Monday, November 7, 2016

A New Monetary System From Scratch, Part 1: Unit-of-Account and Numeraire

Nick Rowe at Worthwhile Canadian Initiative comes up with new thought-experiments at an enviable pace. His subjects often touch my research interests, but with his recent post Synchronisation and the Gross Money Supply he managed to really hit a nerve in me. That blog post is the proximate cause for me starting to blog about research I've been doing the last three years.

Nick begins his post:
You decide to make a new monetary system from scratch. You give everyone a chequing account on your computer, with an initial balance of 0 units. If Andy buys bananas from Betty and pays her 100 units, Betty now has a positive balance and Andy now has a negative balance.[1]

This setup is identical with a monetary system I've been studying intensively that is, I often dream about it and wake up every morning with a deep sense of duty for the last 12 months. Prior to that, I worked 20 months as intensively to arrive at the setup; this is what makes me envious of Nick's ability to come up with thought-experiments!

I have two suggestions which might help us make more sense out of Nick's new system:

  1. Let's explain what a 'unit' is (Nick doesn't). We have to know why Andy and Betty agreed that the price of the goods (bananas) should be 100 units, and not, say, 10 units. Notice that there are no units in existence, not even in the "accounting realm", when Andy and Betty agree on the price.
  2.   Let's not use, uncritically, old language and concepts when describing a new monetary system.

Eugene Fama[2] has touched on both of these points:

Suppose we have... an advanced society in which it is economic to carry out all transactions through the accounting system of exchange provided by banks. The system finds no need for currency or other physical mediums of exchange, and its numeraire has long been a real good, say steel ingots. The society is so advanced that terms like money, medium of exchange, means of payment, and temporary abode of purchasing power have long ago fallen from its vocabulary, and all written accounts of the ancient ‘monetary age’ were long ago recycled as part of an ecology movement.

Suppose now that, for whatever reason, the government of this society decides that it would be more aesthetic to replace steel ingots as numeraire with a pure nominal commodity which will be called a ‘unit’ but which has no physical representation. Although monetary theory has long since passed away, value theory has strengthened with time, and the government’s economists realize that the ‘unit’ cannot be established as numeraire by simple decree. It must be a well-defined economic good, that is, the ‘unit’ needs demand and supply functions which can determine its equilibrium value in terms of other goods.

As Nick's description currently stands, his 'unit' is just like the initial 'unit' Fama criticizes. I don't agree with Fama, though: the 'unit' doesn't need to be a numeraire (I'm not thinking in terms of an equilibrium, like Fama was). But we still have to be able to explain why the price Andy and Betty agreen upon was 100 units and not 10 units.

To start with, I'd like to replace Nick's "unit" with "skilo". It's more convenient to use a word which, for most of us, has no real meaning. But this 'skilo' used to refer to something concrete in the economy under study. A long story short:

Imagine a closed economy where the numeraire is a kilogram of salt; the price of a watermelon might be 1.50 salt-kilos "s-kilos" in short. All goods are priced in s-kilos, which is the unit of account (notice the subtle difference between the numeraire and the unit of account). By definition, the price of the "numeraire good", a kilogram of salt, is 1 s-kilo. Goods are exchanged against other goods, and salt doesn't need to appear as one of the goods in a transaction (because of this, salt is not 'money' as Clower[3] defined it). When we have established (sticky) market prices expressed in s-kilos for most of the traded goods, it becomes feasible to denominate bilateral debts in s-kilos; this arguably makes the prices even more sticky. In most cases these debts didn't arise because the debtor bought salt "on credit", neither do debts need to be paid in salt. The debtor can deliver to his creditor a sack of flour, for instance. (The parties can sue each other if they don't agree on the price, but usually they come to an agreement as trade is seen as mutually beneficial.)

The system works as long as the real cost of procuring salt remains more or less stable, so that prices of other goods don't need to be constantly changed or the nominal value of outstanding debts (usually short-term; < 1 year) adjusted. But let us now imagine that one day well, abruptly anyway the real cost of procuring salt, due to a technological shock, is reduced by 50 %. The community faces a choice: Should they adjust prices of all goods (except salt) and nominal values of all debts a formidable task including menu costs and mental costs , or should they only adjust the price of a kilogram of salt? The majority of our agents are flexible thinkers, so they choose the latter option: the new price of a kilogram of salt is 0.50 skilos. What is a 'skilo'? It's nothing you can touch, nothing you can point at. It's an abstract unit of account. It cannot be a numeraire, because there isn't any supply of, or demand for, it.

