### There’s a Whole Lot of Bubbling Going On

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.

#### 46 Responses to “There’s a Whole Lot of Bubbling Going On”

1. October 22, 2012 at 9:32 pm

I wonder what do you think about Wallace-Sargent “Legal Restrictions Theory” which states that in absence of governamental restrictions, money {as medium of payment} would have to pay interest in order to compete with other assets.

2. 2 BR October 22, 2012 at 10:03 pm

“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.”

I.e. Noah forgot to apply L’Hôpital’s rule! (http://en.wikipedia.org/wiki/L'Hôpital's_rule)

3. 3 Brett Manning October 23, 2012 at 12:32 am

I disagree with your last sentence. Surely the social contrivance argument is a statement of the anthropic principle? We have money as a stable medium of exchange because money is a stable medium of exchange.
There are plenty of examples where this has fallen apart in the past but these are clearly suboptimal equilibria. We therefore have a collective incentive to value and use money which makes the postive value a relatively robust equilibrium.

4. 4 PeterP October 23, 2012 at 3:21 am

Typical academic discussion. Money has value because we need it to pay taxes, otherwise we go to jail. As long as we want to be free and the state can enforce taxes fiat money will have value. Adam Smith, Knapp and Keynes knew this. Historians see it in countless examples when new state introduced its currency. Only modern economists are puzzled.

http://heteconomist.com/?p=4369

5. 5 Christiaan October 23, 2012 at 3:34 am

The point is not that because money has a (social) value proves that it is not a bubble. The point is that this observation makes Williamson’s argument that it is a bubble completely invalid. So, yes, money could still be a bubble, but nobody has given a valid argument why it should. And the fact that money works and has worked for a very long time, as well as common sense, tells you it’s not a bubble. Of course if the money is controlled by some dictator who can at a whim decide to print gazillions of pieces of paper you’d have a good argument that it’s a bubble. But I think you must agree we’re not in such a situation here.

6. 6 Bill Woolsey October 23, 2012 at 4:26 am

So, PeterP, if taxes were to fall to zero, the fiat currency would have no value?

I don’t think so.

I think it would depend on expecations about its future quantity and expectations about real demand.

Radical libertarians take over, abolish taxes, and freeze the quantity of base money. Hyperinflation hits immediately? I don’t think so.

It would only happen if people think that the demand for base money will fall to zero–banks will find alternatives to base money for all purposes.

What bothers me about these sorts of stories is that they implicitly assume that the nominal quantity of money cannot fall.

In my view, the key criterion for money to retain value is the expectation that the nominal quantity will decrease if the demand to hold money falls.

When that is assumed impossible, so that the only equilibrating process is a higher price level and a reduced real quantity of money, then a future death spiral is possible.

If, instead, the quantity is expected to fall to match the demand, then we can imagine a situation where no one wants to hold the money and its quantity falls to zero, but those who continue to hold money until the end don’t lose anything.

This requires the realistic scenario where the money issuer holds assets to match the issued money.

And then, taxes are only relevant if the assets matching the money are government bonds. Why? Because of the assumption that government bonds require taxes to have value.

Suppose a government has no taxes, and solely operates by foreign aid. It borrows money in foreign currency, promising to make payments out of its foreign aid reciepts. It issues paper money, and commits to a nominal GDP level target. It matches the money it issues with some of these bonds. It uses open market operations to keep nominal GDP on target. The exchange rate floats, and so the government has foreign exchange risk.

Of course, we could skip the bonds. The government issues the paper money and stabilizes nominal GDP. It uses part of its foreign aid income to buy back the currency if there is any decrease in the demand to hold it.

Anyway, the point of my example is that there are no taxes and so no question of people being able to use the fiat currency to pay taxes. On the other hand, the government does have some income, which it can use to reduce the quantity of money if the demand to hold it falls. If everyone decides to quit using this money and go to the foreign money, then the quantity of the fiat money will fall to zero. But the last person with it sells it for foreign money (the new domestic money.) The exchange rate is not fixed in terms of foreign money but rather depends the target for nominal GDP.

My story is more realistic than one that assumes the quantity of fiat money is fixed or grows at a constant rate or is printed and spent with no concern about its purchasing power.

In reality, money issuers do hold assets and they both increase and decrease the quantity of money to target inflation.

The examples we have of govenrments that just print money and spend it with no concern about its value don’t really provide much support for the notion that a fiat currency will retain its value.

