Friday, July 24, 2009

A Challenge To (Non-Austrian) Readers

Last month I had a quiz for readers about interest rates, and wrote that I might have more of them, but not necessarily about interest rates.

Now I have a new one, though it differs in important aspects from the previous quiz. Most importantly perhaps is that while I knew the answer the last time, I don't know the answer this time. Or more correctly, I don't think there is an answer. The reason I am having this quiz is to make me more sure about this: To either confirm the belief by absence of valid answers, or to finally enable me to see at least some positive aspects of this practice.

The question is about the use of mathematical modeling in economics. I have repeatedly pointed out the problems with that approach (for example here). What really strikes me though is that I have yet to find a single advocate of that approach really point to any positive function with it in helping to understand the real world. I have directly asked a lot of them, both teachers and others, yet no one has come up with a positive answer.

Usually they have either chosen to ignore the question (as was the case when I asked Menzie Chinn about it in this comment thread), or they come up with irrelevant answers. Examples of the latter include that they think the math is (and I quote) "beautiful" (Which is nice for them, but not for those of us with different esthetical preferences), that math is more "precise" (Which might be true in some cases (though not all), and even in those cases this comes at the cost of the realism of the theory) or that in order to be a science, economics must use math (which is nonsense, as there are lots of sciences that don't use math).

Some defenders also try to deter criticism by the use of insulting hints about the intelligence of heretics. Another line of defense against critics that point to the unrealism created by mathematical modeling is that bad theories have arisen without mathematical modeling. That is true, but is no real defense of the practice, anymore than the fact that some people die prematurely even though they receive good medical care is a defense of the use of witchcraft to cure diseases. Verbal praxeological reasoning enables you to reach the truth, but since people can do it wrong it doesn't guarantee it. Mathematical modeling will by contrast at best (like witchcraft in the case of medical care) be useless in reaching the truth, and will usually be counterproductive.

The quiz, or challenge here, is then for someone to name a (or several) theoretical insight about the real world that mathematical modeling has produced. Obviously, "theoretical insights" that are unrealistic don't count. And neither does empirical findings through econometrics count, as they, even if valid in some sense, are not theoretical. I'll return later to that issue. For now, the focus will be on theoretical mathematical modeling. Since the Austrian part of my readership presumably agrees with me, they will likely be as unable as I am to name a theoretical insight about the real world created through mathematical modeling. The question here is then whether any of the many non-Austrians that I know are reading this will be able to come up with a valid example. I doubt it, but I will find attempts to do so interesting.


Blogger Nima Mahdjour said...

The greatest insight into the real world that mathematical modeling has rendered is the following:

It has shown us how insufficient and useless mathematical modeling is when it comes to understanding economics.

11:18 PM  
Blogger Kevin Feasel said...

Even though I don't count (seeing as how I'm an Austrian reader), I figured I could still try and see if I win any prizes...

When I asked the same question (for the same reason you ask) to an old professor of mine, his response was Ricardian Equivalence. Yeah, the idea did exist long before Robert Barro's proof, but Ricardo himself rejected it.

A less powerful but still reasonable response would, I think, be Robert Lucas's critique of the Phillips Curve and possibly Sargent & Wallace's Policy Ineffectiveness Proposition. These, admittedly, use Rational Expectations, which aren't all that realistic, but as real-world principles, the Lucas Critique is obviously correct.

12:39 AM  
Blogger The Arthurian said...

My background is in mathematics; my skills made economics immediately fascinating to me when I finally looked to it. I am comfortable with economists who use math to express relationships succinctly. I am uncomfortable when math is used to calculate economic results. I am not comfortable, for example, with Mandelbrot's The (Mis)Behavior of Markets, for it seems to me just too tempting to substitute his calculation for the actual world, and make decisions based upon calculation instead of reality.

Further, if mathematics is to be used, it must be used by those who will not misunderstand it. I am thinking in particular of Irving Fisher's equation. As Galbraith presents it in The Age of Uncertainty, we have

MV + M'V'
P = -----------

And as Friedman presents it in Money Mischief:


Friedman has oversimplified the equation. I may have it wrong, but it seems to me Friedman's version considers only final spending. "Income velocity," he calls it. By contrast, Galbraith's form considers total spending (final and non-final) and is clearly a much more honest measure of "how many times the average dollar is spent." My objection is that Friedman's form is worthless, and that it has been simplified because he (or he suspects his reader) fails to understand the significance of the arithmetic. And this is a simple case.

