How Much Math Do Undergrads Need?
Dear Undergraduate Students:
I've updated my letter about econ grad schools. And, yes, here is yet another letter to you. But, don’t despair: I won’t keep up this frantic pace of giving you information, advice, whining, nagging, notifying. I’ve sent you about 4 letters in the last little while, but with regard to these, and to this one as well, I have been saving them up for you over the summer.
Below, are two letters Prof. Barnett and I have sent to 5 of our recent graduates now enrolled in Ph.D. programs in economics. The reason for all of this is that we have recently had a bad experience, and want to do what we can to ensure it never occurs again: One of our very best recent graduates went off to get a Ph.D. in economics, and quit during the first week because of the heavy math stats requirements of the program. We did warn the student of this situation (see attached letter from Eric Mattei, another recent grad also studying economics at the graduate level, but at a different university), but feel we should be even more explicit. Hence this present series of letters.
In my view, if you want to get a Ph.D. in economics, and have a career as a professor of the dismal science, there are two paths open to you.
1. Enroll in a Ph.D. program at a mainstream university in the U.S., Canada, and most places in Europe, Australia, etc., particularly a prestigious one. Here, the best plan for an undergraduate is not necessarily to major in economics (however much it pains me to say this, since I love this discipline above all others) but rather in mathematics and statistics. Alternatively, you may get by with a double major: one in math, the other in economics. If that does not suit you, you might consider only a minor in economics and a major in math and stat. If you go this route, and attend a prestigious university, or, at least, the most prestigious that will accept you, you can look forward to a career on the faculty at any university in the world. In the U.S., there are about 105 Ph.D. degree-granting universities in economics. I am not familiar with all of them. Possibly, there may be some, especially at the lower echelons, that are not so rabid about math and stat.
Before I get to the second choice, a bit of information about myself. I started grad school in the mid 1960s at Columbia University. Even then, there was an emphasis on math in economics. I didn’t like the math, but I was reasonably good at it, so I got my degree. I ask myself, suppose I was about 21 years old right now, didn’t like math, wasn’t good at it, but loved economics. Suppose I was interested not only in free market economics (which is compatible with either a math stat or literary logical approach, but Austrianism, which almost entirely eschews this subject). What would I do to prepare myself for a career of the sort I now have?
I would definitely choose this second option, for more on this see below. However, one caveat: if you go this route, while it is likely that you will be able to get a faculty position in the U.S., it will almost certainly not be at a prestigious research (Ph.D. granting) university. For positions at non-doctoral universities, such as Loyola University New Orleans, employment opportunities will be very difficult, though possible. However, there are many, many college and university economics departments (liberal arts colleges and four year state universities) which will employ people with such degrees.
2a. Enroll in a Ph.D. program in economics at a university that, for lack of better terminology, may be characterized as “non mainstream.” There are several of these around the world. One in Guatemala, another in Argentina, a third in France and a fourth in the Czech Republic. For a full listing of these, see the attached. I have asked the people in charge of these programs, whether or not it is possible to get a Ph.D. without knowing any of the foreign languages utilized in those countries. The answers I get are not fully clear. It appears that if you enroll there with a masters degree in economics already in hand, then you do not need a foreign language.
2b. Enroll in a Ph.D. program but not in economics. For example, in agricultural economics, forestry economics, economic history, plain old history, social thought (at the University of Chicago), etc. It is still possible, although more difficult, to get a faculty position in any economics department with a degree of this sort
2c. Ordinarily, I counsel people against getting a master’s degree in economics at all. If you want to be an academic, a Ph.D. is necessary. With a masters degree only, at best you can be an adjunct professor. This sort of career is very poorly paid, and insecure. I wouldn’t recommend it. However, and this is a big however, if you have a masters in economics, you can then to on to get a Ph.D. at one of these universities in Guatemala, Argentina, France or the Czech Republic. Here, you can avoid math stat almost entirely, and study with Austrian free market (a redundancy) professors.
If you have any questions about any of this, please do not hesitate to come and see me.
Best regards,
8/04
Dear Former Students who are now in Ph.D. programs in economics:
We do not offer econometrics or math-econ courses at Loyola. In my own view, they are, while not exactly worthless, of much less worth than what we do offer: economics!
