THE 'PROBLEM' OF CLOSED MODELS

The Problem of Closed Models.

 

The temptation of every theoretician is to freeze and crystallise reality, to render it 'objective' and thus to reify it, to turn it into an immutable 'thing in itself' impervious to human action. This is what we must avoid. But‚ again‚ we must avoid it not for the sake of an abstract principle to preserve the 'openness' of theory against 'closed' schemata - because otherwise there would be no difference between closed and open systems. The difference between a 'closed' and an 'open' theory cannot be formal, because then we would reify the 'openness' of the 'open' theory, reducing it thus to a 'crystallised' abstraction. Instead, we must specify in what sense a theory is ‘open’ as opposed to 'closed', principally so we may understand (a) how closed systems are possible, and (b) why they are constructed.

 

Although one still sees it repeated incessantly (often from the pens of those

who should know better) that Adam Smith dealt with a world of atomistic

traders, equilibrium, and perfect competition, students of Smith understand

that quite the opposite is the case. One has only to read the first few pages of

The Wealth of Nations to recognize that Smith was concerned with economic

growth — and that the engine of growth is innovation brought about by the

division of labor. (Langlois, Analytical Survey of the Austrian School, p.9)

 

It is incorrect to argue against Arrow and Hahn that Adam Smith’s “invisible hand” was not, or differed from, “equilibrium analysis” in that it had an ‘ontic’ dimension (it was ‘open-ended’ and ‘inter-relational’ and so on) and did not envisage “atomistic” entities unconnected to “social reality”. That may be true of the “wealth-of-nations” or “development” side of Smith’s theory, as Langlois maintains above, but certainly not of the “co-ordination” side (see Loasby’s discussion of Smith in Equilibrium and Evolution). Once one accepts, as one must, that, in Lawson’s own words, (a) “social reproduction of complex, internally related, dynamic, social structures occurs”; (b) that it “occurs in an open world of individuals seeking their own ends”; and (c) that the aim of the theorization of such a system is to optimize the welfare of its individual agents, - then one accepts “the problematic of co-ordination” and the social reality or “social order” viewed as a “sphere of exchange”. And at that precise instant, “the social reproduction” of such “social structures” becomes subject to the “formalistic modeling” of neoclassical theory, that is, to a “closed” theory or Schema – because all its variables are interdependent. In other words, whatever else Smith may have had in mind, his very definition of the problematic of economic theory – the determination of clearing exchange prices in a self-regulating market system, one where agents act self-interestedly and independently – means necessarily that his was a “closed” theory. And this is precisely what Arrow and Hahn argue (in their “Historical Introduction” to General Competitive Analysis), however much Lawson and Langlois may disagree! Smith’s “Invisible Hand” would make no sense whatsoever if this were not the case! (Truly, Langlois “ought to know better”!) Because Smith (unlike Marx, to name one) makes the determination of value of goods dependent on the amount of “labour”, and their corresponding prices - including the price of “labour” - dependent on market-clearing prices, it follows that all of Smith’s system variables are interdependent, his market prices are relative prices, and therefore his is an equilibrium model and necessarily tautological.

 

Although Langlois denies that Smith was an “optimizer” in this sense, he states quite correctly the difficulty involved with closed systems, as is shown here:

 

That economic agents — and economists, for that matter — live in an

open-ended world is hard to dispute. Yet economic theory, especially in its

neoclassical manifestations, finds this an extremely troubling idea. It is

difficult to analyze the optimum allocation of resources if there are always

new resources, techniques, markets, or even tastes yet to be discovered.

Now, one may legitimately choose to construct closed theories (models) in

which all knowledge is ultimately given. For instance, one might argue that

all theories (models) necessarily convey only part of the truth, and that there

are circumstances in which the assumption of fixed-and-given knowledge is

not inappropriate. Similarly, one might argue that economic theory

progresses by successive approximation, and thus that “perfect knowledge” is

only a starting point from which to move to more “realistic” assumptions

about the knowledge agents possess. What sets the Austrians apart is that,

for the most part, they rejected both of these arguments and chose to pursue

theories in which the open-ended character of the world makes itself

unmistakably felt. (Langlois, Analytical Survey of Austrian School.)

