Thursday, September 15, 2016

Better macro theory

What are the terms we hear? Crowding out, bunched trades, jammed ports, buyers queuing up, bottlenecks, a shift shortage of clerks makes for long lines.

OK, the new macro model has to be based on queuing theory over networks.  What we know is that a theorem somewhere says we can make the macro model by assuming agents perform a two coloring partition in their local environment.  That is not to say that we do not do three way deals, we do.  But, to a given precision, we can model the trinaries as binaries, hence  variable window Huffman encoders are guaranteed to remove sufficient redundancy up to a given precision.

So, you have solutions, since some well defined version of duality says the Huffman encoder net is equivalent to the agents distribution net. You can, for example, measure the re-quantization cost, in units of volatility, when the net restructures. In fact, the currency bankers declare losses and gains on re-quantization.

Paul Romer was trying this stuff with his transportation model, as long as he included route restructuring in the face of bottlenecks.  So, passengers queuing up for longer than normal will 'buy a bus' and the entire network branch 'below' restructures (routes get promoted or demoted).  What is 'longer than normal'? When you are fourth or fifth in line, your knowledge of transaction value is very dim, so you are ready to move some mass.

So, Romer's model is equivalent to Shannon, they are trying to create a surface with a derived center, out of scratch.  Agents optimally spread about to minimize interference, but keep enough overlap to adjust the virtual surface.  That is, we do not like standing in long lines. Precision is equivalent to the size of a finite binary digit that generates the typical transaction set when sequenced through the Huffman tree.  The way I have constructed the problem, the number edges should be a power of two.  But that is due to the theorem briefly mentioned above.  So, this model does not eliminate all the control variable issues and requires insight to partition the queue and a working model of mutual entropy. Or how exactly would agents perform the variable window Huffman. All un-resolved issues.

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