## Thursday, October 25, 2012

### More on Bubbles

This will perturb David Andolfatto, who has heard enough about bubbles. But Andolfatto perturbation is enjoyable, for some reason, so here goes. Ben Lester told me about this 1993 paper by Allen, Morris, and Postlewaite on bubbles. Here's the relevant quote:
I think that corresponds quite closely to what I had in mind here (and see this post as well). I'll leave you to judge whether Allen, Morris, and Postlewaite are better or worse economic theorists than Paul Krugman or Noah Smith.

1. Suppose you set up an OLG model with money, just like that. Suppose there exists a central bank that prints that money. How would you ever know, unless you looked into the basement of that central bank, whether or not that central bank held any real assets "backing" that money? In one case the money would be a bubble; in the other case the money would trade at its fundamental value, but the two would be observationally equivalent.

2. Here's an example. Take the OG model from this post:

http://www.newmonetarism.blogspot.com/2012/10/government-debt-and-intergenerational.html

Set n=0, assume r>0, and get rid of the government debt. Now, consider two scenarios: (i) a fixed stock of unbacked fiat money, M, which is an endowment of the initial old; (ii) a central bank that issues money in the first period, buys K goods, stores them until the next period, retires some money with the net return rK, buys K goods, stores them, etc.

In the first case, money is not valued, and only the storage technology is used. In the second case (as long as K is not too large, I think), there is an in which money is valued, and there is deflation at the rate r - essentially money and storage are perfect substitutes.

So the backing for the money matters. And you can think up other examples.

1. Steve: agreed. In that case, where r>n, a ponzi/chain letter/bubble money cannot exist.

But suppose you had r<n, as in Samuelson 58. It wouldn't make any difference whether the central bank issued money that paid a rate of return r, and stored the assets it bought, or simply consumed the assets it bought.

Take a real-world example. The Bank of Canada "promises" a real rate of return of minus 2% on its currency, on average. And people are willing to hold it at minus 2%, and the stock of currency demanded is growing over time, because the growth rate is greater than minus 2%, so the BoC issues new currency every year. Suppose the BoC had a great big party and consumed all of the assets in its basement. Who would ever notice?

3. No. Typically it makes a difference how you back the money - what assets the central bank bought, whether the money was issued to finance lending, whether there is a promise to retire the money in the future. All that stuff is "backing," and in general it matters.

4. The fundamental value of an asset, including "money", is the NPV of dividends, goods, or services which that asset generates.

The difference between Monopoly money, and "real (genuine! fiat!)" money, is that I can and do get food goods, and haircut services for the money, but not for the monopoly paper.

The claim that the "fundamental value" of money is 0, based on some silly pointy-head definition of "money", clearly separates that silly definition from reality. And conclusions based on analysis with that definition, even using calculus or computers or models or magic, such conclusions have relevance in the real world based on coincidence, not based on the silly definition.

Yes, it's important to discuss money as the unit of account, and as the store of value, and as the medium of exchange -- as well as "how much" of it there is. But creating silly claims which are defended by silly assumptions is a silly waste of time.

Which I feel a bit silly to have to point out.
But I do so because there are important issues to argue about, like policies to reduce the re-occurrence of bubbles, rather than wasting time claiming money is a bubble.

What are the best policies to make SS a sustainable Ponzi scheme? seems a much better question.

5. The whole "money being backed by real assets" thing doesn't make much sense if you put much thought into it. Gold and silver are generally the real assets, but how useful would they be in, say, the zombie apocalypse? By its nature, money is an ephemeral substance agreed upon for use by everyone for convenience. Even at the extreme of the government issuing gold specie, the money can still lose significant real value in some apocalyptic situation, or if a huge new gold mine is found.

Money is just a way for a person to create one particular good or service and get paid in the hundreds of thousands of goods that person uses. For loans, money is a way for people to work for free making that one particular good for those thousands of goods at a later date, including interest. If nominal future payments are agreed to, then expected inflation is built into the contract. Unexpected inflation, not inflation in general, is a transfer to the borrow, while unexpected deflation is a transfer to the lender. The role of the people setting the inflation rate, i.e. who prints the money, is to have a steady path of inflation in which it prints or destroys money as needed.