Science or Business, and not always because they couldn't make the grade. More typically they find it more interesting of they prefer our approach to pedagogy. And even if it were true, I think that would be more of an argument for moving Economics out of Arts (as some schools have) rather than not taking an undergrad degree in economics.

[Frances Woolley]

Greg - I have a cartoon on my office wall "Mad? Why yes, I'm mad. But I have tenure."

Jim, "I believe I managed to get through an entire honours BA in economics without seeing calculus applied to theory even once" - things have really changed in this regard. I don't think that would be possible today, certainly not at any university I've taught at.

"that often the spark of creativity comes from seeing a variety of approaches to modeling in a variety of fields, and taking an approach that's useful in one area and applying it in another"

Exactly. That's why a broad undergrad background in biology, history, math, etc is probably much more useful than studying economics of the environment, public finance expenditures, and public policy towards business, all of which spend a week or three teaching the basic theory of externalities. Or, alternatively, perhaps we need a more anarchic approach in grad school. I was just chatting this morning to someone who knows a lot about math grad programs, and she was telling me that it's very common to say to students "O.k., you're interested in this area, go away and work on it and we'll do a directed readings course for you." That does happen in econ, but I wouldn't say it's common.

[Frances Woolley]

Jim, "And even if it were true, I think that would be more of an argument for moving Economics out of Arts (as some schools have) rather than not taking an undergrad degree in economics."

I've thought about that. Moving into business means that econ becomes one of a number of departments, so there's departments of marketing, accounting, finance, economics, etc. That can mean a loss of voice for economists, and also potentially culture clash (many academic economists don't take kindly to being expected to wear a tie and/or pantyhose). Though having said that, the Sauder School of Business (UBC) and also HEC Montreal both have extremely solid and as far as I can tell very happy economics groups. Dalhousie's econ department is in the faculty of science, and that creates other issues (the reaction of scientists to econ candidates at tenure meetings: "What do you mean you're recommending someone for tenure with only six publications and just $25,000 in SSHRC funding?")

[Frances Woolley]

Ian L - "I think this leads the econ programs to be designed to cater to this core of students while giving the opportunity for the more academically inclined students to pursue a more focused degree in with master's and PhD programs."

Yup. That's about it.

But what should the more academically inclined undergrads be told - quit and study math? Relax and take it easy? Or should everything be ratcheted up to the level of the more academically inclined undergrads?

any regrets? do you wish you'd chosen another major? are you going on to grad school?

[Mike Moffatt]

I wonder how many economists just fell into the subject?

I started out as a philosophy major at UWO of all things. The only career path I saw from that was lawyer and I didn't want to be one. I took first year Econ and aced it, so I ended up double majoring in Econ and Poli Sci.

Graduated, did a year at Queen's, then went to Rochester. First year I passed all my courses there (which something many of my classmates couldn't claim), but I got absolutely destroyed because my math skills weren't up to par (I had been warned by UWO profs that I faced that risk, so it's not just Frances letting people in on this secret). I spent the next year as a visiting graduate student in the Applied Math department at UWO - took a bunch of upper year undegraduate/MA courses in math and applied math and spent a summer doing financial math research.

Went back to Rochester, did a whole lot better my 2nd year and did quite well on my comps. But by then I decided that Rochester wasn't for me for a variety of reasons and I wanted to move back to London. Had an opportunity at Ivey and took it.

Not sure what the point of this is, other than as a cautionary note. If you go to a high end PhD Econ program in the States without a math background, you're going to be roadkill.

[Jim Sentance]

"Jim, "I believe I managed to get through an entire honours BA in economics without seeing calculus applied to theory even once" - things have really changed in this regard. I don't think that would be possible today, certainly not at any university I've taught at."

- I don't think it was supposed to be true then either, but my point was that it turned out that while it might have helped, it wasn't necessary.

On the varied course thing, I'd agree that taking a wide variety of things outside of economics as an undergrad helps, but not all economics electives spend three weeks on externalities. I learned very different things in my IO courses than my Labour courses, and the ability to take ideas from the one and use them in the other was very helpful. Excessive specialization is the killer of creativity in my mind.

[Tim Worstall]

"Was Muphry's deliberate?"

Yes.

http://en.wikipedia.org/wiki/Muphry%27s_law

[david]

Hi Frances. Interesting post. A couple of comments. (My background is B.Comm [Queens] and MA Economics [UWO], both early 80s., followed by 27 years of policy and consulting).

Apologies in advance for the long comment.

First, am I the only one that finds it a little bizarre that graduate programs in economics don’t want to consume their own profession’s or department’s output (i.e., those with undergraduate degrees in economics), particularly when the same departments determine what is taught at the undergraduate level and how it is taught? Wouldn’t we all think it was pretty odd if graduate studies programs in physics were actively seeking undergrads from other areas in preference to their own? (The BComm/MBA analogy raised by one of your commenters doesn’t hold- at least when I was at Queen’s, the BComm was at least as hard to get into as the MBA program and had not only more content but more sophisticated content.)

