There is much talk about the zero bound on nominal interest rates and how this is constraining the policy options of many central banks. How can of course ask oneself why there would be such a restriction on nominal interest rates. Would it be possible to tax (nominal) money holdings? It is certainly conceivable to have negative interest rates on some bank accounts, and it has happened before. Switzerland and Germany imposed negative rates on non-resident account holders in the 1970's, and the Swiss National Bank is currently contemplating doing this again (New York Times). Sweden imposed them recently on mandatory reserve holdings of commercial banks. There is, however, very little theory on this.
Cordelius Ilgmann and Martin Menner try to make sense of the existing literature on the topic. There are essentially two strands, according to them: the first is started with Silvio Gesell in the 19th century and proposes taxing money, the second lies within the very recent money-search literature.
Gesell was the proponent of an anarchist free-market utopia, the free-economy movement. He proposed that bank notes would need to have a weekly stamp affixed to remain valid, amounting to a 5% tax every year. The stated reason is that while other goods depreciate naturally, money does not and may be withheld from circulation. The tax alleviates that, and should in particular be used in times of crisis, because it increases the velocity of money and prevents its hoarding. That argument can be made for today, but it neglects the influence of inflation on all this, and that is crucial.
The recent money-search literature uses taxes on money holding as a proxy for inflation. My understanding that this is really for analytic convenience but in no way a policy proposal. Indeed, what this literature cares about is the real return on money, not the nominal one. But Ilgmann and Menner run with it and believe there is an endorsement of a Gesell tax.
PS: a third way is discussed in the paper, recently proposed by Willem Buiter. It is based on the silly idea that the various function of money are taken over by separate currencies and backed up by equally silly arguments with money in the utility function.