Money is just little green pieces of paper!

Have you ever heard people say that "money is just little green pieces of paper"? Well, that is exactly what Steve Williamson claims in this post. Most of the post is an anti-Krugman volley, but buried in one of Steve's points is the following extremely interesting claim:

What is a bubble? You certainly can't know it's a bubble by just looking at it. You need a model. (i) Write down a model that determines asset prices. (ii) Determine what the actual underlying payoffs are on each asset. (iii) Calculate each asset's "fundamental," which is the expected present value of these underlying payoffs, using the appropriate discount factors. (iv) The difference between the asset's actual price and the fundamental is the bubble. Money, for example, is a pure bubble, as its fundamental is zero. (emphasis mine)

Can this be true? Is money fundamentally worth nothing more than the paper it's printed on (or the bytes that keep track of it in a hard drive)? It's an interesting and deep question. But my answer is: No.

First, consider the following: If money is a pure bubble, than nearly every financial asset is a pure bubble. Why? Simple: because most financial assets entitle you only to a stream of money. A bond entitles you to coupons and/or a redemption value, both of which are paid in money. Equity entitles you to dividends (money), and a share of the (money) proceeds from a sale of the company's assets. If money has a fundamental value of zero, and a bond or a share of stock does nothing but spit out money, the fundamental value of every bond or stock in existence is precisely zero.

That's a weird way of thinking about the world.  It would mean that the size of a stock bubble, measured in percentage of terms, is always and everywhere infinite. It would mean that the size of a stock bubble, measured in absolute terms, is just the price of the stock - that Google's stock now has a bigger "bubble component" than Pets.com's ever did, simply because Google's stock price is higher than Pets.com's ever was. If money is a pure bubble, this must be the case.

So it's a weird way of thinking about the world...but is it correct?

It seems to hinge on the definition of "fundamental value". Usually we define "fundamental value" as the (discounted) amount of money you'll have if you hold on to an asset. But if money has no fundamental value, then this is zero.

So what is "fundamental value"? Is it consumption value? If that's the case, then a toaster has zero fundamental value, since you can't eat a toaster (OK, you can fling it at the heads of your enemies, but let's ignore that possibility for now). A toaster's value is simply that it has the capability to make toast, which is what you actually want to consume. So does a toaster have zero fundamental value, or is its fundamental value equal to the discounted expected consumption value of the toast that you will use it to produce?

If it's the latter, then why doesn't money have fundamental value for the exact same reason? After all, I can use money to buy a toaster, then use a toaster to make toast, then eat the toast. If the toaster has fundamental value, the money should too.

So does saying "money is a pure bubble" mean that toasters have no fundamental value, and that therefore, the price of toasters - or, indeed, of any non-consumable good - is a pure bubble? If "fundamental value" = "consumption value", it seems that it must mean exactly that. Now we are into a very weird way of thinking about the world.

Or is there another way to define "fundamental value", besides "expected discounted stream of money payments" or "expected discounted consumption value"? I can't think of one...any takers?


Update: Brad Delong and Paul Krugman weigh in. Paul suggests a more expansive definition of "bubble", while Brad conjectures about what Steve Williamson might mean. And yes, it feels weird calling Paul Krugman by his first name when we've never actually met...

Update 2: Steve Williamson weighs in:

The payoffs on my stocks and bonds, and the sale of my house, may be denominated in dollars, but that does not mean that the value of those assets is somehow derived from the value of money.

Not in general, no. But if the fundamental value of money is precisely, exactly zero then it does mean that. Any finite number multiplied by zero is still zero, so using Steve's definition of "fundamental value" - whatever the heck that is - the expected discounted present "fundamental" value of the stream of (money) payments from any stock or bond is precisely, exactly zero. As for the definition of "bubble", Steve claims that I disagree with his definition ("price > fundamental value"), but actually I do not disagree; that is one of the two main definitions out there (the other being "a rapid rise and crash of prices"), and I think it's perfectly fine.

Update 3: Nick Rowe has some thoughts.

Update 4: David Glasner thinks I've made a mistake. But I haven't made a mistake. If there exists a machine whose only possible function or use is to spit out assets that have zero fundamental value, then that machine has zero fundamental value. There exist many financial assets whose only possible function or use is to spit out fiat money. If the fundamental value of fiat money is always identically zero (as Williamson claims), then the fundamental value of those financial assets is always identically zero.

Update 5: David Andolfatto attempts to rebut my claim that if FV(money)=0, then the FV of most financial assets is also identically zero. Here is his attempted rebuttal:

What of Noah's claim that if money is a bubble, then nearly every financial asset is a bubble? This just seems plain wrong to me. Financial assets are typically backed by physical assets. For example, the banknotes issued by private banks in the U.S. free-banking era (1836-63) were not only redeemable in specie, but they constituted senior claims against the bank's physical assets in the event of bankruptcy. Mortgages are backed by real estate, etc.

I don't think this is a very good rebuttal. Sure, there are examples of financial assets that can be exchanged directly for real assets (without being first exchanged for money). But these are few and far between. Most financial assets only pay you in money, no matter what happens. So I don't think David's rebuttal really works.

Note: None of these critics has yet to offer a concrete definition of "fundamental value". The whole point of my post is to ask for a concrete definition of fundamental value...so far I haven't got one.

Update 5: Steve Williamson finally does provide a definition of fundamental value, cribbing from Allen, Morris, & Postlewaite (1993) (which, by the way, is an excellent paper which you should read if you have time):

To summarize, we are arguing that the fundamental value of an asset is the present value of the stream of the market value of dividends or services generated by that asset.

According to this definition, money is priced above its fundamental value, because money pays no dividends and thus has a fundamental value of zero. Also note that according to this definition, T-bills have a fundamental value of zero, since they pay no coupons. In other words, by this definition, the market value of the redemption payment of a bond does not count toward its fundamental value.

It's not the definition I'd choose; I'd include the redemption in the fundamental (in which case money would have a positive fundamental, since you can "redeem" it for itself). But "fundamental value = dividends" is a perfectly consistent definition. Great! Steve also writes:

I'll leave you to judge whether Allen, Morris, and Postlewaite are better or worse economic theorists than Paul Krugman or Noah Smith.

I can resolve half of this question for you right now: Allen and Morris (and almost certainly Postlewaite, though this is the only paper of his I've read) are better theorists than I am. All you aspiring theorists out there, take a lesson from those guys, and remember to define your terms explicitly and precisely!