It seems to me that if undergraduate programs in economics are felt not to be preparing students adequately for graduate work, isn’t the solution to beef up the undergraduate program or at least increase the requirements for undergrad math (or whatever) before pursuing grad studies?

Second, the notion that it would be considered desirable to have lots of people getting PhDs after, say, a math or physics undergrad with relatively little economics, followed just two years of course work at the graduate level, seems remarkable to me. Technicians are great but can one be expected to have much economic intuition or judgment after that little exposure to the field?

Also, the financial crisis has reminded us that elements of theory or policy that we thought we “knew” and were settled were in fact not so settled. Much of the confusion and current debate is not about the super-sophisticated sub-atomic level of economic theory, it is about all the basic front-end stuff that was bypassed in the rush to focus on the sub-atomic level and all the assumptions of convenience made to make the math work. Is the answer really more people that know lots of math and not so much about economics?

Third, if the problem is a concern about repetitive subject matter then I would suggest the solution is to teach more and different stuff. I now find it utterly astounding that I went through five years of economics without ever being exposed to a) any mention whatsoever of, for example, free banking, the Austrian school and the apparent contradiction of the acceptance of central banking by a profession that normally extolls free markets and competition, or b) any serious treatment of the history of economic thought, disequilibrium and a dynamic conception of the market, the role and evolution of private property (and other institutions) in markets, experimental economics, the various theories regarding the causes and duration of the Great Depression (a good topic for a fourth year or graduate level course), the mechanics and history of the gold standard in its various forms, the economic history of other key eras (e.g. German hyperinflation), the debate (both historical and current) regarding the methodology of economics (positivism and its challengers), etc.

Is there really a shortage of material?

[tomslee]

I was going to say "I wonder if this discussion says something about the lack of empirical content in economics?" because I could not imagine going into postgraduate chemistry (which I did) without the undergraduate degree - there is simply too much factual material to learn.

But on second thoughts, of course I did not use much of that factual material in my graduate studies - being more specialized, I forgot large tracts of chemistry very quickly and did not feel the effects. So maybe it does make sense to be able to go into an economics graduate course without an undergraduate degree.

But on third thoughts - specialization means that just because you have a graduate degree in subject X does not make you an expert X-ist if you don't do the undergraduate (or equivalent). You are building on foundations that may be sand or may be rock - who knows?

[William Hayes]

Any of you U of T grads ever take a class in the old McLuhan Program in Culture and Technology, now part of the Faculty of Information Studies? If so, perhaps you’d know how the guru taught a whole generation of intellectuals. Not that he taught me, but arrived at the same way of educating from different directions. Foundational to his “medium is the message” was using the figure and ground (two principles) of Gestalt psychology (I came onto it through generating substance theory using fuzzy logic). His picture of the whole was to put Medium in the middle with diametrical opposites of Enhances and Obsolesces; Retrieves and Reverses. He’d ask 4 questions, which I think are excellent for any student to ask his prof in an intro class…

1. What does the medium [of economics] enhance?
2. What does the medium [of economics] make obsolete?
3. What does the medium [of economics] retrieve that had been obsolesced earlier?
4. What does the medium [of economics] flip into when pushed to extremes?

The answers that appear about right to me are:
1. Selfishness and false utility
2. Self-interest and utility
3. Enlightened self-interest (self-interest + classic sympathy/new empathy)
4. A flippin gated community fostering narcissistic culture.

And, thank you WCI for having an open door and being so tolerant. However, the only way I can learn how i'm right (sometimes) and where I'm wrong (always in some way) when riding onto your turf is to be challenged. Is the pay dirt from the staked claim gold or fool's gold?

[Frances Woolley]

David, thanks for your long comment. You hit on a point that perhaps I should have clarified:

"Second, the notion that it would be considered desirable to have lots of people getting PhDs after, say, a math or physics undergrad with relatively little economics, followed just two years of course work at the graduate level, seems remarkable to me. Technicians are great but can one be expected to have much economic intuition or judgment after that little exposure to the field?"

That's the point Nick raised in his post that inspired this one. Sometimes, technicians don't, and that's a problem, as Nick points out.

But I don't know what the answer is. If a grad programs only admits people with undergrads in econ it will miss out on many of the best and brightest potential students. Mike Moffat's experience is typical - a good econ undergrad will be slaughtered by math majors in grad school. And that won't change unless the nature of economic research changes and what is valued by the academic economics profession changes.

But if grad programs repeat all of the basic Econ 1000 concepts to bring the technical students up to speed, students with undergrads in econ will be bored.

Sometimes I think we should add an additional comprehensive exam for our PhD students - the Econ 1000 final.

[Josh]

I was going to say "I wonder if this discussion says something about the lack of empirical content in economics?" because I could not imagine going into postgraduate chemistry (which I did) without the undergraduate degree - there is simply too much factual material to learn.

