I was in an econometrics class yesterday where our tutor was walking through a statistical problem concerning an independent normal distribution with us. We calculated 2 probablitlty values for the likelihood a member of the set would be in 2 regions. The next question asked what would be the value the probability would be above 50(the range was between 0 and 100). Now even if this distribution wasn't normal the answer would have been trivial, since the probability of lying in the other regions(covering the range below 50) summed to 1/2.
So, the probability of the value being above 50 was (shockingly!), 1-1/2=1/2. I shouted out the answer before he finished writing the question. He at first fumbled, and then agreed with me, but said that you would not get full marks unless you demonstrated this to be the case presenting a longwinded calculation similar to the one he used to calculate the other 2 values.
This got me thinking. For a while I've had the feeling that economists don't seem to use maths to generate much genuine insight, but merely to pretentiously show off that they know how to play with Greek symbols. When I was a physics student, if I answered in the above way, a professor would either be indifferent or actually enthusiastic that I was using my brain to actually find smarter, easier ways to solve problems than regurgitating from rote memorisation. This doesn't seem to be the case with economists, indeed I am beginning to think this might be why my marks on the econ course I'm currently doing are not as high as they could have been, though they are not bad.
Does anyone else feel this way?
"When the King is far the people are happy." Chinese proverb
For Alexander Zinoviev and the free market there is a shared delight:
"Where there are problems there is life."
two thoughts
#1. econometrics != mathematical economics. econometrics is essentially using statistics to study economic data. any problems you have with econometrics you would have statistics in all of its forms.
#2. i personally don't think mathematical economics (using math to model economic phenomena) is pretentious at all. primarily i'd say it is a tool for clearing one's own thoughts but maybe more importantly a tool for communication. expressing economic theories through mathematics forces one to make every assumption explicit. that may not sound like a big deal, but there is a reason you won't see any papers that ask "what kenneth arrow *really* meant"--mathematics allowed him to make it perfectly clear to begin with! considering all the papers written on interpreting and re-interpreting mises and hayek, i can see why many austrian economists don't like the idea of using math--it could put them out of businees!
now, i am sympathetic to some arguments that there may be an over emphasis on math these days (paul krugman actually had a good blog post recently on the value of less technical econ), but i think arguing that it is merely showing off is missing the point.
Ambition is a dream with a V8 engine - Elvis Presley
Krugman writes in a number of places that without the math he could never have figured out and properly thought through his contributions to trade.
Math offers a useful way to think in an organized, systematic, consistent fashion. Using only words can lead to sloppy thinking in a manner impossible with math (unless you just suck at math).
I do not really have a problem with including math with economics as a tool to help illustrate theories but I oppose the using of math as the only means to explain a theory. If one cannot explain economic law using words and instead uses math, that is a fallacy.
My Blog: http://www.anarchico.net/
Production is 'anarchistic' - Ludwig von Mises
Why?
It's sloppy thinking to think that math expressions are not "words". (The qualitifer in brackets is funny. It's less sloppy if you can't do math?)
Sure, math is language, and it can always be translated to english, although obviously "2 + 2" is often easier than "two plus two" in many situations. Nevertheless, math is a particularly useful language for being organized, systematic, consistent, and logical, much like how French might be a particularly useful language for love or German might be a particularly useful language for doing philosophy.
As for my qualifier, obviously if one cannot do math well one's thinking will appear sloppy--2 + 2 = 5. Some people might do better with words. They might also not have much to contribute to economics.
Symbolic logic is to logic as mathematics is to economics.
Essentially, they wanted to get rid of the ambiguity and equivocation and 'unclear-ness' of wordyness. Both are important, but in the case of symbolic logic, you better well have an appropriate foundation in logic before you move on.
Likewise, you need an appropriate foundation in 'word' economics before you move on--otherwise you're apt to get totally confused.
Why/how/examples?
Math is also more succinct.
If you're asking me, then symbolic logic is used to diagram incredibly complex arguments that are otherwise misconstrued when represented any way other than symbolically.
For instance: ~{[(p v q) -> (r -> s) * ~x] v z}
That's just a small example, but when p, q, r, s, etc., stand for arguments, then it becomes near impossible to represent any other way.
And so someone who doesn't know "word" economics will be limited in that...?
two thoughts #1. econometrics != mathematical economics. econometrics is essentially using statistics to study economic data. any problems you have with econometrics you would have statistics in all of its forms. #2. i personally don't think mathematical economics (using math to model economic phenomena) is pretentious at all. primarily i'd say it is a tool for clearing one's own thoughts but maybe more importantly a tool for communication. expressing economic theories through mathematics forces one to make every assumption explicit. that may not sound like a big deal, but there is a reason you won't see any papers that ask "what kenneth arrow *really* meant"--mathematics allowed him to make it perfectly clear to begin with! considering all the papers written on interpreting and re-interpreting mises and hayek, i can see why many austrian economists don't like the idea of using math--it could put them out of businees! now, i am sympathetic to some arguments that there may be an over emphasis on math these days (paul krugman actually had a good blog post recently on the value of less technical econ), but i think arguing that it is merely showing off is missing the point.
