Formal Theories of the Market Process

|Peter Boettke|

For our Mercatus Center graduate student program this year, several of us have decided to organize 'research clusters" with the PhD students.  My cluster for the academic year will focus on formal theories of the market process.* Topics will range from the "other" Austrian school in Vienna that centered around Karl Menger and also Oskar Morgenstern.  We will start off with a recognition of the shared research program with the more self-consciously identified Austrian school that is associated with Carl Menger, Eugen Bohm-Bawerk, Ludwig von Mises and F. A. Hayek.

We will be reading Robert Leonard's Von Neuman, Morgenstern, and the Creation of Game Theory (Cambridge, 2010) to start our shared inquiry.

A lot of foundational formal theory had Vienna as its birthplace, and in particular in K. Menger's seminar.  See E. Roy Weintraub's "On the Existence of a Competitive Equilibrium, 1930-1950," JEL (March 1983).

The formal proofs of existence and stability of general competitive equilibrium are not what I want to stress, but the effort through the years --- given the existence of a competitive equilibrium --- to formally track the path to equilibrium.  Puzzles and paradoxes at the core of equilibrium theory abound from the very beginning.  Morgenstern identified the paradox of perfect foresight early on, and his collaboration with Von Neuman actually came from the effort to wrestle with this idea.  Theories of the path to equilibrium have continued to vex some of the best minds in economics.  Franklin Fisher's Disequilibrium Foundations of Equilibrium Economics (Cambridge, 1989) pointed out the intellectual stakes involved --- unless we can have good scientific reasons to believe in the path to equilibrium, the equilibrium properties that provide the foundations of modern welfare economics would be little more than science fiction.  The entire enterprise, in other words, is vulnerable to a crisis in intellectual legitimation.

It is my hope that we will study various efforts to model equilibrium path and the role of entrepreneurship -- e.g., Andy Yates, "The Knowledge Problem, Entrepreneurial Discovery, and Austrian Market Process Theory," Journal of Economic Theory, 91 (2000); as well as modern efforts to capture these ideas using experimental techniques and computer simulations.

Ultimately, I am hopeful that our research cluster will stimulate research on the topic.  Personally, I am working on a project about the "Hayek hypothesis" and field studies examining the informational efficiency of markets.

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*David Prychitko and I edited a 2 volume reference work dealing with the varieties of Market Process Theories in 1998.  In those volumes, we provide a documentary history of the efforts -- formal and institutional; orthodox and heterodox --- to explain the process of economic activity.

Comments

[Rafe Champion]

Weintraub wrote (p 2) that there was next to nothing on the history of GE theory, compared with tens of thousands of pages on Keynesianism. That was addressed by Ingrao and Israel who wrote “The Invisible Hand: Economic Equilibrium in the History of Science” translated by Ian McGilvray, the MIT Press, Cambridge and London 1990 (orig 1987).

http://oysterium.blogspot.com/2006/02/maths-invades-economics.html

Interesting to note the role of von Neumann who introduced the great leap from the real world to formalism in both physics and economics.

It seems like mathematical economics showed its mettle in Samuelson's commentary on the Soviet economy. Surely GET belongs in the Maths school.

Interesting to see how general systems theory became so powerful in the 1930s, it captured Talcott Parsons and after his first book in 1937 it is arguable that he produced no theoretical work of lasting value.

This comment started out as a reply to Roger Koppl and Greg Ransom on Mario's thread, to question whether we really need to go the way of mathematical complexity theory. Prompted by Boettke at al on the hourglass of economics I will go away and compose an argument along the lines that the early Parsons/Popper/Mises program would have or could have, or should have kept the hourglass fat and healthy in the middle. At the very least there could have been an alternaive, institutionally focussed program alongside GET. Whether it would have attracted the best talent is another matter, but the great thing about the alternative program is that there is so much low-hanging fruit (love that phrase) that you don't need elite people to stuff their baskets with it.

[Ben]

I have a semi-related question regarding what it takes to be a graduate student in economics.

I'm currently trying to decide where to go and what to do for college as an undergrad. I want to be a professional economist eventually, so I need to learn a lot more economics and math. However, I also think a classical education might be crucial to being a good economist. I got started on this thought-path due to something Hayek said along the lines of "An economist cannot be just an economist," although I can't remember where I read it or the exact quote. Conversations with my dad about the difference between being wise and being smart, and Albert Jay Nock's romantic description of the Great Tradition of classical education solidified the idea in my mind.