I was thinking the same thing. My undergrad was in mathematics and political science, so arguably I would've been well positioned to have pursued graduate study in economics (instead I did a statistics grad degree and proceeded to medical school). Despite being interested in the subject, I never did take an economics course, yet I feel my knowledge is more than adequate to question the simplistic economic arguments made in the media (e.g. in the Globe's business section) and bizarre internet popularity of methodological dead ends like the Austrian "school".

Second, the notion that it would be considered desirable to have lots of people getting PhDs after, say, a math or physics undergrad with relatively little economics, followed just two years of course work at the graduate level, seems remarkable to me. Technicians are great but can one be expected to have much economic intuition or judgment after that little exposure to the field?

I question that there exists some kind economic "intuition" or "judgement" that can be taught through a combination of coursework and research. What can be taught is good scholarship and research methods and an appreciation for theoretical models and principles. As important is the assessment of evidence and data, and those trained in explicitly quantitative and/or abstract disciplines unsurprisingly can hit the ground running rapidly. That said, it's not about math per se, but about the evaluation and analysis of data, i.e. statistics, though given your mention of "positivism" I wonder what your stance on these fuzzy notions of empiricism is.

In political science, at least, we had no shortage of long discussions about methodology and theory. One seminar I took was "Approaches to International Relations", and much of the discussion was given over to Liberalism vs. Realism in the context of differing methodologies for describing or explaining the behaviour of political actors. If economics has long since veered away from the speculations that once dominated such research in favour of empirical study, I'd say this can only be regarded as the maturation of the discipline. That's not to say that "economic thought" is unimportant, but it cannot and must not be separated from discussions of political economy or politics in general. I'm not sure the field is particularly equipped to address such questions, though.

[Mike Moffatt]

"Mike Moffat's experience is typical - a good econ undergrad will be slaughtered by math majors in grad school."

Yep. My mistake was in thinking that an *aptitude* at math would be enough - it's always been a strong subject for me. But you need the actual training, to learn the vocabulary, to polish your skills, etc. For me the year of 3rd-4th year undergrad/MA courses got me up to speed enough where I could hold my own. But without that year, I was completely and utterly lost.

[Frances Woolley]

Josh, I love the idea that people with backgrounds like yours are reading this blog (and will avoid a long digression into realism v. liberalism).

[Ian Lippert]

"But what should the more academically inclined undergrads be told - quit and study math? Relax and take it easy? Or should everything be ratcheted up to the level of the more academically inclined undergrads?

any regrets? do you wish you'd chosen another major? are you going on to grad school?"

Well I think there was a lot of room in my program to accomodate both types of students. If all you want to do is the bare minimum the only really mathematicall difficult courses are 4th year micro, 4th year econometrics, possibly macro too although mine wasnt heavy on the mathematics. Although it sounds like im criticizing it I'm one of the students that couldnt hack it in the math program. Econ actually took me from relatively easy math to rediculous courses like quantitative finance. It definately taught a marginal student like me how to excel academically and now I am starting my MA at Carleton.

No regrets on my major, I love economics and I'm lucky enough for it to all work out and am allowed to pursue studies in something I'm very interested in. Not something everyone can say.

[Frances Woolley]

Ian L - excellent! If you see me please introduce yourself and say hi, Frances

[Chris J]

Frances, ahem, I don't know where to start. Basically you are saying undergrad econ programs have a bad set of course requirements. If you think more math and science is important, teach more math and science. I have physics degrees (BSc, MSc and PhD) and my course training consisted of two things: First, working out really hard problems - ie learning to think about single problems that took a day to solve sometimes and second, learning physics. As an undergrad in physics I learned how the hydrogen atom worked, why the sky is blue, how heat-shrink plastic works,... It was important that I learned this stuff.

Surely in economics there is stuff that a subset of he population actually needs to know. Teach them this stuff. And then give them gruesome problem sets where individual problems take ten hours to solve.

Oh yeah - make them take "lab courses" and work with actual data.

[Sriram]

I've wondered why Economics departments were in Arts faculties. Locating them in the business schools always seemed more natural to me.

[Frances Woolley]

Chris J - "I don't know where to start"

Here's a suggestion: Start by responding to the argument made in the post.

I am saying that an undergrad econ program is not an ideal training for a PhD in economics. Physics degrees teach you to work out really hard problems. That's why a first degree in physics is really useful when it comes to studying economics at a graduate level.

If we gave all of our undergrad students gruesome ten hour problem sets, we would be doing them a disservice. The overwhelming majority are not going on to PhD programs.

To clarify: I'm not saying that undergrad econ degrees are not useful. In my undergrad taxation course last year, we used a simple model to analyze the potential consequences of legalizing and taxing marijuana in California (this has been proposed as a way to reduce their budget deficit). We could get all sorts of fascinating insights into the issue with basic tools from first and second year economics.

But most people with PhDs in economics don't spend their time doing things like analyzing the possible consequences of the legalization of marijuana - the economics are completely straightforward, and there's not enough data to do a sophisticated analysis (in ten years time, though, you could write a really nice paper using the legalization as a 'natural experiment').

