Don't kill the $100 bill

Last week I asked whether the Federal Reserve could get rid of the $100 bill. This week let's discuss whether it should get rid of the $100. I don't think so. The U.S. provides the world with a universal backup monetary system. Removing the $100 would reduce the effectiveness of this backup.

Earlier this week the New York Times took up the knell for eliminating high value bank notes, echoing Larry Summers' earlier call to kill the $100 in order to reduce crime which in turn was a follow up on this piece from Peter Sands. More specifically, Summers says that "removing existing notes is a step too far. But a moratorium on printing new high denomination notes would make the world a better place."

As an aside, I just want to point out that Summers' moratorium is an odd remedy since it doesn't move society any closer to his better place, a world with less crime. A moratorium simply means that the stock of $100 bills is fixed while their price is free to float. As population growth boosts the demand for the limited supply of $100 notes, their price will rise to a premium to face value, say to $120 or $150. In other words, the value of the stock of $100 bills will simply expand to meet criminals' demands. Another problem with a moratorium is that when a $100 bill is worth $150, it takes even less suitcases of cash to make large cocaine deals, making life easier—not harder—for criminals. To hurt criminals, the $100 needs to be withdrawn entirely from circulation, a classic demonetizaiton.

With that distinction out of the way, let's deal with three of the motivations for demonetizing high denomination notes: to reduce criminality, to cut down on tax evasion, and to help remove the effective lower bound.

Criminality

Summer's idea is to kill the $100 bill so that criminals have to rely on smaller denominations like $20s. Force criminals to conduct trade with a few suitcases filled with $20 bills rather than one suitcase filled with $100 bills and they'll only be able to jog away from authorities, not sprint. What sorts of criminals would be affected? The chart below (from this article by Peter Sands) builds a picture of cash usage across the different types of crime.

As the chart illustrates, the largest illegal user of cash is the narcotics industry. So presumably the main effect of a ban of $100s will be to raise the operating costs of drug producers, dealers, and their clients.

But should we be sacrificing the benefits of the $100 bill in the name of what has always been a very dubious enterprise; the war on drugs? An alternative way to reduce crime would be to redefine the bounds of punishable offences to exclude the narcotics trade, or at least certain types of drugs like marijuana. Law enforcement officers could be re-tasked to focus on the cash intensive crimes that remain, like human trafficking and corruption. In that way crime gets more costly and we get to keep the $100 to boot, which (as I'll show) has some very important redeeming qualities.

Tax Evasion

Cash is certainly one of the best ways to evade taxes, but there are other methods to reduce tax evasion. For instance, Martin Enlund draws my attention to a tax deduction implemented by Sweden in 2007 for the purchase of household related services, or hushållstjänster, including the hiring of gardeners, nannies, cooks, and cleaners. In order to qualify the services must be performed in the taxpayer’s home and the tax credit cannot exceed 50,000 SEK per year per person. This initial deduction, called RUT-avdrag, was extended in 2008 to include labour costs for repairing and expanding homes and apartments, this second deduction called ROT-avdrag.*

Prior to the enactment of the RUT and ROT deductions, a large share of Swedish home-related purchases would have been conducted in cash in order to avoid taxes, but with households anxious to get their tax credits, many of these transactions would have been pulled into the open.

We can evidence of this in the incredible decline in Swedish cash demand ever since:

@t0nyyates @jp_koning Starting in July 2007 it became 50% cheaper to buy services (cleaning, ironing, baby-sitting) pic.twitter.com/4EHshRAHWR

— Martin Enlund (@enlundm) February 18, 2016

Sweden has the distinction of being the only country in the world with declining cash usage. The lesson here is that it isn't necessary to sacrifice the $100 in order to reduce tax evasion. Just design the tax system to be more lenient on those market activities that can most easily be replaced by underground production.

Escaping the lower bound

Yep, those advocating a removal of $100s are right. Central banks can evade the effective lower bound on interest rates and go deeply negative if they kill cash, starting with high denomination notes.

But as economists such as David Beckworth have pointed out, you can keep cash and still go deeply negative. All a central banker needs to do is adopt Miles Kimball's proposal to institute a crawling peg between cash and central bank deposits. This effectively puts a penalty on cash such that the public will be indifferent on the margin between holding $100 bills or $100 in negative yielding deposits.

Another way to fix the lower bound problem is a large value note embargo whereby the Fed allows its existing stock of $100 bills to stay in circulation but doesn't print new ones (much like Summers' moratorium). This means that if Yellen were to cut deposit rates to -2% or so, the price of the $100 would quickly jump to its market-clearing level, cutting off the $100 as a profitable escape route. As for the lower denominations, the public wouldn't resort to them since $20s are at least as costly to hold as the negative rate on deposits. Unlike Miles' proposal a large value note embargo doesn't allow for a full escape from the lower bound, but it does ratchet the bound downwards a bit, and it keeps the $100 in circulation.

Why should we keep it?

The $100 bill is the monetary universe's Statue of Liberty. In the same way that foreigners have always been able to sleep a little easier knowing that Ellis Island beckons should things go bad at home, they have also found comfort in the fact that if the domestic monetary authority goes rotten, at least they can resort to the $100 bill.

The dollar is categorically different from the yen, pound or euro in that it is the world's back-up medium of exchange and unit of account. The citizens of a dozen or so countries rely on it entirely, many more use it in a partial manner along with their domestic currency, and I can guarantee you that future citizens of other nations will turn to the dollar in their most desperate hour. The very real threat of dollarization has made the world a better place. Think of all the would-be Robert Mugabe's who were prevented from hurting their nations because of the ever present threat that if they did so, their citizens would turn to the dollar.    

I should point out that the U.S. gets compensation for the unique role it performs in the form of seigniorage. Each $100 is backed by $100 in bonds, the interest on which the U.S. gets to keep. So don't complain that the U.S. is providing its services as backup monetary system for free.

