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Ole Peters

@ole_b_peters

Aug 21, 2019 • 7 tweets • 2 min read • Read on X

1/7 When we started thinking about how to model personal wealth in an economy of interacting people, we soon wrote down an equation we called Re-allocating Geometric Brownian Motion (RGBM). We felt logically forced to use this as a starting point.
dx.doi.org/10.2139/ssrn.2…

2/7 But the economics papers we saw on the topic all used much more complicated, intractable, and from what we could tell quite arbitrary models, i.e. equations trying to represent the same thing we were trying to model.

3/7 Undeterred, we went ahead with our analysis, with somewhat shocking results. It showed an unstable wealth distribution. Where you sit in the distribution is hugely non-ergodic, time scales are much longer than people thought, or non-existent.
ergodicityeconomics.com/2017/08/14/wea…

4/7 Very serious consequences for questions in welfare economics, financial markets, interest rates and on and on.

No economics journal wanted to publish it.

5/7 Then we noticed Bouchaud and Mezard had studied the same equation in 2000: they'd also felt there wasn't much choice in how to model this, and they'd come to similar conclusions. We picked up some great techniques from them.
lptms.u-psud.fr/membres/mezard…

6/7 Later, we saw, Liu and Serota also arrived at this equation, in 2017.
isiarticles.com/bundles/Articl…

And just the other day, we learned that Marsili, Maslov, and Zhang were studying it for the same reasons, in 1998.
arxiv.org/abs/cond-mat/9…

7/7 What does this mean?

4 teams of physicists independently, over 20 years, all arrived at the same equation to model a key economics problem, with alarming results.

I know of no study of this equation published in an economics journal -- do you?

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Ole Peters

@ole_b_peters

Mar 3

1/9
I read @davidbessis book last year. It's brilliant!
It brought back many memories of conversations with Reuben Hersh, who is briefly mentioned.

Mathematics as a human creative act, not as axioms, deductions, and finally theorems. Seeing the answer, and using logic to check.

2/
Pappus wrote (paraphrased by Polya).
'Analysis:' start from what is required (the result) and trace it back to something you know to be true.
'Synthesis:' reverse the process and walk back to the result.

The human process is analysis: see the result, then understand how you know it.

But we write too much synthesis.

3/
@davidbessis emphasizes the most valuable aspect of mathematics: learning to educate our intuition.

This leads him to a critique of Kahneman's System 1 (intuition) and System 2 (logical mechanical 'thought').

System 1 is not fixed. The whole point is to change it: David's System 3.

Read 9 tweets

Ole Peters

@ole_b_peters

May 15, 2024

1/n
A thread about ergodicity economics and world peace, why not.

A quantity is ergodic if its average over an ensemble of systems is the same as its average over time.

Ergodicity economics questions whether ergodicity holds.

But what's that got to do with world peace?

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.

Read 9 tweets

Ole Peters

@ole_b_peters

Nov 22, 2023

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.

Read 5 tweets

Ole Peters

@ole_b_peters

Aug 4, 2023

..emotions also running high on the blog.

Tom is rather upset about the coin toss. Mathematics is an emotional subject.

https://t.co/DNNxVbZbkiergodicityeconomics.com/2023/07/28/the…

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.

Read 8 tweets

Ole Peters

@ole_b_peters

May 20, 2023

https://twitter.com/ole_b_peters/status/1659823460753850368

1/7
Since people seem curious, here's a bit more detail because it's a nice ergodicity story.

The question was: how can paupers and billionaires emerge in a population of identical agents?

I think the ergodicity-economics answer is underappreciated in economics.

https://twitter.com/ole_b_peters/status/1659823460753850368

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.

Read 7 tweets

Ole Peters

@ole_b_peters

Oct 14, 2022

1/4
Hysteresis is a fancy word for "it matters how you got there."

A 5% interest rate is one thing if you've arrived there from 10%; it's something else if it's been 0% for years.

Low and falling rates are systemically ingrained now.

ergodicityeconomics.com/2017/08/14/wea…

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.

Read 4 tweets

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