The examples where governments have a frozen quantity of money or print money and spend it but only according to a rule… what examples?

Seems to me we are confusing what some monetarists advocated with reality. Still, if you assume that the demand for money will grow forever at a very stable rate, and the government prints and spends money at a similar rate, then money will retain its value even if taxes are abolished.

7. 7 PeterP October 23, 2012 at 4:33 am

Bill Woolsey,

Hyperinflation does not hit immediately.

I claimed the reverse: IF sufficient taxes are collected the value of currency is independent of conventions. Look at Africa: colonists imposed an arbitrary “hut tax” and presto, societies with zero conventions to use european money were monetized. I am not talking hypotheticals here, this is historical record.

8. 8 fsateler October 23, 2012 at 6:02 am

“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.”

Indeed. Post WW2, the Japanese Invasion Money quickly found its value go to zero.

9. 9 PeterP October 23, 2012 at 6:59 am

fsateler,

It has nothing to do with pessimism. The issuing state disappeared, stopped collecting taxes payable in Invasion Money and it became just as useful as paper. It has been paper all along, but it had been necessary to pay taxes. After the tax was gone the “convention” collapsed almost immediately.

10. October 23, 2012 at 7:26 am

David: “That’s why the tax argument, as the great P. H. Wicksteed eloquently explained a century ago, is necessary.”

Then explain Bitcoin to me.

I’ve written about it here: Bitcoin steps on the toes of a few popular monetary theories”.

I brought Bitcoin up in Delong’s post and got a touché out of him. What is your parry?

Another thing, I never pay my taxes with government money, I pay with private money.

11. October 23, 2012 at 7:36 am

“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. ”

Interesting. What was Pesek and Saving’s argument?

Are you saying that if a liquidity premium exists in anything, it’ll be arbitraged away? For instance, exchange-listed equities carry liquidity premiums, some bigger, some smaller. Houses carry a liquidity premium, especially during seller’s markets. Are the real quantities of liquid stocks and houses less than optimal in these scenarios? Does a return to optimality mean shrinking the premium by creating more equities and houses?

12. 12 Greg Ransom October 23, 2012 at 8:08 am

The tax argument has real explanatory power.

Something so much of ‘economic’ math play lacks.

13. October 23, 2012 at 10:04 am

BR, That’s a more advanced theorem than I was thinking of, but I’ll take your word that it covers this case as well.

Brett, That’s your interpretation. I am not so sure that the positive value equilibrium is robust unless there is institutional “backing” for it. The collective incentive to value and use money is very fragile; it would break down, despite the collective incentive, if people began to doubt it and started heading for the exits.

PeterP, I agree for the most part, but I don’t think you can prove that a fiat money would not have value without the tax requirement. I think the value of money becomes indeterminate in that case, not necessarily zero, just potentially zero.

Christiaan, But you are begging the question why fiat money has a positive value. If it only has positive value because it is expected to have positive value, then its value may legitimately be regarded as a bubble. I don’t accept Williamson’s definition of a bubble, because it posits a fundamental value that is invariant to expectations. I think that is a very unusual case. All asset values depend on expectations. Expectations are fundamental.

Bill, If taxes fell to zero, the value of money might not fall to zero, but, then again, it just might. You are begging the question whether the demand for money itself depends on the tax requirement. If it does, then the demand for money cannot be unaffected by the elimination of taxes.

There is no assumption that the nominal quantity of money cannot fall, the question is whether the demand for money goes to zero; if people expect money to become worthless in the future, the demand for money now will go to zero unless there is a non-monetary source of demand for money, i.e., demand for an instrument for discharging tax liability. You suggest that if the government can retire outstanding currency fast enough it can manage the decline in the demand for money without allowing the value of its money to go to zero. That may be true and might correspond to certain cases of currency switching. But eventually, when all the old money is retired the value of the old money does go to zero.

fsateler, Good example. Thanks.

PeterP, Cessation of the tax requirement triggers pessimism about the future value of money. There’s no contradiction.

14. October 23, 2012 at 10:09 am

A zero liquidity premium implies not that money is worthless, but that monetary control over credit and spending is zero. A zero liquidity premium world, paradoxically, is an ultra endogenous-money world.

