If a central bank wants to shrink, it must threaten to grow (autographed edition)

[Nothing great or original here, except maybe the metaphor. It's supposed to be a simple teaching post.]

Zimbabwe is only the most extreme recent example of this general rule; the central bank threatened to grow extremely large, and this caused it to shrink extremely small. The Swiss National Bank is another recent example, at the opposite extreme. It grew very large, but slowed down its growth by threatening to grow even faster. Now it has stopped threatening to grow even faster, we will probably see its growth speed up.

(It's the same with interest rates. If a central bank wants lower interest rates, it must threaten to raise interest rates.)

This is very standard economics. It sounds paradoxical, but it isn't. Let me give you an example that has nothing to do with money:

Suppose I were a famous economist (I like this thought-experiment). And bits of paper with my autograph were a valuable asset. But demand curves slope down; so let's assume the market price of my autograph is inversely proportional to the quantity. 10 autographs are worth $10 each, and 20 autographs are worth $5 each, etc.

If that's all there is to it, the total market value of all my autographs would always be $100, regardless of how many I have produced. But that's not all there is to it. Because the demand for my autographs will also depend on whether people expect they will appreciate or depreciate in value.

Suppose the current total market value of my autographs is $100 (10 autographs at $10 each). If I want to shrink it to $50, all I need do is threaten to produce autographs in unlimited amounts if the total market value ever rises above $50. And I must be prepared to carry out my threat, to make it credible. By printing autographs at a faster rate I make them depreciate in value at a faster rate, which reduces the demand for my autographs, which reduces the total market value of my autographs.

And if I wanted to raise the total market value of my autographs to $200, I must threaten to buy back my autographs, in unlimited quantities, if the total market value ever drops below $200. By buying back autographs at a faster rate I make them appreciate in value at a faster rate, which increases the demand for my autographs, which increases the total market value of my autographs.

And we can complicate the story a little, by supposing that my fame as an economist fluctuates, and this causes the demand for my autographs to fluctuate, and this causes the total market value of my autographs to fluctuate too. But I can always offset those fluctuations in demand and prevent fluctuations in total market value by threatening to print autographs more quickly if the total market value rises above what I want it to be, and buy back autographs more quickly if the total market value falls below what I want it to be.

If I want to shrink the total market value of my autographs I must threaten to print more autographs.

Here's where it gets tricky. Suppose I cannot speak, and can only communicate my intentions by actually printing autographs. Or people don't believe what I say, so that my actions speak louder than my words.

If I print an extra 10 autographs, and so double the quantity to 20, what happens? That depends on how people interpret my actions.

1. If they expect that the change is permanent, so there will always be 20 autographs instead of 10, the price of each autograph will halve to $5, so the total market value stays at $100.

2. If they expect the change is permanent, and that I will print an additional 10 autographs next year too, and the year after next, and so on, so that my autographs will be depreciating, demand will drop, and the total market value of my 20 autographs will fall below $100.

3. If they expect that the change is temporary, and that I will soon be buying back those 10 extra autographs, the price will not halve to $5. Because if it did halve to $5, and was expected to increase again to $10, the expected appreciation would cause demand to increase, so price would have to be higher than $5. All we know is that price will fall by less than $5. So the total market value of my 20 autographs will rise above $100.

If I want to shrink the total market value of my autographs, I need to start printing autographs (2). But if people initially think this is just a temporary increase that I will soon reverse (3), the total market value of my autographs will initially grow.

4. Plus, the price of my autographs may be sticky, and respond only slowly to changes in supply or demand. So even if people know I'm doing 2, we may see the total market value of my autographs grow initially, before shrinking.

Bits of paper with my signature are just like bits of paper plastic or silicon with the signatures of Stephen Poloz and Carolyn Wilkins (Governor and Deputy Governor of the Bank of Canada). Except we measure prices of everything else in the latter and not in the former, so a fall in the price of my autographs is equivalent to a rise in the price of everything else in terms of their autographs. And we use the latter but not the former as a medium of exchange (which is why the latter have a demand curve where quantity and price are inversely proportional).

There is no promise or threat written on the bits of plastic that Steve and Carloyn autograph. That promise or threat is written on the Bank of Canada's website instead. Loosely translated it reads: "We promise to ensure that these bits of plastic will depreciate in value at around 2% per year, more or less, though we might change our mind about this promise in future, and we will keep this promise by printing unlimited amounts if they start to depreciate in value by less than 2% per year, and by buying back unlimited amounts if they start to depreciate in value by more than 2% per year."