I have an amateur interest in advanced mathematics (particularly, algorithmic information theory) and I have to say that as an outside observer, I would extend OP's criticism not only to most modern economics but also physics itself.
If you take first year physics (I have), you will learn things like conservation of momentum, and the explanation you are given will be much like that in the linked Wiki and you will learn something like MV = mv. Now, MV=mv is a handy mnemonic, a great tool for calculating momenta in physical problems. But absent the physical experiments and chain of reasoning that led to the equation MV=mv, you have no real comprehension of what you're talking about. You're just an arithmetic monkey.
I read the first chapter of Ernst Mach's Science of Mechanics, in which he presents Galileo's physical argument for the conservation of momentum. Galileo rolled a ball down an incline of angle A and measured how far the ball rolled up an adjoining incline of angle B. He found that the height to which the ball rolled up the second slope depended solely on the height at which the ball was released from the first slope and independent of the angles of the slopes. Therefore, if you fix an angle A, as you decrease the angle B (neglecting the effects of friction) the ball will roll farther and farther in order to reach the height at which it was released on the initial slope. In the limit, the ball will travel infinitely far. Hence, a body in motion remains in motion (Newton's first law or the Law of Inertia from which conservation of momentum follows).
Mathematics is simply a compressed form of natural language. Mathematical objects, therefore, are mental objects, that is, they exist only in the minds of human beings as categories of human thought and language. The only things which mathematical objects fully emulate are themselves, that is, the properties of a mathematical object only correspond to the mathematical object itself. Only pure numbers are perfectly modeled by pure numbers. Correlation between numbers and real objects is dependent on a human brain (or, in the computer age, a machine built by a human brain) to translate some set of observed physical states into a mathematical description which can then be manipulated according to the rules of mathematics. The result of these manipulations can then be translated back to a set expected physical observations. Any information lost in the translation may result in error and the human brain is a fairly "lossy" computational device.
For example, if you lay out 7 rows of 6 rocks each, you can compute the total number of rocks without having to count them one-by-one. First, you translate the phsyical perceptions of the number of rows and the number of rocks in each row (including the physical fact that each row is equinumerous). Once you have "6" and "7" in mind, you can follow the rules of multiplication to arrive at the conclusion that 6x7=42. Finally, you may translate the "42" back to the expected physical perception of having counted 42 rocks one-by-one in order. If you were to count the rocks one-by-one, this is the physical state of affairs that you expect to obtain (to count 42 of them).
Clayton -
A few thoughts:
Symbolic logic is to logic as mathematics is to economics. Essentially, they wanted to get rid of the ambiguity and equivocation and 'unclear-ness' of wordyness. Both are important, but in the case of symbolic logic, you better well have an appropriate foundation in logic before you move on. Likewise, you need an appropriate foundation in 'word' economics before you move on--otherwise you're apt to get totally confused.
You're understating the case. Mathematical (and logical) formalism is the result of a long philosophical search for "irrefutable truth" or "absolute truth." The liar's paradox easily shows that the possbility of finding absolute true or false through ordinary human language is impossible since one may always construct statements that cannot be evaluated into either the category of "true" statements or the category of "false" statements... they belong to a third, unexpected category of "meaningless" or "paradoxical" statements.
Beginning in the 19th century, logicians and mathematicians sought to be more rigorous in their proofs and the idea emerged that perhaps it is possible to establish "provability" or "unprovability" rather than "true" or "false." In other words, perhaps the problem with true and false is that they are "meaningful" concepts and if we just avoided anything to do with meaning and concerned ourselves with the empty manipulation of symbols, we can establish for any given string of formal symbols whether it is provable or not. Then, through a rigorous search of proofs, it would be possible to discover heretofore unknown mathematical truths and use formal methods to vet long-standing mathematical ideas to be sure they are correct.
To this end, Russel and Whitehead wrote their epic Principia Mathematica. It was the first swipe at absolute truth through formal methods. Once completed, it would provide a foundation that could be extended and refined. But then Kurt Godel - inadvertenly - threw a grenade into the whole affair with his 1931 paper On Formally Undecidable Propositions of Principia Mathematica in which he outlined what are today called Godel's First and Second Incompleteness Theorems. In layman's terms, Godel showed that you can't escape the Liar's Paradox by restricting yourself to formal systems. He used a clever trick to encode statements in an artificial mathematical language as numbers (we're used to this nowadays so it doesn't seem strange but, at the time, it was a completely novel technique) and then performed proofs on the encoded statements. In particular, he encoded the statement that says, "This statement is not provable" and showed that the statement - by virtue of what it says about its own provability - is not provable in a consistent mathematical system and he showed that this kind of sentence can be constructed in any mathematical system powerful enough to express the natural numbers (in other words, in any interesting mathematical system). This means there are always true statements which cannot be proved to be true, which makes any formal mathematical system incomplete.