OK. We have a unit of account: skilo. A kilogram of salt has ceased to act as a numeraire. If we stretch the concept of a numeraire a bit, we could say that all goods with sticky prices act as numeraires of sorts. Our economy looks much like the economy Ralph Hawtrey[4] had in his mind here:

Suppose then that society is civilised, and that money does not exist. Goods are brought to market and exchanged. But even though there is no medium of exchange, it does not follow that they must be bartered directly for one another. If a man sells a ton of coals to another, this will create a debt from the buyer to the seller. But the buyer will have been himself a seller to someone else, and the seller will have been himself also a buyer. The dealers in the market can meet together and set off their debts and credits. But for this purpose the debts and credits, which represent the purchase and sale of a variety of goods, must be reduced to some common measure. In fact a unit for the measurement of debts is indispensable. Where a commodity is used as money, it naturally supplies the unit for the measurement of debts. Where there is no money, the unit must be something wholly conventional and arbitrary. This is what is technically called a ''money of account"... This is an approximation to the state of affairs which we are assuming. But however conventional and arbitrary the unit may be, once it is established as the basis of the debts and prices and values of a market, it is bound to assume a certain continuity.


Each dealer in the market calculates his own command of wealth in the same unit; it affords the basis for his valuation both of what he wants to buy and of what he wants to sell, and he looks for only such divergence from the previous prices as variations of supply and demand will justify. The total effective demand for commodities in the market is limited to the number of units of the money of account that dealers are prepared to offer, and the number that they are prepared to offer over any period of time is limited according to the number that they hope to receive. Therefore, arbitrary as the unit is, capricious variations in its purchasing power will not occur.

Arthur Kitson has suggested something very similar to our concept. Cowen & Kroszner[5] explain Kitson's idea like this:

An abstract medium of account can be defined by setting the value of any commodity on a given day equal to “one” and pricing all commodities in terms thereof. For all succeeding market periods, however, this link is severed and only the abstract medium remains. Market participants set prices (in terms of abstract media) by reference to the abstract medium-denominated prices of the preceding period. The abstract medium is derived from a sequential process which ultimately refers back to an original commodity value.

Kitson talks about our 'skilo', doesn't he?

Now we can finally start re-writing Nick's story. Andy buys bananas from Betty, after agreeing with her on a price of 100 skilos for the said bananas.[6]

In the current blog post, we have dealt with this task:
  1. Let's explain what a 'unit' is. We have to know why Andy and Betty agreed that the price of the goods (bananas) should be 100 units, and not, say, 10 units.

In the next post (Part 2), I will start re-interpreting Nick's new monetary system. I will avoid words like "money", "money supply" and "payment". The accounting stays the same. The way we established skilo the "origin myth" of our unit of account will affect our interpretation of the system going forward. (It would be very interesting to hear how Nick establishes his 'unit'. It would probably make comparison of our ideas easier.)

Stay tuned.

Part 2: Records Schmecords


[1] Nick continues: "The Net money supply remains at 0 units, but the Gross money supply is now 200 units."

Having read him often, I should by now understand what he means with the last sentence. But I don't. I know Nick thinks there exists both positive money (which he sometimes calls "green money": for instance, here, here and here) and negative money ("red money"), and he seems to sum the amount of both types of money to arrive at the gross figure, 200 units. Nick is a clever guy, so I'm sure he has a good reason to think like he thinks, but like I said, I haven't fully figured out the reason yet.

[2] Fama, Eugene. 1980. “Banking in the theory of finance” (p. 55). 

[3] Clower, R. W. 1967. “A Reconsideration of the Microfoundations of Monetary Theory”. Clower writes: "Money buys goods and goods buy money; but goods do not buy goods." (p. 5)

[4] Hawtrey, Ralph George. 1919. “Currency and Credit” (p. 2).

