Following this post, I tried to look at some longer run data. In this case I used GNP (and GNP deflator, but still the Adjusted Monetary Base) from FRED for 1929 to the present and plotted two surfaces. One surface (white, blue curve) uses $\kappa \sim \log \text{MB}/\log \text{GNP}$, the second surface (red) uses a constant value of $\kappa = 0.65$. The result for the price level fit does well with varying $\kappa$ (blue line) post WWII, while the constant $\kappa$ (red dashed line) does worse post WWII, but much better with the earlier data (data is the green line)
Here are the surface plots:
The red surface for constant $\kappa = 0.65$ follows the green line on average, while the blue curve (model, white surface) really messes up on the pre-WWII data. Why? I am not sure. The gold standard? Bad data?
One possibility is that for the early data, one or both of the constants $c_1, c_2$ become important ...
ReplyDelete$$
\kappa = \frac{\log \text{MB} + c_1}{\log \text{NGDP} + c_2}
$$