Later, mathematician Gregory Chaitin would go on to show that this is not just an isolated problem that exists in a tiny niche of the mathematical universe of interest only to pedants and quibblers. Rather, incompleteness is the rule in mathematics. As Chaitin says it, "Almost all true mathematical statements are true for no reason." You can watch a lecture on YouTube where he explains this in his own words. It's humorous and engaging:
http://www.youtube.com/watch?v=HLPO-RTFU2o
#1. econometrics != mathematical economics. econometrics is essentially using statistics to study economic data. any problems you have with econometrics you would have statistics in all of its forms. #2. i personally don't think mathematical economics (using math to model economic phenomena) is pretentious at all. primarily i'd say it is a tool for clearing one's own thoughts but maybe more importantly a tool for communication. expressing economic theories through mathematics forces one to make every assumption explicit. that may not sound like a big deal, but there is a reason you won't see any papers that ask "what kenneth arrow *really* meant"--mathematics allowed him to make it perfectly clear to begin with! considering all the papers written on interpreting and re-interpreting mises and hayek, i can see why many austrian economists don't like the idea of using math--it could put them out of businees!
I think you have misunderstood what I was alluding to. This was not really a thread to discuss mathematical economics or its utility, though I have strong reservations about the latter, the case against it would deserve to be made in a separate thread with its own supporting argument (not filed in the category "General"). Neither do I have a problem with statistics, which is all econometrics is, aside of the different conclusions many econometricians have compared to other users of statistics as to what can be concluded from them for open systems.
My point was much more narrow, about the way economists seem to do and use maths. Hence for instance as in the above case, the grinding out of long winded calculations, to gain a trivial result one could gain otherwise by simply using one's logic, is encouraged over doing the latter, for whom marks are penalised in a test. This is by no means the only case, I noticed that my microeconomics professors often made a big deal about "proofs" that displayed nothing more than circular reasoning arriving back at the terms they started their manipulations with(unlike a genuine mathmeatical proof that gains a theorem with some new insight and unpacked informational content). But again, I'm fairly sure such pointless mental masturbation is rewarded and encouraged(and this is definitely not the case in physics; even in theoretical physics, which is my background, I was precisely penalised by one of my viva examiners for this in my first "practice" presentation of my masters thesis).
But again, I'm fairly sure such pointless mental masturbation is rewarded and encouraged(and this is definitely not the case in physics; even in theoretical physics, which is my background, I was precisely penalised by one of my viva examiners for this in my first "practice" presentation of my masters thesis).
The mental masturbation is rewarded because it serves a purpose. It's stops people bullshitting and equivocating about important things in order to find some theoretical support for their preconceived beliefs as many accuse the Austrians of doing (and sometimes quite rightly in my opinion). That's the thing, economics is very complex and almost everybody allows their political values to influence their economic beliefs at some point, so it's absolutely necessary to force people to state their assumptions clearly and to be explicit about the definitions their using. Mathematical formalism allows people to do such a thing.
By the way, I read this the other day and your post reminded me of it
One good way to prove string theory would be to look and see whether strings exist. But the vibrations, according to the hypothesis, take place at a frequency too high for existing equipment to detect. String theorists have still not been able to resolve their equations into testable hypotheses. Instead, they have built their case on the compelling quality of their mathematics, which some find almost incomprehensibly beautiful. Physicists have long looked to higher math for insights into the workings of the universe. “If a figure is so beautiful and intricate and clear, you figure it must not exist for itself alone,” John Baez, a professor of mathematics at the University of California at Riverside, said. “It must correspond to something in the physical world.” This instinct—the assumption that beauty will stand in for truth—has become a habit. Some physicists now worry that string theory’s mathematics have grown permanently unmoored from the real world—an exercise in its own complexity. And so modern theoretical physics has become, in part, an argument about aesthetics. Read more http://www.newyorker.com/reporting/2008/07/21/080721fa_fact_wallacewells#ixzz1DbBgi2QX
Physicists have long looked to higher math for insights into the workings of the universe. “If a figure is so beautiful and intricate and clear, you figure it must not exist for itself alone,” John Baez, a professor of mathematics at the University of California at Riverside, said. “It must correspond to something in the physical world.” This instinct—the assumption that beauty will stand in for truth—has become a habit. Some physicists now worry that string theory’s mathematics have grown permanently unmoored from the real world—an exercise in its own complexity. And so modern theoretical physics has become, in part, an argument about aesthetics.
Read more http://www.newyorker.com/reporting/2008/07/21/080721fa_fact_wallacewells#ixzz1DbBgi2QX
EconomistInTraining, are you really sure that being able to make up equations and graphs stop one of bullshitting?
Are you going to tell me that Paul Samuelson bullshit didn't stink because it was supported by heavy use of math? He used math to tell that war creates prosperity, it's impossible to have inflation with unemployment and that the Soviet Union would be successful.