Also, the acceptance of a certain means of payment for tax is only one possible anchor of its ‘fundamental value’, albeit a socially efficient one if the state is seen as commercially legitimate. When the state is seen to be failing in some sense commercially, the means of payment accepted as tax can lose value regardless.

15. 15 Michael October 23, 2012 at 10:52 am

“Noah forgot to apply L’Hôpital’s rule!”

Glasner also didn’t apply it. Pointing out that infinity/infinity isn’t necessarily 0 doesn’t actually answer the question. You’re right about the need to use L’Hôpital’s rule, but neither of them did so. The answer remains undetermined.

16. October 23, 2012 at 10:56 am

David:

I don’t really agree that the value of money is zero when the quantity of money is zero. More like, it is undefined at best.

Further, if the issue stands ready to issue it if there is a demand for some, I would say it has a price. It is just that the quantity is zero.

Anyway, the notion that the money will someday lose value, so it loses money now fails when the quantity will fall to match any reduction in demnad.

The entire problem is that if the quantity is held fixed, then anyone left with money when no one else wants it takes a loss–a 100% loss.

But, if the quantity falls to match lower demand, then any money you have is still worth the same as it would be. You can still get rid of it at the constant price.

17. October 23, 2012 at 10:58 am

The U.S. dollar was redeemable in gold at one time.

The redeemabilty feature was removed. Did the reason why the dollar maintained value was because people needed them to pay taxes?

I don’t think so.

Or, is the argument that gold only has value because some king demanded taxes?

18. 18 Max October 23, 2012 at 11:26 am

Bill,

I agree that taxes aren’t technically required if the government has another source of income. Saudi Arabia doesn’t need taxes because the government owns all that oil.

But the usual case is for governments to have debts in excess of assets, the debt (and money) being backed by the taxing power. Freezing the money base won’t maintain the value of money if the taxing power disappears. It doesn’t matter that there’s still a demand for *some* issuers money, what matters is that the demand for that particular issuers money will go to zero.

19. 19 Max October 23, 2012 at 11:43 am

“A zero liquidity premium implies not that money is worthless, but that monetary control over credit and spending is zero. A zero liquidity premium world, paradoxically, is an ultra endogenous-money world.”

No, it just means that monetary control can’t be accomplished by varying the quantity of base money. But it can be done very easily by paying interest on reserves.

See:
“Monetary Policy in a World Without Money”:
http://www.columbia.edu/%7Emw2230/IFcashless2.doc

20. 20 Max October 23, 2012 at 12:12 pm

In the case of bitcoins, even if the demand for bitcoins is stable, there is nothing to prevent a mass exodus from bitcoin1 to bitcoin2. There’s no scarcity of bitcoins as a whole, even though bitcoin1 is scarce and bitcoin2 is scarce and bitcoin3 is scarce…

21. October 23, 2012 at 12:52 pm

Max

Yes, of course, IoR still works. My apologies for not being clear.

What I meant to say was that a zero liquidity premium world prices the liquidity put option erroneously at 0. It’s a world of peak credit elasticity. People borrow and lend as they want to, the central bank be damned. They respond to interest rates, of course. But the CB has less traction. For example, I’d expect that in a world with zero liquidity premium, IOR hikes would seldom feed into long rates, credit risk would be underpriced (the system would be under-capitalized) and private credit would be high, and volatile.

Essentially, central banks, banks etc. are all ‘dealers’. They provide the markets they serve with a put option. The marginal cost of liquidity is not zero.

22. October 23, 2012 at 2:00 pm

JP, I have no explanation, but my assumption is that it is just a fad and will quietly fade away as people lose interest. Thanks for the link to your post. Adjusting for the difference between me and Mike Sproul that you are aware of, I would pretty much agree with Mike’s take on bitcoins in his comments to your post. Touche is a pretty good way of putting it. You have a point, but it’s not fatal.

You said:

“I never pay my taxes with government money, I pay with private money.”

Whatever you pay your taxes with is convertible into government currency, and the government thus experiences a net inflow of currency whenever people pay their taxes, whatever instrument they are using.

Pesek and Saving said that money for money to be valuable, it had to represent net wealth to the issuer. If the issuer of inside money, e.g., a bank, paid competitive interest on money the money would not represent net wealth to the issuer because the interest earned on the loan by which the money was created would be exactly offset by the interest paid on the deposit held by borrower or however the borrower paid with the borrowed money. And if money was not net wealth, it is worthless and its value is zero. A competitive supply of money was a contradiction in terms. Harry Johnson annihilated that argument.

“Are you saying that if a liquidity premium exists in anything, it’ll be arbitraged away? For instance, exchange-listed equities carry liquidity premiums, some bigger, some smaller. Houses carry a liquidity premium, especially during seller’s markets. Are the real quantities of liquid stocks and houses less than optimal in these scenarios? Does a return to optimality mean shrinking the premium by creating more equities and houses?”

To what extend liquidity premia are arbitraged away depends on the costs of arbitrage. Financial intermediation is not costless, so banks don’t pay interest on deposits equal to the interest they charge on their loans. Their spread is partly protected by various barriers to entry and other restrictions on competition and the skillfulness of bankers in gaming the system and extracting rents, but there are limits to how much the spreads between borrowing and lending rates can be narrowed. So my statement strictly holds only in an equilibrium with zero intermediation costs. But it serves as a useful benchmark.

Greg, We agree!

23. October 23, 2012 at 2:06 pm

Bill, I read through your long post above and very much liked it. Your point about a central bank holding assets with which it might repurchase unwanted money is similiar to mine here. That surely helps to give modern central bank money its value.

I agree that taxes don’t give money its value. Not that it’s impossible. But no modern money works this way. At best, taxes help contribute to modern money’s liquidity premium, but that’s it.

You said: “In my view, the key criterion for money to retain value is the expectation that the nominal quantity will decrease if the demand to hold money falls.”

I used Bitcoin against David’s chartal theory. But it can also be used against yours. Bitcoin retains its value… yet there is no mechanism in place that guarantees that the nominal quantity will decrease if the demand to hold it falls.

24. October 23, 2012 at 2:31 pm

David, hi!

I haven’t made a mistake, actually. 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.

25. 25 Philo October 23, 2012 at 3:36 pm

“. . . there is a powerful logical argument for why the value of fiat money must eventually fall to zero . . . .” What argument do you have in mind?
There may be an argument that intelligent life will (*must*?) eventually disappear from the universe, a circumstance which would render money (and everything else) worthless. But that “eventually” is probably a long way off, and should be *heavily* discounted.

A network effect supports the value not only of money but of other social contrivances, such as the various natural languages. Take, as a random example, German. If everyone became pessimistic about the likelihood that German would continue to be widely used and understood, that pessimism would be self-fulfilling: people would stop taking the considerable trouble to learn to speak German, and the language would die out. But how likely is that *in the near future*, and why should we worry about *the long run*?

“Optimistic expectations about the value of money require an anchor.” OK, but I don’t see the tax argument as necessary: I think a sufficient premise is human inertia or conservatism.

26. October 23, 2012 at 5:45 pm

Ritwik, I think that I agree with your first paragraph, but I am not exactly sure what you mean by “an ultra endogenous-money world.” And I certainly agree with your second paragraph. A failed state that is not expected to survive or to be able to collect taxes cannot maintain the value of its currency. My impression is that Confederate currency began to depreciate rapidly in late 1864 when the outcome of the war became clear. The cause of the depreciation was not the increase in the quantity of Confederate money, but declining demand, the decline coinciding with expectations that the Confederate army would be defeated.

Michael, Correct. I did not apply it. I gave an intuitive argument for why the value of stocks would not go to zero, but did not provide a mathematical proof.

Bill, If the demand for the money is zero, which I believe is the operative assumption, then I think it does make sense to say that its value is zero.
I agree that when a money is convertible on demand at a fixed redemption rate, the positive value of the money does not depend on a requirement to use the money in paying taxes. Gold has value because it provides real (i.e., non-monetary services) so no tax argument is required to explain its value as a money. You only need the tax argument to explain the value of a money that provides no real services.

Max, I am not sure I follow your point. The tax argument is required to explain why people would have a demand for the money, not why the government is resorting to taxation.

Ritwik, The way I would put is that in a zero-liquidity-premium world, you need a mechanism other than interest-rate targeting by the central bank to pin down the price level. For example, the labor standard devised by Earl Thompson, which I described in Chapter 10 of my book Free Banking and Monetary Reform.

Noah, Thanks so much for your comment. I have two responses. First, although Williamson said that fiat money is a pure bubble, I don’t think that he necessarily meant that the fundamental value of fiat money is identically equal to zero. I think he meant that it is approximately equal to zero. To say that the value of a fiat money is identically equal to zero is self-contradictory. Something that is worthless ipso facto cannot be money, so to say that the fundamental value of a fiat money is identically equal to zero makes no sense. The only way to make sense of Williamson’s bubble statement is to interpret it as as a limiting argument. In other words, the value of a fiat money tends toward zero, but that doesn’t mean that fundamental value is literally zero. After all, the money may be worth the paper that it’s written on. If so, the proper way to evaluate an asset that generates a stream of payments of fiat money is by taking the limit as I described.

Second, even if I were to stipulate that the fundamental value of fiat money is identically equal to zero, the assets would be generating infinite nominal revenues. So you would be dividing infinity by infinity, which is undefined, not zero.

Philo, The fact that everything will eventually be rendered worthless doesn’t make those things that provide real services now worthless. But something whose only source of value is the expectation that it will have value in the future will become worthless now as soon as people anticipate that it will be worthless in the future. If it does not become worthless immediately it is become of some imperfection in the reasoning powers of the actors. I don’t insist that all actors are always and everywhere reasonable, but a model that relies on some imperfection in reasoning powers is vulnerable to a sudden discontinuity once reasoning powers improve. Knowing a language will German provides a lifelong stream of future benefits, so even though there are network effects at work in both cases, they are not strictly comparable.

27. 27 Frank Restly October 23, 2012 at 6:50 pm

David,

“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.”

Nope. You are making a bad assumption. You assume that all transactions can happen simultaneously, that the velocity of money can go to infinity with the price level – it cannot.

Money can be printed (0’s and 1’s on a computer) faster than goods can be manufactured, priced, and delivered. And because of that time discrepancy, even equity takes a hit when production cannot keep up with monetary demand.

So Noah is correct. Because the rate of change in the money supply is bounded by the speed of light (if even that) while the rate of change in the production of goods and services is bounded by the nature of producing anything, real equity valuations do go to zero if the money supply is increased at a fast enough rate.

28. October 23, 2012 at 7:33 pm

Bitcoin has value because it offers a secure electronic system of currency exchange, It’s basically a decentralzied version of Paypal. Bitcoin would have no value in a world without other monies.

It is annoying that the designers of Bitcoin misguidedly promote it as a fiat currency replacement, instead of as an interesting exchange system.

29. October 23, 2012 at 9:40 pm

First, although Williamson said that fiat money is a pure bubble, I don’t think that he necessarily meant that the fundamental value of fiat money is identically equal to zero. I think he meant that it is approximately equal to zero.

Well, see, he said “Its fundamental is zero”. That sounds pretty stark to me, especially when he also says “Money…is a pure bubble”. It sure doesn’t sound like a limiting argument.

I suspect that what’s actually going on is that Williamson has not thought carefully about the term “fundamental value”, and how we ought to define that term. That’s what my post was about.

In fact, I don’t even find it useful to define a “fundamental value” of money. I find the term “fundamental value” to be useful only in situations where there are two or more ways to extract value from an asset (e.g. resell a stock or hold it and collect dividends). In that case, “fundamental value” is just what we call one of the ways. But in the case of (idealized) money, there is only one way to extract value: exchange it for stuff. So I think talking about the “fundamental value of money” isn’t even helpful. But that’s just my opinion.

Now, the question of “why does money have exchange value?”, which is of course what everyone except me (and maybe Steve) is actually talking about here, that is a classic and tricky question.

30. 30 Ken Schulz October 23, 2012 at 10:22 pm

Hi,
Oddly, the only previous time I commented here was to another mention of the Keynesian beauty contest. I agree that it is an insightful illustration.

To a layperson like myself, the word ‘bubble’ suggests an episode of a brisk runup in the valuation of a thing, followed by an even more rapid dropoff, e.g. tulip mania or the housing boom and bust. There are certainly historical episodes of precipitous declines in the value of a monetary unit – we call this hyperinflation. But has any of these ever been preceded by a strong runup in the value of money, i.e. deflation? I don’t recall this ever being reported. If not, then money is not a bubble in the common meaning of the term. Bubbles have to be blown up before they can pop.

31. 31 Max October 24, 2012 at 12:16 am

“I am not sure I follow your point. The tax argument is required to explain why people would have a demand for the money, not why the government is resorting to taxation.”

