Teaching Economics Without Calculus

[Auto-Didact]

Doesn’t the Austrian school reject emperical data, though (I mean, they seem fairly adverse to statistics, which are in fact emperical data)?

I wasn't describing the Austrian school, I have no idea if the Austrian school proposes a non-empirical approach to economics. Let's call the school I am describing above the Complexity school for clarity sake.

To play devil's advocate though, rejecting the use of mainstream statistical methodology is a far cry away from directly rejecting empirical data; mainstream statistical methodology is a way of transforming data in order to demonstrate associations and properties of some data, it is certainly not itself empirical data.

 

[FactChecker]

I wasn't describing the Austrian school, I have no idea if the Austrian school proposes a non-empirical approach to economics. Let's call the school I am describing above the Complexity school for clarity sake.

To play devil's advocate though, rejecting the use of mainstream statistical methodology is a far cry away from directly rejecting empirical data; mainstream statistical methodology is a way of transforming data in order to demonstrate associations and properties of some data, it is certainly not itself empirical data.

What kind of analysis can one do with emperical data that would not be called statistics?

 

[Auto-Didact]

What kind of analysis can one do with emperical data that would not be called statistics?

lol are you serious? For one, directly applying mathematics, e.g. geometry to data is not statistics. Or are you claiming that physics and programming are just forms of statistics now? Mainstream statistics is what is learned in statistics courses (hypothesis testing, probabilistic inference, characterising distributions, using p-values, odds ratios, power, etc); it is a way of intra- and extrapolative reasoning in the face of incomplete/uncertain knowledge where this uncertainty is modeled as due to randomness using probability theory.

Moreover, a lot of empirical data is inherently non-numerical, e.g. written and spoken text. I'm not saying that such data can not ever be handled statistically at all (often it is possible), but that statistical handling is often inappropriate, completely misleading or just plain useless in order to actually find the patterns that are being sought; insisting on purely statistical handling for all possible enquiries is an inadequate point of view. Such data can however usually still be gained and analyzed using purely non-quantitative methods, as is done in language, law, ethics and clinical medicine, or analyzed using non-mainstream statistics tools such as techniques from pure mathematics and physics.

 

[FactChecker]

lol are you serious? For one, directly applying mathematics, e.g. geometry to data is not statistics. Or are you claiming that physics and programming are just forms of statistics now? Mainstream statistics is what is learned in statistics courses (hypothesis testing, probabilistic inference, characterising distributions, using p-values, odds ratios, power, etc); it is a way of intra- and extrapolative reasoning in the face of incomplete/uncertain knowledge where this uncertainty is modeled as due to randomness using probability theory.

Moreover, a lot of empirical data is inherently non-numerical, e.g. written and spoken text. I'm not saying that such data can not ever be handled statistically at all (often it is possible), but that statistical handling is often inappropriate, completely misleading or just plain useless in order to actually find the patterns that are being sought; insisting on purely statistical handling for all possible enquiries is an inadequate point of view. Such data can however usually still be gained and analyzed using purely non-quantitative methods, as is done in language, law, ethics and clinical medicine, or analyzed using non-mainstream statistics tools such as techniques from pure mathematics and physics.

I was just asking. Does that mean that you would draw conclusions from one set of numbers or from one example as an anecdote? If not, how would you use multiple sets of numbers? My impression of economics is that there is a great deal of random variation and that one set of data would not be adequite.

 

[Sorcerer]

lol are you serious? For one, directly applying mathematics, e.g. geometry to data is not statistics. Or are you claiming that physics and programming are just forms of statistics now? Mainstream statistics is what is learned in statistics courses (hypothesis testing, probabilistic inference, characterising distributions, using p-values, odds ratios, power, etc); it is a way of intra- and extrapolative reasoning in the face of incomplete/uncertain knowledge where this uncertainty is modeled as due to randomness using probability theory.

Moreover, a lot of empirical data is inherently non-numerical, e.g. written and spoken text. I'm not saying that such data can not ever be handled statistically at all (often it is possible), but that statistical handling is often inappropriate, completely misleading or just plain useless in order to actually find the patterns that are being sought; insisting on purely statistical handling for all possible enquiries is an inadequate point of view. Such data can however usually still be gained and analyzed using purely non-quantitative methods, as is done in language, law, ethics and clinical medicine, or analyzed using non-mainstream statistics tools such as techniques from pure mathematics and physics.

