<p>I posted a question on the College Search and Selection board and someone advised me to come over here and ask you, saying you were knowledgable on the subject. My question was, how math-intensive is economics, namely in undergraduate, but also overall as a subject. How much of it is calculus based? I do not particulary enjoy math, although I am pretty good at it. Not liking math, would economics be a bad choice as a major?</p>
<p>Not liking math, Caltech might be a bad choice as a school :)</p>
<p>Ben's downstairs eating his dinner so I'll give it a shot answering this question. (I'm a junior econ major)</p>
<p>Yes, economics here is much more math-intensive than at other places. You'll run into proofs every so often and a lot of what you do looks like math: you're introduced to formal definitions of terms and are expected to be able to prove statements in a formal manner. Calculus plays a very important role in microeconomic theory, so you'd be expected to have a firm understanding of basic calculus.</p>
<p>I'd agree with halfthelaw's statement though, if you don't like math, Caltech might be a bad choice as a school. Pretty much everything we do here is math. The only difference is how theoretical the math is and what sort of math it is.</p>
<p>I think joexc07 was asking about economics in general.</p>
<p>Answer: to be an undergraduate econ major at a good university (here I'm thinking anything comparable to any of Caltech, MIT, Harvard, Berkeley, NYU, WashU, UMich, just to take some examples) you will need to work with a lot of mathematics. The least you can get away with is multivariable calculus and linear algebra, (including optimization, Lagrange multipliers, convexity, solving general linear systems, determinants, eigenvalues, differential equations etc.). Even for intermediate macroeconomics you need to be able to do a lot of mathematical manipulation quickly and easily. Everything is calculus based unless you take very weak courses, and then it's not worth doing in the first place.</p>
<p>If you want to consider getting something like a doctorate in economics at a decent place, you need to know mathematics at almost the level of a professional mathematician (not quite, but close). Real analysis is a must, some topology helps, advanced linear algebra, etc. Modern economics is becoming more and more mathematical by the day. Math is become the coin of the realm in almost every subdiscipline. There are exceptions, but overall the trend is unmistakable. That's not universally believed to be a good thing, but normative judgments aside, it's true.</p>
<p>The most common complaint I hear from people who came to college to study economics is that they end up doing a lot of seemingly abstruse manipulations that don't seem very relevant to actual economic questions. If you start out explicitly not liking math, then I would think that this goblin will bother you also. </p>
<p>If you want to think about economics-like things without quite as much analytical machinery, consider things closer to business or management (but NOT finance!) or political science. There's more talking and fewer equations in those fields, in general.</p>
<p>I hope that helps a little, and feel free to ask if you have more questions.</p>
<p>As I was describing this question to someone, I thought of a good way to outline the difference of opinions on the value of math in economics. </p>
<p>Mathematical economists (whose viewpoint is coming to dominate the field) say that mathematical modeling allows us to make rigorous conclusions and test our insights just as it does in any other science. Mathematics disciplines our hypotheses and gives us a language much more precise than English to state them in. Many of them think that "talking economics" is fluffy and lacks substance.</p>
<p>"Talking economists" (in the tradition of Galbraith, for example) and also some political scientists, say that the mathematical approach uselessly replaces genuine insight about social phenomena with pointless abstractions, and that our understanding of the underlying processes isn't yet strong enough to allow such an axiomatic approach. "Stop trying to be physicists" is basically the short version. They think that doing "economics in English" is perfectly reasonable and allows us to get pretty far without getting mired in technical details.</p>
<p>Now that you know what the sides (or caricatures of the sides) say about each other, you can make your own judgments.</p>
<p>Let me add a slightly different perspective.</p>
<p>Most undergrads doing econ will not go on to grad school, nor need much of the technical material in grad school. So just majoring in econ for purposes of getting a job, going to law school, or getting an MBA will usually not require much math beyond calculus. Some upper class courses will be fairly technical, but at most departments, there are ways to structure four years so you can avoid heavy math. Indeed, at some schools, the undergrad econ major is just business lite plus a dose of liberal arts. For the average undergrad, this is not entirely a bad thing.</p>
<p>Learning the economic way of thinking, learning some basic analytic skills and testing them out on various real-world problems is a huge gain for most people.</p>
<p>However, getting a degree for advanced work is a different game entirely. This is why the quality of the grad program is almost irrelevant for most econ undergrads. What the PhD students are doing has minimal overlap with what the typical econ major is doing. For -- let us say -- the typical undergrad econ major who ends up working in sales before going on to an MBA, having a top notch econometrics genius on the faculty will be of zero relevance, and might even be a negative if his classes are too abstruse.</p>
