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.

Alberta Prosperity Certificates and a Greek parallel currency

This post is about the Alberta Prosperity Certificate, one of the world's stranger monetary experiments. Issued in late 1936 and early 1937 by the newly-elected Alberta government, these monetary instruments are the largest-scale example of Silvio Gesell's "shrinking money," or stamp scrip, in action. Gesell, a German business man and self taught economist, had written a treatise in 1891 in which he described a currency that depreciated in value, thus preventing hoarding and encouraging spending.

To make this more interesting, let's jump forward in time. In 2014, Greece's Finance Minister Yanis Varoufakis wrote a blog post that described a new Greek financial instrument that could be used to make payments while circulating in parallel with the already-existing euro. Varoufakis's post, combined with constant rumors that Greece may be planning to issue its own parallel currency in order to make internal payments,* means that a revisitation of Alberta's early dalliance with scrip, which circulated concurrently with Canadian dollars, is more relevant than ever. The attempt by Albertan authorities to issue scrip 80 years ago would end in failure; most of the paper refused to stay in circulation. Understanding why this happened provides some insights into what sorts of conditions might promote the success of a Greek parallel currency—or its downfall.

Virginius Frank Coe

The best source on Prosperity Certificates is a 1938 survey by Virginius Frank Coe, an American economist who visited Alberta in August 1937, five months after the program had been abandoned. Coe's life is interesting enough to deserve its own tangent. An economist educated at the University of Chicago, Coe would go on to hold a number of important positions in various U.S. government institutions both during and after World War II, including monetary research director at the Treasury Department. This brought him into the orbit of Harry Dexter White, then the Assistant Secretary of the Treasury and the architect of the Bretton Woods agreements. Coe himself was a representative at Bretton Woods and would go on to become secretary of the International Monetary Fund in 1946, nine years after having written his Prosperity Certificate paper.

Readers of Benn Steil's The Battle of Bretton Woods will know that much of the evidence incriminates Harry Dexter White as spying for the Soviets, an accusation White himself denied. The same sources who named White as a Soviet agent also fingered Coe, and in 1952 Coe was forced to resign from his post at the IMF. He would appear in front of the McCarran Committee later that year, pleading the fifth in response to all questions posed to him, and would later face Senator Joseph McCarthy. His passport revoked, and unable to find work in the U.S., Coe headed to China to serve as an adviser to Mao until his death in 1980.

Coe's Prosperity Certificate paper betrays the author as someone with a strong interest in alternative monetary systems. While we can't know for sure if his interest in alternative systems extended as far as being a Soviet mole, we shouldn't let this possibility detract from what is otherwise an excellent account of this early Canadian monetary experiment.

Alberta and Social Credit 

Coe describes an Alberta electorate that is facing the same economic backdrop as Greece's voters did prior to the recent election of Syriza. Just as Greeks had endured seven years of famine prior to the 2015 election, Albertans going into the 1935 election had been beset by seven years of distress associated with low farm prices and bad crop yields. The incumbent United Farmers of Alberta government was not willing to implement the more drastic policies that the Albertan electorate demanded, says Coe. Into the void stepped William Aberhart, a pastor and newly-recruited believer in the tenets of Social Credit. Dreamt up by British engineer C.H. Douglas, the idea behind Social Credit was to create a more equal society by augmenting consumers' purchasing power via the payment of a national dividend. Aberhart formed the Alberta Social Credit party in 1935 and won the election a few months later. In electing Syriza, the Greeks, like the Albertans before them, have entrusted their future to a party of political novices.

Reading Coe, one gets the sense that the Aberhart government stumbled into Prosperity Certificates rather than purposefully selecting them as a policy. Gesell's dated stamp scrip was a rival monetary reform to Social Credit, not a complement. Why turn to a non-Social Credit policy? It seems that several months after coming to power, the new Social Credit government was already splintering as one faction had grown impatient with Aberhart's inability to implement economic changes. Coe, speculating that the decision to implement dated stamp money was a token gesture to demonstrate forward momentum and heal internal rifts, says that "any one of a number of plans would have done as well." If a non-Social Credit monetary scheme such as Gesell money were to fail, at least a Social Credit policy option still had a kick at the can. The implication that the government didn't put much thought into the design of the certificates finds some confirmation in the fact that the Free-Economy League, an organization formed by Gesell, published a criticism of the Alberta government's procedure for creating Prosperity Certificates and predicted their failure.

How the certificates worked

Here's how Alberta's stamp scrip worked. In early August 1936, when the program debuted, an unemployed Albertan was paid, say, a $1 certificate for each $1 worth of road maintenance work rendered. This certificate was to be redeemed by the Alberta government two years hence, or in August 1938, for $1 in Canadian dollars. However, redemption required that the certificate have 104 stamps affixed to it (see figure above). Each week during that two year period, the owner of the certificate was to buy a government stamp for 1 cent from an approved stamp dealer and glue it to the note.

The necessity of buying stamps created a fairly onerous fee on cash holdings. As such, any laborer who received the scrip from the government was unlikely to hoard it, preferring instead to spend it on, say at a retailer, who in turn would only accept scrip as payment for goods and services if the correct number of stamps has been affixed. In order to avoid the cost of buying the next weekly stamp in order to keep the scrip current, the retailer themselves would quickly offload it to their suppliers and so on.

The 1 cent stamp fee was collected by the Alberta government and held as a reserve for redemption in two years. With 104 cents being collected over each $1 certificate's life time, this meant that the scheme was entirely self financing. The extra four cents represented a profit to the government.

Failure

We know that the Prosperity Certificate scheme didn't work. The certificates began to be paid to unemployed Albertans in August 1936 for roadwork rendered in July. According to Coe, the maximum amount of outstanding certificates in circulation in August and early September was $239,391 (around $9 million in current dollars). However, by mid-September 1937, just one month after the program's debut, over 60% of the certificates outstanding, or $144,280 out of $239,391, had ceased to circulate.

Where had they gone? The government now held them. The reason for this development was a last minute decision by Aberhart to offer monthly redemption of certificates at par in Dominion currency (i.e. $1 in certificates for $1 in Canadian bills). This short-circuited the original two-year life of the certificates. Rather than continuing to pass the scrip along to the next Albertan, Albertans leapt at the government's offer and converted en masse when the first redemption date presented itself in early September.