There appears to be some sort of disconnect between what you are saying and what I am interpreting, so, can you give specific examples of all the things you are describing?

For example, could you show specific examples where economic statistics and their applications are not based on empirical data, including whatever mathematical analysis comes with it and the source of the data? And why they are not useful?

Or, perhaps, show specific physics equations that are used in economics and demonstrate why they are either inherently invalid or inherently of no use?

 

[fresh_42]

I guess one could avoid calling it calculus, but how can a person do much in economics without discussing rates (derivatives) and cumulative amounts (integrals)?

They (economists) can't. At least they don't. They call it indeed differently, at least here, and yes cumulative was among the words they used. I've stumbled upon all kind of limit words: limit costs, limit profits, limit prices and so on. All have turned out to be derivatives. Without the limit, they put difference in front: difference costs, difference profits and so on. It was irritating. On the other hand, the word derivative would have probably irritated them. The funny part is, that many students started to study economics because they were bad in math, only to be confronted to even more math. Their standard program in the first year was statistics I&II and mathematics I&II which was basically calculus. Now many of these math refugees then turned towards macro-economics. But the models there are even more math: differential equations of all kind, calculus of invariants and so forth. Usually they ended up in legal science.

 

[Sorcerer]

They (economists) can't. At least they don't. They call it indeed differently, at least here, and yes cumulative was among the words they used. I've stumbled upon all kind of limit words: limit costs, limit profits, limit prices and so on. All have turned out to be derivatives. Without the limit, they put difference in front: difference costs, difference profits and so on. It was irritating. On the other hand, the word derivative would have probably irritated them. The funny part is, that many students started to study economics because they were bad in math, only to be confronted to even more math. Their standard program in the first year was statistics I&II and mathematics I&II which was basically calculus. Now many of these math refugees then turned towards macro-economics. But the models there are even more math: differential equations of all kind, calculus of invariants and so forth. Usually they ended up in legal science.

And here is where you find another very practical reason for economics majors to take calculus and higher level math (and it's the same reason we want doctors to as well): to weed out the, how can I delicately put this, less talented people.

Long story short: if you can't handle something as easy as elementary calculus, and even beyond that, to the upper division undergrad math courses, IMHO you have no business putting your hands in anyone's economy in any way, shape or form. The career is not for you. Move to a Business major or the humanities or <insert group> studies.

 

[Auto-Didact]

I was just asking. Does that mean that you would draw conclusions from one set of numbers or from one example as an anecdote? If not, how would you use multiple sets of numbers? My impression of economics is that there is a great deal of random variation and that one set of data would not be adequite.

Ah pardon me then. Yes, things like drawing conclusions from a few interviews, anecdotes and observations. The resulting data sets (video/audio-recording) tends to be non-numeric, not clearly generalizable and nowhere near identical between and within subjects, but by use of transcription, coding and analysis, it is possible to identify recurring broad themes. This empirical methodology is called qualitative research as opposed to quantitative research (i.e. simple statistics) and it has been used for decades now in many of the sciences, but particularly in market research, sociology, education and artificial intelligence (data mining from human experts in order to make expert systems).

There appears to be some sort of disconnect between what you are saying and what I am interpreting, so, can you give specific examples of all the things you are describing?

For example, could you show specific examples where economic statistics and their applications are not based on empirical data, including whatever mathematical analysis comes with it and the source of the data? And why they are not useful?

Or, perhaps, show specific physics equations that are used in economics and demonstrate why they are either inherently invalid or inherently of no use?

You are misinterpreting what I am saying. I never claimed economic analysis is not based on empirical data. Reread what I said. I can however give you an example that premature and overt mathemization, in order to superficially resemble physics and so seem more scientific, can make and has clearly made economic analysis lead to axiomatic reasoning which is not just inaccurate but inappropriate altogether. Even worse taking the resulting calculations serious requires selectively ignoring empirical data or transforming it in such a way that it can be ignored.

Example: There has long been an assumption that risk follows a normal distrubution, i.e. Gaussian distribution. This has led to a systematic undervaluation of risks and gross underestimation of the frequency of crises. The reason for assuming normality of course is due to many factors, among others that it is mathematically more simple and partly a result of misapplying and/or misunderstanding the central limit theorem.

