Many thanks and kudos to Professor Ralph Bradburd, the Economics Department and the CEP for permitting EphBlog to publish the official set of recommendations (all of which have been accepted, I believe) on changes to the economics major. See below the break for the entire report. Comments:

1) The more open and transparent that Williams is about these sorts of decisions, the better for all concerned. Why not publish all the recommendations that CEP received this spring?

2) The more you know about how Williams operates, the more proud you become of the institution and the people who run it. You might not agree with every decision here, but there can be no doubt that some experienced and thoughtful economists spent a great deal of time and energy on the topic.

3) On balance, these are good changes. They are consistent with the direction in which economics is evolving, especially in terms of more focus on empirical work. If I were a member of the department, I would have voted in favor.

4) It is still a shame that the department refuses to offer ECON 101, a one semester introduction to economics for majors and non-majors alike. A biologist or art historian looking for an overview of modern economics should not be forced to sit through 2 semesters.

5) I have strong opinions on how such a class should be constructed. Short version: classical readings (Smith, Marx), lots of writing, topical debates, and a dash of empirical work. Williams has never had a class like this. Longer rant some other day. I wonder if anyone in the department agrees?

CEP Report excerpt:

1. For Faculty Action

a. Changes in major or honors program:

After a year of extensive study and deliberation, the department is proposing a number of changes to the Economics major.

1) Require that students take Economics 110, Principles of Microeconomics, as a prerequisite for Econ 120, Principles of Macroeconomics. This change would be effective as of the 2006-7 academic year.

Motivation: Introductory macroeconomics cannot be taught without at least some microeconomics as background; consequently, faculty who teach Econ 120 must devote their first three or four lectures in that course to teaching material covered in Econ 110. The current system, which allows students to take the two courses in any order, has at least three disadvantages: First, the fact that the first three or four lectures in Econ 120 simply repeat Econ 110 material tends to create a poor classroom atmosphere because the students who have taken Econ 110 can cruiseand are bored in class. Second, because the coverage of the Econ 110 material must be relatively parsimonious, a significant number of the students who have not taken Econ 110 find the presentation of the material to be incomplete and confusing. Third, the classroom time taken for teaching of material from Econ 110 could be better used to cover material in greater depth in Econ 120, to provide more institutional coverage, more policy analysis, and perhaps even greater historical perspective on topics such as economic growth and economic fluctuations.

Practical Considerations:

Given student enrollment patterns, this change would require us to increase (reduce) the number of sections of Econ 110 (Econ 120) offered in the fall semester and reduce (increase) the number of sections of Econ 110 (Econ 120) offered in the spring semester. This should not be difficult to accomplish.

We would continue to allow students to skip Econ 110 (and/or 120) if they meet the current requirements for placing outof them. (These include taking AP microeconomics or macroeconomics and getting a 5on the AP exam, taking introductory microeconomics or macroeconomics as part of an IB or A-levels program.)

2) Change the course catalog number for Econ 301, Economic Liberalism and Its Critics, to Econ 201. (This course is cross-listed as Poli Ec 301 and Poli Sci 333.) This change would be effective as of the 2006-7 academic year.

Motivation: The current course number, Econ 301, creates some confusion regarding the prerequisites for the course. All other economics courses numbered 300 above have as a prerequisite either Econ 251 or 252, or both, and the current course number may discourage some sophomores from taking the course. In addition, all 300-level courses currently in the economics curriculum except for Econ 301 qualify as upper level electivesfor purposes of satisfying the requirements of the major. Our course catalog copy would be less confusing if we could simply say that all 300-level courses qualify as upper-level electives.

3) Replace the current required capstone courseEcon 401, Senior Seminar, which has a two-module structure (the first module common to all instructors and the second one instructor-specific), with 450+ level seminars and tutorials, each in the field of specialization of the faculty member teaching the course, and each with high expectations for the level of rigor of the course material and a requirement of substantial written work. As is currently the case with Econ 401, every 400-level seminar would have as prerequisites Econ 251, 252, and completion of the majors empirical methods requirement. A subset of the 450 + level seminars/tutorials might have additional prerequisites. The proposed system would change as well the electives requirements for the major. Currently, in addition to passing Econ 401, Senior Seminar, all economics majors must successfully complete three electives, two of which must have course catalog numbers 350 (meaning that they have an intermediate theory prerequisite) or above. Under the proposed system, all majors would have to successfully complete four electives, three of which would have to be numbered 350 or above, and of the latter group, one would have to be numbered 450-490. This change would be effective as of the 2006-7 academic year.

