The lower limit to silver's usefulness in coinage

A detectorist in Suffolk, England recently found a beautiful halfpenny minted some time between 1625-1649, during the reign of King Charles I. This coin, captured in the video below, illustrates an important feature of coinage: the lower limit to silver's usefulness as a monetary metal.

As you can see, the halfpenny is tiny compared to the fingers holding it, which would have made it difficult to count, handle, and transfer. Storing it away in a pocket or purse would have been a nuissance, since it might have gotten lost in the folds.

Just chilling this afternoon and pottering about.
So here's a lovely little Charles I halfpenny, simple yet elegent ☺️

Found 2020https://t.co/PiKJjooe7D pic.twitter.com/87BRG2s69u

— Suffolk Detectorist (@SDetectorist) June 11, 2023

The root of the problem is that silver has always had a relatively high value-to-weight ratio, (i.e. it is good at "condensing value," as I once described here) and so attempts to embody lower denomination coins with silver don't function very well, since what is required for low denominations is a material that dissipates rather than condenses. Silver change is just too damn small.

According to the Portable Antiquities Scheme, this particular halfpenny – which is in great shape – weighs 0.27 grams and has a diameter of 10 mm. Compare that to a U.S. dime, already annoyingly small, which weighs 2.3 grams and has a diameter of 18 mm. Doing the calculation for you, a modern dime weighs almost ten times (!) as much as a Charles I halfpenny.

How much was a halfpenny worth in 1625? In short, I'd describe it as the dollar bill of its day.

In England, one penny could buy a penny loaf of bread, the weight of which was regulated by law. In Sheppard and Newton's The Story of Bread (1957), a loaf weighing 4 pounds would have cost 5 pennies in London in 1625. These days, a loaf sold in a grocery aisle usually weighs around 1 pound, so putting things into a modern context, a single 1625 penny was capable of buying one modern-day loaf of bread, and so a halfpenny was worth half a modern-day loaf. Given that a loaf currently retails at Walmart for around US$2 to US$2.50, that means a halfpenny was equivalent to a dollar bill, give or take.

As the dollar bill of its day, a halfpenny would have served a crucial role in England's day-to-day commerce. But being so delicate, it must have done a poor job of it. Even worse would have been the silver farthing, England's smallest coin, worth a quarter-penny, or half a halfpenny. "A still more egregious case [of too small coins] was that of the silver farthings the Royal Mint issued in 1464. Weighing only three troy grains each, these were 'lost almost as fast as they were coined,'" writes George Selgin in Good Money.

How to solve silver's inability to serve as a good medium for lower-denomination coinage? Here's one of the attempts made by the minting authorities:

Halfpenny of King James II, 1687. Source: Yale University Art Gallery

This James II halfpenny is what is called token coinage. Minted out of tin, which had a very low value, a token coin such as this one was worth far more than the amount of tin residing in it. What gave it its value isn't the metal within, but James II's promise to repurchase the coin at its stipulated rate of a half-penny's worth of silver.

Unlike Charles I's feather-light 0.3 gram halfpenny, James II's halfpenny had some heft to it. Weighing in at 10.11 g, which is equal to two modern American quarters, there was no losing track of this beast. The tin halfpenny would certainly have served as a more durable dollar bill of its day than a Charles I silver halfpenny.

Alas, while tokens such as James II's tin halfpennies solve the too-small problem, they introduce a new problem: counterfeiting. Because the amount of metal in a halfpenny was so cheap relative to the face value of the halfpenny, it would have been very profitable for fraudsters to manufacture fakes. Which is indeed what happened. By the middle of the 18th century, close to half of all the farthings and halfpennies, all of which were token coins by then, were counterfeits, according to Selgin (pg 20).

To counter the counterfeiters, James II's 1687 halfpennies have a strange feature on them: a small copper plug. In the image above this plug has fallen out, but this link illustrates what a complete coin would have looked like. By adding a plug to the coin, mint officials were trying to increase the complexity and thus the cost of manufacturing fakes, thus reducing their attractiveness to fraudsters. In concept, we can think of these plugged halfpennies as a clumsy predecessor to Canada's toonie, which has a nickel outer rim and an aluminum-bronze central plug.

Alas, James II's tin halfpennies never worked out. The tin was quick to erode and the copper plug was prone to falling out. If the solution to silver's lower limit was to make token coinage, better to manufacture those tokens out of a tougher substrate like copper. By the 1690s, England's tin halfpenny experiment had ended.

Why Henry III's gold penny failed

English gold penny minted by Henry III in 1257

A lucky metal detectorist just discovered a Henry III gold penny, one of the first English gold coins ever minted, on a farm in Devon in the southwest part of the U.K. My favorite thing about detectorist findings is that they give us a good excuse to learn about old coins. 

Minted in 1257, only eight of Henry III's gold pennies (pictured above) have survived. This is odd given that medieval historian David Carpenter's analysis of historical records indicates that 72,000 of these coins may have been produced within a year or two.

Why are there so few of Henry III's gold pennies still in existence? In this short post I'll suggest that the gold penny was a failure. Rather than circulating in trade, as one would expect of a coin, most of them were melted down within a year or two after issuance. And so there are very few gold pennies left for detectorists to find.

Leading up to the 1200s, the demands of English trade for coinage was mostly met by the workhorse English silver penny. Because the yellow metal was expensive, gold coins fell outside of the day-to-day spending range of the average person.

But Europe was getting wealthier and this was creating more demand for higher denomination coins. According to Alexander Del Mar, gold bezants were already circulating in England by the 13th century (page 236, [pdf]). Minted by the Byzantines, bezants had dominated Mediterranean commerce since 300 AD or so (see Munro). To boot, a handful of 11th- and 12th-century Islamic gold dinars and dinar-inspired coins have been found in England, writes historian Caitlin Green in a blog post, further suggesting a nascent demand for high-value coinage (see photo below). Del Mar cites texts from the era mentioning the circulation of Spanish maravedis, a gold dinar copycat.

Arabic gold dinar (AD 1163-84) found in Suffolk [link]

Meanwhile, the Italian city states of Genoa and Florence had begun to mint their own gold coins in 1252, the Florin and the Genovino. In the century before these two cities had pioneered the creation of large silver coins, the grosso or groat (worth 12 silver pennies) which England had yet to copy.

And so Henry III may have been eager to issue his own gold coin, one with his face on it and not someone else's stamp. But his effort failed .