Foreigners who are being subjected to high rates of domestic inflation will find it harder to get U.S dollar shelter if the $100 is killed off; after all, it costs much more to get a few suitcases of $20 overseas than one case of $100. This delayed onset of the appearance of U.S. dollars as a medium of exchange will also push back the timing of a unit of account switch from local units to the dollar. As Larry White has written, money's dual role as unit of account and medium of exchange are inextricably linked. People will only adopt something as a unit of account after it is has already been circulating as a medium of exchange. A switch in the economy's pricing unit is a vital remedy for the nasty calculational burden imposed on individuals and businesses by high inflation. The quicker this tipping point can be reached, the less hardship a country's citizens must bear. The $20 doesn't get us there as quick as the $100.

So contrary to Summers, I think we should think twice before killing the $100. The U.S. has a very special to role to play as provider of the world's backup monetary system; it should not take a step back from that role. Criminals, tax evaders, and the lower bound can be punished via alternative means. I'd be less concerned about killing other high denomination notes such as the €500, 1000 Swiss franc, or ¥10,000. That's because inflation-prone economies don't euroize or yenify—they dollarize.


Addendum: If Summers is genuinely interested in combing the world of coins and bills for what he refers to as a 'cheap lunch', then there's nothing better the U.S. can do than stop making the 1 cent coin, which is little more than monetary trash/financial kipple. Secondly, replace the $1 bill, which is made out of cotton and supported by the cotton lobby, with a $1 coin. The U.S. lags far behind the rest of the world in enacting these simple cost cutting efforts.


*See here and here for more details on RUT and ROT avdrag,
** Martin Enlund has a great post here on Sweden's cash policies.

Central banks' shiny new tool: cash escape inhibitors

Thomas Jordan, Chairman of the Governing Board of the Swiss National Bank

Negative interests rates are the shiny new thing that everyone wants to talk about. I hate to ruin a good plot line, but they're actually kind of boring; just conventional monetary policy except in negative rate space. Same old tool, different sign.

What about the tiering mechanisms that have been introduced by the Bank of Japan, Swiss National Bank, and Danmarks Nationalbank? Aren't they new? The SNB, for instance, provides an exemption threshold whereby any amount of deposits that a bank holds above a certain amount is charged -0.75% but everything within the exemption incurs no penalty. As for the Bank of Japan, it has three tiers: reserves up to a certain level (the 'basic balance') are allowed to earn 0.1%, the next tier earns 0%, and all remaining reserves above that are docked -0.1%.

But as Nick Rowe writes, negative rate tiers—which can be thought of as maximum allowed reserves—are simply the mirror image of minimum required reserves at positive rates. So tiering isn't an innovation, it's just the same old tool we learnt in Macro 101, except in reverse.

No, the novel tool that has been created is what I'm going to call a cash escape inhibitor.

Consider this. When central bank deposit rates are positive, banks will try to minimize storage of 0%-yielding banknotes by converting them into deposits at the central bank. When rates fall into negative territory, banks do the opposite; they try to maximize storage of 0% banknote storage. Nothing novel here, just mirror images.

But an asymmetry emerges. Central bankers don't care if banks minimize the storage of banknotes when rates are positive, but they do care about the maximization of paper storage at negative rates. After all, if banks escape from negative yielding central bank deposits into 0% yielding cash, this spells the end of monetary policy. Because once every bank holds only cash, the central bank has effectively lost its interest rate tool.

If you really want to find something innovative in the shift from positive to negative rate territory, it's the mechanism that central bankers have instituted to inhibit the combined threat of mass paper storage and monetary policy impotence. Designed by the Swiss and recently adopted by the Bank of Japan, these cash escape inhibitors have no counterpart in positive rate land.

The mechanics of cash escape inhibitors

Cash escape inhibitors delay the onset of mass paper storage by penalizing any bank that tries to replace their holdings of negative yielding central bank deposits with 0%-yielding cash. The best way to get a feel for how they work is through an example. Say a central bank has issued a total of $1000 in deposits, all of it held by banks. The central bank currently charges banks 0% on deposits. Let's assume that if banks choose to hold cash in their vaults they will face handling & storage costs of 0.9% a year.

Our central bank, which uses tiering, now reduces deposit rates from 0% to -1%. The first tier of deposits, say $700, is protected from negative rates, but the second tier of $300 is docked 1%, or $3 a year. Banks can improve their position by converting the entire second tier, the penalized portion of deposits, into cash. Each $100 worth of deposits that is swapped into cash results in cost savings of 10 cents since the $0.90 that banks will incur on storage & handling is an improvement over the $1 in negative interest they would otherwise have to pay. Banks will very rapidly withdraw all their tier-2 deposits, monetary impotence being the result.

To avoid this scenario, central banks can install a Swiss-style cash escape inhibitor. The way this mechanism works is that each additional deposit that banks convert into vault cash reduces the size of the first tier, or the shield, rather than the second tier, the exposed portion. So when rates are reduced to -1%, should banks try to evade this charge by converting $100 worth of deposits into vault cash they will only succeed in reducing the protected tier from $700 to $600, the second tier still containing the same $300 in penalized deposits. This evasion effort will only have made banks worse off. Not only will they still be paying $3 a year in negative interest but they will also be incurring an extra $0.90 in storage & handling ($100 more in vault cash x 0.9% storage costs).

Continuing on, if the banks convert $200 worth of deposits into vault cash in order to avoid -1% interest rates, they end up worsening their position even more, accumulating $1.80 in storage & handling costs on top of $3.00 in interest. We can calculate the net loss that the inhibitor imposes on banks for each quantity of deposits converted into vault cash and plot it:

The yearly cost of holding various quantities of cash at a -1% central bank deposit rate

Notice that the graph is kinked. When a bank has replaced $700 in deposits with cash, additional cash withdrawals actually reduce its costs. This is because once the first tier, the $700 shield, is used up, the next deposit conversion reduces the second tier, the exposed portion, and thus absolves the bank of paying interest costs. And since interest costs are larger than storage costs, overall costs decline.

