Thursday, January 25, 2018

Paying interest on cash

Freigeld, or stamp scrip, is designed to pay negative interest, but it can be re-purposed to pay positive interest.

Remember when global interest rates were plunging to zero and all everyone wanted to talk about was how to set a negative interest rate on cash? Now that interest rates around the world are rising again, here's that same idea in reverse: what about finally paying positive interest rates on cash? I'm going to explore three ways of doing this. As for why we'd want to pay interest on cash, I'll leave that question till the end.


The first way to pay interest on cash is to use stamping. Each Friday, the owner of a bill—say a $50 note—can bring it in to a bank to be officially stamped. The stamp represents an interest payment due to the owner. When the owner is ready to collect his interest, he deposits the note at the bank. For example, say that 52 weeks have passed and 52 stamps are present on the $50 note. If the interest rate on cash is 5%, then the banknote owner is due to receive $2.50 in interest.

Alternatively the note owner can collect the interest by spending the $50 note, say at a local grocery store. The checkout clerk will count the number of stamps, or interest due, and tack that on to the face value of the note. With 52 stamps, the owner of a $50 note should be able to buy $52.50 worth of groceries, not $50. After all, the store has the right to bring the $50 note to its bank and collect the $2.50 in interest for itself.

Stamped currency seems like a pretty big hassle to me. The clerk behind the counter must count out the stamps on the note by hand, and the owner of the note has to trek back and forth to the bank each week to get the stamp affixed. Instead, imagine that each banknote has a magnetic strip that records how long the bill had been in circulation. This would remove some of these hassles. Weekly trips to the bank for stamping would no longer be necessary, and a note reader installed at a bank or retailer would automatically record how much interest was due, precluding painstaking counting of stamps.

"They use this magnetic strip to track you." says Byers to Agent Scully, The X-Files

Apart from stoking conspiracy theories, there's still a major problem with a magnetic strip scheme. Because each note has entered circulation at a different time, each is entitled to a varying amounts of interest. And this means that banknotes are no longer fungible. Fungibility—the ability to cleanly interchange all members of a population—is one of the features of money that makes it so easy to use. Remove it and money becomes complicated, each piece requiring a unique and costly effort to ascertain its value.


Our second way of paying interest on money doesn't destroy the fungibility of banknotes. The central bank needs to sever the traditional 1:1 peg between deposit money and cash, and then have cash slowly appreciate in value relative to deposits.

For instance, a central bank might start by setting an exchange rate of $1 note = $1 deposit on January 1, but on January 2 it adjusts this rate so $1 note is equal to $1.0001 deposits, and on January 3 adjust this rate to $1:$1.0002, etc. So the cash in your wallet is benefiting from capital gains. By December 31, the exchange rate will be around $1 note to $1.0365. Anyone who has held a banknote for the full year can deposit it and will have earned 3.65 cents in interest, or 3.65%. 

The major drawback with this scheme is the calculational burden imposed on the population by breaking the convenient 1:1 peg between cash and deposits. Assuming that retailers price their wares in terms of deposits, anyone who wants to pay in cash will have to make a currency conversion using that day's exchange rate. For instance, if the central bank's peg is currently being set at $1 note = $1.50 in deposits, then a popsicle that is priced at $1 will require—hmmm... let me check my calculator—$0.667 in cash. Phones will make this exchange rate calculation easy, but it is still likely to be a bit of a nuisance.

There are other hassles too. Would a capital gains tax have to be paid on the appreciation of one's cash? How would existing long-term contracts deal with the divergence? For instance, if my employer is paying me $50,000 per year, obviously I'd prefer this sum be denominated in steadily appreciating cash rather than constant deposits, and she will prefer the latter. What becomes the standard unit of account?


The last way to pay interest (at least as far as I know) is to run lotteries based on banknote serial numbers, an idea independently proposed by Hu McCulloch and Charles Goodhart back in 1986.

