Saturday, December 6, 2014

Information equilibrium theories satisfy the Lucas critique

Image from wikimedia commons and modified by me with a random Voronoi diagram to sort of suggest Planck areas measuring the surface units of information.

Despite being annoyed by me, Noah Smith is probably one of the best blogging resources for understanding modern macroeconomics around today, and I frequently go back through his archives and click through the many self-referential links on his blog (a method I have apparently copied). This may be an educational style bias as Noah was an undergraduate physics major, giving us a common point of reference. And there is, of course, the same excellent last name.


Anyway, I was just reading this post of his on the Lucas critique -- the idea that observed macroeconomic relationships may change if you try to use them for policy (the prime example of which is the Phillips Curve which seemed to go away when it was used for policy). Noah quotes Charles Plosser:
Plosser says that "almost no model [has] satisfactorily dealt with the [Lucas Critique]."

Noah then proceeds to ask how one would satisfy the Lucas critique and identifies three methods:

  • Macro experiments (in real or virtual worlds)
  • Real microfoundations and detailed simulations (agent-based models)
  • Vague judgment calls (which is Noah's observation of how things seem to work)

This leaves out a fourth possibility

  • Assume as little as possible about the microfoundations and see how far that can take you

This fourth possibility is the the approach taken in the 19th century to understand thermodynamics (we knew little about atoms at the time), but is also behind maximum entropy methods and -- particularly relevant to this blog -- information equilibrium (such as the information transfer model). Note that I've talked about this before in relation to the Lucas critique.

I'm not sure I've made this clear enough on this blog, but in a sense, whatever theory of macroeconomics turns out to be correct, the information transfer model has to be correct. Note that I've talked about this before as well.

The information transfer model may not be useful, but it has to be correct. The information on one side of supply and demand has to be greater than or equal to the information on the other: I1 ≤ I2. The cases where it is not useful would be where I1 << I2 (most of the information disappears into the information theory equivalent of 'heat') or where I1 ~ I2 doesn't contain enough ... well, enough information to get the details right (microfoundations could matter a lot or the fluctuations around I1 ~ I2 may be the most important part).

In a sense, information equilibrium theories like the one presented on this blog are analogous to assuming isentropic processes in thermodynamics. These will fail if the process produce a lot of entropy or there is more going on that involves additional physics, like say superconductivity. Sometimes assuming energy conservation is all you need to know, but sometimes it's not enough by itself or energy isn't conserved (in a useful way for the problem).

Another useful analogy from physics is black hole thermodynamics.

Stephen Hawking and Jacob Bekenstein, in trying to understand black holes in terms of quantum mechanics, posited that black holes must obey thermodynamics and were able to derive some important relationships that have shed light on how general relativity (Einstein's theory of gravity over long distances) and quantum mechanics (the fundamental theory of small distances) fit together. One really interesting result is that black holes seem to have extremely large entropy meaning they have a huge number of degrees of freedom (entropy is proportional to the surface area of the black hole in Planck units) -- and that you can use string theory to derive that entropy.

Now thermodynamics didn't have to be useful to describe black holes, but it did have to be correct. This is the same for information equilibrium and macroeconomics. In fact, one can construct an elaborate analogy:

Quantum mechanics :: microfoundations
General relativity :: macroeconomics
General relativity may be wrong about black holes :: Lucas critique
General relativity ignores quantum mechanics :: Lucas critique
String theory (quantum theory of gravity) :: microfounded theory of macro
Black hole thermodynamics :: information equilibrium theories

Hawking and Bekenstein's work on black hole thermodynamics would be correct regardless of the final form of the quantum theory of gravity. In the same way, information transfer economics would be correct regardless of the final form or macroeconomics and so satisfies the Lucas critique.

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