How to encourage everyone to lend money

This seems like a really stupid idea, but since he is a renown Harvard prof, its gets published in the NYT as an editorial:

So why shouldn’t the Fed just keep cutting interest rates? Why not lower the target interest rate to, say, negative 3 percent?

At that interest rate, you could borrow and spend $100 and repay $97 next year. This opportunity would surely generate more borrowing and aggregate demand.

The problem with negative interest rates, however, is quickly apparent: nobody would lend on those terms. Rather than giving your money to a borrower who promises a negative return, it would be better to stick the cash in your mattress. Because holding money promises a return of exactly zero, lenders cannot offer less.

Unless, that is, we figure out a way to make holding money less attractive.

At one of my recent Harvard seminars, a graduate student proposed a clever scheme to do exactly that. (I will let the student remain anonymous. In case he ever wants to pursue a career as a central banker, having his name associated with this idea probably won’t help.)

Imagine that the Fed were to announce that, a year from today, it would pick a digit from zero to 9 out of a hat. All currency with a serial number ending in that digit would no longer be legal tender. Suddenly, the expected return to holding currency would become negative 10 percent.

That move would free the Fed to cut interest rates below zero. People would be delighted to lend money at negative 3 percent, since losing 3 percent is better than losing 10.

Mich's Global Economic Analysis points out that if this plan was enacted, cash in the economy would grind to a halt:

What exactly would vending machine operators do? Would owners program all machines to stop accepting dollar bills with a certain digit? What about the bills already accepted? On that line of thinking, I propose a complete shutdown of all vending machines that accept dollar bills would occur several days to a week before the drawing date.

What about merchants? On the date of the drawing and even a few days before, would any merchant accept anything but credit cards, debit cards, checks, or coins? I think not.

No one in their right mind would hold or accept any digit denominated currency. However, quarters would be hoarded! Think of the mounds of quarters people would be hold. A quarter, nickel, and dime shortage would be 100% guaranteed under such a "clever scheme".

Other than buying candy with quarters, the cash economy would literally grind to a halt. And given that people would be carrying less cash than before, spending would actually decline if such a bill were passed.

Thus Mankiw's proposal would do the exact opposite of what he intended.