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.

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.

Tomorrow marks the twenty-sixth anniversary of the 1987 stock market crash. On October 19, 1987 the Dow Jones Industrial Average fell 22.6%, the largest one-day decline in stock market history. The best explanation for the decline, and the least well-known one, was put forth by economist Robert Shiller. This post gives a quick rundown of Shiller's work on understanding crash phenomena, in particular the famous 1987 event.

Eugene Fama, who along with Shiller and Lars Hansen shared the Nobel Prize this week, had very different reaction to the event than Shiller. In an essay penned not long after the crash, Fama, a true believer in the efficient market hypothesis, did his best to square the event with theory. The crash, wrote Fama,

has the look of an adjustment to a change in fundamental values. In this view, the market moved with breathtaking quickness to its new equilibrium, and its performance during this period of hyperactive trading is to be applauded. [Perspectives on October 1987, or What Did We Learn From the Crash? 1988]

Fama's effort to justify the crash as a rational response to economic news falls flat. A 22.6% decline requires something cataclysmic, but no significant events preceded the crash. Sure, there was a skirmish in the Persian Gulf with an Iranian oil station, a new tax proposal in the House, and a sell signal from guru Robert Prechter, but none of these events were capable of moving markets more than a few points.

Robert Shiller, on the other hand, gathered data. The day after the crash, he sent out questionnaires to hundreds of investors. Among other questions, Shiller asked: "Which of the following best describes your theory about the decline: a theory about investor psychology, or a theory about fundamentals such as profits or interest rates?" 67.5% of individual investors and 64% of institutional investors said the crash was about market psychology. When Shiller asked what major news stories people in his survey were reacting to during the day of the crash, the most popular stories were those about past price declines themselves, not fundamental news. Noted Shiller:

It would thus be wrong to say, as many have done, that the market drop on October 19, 1987 ought to be interpreted as a statement of public opinion about some fundamental economic factor, e.g., that there is a lack of confidence in the White House or Congress. At best, any such opinions probably played a role in the crash mainly as they affected the vague intuitive assessments people under great stress made about the tendency of prices to continue or reverse, or about how other investors will react to the current situation.

Put differently, the crash was a purely psychological phenomena.  When it comes to explaining the 1987 stock market panic, Fama and Shiller couldn't have been further apart.

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Let me take this post on a personal tangent and then I'll circle back to Shiller. I first got interested in the 1987 crash back in the late 1990s when I was a student. Fearing that equity markets were getting overextended, I started to mine 1980s price data for clues about what might happen. I discovered that the visual overlay of movements in market indexes in the late 90s was eerily similar to that of the 80s. In October 1999 I went short, sure that we were on the verge of repeating the 1987 crash. At first the markets moved a bit lower. But a week or two later prices found their footing. I didn't know it then, but the bull move that followed would be the last spurt higher before tech mania would be pricked in early 2000. Unable to stomach the losses, I covered my shorts and went back to my studies.

Though I lost money in the debacle, I did gain what I thought was an interesting idea. If enough traders like myself drew analogies to a historical crash, our combined trades -- executed on the same day -- might result in the self-realization of that crash, even though nothing had fundamentally changed about the economy. This idea jived with an observation that many market watchers had made about the 1987 crash: it was eerily similar to the 1929 crash. Wrote George Soros:

Technically, the crash of 1987 bears an uncanny resemblance to the crash of 1929. The shape and extent of the decline and even the day-to-day movements of stock prices track very closely. -The Alchemy of Finance

Both crashes were preceded by multi-year bull markets. They each occurred on a Monday near the end of October, the first crash hitting 55 days after its bull market peak, the second 54 days. In addition to similar timing, the breadth of their declines were almost the same. The 1929 crash resulted in a 23% fall over two days, the 1987 in a 22.6% fall. I append a chart below:


Could it be that the 1987 crash occurred because traders were using the same backward-looking strategy I had when I went short in 1999? The process might have worked something like this, I reasoned: the peaks and troughs in 1987 began to randomly align with those in 1929. Backward-looking traders began to notice this alignment. A feedback loop may have emerged in which scattered fears of a recurrence of 1929 resulted in trades that pushed prices down, in turn rendering the analogy between the two periods ever more clear. A final trigger, say an anniversary date, might have been sufficient to complete the loop, resulting in a realization of the 1929 crash in 1987.