When Henry III issued his gold penny, he rated it to be worth 20 silver pennies. That is, if you were an English merchant in 1256 you were required to accept a new gold penny from a customer at the same rate as 20 silver pennies. As a backstop, Henry III himself promised to redeem the gold pennies at 19 and a half pennies, the other half-penny being a fee. (See Evans, The First Gold Coins of England.)

In bimetallic coin systems, it was crucial for the monarch to choose the proper exchange ratio between silver and gold coins. If the chosen ratio diverged from the market's gold-to-silver rate, then Gresham's law kicked in. Undervalued coins disappear from circulation because they could be better spent elsewhere at their true market metal price.

In his paper Gold and Gold Coins in England in the Mid-thirteenth Century, Carpenter maintains that Henry III picked the right ratio between gold pennies and silver pennies.  A gold penny weighed the same as two silver pennies. At Henry III's chosen exchange rate of twenty silver pennies to one gold penny, this implied a price of ten grams of silver to one gram of gold. Carpenter says that this was in line with the prevailing 10:1 market rate between silver and gold bullion at the time.

But historian John Munro suggests otherwise. What Carpenter omits is that an English silver penny was only 92.5% pure, the remaining 7.5% being comprised of base metals. This means that Henry III's chosen exchange rate of twenty silver pennies to one gold penny actually valued the quantity of gold inside a gold penny at just 9.3 times that of an equivalent amount of silver, not 10 times.

Thus the king's chosen rate undervalued gold. And so Henry III's gold penny would have run smack dab into Gresham's law. It would have been more profitable for an English merchant to melt down 1 kg of gold pennies into bullion and buy 10 kg of silver with the proceeds at the going market rate than to spend that 1 kg of gold pennies as coins (since that would mean getting the equivalent of just 9.3 kg of silver).

Put differently, an English arbitrageur could engage in the following set of trades to make a risk-free return. He or she could spend 9.3 kg of silver coins to get 1 kg of gold pennies at Henry's official rate. Then they could melt that 1 kg of gold coins down and sell the gold bullion for 10 kg of silver at the market rate. Voila, our arbitrageur has magically turned 9.3 kg of silver into 10 kg of silver, earning a free 0.7 kg in silver. They would continue to execute this trade until the entire stock of Henry III gold pennies had disappeared.

There is additional evidence of the undervaluation of the gold penny. In 1265, just eight years after initially issuing them, Henry III increased the gold penny's rated value to 24 pennies from 20 pennies, writes Kemmerer (Gold and the Gold Standard, 1944). This rating would have been more in line with the market rate between gold and silver. But by then it was probably too late. All of Henry III's original issue of gold pennies would have been melted down. Nor was he minting any new ones. Specimens like the coin found this year in the farmer's field in Devon would have been one of a few to escape the melting pot. 

As for England's monarchs, they would only get gold coinage right in 1344 with the successful issuance of the gold noble.

Failed monetary technology

Archaic and ignored monetary technologies can be very interesting, especially when they teach us about newer attempts to update our monetary system. I recently stumbled on a neat monetary innovation from the bimetallic debate of the late 1800s, Nicholas Veeder's Republic of Eutopia coin:

During the bimetallic debates of the late 1800s, one of the more interesting compromises put forward was Nicolas Veeder's cometallic standard. His model 'Republic of Eutopia' coins (1866) had a plug with 12.9 grains of gold and ring with 206¼ grains of silver. A good idea or no? pic.twitter.com/6eZN2YAq6o

— JP Koning (@jp_koning) May 28, 2018

If you've read this blog for a while, you'll know that I like to talk about monetary technology. Unlike financial technology, monetary tech involves a technological or sociological upgrade to the monetary system itself. And since we are all unavoidably users of the monetary system—we all think and calculate in terms of our nations unit of account—each of us is immediately affected by the change.

Veeder's Eutopia coin is an old monetary technology that was never adopted. More recent examples of unadopted (or as-yet not adopted) montech include Fedcoin, NGDP futures targeting, or Miles Kimball's technique for evading the zero-lower bound, which would decouple the value of paper money from electronic money. Examples of recent monetary tech that went on to be adopted include the switch from paper to plastic banknotes, the replacement of older end-of-day clearing systems to real time gross settlement systems, and inflation targeting.

Fintech is more limited in scope than monetary tech. Only that portion of the population that uses these innovations is affected—everyone else's financial habits continues on as before. Recent examples include bitcoin, p2p lending, and roboadvisors. (If bitcoin ever became the standard unit of account, it would have made the trek over to becoming monetary technology, and not just fintech.)

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To make sense of Veeder's Republic of Eutopia coin, we need to understand the problem that his monetary innovation was meant to solve. Most nations were on a gold standard by the 1870s, and with the price of gold rising, the world price level was generally falling. This development provided an unexpected boost to the creditor class, who were owed gold, while hurting the debtor class, who owed gold. A higher price for the yellow metal meant that the loan contract to which a debtor had signed their name now required them to work that much harder to pay it off.

In that context, a broad popular movement for the remonetization of silver emerged. Prior to being on gold standards, nations were generally on a pure silver standard or a bimetallic standard. On a gold standard the debtor class had only one way to settle the debt, by providing the proper amount of gold coins. But if silver coinage was reintroduced at the old rate of sixteen-to-one, debtors could instead sell their labour to buy cheap silver, have it minted into legal tender silver coins, and use those silver coins to pay off the debt. Paying their debts with silver rather than gold meant they'd have a bigger amount of wealth remaining in their pocket.

The movement to restore bimetallism wasn't purely a populist one. The smartest economists of the time--folks like Irving Fisher, Leon Walras, and Alfred Marshall--also preferred bimetallism. A bimetallic standard recruits more monetary material into service than a gold standard. This is advantageous because, as Fisher put it, it "spreads the effect of any single fluctuation over the combined gold and silver markets." In other words, the evolution of the price level under a bimetallic system should be more stable—and thus more fair—than under a monometallic system, since it can absorb larger shocks.

The problem with bimetallism is that it very quickly runs smack into Gresham's law. The traditional way to bring the two metals into service as monetary material was to offer to mint both high denomination gold coins and lower denomination silver coins. So if a merchant needed £20 worth of coins, he could bring either a chunk of raw gold to the mint, or an even bigger chunk of pure silver, and the mint would convert either chunk into £20 for him. The specified amounts of raw silver or raw gold that were required to get a certain number of £-denominated coins constituted the mint's official gold-to-silver exchange rate.

