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The third axiom of neoclassical economics: methodological equilibration

from Christian Arnsperger and Yanis Varoufakis

The third feature of neoclassical economics is, on our account, the axiomatic imposition of equilibrium. The point here is that, even after methodological individualism turned into methodological instrumentalism, prediction at the macro (or social) level was seldom forthcoming. Determinacy required something more: it required that agents’ instrumental behaviour is coordinated in a manner that aggregate behaviour becomes sufficiently regular to give rise to solid predictions. Thus, neoclassical theoretical exercises begin by postulating the agents’ utility functions, specifying their constraints, and stating their ‘information’ or ‘belief’. Then, and here is the crux, they pose the standard question: “What behaviour should we expect in equilibrium?” The question of whether an equilibrium is likely, let alone probable, or how it might materialise, is treated as an optional extra; one that is never central to the neoclassical project.

The reason for the axiomatic imposition of equilibrium is simple: it could not be otherwise! By this we mean that neoclassicism cannot demonstrate that equilibrium would emerge as a natural consequence of agents’ instrumentally rational choices. Thus, the second best methodological alternative for the neoclassical theorist is to presume that behaviour hovers around some analytically-discovered equilibrium and then ask questions on the likelihood that, once at that equilibrium, the ‘system’ has a propensity to stick around or drift away (what is known as ‘stability analysis’). 

It is quite remarkable that the above has been with us since the very beginning. When A.A. Cournot constructed the first model of (oligopolistic) competition in 1838, he immediately noticed a lacuna in his explanation regarding the emergence of an equilibrium. Rather cunningly, instead of discussing this difficulty, he studied what happens when we begin from that equilibrium. Would the system have a tendency to move away from it or was the equilibrium stable? The proof of its stability secured his place in the pantheon of economic theory. Moreover, it established this interesting practice: First, one discovers an equilibrium. Second, one assumes (axiomatically) that agents (or their behaviour) will find themselves at that equilibrium. Lastly, one demonstrates that, once at that equilibrium, any small perturbations are incapable of creating centrifugal forces able to dislodge self-interested behaviour from the discovered equilibrium. This three-step theoretical move is tantamount to what we, here, describe as methodological equilibration.

Note that methodological equilibration is equivalent to avoiding (axiomatically) what ought to be the behaviourist’s central question: Will rational agents behave according to the theory’s equilibrium prediction? Instead, the question becomes: If rational agents are behaving according to the theory’s equilibrium prediction, will they have cause to stop doing so? Note also that methodological equilibration has remained intact since 1838 and Cournot’s first use of it. To see this, consider the two great success stories to have come out of neoclassical economics since WW2: General Equilibrium Theory and Game Theory. In neither case does the equilibrium solution spring naturally from the models’ assumptions.

In General Equilibrium Theory its best practitioners state it quite categorically: convergence to some general equilibrium can only be proven in highly restrictive special cases. More generally, it is not just difficult to demonstrate that a system of theoretical markets will generate an equilibrium in each market, on the basis of rational acts on behalf of buyers and sellers; rather, it is impossible! (See Mantel, 1973, and Sonnenschein, 1973,1974.) In Game Theory the same result obtains: in the most interesting socio-economic interactions (or games) common knowledge that all players are instrumentally rational seldom yields one of the interaction’s Nash equilibria. Something more is required to bring on an equilibrium. That something comes in the form of an axiom that the beliefs of all players are consistently aligned at each stage of every game (see Hargreaves-Heap and Varoufakis, 2004, Chapters 2&3). This assumption is, of course, yet another reincarnation of methodological equilibration: for once we assume that agents’ beliefs are systematically and consistently aligned, they are assumed to be in a state of (Nash) equilibrium. Yet again, equilibrium is imposed axiomatically before stability analysis can test its susceptibility to perturbations. Cournot’s spirit lives on…

Christian Arnsperger and Yanis Varoufakis
WHAT IS NEOCLASSICAL ECONOMICS?
The three axioms responsible for its theoretical oeuvre, practical irrelevance and, thus, discursive power

  1. February 19, 2018 at 3:49 pm

    It’s OK. Economy is not in equilibrium. How then can we construct a theory not based on equilibrium? This must be the first question to be asked. Have the authors given an answer or at least a hint?

  2. February 20, 2018 at 3:28 pm

    I was observing what happens after my intentionally provocative comment. No one responded. It means that few readers were prepared to answer or respond to my question.