In the end, the government might as well have paid for work rendered using Canadian dollars, since the net effect of paying in either Certificates or Canadian dollars was the same. As Coe says, "the dated stamp scrip was in the end little more than a small nuisance." Subsequent issues of scrip were small relative to the original August 1936 issue and the government officially ended the program in April 1937.

"The problem of the wholesalers"

In the planning stages of the program, government officials ran into what Coe refers to as the "problem of the wholesaler." The first to receive the certificates would be farmers on relief, who in turn would make payments to retailers. The payments by retailers would primarily flow to Albertan wholesalers whose dominant payments were to manufacturers and others outside the province. However, those outside the province would not accept Prosperity Certificates, requiring instead hard currency, or Canadian dollars. The Albertan wholesaler would be left holding the bag, so to say, having acquired the entire issue of Prosperity Certificates with no outlet. According to Coe, wholesalers and large retailers were vocal in their opposition to the plan, which they expressed through trade associations and in the press.

One way of solving the wholesalers' problem would have been to establish an exchange market such that wholesalers could sell certificates in order to buy the necessary hard currency and thus fund out-of-Province imports. Banks would normally be an important party to the creation of such a market. Irving Fisher, who wrote a book on stamp scrip, entitled one paragraph "Have at Least one Bank." But the banks who operated in Alberta refused to participate in the Prosperity Certificate scheme—no wonder given that one of the Social Credit party's planks advocated the removal of the "banking monopoly" on the issuance of credit. The tenets of Social Credit thus interfered with the execution of Gesell money, impeding the latter's success.

Even if such a market were to be created, chances are that it would have priced the Certificates at a large discount to Canadian dollars given the onerous fee on certificates relative to Canadian notes and the inferior credit of their issuer. After all, by then the Alberta government had defaulted on its international obligations whereas the Federal government's credit was still good. Such a discount would have been at odds with the Alberta government's policy of using a dollar's worth of certificates to buy one Canadian dollar's worth of labour. If the certificates were trading at 69 cents on the dollar in the wholesale market, workers paid in scrip would be loath to accept them at face value, for if they did, they would probably have problems passing them off at retailers for that amount.

In the end, the government's solution to the problem of the wholesalers was to allow wholesalers (and even retailers) to benefit from free monthly redemption at par. As I noted earlier, this resulted in most of the certificates being returned for redemption just a few weeks after having been issued.** Rather than bad money driving out the good, a garbled version of Gresham's Law had taken hold in Alberta, which Coe describes thusly: "Bad money obviously does not drive out good money when the government is willing to redeem the bad money in good money."

This garbled version of Gresham's law is a phenomenon I've described before to explain a number of monetary puzzles including the failure of the Susan B. Anthony dollar, the European Target2 bank runs of 2011-12, the proliferation of credit cards, and the zero-lower bound problem. See here and here.

What about Greece?

Alberta in 1936 and Greece in 2015 are in similar situations. Both are non-currency issuers within a larger monetary zone, in Alberta's case the Canadian dollar zone and in Greece's case the Eurozone. Both have awful credit. Neither is part of a larger fiscal union. In Greece's case, the mechanism hasn't yet been created whereas in Alberta's case, the Social Credit party was at such odds with the Federal government and the rest of Canada that it could not expect much help.

I'd argue that anyone planning to introduce a Greek parallel currency to circulate alongside euros faces the same problem that Alberta faced; the so-called problem of the wholesalers. If the Greek government starts to pay employees and contractors in Greek parallel IOUs denominated in euros, and employees buy stuff at stores with those IOUs, and stores purchase inventory from wholesalers, these wholesalers will need a mechanism to offload their parallel note surpluses in order to get euros to buy foreign imports. The IOUs can either find their own price, in which case they will most likely trade at a large and varying discount to euros, or the Greek government can offer one-to-one convertibility. They can do this by either redeeming IOUs directly for euros or allowing one euro worth of taxes to be paid with an equivalent number of IOUs.

Neither solution is ideal. If the IOUs trade at a variable discount to euros, then their ability to serve as a competing medium of exchange will suffer. People always prefer to trade using the medium in which a nation's prices are expressed, or, put differently, the medium which functions as a unit of account. For example, people see benefit in the fact that one euro will always discharge a euro's worth of Greek debt or a buy a euro's worth of Greek olive oil. But as long as Greek IOUs trade at a varying discount to euros, it is impossible to know ahead of time how many IOUs will discharge a euro's worth of debt or buy a euro's worth of oil, given that the euro will surely remain Greece's unit of account. This would hinder the IOU's ability to function as a currency. The fact that people prefer to accept stable exchange media in trade to unstable media is one of the reasons that bitcoin hasn't caught on.

So rather than serving as a competing medium of exchange, the parallel IOUs will probably function as illiquid and highly risky speculative fixed income securities. In order to compensate recipients of IOUs for this lack of liquidity, the Greek government will have to issue the IOUs at a larger discount to par than they would for an otherwise liquid equivalent, thus increasing the government's financing costs.

This lack of liquidity militates against one of the key selling points of a Greek parallel unit, which is to finance the government by displacing some of the existing circulating medium of exchange, euros, from citizens' wallets. Preferably, unwanted euros would trickle back to the European Central Bank to be cancelled, reducing the ECB's seigniorage but augmenting the seigniorage of the Greek state as Greek IOUs rush in to fill the void. However, if the new Greek parallel unit cannot compete with the euro's liquidity, then there will be very little 'space' for Greek IOUs to occupy in Greek portfolios, and little relief for beleaguered government finances.

If the Greek government tries to promote the liquidity of its parallel currency by having the units trade at a fixed one-to-one rate with euros, then the same garbled version of Gresham's Law that took hold in Alberta would overwhelm Greece. In Coe's words, the Syriza government's willingness to buy bad money, or parallel currency units, from the public with good money, or euros, will promote mass conversion into euros and thereby drive all the bad money from circulation. Greek parallel units will cease to exist.***

In sum, anyone planning a Greek parallel currency faces a conundrum. In order to pay its bills the government can do little more than introduce a volatile asset that trades at varying discount to euros. This asset's volatility and relative illiquidity won't make it very popular with its recipients. An attempt to render that asset more acceptable in trade by setting a one-to-one conversion rate to the euro will result in a short-circuiting of the scheme as everyone races to redeem IOUs. The issuance of parallel currencies seems like a hard battle to win.

