Information transfer is a state of mind

I am promoting a response to a comment from Tom Brown to a post. Tom's question was: "How would you describe [the original arXiv paper] to someone?"

I personally like the first line of Fielitz and Borchardt's abstract as an answer: "Information theory provides shortcuts which allow [one] to deal with complex systems." The specific thrust of their paper is that it looks at how far you can go with the maximum entropy arguments without having to specify "constraints". This refers to partition function constraints optimized with the use of "Lagrange multipliers". In thermodynamics language it's a little more intuitive: basically the information transfer model allows you to look at thermodynamic systems without having defined a temperature (Lagrange multiplier) and without having the related constraint (that the system observables have some fixed value, i.e. equilibrium [1]).

This is how the information transfer model allows you to use maximum entropy while liberating you from having to either identify a "temperature" or even be in equilibrium. The downside is that the resulting approach has very limited dynamics and may not tell you much.

However this makes it a great approach to economics because it's a complex system with large numbers of things swirling about and there is no real concept of "temperature" or (sorry, economists) equilibrium. That is to say, more generally, there are no constraints in an economic system to use Lagrange multipliers for. There are no few identified conservation laws in economics, so there is nothing little that has a fixed value [2].

The resulting economic information transfer model is successful but with some pretty limited scope. It doesn't capture the "business cycle"; it captures long run trends. However that alone can be seen as a significant success (in my view). It also makes some predictions about low growth and low inflation in the future of advanced economies. Even the rudimentary information transfer model approach may be way more well defined than the current state of economics that has to resort to "expectations" (macro outcomes may be dependent on whether people consider the central bank to be "credible") and where there still are arguments about how money works.

Interestingly, the partition function approach I've been using seems to say is that there may actually be a Lagrange multiplier/temperature we can use that's a function of log M0 (currency component of the monetary base) and the "constraint" may be something that reduces to the quantity theory of money in certain limits (an economy in equilibrium is one that satisfies the quantity theory to some approximation [3]). In this view, a large economy with a large monetary base may be thought of as a "cold" economy that has low inflation and mostly has its low-growth markets occupied (like a cold thermodynamic system has its low energy states occupied).

[1] The constraint is generally that the system have some fixed energy, which involves both energy conservation and thermal equilibrium (i.e. the energy isn't changing).

[2] After originally writing this sentence, I wanted to make sure it was true. It turns out Samuelson identified a conservation law and Ramsey's bliss point may be seen in this light.

I also found this quote by Samuelson:

There is really nothing more pathetic than to have an economist or a retired engineer try to force analogies between the concepts of physics and the concepts of economics. How many dreary papers have I had to referee in which the author is looking for something that corresponds to entropy or to one or another form of energy. Nonsensical laws, such as the law of conservation of purchasing power, represent spurious social science imitations of the important physical law of the conservation of energy; and when an economist makes reference to a Heisenberg Principle of indeterminacy in the social world, at best this must be regarded as a figure of speech or a play on words, rather than a valid application of the relations of quantum mechanics.

Excellent.

[3] As Bennett McCallum puts it: the quantity theory is not just the equation of exchange. It includes long run neutrality. I've made the supposition before that long run neutrality may be an approximate symmetry of economics. This symmetry, via Noether's theorem (vaguely), may be related to the "conservation law" given by the quantity theory. The analogous situation in thermodynamics is that time-symmetry leads to energy conservation (a thermodynamic system that is constant in time is one that is in equilibrium with a fixed value of energy).