Central banks would periodically hold draws entitling the winning serial numbers to large cash prizes. For example, if there was $100 billion in banknotes in circulation, the central bank could set the interest rate on cash at 5% by offering prizes over the course of the year amounting to 5% of $100 billion, or $5 billion.

This technique of paying interest on cash solves the fungibility problem that plagues the earlier stamping technique. Every note has the same chance of winning the lottery, and non-fungible winners are immediately withdrawn. And unlike the crawling peg idea, banknotes and deposits remain equal to each other so burdensome exchange rate calculations don't need to me made.

However, it introduces the threat of bank runs. The day before the big lottery is set to occur, everyone will withdraw deposits for cash so that they can compete in the draw. To prevent a bank run, it may be necessary to randomize the date of the big lottery so that no one knows when to withdraw notes, an idea proposed by Tyler Cowen. Another way to preclude bank runs is to have a regular stream of small weekly lotteries rather than one or two big ones each year.

Another drawback to note lotteries is the cost that is imposed on society by having everyone constantly checking serial numbers. As Brian Romanchuk points out, employees who are working behind their employer's tills may be tempted to switch out winning notes with losers. Employers may protect themselves by setting up scanning hardware to read in serial numbers as banknotes enter the tills, maintaining their own internal database of cash inventories so that winners can quickly be isolated and returned. But all of that is costly. Would it be worth it?

Interestingly, there is some precedent for these sorts of lotteries. In Taiwan, receipts are eligible for a receipt lottery, a neat way to incentivize people to avoid under-the-table transactions (ht Gwern). Lotteries can also be useful in attracting depositors, as outlined in this Freakonomics podcast (ht Ryan). George Selgin and William Lastrapes have gone into the idea of lottery-linked money in some detail:
Though the suggestion may appear far fetched, in many countries lotteries are presently being used with considerable success to market bank deposits. According to Mauro Guillen and Adrian Tschoegl (2002), “lottery-linked” deposit accounts have been especially popular with poorer persons, including many who might otherwise remain “outside the banking system.” ... In two popular Argentine schemes, for instance, depositors receive one ticket or chance of winning for every $200 or $250 on deposit (ibid., p. 221). Lottery-linked banknotes, in contrast, would themselves serve as tickets, allowing persons to play for as little as the value of the lowest note denomination, and with no apparent cost to themselves save that of occasionally inspecting their note holdings.

Some readers may recognize these three techniques for paying interest on cash as the inverse of the three go-to ways of applying negative interest rates to cash being discussed a few years ago. For instance, one of the most well-known ways of imposing negative interest rates on owners of cash is to apply a Silvio Gesell style stamp scheme (see picture at top), whereby a currency owner must buy a stamp and affix it to the note in order to renew the validity of their currency each month. (I once discussed Alberta's experiment with Gesell's "shrinking money" here). Without the appropriate number of stamps, the note is illegitimate. In my first example above, Gesell's stamp tax has been re-engineered into a stamp subsidy. As for the magnetic strip modification, this is Marvin Goodfriend's 1999 update of Gesell, flipped around to award interest rather than docking it.

Miles Kimball has written extensively on escaping the zero lower bound to interest rates by setting a crawling peg on currency. But just as Kimball's crawling peg can impose a negative interest rate on banknotes, it can be used to pay interest, as I described above. Indeed, Miles (along with Ruchir Agarwal) frequently mention this possibility in his blog posts and papers (see this pdf).

Finally, remember Greg Mankiw's controversial 2009 article on imposing negative interest rates by serial number? He wrote:
Imagine that the Fed were to announce that, a year from today, it would pick a digit from zero to 9 out of a hat. All currency with a serial number ending in that digit would no longer be legal tender. Suddenly, the expected return to holding currency would become negative 10 percent.
Mankiw's idea is just the reverse of Goodhart and McCulloch's earlier lottery idea, the lottery replaced by with a demonetization.


