In the social context, the ensemble is usually a population, and the ergodicity question becomes this: does the average over the population represent what happens to the typical individual over time?
So this is about the relationship between collectives and individuals.
You may think: whatever is good for the collective must be good for the individual because the collective is made up of individuals.
In economics, that corresponds to working with "the representative agent," and it's precisely the ergodicity error.
Let's make a list of people who have discovered problems in economics.
Feel free to add your own favorites.
@ThomasHerndon1: as a graduate student exposed the Reinhart and Rogoff paper, which had had trillion-dollar austerity consequences around the world, as jaw-droppingly flawed.
@StephanieKelton: exposed that the public narrative about the mechanics of the monetary system, which is also taught in economics departments, has little to do with the mechanics of the monetary system.
Update: Tom is still rather angry. He has now worked out how to compute expected value.
Perhaps tomorrow he will notice that we agree with his computation of the expected value but are also curious about the time average.
Next update: Tom seems less angry now because he has run his simulation successfully. We don't know what he has simulated, but everybody wins, and that, surely, is a good thing.
2/7 Imagine a population of N agents all of whose growth rates have the same statistical properties.
In the simplest case, at each time step generate N Gaussian random variates and use them as the exponential growth rates.
Everyone's expected wealth is identical for all time.
3/7 However, individually some are luckier and some less so. Because the process is the usual assumption in economics, exponential growth, random differences are exponentially amplified over time.
Result: ever-increasing inequality and log-normally distributed wealth.
2/4 This raises a question I've been wondering about for some years: what happens when we (try to) increase interest rates again?
It's not (just) the level that matters but the path. After 40 years of falling rates, the economic system is used to the trend. Now what?
3/4 You could say "just keep going with the trend." Technically possible but it leads to another dislocation.
The discounted cash-flow value of yielding assets hits a singularity at zero discount rate. It's a phase transition whose critical point we've been flirting with.
Help! I don't know the details of this work. Of course banks are unstable because of their key function in the financial system. Of course that instability manifests through bank runs.
Did these researchers just say as economists what everyone else knew or is it something deeper?
I know that the financial sector is sort of non-existent in a general competitive equilibrium view of the world. Ken Arrow listed it as one of the failings of economics: that finance shouldn't really be there but clearly is. Did they discover the financial sector for economics?
From @philipcball's article I understand that there's a simple set of equations associated with this work, maybe something recognizable to a physicist. What is that set of equations and what is the essential property that provided new insight?