Friday, September 13, 2013

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.

[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.


  1. Another very good post JP. I always wondered about those "imaginary" monies.

    Funny we should both post on MOA vs MOE on the same day.

    1. Great minds, Nick, great minds ;)

      I'm mulling over your post right now. It's succeeded in tying my brain in a knot.

      From what I've read over the last week, there seems to be a consensus among historians that there was no such thing as imaginary money. Since ghost money is defined in terms of a fixed amount of gold, it escapes the imaginary money category.

    2. JP and Nick, thanks for doing your posts (respectively). Scott has done another, calling out Roche. Lot's of activity on this again. (JP, I was hoping you'd update the debate... somehow I knew you'd come through)

      BTW, JP, I can't post links to you on Scott's site. Probably a Wordpress issue. I know someone else who can't use their own name or links to their site on Wordpress sites either: Vincent, the hyperinflationist. You're in good company!

    3. Tom, use html.

      <a href="" > Scott Sumner's post < /a >

      will look like this:

      Scott Sumner's post

  2. JP - are you saying then, that the index coins had more 'moneyness' than other coins?

    I'm not a fan of functional definitions of money. But yes, UOA is big cheese. I'd say however that the relationship between UOA & MOE would have been reflexive (if that makes any sense at all).

    Your post made me grab Joel Kaye's Econ & Nature in C14th off the shelf. He has a reoccurring sub-heading 'Money as Medium and Measure' which looks at how the scholastic community was influenced by its use of money and how this in turn influenced the development of philosophy & 'proto-science'. I'm more inclined to think that the separation of functions is a modern projection onto medieval coinage rather than 'something that our ancestors dealt with on a daily basis'.

    Having said that, when I was looking at coin hoards in the Ashmolean recently it struck me just how tricky it must have been for your average medieval merchant, particularly in port towns, to keep abreast of current coin. Not only that, there must have been people digging up old hoards and trying use them in the market place, too. You'd need to rely on an instinctive valuation to deal with that, I reckon.

    1. Hi Jon, thanks for stopping by.

      I don't think medieval index coins necessarily had more 'moneyness'. I tend to think of moneyness as the relative ease of exchanging some coin or item, or its degree of saleability. A coin's saleability would have depended on people's trust in the mint and the degree of standardization across a given coin. From what I've read, members of the same coin family varied in quality (ie. metal content) so that even though the index coin defined the unit, each individual index coin probably had to be carefully evaluated to determine how far it had deteriorated from the standard. This lack of homogeneity would have inhibited index coin saleability just as much as it would have inhibited non-index coin saleability.

      You make an interesting point about the separation of functions being a modern projection onto medieval coinage. James Steuart's Inquiry into the Principles of Political Economy, published in 1763, goes into some depth on the difference between money-of-account and money-coin.

      Mind you I haven't looked through it in ages.

    2. Jonathan: "I'm not a fan of functional definitions of money."

      Could you explain why not?

    3. JP - Thanks for the reply. I'd like to try your patience with one more question if I may. So, (in the medieval) world the thing that had most 'moneyness' was precious metals? The index coins functioned rather like the marks on a measuring stick. You know there's twelve of them in a foot-long stick, whether they're all the same distance apart, you're not so sure.

      Steuart's name has been mentioned a lot in my reading of late. I had pulled out a couple of quotes - its not really relevant but this is my fav from Marc Shell stressing the importance of his influence

      I've never read him in the raw, so the link is very much appreciated. Thank you.

      Nick - Morris Perlman delivered my macroeconomics lectures. I have a vivid memory of him standing on stage and in (I think) his first lecture, in his thick accent saying 'Money ees, vot money does'. I thought 'that's not really true'. I'd already stuck up my hand in the microeconomics lecture infront of 1200 students to say the same about the assumption of self interest. So I really didn't want to experience the shame of doing the same thing with the wonderful Prof Perlman.

      I guess I must have some sort of unresolved anxiety over functionalist definitions of money :)

      I find they too easily become the totality of our understanding of money. I don't agree that money can be defined in terms of its functions.

