## General equilibrium — economics as ideology

from **Lars Syll**

Although I never believed it when I was young and held scholars in great respect, it does seem to be the case that ideology plays a large role in economics. How else to explain Chicago’s acceptance of not only general equilibrium but a particularly simplified version of it as ‘true’ or as a good enough approximation to the truth? Or how to explain the belief that the only correct models are linear and that the von Neuman prices are those to which actual prices converge pretty smartly? This belief unites Chicago and the Classicals; both think that the ‘long-run’ is the appropriate period in which to carry out analysis. There is no empirical or theoretical proof of the correctness of this. But both camps want to make an ideological point. To my mind that is a pity since clearly it reduces the credibility of the subject and its practitioners.

I can’t but agree. You could, of course, as Brad DeLong has asserted, consider modern mainstream economics to be in fine shape “as long as it is understood as the ideological and substantive legitimating doctrine of the political theory of possessive individualism” and if you manage to put a blind eye to all the caveats to its general equilibrium models — markets must be in equilibrium and competitive, the goods traded must be excludable and non-rival, etc, etc. The list of caveats soon becomes impressively large — and not very much value is left of modern mainstream economics if you ask me …

Still — a century and a half after Léon Walras founded neoclassical general equilibrium theory — modern mainstream economics hasn’t been able to show that markets move economies to equilibria.

We do know that — under very restrictive assumptions — equilibria do exist, are unique and Pareto-efficient. One, however, has to ask oneself — what good does that do?

It’s strange that mainstream macroeconomists still stick to a general equilibrium paradigm more than forty years after the Sonnenschein-Mantel-Debreu theorem — SMD — devastatingly showed that it is an absolute non-starter for building realist and relevant macroeconomics.

As long as we cannot show, except under exceedingly special assumptions, that there are convincing reasons to suppose there are forces which lead economies to equilibria — the value of general equilibrium theory is negligible. As long as we cannot really demonstrate that there are forces operating — under reasonable, relevant and at least mildly realistic conditions — at moving markets to equilibria, there cannot really be any sustainable reason for anyone to pay any interest or attention to this theory.

Stability that can only be proved by assuming ‘Santa Claus’ conditions is of no avail. Continuing to model a world full of agents behaving as economists — “often wrong, but never uncertain” — and still not being able to show that the system under reasonable assumptions converges to equilibrium (or simply assume the problem away) is a gross misallocation of intellectual resources and time.

Life is a tale told by an idiot = the social scientists we are endlessly quoting

Full of sound and fury — rational choice, equilibrium theory, etc.

Signifying Nothing — approximate knowledge is good enough

This should be a critical part of the mathematical discussion. Assumptions of equilibrium ensures the mathematics used is simple and therefore trivial algebra. The mathematics required to deal with reality is to solve appropriate differential equations. The equations are transient differential equations. Until economists accept this they will continue to provide mathematical solutions for a different universe than ours. The papers dealing with transient behaviour are a mere handful. It should not be difficult the understand them. Their are after all mathematicians at universities who will be able to help.

Lars Syll’s citation from Frank Hahn is (a part of) the second paragraph of the introductory section (A General Remark, pp.27-28) of Hahn’s Introduction’s to Petri and Hahn (eds.) (2003) General Equilibrium: Problems and prospects. (London, Routledge)

Let me cite the first paragraph that precedes the citation:

It is of some importance to understand what the argument is about which sadly is not often the case. No economic theory is true, it is at best an approximation to the truth. Unlike what the neo-Ricardians seems to think, general equilibrium theorists for the most part know this as can be seen by the effort which has been devoted by the best of them to improve the theory e.g. by Radner and Mas-Colell, and by their reluctance to use it empirically. It has been found that in general there are too few markets for the invisible hand to do its job, in particular its intertemporal job. One cannot in general exclude multiple equilibria, in the canonical version there is no room for fiat money, indeed exchange or interaction of any kind is not modelled, and so on and so on.

What Frank Hahn wanted to say is rather clear. He is not denouncing general equilibrium as an ‘idelology’. On the contrary, he is defending it against the accusation presented (mainly) by neo-Ricardians. He compared the latter with the Lucasians that he thinks “the currently most extreme neoclassical school”(p.28) and he claimed that both are “the case that ideology plays a large role in economics”. Hahn’s main target of his criticism is against neo-Ricardians’ “long-period analysis” and not against general equilibrium theory. He is contending that neo-Riardians economics is as ideologically motivated as Lucasian economics is.

Lars Syll uses his citation as an introduction to his criticism against general equilibrium theory. But it is extremely misleading and distorting. As we understand by the citation of the first paragraph, Hahn believes that general equilibrium theory can be improved by the effort of the best of general equilibrium theorists (surely including him), although he admits general equilibrium theory has many limitations and defects.

I am not defending Frank Hahn. I am an ardent critic of Hahn. I have written a paper against him from a Sraffian standpoint (See my paper: The Primacy of Stationarity: A case against general equilibrium theory, 1989). But I have no intention to misrepresent what Hahn wanted to say. To persuade mainstream neoclassicals, it is necessary first of all to persuade the person like Frank Hahn. I cannot think Lars Syll has succeeded to proceed toward this challenge even by a step.

I think everyone who knows his history of economics also remembers very well how Hahn looked upon GE in general — and that’s why the quote is so interesting :)

Even if Lars’s assumption that “everyone who knows his history of economics also remembers very well how Hahn looked upon GE in general” is right, the fact that Lars is distorting the Hahn’s main argument on GE theory is not denied. He approved GET despite of many of its caveats, because he believed that GE is the most promising framework and that it is possible to improve any defects that we know actually.

