I might as well join in the fun. Along with Steve Williamson, Noah Smith, Karl Smith, Paul Krugman, David Glasner, and Steve again. [Update: and Brad DeLong and JP Koning. And David Andolfatto.]
Some assets are more liquid than others (they have lower transactions costs of buying and selling). More liquid assets will have a lower desired rate of return than less liquid assets (that means people will be willing to own them even if they expect to earn a lower rate of return than less liquid assets).
Money (the good that is used as a medium of exchange) will be more liquid than other assets. (If some other asset were more liquid than money, people would switch to using that other asset as a medium of exchange instead of the existing money, and that other asset would become the new money).
Money will therefore have a lower desired rate of return (strictly, a desired rate of return that is not higher) than other assets.
A chain letter that is always growing faster than the economy will eventually burst. It would burst immediately, if people didn't think there would be a greater fool coming along who also thinks he can get in and out before it bursts. It is "unstable". A chain letter that always grows more slowly than the economy can exist forever. It is "stable". If the desired rate of return on a chain letter is above the growth rate of the economy, the chain letter would have to grow faster than the economy to get people to participate, and so it is unstable. If the desired rate of return on a chain letter is below the growth rate of the economy, it is [or can be] stable.
Chain letters, ponzi schemes, and bubbles, are all the same thing.
The more liquid an asset, and thus the lower the desired rate of return on that asset, the more likely it is that desired rate of return will be below the growth rate of the economy.
Demand curves, for stuff that doesn't have very close substitutes, usually slope down. If the "stuff" is something like apples, that means the price people are willing to pay (the "desired price", or Marshallian "demand price") is negatively related to the quantity bought. If the "stuff" is an asset, that means the desired rate of return is negatively positively related to the quantity held. [Because the demand price of the asset is negatively related to the desired rate of return, and two negatives make a positive.]
Some assets do not have very close substitutes, and have downward-sloping demand curves. Cars are one example. Money (the medium of exchange) is another. People will want to hold some cars even if the rate of return on holding cars is very low. People will want to hold some money even if the rate of return on holding money is very low. The rate of return on holding money got extremely low in Zimbabwe, before people stopped using that money altogether. It went very very negative.
It is perfectly possible for the desired rate of return on holding money to be below the growth rate of the economy. It nearly always is below the growth rate. That means is it perfectly possible for money to be a chain letter that is stable.
A stable chain letter has two equilibria: one in which it continues forever; and a second in which it bursts immediately. If people always expect it will continue forever, it will continue forever. If people expect it will burst immediately, it will burst immediately. Even a "stable" chain letter isn't totally stable.
In the basement of the Bank of Canada there is a large collection of baskets of consumer goods. The Bank of Canada promises that it will redeem its monetary liabilities on demand for those CPI baskets. It promises that the redemption price will rise at 2% per year, so that the actual rate of return on holding Bank of Canada currency will be minus 2% per year in real terms. It has enough CPI baskets in the basement that it can honour that promise even if all currency were brought in for redemption. Bank of Canada currency therefore trades at a price equal to its fundamental value, that fundamental value is falling at 2% per year, and in equilibrium the desired rate of return is also equal to the actual rate of return of negative 2%. (Purely as a convenience, the Bank of Canada also offers people the choice of redeeming their currency in bonds instead, where the market price of the bonds is the same as the promised price of the CPI baskets. And everybody takes them up on that offer, since CPI baskets are hard to carry around.)
I made up some stuff in that above paragraph. But would anyone ever know, if they hadn't looked inside the Bank of Canada's basement? And even if they did look inside the Bank of Canada's basement, and found it was full of bonds rather than CPI baskets, would they care?
[Update: "Observational equivalence", those are the words I was looking for!]
"A chain letter that is always growing faster than the economy will eventually burst. It would burst immediately, if people didn't think there would be a greater fool coming along who also thinks he can get in and out before it bursts. It is "unstable". A chain letter that always grows more slowly than the economy can exist forever. It is "stable". If the desired rate of return on a chain letter is above the growth rate of the economy, it is unstable. If the desired rate of return on a chain letter is below the growth rate of the economy, it is stable.
"Chain letters, ponzi schemes, and bubbles, are all the same thing."
Your previous paragraph disproved that assertion. Ponzi schemes and bubbles are unstable. You assert that some chain letters are stable. (Not that I have seen one, myself. ;))
Posted by: Min | October 23, 2012 at 12:54 PM
I am not entirely sure what a chain letter is.
I think I know, and I don't really see what it has to do with the growth rate of the economy, so I presume that the chain letter has a monetary element.
Posted by: Bill Woolsey | October 23, 2012 at 01:38 PM
So are you saying that money is sort of like an optical illusion (or like a quantum mechanical wave/particle, or like the traditional Christian conception of Jesus) -- all bubble and all fundamental at the same time (depending maybe on from what angle you look at it)? Or are you saying that bubble-money is perfectly feasible but that, in the case of a strictly inflation targeting central bank, the value of money is fundamental?
(BTW I did see the post on debt burden without full employment. I'm glad you wrote it, but I didn't really have anything else to say.)
Posted by: Andy Harless | October 23, 2012 at 01:49 PM
I think the point that Krugman was making was that he defines bubbles as characterized by individual expectations that are inconsistent in the aggregate. E.g. everyone thinks they can find a greater fool. That is distinct from multiple equilibria that are nevertheless Nash equilibria.