The total size of the Bank of Canada is (roughly) the total (inflation-adjusted) value (in terms of real goods and services) of all the bits of plastic with Steve's and Carloyn's autographs. If they wanted to shrink the Bank of Canada, they would threaten to print autographs more quickly, to target 3% inflation instead of 2% inflation, so their autographs would depreciate more quickly. And if that threat were credible, and if prices adjusted quickly, they would actually need to buy back some of their autographs initially, as demand fell, to stop them depreciating even more quickly than 3%.

Comments

[Roger Sparks]

"Suppose the current total market value of my autographs is $100 (10 autographs at $10 each)."

Now you would like to lower the total market value for the next measuring period to $50.

You, as the producer of the autograph, will always know how the forthcoming market total is advancing. Is it on schedule to reach $50?

The buyer side of the balance has incomplete schedule information. The buyer side will only know the length of the measurement period but not the number of sales. This then takes us to the dilemma of first sale value. What would be the value of the first autograph?

[Nick Rowe]

Roger: if Statistics Canada collects and reports data with a lag, which it does, the Bank of Canada will make random forecast errors in hitting its target, which it does. (Which I have ignored in this post, to keep it simple.)

[Min]

Well, if you print your autographs, I expect that their value drops to 0 very quickly. ;)

Joking aside, what experimental tests might we devise to test some of these plausible hypotheses about autographs? How to assess expectations independently of the market, for example?

[Nick Rowe]

Min: Survey data on expectations (assuming people tell the truth). Or make announcements about future printing (assuming those announcements are believed). Watch what happens when pens unexpectedly run out of ink.

[Fedupguy2004]

Nick last time I looked Mark Carney doesn't sell autographs - the office of debt management sells his autographs and the bank of England no longer has control over that. This matters because in most modern states the central bank no longer controls autograph production (sorry the unit of account) the state does in net unit of account destruction (tax payments) or production (state spending) - unless (legally blocked in most countries) the state allows debt monetisation/helicopter money. All the state can do is affect the futures market for autographs (securities sales a deflationary transfer payment)and similarly central banks (through open market operations). This shifts the consumption of autograophs in time (through deflating or inflating demand in time) but they cannot through these means affect the total consumption of autographs - only net state spending/taxation can do that. Monetary policy shuffles around the deckchairs, only fiscal policy builds battleships.
Andrew Lainton (did you see my post on central bank liabilities https://andrewlainton.wordpress.com/2015/01/20/is-state-outside-money-a-liability-and-if-so-to-whom/ )

[Nick Rowe]

Andrew: Bonds are promises to pay currency; currency is not promises to pay bonds. Currency is alpha; bonds are beta. Alpha leads; beta follows. Bank of Montreal dollars are promises to pay Bank of Canada dollars; not vice versa. Bank of Canada is alpha; Bank of Montreal is beta. The Bank of Canada leads; the Bank of Montreal follows.

[rjs]

This line of reasoning -- treating assets as if they were consumption goods, or bank reserves as if it was something that shares nothing of the characteristics of bank reserves -- is an interesting train thought, and also has some practical consequences:

1. The more bits of capital there are, the less they must be worth, so as investment increases interest rates must go up (because each unit of capital is cheaper).

2. If I start a mutual fund, "RSJ Associates", in which I sell a share for $100 and buy $100 of the SP 500, then the more shares I issue, the less each share must be worth, so I can force a stock market decline as my RSJ Associates fund swells in size.

[Jussi]

Great post!

But I still, even if this has been discussed in the past, wonder whether the analogy is a fair one. I mean in your example autographs are just "issued" against nothing while the money is issued (typically) against a bond - a promise to redeem the money in the future. It looks very different to me from expectations or backing point of view.

[Nick Rowe]

Andrew: sorry. I think I totally missed your point. It was late. The Bank of Canada is a bit weird too. Notes and coins are treated sepeartely. Only notes are on the BoC's books. I tend to lump notes coins and reserves all together. Some are on paper, some are on metal, and some are on silicon, but they are all the same.

[Nick Rowe]

Jussi: thanks!

Jussi and rjs: here's maybe a better metaphor, though more complicated:

Suppose I issue shares in a closed end mutual fund. You can trade them, but only sell them back to me if I choose to buy them back. Suppose the shares trade at a premium to Net Asset Value, because they are more liquid than anything else on the market. People will even want to hold some of them if they expect the yield to be negative. And now suppose I don't pay the asset returns back to the shareholders, but give them away to my favourite charity, so I eliminate the premium to NAV.

