Can lottery tickets become money?

Say that the local lottery system has decided to innovate. Lottery tickets can now be used as money. A ticket with a face value of $x can be used to buy $x worth of stuff at any checkout counter in the country. Or they can be held in digital form and transferred instantaneously across the lottery's new payments system to friends, the utility company, or the government tax department.

With the payments infrastructure in place, will people actually use lottery tickets to pay their bills, transact with friends, or settle their taxes? Can lottery tickets become money-like?

I'm skeptical. Here's my thinking. Say that Jane has just bought $10 worth of digital lottery tickets. At the same time she's chosen to leave $10 in her bank account (she likes the fact that they aren't risky). She spies a coffee stand and suddenly has an urge to buy a $2 coffee. When she arrives at the till, how will she decide to pay? With lottery tickets or deposits?

By paying for the $2 coffee with a bit of both—$1 in lottery tickets and $1 worth of bank deposits—she could end up with $9 of each, re-attaining her pre-coffee 50/50 allocation. But let's assume that every transaction is a bit costly to make, both in terms of time to completion and the small fixed fee associated with each payments network. So paying with both will be too expensive. She'll have to choose one or the other.

A lottery ticket is more than just a bet. Jane is investing in a fantasy in which she is fabulously rich. So from Jane's perspective, swapping her lottery ticket for a mere cup of coffee would be silly. Once she owns it, her ticket is worth more than hundreds of cups of coffee. A form of Gresham's law kicks in. Given that the coffee seller accepts both lottery tickets and deposits at their face value, Jane will only spend her deposits, which she perceives as being overvalued, while hoarding the lottery ticket, which she thinks are being undervalued by the coffee seller. If every lottery player is like Jane, than 'undervalued' lottery tickets will never circulate as money.

Jane could of course consider buying the coffee with lottery tickets only to purchase replacement tickets in time for the draw. But there's always a risk that she'll forget, or not have enough time because something unforeseen suddenly intervenes. By paying with a boring deposit, she doesn't have to fear missing out on a jackpot.

If it seems unlikely that Jane will want to purchase the coffee with a lottery ticket, what about Jim, who owns the coffee stand? Would he prefer to receive lottery tickets or bank deposits?

Again, a mix of the two instruments would be costly for him to accept given a doubling up of payments processing fees. In the unlikely event that Jim is also a lottery player and hasn't yet bought his tickets yet, then he may prefer that Jane buys a coffee with lottery tickets.

Consider that Jim has a constant stream of business expenses ahead of him, but rarely knows precisely when he'll have to make a purchase. Because the lottery tickets will most likely expire worthless in the future, they don't provide him with a suitable means of solving for his future uncertainty. Deposits, on the other hand, will always retain their value. As long as he keeps them on hand, he knows that he can meet his bills. So I think that Jim will probably prefer that Jane pays with deposits. (See more here).

In the unlikely event that Jane insists on paying with lottery tickets, Jim will probably acquiesce—the customer is always right. Since he doesn't want to be exposed to the uncertainty of lottery tickets, he will probably try to exchange them as quickly as possible for deposits, but this will be subject to a conversion fee. Anticipating this expense, Jim could very well decide at the outset to incentivize Jane to pay with deposits. He might place a small surcharge on lottery ticket payments, or offer a small discount if customers pay with deposits. Jim might even pretend that his lottery payments terminal is broken.

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The combination of Jane's reticence to pay with lottery tickets, a form of Gresham's law, and Jim's preference to avoid them will doom lottery tickets as money. Even though the infrastructure is in place for lottery tickets to be transported instantaneously from one person to the other, the incentives just aren't present. Investing in the infrastructure turned out to be a waste of money.

I think this setup also explains why bitcoin has never been adopted as a form of money. Like Jane's lottery ticket, a bitcoin owner's bitcoins aren't just bitcoins, they are a dream, a lambo, a ticket out of drudgery. Spending them at a retailer at mere market value would be a waste given their 'destiny' is to hit the moon. Sure, a bitcoiner can always spend a few precious bitcoins on a coffee, only to replenish his stock later in the day. But this would be dangerous, since bitcoin's price could spike at any moment. Far safer to spend one's deposits and hoard one's bitcoins.

