Economics in General

[whatdoido]

I don't really know anything about economics, being an undergraduate without any research exposure, so I just had a question to all those PhD students out there. At your level, does heavy mathematical rigor seem more like a hindrance that you need to work around, or a very helpful aid. My differential equations teacher said that some mathematicians believe that differential equations can model human choice perfectly, while others think that they can't at all (not sure if that's relevant). What is your take on this?

 

Edit:

To be clear, I'm absolutely for math in economics. Math is great.

Edited November 20, 2010 by whatdoido

[AREStudentHopeful]

I think math can be used to predict (to some extent...it's still a very imperfect science) aggregate human behavior fairly well, but individual human behavior is a lot trickier. There's actually an interesting article about a similar phenomenon in biology/chemistry: Brilliant 10: Christopher Love, the Cell Tracker | Popular Science . In reference to DE's, I think they may be better at predicting natural systems phenomenon than human behavioral systems (that's pure opinion though; I'm sure there's a brilliant mathematician out there who could change my mind).

[El Economo]

I've have personal problems with math before. To an extend that I seriously thought it was invading economics in an awful manner. But after some consideration I realized that they have something to do in clarification of our theories.

 

I wouldn't say that we can't live without them though. They are useful, but there was economics before we mixed math with it.

[ironman6788]

The more fundamental core of economics has become very math intensive but the work done in behavioral economics looks at people's irrationalities and how the math doesn't fit. I read a book called Nudge in an undergraduate behavioral econ class. It was a very fun/ not very technical read that showed how many peoples choices can be influenced by framing the question differently. E.g. if some retirement program an employer offers is opt-in then it will have a much lower participation rate than an opt-out program, but if people's choices are hyper-rational and mathematically based shouldn't opt-in/opt-out not matter because whether it was opt-in or opt-out couldn't factor into how beneficial or costly the program is.

[michaelmas]

“Like so many others in my cohort, I internalized its view that if I couldn’t formulate a problem in economic theory mathematically, I didn’t know what I was doing. I came to the position that mathematical analysis is not one of many ways of doing economic theory: It is the only way. Economic theory is mathematical analysis. Everything else is just pictures and talk.”

 

- Robert Lucas Jr.

[jaimelannister]

Here are are two posts with some arguments for maths:

 

Mathematics and economics - NYTimes.com

 

Dani Rodrik's weblog: Why we use math in economics

 

and two posts with arguments against maths:

 

How Mathematical Economists Overreach « ThinkMarkets

 

Mathematical Economics as an Aid to Economic Thought - Coordination Problem

 

 

Personally I fall in the for camp. I feel the main benefit of using maths is being able to make life easier. Imagine a world without calculus or vectors? Try doing physics without any of those tools. Newton tried and even he ended up inventing calculus to help :p. And this is why I think complexity in human behaviour is an argument for using maths rather than against.*

 

In any case there already exists disciplines that study human behaviour based on non-quantitative methodology e.g. history, anthropology etc. Taking the maths out of economics would just turn economics into a sub-discipline of one of those disciplines.

 

Finally, I think the progress made by economics and it's methodology is borne out in the real world by it's applications. Central bankers, policy makers/politicians, CEOs etc. aren't hired to do their job based on their knowledge of philosophy or human history** but rather being able to successfully apply 'economic principles' (I use this in a very broad sense, for example, I consider Steve Jobs an excellent practitioner of economics even though he might not ever have had formal training in the field) in the real world. I just don't see the impact the non-quantitative based disciplines have on the practical level that I do with economics (and I think this is largely due to the methodology used).

 

Would economics be as influential in today's world if it didn't go down the mathematics path? Personally I don't think so.

 

On the question whether arguments using maths are better than ones without, I think that is clearly independent of the medium and depends on the merits of each argument. At the end of the day it's about the cogency of the argument being made irrespective of it being presented in mathematical form, words, or pictures (or combinations of).

 

 

*Arguably human phenomena are more difficult to explain than physical phenomena. The natural world has four fundamental forces (as far as we know) which determine physical interaction. From these forces physicists have been hugely successful in drawing theorems and relationship that can precisely describe natural phenomena. Unfortunately, as far as we know there is no such equivalent forces governing human interaction. Hence the impossibility of providing precise relationships of human interaction.

