Math knowledge and ability to be a good academic economist???

[Oikos-nomos]

Last semester I took an Intro to analysis course and did well, got 90%, but the course was directed to economics majors, and my classmates had more or less the same training in math than me, so i didn't find myself out of place, in fact, i found myself at the top of the class.

 

Then i decided to enroll this semester in a Topology course for mathematicians...and now i find myself struggling to survive in it: very fast-paced, lots of exercises, etc.:eek:

 

The class is filled with Math-people (those who want to become professional mathematicians) who have taken at least two more upper division math courses than me and most are undoubtely quicker in their math reasoning than me. I think i am beggining to see the limits of my math ability.

 

So the question is: what math knowledge is required, or at least most economist have? and what is the math ability needed to do good research (theoretical, not empirical)...and of course, to survive the Phd.? I mean, economists are not expected to have a command over math comparable to that of mathematicians, are they?

 

I am one of those who regard math as a great tool, but think that there are other factors that are even more important than math.

See for example http://www.www.urch.com/forums/phd-economics/81362-mark-true-research-economist.html

However, i know some math ability is necessary to do good research. I know it depends of what your interest are, but there's got be some standard.

A good example of little math-intuition oriented-research is Paul Krugman, who is quite successful.

 

 

 

 

What do you think?

[nash12]

Math is definately not sufficient to do good theoretical research in economics, but to some extent its neccesary. It is neccesary in two ways: 1) Math is obviously an indespensable tool in economic theory, and 2) Being good in math is a good indication of your ability to think creatively.

 

Note that you can make the math simpler in theory, only when you know the math well. If you've done well very well in a math class for economists, it means you have all the basic ingredients. Don't judge your ability to be a good economic theorist by how you perform with math students in a higher math class like topology. Make sure you get the concepts and give it your best. After doing the course I suggest you read The Thoery of Value by Gerand Debreu. You'll be pleasently surprised to learn how the concepts you studied in Topology have been elegantly used by great economists like him in the past..:)

[Golden Rule]

The class is filled with Math-people (those who want to become professional mathematicians) who have taken at least two more upper division math courses than me and most are undoubtely quicker in their math reasoning than me. I think i am begging to see the limits of my math ability.

I wouldn't sell yourself short. Had you taken the same courses as them leading up to this one, don't you think you'd be a bit more experienced and familiar with the style of thinking? I feel you've more likely built up your skills in different areas. People too often mistake some absolute, static level of ability with differences in priorities.

So the question is: what math knoledge is required, or at least most economist have? and what is the math ability needed to do good research (theoretical, not empirical)...and of course, to survive the Phd.? I mean, economists are not expected to have a command over math comparable to that of mathematicians, are they?

You're right that the math is only valuable insofar as you can use it to generate tractable results with relevant economic interpretations. I thought your post in the thread you linked was spot on.

 

I think once you get specialized, you start to see the same models and techniques over and over again in seminars, and it all becomes very familiar. There's a lot of scope for creativity within a fairly base level of tools. Now I suppose you can be innovative by applying some math technique that hasn't been applied to economics before, but that's not the only way.

[sonicskat]

Math is definitely helpful in converting ideas and thoeries into formulas, which is a tractable way to do economic analysis. However, true breakthroughs in the field, and most successful economists are noted more for their creativity than the ability to do proofs.

 

One little anecdote, I met Roland Fryer about a year and a half ago before I went to grad school. The harvard economist that is on the society of fellows in his late 20s told me that while he is a talented mathematician, his ideas are never driven out of knowing advanced mathematical theory, but by just observing the world around him. In fact, if you look at some of his more popular papers, there is a serious lack of math. In many cases he uses basic topology or linear algebra. Therefore, I think a greater priority than mathematical prowess is creativity... in the worse case, just hire a grad student to do the math for you:)

[Canuckonomist]

I feel obliged to reply, since I am in the same boat. We didn't have analysis for economists, but we had calc I & II for economists. After that, I went on to take math major calc III, analysis I & II, differential equations, abstract algebra and probability. I did about average in those classes, and I questioned my ability to do research, too.

 

That very summer, (the end of my second year,) I did a paper with a professor in Micro/Natural Resource econ, with open and closed loop solutions to a dynamic programming problem. I found it wasn't that hard to pick up dynamic programming that summer, and in terms of using them in an application, I found understanding the math came very quickly. If you can find a good book like I did (Kamien and Schwartz, 1992) then things aren't so bad. All I found it required was a good work ethic.

 

I can say, too, that after taking PhD level Mathecon in third year and ace-ing it, along with PhD financial theory I & II in fourth year, the mathematics used can easily be picked up with the right text and a good work ethic (not to mention stellar profs.) I was lucky to be using Kamien and Schwartz again for Mathecon, too.

 

Also, it's key to have resources that can tell you what "upgrades" there are to certain texts when you find them too easy, and easier versions when you find them too hard. Frank Milne here at Queen's has been great that way for me. He would always give us a text, and say "and if you want more, I can go up the ladder." He wouldn't mention going "down the ladder" in class, but you could always ask him for extra help outside of class. So if you can find a great prof that can provide you that help, you're set as well.