Inevitably the market's gold-to-silver exchange rate would diverge from the mint's official exchange rate, effectively over- or undervaluing one of the two metals. In this situation, no one would bring any of the overvalued metal to the mint to be turned into coins. After all, why bother minting a chunk of gold (assuming the yellow metal was the overvalued one) into £20 worth of coins if that same amount of gold has far more purchasing power overseas? The overvalued metal would thus disappear as it was hoarded and exported, leaving only the undervalued metal in circulation. A monometallic standard had accidentally emerged, and all the benefits of bimetallism were for not.

To prevent Gresham's law from being engaged, the mint had to constantly adjust its official rate so that it stayed in-line with the ever-evolving market rate. Not only would these changes have been politically costly, but they would required an expensive series of recoinages in order to ensure that coins always had the proper amount of silver or gold in them.

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Enter Veeder's Eutopia coin. Nicholas Veeder was no economist, but an executive at C.G. Hussey, a copper rolling mill in Pittsburgh. In 1885, he published a pamphlet with the wordy title Cometallism: A Plan for Combining Gold and Silver in Coinage, for Uniting and Blending their Values in Paper Money and For Establishing a Composite Single Standard Dollar of Account.

Rather than defining a dollar as simultaneously a fixed amount of gold OR a fixed amount of silver, Veeder's pamphlet suggested defining it as a fusion of the two together. Specifically, Veeder's dollar was to contain 12.9 grains of gold AND 206.25 grains of silver. It's worth noting that under a proposed cometallic standard, paper dollars needn't be redeemed with actual Eutopia coins, but could be converted into separate silver and gold bars or coins. The important rule was that each dollar's worth of debt had to be discharged with 12.9 grains of gold and 206.25 grain of silver.

A model of a cometallic gold certificate, from page 60 of Veeder's pamphlet on cometallism

Veeder's cometallic scheme was a neat way to keep all the benefits of bimetallism with none of its drawbacks. Cometallism would draw on the combined supplies of the gold and silver markets, so that the system would be much more elastic than a pure gold standard, and thus fairer to both creditors and debtors. At the same time, Gresham's law would be avoided. Under traditional bimetallic coin systems, the mint established an exchange rate between the two metals. This rate inevitably became the system's undoing when it diverged from the true rate.

But a mint that was operating under a cometallic standard would only accept fixed quantities of silver AND gold before it would mint a $1 coin, and so it would no longer be setting an exchange rate between the two precious metals. The undervaluation of one of the metals, a key ingredient for Gresham's law, could never emerge under cometallism.

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A year after Veeder published his pamphlet, Alfred Marshall—one of the world's leading economists—described a remarkably similar system. Here is part of his response to the Royal Commission on the Depression in Trade and Industry in 1886, which had been convened to address the Long Depression:

"I propose that currency should be exchangeable at the Mint or Issue Department not for gold, but for gold and silver, at the rate of not £1 for 113 grains of gold, but £1 for 56^ grains of gold, together with, say, twenty times as many grains of silver. I would make up the gold and silver bars in gramme weights, so as to be useful for international trade. A gold bar of 100 grammes, together with a silver bar, say, twenty * times as heavy, would be exchangeable at the Issue Department for an amount of the currency which would be calcalated and fixed once for all when the scheme was introduced. (It would be about .€28 or .€30 according to the basis of calculation)."

Marshall's proposal was later dubbed symmetallism. (I wrote about it here.) If you study monetary systems, you'll run into the gold & silver basket idea sooner or later. The concept is invariably refereed to as symmetallism (and not cometallism) and attributed to Marshall (not Veeder). In the 1800s academics were not required to provide references, and from what I understand plagiarism was rampant. Did Marshall develop his idea separately from Veeder, or did he rip it off? Whatever the case, Veeder was an unknown executive at a small manufacturing concern, whereas Marshall a world famous academic. Celebrity carried the day.

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Interestingly, Veeder himself probably borrowed the idea, or at least part of it, from someone else. Almost a decade earlier, William Wheeler Hubbell had tried to get the U.S. congress to adopt the so-called "goloid dollar," a coin containing silver and gold alloyed together.

Another proposed fix was William Hubbell's "goloid" metric dollar (1878). This specimen is 1 part gold, 16.1 parts silver, and 1.9 parts copper. Whereas Vedeer's dollars kept the metals apart, Hubbel's intermingled them. https://t.co/qXpE7EbQrk pic.twitter.com/csNahz1Hhq

— JP Koning (@jp_koning) May 29, 2018

Hubbell owned the patent to the goloid alloy, so he would have made a good profit if the goloid dollar had been adopted by the U.S. Treasury. Unlike Veeder, Hubbell doesn't seem to have been a very good monetary economist, and the case he makes for goloid misses much of nuances of the benefits of bimetallism and the hazards of Gresham's law. He lists a number of advantages for his proposed coin, including: superior durability to gold and silver coins; not susceptible to oxidization (unlike silver); a goloid dollar was smaller than a silver dollar and thus more convenient for consumers to carry around; the mint would be able to make more goloid dollars than silver dollars with its existing capacity; and goloid coins could not be easily melted down for usage in the arts as was the case with gold and silver coins.

Hubbell's idea foundered on the fact that a goloid coin, despite containing gold, has almost the exact same colour as a silver coin. Hubbell's critics believed this set the coin up to be widely counterfeited. A counterfeiter could make a replica with lower gold content, this alteration unlikely to be noticed by the public since the colour of a genuine goloid coin and the fake would be the same.

The difficulties that Hubbell experienced alloying gold and silver were not lost on Veeder. In has pamphlet he mentions that "my first approach, as with many other persons, was to combine the two metals as an alloy for coinage, but, owing to certain difficulties... this idea was soon considered impracticable and abandoned." To avoid Hubbell's color problem, Veeder ended up mechanically wedding the two metals rather than chemically combining them, the Eutopia coin being comprised of a ring of silver and a gold plug embedded inside.

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The topic of goloid and Eutopia dollars seem a bit obscure, but the issues of stability and fairness that concerned monetary technologists in the late 1800s remain relevant today.

Today, most western central banks define the national currency in terms of a basket of consumer goods and services rather than a fixed amount of gold (gold monometallism) or a basket of gold & silver (cometallism, symmetallism). This makes a lot of sense. If we want to create a stable monetary standard, one that provides creditors and debtors with an even playing field, better to use a broad basket of stuff that regular people buy than a narrow basket of metals. That way all parties to a contract know many years ahead of time exactly how much consumer goods they will get (if they are creditors) or give up (if they are debtors). Knowing how much gold and silver baskets they will owe or be owed is less relevant to the average person, since gold and silver are a very small part of most people's day-to-day consumption profiles.

