Monetary Policy for a central bank with no balance sheet

How a central bank can do things with words.

Imagine a central bank with no assets and no liabilities. It does not issue money. It does not buy or sell anything. It does not regulate the commercial banks. The only thing it controls is one word in the dictionary. Every morning it edits the dictionary, announcing what the word "dollar" means today.

If nobody uses the word "dollar", then the central bank is irrelevant. But if people do use the word "dollar", the central bank's monetary policy can have real effects.

To make my thought-experiment semi-concrete, imagine that people use Bitcoin as medium of exchange. All goods and services, and financial assets, are bought and sold for Bitcoin. But to keep it simple, I will ignore Bitcoin mining; there is a fixed stock of Bitcoin. But "dollar" remains the unit of account, from force of custom, even though dollars no longer exist.

Suppose one morning the central bank announces that "one dollar" now means "0.5 Bitcoin", and not "1.0 Bitcoin" like it meant yesterday.

If we measure the stock of Bitcoin in dollars, the central bank has doubled the money supply (and doubled the money supply in every individual's "pocket") simply by making an announcement. If judges consider the central bank's dictionary definition of "dollar" to be authoritative, debtors now owe creditors only half as many Bitcoin as before when they repay debts denominated in dollars. And sellers of goods and services are paid only half as many Bitcoin as before at the same dollar prices, which will create an excess demand for those goods and services. Dollar prices would need to double to restore the original exchange rates between Bitcoin and goods. This is the world of the Quantity Theory of Money, even though the central bank issues no money.

Now make one small change in the thought-experiment. Introduce a one-day delay, so that central bank announcements take effect the following day. So the central bank is announcing the daily rate of change in the exchange rate between dollars and Bitcoin. So the central bank is announcing the daily nominal interest rate (measured in dollars) that will be earned on the Bitcoin balances in your pocket. If the central bank raises that daily nominal interest rate it means that the dollar is depreciating more quickly against Bitcoin than it was before. If dollar prices are flexible, raising the nominal interest rate paid on Bitcoin balances raises the inflation rate. This is the world of the Neo-Fisherian theory (but note that raising the nominal exchange [edit. interest] rate here means raising the growth rate of the nominal money supply).

(I'm heading off to the cottage soon, and will be slow responding to comments.)

Comments

[Mike Sproul]

Nick:
1) "dollar" remains the unit of account, from force of custom"

2) "If judges consider the central bank's dictionary definition of "dollar" to be authoritative"

This is where your argument gets in trouble. As soon as #1 and #2 don't hold (and why should they, when the bank has no assets?) the story falls apart.

On the other hand, the dollar will have value if the central bank maintains convertibility into bitcoin, but convertibility can only be maintained if the bank has enough assets to redeem all of its dollars at par.

[Nick Rowe]

Mike. Yes, 1 is critical. If people stop using the word "dollar" when they trade goods and assets, and make contracts, my central bank is powerless and irrelevant. On 2, I'm not a lawyer, but judges might simply follow custom (like in common law), and it is customary for people to treat the central bank's word as a focal point in saying what is and is not a "dollar". Languages wouldn't have any meaning at all if people didn't follow custom to at least some extent.

[Vaidas Urba]

The only difference when the central bank has no balance sheet is that somebody else earns the seigniorage. In your example, seigniorage is earned by the holders of bitcoin.

[Nick Rowe]

Vaidas: since reading your comment I've been trying to think of other real differences. But I've failed, so I think you might be right. Which is an important point. (And seigniorage is small anyway, for normal countries less than 1% of GDP.)

[Jacques René Giguère]

Humble IO guy think that whoever decide the exchange rate is controlling money and therefore issuing it. Casting coins, printing bills and changing magnetic polarity on a hard drive is manufacturing hardware not monetary policy.
And real central banks have no liabilities (they dontt intend to redeem anything into anything) and no assets (they don't want to have anything redeemed to them).
Talking of CB balance sheet is an origin story. It's cosmogony, not economics.

[Roger Sparks]

It seems to me that a critical issue with your example is the questionable validity of the statement

"debtors now owe creditors only half as many Bitcoin as before when they repay debts denominated in dollars".

Would debts actually be defined in "dollars" or would they be defined in "Bitcoin"?

I think in a fiat money economy, debt would be defined in the fiat currency. In your example, I think the fiat currency would be "Bitcoin".

Now I am thinking that we could substitute the words "Australian Currency" for Bitcoin, and still have the same meanings. If we did that, which currency (dollars or "Australian Currency) would we expect to be used to define debt?

I think debt would be defined in "Australian Currency". If so, the change in "Australian Currency" value would carry through to creditors. After the change in value, it still would still take one Bitcoin to pay one Bitcoin defined debt. The advantage of changed value flows to those holding BOTH debt and Bitcoin, disfavoring those who hold dollar denominated assets.

