Written by Lars P. Syll
Paul Samuelson once famously claimed that the ‘ergodic hypothesis’ is essential for advancing economics from the realm of history to the realm of science. But is it really tenable to assume – as Samuelson and most other mainstream economists – that ergodicity is essential to economics?
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What is ergodicity?
Ergodicity is a difficult concept that many students of econom(etr)ics have problems with understanding. Trying to explain it, you often find yourself getting lost in mathematical-statistical subtleties difficult for most students to grasp.
In the video below, Luca Dellanna has made an admirably simplified and pedagogical exposition of what it means for probability structures of stationary processes and ensembles to be ergodic.
In economics ergodicity is often mistaken for stationarity. But although all ergodic processes are stationary, they are not equivalent. So, if nothing else, ergodicity is an important concept for understanding one of the deep fundamental flaws of mainstream economics.
Let’s say we have a stationary process. That does not – as Adamou shows in the video below – guarantee that it is also ergodic. The long-run time average of a single output function of the stationary process may not converge to the expectation of the corresponding variables – and so the long-run time average may not equal the probabilistic (expectational) average.
Say we have two coins, where coin A has a probability of 1/2 of coming up heads, and coin B has a probability of 1/4 of coming up heads. We pick either of these coins with a probability of 1/2 and then toss the chosen coin over and over again. Now let H1, H2, … be either one or zero as the coin comes up heads or tales. This process is obviously stationary, but the time averages
[H1 + … + Hn]/nconverges to 1/2 if coin A is chosen, and 1/4 if coin B is chosen.
Both these time averages have a probability of 1/2 and so their expectational average is 1/2 x 1/2 + 1/2 x 1/4 = 3/8, which obviously is not equal to 1/2 or 1/4.
The time averages depend on which coin you happen to choose, while the probabilistic (expectational) average is calculated for the whole “system” consisting of both coin A and coin B.
Ergodicity in Economics
Repeating from above:
In economics ergodicity is often mistaken for stationarity. But although all ergodic processes are stationary, they are not equivalent. So, if nothing else, ergodicity is an important concept for understanding one of the deep fundamental flaws of mainstream economics.
Instead of arbitrarily assuming that people have a certain type of utility function – as in mainstream theory – time average considerations show that we can obtain a less arbitrary and more accurate picture of real people’s decisions and actions by basically assuming that time is irreversible. When our assets are gone, they are gone. The fact that in a parallel universe it could conceivably have been refilled, are of little comfort to those who live in the one and only possible world that we call the real world.
Time average considerations show that because we cannot go back in time, we should not take excessive risks. High leverage increases the risk of bankruptcy. This should also be a warning for the financial world, where the constant quest for greater and greater leverage – and risks – creates extensive and recurrent systemic crises.
This article was assembled from two blog posts:
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