Tuesday, April 17, 2018

Yes, I've read Duncan Foley. Have you?

I am not as familiar with the works of Pablo Neruda.
One of the most common comments I get asks (in varying degrees of stridency) whether I am aware of the work of Duncan Foley. Have you read Foley? or This has already been done by Foley. It seems people equate any reference to entropy and thermodynamics in economics with Foley.

The most time I've spent on this was answering an email from someone who read my book. In that context, it was completely understandable since I did not reference Foley in the book (for reasons described below). My recent paper directly cites Foley and even includes a footnote about the differences, and in that context I tend to be less charitable.

I am reproducing my email below (with some minor edits). However let me give a TL;DR
  • Foley and I may both use partition functions, but these are very general things in mathematics and the Lagrange multipliers and constraints are different — which are the only real properties of a partition function, meaning it's completely different. (I also construct the partition function from an ensemble of markets in my recent paper.)
  • Foley asserts prices are Lagrange multipliers (analogous to inverse temperature); in my work prices are measures of information flow and the Lagrange multipliers are related to the size of the economic state space. For Foley, prices determine whether an economy is "hot" or "cold"; for me, a "cold" economy would be large low-growth economy, and a "hot" economy would be a small, emerging one.
  • Foley's approach is so analogous to thermodynamics that you'd even have a second law. One of the most important properties of the information transfer approach is that it explicitly allows second law violations from the beginning (and they seem to be key to understanding disequilibrium scenarios like recessions).
  • Foley uses utility. I think utility is at worst garbage, at best an unobservable effective field.
  • Foley doesn't ever use his theory to describe empirical data, while I do. There are papers where Foley is a co-author that have empirical data in them, but any theoretical description of or lines through the data do not depend on the Foley's thermodynamic theory of economics (and are often just regressions). n.b. Happy to be corrected if I'm wrong about this.
  • It is my opinion (!) that Foley's approach isn't the best, but I don't think Foley is prima facie misguided or his approach will never lead to a successful theory. It could! It doesn't seem to have yielded any major empirical successes yet, however.
Anyway, here's (most of) my response to that email from a reader regarding Foley:


I am aware of Foley's work. One of the first things I did when I started applying communication/information theory to prediction markets and thought I had something new was a big literature search — and any search on entropy and economics brings up Foley. The strongest connection between my work and Foley's work is "statistical equilibrium" (whose terminology I've adopted) that I've talked about on my ... blog where I've also made several other references to Foley and Smith.

However there are also strong differences — in particular the constraint in the partition function and its "temperature" variable [Lagrange multiplier]. For example, in Foley (1996), prices are [analogous] to inverse temperature and the partition function defines an economic state with a well-defined maximum entropy "offer" (i.e. constraint).

The partition function I've looked at uses factors of production as the inverse temperature, and looks at an economy as a maximum entropy state with a well-defined growth rate. This "growth rate" is actually understood in terms of underlying information theory (matching demand "events" with supply "events" which we can think of as messages in communication theory).

There is a similarity in the discussion of entropy (I've made several references to Foley's statement that physics and econ are different because the formalism was set up to study irreversible processes in the latter — no one voluntarily undoes their utility gains — as opposed to reversible processes in the former). However, the information theory treatment tells us not to expect the second law of thermodynamics to hold because the conditions that make it hold are not met. A good example is that traders can all panic and try to sell causing a correlation that would violate the 2nd law; in contrast, atoms don't panic. This makes economics very different from thermodynamics. But I think a consequence of this is that Foley's thermodynamics can reproduce Walrasian/classical economics pretty well because there shouldn't be big market failures in classical economics.

That's just a couple of examples. There are others (e.g. I avoid most discussions of utility, but also show it is probably only a useful concept near equilibrium).

However since I didn't get that deep into statistical equilibrium in the book, and decided to base the book on economist Gary Becker's model (based on the suggestion from economist David Glasner that Becker's approach would be more persuasive/intuitive than my physics jargon), references to Foley fell by the wayside (as a side note, I also edited out a reference to Philip Mirowski because I thought it detracted from the narrative). In general, these references were too technical (I only touch on the 2nd law violation because you can illustrate it with Gary Becker's model) for what was supposed to be a book for a general audience. (I also think the physics jargon and direct analogies with thermodynamics are at least one barrier to traction for Foley and others [in mainstream economics].)

But you are right that I'm mostly focused on understanding empirical problems, partially because that's what I've always done as a physicist (I was technically a nuclear and particle theorist, but most of what I did was build models to explain data) and partially because economics lacks models with anything approaching what scientists would call "empirical accuracy" (and Foley's work doesn't seem to address empirical data much either).



  1. Thanks for the information. No, I haven't read Foley.

    1. Ha! The "Have you?" was my sarcastic response to several of these comments, emails, etc I've gotten from people who are asking me if I've read Foley but who apparently didn't seem to understand what Foley was doing well enough to see the differences.

      He mentioned entropy! It must be the same thing!

      Boltzmann also mentioned entropy. Does that mean Foley's work is the same as Boltzmann's?

      Maybe Boltzmann should read Foley.


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