In Canada, we're seeing a rapid growth in masters degrees in public policy or international relations. Graduates from those programs have a basic undergraduate-level background in economics, and can write and communicate effectively. A lot of employers are looking very seriously at graduates of these programs when they need policy analysis done.

[Stephen Gordon]

To follow up on that last point, I think the point where a standard economics BA fails most is in training students to write. I like writing, and I like to think that I write better than the average economist (an admittedly low hurdle). But much of that came from my poli sci background, where I had to write any number of tightly-worded, well-argued essays.

Our MA program at Laval is one of the few that still requires a master's thesis - at least two sessions of full-time work - and the main stumbling block for our students is getting them to write a comprehensible first draft. But at least by the time they leave, they know what it's like to write up a research report.

[Patrick]

I think it was suggested above, but I'll repeat it anyway...

I studied mech eng at McGill in the '90s. We had required math courses. Lots of required math courses. So why not do like the engineers do and make the required math part of the program? Have a series of math course for econ majors and stagger the econ material so that it's presented after the students have taken the required math. First semester could be econ 101 and the weeder math course (just like first year mechanics is for engineers). And advertise the fact that economics requires math.

[Frances Woolley]

Patrick, click on the link that says '18' in the original blog post above.

Every undergrad econ program in the country requires math.

But there is no level of math that will simultaneously (a) not discourage a large number of potential majors who would enjoy and benefit from an undergraduate degree in econ and also (b) allow someone with an econ degree to compete with someone with a math degree at the PhD level.

An alternative is streaming students and giving some gentle math and others rigorous math. But this requires enough students of each type and, crucially, students need to work out which stream suits them early on.

[Patrick]

Frances, I think my inability to write effectively is letting me down. I wasn't claiming that current programs don't require math.

As to (a), maybe Econ dept. might consider taking a harder line. I'm sure I would have very much enjoyed an easy stroll through plant biology and horticulture (I like gardening) if they skipped all that nasty biochemistry and microbiology. But is that what a university undergraduate degree should be about?

Without really knowing anything about what PhD economics students do, I find (b) above to be somewhat shocking if it's true. I can't think of another field where having a undergraduate degree in the field puts students at a disadvantage relative to students coming from some other field of study. You really should attach a warning label.

Anyway, I'm biased. I was lousy student and had to work my ass off to get even mediocre grads so I tend to be unsympathetic to the view that students should enjoy school or that it should be anything but a horrendous slog - I suffered so everyone else should too dammit!

[Patrick]

Compare the math requirement in honours econ to the math requirements for honours Mech Eng at McGill:

http://www.mcgill.ca/mecheng/undergrad/curriculum/streamc/

(full disclosure: I certainly wasn't honours during my 3 year incarceration, and in fact I bailed on mech and switched to comp sci - much to everyone satisfaction I'm sure).

[edeast]

I can vouch for the masters of policy. I'm a comp sci/bio double major finishing up a summer job with Alberta environment, doing modeling. A number of people in the office working on policy have them. Plus anytime in a meeting with economists, I never had the opportunity to use the 2+ years of econo blog reading. I guess my feeds are tilted heavily toward monetary policy for some reason(0 lower bound/recession) but specific policy analysis is required in a lot of the presentations. And I assume the phd programs tackle the interesting stuff.

[Chris J]

@Frances, Thank you. You clarified something I missed in your argument. You were talking about people who would develop new and different models, not people who would use economics to develop policy. I had not made this distinction. (The economics I read is this blog, Brad DeLong, Tyler Cowan occasionally and a few others - all of whom are academic economists and public-policy people. This caused me not to make this distinction.)

But I stand by my claim that making people think hard about serious problems is great training for everyone. The best way to learn to think is to be made to think about hard problems and then have your arguments read carefully.

[Frances Woolley]

Chris J "But I stand by my claim that making people think hard about serious problems is great training for everyone."

Absolutely.

And as Nick Rowe's posts in this blog show, you don't need mathematical analysis to think hard about serious problems.

Personally, I find questions I can ask in an undergraduate economics course more interesting than graduate economics. For example, here's one that I find fascinating: the big thing in economic development is microcredit loans. These are small loans, usually made to women, and do not require any collateral. Responsibility for repayment is collective, that is, there is a group of women who are jointly responsible for making sure that the members of their group repay their loans.

But here's something interesting: is a woman's optimal strategy to invest her loan in, say, a new stove for her business selling pickles, that will increase her labour productivity, or a new rickshaw, that will increase her husband's productivity? The new stove gives her income that she can control, so she is guaranteed of being able to repay the loan, and may give her greater power within the family. But she risks having to work a double day (doing her regular work+making pickles). The rickshaw may offer a higher financial payoff with less work for the woman, but the woman retains the responsibility of paying off the loan while the husband is the one with the greater earning possibilities.

Undergrad econ is so much fun...

