Why can't the Fed cut interest rates to below zero? Why can't the Fed announce, for example, an interest rate of negative 2 percent? You borrow $100 today and repay $98 a year from now. A negative interest rate would certainly encourage people to borrow and spend, thereby expanding aggregate demand. [...]
The problem, you might reply, is that no one would lend money on those terms. Rather than lending at a negative interest rate, you could hold onto cash by, for example, stuffing it in your mattress. [...]
With this background, I can now state the proposed solution: Reduce the return to holding money below zero. Imagine that the Fed were to announce that, one year from today, it would pick a digit from 0 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.
-- Greg Mankiw, Reloading the Weapons of Monetary Policy