      I remember noticing the negative effect of this functionalist line of thought in Seaford's brilliant 'Money and the early Greek Mind' - for me, it was only once Seaford let go of 'functions' and allowed himself to explore 'features' that he really started to say important things about money. I also found Einzig's work constrained by this idea that because we define money by its functions, if we want to find money in primitive societies we need look for something that performs those functions.

      Thanks for the engagement chaps. It does get lonely in my weird little corner of the moneyverse so I appreciate it. I'm off on my holidays for five days now (literally, I'm just about to load the car) - to New Quay in Wales where Dylan Thomas used to get drunk. I intend to follow his fine example, so won't be able to catch any more of the conversation til I'm back. But thanks again.


    4. Pearlman wrote a great paper on Adam Smith and the real bills doctrine that I've read a few times.

      I view moneyness as saleability. The items that were near the high end of the moneyness scale would appear more often in exchange whereas those that rarely appeared would appear near the low end of the scale. The assumption is that the more occasions on which a commodity or instrument appears in trade, the more saleable it is. In medieval days, gold and silver would have high moneyness, but coined precious metals would probably have ranked higher. Credit, circulating bills of exchange, would also have had high degrees of moneyness.

  3. JP, is this an error?:

    "say 1 pound 6 shillings. A buyer need only look at the 6£ 1s"

    should you have

    "say 1 pound 6 shillings. A buyer need only look at the 1£ 6s"


  4. JP, I'm wondering if all these definitions are meaningless without understanding liquidity and convertibility/arbitrage between various forms of payment. Convenience yield will vary by liquidity of individual media. Even the UOA (e.g. gold,silver) is subject to rumours from the New World of significant discoveries or forgeries. Also, what about legal ramifications; were there laws or customs that required use of certain media?
    Back in the modern world, I've been thinking about puzzles like:
    (a) if we just had one big private bank and all settlement is between depositors, wouldn't Fed Funds become meaningless? What would be the UOA?
    (b) what about if settlement is not via FedWire (e.g. repo, collateral posting, chattel)?
    (c) is "settlementness" the same as "moneyness"?

    1. jt26, I asked JP a similar question here:

      DOB agreed with me there:

      and Sumner doesn't:

      "On your second point, most money is held for reasons of tax evasion, not monetary frictions. In “models” it is sometimes held for reasons of monetary frictions."

      So JP, does that factor into your convenience yield at all: desire to avoid taxes? Certainly not for reserves!

    2. Regarding your part (a): Fed funds would still be required for any transaction in which either the Fed or a Fed deposit holder was at least one of the counterparties: e.g. when you or I pay taxes or gov contractors get paid, etc. In terms of whether they are meaningless or not, I don't know.

    3. Good point about taxes. But, my comment is less about the HPE of base then generally about settlement media. The lender-of-last-resort function of CBs and especially all the emergency programs at the Fed during the GFC shows that settlement actions of the government define the UOA. The Fed observed settlement distress in many markets and intervened with UOA, or future commitments for UOA, at the margin.

    4. Tom and jt26,

      You both asked a good question about what might happen if settlement didn't happen on the Fed's books. Funny enough, I've been planning on writing a post about this next week or the week after, sort of along the lines of what might happen if bitcoin were to outcompete the Fed. What happens if all interbank payments were cleared with bitcoin? How would bitcoin's dominance interfere with the Fed's abilities to conduct monetary policy? So stay tuned, I'll have my answer then.

      "(c) is "settlementness" the same as "moneyness"?"

      Moneyness is more general than settlement-ness. Any medium that can discharge a debt is a settlement medium, at least according to my understanding of the term. Moneyness refers to general saleability, or exchangeability. The ability to use something as a settlement medium surely contributes to its exchangeability, but goods that are not used for settlement can still have a high degree of moneyness.

      "So JP, does that factor into your convenience yield at all: desire to avoid taxes? Certainly not for reserves!"

      Yeah, not for reserves. Criminals can't hold reserves, only bankers can. Bankers' desire to address the uncertainty of the future is what motivates their desire to hold reserves. Why else would they hold a 0% yielding instrument?

  5. JP:

    Your blog was already the best econ blog out there, but with all these historical details, and with external links like Einaudi, Weber, and Spufford, you've left the rest in the dust.

    1. Thanks Mike. Gotta keep the readers happy. And the more of you commenters the better, since you guys keep me honest, provide ideas, and teach me stuff.