Many economic theoretical constructs, like volatility and risk, are nothing more than relabeled statistical concepts like variances and standard deviations in the setting of the normal distribution. Furthermore, much of financial theory is based on this same assumption of normality, most importantly the Black-Scholes equation (BSE), Modern Portfolio Theory (MPT) and the Efficient Market Hypothesis (EMH).

Regarding the EMH, read this paper on arxiv, which shows that among other things that gauge theoretic methods can be used to study curvutare in economic markets and so make money through arbitrage: https://arxiv.org/abs/0902.4274
Standard economic theory of course just claims arbitrage is impossible due to the EMH based on elegant but misleading proofs, which are mathematically sophisticated but have little to do with actual empirical economics (NB: this is analogous to von Neumann's proof of no hidden variables in QM, which is mathematically correct but physically unrealistic).

Like physics, it is posited that these theories (MPT, BSE, EMH) and equations describe economic phenomena, but unlike physics, these theories and their equations are not themselves based on empirical data. They are instead mathematical equations assumed a priori to be valid on the basis of simplicity and ignorance of alternatives, i.e. complete lack of understanding of higher mathematical probability theory. Data which is gathered is fitted to these equations, instead of finding equations which match data and discarding equations that don't, as is done in experimental science. Economists have no experience whatsover of doing experimental science outside of doing simple statistics and simple regression analysis; they will even tell you that that is all experiment is. Practically any undergraduate physics experiment course is far too complicated for them to even try analyzing, while these physical systems tend to be much simpler systems than the economic systems that economists claim to understand.

The result is that economic theory seems because of its mathematical form more scientific than it is, when its core concepts are treated as unquestionable principles when they are actually unjustifiable hypotheses in direct contradiction with experience. An example is the frequency of crises predicted on the basis of crisis frequency following a normal distribution opposed to empirical data of the frequency of crises. A correct analysis required a higher mathematical sophistication than what is taught in economics courses.

What economists should have done to prevent this catastrophe, but didn't do, is start out by actually learning graduate level higher stochastics and mathematical Probability Theory before constructing their theories. Instead it seems they just learned high school level statistics i.e. how to calculate probablities, means and variances using the normal distribution and then relabeled these things as key concepts in economic theory. (NB: this is comparable to physics prior to Newton, where statistical observation led to the mathematically precise Ptolemaic theory of epicycles in celestial mechanics, which in terms of physics was of course pure nonsense.)

Luckily things are starting to change, albeit slowly. Failures of standard economic and financial theory such as above, have crept into curricula and some quick fixes are cooked up for special scenarios, but these fixes tend to be fighting the symptoms, not fighting the disease. And since the late 20th century, at the forefront there are physicists and mathematicians who are trying to reform the entire science of economics completely from the ground up (they are the Complexity school of economics), simply because the problem is a dire one and it doesn't seem economists are willing or capable of solving it themselves. This is not purely an altruistic act on the part of these physicists and mathematicians: developing the correct mathematical theories of economics is almost guaranteed to solve the outstanding theoretical physics problem of open system non-equilibrium statistical mechanics.

The late mathematician Benoit Mandelbrot, discoverer of fractal geometry, has done much work on elucidating the correct mathematics needed for economics. It isn't an exaggeration to say that almost all of econophysics/complexity economics research carried out today are direct offshoots in some manner of Mandelbrot's work. Here is what late MIT economist Paul Cootner said about Mandelbrot's work:

Mandelbrot, like Prime Minister Churchill before him, promises us not utopia but blood, sweat, toil and tears. If he is right, almost all of our statistical tools are obsolete—least squares, spectral analysis, workable maximum-likelihood solutions, all our established sample theory, closed distributions. Almost without exception, past econometric work is meaningless.

 

[FactChecker]

Here is what late MIT economist Paul Cootner said about Mandelbrot's work:
"Mandelbrot, like Prime Minister Churchill before him, promises us not utopia but blood, sweat, toil and tears. If he is right, almost all of our statistical tools are obsolete—least squares, spectral analysis, workable maximum-likelihood solutions, all our established sample theory, closed distributions. Almost without exception, past econometric work is meaningless."

I guess I'm skeptical that they have anything better to replace it with. But it is not my field of expertise.

 

[Auto-Didact]

I'm not an expert either, just an interdisciplinary researcher (trained as a physicist) who happens to have tutored a few economics/finance students.

