Posted on Thursday 17 October 2002 to Miscellanea

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D², anonymous but self-described as "a fat young man without a good word for anyone", sure writes a brilliant blog.

His latest post contains a great backgrounder on this year's joint-winner of the Nobel prize for economics, Daniel Kahneman and the current (sorry) state of economic modelling.

Orthodox economic modelling is still largely based static models which ignore time as an essential component. They do this to keep their mathematics tractable and fudge the time component by modelling people's expectations of future returns and folding that back into the present. Earlier models (which still dominate much thinking in economics) are based on the notion that these expectations are always "rational". That is, for large populations, individual errors in judgement tend to cancel themselves out.

In the popular imagination this leads us to the vulgar maxim that the market is always right but more recent expectation modelling, like that by Kahneman, denies that you can just assume this kind of error cancellation. Rational expectations models have now been largely discredited in academic circles and more recent work uses psychological techniques and laboratory data to build models about how people make imperfect judgements and how this faulty knowledge affects their expectations.

D² goes on to point out that while this in itself is valuable research, the whole raison d'etre of expectation modelling is still about ignoring time and about keeping the mathematics nice and tractable. The problem is that reality is never quite as simple as that.

The real work that needs to be done is in attacking the fundamental assumptions of "expectations" modelling in economics. I mentioned above that Samuelson's assumptions underlying the Law of Iterated Expectations were "innocent-looking", which they are, but they're actually extremely restrictive. Importantly (and this is a topic I've harped on about before), they're only valid for expectations of *ergodic* processes.

What the hell is an "ergodic process" when it's at home?

Ergodicity is a statistical property. A data generating process is "ergodic" if the data that it generates is "well-behaved" in the sense that you can take a sample of it and that sample will be in some way representative of the whole. Imagine a random number generator, spewing out numbers, and yourself sitting in front of it, writing the numbers down. After 1000 numbers, you calculate the mean of the observations. If the random number generator is driven by an ergodic process, you now have a decent estimate of what the mean will be after 10,000 observations. With ergodic stochastic processes, collecting more data gets you a better and better estimate of what the underlying parameters of the process are, as the "noise" cancels itself out in some statistically well-defined way.

But imagine if you were in front of the machine, and you kept on collecting more and more data, but the average after 1000 numbers was completely different from the average after 10,000, which was nothing like the average after 100,000 and so on. Imagine further that it *never* settled down, no matter how much data you collected. That would be a strongly nonergodic process; over time periods of around a week to a month, lots of weather data appears to be nonergodic, which is why medium term weather forecasting is so difficult. It's clear here that to talk about "expectations" of the future states of a nonergodic system are meaningless; people might have opinions about the future, but there aren't the solid linkages between these views and the actual data which one would need to call them "expectations". Certainly, there isn't enough to support the trick used by economists in using the expectations operator to make dynamic processes static so that they can be modelled tractably.

So what? Well, so this:

Most processes which are characterised by positive feedback are nonergodic

Most economic processes of interest are subject to significant, destabilising positive feedback