If banks go all-out and cash in the full $1000 in deposits, this allows them to completely avoid the negative rate penalty. However, as the chart above shows, storage & handling costs come out to $9 per year ($1000 x 0.9%), much more than the $3 banks would bear if they simply maintained their $300 position in -1% yielding deposits.

So at -1% deposit rates and with a fully armed inhibitor installed, banks will choose the left most point on the chart—100% exposure to deposits. Mass cash conversion and monetary policy sterility has been avoided.

How deep can rates go?

How powerful are these inhibitors? Specifically, how deep into negative rate territory can a central bank go before they start to be ineffective?

Let's say our central banker reduces deposit rates to -2%. Banks must now pay $6 a year in interest ($300 x 2%). If banks convert all $1000 in deposits into cash, they will have to bear $9 in storage and handling costs, a more expensive option than remaining in deposits. So even at -2% rates, the cash inhibitor mechanism performs its task admirably.

If the central bank ratchets rates down to -3%, banks will now be paying $9 a year in interest ($300 x 3%). If they convert all $1000 in deposits into cash, they'll have to pay $9 in storage & handling. So at -3%, bankers will be indifferent between staying invested in deposits or converting into cash. If rates go down just a bit more, say to -3.1%, interest costs are now $9.30. A tipping point is reached and cash will be the cheaper option. Mass cash storage ensues, the cash escape inhibitor having lost its effectiveness.

The chart below shows the costs faced by banks at various levels of cash holdings when rates fall to -3%. The extreme left and right options on the plot, $0 in cash or $1000, bear the same costs.

The yearly cost of holding various quantities of cash at a -3% central bank deposit rate

So without an inhibitor, the tipping point for mass cash storage and monetary policy impotence lies at -0.9%, the cost of storing & handling cash. With an inhibitor installed the tipping point is reduced to -3.1%. The lesson being that cash escape inhibitors allow for extremely negative interest rates, but they do run into a limit.

The exact location of the tipping point is sensitive to various assumptions. In deriving a -3.1% escape point, I've used what I think is a reasonable 0.9% a year in storage and handling costs. But let's assume these costs are lower, say just 0.75%. This shifts the cash tipping point to around -2.5%. If costs are only 0.5%, the tipping point rises to around -1.7%.

This is where the size of note denominations is important. The Swiss issue the 1000 franc note, one of the largest denomination notes in the world, which means that Swiss cash storage costs are likely lower than in other countries. As such, the Swiss tipping point is closer to zero then in countries like the Japan or the U.S.. One way to push the tipping point further into negative terriotry would be a policy of embargoing the largest note. The central bank, say the SNB, stops printing new copies of its largest value note, the 1000 fr. Banks would no longer be able to flee into anything other than small value notes, raising their storage and handling costs and impinging on the profitability of mass cash storage.

Good old fashioned financial innovation will counterbalance the authorities attempts to drag the tipping point deeper. Cecchetti & Shoenholtz, for instance, have hypothesized that in negative rate land, a new type of intermediary could emerge that provides 'cash reserve accounts.' These specialists in cash storage would compete to reduce the costs of keeping cash, pushing the tipping point back up to zero.

The tipping point is also sensitive to the size of the first tier, or the shield. I've assumed that the central bank protects 70% of deposits from the negative deposit rate. The larger the exempted tier the bigger the subsidy central banks are providing banks. It is less advantageous for a bank to move into cash when the subsidy forgone is a large one. So a central bank can cut deeper into negative territory the larger the subsidy. For instance, using my initial assumptions, if the central bank protects 80% of deposits, then it can cut its deposit rate to -4.6% before mass paper storage ensues.

Removing the tipping point?

There are ways to modify these Swiss-designed cash escape inhibitors to remove the tipping point altogether. The way the SNB and BoJ have currently set things up, banks that try to escape negative rates only face onerous penalties on cash conversions as long as the first tier, the shield, has not been entirely drawn down. Any conversion after the first tier has been used up is profitable for a bank. That's why the charts above are kinked at $700.

If a central bank were to penalize cumulative cash withdrawals (rather than cash withdrawals up to a fixed ceiling) then it will have succeeded in snipping away the tipping point. This is an idea that Miles Kimball has written about here. One way to implement this would be to require that the tier 1 exemption, the shield, go negative as deposits continue to be converted into cash, imposing an obligation on banks to pay interest. The SNB doesn't currently allow this; it sets a lower limit to its exemption threshold of 10 million francs. But if it were to remove this lower limit, then it would have also removed the tipping point.

What about retail deposits?

You may have noticed that I've left retail depositors out of this story. That's because the current generation of cash escape inhibitors is designed to prevent banks from storing cash, not the public.

As central bank deposit rates fall ever deeper into negative territory, any failure to pass these rates on to retail depositors means that bank margins will steadily contract. If banks do start to pass them on, at some point the penalties may get so onerous that a run develops as retail depositors start to cash out of deposits. The entire banking industry could cease to exist.

To get around this, the FT's Martin Sandbu suggests that banks could simply install cash escape inhibitors of their own. Miles Kimball weighs in, noting that banks may start applying a fee on withdrawals, although his preferred solution is a re-deposit fee managed by the central bank. Either option would allow banks to preserve their margins by passing negative rates on to their customers.

