Considering Taking Micro And Macro Econ..How Much Math Involved?

[ag]

US college, a principles course? Mainly, ability to read basic graphs and diagrams, not much more. Intermediate level courses would/could be more serious. And, of course, underlying what you are taught there is pretty serious math. They do translate it into English for the poor American college kids, though

Still, I would strongly suggest you get rid of the math phobia - it is not a good thing to have.

[ag]

Calc isn't required until intermediate micro/macro, and even that depends on the school.

Anyone that can't do basic calculus shouldn't be awarded a bachelor's degree unless it is something like a fine arts degree.  These pieces of paper should mean something.

Well. There is English Literature, Foreign Languages, History and a couple of others that, I guess, could also be exempt. But, yeah, frankly, it is a shame that one can get even a high school degree without calc.

[ag]

You're allowed to do intro econ without having done calculus?

Worse. In many places you are allowed to do Intermediate Micro/Macro without doing calculus. Don't ask me why. I mean, they talk about "marginal" this or that drawing little triangles

At least, intro courses could be explained. Remember: US "liberal arts" degree is not a professional degree, but a preparation for one. It, basically, produces "an educated person". People have to take a bunch of courses in different areas (one or more of which would be designated as a "major" and some others, possibly, as "minors", implying somewhat greater concentration). So a typical intro course is taken by somebody who is not planning to study economics - either because s/he is just testing waters, or because it allows him/her to fulfill some "core" requirement of the liberal arts program. So you should treat an intro course not as a beginning of serious study of economics but more as a general education "taster" designed to give some idea of what econ is about. Obviously, if you want English Literature and Painting students to feel comfortable, you are not going to put calc as a prerequisite.

[ag]

You're allowed to do intro econ without having done calculus?

Worse. In many places you are allowed to do Intermediate Micro/Macro without doing calculus. Don't ask me why. I mean, they talk about "marginal" this or that drawing little triangles

I know in some schools intermediate micro is required for business students, so they don't make them use calc or they offer a separate calc-based intermediate micro.

That, in fact, is a shame. A business major should have basic calculus skills. Teaching (and learning) intermediate micro without calculus is simply hard: it would have been easier to teach basic calculus in the first place. All it does is perpetuate the myth that basic math is something only very smart people can do. This is a grave mistake.

I am willing to give English majors a pass, though. Actually, if they are really good with,well, English, they can substitute it for math. It works.

[ag]

You're allowed to do intro econ without having done calculus?

In my school, I believe it was a co-requisite though ag probably hit the nail on the head in that it doesn't need to be one.

It is a broader point than micro/macro or economics in general. Intro courses in a liberal arts college are not so much for majors as for the general education of the non-majors or for advertising among the undecided. As such, they should be generally accessible. I mean, an intro music course typically would not require much knowledge of notation, would it?

[ag]

You're allowed to do intro econ without having done calculus?

Worse. In many places you are allowed to do Intermediate Micro/Macro without doing calculus. Don't ask me why. I mean, they talk about "marginal" this or that drawing little triangles

At least, intro courses could be explained. Remember: US "liberal arts" degree is not a professional degree, but a preparation for one. It, basically, produces "an educated person". People have to take a bunch of courses in different areas (one or more of which would be designated as a "major" and some others, possibly, as "minors", implying somewhat greater concentration). So a typical intro course is taken by somebody who is not planning to study economics - either because s/he is just testing waters, or because it allows him/her to fulfill some "core" requirement of the liberal arts program. So you should treat an intro course not as a beginning of serious study of economics but more as a general education "taster" designed to give some idea of what econ is about. Obviously, if you want English Literature and Painting students to feel comfortable, you are not going to put calc as a prerequisite.

There is far too much calculus used in economics.

You can do everything without calculus: it is just a convenient tool, no more than that. But without calculus everything becomes much harder. In fact, one way of setting up a tough graduate question is to prohibit using calculus when answering it ("you may not assume differentiability of" whatever). Trust me, you prefer it this way

But, of course, what you wanted to say is "there is too much math used in economics". Once again, let me be very clear here: math makes things easier, not harder. This has nothing to do with economics as such: understanding and verifying logical reasoning without formal tools is difficult.