However, for grad school, matters are very different. Here, these sorts of things are absolutely necessary to get a Ph.D., at least at most universities. Why, then, don't we offer them at Loyola if only for this reason? Because we send far too few students to grad school to make it worthwhile. I've been at Loyola for 3 years. In that time, you 5 are the only ones to my knowledge who have gone on to enroll in Ph.D. programs in economics. We can't afford to offer classes with only 2-3 students in them.
So, what to do if your math−stat is somewhat deficient? We suggest, urge, that students headed for grad school take a few extra math courses while still undergraduates, either in our math dept, or at Tulane's econ dept. Or, take an extra semester or two after graduating, and before grad school, for this purpose.
But suppose you are already at a grad school, and feel that your math-stat preparation is less than fully adequate for your intro micro and macro classes at the grad level? Then, I suggest you put off your grad micro and macro courses for a semester or two, take all the math−stat you can, even at the advanced undergrad level, and then go thru the program in order.
I'm copying my daughter on this since she's had something of the same experience. She is getting her Ph.D. in neuroscience at Hopkins. Her case is not perfectly analogous to yours, but in her first year, last year, she took an undergrad stat course since she felt a need for it. No big deal. These things happen all the time. Hannah, if you could tell these rotten kids (I mean, former students of mine, sorry, I lost my head) a bit about your experience in this regard, I'd appreciate it.
I'm copying several of my colleagues on this lest I inadvertently lead you astray on any of this. If so, they'll pipe up, I'm sure.
One final note. If you can possibly get out of teaching econ to undergrads during your first year, strive mightily to do so. Put this off as long as possible, hopefully until your third year, after you've passed your comprehensives.
Best regards,
Walter Block
9/8/04
Ladies and Gentlemen,
As you well know, although Walter and I do not agree on everything, we do agree on most things having to do with economics. I do agree with him about our offerings, and will continue to hold this position, even if the number of students we send to Ph.D. programs grows exponentially. The reason is that I think the best preparation for a Ph.D. program in economics is to major in math and either double major or minor in stat, while taking principles, intermediate, and international economics. It would also help, if possible to squeeze in financial accounting and managerial finance, and managerial accounting, if possible. Only this past Friday, I advised an incoming freshman and his parents of my position. Such a course of action would better prepare students for a Ph.D. in economics while still allowing us to use our limited resources to teach economics.
As to what to do if one finds oneself with inadequate preparation in the quantitative areas, I basically agree with Walter. When I was accepted to Chicago’s program, they told me that I would have to spend the first year getting up to speed in mathematics and statistics. And that was for the term that began 35 years ago this fall. (In the event, they didn’t offer me any money so I couldn’t afford to go there.) So, I think that you are better off to delay your basic, and essential and most important economics courses, theory courses until you have sufficient mathematical and statistical skills so that you won’t be handicapped, having to concentrate on the mathematics and statistics to the detriment of the economics.
I wish each of the very best.
William Barnett
-----Original Message-----
From: Erich H. Mattei [mailto:ehmattei@uga.edu]
Sent: Wednesday, September 08, 2004 8:17 AM
To: WALTER BLOCK
Subject: Re: math, stat
Walter and Co.,
Here I am sitting in my office on the sixth floor of the Bank
of America Building in downtown Athens, GA (one of the perks
of being a grad assistant) looking out into the post-remnants-
of-the-hurricane-weather outside.
Since all of us on this little list are former students of
the Subjectivist School at LoyNo, and will be pushing through
graduate school together, albeit at different institutions, I
thought it might fun to communicate via this email list (sort
of like a Live Journal only without all the BS and pictures).
Anyways, I'll take it on myself to make the first entry:
Walter was right, I feel more like a mathematician than an
economist. My first semester classes and their respective
primary texts are listed below:
Micro Theory I: "Microeconomics with Calculus"
Intro. Econometrics: "Statistics: Theory and Methods"
Math for Economists: "Fundamental Methods of Mathematical
Economics"
I must admit, however, that it is not as bad as it may seem
by simply reading these titles. Most of my time is spent
doing problem sets of big long math problems, but at least
it’s not taking some blow-off science or sociology or English
class, and now I am beginning to understand all of those
Greek notations that appear in most articles.