For those interested I do want to mention one recent alternative: multifractal analysis in finance, here's a review from arxiv: https://arxiv.org/abs/1805.04750

 

[FactChecker]

For those interested I do want to mention one recent alternative: multifractal analysis in finance, here's a review from arxiv: https://arxiv.org/abs/1805.04750

Thanks. That gives me a good idea of the directions that they might be going in. (Even if my understanding is rudimentary.) And it does sound legitimate to me.

 

[fresh_42]

The result is that economic theory seems because of its mathematical form more scientific than it is, when its core concepts are treated as unquestionable principles when they are actually unjustifiable hypotheses in direct contradiction with experience.

In my opinion you're mixing a lot of different subjects here in order to make your point. First of all there is a difference between micro and macro economics. The science of national economies is indeed rather complex and involves many mathematical tools like chaos theory, differential equation systems and so on. However, economics itself in the micro sector is about prize building, structure of costs, balances etc. which are all rudimentary arithmetic dependencies which can and are described by basic algebra and basic calculus. The calculus of costs doesn't need chaos theory, but it needs calculus - at least basic calculus. On the other hand if we turn towards macro economic models, things quickly become not only mathematical more complex, but hypothetical as well. Which model applies under which circumstances to predict which behavior of the markets can in large parts only be answered by experiences rather than by strict models (opinion). Think of chartists e.g., they haven't gone away, regardless what has been undertaken to get good models.

So to confuse all these in their most general sense economic questions, will inevitably lead to the arguments which we observe in this thread. It is foul play, because it compares incomparable subjects. Another point is, that probability theory can as well be considered a part of analysis. The two don't have to be complementary: they meet in measure theory. This separation again leads into a discussion which at its kernel is meaningless. I think the answer to ...

Can you really teach economics without calculus?

... is a straight NO. Not because of the fact, that statistics, probability, game and chaos theory weren't needed to understand macro economic phenomena, but because calculus is needed for the everyday business in the micro economic field of calculations done by the financial departments and controllers in all companies. Therefore it is necessary. Nobody has claimed, that calculus alone can solve every macro economic question, and to conclude from the existence of e.g. chaos theory in market research the non-necessity of calculus in general is in my opinion just nonsense.

 

[Auto-Didact]

In my opinion you're mixing a lot of different subjects here in order to make your point. First of all there is a difference between micro and macro economics. The science of national economies is indeed rather complex and involves many mathematical tools like chaos theory, differential equation systems and so on. However, economics itself in the micro sector is about prize building, structure of costs, balances etc. which are all rudimentary arithmetic dependencies which can and are described by basic algebra and basic calculus. The calculus of costs doesn't need chaos theory, but it needs calculus - at least basic calculus. On the other hand if we turn towards macro economic models, things quickly become not only mathematical more complex, but hypothetical as well. Which model applies under which circumstances to predict which behavior of the markets can in large parts only be answered by experiences rather than by strict models (opinion). Think of chartists e.g., they haven't gone away, regardless what has been undertaken to get good models.

So to confuse all these in their most general sense economic questions, will inevitably lead to the arguments which we observe in this thread. It is foul play, because it compares incomparable subjects. Another point is, that probability theory can as well be considered a part of analysis. The two don't have to be complementary: they meet in measure theory. This separation again leads into a discussion which at its kernel is meaningless. I think the answer to ...

... is a straight NO. Not because of the fact, that statistics, probability, game and chaos theory weren't needed to understand macro economic phenomena, but because calculus is needed for the everyday business in the micro economic field of calculations done by the financial departments and controllers in all companies. Therefore it is necessary. Nobody has claimed, that calculus alone can solve every macro economic question, and to conclude from the existence of e.g. chaos theory in market research the non-necessity of calculus in general is in my opinion just nonsense.

I never claimed non-necessity of calculus for economics, I do not adhere to the Austrian school. Quite the contrary, I am claiming, as is the Complexity school, the necessity of basically the entire physics undergraduate curriculum supplanted with fractal geometry, modern network theory, nonlinear dynamics and possibly also differential geometry and symplectic geometry.

Also I'm speaking about macroeconomics, the microeconomic situation is for the birds. The extrapolation of the micro to macro situation unfortunately wasn't as simple as it was in thermodynamics. And I agree, the survival of chartists are a clear demonstration that most financial economic and econometric models (certainly the non-complexity/chaos science based ones) are clearly inadequate, or just terrible approximations.