Calculus is simply a collection of very useful tools that make conversations and understanding easier. Nothing mysterious or esoteric there whatsoever. If a high school diploma required basic calculus (as it should) people would be much less nervous about it. Frankly, it should be a safe assumption that the basic calculus notion are familiar to every 16-year-old - like it is with reading or writing. It is just a useful tool-kit in life.

[ag]

I completely agree that calculus simplifies mathematics a great deal.  It is also amazing that through calculus a great deal of further data can be gathered from having just a few pieces of quantifiable data.

So, calculus is very useful.

However, I was referring to calculus.

There is a reason that many non-economists and some economists refer to economists as having 'physics envy' and this is due to the overuse of calculus in economics.

There are two problems with the obsession mainstream economists have with calculus

1.There seems to be a great deal of opposition to doing research into economics hypothesis that can't be quantified or 'proven' through calculus.  I would think it would be obvious that many economics ideas might be worth investigating but can't be easily quantified or can't be quantified at all.

2.There is a good deal of deceptive use of calculus in economics especially by economists who work for lobbyist organizations.  There seems to be a common view both with most people in the public and with politicians that if a figure has been derived by an economist through the use of calculus that it has been scientifically proven. But, if you actually check into many of the numbers used in the equations, you'll find that many are estimates or are simply made up.  

So, calculus can illuminate many things, but it can also be used to prevent investigation and to obfuscate.  

This is worth a listen: http://www.cbc.ca/radio/ideas/it-s-the-economists-stupid-1.3219471

Interest rates.  Unemployment. GDP.  Markets. Austerity measures.  Economists tell us what we, as societies, can and can't afford.  But how do they decide? What values are at play? IDEAS producer Mary O'Connell speaks with two economists about how modern mantras on the economy limit our choices and shut down civic debate.

Dr. Julie Nelson, Department Chair and Professor of Economics, University of Massachusetts, Boston.

Dr. Richard Denniss, Chief Economist, The Australia Institute, Canberra City, Australia.

I think this simply reflects a fundamental misunderstanding of the usage of mathematical methods in economics (or, for that matter, in other sciences). Just as an aside: calculus is just a routine method - everything that is derived with calculus could be derived directly, but it would be harder. Saying that "too much calculus is used" is like saying "too much multiplication is used" or "too many verbs are used". Ok, If you do not like verbs, I will live with nouns and adjectives. It will be awkward, but I will manage.

Why do we use mathematical tools? Basically, because we do not like making logical mistakes. A simple mathematical model is precisely that - a simple description of a phenomenon of interest, highlighting the features we believe to be of importance. Could it be done with words? Yes, it could. In fact, there are branches of economics that try to do that, at least in published works. For instance, economic historians have to talk to historians - they try to describe their models in the language historians know. Notably, good economic historians still start with a formal model (yes, using calculus, if useful) and then translate it into words. What is the disadvantage of doing this? English is too undisciplined a language - it is easy to hide logical non-sequiturs and implicit assumptions in an English sentence. Math forces these things to be revealed. The first thing I do when looking at a simple undergraduate textbook (without calculus) is try to translate its arguments into a simple math model. If the book is good, this is very easy (it is just a reverse translation to the language the book had been thought up originally). If I cannot do this, chances are the book is bad: it is making arguments that are logically flawed, covering the flaws up with verbiage. In a profession where command of basic math tools is common "plain English", unsupported by a formal model, is naturally viewed as obfuscation.

Now, for being "scientific". Math is not a science: by itself, it is not interested in natural or social phenomena. A scientific proof differs from a mathematical proof in that it is not merely logical, but empirical. Your model can be formally correct, but it starts with assumptions: that is your (likely very simplified) description of how the world is. Empirical observation tests your assumptions. The role of math here is that it helps one to build a logical argument that transforms original assumptions into testable implications. The only thing you can prove with calculus (or trigonometry, or topology, or whatever) is that you made no logical mistakes in that transformation. The real theory is not what you produce using mathematical tools: it is the assumptions you put into the model. And the real "proof" that theory works is not the formal mathematical proof of the implications being correctly derived, but in the empirical test of those implications. This is where we, economists, may indeed have physics envy: their data are so much better!