He referred to ideology only to illustrate that the neo-Ricardians are more motivated by it than scientific mind. In his mind, GET was not ideology at all. It was the most promising scientific framework. We can object Hahn’s belief only by presenting a new frame of analysis that is better than GET. Methodological arguments and detecting flaws or caveats of GET cannot persuade Hahn to change his belief.

Of course, Hahn’s observation on the neo-Ricardians is not fully founded, because he did not understand well what neo-Ricardians are claiming. It is true that neo-Ricardians in their argument with Hahn could not present their ideas clearly and theoretically. For example, Kurz and Salvadori and others argued that neo-Ricardians price theory should only be interpreted as long-period analysis. This contention is extremely defective, because it implies to abandon any arguments in short-period analysis. Another serious defect is that they put too much weight on distribution. To make a long argument short, they preferred distribution than value. (Remind that in Ricardo’s mind economics is a theory of value and distribution. Many of neo-Ricardians concentrated in distribution analysis and neglected theory of value.)

However, if I add in defense of neo-Ricardian or Sraffian or modern classical economics, value theory that can analyze short- and medium-period is now constructed. The core idea is presented in my paper “The Revival of the classical theory of values” (2016). More detailed and extensive account is given in the book “The Microfoundations of Evolutionary Economics” that will soon appear from Springer.

Here is a paper about Frank Hahn´s teacher and doctoral advisor,Nicholas Kaldor,probarly the most outspoken critisizer of the GE-economics among the Cambridge Keynsian´s

“Kaldor on Debreu: The Critique of General Equilibrium Reconsidered’

Thomas A. Boylan and Paschal F. O’Gorman

Department of Economics- National University of Ireland, Galway

ABSTRACT:

“This paper revisits Kaldor’s methodological critique of orthodox economics. The main target of his critique was the theory of general equilibrium as expounded in the work of Debreu and others. Kaldor deemed this theory to be seriously flawed as an empirically adequate description of real-world economies.

According to Kaldor, scientific progress was not possible in economics without a major act of demolition, by which he meant the destruction of the basic conceptual framework of the theory of general equilibrium.

We extend Kaldor’s critique by recourse to major developments in 20th century philosophy of mathematics, and then go on to demonstrate that Debreu’s work, based as it is on Bourbakist formalism and in particular Cantorian set theory, is conceptually incompatible with Kaldor’s requirements for an empirical science. This aspect of Kaldor’s critique has not been explored, and as a consequence a major source of substantiating his critique has remained undeveloped.”

https://aran.library.nuigalway.ie/bitstream/handle/10379/326/paper_0138.pdf?sequence=1

As I have argued many times, it takes a theory to beat a theory. Philosophical attacking and pointing out methodological defects of mainstream economics are not so effective as philosophers and methodologists believe it. Main field of battle lies in the theory construction. What is questioned now is which group of economics schools can present a theory or set of theories that are more feasible and have the wider scope in clarifying economic phenomena such as development, unemployment, globalization and financialization.

I have read the paper cited by Jan Milch:

Thomas A. Boylan and Paschal F. O’Gorman (2008) Kaldor on Debreu: The Critique of General Equilibrium Reconsidered.

http://hdl.handle.net/10379/326

If we omit the section 4 and the related part of the conclusion, this is a good piece of introduction to Kaldor’s critical thought on general equilibrium. However, the authors’ contention about mathematics has no relevance. Boylan and O’Gorman claim that “Debreu’s work … is conceptually incompatible with Kaldor’s requirements for an empirical science” because it is based “on Bourbakist formalism and in particular Cantorian set theory”. This reasoning is not well based.

They contrast two standpoints on the foundations of mathematics: (1) Hilbert’s and Borbakist axiomatic formalism and (2) Poincaré’s constructivism. This contrast is not very exact. As authors emphasize and as it is well known, Hilbert adopted the axiomatic method in The Foundations of Geometry and claimed that meaning of undefined terms can be interpreted in any way as far as a system of interpretation satisfies the set of axioms. Despite of his axiomatic thinking, he also held a subtle standpoint (which he named “finitary” method) toward foundational crises of mathematics.

Hilbert’s system of axioms (in The Foundations of Geometry) was “complete” in the sense that any entities which satisfy the axioms have the same structure. In his understanding, there is no need that a “straight line” of this mathematical entity should be interpreted as “straight line” in the ordinal sense of our life. However, Hilbert has taken a more subtle attitude toward the foundational crisis of mathematics. His “finitary” standpoint required a direct proof without appealing to proof by contradiction. Poincaré’s constructivism and Hilbert’s “finitary” method have many common features and it seems not correct to contrast two’s foundational thought on mathematics.

The authors coin another, similar terms making contrast between Platon, Kantor and Hilbert on one side and Poincaré and Kaldor on the other side. This unconvincing contrast is used to support authors’ main contention that Debreu’s proof of existence of equilibrium is established in the idealized world of Platon and Kantor and has no relevance with the real world.

Boylan and O’Gorman are partly right in the sense that Debreu (and Arrow)’s proof of existence of competitive equilibrium is based on Kakutani’s fixed point theorem and the standard proof of this theorem is based on indirect proof. In this sense we can say that Debreu’s proof is the one in the transcendental ideal world. But the authors are forgetting that Kakutani’s fixed point theorem can be proved by a more direct method. It is well known result that fixed point theorem can be proved by using Sperner’s lemma. Herbert E. Scarf used this method for giving an approximation procedure to find equilibrium. As far as I understand, both Hilbert and Poincaré admitted this method by mathematical induction as strictly valid, in other word, “finitary” and constructive.