When statistical things go wrong, it’s often because someone unknowingly assumed ergodicity where that wasn’t ok. This can have dramatic effects in everyday language: I will use the example of incarceration rates. I will then present a visual illustration to discuss the role of time scales.
Growth rates are at the heart of ergodicity economics, and economic news are full of them, too — “GDP grew by 3% last year,” something like that. Sometimes we also hear “national debt grew by $1,271,000,000,000 over the last year” (which is dimensionally different from 3% per year). So since growth rates come in very different forms: what are they, really?
A few weeks ago I was made aware of an experiment that was recently carried out in Copenhagen, by a group of neuroscientists led by Oliver Hulme at the Danish Research Center for Magnetic Resonance. Results of the experiment have not been published yet, so this is an exciting time to speculate. The experiment’s primary focus was neurological, but — almost as a by-product — it may yield an answer to the following provocative question: who is right, ergodicity economics or expected utility theory? I was not involved in the design or execution of the experiment, nor was I even aware it. But it is directly relevant to the falsification or corroboration of our work. Below I will describe my understanding of the setup, and of the significance of the possible findings.
If we assume that a false proposition is true, we can prove anything (ex falso quodlibet). Bertrand Russell, so the story goes, once mentioned this in class. A student raised his hand and challenged: in that case prove that 1=0 implies that you’re the Pope. Russell promptly obliged, see below. Bernoulli 1738, as discussed in an earlier post, contains two contradictory definitions of expected utility theory. This contradiction amounts to a false proposition, and that means any statement can be proved using expected utility theory. As an illustration, let’s prove that Bertrand Russell is the Pope.
Not all academic fields have a clear starting point, a seminal paper that constitutes the foundation of the entire discipline. But economics does. The paper that defines modern formal economics was written by Daniel Bernoulli in 1738. It introduces expected utility theory. The main thrust of our work is, of course, to replace expected utility theory and instead work with time-average growth rates of wealth. I’ll mention how that works, but the focus of this post will be on something else. Bernoulli’s paper is not only conceptually misleading but also technically flawed in a sneaky way that keeps confusing everyone. Where Bernoulli determines the price to be paid for a risky prospect, he contradicts himself. I wouldn’t make such a fuss about this if the paper wasn’t so absolutely crucial. This basis of economics contains an error that invalidates commonly held beliefs and puts tens of thousands of studies into a different light. I recently encouraged people, using twitter, to read the paper and see for themselves. In this blog post I go through the relevant analysis step by step and address questions that came up in response to the tweet.
In June 1946 Max Planck spoke in the Göttingen physics colloquium. Planck was 88 years old, had received the highest honors of his community, including a Nobel Prize in 1918 for his discovery of the quantum, and had profoundly changed how we think about physical reality. He knew something about problems, both in science and in life. He postulated the quantum, famously, “in an act of desperation.” His first wife died young, as did four of his five children, the fourth, Erwin, killed by the Gestapo in 1945. Having lived through all of this, Max Planck decided to talk about problems that are nothing but distraction — scheinproblems.
The most interesting scientific projects are those that surprise, when the mathematics, or the code, tells us something we didn’t expect. In our study of US wealth dynamics that’s what happened. We wrote it up in a paper, but that’s only the end product not the curious route by which we got there. Hence this post.