Even if banks don't adopt cash escape inhibitors of their own, I'm not too worried about retail deposit flight in the face of negative central bank deposit rates of -3% or so. The deeper into negative rate territory a central bank progresses, the larger the subsidy it provides to banks via its first tier, the shield.  This shielding can in turn be transferred by a bank to its retail customers in the form of artificially slow-to-decline deposit rates. So even as a central bank reduces its deposit rate to -3% or so, banks might never need to reduce retail deposit rates below -0.5%. Given that cash handling & storage costs for retail depositors are probably about the same as institutional depositors, banks that set a -0.5% retail deposit rate probably needn't fear mass cash conversions.

So there you have it. Central banks with cash escape inhibitors can get pretty far into negative rate land, maybe 3% or so. And with a few modifications they might be able to go even lower.

Andy Haldane and BOEcoin

The 1995 British two pound "Dove" coin

The Bank of England's chief economist Andrew Haldane recently called for central banks to think more imaginatively about how to deal with the technological constraint imposed by the zero lower bound on interest rates. Haldane says that the lower bound isn't a passing problem. Rather, there is a growing probability that when policy makers need three percentage points of headroom to cushion the effects of a typical recession, that headroom just won't be there.

Haldane pans higher inflation targets and further quantitative easing as ways to slacken the bound, preferring to focus on negative interest rates on paper currency, a topic which gets discussed often on this blog. He mentions the classic Silvio Gesell stamp tax (which I discussed here), an all out ban on cash as advocated by Ken Rogoff, and Miles Kimball's crawling peg (see here).

According to Haldane, the problem with Gesell's tax, Rogoff's ban (pdf), and Kimball's peg is that each of these faces a significant 'behavioural constraint.'  The use of paper money is a social convention, both as a unit of account and medium of exchange, and conventions can only be shifted at large cost. Tony Yates joins in, pointing out the difficulties of the Gesell option. Instead, Haldane floats the possibility of replacing paper money with a government-backed cryptocurrency, or what we on the blogosphere have been calling Fedcoin (in this case BOEcoin). Unlike cash, it would be easy to impose a negative interest rate on users of Fedcoin or BOEcoin, thus relaxing the lower bound constraint. Conventions stay intact; people still get to use government-backed currency as a medium of exchange and unit of account.*

While I like the way Haldane delineates the problem and his general approach to solving it, I'm not a fan of his chosen solution. As Robert Sams once pointed out, Fedcoin/BoEcoin could be so good that it ends up outcompeting private bank deposits, thus bringing our traditional banking model to an abrupt end. Frequent commenter JKH calls it Chicago Plan #37, a reference to a depression-era reform (since resuscitated) that would have outlawed fractional reserve banking. If Haldane is uncomfortable with the Gesell/Rogoff/Kimball options for slackening the lower bound because they interfere with convention, he should be plenty worried about BOEcoin.

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I do agree, however, with Haldane's point that the apparatus adopted to loosen the constraint should interfere with convention as little as possible. We want the cheapest policies; those that only slightly impede the daily lives of the typical Brit on the street while securing the Bank of England a sufficient amount of slack.

With that in mind, here's what I think is the cheapest way for the Bank of England to slacken the lower bound: just freeze the quantity of £50 bills in circulation. Yep, it's that easy. There are currently 236 million £50 notes in circulation. Don't print any more of them, Victoria Cleland.**

I call this a policy of embargoing the largest value note. How does it work?***

Say that in the next crisis, the Bank of England decides to chop rates from 0.5% to -2.0%. Faced with deeply negative interest rates, the UK runs smack dab into the lower bound as Brits collectively try to flee into banknotes. After all, banknotes offer a safe 0% return, the £50 note being the chosen escape route since those are the cheapest to store and convey.

Flooded with withdrawal requests, banks will quickly run out of £50s. At that point the banks would normally turn to the Bank of England to replenish their stash in order to fill customers' demands. But with the Bank of England having frozen the number of £50s at 236 million and not printing any new ones, bankers will only be able to offer their customers low denomination notes. But this will immediately slow the run for cash since £20s, £10s, and £5s are much more expensive to store, ship and transfer than £50s. Whereas people will surely prefer a sleek high denomination note to a deposit that pays -2%, they will be relatively indifferent when the choice is between a bulky low denomination cash and a deposit that pays -2%. Thus the lower bound has been successfully softened by an embargo on the largest value note.

Once negative interest rates have served their purpose and the crisis has abated, they can be boosted back above 0% and the central bank can unfreeze the quantity of £50s. Everything returns to normal.

A few conventions will change when the largest value note is embargoed.

1. People will no longer be able to convert £50 worth of deposits into a £50 note. Instead they'll have to be satisfied with getting two £20s and a £10. That doesn't seem like an expensive convention to discard. And if folks really want to get their hands on £50s, they'll still be able to buy them in the secondary market, albeit at a small premium.

2. In normal times, £50 notes always trade at par. Because their quantity will be fixed under this scheme, £50s will rise to a varying premium above face value whenever interest rates fall significantly below zero. For instance, at a -2.0% interest rate a £50 note might trade in the market at £51 or £52.

The par value of £50 notes is a cheap convention to overturn. The majority of the British population probably don't deal in £50s anyways. Those who do use £50 notes in their daily life will have to get used to monitoring their market price so that they can transact at correct prices. But the inconveniences faced by  this tiny minority is a small cost for society to pay in order to slacken the lower bound.

3. Importantly, there will be no need to proclaim a unit of account switch upon the enacting of an embargo on £50s; the switch will be seamless.

Because the £50 was never an important part of day-to-day commercial and retail existence, come negative interest rates no retailers will set their prices in terms of a £50 standard. If they do choose to set sticker prices in terms of the £50 note, they will find that if they want to preserve their margins they will have to levy a small surcharge each time someone pays with £20s, £10s, and £5s and bank deposits. Given the prevalence of these payment options, that means surcharging on almost every single transaction. That's terribly inconvenient. Far better for a retailer to set sticker prices in terms of the dominant payments media—£20s, £10s, and £5s and bank deposits—and provide a small discount to the rare customer that wants to pay with £50s.