If possible, I would like to spend my undergraduate years getting an education in the classics, continuing my economics and mathematical education only independently, as I currently do (or indirectly through my classical studies--I may end up reading Euclid and Newton, for example). However, posts like this make me wonder if this might be an utterly unrealistic plan; I had no idea that whether markets moved towards equilibrium was a controversial subject to any degree. However, it does sound like a fascinating subject, and I'd hate to pursue a classical course only to find myself locked out of advanced economics and mathematics.

So, Professor Boettke, I would be extremely grateful if you or anyone competent to answer could tell me if my plan for my undergraduate years is feasible if difficult or completely preposterous if I want to pursue an advanced degree in economics (I know I can double major in the classics and economics at plenty of colleges, but I'm considering, among others, a college that offers solely a four-year classical education, which would definitely be my first choice if I could be reasonably confident that attending there would not mean hobbling myself). A brief answer would do much to simplify my life and help me make a decision. In any event, good luck with your graduate program, even if exactly what you and your students will be doing is currently beyond me.

[Troy Camplin]

Ben,

You need to double major in math (concentrating in as much systems, complexity, chaos, network, and process theory as possible) and economics, and minor in philosophy. And for your science classes, take as much biology as possible, not physics. Physics will make you a bad economist. Biology and cognitive psychology will bring you much closer to what you need to know to be a good economist. And read two books by an Austrian economist for every mainstream economics book, to keep you rooted in economic reality rather than the fantasies of mainstream economics.

[Mario Rizzo]

Pete,

I think it would be also useful to look at Debreu's view of mathematical economics. A very interesting article by Till Duppe appears in the Eramus Journal for Philosophy and Economics (Spring, 2010):

http://ejpe.org/pdf/3-1-art-1.pdf

[Nick]

Pete - if you haven't already, take a look at Francis Spufford's new book 'Red Plenty'. There isn't a better 'fictional' book on the Soviet fairytale of the planned economy. It is a work of real genius. It even cites Hayek at the back.

By the way, I am not the author, or related in any way to him.

[Roger Koppl]

Ben,

Given your ambitions and your big head start in economics, I think you need to be sure to major in math. Reading Euclid and Newton simply won't do. You need math training in the college classroom, for which there is no substitute, period.

Whether to double math with economics, or classics, or history, or something else is a relatively minor point, at least in your case.

First, Go to the best school you can get into and work hard. Second, in your case a math major seems in order. Third, everything else is a detail.

[Ben]

Professor Koppl and Mr. Camplin,

Thanks for the quick and detailed responses. That certain makes my life easier. I am rather surprised, however, at the emphasis both of you placed on mathematics above all else. My (apparently false) impression of the state of math in economics is that it is on a relatively low level (compared to something like physics), and therefore at the most I could get away with minoring in it. Fortunately I enjoy math, so it's not a problem.

Thanks for both of your advice. It'll definitely help me make a decision about where to go in pursuit of higher education.

[Troy Camplin]

The state of math *is* horrible in economics, but 1) it has to be done to succeed in economics, and 2) there is in fact some mathematics which is appropriate to economic analysis. I gave a list above of areas. There is a great opportunity for using the *right* mathematical approaches and models. But to do that, you have to know the math.

Knowing math is vital, but knowing the proper position of math in the hierarchy of knowledge is equally important:

In order from simplest to most complex:

1.) math
2.) physics
3.) chemistry
4.) biology
5.) psychology/cognitive science
6.) the social sciences (sociology/economics/anthropology)
7.) philosophy
8.) literature and the arts

Math can be used to describe/model each of the levels of complexity above it, but with increasing inaccuracy and the need for ever-greater mathematical complexity.

As we can see, the social sciences are much closer to philosophy than to math. But they are equally close to psychology/cognitive science as to philosophy. Hayek was right to be more interested in the brain (The Sensory Order) and philosophy (Individualism and Economic Order, LLL, The Fatal Conceit, etc.) than math. At the same time, I think he would be very interested in some of the math of complex adaptive systems, process theory, etc. if he were a young economist today. (Reproduced from a response at Thinkmarkets)

[Roger Koppl]

Ben,

Benoit Mandelbrot got the idea for fractals from looking at cotton prices. The great economist W. S. Jevons was also a pioneer in mathematical logic. The mathematical field of game theory was created by the collaboration of John von Neumann with an economist, Oskar Morgenstern. And so on!

[greg ransom]

Math is the great and objective granter of intellectual status.

Academics is a status game and a "whose the smartest man in the room" game and a political cpgame and -an advance the ball game -- and a "make it easy to teach" game.

Math genius and ability is an ultimate trump card.

When you've advanced the ball, there are formal objective ground to prove it.

And you've created something easy to teach and grade and something others can build a resume upon with additional publications in the new math territory.

These are reasons that math trumps successful understanding.