Although I believe some of this may be more challenging for
me than other students (a number of whom already have MAs or
actually have degrees in Math and Physics), I make up for
my 'math-stupids' with my 'econ-smarts' (which, personally,
means much more to me). I may not grasp the mathematical
notations of theorems immediately, but I more than make up
for it with my understanding of the economic theories it
applies to. Based on my participation in class, and the lack
of others' participation, I sometimes feel like I'm the only
one who is an economist, the only one who knows anything
about economics!!!
Anyways, that’s all for now
later,
Erich H. Mattei
Department of Economics
University of Georgia
-----Original Message-----
From: ddamico@gmu.edu [mailto:ddamico@gmu.edu]
Sent: Wednesday, September 08, 2004 1:01 PM
To: ehmattei@uga.edu
Subject: Re: math, stat
Erich,
Not to sound like I'm bragging but all I can say is you picked the wrong school to go to my friend. One of the most important things I've taken note of so far is that we are supposed to learn more from our peers than classes or books. If you don't have anyone to engage in debate with or grapple over the material with I worry for you. The kids at GMU are impressive, and matched by the faculty so far. Russell Roberts is awesome, he took over for Walter Williams as the micro lecturer. Emily and I already noticed that the Loyola crew has a leg up on his syllabus as we've read about three fourths of it already.
Math isn't going to be fun but it doesn't seem to be too hard. I don't have time to get into all the specific nuances of how great the program appears to be so far, but let's just say I'm sure that no other PhD program in economics is quite like it. After reading your summary of Georgia, I'm sure of it.
Sincerely,
Dan
Dear Erich and Dan:
It is always very good to hear from you.
You always were snarky kids when you were here, and I'm glad that none of that has rubbed off of you in your new intellectual homes.
I give you fair warning; I don't have exact figures on this, but it is my impression that of 100 students who begin doctoral studies in economics, fewer than half emerge with the Ph.D. degree. I don't say that all who fall by the wayside do so for lack of mathematical and statistical sophistication, but a goodly number of them surely do.
TAKE THIS STUFF SERIOUSLY. You have only been at grad school a few weeks. You've not passed any course exams, let alone orals, or dissertation defense. Professors at most grad schools are rabid on math and stat. Get in as many of these type of courses as you can, and work hard at them. Math stupids and econ smarts are not likely to be appreciated at doctoral universities. Your chances of success, there, would be increased with the very opposite talents.
Best regards,
Walter
Dr. Walter Block
Harold E. Wirth Eminent Scholar Endowed Chair in Economics
College of Business Administration
Loyola University New Orleans
6363 St. Charles Ave., Box 15
New Orleans, LA 70118
http://cba.loyno.edu/faculty/wblock
Office location: Miller Hall 321
work: (504)864-7934
secy: (504)864-7944
fax: (504)864-7970
wblock@loyno.edu
Comments (11)
That's interesting, I never knew there was so much math in econ. As a computer science/math major I've taken a lot of calculus and differential equations, but not any stats. I think I would find stats to be quite boring. Good luck to the econ grad students.
Published: September 15, 2004 1:30 PM
Here at the U of Oregon, the teachers I've talked to have recommended to me that I take the RIGOROUS econometrics and calc that they have to offer if I even want a chance of admission to grad school. My upcomming sophomore year is going to include integration and differentials. My favorite program is Maple ;) Thank you for the letter Walter. My plan so far is to graduate from UO, then work for a few years, then get a masters and hopefully start a business. I love reading mises and studing the economics, but i'm not sure if academics is my lifes calling.
Published: September 15, 2004 2:00 PM
There does not have to be so much math. It only adds another level of abstraction to the abstraction. It enhances the effect of the smoke and mirrors. It also weeds out most of the wannabes.
In economics, econ smarts aremore important than math smarts. In physics, physics smarts are more important to math smarts. In any field of study, that fields smarts are more important than math smarts. That is, if you want to create something new in that field.
No new theory ever came out of manipulating greek letters. Every theory starts with an observation or flash of insight. The math is there to provide formal proof of such.