[5] Cowen & Kroszner. 1994. “Explorations in the New Monetary Economics” (p. 126). They refer to Kitson: "Mr Kitson's Defence", 1895.

[6] Andy could have bought 200 kg of salt from Steve for the same price, so in our economy bananas might be a luxury item, salt supply abundant or then we are talking about a lot of bananas... I'll go for the latter.


  1. Welcome to Blogland in English!

    After looking forward to learning more about your ideas for several days, I am beginning to see them. Thanks for sharing.

    My thoughts so far: I notice that bananas and skilos are both off-ledger assets. They both first appear on-ledger when a trade occurs.

    Bananas and skilos have an assumed beginning ratio to each other.

    Andy (in Nick's reference model) has neither bananas nor skilos but still his transaction is recorded in the ledger.

    Betty (in Nick's reference model) trades bananas for a positive ledger entry. Betty has gone from off-ledger to on-ledger.

    Andy has assumed Betty's pre-trade off-ledger position. He has also been entered on-ledger with a negative entry. Andy has gone from invisible to become a holder of off-ledger bananas and on-ledger negative entry.

    An interesting start. I wonder where this will go?

    1. Thanks, Roger!

      I like your off-ledger/on-ledger approach. On-ledger world is what I called an "accounting realm". To avoid misunderstandings, I'd like us to clarify a couple of things you said:

      "I notice that bananas and skilos are both off-ledger assets. They both first appear on-ledger when a trade occurs."

      Skilos are no off-ledger assets, right? Think of the barter-credit, pre-monetary system world (ie. no entries are yet made on accounts in the new ledger). 'Skilo' is just a unit in which the price of goods is expressed. We shouldn't call it a "unit of measurement", but it is similar to a 'meter' (or 'metre') in the sense that neither of them exist: no one can hold a 'meter' either. It is impossible to think of someone holding a 'skilo', even in a figurative sense, so it cannot be an asset.

      You say that bananas appear on-ledger when a trade occurs. But then, in the end, you say that Andy holds off-ledger bananas. The latter is correct, right? Bananas don't appear on-ledger. They exist in the "real world" (vis-à-vis "accounting realm").

      Where will we go from here... It seems clear to me that we need to first motivate the use of the new monetary/accounting system. There is no money in our economy, so I don't see that we can just declare that we establish a CENTRAL BANK which issues money called 'skilos' by crediting Betty's account (Nick's Language: "positive skilos") and debiting Andy's account (NL: "negative skilos"), and in this way skilos not only come into existence but become a "means of payment". That doesn't sound plausible -- especially if we assume that there has never been money in our economy.

      How does this sound?

    2. A short comment on bilateral debts which might make the expression "unit-of-account" more concrete:

      If Betty had previously bought apples from Andy for 50 skilos (or s-kilos; it doesn't matter what the price of one kg of salt was at the time) without giving him anything in return, Andy and Betty would have both recorded in their personal ledgers/books, mental or physical, that there is a skilo-denominated debt, priced at 50 skilos, from Betty to Andy. A&B being used to trade with different people, the ledgers would probably be physical (or electronical), and Andy's ledger would have an account named "Betty", and vice versa.

      It makes sense to call 'skilo' a unit-of-account, doesn't it?

    3. First some humor: It's early morning here and I am reading deep thought! Like you, I think the details are important (very important). The problem is that the details are viewed from so very many angles, with so many colors, and even in different time frames. I smile at the complexity!

      Well,,, I certainly agree that the skilo is a valid measure of account.

      Next we can think of the VALUE of the skilo. Value can be seen from many perspectives, none of them equal. In Nick's example, Betty thinks Andy's 100 POSITIVE units (skilos?) on-ledger is a fair trade and (in my view) establishes value. Betty begins the trade with bananas and ends the trade with 100 POSITIVE credits on-ledger.

      Are you thinking that Betty's 100 POSITIVE credits on-ledger have no future value?

      Still thinking about establishing value for the skilo, let's think from Andy's perspective. Andy is willing to acquire the bananas and 100 NEGATIVE units (skilos?) on-ledger. Andy seems to have acquired two physical objects, but what is a NEGATIVE unit (skilo)?