[William Hayes]

Interestingly, my wife Wan is dealing with a case right now here in Asia. A husband (who is a policeman) wants his wife to borrow money for him. And, he has hit her to get it, but she has resisted so far. She hid in the back room of my wife’s shop for three days but the husband found her and she went with him. The reason she did so was she didn’t want anyone to hear angry voices in public; she'd loose face; and would rather be beaten in private. That's the situation now. Wan just got off the phone pleading with her not to give in to him...

I’ve had to deal with black-shirts on motorbikes who regularly come to the village to extract money, beat up people and take what they want. They back off with a foreigner present. On some loans people can pay 30% a month interest. Many are forced into it with hospital bills and the men tend to gamble a lot. I’ve eliminated most of this by being the major microcredit lender in the village. I usually make $100 loans at 0% to the women (never to men): one is with a family with a child that's chronically ill (and I've forgiven some of the loan), but most are with a project and a plan. When they pay it back (which they do in their own time; I just insist on something minimal which they determine each month) the amount they can borrow goes up depending on the project they have in mind. They usually buy products cheap on a rural market and make a profit on them in an urban public market.

[William Hayes]

With my McLuhan post I dangled a carrot to get a challenge; to give someone a friendly poke with my stick. Perhaps the contradiction appearing in “right (sometimes) and wrong (always in some way)” was too simple. The point: the phrase has an underlying “double-truth”: true to the part; true to the whole. In other words, I’m right sometimes with the core or pivotal principle; always wrong in some way with the details (rough around the edges).

[William Hayes]

Just some correction, clarification and a little extension.

Wan suspects the woman has been hit. She doesn’t really know: the woman won’t talk to her about that.

“Black-shirts” are literally and figuratively true: a double-truth. Also, I infiltrated the police force to became a “volunteer”: supposedly to help tourists. Never helped a tourist yet when I put on my police hat (I've no authority and say nothing other than to inquire as to the problem) the bullies back off; and the police don’t extort me when they stop my car (seldom) or motorbike (often). Also, the uniform is occasionally worn for the the big bosses, politicians, police, army, who like very much to have their pictures taken with me all dolled up in a white uniform. Look like a bald big-wig navy officer.

Loans were usually up to $100 but with trust more often give $20 here and $30 there kinda thing. They keep track; I can’t be bothered with details. No big deal really, though it does cut into my teacher's pension. And, I did give money to a man. Indeed, the largest of a $1000 to help build a new house, but I got the broken down house in return on the family land, which they still own. And, I’ve a good guy that helps an old man, whose head spends more time in the air than his feet are on the ground. Still the idea is to renovate the old house as it can get crowded in our home. We can have up to 4 girls from the outer villages staying at our place and taking the 7km ride into the city to go to university. They are poor people, stay here for free. (An interesting aside: Wan gives her former teachers money occasionally, and she will for the rest of their lives.)

You've heard of red-shirts, yellow-shirts, now black-shirts; anyone hear of the green-shirts? They are comprised of women over 50 from a couple of dozen villages battling (for about 10 yrs now) big government-big business on a huge potash project that will undermine (double-truth there) their villages and rice fields. They are remarkable, wonderful - and that's where you'll find me wondering. Just look for the silent old white guy in the shadows surrounded by a bunch of old women chattering away.

I should mention that what i do is officially illegal. Some people think I've been red-flagged but I don't think so. Wan worries too much. Still, the government watchdogs might be reading this.

[Matthew]

"Graduates from those [public policy and international relations masters] programs have a basic undergraduate-level background in economics.

Would you really go so far as to say they have a basic undergraduate level background in econ? As far as I can tell most of these programs only require one course in undergraduate micro (taught one half of the year) and one in macro (taught the other half) - sometimes even these are "dumbed down" because so many of the students have difficulty. Better than nothing perhaps, but probably not even amounting to a minor concentration.

[Frances Woolley]

Matthew, all I can say that, if that is true, then the following should make you very worried about the Department of Finance, economics graduate programs, or both:

(the following is cut and pasted from the recruitment information on the department of finance website, www.fin.gc.ca)

What are the different recruitment streams?

Finance Canada hires university recruits through three streams. Most recruits are hired through the Economist and Policy Analyst stream, which is open to recent graduates at the Master's level in our four target disciplines:

* Economics.
* Public policy/administration.
* International relations/studies.
* Finance.

The two other streams are highly specialized. The Tax Legislation stream is open to those with training in law, taxation or accounting and who wish to pursue a career as a specialist in income or sales tax. The Doctoral Researcher stream is aimed at recent Ph.D. graduates who wish to conduct theoretical and empirical research. Information about the application process for these two streams can be found here.

[Gregory Sokoloff]

Frances, you might be interested to read Greg Mankiw's comments from a few years back in "Why Aspiring Economists Need Math" (gregmankiw.blogspot.com/2006/09/why-aspiring-economists-need-math.html). I don't think you need worry about having revealed any shocking secrets about Econ grad admissions.