These models such as GARCH, NARMAX etc are clear indications that blindly increasing mathematical sophistication without rethinking fundamental concepts and postulates in economics is the wrong method of going about solving the problem. Just imagine if physics theories were made on the basis of such infinitely tunable free parameters...

 

[Auto-Didact]

And here is where you find another very practical reason for economics majors to take calculus and higher level math (and it's the same reason we want doctors to as well): to weed out the, how can I delicately put this, less talented people.

I used to have the same perspective as you before finishing medical school. During clinical rounds and especially after finishing it, my point of view has changed enormously. Biomedical research has tonnes to learn from calculus/physics, but clinical doctors have practically nothing to benefit from knowing calculus if they aren't involved in research.

They (economists) can't. At least they don't. They call it indeed differently, at least here, and yes cumulative was among the words they used. I've stumbled upon all kind of limit words: limit costs, limit profits, limit prices and so on. All have turned out to be derivatives. Without the limit, they put difference in front: difference costs, difference profits and so on. It was irritating. On the other hand, the word derivative would have probably irritated them. The funny part is, that many students started to study economics because they were bad in math, only to be confronted to even more math. Their standard program in the first year was statistics I&II and mathematics I&II which was basically calculus. Now many of these math refugees then turned towards macro-economics. But the models there are even more math: differential equations of all kind, calculus of invariants and so forth. Usually they ended up in legal science.

There is a general theme I see among economic students and economists:
they do not really care how the economy works. Contrast this with physics students and physicists who seem to be obsessed with learning and figuring out how nature works, so obsessed they will willingly learn tonnes of abstruse mathematics.

They also tend to have an aesthetic appreciation of mathematics and get enjoyment from finding novel patterns, this is culminated in the goal of theoretical and mathematical physics. Contrast this again with the goals of economics students and economists, i.e. making money and having a career. I think this explains a lot about the state of economic science.

 

[bhobba]

I guess one could avoid calling it calculus, but how can a person do much in economics without discussing rates (derivatives) and cumulative amounts (integrals)?

A key concept in economics is marginal rate. Consider the utility of a product. The marginal utility would be how much the the utility varies when the product changes by one. That's the English version - calculus version - derivative. It is normally increasing - but the rate of increase gets smaller as the amount of product increases. That's now trivial with calculus - the first derivative is positive and the second derivative negative. As can be seen it makes understanding concepts easier. Instead of saying its concave increasing and drawing graphs to illustrate it - you know what it means immediately. You probably will still do it anyway to reinforce intuition but its easier with the calculus definitions.

Thanks
Bill

 

[bhobba]

Contrast this again with the goals of economics students and economists, i.e. making money and having a career. I think this explains a lot about the state of economic science.

Mathematicians like Mandelbrot warned about some of the methods used by those that got carried away with the beauty and power of the concepts used in creating the derivatives that blew up and created the global financial crises. The error was the statistical models, taking the central limit theorem at face value, assumed normal distributions. Mandelbrot showed that was not true - it wasn't normal - it had fat tails. The reason the theorem failed is you need to look at its assumptions. It requires independence. But with dollars clouding their judgement they ignored this fundamental fact.

Thanks
Bill

 

[BWV]

To be fair, economics is a lot more complicated than physics. Everything knowable about subatomic particles can be defined completely by math, whereas economics is a historical and social science. What use is math in determining the causes of WW1? - there is none, and that question is not far removed from why was there a global financial crisis in 2008. Economics is in that grey area between something where a legal / historical type of qualitative analysis rules and a quantitative / statistical discipline. Calculus is useful for models but the models are just that, they are not like theories in physics. The only quantitative 'truths' in economics are accounting identities that rely on simple arithmetic.

 

[Auto-Didact]

To be fair, economics is a lot more complicated than physics. Everything knowable about subatomic particles can be defined completely by math, whereas economics is a historical and social science. What use is math in determining the causes of WW1? - there is none, and that question is not far removed from why was there a global financial crisis in 2008.

Historical course making a difference is not as mathematically foreign as one would think, it actually is equivalent to having a path-dependent description, in direct opposition to the path-independence characteristic of classical physics when doing line integrals in conservative vector fields. All of this is part of undergraduate calculus theory, perhaps more expanded upon in analysis, and known as non-conservative vector fields. This can be generalized in a multitude of ways using among others differential geometry and exterior derivatives.

