Medium of Account vs Unit of Account: Brazil Anyone?

I’d like to interject a very concrete example into the large swirl of quite theoretical, thought-experiment discussion about whether “demand for money” means “demand for the medium of exchange” or “demand for the medium of account.” Scott Sumner and Nick Rowe are, as so often, at the center of this discussion. But before I do, I need to work through some conceptual and terminology issues.
Nick — who so often cuts so clearly to the crux of things — injects what he seems to feel (rightly so, I think) is a necessary update and clarification into his sally on the subject:

…in my model, gold is the medium of account; and (say) an ounce of gold is the unit of account.

I’m not clear whether or not the update was in reply to M.R.’s comment, which addresses exactly the point I want to make:

I’m still not convinced that the concept of a “medium of account” is well enough specified. “Unit of account” is fairly straightforward; we measure everything in units (inches, kilograms, minutes, etc.) What is the “medium of account” in the current U.S. monetary system, analogous to the role that gold plays in your simple model? If your answer is “dollars” then I think you may have a very serious specification problem. This is very subtle and difficult.

Nick does reply directly to that comment, and his reply’s uncertain nature fully supports my thinking:

OK, but the unit of account (in my model) isn’t “ounces”, it is ounces of gold, as opposed to ounces of silver or ounces of hair.
Medium of account in the US? Hmm. Fed liabilities?

Here we see Nick Rowe — who thinks as deeply and curiously (but I think misguidedly) about monetary economics as anyone out there — wondering what the U.S. medium of account is. This, after hundreds of years of very hard thinking by very smart people about the nature of money. It’s enough to make you question economists’ understanding of economics. They don’t even understand money?
The more I think about it, the more I think that “medium of account” is an incoherent concept (and even worse, “demand for the medium of account,” which seems doubly incoherent) — a will o’ the wisp that lures otherwise coherent thinkers into dangerous and bottomless conceptual b(l)ogs.

Think about “medium” and “media” in a very common usage — relative to information and entertainment. In this context media are vehicles for transmission — books, newspapers, TV, web pages.
This meaning kind of works for “medium of exchange” — dollar bills and bank interchanges are vehicles for transmitting something — value. Just like power lines and cans of gasoline are media for transmitting energy.
There are many media of monetary exchange (especially if you include purely financial transactions) — physical pieces of currency, credits in bank (and money-market) accounts, credit-card lines of credit, treasury bonds, bank reserves, etc. Dollar bills and bank-account credits have traditionally been the dominant media of exchange for exchanges involving real-world goods and services, but even that is far less true these days, given the quantity of credit-card sales. “Medium of exchange” at least makes conceptual sense. But “the medium of exchange” doesn’t. There are many. To steal M.R.’s words, it has “a very serious specification problem.”
“Money as the medium of account” is really far worse. What is being transmitted, and what is the vehicle? What does this term — in particular the word “medium” here – mean? It’s obviously about counting and measurement. But what is being measured, counted? I would say: value — just like a thermometer measures temperature, or a ruler measures length. But in those contexts, the media of account are temperature and length. (The units of account are degrees and inches, or whatever.) I’d like to suggest that in economic thinking the medium of account is always value — not “money” (however you choose to define that word), and never dollars or ounces of gold, which are units of account. If this is safe, “demand for the medium of account” would mean “demand for value” — which strikes me as obvious, or tautological, or just not very useful, conceptually. And “demand for the unit of account” obviously makes no sense at all; is there demand for inches or degrees?
This is where M.R. gets it right, and Nick in his update glances toward more useful thinking: we should be talking, thinking, about units of account, and how value is ascribed to those units.
In the normal course of things, a (physical or electronic) dollar has the same designated, ascribed, agreed-upon value as “the dollar.” But as Miles Kimball points out in what he describes as “the most important thing I have ever said about monetary policy,” this need not necessarily be true. A physical dollar can, conceptually at least, have a different value than an electronic dollar. (Once again I would say that each of these is a financial asset, an embodiment of money or exchange value, with particular properties and characteristics which may be in greater or lesser demand — and supply — at different times.) Different kinds of dollars could have different values, as designated in dollars! We really need different words for these things. (See: concrete example, below.)
Let me put it another way: I think Nick, Scott, and most economists don’t fully understand that “a dollar” is, conceptually, a completely different type of thing from “the dollar.” (At least they talk as if they don’t.) One is a unit (and vehicle) of exchange, the other is a unit of account, or measurement. And as Miles points out, even “a dollar” is not sufficiently specified.
I promised a concrete example, and here it is, courtesy of This American Life‘s typically brilliant “The Invention of Money” episode: how Brazil ended years of rampant hyperinflation. I’m rather astounded that, searching through my blog reader, I find that nobody has looked at this real-world example, even though it’s exactly the situation that Scott and Nick are talking about. (I’m sure there are others like it. Readers?)
Here’s the short story, but I recommend the whole thing; it’s short and very entertaining.
The cruzeiro had been plummeting in value (relative to real goods) for years. This was true both of the units of exchange (“cruzeiros” of all types — physical, electronic, etc.) and the unit of account (“the cruzeiro”) — necessarily so, because they were uniformly conceived as the same thing.
The solution was to introduce a new unit of account — rather cravenly titled the real in an effort to get people to ascribe real market-basket value to it — and to require its use in designating the value of everything, regardless of what units were exchanged. (Conceptually, they could have just revalued “the cruzeiro,” but nobody would have fallen for it because nobody trusted either the cruzeiro or cruzeiros. They would have continued to ascribe low — and ever-lower — value to it.)
By legislative fiat, all wages, taxes, and prices were to be designated in the new “real” unit of account.

