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Jacques Rene: well, you could reasonably argue over whether we should or should not call it a "Ponzi scheme". It is like what Mr Ponzi did in some respects, because the proceeds of the loan are not invested in any real assets; Mr Ponzi just consumes them, and borrows more to pay interest and redemptions. But it is unlike what Mr Ponzi did in that it is possible for it to go on forever, without exploding, so rational people would lend even if they fully understood how the scheme works, and assumed everyone else is rational too.

Some economists call it a "rational bubble". I call it a "sustainable Ponzi".

Nick: if you never default,then it is not a Ponzi scheme

The definition of a Ponzi scheme here is an economic unit that repays its past borrowing only by issuing new debt. Such a unit may not ever default, even if it has no income.

Nick: I don't find your story quite convincing because you can also carry out your Ponzi scheme when r is greater than g. In that case, it's true, your debt-income ratio rises without limit, but so what? The basic setup does not have any limits on allowable debt-income ratios. And if we introduce a maximum debt-income ratio, that will exclude some non-Ponzi paths as well.

JW: if the flow of debt the old agents are selling exceeds the total income of the young agents, they won't be able to buy it. So if the debt/income ratio gets too high, the Ponzi scheme must collapse.

if the flow of debt the old agents are selling exceeds the total income of the young agents, they won't be able to buy it.

In that case, the debt will be repriced so that the younger generation *can* buy it. The repricing of debt (e.g. making it cheaper) is equivalent to an increase in interest rates. There is a finite amount of free lunch to be eaten, after which interest will go up if you try to eat more.

rsj: yes, and if the old agents who are now selling the debt understood that that will happen, they would not have bought the bonds in the first place, so the Ponzi scheme unravels back to the beginning.

Nick,

So you are saying that negative interest rates never occur?

Losing some asset value is the same as a (total) return that might be negative. If that is the equilibrium return, then that is what would clear the market.

I don't see how you can talk about the zero lower bound with a straight face while insisting that no one would ever tolerate a capital loss.

@rsj: Nick Rowe's argument refer to steady states. The presence of land rules out a steady state where r < g. By the Turgot-Homburg argument, you necessarily have r > g.

But, answering your question, this does not imply that negative interest rates can never be observed outside steady states. In a period model, rt < gt can hold for some time, but not forever.

This is what Nick Rowe already indicated in the title of this thread: Land is a long-run stabilizer, as it rules out dynamic efficiency, but also a short-term troublemaker, as it induces people with adaptive expectations to try Ponzi games.

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