by From Lars Syll To understand real-world decisions and unforeseeable changes in behaviour, ergodic probability distributions are of no avail. In a world full of genuine uncertainty — where real historical time rules the roost — the probabilities that ruled the past are not necessarily those that will rule the future. Time is what prevents everything from happening at once. To simply assume that economic processes are ergodic and concentrate on ensemble averages — and a fortiori in any relevant sense timeless — is not a sensible way for dealing with the kind of genuine uncertainty that permeates open systems such as economies. When you assume the economic processes to be ergodic, ensemble and time averages are identical. Let me give an example: Assume we have a market with an asset
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from Lars Syll
To understand real-world decisions and unforeseeable changes in behaviour, ergodic probability distributions are of no avail. In a world full of genuine uncertainty — where real historical time rules the roost — the probabilities that ruled the past are not necessarily those that will rule the future.
Time is what prevents everything from happening at once. To simply assume that economic processes are ergodic and concentrate on ensemble averages — and a fortiori in any relevant sense timeless — is not a sensible way for dealing with the kind of genuine uncertainty that permeates open systems such as economies.
When you assume the economic processes to be ergodic, ensemble and time averages are identical. Let me give an example: Assume we have a market with an asset priced at 100 €. Then imagine the price first goes up by 50% and then later falls by 50%. The ensemble average for this asset would be 100 €- because we here envision two parallel universes (markets) where the asset-price falls in one universe (market) with 50% to 50 €, and in another universe (market) it goes up with 50% to 150 €, giving an average of 100 € ((150+50)/2). The time average for this asset would be 75 € – because we here envision one universe (market) where the asset-price first rises by 50% to 150 €, and then falls by 50% to 75 € (0.5*150).
From the ensemble perspective nothing, on average, happens. From the time perspective lots of things, on average, happen.
Assuming ergodicity there would have been no difference at all. What is important with the fact that real social and economic processes are nonergodic is the fact that uncertainty — not risk — rules the roost. That was something both Keynes and Knight basically said in their 1921 books. Thinking about uncertainty in terms of ‘rational expectations’ and ‘ensemble averages’ has had seriously bad repercussions on the financial system.
Knight’s uncertainty concept has an epistemological founding and Keynes’ definitely an ontological founding. Of course, this also has repercussions on the issue of ergodicity in a strict methodological and mathematical-statistical sense. I think Keynes’ view is the most warranted of the two.
The most interesting and far-reaching difference between the epistemological and the ontological view is that if one, as Kay do, subscribes to the former, Knightian view, you open up for the mistaken belief that with better information and greater computer-power we somehow should always be able to calculate probabilities and describe the world as an ergodic universe. As Keynes convincingly argued, that is ontologically just not possible. To Keynes, the source of uncertainty was in the nature of the real — nonergodic — world. It had to do, not only — or primarily — with the epistemological fact of us not knowing the things that today are unknown, but rather with the much deeper and far-reaching ontological fact that there often is no firm basis on which we can form quantifiable probabilities and expectations at all.
Often we do not know because we cannot know.