BS in fancy equations is still BS.
You can spin as much BS with English as with math. Ever heard of deconstructionism? Or the (in)famous Sokal paper?
What bullshit of Samuelson's are you talking about? His contributions to economics are numerous so it's important to distinguish between those contributions which reveal his true insight and those areas where he was, perhaps, simply being partisan. The thing is the Soviet Union example, as far as I can tell, was simply an extrapolation of bad Soviet data into the future, whatever your opinions on formalism there is always need for some sort of speculation but also some numerous difficults involved. But your inflation and unemployment example is precisely an example where mathematical formalism has helped remove controversy. The fact is that the crude Keynesian models of the time (as far as I'm aware) didn't use anything like maximising agents and weren't particularly explicit about expectations, this only came with Lucas.
The ABCT in the other hand is being credited for every business cycle from the big bang to all the way in the future. Precisely because it's so easy and tempty to make ad hoc changes to what you mean by ill defined terms like "higher order goods" and even the business cycle in and of itself. By the way, in an of itself formalism only assures that the theory is internally consistent, not that it really corresponds to anything "out there". More empirical work is needed to reach the latter result.
What bullshit of Samuelson's are you talking about? His contributions to economics are numerous so it's important to distinguish between those contributions which reveal his true insight and those areas where he was, perhaps, simply being partisan. The thing is the Soviet Union example, as far as I can tell, was simply an extrapolation of bad Soviet data into the future, whatever your opinions on formalism there is always need for some sort of speculation but also some numerous difficults involved. But your inflation and unemployment example is precisely an example where mathematical formalism has helped remove controversy. The fact is that the crude Keynesian models of the time (as far as I'm aware) didn't use anything like maximising agents and weren't particularly explicit about expectations, this only came with Lucas. The ABCT in the other hand is being credited for every business cycle from the big bang to all the way in the future. Precisely because it's so easy and tempty to make ad hoc changes to what you mean by ill defined terms like "higher order goods" and even the business cycle in and of itself. By the way, in an of itself formalism only assures that the theory is internally consistent, not that it really corresponds to anything "out there". More empirical work is needed to reach the latter result.
You have an incomplete understanding of Austrian claims about the market - Austrian theory, including business cycle theory, eschews any claim of predictions about the future state of the market. Business cycle theory itself is an ex post facto explanation of why past business cycles have happened in the past but explicitly rejects crystal-ball gazing regarding future business cycle events.
The Austrian view is that the only individuals who actually engage in meaningful prediction about the future state of the market are entrepreneurs. Academic economists can offer nothing more than an analysis of cause and effect in past real economic events or "praxeological" theories explaining human choice under conditions of voluntary exchange ("catallactics"). Thus, any academic economist who says, "If you follow policy X, employment will increase by X%" is just a charlatan. This agnosticism regarding the real outcomes of government policies is what motivates Austrian criticism of any government policy intervention in the market. Since we cannot know ex ante what the real outcome of any government policy will be, no government policy can be justified on the supposed benefits it will provide to the market.
One deficiency I see in Austrian theory as it stands is that it does not talk about political entreprenuerialism, that is, the entrepreneurial aspect of political means. This is becuase the political means fall outside the scope of voluntary exchange and, therefore, do not conform to the axioms of catallactics. However, I believe it would be possible to formulate a set of axioms that describe human choice where coercion can be given and received and this would greatly assist in analyzing the behavior of the political class. For example, governments are themselves subject to evolutionary forces similar to those which govern the free market - governments which adopt policies that are too aggressive or oppressive tend to be replaced by governments which adopt more reasonable policies and government which adopt policies that do not extract sufficient resources from their subject population or allow their subjects too much liberty tend to be replaced by governments which are more austere in disciplining and subjugating the population.
Not exactly the mainstream way of analyzing government action but mainstream political analysis is more useless than theology.
Clayton: You have an incomplete understanding of Austrian claims about the market - Austrian theory, including business cycle theory, eschews any claim of predictions about the future state of the market. Business cycle theory itself is an ex post facto explanation of why past business cycles have happened in the past but explicitly rejects crystal-ball gazing regarding future business cycle events.
Then what's the point?
If I wrote it more than a few weeks ago, I probably hate it by now.
Business cycle theory itself is an ex post facto explanation of why past business cycles have happened in the past but explicitly rejects crystal-ball gazing regarding future business cycle events.
someone should probably tell that to the posters here claiming that bernanke is flooding the market with cash and setting up the foundation for the next boom-bust cycle.
or is that level of crystall-ball gazing alright?
Clayton: You have an incomplete understanding of Austrian claims about the market - Austrian theory, including business cycle theory, eschews any claim of predictions about the future state of the market. Business cycle theory itself is an ex post facto explanation of why past business cycles have happened in the past but explicitly rejects crystal-ball gazing regarding future business cycle events. Then what's the point?