It's entirely possible that the majority of retailers will not bother offering any discount whatsoever on £50s. This would effectively undervalue the £50 note. Gresham's Law tells us that given this undervaluation, the £50 will disappear from circulation as it gets hoarded under people's mattresses. For the regular British citizen, never seeing £50s in circulation probably won't change much. And anyone who does want a £50 can simply advertise on Craig's list for one, offering a high enough premium to draw it out of someone's hoard.

In closing, a few caveats. The figures I am using in this post are ballpark. It could be that a policy of freezing the supply of £50 notes allows the Bank of England to get to -2%. But maybe it only allows for a level of -1.75%, or maybe it slackens the bound so much as to allow a -2.5% rate.

Haldane mentions that the Bank of England could need 3% of headroom to combat subsequent recessions. But as Tony Yates has pointed out, in 2008 bank officials calculated that a -8% rate was needed. The Bank could get part way there by not only embargoing the £50 but also the next highest value note; the £20. But that probably wouldn't be enough. As ever smaller notes have their quantities frozen, this starts to intrude on the lives of the people on the street, making the policy more costly. If it needs to slacken the lower bound in order to allow for rates of -8%, I think the Bank of England should be planning for a heftier policy like Miles Kimball's crawling peg. After all, when the sort of crisis that requires such deeply negative rates hits, the last thing we should be worried about is disturbing a few conventions. Until another 2008-style crisis hits, embargoing large value notes might be the least intrusive, lowest cost option. 

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*Of these policies, I think Miles Kimball's plan is by far the best one.
**Specifically, the Bank would only print new bills to replace ripped/worn out bills. Otherwise the outstanding issue will wear out and become easier to counterfeit. As for Scotland, which issues 100 pound notes, their quantity would have to be fixed as well.
*** I first mentioned the idea of embargoing large notes in relation to the Swiss 1000 CHF note, and later elaborated on it in the Lazy Central Banker's Guide to Escaping Liquidity Traps.

Plumbing the depths of the effective lower bound

Unfathomable Depths by Ibai Acevedo

Denmark's Nationalbank and the Swiss National Bank are the world's most interesting central banks right now. As the two of them push their deposit rates to record low levels of -0.75%, they're testing the market's limit for bearing negative nominal interest rates. The ECB takes second prize as it has been maintaining a -0.2% deposit rate since September 2014.

At some point, investors will flee deposits into 0%-yielding cash. This marks the effective lower bound to rates. Has mass paper storage begun? The last time I ran through the data was in my monetary canaries post, which was inconclusive. Let's take a quick glance at the updated data.

To gauge where we are relative to the effective lower bound, I'm most interested in the demand for large denomination notes, which bear the lowest costs of storage. Once a central bank reduces its deposit rate so deep into negative territory that the carrying cost of deposits exceeds the cost of storing a nation's largest value banknote, then it has hit the effective lower bound. Small denominations notes, which have higher storage costs, are not a pivotal part of the picture given the ability of note holders to freely convert low value notes into higher ones.

European Central Bank

The ECB issues the €500 note, which has the second highest purchasing power out of the world's currency notes. I've charted the quantity of €500 euro notes in circulation below, as well as the percent change in the value of all euro denominations:

After declining through 2012 and 2013, we saw a sharp rise in demand for €500 notes, particularly in December 2014 and the first few months of 2015. The red line illustrates the general demand for all denominations of euro cash. Over the last four months the seasonally-adjusted growth rate of banknotes outstanding has risen to its highest level in the last five years.

It's hard to determine how much of this increase can be attributed to the ECB's negative rate policy, initiated when Mario Draghi brought the deposit facility rate to -0.1% in June and -0.2% in September, and how much is due to the Greek fiasco. Growing fears that Greece will either leave the euro or impose capital controls have led to a steady jog out Greek banks. There are two escape routes: Greek's can convert their deposits can into German deposits or into cash.

In an interesting article, Bloomberg's Lorcan Roche Kelly backs out the Greek-specific demand for European cash. Read it for the full details, but the shorter rendition is that a line item on the Bank of Greece's balance sheet allows us to see how many banknotes Greeks are demanding in excess of the Bank of Greece's regular allocation. Kelly finds a large spike beginning in December and extending into 2015, which we can attribute to the bank jog. I've recreated the chart below:

Source: Bloomberg, data to end of March

The approximately €12 billion jump in Greek cash demand corresponds nicely with the recent €7.2 billion spike in €500 notes in circulation across the entire eurozone. The upshot is that a large chunk of the rise in €500 notes over the last few months is probably due to a run on Greek banks, not an escape from negative-yielding ECB deposits. Remove the run and the rise in demand for €500 notes would have been unremarkable, indicating that the eurozone is still far from hitting the effective lower bound.

Swiss National Bank

Because Swiss banknotes are not a direct escape route from the ongoing Greek bank run, SNB cash data should provide a clearer signal of the whereabouts of the effective lower bound than ECB data. The SNB issues the world's most valuable banknote in terms of purchasing power; the 1000 franc note. Below I've plotted the yearly percent change in demand for both the 1000 note and Swiss cash-in-general to the end of February.

There's been slight pickup in the demand for Swiss cash, but nothing dramatic. Its worth pointing out that Swiss paper currency has historically played a safe haven role. Demand tends to spike during episodes of uncertainty, including the 2008 credit crisis and the 2011-12 period, when it seemed like the euro could be torn apart. This means that it is difficult to be sure how much of the recent pickup in demand for Swiss cash stems from the SNB's -0.75% deposit rate and how much is due to fear of a Greek government default, which would create havoc in world markets.  

Danmarks Nationalbank

Our final canary is the Danmarks Nationalbank. Unlike the demand for Swiss paper francs, the demand for Danish paper krone does not usually spike during times of crisis. For instance, during the 2008 credit crisis demand remained muted. This leads me to believe that demand for paper krone provides the clearest indicator yet of the presence (or not) of the effective lower bound. I've charted the year-over-year change in Danish currency in circulation.