[Min]

@ Nick Rowe

Continuing with the autograph experiment idea, we have this: "And bits of paper with my autograph were a valuable asset. But demand curves slope down; so let's assume the market price of my autograph is inversely proportional to the quantity. 10 autographs are worth $10 each, and 20 autographs are worth $5 each, etc."

One possible way to do that kind of thing in an experiment would be to have the "autographs" be lottery tickets for a drawing at the end of the experiment for a prize of $100. Or, equivalently, bookkeeping entries in a ledger. :)

However, we also have this: "Suppose the current total market value of my autographs is $100 (10 autographs at $10 each). If I want to shrink it to $50, all I need do is threaten to produce autographs in unlimited amounts if the total market value ever rises above $50."

How do we implement that in the experiment?

[baconbacon]

I would disagree with the strength of the conclusion. In the US, at least, money supply flows through banks, and from a banks perspective regulatory mandates are alpha. In terms of cash vs bonds- bonds (mortgages not government) banks don't care about a loss of purchasing power (its not their money) but they do care about inflation as it effects interest rates and thus the value of their current portfolio.

http://sebwassl.blogspot.com/2015/02/nick-rowe-gets-lost-taking-shortcut.html

[rjs]

Nick:

"Suppose the shares trade at a premium to Net Asset Value, because they are more liquid than anything else on the market. People will even want to hold some of them if they expect the yield to be negative.:"

Kinda, maybe a little you have variations due to "frictions". Not something to worry about putting into a model, though.

"And now suppose I don't pay the asset returns back to the shareholders, but give them away to my favourite charity, so I eliminate the premium to NAV."

And now comes the fiscal policy/illegal activities. Damn why keep slipping accounting fraud into these toy models? If you are buying a basket of securities, the advisor doesn't get to give yield away to charity. No, no, no!

More importantly, bank reserves are not a "closed ended fund", as any citizen holding bank reservers in the non-bank sector can exchange them for bank bonds and stocks -- e.g. they are redeemable on demand. The banks may be stuck holding the bag because, in aggregate the banking sector cannot redeem federal reserve notes, even though the non-bank sector can. The purpose of the banking is to transform the liabilities that issued by the non-bank sector (including the govt sector) into liabilites that the non-bank sector wants to hold. That means that the shift in balance sheets happens in the private banking sector to undo the shift in liabilities of the CB -- think of it as (Financial) Ricardian Equivalence that undoes the effects of QE.

But since pretty much all the income earned by the banking sector is seignorage income, this just means that their margins get squeezed, not that they rush and use customer deposits to give gifts to charity or "spend" the money invested in them by non-bank households.

[rjs]

In the above, instead of "federal reserve notes", it should read "federal reserve liabilities", sorry.

[Too Much Fed]

Nick said: “Andrew: Bonds are promises to pay currency; currency is not promises to pay bonds. Currency is alpha; bonds are beta. Alpha leads; beta follows. Bank of Montreal dollars are promises to pay Bank of Canada dollars; not vice versa. Bank of Canada is alpha; Bank of Montreal is beta. The Bank of Canada leads; the Bank of Montreal follows.”

Andrew, I disagree with that. I believe it is both ways. Assume the central bank is set up to handle liquidity events for the commercial banks and deposit insurance handles solvency events.

If there is a bank run and the bank is solvent/the assets will hold their value/the loans will perform, the central bank will buy something demand deposit like from the commercial bank and sell currency to the commercial bank to meet demand.

If there is a bank run and the bank is not solvent/the assets will not hold their value/the loans will not perform, the commercial bank will get what I call FDIC’d.

In either case, demand deposits remain 1 to 1 fixed convertible with no demand deposit writedown.

For example, say a bank creates $9 billion in new demand deposits. They will most likely affect the price level. Then at a later period, have a bank run where the commercial bank is solvent. The central bank will buy something demand deposit like from the commercial bank for $9 billion and sell $9 billion in currency to the commercial bank to meet demand.

I don’t see the central bank ever saying sorry we won’t meet the extra demand for currency.

Also, I’d say almost all bonds can involve either currency or demand deposits. If I buy a bond from a commercial bank that the commercial bank uses for bank capital, it can repay me with either currency or demand deposits. Same if I buy a bond from United Technology.

[Jussi]

Thanks Nick. I like it better. It is a cute and useful model, I think.

But even the improved version is not totally accurate/realistic IMO as e.g. in Europe banks can, at will, pay the LTROs back and there might be other ways too. So I think that the base money and its velocity is a quite elusive concept - yet maybe still useful.

And I'm not sure the cash premium / positive NAV is due to liquidity because the CB can by and large decide the rate (of the deposit facility) it pays. Isn't it more like a banking tax.