<p>For those going on to grad school, a math major combined with an econ minor or major is arguably more valuable than a pure econ degree from any top school. I recently spoke to a bright European MA student at a good development program who was shocked that she was underprepared for applying to US PhD programs because she had had no math since high school calculus.</p>
<p>As to Ben's second point, I also have a slightly different view. Econ is becoming mroe mathematical but for both good and ill. On the one hand, more rigor is useful in many circumstances. On the other a lot of rigor is borrowed from the math not physics departments. That is, there is a subset of economists for whom formalism or formal elegance is valuable in and of itself. This point of view is quite different from that of the theoretical physicists I knew at Caltech for whom math was important for operationalizing ideas not for elegance. [Compare how physicists used the Dirac delta function before the mathematics of it had been fully worked out. In econ, the temptation would have been to formalize first, then use it later.]</p>
<p>As I've grown older I've become a lot less mathematical, not because I dislike math but because I dislike the way many economists use math. Some professors I know almost don't seem to care whether a theory is true or not. I know many -- I won't name names -- who prefer an interesting though inaccurate model to a simple, parsimonious, but technically unimpressive explanation.</p>
<p>I went into econ planning to do formal theory but rapidly shifted to more applied work. Moreover today, there is a big diffference between those who use clever econometrics and math to get solutions empirically to those who build models just because a technical puzzle needs to be solved. As Ben noted, this is a caricature and there are many great minds who straddle both. But it is not entirely inaccurate.</p>
<p>I remember Vernon Smith telling me that some of his earlier experimental findings were dismissed by many theorists because "They contradicted what trivial math models told us couldn't happen." This attitude has changed quite a bit in recent years but it is still a tension in most econ departments. This however, is probably too much information, and too much "insider baseball" for a forum like this.</p>
<p>On NQO's #6 -- I agree that many econ departments offer an 'econ-lite' which can be quite entertaining and not too mathematical. At a minimum, I'd recommend talking to a professor to see if an econ degree will require anything like (a real course in), for example, intermediate microeconomics. If they do, then that's probably too much math for someone who doesn't like math. But if they have a track which is more business and applications focused, then you'll be happy with that. Just be aware that if you blindly go for the "economics major" at a good school you may wind up with preparation in a mathematical discipline that doesn't interest you. Make sure to ask what you are buying. </p>
<p>On #7 -- from my naive and green perspective, I actually don't think the formalist tendency which we see is such a great thing. I wanted to keep my own views out of it, but I may have inadvertently suggested that I think it's great. On the one hand, it's good for me -- more math, more proofs, fun. But as far as understanding economic activity, I think often the answer is less flashy and more data-oriented and common-sense, as you say. </p>
<p>But hopefully the OP was able to gain some insight about what things are like and what questions to ask if he ends up considering econ programs.</p>
<p>I am all for using math in economics (and elsewhere, e.g. in biology) but I think Ben and NQO may have somewhat overstated the amount of math needed at top econ grad schools. Students who don't plan to be theorists don't need abstract topology, and they don't need to have taken a semester of Rudin-like analysis; all that's really needed is metric-space defintions of open and closed sets, continuous functions, and compactness. Linear algebra and some elementary probability are a must for the required econometrics classes. Students who want to be theorists (or theoretical econometricians) would indeed do well to know some topology, as well as probability theory, and a little about dynamical systems and stochastic processes, but even that is well short of what a typical student would know entering math grad school.</p>
<p>My experience has almost universally been that people (even people who are not naive) are surprised by the amount and level of serious math required at top econ grad programs, so I think it's hard to overstate the point. Sure, people get into top programs knowing a very modest amount of math, and even do quite well, but I think that's closer to the exception than the rule.</p>
<p>I do see your larger point -- only theorists would routinely use topology or big analysis theorems in their day to day work. On the other hand, everybody is made to take courses in things that were not so long ago considered pretty sophisticated theory: e.g. general equilibrium or game theory. Sure, it's possible to stay afloat in these courses taking many of the mathematical results for granted, but that isn't fun at all. To really "get" all the fixed point theorems other subtle arguments, one needs to have a fair amount of mathematical sophistication about analysis and topology. (Just imagine reading something like Fudenberg and Tirole without having ever seen all the standard correspondence machinery.)</p>
<p>Anyway, I agree that one doesn't absolutely need a lot of hardcore mathematics to be an economist, but someone who doesn't (I think) would be pretty out of breath most of the first year of grad school. If I were giving advice to a friend, I'd say that it's very hard to have too much math. But you probably know more about this than I do, so correct me if I remain wrong.</p>