    2. Second that. Also love the Canadian content, like the Molsons Bank money (and $7 bills!) and the BoC balance sheet views. BTW somewhat related to settlement, I once asked David Beckworth about the (mythical?) shortage of safe assets as settlement media and used the Canadian Payments System as an example:
      ... so it's fun to see more Canadian-ness on the econ blogosphere!

  6. JP, recalling your definitions for MOA and UOA with inflation targeting:

    MOA = CPI basket of goods
    UOA = dollar = certain sized slice of that basket, shrinking at the targeted inflation rate each year.

    How would that change with NGDP targeting?

    1. See this post:

    2. Great, thanks JP. Going back to inflation targeting for a moment, say the target inflation rate is 1% and the CB is hitting its target, then on Jan 1, they announce a new target of 2%. A year later, Dec 31, the inflation rate was calculated to have been instead 3%.

      When did the UOA change? Jan 1? What did it change to? Is the proper way to conceptualize this that the UOA is a ever shrinking slice of the CPI basket of goods (with each good in the basket present in the proper proportion to other goods), but that the actual size of the slice at any one time is a hidden variable that can only be estimated? Do you see what I mean? In other words, say the 3% figure for the year was 100% accurate, then is the CPI basket slice which defines the UOA 3% smaller even though 2% was targeted? I would think so, right?

    3. Tom, the unit of account stays the same, since it is just a sign like $ or £.

      When the central bank hits 3% instead of 2%, it has accidentally allowed its circulating media of exchange -- paper bills and reserves -- to fall faster in value against the CPI basket than the idealized 2% target.

      If shopkeepers use the ideal 2% declining basket to define how many £ or $ they ask for (ie. as the MOA), then no problem. Pricing behaviour needn't change and sticker prices will continue to fall 2% annualized each day. If shopkeepers use the central bank's media of exchange to define how many £ or $ they ask for, then pricing behaviour will change and they will begin to mark down prices at a rate of 3%, not 2%.

      This dichotomy is very similar to the idea of using either a current silver coin to define the £ or using a historically fixed/idealized index coin to define the £. The former is similar to using circulating central bank notes and deposits to define the £, the latter is like using the 2% ideal target to define the £.

    4. JP, Thanks for that. One question about your first sentence: I mistakenly thought that you'd lumped the sign (e.g. $) in with the definition of the sign in terms of the MOA and called both the sign and the definition the UOA! I thought that was a difference between you and Woolsey, but I guess not.

      Then it seems to me we need in addition to an MOA and a UOA a third entity: a "definition" which relates the UOA to the MOA. True? Do you just refer to this as "the definition?" Say for example in a simple fixed gold standard with $1 = 1/35 oz.

    5. Oh wait... so you're combining the definition into the MOA?

      Back to the gold standard example. I thought w/ the gold standard, we have:

      MOA = gold

      No mention of how much gold, just gold. Wasn't that Bills point? Didn't he say it could just as well be:

      MOA = electric energy

      It's not until you adopt a UOA (e.g. $) an a definition for that UOA in terms of the MOA, e.g.:

      $1 = 1 kw-hr of electric energy

      That you have to full story?

    6. Apologies if I may have shifted definitions over time. This research that went into this post really clarified my understanding of what is often a confusing set of distinctions between MOA, UOA, and MOE. Here's where I am now:

      UOA: the various signs like £/s/d and $/¢ and the ratios between them (ie 100 cents in a dollar)
      MOE: the entire range of gold, silver, and copper coins in circulation, many of them foreign.
      MOA: the thing that is used to define the UOA. In medieval days, it was an index or link coin, typically the penny. Should we say that the penny itself was the MOA or was the quantity of silver residing inside the penny the MOA? Did the MOA change when the metal content of the link coin was debased? What if the link coin was recalled and reissued as a gold coin? Did the MOA change from silver to gold, or was the MOA still the penny? Much of this is semantic, but whatever the case, the MOA is a complex feature and we need to understand its various facets if we want to understand what determines the price level. (So long story short, I'm combining the definition into the MOA).

