Non-Ergodicity and Trends and Cycles

Non-ergodicity is a tricky concept relevant to economics.

Yet any particular economy is not purely non-ergodic, but a complex mix of ergodic and non-ergodic elements, and non-ergodicity is a property of those processes or phenomena in which time and/or space averages of certain outcomes or attributes of that system either do not coincide for an infinite series or do not converge as the finite number of observations increases. That is to say, there will be no stable long-run relative frequencies, and even a large sample of the past does not reveal the future in an non-ergodic process to allow objective probabilities to be calculated for the likelihood any specific future outcome.

But, as already noted, any real world economy is a complex mix of both ergodic and non-ergodic processes, and the important point is that non-ergodicity does not mean no trends, cycles and oscillations occur in non-ergodic systems or in the economy at large.

We have, for example, no difficulty identifying high unemployment in the present or immediate past, or rising unemployment or rising or falling real output growth. Or trends like bear or bull markets in stock markets, even though future prediction of the value of any one share with objective probability scores still cannot be given.

What cannot be done in a pure non-ergodic system is to give an objective probability score for some specific future state of the system.

Things can become more complex because some processes have short-term stable relative frequencies but may not have such stability in the long run:

“[s]ome economic processes may appear to be ergodic, at least for short subperiods of calendar time, while others are not. The epistemological problem facing every economic decision maker is to determine whether (a) the phenomena involved are currently governed by probabilities that can be presumed ergodic – at least for the relevant future, or (b) nonergodic circumstances are involved.” (Davidson 1996: 501).

The long-run instability of certain human ensemble averages is an example of this.

Furthermore, some processes – and perhaps long term climate is one – may be so complex that they have elements that are ergodic and other elements that are non-ergodic, so that how one characterises the overall system can be an epistemic problem.

Links
“Physical Probability versus Evidential Probability,” July 9, 2013.

“Keynes’s Interval Probabilities,” July 15, 2013.

“Davidson on “Reality and Economic Theory,” July 10, 2013.

“Probability and Uncertainty,” July 11, 2013.

“A Classification of Types of Probability and Theories of Probability,” July 14, 2013.

“Is Long Term Climate Non-Ergodic?,” July 18, 2013.

BIBLIOGRAPHY
Davidson, Paul. 1996. “Reality and Economic Theory,” Journal of Post Keynesian Economics 18.4: 479–508.