So maybe you (economists) are just arguing over definitions, or perhaps there is some substantive disagreement. I would be interested to know if this was the case.
Plus, the Giants won!
Posted by: rsj | October 23, 2012 at 02:04 PM
It could also be that different groups of people have different needs and define "money" differently.
E.g. for a household, "money" is a depost, because that is much easier for them to use than paper currency.
For a depository institution, "money" is reserves.
For an investment bank or currency trader, "money" is a treasury bill -- because that is the most convenient form.
There is no requirement that the most convenient store of value for one type of market participant be the most convenient for another.
Posted by: rsj | October 23, 2012 at 02:07 PM
Min: bubbles and Ponzi schemes can be stable. Suppose Mr Ponzi offers a rate of interest below the growth rate of the economy. And suppose people take him up on his offer, because (for some reason) they really like lending to Mr Ponzi, even if he offers a lower rate of interest than anyone else. And he spends what they lend him, and keeps rolling over the debt, and for every person that wants to withdraw his money, someone else comes along who wants to lend him money. His liabilities grow at the rate of interest he pays. But if the economy is growing more quickly than that, it never needs to end.
Bill: you didn't get chain letters when you were a kid? Here's the simplest version. You get a letter telling you to mail $1 to the person who sent it to you, and to mail a copy of the letter to 2 other people. If the delay between paying $1 and getting $2 is one year, the rate of interest on the chain letter is 100%. (More complicated letters tell you to mail $1 to the person who sent it to the person who sent it to you.)
Andy: I think I'm saying that bubble money and strict inflation targeting money are observationally equivalent. And we could expand that to cover the case of other monetary regimes, not just IT.
rsj: I think that Paul Krugman has changed his definition of bubbles/ponzi over time, so that, by definition, only unstable ponzis are now called "ponzis". I don't think that's a useful definition. I can imagine cases where Mr ponzi does exactly the same thing, but whether it is stable or unstable is an empirical question, depending on future r and g. There are two questions: does Mr Ponzi actually buy assets with what people lend him (or does he spend the lot); and is it unstable? Those are two empirical questions, and we need to keep them separate, so we can ask: under what conditions are those two answers related?
Posted by: Nick Rowe | October 23, 2012 at 02:27 PM
rsj: "There is no requirement that the most convenient store of value for one type of market participant be the most convenient for another."
I'm not talking about stores of value. My house, stocks, land, cars, and canoes are all very convenient stores of value for me, but they are not media of exchange.
But yes, different people may choose different media of exchange. (Though it depends a lot on what other people around you are using, so there's a network effect.)
Posted by: Nick Rowe | October 23, 2012 at 02:31 PM
Nick Rowe: "Suppose Mr Ponzi offers a rate of interest below the growth rate of the economy."
Then he is not Mr. Ponzi.
You may recall that some time ago, Nick, I often took took you to task over sloppy language. Later I realized that that was part of your creativity. :) Fine. But talking about Ponzi schemes and such introduces emotional elements that "cloud men's minds", even if it does not cloud yours. Ponzi talk is for the nut jobs.
Posted by: Min | October 23, 2012 at 02:40 PM
Min: OK. Suppose Mr Smith offers a rate of interest below the growth rate of the economy, and then consumes what people lend him, instead of investing it.
Posted by: Nick Rowe | October 23, 2012 at 03:07 PM
Nick: I think that Paul Krugman has changed his definition of bubbles/ponzi over time, so that, by definition, only unstable ponzis are now called "ponzis".
Yes, he explained here why he changed:
http://krugman.blogs.nytimes.com/2011/09/14/the-ponzi-thing/
Posted by: Kevin Donoghue | October 23, 2012 at 03:13 PM
Kevin: thanks. I'm not sure if it was a good decision by PK though. Suppose we call an unfunded but stable plan a "Smith scheme". If the growth rate drops, or if the desired rate of return rises, a Smith scheme might suddenly turn into a Ponzi scheme. (I would prefer to say a stable Ponzi had now become unstable, but whatever.)
Posted by: Nick Rowe | October 23, 2012 at 03:18 PM
Or, better, that a Ponzi scheme that we thought was stable turned out to be unstable.
Posted by: Nick Rowe | October 23, 2012 at 03:19 PM
Nick,
"And even if they did look inside the Bank of Canada's basement, and found it was full of bonds rather than CPI baskets, would they care?"
Sure, they would.
The BoC has CPI baskets in the basement by virtue of the fact that the government of Canada has broad discretion to confiscate them from Canadian taxpayers. Should that fail, I don't think the market would think very highly of BoC liabilities backed by future claims on the crown denominated in BoC liabilities. In fact, don't hyperinflations generally follow the failure to collect adequate tax revenues?
Also, didn't you once to a post about instability of the "money backed by money" CB valuation? (It's a geometric sequence, the limit of which is either zero or infinity depending on whether assets exceed liabilities). CB balance sheets only make sense if you consider the fact that there is an equity claim *and* a tax asset (the govt always tries to make the CB whole). The nominal backing is a debt from the government to itself, pure accounting smoke and mirrors. The real asset is the tax asset.
The BoC *could* keep CPI baskets in the basement by holding a broad basket of capital assets. It would be an uncertain amount of future consumer basket, but then there are no certain claims on future consumption (taxes also are limited by the size of the economy). That might be a good idea, as we've discussed before.