    7. Ah, OK. So you're saying it's not always a simple story. But Let's translate to a simple story. Say we have a gold standard with $1 fixed equal in value to 1/35 oz gold (not in any particular format... just pure gold). Then how would this work:

      UOA = $ is the "dollar"... divided into 100 equal cents.
      MOE = reserve notes, coins, etc.
      MOA = {the following definition: 1 dollar = value of 1/35 oz gold}

      How's that?

    8. BTW, I've never been swayed by gold standard arguments, but it does seem to me it has one advantage:

      It the CB is responsible for defining the UOA, MOE, MOA etc. Instant inflation or deflation available. $1 defined as 1/20 oz?... and deflation is looming? No problem: $1 is now defined as 1/35 oz. Voila! (I know that leaves open the sticky issue of convertibility, etc... and there are plenty of things I'm overlooking there... but still, compared to endless hand-wringing over QE and transmission mechanisms and what kind of assets to purchase and tapering, and IOR.... it sure seems simple! No "forward guidance" required... it happens today!).

    9. "MOA = {the following definition: 1 dollar = value of 1/35 oz gold}"

      That depends. The MOA could be a link gold coin, say the gold guinea. Or it could be some ideal quantity of gold "grains". Or it could be a gold-backed note. All three are similar in that they are fixed quantities of gold or embodiments thereof. This means that in each case, if gold becomes relatively more valuable, shopkeepers will universally react by reducing prices in terms of the unit of account.

      But it's useful to drill down into the specific nature of each MOA because the locus of control is different. If the link coin is manufactured by a specific mint, any debasement on the part of that mint's mint-master will cause a change in sticker prices, even if the gold's relative price hasn't changed.

      If some ideal number of grains has been adopted as the MOA, then changes in the quantity of gold in coin will have no effect on prices since coin is no longer the MOA. However, if this ideal quantity is set by edict, then whoever sets this amount can change sticker prices, even if the relative price of gold is constant over the interim.

      Finally, if a particular brand of gold notes functions as the MOA, then the locus of power over the price-level resides with the note-issuer, since they get to choose the amount of gold into which a note can be converted. Even if the price of gold stays relatively constant, the issuer can increase the price level by setting notes equal to a smaller quantity of gold.

  7. JP, I'm wondering what you think of this description of "paper gold" that Sumner gives:

    "Regarding paper gold, cash provides a flow of liquidity services. That’s what gives it value. If you double the supply of cash it doesn’t provide any more liquidity services, hence it’s value in aggregate is unchanged. It’s value per dollar falls in half."

    How do these "liquidity services" relate to your convenience yield? Is there a difference?

    1. "How do these "liquidity services" relate to your convenience yield? Is there a difference?"

      I see that he brings the term up again here. There could be a similarity. But it's the only time he talks about it, so it's probably not an important concept in his world view. I guess I'd need some more color from him to be sure.

  8. Hi JP, O/T: have you ever looked into the economy under the Anarchists of Barcelona during the Spanish Civil war? I saw a documentary on the war the other day... it seemed like an incredibly strange situation there.

  9. JP, I recently engaged in a thread with Scott Sumner, using your concept of the CPI slice as the MOA, but I could not understand his two word reply. First here's a link:

    Now I'll copy and paste the pertinent bits:

    Fed Up (another commentator):
    "I am pretty sure monetary base (currency plus central bank reserves) can be zero with the economy still being fine. MOA would equal demand deposits here just like they are now because of 1 to 1 convertibility (relative pricing).”

    Scott Sumner:
    "Sure, but then DDs [demand deposits] are the medium of account. BTW, what exactly is available “on demand” in a DD when there is no cash or reserves?"

    Tom Brown:
    "A small slice of the CPI basket of goods?"

    Scott Sumner:
    "Transactions costs?"

    It's not terrible important... but perhaps you know what he's getting at there. Why, do you think, is that his response and what does he mean by it? (this particular thread on Scott's site is LONG past stale, so I'm a little surprised he's still answering questions there). Of course the thing to do is ask Scott!... but I thought perhaps I'm just missing something simple here. Any idea?

    1. "BTW, what exactly is available “on demand” in a DD when there is no cash or reserves?"

      If deposits are inconvertible, what would determine their value? Some people like Scott that they will still be valued for their ability to avoid transaction costs. That could be it.