I think it’s less confusing to think of taxes as backing money rather than creating a demand for money. Then it’s easy to see that the backing could be provided by assets (e.g. oil fields) instead. Or by the credible commitment to levy taxes in the future if required to maintain stable prices.

32. October 24, 2012 at 7:21 am

Noah, I defined fundamental for you a few days ago in the comments section of your website. The ensuing blog post I link to talks about the fundamental value of money. If you drill down further, I don’t think Stephen thinks that modern central bank money is fundamentally worth nothing.

David, thanks for your comments. I’ll mark you down in the list of economists who think bitcoin is going to zero. I’ve been leaning towards that pole too myself, although not because it’ll never be accepted for taxes, but because it has almost no fundamental value (ie. no non-monetary value). In the meantime I’m holding on to my bitcoin… it’s going to the moon! But I maintain that if bitcoin is still around in a few years, all of use are going to have to revise our monetary theories.

“Whatever you pay your taxes with is convertible into government currency, and the government thus experiences a net inflow of currency whenever people pay their taxes, whatever instrument they are using.”

Touché.

33. 33 Frank Restly October 24, 2012 at 1:35 pm

Using the following symbology:

P(t) = Nominal production at time t
M(t) = Money supply at time t
PRM = Profit Margin as a percentage of nominal production
S = Shares outstanding
P/E = Price to earnings ratio
E(t) = Market cap of equities

E(t) = PRM * S * P/E * P(t)

What is the ratio of P(t) / M(t) as M(t) approaches infinity?
Because P(t) cannot grow as quickly as M(t) we know that dM / dt can be much larger than dP / dt. If the ratio between the growth of M(t) and the growth of P(t) is a constant C, we write:

dM / dt = C * dP / dt
dM = C * dP
M(t) = C * P(t)

Lim P(t) / M(t) = 1 / C as M(t) approaches infinity which is non zero for all constant C.

However if the ratio between the growth of M(t) and growth of P(t) is a function of time, for instance:

Letting dP / dt = exp (t), then dM / dt = t * exp(t)

P(t) = exp (t)
M(t) = t * Integral ( t * exp(t) )

Integrate by parts
u = t du = dt
v = exp (t) dv = exp(t) dt
M(t) = exp(t) * ( t – 1)

P(t) / M(t) = exp(t) / [ exp(t) * (t – 1) ] = 1 / (t – 1)

And so P(t) / M(t) goes to zero at t = 1.

Which is not to say that the market cap for equities will be zero at that point.

E(t) = PRM * S * P/E * P(t) = [ PRM * S * P/E ] / (t – 1)

If the number of shares times the P/E ratio rose just as quickly (people accepting less earnings per share) then the market cap could continue to rise.

34. October 24, 2012 at 1:39 pm

Frank, I don’t think that I am assuming that all transactions take place simultaneously. If the value of money is zero, the price level is infinite. That sounds like infinite velocity to me.

AH, Thanks for your interpretation. I must admit that I don’t understand how bitcoin works, but what you say sounds, at a minimum, very plausible to me. Maybe there others out there who will weigh in on this.

Noah, You are right Williamson said “its fundamental value is zero.” It is not my general practice to speak on Williamson’s behalf, but I would think that rather than interpret his statement literally in a way that leads to an absurdity, it is preferable to interpret his statement as an approximation, so that his statement is not absurd. After all we’re only talking about a difference of epsilon here. You say that his statement doesn’t sound like a limiting argument. We are talking about something he wrote on his blog, how carefully did you weigh every last word that you have written on you blog?

If your intention is to show that the term “fundamental value” is hopelessly confused and lacking in any clear meaning, I would fully agree with you. That was actually the (or at least a) point of my post. So, although we differ on how to get there, we actually seem to be headed in the same direction.

Ken, Welcome back. I think that you are correct to observe that the term “bubble” usually denotes both a period of increasing and then rapidly decreasing prices. And in that sense, bubble is probably not the best way to describe a hyperinflationary fall in the value of money. The idea of a bubble generally involves some implication that high value of the asset in question was really not sustainable. In that sense, I don’t think that the assertion that the value of fiat money is a pure bubble is at all accurate.

Max, You probably would agree with Mike Sproul who explains the value of money in terms of backing. I think that, although we use different terminology, there is not a great deal of substantive difference between us in how look at the operation of the monetary system, so chances are the we are discussing semantics rather than substance now.

