On mathematics and economics

22 Aug, 2013 at 10:57 | Posted in Economics, Theory of Science & Methodology | 6 Comments

Neoclassical economic theory today is in the story-telling business whereby economic theorists create mathematical make-believe analogue models of the target system – usually conceived as the real economic system. This mathematical modeling activity is considered useful and essential. Since fully-fledged experiments on a societal scale as a rule are prohibitively expensive, ethically indefensible or unmanageable, economic theorists have to substitute experimenting with something else. To understand and explain relations between different entities in the real economy the predominant strategy is to build mathematical models and make things happen in these “analogue-economy models” rather than engineering things happening in real economies.

Formalistic deductive “Glasperlenspiel” can be very impressive and seductive. But in the realm of science it ought to be considered of little or no value to simply make claims about the model and lose sight of reality.

With his profound knowledge of mathematics, Keynes realized the limits of its applicability to the real world — and that it was certainly not enough for a relevant social science to prove things about thought up worlds:

But I am unfamiliar with the methods involved and it may be that my impression that nothing emerges at the end which has not been introduced expressly or tacitly at the beginning is quite wrong … It seems to me essential in an article of this sort to put in the fullest and most explicit manner at the beginning the assumptions which are made and the methods by which the price indexes are derived; and then to state at the end what substantially novel conclusions has been arrived at … I cannot persuade myself that this sort of treatment of economic theory has anything significant to contribute. I suspect it of being nothing better than a contraption proceeding from premises which are not stated with precision to conclusions which have no clear application … [This creates] a mass of symbolism which covers up all kinds of unstated special assumptions.

Keynes to Frisch 28 November 1935

Neoclassical economists often hold the view that criticisms of its one-sided, almost religious, insistence on mathematical-axiomatic-deductivist modeling as the only scientific activity worthy of pursuing in economics, are the conclusions of sadly misinformed and misguided people who dislike and do not understand much of it. This is really a gross misapprehension. To be careful and cautious is not the same as to dislike. And as any perusal of the works of people like for example John Maynard Keynes or Tony Lawson shows, the critique is put forward by respected authorities. I would argue, against “common knowledge”, that they do not misunderstand the crucial issues at stake. Quite the contrary. They know them all too well – and are not satisfied with the validity and philosophical underpinning of the assumptions made for applying its methods:

The fundamental problem of modern economics is that methods are repeatedly applied in conditions for which they are not appropriate … Specifically, modern academic economics is dominated by a mainstream tradition whose defining characteristic is an insistence that certain methods of mathematical modelling be more or less always employed in the analysis of economic phenomena, and are so in conditions for which they are not suitable.

Fundamental to my argument is an assessment that the application of mathematics involves more than merely the introduction of a formal language. Of relevance here is recognition that mathematical methods and techniques are essentially tools. And as with any other tools (pencils, hammers, drills, scissors), so the sorts of mathematical methods which economists wield (functional relations, forms of calculus, etc.) are useful under some sets of conditions and not others.

The specific conditions required for the sorts of mathematical methods that economists continually wield to be generally applicable, I have shown, are a ubiquity of (deterministic or stochastic) closed systems. A closed system is simply one in which an event regularity occurs. Notice that these closures are as much presupposed or required by the ‘newer’ approaches to mathematical economics, those often referred to as non-linear modelling, complexity modelling, agent-based modelling, model simulations, and so on (including those developed under the head of behavioural or neuro- economics), as they are by the more traditional forms of micro, macro and econometric modelling.

The most obvious scenario in which a prevalence of such closures would be expected is a world 1) populated by sets of atomistic individuals or entities (an atom here being an entity that exercises its own separate, independent, and invariable effect, whatever the context); where 2) the atoms of interest exist in relative isolation (so allowing the effects of the atoms of interest to be deducible/predictable by barring the effects of potentially interfering factors). Not surprisingly the latter two (ontological) presuppositions are easily shown to be implicit in almost all contemporary economic modelling contributions …

However, explicit, systemic and sustained (ontological) analysis of the nature of social reality reveals the social domain not to be everywhere composed of closed systems of sets of isolated atoms. Rather social reality is found to be an open, structured realm of emergent phenomena that, amongst other things, are processual (being constantly reproduced and transformed through the human practices on which they depend), highly internally related (meaning constituted though [and not merely linked by] their relations with each other – e.g., employer/employee or teacher/ student relations), value-laden and meaningful, amongst much else …

Clearly if social phenomena are highly internally related they do not each exist in isolation. And if they are processual in nature, being continually transformed through practice, they are not atomistic. So the emphasis on the sorts of mathematical modelling methods that economists employ necessarily entails the construction of economic narratives – including the sorts of axioms and assumptions made and hypotheses entertained – that, at best, are always but highly distorted accounts of the complex phenomena of the real open social system … It is thus not at all surprising that mainstream contributions are found continually to be so unrealistic and explanatorily limited.

Employing the term deductivism to denote the thesis that closed systems are essential to social scientific explanation (whether the event regularities, correlations, uniformities, laws, etc., are either a prior constructions or a posterior observations), I conclude that the fundamental source of the discipline’s numerous, widespread and long lived problems and failings is precisely the emphasis placed upon forms of mathematical deductivist reasoning.

Tony Lawson