 

 

There are two ways to escape closed systems. The first is to turn the notion of equilibrium into a “process” ex ante facto (inter-temporal equilibrium). The other is to point to the existence of co-ordination in the economy – the fact that “it works” to a given extent - to show, ex post facto, that it exists empirically and from there advance an inductive theory of the operational equilibrium of the economy. Both these approaches dispense with treating the inter-est of economic activity because they focus exclusively on its modus operandi – and specifically on that peculiar point called “equilibrium” where all prices are necessarily relative, and therefore dispense with the need to indicate what absolute prices are about! Hence, the emphasis on “spontaneous [unplanned, organic] order” (Hayek) or co-ordination. In the absence of such assumed “spontaneity” or synallagmatic catallaxy, the equilibrium of such absolutely selfish and atomic agents necessitates a totalitarian entity, an external “demon” (Clower) or a providential entity (Adam Smith’s Invisible Hand), or a “hidden God” (deus absconditus), or a Sovereign (Hobbes’s Leviathan, a deus mortalis), or even a neutral arbiter (Walras’s auctioneer) to ensure the “closed functioning” of the system, which otherwise would be unstable axiomatically (because obviously its selfish and atomistic  agents are antithetical to its cohesion).

 

Here we wish to throw more light on the conceptual characteristics of “closed systems” and then see how they apply to, or assume the form of, socio-political categories. What Langlois fails to perceive is that the problem of orthodox economic theory is not that “closed systems” or “formal models” cannot take account of a necessarily changing reality – because, as we shall show presently, they cannot do so by definition! The problem is instead that bourgeois orthodox economic theory erects closed systems or models precisely because it does not wish to identify, let alone confront, what it is that market agents are seeking in a competitive market (Latin, com-petere, covet or fight together over a common bone of contention). Neoclassical theory studiously avoids the most essential element of capitalism:- the real political antagonism at the heart of capitalist social relations of production that makes these social relations categorically impervious to their description or encapsulation by a logico-mathematical Schema.

 

To exemplify, when Bohm-Bawerk exulted for his proof that Marx’s transformation of values into prices  – which he called appropriately “the ‘close’ [Ab-schluss] of Marx’s system” – was categorically impossible (thereby earning for himself the sobriquet of “the bourgeois Marx”), he inadvertently and ironically was celebrating the demise of his own attempt at squaring the circle with yet another stab at “the Law of Value” – his theory of “roundaboutness”. The fundamental characteristic of all theories of value – including Marx’s - is that they seek to find a univocal relation between prices and values – a Law of Value. But this is attempting the impossible – because value is a political category whereas prices are the empirical institutional monetary manifestation of the transformation of value from the production of goods (valorization) to their sale (realization of value). Per contra, the existence of a Law of Value would signify the end of economic activity as a conflictual and antagonistic reality – thereby turning economic theory into pure engineering! If we could measure all the inputs to economic production according to a Law of Value in the same way we measure the material quantities needed to produce material goods, then economics would be indistinguishable from engineering.

 

(Indeed, let it be said parenthetically, the origins of Neoclassical Political Economy is to be found in Anglo-Saxon academic circles firmly implanted in engineering faculties. From Gossen to Gottl to Menger, Wieser, Jevons and Walras, the engineering stamp of these neophyte “political economists”, for whom economics was only an appendage to their technico-mathematical bent, is utterly unmistakable.)

 

Langlois’s conclusion that the problem with closed systems is “that economic agents — and economists, for that matter — live in an open-ended world” both mystifies the issue and misses the mark. It misses the mark because the fact that “the world is open-ended” has nothing to do with anything – because it can be applied to any aspect of “the world”, of human experience – and therefore to any scientific hypothesis. And it mystifies the issue because it dissolves the political antagonism of capitalist economic reality into the ethereal vault of “the open-ended world”! In other words, it attributes the transformation of economic relations philosophisch to the becoming of “the world”.

 

The first question that the critics of equilibrium analysis fail to ask and confront is (a) why bourgeois economists feel the need to try to achieve the impossible – to encapsulate economic relations into a Schema whose very formalism obliterates, nullifies the substance and purpose of economic activity – to leave out the political element. (Gunnar Myrdal was wrong to title his study “the political element in economic theory” – because the real political element of bourgeois economic theory is: – to conceal and obliterate that very political element! – With the consequence that there is no political element in economic theory outside of the theory itself. Economic theory eschews politics – and that is precisely why it is political!) And the second question – by far the most important of all – is, (b): given that a closed system or model is intrinsically tautological and therefore meaningless in and of itself – how is it then possible for the bourgeois economists to make any use of it, to give it a purpose?