There is an important debate going on today about whether to continue defining national currencies in terms of a consumer goods & services basket, or whether to move to something more fluid like a nominal gross domestic product (NGDP), or output. One problem with using a consumer goods basket is that, in the event of a large economic shock that leads to significant loss of jobs, debtors take on all the macroeconomic risk. After all, they owe just as many CPI baskets as before, but have less capacity to meet that obligation because they might not have a job. This doesn't seem like a fair splitting up of risks and rewards.

The nice thing about defining the national currency in terms of NGDP, or output, is that the risk of a large shock, and the associated loss of jobs, is shared between creditors and debtors. This is because if a recession occurs, debtors will owe a smaller amount of real wealth to creditors than they otherwise would. And during a boom, when the job offers are rolling in, creditors will owe more.

Cometallism was never adopted. Perhaps it was a bit too fancy. NGDP is a bit exotic too, but then again so were many forms of monetary technology, until they were actually adopted and became part of the background. We'll have to see what happens.

A 21st century U.S. trade dollar

"America's only unwanted, unhonoured coin." 

- John Willem on the silver trade dollar.

The inspiration for this post comes from the old trade dollar, a U.S. silver coin that was minted in the 1870s and 1880s for the sole purpose of circulating in China. Taking the trade dollar as a model, I'm going to discuss the idea of converting the U.S. $100 bill into a trade bill; i.e. to limit it to foreign and not domestic usage.

Why bother modifying the $100 in this way? While not entirely convinced, I do lean towards Ken Rogoff's idea of getting rid of high denomination banknotes like the Canadian $100, the Swiss 1000 franc, and the Europe's €500. These bills are used primarily by criminals and tax evaders; their removal will make these activities more costly. The public's licit demand for a private means of payment can be met by low denomination notes, as can the necessity for a convenient physical payments medium on the part of the unbanked.

But as I wrote here, the Federal Reserve's $100 is categorically different from the above banknotes. The dollar plays a special role as the world's backup medium of exchange and unit of account. Abolish the $100 and not only will those dollarized countries already using U.S. banknotes (many of them poor) be hurt, but so will the desperate citizens of foreign countries who might try to flee to the dollar in the future due to the awful monetary policies of their leaders, usually dictators.*

By converting the $100 into a trade bill, everyone can have their cake and eat it too. Like the old silver trade dollar, the $100 trade bill will be barred from playing a role in the U.S. economy, thus doing damage to the domestic underground economy. But it will be free to be used in places like Venezuela which, thanks to misgovernance, are in urgent need of a better monetary standard.

To help determine the structure of a modern $100 trade bill, let's explore the design of the 19th century silver trade dollar. China had a long history of using silver as money, and as trade with the west grew the Spanish silver dollar—minted in Mexico—had become quite popular with Chinese merchants. U.S. traders were penalized as they had to acquire Mexican dollars at a premium to the coin's intrinsic silver value in order to do business with China. Enter the trade dollar. The idea was to introduce a U.S. equivalent to the Mexican dollar in order to help out U.S. merchants, who would no longer have to pay a premium. The trade dollar would also provide domestic silver producers, an important political constituency, with an outlet for their production.

While U.S. legislators liked the idea of having U.S. silver coins circulate overseas, they did not want the trade dollar to be used in the U.S. After all, the U.S. was in the midst of giving up the old bimetallic standard (silver and gold) in favour of a gold standard, and a new silver coin might interfere with this process.

Thus, we arrive at the Coinage Act of 1873, which simultaneously took the U.S. off of silver (by ending the free coinage of silver) while also introducing the trade dollar. To ensure that the trade dollar would not be "made a part of or be in any way confounded with our monetary system," its legal tender status was limited to $5 i.e. no domestic debt could be extinguished with more than $5 in trade dollars (for a review of legal tender, go here). To further hurt its domestic usefulness, this legal tender status would be completely revoked in 1876.

While the trade dollar was well-received in China (most of them were chopped), it wasn't entirely successful in staying out of domestic U.S. circulation. According to Garnett, of the $35.9 million in trade dollars coined, $29.4 million were exported. Of this amount, $2.1 million returned to the U.S., joining the $6.6 million that had never left the country.

It's important to understand why trade dollars sometimes stayed in the U.S.—after all, the idea of a trade bill simply won't work if $100 notes continue circulating in the U.S. There seems to be two reasons for this. From 1873 until 1876, trade coins still had a limited value as legal tender. At first, this wasn't an issue. Since the intrinsic value of the coins' silver content exceeded their official legal tender value, it made little sense for Americans to use them to settle local debts—debtors would be effectively overpaying if they did so. However, as silver prices fell through the 1870s the official legal tender value of trade dollars began to exceed their intrinsic value, at which point it was profitable for debtors to pay off their bills in overvalued silver trade dollars. This would have diverted trade dollars from China in order to meet local demand.

Secondly, speculators began to buy trade dollars in China and bring them back home on the expectation that the U.S. government would eventually redeem them at their original value of $1, even as they traded at around 80 cents on the dollar. This belief was eventually realized in 1887 when Congress compelled the government to redeem all trade dollars at par.

So with these design flaws in mind, let's design our $100 trade bill. To begin with, on January 1, 2017 the U.S. government will announce  its intention to rescind the legal tender status of $100 bills. That means the $100 can no longer be used by a debtor to discharge any U.S. debt. Legal tender status must be entirely rescinded to avoid the mistakes of the trade dollar.

Next, the Federal Reserve announces that after a certain date (say January 1, 2019), all domestic deposits and withdrawals of $100 notes will be illegal. Until then, the public enjoys a two-year window for bringing bills into banks or Federal Reserve branches for conversion into $20 bills or deposits. To prevent local hoarding of $100 bills, the domestic closure of the "$100 window" must be perceived to be permanent. Remember that trade dollar inconvertibility was perceived to be temporary, thus encouraging domestic demand. Likewise, if they anticipate a re-opening of the "$100 window," Americans will simply keep their $100s at home.

Banning local redemption will likely force all local retailers, wholesalers, and other businesses to stop accepting $100 bills. A retailer like Walmart that receives a $100 bill during the course of business will have to ship it overseas to be spent or deposited, and that would be quite expensive. Likewise, licit person-to-person exchanges of $100s will be crimped. Lacking domestic acceptance by banks and retailers, the $100 will have no liquidity, and regular people will no longer be willing to accept them.

