What has become of the Axiomatic method of economics?

Economists have not paid much attention — and so modern economics has become increasingly irrelevant to the understanding of the real world. "Why anyone should be interested in that kind of theories and models is beyond imagination. As long as mainstream economists do not come up with any export-licenses for their theories and models to the real world in which we live, they really should not be surprised if people say that this is not science." LARS P. SYLL (https://larspsyll.wordpress.com/) Apud Tony Lawson, Economics and Reality (1997).

Dear Marcelo: We need to keep in a constant production of new research and development to promote our ideas that it is based on propose alternative economic theories and models that can help explain our real world. 

The generation of economist that developed the Arrow-Debreu model has retired or is about to retire. According to Susan Coyle in her book "The soulful Science, what economist really do and why it matters": 1.  the public image of economics is one of the neo-classical model prescribing liberalizing markets; 2. Economics has moved beyond this framework. For instance, her view in Chapter 5 is that psychology and behavioral economics lack an overarching framework and that we are left with many pieces of a puzzle and no idea how to put them together into a coherent framework. Whether this is temporary or structural is heavily debated. There are economist working successfully from within the axiomatic tradition, e.g., Douglas Bernheim, Faruk Gul, Wolfgang Pesendorfer and Antonio Rangel, to enrich and extend theories such that these capture anomalies. This has not yet reached textbooks. But the importance of solid theory explaining observations has grown over the past decades. Although there are also areas where neoclassical economics does work, much interesting work needs to be done still.

I thank you all for your responses.

Marcelo Negri Soares plagiarized this:

Dear Victor,

Thanks for the post. The dominant theme in it seems to be that the social sciences are different from the physical sciences. But I recall that Adam Smith wanted to do for the social sciences what Newton did for the physical sciences. Smith evolved the notion of the spectator in his TMS which became the invisible hand in the WN. People are not satisfied with his solution, but, as I see it,  the Axiomatic Method is trying to lay bare the conditions that must be met for Smith's model to hold.

Marcelo-

On 28 December 2014, Lars Syll wrote:

"Why anyone should be interested in that kind of theories and models is beyond imagination. As long as mainstream economists do not come up with any export-licenses for their theories and models to the real world in which we live, they really should not be surprised if people say that this is not science, but autism!"

Ten days later, on 7 January 2015, you wrote:

"Why anyone should be interested in that kind of theories and models is beyond imagination. As long as mainstream economists do not come up with any export-licenses for their theories and models to the real world in which we live, they really should not be surprised if people say that this is not science."

Clearly, you are a plagiarist. But I am curious: Why did you edit out the word "autism" when copying and pasting your comment? You are not ashamed of the history of your profession, are you?

In this recent paper I summarize the history of your profession.

Lall-

Thank you for your interesting comment regarding Adam Smith. However, my book, Axiomatic Theory of Economics, is not trying to lay bare the conditions that must be met for Smith's model to hold. I see Carl Menger, not Adam Smith, as the precursor to axiomatic economics. In this paper I critique Austrian economics:

Today, every economist of Austrian birth is lumped together, but I feel that, after Menger, there was a Y with Mises and then myself going in one direction and Böhm-Bawerk and then Hayek going in another direction, towards what is today known as “Austrian” but which I reject.

Dear Victor,

Your comments are enlightening. I did not mean to give precedent to Adam Smith over Carl Menger for the founding of the axiomatic method. I am aware of the force of this method in the Austrian school. We find Stanley Jevons also using the term in the following sense.

“That every person will choose the greater apparent good; that human wants are more or less quickly satiated; that prolonged labour becomes more and more painful, are a few of the simple inductions on which we can proceed to reason deductively with great confidence. From these axioms we can deduce the laws of supply and demand, the laws of that difficult conception, value, and all the intricate results of commerce, so far as data are available.” (The Theory of Political Economy)

Joseph Schumpeter ascribed the term to N. Senior in his chapter titled the “AXIOMATICS. SENIOR’S FOUR POSTULATES.”(Ch. 6 of Schumpeter’s His. Of Eco. Thought).