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*There are a number of plans including that of Biagio Bossone & Marco Cattaneo, Thomas Mayer, and Robert Paranteau
** Compounding the problem was that redemption at face value put a premium upon redemption, says Coe. "The holder who redeemed received face value; the person who did not redeem ran the risk of losing 1 per cent of the face value if he failed to pass the certificates within the next few days, and more for longer periods. This premium placed upon redemption could only have been eliminated by redeeming the certificates at a discount of more than 1 per cent-say, 2 or 3 per cent." So the government accidentally created an even greater incentive for certificate owners to redeem.
*** This is particularly damaging in Greece's case at will result in a perpetual draw down in the state's euro balances. These reserves are vital since the Greek government needs to service its (existing or renegotiated) Euro debts to the IMF and pay external suppliers, and can only do so with hard currency. 

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.

When the good drives out the bad

There's a fairly regular monetary phenomenon that needs a name. It's similar in nature to Gresham's law, yet the inverse version.

Gresham's law is commonly stated as the phenomena by which "bad money drives out the good". But as any economist will tell you, that's not quite it. Bad money chases out the good, but only if authorities have chosen to enforce a fixed exchange rate between the two moneys. When the market ratio diverges from the fixed ratio, the undervalued money—the "good" one—will disappear from circulation while the overvalued money —the bad one—will become the exchange medium of choice. Bad money drives out good money because they pass by law at the same fixed price.

That's the classic Gresham's law. However, it's possible to show how an authority can set a fixed price between two moneys yet rather than the bad coin chasing out the good, the opposite happens: the good coin chases out the bad.

Before I show how, let's first give an example of Gresham's law. Say that new full-bodied silver coins and debased silver coins with the same face value circulate concurrently. If authorities set a law requiring that all coins must be accepted by the populace at face value, buyers and debtors will only settle their bills in debased silver coin (the "bad" money). Full-bodied coins (the "good" money) will be held back as hoarders clip off a bit of each coin's silver content, converting the entire full-bodied coinage into debased coinage. After all, why spend x ounces of silver on goods when a smaller amount will suffice? Thus the bad chases out the good.

Now let's vary our example to have good money chase out the bad. Say authorities promise two-way conversion between all silver coins at face value. Everyone will bring debased silver coins, the "bad" money, to the authorities for conversion into full bodied coins, the "good" money. In essence, they are bringing in x ounces of silver and leaving with x + y silver. This will continue until every bad coin has been deposited into the authority's vaults so that only the good money circulates.

So why in the first case does bad silver coin chase out good yet in the second good chases out bad?

When coins circulate at face value while their true market price differs, a mispricing is created. Any mispricing provides an arbitrage opportunity. In our first example, the arbitrage is such that all those holding full-bodied coin can take a full-bodied coin, file off some silver, and purchase the same amount of goods as before with the now debased coin, all the while keeping the silver clippings to themselves. A different sort of arbitrage opportunity arises in our second example. Because the authorities offer a two-way conversion feature, everyone holding debased coins gets to enjoy a risk-free return by bringing those coins in for conversion into full-bodied coins. They get more silver with less.

So the way that the arbitrage opportunity is structured will either incentivize the population to switch to bad money or to good. We get Gresham's law if people switch en masse to bad coins, and we get an inverse-Gresham effect if they take advantage of conversion and switch en masse to good coins. Since I'm not feeling especially creative, I'll call this effect Mahserg's law (Gresham spelt backwards).

My favorite modern example of Gresham's law is the proliferation of credit cards. In the same way that an owner of a full bodied coin could clip a bit of "bonus" silver off the coin while still being guaranteed the same purchasing power, payment with a credit card allows its owner to maintain their purchasing power while getting rewards to boot.

There are a few modern examples of Masherg's law. In 1978 U.S. authorities created a situation in which two different exchange media with the same denomination circulated concurrently, the Susan B. Anthony dollar and the good old $1 US bill. Because it was novel and untrusted, the Susan B. Anthony was considered to be "bad" money. The dollar bill, which enjoyed network externalities that had been established over a century of use, was the "good" money. The Federal Reserve offered two-way conversion between coin and paper. The inevitable result was that whatever Susan B. Anthony dollars were emitted into the economy were quickly brought back to the Fed to be converted into paper dollars. The good money drove out the bad. To this day Susan B. Anthony dollars are nowhere to be seen.

Another example of Masherg's law is a good old bank run. Take the intra-Eurosystem bank run that began after the credit crisis. There exist many different brands of euros, some issued by Germany, some by Greece. As a condition of membership in the Eurosystem, all nations are required to accept each other's euros at par. With the spectre of euro breakup growing in 2010 and 2011, Greek euros came to be viewed as inferior to German euros. Since it was possible to convert the bad into the good at par, everyone leaped at the opportunity. The quantity of bad Greek euros rapidly contracted while the quantity of good German euros grew, a process that would have eventually resulted in the complete extinction of Greek euros if Mario Draghi hadn't stepped in to short-circuit the run.

My favorite modern example of Masherg's law is the zero-lower bound. A central bank issues two media, dollar bills and dollar deposits. It allows free conversion between the two at par. Say that the central bank reduces the interest rate it pays on reserves to a negative rate so that reserves are inferior, or "bad", relative to 0%-yielding bills, which are now good. Anxious to avoid the negative rate penalty, everyone will race to convert their reserves into cash at the central bank until reserves no longer exist. The good has chased out the bad.

The zero-lower bound can be thought of as the lowest rate that a central bank can institute before setting off Masherg's law. Modern central banks are petrified of encountering this particular law—that's one reason that they aim for a positive inflation target

And what about Gresham? Say our central bank reduces rates below zero. If the central bank ceases allowing convertibility between dollar notes and deposits but continues to require merchants to accept the two media at par, then the incentives change such that the good no longer chases out the bad. With no conversion outlet for bad currency, people will hoard notes while only deposits will circulate. After all, why use good cash to pay for groceries when a negative yielding deposit will suffice? We're back at Gresham's law, or the chasing out of the good by the bad.

