Miles Kimball has an article on Quartz about electronic money. He advocates making electronic money the medium of account, and allowing tangible paper currency to trade at a discount during national economic emergencies.
He proposes that households and firms have electronic money created by the government available, though he doesn't really spell that out. He mentions in passing that the interest rate paid on that electronic money (effectively "reserve balances" held by firms and households at the central bank) should be set below the interest rate target set by the Fed. Perhaps I was reading between the lines, but he seems to be advocating a system of using the interest rate paid on the banks' reserve balances as the instrument of monetary policy. His major emphasis is that this target interest rate could be reduced below zero if the Fed found it necessary to do so in order to maintain spending on output.
As for tangible hand-to-hand currency, it would trade at a growing discount relative to the electronic money held by households and firms. While Kimball doesn't explain, I suppose he is assuming that by reducing the price at which currency can be deposited in exchange for electronic money in the future, its actual market value would fall. (I think this is likely true.)
This discount on tangible currency would only occur in national economic emergencies--that is--when the interest rate that banks earn on reserve balances is reduced to very low levels. Again, while Kimball wasn't too clear, when the interest rate the Fed pays to banks rises enough that the lower one paid to firms and households rises enough, so that the still lower rate of price decrease on the tangible currency hits zero, then tangible currencywould no long fall in value. When good times return, he explains, the discount would be reduced (the price of currency would rise again) creating a positive rate of interest, presumably still slightly lower than that on electronic money. The point is to make tangible currency perform slightly worse than a balance in an electronic money account.
In my view, there is no need to set up deposit accounts for households and firms at the central bank (Kimball's "electronic money.") The private banking system already provides those--they are called checkable deposits. It would be possible for the government to adjust the rate of exchange between reserve balances and currency at the central bank and allow private banks to use that same rate of exchange for withdrawals and deposits of the tangible currency. The key, however, isn't how much currency can be withdrawn from deposits, but rather the price at which it will be accepted for deposit in the future. A dollar withdrawn when interest rates turn negative must be only accepted for deposit when interest rates turn positive again at a lower price reflecting the negative interest rate on deposits during the interim.
I still believe that rather than have the government develop a new sort of money for households and firms (electronic deposits held directly at the central bank,) it would be better to leave the issue of the tangible currency to the private sector.
In my view, a situation where extremely low (and even negative) yields on short and safe assets makes currency more attractive to hold, is not a time to start reducing the price of currency. The growing discount on currency means that each dollar-dominated deposit is being redeemed with progressively more hand to hand currency. While that make it more attractive to hold deposits, (with the nominal interest rate calculated in terms of the currency remaining approximately zero,) for this to all work out, the government must stick to its commitment to only allow the currency to be redeposited at that lower price. Or rather, to only gradually raise the price at which it can be deposited at a rate reflecting interest rates on other short and safe assets when they are again positive. Allowing that process to be short circuited, and having the currency jump back to par would be a problem. And why wouldn't everyone in the private sector clamor for such a jump in the value of their currency holdings?
In my view, private hand-to-hand currency, where banks just cease issuing it when it is no longer profitable, and have a call provision when maintaining the outstanding balance is too costly, is a much better system. Rather than trying to reduce the price of currency, the central bank just sets the interest rate it pays on deposits where it thinks it is best. Banks set interest rates on "electronic money" as they think is best. And if no one wants to issue currency, then none is issued.
Sure, the lack of hand-to-hand currency is inconvenient. Let the private sector come up with substitutes to solve the problem of currency shortages. I think it is simpler than managing a currency deposit exchange rate.