Monday, March 9, 2015

What Is Money?

Money is an abstract unit of account.

This is all there is to money. If something else is called "money", it is a matter of convention.

In economics, the term "unit of account" is synonymous with "(monetary) unit of measure". "Measure of value" carries very much the same meaning, too. There are various units of account in use around the world and worldwide, for instance "US Dollar", "Euro" and "Malaysian ringgit" (all abstract).

Here is a formal expression which might further illustrate my point:

P = r  x  [P]

where P is a monetary value ("price"), r is any real number and [P] is money (e.g, US Dollar).

The monetary value of various objects and contracts is expressed as P (price), which in turn is denominated in [P] (money). It logically follows that money can never be touched, nor can it be lent or owed. In other words, [P], money, cannot take the form of any object. In this sense it is no different from a "metre", a unit of length. Let's say we have an iron bar which is 1-metre long. The iron bar can have many functions, for instance "building material" or "a weapon". But no scientist would posit that the iron bar, in addition to its other uses, functions as a "unit of length".

Why should we define money in this narrow way?

First, I haven't seen any other definition of money that would be both logical and meaningful. Just like that, the enigma called "money" disappears; money is not what money does, but an abstract unit of account. Second, this definition allows us to build an economic theory which is both simpler (more elegant) and better in explaining various economic phenomena than any of our prevailing theories. Unlike the prevailing, often competing and contested, theories, this new theory helps us answer a wide range of pressing economic questions of our times -- questions related to the amount of global debt and its sustainability; and also to the widening income and wealth inequality in our societies.

Do you find any reasons why we shouldn't define money in this way?


J.M. Keynes used the term "money-of-account" when talking about our narrowly-defined money in his A Treatise on Money (1930):

“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.... Money itself, namely that by delivery of which debt-contracts and price-contracts are discharged, and in the shape of which a source of General Purchasing Power is held, derives its character from its relationship to the Money-of-Account, since the debts and prices must first have been expressed in terms of the latter”

It seems he wasn't able to let go of the conventional concept of "money", so he only separated it in two: "money-of-account" and "money itself". It was a good start, but it was clearly not enough to bring clarity into the matter.


  1. Ok, I'll bite. This definition seems extremely narrow. I.e. your money is no different from "kilogram" or "joule". This omits at least one *crucial* role that "money" must play:

    - it is a "medium of exchange"

    As every physicist (or just a studen having taken some physics classes) learned from "dimensional analysis", there are some basic, irreducible, units that can NOT be converted to each other:

    - while "gram" and "kilogram" are commensurate, "gram" and "meter" are not.

    Thus, try as you might, you will never be able to view 1 gram and 1 meter as commensurate -- and hence exchangeable.

    Thus if I measure my fish catch in grams and somebody measures their berry harvest in meters (ok, a bit of a stretch, I know, but just to be able to continue with fundamental physics units), there is no way for us to trade.

    Have I just ruined one of the starting points of your money theory?

  2. I don't think it's that easy to ruin! :-) As with any simple theory, it has taken a lot of effort (sweat and tears) to build and test it. I have really tried to break it, but it keeps on getting stronger.

    You read me correctly. Money is not that much different from "joule", although money is not "a definite magnitude of a physical quantity" (

    Here's a question to you:

    Is this "medium of exchange" really money, or is it just denominated in money [P], as I suggest? If we believe that money functions both as a "unit of account" and a "medium of exchange", then we are basically saying that money is denominated in money. And if we say so, then we could as well say that the iron bar I mention in my post is both "1-meter long" and "meter".

  3. I cannot quite answer your last paragraph's question because it starts with a wrong premise...and then you get yourself confused, I think...

    Here is how I would define money:

    - whenever we think of a "unit of account", "money" is that "account" -- NOT the "unit" part of it.

    To put it differently, "money" is an "account" in the same sense that it is an "IOU", an "asset" that can be exchanged for something else (importantly, "something else" that is not necessarily money). Note how "exchange" comes into the definition again.

    Without the "exchange" part, you have no money. I.e. you have no fungibility. "Money" has to be a special/universal unit that lots of other things convert to (fish, berries, but presumably not "love" :). This universal scale of measurement reduces the M*(M-1)/2 problem of figuring how to exchange M pairs of items to just an M+1 problem.

    So then, what is left in a formula like yours? "1000 dollars" is a quantitative amount of "money" where 1000 is the amount (or "price", or "ratio scale value") and "dollar" is the "physics unit"/currency.

