Economics for Mathematicians

November 16, 2012 2:25 AM

Economics Mathematics: I have a Maths degree but lately I've become interested in Economics (Microeconomics and Macroeconomics) and have been reading some textbooks and classic texts and doing some online lecture courses on Economics. But find many of that the "handwaving" graphical "proofs" of economic theories lack a sense of mathematical robustness. Do more thorough mathematics for these ideas exist? Where can I find them?

Secondly, what mathematical theory would be most useful in Economics? Statistics seems the obvious thing ( Statistical Methods / Regression Analysis etc..) - unfortunately that was never my favourite subject at Uni.

(I was more of an Algebras, Group theory, Combinatorics type.)

posted by mary8nne to education (9 answers total)

Any graduate level micro book will feature a lot of stuff that looks like modern analysis in equilibrium proofs. Not sure about the macro side; I believe they will look more hand-wavey than the micro side. I don't know think you'll see much that looks like algebra, though.

Coincidentally, the most recent Nobel Prize winners have a paper where there is a meditation on mathematical argument at the end.

Shapley deferred choice algorithm
posted by chengjih at 2:57 AM on November 16, 2012 [1 favorite]

Introductory Economics is, as you say, rather hand-wavy. It does get more mathematically robust. Some of the major areas:

- Statistics is the main tool in Econometrics (analysis of data sets, particularly regressions)
- Micro uses equilibrium analysis, and also game theory
- Macro also involves a great deal of equilibrium analysis

A caveat: IMO, orthodox classical economics has a tendency to glorify the elegant mathematical model over the frequently rather murkier empirical data.

For reference, Mathematics for Economics was the core maths text for the masters course I attended.
posted by Bodd at 3:14 AM on November 16, 2012 [1 favorite]

My sense is that models in Macro are more for building intuition. If you want to get a handle on the math-y parts of macro you could look for stuff that covers Dynamic Stochastic General Equilibrium models as that seems to be the most sophisticated model in common use. You are right that a lot of the math that economists worry about is covered under time series regression, ie econometrics. If its the math you like, you might also be interested in the economics of finance.

If you want to rank economics subjects by math content I think it would go something like: econometrics > finance > micro > macro.

There is a really interesting high level discussion of the mathification of economics in the first chapter of Paul Krugman's 1995 Book The Rise and Fall of Developmental Economics, if you have access to a good library.
posted by shothotbot at 5:54 AM on November 16, 2012

Have you looked into game theory? AT UCLA, for example, there is a game theory course taught by the math department. Game theory has plenty of proofs, and often uses combinatorics and graph theory.

Students who are getting their masters/ phd in economics go to math camp. (If you google you can find some syllabi for such "camps.")
posted by oceano at 6:34 AM on November 16, 2012

I guess I'm looking for more of a Economics for Mathematicians rather than "Mathematics for Economists".

One of the problems is that I am more interested in the Macroeconomics / Foreign Trade / Whole industry side - which seems to be the least mathematically robust. Trying to read Keynes General Theory at the moment and its well - rather difficult.

Oh and I"m not expecting it to look like Algebra. I just meant that I haven't done a lot of Statistics. (I have done some years ago though and of course loads of Calculus.)
posted by mary8nne at 7:20 AM on November 16, 2012

One thing mathematics genius Husbunny did was check out Actuarial Sceince. Mathematicly robust, oh my yes.

It ties into Economics, and a bunch of other stuff.

Look at that and see if Actuarial Science is something you want to try. Husbunny has been an actuary for 6 years now and he LURVES it!
posted by Ruthless Bunny at 7:47 AM on November 16, 2012

One comment I'll add, as a mathematician who did some work in econometrics a while back: I found, while reading papers, that a lot of the rigorous mathy stuff depended on super strong assumptions about people/preferences/states of the world. And not in a, "this makes the arithmetic easier without changing the qualitative result" way, in a "if this is deviated from at all the whole result falls apart" way. Sorry, don't have anything to point to, this was 6 years back or so. It's possible this is less true now.

Other thing I tended to notice is the flip side of equilibrium analysis: There was a real lack of investigation into dynamics on the way to equilibrium. (Presumably this is because dynamics is generically HARD, but to paraphrase Keynes, in the equilibrium state we're all dead.)
posted by PMdixon at 8:31 AM on November 16, 2012

The standard textbook for consumer and producer theory is Mas-Colell, Whinston and Green. They prove all the basic results using (vector) calculus. If you're looking for something mathematically "elegant", then Debreu's "Theory of Value" is supposed to be good (but hard!). The textbook by Jehle and Reny is sort of nice and might be more accessible.  For game theory, Osborne & Rubinstein have made their graduate text available for free online.

The reason most macro trade stuff is not mathematically rigorous is because it's *extremely* hard. Most rigorous macro models (DSGE) are quite abstract and very complex (must always be solved numerically). Expanding these models to incorporate multiple countries is a huge effort with highly doubtful returns. On the micro side of trade, Helpman and Krugman's "Market Structure and Foreign Trade" is a modern classic. One of the most influential papers in recent years is that of Melitz (Econometrica, 2003).

For macro, the standard graduate text is by Stokey, Lucas and Prescott, but it's verrry dry. The book by Sargent & Ljungkvist might be a much more pleasant read.
posted by yonglin at 9:20 AM on November 16, 2012

A lot of the more mathematical side of game theory and risk is under "Decision theory" in textbooks.
posted by Ashlyth at 5:22 PM on November 16, 2012