This isn't as clear as I want it to be. Sorry.
Mr Ponzi issues a financial asset. Assume that the demand to hold that asset grows at the same rate as GDP. If people are willing to hold that asset at a rate of return less than the growth rate of GDP, Mr Ponzi can run a sustainable Ponzi scheme. He can issue new assets to pay the interest on the existing assets, and still issue a few more to provide some income for himself. Another name for a sustainable Ponzi scheme is a rational bubble.
Consider paper currency. Bank of Canada notes, for example. The Bank of Canada promises that this asset will earn a rate of return, in real terms, equal to minus 2% on average. That is below the expected growth rate of the economy. It is a sustainable Ponzi scheme, and a profitable one for the Bank of Canada. It is a rational bubble.
"Does the economy need a bubble?" is the wrong question. We know it needs a bubble. The empirical evidence is right there in our pockets. The only question is: how big a bubble does it need? Or, what does it depend on?
People willingly hold paper currency, even at a very low rate of return, because it is more liquid than other assets, which need to pay a higher rate of return.
We can imagine an economy in which the only liquid asset is paper currency, and all other assets are much less liquid, and in which paper currency is the only Ponzi asset, and all other assets pay a rate of return greater than the growth rate of GDP. If the issuer of that paper currency promises a real rate of return of minus 2%, and people choose to hold (say) 5% of their annual income in paper currency, then that economy needs a bubble equal to 5% of GDP.
Now suppose the issuer of that paper currency promises a 0% real rate of return instead. (The Bank of Canada targets 0% inflation instead of 2% inflation). And suppose people now want to hold (say) 10% of their annual income in paper currency. Then that economy needs a bubble equal to 10% of GDP.
Let's keep going. What would happen if the issuer of paper currency promised a rate of return equal to the growth rate of GDP? (The Bank of Canada targets zero growth in nominal GDP, so the inflation rate is minus the growth rate in real GDP.) Suppose people now want to hold (say) 123% of their annual income in paper currency. Then that economy needs a bubble equal to 123% of GDP. That is the exact borderline between paper currency being a bubble asset and not a bubble asset. The Bank of Canada issues an amount of paper currency equal to 123% of GDP, then issues no more ever again (assuming the demand for currency is proportional to GDP).
Now suppose there were some exogenous change in the demand for currency, that caused it suddenly to double, as a percentage of people's annual incomes. The economy would need a bubble twice as big as before. And if the issuer of paper currency didn't satisfy that need for a bubble twice as big, the price level would have to halve to satisfy it. And if the price level couldn't halve instantly (because prices are sticky) there would be a recession, because of the excess demand for currency, which serves as the medium of exchange.
But currency is not the only liquid asset. Some assets are more liquid than others. Some may be liquid enough that people will hold them even if they expect a rate of return that is permanently below the growth rate of the economy. Any such asset can be used for a sustainable Ponzi scheme (a rational bubble).
Let us imagine an economy with a spectrum of Mr Ponzi's. And let's line up all the Mr Ponzi's in order of how liquid their liabilities are.
The first Mr Ponzi (the Bank of Canada) can issue the most liquid liabilities. The second Mr Ponzi (the Government of Canada?) can issue the second most liquid liabilities. And so on down the line of Mr Ponzi's.
If he wants to, the first Mr Ponzi can drive all the other Mr Ponzi's out of business. He simply needs to promise a rate of return just slightly below the growth rate of the economy. Since all the other Mr Ponzi's, who issue less liquid liabilities, would need to pay a rate of return above his if they wanted people to buy their liabilities, they wouldn't be able to run a sustainable business.
Suppose the first Mr Ponzi doesn't do that. He then leaves room for the second Mr Ponzi. And if the second Mr Ponzi wants to, he can drive all the other Mr Ponzi's out of business. Suppose the second Mr Ponzi doesn't want to do that. He then leaves room for the third Mr Ponzi. And so on.
You can think of this post as a continuation of my post on Turgot's land beating Samuelson's money.
Samuelson said you could have an economy which needed a bubble, because the rate of interest is below the growth rate of the economy. People would want to hold what Samuelson called "money" (but which might better be called "government bonds") purely as a way of saving, even if they knew it was a pure Ponzi asset.
Stefan Homburg said that Samuelson was wrong, because land would be just as good a savings vehicle as Samuelson's "money", since land too lasts forever, and land is even better, because land pays rent, because land is productive.
But if land is less liquid than Samuelson's "money", the economy might still need a bubble. We know that land is less liquid than currency, and we know that the economy needs a bubble, because people are willing to hold currency even though its rate of return is below the growth rate.
But what Finance tries to do is convert less liquid assets into more liquid assets. For a while, Finance succeeded in making land (in particular, the land on which houses are built) into a more liquid asset. If Finance succeeded in making land as liquid as currency, the economy would not need a bubble. If Finance succeeded in making land nearly as liquid as currency, the economy would only need a small bubble. But if Finance suddenly fails, and land becomes less liquid, the economy suddenly needs a much bigger bubble.