Motivation: Neither students nor faculty are satisfied with Econ 401 as it is currently structured. Students seem to feel that they are wasting their time and/or that the first-module topic is not really interesting to them; faculty members assigned to teach Econ 401 frequently themselves teaching first-module topics that are greatly removed from their area of expertise, a particular problem for new faculty; and faculty also feel that the course compression inherent in a two-module system creates a situation that complicates their ability to require students to utilize the full range of skills that we expect them to have acquired by their senior year. (This is consistent with the comments of last years External Review Report.)

Practical Considerations:

Offering 450-level seminars would not require more staff than the current system. When the department members were queried regarding interest in teaching a 450-level seminar, there was great interest, far more than is expressed for teaching Econ 401. One possible disadvantage of the proposed change is that currently, some faculty members teach multiple sections of Econ 401, and it might be the case that under the new system, faculty would lose the advantage of such double preps. However, with sufficient student interest, it might be possible to offer more than one section of a seminar, thereby preserving the double prep. A second consideration is that, as is the case currently with Econ 401, particular sections of the 450-level seminars may be under- or over-enrolled. Currently, students are asked in the spring semester of their junior year to rank the various Econ 401 second-modules to be offered the following year, and the department attempts to match students with their preferred module, while keeping class sizes in the different sections close to equal. We anticipate that registration for the new 450-level electives will work more like that for other courses, with less centralized coordination of registration. However, some coordination among instructors would still be possible if problems arise.

Another consideration is that currently, only senior economics majors are allowed to take Econ 401. We propose that the new 450+ electives be open to others (juniors, non-majors). But to ensure that seniors can fulfill the requirements of the major, and to reduce the likelihood of seniors obtaining a poor match,we would give priority to senior majors in admission to the classes, and would require that anyone who is not a senior econ major receive permission of instructor before registering.

4) Modify the specialization route to honorsin response to the elimination of Econ 401. This change would be effective as of the 2006-7 academic year.

Motivation: the economics departments procedures for the senior thesis are integrated closely with the current design of Econ 401. Replacing 401 with 400-level seminars requires us to specify how the procedures for a senior thesis would change in response.

Current system: Students can pursue honors in economics either through the full-year thesis routeor through the specialization route. A student who pursues the full-year thesis route to honors submits a proposal late in the spring of his/her junior year, and if the proposal is accepted, works on the thesis for the whole of the fall semester, WSP, and the whole of the spring semester. (Students who pursue the full-year thesis route to honors may apply one semester of thesis work toward the majors upper level elective requirement.). A student who pursues the specialization route to honors submits a mini-proposaltypically one page in length and indicating the proposed topic and faculty advisorhalfway through the fall semester of the senior year, and if that mini-proposal is accepted, the student then withdraws from the second module of Econ 401, Senior Seminar, in order to write a full thesis proposal, which is expected to be about 20 pages in length and to include a statement of the thesis topic, a review of the relevant literature, and a proposed timetable. If that proposal is accepted, the student then spends WSP and the spring semester writing the honors thesis.

Proposed System: Students wishing to pursue the specialization route to honors in the spring of the senior year would not be excused from the second halves of their fall 450+ seminars. Rather, any economics major would be allowed to submit a 20-page thesis proposal during December of the senior year. If this proposal is approved, the rest of the specialization route to honors would work as it does now. The 450 + level seminars would generally require a substantial research paper as part of the course, and our intention is that in most cases, the December thesis proposal would grow out of the research paper in the 450+ level seminar. We would also expand the current specialization route to honorsto also allow students to write their honors theses in the fall semester and WSP. This change would be effective as of the 2006-7 academic year.

Motivation:

We would like to avoid unnecessary obstacles to pursuit of honors, and we see no compelling reason why students should not be able to pursue the specialization route to honors by submitting a proposal in the spring of the junior year, and then, conditional on acceptance of the proposal, work on the thesis in the fall semester and WSP.

6) Require all majors to complete the equivalent of Econ 255, Econometrics, and eliminate the possibility of satisfying the empirical methods requirement with Econ 253, Empirical Economic Methods. This change is effective for students in the Class of 2009.