      Are you thinking that the NEGATIVE skilo has no future value?

      I will speculate as to what you are thinking. You are thinking that ledger entries by-themselves have no value. They are just ledger entries.

      Am I right?

      It seems to me that ledger entries by-themselves would need to have an enforcer before they would have value. They would only be an asset if the entries could be enforced.

      I apologize for the step-by-step detail. Step-by-step is the mechanical way that has become my guide in macroeconomics. I think your accounting perspective may be more like snap-shot by snap-shot.

      Does this make any sense?

    4. Antti,

      By now, you are probably coming to the same conclusion that I find. If we have an enforcer who keeps the ledger, we have just built a monetary system. We have just created money (the positive skilo) and debt (the negative skilo). The ledger could be electronic; the positive entry could be replaced with a paper equivalent; the negative entry could be a bond.

      Is this where you were going all along?

    5. Roger: One could say it's about an "enforcer", but I will provide a much more detailed explanation later.

      I think you're jumping from our abstract skilo to a "skilo-thing" too fast. People who insist that the medium of exchange ("positive money") acts also as a unit-of-account make the same mistake. Those are two separate concepts. I've so far introduced the concept of a unit-of-account and it didn't require the existence of any "money". When we get a positive balance on an account later, we must ask ourselves if we should call that balance so and so many 'skilos' or not. In my example of a bilateral debt it wouldn't occur to Andy to say that he has 50 skilos, would it? It's a debt DENOMINATED in skilos.

      About the VALUE of skilo. Our abstract unit-of-account doesn't really have any value, does it? To talk about its value would be to talk about the prices of goods. If you can sell something for 100 skilos, you ask yourself what can you buy for the same price. Skilo has no value. But you were already thinking about "a positive skilo" on an account. As I hinted, I won't call those 'skilos'. I will ask what is the purpose of this record, what does it mean to have a certain balance on your account. Just like in the case of a bilateral debt, when no banks nor money exist.

      I should save you from second-guessing by writing a post or two! Let's see. Perhaps later this week.

    6. Thanks Antti.

      I took a gambit to create a post describing how the NGC model can be used to illustrate the creation of money. The post is found at

      I stay away from assigning a value to any money created. Just as a comment, I lean toward the idea that money is re-valued each time it is received. Certainly, historical valuations have an influence on making that repeated value judgement.

    7. Roger, what do you mean by "money is re-valued each time it is received"?

      And how does my new post (Part 2) compare with you NGC model?

  2. Replies
    1. I've never heard of Kitson before. Thanks for introducing me to him. I very much agree with your post.

    2. Good to hear, Oliver!

      There was a lot going on in monetary theory around the fin-de-siècle. It must have had something to do with the rapid evolution of the banking system (although that must have marked the whole 19th century). You might want to have a look at this less-known source which is also related to my work:

      Boianovsky & Erreygers:

      A well-known and good source, although perhaps not as much appreciated for its contribution as a description of the banking system as its line "double coincidence of wants" is Jevons: (mainly Chapters XIX->)

      J.S. Mill recommended those chapters of Jevons' for an overview of the bank credit system. Reading them, it occured to me that I should have read them before reading Bagehot's Lombard Street, and if I remember correctly, later I found out that Jevons himself suggested one should read Bagehot for further information!

    3. Just to leave no room for misunderstandings: I mention basic texts like Jevons not because I think you are not on a very advanced level -- which you obviously are -- but because I myself like to dwell on the fundamentals.

    4. Advanced, moi? Hardly! The only thing I'm guilty of is reading my way through more or less sympathetic monetary theories on the internet for the past couple of years. There are humongous holes in my knowledge, right down to the basics. Starting with Jevons :-).

    5. Then you're much like me, although I might have read by now a bit more. It helped to quit my day job more than two years ago -- lots of time to read and think.

      I came a bit late to monetary theory, having first tried to figure out how debt works on macro level without a deeper understanding of monetary theory. I set myself to solve this question about 4-5 years ago when I concluded that the level of indebtness around the world is the gravest problem our generation faces, and that there is no common understanding on how this all works (e.g, BIS vs. Krugman et al; I'm on the BIS side, mostly...).