Noah Smith picked up on the following comment, made in passing by Stephen Williamson in a blog post mainly occupied with bashing his (Williamson’s) nemesis, Paul Krugman. Maybe I’ll come back with further comments on the rest of Williamson’s post anon, but, then again, maybe not; we’ll see. In the meantime, here’s Williamson on how to identify a bubble and pointing to money as an example of a pure bubble:
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. There is a bubble component to government debt, due to the fact that it is used in financial transactions (just as money is used in retail transactions) and as collateral. Thus bubbles can be a good thing. We would not compare an economy with money to one without money and argue that the people in the monetary economy are “spending too much,” would we?
Noah (I actually don’t know Noah, but since he has written a few complimentary posts and tweets about me, I consider him one of my best friends) was moved to write a whole blog post about this paragraph. But before quoting Noah’s response, I will just observe that what Williamson describes as a bubble is what Keynes described as a liquidity premium. People are willing to accept a lower rate of return on money than on other assets that they could hold, because, at the margin, money is providing them with valuable liquidity services. The reduction in the rate of return that they are willing to accept is achieved by bidding up the value of money until the expected service (liquidity) yield on money just compensates for the reduced pecuniary rate of return associated with holding money compared to alternative assets. This liquidity premium, by the way, is a result of the real quantity of money being less than optimal. If the real quantity of money were optimal, the liquidity premium would be zero, but a zero liquidity premium would not imply, as Pesek and Saving notoriously argued about 40 years, that the value of money would be annihilated. I don’t think that Williamson is making the mistake that Pesek and Saving made, but he is (to engage in a bit of metaphor mixing) skating on thin ice. Anyway, now to Noah:
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.
Noah is making a good argument, a sort of reductio ad absurdum argument, but I think it’s wrong. The reason is that what Noah is looking at — the real value of non-money assets — is really a ratio, namely the nominal value of an asset divided by the price level measured in terms of the money (unit of account) whose value is supposedly a bubble. Noah says OK, suppose Williamson is right that money is a pure bubble. What would happen once people caught on and figured out that the money that they used to think was valuable is really worthless? Well, when money becomes worthless, the price level is infinite, so the real value of any asset must be zero. Really? I don’t think so. Noah is making a category mistake. Not all financial assets are alike. Some financial assets (bonds) are claims to a fixed stream of payments. But other financial assets (stocks) are claims to a variable stream of payments. Certainly bonds would become worthless as the price level was expected to rise without limit, but why would that be true of stocks? The cash flows associated with stocks would rise along with the increase in the price level. What Noah is doing (I think) is evaluating a ratio, the price of a stock relative to the general price level, as the price level (the inverse of the value of money) goes to infinity. If the denominator is infinite, then the ratio must equal zero, right? Not so fast. Just because the value of the denominator of a ratio goes to infinity does not mean that value of the ratio goes to infinity. That’s a fairly elementary mathematical error. To evaluate the ratio, if both the numerator and denominator are changing, you must look at the behavior of the ratio as the value of the denominator goes to infinity, not just at the denominator in isolation. For a stock, the numerator would go to infinity as the price level rose without limit, so you can’t infer that the real value of the stock goes to zero.
So the way to do the thought experiment is to ask what would happen to the value of a stock once people realized that the value of money was going to collapse. The answer, it seems to me, is that people would be trying to exchange their money for real assets, including stocks, as a way of avoiding the loss of wealth implied by the expected drop in the value of money to zero. Under the standard neutrality assumptions, a once and for all reduction in the value of money would imply a proportional increase in all prices. But the bubble case is different, inasmuch as everyone is anticipating the loss of value of money before it takes place, and is therefore trying to switch from holding cash balances to holding real assets. The value of real assets, including financial assets like stocks, would therefore tend to rise faster than the prices of the anticipated service flows embodied in those assets. Asset and stock prices would therefore tend to rise even faster than the general price level, which is to say that the real value of those assets would be rising, not falling, let alone falling to zero, as Noah suggests. So I am sorry, but I don’t think that Noah has succeeded in refuting Williamson.
But in a sense Noah does get it right, because he goes on to question whether there is any meaning to the whole notion of “fundamental value.”
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.
Well, the problem here is that the whole question is whether you will be able to buy a toaster with money once people realize that the true value of money is zero. The toaster will remain valuable after money becomes worthless, but money will not remain valuable after money becomes worthless. Nevertheless, the value of a toaster to you is itself not invariant to the tastes and preferences of people other than yourself. Toasters have value only if there are enough other people around that demand sliced bread. If the only kinds of bread that people wanted to eat were baguettes or matzah, your toaster would be worthless. The only goods that have unambiguous consumption value are goods for which there are no network effects. But there are very few such goods, as my toaster example shows. If so, the consumption value of almost any good can be negatively affected if the demand for that good, or for complementary goods, goes down. What you are willing to pay for any asset embodying a future service flow depends on your expectations about the value of that flow. There is no way to define a fundamental value that is independent of expectations, or, as I have previously observed, expectations are fundamental. That is why Keynes’s much reviled comparison, in Chapter 12 of the General Theory, of the stock market to predictions about the outcome of a beauty contest, while surely a caricature, was an insightful caricature.
Noah’s post prompted Paul Krugman to weigh in on Williamson’s assertion that money is a pure bubble. Invoking Samuelson’s overlapping generations model of money, Krugman rejects the notion that fiat money is a bubble. It is rather a “social contrivance.” Social contrivances are not bubbles; they depend on a web of conventions and institutions that support expectations that things will not fall apart. Similarly, Social Security is not, as some maintain, a grand Ponzi scheme. Krugman concludes on this note:
[T]he notion that there must be a “fundamental” source for money’s value, although it’s a right-wing trope, bears a strong family resemblance to the Marxist labor theory of value. In each case what people are missing is that value is an emergent property, not an essence: money, and actually everything, has a market value based on the role it plays in our economy — full stop.
I agree with this in spirit, but as an analytical matter, we are still left with the problem of explaining how fiat money can retain a positive value, based on the expectation that someone accepting it now in exchange will, in turn, be able to purchase something else with it further in the future, even though there is a powerful logical argument for why the value of fiat money must eventually fall to zero, in which case backward induction implies that its value falls to zero immediately. Krugman actually alludes to one possible explanation for why the value of fiat money does not immediately fall to zero: the government makes it acceptable as payment for the taxes it imposes, or actually requires that tax obligations be discharged using the currency that it issues. By putting a floor under the current value of money, the creation of a non-monetary demand for money as way of discharging tax liabilities excludes the class of potential equilibria in which the current value of money goes to zero. Brad DeLong spells this out in more detail in his post about Noah Smith and Stephen Williamson.
So what is my point? Yes, I agree that money is not a bubble. But merely asserting that money performs a useful social function from which everyone gains is not enough to prove that it is not. That assertion doesn’t explain why that high-value social contrivance is robust. Expectations about the value of money, unless supported by some legal or institutional foundation, could turn pessimistic, and those pessimistic expectations would be self-fulfilling, notwithstanding all the good that money accomplishes. Optimistic expectations about the value of money require an anchor. That anchor cannot be “fundamental value,” because under pessimistic expectations, the “fundamental value” turns out to be zero. That’s why the tax argument, as the great P. H. Wicksteed eloquently explained a century ago, is necessary.