Even when they claim to be accepting bitcoins, retailers like Jim actually rely on intermediaries like BitPay to step in and purchase the bitcoins while relaying dollars to the retailer. For instance, see last month's post on Ohio tax payments.

I also wonder how well my story fits with other examples of volatile media being used as money. For instance, John Cochrane has blogged about a world where one might trade an "S&P500 index share for a candy bar." If lottery ticket buyers and bitcoin owners are consuming a dream, then perhaps an  owner of an equity ETF is doing the same. In which case, no one would bother buying candy bars with stocks, and so building out the payments infrastructure necessary to facilitate this would be pointless.

Central banks deposits for you and me

The Bank of England recently announced that it will end a 300-year tradition of allowing employees to keep chequing accounts at the Bank. You can see an example of a cheque above, which is marked with the sort code 10-00-00. Traditionally, folks like you and me have only been able to get a piece of the central bank's balance sheet by holding banknotes. Central bank deposit accounts, which are far more convenient, have been limited to banks and other financial institutions. But the BoE provides a rare example of regular people, specifically employees, being permitted to directly own fully transferable central bank deposits, at least until recently.

The BoE's termination of this seemingly archaic practice is especially interesting in the context of growing efforts to crack open central bank balance sheets to those who have traditionally been hived off from them. A concrete step in this direction is the Federal Reserve's overnight reverse repurchase facility, which allows money market mutual funds to hold overnight balances at the Fed. More ambitious (but less concrete) is the Bank of England's Ben Broadbent, who describes the idea of a central bank adding more counterparties-

"perhaps a wide range of non-bank financial companies, say.  It might mean something more dramatic:  in the limiting case, everyone – including individuals – would be able to hold such balances."   

Echoing Broadbent, BoE Deputy Governor Minouche Shafik has spoken of the need to rethink "about to whom we give access to the advantages of central bank money with its unique qualities of finality of settlement." The idea here is to allow non-banks involved in fintech direct access to the Bank's real time gross settlement system, as Mark Carney goes on to illustrate here.

Turning to the blogosphere, John Cochrane has recently written about having all money backed by the government in order to end bank runs. And in the same vein, here is David Andolfatto's idea of allowing TreasuryDirect balances to be tradeable, thus providing individuals and firms with a safe place to keep cash other than the banking or shadow banking system.

This democratization of central banking sounds like a novel idea. Nosing deeper into the Bank of England's history, however, we learn that it was not just employees who could hold Bank of England deposits; most people could. Some of them were quite famous. An interesting anecdote from the 1700s has Sarah, Duchess of Marlborough, asking her bankers at the Bank of England to provide her with a freebie, namely some pens because she 'could get none that were good.' [1]

Moving forward a century, we learn that upon opening for business in 1855 the Bank of England's Western branch tended to attract small businessmen and private individuals "of modest means" as clients, including the accounts of the University of London, a Regent Street hatter, and a Sackville Street clothier—all on its first day of operations. Later that year the household of Queen Victoria left its private bank in order to do business with the Western branch. By all accounts, the Bank of England seems to have had excellent service:

"Staff were expected to recognize customers on sight and have a good, clear hand for writing up passbooks. Two porters were always on duty at the main entrance, clad in the pink livery of the Bank of England with silk top hats, and even the cashiers wore top hats when serving at the counter." [2]

The Bank of England kept up a retail presence well into the 1900s. But as public service came to be regarded as the Bank's main role, the aggressiveness of its commercial and retail businesses was reduced and it transitioned into a purely bankers' bank. The Western branch would be sold in 1930 to the Royal Bank of Scotland. [3]

By 1963 the Bank of England's services to the public were limited to a small number of accounts for existing customers. Presumably as they died, these accounts were closed. The most recent example of the Bank of England allowing non-banks to set up accounts comes from 2003, when Bank officials decided to provide Huntingdon Live Sciences, a drug company facing threats from animal rights activists, with a BoE account because commercial banks refused to offer their services.

So while it may seem that the Bank of England's Broadbent and Shafik are introducing a modern approach to central banking, the practice of allowing private individuals and non-financial businesses to directly hold central bank balance sheet space (in a non-cash form) is actually an old one. What lessons can we take from this historical example?

