Recently I was asked to contribute to a German journal on the topic of the failure of the vast majority of mathematical economic models to anticipate the Global Financial Crisis, and whether mathematics itself was at fault. This was part of my response.

Part One: The core fallacies in conventional economics

The vast majority of mathematical economic models developed by the world's Treasuries, Central Banks and economic research institutions completely failed to anticipate the Global Financial Crisis. The most egregious example of the failure to see what was imminent can be found in the OECD Economic Outlook of June 2007. Right on the verge of the collapse, the OECD summarised the findings of its economic model thus:

Indeed, the current economic situation is in many ways better than what we have experienced in years. Against that background, we have stuck to the rebalancing scenario. Our central forecast remains indeed quite benign: a soft landing in the United States, a strong and sustained recovery in Europe, a solid trajectory in Japan and buoyant activity in China and India. In line with recent trends, sustained growth in OECD economies would be underpinned by strong job creation and falling unemployment. (OECD Economic Outlook, Vol. 81, June 2007, p. 5)

This statement may well be the 21st century equivalent of Irving Fisher's ill-fated observation, days before the Stock Market Crash of 1929, that:

“Stock prices have reached what looks like a permanently high plateau. I do not feel that there will soon, if ever, be a fifty or sixty point break below present levels, such as Mr. Babson has predicted. I expect to see the stock market a good deal higher than it is today within a few months.” (Irving Fisher, New York Times, Wednesday, October 15, 1929)

Many critics of economics have taken this abject failure as yet another sign that economics cannot be a mathematical discipline – that mathematics itself is the problem

I disagree. Though there are indeed far more stringent limitations on the effectiveness of mathematics in economics than conventional 'neoclassical' economists appreciate, I instead point the blame at the core beliefs of neoclassical economics itself. It is these beliefs, whether expressed in words or equations, which explain why most economists completely failed to anticipate the crisis. Nonsense is nonsense, whether expressed in words or equations.

There are so many core beliefs in neoclassical economics that are manifestly false that it is hard to decide where to start. But the most apt fallacies that led to its myopia in the face of this crisis were (a) that money – and hence debt – does not affect real output and (b) that the economy can be modelled as if it is always in equilibrium (except when disturbed by exogenous shocks).

Money doesn't matter?
The most strident advocate of the first fallacy was Milton Friedman, who began his paper "The optimum quantity of money" with this proposition:

It is a commonplace of monetary theory that nothing is so unimportant as the quantity of money expressed in terms of the nominal monetary unit… let the number of dollars in existence be multiplied by 100; that, too, will have no other essential effect, provided that all other nominal magnitudes (prices of goods and services, and quantities of other assets and liabilities that are expressed in nominal terms) are also multiplied by 100. [Friedman, M. 1969, ‘The optimum quantity of money’, in The Optimum Quantity of Money and Other Essays, MacMillan, Chicago, p. 1; emphasis added]

The Post Keynesian economist Joan Robinson once described Milton Friedman as a magician who would put a rabbit into a hat in full view of the audience, and then expect applause when he pulled it out again sometime later. This is an excellent example of this, because Friedman's proposition that the nominal amount of money doesn't matter was based on the assumption that if there were inflation, then all other nominal quantities – including money wages, money profits and the money value of outstanding debt – would also be increased at the same rate.

This is nonsense. On this planet Earth, when inflation drives up the cost of commodities today, that does not guarantee that wages and profits will rise by the same amount. Most importantly, nominal debt levels are unchanged. For Milton Friedman's rabbit to be a live rather than a dead bunny, you would need an economic system in which all nominal quantities were indexed to each other. No such economic system exists.

As a result, Friedman's initial proposition is false: "the quantity of money expressed in terms of the nominal monetary unit" is important, primarily because it is the link between income flows today and financial commitments entered into in the past. This matters during times of inflation, but especially during times of deflation – falling prices – as occurred during the Great Depression, and as Japan has experienced periodically for the last two decades.

Economic models that follow Friedman's fallacious advice and ignore the nominal amount of money are therefore going to miss the crucial dynamics of credit and debt formation. In fact most economic models go far beyond Friedman's stricture – which at least still allows that the inflation-adjusted quantity of money might matter – and abstract from money entirely. They instead work in "real" values only, and omit private debt completely from their analysis.

It is no wonder then that they missed a crisis caused by an excessive level of private debt. Rather than the mathematics itself being to blame, their decision not to incorporate debt into their models meant that they suffer from what is technically known as "omitted variable bias". A mathematical model that does not contain variables that are in fact crucial to the system it is supposed to represent must ultimately be wrong. This is not the fault of the mathematics per se, but of the mathematician who left out the crucial variable.

The economy is always in equilibrium?
The second error, of modelling the economy as if it is always in equilibrium, or will tend back to equilibrium after any "exogenous shock", is the coup de grace for the capacity of neoclassical mathematical models to accurately model the economy.

This itself is not so much a case of ideology – though there is certainly that to it – than of ossified intellect. The founding fathers of the neoclassical school of thought knew that they were making a stop-gap decision when they attempted to model the economy as if it were in equilibrium at all times. But they hoped that their successors would build on their work to develop a truly dynamic model of the economy, which would cope with both equilibrium and disequilibrium equally well. These expressions of hope for the future – and the realisation that equilibrium modelling was inadequate – occur throughout the original "Great Works" of the neoclassical school. Jevons wrote that:

We must carefully distinguish, at the same time, between the Statics and Dynamics of this subject. The real condition of industry is one of perpetual motion and change. Commodities are being continually manufactured and exchanged and consumed. If we wished to have a complete solution of the problem in all its natural complexity, we should have to treat it as a problem of motion – a problem of dynamics. But it would surely be absurd to attempt the more difficult question when the more easy one is yet so imperfectly within our power. It is only as a purely statical problem that I can venture to treat the action of exchange.. (William Stanley Jevons,1871 , The Theory of Political Economy, Chapter ,5 Paragraph 25)

