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!]
Worthwhile Canadian Initiative 
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'”.
“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.
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?
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.
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….
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.
As I suspected….you don’t find those other problems interesting.
But I will go back and read about your trills again.
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?
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.
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.
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.