Posted by: K | October 23, 2012 at 03:34 PM
K: Let's take the extreme case. Suppose the government of Canada declared all its bonds null and void. So if the BoC held government bonds, they would be worthless. The BoC currency would now become a stable Ponzi. If the BoC could keep its independence (a big if), and if the demand for BoC currency continued to grow over time, or at least never fall below where it is right now (a second big if) it would be perfectly possible for the BoC to continue to keep inflation at the 2% target. It would just pay less profits to the government (because it gets those profits from the interest on government bonds). Though if everybody expected everybody else to refuse to accept Loonies, Loonies would drop to zero value, and not be used as media of exchange. (Maybe you could argue that couldn't happen, since their value for recycled paper would rule out that equilibrium.)
Posted by: Nick Rowe | October 23, 2012 at 03:49 PM
Nick:
This might be a good time to ask if you have changed your mind about whether the central bank must hold enough assets to buy back ALL of the money it has issued, or if the central bank can get by with enough assets to buy back maybe only 30% of the money it has issued. You sound like you might be wavering.
Posted by: Mike Sproul | October 23, 2012 at 04:19 PM
Mike: If there's a chance the demand for money might drop by a maximum of (say) 30%, the BoC will need to keep 30% assets (if it wants to keep inflation on target). The only point to keeping 100% assets is to keep the accountants happy, and because there is no cost to keeping assets, since the seigniorage profits from those bonds goes right back to the government anyway. (It's maybe different for the ECB, where what "ownership" might mean is a bit more confused.)
I think that means I haven't changed my mind on that question. (But I can't actually remember what my mind used to think.) (But I have changed my mind, a bit towards your view, on the bigger question, ever since my "gold standard to CPI standard post").
Posted by: Nick Rowe | October 23, 2012 at 04:34 PM
Nick Rowe: "Suppose Mr Smith offers a rate of interest below the growth rate of the economy, and then consumes what people lend him, instead of investing it."
Ah! The Smith scheme. I like it. ;)
Posted by: Min | October 23, 2012 at 04:36 PM
And even if they did look inside the Bank of Canada's basement, and found it was full of bonds rather than CPI baskets, would they care?
I think so. Because in some of the world-states where people do look inside the BoC's basement, the bonds are also worthless.
I'm imagining the zombie apocalypse, for instance. Money loses its liquidity premium, because trade and exchange collapse. So people carry their loonies and worthless paper to the BoC, hoping to exchange them for the bags of ammo and food in the basement. But they find that the only things in the basement are other pieces of worthless paper (bonds).
I think you get the same result when people expect devaluation. If the central bank has goods (or foreign-denominated assets) in the basement, then it can support the value of money. If they only have domestic-denominated bonds, it can't.
Posted by: Ryan V | October 23, 2012 at 04:46 PM
Ryan: OK. Assume that every year there is a 5% chance of Zombie apocalypse (or Zimbabwe). So there's a 5% chance your money would be worthless. That reduces the actual rate of return (for the same target rate of inflation if there's no zombies) by 5%. So you hold a little bit less money to bring your desired rate of return back into equality at the margin with the actual rate of return. It's the same as having 7% inflation.
Posted by: Nick Rowe | October 23, 2012 at 05:09 PM
If people expect devaluation, even if the central bank has 100% foreign currency assets, the rise in domestic interest rates, and domestic recession, can make devaluation a self-fulfilling expectation. Because central banks will devalue rather than allow a very big recession.
Posted by: Nick Rowe | October 23, 2012 at 05:13 PM
Re: CPI basket/bond redemption.
I was going to say that Mike Sproul wrote this post, not Nick Rowe, but then saw you two had already conversed.
"I think that means I haven't changed my mind on that question. (But I can't actually remember what my mind used to think.) (But I have changed my mind, a bit towards your view, on the bigger question, ever since my "gold standard to CPI standard post").
Mike, you can frame that and hang it on your wall.
I could be wrong, but Bill Woolsey seems to be saying the same thing here. I wrote something similar here.
Posted by: JP Koning | October 23, 2012 at 05:29 PM
JP: I liked your post (and just now remembered to add it to my links before reading your comment, honest!). But I was wondering about the case where the asset lives longer than the buyer, or where the buyer may not want to hold that asset in future, because his kids have left home and he wants to get rid of the minivan and buy a sports car. He would pay a lot less for the asset if he knew he would have to hold it forever, even if it did trade at its fundamental value. I was thinking about that (and also thinking about another post I have in the pipeline about the relation between liquidity and velocity), when I decided to try to approach it this way.
The ironic thing is, I was reading some MMT (I think) bloggers arguing that modern monetary theory is so very different from under the gold standard, and thinking about why that might be true, when I realised it really wasn't correct, and wrote my gold standard and CPI post. It was MMT that pushed me towards Mike!
Gotta read Bill.
Posted by: Nick Rowe | October 23, 2012 at 05:40 PM
"Money (the good that is used as a medium of exchange) will be more liquid than other assets. (If some other asset were more liquid than money, people would switch to using that other asset as a medium of exchange instead of the existing money, and that other asset would become the new money)."
What if the medium of exchange is defaultable?
