Sunday, May 3, 2015

Information equilibrium as an economic principle


One thing I've noticed is that economists who wouldn't politically disagree with the results of the information equilibrium framework -- especially because it comes up with some of the same models as mainstream approaches -- would ask why this approach is useful or how it adds to mainstream approaches. Additionally, when I bring up information theory, the first thing that comes to mind is information economics and a quick dismissal: "been there, done that".

I downloaded a trial Kindle copy of Krugman and Wells Macroeconomics and in Chapter 1 there is a list of economic principles that is a useful guide to the differences between the information equilibrium approach and why economists haven't already looked at information theory in the way I am looking at it.


"Principle #1: Choices Are Necessary Because Resources Are Scarce"

Basically what this means in the most objective language is that economics is an allocation problem. As it is stated, though, it assumes the method of solution: optimizing agents. Money could be used to set up optimization through agents to find the e.g. maximum utility solution. Money could also be used to set up a path to the maximum entropy solution.

That is to say the allocation problem could be solved by:
  1. Finding the allocation that optimizes some objective function that humans defined (e.g. utility)
  2. Taking the most likely allocation
This blog takes the second path -- that money sets up a maximum entropy solution to an allocation problem, not an optimized solution. Here's more on how these two views are related (and how they differ).

Overall in this first principle you can see the primary difference and the reason why I don't think economists have discovered this approach -- information equilibrium abandons the human decision element and says the allocation problem is a maximum entropy solution (actually it is agnostic about how the allocation problem is solved, just that the solution is consistent with MaxEnt).

Here's how I'd restate this first principle;

Principle #1: Economics is the study of allocation problems.

"Principle #2: The True Cost of Something Is Its Opportunity Cost"

The best I can do for this is to say that the difference between two different allocations is not just the difference between the filled states, but depends on the states left unfilled as well. This is a critical piece of knowledge when trying to understand entropy.

Principle #2: Unfilled states matter too!


"Principle #3: “How Much” Is a Decision at the Margin"
This was a huge 'revolution' in economics, but in the information equilibrium view all this means is that the generalized price P of A in terms of B is P = dA/dB. Marginal thinking is formally enforced by sticking to information equilibrium relationships P : A → B.

Principle #3: P = dA/dB when A and B are in information equilibrium.


"Principle #4: People Usually Respond to Incentives, Exploiting Opportunities to Make Themselves Better Off"
I wrote a whole piece on how incentives are an attempt to come up with a microfoundation for an macroeconomic entropic force. However this is essentially the idea that random dither can discover new areas of state space. If you add volume to an ideal gas, molecules will move into it. So I'd like to re-work this principle into the language of entropy:

Principle #4: Market forces are entropic forces that can move people into and out of states


"Principle #5: There Are Gains from Trade"
The whole of a macroscopic system is more than the sum of its parts -- in physical systems there is an emergent concept called entropy that encapsulates this. In economic systems there is an analogous concept in the information equilibrium framework; see here or here. This principle becomes:

Principle #5: There is an entropy term T S in economic potential


"Principle #6: Markets Move Toward Equilibrium"
This one is easy. This has the added benefit of being the same definition of equilibrium in thermodynamics.

Principle #6: Markets move towards maximum entropy


"Principle #7: Resources Should Be Used Efficiently to Achieve Society’s Goals"
Sounds good to me. Let's keep this one -- but it's more of a philosophical axiom (as are #9-#12 below) than an axiom that would appear in the Principia.


"Principle #8: Markets Usually Lead to Efficiency"
Truthfully, this principle better maps to accepting the idea that maximum entropy solutions are usually close to optima for most relevant objective functions. But as those objective functions aren't especially relevant -- just take the MaxEnt solution on its face -- I thought I'd go with the idea that assuming information equilibrium is a remarkably good starting point ...

Principle #8: I(A) ≈ I(B) is a good first order approximation



That's about as far as I want to go for now. The remaining principles #9-#12 get into more philosophical ideas -- government intervention and one person's spending is another's income (the economic equivalent of the 'golden rule'). It's not that I don't agree with them, it's just that they aren't necessary to build the information equilibrium macroeconomic theory.

Also, the "usually" appearing in the principles above are incorporated in the fact that sometimes we have non-ideal information transfer and I(A) > I(B).

For easier cutting and pasting, here are the eight seven principles:
Principle #1: Economics is the study of allocation problems. 
Principle #2: Unfilled states matter too! 
Principle #3: P = dA/dB when A and B are in information equilibrium. 
Principle #4: Market forces are entropic forces that can move people in and out of states 
Principle #5: There is an entropy term T S in economic potential 
Principle #6: Markets move towards maximum entropy 
Principle #8: I(A) ≈ I(B) is a good first order approximation

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