To sum up,  math is not used to obfuscate, but to clarify. That the public at large sometimes views it otherwise is, to a large extent, a product of poor education: not even at college, but at the high school level. This is why I firmly believe that calculus should be taught to everyone and early: it is as essential as knowing multiplication tables. It is not some fancy math - it is very basic. It is not difficult, if properly explained. It is a lot harder to teach a student basics of economics (or any other science) without calculus than to spend first a semester teaching basic calculus tools and then doing economics using that. Calculus is not magic - it does not make anything happen. Things are true or false irrespective of what math tools are used to analyze them. But it sure helps to have the tools.

[ag]

First a public apology:

I accidentally modified the message I was responding to, instead of simply quoting it. I really had no intend of doing that damage, but, unfortunately, I canno reverse it. I do apologize: this is very stupid of me.

Yeah I can definitely see that.  But the fact the OP is talking about grad school is a bit scary.  If someone wanted to do grad work in history and ran away from math I would be a bit concerned.  Ignoring the quantitative side is how we end up with so much skewed history.  It's like if you read an account of an army that is a certain size.  Well you need to calculate crop yields and economic yields to see if a particular government could even field an army that large or whether some ancient historian was just telling a tall tale.

Well, History is a large field. Definitely, an Economic Historian needs to have basic math tools. But for an Art Historian it will be more important to memorize how Rhode Island chairs differ from those produced in Massachussetts, how to read 17th century shorthand on the back of a painting or what sort of wood was used in Bulgaria for icons in the 12th century. A historian of Shakespeare will be better served with a paleography semester than with a calculus class.

[ag]

I don't understand the discussion here. Or more precisely I don't get Adam T's points.

Formally, his point is that vowels are more useful than consonants (or the other way around), so it is absolutely unintelligible. Nst hrrd clcls.

Of course, what he has in mind, I guess - or, more specifically, he read it somewhere - is that people sometimes take certain "numbers" a bit "too literally", forgetting that many econ models are better viewed as mathematical parables, designed to elucidate a point, not as literal descriptions of reality (there are circumstances when it is not the case: in parts of market design literature - auctions, matching algorithms, etc. - economists have achieved almost engineering-like precision; but these are, of course, exceptions). Now, that point is, in fact, quite valid in my view: I myself like to pull the leg of my macro colleagues on this Unfortunately, that point is almost unrecognisable in his attempt at formulating it. An attack on vowels calculus is as bizarre as it looks.

BTW, if you insist on blaming some math toolkit, blame numerical methods, not calculus. I mean, if the model has a closed-form solution, chances are it is simple and elegant precisely because nobody has tried to make it as ugly and complex as the actual world around us, so its metaphorical meaning is clear It is when people get into "calibrating" things to the "real" economy that they become too literal in their meanings. But that you almost never can do just with your calculus toolkit. Big nasty computers are to blame  
 

[ag]

math.

2.Mathematics/calculus are frequently used by economists who work for lobbying organizations to present dishonest arguments

Well, English is used for these purposes much more frequently and in much more obscure ways. For this reason, I strongly suggest strict prohibition on using English for any sort of argument related to economics

[ag]

One of the funny misconceptions in all these posts above is the confusion between "mathematical" and "quantitative". Most fancy math usage in econ has nothing to do with quantification of anything: "math" does not mean "numbers". Math is simply the formal language in which this profession expresses itself. In any case, if your objection is to "numbers" please object to things that, actually, produce "numbers." Calculus - and its usage in economics - is, at worst, a very minor culprit here Frankly, if I had to give a very unscientific estimate here, I would say that the quantity of numbers in the output of an econ study and math usage in the process of conducting it are very much inversely correlated

And, of course - and this is very much a separate issue - I strenuously object to economics "not being a science". Saying that is like saying that economics is not dealing with empirical facts about this world. If that were the case, it would have been a useless field. In fact, even (good) history is a science. Science is the way we understand the world around us. We study what happens, we pose hypothesis about the underlying mechanisms, we test them, using empirical data (both observational and experimental). That is what makes it science. This process is made easier by math, but good historians sometimes do it without using math explicitly. Their data is, generally, pretty bad, so they do not have to build very precise models: makes sense not to take position on things one never can test (in contrast, they spend the bulk of their time collecting the data - what for an economist is a data point, for a historian is 3 years of archival work). Our data is somewhat better, so we do a more careful job. Physicists have even better data, so they try to understand even more. Standards might vary by field, but the fundamental approach is very much the same, math or no math. If economics (or history) is not a science, than what is it? Religion?