I think this is why the majority of Austrian economics is praxeological in nature. We can reach praxeological conclusions regarding how human beings will behave in the future, for example, that they will prefer to possess things which seem more valuable to them than things which seem less valuable to them. This preference is purely subjective and, therefore, cannot be directly observed except in the case of one's own preferences but we can observe the revelation of preference in others when they leave behind or exchange away less valuable things and seek or exchange for more valuable things. Of course, this praxeological line of thinking is completely devoid of any concrete application to the real world, particularly with respect to predicting the future course of human events. Nevertheless, praxeology is valuable for comprehending why the market process emerges as it does, just as evolutionary theory (which is, by and large, un-testable in the physics laboratory sense) is valuable in understanding why the natural world has emerged as it has over the last four billion years. You cannot use evolutionary theory to predict how species will evolve in the future. But it does explain how they have evolved in the past.
someone should probably tell that to the posters here claiming that bernanke is flooding the market with cash and setting up the foundation for the next boom-bust cycle. or is that level of crystall-ball gazing alright?
ABCT explains how inflationary expansion by central banks has systematically led to discoordination in the structure of production, including labor, as well as the misallocation between consumer demand and producer capacity. This does not lead to the conclusion that every expansion of the money supply will result in a subsequent economic collapse since central banks have certainly learnt from their own past and are cleverer today than they were 100 years ago. Nevertheless, the Austrian approach would reject any claim on Bernanke's part that his money printing will not result in another business cycle. It is obvious, therefore, that if Mr. Bernanke does not want to risk causing an economic collapse, he should not print money.
To make an analogy that I think make things easier to picture:
There's the old, historically innacurate but engaging anecdote about both NASA and the Soviets facing the issue of the fact that pens wouldn't work in zero gravity. NASA spent and invested in millions of dollars to solve this problem building a pen that could write in zero gravity. How did the Russians solve the problem? They used a pencil.
My gripe was about economists taking the "NASA" route almost every time.
"What bullshit of Samuelson's are you talking about? His contributions to economics are numerous so it's important to distinguish between those contributions which reveal his true insight and those areas where he was, perhaps, simply being partisan. The thing is the Soviet Union example, as far as I can tell, was simply an extrapolation of bad Soviet data into the future, whatever your opinions on formalism there is always need for some sort of speculation but also some numerous difficults involved."
The thing is, he extrapolated bad Soviet data til the very end, in the late 80s he was saying that the Soviet Union could surpass the West. Late 80s, when anyone could turn on the TV and see the USSR was crumbling.
So you say "he was fed bad data!". He was limiting himself quite a lot, he could have done something extremely simple to actually know about the real conditions of the soviet economy. He could just have asked one of thousands of people who fled the Soviet Union about how things there were like. Or could seem some video footage that were already common of the long lines.
But no, he prefered to drink the kool aid of his own equations, hoping they would shape reality somehow. In essence, he forgot that economics is, afterall, about people.
I'm not sure if your complaint is with the way economists use it, so much as the education system.
Perhaps you're right. I perhaps was very lucky to have studied in an environment that emphasised problem solving over simply rote learning for my first degree. If more people approached mathematics(and thinking in general) in the way of the following author, the world would be a very different place:
http://www.amazon.com/Mathematical-Puzzling-Gardiner/dp/0486409201
It was writtent by a former lecturer I had in an isolated module outside the main discipline. I failed it first time, but excelled in the resit. Probably one of the most immense growing experiences of my life was to learn to appreciate books like this.
I perhaps was very lucky to have studied in an environment that emphasised problem solving over simply rote learning for my first degree.
This has certainly not been my economic grad school experience. I know for a fact all my professors and TAs have been bright people who value simple approaches to complex problems. If this has not been your experience I would say it has more to do with your institution than the discipline as a whole.
Here is an old (but still popular) ranking of econ grad programs world wide: http://econphd.econwiki.com/rank/rallec.htm
see where your institution falls.
"By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race." -- Alfred North Whitehead
I will never understand the Austrian portrayal of mathematics. It's downright anti-intellectual. In fact, I'm also sick of critics who argue along lines of, "Economics isn't like physics; it's like biology." Well, if that's the case, then how does serious biology work?