Become king of the math hill, and you can didctate what understanding comes to in your field -- because you've proven you are "the smartest man in the room", and you've laid out the bound for endless new publications using your math innivations.

[Roger Koppl]

I think you overstate the case, Greg. Sure, math is good for showing off and the culture of economists can be rather ostentatious. Yep. And you had better understand the math you're reading if you want play in the economic-theory sandbox. But the really successful guys all have something to say and many of them are quite low tech on the math as illustrated by Avner Greif among others.

[fundamentalist]

However, there seems to be an inverse correlation between the good math economists and economic understanding.

[Greg Ransom]

Roger, I'm riffing on themes from Coase and Kuhn and philosopher Larry Wright -- and brightening the edges to illustrate a point.

Differences in understanding cannot be adjudicated formally -- but math result can.

The teaching of an achieved understanding takes hard work and lots of training, reading, and conversation over time -- and the evaluation of the successful acquisition of a new understanding cannot be evaluated with a mark-sense form, or by a grad student checking a formal result.

The teaching of math is straight forward and can be evaluated very simply by a grad student checking a set of formal problems for correct solutions.

When a formal project is FAIL it takes sometimes decades for people to identify and explain what has gone wrong (e.g. Wittgenstein on the failure of the Frege project, all sorts of people on the failure of the Hilbert project, Hayek and Popper and Kuhn on the failure of the Mach/Mill/Hume project, Hayek and Mises on the failure of pure theory / pure math economics).

And there is no simple "crank it out" formalism that establishes what has gone wrong.

[Greg Ransom]

Example.

Math results typically instantly recognized.

New insights and understandings, often, not so much.

Coase says Hayek and Robbins failed to see anything of significance in his 1937 paper on the firm.

Friedman, Stigler and the Chicago economists read Coase's 1960 paper, and rejected its argument -- until a long conversation late into the night with a large group of them help them to understand the point.

Coase's results were very close to formal results -- but they weren't math, and failed to have that wonderful property of math -- the ability to compel assent.

[Greg Ransom]

No, math is good for compelling assent.

It's also good for producing material that is easy to teach.

Etc.

This isn't about showing off.

Roger wrote,

"math is good for showing off"

[Greg Ransom]

Math provides an objective template for a uniform curriculum of economics across university campuses.

That's another advantage -- it gives the profession a univocal criterion for what it is to "understand" economics.

Even if much of that understanding is bogus -- as a majority of tenured economics say of modern macro.

[Barkley Rosser]

Troy,

Most would pull econ out of social sciences in your list and put it third, after math itself and physics, in terms of mathiness, although the logic parts of philosophy are pretty highly mathy also. The parts of chem and bio that get mathy are either the parts related to physics (physical chemistry) or stats, where they are about at the same level as econometrics.

[greg ransom]

Darwinian biology has the same math model vs sound understanding problem as does economics.

Fortunately, there is more to do in biology, and field research is not viewed as "unscientific".

So the pure math guys creating constructs with embedded pathologies of interpretation do not dominate.

But for all that biologist found it necessary to set up a committee to support work on working the bugsmoutnof the general and global explanatory strategy of economics (the sort of work that Ernst Mayr did). Their simply was no instittutional support or professional incentive for work by grad students in that area.

Most such work is now done in philosophy departments.

And the pathologies remain -- no one yet has worked out a stable and fully coherent model of Darwinian explanation (see for example David Hull's or Elliott Sober' attempts and commentary on these).

And the relative prestige remains with the math guys -- and so does much of the content of the textbooks.

[greg ransom]

Make that:

"But for all that biologist found it necessary to set up a committee to support work on working the bugsmoutnof the general and global explanatory strategy of biology."

[George Machen]

I know everyone here has heard the story, but I nevertheless can't resist invoking it in the context of this thread vis-a-vis mathematics: In _The Worldly Philosophers_, Robert Heilbroner tells a story of a dinner John Maynard Keynes had with Max Planck, the physicist who was responsible for the development of quantum mechanics. Planck turned to Keynes and told him that he had once considered going into economics himself, but he decided against it - it was too hard. Keynes repeated this story with relish to a friend back at Cambridge. "Why, that's odd," said the friend. "Bertrand Russell was telling me just the other day that he'd also thought about going into economics. But he decided it was too easy."

[Troy Camplin]

They were both right. Economics is much more complex and, therefore, far more difficult than physics, while philosophy is more complex than economics.

[K Sralla]

Ben,

My son is in high school and thinking about his after life. He did not ask me, but I offered my advice to him nonetheless. Squats for success in athletics (he is starting defensive end on his high school team) and math for success in just about whatever academic challenge he decides to tackle. Math, Math, Math. It is the key to academic success whatever you decide to study.