Motivation: Because there is no statistics prerequisite for Econ 253, Empirical Economic Methods, too much of that course must be devoted to presentation of elementary statistics (probability, moments of probability distributions, hypothesis testing, confidence intervals, t-tests, etc.) with the result that too little course time is available for covering essential topics for empirical economic analysis. If students are not familiar with these topics, the vast majority of empirically-oriented articles in professional journals are not within their reach. This greatly constrains faculty in creating their course syllabi and in their ability of cover material at an appropriate level of rigor in upper level courses.

Practical Considerations:

a) Econ 255 (and Statistics 346) has Statistics 101 or 201 as a prerequisite. In effect, then, we would be adding an additional requirement for the major. Currently, a substantial percentage of majors take Statistics 101 or 201, and would therefore be unaffected by the change. (Note: We would allow AP statistics to substitute for Stats 101 or 201 if the student received a 5 on the statistics AP exam.)

b) At present, Math 105 is also a prerequisite for Econ 255. Rather than add another course requirement for the major, we will teach Econ 255 in such a way as to only require the equivalent of Math 103 as a prerequisite, and as this level of proficiency in calculus is already required for students taking Econ 251 and Econ 252, this will avoid adding a hidden requirement to the major.

c) Given the number of students who choose to major in economics, a shift to requiring Econ 255 may necessitate some increase in offerings of Statistics 101 and/or 201 by the Mathematics Department. The change may not be all that significant; for example, of the 28 students currently enrolled in Econ 253 for the spring semester of 2006, 19 have taken Statistics 101, 4 have taken Statistics 201, and only 5 have taken neither one.

d) Currently, students can satisfy the economics major econometrics requirement by taking Statistics 346 instead of Econ 253 or Econ 255. Statistics 346 provides greater coverage of essential empirical methods than Econ 253. However, our motivation for requiring Econ 255 for all majors is to ensure that all our majors are capable of reading empirically oriented journal articles, and because there are differences in the topics covered, it is not clear that students who take Statistics 346 will be able to do so. We are still in the process of determining whether Stats 346 will be an acceptable substitute for Econ 255, and hope to have the answer to this question in the near future.

7) Eliminate Econ 251M from course offerings. This change would be effective as of the 2006-7 academic year.

Motivation: There are two disadvantages of our current practice of offering Intermediate Microeconomic Theory as both Econ 251 and Econ 251M, where the M designation is meant to imply math intensive. First, the current system creates an incorrect expectation among some students that Econ 251 offers a way to complete the microeconomic theory requirement for the major without having to know calculus and/or without significant effort. Second, the current system encourages strong students to self-select into Econ 251M, and given that we only offer one section of 251M each semester, this can lead to frustration for serious students who for scheduling reasons find themselves in Econ 251 classes in which very few students are really engaged with the material. Another motivation for eliminating the distinction between 251 and 251M is that, frequently, there is not a significant difference between the material covered in Econ 251 and 251M. To be clear, our goal here is not to lower all sections of intermediate microeconomic theory to the lowest-common-denominator sections of the current 251. Rather, it is to raise them all to the level of 251M.

Currently, Econ 251 has Math 103 as a prerequisite, and Econ 251M has Math 105 as a prerequisite. In practice, both Econ 251 and Econ 251M make use of calculus tools (in particular, partial differentiation and constrained optimization) that are only covered in Math 105. However, these tools represent a tiny fraction of the material covered in Math 104 and 105, and for this reason we do not feel it is necessary to require both of those courses of all majors. It should be possible to teach these topics to any student who has had at least Math 103 in approximately a single class during Econ 251, and in practice this is often what we do already. All instructors in Econ 251 would give a short in-class lecture early in the semester on how to take derivatives of multivariate functions, and would then make use of this material in their lectures, problem sets, and exams throughout the semester.

Practical Considerations: There are no staffing implications of implementing this change, and we do not see any other problems that could arise.

8) Eliminating the Oral Exam

Motivation: There are three reasons for making changes to the current oral examination process, one having to do with timing, the second having to do with the nature of the exam itself, and the third having to do with the costs of the oral exams to students and faculty relative to the benefits.

Timing: At present, the Senior Oral Examination is given in conjunction with Econ 401, which consists of two five-week modules. At the conclusion of the first module, students are given a list of roughly a dozen questions to study that, as a whole, are meant to cover the topics with which, as a minimum, every senior economics major should be familiar; the following week they are given an oral examination on those questions. The second module begins the week after the oral exams. When we eliminate Econ 401 and replace it with 450+ level senior courses as planned, we do not anticipate having a two-week break in those courses in which to give oral examinations.