Similarly, Marshall wrote that:

the problem of normal value belongs to economic Dynamics: partly because Statics is really but a branch of Dynamics, and partly because all suggestions as to economic rest, of which the hypothesis of a Stationary state is the chief, are merely provisional, used only to illustrate particular steps in the argument, and to be thrown aside when that is done.(Alfred Marshall, 1890, Principles of Economics, Book V,Chapter V, Note 19)

These 19th century economists clearly hoped that the 20th century would see the development of a truly dynamic model of economics. Poignantly, at the turn of the 20th century, the developer of the marginal productivity theory of income distribution, John Bates Clark, predicted that the hallmark of economic theory in the 20th century would be the development of dynamics:

“A point on which opinions differ is the capacity of the pure theory of Political Economy for progress. There seems to be a growing impression that, as a mere statement of principles, this science will soon be fairly complete… It is with this view that I take issue. The great coming development of economic theory is to take place, as I venture to assert, through the statement and the solution of dynamic problems.” (John Bates Clark 1898, "The future of economic theory", Quarterly Journal of Economics Volume 13, p. 1)

Clark's prediction about the future development of economic theory was clearly wrong: rather than having developed models that function both in equilibrium and out of it, neoclassical economics has continued to give equilibrium a primary role in its thinking. Today, what neoclassical economists describe as dynamic modelling – such as so-called "Dynamic Stochastic General Equilibrium" models – are dynamic in name only (if they were truly dynamic, they would be "Dynamic Stochastic General Disequilibrium" models).

Why have modern neoclassical economists failed to do what their founding fathers expected? Here mathematics, ideology and ignorance come into play – with mathematics as the hero, and ignorance and a largely unconscious ideology as the villains.

To address ideology first, the effective hijacking of the preceding classical school of economics by Marx played an important role in the rise of neoclassical economics. Classical economics, in the hands of Smith and Ricardo, was a weapon to argue for capitalism over its then feudal counterpart. But Marx took this tool and turned it into a critique of capitalism and an advocate for socialism. The neoclassical school, with its emphasis upon subjective value and marginal analysis, took up the cudgels for capitalism, and put into marginal form Smith's proposition that a free market would lead not to chaos and breakdown but order: the "invisible hand" would ensure that market outcomes were not merely beneficial to capitalists, but beneficial to all.

An essential aspect of this vision of capitalist beneficence was equilibrium: whereas its detractors might say that a free market would lead to chaos, neoclassical economists set themselves the task of proving that the capitalist market system would lead to a utility-maximising equilibrium.

The crowning glory of early neoclassical economics was Leon Walras's model of "general equilibrium"; whereas Marshall considered what happened in one market in isolation from all others, Walras attempted to model what happened when markets interacted with each other – in the belief that the process of supply and demand responding to changes in prices would lead all prices in the economy towards equilibrium, so that supply would equal demand in all markets.

However, this raised the problem that a move towards equilibrium in one market could disturb equilibrium in others. Walras conjectured, but he could not prove, that the stabilising effect of prices in one market would outweigh the destabilising effect of this market on others.

Now enter mathematics as the hero. In a totally unrelated piece of research into pure mathematics, Oskar Perron and Georg Frobenius incidentally showed that Walras's conjecture was false. They were simply examining the properties of matrices – square arrays of numbers that play a significant role in mathematics – and were concerned with the properties of a matrix that consisted only of positive numbers or zeros. One property they found was that any process that depended both on a given matrix and its inverse would be unstable.

General equilibrium economic models inherently are of that type: the price dynamics depend upon a given matrix, and the quantity dynamics depend upon its inverse. Therefore the equilibrium of a general equilibrium model must be unstable. Walras's conjecture was therefore false: the movement of prices towards equilibrium in one market would be more than offset by the destabilising impact of this price change in other markets, and a model of a multi-market system – to say nothing of a real economy – would never reach equilibrium.

The obviously correct conclusion from this mathematical result was that prices must be set in disequilibrium – but economists remained so ideologically wedded to the belief that a market economy tended towards equilibrium that they misinterpreted and ignored this result.

Consequently, every time neoclassical economists make a foray into genuine dynamic modelling, they get a result they don't expect – an unstable equilibrium. Since they are often ignorant of the basic mathematical reason as to why, they tend to stray back to a framework in which this particular force for disequilibrium can be ignored – as with "Dynamic Stochastic General Equilibrium" models that pretend that the entire economy can be modelled as a single agent producing and consuming a single good – or they impose equilibrium solutions on systems that fundamentally have disequilibrium dynamics.

This mathematically invalid past-time would not be a problem if it didn't have real-world impacts. But of course it did. Because neoclassical economists treated any economic variable generated by a market economy as being in equilibrium, they fantasised that stock and house prices were in equilibrium when clearly they were in a bubble, and they ignored rising levels of private debt in the belief that whatever level of debt applied was an equilibrium one – and therefore justified by market fundamentals.

Nowhere was that fantasy more damaging than in the reception that neoclassical economics gave to the ideas of Irving Fisher as he attempted to explain how the Great Depression occurred in 1933. Intellectually chastened and effectively bankrupted by his false beliefs about the market in 1929, Fisher set about working what in his model of the economy had led him so badly astray. The fundamental flaw, he concluded, was his belief that the economy was in equilibrium – and therefore that observed market prices, debt levels, and everything else reflected the equilibrium values of these variables. In 1933, he reasoned that this could not possibly be the case in the real world, and therefore if it were to have any relevance to the real world, economic theory had to model disequilibrium dynamics.