For these same reasons, illicit domestic usage of $100s will suffer. Since no legitimate businesses will accept them, criminals won't be able to spend $100 notes into the local economy. To launder $100 bills, it will now be necessary to send them overseas for deposit into foreign banks. This will impose significant handling costs on money launderers, especially if the government institutes laws that limit large cash exports. These handling costs will  probably be high enough to force domestic illegal currency users to migrate to $20 bills as their preferred medium.

While domestic usage of $100s will rapidly decline, foreign-based banks will be completely free to allow deposits and withdrawals of $100 banknotes, much as they do now. To get $100 notes shipped from the U.S., foreign banks will have to put in orders with a Federal Reserve bank (they tend to prefer the New York Fed's cash office and, in the West, the San Francisco Fed's Los Angeles cash office). To redeposit $100 bills, they will have to send them by plane back to New York.

This setup should be sufficient to flush most $100 bills out of domestic circulation, forcing U.S.-based criminals and tax evaders to fall back on less convenient $20s. And just as the trade dollar successfully met Chinese demand for silver money, the $100 trade bill will meet Panamanian, Zimbabwean, and other foreign demand for U.S. high denomination cash.

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*Rogoff believes that a policy of removing high denomination notes should only be enacted by developed nations. But since so many undeveloped nations use the dollar, Rogoff is being inconsistent in calling for an end to the $100.

To read more about U.S. trade dollars, here are some good sources:
A Trade Dollar Song and Chorus, 1883 (link)
Collecting Trade Dollars (link)
The History of the Trade Dollar (link)

The British (link), Japanese (link), and French (link) also issued trade dollars

Milton Friedman wrote an excellent account of the switch from bimetallism to the gold standard (pdf).

From ancient electrum to modern currency baskets (with a quick detour through symmetallism)

Electrum coins [source]

First proposed by economist Alfred Marshall in the late 19th century as an alternative metallic standard to the gold, silver and bimetallic standards, symmetallism was widely debated at the time but never adopted. Marshall's idea amounted to fusing together fixed quantities of silver and gold in the same coin rather than striking separate gold and/or silver coins. Symmetallism is actually one of the world's oldest monetary standards. In the seventh century B.C., the kingdom of Lydia struck the first coins out of electrum, a naturally occurring mix of gold and silver. Electrum coins are captured in the above photo.

While symmetallism is an archaic concept, it has at least some relevance to today's world. Modern currencies that are pegged to the dollar (like the Hong Kong dollar) act very much like currencies on a gold standard, the dollar filling in for the role of gold. A shift from a dollar peg to one involving a basket of other currencies amounts to the adoption of a modern version of Marshall's symmetallic standard, the euro/yen/etc playing the role of electrum.

The most recent of these shifts has occurred with China, which late last year said it would be measuring the renminbi against a trade-weighted basket of 13 currencies rather than just the U.S. dollar. Thus many of the same issues that were at stake back at the turn of the 19th century when Marshall dreamt up the idea of symmetallism are relevant today.

So what exactly is symmetallism? In the late 1800s, the dominant monetary debate concerned the relative merits of the gold standard and its alternatives, the best known of which was a bimetallic standard. The western world, which was mostly on a gold standard back then, had experienced a steady deflation in prices since 1875. This "cross of gold" was damaging to debtors; they had to settle with a higher real quantity of currency. The reintroduction of silver as legal tender would mean that debts could be paid off with a lower real amount of resources. No wonder the debtor class was a strong proponent of bimetallism.

There was more to the debate than mere class interests. As long as prices and wages were rigid, insufficient supplies of gold in the face of strong gold demand might aggravate business cycle downturns. For this reason, leading economists of the day like Alfred Marshall, Leon Walras, and Irving Fisher mostly agreed that a bimetallic standard was superior to either a silver standard or a gold standard. (And a hundred or so years later, Milton Friedman would come to the same conclusion.)

The advantage of a bimetallic standard is that the price level is held hostage to not just one precious metal but two; silver and gold. This means that bimetallism is likely to be less fickle than a monometallic standard. As Irving Fisher said: "Bimetallism spreads the effect of any single fluctuation over the combined gold and silver markets."  Thus if the late 1800s standard had been moved from a gold basis to a bimetallic one, the stock of monetary material would have grown to include silver, thus 'venting' deflationary pressures.

Despite these benefits, everyone admitted that classical bimetallism had a major weakness; eventually it ran into Gresham's law. Under bimetallism, the mint advertised how many coins that it would fabricate out of pound of silver or gold, in effect setting a rate between the two metals. If the mint's rate differed too much from the market rate, no one would bring the undervalued metal (say silver) to the mint, preferring to hoard it or export it overseas where it was properly valued. The result would be small denomination silver coin shortages, which complicated trade. What had started out as a bimetallic standard thus degenerated into an unofficial gold standard (or a silver one) so that once again the nation's price level was held hostage to just one metal.

The genius of Alfred Marshall's symmetallic standard was that it salvaged the benefits of a bimetallic standard from Gresham's law. Instead of defining the pound as either a fixed quantity of gold or silver, the pound was to be defined as a fixed quantity of gold twinned with a fixed quantity of silver, or as electrum. Thus a £1 note or token coin would be exchangeable at the Bank of England not for, say, 113 grains of gold, but for 56 grains of gold together with twenty or so times as many grains of silver. The number of silver and gold grains in each pound would be fixed indefinitely when the standard was introduced.

Because symmetallism fuses gold and silver into super-commodity, the monetary authority no longer sets the price ratio between the two metals. Gresham's law, which afflicts any bimetallic system when one of the two metals is artificially undervalued, was no longer free to operate. At the same time, the quantity of metal recruited into monetary purposes was much larger and more diverse than under a monometallic standard, thus reducing the effect of fluctuations in the precious metals market on aggregate demand.

While symmetallism was an elegant solution, Alfred Marshall was lukewarm to his own idea, noting that "it is with great diffidence that I suggest an alternative bimetallic scheme." To achieve a stable price level, Marshall preferred a complete separation of the unit of account, the pound, from the media of exchange, notes and coins. This was called a tabular standard, a system earlier proposed by William Stanley Jevons. The idea went nowhere, however; the only nation I know that has implemented such a standard is Chile. As for Fisher, he proposed his own compensated dollar standard plan, which I described here.

The urgency to adopt a new standard diminished as gold discoveries in South Africa and the Yukon spurred production higher, thus reducing deflationary pressures. None of these exotic plans—Marshall's symmetallism, Jevons tabular standard, or Fisher's compensated dollar—would ever be adopted. Rather, the world kept on limping forward under various forms of the gold standard. This standard would be progressively modified through the years in order to conserve on the necessity for gold, first by removing gold coin from circulation and substituting convertibility into gold bars (a gold bullion standard) and then having one (or two) nations take on the task of maintaining gold convertibility while the remaining nations pegged to that nation's currency (a gold exchange standard).

