I teach how to break through the zero lower bound in my “Monetary and Financial Theory” class. I got an interesting question from one of my students, Matthew Hoffman (who chose fame over anonymity when I told him I wanted to write this Q&A post. Here are his questions and my answers. 

Matthew: I understand that electronic money would be the unit of account, and that the deposit fee, in a time of negative interest rates, would eliminate the ZLB as the paper currency is charged roughly the value of the negative rate upon deposit. So my question is what stops people from just taking all of their money out and holding it as cash? You give three ways to act against paper currency storage, but since you advocate the third method (the fee on deposits) why can’t people still withdraw all of their money in cash and then not re-deposit until the deposit fee is “allowed to shrink when the interest rate is positive?”

Is the answer to my question explained in part “B. The Paper Currency Interest Rate,” in that since the electronic money is the unit of account, then the deposit fee still affects the value of paper currency regardless of whether it’s in the bank or under the mattress? For example, if I take a $100 bill out of the bank when the deposit fee is 2%, then is the value of my bill only $98 if I go to the mall? Or is it still worth $100, but when I go to re-deposit it, at that point it will be worth only $98 and I essentially lost $2 by putting it in the bank? 

Miles: Excellent questions!

1. Note that over the horizon where paper currency earns a zero interest rate, money in the bank also does. So that creates no incentive to take out paper currency–though it also provides no disincentive. 
2. At retail, paper currency will be at par for a while. If I take out cash and spend it, that stimulates the economy. So that is OK. It doesn’t stop the policy from working.
3. The interest rate for small checking and saving accounts may stay zero if interest rates are not too low, and to somewhat lower interest rates if the central bank subsidizes zero interest rates in small checking and saving accounts. If so, then those folks wouldn’t have any temptation to withdraw paper currency in any case.

Notice that in no case is there an arbitrage that stops interest rates from being deeply negative.

Matthew: One follow up question…so would cash that was already under the mattress when the Fed increases the deposit fee still be worth its face value? It would only be worth less if it were deposited? This is like your second point in your previous email I believe…the value will stay at par for awhile and that cash can stimulate the economy if spent.

Miles: If used for purchases reasonably promptly, paper currency households already had could probably be spent at par. And most business try to deposit their paper currency in the bank quickly, while the exchange rate changes very slowly. So paper currency on hand at the beginning of the electronic money system should not be a big deal for them.