Reading through accounts of the 1987 crash, I found ample evidence of traders basing their strategies on 1929 analog models. In a famous but hard-to-come-by documentary filmed prior to the crash, 1980s wunderkind Paul Tudor Jones explained how he was using a 1929 analog model developed by his research director Peter Borish to put on a large short position in October 1987. The documentary is here, for now at least.* The Friday before the crash, hedge fund giant George Soros received a copy of Tudor Jones's study and showed it to Stanley Druckenmiller, manager of Soros's famous Quantum Fund.** On the morning of the crash, the Wall Street Journal published a chart of stock price in 1987 superimposed on stock prices leading up to the crash of 1929. News of the analog was spreading across Wall Street, and by Monday, October 19, enough momentum may have built for the analog to self-realize itself.

Paul Tudor Jones circa 1987

The 1929-87 event taught me that investor's minds don't react passively to underlying fundamental phenomena. Investors create stories that, when acted upon by enough people, actually shape the fundamentals. In 1987, a psychological "worm-hole" linked to an event fifty-eight years prior seems to have emerged, leading to the greatest one-day drop in market history. It was a mistake, a mental glitch, or a wrinkle in time.

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Back to Shiller. I later found out that all of this had been anticipated by Shiller long before I was even old enough to buy and sell stock. In his post-1987 survey, Shiller found that 35% of individual investors and 53.2% of institutional investors reported talking of events of 1929 on the few days before October 19, 1987. Memories of 1929 were therefore "integral" in creating the 1987 crash, wrote Shiller:

Investors had expectations before the 1987 crash that something like a 1929 crash was a possibility, and comparisons with 1929 were an integral part of the phenomenon. It would be wrong to think that the crash could be understood without reference to the expectations engendered by this historical comparison. In a sense many people were playing out an event again that they knew well.

Nor was this the end to Shiller's work on crashes. The memory-of-crashes effect would reappear two years later. On Friday, October 13, 1989, a mini-crash occurred, the Dow falling 6.9%. Once again Shiller sent out a questionnaire. The most likely reason for the mini-crash, wrote Shiller, was the fact that the coming Monday was to have been the second anniversary of the 1987 crash.*** The mental image of the two biggest crashes in history possibly happening that Monday would have been sufficient to amplify any random price decline into an all-out panic. Wrote Shiller:

It may be a silly notion, but silly thoughts may have come to the minds of people trying to decide whether to sell as prices plummeted in the last hour of trading. They did not then have all of the reassuring commentary that came later, and they had to act then or risk having to sell on the following Monday. - Fear of the Crash Caused the Crash, NYT, 1989

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In sum, Shiller long ago provided the world with what is probably the best explanation for why the 1987 crash happened when it did, and why it fell so far. Because Fama was so closely wedded to the EMH, his only option was to stay mute on the causes. "What caused this shift in expectations? I do not know" he wrote. Fama gives us a good-enough framework for understanding 99% of market moves. But for the remaining 1%, we really do need Shiller.

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* The documentary has an interesting history. See Ritholtz, the WSJ, and Business Insider, among others. Apparently Tudor Jones threatens to sue anyone who puts it up, so getting ones hands on it is challenging. While the documentary is the best place to learn about the 1929 analog model, it also appears in the first edition of Jack Schwager's Market Wizards. But do try to watch the video, it's quite fascinating in its own right.


** Said Druckenmiller: "That Friday after the close, I happened to speak to Soros. He said that he had a study done by Paul Tudor Jones that he wanted to show me. I went over to his office, and he pulled out this analysis that Paul had done about a month or two earlier. The study demonstrated the historical tendency for the stock market to accelerate on the downside whenever an upward-sloping parabolic curve had been broken – as had recently occurred. The analysis also illustrated the extremely close correlation in the price action between the 1987 stock market and the 1929 stock market, with the implicit conclusion that we were now at the brink of a collapse. I was sick to my stomach when I went home that evening. I realized that I had blown it and that the market was about to crash." - Market Wizards, Jack Schwager (1988)

*** The 1929-87 analog revisited markets once again in 1997. On Monday, October 29, 1997, the Dow went into a freefall, eventually tumbling 7% . See my explanation of the 1987-1997 analog here. 