Nature of the Exam: Quite a few (though not all) faculty members in our department feel that the current examination process, in which students study a set of specific questions for roughly a week, and then, in pairs, engage in a 50-minute discussion of a subset of those questions with a pair of faculty members, is neither an effective testing instrument nor an effective means of encouraging students to master the material that we want them to know.

Costs/Benefits: Students report that they spend a great deal of the week (or weeks, in the case of students whose oral exam is at the end of the exam week) preceding the exam in preparing for it. Given the number of economics majors in each graduating class (88 in the class of 2006, 134 in the class of 2007), and given that each pair of students requires two hours of faculty time for the oral examination, faculty are very hard pressed during oral exam week. It was not clear that the benefits of the exercise, as currently structured, exceeded the costs.

Comments Disabled To "Reasonings for Econ Changes"

#1 CommentByJeff Z.On May 3, 2006 @ 8:01 amFirst, all of these suggestions look great. The greatest benefit will be to scare off people who view econ as a relatively easy major, by eliminating the 251 / 253 path. By requiring more math, I guarantee the number of econ majors will, in the future, approach a more manageable level. The intellectual level in classes, overall, will rise. And the more rigorous quant. coursework will better prepare most econ grads for either a career in finance / banking /business / accounting, or for grad school (in which you’re better off as a math major in any event), which are the most common destinations for econ grads.

On another note, Econ 101 was offered when I was an econ major, and it was a major waste in my view. It was basically a joke and totally duplicative of material later covered in 251 and 252. I think 251 provides a great introduction to economic thinking for various disciplines and that you don’t really need 252 if you have a casual interest in understaning the economic approach to thinking — 252 is more about policy and whatnot, while 251 gives you an elementary tool kit that is applicable not only to econ but a whole variety of disciplines (see, e.g., freakonomics). Just like having a poly sci 100 that attempts to cover all political science topics for an interested non-major could never really work; better to avoid a class being so overbroad that it can cover material in only the most cursory fashion.

#2 CommentByfrank uibleOn May 3, 2006 @ 8:47 amShould reduction in the number of the College’s Economics majors be a goal? Shouldn’t the College have room for generalists who want to major in Economics but who don’t plan to be professional economists or otherwise ultimately use any of the material of an Economics major in their day-to-day lives except in a very general way and who consequently do not desire or need to submit themselves to academics of the extremely rigorous nature required or advisable for graduate work in economics? Aren’t the College’s production of generalists of that sort the mission of a liberal arts education?

#3 CommentByJeff Z.On May 3, 2006 @ 9:19 amYes, the mission should be to produce generalists. But the college should not turn into an econ factory where 25 percent of the class are econ majors because, at least for some, they feel it will be an easy major or impress consulting recruiters. Replace “Biology” or “Chemistry” with econ and the same logic holds, yet no one says, let’s let Chem majors skip out on Organic Chemistry, etc. Majoring in a subject signifies some depth of interest beyond a mere generalist, and to have any serious understanding of Econ today, folks need to be fluent in econometrics and basic calculus, just like a Chem major needs to understand organic chemistry. A generalist like you describe can take 3 econ classes and have a basic fluency in economic concepts; but majors should have at least a somewhat deeper grasp of their chosen field.

#4 CommentByfrank uibleOn May 3, 2006 @ 11:00 amIrrespective of student opinion about the rigor of a major and irrespective of the actual presence or actual absence of rigor, should the level of rigor of a major be set for the primary purpose of encouraging or discouraging certain students from undertaking it? Perhaps that is a better question.

#5 CommentByAnonymousOn May 3, 2006 @ 11:14 amIt is a great shame that the department does not make students take MATH 105. I feel that requirement would be the real weed-out for disinterested people.

#6 CommentByJared ’96On May 3, 2006 @ 1:01 pmI agree with Jeff Z. that these changes look good. When I was an econ major, the curriculum was a real mess. It’s heartening to see that they are actively thinking about how to structure the major in a way that makes sense. I don’t think they always did so.

As for Jeff’s view on the benefits of making the major harder, I couldn’t agree more. When I was a major, there was no 251M (it came around during my senior year, I think), but it was clear that at least some majors (including myself) were frustrated at the lack of seriousness and rigor in the required classes.