In any case, what you are saying is exactly why an actual economic theory requires more advanced mathematics than is used in physics. If the day came that economists could model their theories anywhere close to how physicists are able to model their theories i.e. even utilizing and developing special branches of mathematics in this process, then most of physics would seem like a joke to economists. Suffice to say, economic science today is nowhere close to being able to do this.

 

[BWV]

Historical course making a difference is not as mathematically foreign as one would think, it actually is equivalent to having a path-dependent description, in direct opposition to the path-independence characteristic of classical physics when doing line integrals in conservative vector fields. All of this is part of undergraduate calculus theory, perhaps more expanded upon in analysis, and known as non-conservative vector fields. This can be generalized in a multitude of ways using among others differential geometry and exterior derivatives.

In any case, what you are saying is exactly why an actual economic theory requires more advanced mathematics than is used in physics. If the day came that economists could model their theories anywhere close to how physicists are able to model their theories i.e. even utilizing and developing special branches of mathematics in this process, then most of physics would seem like a joke to economists. Suffice to say, economic science today is nowhere close to being able to do this.

One can say most anything using mathematics, but it is often meaningless to do so. Your observation about line integrals is an analogy, not a route to a predictive model. Confused about rest of your post makes no sense. Biology studies far more complex systems than physics (but still less complex than economics)- should biology be using more complex math than theoretical physics? Its simple things, like electrons, that lend themselves to complex mathematical relationships. I have a book on my desk called The Physics of Finance where the author uses Fibre Bundles to model foreign exchange conversions - perhaps this is a productive analogy for introducing finance to people with PhDs in physics, but is worthless to anyone else. People in quantitative sciences overvalue math because it perfectly describes everything in their field, but that is not the case for most disciplines.

 

[Sorcerer]

Ah pardon me then. Yes, things like drawing conclusions from a few interviews, anecdotes and observations. The resulting data sets (video/audio-recording) tends to be non-numeric, not clearly generalizable and nowhere near identical between and within subjects, but by use of transcription, coding and analysis, it is possible to identify recurring broad themes. This empirical methodology is called qualitative research as opposed to quantitative research (i.e. simple statistics) and it has been used for decades now in many of the sciences, but particularly in market research, sociology, education and artificial intelligence (data mining from human experts in order to make expert systems).
You are misinterpreting what I am saying. I never claimed economic analysis is not based on empirical data. Reread what I said. I can however give you an example that premature and overt mathemization, in order to superficially resemble physics and so seem more scientific, can make and has clearly made economic analysis lead to axiomatic reasoning which is not just inaccurate but inappropriate altogether. Even worse taking the resulting calculations serious requires selectively ignoring empirical data or transforming it in such a way that it can be ignored.

Example: There has long been an assumption that risk follows a normal distrubution, i.e. Gaussian distribution. This has led to a systematic undervaluation of risks and gross underestimation of the frequency of crises. The reason for assuming normality of course is due to many factors, among others that it is mathematically more simple and partly a result of misapplying and/or misunderstanding the central limit theorem.

Many economic theoretical constructs, like volatility and risk, are nothing more than relabeled statistical concepts like variances and standard deviations in the setting of the normal distribution. Furthermore, much of financial theory is based on this same assumption of normality, most importantly the Black-Scholes equation (BSE), Modern Portfolio Theory (MPT) and the Efficient Market Hypothesis (EMH).

Regarding the EMH, read this paper on arxiv, which shows that among other things that gauge theoretic methods can be used to study curvutare in economic markets and so make money through arbitrage: https://arxiv.org/abs/0902.4274
Standard economic theory of course just claims arbitrage is impossible due to the EMH based on elegant but misleading proofs, which are mathematically sophisticated but have little to do with actual empirical economics (NB: this is analogous to von Neumann's proof of no hidden variables in QM, which is mathematically correct but physically unrealistic).

Like physics, it is posited that these theories (MPT, BSE, EMH) and equations describe economic phenomena, but unlike physics, these theories and their equations are not themselves based on empirical data. They are instead mathematical equations assumed a priori to be valid on the basis of simplicity and ignorance of alternatives, i.e. complete lack of understanding of higher mathematical probability theory. Data which is gathered is fitted to these equations, instead of finding equations which match data and discarding equations that don't, as is done in experimental science. Economists have no experience whatsover of doing experimental science outside of doing simple statistics and simple regression analysis; they will even tell you that that is all experiment is. Practically any undergraduate physics experiment course is far too complicated for them to even try analyzing, while these physical systems tend to be much simpler systems than the economic systems that economists claim to understand.