PS: If market's plunge this coming Monday, you know why.  ;) 

Hand operated rolling mill, for putting the edge impression on to coins

I've been reading about the medieval monetary system lately. What a fascinating and complex mechanism, and a good reminder that we should not be using the word medieval as a synonym for primitive or unenlightened. Medieval coinage, I've come to discover, is also a highly confusing subject. A quote that John Munro attributes to Karl Helleiner seems apropos: "There are two fundamental causes of madness amongst students: sexual frustration and the study of coinage."

Studying odd, imaginary, or historical monetary systems is rewarding not only because of the aha! moment that understanding provides, but also because of what these systems reveal about our modern one. Readers may have noticed that for the last two months I've been posting rather obsessively on monetary policy, a topic I've typically avoided. Here's my attempt to combine monetary policy and medieval coinage into one post, hopefully as a useful way to consolidate all my points in an interesting way.

In medieval days, mints were generally owned by a prince. A mint-master was put in charge of coining silver bullion into coin (gold and copper were also coined, but for simplicity I'll focus on silver). The prince set the official rate at which the mint-master could convert raw silver into a specific coin. For instance, one pound-weight of silver might be coined into 240 silver pennies, each with 1/240th a pound-weight of silver in them. Under the principle of free coinage, anyone could bring raw bullion, plate, jewelry, and foreign coin to the mint to be converted into coin of the realm.

Coins were far more convenient in trade than raw silver because they saved transactors from the laborious process of weighing and assaying silver powder or ingots. Because of this superior marketability, coins usually traded at a premium to an equivalent amount of raw silver. A coin with 1 gram of silver therein, for instance, might exchange in the market at a price of 1.1 grams of pure silver bullion. Munro refers to this premium as the agio.

The existence of an agio represented a potential arbitrage opportunity for the public. A merchant need only buy raw silver, bring it to the mint to be coined, and leave with the same weight of silver, but now in coin form and capable of purchasing, say, 10% more goods. He could then buy more bullion with this new coins, repeating the process and earning a 10% risk-free return each time.

While coinage was free, it was not gratuitous. The mint-master required a certain amount of silver as payment for the use of his time, minting tools, and wages for his employees. Since silver was usually mixed with base metals like copper to produce the final coin, the mint-master also required compensation for supplying the baser metals. This fee was called brassage. The prince exacted a fee too, or a tax. This was called seigniorage.

These costs restricted the opportunities for arbitrage. If the brassage and seigniorage costs were higher than the agio, the public would avoid the mint altogether since the transaction would result in a loss in purchasing power. Better to keep their silver in bullion form or search for a mint that produced identical coin at less cost.
However, as long as the agio was more than brassage and seigniorage, citizens would continue to bring bullion to the mint and enjoy a small return.

This process had a natural limit. Much like the water-diamond paradox (which tells us that the usefulness of something does not necessarily equate to a higher price) the fact that coins were more useful than raw bullion in transactions didn't mean that people would always pay to enjoy that benefit. As the public flocked to the mint, a coin glut would develop. The marginal value that the market placed on coin-as-transactions-medium would deteriorate, driving the agio down to the twin costs of brassage and seigniorage. Put differently, an increase in coin supply would push the marginal value of coin towards the cost of production. Just as water is extremely useful but essentially free, the marketability value of coins -- though still useful -- could be had at no cost once the quantity of coin was sufficiently plentiful.

Let's bring this back to monetary policy. The initial agio of coin over silver is very much akin to the liquidity premium I've mentioned in previous posts. The existence of an agio, or liquidity premium, is justified by the convenience, moneyness, or non-pecuniary return on a medium-of-exchange. As the supply of coin is allowed to increase, all other things staying the same the market's marginal valuation of this non-pecuniary return will fall, as will the associated agio/liquidity premium.

A modern central bank keeps the supply of reserves artificially tight and restricts competition. In doing so, it creates a positive marginal non-pecuniary return on reserves (or a convenience yield, see here). This drives the market value of reserves above the price at which they would otherwise trade were they subject to competition. In other words, a central bank creates a permanent agio.

In order to execute monetary policy, central banks will typically massage this agio. By emitting a small amount of reserves or sucking them in, a central banker can alter the marginal valuation that the market places on the convenience of reserves. This pushes the agio higher or lower. Any change in the agio translates into an economy-wide change in the price level.