The department was especially weak on math–Econ 251 didn’t even require any calculus. And until DeVeaux arrived (again, I think it was my senior year), there were no statistics classes offered on campus except for Econ 255, so econ majors couldn’t even look to the math department for further study.

As for Frank’s question about the appropriateness of setting a level of rigor for the “primary purpose” of discouraging certain students, I think it’s off-point. Williams is (supposed to be) a rigorous institution. If the “certain students” that will be discouraged are less intellectually serious students, then by all means it should discourage them.

I should say that as a liberal arts institution, Williams should not be in the business of primarily preparing its students for professional careers, including careers as professional academics. I would certainly not approve of the econ department (or any department) shutting its doors to anyone who wasn’t aiming for a PhD. However, that is not to say that Williams students should be able to get by without taking their chosen course of study seriously, and that’s just what used to happen with econ majors.

#7 CommentByDavid ROn May 3, 2006 @ 1:04 pmFrank: I think this boils down to a question of resource constraints. As it stands, there are clearly more Econ majors than would be optimal given current resources. In making the Econ major more demanding, I think it’s clear that you will get rid of the people who happen to be Econ majors out of convenience and are likely less interested in the material. This removes the current burden on the Econ faculty and students who have much more sincere interest in the material.

This carries the added benefit of giving Econ majors a true taste of modern economics and a better background in empirical data analysis. That said, it’s slightly disappointing to see that, as the anonymous poster says above, the department will only require Math 103 for the empirical methods course. Stat 346, by comparison, requires that the student take Stat 201 and Linear Algebra (Math 211). Both Linear Algebra and Stat 201 require having taken Math 105, which fosters a level of mathematical rigor that I’ve found invaluable to my understanding of empirical data analysis/econometrics.

I truly hope that this does not become a policy of finding the “lowest common denominator” among students’ abilities. With those concerns I mention above, I fear that this may eventually happen. Hopefully, however, these new policies will weed out those who have very little real interest in the material, and raise the bar for all Econ majors.

#8 CommentByDavid ROn May 3, 2006 @ 2:35 pmAs an afterthought to my comments above, I’d like to mention that I think Math 105 would be an important prerequisite to Econ 255 not because the single variable calculus in 103 would be insufficient, but because it would weed out students without advanced quantitative reasoning skills.

If you were to run a very mathematically advanced econometrics/regression class, you would clearly require familiarity with methods in multivariable calculus (Math 105) that would be absent in Math 103. This knowledge would be largely useless, however, if the students were not also familiar with concepts in Linear Algebra, which would be key in understanding advanced concepts in multivariate regressions.

I think that Math 105 should be a prereq for Econ 255 because it would raise the bar for the required level of mathematical/quantitative skills for students taking the class. This would in turn allow the professor to conduct a more mathematically intensive course than would otherwise be possible.

#9 CommentByLoweeelOn May 3, 2006 @ 2:46 pmI’ll go a step further than this crowd and argue that all students should have to pass at least Math 104 (or the equivalent through AP/IB exams in high school) to graduate. Williams should not be graduating people who aren’t able to take an integral and a derivative of one variable — it’s a basic life skill, and unlike learning about income inequality, or other peoples and cultures, it’s not likely something that people will develop an interest in after graduation.

Furtheromre, it’s also a lot harder for the average person — even the average Williams student — to develop math skills on their own time than it is to learn about most other areas. Math is kind of a prude, and does not reveal her even her low-level secrets easily to the dilletante, in contrast to certain other fields, which are more like the last folks “standing” at Brooks Late Night.

Then again, I just really like Math, so just about any “more math” requirement is fine with me!

#10 CommentByRichard DunnOn May 3, 2006 @ 2:56 pmI have completely changed my thoughts on this since graduating, but I think quantitative skills should be less emphasized in the econ major.

It is shocking how much can be “derived” in econ without resorting to complicated math, even calculus. Math is not an end-in-itself and to varying degrees it is a crutch and a language. We resort to calculus because it is difficult to understand immediately all the conflicting forces on a particular decision. At the end of the day, however, the longest string of greek symbols must be met with–“this is intuitive because each symbol is representing a force and here is how the interact.” I am not sure of the benefits of teaching people how to produced these equations as undergraduates versus understanding the intuition behind them.