[Frances Woolley]

Gregory S, thanks for that link, very interesting article, especially what Mankiw says at the end, "Is it possible that admissions committees for econ PhD programs are excessively fond of mathematics on student transcripts? Perhaps."

I think what's slightly different about the argument I'm making here is that I talk about the supply and demand in the market for graduate students - the large potential supply of students/demand for places that a department can tap into by marketing their program to underemployed mathematicians and physicists. Those people who are really smart but just a little bit too sensible/not quite crazy enough to be successful as pure mathematicians.

[Frances Woolley]

William Hayes, thanks for sharing these stories, they're fascinating. It sounds like microcredit deserves a post on its own!

[Matthew]

"Matthew, all I can say that, if that is true, then the following should make you very worried about the Department of Finance..."

I would be worried if policy analysts actually did anthying except drinking coffee and trolling economics blogs!

[William Hayes]

Thank you, Frances. Muhammad Yunus recently opened a school to teach microcredit and microfinance here. It’s evolving well. So yes, please, do a post on it’s own.

[William]

OK. Let’s see if I can kill two flies with one swat: the problem of circular curriculum being boring and Francis’ concern about learning retention with what’s being taught.

Her concerns have no substance; actually the opposite: because the prof in NZ ONLY remembers Frances cooking cookies at midterm (and nothing else) precisely tells me that her teaching was a success, the cookies were a winner - and indicates she’s a good teacher.

Why? Because cooking cookies was a big positive that only happened once and perhaps only once in all his schooling: it was an accented or WOW moment. Think about it. When a child first observes an airplane it makes a big impression the first time: like wow! Next day, hears it; sees it – heh, neat…3rd day ok…until the plane goes over and over and the child is not even conscious of it. But, it’s not really forgotten. As soon as something different happens with that plane, different noise perhaps, the child will become conscious of it, if for only a short unaccented moment. Same with what she taught her students; it’ll become conscious when something is different, a negative, something that challenges what was learnt and internalized from Frances’ class. With circular curriculum, it appears (and notice phenomenology is the main tool i use) they keep getting students to look at that damn plane over and over again. They eventually loose interest and booorring. They need to change to accent cars or horses or whatever...for a theme on transportation perhaps.

[Nick Rowe]

William: Wow!

Matthew: Last Winter, I taught Macro (half course) to Carleton's MA Public Admin students. They had already had a full course of Intro Micro and Macro (Mankiw). I taught them using the intermediate text Blanchard and Kneebone, minus the math, plus a bit more intuition and policy. They get similar micro, plus a lot of more applied stuff. A lot less math and technique than economics majors, but they are grad students, so you can stretch them a bit more on other dimensions. I don't know about other Universities.

[TJM]

I TAed for first year Econ last year and I was amazed at how many students who were planning on attending graduate school for other programs had so much difficulty with the material. As a student I found Econ1000 almost too easy at Carleton. Come to think of it I found intermediate Macro and Micro to be too easy (in a relative sense) as well, so that when I got to fourth year Micro theory I felt side-swiped and totally unprepared for the extremely difficult theory and application problems we were forced to deal with. This almost completely dissuaded me from applying to graduate school for Econ.

One complaint I have (if I'm permitted one) was that many of the compulsory courses focused too narrowly on theory. While I understand it to be useful, it can get pretty dreary the third time through. If the concepts really are going to be repeated in the Master's program, perhaps undergraduate students would benefit more from a focus on real world applications and examples in core courses. The memorization of relevant real world economic history and case studies seems like it is very underrated by the econ department at Carleton.

[Nick Rowe]

TJM: For any course: there is a variance of students in terms of how easy/difficult they find the course; and there is a covariance between how easy/difficult they find this course and how easy/difficult they find other courses across the university.

What you say matches my experience. For ECON1000, the variance is higher, and the covariance is lower, than for most courses across the university. Some students find it really easy, others find it really hard. And it doesn't correlate well with how easy or hard they find other subjects.

Those would be grad students, or prospective grad students, in Public Admin or International Affairs. Yep, they are bright, but some of them find economics hard.

[Frances Woolley]

TJM: "One complaint I have (if I'm permitted one) was that many of the compulsory courses focused too narrowly on theory. While I understand it to be useful, it can get pretty dreary the third time through."

You are the person I wrote this post for.

Don't write off people who struggle with Econ 1000, though - it's a particular way of viewing the world, and it comes naturally to some people and not to others. And what's important in teaching is the marginal product, not the total product - making a difference to someone's life. Econ 1000 has more potential to change the world view of someone who doesn't already think like an economist.

[Matthew]

"Matthew: Last Winter, I taught Macro (half course) to Carleton's MA Public Admin students. They had already had a full course of Intro Micro and Macro (Mankiw). I taught them using the intermediate text Blanchard and Kneebone, minus the math, plus a bit more intuition and policy. They get similar micro, plus a lot of more applied stuff. A lot less math and technique than economics majors, but they are grad students, so you can stretch them a bit more on other dimensions. I don't know about other Universities."