 

I know this is long-winded, but in short, in terms of research and surviving Ph.D courses, a strong work ethic is the number 2 thing I can recommend, next to the will to ask for help. Don't be afraid to ask around to find someone who can help you "go up the ladder".

[decide_aposteriori]

2) Being good in math is a good indication of your ability to think creatively.

 

I would have to disagree. Why then are artists, musicians, etc not required to take loads of math? You may have intended to say that math is a good indication of thinking creatively in economics but I would still disagree. I'll quote Boettke on Amartya Sen, "[sen] (1987) has argued that our discipline has both an engineering component and a moral-philosophic component to it, and that unfortunately the past few decades have witnessed an overemphasis on the engineering side to the exclusion of the moral-philosophical."

 

Good mathematicians are creative within the abstract world of "mathematics", that doesn't necessarily translate into good economics. I think this gets at deeper epistemological questions about economics, and this isn't necessarily the place to debate those questions. Pressed though I would have to sympathize with the Austrian arguments about the foundation of economics and how much mathematics can do for economics (not what can economics do for mathematics).

 

As for the OP, my point is, math knowledge alone won't determine your ability to be a good academic economist: Original ideas will. Sometimes hard math classes take time to digest and when you come back to the material it's quite a bit easier to understand.

[asianeconomist]

I read it in TM perhaps: An Economics professor tells his students "If you follow the righteous path and live a good life then you'll be reborn as a Mathematician. But if you stray and spread evil then you'll be born as a sociologist".

 

Sorry for the Cheap Shot !

[AspiringEconomist]

This isa great quote!

[hips]

Well, I am an undergrad in Econ and I am taking a grad micro course this semester. We use MWG and covers Part II and related applications

(asymmetric info.,repeated games,etc). So far we didn't use any math beyond calculus. The most mathematical part until now is perhaps Bayesian auction but that's just calculus.(Or the existence of NE, but I think it's nothing but verifying the conditions of kakutani.)

When teaching repeated games, the professor proved a folk theorem in Fudenberg-Tirole, the one using carrot-stick strategy, but to prove it, one just check whether the constructed strategy is an SPNE. It really doesn't involve any high level math(unless you think the term "the dimension of the convex hull of..." is abstract, but it's just an expression.)

 

I think the difficulty lies not in the math but in the game theoritic thinking.

For example, to derive the the symmetric NE of Bayesian auction where each

players' valuation is uniformly distributed , say b(v_i) is the strategy (valuation-bid relationship), the solution manual of MWG solves this by saying that bidders maximize

(V_i - b(v))(v/v_lower bar) ---(1)

and diff w.r.t v, get an FOC, then put v = v_i, arguing that "it is optimal for bidders not to pretend to have a different valuation"

I think the above is very counter-intuitive, and I have never seen such operation being taken in any math courses. Later on I tried very hard to convince my self that the operation makes sense, in that b(v) is the strategy chosen, and (1) is just the expected payoff, hence by diff. w.r.t v, we get the FOC, and since we assumed b(v_i) is NE, it must satisfy the FOC. However, I still prefer to differentiate w.r.t. b, I think this makes more sense.

(this approach uses inverse function differentiation, and is adoped in Osborne's undergrad text Game Theory.)

 

Since I take the second-semester micro directly,I missed all the consumer/producer theory and GE, I can't tell whether there involves a lot of math. By the way, the professor require the students to present some papers along with the course, so far I have presented Aumann's "Agree to Disagree" and will be presenting "Learning, Mutation, and LR Equil. in Games",both papers are not very mathematical; the latter even comes from Econometrica. The math involved are just conditional probabilities, Markov matrix, taking limit, and a pretty strange but interesting z-tree argument. It is the innovative way to construct the model that sets the paper apart from others, not any fancy math.

 

BTW, I have already completed a double in Math(in 4 years:D,along with the Econ major, this is my last semester.) So maybe my "mathematical maturity" helps in an implicit way. But I am not sure;after all, there is no control group.

[mentalitysurf]

I read it in TM perhaps: An Economics professor tells his students "If you follow the righteous path and live a good life then you'll be reborn as a Mathematician. But if you stray and spread evil then you'll be born as a sociologist".

 

Sorry for the Cheap Shot !

 

Krugman mentioned this quotation in his book, peddling prosperity, but it is a bit different from TM's version. He says, "if you are a good, virtuous economist, you are reborn as a physicist, but if you are an evil, wicked economist, you are reborn as a sociologist."

[israelecon]

it seems to me that you have the problem that since you studied math before economics, you still do not have the necessary economic intuition. what you call "game theoretic" - thats just economics. the point from all this is very simple, sure you may know a lot of math, but you don't know how to use it to solve simple economic problems like the auction. the mathematics used is trivial (for a mathematician), but you have to know what math to use. the problem with mathematicians is that sometimes they let the math dictate the model instead of letting the economics dictate the model and use the math as a tool.

anyway, the point of this is clear for those of you worried about not knowing enough math. sure it nice to know math, but it is not more important than having sound economic understanding, and sometimes to much math can drown out the economics behind a result. so a mathematician may know better than everyone else how to differentiate etc., but what good is that if you don't know, or can't understand with respect to which variable to differentiate?

[Oikos-nomos]

Thanks some of you guys for your comments...and support!!:tup: