Angolan macutes: Imaginary money

Economists are sometimes guilty of misrepresenting real-world liquid objects as living examples of the abstract variables populating their favorite monetary model. A good example of this is the incorrect reliance on Yap stones to illustrate the idea of fiat money by economists as varying as Keynes, Milton Friedman and James Tobin. Whereas fiat money is intrinsically useless, inconvertible, and unbacked, Yap stones certainly aren't, the anthropological evidence revealing that the stones had cultural and religious significance apart from their monetary value.

Similar in concept is the story of the macute, a unit of account used in Angola hundreds of years ago. Much like the exotic Yap stone, the existence of the macute (or macoute) came to the attention of Western thinkers as trade and conquest revealed ever large parts of the globe. Montesquieu was one of the first to describe the macute, noting:

The negroes on the coast of Africa have a sign of value without money. It is a sign merely ideal, founded on the degree of esteem which they fix in their minds for all merchandise, in proportion to the need they have of it. A certain commodity or merchandise is worth three macoutes; another, six macoutes; another, ten macoutes; that is, as if they said simply three, six, and ten. The price is formed by a comparison of all merchandise with each other. They have therefore no particular money; but each kind of' merchandise is money to the other. - Montesquieu, Esprit des Lois, 1748

Montesquieu's macute was later picked up by Sir James Steuart, an 18th century economist ranked just a notch or two below Adam Smith:

That money, therefore, which constantly preserves an equal value, which poises itself, as it were, in a just equilibrium between the fluctuating proportion of the value of things, is the only permanent and equal scale, by which value can be measured.

Of this kind of money, and of the possibility of establishing it, we have two examples: the first, among one of the most knowing; the second, among the most ignorant nations of the world. The Bank of Amsterdam presents us with the one, the coast of Angola with the other.

The second example is found among the savages upon the African coast of Angola, where there is no real money known. The inhabitants there reckon by macoutes; and in some places this denomination is subdivided into decimals, called pieces. One macoute is equal to ten pieces. This is just a scale of equal parts for estimating the trucks they make. If a sheep, e. g. be worth 10, an ox may be worth 40, and a handful of gold dust 1000. - An Inquiry into the Principles of Political Oeconomy, 1767

To Steuart and Montesquieu, the macute was an example of "ideal" money of account. The term money-of-account refers to the economy's pricing sign, or unit-of-account. It could be pounds (£), yen (¥), or dollars ($). Some real good typically defines this unit. For instance, the $ is the unit used to record prices in the US. The real good that defines the $ is base money issued by the Federal Reserve. In medieval times, prices were recorded in terms of £/s/d, with silver pennies being the defining real item (the "link coin"). To put this in the lingo of the econ blogosphere, the real good that defines the unit of account is the medium of account, a term popularized by Scott Sumner.

James Steuart's ideal money of account was a unit that, somewhat unusually, had no underlying real good defining it. It was a purely abstract accounting unit. There were prices in Steuart's economy, but no medium of account. Presumably Angolans were to keep the macute scale in mind, much like they might have a good sense for how long a foot was, or how much liquid a litre might contain. But at least with litres or feet there was a standard to which one might refer back to, say a metre stick or a measuring cup. Since the macute had no physical representation, goes the theory, it could only ever exist in people's heads.

Steuart and many others in his day believed in the necessity of an invariable scale of value. What was important to Steuart was the relative prices of real goods, not the price of some superfluous intervening good who's only job was to provide a measuring stick. If the money-of-account was a gold coin, for instance, then the "smallest particle of either metal added to, or taken away from any coin" would cause the entire price level to rise, destroying the ability of coins to measure the value of things. This would create macroeconomic difficulties:

any thing which troubles or perplexes the ascertaining these changes of proportion by the means of a general, determinate and invariable scale, must be hurtful to trade, and a clog upon alienation. This trouble and perplexity is the infallible consequence of every vice in the policy of money or of coin.

Fixing the money of account to a coin rather than allowing it to have an independent and abstract value caused distributional unfairness, since the relative interests of debtors and creditors were now at the disposal of anyone who could reduce the quality of coin,

not only of workmen in the mint, of Jews who deal in money, of clippers and washers of coin, but they are also entirely at the mercy of Princes, who have the right of coinage, and who have frequently also the right of raising or debasing the standard of the coin, according as they find it most for their present and temporary interest.

To those like Steuart, the advantage to society of an imaginary accounting unit like the macute was that, unlike physical coin, no prince or money clipper could ever debase it. It existed safely in the collective imagination where it could not be damaged, and therefore trade would no longer be held hostage to a fluctuating price level.

This idea spread. Around the time of Steuart, A.R.J. Turgot would also write of the macute as a purely imaginary unit:

The Mandingo negroes, who carry on a trade for gold dust with the Arabian merchants, bring all their commodities to a fictitious scale, which both parties call macutes, so that they tell the merchants they will give so many macutes in gold. They value thus in macutes the merchandize they receive; and bargain with the merchants upon that valuation. - Reflections, 1766

Macutes-as-ideal-unit would go on to be upheld a century later by John Stuart Mill:

This advantage of having a common language in which values may be expressed, is, even by itself, so important, that some such mode of expressing and computing them would probably be used even if a pound or a shilling did not express any real thing, but a mere unit of calculation. It is said that there are African tribes in which this somewhat artificial contrivance actually prevails. They calculate the value of things in a sort of money of account, called macutes. They say one thing is worth ten macutes, another fifteen, another twenty. There is no real thing called a macute: it is a conventional unit, for the more convenient comparison of things with one another. - Principles of Political Economy, 1848

As lovely as the idea of an imaginary macute was, it simply wasn't true. The macute was not so abstract as Montesquieu, Steuart, Turgot, and Mill would have liked it to be. William Stanley Jevons, for instance, scolded Montesquieu for misunderstanding the nature of money of account, since macutes served as "the name for a definite, though probably a variable, number of cowry shells, the number being at one time 2000." Lord Lauderdale accused Steuart of ignorance, noting that macutes were "pieces of net-work, used by the people of Angola for a covering." Like Lauderdale, John Ramsay McCulloch also found macutes to be bits of valuable cloth. Other writers declared that slaves were the missing medium-of-account used to describe the macute.

With the benefit of modern ethnographic accounts, we know that McCulloch and Lauderdale were right—macutes were neither imaginary, nor slaves, nor cowries, but cloth. In Power, Cloth and Currency on the Loango Coast, Phyllis Martin describes a coastal economy in which domestically produced cloth currency circulated. These libongo (pl. mbongo) were fourteen inch square pieces of cloth about the size of a hankerchief (see photo below). Mbongo had multiple uses. Not only could it be used in local markets to buy food and other consumption goods, but it could be made into clothes, wall hangings, bags, and floor coverings, and used for ceremonial purposes.

Kongo or Angola cloth, 17th century, raffia pile (source)

Martin also describes a traditional unit of account called a makuta (macute), defined as ten mbongo wrapped together in a strip. European trade brought foreign substitute cloth, and with that a decline in the purchasing power of the makuta, or inflation, resulted. As a result, copper coins came into increased use, although Martin finds that mbongo remained in circulation well into the eighteenth century. By the 1700s, around the time that Montesquieu was writing, the nature of the makuta unit of account had changed:

At Loango Bay traders used an abstract numerical unit of account based on a makuta, one mukuta being equal to 10. The unit may have developed from the older association of the mukuta with ten mbongo. Thus a slave-trader at Loango in 1701 wrote, "we bought men slaves from 3,600-4,000, and women, boys and girls in proportion." The goods to be exchanged were also valued in the numerical unit of account for example, a piece of "blue baft" or cotton cloth from India counted as 1,000, a piece of painted calico was 600, a small keg of powder was 300, and a gun was 300.40 

- Martin, Power, Cloth and Currency on the Loango Coast, 1986

What we have here is an example of "ghost money", not ideal money. An ideal money, having been divorced from any traded good, would have no commodity definition whatsoever. The mukuta (macoute) as described by Martin, however, was defined as a historically fixed, or "ghost" quantity, of mbongo. Though no longer prized as a highly liquid medium of exchange—copper coinage would have filled this place—mbongo were still desired for their non-monetary qualities. Thus any alteration in the real value of mbongo would continue to have an effect on all prices. It may have been this historically fixed "ghost" nature of macutes and their relative rarity in actual trade that confused Montesquieu into describing them as an ideal accounting unit.

In sum, macutes were not the ideal unit of Steuart and Montesquieu's imagination. Does that mean that ideal units of account can't exist? I'm hard pressed to come up with a logical explanation for how they might work. And I surely don't have any historical examples, the macute having been confined to the dustbin. I vote we toss the idea out, along with fiat money. Beware economists toting imaginary accounting units, abstract numeraires, and ideal money of account.

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P.S. Indexed units of account like the Chilean Unidad do Fomento, which I wrote about here, are not imaginary units. Instead, I think they should be thought of as ghost monies.

Separating the functions of money—the case of Medieval coinage

Florentine florin

Last year Scott Sumner introduced the econ blogosphere to what he likes to call the medium-of-account function of money, or MOA, defined as the sign in which an economy's sticker prices and debts are expressed. Here and here are recent posts of his on the subject.

I think Scott's posts on this subject have added a lot of depth to the interblog monetary debates. However, I've never been a big fan of Scott's terminology. As I've pointed out before, what Scott calls MOA, most modern economists would call the unit-of-account function of money. Older economists like Jevons and Keynes[1] referred to the unit-of-account as the money-of-account, and modern economic historians also prefer money-of-account. Terminological differences aside, in today's post I want to focus on what I'll call from here on in the unit-of-account function of money.

Scott's UOA posts often emphasize the idea of separating the unit-of-account function from the medium-of-exchange. This isn't a new approach. Back in the 1980s, a trend in monetary economics began whereby economists began to dissociate the various bundled functions of money into constituent components. In fact, a few contributors to the modern econ blogosphere were participants in what was then called "New Monetary Economics", or NME, including Tyler Cowen, Bill Woolsey (pdf), Scott, and Lawrence White (pdf). White, it should be noted, was a critic. Cowen doesn't blog much about NME these days, his last post on the subject was in 2011, but I'm sure every time he goes to a restaurant he can't help but wonder what the world might be like if the menu prices were in different units than the media he expected to pay with. Here is an old Cowen paper (with Krozner) on NME that is worth reading, as well as the bibliography which serves as a good jumping off point to understand more about NME.

But let's turn to an actual example. The separation of the medium-of-exchange from the unit-of-account envisioned by NME isn't mere speculation. Indeed, such a separation has been very much the norm over the last thousand years or so. The medieval monetary system operated with what was essentially a number of heterogeneous media of exchange and an independent unit of account.

Medieval Europe was politically fragmented and many different mints issued coins. Einaudi (pdf) tells us that some 22 gold coins and 29 silver coins (most of them foreign) circulated in the Duchy of Milan alone in the 18th century. This does not include the many varieties of copper coins that would also have been current. Weber (pdf) describes Basel in the 1400s, which had a heterogeneous coinage acquired through trade that included florin and ducats from Italy, and German rhinegulden, along with the local silver penny.

Because most of these coins had different metallic content, and the market value of coins was determined to a large extent by the quantity of metal therein, would this not have caused a terrific amount of confusion? Silver and gold traded at a constantly fluctuating ratios, contributing to the calculational morass. How could shopkeepers and shoppers keep track of the prices at which transactions were to be consummated with such an incredible variety of ever changing units?

The answer is that prices were expressed in terms of a universal unit of account. The name for this unit was the pound, or in French, the livre. The pound (and livre) were further divisible into 20 shillings (sous) and each shilling into 12 pence (deniers). A pound was therefore divisible into 240 pence. Prices and debts were recorded not in terms of individual circulating coins, but in terms of this pound unit of account. Indeed, pound coins never actually existed in Medieval Europe, the pound being a purely abstract accounting unit.

According to Einaudi, local mint officials maintained a list of coin ratings whereby each coin in local circulation was rated at a certain amount of £/s/d. Officials determined the rating by assaying the quantity of gold or silver in each coin. Thus a shopkeeper need only list the price for, say, a horse in terms of the universal unit of account, say 1 pound 6 shillings. A buyer need only look at the 1£ 6s sticker price, determine what sorts of coins he had in his pocket, refer to their public ratings, and compute the proper number of coins to hand over as payment.

Over time, the precious metals content of coins would deteriorate as people 'sweated' coins, filed them, clipped them, or bathed them in aquafortis [2]. The price ratio of gold to silver would often change subject to the whims of market demand as well as mine supply. Sometimes a sovereign might call in an existing issue of coins and reissue them with more or less precious metals therein. When the metallic content of a given coin was changed, or when the market silver-to-gold ratio fluctuated, local mint officials would quickly account for this change by re-rating the altered coin in terms of the £/s/d unit of account.

The advantage to shopkeepers with this system is that they needn't update their sticker prices. After all, via constant re-ratings, the prices of coins were made to fluctuate around the unit of account. For example, if the Spanish doubloon was re-rated due to a debasement in its gold content, our horse-seller could keep his 1 pound 6 shilling price constant, and need simply ask for more doubloons [3]. In this way, the chaos of the medieval coinage system was rendered orderly by a universal £/s/d unit of account.

There is one important issue I haven't dealt with. What defined the medieval pound unit of account? Anyone who's read my old post will know that this question boils down to this—what was the medieval medium of account? The unit of account is always defined in terms of something else, a medium of account, and it is this MOA (which is different from Sumner's MOA) that anchors the price level.

Although city states never minted pounds (and only rarely shillings), they did mint their own pennies. Weber (pdf)(RePEc) and Spufford hypothesize that these pennies served as a foundation, or "link" coin. The penny unit of account was set equal to the penny coin, either spontaneously or via enactment, and thereafter any alteration in the silver quantity of the penny link coin modified the unit of account.

To illustrate, if the sovereign reduced the amount of silver in the local penny, the penny's linkage to the unit of account meant that the penny-as-unit of account now contained a smaller quantity of silver. The pound unit of account (a multiple of 240 pennies) by definition now also contained less silver. So a debasement of the link penny coin meant that all £/s/d sticker prices would need to be raised by shopkeepers if they desired to preserve real purchasing power [4]. In modern days, we call this inflation. Nor was princely debasement of the link coin the sole cause of medieval unit-of-account inflation. After many years of passing from hand to hand, link coin's naturally wore out, and therefore a steady inflation in prices resulted.

A debasement in a foreign penny circulating locally, however, would have no effect on the local unit of account, insofar as the foreign penny didn't serve as the link coin. Rather, a debasement of a foreign penny would result in that particular coin being re-rated in terms of the unit of account. £/s/d sticker prices would stay constant.

In some cases, however, foreign pennies were the link coin, so changes to the silver content of the local penny would have no effect on the price level. Inflation or deflation were imposed exogenously. Even more interesting, in a few rare cases the precious metal content of a famous coin of a previous era that no longer existed was used as the link coin. Monetary historians such as Munro call these "ghost monies". The advantage of having a ghost link coin rather than a current coin is that the unit-of-account could now stay constant over time, preserving the real value of debts and contracts.

To sum up, the medieval unit of account, as we already know, was £/s/d. We also know that there was no single medium of exchange, but a chaotic mix of coin media of exchange. The MOA was a single "index" coin, usually the locally-coined penny, but at other times a foreign coin or an antiquated "ghost coin". While link coins would come and go over the centuries, the £/s/d unit of account stayed constant.

At what point in history did the unit of account and medium of exchange finally fuse together? Weber (pdf) hypothesizes that the Industrial Revolution brought with it improvements in the quality of coin production. Milled edges prevented filing and clipping. The introduction of steam driven coining reduced minting costs and made it more feasible to replace worn coins. These technological improvements meant that it was now possible for coins to serve as stable units of account. The best evidence that Weber finds for this is the appearance of "value marks", or numbers, on the faces of coins. Medieval coins did not carry numbers on them, only the faces and names of the various personages responsible for their issue. The blank nature of these coins allowed the market to determine their exchange rates in terms of the unit of account. The appearance of value marks in the 19th century indicated that the coinage was now of a high enough quality that a separate unit of account was rendered unnecessary. It was now possible to inscribe the unit of account directly on the coin's face.

As a result of these developments, the modern day individual is incapable of imagining a split between the unit-of-account and the media-of-exchange. But this complex institution is something that our ancestors dealt with on a daily basis. Understanding the medieval monetary system is a great way for us to throw off the cobwebs and understand the difference between media-of-exchange and unit-of-account. After all, who knows what future monetary systems might have in store for us — perhaps another divergence between the two functions? It also crystallizes how important the unit-of-account function is. Whoever controls the unit-of-account controls prices, and therefore monetary policy.

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[1] The first line of Keynes's Treatise on Money is: "Money-of-account, namely that in which Debts and Prices and General Purchasing Power are expressed, is the primary concept of a Theory of Money.
[2] Sweating coins involved putting many coins in a sack, shaking the sack, and removing the fine metal grains that shaking had dislodged from the coins. Aquafortis is nitric acid, or HNO3.
[3] The doubloons re-rating due to lower metallic content was called a "crying down" the value of the coin. If the doubloon had been reminted to contain more gold,  its value would have been "cried up". [Editor's Note: this is wrong|
[4] When the link coin's metallic content was debased, this was referred to in the medieval literature as an 'augmentation' or 'enhancement' of prices. When link coin's metallic content was rebased (increased), this was referred to as 'diminution', or 'abatement'. 

Update: By coincidence, Nick Rowe has simultaneously posted on the separation of the functions of money.

Scott Sumner ignores banks, so what?

In response to a recent comment by Cullen Roche, Scott Sumner wrote that "I have no interest in banking or bookkeeping. My interest is monetary policy."

Now this is a point that Sumner has made before. For instance, he wrote an old post back in January entitled Keeping Banks out of Macro, in which he claimed that bank lending "is not a causal factor—it mostly reflects the growth rate of NGDP."

To Minskyites and Post Keynesians like Cullen, who put a lot of importance on the banking system and the financial instability that results from bank failures, this claim is blasphemous. But given the side of the field from which Sumner comes from, I think he makes a lot of sense. As Sumner points out in his comment, his main interest is monetary policy, and Sumnerian monetary policy boils down to exercising control over NGDP. Sumner usually explains this by reference to the medium of account role of money, and though I think his terminology is a bit buggy, I agree with him.* By wielding its control over base money, or what Sumner calls the medium of account, the Fed can push up the price level, and therefore NGDP, to whatever heights it wants to.

This relates back to my previous post in which I made the analogy of a central bank's power to Archimedes's boast that he could move the world. Give a central banker a long enough lever and a fulcrum on which to place it, and he'll move prices and therefore NGDP as high as he wishes.

Whether there is a banking system or not in the picture will interfere in no way with a central banker's Archimedean lever. Here's a very short explanation for why banks don't change anything. Think of a private bank deposit as a call option on central bank base money. Any bank that holds another bank's deposits can "put them back" to the issuer whenever they wish in return for an equivalent amount of central bank deposits or notes. Similarly, a consumer or business holding a bank deposit can always convert them into an identical quantity of central bank cash. This one-to-one correspondence between underlying central bank money and bank deposits, enforced by the option to convert, means that if the purchasing power of base money declines, then so must the purchasing power of a bank deposit.

The correspondence between option and underlying is fairly non-controversial. If Apple's stock price falls, then options to buy Apple will fall too. If the options fail to fall in sync with the underlying stock, arbitrageurs will sell options and buy Apple until the gap has disappeared. Just so, if a central bank drives down the purchasing power of base money, a failure of bank deposits to corroborate the fall of the underlying will be exploited by arbitrageurs until that failure has disappeared. Of course in practice we almost never see a difference between the price of central bank money and bank deposits. The process is so automatic that we never think about it.

I'm not being original here. For instance, in an article on calling for the death of the money multiplier, David Glasner described the equality of inside and outside money, noting that

it is convenient to view the value of money as being determined by the supply of and the demand for base money, which then determines the value of inside money via the arbitrage opportunities created by the convertibility of inside into outside money.

In David's quote, inside money is bank deposits, and outside money is central bank notes and deposits.