 

**I'm not saying philosophy or history isn't useful but being able to apply economic principals is a lot more important in those jobs. I remember reading about a blog debate flowing from the GFC between Steven Levitt (or was it Tim Harford?) and some well known historian who claimed that it would be better that there were less economists in important jobs (or an argument along those lines) and I remember thinking at the time if historians were better equipped (or had something more useful to contribute) to say financial crises or managing the economy/firm better than we would see more historians in those jobs.

[michaelmas]

Krugman sums it up neately as usual: "So by all means let’s have math in economics — but as our servant, not our master."

[whatdoido]

I like the Krugman quote, a similar sentiment was also presented in the "Coordination Problem" article in one of the posts above.

[zurich_econ]

The more fundamental core of economics has become very math intensive but the work done in behavioral economics looks at people's irrationalities and how the math doesn't fit.

 

This is a blatantly wrong assertion. True, "Nudge" doesn't contain any formulae, but try selling an economics book with formula to a general audience. If you have a look at the actual research papers the book is based upon, you'll realize that they rely very heavily on mathematical models. If you have a look at what the big researchers in behavioral economics are doing (e.g. Matthew Rabin but there are many more), you'll see that their research is very heavily mathematical. They don't try to find "where the maths doesn't fit", they try to find where the economic assumptions do not fit and make refined mathematical models with refined economic assumptions.

 

Also whoever says that the mathematical method makes more assumptions than the verbal method because it sometimes assumes differentiability and so on probably has not had a good course in microeconomic theory. At no point is it necessary to assume differentiability of the functions of interest. Sometimes, differentiability arises endogenously (e.g. the profit function is differentiable at a point if and only if the solution to the firm's profit maximization problem at this point is unique), but it doesn't need to be assumed for almost all the results in micro theory. On a related note, the axiomatic approach allows, or even require you, to be very explicit about what you are assuming. If you make an assertion about some alleged implications of a set of verbal assumptions and are not able to formulate these assumptions mathematically (note that you do not require functions or even numbers to do so) and to derive your alleged implications from these mathematical assumptions, then your alleged implication is most likely not really implication of your assumptions.

[dreck]

I agree with Zurich_econ. Math is perhaps most powerful when applied to decision theory, where you can make minimal assumptions and generate a powerful theory.

 

The only thing that I would add is that math makes macro very, very difficult. You need a ton of assumptions, and which ones to pick is a nightmare. As a result, certain conventions have taken root. These conventions are definitely not the only way to mathematically model the macroeconomy, but each new theory takes much longer to build and is uber-complex, so there's little incentive for a paradigm shift. That's what PK means, I think, when he compares math as a servant or a master.

 

Another point, which you may not realize until you get to grad school: Math is nothing more or less than the language of pure logic. In order to model behavior with mathematics, we need to be able to think about human behavior logically. We do NOT need the people themselves to think or act logically. We just need their craziness to have patterns.

[whatdoido]

I agree with Zurich_econ. Math is perhaps most powerful when applied to decision theory, where you can make minimal assumptions and generate a powerful theory.

 

The only thing that I would add is that math makes macro very, very difficult. You need a ton of assumptions, and which ones to pick is a nightmare. As a result, certain conventions have taken root. These conventions are definitely not the only way to mathematically model the macroeconomy, but each new theory takes much longer to build and is uber-complex, so there's little incentive for a paradigm shift. That's what PK means, I think, when he compares math as a servant or a master.

 

Another point, which you may not realize until you get to grad school: Math is nothing more or less than the language of pure logic. In order to model behavior with mathematics, we need to be able to think about human behavior logically. We do NOT need the people themselves to think or act logically. We just need their craziness to have patterns.

 

So I actually have another, somewhat unrelated, question. Is the math that you get to do in graduate school exciting, given that you were kind of excited and actually liked the math you were doing in undergrad.?

[Norsker]

So I actually have another, somewhat unrelated, question. Is the math that you get to do in graduate school exciting, given that you were kind of excited and actually liked the math you were doing in undergrad.?

 

Not usually.

[dreck]

So I actually have another, somewhat unrelated, question. Is the math that you get to do in graduate school exciting, given that you were kind of excited and actually liked the math you were doing in undergrad.?

 

This is my opinion: in Micro, yes (at least the first micro quarter); in macro, no way; in metrics, it depends on whether you like that flavor of math, and how the course is taught.