Gresham's law and credit cards

This is a follow up to my previous post on the monetary effects of credit cards. In this post I'll explore the idea that the use of credit cards in payments is driving a modern Gresham effect, the result of which is a displacement of cash and an inflationary race to the bottom of sorts. This downward spiral resembles the same dynamic set off by coin clippers in the medieval age, the era when Gresham's Law was first enunciated.

First, we need to revisit the idea of Gresham's law, or the idea that the bad money drives out the good. Imagine that it's 1592 and you're a fish monger in a busy market in London. Like everyone else, the unit of account that you use to price your wares is the pound unit of account, further subdividable into twelve shillings and 240 pennies. The actual medium that you and most other merchants have chosen to represent that unit (ie. the medium of account) is the English penny, coined by the Royal Mint from twenty-four grains of silver.

However, not all English pennies are the same! You've been selling fish for most of your career at 1d (d is the sign for the penny unit). But lately you've noticed that a growing number of the pennies you've been receiving have been altered. Small notches have been clipped from these coin's edges. The imprints on them look increasingly worn, and you hear stories about people who "sweat" coins. These ruffians are putting pennies into a sack, shaking them, and removing the small pieces of silver that have been scratched off.

Which means that in a growing minority of your transactions you are receiving the same amount of coin per fish but earning less silver. Clippers and sweaters are stealing the difference. To solve this problem, what you'd really like to do is weigh and assay each penny proffered and charge a unique price based on that coin's silver content. But you don't have the expertise to do this, and in any case, the chaos of the market doesn't offer enough time. Even if you could, accepting coins by weight rather than tale (their face value) is probably punishable by something grisly like getting your finger chopped off.

So instead you raise your prices a bit. By selling fish for 1¼d, you get more pennies than before, but roughly the same amount of silver. What you've done here is switch the medium you use to define the "d" unit of account, or your medium-of-account. You've adopted clipped and sweated shillings as your definition of the penny unit rather than full bodied shillings.

Here's where Gresham's law kicks in. Anyone who has undebased pennies (i.e. good pennies) in their pockets now has to pay 1¼d for your fish rather than 1d. But this is a bad deal for them. Our fish buyer can simply pay with with clipped and sweated pennies that contain less silver, say twenty-three grains of silver... and buy the same quantity of fish. Good pennies containing twenty-four grains of silver are being undervalued in the market place. Owners of these good pennies will choose to hoard them in their pockets and never use anything other than bad pennies to buy things or pay debts.

Where will all the good pennies go? They'll eventually be sent to wherever their silver is not being undervalued. In 1592, people would most likely have melted their good coin down into bullion and shipped this bullion across the Channel to France, only to have it re-minted into French coin and used to buy a larger quantity of fish (or more likely some durable good) than the London market allowed. That is Gresham's Law: when the price of various exchange media are fixed by law or custom, if the true market value of these media diverge, the market will tend to adopt the overvalued medium as their preferred payments option. In short, the bad English pennies drove out the good.

Now it's 2014 and you're a fish monger in a busy market in downtown Toronto. You use the dollar unit of account, the medium that represents this unit being Canadian banknotes.

However, not all dollars are the same! You've been selling fish for $10 for the past few years, but lately you've noticed that the use of credit cards has increased. Furthermore, the credit card networks are charging you ever higher transaction fees, say twenty cents rather than just two cents. This means that people are paying you the same amount of dollars per fish, but after fees you're earning the equivalent of just $9.80 worth of paper dollars in your account.

To solve this deficit, you'd like to charge the transactor a 20c fee, similar to how in 1592 you would have liked to assay each coin and charge a discount to face value based on the coin's actual silver content. By placing a 20c surcharge on credit card transactions, you'd end up with $10 per fish. However, the credit card companies stipulate in their contract with you that card payments can't be surcharged, the penalty being banishment from the card network. (Banishment certainly seems more humane than having your finger cut off.)

So instead you raise your prices a bit, just like you did in 1592. By selling fish for $10.20 you receive more in payment than before, but once the twenty-cent fee kicks in you end up with the same $10 quantity of paper dollars. Just like the medieval fish monger switched from full bodied pennies to clipped pennies, you've switched the medium you use to define the $ unit of account from paper money to credit card money. By doing so, you've preserved your margins.

As it did in 1592, Gresham's law kicks in. All things staying the same, anyone with paper money in their pocket now has to pay $10.20 for a fish rather than $10. But this is a bad deal for them since it undervalues their paper dollars. Better to pay $10.20 in credit card money and get all the associated rewards (air miles, cash back, etc) then pay $10.20 in cash and get no rewards. People will keep their paper dollars in their pockets and only make purchases by credit card.

Where will all the hoarded banknotes be exported? Well, people can't ship them down to the U.S. Americans aren't fond of Canadian dollars. But there will still be places in Canada that don't undervalue banknotes, namely all those retailers who only accept cash. Perhaps there's a competing fishmonger on the other side of town, say Scarborough, who won't accept credit cards and still charges $10 per fish. People will export undervalued banknotes to Scarborough where their dollars earn their full value. Or maybe they'll be exported to Toronto's drug market, or its prostitution market, or anywhere else where cash is still king. At the end of the line is the Bank of Canada, which will always offer to repurchase and shred all of the unwanted old notes that it has issued.

So the point of my little exercise has been to illustrate how 1592 is no different from 2014. Just substitute out the word "coin" with "credit cards" and the same Gresham effects are generated.

In both eras, one of the ways to remedy the displacement of good money by bad money would be to allow the price of the various exchange media to float. In the case of medieval coins, if merchants were allowed to charge varying prices based on the quality of coins proffered, then good coins would once again be properly valued and return into circulation. In the modern case of cash and credit cards, if retailers could charge surcharges on credit card payments, then cash would no longer be undervalued and would return to universal circulation.