Many people believe that an open central bank balance sheet has the potential to render our traditional banking system extinct. Banks are special. They provide the world's most popular exhange media—deposits—as an offshoot of their primary business, lending. But as Robert Sams points out, if individuals are allowed to own safe central bank deposits directly there may no  longer be a reason for them to hold risky bank accounts. Demand for bank deposits falling to zero, banks will have to fund their loans to the public with regular bonds or equity, even as payments are re-routed through the books of the central bank. Fractional reserve banking as we know it is dead.

Depending on who you ask, the replacement of fractional reserve banking with so-called narrow banking, or 100% reserve banking, can be either good or bad. I'll leave that discussion for another day. Whatever the case, Bank of England history illustrates that private bank deposits can coexist with an open central bank balance sheet. Given the choice between keeping accounts with the safe Western branch or a risky private bank, individuals did not collectively flock to the former.

No doubt this was partly due to the two things, the Bank of England's policy of charging for servicing unprofitable accounts and of not paying interest on deposits. Its competitors, on the other hand, did pay interest. In essence, private banks had to retain customers by offering better services.

Which brings us back to the Bank of England's recent decision to close employee accounts. Given the Bank's stated intention of opening up its balance sheet, wouldn't it have been an opportune time to open up its retail banking business to all of England rather than shutting it down? The Bank maintains that it had been having trouble competing with services like online banking being offered by private banks. But as history shows, since a central bank offers something private banks can't —safety—it needn't be as competitive in the services it provides. Alternatively, it could be that the Bank will be following a different strategy of opening itself up, say through a distributed ledger or something like PositiveMoney's Digital Cash Accounts. Whatever the case, don't be fooled by the technological terminology; if the Bank were to open itself up, this would be more of a returning to the fold than a bold new future.

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[1] Bank of England: first report, session 1969-70 (link)
[2] Western Branch of The Royal Bank of Scotland - The Story of a Bank and its Building (pdf)
[3] Branches of the Bank of England, 1963 (pdf)

John Cochrane is too grumpy about negative rates

John Cochrane has written two posts that question the ability to implement negative interest rates given the wide range of 0%-yielding escape hatches available to investors. These escapes include gift cards, stamps, tax & utility prepayments, and more. In a recent post entitled However low interest rates might go, the IRS will never act like a bank, Miles Kimball and his brother rebut one of Cochrane's supposed exits; the Internal Revenues Service. I've responded to Cochrane's other schemes here.

Think of Cochrane's exits as arbitrage opportunities. As nominal rates plunge into negative territory, the public gets to harvest these outsized gains at the expense of institutions that issue 0% nominal liabilities. The Kimballs' point (and mine here) is that because these institutions will lose money if they continue to issue these liabilities, they will implement policies to plug the holes. Cochrane's multiple exits aren't the smoking gun he takes them to be.

In a new post, Cochrane tries to salvage his argument by making an appeal to symmetry. He points out that in the symmetrical case—a world with positive inflation and higher nominal rates—we don't actually observe people adopting the sort of behavior that Miles believes they would adopt in a negative rate world. So in practice, Cochrane doesn't believe that removing cash in order to implement negative interest rates will work.

This is a fair tactic to take. In general, people should demonstrate similar behavior whether nominal rates are positive or negative. However, is it true that in an environment with positive inflation and high nominal rates, institutions issuing liabilities (or those purchasing those liabilities) allow themselves to be systematically made the targets of arbitrage?

Take Cochrane's main example; gift cards. As I described here, once rates fall deep into negative territory, retailers will simply stop issuing gift cards since they won't care to earn a negative spread. Cochrane's appeal to symmetry implies that gift card issuers behave differently when rates are positive. Well let's imagine that rates are at 5%. An issuer of 0% gift cards is certainly not setting itself up to be arbitraged—in fact, given that it is funding itself at 0% in a 5% yield environment, it will be earning an excess return on each card issued. Nor will the liability-using public choose to subject itself to the money-losing obverse side of the trade. People can simply choose to avoid investing in 0% gift cards in favor of a 5% alternative. Likewise for the other liabilities that Cochrane mentions. Rather than prepaying taxes and earnings 0%, the public will pay at the last moment and harvest a 5% return until then. Instead of delaying the cashing of a check, they'll deposit it the day they receive it in order to earn interest.

So when interest rates are positive, people will try to avoid behaviour that allows them to be taken advantage of, whether they be an issuer or buyer or liability. Symmetrically, it follows that this same behaviour should prevail when rates are negative.