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Let's bring this back to the present. In the same way that conditions in the gold market caused deflation among gold standard countries in the late 1800s, the huge rise in the U.S. dollar over the last few years has tightened monetary conditions in all those nations that peg their currency to the dollar. To cope, many of these countries have devalued their currencies, a development that Lars Christensen has called an 'unraveling of the dollar bloc.'

A more lasting alternative to re-rating a U.S. dollar peg might be to create a fiat version of electrum; mix the U.S. dollar with other currencies like the euro and yen to create a currency basket and peg to this basket. China, which has been the most important member of the dollar bloc, has turned to the modern version of symmetallism by placing less emphasis on pegging to the U.S. dollar and more emphasis on measuring the yuan against a trade-weighted basket of currencies. This means that where before China had a strictly made-in-the U.S. monetary policy, its price level is now determined by more diverse forces. Better to put your eggs in two or three baskets than just one.

Bahrain, Oman, Qatar, Saudi Arabia and United Arab Emirates are also members of the dollar bloc. Kuwait, however, links its dinar to a basket of currencies, a policy it adopted in 2007 to cope with the inflationary fallout from the weakening U.S. dollar. In an FT article from April entitled Kuwaiti currency basket yield benefits, the point is made that Kuwait has enjoyed a more flexible monetary policy than its neighbours over the recent period of U.S. dollar strength. Look for the other GCC countries to mull over Kuwaiti-style electrum if the U.S. dollar, currently in holding pattern, starts to rise again.

Modern day electrum can get downright exotic. Jeffrey Frankel, for instance, has suggested including commodities among the basket of fiat currencies, specifically oil in the case of the GCC nations. Such a basket would allow oil producing countries to better weather commodity shocks than if they remained on their dollar pegs. If you want to pursue these ideas further, wander over to Lars Christensen's blog where Frankel's peg the export price plan is a regular subject of conversation.

A brief history of the Guinea

1685 Guinea with the bust of James II (link)

The guinea makes a fascinating story because its evolution reveals so many different monetary phenomena. It began its life in 1663 in the Kingdom of England as a mere coin, one medium of exchange in a whole sea of competing exchange media that included crowns, bobs, halfpennies, farthings, not to mention all the foreign coins that circulated in England, Bank of England paper notes, as well as the full range of portable property—like jewelery and art—and property-not-so-portable, say houses and land and such. If things had stayed that way, the guinea's life would be a boring one and I wouldn't be writing about it.

But in the late 1600s the guinea crossed a line and became a very different thing. Rather than functioning as just one exchange medium among many, the guinea suddenly emerged as one of Britain's two media of account, the items used to define a nation's unit of account, in this case the £. Within a few decades it had wrested the medium of account function for itself, holding this pre-eminent spot until 1816, at which point the guinea was decommissioned.

Interestingly, while the guinea ceased to exist in 1816, its memory was sufficiently strong that it continued to function as a unit of account, albeit a relatively unimportant one, well into the 1900s. More on that later.

Just a regular coin

Whereas most of England's coinage at the time was silver,  the guinea was a gold coin. Introduced in 1663 during the reign of Charles II, it was initially rated at 20 shillings, or one pound (£), by the monetary authorities (the mint and the king). Pounds, shillings, and pence, or £sd, comprised the English unit of account—the set of signs that merchants affixed to their wares to indicate prices. The pound unit had been defined in terms of silver coins for centuries, but the the decision by the mint to give a 1 pound (or 20 shilling) rating to the guinea meant that the pound would now be dually defined in terms of both gold and silver coins.

However, according to Lord Liverpool, both the public and the authorities ignored this 20 shilling rating so that a market-determined price emerged for the guinea. In this way the guinea was no different from any other item of merchandise; its price floated independently according to the whims of buyers and sellers.

This stands in contrast to England's silver coinage. Silver pennies, halfpennies, and farthings had an extra function; they served as the nation's medium of account. The pound unit, the £, the symbol with which merchants set prices or denominated debts, was defined by the nation's silver coinage. Put differently, by setting a farm's price at £10, a seller was stipulating that the farm was worth the amount of silver residing in a collection of pennies and farthings.

When something serves as the medium of account, it's price doesn't float independently. Rather, the whole universe of other prices shifts to accommodate changes in the value of the medium of account. For example, if the value of silver were to have risen in the 1670s due to increased demand for silver jewelery, then the entire English price level would have had to fall. Alternatively, if the amount of silver in the nation's coinage was debauched, then the English price level would have risen. A change in the demand for gold in the 1670s, however, would have produced an entirely different result; the relative price of the guinea would have shifted, but little else. That's why a medium of account is so special. Unlike all other items, the price of everything pivots around it.

The fact that the guinea's initial 1663 rating had been ignored was very important. Imagine that the authorities had been stern about enforcing it. Returning to our farm example, in setting the farm's price at £10, our seller would have been stipulating that the farm was worth either the amount of sliver residing in a collection of pennies and farthings, or the amount of gold residing in the guinea. A very different monetary system would have emerged; bimetallism. But more on that later.

Liverpool tells us that the guinea fluctuated between 21 and 22 shillings in its first decades, but in 1695 its price rose rapidly to 30 shillings. This wasn't because of an increase in the demand for gold but a function of the quickening pace of clipping and sweating of pennies, which reduced the quantity of silver in the coinage. Guineas weren't the only commodity to rise in 1695; the entire array of English prices had to pivot around the diminishing value of the silver penny. Once the silver coinage was reformed (its silver content being restored) in the Great Recoinage of 1696, the price of guineas quickly returned to 22 shillings.

The switch to bimetallism

Things all changed in 1697 when the Exchequer, the department responsible for receiving taxes, announced that all guineas were to be accepted by the Exchequer's tellers at 22 shillings. Prior to then, the Exchequer had accepted guineas at the going market rate. As Sykes points out, after 36 years of floating this was tantamount to fixing the price of the guinea relative to silver. Guinea couldn't circulate for less than this stipulated amount, say 21 shillings, because an arbitrageur would mop up those guineas at 21 shillings and use them to pay 22 shillings worth of taxes, earning him or herself a 1 shilling gain. (The next year, the Exchequer would reduce this rate to 21 shillings 6 pence.)