Posted by: Too Much Fed | October 23, 2012 at 10:07 PM
Nick:
"If there's a chance the demand for money might drop by a maximum of (say) 30%, the BoC will need to keep 30% assets"
But a bank with 30% assets (or even 99% assets) is a run waiting to happen. As soon as people realize that the bank's assets are enough to buy back only 30% of its assets, they rush to redeem their dollars at full value. By the time 30% of the dollars have been redeemed, the bank will have no assets left, and no way to buy back the other 70% of its dollars still in private hands. Meanwhile, currency traders will be shorting the dollars like crazy, profiting as it falls in value.
Posted by: Mike Sproul | October 23, 2012 at 11:49 PM
Correction:
"only 30% of its assets" should say "only 30% of the dollars it has issued"
Posted by: Mike Sproul | October 23, 2012 at 11:52 PM
A commercially legitimate central bank sets the price of its own assets (mostly). The only constraints it faces are on count of 1) its own policy goals 2) the value of those assets that it holds for some reason but whose price it doesn't control, i.e Fx reserves, gold 3) the equilibrium neutral real rate.
Therefore, it has assets even when it doesn't have them. And vice versa.
All differences on this count between backing theory, hot potato theory, MMT etc. are Wittgenstein-ian. What matters is the real interest rate on the financial numeraire, the asset with the lowest real rate. That alone determines what is the inflation tax, what is the hotness of the potato, how much of the liquidity premium is 'fundamental' and how much of it is a bubble, etc.
Not all liquidity is a bubble. Karl Smith is wrong. He mistakes the ability to borrow against higher equity, a question of wealth, for a liquidity effect. It isn't. It's a wealth effect.
If the real interest rate is too low, money is in a bubble.
A fall in money demand can be countered by paying higher interest on reserves. At any point of time, a central bank can have all (most) of its assets as short term t-bills at the same yield as the interest it pays on reserves, that it rolls over indefinitely. If the average reserve is turned over say once in 30 days, the central banks holds 30 day t-bills, and transfers its profit/loss to the treasury at intervals of 30 days, these can be pure accounting entries.
Posted by: Ritwik | October 24, 2012 at 03:13 AM
Let's take the extreme case. Suppose the government of Canada declared all its bonds null and void.
The problem is that interest rate policy is determined by the rate of discount on government debt. So you are assuming that the CB does not control interest rates, because the rate of discount of government debt is high in this case.
To think about it another way, the CB guarantees to redeem government debt (e.g. discount government debt) at the policy discount rate. Any and all takes are always able to show up at the CB and sell their government bonds to the CB at the announced rate of discount.
This requires some coordination between the CB and the Treasury, and you are assuming that this coordination breaks down, but the CB somehow manages to keep its doors open.
In this situation, it can't keep its doors open. The CB defaults at its promise to discount debt just as much as the government defaults in its promise to repay debt. Both sides default equally or no one defaults.
If you look at those situations in which governments have defaulted on debt, they all correspond to situations in which there was no sovereign interest rate policy. E.g. the government was trying to maintain a peg to something that it did not control. In that case, arguing that the government defaults is equivalent to arguing that the CB cannot maintain a target rate of discount, which is itself equivalent to arguing that the CB does not control the money supply.
In both cases, it's logically inconsistent to assume that the CB can continue to control the money supply even as Treasury defaults on risk-free debt. The treasury can continue to sell debt at the policy discount rate if and only if the central bank can continue to discount that debt and so set interest rates.
Posted by: rsj | October 24, 2012 at 05:22 AM
TMF: what would "default" mean? See my answer below to Mike.
Mike: good point. I had to think about that one. Here's my answer:
Suppose there were a run. The central bank could suspend convertibility at the old price, and restore convertibility at a new lower price, so that it had 100% assets at that new lower price (this would mean, of course, that inflation would have risen above the 2% target). But the real stock of money is now lower, so there would be an excess demand for money (if there were no close substitutes for central bank money). So the value of money would rise back up again to its original equilibrium. Anticipating that rise, other speculators would take the other side of the market against the shorters.
One thing that could go wrong with my counterargument is this: if there were a run, and the value of money fell to zero, it could no longer work as a medium of exchange, so it could never recover its value. So the central bank would need to have some assets to prevent this happening. (Or, maybe, paper money could still work as money, even if it were only worth the paper it's on??)
My counterargument would not work for commercial banks, because there are close substitutes for the money of any one commercial bank.
Posted by: Nick Rowe | October 24, 2012 at 06:18 AM
Ritwik: "Therefore, it has assets even when it doesn't have them. And vice versa."
You lost me a little there. Are you saying that the most important asset of a central bank is one that doesn't appear on its balance sheet? Namely the present value of its future monopoly profits? If so, I agree.
rsj: if the assets it held became worthless in real terms, the central bank would have to choose between fixing the value of its money in terms of those same assets (in which case its money would become worthless too) or letting the monetary value of those assets drop to zero, so that its money would continue to be worth something. I am assuming the central bank has enough independence that it would choose to do the latter. It would have to close its Open Market Operations desk, obviously. But why would it have to close its "doors"? What doors? Why couldn't I keep on using those bits of paper to do my shopping?
Yes, if there were a fall in the demand for those bits of paper, the central bank would be unable to buy them back, so the value of those bits of paper would fall. (It would be unable to keep inflation at the 2% target in the face of a fall in the demand for money). But unless people stopped using its money altogether, so the demand fell to zero, the money would still have value. Look at Zimbabwe, where people kept using the money despite massive numbers of new notes being created. It takes a truly massive amount of printing to destroy a currency, not just a failure to burn notes when the demand for those notes falls.