In his post, Cochrane seems to be changing the subject of the conversation from arbitrage to the indexing of contracts. His point is that during periods of positive inflation and high interest rates, nominal payments were not indexed to the nominal interest rate. His example is the IRS, which does not offer interest for early payment when market interest rates are high. Factually he is right. But this criticism is besides the point. The IRS doesn't offer interest to those who pay their taxes early because prepaid taxes aren't the government's main form of funding, treasury debt is. If the government's main form of financing *was* to offer savings accounts to tax payers, then you can be sure that those accounts would have to promise nominal payments that rise in line with the market's nominal interest rate—otherwise no one would open an account and the government would suffer a cash crunch. Nor would the government offer an excess nominal rate, since every American would exploit the situation and open an account—at the government's expense.

No one wants to be the dupe and end up on the wrong side of an arbitrage. If anyone is arguing for asymmetry, it is Cochrane. He needs to explain why liability issuers and users would exhibit such a degree of irrationality as to allow themselves to be exploited as rates fall into negative territory, but so rational as to avoid being exploited at positive rates.

A libertarian case for abolishing cash

Last week Citi's Willem Buiter published a note on the three ways to get rid of the effective lower bound to nominal interest rates, one of which is to abolish cash. He goes on to say that

politically, the abolition of currency would run into opposition from some of the legitimately cash-dependent poor and elderly, from those for whom the anonymity of cash is desired because they are engaged in illegal activities and from libertarians. The first constituency can be helped, the second can be ignored and the third one should take one for the team.

I think that Buiter is wrong to characterize libertarians as necessarily opposed to the abolition of cash. Their take on cash is probably (or at least should be) a bit more nuanced. Since libertarians generally advocate government withdrawal from lines of business like health care or liquor retailing, an exit of central banks from the cash business should be a desirable outcome.

What Buiter is advocating is a bit more extreme than just government exit, however. An across-the-board banning of cash would not only take the government out of the cash business but also prevent individuals and businesses from entering the product niche. The participation of the private sector in the provision of cash isn't just science fiction. Historically, commercial banks were intimately involved in the production of paper currency. In modern times, the majority of banknotes that circulate in Scotland are issued by three private banks—the Bank of Scotland, the Royal Bank of Scotland, and the Clydesdale Bank, while in Hong Kong, the major commercial banks are charged with issuing currency.

Buiter would probably object to private banknotes. After all, if private banks are able to issue negotiable bearer instrument that pay a zero nominal interest rate, a central banker will continue to be plagued by the problem that he/she can't reduce interest rates below zero—instead of fleeing into 0% government paper, the public will hide in private banknotes. It's the same liquidity trap as before, with private currency in the place of central bank currency.

However, there would be one key difference. Private banks must abide by the Darwinian calculus of profit and losses, central banks don't have to. Take a world with privatized cash. A recession hits and the rate of return on capital falls plummets. At the same time, the central bank drops its deposit rate deep into negative territory. As a private bank tries to match with deposit rate reductions of its own, say to -2%, customers will convert negative yielding deposits into the bank's higher-yielding 0% bank notes. The bank, whose survival depends on a healthy spread between the rates on borrowing and lending, faces a sudden spike in borrowing costs to 0%, the rate on their cash base. Spreads will shrink, even invert. Bankruptcy looms.

In order to avert this disaster, private issuers will quickly institute limits on their cash business. This could involve adopting any one of Buiter's three remedies: 1) cancel their note issue; 2) impose a fee on cash, or; 3) remove the fixed exchange rate between deposits and cash. Thus,the lower bound probably wouldn't be a problem in a banking system characterized by privatized paper issuance. The necessity of maintaining a spread would force private banks to rapidly innovate any one of these three escapes come recession and negative nominal rates. Upon recovery, they can remove these limitations and continue with their regular cash business.

Imagine that private banks all choose the first option when nominal rates fall below zero, cancellation. With cash no longer in existence, banks will have succeeded in restoring their margins to health. The population, however, will have effectively lost their ability to make anonymous transactions. This puts a libertarian in a tough philosophical position. On the one hand, a cashless world poses a serious threat to personal liberty. John Cochrane calls it an "Orwellian nightmare," and Chris Dillow has referred to banning cash as "a grossly illiberal measure - the banning of capitalist acts between consenting adults."