So why pay interest on currency? I can think of two reasons. One is based on fairness, the other on efficiency.

The decision to avoid paying the market rate of interest on currency amounts to a tax on currency users. Who pays this tax? Cash is often the only means for the poor, new immigrants, and unbanked to participate in the economy. So the tax falls on those who can least afford it. This hardly seems fair. By conducting note lotteries or stamping notes, those consigned to the cash economy can get at least the same return on banknotes as the well-off banked receive on deposits.

Now hold up JP, some you will be saying at this point. What about criminals? Yep, the other group of people who suffer from the lack of interest on banknotes are criminals and tax evaders. Rewarding them with interest hardly seems appropriate. One would hope that if central banks did adopt a mechanism for rewarding currency with interest, it would be capable of screening out bad actors. For instance, criminals may be leery of collecting their interest or lottery prize if making a claim at a bank means potentially being unmasked. Another way to set up the screen would be to pay interest or prizes on small denominations like $1-$10 notes, and not on $20s and above. Since criminal organizations prefer high denomination notes due to their compactness, they wouldn't benefit from interest.

As for the efficiency argument, this is nothing but the famous Friedman rule that I described in my previous post. All taxes impose a deadweight loss on society. When a good or service is taxed, people produce and consume less of it than the would otherwise choose, tax revenues not quite compensating for this loss. From a policy maker's perspective, the goal is to reduce deadweight loss as much as possible by selecting the best taxes.

In the case of cash, the deadweight loss comes from people holding less of it than they would otherwise prefer, incurring so-called shoe leather costs as they walk to the bank and back to avoid holding too much of the stuff. If a 0% return on cash is an inefficient form of taxation relative to other alternatives types of taxes, then it would be better for the government to just pay interest on the stuff and recoup the lost revenues elsewhere, say through consumption taxes or income taxes.


  1. The Post Office sells 'cash' stamps from a machine one can buy. Each time the customer needs some stamps, they turn the crank and charges are applied automatically. The Post Office has to hold some pre-printed stamps in inventory when issuing fee based stamp allocation so as not deviate from planned delivery capacity.

    Then there are ATM machines which charge a fee. The ATM banks allocate the fee based schedule to match the typical consumer who ends up paying a typical monthly fee for the typical quantity of cash.

    So, this leads to the idea that if everyone can have an honest ATM machine in their chip card. If everyone had the intelligent ATM machine then all the congestion problems go away because all queues can be balance with congestion fee.

    Interest charges always set so as to avoid money congestion, as long as you do not introduce time. The digital bearer cash concept allows all of the monetary network to be congestion managed.

    1. Interesting. Not sure what it has to do with my post, though.

    2. Just that we now have many methods to charge a cash use fee. There seems to be no restriction except selecting a mechanism. That is the goal? Maintain the bearer cash concept otherwise the fiat system won't work with the new tech, the new tech is offering bearer cash.

    3. OK, I get it. You want cash users to earn interest on cash held, not pay. Why?

      "Cash is often the only means for the poor, new immigrants, and unbanked to participate in the economy. So the tax falls on those who can least afford it."

      All that security needed is a cost, it is part of banking. We currently charge these folks about 1.5%, typically for cash. If we want to reduce the cost of cash, then make more of it, what happened to free market, remember chapter 1 of Econ 101?.

    4. Matt, you either didn't read my post and quickly commented, in which case shame on you. Or you did read it before you commented, and didn't understand, in which case shame on me.

      The reason for paying interest on cash is to correct an inefficiency. If cash wasn't a government monopoly, competing banks would have long since figured out how to make their notes yield interest. So by paying interest, the government would be acting as if it was operating in a free market. And that should make everyone better off.