Paul Krugman (The 90s Krugman, to be exact):Academic economics, the stuff that is in the textbooks, is largely based on mathematical reasoning. I hope you think that I am an acceptable writer, but when it comes to economics I speak English as a second language: I think in equations and diagrams, then translate. The opponents of mainstream economics dislike people like me not so much for our conclusions as for our style: They want economics to be what it once was, a field that was comfortable for the basically literary intellectual. [ ... ] A similar situation exists in other fields. Consider, for example, evolutionary biology. Like most American intellectuals, I first learned about this subject from the writings of Stephen Jay Gould. But I eventually came to realize that working biologists regard Gould much the same way that economists regard Robert Reich: talented writer, too bad he never gets anything right. Serious evolutionary theorists such as John Maynard Smith or William Hamilton, like serious economists, think largely in terms of mathematical models. Indeed, the introduction to Maynard Smith's classic tract Evolutionary Genetics flatly declares, "If you can't stand algebra, stay away from evolutionary biology." There is a core set of crucial ideas in his subject that, because they involve the interaction of several different factors, can only be clearly understood by someone willing to sit still for a bit of math. (Try to give a purely verbal description of the reactions among three mutually catalytic chemicals.) But many intellectuals who can't stand algebra are not willing to stay away from the subject. They are thus deeply attracted to a graceful writer like Gould, who frequently misrepresents the field (perhaps because he does not fully understand its essentially mathematical logic), but who wraps his misrepresentations in so many layers of impressive, if irrelevant, historical and literary erudition that they seem profound. Unfortunately, Maynard Smith is right, both about evolution and about economics. There are important ideas in both fields that can be expressed in plain English, and there are plenty of fools doing fancy mathematical models. But there are also important ideas that are crystal clear if you can stand algebra, and very difficult to grasp if you can't. International trade in particular happens to be a subject in which a page or two of algebra and diagrams is worth 10 volumes of mere words. That is why it is the particular subfield of economics in which the views of those who understand the subject and those who do not diverge most sharply.
[ ... ]
A similar situation exists in other fields. Consider, for example, evolutionary biology. Like most American intellectuals, I first learned about this subject from the writings of Stephen Jay Gould. But I eventually came to realize that working biologists regard Gould much the same way that economists regard Robert Reich: talented writer, too bad he never gets anything right. Serious evolutionary theorists such as John Maynard Smith or William Hamilton, like serious economists, think largely in terms of mathematical models. Indeed, the introduction to Maynard Smith's classic tract Evolutionary Genetics flatly declares, "If you can't stand algebra, stay away from evolutionary biology." There is a core set of crucial ideas in his subject that, because they involve the interaction of several different factors, can only be clearly understood by someone willing to sit still for a bit of math. (Try to give a purely verbal description of the reactions among three mutually catalytic chemicals.)
But many intellectuals who can't stand algebra are not willing to stay away from the subject. They are thus deeply attracted to a graceful writer like Gould, who frequently misrepresents the field (perhaps because he does not fully understand its essentially mathematical logic), but who wraps his misrepresentations in so many layers of impressive, if irrelevant, historical and literary erudition that they seem profound.
Unfortunately, Maynard Smith is right, both about evolution and about economics. There are important ideas in both fields that can be expressed in plain English, and there are plenty of fools doing fancy mathematical models. But there are also important ideas that are crystal clear if you can stand algebra, and very difficult to grasp if you can't. International trade in particular happens to be a subject in which a page or two of algebra and diagrams is worth 10 volumes of mere words. That is why it is the particular subfield of economics in which the views of those who understand the subject and those who do not diverge most sharply.
http://www.slate.com/id/1911/
Using derivatives to understand marginal analysis is so easy that it's shocking other strategies are even considered. Calculus > Austrianism.
"I'm not a fan of Murray Rothbard." -- David D. Friedman
StrangeLoop,
Austrians have nothing against math or number and you know that. What austrians are against is the very loosy and arrogant methodology used by many of the mainstream where any pretty equation or graph goes . And I've seen mathmeticians and physicist siding with the austrians because they love math and hate to see it so randomly misused by economists.
Vitor: What austrians are against is the very loosy and arrogant methodology used by many of the mainstream where any pretty equation or graph goes .
Claiming that to be the norm of economic scholarship shows prejudice, not evidence.
Vitor:Austrians have nothing against math or number and you know that.
I'm not quite sure about that. I've encountered open hostility (including in my recent reading of Rothbard).
Essentially, if you're claiming that an undisciplined methodology is undesirable, then we agree (and I imagine most economists--mainstream or not--would). Such a criticism does not divide Austrians from others. Where the line is drawn, perhaps, needs to be clearly drawn by Austrian methodologists (e.g., is finding the maximum of a function--i.e., optimization--necessarily a dead end in economic inquiry?).
It might be easy, but it's still wrong. You may not have noticed but even on a conceptual level, both neoclassical and austrian marginal utility are not analogous to each other. The latter referes to a ranking, albeit of the least valued of a good held, or the most valued not served, and these rankings are only made derivative to an ultimate ordinal ranking of ends(with complications arising due to the strict quantiative relations between means and ends and the ratios in which the former can be employed to achieve the latter). Every ranking is made in reference to all others implicitly, and so does every change in marginal utility contains a reference to all others it overlaps. The neoclassical conception of "marginal utility" refers to the partial derivative of the utility function with regard to one of the goods, and floats altogether without such referential content altogether.
In fact, many unsurprisingly, using this definition of marginal utility hardly consider the law a "law" at all, and only a general hypothesis[cf. Baumol, Economics: Principles and Policy p.86-87], with exceptions such as when a man gains more stamps in his collection "approaching" 10. Aside of assuming the relevant consideration of utility (and the one to be relevant for price formation) to be a temporal one comparing past utilities to present when concerning the problem of present price formation, this approach also makes the error of formulating the law of marginal utility with ignorance to human purpose and the quantitative means end relations relevant for achieving action[See Mises, Human Action, p.124-5 for a delightful disquisition on this misunderstanding of the nature of utility].