On the other hand, if cash threatens a bank's existence, no libertarian would advocate the use of force to prevent said bank from exiting the business of cash provision. Capitalistic acts cannot be forced upon non-consenting adults, or, put differently, Jack's desire for anonymity-providing products doesn't justify Jill being put into chains in order to provide those products. Therefore, a withdrawal of cash by banks as nominal rates fall below zero, and the loss of anonymity that comes with it, is consistent with libertarianism.

So oddly, Buiter's proposed end point—a cancellation of cash in order to rid the world of the lower bound—is very similar to what a libertarian end point could look like. Both institutions will elect to withdraw cash from circulation because it interferes with their institutional prerogatives. For a central bank, this mission boils down to the targeting of some nominal variable like inflation while in the case of a private bank it is its ability to earn a competitive return. That's not to say that a libertarian ought to support Buiter's abolition, only that the subject is more nuanced than it might seem upon a superficial reading.  

As a postscript, it's worth noting that neither Buiter's central banker nor a libertarian's private banker need go as far as abolishing cash in order to remove the effective lower bound. Buiter provides two other options, the best of which (in my opinion) is removing the fixed exchange rate between cash and deposits. Miles Kimball has gone through this option exhaustively. I've outlined some even less invasive, though not as effective, options here.

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Related links: 

Does the zero lower bound exist thanks to the government's paper currency monopoly? (link)
Is legal tender an imposition on free markets or a free market institution? (link)
Bill Woolsey on how the private sector would withdraw cash at negative rates (link | link )
FTAlphaville: Buiter on the death of cash ( link )

Note: I changed some wording on September 26, 2015. The message remains the same.

Cracks in the zero-lower bound

Shibboleth, by Doris Scalcedo

John Cochrane writes an interesting post that makes the case that removing or penalizing cash would not remove an economy's 0% lower bound. Briefly, the zero lower bound problem arises when a central bank tries to reduce the interest rate on central bank deposits below zero. Because cash always yields a superior 0% yield, everyone will race to convert their deposits into cash, thus preventing a negative interest rate from ever emerging. By removing cash, this escape route is plugged and a central bank can safely guide rates to -4 or -5%.

Cochrane's point is that even if cash is removed, there are a number of alternative 0% yielding 'exits' to which people will flee, the effect being that rates will be inhibited from falling much below 0%. The examples he provides includes prepayment of taxes, bills, and mortgage payments, and the hoarding of gift cars or stored value cards like subway passes. In a follow-up post, he mentions a strategy of rolling over cheques.

There are two points I want to make:

1. Even with alternatives, a central bank can still create inflation

Scott Sumner points out that even in a cashless world at the zero lower bound, the existence of these alternatives cannot impede a central bank from driving up inflation. This is because the other alternative assets that Cochrane discusses are not media of account. To be a medium of account is to be that good which defines the $ unit that appears on a retailer's website and their aisles. What this means is that the the sorts of dollars that a retailer has in mind when setting sticker prices are those issued by the nation's central bank (in a cashless world, this would be central bank deposits). Retailers aren't using gift card dollars or stored value card dollars as the 'reference dollar' for their sticker prices.

Keep in mind that the use of central bank deposits as the medium of account does not preclude retailers from accepting gift cards in payment at the till. However, if they accept them, they'll probably apply some sort of reduction/addition to a good's advertised sticker price. If we assume that gift cards have become quite liquid in the absence of cash, I think it's conceivable that retailers would offer a reduction (ie. take gift cards at a premium) since gift cards would be a better asset than a deposit; in addition to being useful as media of exchange, they yield 0% rather than negative yielding deposits. We could imagine a range of different gift card premia developing based on their perceived quality, with cashiers consulting some sort of electronic guide to calculate the final bill.

In any case, Sumner's point is that as the central bank reduces rates into negative territory, sticker prices will all rise, despite the fact that alternative media exist that can be used to make payments. I think he's dead right.