So, Yes, I would agree that dollar denominated assets would quickly be marked up in price.

[Nick Rowe]

Jacques Rene: "Talking of CB balance sheet is an origin story. It's cosmogony, not economics."

That does seem to be where the logic of this post is leading. Funny thing is though, some years ago a deputy governor of the Bank of Canada said: the only thing we really control is our own balance sheet. And I used to think that was right. I was myself surprised at where this post is leading.

Roger: It's not obvious whether debts would be denominated in dollars or Bitcoin. But if the central bank keeps the value of the dollar more stable than Bitcoin (against real goods) that might help preserve "Dollarisation".

[Scott Sumner]

This reminds me of two things:

1. My earlier posts on NeoFisherism, where I talked about a central banking with a crawling peg against the dollar. Increasing the rate of depreciation raises both interest rates and inflation. With no lag.

2. The example also reminds me of FDR's monetary policy in 1933, where he did daily adjustments in the "dollar" price of gold, to affect inflation. However in that case there were also actual dollars in existence.

[Jacques René Giguère]

Scott: "raises...inflation".
Are you talking inflation as a monetary phenomenon or real prices rises due to falling terms of trade? They're so not the same thing....

[Nick Rowe]

Scott: I was thinking of you as I wrote this post. In terms of our long-running battle, between you as a unit of account guy and me as a medium of exchange guy, this post has turned traitor, and supports your side.

Good points. Yep, my central bank could define the "dollar" in terms of something other than the medium of exchange, which doesn't have to be Bitcoin. Gold would be a good example. It could be commercial bank money.

[Vaidas Urba]

Nick,

if you capitalize the net present value of seigniorage, you get a company which is more valuable than any other company in the world. So this balance sheet issue is quite important. Yellen is running a business which is more valuable than Apple, yet there are some members of FOMC who want a return to a small-balance-sheet Fed. Well, if the Fed set a margin between interest on reserves and discount rate wide enough and privatized the coinage, it could run the policy without any balance sheet whatsoever.

[dlr]

Scott: I was thinking of you as I wrote this post. In terms of our long-running battle, between you as a unit of account guy and me as a medium of exchange guy, this post has turned traitor, and supports your side.

Heh, I was glad to see you say this. You have long described the NK model as doing away with money. William Buiter once criticized the cashless version of the Woodford NK model as sneakily turning the MOA into phlogiston, a "disembodied, abstract numeraire or virtual currency." Here you have done the same, except proudly. The Woodford cashless model seems different at first from a mere focal point, because the MOA is described as CB liabilities. But it's a red herring, because those liabilities are not the MOE and in fact do not have to exist at all in the model, which is instead ultimately all about coordination, i.e. equilibrium selection -- just like yours. This is why I disagree with your complaint that the problem with the NK model is that it ignores money, and also with the NK experts who believe the cashless model somehow can admit "barter" but also experience price rigidity. It only drops the MOE. It always and everywhere retains an MOA, and the MOA is what really, really matters to the extent that sticky prices matter. What I like about John Cochrane's valiant paper attempting to fly the Neo-F flag is that he explicitly acknowledges your argument here: It's all about how the coordination game for the MOA plays out. Here is the kind of past discussion I'm thinking about. Sorry for the digression:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2015/04/noah-vs-steve-a-suggested-interpretation.html?cid=6a00d83451688169e201b8d1091cc4970c#comment-6a00d83451688169e201b8d1091cc4970c

[Roger Sparks]

I've been thinking about divergence between MOA and MOE. A version of Nick's example plays out in the real economy every day. It happens when a gift certificate owner encounters changing prices in the issuing store. Let's explore this concept for a minute or two.

A gift certificate is nothing more than a general MOE converted into a store specific MOE. For example, when a Lowe's gift card is purchased with money, a store specific MOE has been purchased with a general MOE.

When a gift certificate is presented at Lowe's for redemption, it is first converted back to money (the general MOE). THEN the purchase and MOE exchange is completed.

In this example, we see that both money and the gift certificate are vulnerable to a divergence between MOA and MOE. All the goods in Lowe's are priced in MOA. Prices in the store can change at any time. If an event causes the MOE to diverge from MOA, then a person owning either money or gift certificates would first think that MOA and MOE have one value but, upon arriving at the issuing store, would find that a change in relative value had occurred.

We might ask who has the ability to cause this divergence between MOA and MOE? Nick gives this power to the central bank. In my example, the owner of the store has this power.

A divergence between MOA and MOE represents a dynamic situation. Prices are no longer stable across time.

The tie between MOE and Gift Certificate serves to highlight the time-enduring nature of money.

[Jacques René Giguère]

A store gift certrificate is restricted form of MOE in its use but not in value.
Points are a restricted use MOE but they have their own exchange rate.
The C$ has gone down against the US$ but my vacations in the US will cost me the same in Aeroplan and Choice Hotels points. These currencies hold up their value. They're like Keynes Bancor. National currencies waltz around but they retain their purchasing power.
They can be devalued but internally: now it takes Y K points instead of X K to go from FK to LAX.

