People adjust their borrowing to interest rates all the time. But cash balances? That's hard to believe.
Who cares? In practice, the Fed has its famous three tools--the discount rate, the reserve requirement(s), and open market operations. In the latter, it fiddles in the repo market.
When the Fed fiddles in the repo market, Bryan says that he does not adjust how much cash he carries in his wallet. Neither do I. But that just means that there is a loose relationship between Fed fiddling and measures of the money supply.
But there is a very tight relationship between Fed fiddling and one measure of the money supply--H, or high-powered money. H is equal to the liabilities on the Fed's balance sheet. The Fed does control that.
There is slack in the relationship between H and cash held by the public. There is slack in the relationship between H and M1, the traditional measure of cash plus checking accounts. There is slack in the relationship between H and M2, which is M1 plus some savings accounts, and is Milton Friedman's favorite definition of "M."
The slack does not stop there, by any means. There is slack between any of the M's and nominal GDP. There is slack between the repo rate (where the Fed does its fiddling) and every other interest rate in the economy. There have been plenty of times where the Fed leaned one way on interest rates and bond market vigilantes, who affect mortgage rates and corporate bond rates, sent rates in the other direction.
If Bryan wants to fight like heck for his theory of the inelastic money demand function, let him. I think it's pointless. In going from textbook monetary theory to reality, there are plenty of more important problems to worry about. Because there are so many problems, my guess is that a good case can be made for all sorts of values for the interest elasticity of money demand, including very low values.
It's a stupid fight to get into. My initial instinct was to stay out of it, and I wish I'd stuck with my initial instinct.