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Wednesday 18 May 2011

Exit the Walras, followed by Equilibrium


As we saw in Economics and Psychology: The Divorce, the two queenly social sciences long ago parted ways. What we haven’t yet seen is quite what the economists did next, when they abandoned the idea that people had any part to play in economic behaviour.

To do this they chose to follow a path predetermined for them by physicists, which would have been all very well were it not for the fact that the bit of physics they choose to use turned out to be incomplete. Unfortunately, by cloistering themselves away from new research for nearly a century, this new reality was missed and by the time they emerged from their bunkers economics wasn’t so much wrong as irrelevant.


In Metaphors of Mind and Money we showed how the social sciences are rather too willing to leap on the latest novel theory to appropriate it for their own rather than coming up with their own ideas. Everything from fluid mechanics to chaos theory has been expropriated, usually to no good effect. At the end of nineteenth century economists, looking for a way of making their subject quantifiable, alighted on just such a metaphor.

As usual the one they chose was the latest and greatest scientific theory and, as usual, they chose this metaphor without really understanding whether it genuinely modelled the phenomena under investigation. And then, just to make sure they weren’t so much barking up the wrong tree as exploring the wrong solar system, they ignored the fact that the basis of their metaphor was shortly shown by physicists to be, at best an partial truth.


This metaphor was thermodynamics and, in particular, the First Law which we probably know better as the Law of Conservation of Energy. It states that no matter what we do we can’t destroy energy, we can only move it from one state to another. Under the first law the critical idea is of equilibrium: because energy can’t be destroyed then the system must always tend to a stable state where energy is conserved.

Economists, primarily Léon Walras, seized upon the idea of equilibrium and the mathematics of the First Law as a way of making economics a quantifiable, hard science. To this day equilibrium is the dominant paradigm of standard economic theory and, if you look hard enough, it’s everywhere: see, for example, Tâtonnement: Groping For Stock Equilibrium.


To verify his theory Walras put it in front of the eminent scientist Henri Poincaré who acknowledged that the math looked good but pointed out there were a couple of tiny potential problems:
"At the start of every mathematical investigation, there are some hypotheses and, to make that investigation successful you must (just as in physics) be aware of those hypotheses. Forgetting this condition means going beyond the reasonable limits. For example, in mechanics, we often ignore friction and consider bodies as perfectly polished. You look at human beings as infinitely selfish and infinitely farsighted. The first hypothesis may be admitted in a first approximation, but second requires further consideration".
(Any errors in the French translation are entirely down to my faulty education).

Or, to put it another way, you might just allow that people are perfectly selfish but it’s almost impossible to believe that they’re perfectly rational. Indeed, to make this work in markets, economists had to make the assumption that there was some illusory Walrusian Auctioner who enabled prices to find their equilibrium.

As Alan Kirman has observed the problem with this is that it makes assumptions about people that simply aren’t realistic:
“How do agents know when to stop calling out prices or to trade? Walras seems to suggest, that by looking around, they would be able to see or hear the opportunities available and to trade accordingly. Yet, if there were enough traders to make the assumption of free competition plausible, then checking who had an excess demand or supply and how much was involved, would be a daunting task”.
Indeed Walras himself never seems to have quite managed to sort out this contradiction in his own mind, but when pushed clearly favoured mathematical rigour over realism. None of which means that his successors needed to follow his lead: but they did, and equilibrium based theories became the norm, despite the difficulties they caused.


Economists are, however, nothing if not bright and what would have seemed insurmountable problems for most of us they merely regarded as the next challenge. Take growth, for instance. In an equilibrium based system everything is conserved: although you can transform kinetic energy in potential energy or goods into money you can’t actually create more energy or more money. So how do you account for growth?

Well, that’s a long story in its own right but suffice to say a number of brilliant men spent their careers showing that it was possible and were lauded for their achievements. Unfortunately, as it turned out, this was a bit like giving Einstein a Nobel Prize for spending thirty years developing better ways of solving the Rubic’s Cube: utterly brilliant, perfectly pointless and a dreadful waste of talent.


Now this idea of economic equilibrium may be a metaphor, but it’s not simply enough to argue that economics is similar to thermodynamics if you want to make the equations work. This was one of Poincaré's points: if you want to use the mathematical structures behind thermodynamics you’re arguing that the economy is an equivalent system.

Which is all very well but leads to a range of issues, not the least of which is that there are two laws of thermodynamics and economic equilibrium relies only on the first of them. The reason for this is a quirk of history, for when Walras first developed his model the Second Law hadn’t yet been properly understood and wasn’t part of the general physical models he was using.


We’ve met the Second Law in these pages before: in the ideas in Maxwell’s Demon Investor. The key concept is that of entropy, the idea that a thermodynamically closed system gradually moves from order to disorder. Think about a teenager’s bedroom if an adult doesn’t input energy into keeping it vaguely tidy: that’s entropy for you.

So if the thermodynamic metaphor of economics is to hold it implies that the Second Law must also be hold in economies. And if the Second Law is true it tells us that the economy must be moving from a state of order to one of disorder. Things should be going badly awry.

Now, while there is an argument that this may be true it’s probably not. If anything we’re seeing economic growth and improvements in the longevity and wealth of most of humanity. If the laws of thermodynamics apply to the economy this shouldn’t be happening and we should all still be wandering around banging rocks together. And wondering where all the rocks had gone. And why there was so much damn gravel about.


Of course the reality is that economics can't be equivalent to a thermodynamically closed system because there aren't any such systems on Earth, outside of scientists' labs and engineers' systems. However, that doesn't explain why economists ignored the developing understanding of the Second Law which should, at least, have told them that there was something awry with their equilibrium approach.

So why did economics not follow the models of physics it started with? Well, Kirman reckons it’s because:
“Had it done so it would have found itself in a contradictory position. Thermodynamics and emphasis on entropy would suggest a system which was constantly moving towards disorder”.
Or to put it another way: if economists had acknowledged the problem they’d have had to rip up their lives’ work and admit that most economic theory – and therefore policy made from it – was bunkum. And if you don’t believe that’s true think back to the financial panic of a few years ago when regulators and politicians abandoned all their carefully thought out models and freely admitted they were making policy up on the hoof.

An economics that tells us what to do when times are good but abandons us in times of trouble is about as useful as a concrete lifebelt. It’s time to exit the Walrasian legacy, abandon equilibrium and start again, from somewhere more useful.

Related articles: Metaphors of Mind and Money, Maxwell’s Demon Investor, Economics and Psychology: The Divorce

1 comment:

  1. Excellent points, well-made. There is more along similar lines in "The Origin of Wealth" by Eric Beinhofer (which you may or may not have seen).

    A relation of mine is a professor of finance in a UK university; this is someone who has spent all of their life in the mathematical economic paradigm, and has no interest in changing the status quo. This is an example of why I see no quick way of changing things since there are too many vested interests.

    It is frustrating if you're a non-mathematician to be constantly told that 'you don't really understand it' when the 'it' in question is so philosophically absurd so that the underlying math is irrelevant.