2. Alternative escape routes will be resolved by simple product alterations, not a legal revolution

Cochrane's posts emphasize that in a negative rate world, all sorts of odd financial loop holes will be exploited in order to earn superior 0% returns. I think he's right on this. However, Cochrane seems to believe that that the government will have to upend 'centuries of law' in order to plug these alternative 0% instruments. I am more sanguine than him. If someone is exploiting a loophole in order to earn a superior 0% return, someone else is bearing that negative return. Institutions forced to bear the negative impacts of these loopholes will have an incentive to quickly evolve simple strategies to plug them, thus precluding any need for either Cochrane's rather dramatic 'legal revolution' or the heavy hand of the government.

Take Cochrane's first 'escape', gift cards. Consider a retailer that issues 0% gift cards in various denominations like $50s and $100s. Assume that in a world without cash, these cards have become relatively liquid. The central bank suddenly pushes rates to -5%. People who own negative yielding bank deposits will flock to buy the retailer's gift cards (assume that both instruments are equally risky) with the goal of immediately improving their expected return from -5% to 0%. The retailer, however, is left holding a -5% asset while owing a 0% liability, an awful position to be in. To remove the burden of this negative spread, our retailer need only reduce the return on newly-issued gift cards to -5%, say be introducing a redemption fee of 5%. A gift card worth $100, when redeemed, now only buys you $95 worth of stuff. Either that or just stop issuing the things. The loophole is closed and the problem solved.

The same goes for Cochrane's other 0% exit, prepayment if bills. A firm that allows for prepayments is accepting a 0% liability on itself; it effectively owes x dollars worth of some service or item. So we are back to our gift card example above, since gift cards are basically prepayments. Impose an appropriately sized fee on those who want to prepay and the problem is solved. Banks have always charged prepayment penalties on mortgages, car loans, and business loans, so this is nothing revolutionary in turning to this solution.

The next of Cochrane's 0% exits is a string of constantly renewed personal cheques. Rather than cashing a personal check, a cheque holder waits for that cheque to go 'stale', usually after 6-months, and then asks the issuer to issue a new one, rinsing and repeating as often as necessary. As physical bearer instruments, cheques (much like cash) cannot be made to pay negative interest, which allows the holder of a cheque to earn a perpetual 0% return. The unfortunate issuer of the cheque is left bearing a 0% liability in a world where their assets are yielding just -5%. This problem will quickly be resolved by people no longer writing checks. There is a less extreme alternative. Banks, unwilling to lose revenues from their cheques businesses, will simply increase cheque cancellation fees. Before a stale check is re-issued, it must be canceled, which traditionally incurs a cancellation fee. If the person running the scheme is required to pay an appropriately sized fee to carry over the cheque, the scheme can be rendered no more profitable than owning a -5% deposit.

Cochrane also points to Kenneth Garbade and Jamie McAndrews's scheme whereby depositors can purchase certified cheques from banks and thereby evade negative rates. According to Garbade and McAndrews, commercial banks "might find their liabilities shifting from deposits (on which they charge interest) to certified cheques outstanding," with this shift imposing significant costs on banks since certified cheques are less stable than deposits. If such a shift were to occur, banks would find themselves bearing a negative spread (liabilities yielding 0% while assets yielding -5%), a position they would be quick to remedy. One option would be to cease the issuance of certified cheques altogether. Alternatively, banks have always charged a fee for certified cheques. They could simply increase this fee to the point that the cost of holding a certified cheque is brought in line with the negative deposit rate. Once again, problem solved.

This fee strategy shouldn't be unfamiliar. It is the mirror image of the strategy adopted by U.S. commercial banks when interest rates were capped during the inflationary 1960s and 70s. Unable to reward depositors with sufficiently high interest rates, banks evaded the ceilings by offering implicit interest in the form of under-priced banking services, say by reducing fees on certified cheques. In our modern era in which deflation is pushing rates towards an equally artificial 0% barrier (in this case arising from the circulation of personal and certified cheques rather than a government imposed cap), all those services that a bank had been underpricing or pricing at market will now be adjusted upwards so that they are overpriced.

In sum, no revolutions here, just markets adaptation via boring old fee changes.

