Cameron Murray's Thumbnail Summary of Ole Peters on Non-ergodicity

This article (Revisiting the mathematics of economic expectations) by Cameron Murray, a self-bio-ed economist is a good thumbnail summary of the difference between time and ensemble averages and does a good job doing a cover on what Ole Peters discusses often on Twitter and at his blog at ergodicityeconomics where Ole can sometimes be more opaque (to me) than not.  

These are economists conveying economic info from their econ baseline and I think it is helpful. People coming from a finance baseline, on the other hand, should(?) recognize it immediately as the effect of time and multiple periods on returns or, in this case as an example, terminal wealth.  The terminal wealth effect is non-ergodic. You get in the end over time a lognormal-ish distribution where the average is more or less meaningless, the median represents the outcome of the geometric mean return and is helpful and the mode, too, is a helpful stat for how and where relative likelihood stacks over time. I did my amateur cover of this effect here.

Mr Murry pulls some pretty quick deft insights out of his summary though. It's a short read so I'd recommend his note rather than my extract but here are a few things I took away that are relevant to retirement finance, a place where econ and finance sometimes love each other ;-) Note that I am not necessarily endorsing or agreeing with his conclusions: 

• We hate losing what we have because it decreases our ability to make future gains. Mathematics tells us we should avoid being on one of the many losing trajectories in a non-ergodic process. 

• You can immediately see the problem here. If the process of earning and saving is non-ergodic and similar in character to the example above, such a system won’t be able to replace public pensions at all. Many earning and saving paths of individuals will never recover during their working life to support their retirement. Unless you want the poor elderly living on the street, some public retirement insurance will be necessary. 

• Undoubtedly there are many more areas of economics where this subtle shift in thinking can help improve out understanding of the world. I’m thinking especially about Gigerenzer’s idea of a heuristics approach as a generally effective way for humans to navigate non-ergodic processes. 

• Murray quoting Robert Solow: 

"I ask myself what I could legitimately assume a person to have rational expectations about, the technical answer would be, I think, about the realization of a stationary stochastic process, such as the outcome of the toss of a coin or anything that can be modeled as the outcome of a random process that is stationary. If I don’t think that the economic implications of the outbreak of World war II were regarded by most people as the realization of a stationary stochastic process. In that case, the concept of rational expectations does not make any sense. Similarly, the major innovations cannot be thought of as the outcome of a random process. In that case the probability calculus does not apply." 

• My take is on the economic implications of this is that if people can individually [i.e., vs doing it via a pool, private or social] smooth consumption through time for retirement than there is no logic to social insurance.