<p>I agree that the extra math is not "needed" and is often genuinely superfluous. But Aedar doesn't note that excess math is often used as a signal by departments in selecting students for the top programs. Moreover, having entered a top program, a student with a lot of math is likely to do better in the first year core and hence, more likely to attract the attention of a good adviser even if he or she uses nothing more sophisticated than basic game theory or instrumental variables econometrics.</p>
<p>Of course, as a recent survey by Athey, et al. showed, performance in the first year is only weakly tied to job market performance. Doing well in class (conditional on finishing) doesn't guarantee the ability to come up with a creative research project. Indeed, the stats seemed to suggest that graduating from an elite undergrad school (US News top 15) was more important for eventual job success than doing well in the first year of a top 5 PhD program.</p>
<p>But as I noted in a different post, this signalling game means that even top notch undergrads with econ degrees can get dinged by grad schools for not having enough math. [The most recent example being the Harvard honors grad that Mankiw mentioned on his blog who was rejected by every single top PhD program to which he applied.]</p>
<p>I think it is indeed a good thing for would-be econ PhD students to learn some analysis; I was only trying to say that somone who didn't want to do that could still be admitted and do good work, and to indicate what I thought a reasonable minimal preparation would be. I definitely agree that it is more fun (for the mathematically inclined, e.g, you and me) to have some understanding of fixed point theorems, but I don't think that understanding is needed in most programs. As to the "too much math," I agree that it's hard to know what that would be, except in the sense of opportunity cost and too little knowledge of economics- a student who had taken lots of math but only intro econ would have quite a struggle. More conretely, it might be better for most students to take an advanced economics class in a field of interest instead of e.g. topology or graduate real analysis (and those are two of the more useful post-analysis math classes, it would definitely be better to take econ as opposed to abstract algebra, complex analysis, or differential geometry.) </p>
<p>NQO, that Athey et al article is very interesting, thank you for linking it. But their abstract seems to spin the findings a bit differently than you do: they abstract says that performance on first-year micro and macro is a statistically significant predictor of job placement, and the paper says that "an increase in both of these core grades by 20 percentile ranks is predicted to increase a student's chance of being placed in the top 20 by a sizable 10 percentage points." They then conclude by saying that (a) the reason for this effect isn't clear and that (b) their model only explains a small part of placement (R^2=.12).Too bad they don't have data on which students took analysis, and an instrument to control for the fact that students self-select into classes- otherwise we'd know how much it does help to take analysis. :) I wonder if the students from those top-15 undergrad schools have had more math than the average?</p>
<p>Just a minor point, the claim I made was based on the following line from page 11: "Some background characteristics, such as attendance at a top undergraduate institution, do a better job of predicting job placement than grades." And as they note, this is already conditional on being accepted into the program and doing well the first year, so in theory, the explanatory variance of undergrad degrees should have been "used up."</p>
<p>But they also note that these models are generally weak predictors and there are serious errors in the measurements of success and productivity.</p>
<p>As for real analysis, the real issue isn't whether analysis helps you do well, it's whether analysis helps you get IN. [Although the former might be true as well.]</p>
<p>One other point, I sincerely doubt that any Caltech undergrad has ever been rejected by an econ program because he didn't have enough math. Low grades, yes. Math, no.</p>
<p>The issue isn't which math classes per se, it's having the right ones to signal you know that PhD econ is a different world than undergrad econ.</p>
<p>
[quote]
More conretely, it might be better for most students to take an advanced economics class in a field of interest instead of e.g. topology or graduate real analysis (and those are two of the more useful post-analysis math classes, it would definitely be better to take econ as opposed to abstract algebra, complex analysis, or differential geometry.)
[/quote]
</p>
<p>It's funny -- when I was facing pretty much this exact choice, my economics professors were very certain about saying "Take more math now -- you can pick up the rest of the econ in grad school." I will tell you how it goes next year (if anyone takes me).</p>
<p>No worries, Ben; my advice was for "most students" and not for those at Caltech, who tend to have both more interest in and facility with math than most other undergrads thinking about econ grad school :)</p>
<p>If no one minds, I think I'll pop in here and ask a somewhat related question, one that I've been wondering ever since I got interested in econ (I'm a HS senior):</p>
<p>Why is graduate economics so vastly different from undergraduate economics? Why is the former so incredibly saturated with mathematics, while the latter is much more verbal and topical? I'm really asking a few different questions here (some of which have already been discussed a little):</p>
<ol>
<li> Why are PhD-level economists so obsessed with math?
--1a. Does the math actually bring economists closer to truth than verbal analysis (a la Adam Smith) can?
