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:

http://informationtransfereconomics.blogspot.com/2013/10/the-phillips-curve.html

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:

http://informationtransfereconomics.blogspot.com/2013/10/sticky-wages.html

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

Comments are welcome. Please see the Moderation and comment policy.

Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.