In Australia and the U.S., authorities have adopted policies that should relieve these modern Gresham effects. Merchants in both nations are allowed to put surcharges on credit cards transactions. In Canada, surcharges are not allowed, despite efforts by the Competition Bureau to allow them. Gresham's law, it would seem, is still in effect up here.

Left unchecked, the Gresham effects kickstarted by both coin clippers and credit card networks contribute  a race to the bottom of sorts. In 1592, the incentives to clip coin would have been huge since the payor would be able to buy a greater real quantity of goods with a clipped coin than an unclipped coin. In reaction to the appearance of newly clipped coin, merchants would defensively raise their prices. The rest of the populace could only tag along and adopt the newly clipped coin as their standard payment medium. After all, using their good coin in local trade would be madness, since good coin was always and everywhere undervalued. The clippers would attack once more, prices would rise, and once again non-clippers would have to shift their cash holdings into inferior coin. Unless something was done to break out of this downward spiral, there was a tendency for the standard to be perpetually debased and prices to rise forever.

The same dynamic set off by clippers also emerges when credit card networks issue new premium cards that offer better rewards. Say that the networks introduce a "super" card that offers 5% cash back. Early-moving consumers will quickly adopt these cards—after all, they can buy the same quantity of goods at the same price... and get a large cash reward to boot. The higher the reward, the higher the fees a merchant must pay. They now find themselves ponying up 5% of the value of each transaction to the networks. In defense, merchants will belatedly raise their prices.

However, while early movers have adopted 5% cards, the general populace may still only be using cards that allow, say, a measly 1% cash back reward. Their existing cards are now undervalued, since merchants' prices are implicitly being marked up to a 5% card standard. What retailed for $100 now retails for $105. Anyone purchasing $105 worth of goods and getting only $1 cash back incurs a loss of $4. To avoid real losses, the population has no choice but to play catch up and apply for 5% cash back cards. By then, the card networks may be offering 6% cash back cards, which early movers will quickly adopt in order to enjoy the increased purchasing power that these cards afford. Once again merchants will raise prices to defend their margins, adopting a 6% card standard (in other words, their chosen medium-of-account is now 6% cards). But now the 5% cash back cards adopted earlier by the general populace will be undervalued, forcing them to transition to the use of 6% cash back cards. And on and on and on till we have a 100% cash back Visa card standard.

Empirically, we can see this effect over the last decade by the proliferation of premium credit cards, as well is the growing fees that merchants must pay to the card networks.  See this GAO report, especially Figure 3 which I've appended below.

In closing, here's a rare bit of practical advice from the Moneyness blog. If you live in a nation that doesn't allow credit card surcharges (like Canada), and you use cash to pay for most things, YOU ARE LOSING MONEY. Many merchants are implicitly setting prices based on the expectation that credit cards will be used and are pricing in a premium to cover the fees they must pay to the card networks. Either demand a 2-3% cash discount on everything you buy, or get yourself a credit card that yields decent rewards. Save your cash for buying stuff at your local farmer's market or any other cash-only venue where your cash isn't being undervalued. Put differently, if you aren't behaving according to the strictures of Gresham's law, you should be.

The three lives of Japanese military pesos

1942 Japanese Invasion Philippines Peso with a JAPWANCAP Stamp

In his reply to Mike Sproul, Kurt Schuler brings up the question of the determination of the value of a very peculiar kind of money: military currency. Curious, I investigated one example of such money, Japanese-issued "invasion money" in Philippines both during and after World War II. As best I can tell, the mechanism by which the value of these military notes has been mediated has gone through three different phases, each of them teaching us something interesting about money.

In January 3, 1942, a few weeks after successfully invading Philippines, the Japanese Commander-in-Chief announced that occupying forces would henceforth use military-issued currency as legal tender. Notes were to circulate at par with existing Philippines "Commonwealth" Pesos. Since this military scrip was not directly convertible into existing pesos, the trick to get it to circulate at par can probably be found in the tersely titled proclamation Acts punishable by death which, among seventeen acts that could result in loss of life, listed the thirteenth as:

(13) Any person who counterfeits military notes; refuses to accept them or in any way hinders the free circulation of military notes by slanderous or seditious utterances.

This is a great example of a Warren Mosler fiat money. According to Mosler, the state's requirement that citizens discharge their tax obligation with a certain intrinsically worthless medium on pain of being shot in the head is sufficient to give that medium a positive value. Likewise, requiring citizens to use the same medium in the course of regular payments and accept it to discharge debts, all on pain of death, would probably have promoted a positive value for intrinsically worthless paper.

Over time, those bits of "forced" paper will enjoy constant purchasing power as long as the issuer withdraws excess currency or adds it when desired. This is the quantity theory of money.

By 1943, however, it seems that the Japanese occupying forces, now being pushed back by the Allied forces, were desperately issuing excess notes to pay for operations. The Filipino monetary system proceeded to run smack dab into Gresham's law. The unit of account, the peso, was defined in terms of two different media—original pesos and military pesos. This meant that debtors could choose to discharge their debts with either. However, if one was perceived to be more valuable than the other, this superior medium would be hoarded and the inferior one used to pay off the debt. Legacy pesos had completely disappeared from circulation by 1943—only war pesos were being used to discharge debts and pay for goods, a decent indicator that the value of Japanese invasion pesos had fallen below that of original pesos. Bad money had chased out the good. (See [1] and [2] for evidence of Gresham's law)

Through 1944 and 1945, the war peso would endure extreme inflation. 10P had been the largest denomination in 1942. The military introduced 100P, 500P, and 1000P notes in subsequent years. In Neil Stephenson's Cryptonomicon, a wide-ranging historical/science fiction novel filled with monetary themes, there's an interesting passage in which Japanese soldier Goto Dengo describes the use of military scrip, probably sometime in 1943 or 1944:

The owner comes over and hands Goto Dengo a pack of Lucky Strikes and a book of matches. "How much?" says Goto Dengo, and takes out an envelope of money that he found in his pocket this morning. He takes the bills out and looks at them: each is printed in English with the words THE JAPANESE GOVERNMENT and then some number of pesos. There is a picture of a fat obelisk in the middle, a monument to Jose P. Rizal that stands near the Manila Hotel.
The proprietor grimaces. "You have silver?"
"Silver? Silver metal?"
"Yes," the driver says.
"Is that what people use?" The driver nods.
"This is no good?" Goto Dengo holds up the crisp, perfect bills.
The owner takes the envelope from Goto Dengo’s hand and counts out a few of the largest denomination of bills, pockets them, and leaves.
Goto Dengo breaks the seal on the pack of Lucky Strikes, raps the pack on the tabletop a few times, and opens the lid.