Britain, which had been on a silver standard up to 1697, was now on a bimetallic standard, with the £ unit defined as the amount of silver residing in the English penny, and simultaneously the amount of gold residing in the guinea.

The guinea takes over

The problem with the new standard was that in setting the guinea at 21s 6p, the Exchequer had overvalued gold relative to the market price, more specifically the silver-to-gold ratio prevalent in the rest of the world. By how much? In 1702 Sir Isaac Newton, Master of the Mint since 1699, concluded that 'Gold is therefore at too high a rate in England by about 10 pence or 12 pence in the Guinea.' In other words, the Exchequer should have announced it would only accept guineas at around 20s 6p, or 4.6% less than it had.

What were the consequences of this over-valuation? All of the silver pennies began to leave Britain, gold coins filling the void. Given the choice between paying a debt or a tax in either an overvalued or undervalued instrument, people will always select to use the overvalued one. After all, buying 20 shillings 6 pence's worth of gold in France and using it to discharge a 21s 6p shilling tax liability in England resulted in a 4.6% profit (less transportation and minting costs). The undervalued instrument, in this case silver, is best used in other parts of the world where it is capable of purchasing a larger real amount of goods (or discharging a larger real quantity of taxes) than in the country in which it is artificially undervalued. This is, of course, Gresham's law; the bad drives out the good.

So our guinea, which had started its young life as a mere medium of exchange, had not only graduated to becoming one of only two English media of account, but was responsible for the mass flushing out of silver from England.

By 1717, the silver outflow was getting significantly bad that the authorities decided to do something about it. Newton, still Master of the Mint, noted that the market price for the guinea was around 20s 8d, given the exchange rate between silver and gold in other European markets, and suggested an initial rate reduction from 21s 6d to 21 shillings.

But even at this lower price the English authorities were still overvaluing the yellow metal. They had now fixed the silver to gold ratio at 15.069 to 1, but because the rate was 14.8 to 1 in Holland and France, a profit still remained on exporting silver and importing gold. This silver outflow would continue over the decades until most silver was gone. England had gone from a bimetallic standard to a monometallic standard. Though it was still de jure bimetallic, de facto it had become a gold standard. And the guinea, which was now the controlling element in English prices, was to blame (or at least the decision to misprice it was).(1)

The end of the guinea

For the next century, the English price level pivoted around the value of the gold guinea, until the Great Recoinage of 1816, at which point the guinea's life suddenly came to an end. Since the days of Isaac Newton, the guinea had been awkwardly rated at 21 shillings, or one pound one shilling. This must have made payments somewhat arduous since there was no coin that could satisfy an even 1 pound bill or debt, and people like round numbers. The decision was made to introduce a less awkward gold coin, the sovereign, with slightly less gold. The sovereign was conveniently rated at exactly 1 pound, or 20 shillings, the upshot being that the pound unit of account still contained just as much physical gold as before, but now a coin existed that corresponded with the exact pound unit. The guinea was dead.

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Well, not entirely. Though is was no longer being minted, the guinea continued to be used as a way to price items. According to Willem Buiter (pdf), auction houses and "expensive and pretentious shops" continued to set prices in terms of guineas through the 1800s and 1900s. Bespoke tailoring and furniture, for instance, was quoted in the legacy gold coin. The unit used was g, or gn, with the plural being gs or gns, although payments were made in sovereign coins or Bank of England notes.

Gillette advertisement (link)

Doctor's and lawyer's fees, often known as "Guinea fees" we're advertised in terms of the legacy gold coin. Whereas common laborers were paid in pounds, payments in guineas was considered more gentlemanly. You can see it pop up in the literature of the time. In Arthur Conan Doyle's Sherlock Holmes tale the Adventure of the Engineer's Thumb a stranger offers Mr Hatherly, a hydraulic engineer who is down on his luck, a unique proposal. "How would fifty guineas for a night's work suit you?"

An ad from 1929 (link)

The standard rate paid by Charles Dickens for contributions to his weekly periodicals Household Words and All The Year Round was half a guinea a column or a guinea a page. In his novels, the guinea pops up often. In Oliver Twist (set in the 1840s), a 5 guinea reward for information on Oliver is posted by the kind Mr. Brownlow.

In more modern times, horses continue to be auctioned in terms of guineas.

Dancing Rain sold for 4 million guineas (link)

Now of course this is a bit of a come-down for the once almighty guinea. Serving as the unit at Tattersalls isn't the same as underpinning the entire price level. But at least its better than the sovereign, the coin that replaced the guinea, which has gone silent, or most other medieval coins for that matter, which neither circulate nor serve as legacy units.

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(1) The 1717 reduction of the guinea to 21 shillings was accompanied by the requirement that those guineas be accepted as legal tender at that price. Prior to then, only silver had functioned as legal tender, meaning that a debtor could only discharge a debt with silver coins. After the change, a debtor could choose to use either guineas or silver coins to pay off their debt, a decision made easier given gold's overvaluation.

Some References:

Lord Liverpool, A Treatise on the Coin of the Realm, 1805.
Sargent & Velde, The Big Problem Of Small Change, 2001.
Selgin, Good Money, 2008.
Sykes, Banking and Currency, 1905. 
Macleod, Bimetallism, 1894.

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.

A history of the pound sterling's medium-of-account

Shillings issued during Queen Elizabeth's reign

There are plenty of rumours that Mark Carney will implement some sort of NGDP targeting regime when he arrives at Threadneedle Street. If so, this will mark the seventh medium-of-account used to define the pound sterling since the pound's establishment in the early part of the last millennium. This storied list of media-of-account includes silver, silver/gold, gold, the US dollar, the Deutsche Mark, CPI, and perhaps NGDP.

First, some definitions. The pound sterling is a unit-of-account. Think of it as a word, a unit, or a brand name. The unit-of-account is generally defined in terms of some other good. This other good is called the medium-of-account. Some quantity x of the medium-of-account equals the unit-of-account. (See this older discussion of the definition of the word medium-of-account.)

1. Silver

The pound's first medium-of-account was silver.  A pound sterling was defined as 5,400 grains of 92.5% fine silver. We don't use grain measurements much these days, but a grain was legally defined as the weight of a grain seed from the middle of an ear of barley. So whatever weight of silver equated to 5,400 grain seeds defined the pound sterling.

