# A crude attempt to translate Rowe/Krugman/DeLong into monetarism

As readers know I’m not very good at mathematical economics. Actually that’s not quite right, I’m pretty good at that part of math called “geometry,” but not so good at that part of math called “algebra.” Unfortunately most economists don’t consider geometry to be math. So most people will want to skip this post, where I try to translate **Paul Krugman’s** geometric critique of Steve Williamson into monetarist language. There’s about an 85% chance I am wrong, but I’m hopeful that my smarter commenters can tell me why.

Even worse, I cannot draw graphs, so I will verbally describe changes on a graph. Anyone still reading? I did find a graph on the internet that looks roughly like what I have in mind, however the horizontal axis in my graph is next year’s NGDP (or price level) and the vertical axis is next year’s monetary base.

Why the U-shape? Recall that countries with no NGDP growth have low interest rates and hence a high demand for base money. In Japan the base is more than 20% of GDP. In Australia, a country that averages 6% NGDP growth, it’s only 4% of GDP. In Zimbabwe it is (was) still lower. However the growth rate of NGDP in Zimbabwe is so fast (or was a few years ago) that the total base is still much higher than it would have been with 6% NGDP growth, despite being even a lower percentage of GDP. On the other hand the difference between 0% NGDP growth and 6% NGDP growth is trivial compared to the difference between the base being 20% of GDP and 4% of GDP.

Let me illustrate this with a specific example. We start at the Australian position, near the bottom of the U-shaped graph. Now the central bank contemplates three possible policies: status quo, the Japanese option, and the Zimbabwe option. (No idea why they’d want to move.) Assume policy is 100% credible. My claim is that a move toward the Japanese option would actually require a larger monetary base, as the slowdown in NGDP growth would be trivial compared to the jump in demand for base money as a share of GDP, from 4% to 20%. Moving that way would force the central bank to print lots more base money, despite the slower NGDP growth and inflation. Sound far-fetched? Check out the US since 2008. We’ve seen the slowest NGDP growth since Herbert Hoover, and a big surge in the base.

The other direction is easier to explain. It’s common sense that moving toward Zimbabwe hyperinflation would require a bigger base, despite being a smaller share of GDP. After all, they had individual currency notes of $100 trillion.

Now draw a horizontal line that cuts the graph in two places. The intersection on the left is likely to be at the zero interest bound, or very close. The right is the more “normal” equilibrium. I believe the dual equilibrium is related to the indeterminacy problem in ratex fiat money models, but am not sure. (Here I mean “indeterminacy” in the “multiple equilibria” sense of Bennett McCallum.)

Now we finally get to the Krugman thought experiment. The liquidity premium for government bonds increases. That reduces the yield on government bonds relative to other assets. That then reduces the hot potato effect, as the gap between the yield on government bonds and base money declines. Less HPE is just another way of saying the demand for base money increases at any given level of NGDP. This means the U-shaped graph shifts vertically upward. At the equilibrium on the right side (the “normal” case) the equilibrium point shifts to the left. Next year’s NGDP declines, just as you’d expect. But the equilibrium on the left side moves to the right, suggesting that more demand for base money is expansionary. That’s the case where Krugman criticized Williamson, translated into monetarism.

Or perhaps I’m in way over my head.

PS. This post is motivated by posts by **Nick Rowe**, Paul Krugman, and **Brad DeLong**.