Out of all of Arnold's macroeconomic views, only one strikes me as truly absurd: His skepticism about the ability of central banks to affect nominal GDP and other nominal variables.
Here is my problem. Nominal GDP is measured in a way that uses money as a unit of account. The central bank affects the quantity of some physical monetary aggregate. Those are not necessarily the same.
For example, suppose that the Fed swaps dimes and pennies for nickels, cutting the supply of nickels in half. I contend that nominal GDP, measured in dollars, will stay unchanged. Scott Sumner is prepared to argue differently, but I find that odd on all sorts of counts. If you think of currency as the key nominal aggregate, exchanging dimes and pennies for nickels does not change the total amount of currency outstanding, so why should it change nominal GDP, even if you believe the quantity theory of money?
So, if you are with me so far, then you agree that the Fed cannot just engage in any old open market operation and change nominal GDP. It has to increase an M that "matters" for nominal GDP. What I want you to do is choose a definition of M, stick to it, and then tell the empirical story.
If you choose the monetary base, you will have a big problem with the fall 2008 episode, when the Fed pretty much doubled the monetary base and nominal GDP did not even rise, much less double. If you choose a broader definition of money, then you are choosing an aggregate that the Fed does not exactly control.
We know that a country can debase its currency if it really is determined to do so--which is what happens under hyperinflation. This occurs when a country whose budget deficit far exceeds the amount it can borrow, and it just prints money to cover the shortfall.
I think that the Fed could debase our currency, too, if it were really determined and followed pretty drastic policies for quite a long time. However, within the range of realistic policy moves, there is only a loose relationship between the monetary aggregate that the Fed controls and any monetary aggregate that will correlate closely with nominal GDP. Hence, the relationship between what the Fed does and nominal GDP is going to be a loose one.
So my challenge for Bryan (and for the rest of the profession, because I am the one who is out on a limb on this) is to come up with a definition of money that satisfies two criteria. First, your monetary aggregate is correlated with nominal GDP in a reliable way (with "reliable" including that if you were to target it, the relationship would not fall apart). Second, the Fed controls that monetary aggregate reasonably closely.