[Majromax]

@Nick Rowe:

> Roger: It's not obvious whether debts would be denominated in dollars or Bitcoin. But if the central bank keeps the value of the dollar more stable than Bitcoin (against real goods) that might help preserve "Dollarisation".

I think that's an important but de-facto restriction. The CB can't use its powers arbitrarily while also keeping the value of the dollar more stable than the value of bitcoin.

My conceptualization is that real central banks have a balance sheet to allow for reversible monetary policy. Any central bank can run printing presses, but it takes a balance sheet (or integration with the fiscal authority) to run the money shredder. Because there's a balance sheet and some sort of market transaction, OMO-type monetary policy automatically ensures that the named money market clears.

In Canada and the US, the named money market is one of interbank lending. In Scott Sumner's example, the named money market is the exchange of dollars for gold (and where money policy was constrained by nations' bullion stocks). In this example, it's the implied exchange of dollars for bitcoins, where this market clears (and dollars are the unit of account) only by a priori constraint.

[csissoko]

Glad that installing the hitch didn't prevent the post from being written!

What this post brings to mind for me is an interesting story from J.K. Horsefield's British Monetary Experiments 1650-1710. In the years preceding the birth of the British gold standard, Britain was on an effective silver standard with a steadily deteriorating silver coinage (that circulated at par -- e.g. as "dollars" despite decreasing silver content over time) and gold guineas that floated in value relative to silver. Just after the Bank of England was founded, Britain reformed its coinage by recalling the low quality silver coins and recoining them into higher value (i.e. the reverse of your experiment). Everybody knew the process would be disruptive and in fact over the course of 1696 there was some doubt as to whether the government would indeed hold the line at a high value coinage.

What's most interesting (and makes gold look a little like bitcoin today) is that in the year preceding the year of recoinage, the gold guinea which was not recoined, jumped in value from 22s. at the end of 1694 to 30s. in the third quarter of 1695 and stayed elevated until the government (attempted?) to legislate the gold-silver exchange rate in February-April 1696. The concern at the time was that the high market rate for gold risked causing the new silver coins to be melted down and exchanged abroad for gold. The event remains largely unexplained, but I think provides some evidence of how efforts by monetary authorities to exercise their ability to change the unit of account at least in the short-term can create very wild results due the public's need for a means of exchange.

Anyhow, thought you'd like the anecdote.

[Nick Rowe]

dlr: I'm still trying to get my head round the implications of this post! Funnily enough, I didn't see the connection to Woodford's model (where the central bank also has no balance sheet) until Tony Yates tweeted it!

As you may remember, the only way I can make sense of Woodford's model is to interpret it as assuming (regardless of what Woodford might say) that each agent has a chequing account at the central bank, which serves as MOE, which can have a positive or negative balance, where those balances in aggregate must sum to zero, and where the identical agents assumption means that each individual's balance must also be zero in equilibrium. But with heterogenous agents the central bank would have a balance sheet with both assets (agents' negative balances) and liabilities (agents' positive balances). My thought-experiment here is more extreme than that, because the central bank's balance sheet is identically zero for all individuals.

Majro: "My conceptualization is that real central banks have a balance sheet to allow for reversible monetary policy."

Yes, if the central bank has money on the liability side. But in my example here there is no liability side. And my central bank does not fix the exchange rate by buying and selling dollars for Bitcoin; dollars don't exist, and it doesn't buy or sell anything.

Thanks Carolyn! Installing the hitch turned out to be relatively easy, and I learned the technique of "fishing" a bolt through a tube and out a hole with a wire.

I like your anecdote. The historical episodes I thought of when writing this post was about those "imaginary money" cases (Eunadi? IIRC), which I have never really understood.

[C Trombley]

I have one small caveat. You say "This is the world of the Quantity Theory of Money, ..." which is fine. But then you say "...even though the central bank issues no money.", when surely a better end to that sentence is "...unlike the real world where the central bank issues money.". ;P

[JP Koning]

Nick, that sounds like William Stanley Jevons's tabulated standard, the only modern incarnation of which is Chile's Unidad do fomento. See here.

[Nick Rowe]

JP: Chilean case is a great example. God only knows why I had forgotten about that. My science fiction thought-experiment is a lot more real world than I thought it was.

[Too Much Fed]

JP, in your Chilean example, there is nothing preventing entities from posting prices in pesos, right?

[Scott Sumner]

Jacques, I am primarily focused on inflation as a monetary phenomenon, but the real price changes you describe may also occur.

[Andrew]

This reminds me of an episode in Rick & Morty, season 3 episode 1. The galactic government has one form of currency and it's value is = 1. Rick(Protagonist)then destroys the government by changing it to zero, haha.