[ironman6788]

Only grad class I've taken was a master's micro course. I enjoyed how much more mathematical the class was (using multivariable calculus) compared to undergraduate intermediate micro. In undergrad micro when you are looking at the substitution effect of the price change on a consumption bundle the prof says "now draw a line that has the same slope as the new budget constraint but tangent to the old utility curve" and the class says "lol, what?". Then in the grad class you learn how to find the expenditure function then use Shepard's lemma so you get compensated demand, it made more sense to me. It's like trying to derive switching from xy to polar coordinate integration through graphical representations and then learning the Jacobian later, ya it's the way its done but when you learn the Jacobian it becomes much clearer in my opinion.

[whatdoido]

This is my opinion: in Micro, yes (at least the first micro quarter); in macro, no way; in metrics, it depends on whether you like that flavor of math, and how the course is taught.

 

Cool, thanks.

[michaelmas]

To much math makes economics much more difficult, but also much more helpful if one knows how to appreciate it.

 

To little math, however, is downright boring and completely unhelpful - I believe - if one want/needs to explore economics at a deeper level than the supply-and-demand diagram.

 

This is from an interview with Thomas Sargent last summer:

 

Sargent: I know that I’m the one who is supposed to be answering questions, but perhaps you can tell me what popular criticisms of modern macro you have in mind.

 

Rolnick: OK, here goes. Examples of such criticisms are that modern macroeconomics makes too much use of sophisticated mathematics to model people and markets; that it incorrectly relies on the assumption that asset markets are efficient in the sense that asset prices aggregate information of all individuals; that the faith in good outcomes always emerging from competitive markets is misplaced; that the assumption of “rational expectations” is wrongheaded because it attributes too much knowledge and forecasting ability to people; that the modern macro mainstay “real business cycle model” is deficient because it ignores so many frictions and imperfections and is useless as a guide to policy for dealing with financial crises; that modern macroeconomics has either assumed away or shortchanged the analysis of unemployment; that the recent financial crisis took modern macro by surprise; and that macroeconomics should be based less on formal decision theory and more on the findings of “behavioral economics.” Shouldn’t these be taken seriously?

 

Sargent: Sorry, Art, but aside from the foolish and intellectually lazy remark about mathematics, all of the criticisms that you have listed reflect either woeful ignorance or intentional disregard for what much of modern macroeconomics is about and what it has accomplished. That said, it is true that modern macroeconomics uses mathematics and statistics to understand behavior in situations where there is uncertainty about how the future will unfold from the past. But a rule of thumb is that the more dynamic, uncertain and ambiguous is the economic environment that you seek to model, the more you are going to have to roll up your sleeves, and learn and use some math. That’s life.

[michaelmas]

I'm not trying to paint a picture of myself as a math wizard who has taken all PhD math coursework from the 1st and 2nd year at MIT (in fact, I haven't even taken Real Analysis, and I'm taking an Economics Masters at a European school far away from top 50) but there is a certain quote from John von Neumann that completely revolutionized my view on math:

In mathematics, we don't understand things, we just get use to them.

[anarchist]

I don't really know anything about economics, being an undergraduate without any research exposure, so I just had a question to all those PhD students out there. At your level, does heavy mathematical rigor seem more like a hindrance that you need to work around, or a very helpful aid. My differential equations teacher said that some mathematicians believe that differential equations can model human choice perfectly, while others think that they can't at all (not sure if that's relevant). What is your take on this?

 

Edit:

To be clear, I'm absolutely for math in economics. Math is great.

 

You might find this article quite interesting :-)

 

http://www.ederman.com/new/docs/beware.hbr.pdf

 

It was written by Emanuel Derman, Emanuel Derman - Writings on Quantitative Finance

[santacanyon]

Only grad class I've taken was a master's micro course. I enjoyed how much more mathematical the class was (using multivariable calculus) compared to undergraduate intermediate micro. In undergrad micro when you are looking at the substitution effect of the price change on a consumption bundle the prof says "now draw a line that has the same slope as the new budget constraint but tangent to the old utility curve" and the class says "lol, what?". Then in the grad class you learn how to find the expenditure function then use Shepard's lemma so you get compensated demand, it made more sense to me. It's like trying to derive switching from xy to polar coordinate integration through graphical representations and then learning the Jacobian later, ya it's the way its done but when you learn the Jacobian it becomes much clearer in my opinion.

 

we do that in undergrad intermediate...

[ironman6788]

ya i don't see any reason why my undergrad intermediate course didn't cover it. It's not difficult to do mathematically.

[dreck]

There's obviously a lot of variance. On the other hand, you might think you've seen something in undergrad intermediate only to see it's full blown form in your first year, and realize how little you actually saw before :)