I did not mean to implicate Smith directly to the axiomatic method, but only indirectly in that sense in which Gerard Debreu “Theory of Value: An Axiomatic Analysis of Economic Equilibrium,” tries to address perfect competition.  Arrow-Debreu were explicit in saying that they wanted to improve Leon Walras effort to find a GE solution. We find in Arrow-Debreu work that “…perfect competition prevails, in the sense that each producer and consumer regards the prices paid and received as independent of his own choices.” (Arrow and Debreu, Eonometrica, 22 (1954) p. 265. I attach an excerpt from one of Debreu article explaining the role of the the axiomatic in his work.

Lall-

With varying degrees of success, many people have attempted to use the axiomatic method in economics. Extant are Egmont Kakarot-Handtke and I – everybody else is long dead and their theories forgotten. I reply to Kakarot-Handtke here and also touch on Senior’s early use of the method:

I consider Mises a precursor to my own work because his Regression Theorem somewhat inspired my third axiom. Mises was wrong to call it a theorem because he never proved it and he was wrong to call his Action Axiom an axiom because it is a platitude from which nothing is proven. Also, he was thinking too small; what he called the Regression Theorem applies not just to money but to everything.

But, in spite of these shortcomings, I give credit where credit is due. Mises’ Regression Theorem is actually the only thing of value in his work; originary interest was wrong as Keynes so cuttingly pointed out in a footnote on page 192-193 of his General Theory. But, reformulated as an axiom that applies to everything, Mises’ idea became one of the three axioms from which I deduce all of my theorems.

But Debreu is a not a precursor to my work because I do not believe in supply and demand. My theory is about price and stock. I discuss more thoroughly my rejection of supply and demand here:

In the excerpt you attach, Debreu writes, “as axiomatized theory has a mathematical form that is completely separated from its economic content. If one removes the economic interpretation of the primitive concepts, of the axioms, and of the conclusions of the model, its bare mathematical structure must still stand. This severe test…”

So we see that he meant this disassociation from economic interpretation as a test, like putting a race car on a dyno to test the power and torque of the engine, though with full realization that, while it is hooked up to the dyno, it is not actually going anywhere.

I make clear that there are three senses to the term “truth” in Section 3.1 of my book. (And in Section 12 I make clear that I am not addressing perfect competition, which does not actually exist.) Here is the table of contents:

But most economists create a conflict where there is no need for conflict by insisting on pitting these different senses of the term “truth” against each other as though only one can prevail. In fact, they work hand-in-hand to create sound and useful theory.

Incidentally, note that Debreu refers to his axioms as “primitive concepts,” which is the same term used by Lewis Fry Richardson when he used the axiomatic method to found numerical weather prediction. Richardson’s use of the axiomatic method is a good role model for economists. I discuss how numerical weather prediction relates to economics in more detail here:

This paper now has a different URL than what I linked to above:

The History of Economics from 1974 to 2014

Lall-

I forgot to mention Dirk Helbing.  Here he proposes a "research program of grand scientific challenges in economics - a Hilbert program for economics and the social sciences as I call it."

Frankly, I am not sure that soliciting "a list of the greatest deficiencies and challenges of currently applied economic theories" is accurately described as a Hilbert program.  But the fact that he invoked Hilbert's name warrants mention on this thread.

Thinking in terms of recursive economics, perhaps a rule or pattern could be found to overcome the curse of dimensionality that often defeats an attempt to axiomatize economics. From this vantage point perhaps the search for recursive algorithms in economics is the way forward - a rule that will allow for the universal computation of economic phenomena. Ultimately what constitutes an axiomatization in economics has to be resolved.

Dear Shian-Loong,

Thank you for your suggestion. I too think that the axiomatic basis of recursive method is worth exploring.

Dear Lall,

Most welcome, was a pleasure- the ideas put forward here is really an indication that economics is still very much a formal system of thinking and not purely a vehicle for politics or opinions in current affairs.

Best Regards

Dear Shian-Loong:

I am pleased to meet an economist who states his assumptions clearly and then deduces a theory from the stated axioms and from nothing else, with no hidden assumptions.

Here I quote Aditya Chakrabortty, who laments that, "instead of a real, all-encompassing economic theory, we get conferences that devote as much time to discussing the holistic massage industry ('using a Foucauldian lens') as to analyzing financiers. "

There are all too many economists today who eschew all theory in favor of finding and/or fabricating whatever data will push their political agenda or "prove" the opinion of whoever is funding them.

Dear Victor,

You make an excellent point. I have been thinking of Shian-Loong view on Axiom and recursive methods. I looked into Lars Ljungquist and Thomas Sargent "Recursive Macroeconomic Theory", MIT Press 2000. The did not make clear the axioms they follow. Have you any thought about this.