People had to be tricked into thinking money had value, when all signs told them that was absolutely not true. So Basha says, they wrote a plan for a new currency, one that was stable, dependable, trustworthy. The only catch was this currency would not be real. It would not be printed. There would never be coins. It was fake. They called it a virtual currency.
Edmar Basha
We called the unit of real value, URV. Yeah, it was a virtue that didn’t exist in fact.
Chana Joffe
People would still have cruzeiros, the local currency in their pockets. But when they got paid, their wages would be listed in URVs. Taxes were in URVs and all prices were listed in URVs. And URVs were stable. And so, for example, when you went to the store and bought some milk.
Edmar Basha
How much does it cost? Say well, know we have it cost X. Let’s say one URV. Well, how much is that because I cannot pay with URV. Well, I have this little table here and today’s value of URV in cruzeiros is seven cruzeiros per URV. So it cost one URV, seven cruzeiros.
You go next week, well, it’s still one URV. But then you say, how many cruzeiros? You look, well, 14.
Chana Joffe
Every night the central bank would put out a memo with the official conversion rate. And a table would get printed in the newspaper. The store clerk could look at the table in the newspaper and see, Monday, one URV is equal to seven cruzeiros. Tuesday, 12 cruzeiros. Wednesday, 14. Milk or whatever it was you were buying would stay the same price. There was no need for the sticker man.

Eventually they phased out cruzeiros and issued physical reals. It worked:

Brazil went from being an irrelevant, economic basket-case to one of the most important economies out there. The eighth largest in the world.

Notice “unit” in the name. (Not “medium.”) The stability of the unit of account was what mattered — what value people ascribed to it. That ascription was anchored to real value because wages and taxes were designated in that unit, which also made “reals” into units of electronic exchange. (For the former: labor theory of value, anyone? For the latter: got chartalism?)
You’ll notice I never used the word “medium” to describe what happened here. At best it was unecessary, and at worst it would have sown all sorts of confusion and incoherence. We don’t need no stinking mediums.
Update: I should add that “unit” here is also used in two senses: 1. Exchange units of which there are many, that can be shuffled around physically or electronically, and 2. a more abstract and necessarily singular measurement or accounting unit. The value of the former are designated in the latter.
Cross-posted at Asymptosis.

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