## Monday, April 17, 2017

### Organization of information equilibrium concepts

The blog's 4th birthday is coming up, so I started writing up a post that'll come out next Monday. However in writing that post I realized that there's a logic to the different techniques I've used that all stem (ultimately) from the basic information equilibrium condition. Here's an organization chart:

Each circle has a post or presentation that sums up the ideas:

Information Equilibrium: This is the circle at the center of it all. An overview of the ideas are in this presentation, this blog post, and my paper (choose your favorite format). The information transfer index k is a key property of an information equilibrium system.

Single-factor production, Supply and Demand: I illustrate both of these circles as well as their connection via scope conditions and scale (time to adjust) in this recent blog post. These scope conditions are shown in the diagram. This is also discussed in the paper.

Multi-factor production: This is behind the Solow model, and is best explained in the paper. This blog post on the so-called "Kaldor facts" is useful as well. It comes from assuming output ("demand") is in information equilibrium with more than one input factor ("supply"). Another example is the "quantity theory of labor and capital" I came up with.

Matching models: In this post, I show how matching models fit into the information equilibrium framework and connect it to dynamic equilibrium (below). The idea is not very different from the two factor approach above where two factors (an unemployed person and a job opening) come together to form an output (a hire).

Dynamic equilibrium: This presentation goes over the main ideas and some results of the dynamic equilibrium approach. It follows from making assumptions about the time dependence of the quantities in information equilibrium (in particular that both are exponentially growing).

Ensembles: This sets up an ensemble of information equilibrium conditions (with one or more input factors of production and information transfer indices k) and uses a maximum entropy distribution (partition function Z) to deal with multiple markets, industries, or firms. It makes rigorous the idea of how the system must behave if there is to be a single "economic growth rate" (i.e GDP growth) that is a well-defined aspect of a macroeconomy. This is also discussed in the paper, though probably not as clearly as the blog post. An explicit example using labor as the single factor of production is shown in this blog post.

Statistical equilibrium, k-states: Going a step further than just looking at ensembles, this looks at behaviors of the distributions of economic "k-states" P(kᵢ) ‒ with information transfer indices kᵢ ‒ and shows how to understand stock markets, government spending, secular stagnation and nominal rigidity. Again, this is also discussed in the paper, but not as clearly as the "mini-seminar" I link to in this paragraph.

#### 2 comments:

1. Do you have any applications in mind, such as stress testing software, or is your interest purely in theory?

1. I am not sure what you mean by stress testing software -- do you mean software that performs "stress tests" for banks (as the post-financial crisis Fed)?

I do have a primary interest in theory, but if I could find useful applications I would definitely pursue them.

The original application was going to be developing metrics for prediction markets (e.g. SciCast/DAGGRE), but that was never funded. The framework seems to be more interesting for macro ... so I went to the blogs.

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