Thursday, July 11, 2013

Short course on information transfer and the quantity theory

In order to shop around this idea in the blogosphere for real (as opposed to writing only for myself), I thought I should assemble a "best of" single link to my posts and create something of a short course on the information transfer model/framework and its application to the quantity theory of money. One point to make at the beginning is that the information transfer model is a framework for doing things supply-and-demand-y (i.e. making economic arguments). You need to include other things in order to describe the real world. In this case I describe a quantity theory of money in the information transfer framework and find that it does a little better that the real than the traditional quantity theory which seems to work only for high inflation countries. The theory presented works for low inflation countries as well as high. Anyway, here are the posts you should read (other posts are speculative musings and numerical games):

Basics of the Information Transfer Model (ITM)
Deriving "supply and demand" from the information transfer model

Aggregate Demand/Aggregate Supply
I don't have a good post on using the ITM as an AD/AS model ... perhaps I should write one. But all it would say is if you took
$$ Q^s = AS \text{ and } Q^d = AD \text{ and } P = P $$
then you get what you'd expect. It doesn't have vertical $\text{LRAS}$ curves (with perfect information transfer), but it gets the basic ideas across. Having the information transfer index $\kappa$ become a function of $\text{AD}$ and $\text{AS}$ brings you to what I think is the best use of the ITM so far ...

Information Transfer Model and the Quantity Theory of Money
This series of posts catalogs some numerical work where we take $Q^s = AS = MB$ and $Q^d = AD = NGDP$ and culminates in deriving the quantity theory of money from information transfer. The equations do an excellent job of calculating inflation from NGDP and the monetary base in the US from 1960 to the onset of the financial crisis in 2008. The derivation of the traditional quantity theory of money (which only works well for high inflation countries) using the information transfer model framework not only recovers the traditional quantity theory but extends the application it to low inflation countries.

Empirical results with the Information Transfer Quantity Theory
This final series shows a better way to visualize the information transfer model (the equation determining the price level is best envisioned as describing a surface on which the $MB$ and $NGDP$ perform a random walk with drift). The results do a good job of describing the US, Japan and Germany. I also venture an inflation prediction with the model (the price level will stay flat  -- low inflation -- until 2020) even with monetary moves comparable to the QE already conducted by the Fed.


  1. I should note that the solution to the differential equation for "floating" information source/destination is
    \frac{Q^d}{Q^{d}_{ref}} = \left(\frac{Q^s}{Q^{s}_{ref}}\right)^{1/\kappa}
    And that substituting that in the equation for the price yields
    P = \frac{1}{\kappa}\left(\frac{Q^d_{ref}}{Q^{s}_{ref}}\right) \left(\frac{Q^s}{Q^{s}_{ref}}\right)^{1/\kappa - 1}
    This is used as the starting equation analogous to $M V = P Y$ in the quantity theory of money. In it we take
    \kappa \sim \frac{MB}{NGDP}

    1. Forgot the logs!
      \kappa \sim \frac{\log MB}{\log NGDP}


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