 

 

When heterodox critics of closed systems complain about their formalism, their failure to describe reality and therefore also to predict it, they pose an ideal value (a veritable Kantian Sollen [Ought, Categorical Imperative]) that underlies “social reality”, as if this mythical “social reality” were a neutral, objective state of affairs and not an antagonistic one that requires a hortatory or even partisan theory or analysis – what Schumpeter calls “a heuristic tool”. The crucial difficulty with this criticism of closed systems is that “social reality” as an objective neutral entity simply does not exist! The problem is not in the theory or the analysis or the “system”, then: the problem lies with the reality because the reality is a problem! The fact is that social reality changes constantly because it is antagonistic and conflictual. And this is the greatest problem with closed systems: they leave out logically the political antagonism central to the “social reality” that they wish to capture or describe but in fact can only prescribe! By contrast, the problem with “open systems” is that they reify the sources of change by seeking “to freeze” them, or else do not specify them sufficiently so that the system is rendered useless (Robinson’s “one to one map”).

 

Neoclassical theoreticians never pretended to imitate or encompass “social reality”. Under their stated aim “to formulate” reality lay the ideological and strategic goal which consisted, in Lawson’s express words,

 

“[in] inventing ‘a reality’ of a form that their modeling methods can address (i.e., a world of isolated atomistic individuals possessed, for example, of perfect foresight, or rational expectations, omniscience, pure greed, and so forth)”.

 

If Lawson had bothered to look more into this ‘social reality’, he would have found the problems that equilibrium analysis reflects and mirrors! But Lawson does not even bother to examine the assumptions of the analysis except to oppose to it his ‘post-modern’ late-romantic progressive ideals – pathetic and powerless – but still in the same world of meaning that belongs to Neoclassical theory, namely, the sphere of exchange and its axiomatic assumptions. Lawson and Langlois assume that there is a “reality” that theory can disclose or represent. But this “reality” is itself subject to distortion by conflict and antagonism! Theory and analysis then must reflect this conflicting “reality”; they must be one-sided.

 

The kind of ‘ontic’ assumptions that Lawson would substitute for those of equilibrium analysis are not much better or realistic than those of equilibrium analysis itself - and would end up as ‘reifications’ capable of “formalization/formulation” in an equally “dynamic equilibrium” model. Heterodox economists should ask not whether equilibrium analysis is “true” or even “realistic”, but whether it is effectual – and above all why and how it can be effectual! What they should challenge are not the claims to “realism” but what kind of “practical assumptions” lie behind the “theoretical assumptions” of neoclassical analysis. As Hahn put it in his own defence:

 

The great virtue of mathematical reasoning in economics is that by its

precise account of assumptions it becomes crystal clear that applications

to the “real” world could at best be provisional. When a mathematical

economist assumes that there is a three good economy lasting two periods,

or that agents are infinitely lived (perhaps because they value the

utility of their descendants which they know!), everyone can see that we

are not dealing with any actual economy. The assumptions are there to

enable certain results to emerge and not because they are to be taken

descriptively. (Hahn, 1994, p. 246)” (434)

 

Hence, the question remains of how a formal logico-mathematical tool - that possesses no meaning because it is a pure identity – can be applied practically to a society so as to guide political decision-making or policies. The obvious immediate way out is to insist on the objectivity and mechanical properties of the equilibrium Schema – to insist not on its substantive merits, the creation and distribution of “wealth”, but on the equally formal fact of co-ordination. But the co-ordination of productive activities cannot in and of itself justify its actual existence without referring to what is being co-ordinated, that is, the purpose of economic activity. Co-ordination is simply a relation between several activities. But the existence of co-ordination can be justified, can have any sense or meaning at all, only if it is founded on an aim or goal or purpose or interest that is conducive to that co-ordination! Co-ordination of anything for its own sake is quite simply meaningless! In the absence of an interest for which market agents can agree to co-ordinate their activities, there is no point to the co-ordination at all!

Interestingly, Loasby (in “Closed Models and Open Systems”) sees “closedness” not as tautology or even as determinateness of relative prices but rather as “rest”, absence of “development” or “growth”. The central question becomes then how “to open” this “closed system” so that “co-ordination” allows for “evolution” and “growth”. This is where Adam Smith and Schumpeter differ from the other theoreticians – although, significantly, Loasby allows, contra Lawson and Langlois, that Smith was also an equilibrium thinker.