Tuesday, September 6, 2016

The economic state space: a mini-seminar

I thought I'd curate a mini-seminar of information equilibrium blog posts chosen from over the past two years that draw on a particular visualization of the economic state space:


The picture above represents a histogram of different markets', individuals', households', firms', goods, or generic agents' "growth" states. For example, if firm X grows in revenue at 10% per year, then firm X gets a box at the 10% mark. But those boxes could well be wage growth or productivity growth for example.

The concept of "information equilibrium" is based on the idea that the distribution is stable, but e.g. the box for firm X moves around in it. Additionally non-ideal information transfer (information loss) results in the over-representation of the lower growth (or negative growth) states relative to e.g. a Gaussian distribution. Economic forces that maintain the distribution would be entropic forces like diffusion -- they'd have a macroeconomy-level description but no agent-level description.

If you need background on the basics of information equilibrium, here are some slides.

Here are six seven nine posts that expand on this idea of the economic state space (plus one link to a picture of a version using CPI components):


This post shows some empirical evidence that these stable distributions (which may actually be stable distributions) may exist for profit rates.


The movement of particular goods or labor growth states inside the distribution while the distribution itself stays relatively unchanged allows for nominal rigidity at for the aggregate economy, but without requiring individual wages/prices to be "sticky". This potentially resolves a conundrum because individual prices aren't empirically observed to be sticky, but aggregate stickiness is needed e.g. to make monetary policy have an effect on the economy.

3. Balanced growth, maximum entropy, and partition functions

We capture the concepts of the previous two posts in a single framework by defining a partition function (based on a maximum entropy distribution with constrained macroeconomic observables such as the existence of "economic growth"). This is used in the next post (#4).


In this post we build a very simple model of an economy that exhibits a productivity slowdown simply because it is more likely to organize a large economy out of a distribution with many low productivity states than a few high productivity states.


The picture at the top of this page gives a possible interpretation of national income accounting identities like Y = C + S + T + NX as more than just definitions.


The over-representation of the low/negative growth states has many implications for economics. In particular, although the information transfer approach is built on a generalized thermodynamics, the "econo-dyanmics" theory is very different from thermodynamics. The over-representation of low/negative growth states means "econo-dynamics" does not have a second law that entropy always increases. Thermodynamics has an exception for very small decreases in entropy (the fluctuation theorem), but econo-dynamics may have an even larger deviation that are at the heart of recessions.



The large deviations from the second law of thermodynamics may have their source in large scale coordination -- periods when agents behave in the same way such as a panic in a financial crisis or having the same reaction to a piece of economic news. Recessions could be viewed as a spontaneous fall in entropy. That is something that does not occur in physics or in many other maximum entropy approaches meaning that economics is a very different field of study.

8. Price growth (i.e. inflation) state distribution (NEW!)

An empirical look at a stable "statistical equilibrium" of price changes (price change state space) based on the MIT billion price project. The results support the economic state space picture.

9. Stocks and k-states (NEW!)

A theoretical and empirical look at the application of "statistical equilibrium" of k-states (in economic state space) to stock markets. The economic state space picture allows us to understand the Fama-French three-factor investing model.

3 comments:

  1. I am a bit puzzled on the last point. Large scale coordinated action reducing entropy is a phase change. And it happens all the time. I suspect it is more akin to grain growth models in soluds, but this is by no means outside of basic thermodynamics. The implication of a phase model is multiple local equilibria. That seems hard to prove.

    You can even get coordinated pseudo phases like dislocation arrays. What you need then is an equivalent of Gibbs free energy to minimize, not just entropy maximization...

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    1. That is an important point and I agree that I should've addressed it. It may even be useful to talk about e.g. some recessions triggered by Fed announcements with an analogy using supercooled liquids and nucleation sites, respectively.

      However in the economics case the entropy of an isolated system can spontaneously drop. In a phase transition, there is usually some heat exchanged with the environment (the system isn't isolated and the drop in entropy is accompanied by a rise in total entropy for the whole system).

      One way to think about it is that there can be a global recession (even though we do not trade with other planets); a second law preserving statistical economics would involve increased output for some alien civilization.

      US imports and exports are only a fraction of GDP -- nearly all of which is accounted for by trade with Canada and Mexico -- so to a good approximation North America could be considered an isolated system, yet North America experienced a recession in 2008.

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    2. This is all contingent on these ideas not being wrong in the first place :)

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