Wednesday, April 24, 2013

An informal abstract

First, I like to follow economics blogs in my spare time in the political and academic spheres (in particular, Noah Smith -- n.b. his post about scientists commenting on blogs, Cosma Shalizi and Scott Sumner). I briefly thought about going to graduate school for economics both before and after my Phd in physics but I went into industry instead -- which would make it difficult to submit an economics paper that would be taken seriously. The idea here is blog as working paper.

Second, I was recently (2011-2012) involved in a project that relied heavily on information theory and I came across this interesting paper:
Information theory provides shortcuts which allow to deal with complex systems. The basic idea one uses for this purpose is the maximum entropy principle developed by Jaynes. However, an extensions of this maximum entropy principle to systems far from thermal equilibrium or even to non-physical systems is problematic because it requires an adequate choice of constraints. In this paper we apply the information theory in an even more abstract way and propose an information transfer model of natural processes which requires no choice of adequate constraints. It is, therefore, directly applicable to systems far from thermal equilibrium and to non-physical systems. We demonstrate that the information transfer model yields well known laws, which, as yet, have not been directly related to information theory, such as the radioactive decay law, Fick's first law and Hubble's law.
http://arxiv.org/abs/0905.0610

Some time later, I came across this blog post by Paul Krugman where he says:
It is not easy to derive supply and demand curves for an individual good from general equilibrium with rational consumers blah blah. And it’s definitely not easy to justify consumer and producer surplus as measures of welfare. And there have always been some purists who condemn any use of the S and D curves we all grew up with, the use of triangles to measure welfare loss, and all that. But for the most part nobody pays attention. The supply-and-demand framework is so convenient, while pretty much getting at what you want to get at, that it’s what almost everyone uses to get a first-pass analysis of economic issues. 
Which made me think of the Fielitz and Borchardt information theory paper cited above along with Hayek's description of the price system as a mechanism for transferring information:
We must look at the price system as such a mechanism for communicating information if we want to understand its real function—a function which, of course, it fulfills less perfectly as prices grow more rigid. (Even when quoted prices have become quite rigid, however, the forces which would operate through changes in price still operate to a considerable extent through changes in the other terms of the contract.) The most significant fact about this system is the economy of knowledge with which it operates, or how little the individual participants need to know in order to be able to take the right action. In abbreviated form, by a kind of symbol, only the most essential information is passed on and passed on only to those concerned. It is more than a metaphor to describe the price system as a kind of machinery for registering change, or a system of telecommunications which enables individual producers to watch merely the movement of a few pointers, as an engineer might watch the hands of a few dials, in order to adjust their activities to changes of which they may never know more than is reflected in the price movement.
I thought: it could potentially be easy to derive supply and demand from first principles using information theory using the framework of the Fielitz and Borchardt paper. And I basically started to put together my own paper. Here was the abstract:
Abstract: A generic information transfer model in the case of ideal information transfer is used to derive the relationship between supply (information destination) and demand (information source) with the price as the signal of information transfer. We recover the properties the traditional economic supply-demand diagram. In the case of non-ideal information transfer, prices are observed to be sticky downward.
Instead of trying (and probably failing) to publish it as a paper, I was inspired by Igor Carron to just think out loud with a blog. This blog will be focused on determining if the framework established here is good for anything or just an interesting toy model. Or if it is completely wrong!

The next few posts will consist of what I have done so far: a summary of the Fielitz and Borchardt paper (since I kind of used their notation), deriving supply and demand from ideal information transfer, and demonstrating sticky prices from imperfect information transfer.

2 comments:

  1. Jason, I've decided to start at the beginning with your blog and work my way through... I'm tired of only being able to grasp bits and pieces. :D

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    Replies
    1. You'll get to see the slow evolution of how I thought about stuff. There's a whole period where I was into simulating stochastic processes. That was a wrong turn :)

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