The result is that economic theory seems because of its mathematical form more scientific than it is, when its core concepts are treated as unquestionable principles when they are actually unjustifiable hypotheses in direct contradiction with experience. An example is the frequency of crises predicted on the basis of crisis frequency following a normal distribution opposed to empirical data of the frequency of crises. A correct analysis required a higher mathematical sophistication than what is taught in economics courses.

What economists should have done to prevent this catastrophe, but didn't do, is start out by actually learning graduate level higher stochastics and mathematical Probability Theory before constructing their theories. Instead it seems they just learned high school level statistics i.e. how to calculate probablities, means and variances using the normal distribution and then relabeled these things as key concepts in economic theory. (NB: this is comparable to physics prior to Newton, where statistical observation led to the mathematically precise Ptolemaic theory of epicycles in celestial mechanics, which in terms of physics was of course pure nonsense.)

Luckily things are starting to change, albeit slowly. Failures of standard economic and financial theory such as above, have crept into curricula and some quick fixes are cooked up for special scenarios, but these fixes tend to be fighting the symptoms, not fighting the disease. And since the late 20th century, at the forefront there are physicists and mathematicians who are trying to reform the entire science of economics completely from the ground up (they are the Complexity school of economics), simply because the problem is a dire one and it doesn't seem economists are willing or capable of solving it themselves. This is not purely an altruistic act on the part of these physicists and mathematicians: developing the correct mathematical theories of economics is almost guaranteed to solve the outstanding theoretical physics problem of open system non-equilibrium statistical mechanics.

The late mathematician Benoit Mandelbrot, discoverer of fractal geometry, has done much work on elucidating the correct mathematics needed for economics. It isn't an exaggeration to say that almost all of econophysics/complexity economics research carried out today are direct offshoots in some manner of Mandelbrot's work. Here is what late MIT economist Paul Cootner said about Mandelbrot's work:

I think I confused you with the other guy, because you seem to be saying not that economics math is too complicated, just that it is wrong (and possibly not sophisticated enough).

As I see it, given the immense amount of variables inherent to economics, a “correct” theory would have to have the most sophisticated mathematical formulation there is. But then I know very little of the subject.

I still believe, however, that all economics students should be forced to run the gauntlet of mathematics during the course of their education. The worst it would do is weed out the people who should be business majors instead.

 

[Sorcerer]

I used to have the same perspective as you before finishing medical school. During clinical rounds and especially after finishing it, my point of view has changed enormously. Biomedical research has tonnes to learn from calculus/physics, but clinical doctors have practically nothing to benefit from knowing calculus if they aren't involved in research.

Yeah, but they function as gateway courses. For example, we presumably only want reasonably smart people as doctors, etc. If you can’t pass elementary calculus as an undergrad, you have no business diagnosing someone’s illness, IMHO.

 

[bhobba]

I was just asking. Does that mean that you would draw conclusions from one set of numbers or from one example as an anecdote? If not, how would you use multiple sets of numbers? My impression of economics is that there is a great deal of random variation and that one set of data would not be adequite.

If you haven't studied it I can see how its a reasonable question.

Typically the type of thing you want to do is find the amount of some product that optimizes a utility function. You want to answer questions like does such an optimum exist, is it worthwhile even producing at all, if it exists what is the value. Sometimes a correct calculus based analysis shows some surprising things. As I mentioned you might think your best profit is what maximizes the profit per thing you are producing. Seems reasonable doesn't it? But its wrong.

Can I suggest people that don't have experience in this simply have a look at the few units of the course. Its in EDX under Principles Economics With Calculus then ask something that not's clear ie why is this easier than doing it with words. When you see the material that's a pretty easy question to answer - but it may still not be clear:
https://www.edx.org/

Thanks
Bill

 

[bhobba]

and that question is not far removed from why was there a global financial crisis in 2008.