Japanese invasion currency, already being well on its way to being repudiated, would become completely worthless upon Japan's unconditional surrender in 1945.

Well, not entirely valueless. The second chapter in the life of military scrip begins with The Japanese War Notes Claimants Association of the Philippines, or JAPWANCAP. Formed in 1953 on behalf of Filipinos left holding stranded quantities of worthless Japanese invasion money, JAPWANCAP's mission was to hold both the US and Japanese government's liable for the redemption of war currency (the US had also issued counterfeit Japanese military currency). So while pesos had been valued prior to the war's end upon pain of death, and their value regulated by limiting the quantity outstanding, those same pesos were now valued on the margin as a liability of their issuer. Given the possibility of redemption, an old invasion note was worth more than zero.

Was JAPWANCAP successful? While the case was heard in a United States Court of Claims in 1967, it was thrown out on a technicality, the statute of limitations having had passed. Put simply, the court would not hear a claim that had not been filed within six years of that claim first being accrued, and in JAPWANCAP's case many more years than that had already passed.

This makes one wonder, if Filipinos in 1953 were already convinced that Japanese invasion pesos were the liability of the issuer, and therefore redeemable in some quantity of yen or dollars, did that same motivation also lead them to originally accept new military pesos in 1942? To what degree was the initial acceptance of pesos driven by the threat of force (& subsequent changes in value regulated by their quantity), and to what degree was their value dictated by their status as a liability of a well-backed issuer? That's a question we can never be entirely sure of. But while the force/quantity theory story fits the facts, the liability story does too. The military peso's inflation, for instance, can be attributed to the rising quantity of money, but also to the increasing likelihood of Japan losing the war, a loser's liability's being worth far less than a winner's.

Which brings us to the third chapter in the evolution of Japanese military pesos. Nowadays you can buy the notes on eBay for a few bucks. Their value is no longer dictated by gunpoint, nor by their liability nature, but their existence as a unique commodity, much like gold, bitcoin, or some rare antique.

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To learn more, here is a paper called "Financing Japan’s World War II occupation of Southeast Asia"

Note: I will be posting sparsely over the next two months, probably once every two weeks.

The zero-lower bound as a modern version of Gresham's law

Sir Thomas Gresham, c. 1554 by Anthonis Mor

The zero-lower bound may seem like a new problem, but I'm going to argue that it's only the most recent incarnation of one of the most ancient conundrums facing monetary economists: Gresham's law. A number of radical plans to evade the zero-lower bound have emerged, including Miles Kimball's electronic money plan. When viewed with an eye to history, however, plans like Miles's are really not so radical. Rather, they are only the most recent in a long line of patches that have been devised by monetary tinkerers to spare the monetary system from Gresham-like monetary problems.

Here's an old example of the problem. At the urging of Isaac Newton and John Locke, British authorities in 1696 embarked on an ambitious project to repair the nation's miserable silver coinage. This three-year effort consumed an incredible amount of time and energy. Something unexpected happened after the recoinage was complete. Almost immediately, all of the shiny new silver coins were melted down and sent overseas, leaving only large denomination gold coins in circulation.

What explains this incredible waste of time and effort? Because it offered to freely coin both silver and gold at fixed rates, the Royal Mint effectively established an exchange ratio between gold and silver. English merchants in turn accepted gold and silver coins at face value, or the mint's official rate, and debts were payable in either medium at the given rate. Unfortunately, the ratio the Mint had chosen overvalued gold relative to the world price and undervalued silver. Rather than spend their newly minted silver coins to buy £x worth of goods or to settle £y of debt, the English public realized that it was more cost-effective to use overvalued gold coins to purchase £x or settle £y. Then, if they melted down their full bodied silver coins and sent them across the Channel, the silver therein would purchase a higher quantity of real goods, say  £x+1 goods, or settle more debts than at home, say £y+1 debts.

Newton and Locke had run into Gresham's law. When the monetary authority defines the unit-of-account (£, $, ¥) in terms of two different mediums, the market will always choose to transact using the overvalued medium while hording and melting down the undervalued medium. "Bad" money drives out the "good". (For a better explanation, few people know more about Gresham's law than George Selgin.)

The abrupt switches between metals that characterized bimetallism weren't the only manifestation of Gresham's law. Constant shortages of silver change in the medieval period were another sign of the law in operation. Over time, a realm's silver coinage would naturally wear out as it was passed from hand to hand. Clippers would shave off the edges of coins, and counterfeiters would introduce competing tokens that contained a fraction of the silver. Any new coins subsequently minted at the official standard would be horded and sent elsewhere. After all, why would an owner of a "good" full-bodied silver coin spend it on, say, a chicken at the local market when a "bad" debased silver coin would be sufficient to consummate the transaction? The result was a dearth of new full bodied coins, leaving only a fixed amount of deteriorating silver coins to serve as exchange media.

This sort of Gresham-induced silver coin shortage, a common phenomenon in the medieval period, was the very problem that Newton and Locke initially set out to fix with their 1696 recoinage. Out of the Gresham pan into the Gresham fire, so to say, since Newton and Locke's fix only led to a different, and just as debilitating, encounter with Gresham's law — the flight of all silver out of Britain.