Published: September 15, 2004 2:02 PM
I believe that all economists should have a damn good understanding of math, so they could immediately recognize stupidity of mainstream economics. But by "understanding math" I do not mean the math that is taught at economics schools, but rather the Math. Analysis in math programs. I had both. The difference?
Math at economics school: 2 hours/week, one year covered linear equations, matrices, derivatives, integrals, partial derivatives, differential equations.
Math analysis at math faculty: 3hours/week: one year covered convergence, derivatives, integrals - but you could prove every word. I can tell you that one semester of this math gave me more then 3 years of economy.
If mainstream economists had basic understanding of math, they could not believe a word of what they teach. They can COMPUTE but they do not understand math.
Published: September 15, 2004 4:52 PM
Ideally, in addition to fundamental math and stats, I think physics (or at least applied math) courses could be very helpful in understanding mainstream economics (or its flaws). In facts, mainstream economics/finance use much the same methods as physics, i.e. model "reality" as optimization problems under constraints. Therefore, an exposure to boundary value problems, partial differential equations, Lagrange mutipliers, linear programming, and the like, would certainly not be a waste of time.
At a higher level (and for the real keeners) an exposure to chaos theory and non-linear dynamics could be enlightning as it shows how self-regulating systems can spontaneously emerge out of apparent chaos, just like the free market economy that Austrians like to describe "with words".
Published: September 15, 2004 6:12 PM
The Math Question
Steve Kane’s point, that it is rather basic statistics that economists use, is a point that Murray Rothbard used to make all the time. He would say that real mathematicians were never impressed by the math employed by economists.
That being said, it will come as a shock to many new Austrian type Ph D candidates as to the extent of the math used at the graduate school level in economics courses. That was the case for me near 30 years ago.
I remember my macro course was taught by a professor that started each class on the far upper left hand corner of the blackboard and continued during the hour to just add one equation after the other until he ended up on the lower right hand corner of the blackboard.
I had no clue as to what he was writing.
I was doing very well in the Math for Economists course, but this guy was just throwing up equations in the macro course that could just as well have been some newly discovered ancient writing . I should have never been in that course. I didn’t have the basics to understand what he was talking about.
With little guidance given to me by my Austrian professor that I went to for help, instead of getting the fundamentals in the math and statistics courses, I dropped out.
Walter Block has it absolutely right, I wish his advice was around for me. Get the math down cold first, before you take the econ courses.
Published: September 15, 2004 8:58 PM
Professor Block mentions "economic history" as a separate study. Can anyone here comment on that?
Published: September 15, 2004 10:20 PM
We shouldn't forget that if dissatisfaction with current institutions grows too severe, a new arrangement to preserve learning can be created. Where do you think the institutions that we are in now came from? Are they degenerate?
NJR
Published: September 16, 2004 2:20 AM
On Economic History as a separate field:
Many European universities have separate depts of "economic history." In the US, EC history isn't that different from other sub-fields; however, there is a rather unique emphasis on explaining the real world. It's a good field for austrians. For more info on economic history, see www.eh.net(Link).
Published: September 16, 2004 9:41 AM
For a good critique of how economics is taught at the graduate level, I recommend David C. Colander. He has written many articles and at least three books bemoaning the methodology that is taught at most graduate schools. He feels that mathematics is stressed at the expense of relevant economic theory. Some of his arguments are borderline Austrian, but he explicitly rejects the larger Austrian paradigm. He refers to the grad program at George Mason as a free market "mafia". Whatever that means.
Published: September 17, 2004 9:00 PM
Truth of the matter is no one will ever give you a job as an economist if all you can do is say "free market!" I've been on job interviews where the first question was "what are the assumptions of the Best Liner Unbiased Estimators?" And this wasn't at the World Bank but on Wall Street! If I hadn't had a strong background in econometrics it would have surely been my last.
I've just started looking at this website, but it seems all that is said is "get off my land," which if you are talking (or working) in monetary policy won't get you in any door. If you kids don't know the basic language of say the Dornbusch model (overshooting), you should ask for a refund on your education.
I’m not going to get into the details of why mainstream theories are important for concentrating on a specific issue (most people seem to have a made mind on that issue here), but I would like to see how the context of these discussions can get anyone either tenure or a non-political job in policy (say development).
Published: September 27, 2004 12:21 PM