    And yes, various *amounts* of money may *seem* to be defined in terms of each other -- but only in the same sense as 1 kilogram is "defined" as 1000 grams. But "1 kilogram" is not a *definition* of "weight" -- it is merely an expression of the fact that something called "weight" is measurable on the ratio scale ( If you don't object to 1 kilogram being 1000 grams, you should not object to $10 being ten $1's. Something *else* needs to be provided to *define* "weight" (Newton's laws, it has inertia, general theory of relativity, etc) and by the same token something else needs to be provided to *define" "money" (it is exchangeable for other non-money assets, it is measurable on a ratio scale, etc).

    How is my theory doing vs yours now?

  4. First, let me be clear: I have a theory ("my theory"), but I don't see "your theory" -- instead, I see the prevailing theory behind what you say :-)

    What you are saying is that money is both a UNIT of account and an ACCOUNT -- right? Think about it for a moment. I say that money is an abstract *unit* of account. This must be the original meaning of "unit of account", because the word "unit" comes first. I assume you don't want to twist this? Instead, you want us to focus on money being *also* not-so-abstract *account*, and with that you mean money-as-an-IOU, something fungible, something that can function as a "medium of exchange".

    What I am saying is that these IOUs, also the ones which serve as our common (more or less legal tender) "medium of exchange", are only denominated in money (an abstract unit of account). No matter what we have thought and believed before -- no matter what we are used to call "money". If we, in macroeconomics, are able to dismiss money as "medium of exchange" and a "store of value", and understand how various kinds of IOUs serve these two functions, then everything makes much more sense. Economic cycles, current debt problems and inequality. I'm not going to force anyone to adopt my view, my theory. All I say is that my theory explains so much more than any prevailing theory is able to explain :-)

  5. >"What you are saying is that money is both a UNIT of account and an ACCOUNT -- right?"

    No, I am not saying that. I am saying that money is an ACCOUNT (which is a record of an IOU). The UNIT part is not money, it is an artifact of the measurement scale (positive and negative real numbers with decimal point :).

    That is all. I am not saying I have my own theory, I am just saying that your definition of money seems too restricted compared to the prevailing one, restricted to a point where it clearly can't be operational in our real world. There have been economics schools that didn't *any* money in them at all -- they are not much use now. By comparson, the attractiveness of MMT is that it actually does not abstract away too much operational realities.

  6. This is then good news. We agree that we have to separate these two concepts that have traditionally been combined in the "three functions of money":

    1) "Unit of account", or "monetary unit of measure" -- which for me is "money", for you "an artifact of the measurement scale" and for Keynes "Money-of-Account"

    2) "Medium of exchange" -- which for me is "just an IOU", for you "money" and for Keynes "money itself"

    Do you agree?

  7. I admit to not knowing Keynes' exact definition of money, but yes I would choose #2 above as my definition if I had to pare it down to its bare minimum:

    - the "units" I could conceivably do without, especially with fractions etc. For example, we could use whole chickens for counting and disallow half-chickens. But money at least needs to have what I'd call "total ordering": it should be possible to say that "money X < money Y" and the relationship should have the usual reflexivity, transitivity, etc properties. It may be desirable for "money" to have a "ring algebra".

    Note: I said "if I had to pare it down to bare minimum". In practice, I feel like it gives up too much. For example, I'd like "money" to also have durability (for "store of value" functionality) and have some wide scope of acceptance.

  8. I think you still mix these two things... My money works just fine in any calculations and comparisons. $100 + $20 = $120. It's only that I'm not talking about cash or deposits -- only abstract ideas of (monetary) value. Let's say I make $15/hour. How many hours do I want to work today to pay for my dinner? One hour. Ok, then I don't buy a dinner that costs me more than my hour's pay after tax, in this case something around $10-$12. Here I'm talking about money as defined by me.

    The moment you imagine yourself a 10-dollar note when I write "$10", you move away from money to an IOU with a nominal value of $10, measured in money. Only these IOUs can function as a medium of exchange and a store of value -- and conversely, they cannot function as a monetary unit of measure, a role which I leave for my abstract money.

    Are you sure you haven't misunderstood what is meant by "unit of account"? For instance, an MMT advocate, Pavlina Tcherneva, seems to agree with me, judging from what she wrote me on Twitter: "Think of 'money' as a 'foot', 'centimeter', 'kilo', that is a measuring unit of a credit (i.e. debt) relationship".