Over the centuries, a number of technical fixes have been devised to fight silver coin shortages. By milling the edges of coins, clipping would be more obvious to the eye, thereby deterring the practice. High quality engravings, according to Selgin (pdf), rendered counterfeiting much more difficult. Selgin also points out that the adoption of restraining collars in the minting process created rounder and more uniform coins. Adding alloys to silver and gold strengthened coins and allowed them to circulate longer without being worn down. These innovations helped to prevent, or at least delay, a distinction between good and bad money from arising. As long as degradation of the existing coinage could be forestalled by technologies that promoted uniformity and durability, any new coins made to the official standard would be no better than the old coins. New coins could now circulate along with the old, reducing the incidence of coin shortages. Gresham's law had been cheated.*

Let's bring this back to modern money. As I wrote earlier, Gresham's Law is free to operate the moment that the unit of account is defined with reference to two different mediums rather than just one. In the case of bimetallism, the pound was defined as a certain amount of silver and gold, whereas in a pure silver system the unit was defined in terms of old debased silver coins and new full bodied silver coins. In our modern economy, £, $, ¥ are defined in terms two different mediums—central bank deposits and central bank notes. 

Normally this dual-definition of modern units doesn't cause any problems. However, when economic shocks hit a central bank may be required to reduce interest rates to a negative level in order to execute monetary policy. Say it attempts to do so by setting a -5% interest rate on central bank deposits. The problem is that bank notes will continue to yield 0% since the technical wherewithal to create a negative rate on cash has not yet been developed. This disparity in returns allows a distinction between good and bad money to suddenly emerge. Just as full-bodied silver coins were prized relative to debased silver coins, the public will have a preference for 0% yielding cash over -5% yielding deposits. It's Gresham's Law all over again, with a twist...

...when rates fall to -5% it isn't the bad money that chases out the good, but the mirror image. Everyone will convert bad deposits into good cash, or, as Miles describes it, we get massive paper storage. All deposits having been converted into cash, the central bank loses its ability to reduce interest rates below 0% — it has hit the zero lower bound.

In this case, the reason that the good drives out the bad rather than the opposite is because a modern central bank promises to costlessly convert all notes into deposits and vice versa at a 1:1 rate. If bad -5% deposits can be turned into good 0% notes, who wouldn't jump on the opportunity?

To make our analogy to previous standards more accurate, consider that this sort of "reverse-Gresham effect" would also have arisen in the medieval period if the mint had promised to directly convert debased silver coinage into good coins at a 1:1 rate.** As it was, mints typically converted metal into coin, not coin into coin. If mints, like central banks, had offered direct conversion of bad money into good, everyone would have jumped at the opportunity to get more silver from the mint with less silver. Good coin would have rapidly chased bad coin out of circulation as the latter medium was brought to the mint. In offering citizens such a terrific arbitrage opportunity, the mint could very quickly go bankrupt.

Here's a medieval-era example of the "reverse Gresham-effect". When it called in the existing circulating silver coinage to be reminted in 1696, Parliament decided to accept these debased coins at their old face value rather than at their actual, and much diminished, weight. In the same way that everyone would quickly convert bad -5% deposits into good 0% cash given the chance, everyone jumped at this opportunity to turn bad coin into good. John Locke criticized this policy, noting that upon the announcement, clippers would begin to reduce the existing coinage even more rapidly. After all, every coin, no matter how debased, would ultimately be redeemed with a full bodied coin. Why not clip an old coin a bit more before bringing it in for conversion? Even worse, since the recoinage was to take two years, profiteers could repeatedly bring in bad coin for full bodied coin, clip their new good coins down into bad ones, and return them to the mint for more good coin. Locke pointed out that this would come at great expense to the mint, and ultimately the tax-paying public. [For a good example of Locke's role in the 1696 recoinage, read Morrison's A Monetary Revolution]

Just as the reverse-Gresham effect would cripple a mint, allowing free conversion of -5% deposits into 0% notes would be financial suicide for a bank. As I've suggested here, any private note-issuing bank that found it necessary to reduce rates below zero would quickly try to innovate ways to save themselves from massive paper conversion. Less driven by the profit motive, central banks have been slow to innovate ways to get below zero. Rather, they have avoided the reverse-Gresham problem by simply keeping rates high enough that the distinction between good and bad money does not emerge.

In order to allow a central bank to set negative rates without igniting a reverse-Gresham rush into cash, Kimball has proposed the replacement of the permanent 1:1 conversion rate between cash and deposits with a variable conversion rate. Now when it reduces rates to -5%, a central bank would simultaneously commit itself to buying back cash (ie. redeeming it) in the future at an ever worsening rate to deposits. As long as the loss imposed on cash amounts to around 5% a year, depositors will not convert their deposits to cash en masse when deposit rates hit -5%. This is because cash will have been rendered equally "bad" as deposits, thereby removing the good/bad distinction that gives rise to the Gresham effect. The zero lower bound will have been removed.

To summarize, Kimball's variable conversion rate between cash and deposits is a technical fix to an age-old problem. Gresham's law (and the reverse-Gresham law) kick in when the unit of account is defined by two different mediums, one of which becomes the "good" medium and the other the "bad". When this happens, people will all choose to use only one of the two mediums, a choice that is likely to cause significant macroeconomic problems. In the medieval days, it led to shortages of small change. Nowadays it prevents interest rates from going below 0.

In this respect, Miles's technical fix is no different from the other famous fixes that have been adopted over the centuries to reduce the good vs bad distinction, including milled coin edges, high quality engravings, alloys, mint devaluations, and recoinages. Milled edges may have been new-fangled when they were first introduced five centuries ago, but these days we hardly bat an eye at them. While Miles's suspension of par conversion may seem odd to the modern observer, one hundred years from now we'll wonder how we got by without it. In the meantime, the longer we put off fixing our modern incarnation of the Gresham problem, the more likely that future recessions will  be deeper and longer than we are used to — all because we refuse to innovate ways to get below zero.

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*Debasing the mint price, or the amount of silver put into new coins (other wise known as a devaluation, explained in this post), was another way to ensure that old and new silver coins contained the same amount of silver. A devaluation rendered all new coin equally "bad" as the old coin, ensuring that Gresham's law was no longer free to operate. In addition to devaluations, constant recoinages re-standardized the nation's circulating medium. Much like a devaluation, a recoinage removed the distinction between good and bad coins, at least for a time, thereby nullifying the Gresham effect and putting a pause to coin shortages.

** In a bimetallic setting, the process would have worked like this. Say that the mint promised to redeem gold with silver coins and vice versa at the posted fixed rate. When this rate diverges from the market, buyers needn't send the overvalued coin overseas to secure a market price. They only had to bring all their overvalued coins (the bad ones) to the mint to exchange for undervalued ones (the good ones), until at last no bad coins remained. Thus the good drives out the bad. In the meantime, the mint would probably have gone out of business.