So to sum up, since a central banker has precise control of the purchasing power of the liabilities that it issues (explained in my previous post), it will automatically exercise that same control over the purchasing power of the liabilities of the entire banking system, insofar as private banking deposits function as call options on underlying central bank liabilities. Should Ben Bernanke desire to push up NGDP by 10%, he need only hurt the purchasing power of his own liabilities, and this will be immediately reflected in a fall in the purchasing power of all derivative US dollar bank deposits. In a world without banks, Bernanke would exercise just as much control over the price level. Given the observational equivalence of a world with banking and one without, I don't think Sumner, who is primarily interested in manipulating NGDP, is off base in his lack of interest in banking.

Of course, Sumner may have an entirely different reason for ignoring banking than the explanation I've put forward. As for banking in general, I do I think it is important to understand it since there is more to understanding economies than the range of issues that interest Sumner.

*I think the unit of account role is a more accurate word to use than medium of account. Shops post prices in terms of the unit of account, not the medium of account.

Update: Cullen Roche adds a response.

IMF SDRs: the world's largest LETS

IMF board room, 1977

I like to think of the International Monetary Fund's special drawing rights (SDR) program as the world's largest Local Exchange Trading System, or LETS. A truly unique part of the monetary landscape, what follows is a short visual essay on SDRs.

What is an SDR?

An SDR has two aspects. First, an SDR is a unit of account, or, put differently, a measure of value. As a unit-of-account, the SDR is defined by the IMF in terms of a reference good, or a medium of account. When the SDR was first introduced in 1969, an SDR was defined as 0.888671 an ounce of gold, so the yellow metal was the SDR's first medium of account. The IMF later redefined the SDR as a certain quantity of central bank currencies. As of 2012, an SDR is comprised of a basket of 0.423 euros, 12.1 yen, 0.111 pounds, and 0.66 US dollars. Thus the modern day SDR is defined in terms of multiple media of account.

The Suez Canal Authorities currently uses the SDR to calculate the Suez Canal Tariff, while the the Universal Postal Union, which coordinates international postal duties, uses the SDR as a unit of account. Apart from these and a few other rare examples, the SDR is not a popular unit of account.

In addition to existing as a unit of account, SDRs also function as media of exchange. This is the aspect of SDRs I'll focus on from here on in.

SDRs as LETS

In many ways, the SDR system represents a souped-up Local Exchange Trading System, or LETS. In a LETS, each member of a local community gets an initial line of credit. These credits, which are accepted by all members of the LETS, are liabilities, or claims, of all LETS members on each other. A LETS member can spend down their line of credit by purchasing stuff from other members, and replenish their line of credit when others spend at their own shop. No one can spend more than their line of credit.*

All LETS need an administrator. The administrator takes on no risk, nor are they liable for credits issued. They simply maintains the books of the LETS and ensure that the system operates efficiently.

Much like a LETS administrator maintains a LETS, the IMF "SDR Department" maintains the SDR system. SDRs are not issued by the IMF, nor are they claims on the IMF. Rather, the community of nations jointly issues SDRs. In the SDR system, each country's respective line of credit is referred to as its "allocation" of SDRs. In general, the larger a nation's GDP, the greater its allocation. The US's current allocation is around SDR 35 billion, whereas Canada's is SDR 6 billion. Cyprus's allocation amounts to a meager SDR 132 million. (One SDR is worth about US$1.50, so Canada's stash of SDRs comes out to around $9 billion)

SDR holdings vary over time as SDRs are spent from nation to nation and as new credits are created. The chart below shows total SDRs in existence. It gives a sense of how SDRs are distributed between some of the program's largest members and blocks.

Individual members can't simply create new SDRs willy nilly. All members must jointly agree to create them. In 1971, 1972, 1979, 1980, and 1981 the total amount of SDRs was increased, but after that a long freeze set in. In 2009, in the midst of the credit crisis, members agreed to an increase in SDR credits from $21 billion to $204 billion. You'll notice in the chart that the BRICs received a far larger shot of SDRs than they did during previous allocation top-ups because their relative position in world GDP has increased so much.

It's particularly interesting to break down the distribution of SDRs. Over time, members will either spend away their SDR credits so that they are holding less SDRs than originally allocated, or they will acquire SDRs so that they are holding more than they were originally allocated. Surplus nations receive interest payments from deficit nations.** We can see the distribution of surplus and deficit countries in the histogram below. In general, far more countries are in an SDR deficit position than a surplus position. Put differently, most counties hold less SDRs than they were initially allocated.

