Friday, August 30, 2013

Scott Sumner's Model (Part 1)

I've been working on trying to build different economic models in the information transfer framework. I have had some success with the quantity theory of money (here, here and here) and the IS-LM model (here and here). The "holy grail" as it were is Scott Sumner's model. Not because it is the best, but because it doesn't exist!

I started to believe it would fall out quickly when I saw the following graph on a flight from LA back to Seattle (from this post from a couple days ago):

At least that's my version of the graph from FRED data. It plots the unemployment rate and the ratio of hourly nominal wages to NGDP. I saw that and thought (in the information transfer framework) is the unemployment rate a "price" detecting a signal from the aggregate demand to nominal hourly wages? ($r:NGDP \rightarrow NHW$) In the information transfer framework we'd write the "price equation" like this:

$$ r = \frac{1}{\kappa}\frac{NGDP}{NHW} \text{ ???} $$

Unfortunately, my initial idea crashed and burned when I realized after I got a chance to plot it myself that the correlation in the graph is a trick of normalization and selective windowing. Here is a version over a longer period:

Apparently the model in Scott Sumner's head has more variables than the version he writes down. You can see that there is an approximate overall $1/\text{year}$ bias. However this graph was useful in the sense that it helped me write down the real thing, which is the subject of the next post.

1 comment:

  1. The "correct" model with the unemployment rate is here:

    And the information transfer model is P:NGDP→U, not u:NGDP→NHW, where U is the total number of unemployed and u is the unemployment rate. The model for wages can be seen here:

    The information transfer model is P':NGDP→NW where P' is some unknown constant price (hence sticky wages) and NW are total nominal wages.


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