In the standard model, central banks earn seignorage (sometimes called "inflation tax revenue") because their liabilities (cash and bank reserves) pay zero interest and their assets (government bonds) are interest earning. Thus imagine the Fed back in 2007, with a monetary base of $800 billion and 4% interest on its portfolio of bonds. In that case, the Fed would earn about $32 billion each year in profits. Most of that money is passed on to the Treasury, with the Fed just keeping enough to finance its operations.
Because of the zero lower bound on interest rates, I don't think anyone imagined seignorage ever turning negative. But risk-free German interest rates are now negative, so does that mean central banks in the eurozone can expect to earn negative seignorage? Perhaps, although as a practical matter it's probably still positive, as the Swiss National Bank, for instance, has a negative 0.75% rate on reserves. That's much bigger in absolute value that the minus 0.05% yield on the 5-year bund.
Nonetheless, it is probably impossible to pay negative interest rate on currency. Nor do I think it is feasible to make it so that currency is no longer a medium of account (as Miles Kimball proposed.) Just to be clear, however, I do expect negative interest-bearing currency to be feasible within 25 years, and to be implemented within 50 years. So Miles is just ahead of his time.)
Over at TheMoneyIllusion, Bill Woolsey left an excellent comment. Here's one part of it:
If the Swiss central bank's goal is to provide nominal stability within Switzerland, then it needs to be able to reduce the quantity of base money when necessary. When Switzerland's safe have status results in what looks a temporary spike in the demand for base money, even if this "spike" might look to last for some years, the Swiss central bank must be especially concerned about the need to reverse any increase in the quantity of base money. This suggests that risk on the assets purchased to expand the quantity of base money is a significant concern.
A quantity theoretic analysis that assumes a given quantity of money with nominal values changing until the real quantity meets the real demand can lead to confusion. As Nick Rowe points out, expected future seignorage is a key asset for a central bank. But that "asset" is due to the central banks monopoly on issuing currency. How important is that to a small open economy located in the middle of Europe, especially one with tradition of financial freedom for its citizens?
Of course, to maintain nominal stability the Swiss central bank must accommodate increases in the demand for base money. As it is doing, the way to dampen increases in the demand for base money is to charge people for holding it-negative interest rates on central bank balances. And as Koning has pointed out, they need to stop issuing high denomination currency immediately. When borrowing at a zero interest is not attractive because of risk, they need to focus on issuing currency in the sorts of small denominations appropriate for small face-to-face transactions in Switzerland.
I think this is about right, but I'd slightly disagree on the large denomination currency. Let's step back and ask what's so bad about more rapid inflation? One answer is that it hurts savers. But does it? Aren't they compensated via the Fisher effect? The counterargument is that holders of cash are not compensated for inflation. But surely that's not a big problem for the amounts of cash that people typical carry in their wallets. But what about the hoarders of massive quantities of Swiss currency? Isn't inflation unfair to them? Yes it is. But here's my question; if we are going to avoid inflation in order to protect major cash hoarders, then what sense does it make to eliminate restrict large denominations notes in order to discourage cash hoarding? In other words, the Swiss have to make up their minds---what do they want to do? Do they want low inflation or a small central bank balance sheet? So far they (and their supporters) seem to be talking and acting as if they think they can have both. But they cannot, at least not in the 21st century world of ultra-low Wicksellian equilibrium interest rates.
Another cost of inflation is excess taxation of nominal returns on capital. But in a world where nominal returns on risk-free assets are negative, that's the least of our worries. Here again, NGDP targeting offers a nice compromise. In the long run, returns on capital are likely to be strongly correlated with NGDP growth. It probably makes sense to target NGDP growth at a high enough rate so that nominal returns on government bonds are at least slightly positive, at least until we have invented negative interest currency. For instance, look at how the Japanese were able to sharply depreciate the yen without having to pay a penny more in interest on their debt. How many other central banks are leaving $100 bills on the sidewalk?