"If you look at those situations in which governments have defaulted on debt, they all correspond to situations in which there was no sovereign interest rate policy."
Are you sure about that? I can see why it would generally be true. Why default on your debt when you can print money? But didn't someone in comments a couple of years back give a couple of counterexamples? (My memory has failed.)
Posted by: Nick Rowe | October 24, 2012 at 06:39 AM
Nick
What I mean is imagine that all reserves of the central bank are in essence backed by short term t-bills of the government, even if they are not *actually* backed by them. Monopoly profits, whether from the difference between currency & bank deposits, or from making the market in overnight reserves, or from collateralised lending in distressed times, are only cherries on top. They allow a central bank some room to make mistakes on the inflationary side and still get away with it. But the system survives and thrives and is coherent even when you assume such profits to be 0.
The 30% fall in money demand --> back by 30% assets or 99% < 100% causes inflation etc. are all unnecessary scenarios and don't yield much insight. Inflation is a fall in money demand (or a reduction in the net worth of a central bank). If so, hike the interest paid on reserves. Create money demand. You can see this as a central bank hiking the value of its assets, and hence net worth, by fiat. There can never be a run on a central bank, a central bank that discounts its assets and liabilities properly is never insolvent. The discount rate (real)is all that matters, for a first order approximation.
In fact, a central bank should almost always be run on a 'high frequency netting of profits with the treasury' basis, whether this consists of the CB handing over its market making profits, or whether it consists of the Treasury instituting a payment to the CB to cover the interest it pays on reserves. The net worth of a central bank - its non monetary liabilities - must always be kept at identically zero.
Posted by: Ritwik | October 24, 2012 at 07:42 AM
Nick: Isn't your counterargument to Mike are you sure about that? How could real value of money increase to its previous level if it is now convertible only for 30% of quantity of whatever asset is backing it compared to previous state? That would mean that there needs to be a one-time change in relative prices of redeemable assets and all other assets in an economy coinciding with the bank announcement - which could be possible for supply reasons, but I do not think it is anything behind Mike's argument.
Maybe you wanted to say, that immediately after CB declared its willingness to inflate (increase the price of redeemable good in terms of money it issues), markets would realize that this is new stable equilibrium and would thus stop their bank run and so bank could restore back its original policy and actually not inflate? I still think that this is false, because it is equal to an assumption that there can be no bank run if the bank is willing to inflate. If your assumption is that there can be no bank runs, then there simply won't be any.
Posted by: J.V. Dubois | October 24, 2012 at 08:50 AM
Ritwik: I'm still not sure I'm following you. Let me try this:
A central bank which issues currency at -2% real when other interest rate are (say) 1% real has a stream of future profits equal to 3% on all the future currency it issues, so it can borrow against that stream of future profits, even if it has no other assets. It can sell its own Tbills, or pay interest on reserves. ?
JV: The only equilibrium is where Md/P=Ms/P. If people want to hold a stock of money to use as a medium of exchange, Md/P > 0. Why should a change in the price *level* affect the real demand for money? Suppose for example there is a run on the bank, and the price level doubles, and stops there. That means Ms/P is now halved. But Md/P should be unchanged. So now there is an excess demand for money, and the price level must halve again.
The only danger is if the price level goes to infinity, because now the value of money is zero, it can't be used as a medium of exchange, so Md drops to zero too. (OK, maybe if the price level gets very high, you physically can't carry the notes you need to do the shopping, so they don't work as a medium of exchange either).
Posted by: Nick Rowe | October 24, 2012 at 09:14 AM
Nick: "Why should a change in the price *level* affect the real demand for money"
Ok, maby we started it in the wrong way. Bank run on central bank means that people want to decrease the stock of money in exchange for whatever asset serves as backing given the current price level. So we already start in disequilibriuml. So as reaction CB can decrease the Ms (buying money for backing) or they can let P increase so that the equilibrium restores. Then there is no need for P to be halved again. Or am I missing something?
Posted by: J.V. Dubois | October 24, 2012 at 09:58 AM
JV: OK I misunderstood you.
I was starting in equilibrium, and seeing if a run could be a second equilibrium.
If we start in equilibrium, then there's a shock which halves the real demand for money, the central bank will run out of assets if it has less than 50% backing. So it will be forced to allow the price level to rise. (Unless it borrows against its future seigniorage revenue).
Posted by: Nick Rowe | October 24, 2012 at 11:05 AM
Nick
Assume a world without currency. Reserves pay 1% real. Say 1% real is the 'right' short rate for the economy.
This central bank has a guaranteed 1% income stream from the Treasury. This could be through actual 1% yielding t-bills. Or simply a legal arrangement which says that the Treasury must pay the interest the central bank promises on reserves. The legal arrangement is implicit. The central bank always has the assets it needs. It can't be insolvent. Any runs would be the result of nonsensical institutional arrangements, not economic/finance theory.
There could be a bubble. Say the right rate is 1%. And reserves/t-bills only pay 0%. This is a central bank created 'bubble' in money.
But let's go back to the case where there is no such bubble. Reserves pay 1% real. Now add currency, which pays only -2% real. The public's wish to transact in and hold this currency allows the central bank to make seigniorage, boosting its capital. Call this the revenues realised for providing 'currency services'.