I would prefer to see students learn the ability to translate between mathematical symbols and economic theory than plug through derivatives and linear algebra. Those are skills best left to grad school. Instead, focus on the fundamental relations the recur time and again across economic fields. By far, this is a harder skill to learn and occurs much later in the progression through grad school than the mindless use of calculus. Students should learn how to take an equation apart and explain it in basic economic terms rather than spend hours churning through arithmetic

As for econometrics, I believe an undergraduate econometrics course should focus on applications rather than theory. The theory of econometrics is adequately confusing that many a grad student leaves with only enough metrics to accomplish the simple techniques they require. I just don’t see the benefit of doing linear algebra and matrix derivatives. At the undergrad level, you should be able to explain why something is a bad estimator without resorting the mathematical proof. People should be able to read a table of results without having to know why precisely the estimator was the best estimator available. It is just too difficult to do so with little real benefit at that level.

I think the “mathing” of econ at the undergraduate level as a weeding tool is unnecessary and speaks of a little math arrogance.

#11 CommentByRichard DunnOn May 3, 2006 @ 3:01 pmAnd I totally disagree with Lowell’s comment:

Math is kind of a prude, and does not reveal her even her low-level secrets easily to the dilletante, in contrast to certain other fields, which are more like the last folks “standing” at Brooks Late Night.

Nothing could be farther from the truth. The most beautiful math is often the simplest requiring little more than an inquisitive nature.

Math, in large part, is an organizational tool for economists. Yes, we need math to establish nasty things like “existence” and “uniqueness,” but for the majority of econ work, this is the unsavory march that must be made before the economics can actually begin.

#12 CommentByBill ’04On May 3, 2006 @ 3:03 pmI think that David is right, and a non-major economics class is great idea. Economics is the basis for modern society, and it is vital that everyone has the ability to get a basic understanding of these concepts. A class that approaches economics from a historical perspective would be a great idea overview for non-majors, and could hopefully turn a few of them away from evils of socialism.

I do disagree with getting rid of the oral exam though. I think that this was a very important part of the economic major. Being able to articulate an argument is an important skill, and I think that it should be kept in the major.

#13 CommentByRichard DunnOn May 3, 2006 @ 3:18 pmI do disagree with an econ for non-majors class, mostly because I think the way we teach econ is broken in general.

The fact that “decreasing marginal utility” is still a concept widely discussed in intro classes is disturbing. Instead of learning silly play models, we would be better off with a first course in economics that was a combination of econ history and the philosophy of economics with simple models used as illustrations.

Too many students walk away with an interpretation of economics that is perversely incorrect and far different from how professional economists think.

The goal shouldn’t be a course for non-majors, but a better intro class that placed econ in a fuller context…you know, in the liberal arts style. There is no need to teach econ just like everyone else teaches econ.

#14 CommentByDavidOn May 3, 2006 @ 3:43 pmTo be clear, I am not recommending a course for non-majors. I despise non-major courses. At a place like Williams, if a class is too gutty to not count for a major, it shouldn’t be offered.

That aside, I suspect that Richard and I agree on what an ECON 101 course should look lie. It should give people an overview of economics in a serious fashion, but with a focus on classical readings and contemporary debates.

The math can be avoided, but students should be able to understand “adverse selection”, “moral hazard’, “diminishing returns” and all the other economic terms that make regular appearences in public policy debates.

After this class, majors would go on to take 251 and 252. There is no need for 110 and 120.

At some point, I would like to design — perhaps in conjunction with our next CGCL! — such a class.

#15 CommentByAnonymousOn May 3, 2006 @ 9:05 pmMr. Dunn said:

“Nothing could be farther from the truth. The most beautiful math is often the simplest requiring little more than an inquisitive nature.

Math, in large part, is an organizational tool for economists. Yes, we need math to establish nasty things like “existence” and “uniqueness,” but for the majority of econ work, this is the unsavory march that must be made before the economics can actually begin.”

Mr. Dunn, can one really understand the concept of Nash equilibrium without having a basic grasp of Topology and the Brower Fixed Point theorem? Can one really comprehend the Black-Scholes equation without having an understanding of the calculus of variations? Can one really do the econometrics without being able to explain what the eigenvalues of a matrix are?

I am appaled by the people who think that the

“Steven Levitt”-like analysis is what the economics is all about. Anyone can hypothesize, put a buntch of numbers in a regression, and see what it spits out. To be able to advance the Economics, one needs to be able to advance, first and foremost, the Economic Theory, and that is impossible without at least a graduate-level mathematics in your tool box.