    I am more interested in the reaction from the part of Post Keynesian economists. I am one of Post Keynesians because I belong to Sraffians which is often included among Post Keynesian economics. (I know there are historians of economics who argue that Sraffa and Sraffians should be excluded form Post Keynesian economics.) I was against equilibrium framework since I read Kornai’s Anti-Equilibrium (1971) and Kaldor’s Irrelevance of equilibrium economics (1972). My third book (written in Japanese, 1990) is subtitled “From anti-equilibrium to complexity.” In my second book Reflections on modern economics (1983), I argued that “equilibrium is the epistemological obstruct” which is now the major hurdle for the further economics development. The same viewpoint is emphasized in the introduction of my first book (1981).

    From my long personal experience as a vehement anti-equilibrium stance in theory making, I know well that most of heterodox economists are indifferent from the danger of equilibrium framework. Post Keynesians (PK) are normally thought to be against neoclassical economics including New Keynesian economics. However, many (or majority) of PK theories are constructed on explicit or implicit equilibrium assumptions. Needless to say, their patron saint John Maynard Keynes in his General Theory (1936) adopted equilibrium as its analytical framework. But most of PK economists are not aware of this defective fact ant often repeat Keynes’s erroneous propositions.

    Of course, there are a few economists who acknowledged that Keynes retracted from sequence analysis to equilibrium method and prepared the way to the anti-Keynesian revolution in 1970’s. Please read for example Meir Kohn’s Monetary analysis, the equilibrium method, and Keynes’s “General Theory” (JPE 1986).

    In my first comment, I asked what would be a theory that is not based on equilibrium. The essence of the new method is already given. Only those people who are indulged in Keynes’s General Theory do not know this.

    Why did this kind of peculiar phenomenon occur? In my opinion, it is because PK economics are not aware that they do not have its firm theoretical foundations. I am discussing this point in the question page on ResearchGate. Please read and participate to the discussion:

    Does Post Keynesian Economics need no theoretical foundations?
    https://www.researchgate.net/post/Does_Post_Keynesian_Economics_need_no_theoretical_foundations

    • February 20, 2018 at 4:26 pm

      Two points.

      1. One can very reasonably base the theory of economics on equilibrium, but not as a fact: as an AIM. What has become desperately important is that the theory of economics should be about what do we have to DO to achieve equilibrium within our economies and our solar-powered ecology? See https://rwer.wordpress.com/2018/02/20/the-debate-continues-in-the-same-absurd-polarized-and-simplified-form/#comment-132297.

      2. Post-Keynesianism is not Keynesianism. Post-Keynesianism is about maintaining an equilibrium we already have. Keynesianism was about recognising a disequilibrium in the market’s provision of employment and putting it right directly, with non-market infrastructure maintenance and development. That having been done, the post-Keynesians bought up the improved public facilities and went back to profiteering by marketing the use of them.

  3. February 20, 2018 at 6:00 pm

    “It is quite remarkable that the above has been with us since the very beginning. When A.A. Cournot constructed the first model of (oligopolistic) competition in 1838, he immediately noticed a lacuna in his explanation regarding the emergence of an equilibrium.”

    Here’s a bit of fun. I mistook Cournot for Carnot, inventor of the four stroke cycle in heat or internal combustion engines, but in looking up “the Cournot cycle” came up with an explanation involving the same 4 x 4 structure my own theory of economics is based on, as indeed is the Myers-Briggs map of personality types. I am looking at p.86 of Tonu Puu’s “Oligopoly: Old Ends, New Means”.

    The section is about two competitors learning the periodicities they produce. In my scheme these are the real and the monetary economies. There is just one four period cyclic attractor, and a unique basin. In the first of the four periods the first competitor reacts to the lead of the second, who then follows the reaction; the first repeats his action and the second reverts to his. Given the simple regularity, suppose the agents learn the periodicity and react, not to the competitor’s action the period back, but FOUR periods back. What would be the outcome?

    “If one considers the dynamic every fourth period, the outcome is exactly the same as before. But in the three intervening periods, the system will settle to an indeoendent cycle of the same type. The total result is a composition of four 4-cycles successively displaced in time. The outcome is a 16-period cycle”. I would add that the same cycle is displaced in time for the two competitors.

    My theory interprets the points in the maths as different subgroups of people performing different functions, and ties in well with Soddy’s money keeping the system going between their doing their jobs. I find it a lot easier to follow my flow diagram rather than this interpretation in words. Still, with all the non-reaction one gets here (particularly from the posters) it is encouraging to find someone else having similar thoughts.

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