Now let's add banks and overnight call money markets. The central bank makes a market in reserves at 1%-2% real. The inter-bank rate fluctuates in this range. This bid ask spread, the interest rate corridor, makes the central bank some more profits. Call this the revenues realised for providing LoLR services.
Now add asset markets of all sorts. Now the CB makes markets not just for reserves, but also for illiquid but solvent assets. Let's say the market for MBSs is 3%-6% real. In normal times no one will trade with the central bank. In bad times people will happily hit the market that it makes. This is a third source of revenues. Call this revenues realised from providing 'market maker of last resort (MMLR)' services.
Now if the CB adds all three revenues, after paying for its costs, it will have some profits and hence capital left over. It needs part of this capital for
1) Holding some inventory of assets to make the markets in MBS etc.
2) Financing Fx/gold/ SDR purchases
3) Creating a cushion for making some inflationary mistakes. Thus if the equilibrium real rate is 1% and CB sets it at 0% for a while, it will stoke some inflation above its target, a mini 'run' on its liabilities.
The rest of the profit it hands back to the treasury. Also, if it has completely run out of capital and net worth threatens to go negative, i.e. the short rate is too low, it hikes the interest paid on reserves. And the treasury just makes regular payments to CB to enable it to make the interest payments on reserves.
This is already a full blown model of a CB. There is no run conceivable on this CB. You can model the no run scenario through assets/liabilities and backing theory ala Mike Sproul. Or you can model it through money demand/ money supply ala you. Doesn't matter. It's isomorphic. The only thing that matters is getting the real discount rate right. Or atleast, not *too wrong*.
Posted by: Ritwik | October 24, 2012 at 11:09 AM
"also thinking about another post I have in the pipeline about the relation between liquidity and velocity."
Sounds interesting.
Maybe off topic, but a question on definition of the growth rate of the economy variable that you use in your post. Can I think of it as a universal return we expect from holding generic durable assets over time (assuming away differences in riskiness, liquidity, storability among durable assets).
Posted by: JP Koning | October 24, 2012 at 11:16 AM
JP: "Maybe off topic, but a question on definition of the growth rate of the economy variable that you use in your post. Can I think of it as a universal return we expect from holding generic durable assets over time (assuming away differences in riskiness, liquidity, storability among durable assets)."
No. I don't think you can think of it like that. That sounds closer to a rate of interest than to a rate of growth. We could have no investment possibilities at all, and still get growth, if we have population growth, or exogenous technological improvement in productivity.
Posted by: Nick Rowe | October 24, 2012 at 01:53 PM
Nick's post said: "TMF: what would "default" mean? See my answer below to Mike."
I don't think we are on the same page.
Medium of exchange is apples. I have apples. Next day I wake up, and some of my apples have rotted. Amount of medium of exchange has gone down.
Medium of exchange is currency plus demand deposits. I have demand deposits of bank A. Next day I wake up, and some of my Bank A demand deposits have gone down (the bank failed). Amount of medium of exchange has gone down.
Posted by: Too Much Fed | October 24, 2012 at 02:41 PM
"In the basement of the Bank of Canada there is a large collection of baskets of consumer goods"
Even if the basement was empty, and even if the bonds were cancelled, it is likely the value of the currency would not change. I am sure Canadian dollars are backed by the future profits of the central bank, and most of the time the users of the currency will be willing to discount these profits at some very bubbly rates.
The main question we need to ask is if the goodwill on the central bank's balance sheet has got a bubble valuation. Bonds and CPI baskets are a distraction.
Posted by: 123 | October 24, 2012 at 04:52 PM
"Chain letters, ponzi schemes, and bubbles, are all the same thing." Et tu Brutus?
Nick, I don't think you're helping with statements like that.
You know every well that there are lots of alternative definitions of Ponzi schemes and bubbles around. Much of the debate over whether some things can be classed as one of these (PAYGO pension schemes? US government debt? paper money?) depends on which precise definition you use. The comments you've gotten so far reflect much of that; people can't agree on what a Ponzi scheme is, in part because you've given no definition. I think a necessary condition is that the scheme always has negative equity -- so it includes money and PAYGO pensions schemes -- but many others think "Ponzi" is a pejorative term and so prefer definitions that exclude such things.
Posted by: Simon van Norden | October 25, 2012 at 01:29 AM
Look, instead of rehashing the same old classic monetary thinking about Ponzi schemes and bubbles (zzzzz!) why not try thinking about a more useful setting? Suppose you're in a world where interest rates and growth rates are stochastic and their movements are hard to predict? where we can't reliably tell which of several different forecasts for these variables are "best"? How would you define a Ponzi scheme in a world like that? a bubble?
Posted by: Simon van Norden | October 25, 2012 at 01:36 AM
Simon: "Suppose you're in a world where interest rates and growth rates are stochastic and their movements are hard to predict? where we can't reliably tell which of several different forecasts for these variables are "best"? How would you define a Ponzi scheme in a world like that? a bubble?"
YES! That is indeed a much more interesting question to answer. And much more important, for policy.
But I have already answered it! Or, more precisely, I have already answered a more policy-relevant version of the same question, namely: what should government debt policy be in a world where interest rates and growth rates are stochastic and hard to predict?
