# Economics: we find the truth axiomatically

## How economists implicitly assume what they claim to know

By way of Casey Jaywork, I stumbled across this insightful, if somewhat philosophical, paper from 2006 by economists Christian Arnsperger and Yanis Varoufakis. I've often marveled at the ability of mainstream economists to reject criticisms of their work using any of an apparently infinite set of slippery and, I think, ultimately disingenuous defenses. "We don't really believe what you claim we do," perhaps, even though you find such assertions clearly in their papers. Or "you're just ignorant of the literature, because so and so showed long ago that these assumptions aren't necessary," even though, if you look up so and so's paper, you find that it "shows" nothing of the sort. No worries; there are always other papers to be referred to in further defenses.

Arnsperger and Varoufakis suggest that there is good reason for this; that many of the common criticisms of mainstream economics do not aim for the right targets, and hence make these kinds of defenses too easy. However, they suggest there are REAL and legitimate targets, these being axiomatic assumptions of several kinds that economists make habitually, most now without even realizing it. These assumptions provide the framework for all analysis; they go unquestioned by assumption. I won't go into detail -- the paper is well worth a 15 minute read -- but I’ll just quote one small section on what they refer to as the "axiomatic imposition of equilibrium."

Why do economists so pervasively assume an equilibrium? I wrote a whole book attacking the idea, and was probably in large part wasting my time! Equilibrium is not widely assumed in economic analyses because it is plausible, based on evidence, but because, the authors suggest, the theoretical edifice of all economics would crumble without this assumption:

The third feature of neoclassical economics is, on our account, theaxiomatic 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 methodologicalequilibration.

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…

One day, I believe, people will look back in wonder at the immense volumes of economic literature we have produced at vast expense to prove various theorems concerning “economic systems”. Modern scientists from many other fields look into economics and wonder this already.

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