In closing, Cochrane has much more legitimate worries about two other problems: Big Brother and the disproportionate effect on the poor if cash is removed. Agreed, these are big issues. Now it could be that the emergence of cryptocurrencies such as bitcoin solves the Big Brother problem so that there is no role left for cash in preserving anonymity. Let's put bitcoin aside though. The simple answer to both of Cochrane's concerns is that we don't need an outright ban on cash to remove the 0% lower bound. Just adopt Miles Kimball's proposal for a crawling peg between cash and deposits. Kimball's peg is designed in a way that it would impose the same penalty on cash as that incurred by deposits. This would allow central banks to push rates to zero without mass flight into cash, all the while preserving the institution of cash for the poor and those requiring anonymity. (I've written in support of Kimball's plan here and here)

There is also my lazy man's route toward getting below the lower bound (here, here, here). I call it lazy since it's not nearly as complete as Kimball's solution, nor as complicated. Simply withdraw high denominations of bills like $100s, $50s, and $20s. When a central bank sends rates to -3% or -4%, people will balk at fleeing from deposits into $1s, $5s, and $10s since low denominations are very inconvenient to store. That way the poor still get to use cash and the zero lower bound can be breached.

Sign Wars

Does a lowering of a central bank's interest rates create inflation or deflation? Dubbed the 'Sign Wars' by Nick Rowe, this has been a recurring debate in the economics blogosphere since at least as far back as 2010.

The conventional view of interest rate policy is that if a central bank keeps its interest rate too low, the inflation rate will steadily spiral higher. Imagine a cylinder resting on a flat plane. Tilt the plane in one direction —a motif to explain a change in interest rates—and the cylinder, or the price level, will perpetually roll in the opposite direction, at least until the plane's tilt (i.e. the interest rate) has been shifted enough in a compensatory way to halt the cylinder's roll. Without a counter-balancing shift, we get hyperinflation in one direction, or hyperdeflation in the other.

The heretical view, dubbed the Neo-Fisherian view by Noah Smith (and having nothing to do with Irving Fisher), is that in response to a tilt in the plane, the cylinder rolls... but uphill. Specifically, if the interest rate is set too low, the inflation rate will jump either instantaneously or more slowly. But after that, a steady deflation will set in, even without the help of a counter-balancing shift in the interest rate. We get neither hyperinflation nor hyperdeflation. (John Cochrane provides a great introduction to this viewpoint).

Many pixels have already been displayed on this subject, about the only value I can add is to translate a jargon-heavy academic debate into a more finance-friendly way of thinking. Let's approach the problem as an exercise in security analysis.

First, we'll have to take a detour through the bond market, then we'll return to money. Consider what happens if IBM announces that its 10-year bond will forever cease to pay interest, or a coupon. The price of the bond will quickly plunge. But not forever, nor to zero. At some much lower price, value investors will bid for the bond because they expect its price to appreciate at a rate that is competitive with other assets in the economy. These expectations will be motivated by the fact that despite the lack of coupon payments, the bond still has some residual value; specifically, IBM promises a return of principal on the bond's tenth year.

Now there's nothing controversial in what I just said, but note that we've arrived at the 'heretical' result here. A sudden setting of the interest rate at zero results in a rapid dose of inflation (a fall in the bond's purchasing power) as investors bid down the bond's price, followed by deflation (a steady expected rise in its value over the next ten years until payout) as its residual value kicks in. The bond's price does not "roll" forever down the tilted plane.

Now let's imagine an IBM-issued perpetual bond. A perpetual bond has no maturity date which means that the investor never gets their principle back. Perpetuals are not make-believe financial instruments. The most famous example of perpetual debt is the British consol. A number of these bonds float around to this day after having been issued to help pay for WWI. When our IBM perpetual bond ceases to pay interest its price will quickly plunge, just like a normal bond. But it's price won't fall to zero. At some very low level, value investors will line up to buy the bond because its price is expected to rise at a competitive rate. What drives this expectation? Though the bond promises neither a return of principal nor interest payments, it still offers a fixed residual claim on a firm's assets come bankruptcy, windup, or a takeover. This gives value investors a focal point on which they can price the instrument.

So with a non-interest paying perpetual bond, we still get the heretical result. In response to a plunge in rates, we eventually get long term deflation, or a rise in the perpetual's price, but only after an initial steep fall.  As before, the bond's price does not fall forever.

Now let's bring this back to money. Think of a central bank liability as a highly-liquid perpetual bond (a point I've made before). If a central banker decides to set the interest rate on central bank liabilities at zero forever, then the purchasing power of those liabilities will rapidly decline, much like how the cylinder rolls down the plane in the standard view. However, once investors see a profit opportunity in holding those liabilities due to some remaining residual value, that downward movement will be halted... and then it will start to roll uphill. Once again we get the heretical result.