My answer is: the government should issue one trill perpetuity (maybe split up into 30 million pieces).
(I don't know for sure if my answer is right, but it is an answer.)
Posted by: Nick Rowe | October 25, 2012 at 10:26 AM
Simon: "You know every well that there are lots of alternative definitions of Ponzi schemes and bubbles around."
They all have the feature that they define a bubble/ponzi/chainletter as where the price exceeds the fundamental value. And the point of this post is to say that there can be an observational equivalence between cases where the price is or is not above the "fundamental value". So I am questioning whether all those definitions make any sense.
Posted by: Nick Rowe | October 25, 2012 at 10:33 AM
Nick:
At least you recognize that your answer wouldn't work in the presence of rival moneys. So, for example, if the Mexican central bank suddenly went from 100% assets to 30% assets, the peso would drop to 30% of its old value, and the resulting tight money void would be filled with US dollars, Mexican checking account dollars, credit card dollars, etc.
But you seem to think that, absent rival moneys, the peso would immediately rebound to its old value just because that's what it has to do to keep Ms=Md. That's sort of like saying that if a builder reduced his labor force by 2/3, the remaining workers would just work 3x as hard because that's what they have to do to keep the work supplied=work demanded. (Wicksteed said something similar way back when.)
Anyway, if your answer were right we should be able to find lots of examples of central banks that hold 30% assets, and of course there are no such central banks. All we ever find is central banks that hold 100% (or more) assets, and in the few cases where those banks lose assets, their money loses value.
Posted by: Mike Sproul | October 25, 2012 at 01:13 PM
Mike: "At least you recognize that your answer wouldn't work in the presence of rival moneys. So, for example, if the Mexican central bank suddenly went from 100% assets to 30% assets, the peso would drop to 30% of its old value, and the resulting tight money void would be filled with US dollars, Mexican checking account dollars, credit card dollars, etc."
I don't agree with that. If the Mexican peso had very close substitutes, a lower rate of return on holding pesos might cause the demand for pesos to drop to zero. But no individual Mexican will switch from pesos to Canadian dollars unless a lot of other Mexicans do too. So Canadian dollars are not a close substitute for pesos at the level of individual choice. Network effects.
Posted by: Nick Rowe | October 25, 2012 at 01:40 PM
NO.
"Chain letters, ponzi schemes, and bubbles, are all the same thing."
You are falsely assuming people have more knowledge than they do -- a grossly false assumption with massive explanatory consequences.
What don't you get about this?
If you don't know what is more or less risky or what will more or less risky or why things are more or less liquid or what will be more or less liquid, the explanatory situation is VERY different.
Again, can you really not see this?
Unknown unknowns are NOT mathematically given probability distributions.
Posted by: Greg Ransom | October 25, 2012 at 10:40 PM
Simon van Norden: "but many others think "Ponzi" is a pejorative term and so prefer definitions that exclude such things."
If economists were only talking among themselves, who would care what terms they used, as long as their terminology did not cloud their minds. However, economists, especially when talking about macroeconomics, have a broad audience of politicians and citizens. Under such circumstances, it is well to avoid charged and biased terminology.
Posted by: Min | October 26, 2012 at 01:53 AM
Min and Simon: I think it is better and more honest to use the same pejorative word, and explain to the public that ponzi finance is not necessarily wrong, and that it is sustainable under some conditions. In doing so, we acknowledge the risk that what looks like a sustainable form of finance might turn out to be an unsustainable if things change.
"Yes I'm queer/ponzi, and there's nothing wrong with being queer/ponzi!"
(The Brits have used this same tactic very successfully over the years; IIRC "Brit" was originally pejorative, and invented by the Irish Republican Army.).
Posted by: Nick Rowe | October 26, 2012 at 08:52 AM
With 'bubbles' in finance and across differentially time consuming production processes, there are *systematic* yet never fully known or understood network relations between vast numbers of different assets, financial instruments, production processes, inputs to production, consumption streams, etc.
With chain letters and ponzi schemes ... NOT.
Can you please address this signal fact and its explanatory & causal consequences, Nick?
Nick writes,
"Chain letters, ponzi schemes, and bubbles, are all the same thing."
Posted by: Greg Ransom | October 26, 2012 at 11:06 AM
Nick:
About network effects: US dollars are widely used in Mexico, circulating as easily as pesos. When I was there in 1990 people said that real estate prices are always quoted in US dollars, not pesos. Also, of course, if there is a sudden void of paper pesos from the central bank, the void can be filled with checking account pesos, credit card pesos, gift certificate pesos, etc, all without people ever having to "go outside the network" (i.e., use money that isn't denominated in pesos.)
Posted by: Mike Sproul | October 26, 2012 at 11:17 AM
Is this a basket of 1920s consumers goods? Likely they would be worthless today.
Nick writes,
"a large collection of baskets of consumer goods."
Production goods and consumers goods have *changing* valuational significance in a changing network of production processes and relative prices -- sometimes this network gets systematically twistes, and then is systematically untwisted -- in dimensions epistemically *unknowable* in advance.
This *matters* when it comes to the "backing" of a currency or a set of money substitute assets.
LOOK AT HISTORY -- sometimes this systematic twisting and untwisting created unknowable-in-advance cascades of liquidity, value, and risk changes, as we saw in the period 2003-2010.
How much detail do I need to provide to bring this point home/
What part of it can you challenge?