[ag]

To sum up. It makes no sense to read "heterodox economics" unless you happen to know what "orthodox economics" is about and what it does. Now, there are many things you can object to: a lot of it with great reason. But objecting to usage of a - very basic and easy - math toolkit is ridiculous. Using calculus is no different from using, I do not know, a present tense. And, of course, it is infinitely easier to lie in English, without any usage of math. If you cannot translate a simple spoken argument into baby math, it is, probably, a lie - or, at best, has flaws/unclear things in it. That concerns not merely math, but any kind of human conversation. This forum would have been a lot clearer if we used LaTex and wrote using notation. And that, by itself, would have made it not at all "more scientific". I mean, I have been in seminars that could be best described as standup comedy - all using beautiful mathematical modelling and reasoning. It was as funny - and as scathing - as anything produced by John Stewart. You just needed to know a little math :)

[ag]

I don't understand the discussion here. Or more precisely I don't get Adam T's points.

Anyway, understanding calculus is super useful to make sense of life, IMO. I learnt the basics in early high school and I think that was good.

I think I figured out the cause of your confusion.  

It is, of course, a logical fallacy to blame all of the use of mathematics in economics for some economists misusing that mathematics/calculus.  The problem is, as Richard Denniss explained in that radio program that many economists like the idea or being regarded as some kind of scientist or some kind of guru and don't want to inform the public that a great deal of economic forecasts, and not just the deliberately dishonest ones from lobbying groups, are, if not outright garbage in and garbage out, are based on all sorts of assumptions that render the specificity of the forecast as essentially meaningless.

Garbage in/garbage out is a general rule, applicable to all endeavours. This has nothing to do specifically with economics, math, or interaction of the two: though, of course, it is the rule very much applicable to us as well About 99.9% of the time an economist is trying to use mathematical reasoning s/he is not producing a macroeconomic forecast (frankly, as an economist, I have no clue how these are done - from what little I understand, it has very little to do with economics, as science). And most of the time lying happens in conversation about economics, it is the English verbiage that is used to do the trick. At least, if math is used, than if you know the math you can understand what is going on. I am pretty sure that without math I could get you a reasonably plausibly looking argument why you should be killing your grandma in such a way that you will never see where I got you sold on it. Plato's dialogues are much harder to unravel than Arrow's theorems

Of course, people who have a religious faith in some mysterious and esoteric "math" that magically makes things into "science" are not the intended audience of an academic paper. If one of these happens to be your congressman, I fully agree that presenting him with a bunch of mathematically-looking pages is fraud. Pretty much everything of interest we say with math can be explained in words - and should be, if the task is to explain. Unfortunately, it would take a very smart person to figure out whether that explanation is correct or flawed. It is exactly what happens to me when I go to a medical office for a procedure. I ask the doctor to explain me what is going on, and the doctor, generally, does. But I have no clue whether his explanation makes sense - I know little biology or chemistry and pretty much no pharmacology or medicine. I haven't written a chemical formula in a quarter century and have no clue what happens in my body. If a doctor starts writing formulas for me, I will gain nothing from this. But that does not mean that medical students should not learn chemistry.

[ag]

2.http://www.scmp.com/lifestyle/technology/article/1737875/what-proper-role-mathematics-economics
The proper role of maths in economics.  Written by a physicist.

Unfortunately, it does not discuss the actual proper (or improper) use of math in economics. In fact, it suffers from the same problem it describes: there is a theory (of math usage in econ) not grounded in data. And, notice, it is done entirely without math

Now, I happen to understand some of the things he is trying to allude to. And some of the issues are quite serious indeed (I myself firmly believe that much of what we are doing is best described as building "mathematical parables" and object to overinterpretation of many results). But he most definitely is not saying that intermediate micro should be taught without calculus

[ag]

To my knowledge, it's nearly impossible to be a proficient statistician/econometrician without understanding the theoretical basis of statistics (probability theory and mathematical statistics) and this requires calculus.

