## Saturday, March 15, 2014

### Unsolved problems in information transfer macroeconomics [update: solved]

Once the theory was invented, [Einstein] didn’t have a monopoly on it; it was out there for anyone to understand and move forward with. ... Your theory should have a life of its own; it should be a machine that I (or anyone) could use to make predictions.

To this end, I'd like to put forward a (living) list unsolved problems information transfer macro that maybe people out there can help with or solve themselves:

1. In the interest rate market r:NGDP→MB, the interest rate r itself is not the "price" ... it's actually r^c where c is a constant (≈ 2.8). This is a bijective function on the domain [0, ∞), so from a mathematical standpoint there really isn't a meaningful difference. However it's an additional parameter that may be derivable from e.g. the byzantine system of determining a bond's price. It doesn't appear at first glance to be related to the term of the bond (my initial guess).
2. In the labor market P:NGDP→L, there is a significant component that isn't explained that is approximately linear with time if you take the ratio P/(NGDP/L). Including this ratio to incorporate this unknown effect is critical to understanding the unemployment rate. Originally, I thought it might be related to nominal wage flexibility and that does seem to explain a piece of it. I also considered inequality might be involved. I haven't nailed this down yet.

Update 26 November 2016

Both of these have been solved. In 1), the interest rate model should be seen as a pair of information equilibrium relationships (where the interest rate is in information equilibrium with the "price of money"):

p:NGDP→MB
r→p

See here (draft paper) or the actual paper.

In 2), the labor market ends up relying a bit on the Solow model, and the difference mentioned above is due to capital (and is different for different countries that have different capital-labor mixes). Here is the description of the "quantity theory of labor and capital".