In the 55 days that have passed since the Danmarks National bank reduced its rates to -0.75% (February 5), there has been a sustained rise in the demand for cash, as the red data indicate. But I don't think we can describe it as anything out of the ordinary, at least not yet.

Interestingly, in late March the Nationalbank granted Danish banks some wiggle room by providing them with greater access to the Bank's 0% current-account facility. This small adjustment would have reduced Danish banks' incentives to emigrate from -0.75% deposits into cash. Was the central bank's decision to provide this wiggle room a response to private data showing that it had hit the effective lower bound? Who knows.

It may be worth noting even if a central bank finds itself at the effective lower bound, it can forestall the demand for large denomination notes by using moral suasion. Willem Buiter mentions this possibility in his recent note High Time To Get Low, but maintains we have no evidence of this sort of pressure. I'm tempted to agree with him. If either the Danish or Swiss central bankers have put informal embargoes on cash, we would have known about it by now.

The use of moral suasion to prevent large denomination banknote storage would effectively freeze the quantity of high value notes in circulation. In such a scenario, we'd expect the 1000 Sfr note to rise to a slight premium to face value, say 1050 Sfr in bank deposits for each 1000 Sfr in banknotes. Traders would be willing to pay this premium as long as the storage costs on high value notes are lower than the -0.75% penalty set by the SNB on deposits, thus allowing them to earn an excess return on their note holdings. As long as moral suasion remains successful in choking off Swiss banks' demand for cash, each subsequent cut by the SNB into ever deeper negative territory would drive the premium on notes higher. (Assiduous readers will recognize this as the second of three ways for a lazy central banker to escape a liquidity trap.)

In sum, we probably haven't hit the effective lower bound yet. Stay tuned.

A lazy central banker's guide to escaping liquidity traps

For lazy central bankers, this post describes three lite strategies for getting interest rates below the zero lower bound. Rather than requiring drastic action, these methods can be quickly deployed without having to spend too much energy—leaving plenty of time for the afternoon squash game.

1) Let's start at the beginning. What is the zero lower bound? If a central bank reduces interest rates below 0% then banks will rapidly convert all their central bank deposits into cash. No point accepting a -2% return if you can get 0%, right?

2) The zero lower bound is a problem. From time to time, a central bank may need to venture into negative territory to hit its monetary policy targets. Cash impedes the smooth descent into negative territory.

3) We already have a few go-to plays for dealing with our inability to get below zero: quantitative easing, forward guidance, and fiscal policy, each with its own set of warts. While quantitative easing has become a popular tool over the last few years, theory tells us that purchases are irrelevant at the zero lower bound. Promising to keep rates at 0% for longer than is prudent has also been used by a few central banks, notably the Bank of Canada. Unfortunately the market finds forward guidance confusing and may see little credibility in it, given the fact that the central banker who initiates the promise may not be in office to carry it out. This problem is called time inconsistency. And lastly, while fiscal policy may be a good way to evade the zero lower bound problem, it hinges on flaky political processes and arduous negotiations.

4) A more direct way to get around the zero lower bound problem may be necessary. Our lazy central banker might have to make alterations to the very nature of cash itself.

5) A sure-fire way to remove the lower bound is an outright abolition of cash. It gets around the time inconsistency problem and the flakiness of politics. But abolishing cash is a drastic step. Banknotes serves a role in protecting privacy and are popular with the unbanked. Abolish cash and you hurt both. Given the degree of preparation and effort needed to remove cash, and the political wrangling this option would require, a lazy central banker may want to take a pass.

6) Rather than removing cash, just harm it. Silvio Gesell's stamp tax, for instance, attacks cash's pecuniary return. In this spirit, Miles Kimball's crawling peg between electronic currency and paper currency burdens those who own cash with a capital loss. The crawling peg banishes the zero lower bound—without requiring the drastic step of immediately removing all banknotes. It's an elegant solution, you can read the details here (pdf).

7) There are a few drawbacks to a crawling peg. Driving a wedge between paper and electronic currency creates two different sets of prices at the till, one for deposits and the other for cash. A chocolate bar, for instance, might have a sticker price of $1.00 in electronic money, but require a cash payment of $1.05. This will be confusing and inconvenient for shoppers, necessitating an expensive and costly education campaign by our central banker. According to Kimball, instituting a crawling peg requires that a nation enact a unit of account switch. Prices must be set in terms of electronic currency, not paper currency, otherwise the central bank will lose control over the price level. While a switch in standards is by no means impossible, it does require time and effort.

8) Which finally gets us to our lite strategies for lazy central bankers. These options don't suffer from time inconsistency or flaky politics. They get us below zero without requiring the abolition of cash, nor do we get two different sets of prices at the till, nor do we need a nation to switch to a new unit of account. In short, if enacted, they'd keep our system pretty close to the current system.

9) Laziness isn't without a cost. Unlike the abolition of cash and Miles Kimball's crawling peg, the lite methods don't free us entirely of the lower bound. They only soften it up a bit, re-situating the bound a few percentage points lower. This buys room for central banks to cut rates,  but not infinite amounts. If extremely negative rates are necessary, say -6%, then there is no lazy option: best get off the couch and go with a full-out crawling peg.

10) There are a number carrying costs on cash holdings, including storage fees, insurance, handling, and transportation costs. This means that a central bank can safely reduce interest rates a few dozen basis points below zero before flight into cash begins. The lower bound isn't a zero bound, but a -0.5% bound (or thereabouts).