Nick, if both these intro and intermediate courses are actually required then, in my understanding, that would be on the upper end of economics intensivity for Canadian public admin programs. Also, it is good that you teach it the way you do - less math, more understanding principles - because this is what the vast majority of future policy analysts need. Pretty much anyone in govt doing real applied economic analysis will have a full econ degree (probably a masters), but there are lots of other areas where people aren't crunching numbers, but need to have an appreciation of economic principles.

[Frances Woolley]

Matthew - "Pretty much anyone in govt doing real applied economic analysis will have a full econ degree (probably a masters), but there are lots of other areas where people aren't crunching numbers,"

real applied economic analysis=crunching numbers?

[Matthew]

Frances,

What I mean to say is that most anything in govt involving a heavily quantitative application of economic priciples (i.e. econometrics, input-output analysis, simulations, etc.) tends to be done by people who were trained as economists. There are a lot of people though (easily the vast majority of analysts, in my experience) who more qualitatively or intuitively apply economic reasoning when analyzing/making policy - these people come from a wider variety of backgrounds.

[Frances Woolley]

Matthew - interesting. Your perception of what economists do suggests that perhaps even people wanting a career as an economist in government should load up on the math courses. Which is a stronger claim than I'm making - I'm saying a math background is useful for a PhD in economics and a job in academia.

[Matthew]

Frances,

Is my perception mistaken? Please explain if you feel it is.

I don't necessarily think people wanting a career in govt as an economist should load up on the math courses as per Mike Moffatt's experience - but comfort with econometrics, which can cause a certain amount of trauma among the less mathematically inclined (it did for me) is recommended.

[William]

Excellent question, Frances: that real applied economic analysis=crunching numbers? I'd put 'ideal economic theory crunching numbers' to balance the right side though.

First, let me apologize for misspelling your name occasionally. I’m literally blind, have a blind spot with detail – and lack the sort of clear thinking that will eliminate them. Anyway, with that question not sure how many flies I can swat with my left hand while simultaneously grasping them with the right one. However, I will gently push aside the flies and problematic view (and growling experience) I have about the applied economics of cost/benefit analysis equated with welfare economic number crunching.

Your question is excellent as it points to an absolute extreme with co-consciousness. Appears evolution about mind and matter is co-conscious evolution or co-evolution. And, the two are very well meshed, and complement better in women than in men, I believe.

Nonetheless, at the extreme lets not just put the number crunchers also include that “mighty thinker” (as Marx called him and Hegel was) and his theory of absolute idealism. This means Marx’s theory of absolute materialism is there too (but he’s not a problem being contained now, but not in the trash can as you people probably believe). I see Hegel’s three-fold march about the world to be really dangerous now, and could destroy humanity if not contained. While not quite correct, its in the ballpark to say that Hegel is to capitalism and idealism as Marx is to communism and materialism is apt.

Another way of looking at this is that Heraclitus and Hegel (‘the rational is real and the real is rational’) are close to correct and absolutely wrong. They believed the way up and the way down are one and the same. It appears the way up into theory and way down into application is only alike and never the same.

Anyway, this is a reason I believe the best math for undergraduates is to work with mindfulness (like wow, to get big, bigger and best positive pictures) centering on One. Developing rules by thumb is doubly handy to say the least and in application everyone will be in the ballpark of understanding. Then bring in sophisticated 0-centered maths in graduate school. These guys will be the best at hitting home runs. Almost nothing better for me than to die watching you guys playing ball and hitting home runs.

Gotta go. Know the look. Wan wants me to be mindful about baking bread.

Hope there are some accented moments, wows for you people, in this post.

[TJM]

Nick and Frances:

Thanks very much for your responses, I enjoy this blog immensely.

[Frances Woolley]

Matthew - "Is my perception mistaken? Please explain if you feel it is." It sounds as if you have better information than I do. I'm going to re-evaluate the advice that I give econ MA students interviewing for Finance.

[Matthew]

Frances,

Just to be clear, I don't mean to say that all govt economists do math intensive economic analysis, but rather that pretty much all of this type of analysis happens to be done by economists. There are quite a few govt economists who don't really do this sort of work and just use StatsCan data to tell economic stories. In fact, I have seen people with very minimal formal economics training do this well enough. However, the people who are capable of some of the more math intensive modes of applied analysis are an especially valuable commodity because they are relatively few, so if students have the ability, its probably not a bad idea to point them in that direction. I have no first-hand experience of the federal dept. of finance, but I'd be surprised if it is any *less* mathematically demanding than the provincial agency I work for.

[Jonathan]

Funny, my first year econ prof at Carleton never mentioned this (I don't think he's there anymore), nor any of my other econ profs.

My first year law prof, however, did. He told us that if we wanted to go to law school (which I didn't), we shouldn't take any undergrad law courses. My understanding was that the law schools thought all undergrad programs did was fill students' heads with bunk, and they didn't want to waste time un-teaching it all.