Worthwhile Canadian Initiative 
rp1: “Do you own any stocks that don’t pay a dividend?”
Yes. But I think (and hope) there are some real assets matching those stocks, and the returns from those real assets will eventually be used to either pay me dividends or to buy back stocks (same thing). So I expect those stocks to appreciate over time. I wouldn’t hold them unless I expected them to appreciate.
But that doesn’t work with paper currency. I know the Bank of Canada has assets, but I also know they will simply hand over the returns from those assets to the government, and not use those returns to pay dividends and buy back currency. I expect that currency to depreciate over time, at 2% per year. The Bank of Canada has promised it will try to make it depreciate at 2% per year.
Nick,
I was inspired by your comment “currency is a bubble” (written in response to Nick Edmonds) to write a post “Fiat Money is a Bubble” (found at http://mechanicalmoney.blogspot.com/2013/12/fiat-money-is-bubble.html).
The comment struck me as SO TRUE! In the post, I mention your comment as containing a startling depth of insight.
I expect you might not agree with my further associations but such is the stuff of economic exploration. Thanks for your post and comments.
I think you’re misunderstanding. We agree that cash should not be a long term investment. It’s a defensive measure that one might hold if they discern a predatory investment climate. Because it is an extremely valuable option in such an environment. That is, in addition to protecting you, it can also make you lots of money which you might need if things continue on their trip to hell.
Here is a weekly chart of the DJIA. http://i.imgur.com/akKU7o4.png
Your arguments against holding cash were proclaimed just as loudly in 2000 and 2007, and by American homeowners in 2005, and by Canadians 2010-present. If you have not considered the possibility that we are in a secular bear market, then I suggest you do so. That is my contention, but I have also considered a secular bull market and managed risk as best I can. It’s easier with global investment options.
I would like to point out that much of what has been called investment since the mid 1990’s is purely speculation on price, and the trend towards speculation has intensified as interest rates and real yields fell. This is not conductive towards productive investment that leads to future growth.
I would also like to point out that the financial system has been abused to such an extent that it has damaged the real economy and the prospect of earned income for large swaths of the population in the developed world, and we now have governments and central banks running wild experiments which affect financial markets greatly but do little for the real economy.
My point here is that risk and opportunity are two sides of the same coin, and to take advantage of an opportunity, you need cash. For five years we have had financial assets rising seemingly without limit as real economies stagnate, with many choosing to put 100% of their net worth into that. I think this lacks common sense. History is replete with strange trends that persist longer than anyone expects before coming to an end. The only real surprise is that anyone is surprised when things change.
To Roger: of course fiat currency is a bubble. It has to be. Without such a bubble you would not have economic freedom.
So maybe the great moderation wasn’t due to CB policy so much as a combination of low currency growth and a free-banking alternative (shadow banking)
Mr Ponzi, in trying to put lower tier Ponzi’s out of biz, will cause hyperinflation, and the selection by investors of a sane currency. If the expected growth rate of the economy is 3.0%, and Ponzi ups the return from 1.5% to 2.9%, next years expected return will be 4.4%, and Ponzi will have to pony up a 4.3% return…The Senate would stop such a Central Banker in this country, at least for 8 years.
You guys have all gone nuts. I sincerely hope nobody in a position of actual authority is listening to you.
Roger: thanks!
rp1: we are not talking about the same things. Currency is a good long term investment. I like to hold about $100 on average. It is a good investment because it makes it easier for me to buy stuff like cups of coffee and pints of beer.
TKG: No it’s the other way around. The central bank would need to target lower inflation to increase the size of M/NGDP.
Dan: it probably looks like that. IIRC, US social security(?) was designed according to Samuelson 58.
I thought the Central Bank was Mr Ponzi. I thought he was targetting the GDP growth rate minus 0.1%. If the central makes GDP growth the only factor in setting the interbank overnight interest rate, it will be hyperinflationary. Whoever Mr Ponzi is, he is hyperinflationary. In a recession, he is hyperdeflationary.
An added tanget about land: The USA subscribes to inferior suburbia becuase of the idiosyncracies of Thomas Jefferson. Someone probably threw out garbage on him while he was on his way to a date or something. They have an inferior myth to the rest of the world and too much market forces ideology is preventing them from correcting this error and having liveable cities. So urban land would be a better store of wealth here.
…it is calculus. A given interest rate will induce a given “natural” rate of GDP growth. As you allude to this morning, interest rates and inflation tend to run inversely. If anyone basis interest rates upon GDP growth, in a naturally growing economy, the rates will run away to infinity. In a market of alternative investments, it isn’t just overnight bank lenders that get the Ponzi rate, it is every chequing account holder. Maybe the savings account holders too. Different levels of Mr Ponzi’s have different levels of public trust and different insurance capabilities. Jeffereson may have been a good editor, but I wouldn’t trust anything that guy wrote.