11) The various lite strategies all exploit the fact that differences in carrying costs among the various note denominations mean that banknotes are not naturally fungible. Put differently, bills aren't perfect substitutes for each other. Large denomination notes, say $100 bills, incur lower storage and handling fees than small denomination notes like $10s. After all, a hundred-thousand $10 bills (worth $1,000,000) take up ten times more storage space than a ten-thousand $100s (also worth $1,000,000). However, a central bank renders the two types of notes equivalent by offering to convert pesky low denomination $10s into sleek large denomination $100s at no cost to the owner. This means that the public can avoid the nuisances of small denomination note storage, for free. So at any point in time the note-owning public is bearing the carrying cost of the highest denomination note, not the lowest ones.

12) To get a bite, the following three lazy techniques all boost the carrying cost of cash.

13) They do so by interfering with the traditional smooth switch out of small denomination notes and deposits into large denomination notes afforded by a central bank. The effect is to put an end to banknote fungibility. The public, previously sheltered from the hassles of holding pesky low denomination notes, must now bear those costs, while being barred from racing into sleek high denomination notes.

14) By implementing any one of these lite techniques, the additional carrying costs now imposed on cash remove any incentive to convert increasingly negative yielding deposits into banknotes. A central bank that had previously reduced its deposit rate to, say, -0.5% before finding itself snug against the lower bound, will now be able to reduce its deposit rate to a much lower level, say -2.5%, without fear of mass flight into cash.

15) The first method a lazy central banker should consider is the abolition of large denomination notes. A central bank issues a proclamation giving people one month to bring in all $100s for conversion into ten $10 bills. Any large denomination notes remaining in circulation after one month will be disavowed. Once all high-value denomination are demonetized, the market clearing carrying cost on cash holdings will no longer be the superior rate on $100s, but the much heftier one on $10s. The expected return on cash holdings having been diminished, a central banker who had previously found him or herself stuck against the lower bound now has room to go lower without fear of mass flight into cash.

16) Even with the $100 having been abolished, the remaining low denomination notes in circulation can continue to serve a role in protecting privacy and serving the unbanked.

17) The second method involves closing the high denomination "conversion window." Specifically, a central bank ceases converting both low denomination notes and deposits into high denomination notes. The only window the central bank will keep open is between deposits and low denomination notes. This means that anyone who converts deposits into cash can now only get pesky small notes, forcing them to bear the higher carrying costs of $10s rather than the minimal inconveniences of sleek $100s. A central bank can now cut its deposit rate much deeper into negative territory than before since depositors are far less likely to flee into bulky cash.

18) If we close the conversion window, won't those who hold negative-yielding deposits and low denomination notes simply trade them for zero-yielding high denomination notes on the secondary market? Sure, but the opportunity will be a fleeting one. The closing of the conversion window effectively freezes the quantity of high denomination notes in circulation. The price of $100s will immediately rise to a premium over bulky low denomination $10s and negative-yielding deposits. After all, $100s impose much lower carrying costs than the other two instruments. This premium removes any incentive to flee deposits and low denomination notes.

19) Won't the public suffer the inconveniences of having two different sets of prices? Not really. Rather than having an electronic currency price and a cash price (as in point 7), the closing of the high denomination conversion window will create a combined electronic/low denomination price and a high denomination price. The public, which almost never transacts in high denomination $100s anyways, can conveniently ignore the high denomination price level.

20) Nor does our lazy central banker need to worry about switching standards. Given that consumers only rarely pay with high denomination notes, it's highly unlikely that retailers currently set prices in terms of $100s. In fact, even now retailers often refuse to accept large value notes. It's likely that we probably already live in a world with a low denomination/electronic currency standard.

21) Which brings us to our third method: vary the conversion rate between low denomination notes/electronic currency and large denomination notes. Central banks currently allow free conversion between deposits, low value notes, and high value denominations. The idea here is to keep the conversion window open, but levy a fee, say three cents on the dollar, on anyone who wants to convert either deposits or low denomination notes into high denomination notes. Conversion between low value notes and deposits remains free of charge.

22) A central banker can now safely guide rates to a much more negative rate than before, say to -2.5% rather than just -0.5%. Prior to instituting a conversion charge, the public would have fled from deposits to cash at such low rates. Now, while people can still convert deposits at no cost into low denomination notes, this offers them no real advantages given the high carrying costs on such notes. And flight into high value notes is forestalled by the conversion fee.

23) As with the second lite method, the third creates two different sets of prices: one for low denomination notes/deposits and one for high denomination notes. But this doesn't matter, see point 19. Nor do we have to switch standards, see point 20.

24) The main difference between the second method and the third one is that the exchange rate between high denomination notes and low denomination notes/deposits is allowed to float in the former versus being fixed under the latter.

25) The third lite method is akin to Miles Kimball's crawling peg, except that the conversion penalty is set on high denomination notes only, not cash in general. But if we steadily widen the peg so that it includes mid-value denominations, and then add small denominations, then the third lite technique isn't so lite anymore. It has basically become Kimball's peg. At some point along that transition, we start to inherit the inconveniences of the crawling peg (see point 7). For instance, the dual price level becomes much more inconvenient, especially once $10s (and lower) are included. However, the advantage is that we can now push rates much deeper into negative territory.

26) Which means its possible to incrementally transition from a lite program to an all-out option like a crawling peg or total abolishment of cash. Lazy central bankers may prefer to stick their toes in the water before jumping all the way in.

27) By the way, I've mentioned the first lite technique here, here, here, and here. I mentioned the second lite technique here. I haven't mentioned the third before.

28) If I was a lazy central banker, of the three lite programs I'd be partial to the second one; the closing of the high denomination conversion window. Removing high denomination notes from circulation would probably have messy political implications and draw the public's wrath. Levying a fee is an assertive, some might say aggressive stance necessitating the creation of new processes and administration expenses. Simply closing the $100 window seems like it would take the least amount of effort. It doesn't require that any new infrastructure or the decommissioning of existing machinery. As for the pricing of high denomination notes, this gets outsourced to the market.