[William]

I’ll second Matthew and also add thanks to Mike and Stephen. But, does anyone have a theory why these four economic professors are so good?

Well, my theory is this: they are, what I call, a “complete team” (comprise a very good four-folded whole). And, the “good” has multiple truth: good team, good people, good professionals, as well as good, well-suited, for my elemental root metaphor. Whenever I make up teams to venture into, infiltrate, opposition lines (not “enemy lines” as I’ve none, not even fascists: i.e. corrupt police and bully boys) to gain new knowledge, capture the flag at the centre, stake a claim or head off into the wilderness (the English psychologists nicknamed me Wilderness Man) a complete team is four-folded and an efficient team (adding 3 specialists in any of the four subfields as necessary) is never more than 7 to accomplish any given task. And, while I no longer have a classroom, the group dynamics of 7 was found to be best for the Sphairos in the middle shaping a field and actualizing the selves within it - the wows, self-actualized, hopefully, into peak experiences.

Yup, I’m a shape-shifter. Welcome to Wonderland! I look a lot like Humpty Dumpty, but different in some ways (like if I fall, bounce back; don’t break. So I guess I’m a hard-boiled egghead without a shell who looks like a nut :) - and Frances appears like playful Alice looking through the looking glass wondering and questioning. Take yesterday, her question about the “real applied economic analysis=crunching numbers?” Notice, I first balanced the overall shape of the question. In re-visiting it today, mistakes were made (mainly in centring it but can't be bothered reshaping it) in the answer and one huge fly got away. Another “ideal theory” to swat dead and grasp alive simultaneously would include the Positivists: however, they are now contained too and no longer bent by absolutes, i believe.

Further, two key images mirrored involve the two natural symmetries: bilateral and radial. it’s as if the former is to the left higher hemisphere and moves, evolves, a right-handed consciousness to overcome Strife and provide security like constructing a house, for instance. With the left hand, radial symmetry involves Love, empathy to create the home. Specifically, I'd bet Frances' class would feel like a home for the students: become like family/friends (wow, she bakes cookies!). Part of the work would be play, having some fun and wonder a lot. And, there is no better teacher than one who gets students to think and work hard, get the job well done, in part by utilizing play and instilling the love of learning.

[Lingwhatics]

An addition to Stephen Gordon's note on failing to train students to write, I did a civil engineering and linguistics double degree in undergrad and neither of those programs provided much in the area of improving writing. I learned most about writing in elective courses, but most students do not choose courses where writing is a requirement.

Sadly, as a TA, I have found that the quality of writing produced by 3rd year engineering students is generally poor, and like many other science and arts programs there is no sense of how important communication is regardless of the field. Those who know how to write seem to end up in those public policy and international relations programs.

[William]

Let me start here with a little proof for the team I believe would be well suited for a venture on Pangaia (like Middle Earth except no humans there; homanity comprises the fourth in my wonderland in Middle Heaven) or take on any undergraduate task coursing any discipline. I simply suit them with my root elemental metaphor. Stephen appears sensible, well grounded, good for mining information and arranging supplies. Mike, the homan on the team, appears as the planner, arranging finances for the venture, making sure all our documents (legal & illegal) are in perfect order. Frances (not sure if she’d make a good thief if need be) for sure would start a list of how to keep the rest of the team, especially those male egos, in check and sober. She’d attend to some comforts for the venture and would certainly bake some cookies! Nick is the group leader; the Elf on the team: the pathfinder with the ability to go up in the air and come down to ground with positive ‘focal points’ to keep the team on tract as they wander the wilderness. He’d be key for finding the negating ‘focal point’ too in the opposition’s square once the Trojan horse has penetrated opposition lines. Me, well I’m normally invisible but will become visible as a Trojan horse to get them through the gate. During the trip I can shift-shape into any living form really using 'rubber sheet geometry'; however my favorites are Raven the Trickster during the day and the Owl of Minerva at night.

So that’s my theory and a simple proof of why I believe the four at WCI make a complete team, not perfect but a good team, rough and soon ready – if they ever choose to venture and take on tasks in the wonderful world of Pangaia.

[econometrician]

Patrick hit the mark with this comment: "I can't think of another field where having a undergraduate degree in the field puts students at a disadvantage relative to students coming from some other field of study."

I teach econometrics at both the undergraduate and graduate levels. When I look at econometrics textbooks designed for undergraduates, it is immediately clear that students who are exposed to such texts (and only such texts) will not even be remotely prepared for graduate-level econometrics courses. My approach has been to prepare my own set of lecture notes which (I hope) will provide the right background. Does this risk alienating the weaker students? Absolutely. But I'm sure advanced undergraduate physics/psychology/philosophy courses also risk alienating students who wouldn't be able to handle graduate work in those fields. Can the type of students who don't have a chance in hell of succeeding in an economics graduate program benefit from undergraduate courses in economics? Absolutely - just like how students who wouldn't succeed in a graduate program in physics/psychology/philosophy can benefit from undergraduate courses in those fields.