Here are some important statements that come up in economics:
"Nice estimators are consistent even in complicated models."
"Nice financial markets are informationally efficient."
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"Nice markets have price equilibria."
"Nice games have Nash equilibria."
The way these ideas are taught to Ph.D. economists in any field, even in core courses, involve very explicitly and extensively ideas extending ones in basic analysis.
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In particular, those ideas are: convergence (in fairly big spaces), integration and probability/martingales, continuity and fixed points.
Though you could get across aspects of these ideas at a high school level, econ grad school doesn't do them that way.
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Relatedly, an interesting feature of academic econ is that it seems much more interested in mathematical rigor than, say, physics. So most working economists need not only to understand these ideas but to work, at least a little, with proofs.
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While there's no standard math course that perfect practice for the econ kinds of proofs, the one that's the closest is probably basic real analysis, so think of this as the closest-to-relevant training in "proof weight lifting" for what you'll do.
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Much more down-to-earth: people interested in social science, finance, etc. who want something to "read along with" a real analysis course might enjoy Efe Ok's book. It develops economic applications right alongside the math.
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Despite the fact that basic real analysis can seem a little abstract, the applications in the above screenshot (along with game theory and basic finance theory) might be some of the most direct "practical applications" of real analysis in any field.
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One amusing feature of math classes at the master's level or above is that they almost take pride in not motivating the subject in external terms. For example, here's a page from a canonical textbook in algebraic geometry.
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This does a good job of reminding me of how Lecture 1 in such classes often felt, which is roughly, "The motivation for this class is fuck you. Let k be an arbitrary algebraically closed field. Now..."
Which was not a problem when I had my own motivations!
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At some point it stopped being enough. Incidentally, I don't think my economics courses were much better in the way of giving some great external motivation: I just found a cycle of self-reinforcing curiosity that kept me happily studying that subject.
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Was grateful to share at an #ASSA2021 session today a bit on what I've learned in teaching an undergraduate course on the Economics of Networks.
A short thread to serve as a focal point for any follow-up conversation.
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What networks is about (very rough and probably somewhat idiosyncratic description)
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I taught several variants of an undergraduate elective on this exciting and growing area. It was at the applied math/econ/CS intersection -- sometimes cross-listed, sometimes just economics but open to (and taken by) applied math, CS, other students.
This thread gives my own gloss and expansion of some points Doctor et al. raise.
Peters and co think there is a hidden assumption of economic theory: specifically, they think expected utility theory secretly assumes a mathematical property called ergodicity.
This is false.
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Expected utility theory makes 4 assumptions, which are stated precisely and concisely in every graduate textbook. Ergodicity is not among them.
EU is not the kind of theory that can hide assumptions: it is like Newtonian mechanics, not like Freudian analysis.
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Let me very briefly jot down some notes as I read...
Take a basic static input/output model, and suppose we don't worry about nonlinearities in static equilibrium (as Baqaee and Farhi very productively have done).
Then it's easy to know which shocks matter for welfare...