Bringing this back to a medieval setting, imagine that the prince ceases free coinage (much like how a modern central banker would restrict reserve supply and competition). From time to time the public might be allowed access to the mint, and in limited numbers, but usually the mint would be closed to business. The supply of coin, therefore, is henceforth restricted. The ensuing lack of transactions media will cause a large agio to emerge as the market value of coin rises relative to bullion. I'm assuming here that counterfeiting is too dangerous to justify. If not, counterfeiters will be motivated to establish black market mints once the agio significantly exceeds brassage.

The prince is now in the same position as a modern central banker. By bringing a bit of silver bullion to the mint, turning it into coin, and spending it, he can increase the quantity of coin in the economy and thereby decrease the marginal non-pecuniary return on coin. The agio would thereby shrink, pushing the market value of coin down, or the price level up.   After all, the economy's unit of account in the medieval period was determined by a given link coin, usually the penny, so any change in the penny's value resulted in an economy-wide change in prices.

Both the prince and a central banker face a limit to the effectiveness of expansionary monetary policy. Once a prince has issued enough coin to drive the agio down to zero via mass "coin quantitative easing", further coin emissions will have no effect on the price level. A coin will now be worth no more than its intrinsic silver value. Nor can it fall to a discount to its silver content, since the public would simply buy coin and melt it into bullion until the discount has been removed. As for a modern central banker, once QE has reduced the convenience yield provided by reserves across the entire curve to zero, then further reserve emission cannot push the price level down any further. The agio has disappeared. In the same way that coin falls to its silver content, reserves will have fallen to their intrinsic "backing" value -- and will go no lower.

The prince still has an alternative. He can engage in outright debasement. By reducing the intrinsic silver content in coin, the price level will once again start to rise. Likewise, a central banker might attack the intrinsic value of central bank liabilities by destroying assets, or purchasing assets at bloated prices, or engaging in helicopter drops. Princes did in fact tend to reduce the price level via debasement and not by manipulating the agio, although they usually did so as a way to earn higher revenue, not to help the economy. No doubt due to the irresponsibility of the prince's who preceded them, modern central bankers are legally prohibited from outright debasement. Manipulating the agio on reserves, or playing with the interest rate on reserves, are the only tools left to them.

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Most of the actual facts about medieval coinage in this post come from John Munro's Warfare, Liquidity Crises, and Coinage Debasements in Burgundian Flanders, 1384 - 1482 (RePEc) and The Coinages and Monetary Policies of Henry VIII (RePEc), among other papers. Munro shouldn't be blamed for mistakes in my theorizing, nor the analogy to modern central bank QE. 

Does it matter what the Fed buys? ...from whom? ...or how? I don't think so.

The Fed currently buys and sells government-issued and guaranteed securities from designated primary dealers. It does so publicly and transparently. In the case of QE, it announces ahead of time the quantities it will purchase. Prior to 2008, it announced that it would conduct enough purchases to drive the fed funds rate up or down by x%.*

But let's modify the monetary policy transmission mechanism a bit. Say that a few years from now the Fed decides to buy and sell bitcoin, bitcoin claims, and other cryptocoins instead of government securities. Rather than executing these trades through a select posse of firms, it'll transact broadly with Joe Public. And rather than announcing purchasing intentions, it will carry them out surreptitiously. Big as these changes may seem, altering the route won't impede the transmission of monetary policy. Whether it quietly buys bitcoin from the public or pre-announces government bond purchases with primary dealers, the Fed will still continue to keep a firm grip on the economy's price level.

There are a few ways for a hypothetical bitcoin transmission mechanism to work. Here's one way. Say the Fed wants to loosen policy and push prices up by, oh, 5%. Fed officials fan out across the US, looking for local bitcoin over-the-counter exchanges. Bitcoin OTC markets exist on street corners, in coffee shops, houses, cafés, public libraries, city parks, and bars. These informal OTC exchanges are where Joe Public congregates to truck and barter bitcoin. Once located, the Fed officials begins to write out cheques to OTC traders in exchange for bitcoin at the going market price. The Fed now has bitcoin on the asset side of its balance sheet. OTC traders have Fed cheques which they proceed to deposit at their local bank.**

So far the Fed's purchases haven't had an effect on the price level — neither the price of bitcoin nor the price of goods have budged. Note that even if Fed officials accidentally nudge bitcoin OTC prices up a bit through their buying, arbitrageurs will quickly counterbalance this by routing sales away from centralized bitcoin exchanges like Mt-Gox (assuming it still exists in a few years) to OTC markets, driving OTC prices back to their fundamental value.

