Chapter 9 of Steve Keen’s Debunking Economics criticises economist’s reliance on static models in a clearly dynamic system. He first shows both Walrasian equilibrium and Gerard Debreu’s related models to be highly questionable – this is, of course, not difficult, and will be met with ‘we have improved on those!’ However, the real message of the chapter is that static analysis is fairly worthless, and dynamic analysis does not simply ‘fill in the gaps’ between different equilibria.
If you are not familiar with Walras or Debreu, prepare to be amazed at how clearly unlike the real economy these models are.
Walrasian equilibrium supposes that an auctioneer has control over the buying and selling of every commodity, and determines the ‘market clearing’ price – where supply equals demand for every commodity – before any trade takes place. Walras suggested that the auctioneer start with a random guess, which would probably be wrong. They’d then go on to adjust prices until equilibrium was reached, at which point trade would take place.
Keen refrains from commenting substantially on the realism of this approach, instead taking his usual route of accepting economist’s logic, then showing that the model still can’t work. The maths is somewhat over my head, but Keen channels John Blatt, who uses a theorem of matrices – a mathematical system by which a Walrasian auction can be explained – to show that the auctioneers prices will not converge towards equilibrium.
Simply put, there are two conditions required to Walras’ auction to ‘work:’
- The system must be able to reproduce itself e.g. produce enough iron for the required inputs of iron in the next period.
- The prices must be ‘feasible;’ basically, they cannot be negative.
According to Blatt, these two conditions require the matrix and its inverse to have the same properties. In English, this means that something and its opposite have to have the same properties, which is obviously logically impossible. Hence, the auction will not converge to equilibrium.
Debreu did not worry about whether an economy would converge to equilibrium, but simply whether or not an equilibrium existed. However, the same conditions outlined above – not to mention the incredibly restrictive assumptions of Debreu’s model, such as virtually identical, prophetic actors – showed that even if equilibrium were achieved, it would be unstable.
Keen concludes that the elusive search for equilibrium is a dead end, and moves on to chaos theory, in which equilibria are unstable and rarely or never, reached, but clear patterns emerge:
The two ‘eyes’ here are the equilibria, and as you can see they are quite clearly not worth studying – what is instead needed are differential equations that describe the dynamic evolution of the system. Economists do have a more advanced definition of equilibrium, which states the time path for the economy, but it involves restrictive assumptions similar to Debreu’s, and is not on the same level of dynamism as chaos theory. Anyone untainted by neoclassicism will be able to see that the above pattern is similar in type to the cyclical behaviour of a capitalist economy, and that applying chaos theory to economics is surely an idea with potential.
Keen ends the chapter by giving a couple of examples of attempted dynamic (though not chaotic) analysis – the Goodwin model, based on Marx’s analysis of the relationship between wages, investment and capital, and A .W. Phillip’s ill-fated attempts to bring dynamic modelling into economics. Contrary to popular belief, Phillips was well aware of expectations and how they changed, and incorporated this into his model. Both of these models produced realistic business cycles, as do Keen’s similar model (which we will come to in a later post).
But economists reject this type of analysis because…engineers don’t know what they are doing? The empirically successful microfoundations project? Assumptions don’t matter but do when they aren’t ours? I honestly just don’t understand.