    My references to Keynes relate to the quote I used in the end of the blog post.

    1. I use money definition pretty much like in BoE 2014 papers: money is an IOU. It has 3 important roles: store of value, unit of account, medium of exchange.

      I quote BoE on what they mean by "unit of account":

      >"the thing that goods and services are priced in terms of, for example on menus, contracts or price labels."

      I remain convinced that it is you (and perhaps Pavlina) who are confused: you confuse "gram" and "weight". One is a unit, the other is an aspect of an object in a gravity well. Analogously, in "$100" the "$" is a "unit", "100" is its measure, but what "$100" is we don't know without additional context: it could be a price label, it could be available funds in my savings account, or the amount I won in a bet with my friend which he hasn't paid me yet. The first is not "money", the second and third are "money" because they are someone's liabilities (my bank's or my friend's) to me. Clearly, on the scale of "money-ness", the $100 in the bank is higher than my friend's promise to pay, because the probability of payout (should a claim be called in) is higher.

      To sum up my position: the most important feature of "money" is its IOU-ness.

    2. Yes, but $ as a "unit" must refer to $1. $100 is 100 monetary units, in this case $-units. Right?

      Take your price label. What I'm saying is that the price on that label is expressed in monetary terms. Alternatively, it could be expressed in "hours of labor", for instance. But now it says "$100". What is this $100? To me, it is money. It clearly is not any fungible thing, and I see no reason to start thinking about in terms of cash or deposits (which you call "money"). Based on the information on the price label, I form an idea of how much goods or services (incl. labor) I need to sell in order to pay for my purchase (let's assume I buy the good the price label is related to). It might be that I have already sold goods or services and I'm holding credits, or IOUs, (your "money") issued by others worth $100 -- then I'm in a situation where I have already paid for the purchase I now make.

      If you want to call my money "price label", fine. My point is that this "price label" gives you price information, and the price is measured in money. And there is no need to relate this price to some IOUs -- we can relate it to the effort it takes us to pay for it. Nothing keeps us from performing a service to the seller in return, a service he judges to be worth $100. If the good we bought was created by the seller, it can very well be that we have created $200 worth of GDP without a single IOU changing hands.

      I don't ask you to let you go of your "money". I'm only asking you to recognize what is money for me. You can call it what you like. There are reasons why I call it money, and why I don't call the IOUs money. Those are very well known reasons. But we won't get there before we can agree what my money is and what your money is.

    3. I hope I am not frustrating you but when you say

      >"And there is no need to relate this price to some IOUs -- we can relate it to the effort it takes us to pay for it."

      isn't "pay for it" just a synonym for "exchange"? You are back to exchangeability of money as one of the defining characteristics... Exchangeability and "being able to pay for things with it" are almost the same thing, are they not?

      Next, "labor" or "effort" are unreliable bases for defining money (that was Marx's mistake). Imagine that two guys are expending the same amount of labor/money but if one of them is just digging ditches and the other one is mining diamonds they make different amounts of "money".

      Finally, don't get upset, I am still trying to understand your definition. Let me try further by asking this:

      You say: "What is this $100? To me, it is money". And I say: "how do you know it is money? what is it that makes you certain you can use this item to exchange for goods and servies? As a way of answering, imagine you're an alien just landed on Earth and found a piece of paper that has "$100" written on it -- how do you learn that it is "money"?"

    4. Let me try to answer in the way I was hoping to lead you to answer:

      "I know that $100 is money because I have an agreement with some seller for a rate of exchange of this money for his goods and services. The alien will know that the $100 piece of paper is money when he receives the knowledge (already common among all Earthlings) that such pieces of paper can be so exchanged. "

      Fine! You have an agreement... which is basically a claim you have: the seller has guaranteed to you that he will accept $s and give you goods and services. Thus, the seller has an obligation to accept $s and you have a claim on his obligation to do so.

      Next, when there are more than just the two of you, a central guarantor emerges: the government/central bank/some kind of an exchange. But there is always a system of mutual obligations and claims + an entity ensuring trust by guaranteeing these claims. And so this system of claims, guarantees, and associated bookkeeping is precisely a system of IOUs.