Lall-

Shiang-Loong said, “perhaps a rule or pattern could be found,” so he does not have a set of axioms that works either.  But at least he is trying, which is more than can be said for the other 99% of economists who despise the axiomatic method and are content to do endless statistical studies – none of them consistent with each other – that “prove” the opinion of whoever is funding them that day.

Frankly, I believe that what constitutes an axiomatization in economics has already been resolved, in 1999 when I published Axiomatic Theory of Economics.  But I welcome Shiang-Loong’s efforts to devise a new axiomatic theory along recursive lines.

Incidentally, recursion – as the term is used in computer programming – was first introduced in economics by Ludwig von Mises.  Notice that his regression theorem is like a subroutine that calls itself until it reaches a stopping point where money had only use value.  This is similar to the minimax algorithm for playing tic-tac-toe, which regresses all the way to the end of the game, or for playing chess, which regresses as far as it can within the time limit and then assigns values to all those end positions based on material remaining and pawn position.

“I went beyond Mises by recognizing that his Regression Theorem is not a theorem but an axiom and that it applies to all phenomena, not just money.”

Dear Victor; Shian-Loong,

The recursive macroeconomic theorists start with a vector of variables that characterizes the current position of the system. Then, they use two transition functions, one mapping today's state to tomorrow's state; and the other mapping the state variables to other endogenous variables in their model to do the recursive procedure.

Now, it seems that the state vector they started with resembles say the Axiom of Leonard Savage, who was working on Maurice Allias Axioms, who in turn was reacting to John von Neumann and Oskar Mergenstern axioms. So, can we regard such recursive state vector of variables as their fundamental axiom?

Dear Lall,

It has been quite some time. Thanks for the insight and illustration from the economic methodology of recursive macroeconomic theorists. It is always beneficial to know where we are/have been in order to attempt a quantum leap. 

Thinking in terms of a cellular automata and extrapolating this to the way the economy works- artificial economy: interesting to note that John von Neumann was instrumental in promoting the use of cellular automata. The kind of recursive rule I am referring to would most probably resemble the 1st of the set of two transition functions- the set that maps today's state to tomorrow's state. This first set of transition function though more abstract compared to the second set (the mapping of variables), is nonetheless more general, as a recursive rule and hence would fulfill the criteria of universality for axioms (my assumption of what axioms should be).

I believe this sort of recursive structure approaches the kind of mesoeconomics that Schumpeter was referring to when he focused on creative change (transition from current to future states) vis-a-vis adaptive change (transition between state vector of variables).

Neo-Schumpeterians and evolutionary economists have reworked this idea somewhat and a formal categorization of rules leading to a general theory of economic evolution can be found in:

http://www.amazon.com/General-Theory-Economic-Evolution/dp/0415279429/ref=mt_hardcover?_encoding=UTF8&me=  

Cheers

Victor Aguilar has mentioned an interesting list of Hilbert problems in economics. I was not aware about them before, but after reading the list I found high correlation with my way of thinking. In fact, in some of my papers I tried to follow this agenda.

Human language is polysemantic. It is a problem for any praxeology, i. e. what meaning to use in order to formulate the action and get a predictable result. For example, a basic economic concept "exchange" has 9 meanings in Collins English dictionary and all of them are being reduced to the two ones: debt-free ("at the same time", "something similar", "as an equivalent") and debt ("securities", "money", "currencies", "debts"). When you choose amongst these two groups of meanings you can formulate the axiom of exchange and some others to complete the axiomatics. The approach has a cultural dimension. But human actions and culture/language are interconnected.

Dear Nikolay,

Thank you for the answer. One can ask whether the meaning in the term "action" in the libertarian's "action axiom" matter. It seem that people are free to act in any way they choose, only that they must bear the consequence of their action.

Also, I see that axioms in general equilibrium tries are made precise in using mathematics as their language.

One wonders also if Wittgenstein's picture theory of facts is not another way to get a precise meaning of proposition.

Lall - each economic theory has its own set of axioms; once you have several economic theories, the axioms may (and do) vary, leading to incompatibilities, overlapping, paradoxes, etc. This is because in economics you have competing theories (e.g., Keynesian, Friedmanite, Fisherian, etc), unlike, say, geometry, where the theories are mutually exclusive.