...which doesn't make much sense. If countries spend away SDRs, someone must be left holding the bag. SDRs cannot be uncreated. This is where the IMF once again re-enters our story. While only states can enjoy SDR allocations, certain supranational organizations like the IMF are allowed to purchase SDRs from states after SDRs have been created.*** As my first chart shows, the IMF is a large holder of SDRs and possesses a portfolio that shows much more volatility in scope than the other nations and blocks.

Let's explore this more. The chart below ranks all countries by the excess of holdings over allocations. Deficit countries lie below 0, surplus ones are above. I've added the IMF too which, as the chart shows, is by far the system's largest accumulator of SDRs. The IMF currently holds around SDR 12.7b. The only reason that most countries on the chart are able to be in deficit positions is because the IMF serves as an SDR sop.

Try playing with the slider above by pulling the top tab from 12,691 down to 0 or so. This filters out the IMF and the surplus nations, thereby providing more resolution on the system's greatest deficit countries, which includes the Ukraine, India, Romania, and Hungary. The Ukraine, for instance, has sold of SDR 1.3 billion of its initial allocation (more on this later).

It's also useful to rank countries by their percent surplus/deficit rather than their absolute surplus/deficit. In the chart below, those countries distributed close to the 100% level have about the same number of holdings that they were initially allocated. Anyone over the 100% line holds more SDRs than they were allocated, and those below 100% have been sellers.

Use the slider above to zoom in on the biggest surplus countries. Oddly, you'll see that Libya leads the pack, holding 150% of its initial allocation. One reason for this may be the fact that the Libyan dinar is pegged to the SDR, a link that has been in place since 1986. A buffer of SDRs would be necessary for the Libyan monetary authority to protect the peg. According to the Sadeq Institute, the choice of the SDR was made by the Gadaffi regime in "symbolic retaliation" to the US. Prior to 1986, Libyan dinar's had been pegged to USD. Botswana also has an outsized SDR portfolio. The Botswanan Pula has been pegged to a mix of the South African rand and the SDR since 1980, a policy that would presumably require a large stock of SDRs.

Zooming in on the deficit side of the chart, you'll see that the Ukraine is the third largest deficit nation, having sold all but 0.45% of its initial allocation. Ukraine was hit hard by the 2008 credit cirsis. It also imports terrific amounts of natural gas, much of which gets exported on to Western Europe. In order to pay its natural gas bill late in 2009, it used almost its entire SDR allocation.

Is a nation's per capita GDP related to its status as SDR debtor or SDR creditor? The chart below charts per capita GDP along the x-axis and SDR position along the y-axis.

Most rich nations, those in the two right quadrants with per capita GDP in excess of $10,000, tend to cling closely to 1.0. They are neither in large surplus nor deficit positions relative to the system. Iceland and Hungary, which hover near the bottom of the bottom-right quadrant, are outliers. Both have per capita GDP's above $10,000 but have largely drawn down their SDR balances. Hungary, which only received its first allocation of SDRs in 2009, was hit hard by the financial crisis and  forced to liquidate many of its new SDRs in order to meet bills.

What all these charts illustrate is that except for the IMF (and a few countries that fix to the SDR), only a minority of countries have been net purchasers of SDRs. Most have been sellers. Put differently, members of the SDR LETS have been quite content to be short SDRs, not long. Why? Many poorer countries are no doubt forced by circumstances to sell off a large part of their allocation. But even then, a large proportion of wealthy countries including almost every European nation, the UK, Australia, India, Brazil, and Canada are in deficit.

I'm speculating here, but the general aversion among states to holding SDRs may be due to a weak point that the SDR system shares with any other LETS system. Consider this: what happens to a LETS when a member in deficit splits town only to never be seen again? If the departing member fails to rebalance their account prior to leaving, then the amount by which they are in deficit will never be recouped by remaining members. All members must collectively absorb the loss. The same goes for SDRs. If Iran wishes to leave the system, what guarantees that prior to departure they'll honour their obligation to the system by purchasing enough SDRs to return them to an even level?