JP, OK mark me down that way, but, as I admitted to AH, I don’t really understand the mechanics of how bitcoins work. What do you think of what AH has to say about bitcoins?

35. 35 Frank Restly October 24, 2012 at 4:56 pm

“Frank, I don’t think that I am assuming that all transactions take place simultaneously. If the value of money is zero, the price level is infinite. That sounds like infinite velocity to me.”

Uh, no. If the value of money is zero, that means that the money is not exchangeable for other goods (value of money = zero and velocity of money = zero). When that happens, money ceases to be a unit of account and cannot be used to calculate the price level. The price level is set in the exchange of money for goods. If money is not accepted for goods (value of money is zero) then the price level cannot be calculated.

Money can be printed (0′s and 1′s on a computer) faster than goods can be manufactured, priced, and delivered. Meaning the federal reserve can print money faster than it can be spent. And so the rate of change in the money supply (dM/dt) can exceed the velocity (V).

Because stocks depend on that velocity to justify valuations, when the supply of money rises faster than the velocity of money, then the ratio of nominal production, profits, and ultimately equity capitalization to the money supply can go to zero.

I overstepped in my statement. I should have said you are assuming that the velocity of money rises in lockstep with the supply of money. That is not a guaranteed condition.

36. October 24, 2012 at 5:58 pm

I think that AH is right that bitcoin is a very interesting exchange system, even revolutionary. The bitcoin mechanism maintains a decentralized and evolving history of all bitcoins exchanged. By keeping good records, the integrity of the payments system is ensured. By integrity, I mean double-spending is prevented – the passing off of non-existent currency. Double spending would quickly cripple the system. In our regular banking system, banks maintain these histories and use this information and other safe guards to prevent double spending.

While the bitcoin record keeping mechanism is great, the inherent problem is that the underlying asset being tracked – bitcoin – is fundamentally worthless. It’s like having a library with the best archival system in the world, yet the only books in the library are filled with empty pages.

37. 37 Ken Schulz October 25, 2012 at 8:30 pm

David,
Thanks for your response. My viewpoint as a psychologist again; things that don’t _behave_ the same shouldn’t be called by the same name, in general. Nice to know I wasn’t totally talking through my hat!

38. November 4, 2012 at 12:38 pm

Frank, You are right that a zero value of money is a contradiction in terms. My point was that as money approaches worthlessness, the velocity will be increasing because people are increasingly unwilling to hold it, making prices rise faster than the increase in the quantity. I was not saying that velocity rises in lockstep with the supply of money (I am not even sure what that means). But I think that it is a well-established empirical fact that in hyperinflations, velocity rises as prices rise faster than the quantity of money.

JP, Perhaps then bitcoin is charging combining a medium of exchange with a bookkeeping service. The real value of the bitcoin reflects the valuable bookkeeping service bitcoin provides. Once there is a value associated with the bitcoin because of the bookkeeping service, there can be network effects that increase the demand for bitcoins as a medium of exchange. Just thinking out loud here.

Ken, Thanks for sharing your viewpoint. Economists have an imperialistic attitude toward other social and behavioral sciences, but part of an effective imperialistic strategy is to make use of the local resources of subject states. So economists can certainly benefit from listening to what psychologists and sociologists are thinking and then incorporate those ideas into economic discourse.

39. 39 Tas von Gleichen December 15, 2012 at 9:20 am

We have no choice this is why fiat money has any value at all. At least before the 1971 money was backed by gold. If we still had that system in place I would say that fiat money has a role to play since I could exchange it for real money (Gold).

40. 40 Barry January 2, 2014 at 9:26 am

David: “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.”

Doesn’t that hold for most, if not all assets? For any commodity, the pessimistic assumption about value would be for a drastic fall in price. For any stock or bond, the pessimistic assumption would be default and bankruptcy.

41. 41 Barry January 2, 2014 at 9:29 am

David: “…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. ”

I smell proof by contradiction, since there is a lot of money with non-zero value.

42. January 3, 2014 at 8:48 am

Barry, For most assets market value corresponds to some intermediate point between optimistic and pessimistic expectations, but for assets for which demand is largely based on a network effect, the value is highly vulnerable to a tipping point where the value plunges toward zero.

The empirical observation that there are many fiat moneys that retain positive value doesn’t prove that there is nothing problematic about a positive value for fiat money, because it may be that the tax argument is what provides a floor to expectations.

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