    5. Of course this is frustrating, but then again, learning is often frustrating (think of a pianist practising and practising). I'm confident we'll get forward! Perhaps tomorrow :-)

      You have misunderstood. Read carefully. I said that the "$100" *on a price tag* is money *as I define it*. The price itself is not money, but it is expressed in money. And when I say money, it seems you automatically think of an IOU. And that's wrong. Remember now that money is totally *abstract* to me. It is part of a value/price system inside our heads.

      When we write that "$100" on a debt contract, then we have an IOU (the debt contract!) which is worth $100 (it is denominated in dollars -- my money). And this IOU can be, for instance, a 100-dollar bill.

      I understand that this might be confusing for you. But you must be able to realize how "$100" can be abstract, a non-thing, just numbers in your head, and still it is part of a useful system even if it doesn't refer to any IOU? I tried to show how we use this "monetary measure of value" when we exchange things, without ever needing any IOUs (your money).

  9. Ok. Let "price tag" be money according to your definition. I will probably not understand why you wouldn't just call it "price" then, but assuming I can keep your definition in my head, what do you do with it?

  10. Actually, I probably chose it wrong again. Going back to the start of the thread, you want to define "money" as the measurement unit ("meter", "dollar", etc). Ok, fine, what next?

  11. Yes, the latter is correct. But when we talk about a "unit", we don't talk about the word "meter" or "dollar" but "one metre" or "one dollar". 100 units = 100 x 1 unit. Here's from Wikipedia:
    "1 (one; /ˈwʌn/ or UK /ˈwɒn/, also called "unity" or, in technical contexts, "monad") is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of "unit length" is a line segment of length 1."

    So we can perform various calculations by using these monetary units (my money). I'm talking about a concept which for you is *not* money. Here's what you wrote:

    "...but what "$100" is we don't know without additional context: it could be a price label, it could be available funds in my savings account... The first is not "money""

    Let's say we had two price labels, one with "$100" on it and another with "$20" on it. This would allow us to add the prices together, deduct them from each other, and compare them -- for instance, "Product X is $80 more expensive than Product Y". All this, and we still are talking only about something you say is not "money".

    What I want you to see is that "my money" exists *independently* from the IOUs you refer to. You're right, the IOUs you refer to, are called "money". But the "unit of account" is also called "money" (this is "my money", which I want to divorce from the IOUs), and it exists independently from the IOUs. I haven't made this mess. It has always existed via the three functions of "money". That's also why Keynes tries to separate "Money-of-Account" and "money itself".

    Once again: My money refers to the "system of prices" which each of us carries in our brain. Are you from eurozone? When euro notes and coins started to circulate and prices were expressed in euros instead of whatever currency was in use before it, most of the people kept on carrying their old "system of prices" with them -- they were thinking in terms of Marks and Liras long after the corresponding notes and coins (IOUs) had ceased to circulate. Similar thing has happened on many occasions in history. We think of prices, of value, in terms of this system which exists independently from the IOUs (your money).

    This is monetary economics. This is not my own making. Based on this, I want us to agree that we can separate the "unit of account" from the "medium of exchange".

  12. Ah, terminology! It could be frustrating but it's best to get it out of the way at the very beginning.

    It is a bit inconvenient to speak using "money type A" (account/IOU) and "money type B" (unit of account), but I suppose we can deal with it unless we come up with better terminology.

    The BoE definitions (type A) are convenient when talking about monetary bases of a country: base money, broad money, etc. So when some commenters at FT complain about "central banks printing money" I like to counteract by asking "which money? base? broad? do you know that most money is printed by non-central banks via loans?" etc. Surprisingly few people know that most money (type A) is created "out of thin air" as IOUs/loans and the central bank is not involved directly.

    What you call *your money* definition I can deal with. I think you were right in claiming that MMT uses type B, at least some authors I read. Mosler's early writings did not define "money" specifically but he used various accounts when describing Treasury/gov funding process etc. In "Soft Money Economics" he says:"

    "Historically, there have been three categories of money: commodities, credit, and fiat."

    (He then says that commodity money is money with intrinsic value, like gold coins, credit money is the liability of some individual or firm, usually a checkable bank deposit (type A), and "fiat money is a tax credit not backed by any tangible asset"... "fiat money is an accepted medium of exchange only because the gov requires it for tax payments". Basically, his "fiat money" is also type A but applied to the Treasury account or "national debt".)

