# Tony Yates’s Worries about Breaking Through the Zero Lower Bound Are Unfounded for a System Built around Electronic Money that Keeps Paper Currency in a Subsidiary Role

I wanted to reply to Tony Yates’s post “Haldane on coping with the zero lower bound.” Tony was reacting to this passage from Bank of England Chief Economist Andrew Haldane’s recent speech, discussing the basic options for eliminating the zero lower bound that Willem Buiter detailed in the first decade of this millenium:

Over a century ago, Silvio Gesell proposed levying a stamp tax on currency to generate a negative interest rate (Gesell (1916)).  Keynes discussed this scheme, approvingly, in the General Theory.  More recently, a number of modern-day variants of the stamp tax on currency have been proposed – for example, by randomly invalidating banknotes by serial number (Mankiw (2009), Goodfriend (2000)).

A more radical proposal still would be to remove the ZLB constraint entirely by abolishing paper currency.  This, too, has recently had its supporters (for example, Rogoff (2014)).  As well as solving the ZLB problem, it has the added advantage of taxing illicit activities undertaken using paper currency, such as drug-dealing, at source.

A third option is to set an explicit exchange rate between paper currency and electronic (or bank) money.  Having paper currency steadily depreciate relative to digital money effectively generates a negative interest rate on currency, provided electronic money is accepted by the public as the unit of account rather than currency.  This again is an old idea (Eisler (1932)), recently revitalised and updated (for example, Kimball (2015)).

Tony responds:

Andy points out that inflation is costly, and so an extra 2 percentage points of it is proportionately more costly.  Yet it seems to me that allowing negative interest rates on digital cash increases the cost of 2 per cent inflation somewhat.  Formerly, consumers get zero interest on their notes and coins holdings, while they depreciate at an average of 2 per cent a year.  With occasionally negative rates, these ‘shoe-leather costs’ of inflation increase a bit, proportional to the time spent below zero, and just how negative they go.  A reminder:  during the dark days of the previous crisis it was commonly thought that rates would ideally have gone down to about negative 7% or 8%.

Second, I query the judgement that eliminating cash and using negative rates would be less damaging to the credibility of monetary institutions than bumping up the inflation target.  Ultimately, in the absence of good models of how reputations are won and lost, this argument is really about trading hunches.  But mine is that there is a risk of a serious WTF moment when the no-cash system is explained, or people find out that they actually have to pay large sums of money simply for the privilege of having it.  Anecdotally, we know from many models of money that equilibria where money is valued are quite fragile – specifically, it’s quite easy to write down models in which it is not.

I am not going to defend Silvio Gesell’s direct taxation of paper currency or the total abolition of paper currency. But I will defend my own recommendation, which builds on Robert Eisler’s idea of having an exchange rate between paper currency and bank money (which in modern times can be called “electronic money” since it is encoded in the memory banks of computers).

Tony has two worries. The first is a worry about “shoe-leather costs”–people being overly discouraged from using paper currency. But shoe-leather costs are all about the spread between the paper currency interest rate and other safe interest rates. My recommendation to central banks is to keep the paper currency interest within 50 basis points of the target rate at all times, except when that would push a paper dollar toward being worth more than an electronic dollar. Consider in particular the baseline case of a paper currency equal to the target rate whenever that doesn’t take paper currency above par. Then there are no shoe-leather costs when paper currency is away from par.

If a central bank follows this recommendation, paper currency is at par only during periods of time when the target rate is positive, and things are very much as under the current system when the target rate is positive. One might lament the shoe-leather costs during those periods, but it is a lament one could equally have in the current system. And over time, as central banks gain confidence that the zero lower bound is no more, they are likely to lower the target inflation rate, bringing shoe-leather costs during those periods at par down as well.

Tony’s second worry is that confidence will be shaken by the dramatic change in the system. He is certainly right that the formal models give little guidance on this point because under any fiat money system, the formal models allow the value of money to suddenly drop to zero at any time for no real reason. So any answer must be based solidly on intuitions about the real world rather than on a formal calculation.

Part of my reply to Tony’s second worry is to note that a straightforward arbitrage argument ensures that how the central bank treats paper currency at the cash window determines the value of paper currency relative to electronic money. (See An Underappreciated Power of a Central Bank: Determining the Relative Prices between the Various Forms of Money Under Its Jurisdiction.) So the danger at issue has to be something about all the forms of money controlled by the central bank put together.

But the main point I want to make is that the approach I recommend changes everything very gradually. At the moment of introducing the new system, paper currency starts at par, just as it is under the current system. Even at a quite low nominal interest rate of -4% per year, the value of paper currency relative to electronic money would only be changing by about 1.1 basis points per day. For example the exchange rate would go from 1000 electronic dollars per 1000 paper dollars on day zero to 999.89 electronic dollars per 1000 paper dollars the next day–an 11 cent paper currency deposit fee on $1000. The paper currency deposit fee on$1000 would escalate by roughly 11 cents each day, to 22 cents, then 33 cents, etc., until compounding kicked in a little more to make the absolute amount of the addition to the fee each day a little less. (Note that to fully establish the exchange rate, the paper currency deposit fee is levied on net deposits, meaning that on the day a deposit by a private bank at the Fed’s cash window of p$1000 would become e$999.89 in the bank’s reserve account, a withdrawal of p$1000 would only result in a deduction of e$999.89 from the bank’s reserve account. Or if the bank wanted to withdraw e$1000, it would receive something close to p$1000.11.)

Of course, 1.1 basis points per day adds up over time, so this is a big deal. My point is not to minimize the importance of what is being done with the exchange rate between paper currency and electronic money, but to say that the exchange rate is moving very gradually each day. There is plenty of time for people to get used to the new system. And the continuity from one day to the next means that for private agents, behaving more or less as they did yesterday is a viable option until they figure things out. By the time they figure things out, the system already has a track record of day after day looking stable.

All of the above is to argue that getting paper currency out of the way of negative interest rates will not cause any drastic change in behavior. The electronic negative interest rates themselves can and should cause a significant change in behavior–after all, the point is to stimulate the economy, as was needed in 2009 in the US, and as is needed now in the eurozone and in Japan. But I suspect that central banks will be fairly gradual in going to deeper negative rates as well. If the Swiss National Bank goes to deeper negative rates, for example, I will be surprised if the next step down from -.75% per year is to any lower than -1.25%. (And it is even more unlikely that the next step down would be to lower than -1.5%.)

Gradualism in going to deeper negative rates, (associated with gradualism in lower the paper currency interest rate to get paper currency out of the way) has costs in the slowness of the extra stimulus, but it tends to allay the kinds of worries that Tony is expressing. If the first step down in the paper currency interest rate is to -.5%, at that rate, after a full quarter, the paper currency deposit fee would only by 1/8 %, meaning that the exchange rate was .99875 electronic dollars per paper dollar after three months. That is nowhere near as disruptive as many other things central banks have done in the past, such as the sudden change in the exchange rate for the Swiss Franc back in January, 2015 (which I wrote of in my column “Swiss Pioneers! The Swiss as the Vanguard for Negative Interest Rates.”)