Talk:Mathematical economics/Archive 1

what is real
Mathematical Economics is a beautiful and interesting way to link what is real to what is just a theory. By writing the situations that occurs in local markets in the mathmatic language, we assure that they are not anymore local, but are now open to the whole world to be discussed and solved.

Yes, i have realized that by reading many books of the are.

BUT: (and thats why i'm posting here)

I'm kind of concerned about the relationship between what is real and what is in the numbers...i mean...is mathematics a real, usefull tool in the analysis and in the solving part of a problem in a industry or in finace-related work like a bank?!

Does a mathematical model works in the real life?

waintg answers here! - Dionisio (sorry for the mistakes in the english write...i'm from Brasil)


 * Answering from Turkey: They don't work all the time. See post-autistic economics.

JET
If JET is the apotheosis of mathematical economics, what is Econometrica? JET is an almost normal journal i think...
 * I agree. If there are no opposes I'll fix this in a few days. EconomicsGuy (talk) 18:35, 22 March 2008 (UTC)

Changes
I intend to change a few things in this article. I won't do so until I see some sort of consensus or no response for a while. I'll probably post the intended new text here tomorrow or so.Protonk (talk) 04:55, 18 April 2008 (UTC)

criticisms
there are a few reasonably good sources from within the profession (and a few from without) that criticize the notion of mathematical economics. I'll add those in. Namely, Heilbroner, Henderson and others. However. I intend to remake this section to show that these views do not represent a large slice of the profession and are not widely respected at a research level. Obviously it will stay NPOV, but that is the intent.

Ok, here are a few quotes:

First, I've decided NOT to use the quote from Henderson, which I think is pretty slanted (appears here, in an adbusters article. If someone selse feels that it is appropriate, please tell me). I'm not going to go so far as to suggest that it be removed from the Samuelson page (Here, as it is a direct criticism of Samuelson, but I'm not going to spread it here. The passage I'm interested in is this one:

"I guess the scientific approach began to penetrate and soon dominate the profession in the past twenty to thirty years. This came about in part because of the 'invention' of mathematical analysis of various kinds and, indeed, considerable improvements in it. This is the age in which we have not only more data but more sophisticated use of data. So there is a strong feeling that this is a data-laden science and a data-laden undertaking, which, by virtue of the sheer numerics, the sheer equations, and the sheer look of a journal page, bears a certain resemblance to science. You will find few of the curves and the equations that are characteristic of economic writing in writings of political science or sociology. Those undertakings, which I consider to be of great importance in establishing the tone, the character of the economy; are not generally regarded as scientific. Now, that is another reason. Economics, what we call economic activity - buying and selling is a central one - is the only activity I know of in this society in which a given stimulus separates the population into two halves, one half moving to the right, one half moving to the left. When prices go up, buyers buy less and sellers try to sell more. When they go down, buyers want to buy more, sellers try to sell less. There is no other aspect of the complicated society in which we live where you have such an extraordinary cost-effect phenomenon. Bang goes the cost, up goes the price, and you know with some certainty that the sellers are going to move that way; the buyers are going to move the other way. Never mind for the moment how fast they move, or the elasticity. You know there is going to be overall change in the structure, in the arrangements. That one central activity looks scientific. I understand that. I think that is genuine. It approaches being a universal law. But resembling a science is different from being a science."

That's actually from an interview (Challenge Magazine interview) with Heilbroner. I'd include a passage from The Worldly Philosophers but I've lent my copy out. I've got to stop doing that. :)

In another, very serious sense, we have to accept that criticism of mathematical economics is not a new position and while it is held by very few practicing economists (for many reasons, not least of all social), it is not a fringe view. There is a article discussing Karl Popper that mentions his fundamental criticism of economics (Seven Decades of Economic Methodology). this debate is the one that prompted Milton Friedman to announce that "all assumptions are unrealistic" in order to argue against the Popperian disdain for unverifiable assumptions. In my opinion, Popper's criticisms, while they do not result in a viable alternative (see later in the article) are notable.

Despite there being much talk about testability in economics in the 1960s, none of this had to do with Hutchison’s path-breaking view of methodology. Instead, the 1940s and 50s were the battle ground for the movement to make economics a mathematical science. A main criticism of mathematical economics was that mathematics could only provide tautologies – which were claimed to be statements or theorems that are true by virtue of their logical form rather than their empirical content. More correctly, a tautology is a statement which does not depend on the definition of its non-logical words but only on its logical words such as ‘and’, ‘or’, ‘is’ and ‘not’. Thus, a tautology is a statement which is true simply because one cannot conceive of a counter-example. For example, the statement ‘I am here or I am not here” is true regardless of who ‘I’ am or where ‘here’ is.

The article goes on to describe the arc of that methodology, which is probably notable but not relevant to this article.

there is also an article, not yet peer reviewed, that suggest that future work in economics is trending toward empirical work and away from purely theoretical work. Some of the conclusions in this paper are suspect, in my opinion, but the notion that empirical and experimental work is becoming more popular is certainly true. Blog link to the paper.

Here is the current article:

The methods of mathematical economics are widely, though far from exclusively used, in professional publications, but there are opponents, notably the Austrian School. Within it, the use of formal techniques has been criticized as projecting scientific exactness that, by nature of the eccentricities of its human subject matter, is infeasible, even in principle.

Proponents argue that the validity of the mathematical method derives from the distinctive modeling of economic decision-making and economic systems. These parallel mathematical concepts, such as optimization, to describe (i) rational, self-interested agents interacting in economic systems. From such assumptions and concepts, behavior of an agent or an economic system may in principle be compared against properties of the model using formal analytical techniques.

thoughts?Protonk (talk) 19:59, 19 April 2008 (UTC)


 * First of all the rewrite of the criticism section is much needed so something needs to happen. I see nothing wrong with citing Popper, indeed not doing so would be ignoring a significant part of the more constructive criticism of mathematical economics. Regarding the current section I especially dislike the way it suggests that agents are assumed to be rational and self-interested. It is entirely possible to use mathematics to model economic systems where this is not the case. The point that the assumptions are just that, assumptions, and not proven verifiable facts is the point that should be made and that is neither fringe nor hard to source. Such a section would be a huge leap forward considering the sad state that many of these criticism sections in our economics articles are in. EconomicsGuy (talk) 20:27, 19 April 2008 (UTC)

Subsections
I intend to expland the applied mathematics sections and to add a few more to show that mathematical economics (as samuelson or Marshall would define it) is not just some branch of economics, but the foundation of a considerable amount of work in the field.