The residual claim that tempts fundamental investors to step in and anchor the price of a 0% yielding central bank liability could be some perceived fixed claim on a central bank's assets upon the bank's future dissolution, the same feature that anchored our IBM perpetual. Or it could be a promise on the part of the government to buy those liabilities back in the future with some real quantity of resources.

However, if central bank liabilities don't offer any residual value whatsoever, then we get the conventional result. The moment that the central bank ceases to pay interest, the purchasing power of a central bank liability declines...forever. Absent some residual claim, no value investor will ever step in and set a floor. In the same way, should an IBM perpetual bond cease to pay interest and it also had all its residual claims on IBM's assets stripped away, value investors would never touch it, no matter how low it fell.

So does central bank money boast a residual claim on the issuer? Or does it lack this residual claim? The option you choose results in a heretical result or a conventional result.

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What does the data tell us, specifically the many cases of hyperinflation? As David Beckworth has pointed out, the conventional explanation has no difficulties explaining the Weimar hyperinflation; the Reichsbank kept the interest rate on marks fixed at very low levels between 1921 and 1923 so that the price level spiraled ever upwards. Heretics seem to have difficulties with Weimar—the deflation they predict never set in.

Here's one way to get a heretical explanation of the Wiemar inflation. Let's return to our analogy with bonds. What would it take for the price of an IBM perpetual bond to collapse over a period of several years, even as its coupon rate remained constant? For that to happen, the quality of the bond's perceived residual value would have to be consistently deteriorating. Say IBM management invested in a series of increasingly dumb ventures, or it faced a string of unbeatable new competitors entering its markets. Each hit to potential residual value would cause fundamental investors to mark down IBM's bond price, even though the bond's coupon remained fixed.

Now assuming that German marks were like IBM perpetual bonds, it could be that from 1921 to 1923, investors consistently downgraded the value of the residual fixed claim that marks had upon the Reichsbank's assets. Alternatively, perhaps the market consistently reduced its appraisal of the government's ability to buy marks back with real resources. Either assumption would have created a consistent decline in the purchasing power of marks while the interest rate paid on marks stayed constant.

Compounding each hit to residual value would have been a decline in the mark's liquidity premium. When the price of a highly-liquid item begins to fluctuate, people ditch that item for competing liquid items with more stable values. With less people dealing in that item, it becomes less liquid, which reduces the liquidity premium it previously enjoyed. This causes the item's purchasing power to fall even more, forcing people to once again turn to alternatives, thus making it less liquid and igniting another round of cuts to its liquidity premium and therefore its price, etcetera etcetera. In Weimar's case, marks would have been increasingly replaced by dollars and notgeld.

So consistent declines in the mark's perceived residual value, twinned with a shrinking in its liquidity premium, might have been capable of creating a Weimar-like inflation, all while the Reichsbank kept its interest rate constant.

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That's not to say that central bank liabilities do have a residual value and that the heretical result is necessarily the right one. Both possibilities make sense, and both can explain hyperinflations. But to determine which is right, we need to go in and do some gritty security analysis to isolate whether central bank money possesses a fixed residual claim on either central bank assets or future government resources. Parsing the fine print in central bank acts and government documents to tease out this data is the task of lawyers, bankers, historians, fixed income analysts, and accountants. And they would have to do a separate analysis for each of the world's 150 or so central banks and currencies, since each central bank has its own unique constituting documents. In the end we might find that some currencies are conventional and others are heretic, so that some central banks should be running conventional monetary policies, and others heretic policies. 

In closing, a few links. I've taken a shot at a security analysis of central bank liabilities in a number of posts (here | here | here), but I don't think that's the final word. And if you're curious how the Weimar inflation ended, go here.

Drachmas or not?

John Cochrane has had a few interesting comments on Greece leaving the Euro, here, here, and here.

Cochrane doesn't believe in the consensus view that a Greek default means a Greek euro-exit. He thinks Greece can default and stay in the Euro. He also makes the good point that Eurobonds already exist... in the form of Target2 transfers. His last post illustrates how difficult it would be to create a new drachma. I am sympathetic to many of his views.

I had an interesting debate in the comments section of his last post on the difficulties of creating a new drachma.