The ZLB and the impending race into Swiss CHF1000 bank notes

Two things worth noting:

1. As many of you know by now, the Swiss National Bank (SNB), Switzerland's central bank, just reduced the rate that banks earn on deposits held at the SNB by half a percentage point to -0.75% (from -0.25%). The SNB had only recently instituted a negative deposit rate, having reduced it to -0.25% from 0% this December. The SNB will also be targeting a 3-month LIBOR rate of -1.25% to -0.25%, down from the previous range of -0.75% to +0.25%


2. The SNB issues the world's largest paper bearer note denomination, the hefty CHF 1000 note (pictured above). It's worth around US$1143.

The first is significant because as yet, no central bank has ever brought rates this deep into negative territory. The ECB's current deposit rate is set at -0.2% while Denmark's central bank, the Danmarks Nationalbank (DNB), applied a negative deposit rate of -0.2% on deposits that banks placed with the DNB in 2012. Neither of these top the SNB's ultra-low -0.75% rate.

The second point is significant because neither the ECB nor the DNB issue a note that approaches the real value of the CHF 1000.

Why is the conjunction of these two observations important? In short, we get to observe in real time how tightly the so-called zero-lower bound (ZLB) binds. When a central bank reduces the rate it pays on central bank deposits below 0%, arbitrage dictates that all other short term interest rates will follow along, including rates on government t-bills and insured bank deposits. However, one asset interferes with this adjustment: cash. Cash carries an implicit yield of 0%. If deposits or t-bills are being penalized at a rate of 0.25% per year, there are significant incentives for everyone to convert these assets into zero-yielding paper equivalents in order to avoid the 0.25% penalty. Not only will commercial banks all convert their deposits at the central bank to cash, but the public will clear out their bank accounts in order to hold paper. The upshot is that interest rates can't fall below 0% lest the  entire country turn into a 100% cash economy.

In practice, the 0% bound isn't a tight one since paper currency incurs storage and transportation costs whereas electronic deposits don't. What this means is that a depositor will grudgingly accept a slightly negative deposit rate in order to avoid having to bear the inconveniences of ungainly cash. So the zero lower bound actually lies a bit lower than 0%, let's say -0.4%. However, reduce rates far enough below that and the dash to cash beings.

This is where the CHF 1,000 note comes into the picture. The larger the denomination of paper currency issued by a central bank, the lower the storage and transportation costs. Take CHF 1,000,000 worth of CHF 20 notes. That's 50,000 paper notes. The costs incurred in counting, double counting, checking for counterfeits, packaging, loading into an armoured car, unloading into a vault, paying storage costs on that vault, and finally insuring the hoard will be quite high. Now imagine CHF 1,000,000 worth of CHF 1000 notes. That amount to just 1,000 slim paper notes, a fiftieth of the amount. Handling and storage costs come out to much less. The point being that thanks to the CHF 1,000 note, the zero lower bound binds a bit more tightly in Switzerland than anywhere else in the world.

What I'd expect over the next few months is a mad dash out of deposits into these colourful bits of paper. Luckily, the SNB provides data on its note denominations, which I've charted below going back to 1990.

The value of CHF 1000 denomination notes in circulation. Source: SNB

You can see that in general, the value of CHF 1,000 notes outstanding has grown quite quickly since 1990 and now comprises around 61% of the entire value of the Swiss note circulation. While that tally retreated a bit in 2014, it should start to grow at an above-trend rate in 2015 now that negative rates are in effect. The actual process will go something like this; the Swiss public will ask to convert their bank deposits into CHF 1000 notes, the banks being obliged to provide these notes by going to the SNB and converting their SNB deposits into cash.

If this process doesn't occur, the implication is that the costs of holding 1000 notes are even higher than 0.75% a year, thus giving the SNB even more breathing room to reduce rates.

I'd expect ongoing conversion into 1000 notes to impose a significant burden on the SNB, threatening both the banking system's deposit base and the effectiveness of monetary policy. There are a number of fixes that the Swiss might consider to offset this burden. First, the SNB can bump interest rates back up in order to stem the mania for 1000 notes, hardly an alternative if it is trying to get inflation back up to  its target. Alternatively, the Bank may decide to call in and demonetize the CHF 1000 notes, forcing everyone to accept five CHF 200 notes in its place (an idea discussed here). Since the 200 incurs more carrying costs than the 1000, the conversion into cash will be forestalled and the lower bound will have effectively been loosened downwards. Lastly, the Swiss might consider adopting a crawling peg between cash and deposits, as advocated by Miles Kimball.

The next and last option is the most interesting. When the public asks the banks for CHF 1000s, and the banks ask the SNB for 1000s, the SNB can just say no. In doing so, the SNB will have frozen the quantity of 1000s in circulation.

What will happen next will amount to an instance of Gresham's law. Since a CHF 1000 note is better than five CHF 200 notes due to its lower carrying costs, and 200s can no longer be converted on demand into 1000s thanks to the SNB's freeze, the 1000 should trade in the market at a premium to its face value, say CHF 1012 or 1013. However, legal tender laws typically stipulate that a note cannot discharge debts at more than its face value, thereby resulting in the forced undervalution of the 1000 note in trade. As a result, the Swiss public and its banks will hoard their 1000s rather than spending them, preferring instead to make payments and settle debts with lower denominations notes. Thus we get a modern version of Gresham's law, whereby 'good' CHF 1000 notes are driven out of circulation by 'bad' lower-denomination CHF notes. Think of it as an unofficial demonetization of the 1000.

Ultimately, I think that this last solution is the easiest and lowest cost alternative for the Swiss to fix their impending problem of mass paper storage at the negative interest rates. It's a temporary fix, however. A permanent solution will require outright demonetization of large denomination notes, or something like Miles Kimball's plan.