I did not even touch on that for lack of time

[ag]

2.Whether economics should be considered a (hard) science or not is not at all a separate debate/discussion.  It's pretty obvious that you think one of the major reasons economics should be considered a (hard) science like physics is due to the use of mathematics/calculus in economics.

This pretty much directly contradicts everything that I have written over multiple posts. Have you bothered reading them?

I do not know what a "hard science" is. It is either science, or it is not. But the scientific approach means formulating hypothesis and testing them with data. I have several times mentioned that, in general, one can do this using English: it is just much harder to do so. Economics uses math because that makes it easier and more transparent. Overwhelmingly, those who oppose math usage in economics, are doing so for the purposes of obfuscation, to cover up bad and imprecise reasoning.

[ag]

2.Whether economics should be considered a (hard) science or not is not at all a separate debate/discussion.  It's pretty obvious that you think one of the major reasons economics should be considered a (hard) science like physics is due to the use of mathematics/calculus in economics.

This pretty much directly contradicts everything that I have written over multiple posts. Have you bothered reading them?

I do not know what a "hard science" is. It is either science, or it is not. But the scientific approach means formulating hypothesis and testing them with data. I have several times mentioned that, in general, one can do this using English: it is just much harder to do so. Economics uses math because that makes it easier and more transparent. Overwhelmingly, those who oppose math usage in economics, are doing so for the purposes of obfuscation, to cover up bad and imprecise reasoning.

1.I've read everything you've written. If I've misunderstood anything you've written, I'm sure the fault is mine.

2.Hard science vs. soft science: https://en.wikipedia.org/wiki/Hard_and_soft_science
The scientific method also requires repeatability of experimentation and the ability to produce laws or theories that can be applied universally.  Physics and chemistry and most of the time biology can do that, economics can't.  You can call economics a science if you want, but it is not a science in the same way that physics, chemistry and biology are, though, for some reason that I can't understand, you seem to either wish it were or believe it is.

What do ou mean we "can't"? We have a large body of repeated experiments (both lab, field, and natural) and we have established regularities that are pretty damn repeated across the world.

The main problem with you argument is that you do not know what economists are doing. You come back to (macro) economic forecasting - something generally not done by academic economists and viewed very sceptical in the academic community. I will fully agree that much of that is not science. But neither it is economics, really I mean, doctors in the field routinely do unscientific things, but you are not going claim that biology is not a science because of that

[ag]

I think Ag should have become a professor of calculus and not a professor of economics.

A student newspaper has once quoted me saying "calculus is not a religion: do not differentiate everything that moves" If anything, I am the sort of an econ prof who likes asking questions where calculus will not help. This is why students hate me

[ag]

3.With garbage in/garbage out I was specifically referring to the use of estimates or essentially made up numbers being used in economic forecasts, especially those used by lobby groups.

4.Economic forecasts made and/or used by lobby groups are rarely attended for an academic audience, not strictly for an academic audience anyway.

If anything, that is the argument against using English: 99.9% of lying there happens in English. You do not need calculus to produce made-up numbers.

[ag]

5.My guess is, and I admit that this is strictly a guess myself, is that were it not for economists claiming to be scientists and producing economic forecasts with precise numbers, that most ordinary people would not take the 'english language' claims made by economists as 'gospel' either.

People doing forecasts and people who do economic science tend to be very different people. Doctors also tend to be pretty crappy scientists in my experience. The reason you trust doctors is not because they are good biologists.

[ag]

All the poor kid wanted to know was how much math is in Econ and if he should take it or not.  I answered it in the first post... geez!

... and (un)fortunately I was traveling while most of this exchange was happening. As a particle physicist with a degree in mathematics and many published statistical analyses, who also works extensively with governmental economics and accounting, I probably could not have resisted jumping in. Comparisons of economics to physics and string theory are nigh irresistible. I suppose if anyone wants my opinion on any of that they can ask.

You are welcome