The OTC traders' Fed cheques having been deposited in the banking system, banks proceed to load them into Brinks trucks for delivery to the local district Fed for clearing and settlement. During the clearing process, a large settlement imbalance in favor of private banks emerges, an imbalance that has arisen thanks to the Fed's cheque-writing campaign. The Fed settles its debts by crediting the reserve accounts of creditor banks with newly created deposits.

Only now is our bitcoin transmission mechanism poised to push prices higher. Banks collectively find themselves with an excess stock of reserves. But there is no place for this excess to go. Within the next few hours, banks will madly compete to get rid of their reserves. They'll do so by buying up financial assets like bonds, stocks, MBS, and bitcoin from other banks.*** As a result of their combined efforts, the prices of all these assets will quickly rise. Put differently, the purchasing power of reserves will fall. This decline will only stop when the purchasing power of reserves has fallen to a low enough level that they are once again willingly held by bankers. While this will happen very fast with financial asset prices, stickier prices like goods and labour will take longer to adjust upwards.

In a nutshell, that's how the Fed's bitcoin purchasing policy succeeds in increasing the price level. And if the Fed falls short of hitting its 5% growth target, it need only send out more officials to write more checks for more bitcoin until it hits its mark.

Let's make a few changes to our transmission mechanism. To streamline the process, the Fed decides to funnel purchases to a select number of bitcoin dealers rather than spraying them broadly. Should the Fed require it of them, these chosen dealers are required to quote the quantity of bitcoin they are willing to sell and at what price.

Does the decision to funnel purchases rather than spray them change anything? Not at all. Fed cheques are still deposited by bitcoin sellers at their banks and these checks are settled with reserves. Whether funneling or spraying, banks still end up with an excess reserve position which they will try to rectify by simultaneously buying up assets. The only resolution to this will be a quick rise in prices. A primary bitcoin dealer system, it would seem, is no different a transmission mechanism than our earlier broad Joe Public approach.

The Fed may even require that bitcoin dealers hold inventories of government bonds and submit bond quotes from time to time in addition to bitcoin quotes. Even if the Fed decides to purchase bonds rather than bitcoin, nothing about the transmission mechanism changes—Fed cheques still result in excess reserve positions at banks, and these can only be equalized by a rise in prices. But now we're back at our current system in which primary dealers sell bonds to the Fed.

The Fed may even start to publicly announce its intentions to make bitcoin purchases rather than surreptitiously writing checks. Anticipating that they will soon be inundated with excess reserves upon hearing the announcement, banks won't wait for the reserves to arrive before trying to offload them. Rather, they'll sell immediately. This will quickly push asset prices higher. Smart speculators and investors, anticipating that forward-looking bankers will quickly spend their reserves after the Fed announces its intention to buy bitcoin, will try to beat the bankers to the punch by purchasing assets the moment an announcement is made.

So when the Fed's purchasing intentions are announced, market prices adjust even before the Fed carries out the actual purchases. Without an announcement, however, the cheques must physically enter the economy and cause a reserve imbalance before prices begin to adjust, a process that will only start a day or two after and will proceed in a jagged manner.

The upshot of all this is that it doesn't matter what the Fed buys, nor from whom. Monetary policy works irrespective of the route. As for the "how",  the Fed's decision to publicize their intention to make bitcoin purchases rather than quietly writing out cheques has the effect of dramatically speeding up what would otherwise be a circuitous transmission process.

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* For simplicity, I'll be assuming a world in which the Fed doesn't pay interest on reserves.
** Even if OTC traders don't accept cheques, they'll accept bank notes, and the same analysis applies.
*** In addition to purchasing financial assets, banks will try to lend them away to other banks in the interbank market, receiving the overnight interest rate in return. This will cause the interbank lending rate to fall. 

What effect does a stock market listing have on the value of equity? Companies can always choose to issue shares privately rather than list them on public centralized exchanges. That the world's biggest corporations are all publicly-listed implies some sort of advantage to being listed.