  2. JP, you might want to remark upon the implications of a strict, conventional Friedman rule based on interest payments on both bank reserves an deposits, under which the rate on M0 must equal the rate on short-term Treasuries. In that regime, setting aside GSEs, the Treasury balance, and long-maturity securities, the Fed's portfolio earnings all go to pay interest--there is not even an allowance for Fed operating expenses, let alone dividends and remittances to the Treasury. So the Fed cannot manage without a Treasury appropriation, which has big potential implications for its independence. Holding long-maturity assets, and a bigger balance sheet of such, assuming a normal yield curve, only gains net income at the expense of greater risk of loss, so no real gain. Inflation is another way out--but not one consistent with the Fed's mandate. In short, one can have one's interest-on-all B based Friedman rule, or have the Fed retain its current degree of independence (while meeting its mandate), but you probably can't easily have both.

  3. Sorry, for "both bank reserves and deposits" read "both bank reserves and currency."

    1. George, great points. I agree that the existence of 0% yielding cash is what buys central banks their independence. That's one reason I think the Riksbank is trembling with fear right now.

      Is a more democratic, less technocratic central bank really so bad, though?

      "In short, one can have one's interest-on-all B based Friedman rule, or have the Fed retain its current degree of independence (while meeting its mandate), but you probably can't easily have both."

      You say you can't easily have both. Ok. But what about the idea I mentioned in the post of offering interest on just low denomination bills? That allows the central bank to continue collecting seigniorage on high denominations, thus preserving independence, but implements the Friedman rule on notes that regular people are more likely to use.

  4. Of course one can try to compromise as you suggest. But banning certain denominations will cause people to sub, into interest-yielding ones, adding a new distortion.

    Regarding criminals: well, you can't have it both ways here, either: if they are reluctant to collect interest on currency, then the interest will not serve to encourage them to hold "optimum" quantities.

    Of course, my own ideal--leaving currency provision to the private sector--might also leave central banks without means for covering their expenses if they abided by the Friedman rule. But then, I think that rule, as usually understood, a bad guide. The CB should pay IOR at a competitive rate, after deducting its (ideally minimal) operating expenses, perhaps including ordinary dividends. Under this scheme the Treasury would still get diddly, which is as it ought to be: consumers' surplus trumps producers' surplus.

    1. "Regarding criminals: well, you can't have it both ways here, either: if they are reluctant to collect interest on currency, then the interest will not serve to encourage them to hold "optimum" quantities."

      I'm not convinced that paying interest on criminals' high denomination notes is consistent with the Friedman rule. The government's marginal cost of producing $100s and €500s isn't zero--each additional note facilitates tax evasion and increases the government's costs of law enforcement. I like the idea of limiting interest to small denomination notes. Put differently, the Friedman rule shouldn't be universally applied to cash-in-general but calibrated for each unique note denomination.

      "But then, I think that rule, as usually understood, a bad guide. The CB should pay IOR at a competitive rate, after deducting its (ideally minimal) operating expenses, perhaps including ordinary dividends."

      I think what your saying (but I could be wrong) is that the Friedman rule is wrong because it implies that the costs of running the currency apparatus is zero, when in actuality the cost is greater than zero. If so, I'd agree with that.

    2. "I think what your saying (but I could be wrong) is that the Friedman rule is wrong because it implies that the costs of running the currency apparatus is zero, when in actuality the cost is greater than zero. If so, I'd agree with that."

      Yes, that's what I meant.

  5. The current technocratic version of central banking defers all social insurance to central government but goes a long way toward insuring central government makes it budget. Mainly because this debate is an old one, the consensus view is provide accommodation to government, let it differentiate the social issues.

    The big paradox is that the new tech actually allows a much greater degree of differentiation of the various social insurance programs. We can make money more neutral, lower its cost, and allow it to be competitive. In that case, all the social insurance programs are much more accurate in targeting their clients, social insurance programs have independent access to fair banking, directly keeping themselves optimum and deferring their relative priority back to the legislature. Keep the old consensus, just drive its efficiency as far as we can.