Indeed, neither is it surprising that the concept important for neoclassicals for price determination is the MRS and not this "floating" partial derivative marginal utility[For an example of this admission of the arbitrary character of this partial derivative and subsequent application along these lines using the MRS, see Varian, Intermediate Microeconomics, p. 65-66 in the 7th edition(International Student Edition)]. The former at least mimics the referential character of the Austrian formulation of law of marginal utility, allowing for the quantity traded to be arrived at the tangency point of the indifference curve for any given price, allowing for general derivation of a demand function from solving the Lagrangian optimisation problem of utility with the budget constraint. What's funny, is this derivation, as a consequence of the chain rule; is invariant of the form of the utility function following any transformation, monotonic or not, or whatever. e^-u(x,y) allows the same demand functions to be derived as for u(x,y), and similarly, to get the actual marginal consideration between 2 goods as one of them increases, the relevant consideration is the diminishing character of the MRS. Interestingly this characteristic was admitted to be a rabbt out of a hat by John Hicks himself in Value and Capital[see Hicks, Sir John Richard; Value and Capital, Chapter I. “Utility and Preference” §8, p23 in the 2nd edition.]. We can understand it rather as a necessary way to replicate the character of the marginal utility law for the Austrians from the mathematical framework of representation disconnected from action utilised by the neoclassicals, since it allows the "referential" marginal utility. Note also, the diminishing character of the MRS, in just the same way the MRS itself is invariant under all transformations as a consequence of the chain rule, can itself be achieved by using negative, increasingly increasing, diminshing utility functions of whatever type you please.
Furthermore, we cannot be anything more than uncertain about the necessary meaning of these mathematical operations on the utility function, since only the latter was established with regard to actual preferences(although not for ends or means, but abstract "bundles" of goods), and this was done via a relation of representation, not of equivalence(On this point, see the following paper by Dan Mahoney).
So yes, perhaps it is "shocking" you don't seem to understand the mathematics you claim to be applying. The Austrians on the other hand have far less of a problem applying mathematics to real things like production. On this point cf. Rothbard's masterful account of the law of returns on p.466-478 of Man, Economy and State. (His derivation, like Stigler's is algebraic, I guess as a matter of taste I would have employed calculus to arrive at the equivalent result).
Wow. Looks like someone has an affinity for using the passive voice ("neither is it surprising??") and talking like they're in the 19th century. Disquition!? trying a little hard, eh?
Honestly, I am only picking up half of what you're throwing down here. It's very hard to understand the points you're making. No offense, but if you pose questions like this in class its probably why your TA gets flumuxed and it certainly isn't his fault.
Anyways, I'll just take this opportunity to warn StrangeLoop to avoid going down the road that post is headed. I know on HeroicLife's old Austrian Econ forum I got into a similar argument about the "real meaning of neoclassical utility, ordinality, etc" that lasted for days before everyone just gave up and quit posting. And that hasn't just been my experience. That's essentially what Bryan Caplan had to do when arguing the same topic with Block and Hulsman after his "Austrian Search for Realistic Foundations Paper" was published. This entire line of conversation is an unsatistfying time suck.
That's why these days I don't even bother getting into it. I figure live and let live. If some rothbardians (not all austrians actually believe this stuff) really want to believe that they don't use neoclassical choice theory because they just have a deeper understanding of mathematics than everyone else on the planet that's fine with me. But I still think it is funny that after all the huffing and puffing about methodology, ordinality, rankings and ties, the conclusions of rothbardian price theory are almost identitical to those of neoclassical price theory.
I say almost because, as Caplan notes, rothbard's approach seems to have a problem with handling income effects of price changes. Of course, that didn't stop Rothbard from lifting the conclusions he desired from neoclassical sources, even if he couldn't be bothered to derive those conclusions himself using his own value scale framework (i'm thinking about the backward bending supply curve for labor). This isn't a small problem. Especially considering that whether income effects *even exist*, let along whether they can actually be replicated in the rothbardian framework, was debated by Rothbardians as recently as *10 years ago!!!!*. What a lovely and clear theory that is, right? Neoclassical economists settled this internally at least 50 or 60 years ago. Welcome to the 1950's guys!!!
Anyways, like I said, not all Austrians are Rothbardians. You won't find any mention of value scales in Peter Leeson's work. Seek out *those* Austrians imo.
But this all just a long winded way of saying that the introduction of this topic my cue to exit, stage riggggghhttt.
Post Script for absk:
"So yes, perhaps it is "shocking" you don't seem to understand the mathematics you claim to be applying"
Strange Loop and the entire mainstream economics profession, right? But neither is it suprising to moi that thee believes that thou is not only smarter than the TA teaching his econometrics class, but the entire economics profession as a whole. Zounds!!!!