Was coin debasement always bad?

Dante's 8th level of hell, which housed counterfeiters, among others. Illustration by Doré

In this post I'll argue that debasement wasn't necessarily a bad thing. Periodic debasements initiated by a prince may have been a wise solution to a certain set of problems imposed on an economy by the nature of coins.*

Debasement is a reduction in the metallic content of a realm's unit of account. Most descriptions of debasement focus on the prince's role in the affair. This is usually a sordid story. The prince would have his mint surreptitiously reduce the amount of silver it put in coin. Next he and his friends would bring some quantity of silver bullion to be coined at this new rate, then quickly spend the coins before the public had the chance to learn about the debasement and defensively raise their prices. The prince and his gang gained at the expense of others.

But the prince was rarely the only debaser. Much like the prince, the public actively tried to improve their position by reducing the silver content of coin. They did so by clipping and counterfeiting coin. The latter is self explanatory. In the former, a clipper used scissors to remove small bits off the edges of each coin he or she received before passing them off. The clipped bits could be melted down and turned back into new coins, earning the clipper a good return.

Though clipping and counterfeiting were fraudulent, the public also engaged in non-fraudulent debasement by contributing to the natural wearing-out of coin. The constant passage of coins from hand to hand, clinking together in pockets and purses, etc steadily reduced the metallic content of coin below its stipulated amount.

To simplify matters, let's assume that the royal mint adopted the practice of milling the edges of coin. A clipp'd coin would quickly be outed if its milled edge was scarred, and therefore would cease to circulate. And say that the prince outfitted the mint with good technology and skilled engravers so as to prevent counterfeiting. Having removed the influence of clipping and counterfeiting, this leaves a natural rate of debasement of a realm's silver coinage due to wear & tear of, say, 1% a year.

Two stylized facts about the medieval economy. Mints fixed the number of coins they would cut from a given weight of silver brought to it by any member of the public. A merchant's pound of silver, for instance, might be coined by the mint into 240 pennies so that each penny held 1/240th a pound of silver. The mint, in other words, set the standard. The second stylized fact is that silver coins usually circulated by tale, not by weight. Just as in modern times, shopkeepers accepted coins by looking at their face in order to ascertain their value, not by weighing them on a scale.

So why might princely debasement be a boon in this environment? A perverse interaction between the mint's fixed standard and the constantly deteriorating coinage might emerge. As the coinage was debased by regular and legitimate public use, prices in terms of the unit-of-account would slowly be bid up. Each year a given coin, which now contained less silver, would buy less consumption than before. The twin demands of a higher price level and population growth required that more coin be produced to satisfy the population's expanding transactional demand.

However, our first stylized fact interfered with this process. Any silver brought to the mint would be turned into new coins at the fixed standard of 1/240th pounds of silver per penny. This meant that new coins would effectively contain more silver in them than already-circulating coins which, having undergone a few years of wear and tear, might contain by then only, say, 1/300th pounds of silver.

Once coined, the new and heavier coins *should* have commanded a premium in the market thanks to their higher silver content. Shopkeepers, for instance, might have quoted a higher price in terms of old coins and a lower price in new coins. However, as per our second stylized fact, coins in medieval times circulated by tale, not weight, and therefore a buyer could not get a better price when paying with new coins.

The inability of new coins to purchase the correct market equivalent in goods meant that they were artificially undervalued. All new coins that were brought into circulation would quickly be hoarded, melted down, and sent overseas where the silver therein could purchase a more appropriate real quantity of goods. The effect this had was that no new coins were put into circulation. It made no sense for a member of the public to bring silver bullion to the prince's mint to be coined since the resulting coin would always purchase less than it would have if left in raw bullion form.

This is Gresham's law. The bad, or artificially overvalued silver coin, pushes the good, or undervalued silver coin, out of the realm.

Since citizens no longer saw it fit to bring their silver to the mint to get coin, coin shortages would develop. To meet transactional demand, existing coins would exchange at ever higher velocities, but this would only debase them further, exacerbating the problem.

One answer to this problem would be for the prince to change the mint price in order to encourage people to once again bring silver bullion to the mint. For this to happen, the old standard of 1/240th a pound of silver per penny had to be reduced to a rate equivalent to the silver content of existing circulating coinage. In essence, to relieve the shortage of coin the prince needed to debase the standard. By reducing the amount of silver in a newly minted coin to, say, 1/300th pounds of silver, citizens would once again find it worthwhile to return to the mint. Since new coins now contained the same silver quantity as old coins, they would circulate together with their older counterparts rather than be subject to Gresham's law.

As long as the prince periodically debased the standard in order to keep up with the natural wear & tear of coins, then the supply of coin would be kept in line with the demand. Princely debasement could be a solution to a very real problem. To say that it could be a good solution, however, doesn't mean that all debasements were benevolent and/or beneficial.**

My justification of princely debasement of coinage as good policy in some way parallels the modern justification for fiat debasement as good policy. Sure, we can always attribute certain malign motives to central bank debasement. A central bank might surreptitiously monetize a government's debt at subsidized prices to help it pay for wars, thus causing high inflation. But there are some very good reasons to ensure that currency is constantly falling in purchasing power. The higher the rate of inflation, the lower the chance of running into the zero-lower bound. And if nominal wages are sticky downwards, then a positive inflation rate will ensure that wages adjust more easily on a real basis should the necessity arise. That debasement could be simultaneously both a good and predatory policy makes it a somewhat difficult topic to unpack.

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* Much of this post echoes a comment left by Mike Sproul in my last post on medieval coinage.

**We shouldn't idealize princes as wise monetary doctors. Munro has noted that while princely debasement may have helped solve coin shortages, the motives for debasement were usually personal gain. In medieval times, a large component of a prince's revenues came in the form of seigniorage from his mint. If the standard was kept too high relative to the ever-deteriorating silver content of circulating coin, the mint would do no business and this would impair the prince's revenues. By periodically reducing the standard, the prince could ensure that business would return to the mint and seigniorage restored.

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.