Nobel prizes in Economics are not given to the people who do regressions. Nobel prizes are given to the people who can prove the ‘ [***]nasty things[***] like “existence” and “uniqueness.”‘ And it should be that way, because that is what Economics is about.

#16 CommentByfrank uibleOn May 3, 2006 @ 9:19 pmAu contraire, economics is about growth and jobs.

#17 CommentByRichard DunnOn May 3, 2006 @ 10:04 pmDear anon:

Maybe you are a professional economist, but I doubt it. I don’t know a single economist who would agree with you. Your opinion of economics is so far removed from what we think of economics I don’t know where to begin. The answer to all your questions is: Yes, you can understand all of those with out deep knowledge of the math.

Very few economists can reproduce Brouwer’s fixed point theorem, but we do know the requirements for it and invoke them when necessary. These results are never in the paper proper, but relegated to the Appendix (browse AER or Econometrica).

Sorry to bore those who aren’t economists, but no, you do not need to know Brouwer’s fixed point theorem to understand Nash equilibrium. First, Nash’s original proof did not make use of it. Second, you need Brouwer to prove the incredible result that every game has at least one Nash equilibrium, but you don’t need Brouwer to find the Nash equilibrium.

Here is the concept of a Nash equilibrium: If you don’t think anyone else is going to change what they are doing, then you don’t want to change what you are doing. If everyone thinks this way, then you are at a Nash equilibrium.

See, I didn’t need Brouwer at all. If you understand that, the only other thing you need to do is translate my words into math so the analysis is neater.

Given the choice between people being able to find the Nash equilibria and people understanding the proof that they exist, I’ll take the latter. Indeed, given the choice between finding Nash equilibrium and understanding what the concept means, I’d still take the latter.

As for Black-Scholes, I simply don’t know economists who do it. This is a useful relation from the finance literature, but economists will admit that our models of stock prices based on rational expectations are woeful when it comes to predicitons of individual stock prices. A great number of economists work in discrete time rather than continuous, in which case you don’t need Calculus of Variation at all.

To really understand econometrics you have to be from another planet. There are plenty of people who are excellent at linear algebra who don’t grasp econometrics. You don’t just sit there with your matrices and go to town. There is an intuition behind it all that is directing you all the time, and the algebra, as we say, just keeps you honest.

I suggest you actually read a paper by Steven Leavitt. He has all the mathematical tools an economist could want.

The point is, if you understand the intuition behind a decision, you become less dependent upon the math to get you there. I read papers, look at long equations with many constraints; wonder at how the person is ever going to solve this; and discover their result is a simple application of marginal cost equaling marginal benefit. They probably knew what the answer would look like at the end before they started all the calculus.

Anon, you are far scarier to economics than anything Leavitt has or will ever do.

#18 CommentByrOn May 4, 2006 @ 2:37 amWilliams does in fact have a class similar to what you describe as Econ 101. It’s Political Economy 301 (also Econ 301–soon to be 201). It starts with Wealth of Nations and continues on through history, including works by Marx, Keynes, Milton Friedman, etc.

It’s not an intro class, but it only requires one econ and one poli sci class as prerequisites.

#19 CommentByRalph BradburdOn May 9, 2006 @ 1:11 pmI’d like to correct what I think may be a misinterpretation of the nature of Econ 255. The course will not have a linear algebra prerequisite nor will knowledge of linear algebra be necessary for required coursework.

#20 CommentByJohnOn May 12, 2006 @ 3:48 amOk, now some of this is just sloppy. And before I digress off topic, I’d like to note that I really think these changes are quite a good idea…much as I think of economics as a liberal arts discipline, the field has progressed to a level where mathematical rigor is a requirement for serious analysis.

That out of the way, I guess that I am the serious economist that contradicts the preceding proof. While I might disagree with anon’s prose, his points are more valid than the dismissive treatment that they receive. Having employed both economists on Wall Street and taught graduate students, undergraduates, and high school students in the discipline, I can certainly assert that “Leavitt(sic) style” economics is not sufficient for serious inquiry, or continued employment. And as a side note, I’ll add that Steven Levitt has exceptional math skills which are on display in his published articles; none of these stopped him from committing serious econometric oversights that others, also with exceptional math skills, are now rectifying.