--1b. If the math doesn't do so, then why are the economists unwilling to admit this and give up the whole charade?<br>
--1c. If the math doesn't do so, why haven't other fields been infected with such mathematician-wannabes? I'm sure that if political scientists, for example, were desperate to prove they could do math, they could find some sophisticated-but-dubious mathematical connections with their field---but they don't bother (for the most part, anyway).<br></li>
<li> Why hasn't this obsession with math trickled down into undergrad econ training?</li>
</ol>
<p>Some may think the answer to #2 is obvious: "Not every econ major wants to be an economist." Yes, just like not every physics major wants to be a physicist. But if you major in physics you will still be required to learn ACTUAL physics (and math), in such a way that you'll be on track for grad-level physics, if you so choose. Same thing with history, English, chemistry, and every other field out there. Why is econ the exception? Is it simply because the answer to question 1a is "Hell no," and undergrad instructors are the only ones who know that?</p>
<p>This is all just a guess, I'm not really familiar, so I shouldn't even be commenting.. But perhaps it is because the undergraduate topics are simple enough to describe verbally. Once the concepts get too complex to make much sense verbally, one has to fall back on math to describe them.</p>
<p>Just a guess, though.</p>
<p>A'ight -- thanks for a very thoughtful post.</p>
<p>
[quote]
1. Why are PhD-level economists so obsessed with math?
--1a. Does the math actually bring economists closer to truth than verbal analysis (a la Adam Smith) can?
[/quote]
</p>
<p>Yes, sometimes. Some questions are just impossible to analyze informally, but have extremely beautiful and important solutions that we can find through formal analysis. The best example I have offhand is Arrow's</a> impossibility theorem, even though the Wiki exposition is a little clunky. The revenue equivalence theorem, which says that any auction format will yield the same revenue to the auctioneer (assuming bidders are rational) is another example.</p>
<p>Math in social science, at its best, is definitely not obscurantist in intent or in practice. Some systems, like the economy, are just incredibly complex; if we really want to think seriously about them, we need a framework robust enough to contain all that complexity -- and English is unfortunately insufficient. (The proof of Arrow's theorem is fairly simple mathematically, but just try to explain it "without math".)</p>
<p>
[quote]
2. Why hasn't this obsession with math trickled down into undergrad econ training?
[/quote]
</p>
<p>I think part of this may just be an idiosyncrasy, but there's also probably a systematic component to the explanation. Physics, chemistry, etc., are very mature sciences. The level of sophistication in the applications is very close to the level of sophistication in the research universities. Economics is still very young, and many of the academic insights are not yet ready for everyday use -- they need to be refined more. Teaching undergrads (in most places) the commonsense basics is economists' way of admitting that they're not yet so confident about the hardcore mathematical theories, but they're pretty sure about these few commonsense consequences of those theories, so let's talk about those. As economics ages and becomes more established, the applications will increasingly come to resemble the most refined theory.</p>
<p>Just my two cents -- I'd be curious to hear what you think of these answers, and obviously my economic elders should chime in too.</p>
<p>Too difficult a set of questions for these posts but let me see if I can hit the high points:</p>
<p>Economics is really trying to be many different things. Some of it is closer to applied math and some is more akin to a social physics. The overlap is not always perfect. There is also an aspect of it that is philosophical and normative.</p>
<p>The theoretical impetus is to try to state things as cleanly and rigorously as possible. Math does this well. However, because the feedback from empirics to theory is not straightforward this leads to a problem whereby some kinds of theory become math for the sake of elegance whereas others are genuinely interested in operationalizing difficult ideas as simply as possible. The closest split in physics is between the generation of Feynman -- for whom theory was about generating better calculations and testable hypotheses and the string theorists where the difficulty in testing has led to an emphasis on elegance rather than operationalizability. It's worse in econ, partly because the field is so immature.</p>
<p>This is quite distinct from applied statistical work which is nowhere near as formal as the theories. Indeed, the quality of research by people such as Levitt, Krueger, Oster, or Murphy indicates that very good empirical work only weakly depends on the most formal models.</p>
<p>Sadly, there is an increasing disappearance of the "soft theory" group. In my view, the work of people such as Coase, Friedman, Schelling, Akerlof, Spence, Alchian is very good but not very formal theory. Today, theorists say their work is outmoded in that the level of acceptable math has moved upwards. This is a mistake in my view because the level of maturity in econ has not been so great as to invalidate this level of model-building. Nonetheless, it is a sociological given that to succeed in theory you need much fancier math models than Friedman or even Spence could get away with 30-40 years ago. Ironically however, the star empiricists today are basically working with models not much different from that of the aforementioned group.</p>
<p>This is a constant source of friction even within the very top departments.</p>