To answer this question, it helps to see what happens to listed share prices upon the sudden dissolution of a stock market. The cryptocoin universe has just provided us with a great natural experiment (which, unluckily for me, resulted in a loss). Due to what it called "recent changes in the virtual currency regulatory environment," LTC-Global, a litecoin-denominated stock market, and sister exchange BTC-TC, a bitcoin-denominated exchange, announced that they would be shutting their doors. Both exchanges listed twenty to thirty securities each, including shares, bonds, and ETFs. BTC-TC did ~2,000 BTC in daily volume or ~$350,000, while LTC-Global was doing 5,000 LTC a day in business, or around $10,000.

The fateful announcement was made on the morning of September 23. Trading was immediately halted and order books cleared, presumably to allow investors to digest the information. When trading was re-opened, the immediate reaction of almost all share prices was to plunge in value. Shares continue to trade almost exclusively below their pre-September 23 price. All trading will be halted on October 7. After that point, de-listed companies will have to reconfigure the way by which their shares are traded. They may either relist on another crypto share market (there are a few), they might provide their own venue for trading on their personal website, or they might simply leave it to the shareholders to locate each other and trade over-the- counter, say on forums or message boards.

Here are a few charts showing the reaction of some of the more liquid stocks to the closure. I get them from Coinflow:

Labcoin (BTC-TC):  Labcoin is in the business of manufacturing and marketing cryptocoin mining equipment. It immediately fell from 0.0023 BTC to 0.00025 BTC, or around 90%, soon recovering to 0.001 BTC, about 50% below pre-announcement prices.


Basic Mining (BTC-TC):  Basic Mining units offer a share of revenues earned from a bitcoin mining operation. They stabilized the day after the announcement at around 40% below their previous price.


LTC-Miner (LTC-Global):  The share price of LTC-Miner, a cryptocoin mining farm's value, was halved on September 23.


This event clearly illustrates how an unanticipated de-listing affects a firm's stock price. Despite no change in underlying fundamentals—the earnings of most of the listed cryptofirms would have been unaffected by the stock market's closure—the market value of most firms' shares declined. Alternatively, we might say that the listing of a stock on a stock market would cause a rise in the market's valuation of a firm, despite no improvement in underlying fundamentals.

There are two non-mutually exclusive reasons that might explain the collapse in crypto shares upon the closure of LTC-Global and BTC-TC, a real and a monetary one:

1. Stock markets vet firms to ensure they are legitimate. They also set standards for communication and governance, and this forces firms to be more accountable to shareholders. The graduation of a firm's shares to an exchange like LTC-Global or BTC-TC may be taken by investors as an indicator that the shares are less risky than before, and therefore they can be discounted by a smaller factor. When LTC-Global and BTC-TC were suddenly closed, shareholders had no guaranty that the issuer, no longer under the glare of the public eye, would treat them as fairly as before, and therefore the large selloff. Or put differently, investors chose to suddenly put a larger risk premium on cryptoshares.

2. By bringing together many stocks and investors in one space, stock markets promote the liquidity of shares. Liquidity is its own return. By that I mean that investors "consume" liquidity in the same way that they consume other durable goods that provide protection, say house alarms, guns, or fire extinguishers. Though these goods are unlikely to ever be used, the services they provide are steadily consumed through time in the form of comfort and security. By ensuring liquidity, stock markets increase the non-pecuniary flows of comfort and security provided by listed stock. A liquid share, after all, can be easily sold should some unforeseen arise—an illiquid share can't. All other things staying the same, this improvement in a stock's non-pecuniary yield should result in a rise in its price (see this post for more).

So upon the announced shutdown of LTC-Global and BTC-TC, expectations about future liquidity were reduced, the non-pecuniary return on shares declined, and thus prices fell. The fallback option—that shares trade over-the-counter—results in inferior liquidity since there are significant search and monitoring costs entailed when exchanging stock via forums or email.

One wonders when some bright programmer creates a decentralized ledger to store a stock market's order book. Just like it is impossible to shutdown bitcoin since it doesn't exist in one particular location, it would be impossible for authorities to shutdown a decentralized cryptocoin stock market. Companies operating in the bitcoin universe would flock to list on this market since it would provide them with the most legitimate guarantee of future liquidity, and a higher stock price. All for a juicy fee, of course.