Of course you don’t need a fixed point theorem to understand a Nash equilibrium. Hell, I saw the movie. To prove that a strategy is actually a Nash equilibrium it is a help though, and last I checked, applying equilibrium concepts to the study of (for instance) corporate or labor decision making was still a major thrust of economic theory. Simply put, if I wanted to merely absorb knowledge, your characterization might suffice (and it would be really cool to watch a movie in class!); if I’d actually care about advancing the field in a manner I’d hope most Williams students would aspire to, your prescription is woefully inadequate.

And no, Nash didn’t use Brouwer in his original proof…he used a variation of Kakutani’s extension (which is a bit harder to grasp actually) in his NAS article, and then reverted to a “simpler” Brouwer explication in his “Non-Cooperative Games” article. And while it is true that all finite games have Nash mixed-strategy equilibria, the truly relevant issue is usually how to find reasonable candidates among a plethora of candidates in infinite games (i.e. those with a continuum of players or time). For this, both theoretical, and more importantly, numerical implementation of fixed point theorems are essential.

I won’t begin to dignify the comments on Black-Scholes. No, there aren’t economists who do it, since we all understood it a long time ago. And yes, Ito calculus is important, essential even, to access any recent results on interest rates or credit insurance…and to ask it to explain the cross-section of individual stock returns is a straw man of Ozian proportions. B-S actually doesn’t rely on any presumption of rationality in stock returns at all, and can be directly derived via no arbitrage and assumptions regarding the diffusive motion of an individual underlying asset.

And thanks for suggesting that we relocate the econometrics class to the interplanetary biology department. The sad fact is that probability is an especially slippery subject, and that intuition, even that of accomplished statisticians is not so reliable. Think about the theory of long leads for instance, or the return to origin tests of randomness. I hardly think knowing when to type xtreg into Stata is becoming of a Williams education. That is, as they say, what manuals are for.

And if you’re looking for econometric role models, Levitt might be not be the best choice; first, because he clearly understands the theory behind the technique, and still let intuition lead him astray.

Sad really, that I like defending the anonymous.

#21 CommentByRichard DunnOn May 12, 2006 @ 11:23 amThis is clearly a case of refusing to differentiate between what should be taught in graduate school and what should be taught to undergrads.

To be a professional economist requires a large mathematical toolbox. The math everyone is speaking about would require every econ student to come close to completing a math major as well. Until we want to make linear algebra, differential equations, real analysis, and topology required for the major, there is no way to teach with the rigor y’all are asking for. And I am not sure I see the benefit of doing so anyway.

To address your questions without whipping out my math:

Remember, a Nash equilibrium is just a place where no one wants to move from if no one else is going to move. For example, you are on a date at a shitty movie. The movie is so bad you would love to be grabbing a beer instead. Your very attractive date is thinking the same thing. Because its a movie, you can’t talk and so you don’t leave because you would prefer to watch a shitty movie with a hot date than drink alone. Your date thinks the same thing (lucky you).

The problem is the Nash concept guarantees an equilibrium but often gives us too many and some of these may be really illogical. I don’t need a fix point theorem to understand this. I also don’t need a fixed point theorem to find solutions.

Fixed point theora are used for one reason and one reason only: to prove the existence of an equilibrium. It is an important detail, but just a detail, and one that can wait until grad school.

You write as if you expect Williams undergrads are going to be publishing in AER right out of college. That is just silly. Williams will send plenty of good people to grad school who will advance the field. And this should not be the goal of a Williams education in the first place. The point should be that they understand enough economics to see the flaws in many arguments and enough to formulate their own arguments.

It is my belief that they should leave undergrad understanding that economics is not applied mathematics. Math will never lead you to building your own model, and that should be the goal of a Williams undergraduate education. How can we get you at the end to write down and solve a simple 2 period model where you make a choice between 2 options. I don’t care if you can re-invent the proof that simultaneity biases OLS results. I care that you can think up a simple example of simultaneity (stadium attendance and winning percentage: do fuller stadia cause more winning or does winning cause fuller stadia) and come up with a way to solve it. Yes, I am ok with someone just using ivreg in stata, as long as they understand why they are using IV instead of OLS and they meet the conditions for doing so. That is doing economics, not twiddling around with system of differential equations.

#22 CommentByRichard DunnOn May 12, 2006 @ 12:43 pmI have deeper problems with all the pro-math comments: where are we teaching fixed points and ito calculus. I mean, what undergrad class grinds to a halt without these things? Where in the curriculum is it necessary to have all these tools?