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Since I know a couple of mathematicians (and like to pretend I understand what they work on) I am always a little skeptical of economists' claims to be mathlord

by slurry 13y ago

Since I know a couple of mathematicians (and like to pretend I understand what they work on) I am always a little skeptical of economists' claims to be mathlords. But perhaps my skepticism is misplaced? How rigorous/sophisticated is the math in research-level econ, really? The econ undergrads I knew went up to basic engineering math (calc 3, linear algebra, diff eq's) at most, and those who did were considered to be really hardcore. Do research economists use higher-level math than that?

rvn1045 13y ago
A lot of economists who have a phd in in economics, were Engineering, Math and Physics majors as undergrads. To get into a good phd program in Econ, you have to have taken and aced a lot of math classes such as Real Analysis and some very advanced Probability courses. Taking some grad level math classes would probably increase an applicants chance. So yes a lot of economists are really really good at math. And yes a lot of it is used in research.
- slurry 13y ago
  I know economists are good at math, I'm more curious what kinds of math they tend to use.
  - tedsanders 13y ago
    It very much depends on the application. Econometrics uses lots of statistics. Finance uses stochastic calculus. Microeconomics uses linear algebra and calculus. To see how incomprehensible things can get, here's a paper by one of my old econometrics professors: http://econweb.ucsd.edu/~bbeare/pdfs/vinecopula.pdf http://econweb.ucsd.edu/~bbeare/pdfs/vinecopula.pdf
  - mathrat 13y ago
    Financial economics literature is quite heavy on stochastic processes. This requires a sophisticated treatment of probability, which in turn necessitates familiarity with measure theory. Throw some stochastic differential equations into the mix and you're probably also going to need some background in functional analysis. Not so familiar with the rest of the econ literature, but even basic econometrics requires familiarity with point set topology.
  - aet 13y ago
    Game theory
tristanz 13y ago
It's not necessarily about pushing the boundaries of math. The simpler you can make the math the better for a given level of insight. But I don't think it's "easy" to derive clean mathematical results for many economic models. It's a combination of math, insight, and style. Imagine this: prove to me some conditions under which equilibrium exist for prices in a market of consumers and producers with heterogenous preferences and skills, that can only communicate on a network with a cost per interaction. Now introduce time and savings and prove the equilibrium interest rate over time. Now prove the optimal tax rate on capital and labor over the agents lifecycle. Now prove that when skill and preferences are not observable to the government. Now introduce default and unobservable savings. Are there conditions under which the markets unravel when faced with exogenous shocks to productivity or beliefs. What is the optimal interest rate policy? These are classic questions in economics in a more realistic market that captures heterogeneity, limited information, and locality or search costs.

by slurry 13y ago

rvn1045 13y ago

A lot of economists who have a phd in in economics, were Engineering, Math and Physics majors as undergrads. To get into a good phd program in Econ, you have to have taken and aced a lot of math classes such as Real Analysis and some very advanced Probability courses. Taking some grad level math classes would probably increase an applicants chance. So yes a lot of economists are really really good at math. And yes a lot of it is used in research.

slurry 13y ago
I know economists are good at math, I'm more curious what kinds of math they tend to use.
- tedsanders 13y ago
  It very much depends on the application. Econometrics uses lots of statistics. Finance uses stochastic calculus. Microeconomics uses linear algebra and calculus. To see how incomprehensible things can get, here's a paper by one of my old econometrics professors: http://econweb.ucsd.edu/~bbeare/pdfs/vinecopula.pdf http://econweb.ucsd.edu/~bbeare/pdfs/vinecopula.pdf
- mathrat 13y ago
  Financial economics literature is quite heavy on stochastic processes. This requires a sophisticated treatment of probability, which in turn necessitates familiarity with measure theory. Throw some stochastic differential equations into the mix and you're probably also going to need some background in functional analysis. Not so familiar with the rest of the econ literature, but even basic econometrics requires familiarity with point set topology.
- aet 13y ago
  Game theory

tristanz 13y ago

It's not necessarily about pushing the boundaries of math. The simpler you can make the math the better for a given level of insight. But I don't think it's "easy" to derive clean mathematical results for many economic models. It's a combination of math, insight, and style. Imagine this: prove to me some conditions under which equilibrium exist for prices in a market of consumers and producers with heterogenous preferences and skills, that can only communicate on a network with a cost per interaction. Now introduce time and savings and prove the equilibrium interest rate over time. Now prove the optimal tax rate on capital and labor over the agents lifecycle. Now prove that when skill and preferences are not observable to the government. Now introduce default and unobservable savings. Are there conditions under which the markets unravel when faced with exogenous shocks to productivity or beliefs. What is the optimal interest rate policy? These are classic questions in economics in a more realistic market that captures heterogeneity, limited information, and locality or search costs.