This does not constitute a coherent argument and it entirely ignores the actual arguments made by Austrian economists regarding untenable assumptions and general problems associated with mainstream price theory and welfare analysis. Even if mathematics is useful as a demonstrative tool in economics, which I believe it is, the arguments put forth by Mises, Kirzner, and Lachmann still hold.
Basic problems with mainstream price theory:
"If we wish to preserve a free society, it is essential that we recognize that the desirability of a particular object is not sufficient justification for the use of coercion."
if you think that sentence was intended as an argument against any austrian critique, and not a commentary on absk's apparent ego-tripping, then i think you may be posting too late in the evening. take a nap, then give it another shot.
Personally, I always check my cognitive faculties before posting by replicating euler's proof of euclid's theorem. true story!
Student, yes perhaps I do indulge myself with my language nowadays. I find reading older works of literature like I have been introduces me to a vocabulary that also allows me to broaden in a sense the scope of my thinking, but i guess I am being rather "19th century" if you want to use that term in a derogatory sense as it appears.
Furthermore, a lot of the points I made above are rather original to a critique I've been writing(not original to RB or Mises, but inspired by parts of their work though) I presented at a conference and will be presenting to some of my own professors. Neither have I been rude in any of my discussions with my professors, in fact considering one of the points I made using Mises critique'[p.124-5], my econometrics professor acknowledged problems with standard consumer choice theory in describing certain kinds of scenarios like these. I respect that, even though I thought the solution he proposed was rather ad hoc and unsatisfactory, as he alluded to work in consumer demand theory that has been used to produce mathematically exceptional (often discontinuous) utility functions that can account for this kind of behaviour.
In any case when I first saw your post I was looking forward to a good counter argument. Some old forum members like "Neoclassical" could at least provide that. But if you can only resort to ad hominem attacks then whatever. (zounds...)
Actually, my post wasn't all complaints about your writing. I said that after all the huffing and puffing about methodology, rothbard's alternative framework yielded nearly identical positive conclusions to that of neoclassical theory. Are your criticisms different in this regard?
Specifically, do you think your "original critiques of neoclassical choice theory" will overturn any of the typical neoclassical predictions? For example, think about the slutsky equation. Neoclassical choice theory predicts that price changes will be associated with and income effect and a substitution effect. And depending on the size of each of these effects the real-world consequences of a price change of a single good could be ambigious. Do you expect anything different?
They see me writing...I'm trollin'..My math is so loud...they hate it...
Math is not economics. It's that freaking simple. Economics is a teleological science, it has to do with purposivity and not any BS like 'maximization functions' which do not exist.
It's still a work in progress tbh (on that matter I do sincerely apoligise for saying I finished it above, it's the most ambitious piece of work on economic theory I 've attempted yet, and it's been taking me a very long time, so I do often want to say I've finished it...), there are some aspects of what you mentioned with the income and substitution effect that I intend to go into more detail on, but even more so as regards to the backward bending supply curve for example, I show can be derived without having to consider leisure as some sort of strange homogeneous good with inferior proerties and normal properties depending on the level of a person's income. Instead this property is derived simply acknowledging that consumption is the end of all production, and that it takes time which must fit within an actor's general time-horizon(a concept Rohtbard introduces in MES, but doesn't use explicitly for any analytical purposes).
So I guess my answer is: I'm not completely sure yet. Many results are similar, but with different nuances in their formulation and interpretation. Like i said, even though the MRS is a concept without connection to action, due to its referential characteristic, in actually being formulated in a way that allows one to compare both partial derivatives of the utility function in a ratio, it nicely allows one to replicate or mimic some(but not all) of the price clearing conclusions of Bom Bawerkian - Wicksteedian price theory. In a sense this should not necessarily be out of this world surprising.
One of the basic results of logic is the possibility to derive true results from false premises, e.g. all books are dogs, all dogs have pages, therefore all books have pages. A mistake of many positivists is thinking that one can start with premises that one already knows to be false as opposed to real hypotheses(ever seen an atom?), and thinking that one can treat these premises as constructing reliable theories when they yield correct predictions. Doing so is an abject misunderstanding of the scientific method. (Not that I'm claiming either MRS or parital derivative marginal utility to be "false", it's just that we cannot be anything more than unsure about the actual meaning of these identities with regard to actual action, and given what I have alluded to above, we have good reason to have strong reservations about this not being the case).
Finally, perhaps as a "peace offering" in this argument of ours, I can tell you something where I think we do have common ground. I do really think many Austrians(especially younger ones) need to brush up on mathematics and learn it well. A lot of people had much more difficulty with my presentation than I anticipated. Avoiding mathematics was certainly nothing done by the likes of Mises and Rothbard. Indeed I'm pretty sure Mises himself said the best way to avoid the pitfalls of mathematical economists was to properly master mathematics(I think he said the same vis a vis psychology and psychologism).