P.S. I made this connection thinking of Samuelson - he insisted that mathematics was essential, and his numerous and groundbreaking contributions provided the foundation on which modern economics is built.

Dear Lall,

One can think it is all about words organized in sentences that causes difficulties to define what "action" is. Rudyard Kipling with "I keep six honest serving-men" and James Frederick Ferrier were close to defining "action" and "knowledge", but it is beyond economy. Yes people are free to act... knowing nothing about the structure of action and it is doubtful they can always choose a correct variant because they do not see all of those variants embedded in sentences. The responsibility becomes a declarative desire in these conditions.

Dear George; Nikolay

It appear that some economists are not convinced about the usefulness of the axiomatic method. In the area of utility analysis we find among the axiomatic approach, studies about work and living condition of people, probability choice experiment under decision-making environments, and research such as by Leyden that allows individuals to verbally qualify their utility level. One can also mention the early absolute income hypothesis by Keynes that started the research program of the relative income hypothesis by Duesenberry, the permanent income model by Friedman, the life-cycle hypothesis by Modigliani, and the current random walk model by Hall as alternative approach that are not axiomatic. I think it was Angus Deaton that got the last Nobel prize in that area of consumption.

But the axiomatic utility framework of von Neumann and Morgenstern is also setting a research program that is still current. Debreu and Arrow were influenced by that work in their creation of General Equilibrium analysis. From that work also Samuelson developed his revealed preference theory, which was followed by a Weak axioms of revealed preference (WARP), a strong one (SARP) and a Generalized one (GARP). Also this research framed many investigations into risk analysis. All this goes to show that the axiomatic method co-exist and is useful in utility analysis.

Lall - I know of graduate programs in Economics, at rather good universities, that choose not to include any of the contributions by von Neumann, Morgenstern, Debreu, Arrow and Samuelson - after all methodological discussions on the subject that took place along the years.

Dear Lall,

I wrote a book about axiomatics of interest free political economy (it is not translated in English) and started there from the axiom of exchange. It was a look through various arts: painting (Jacques-Louis David, Viktor Vasnetsov, Élisabeth Sonrel, Evelyn De Morgan, Robert Wilhelm Ekman, Edvard Munch, Charles Sprague Pearce and others), classical literature and so forth because some economic concepts are result of the broader agenda than economy itself.

Consider "debt" as a kind of non-equivalent exchange where obligations are stretched over time. Many economists and probably all politicians think that "debt" is a kind of natural law, but it is not. After the invention of Purgatory "debt" became widely accepted and first English political economists perceived "debt" to be natural practice. At least Dante described 3 currency systems in his "Divine Comedy": based on grain, silver and interest. 2 of them have exhausted themselves: silver and interest.

That experience helped me to formulate the theorem of competitiveness:

In general, maximum competitiveness means:

- Co-operation instead of purchase to produce (different type of contracts);

- Debt free cost price;

- Domestic production and a buoyant domestic market;

- Keeping to the law of mutual aid inherent in the people and their networks.

So I just want to say that I confirm the usefulness of the axiomatic method.

Nikolay,

You have provided wonderful news. Most people think of debt as borrowing as in the case of debt vs. equity. Your analysis is broader in scope and deeper in thought. Hope you can get your book translated in English to reach a broader audience. Thanks you.

Dear George,

I agree in what you say. In my experience most business schools link their graduate programs to the expected job market. Also, I think students are not encouraged to learn the math needed to understand the subject. I would like to see more schools offering the subject. What do you think?

Of course that I agree with you, Lall - some of the order generations are still reticent ("why fixing it, if it's not broken"), whereas the younger generations tend to go beyond their (and their teachers)' "limitations". It's too late for the former to change, but we can help the latter with appropriate academic courses.

P.S. I hear a lot "Mathematical Economics programs, but go easy on mathematics"

Thanks, Lall, for your kind words. To translate - sounds simple. But the book's language is full of allegories that makes it difficult to understand even for the Russians, as I was told. I could not find another approach to represent "the taste" of the basic economic concepts in their cultural environment. You can see the book file https://www.researchgate.net/publication/272180442_N_Krackov_Aksiomatika_politiceskoj_ekonomii_bez_procenta

Is there something in the middle to generate professional criticism (a book review by someone who knows Russian, etc,)? Could you please give me your advice?