Taking this even further, imagine if a large block of deficit nations left the SDR system. What guarantees that SDRs will continue to be valued at their stipulated value of 0.423 euros, 12.1 yen, 0.111 pounds, and 0.66 US dollars? Remaining nations may start to bid SDR prices down until SDRs trade at a wide deficit to their ideal value in terms of media of account. At some point, the IMF might be required to announce a lower value for the SDR in order to catch up to its declining market value.

Alternatively the IMF could prop the system up by purchasing all SDRs at their ideal value of 0.423 euros, 12.1 yen, 0.111 pounds, and 0.66 US dollars. If it did so, the IMF would be left holding a large chunk of the system's SDRs.

But hold on a sec... isn't that already the case? Most countries have been net sellers, leaving the IMF (and other supranationals) currently holding some 6.2% of the total SDR float. This might be a sign that member nations have from time to time valued the SDR at somewhat less than 0.423 euros, 12.1 yen, 0.111 pounds, and 0.66 US dollars and, given the opportunity to sell at an overvalued rate to the IMF, they have seized that opportunity. The asymmetric distribution of SDRs does not give one much confidence in SDRs as assets.

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*Many LETS do not limit member lines of credit. They leave it up to members to self-monitor the system.
**The SDR system defers markedly from a LETS in this respect. Most LETS frown on interest payments.
*** Other parastatals currenlty holding SDRs inclue the Arab Monetary Fund, Bank for International Settlements, Bank of Central African States, Central Bank of West Africa, European Central Bank, and the Islamic Development Bank. Total holdings of these instituitions comes out to about 1/12th that of the IMF's SDR holdings.

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.

Discussions of the medium-of-account could be more well-done

Nick Rowe, Scott Sumner, and most recently, David Glasner, all say that the US's current medium of account is the dollar. I disagree. I think that the current medium of account is CPI units. Here's why.

First, there's been some sloppiness with definitions in the links above, so let's define the term. The medium of account is whatever defines the unit of account. I think this a pretty standard definition. That's Bill Woolsey's definition here. David echoes this definition in his comment here.

Take an old-style central bank that holds 100% gold reserves in its vault. It chooses the word "dollar" to stand as the unit of account. The bank then goes on to define the dollar as equal to x grains of gold. Thus the medium of account is gold. Our central bank issues paper notes which are to be used as the medium of exchange. Shopkeepers post prices in terms of the unit of account, the dollar, and accept notes as payment. Some shopkeepers might even choose to post prices in grains of gold rather than the dollar unit of account. If they do, this won't affect the fact that gold remains the medium of account.

Inspired by the Bank of Canada, our 100% gold bank chooses to sell all its gold for bonds. Next it chooses to redefine the value of the dollar as an idealized basket of consumer goods that declines in size by 3% a year. It threatens to do open market operations in a manner that ensures that its definition sticks.

What has changed? Shopkeepers continue posting prices in the unit of account, the dollar. Notes issued by the central bank are still the medium of exchange. But the definition of the dollar, the medium of account, has changed from a quantity of gold to a gradually shrinking quantity of consumer goods.

Some shopkeepers might even post prices in terms of this imaginary basket of goods. When shoppers arrive at the till to pay, they obviously can't hand over CPI baskets. Rather, the shopkeeper will download the central bank's most recent CPI-to-dollar ratio and quote the customer their final price in terms of notes, the medium of exchange.

To sum up, in moving from a fully-reserved gold bank to a modern CPI targeter, all that's happened is that our central bank has changed the medium of account from gold to CPI. Nick has to understand where I'm coming from since I'm just using the same technique he used in this post.

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.

My synopsis of the MOE vs MOA debate

Bill Woolsey, Scott Sumner (here and here), and Nick Rowe and a debate that was fun to follow. It seems to me that they more or less end up on the same page. Here's my rough synopsis.

The argument seems to have started as a semantic battle over the definition of the word money. Scott holds that money is the medium of account (MOA), Nick and Bill say it's the medium of exchange (MOE). I say ignore this part of the conflict. Pretend the word money doesn't exist. Money. The semantics detract from the main points of the debate which, to me at least, is about how price rigidity, MOA, and MOE interact to cause recessions.