Or is the continued preference of the profession just to pretend that this can't exist, because it isn't considered in the easily graded textbook 'models' -- which abstracted away from these causal mechanisms in the 1930s, for the benefit of easy modeling and easy textbook writing and easy formal assessment of "who is a 'good 'scientist'".
Posted by: Greg Ransom | October 26, 2012 at 11:20 AM
"They all have the feature that they define a bubble/ponzi/chainletter as where the price exceeds the fundamental value. "
I don't think so. I think an alternative definition of a ponzi game is one where the scheme will always have negative equity, and no reference is made to fundamental values. That's the approach Zeldes and O'connell take in their classic 1988 IER paper, for example.
That makes a difference when you talk about pension schemes, for example, where prices and fundamental values may be hard to put a finger on.
Posted by: Simon van Norden | October 27, 2012 at 07:55 AM
As for my question about defining bubbles in a world with variables growth and interest rates, I'm surprised that you think you can answer it. But since you think you have, could you please tell us which major assets (exchange rates, government bonds, and stock market indices would be a good start) are trading above their fundamental value and which are below? I really have a hard time figuring this out sometimes....
Or, to save yourself some time, can you just tell us your method? how are we supposed to handle the interest rate uncertainty? the growth rate uncertainty? the knowledge that some agents are better informed about these things than others and we can't be sure how we rank against other market participants?
Posted by: Simon van Norden | October 27, 2012 at 08:04 AM
Simon: OK. I wasn't answering that question. I was thinking about government bonds, in a world where the rate of interest might or might not be above the growth rate, in future. The government issues one trill perpetuity. That ensures (if I'm right) that the interest rate must be above the growth rate, so the economy must be dynamically efficient. That solves the policy question, and makes the forecasting question redundant.
Posted by: Nick Rowe | October 27, 2012 at 09:07 AM
wait.....didn't a trill ensure that the ex post growth rate would equal the ex post rate of return? So what if trills trade in the market alongside conventional fixed-interest-rate debt that pays less than the expected rate of growth. Is that a dynamically efficient outcome?
BTW, your answer doesn't solve the policy question (a) in any country whose debt has yet to be converted into trills, or (b) for any asset other than government debt (e.g. little things like public pensions, real estate markets, private sector debt and equity, exchange rates, etc.) Of course, you might no longer find such problems interesting....
Posted by: Simon van Norden | October 28, 2012 at 03:40 AM
Simon: "wait.....didn't a trill ensure that the ex post growth rate would equal the ex post rate of return?"
No. The yield on a regular trill will depend on the market price of that trill. If the yield on a trill perpetuity were equal to the growth rate, the price of that trill perpetuity would be infinite. So if one trill perpetuity exists, and it must have a finite price, the yield would have to be more than the growth rate. A single trill perpetuity would make a dynamically inefficient economy dynamically efficient.
Posted by: Nick Rowe | October 28, 2012 at 08:32 AM
As I suspected....you don't find those other problems interesting.
But I will go back and read about your trills again.
Posted by: Simon van Norden | October 29, 2012 at 12:16 AM
Okay, you've straightened me out about trills. (Thanks!)
But to claim that the existence of a single trill (or, more precisely, a finite market price for a single trill) guarantees dynamics efficiency still confuses me. When I think of dynamic efficiency, I think of the relationship between expected growth rates and the risk-free rate. A finite market price for a trill (okay....in an otherwise efficient market) implies that a risky interest rate is higher than the expected growth rate.
Where did your risk premium go?
Posted by: Simon van Norden | October 29, 2012 at 12:25 AM
Simon: I do find those other problems interesting. But I don't think I've got any good answers.
"Where did your risk premium go?"
That's the bit I can't quite get my head around. I know what dynamic inefficiency means in a world where we know future growth rates and interest rates, and I'm confident trill perpetuities would work to eliminate dynamic inefficiency in that case. But the whole point of trill perpetuities is to find something that works in the case where future growth rates and interest rates are uncertain. What exactly does "dynamic inefficiency" mean in the uncertain case? And would trill perpetuities *always* work to eliminate dynamic inefficiency in that case? My gut intuition says they would work. But to really convince anyone I would need to build an OLG model where future growth and interest rates were uncertain, then introduce x trill perpetuities, and show that as x approaches zero, welfare is higher, and higher in the limit than at the limit where x=0. In other words, introducing just a very small number of trill perpetuities causes a discontinuous jump in welfare, just as it would in the case where r and g are certain. And I don't think my math/modelling skills are good enough to do that.
Posted by: Nick Rowe | October 29, 2012 at 07:29 AM
Intuition: imagine an OLG model like Samuelson 58, where r < g most of the time, except that future population is uncertain. Introducing just one trill perpetuity (but divisible so everybody can own some) will cost each cohort one trillionth of their income to pay the taxes to service the trill. That's peanuts, and can be almost ignored. But that trill perpetuity would have a very high value, and provides a big savings vehicle and causes a big jump in r and welfare.
Posted by: Nick Rowe | October 29, 2012 at 07:38 AM
Nick Rowe: " I think it is better and more honest to use the same pejorative word, and explain to the public that ponzi finance is not necessarily wrong, and that it is sustainable under some conditions."
The problem is that, while you are doing that, you are joining the propagandists of scare tactics and the crazies.
Posted by: Min | October 30, 2012 at 09:49 PM