The pound's 5,400 grains of silver was subdivided into a smaller unit of account, the shilling. Twenty shillings made a pound, each shilling equal to 270 grains. Over the centuries, monarchs redefined the unit-of-account by increasing the amount of shillings in each pound. For instance, Henry V divided the pound unit into 30 shillings, not 20, while Henry VII increased the amount of shillings in a pound to 40. This allowed the monarchy to issue more shilling coins from the same 5,400 grains of silver. By Queen Elizabeth I's time, a shilling only had 93 grains of silver, down from 270 grains a few centuries before. This meant that instead of coining just 20 shillings from 5,400 grains of silver, Elizabeth could issue 62 shillings from that amount.

2. Silver & gold - bimetallism

Gold coins called "guineas" were issued in 1663. Each guinea containing 118.6 grains of pure gold. While the value of the guinea was allowed to float relative to silver, this policy changed in 1696 when the monarchy declared one guinea equal to 22 shillings. Since 5,400 grains of silver was defined as 62 shillings, and 22 shillings was now defined as 118.6 grains of gold, the shilling was now dually-defined. Enter bimetallism, a system in which both silver and gold were the medium-of-account. The dual definition would be slightly modified by Sir Isaac Newton so that a guinea equaled 21.5 shilling in 1698 an 21 shillings in 1717.

3. Gold

In 1816, the bimetallic standard officially ended. The pound continued to be defined in terms of a quantity of gold grains and silver grains, but silver was confined to serving as the medium-of-account on payments below two pounds. For all practical purposes, gold had taken over the task of serving as the pound's medium-of-account. From 1816 to 1931, the pound would be defined as 113 grains of pure gold.

4. US dollar

After going off the gold standard in 1931, the pound had no publicly-disclosed medium-of-account until 1940, when it was redefined as US$4.03. While the USD served faithfully as the pound's medium-of-account, the specific amount of USD used in this definition changed three times over the next decades. In 1949 the pound dropped to $2.80 and in 1967 to $2.40. After Nixon closed the gold window in 1971, the ensuing Smithsonian Agreement redefined the pound upwards to $2.6057. This definition would only last for a few months when in June 1972 it became impossible to defend that rate. The dollar ceased to be the pound's medium-of-account.

5. Deutsche mark

In October 1990, John Major entered the European Exchange Rate Mechanism by defining the pound as 2.95 deutsche marks. As a result, the deutsche mark was now the pound's medium-of-account. The Bank of England was allowed to let the pound diverge from this underlying definition by a band of +/-6.5%, but the pound fell out of this band in September 1992 due to massive speculation by the likes of George Soros.

6. CPI

Since September 1992, the pound unit-of-account has been defined in terms of the consumer price index (CPI). In short, the medium-of-account is now the CPI basket, and an ever-shrinking basket at that. For the first few years, the pound was defined such that it bought a basket that declined in size by 1-4% each year. After 1997, the rate of decline was made more precise, 2.5% each year. The Bank of England is held accountable should the pound-denominated liabilities it issues fail to fall in the line with the ever shrinking medium-of-account.

7. NGDP?

If a switch is made to NGDP targeting, then the pound's medium-of-account will be updated from a variably-sized CPI basket to a varying NGDP basket. A pound sterling will be equal to a trillionth (or so) of UK nominal output. One could do so even more formally by adopting an NGDP futures market. Here is Scott Sumner describing such a scheme as "analogous to a gold standard regime, but with NGDP futures contracts replacing a fixed weight of gold as the medium of account."

You'll notice there are plenty of large gaps in the above history where the pound had either no public definition or was undefined altogether. Perhaps it's not necessary to always have a medium-of-account. Changes in the medium-of-account tend to be acrimonious and attract intense public attention. The bimetallism debates defined the 1896 US election, as evinced by the famous cross of gold speech. The drive to adopt NGDP as a medium-of-account seems no less controversial, at least if the debate  in the blogosphere is any sign.

Bimetallism redux

Isaac Newton, Master of the Mint

Miles Kimball's proposal for subordinating paper money to electronic money sounds to me a bit like abandoning bimetallism.

Beginning in 1717, Isaac Newton, Master of the Royal Mint, put England on a bimetallic standard. Under bimetallism, the pound sterling was defined as a fixed quantity of silver or gold. In other words, where before England's medium of account was a certain quantity of silver, the new medium of account was a certain quantity of both metals. The unit of account through all of this remained pounds. As the market prices of gold and silver varied due to technological advances and new discoveries, the fixed silver-to-gold ratio meant that one or the other would be undervalued relative to its actual market price. As a result, the entire nation's stock of circulating coin would either flip to gold (if gold was overvalued by the mint) or silver (if silver was overvalued). After all, why bring your silver to the Royal Mint in London when you might sell it for more overseas? The overvaluation of gold, which in England's case was accidental and not intended, quickly moved the nation from a mixed standard to a gold based monetary system.

Just as England once fixed the quantity of gold equal to a quantity of silver, the modern Bank of England declares a fixed relationship between a paper pound and an electronic deposit at the Bank. The relationship is 1:1. This fixed relationship causes significant problems at the zero-lower bound. Say interest rates on BoE deposits fall below zero. At this point, the entire nation's stock of circulating pounds will be converted into paper pounds. Why hold a -2% deposit when you can hold cash at 0%? Very quickly, England will have moved from a mixed deposit/currency standard to a straight paper currency standard. It's exactly like the old bimetallic flips of yore.

The way to solve the bimetallic switching problem was to periodically adjust the fixed ratio between gold and silver to approximate actual market rates. That way neither of metals would ever be undervalued and, as a result, England would have been able to stay on a mixed standard with both silver and gold coinage. Miles's proposal is very much the same. If you relax the 1:1 ratio between Bank of England deposits and Bank of England paper currency, then as rates fall you can prevent the flip to paper currency from happening. Say rate on deposits falls to -2%. The Bank can declare that paper currency is now only worth 0.98 of a deposit, nipping at the bud the incentive to switch into paper currency. With neither asset superior to the other, people will choose to hold the same mix of currency and deposits as before.

The other way to solve the switching problem was to simply get rid of bimetallism altogether. Define the pound in terms of only one metal and let the free market take care of dealings in the rest. This is Bill Woolsey's answer to the modern zero-lower problem (here and here). It's similar in nature to Miles's. Have the central bank cease all dealings in paper currency and define the pound only in terms of deposits at the BoE. Private banks will take over the business of issuing 0% paper money. When rates fall to zero, private banks will immediately contract their issues of outstanding paper currency to nothing since maintaining a stock of 0% liabilities when the assets that support them are also paying 0% is not profitable.

In either case, you can get below the zero-lower bound pretty easily. The long gone era of bimetallism isn't as dead as we think. Differentiating between currency and deposits is very much like differentiating between silver and gold.