    Finally, Wray offers these definitions in his "MMT, A Primer ..." book:

    "The word "money" will refer to a general, representative unit of account. We will not use the word to apply to any specific "thing" -- that is a coin or central bank note.

    Money "things" will be identified specifically: a coin, a bank note, a demand deposit. Some of these can be touched (paper notes); others are electronic entries on balance sheets (demand deposits, bank reserves). So "money things" is simply shorthand for "money denominated IOUs".

    A specific national money of account will be designated with a capital letter: US Dollar...

    The word "currency" is used to indicate coins, notes, and reserves issued by government..."

    I am ok with using Wray's terminology as well: "money" (unit) and "money things" (money denominated IOUs), although it's a bit silly when used outside of an academic book.

    As a footnote, I'll mention that while in the USA dollars are used both for account units and for exchanges, several books and papers tell stories that it has not always been the case in other countries (and effectively remains not the case when you consider how some trades (oil) are done in US $ by countries that have different national currencies).

    Are we getting closer to the same page? I would prefer "type A/B" or "money/money things" or "unit/account" to "yours and mine", to be honest.

  13. Great!

    I fully agree with you: It is best to tackle the terminology right away. Sure, it feels somewhat pointless at times, but it's about building a firm foundation. Good to see that you possess the perseverance needed to do this.

    We seem to be on the same page. As I guessed: "Perhaps tomorrow" :-)

    I'd say we go with this:

    "I am ok with using Wray's terminology as well: "money" (unit) and "money things" (money denominated IOUs)"

    This is consistent with my definition of "money". Wray uses "money things" when talking about the IOUs, and I can live with it -- at least for now :-) When we move to these IOUs (another blog post), I will try show why I'd rather not call them "money things", but only "IOUs" or "credits" -- but almost without exception I'd refer to more precise categories, like "commercial bank deposits" and "central bank reserves". (Behind my reasons is Mitchell-Innes and Chartalism -- just in case you want to study those a bit more. I see that you are well read, though!)

    Btw, do you perhaps refer to this later in your comment:

    "With many forms of domestic and international money (with different weights, purities and quality) circulating throughout Europe in the late Middle Ages and the early modern period, the use of an accounting currency became a financial necessity. In the world of international banking of the 13th century, it was the florin and ducat that were often used. In France, the livre tournois and the currency system based on it became a standard monetary unit of accounting and continued to be used even when the "livre tournois" ceased to exist as an actual coin. For example, the Louisiana Purchase treaty of 1803 specified the relative ratios of the franc, dollar and livre tournois.

    The official use of the livre tournois accounting unit in all contracts in France was legislated in 1549, but it had been one of the standard units of accounting in France since the 13th century. In 1577 the livre tournois accounting unit was officially abolished and accountants switched to the écu, which was at that time the major French gold coin in actual circulation, but in 1602 the livre tournois accounting unit was brought back."

    Monetary history is interesting, and we should be familiar with it. But we need to be cautious: If we have something to say about the current monetary system, it is then best to talk *only* about the current monetary system. I have tested my theory against past data and looked at it in light of historical monetary systems, and I have also used my theory in attempts to interpret the past (basically all the way to the "Debt Jubilees" thousands of years ago). It seems to pass these tests too. But the moment I start to argue about some historical facts related to monetary systems, I -- like anyone else -- am walking on thin ice. That's a mistake nearly all monetary economists have made -- Mitchell-Innes made it too! What often follows is an endless argument where opponents attack some historical "fact" -- those can always be contested.

  14. Ok, cool. So we can move on to the next stage of theory development.

    One last comment within this thread: monetary history is not just interesting. I find that its effect are surprisingly lingering to this day. Example: everyone talks about "Japanification" of the US or Europe, but not everyone is aware of how different Japan's monetary system has actually been:

    - most of its WWII mobilized structure was allowed to be retained by the US occupation administration, in order to build a reliable Cold War ally;
    - much of credit creation by BoJ was done in a semi-obscure way via top-down "window guidance" (an idea the Japanese ultimately learned from the success case of German financing during pre-WWII years) and much of Japan's economy development was colored by BoJ's power struggles with the Ministry of Finance.

    This continued until early 2000s, at least. Of course, the IMF and the US did their best to force Japan to switch to the "open markets" model in exchange for letting them join WTO but to what extent that has transformed Japan's "true" monetary policy needs to be studied. Until that is done, using Japan as an example of *anything* that might or might not happen in the West is fraught with peril.