Actually math is central to that - as I explained in another post it was caused by too much faith in beautiful mathematics used in securitising low grade investments and greed clouding what should have been done ie carefully checking the math they were using.. High profile experts like Mandelbrot did and warned about it, but with dollar signs clouding their vision he was ignored. He has seen it all before. When he was a junior researcher at IBM someone come up with a surefire way to make money on the stock market. They ran simulation after simulation and it never failed. But as a final check they gave it to him and he spotted the issue immediately - they did not take into account transaction costs. When that was done it failed. That is not to say math can't be used for such things - look into a mathematician called Jim Simons - you will find it interesting.

Thanks
Bill

 

[bhobba]

Yeah, but they function as gateway courses. For example, we presumably only want reasonably smart people as doctors, etc. If you can’t pass elementary calculus as an undergrad, you have no business diagnosing someone’s illness, IMHO.

Can we stay on topic please. Basic knowledge of Economics IMHO is necessary for all citizens - the question here is can it really be taught properly without some basic calculus. There will undoubtedly be people that simply find calculus too hard and other ways of teaching it need to be found for them. Personally I think they are rare - basic calculus is not that hard - the vast majority of people can do it. Contrast this with an interesting debate going on where I live that English is necessary to go to university. Here English means literature. I do not agree - I think professional communication is what is required. But this thread is not the place to discuss it - I simply mention it as a related issue that is off topic and is the type of thing we must watch out for to stay on track.

Thanks
Bill

 

[FactChecker]

If you haven't studied it I can see how its a reasonable question.

Typically the type of thing you want to do is find the amount of some product that optimizes a utility function. You want to answer questions like does such an optimum exist, is it worthwhile even producing at all, if it exists what is the value. Sometimes a correct calculus based analysis shows some surprising things. As I mentioned you might think your best profit is what maximizes the profit per thing you are producing. Seems reasonable doesn't it? But its wrong.

Thanks. Actually, @Auto-Didact mentioned multifractal analysis, which opened my eyes to an entirely new (to me) line of analysis. ( https://en.wikipedia.org/wiki/Multifractal_system )
And I admit that there may be other analysis subjects that I am not aware of.

 

[BWV]

Actually math is central to that - as I explained in another post it was caused by too much faith in beautiful mathematics used in securitising low grade investments and greed clouding what should have been done ie carefully checking the math they were using.. High profile experts like Mandelbrot did and warned about it, but with dollar signs clouding their vision he was ignored. He has seen it all before. When he was a junior researcher at IBM someone come up with a surefire way to make money on the stock market. They ran simulation after simulation and it never failed. But as a final check they gave it to him and he spotted the issue immediately - they did not take into account transaction costs. When that was done it failed. That is not to say math can't be used for such things - look into a mathematician called Jim Simons - you will find it interesting.

Thanks
Bill

Yes, that was my point, just as you cannot reduce an the causes of WW1 to some mathematical analysis, there was no math used in your explanation of what caused the financial crisis.

 

[bhobba]

Yes, that was my point, just as you cannot reduce an analysis of the causes of WW1 to some mathematical analysis, there was no math used in your explanation of what caused the financial crisis.

I gave it my like - but IMHO its cause was too much FAITH in flawed math. Math doesn't explain why you would do that - but it was indeed caused by faith in flawed math. So in one sense you are correct - in another not.

Economics can use math to explain what a rational person should do but not why they can be, and often are, irrational. I was speaking to my doctor yesterday and he mentioned Freudian Analysis has been totally discredited yet especially in the US tons of Psychiatrists use it. Board Certified Psychiatrists must pass exactly the same exam as Neurologists in the US - they are no dummies - yet many use a totally discredited method. What is the modern approach? Well aside from diseases caused by a brain chemical issues eg bipolar disorder, it's to find something that simply is not logical. The tension and worry because they really know its illogical, is what needs to change to fix it. I have a number of those but that is getting way off topic. When you realize that you see math can never explain human behavior, just help in finding the best behavior if you are rational. Many are not.

Thanks
Bill

 

[BWV]

Yes, but I would argue that every actor in the mortgage supply chain, from the borrower to the mid-level bankers to the corporate execs to the institutional investors who bought the paper acted rationally under the incentives they had at the time

Not arguing that the economic models of rational behavior (which employ calculus) are not useful, but they are not the analogs of physical theories

in physics, the usefulness of your model is not impacted by other physicists trying to game it

 

[bhobba]

The last post was on Tuesday, its now Sunday so I think it can now be closed. Its been milked pretty dry IMHO. But of course if anyone wants to add something drop me a line.

Thanks
Bill