This is perhaps my third comment on Stefan Karlsson's blog. From the first, however, it was clear to me that I am an amateur in the presence of professionals. So I keep my comments to a minimum. I note, however, that Irving Fisher was "a learned mathematician" as Galbraith puts it. So perhaps there is hope for me. Meanwhile, I come here because here I have proof that there is indeed intelligent life on this planet.

Stefan writes: "The question is about the use of mathematical modeling in economics. I have repeatedly pointed out the problems with that approach .... What really strikes me though is that I have yet to find a single advocate of that approach really point to any positive function with it in helping to understand the real world. I have directly asked a lot of them, both teachers and others, yet no one has come up with a positive answer."

I'd like to take a crack at that, sir. In particular, I'd like to offer a simple mathematical analysis of the U.S. economy. It is how I understand the real world, and I expect it can help others understand it as well. Only 12 pages... Your choice:




2:23 AM  
Blogger stefankarlsson said...

Kevin, I have taken advanced macro courses (where focus has been on New Classical and New Keynesian mathematical models) and where the subject of Ricardian equivalence was discuseed, but I don't think I ever heard the teacher or the textbook or anyone else claim that Robert Barro theoretically proved Ricardian equivalence. Instead, it was pointed out (using verbal logic before the mandatory translation of it into differential equations with Greek letters) that there are good reasons to believe it won't hold, such as population growth, limited life span, borrowing constraints etc. I would have thought the relevance of these factors would be empirical. Has Barro somehow mathematically proved that these factors must always in all empirical circumstances be irrelevant? If so, how?

The Lucas critique really doesn't count as it is based on unrealistic assumptions. While the conclusion that government can't achieve a permanent increase in employment through inflation is basically true, it arives to that conclusion in a twisted way. Using Austrian economics it can be demonstrated that through malinvestments employment will in the long run often be lowered by increased inflation. The Lucas critique says nothing of this.

And the Policy Ineffectiveness Proposition is even worse, with its assumptions of the neutrality of money.

Particularly the Policy Ineffectiveness Proposition is in fact an example of how math can create fallacies, not to how insights can be created.

The Arthurian: The equations you're talking about are not the kind of mathematical modelling discussed here, as they are accounting identities.

And please note that a general link to your blog is not a substitute for arguments, especially since you have no arguments related to this issue presented there.

10:28 AM  
Blogger Celal Birader said...

Hi all,

Does Einstein's Theory of Relativity count ?

Somehow Einstein came up with a)the physical insight then b)it was expressed using mathematics and then c) experimentation later proved him to be correct.

It seems to me the hard sciences (physics, chemistry) have demonstrated that the creation observes or rests on mathematical relationships.

So taking courage from this fact, people have been extrapolating in a simplistic fashion to the social sciences with absurd results (as this blog points out to us over and over again).

HOWEVER, if we accept that man is not an infinite or an infinitely free being but a created being with internal and external limitations, then isn't it logical to posit that human behaviour is also subject to some laws of creation ?

If that is the case then there remains hope that mathematics will eventually explain fields such law or economics correctly.

We are very far from that point; but, perhaps the work of Mandelbrot, Taleb and Kahneman are an indication that baby steps are being taken in that direction.

10:42 AM  
Blogger Flavian said...

Well, if you take a look at Irving Fisher's economic "predictions" you will find out that maths will teach you absolutely nothing about economics....................

1:02 PM  
Blogger stefankarlsson said...

Celal, human behavior is subject to the laws of creation. But it is not subject to unrealistic assumptions designed to enable the use of Lagrange multipliers, such as perfect rationality, neutrality of money etc.

10:34 PM  
Blogger Celal Birader said...

Absolutely right Stefan. I agree with you. Money is not neutral it is subject to 'animal spirits' which follow a reproducible pattern across different markets, across different cultures and across different times.

This tells me that there is a fundamental relationship which may be expressed through some form of mathematics -- perhaps not with Lagrange multipliers and certain types of statistical assumptions.

HOWEVER, Mandelbrot has pointed out some striking mathematical similarities between hydrological systems and human markets like the wheat market --- fractal economics or fractal finance as it has been called.

These may be fruitful lines or research

4:02 PM  

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