Sunday, October 21, 2012

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!

148 comments:

1. Anonymous7:29 PM

What isn't a 'little piece of paper'?

If I 'own' a house, don't I hold a 'little piece of paper' that affords me property rights? How is that any different for gold, or any other physical thing?

Our entire system of property rights is founded on pieces of paper, and makes the money critique even sillier.

1. not only that, people same who seem to think those pieces of paper are valueless complain bitterly when the government tries to collect (strike: confiscate) that paper via taxes. Sounds like your money is a bubble, mine is valuable.

oh, by the way, most money is in the form of electrons these days not paper.

2. Except the pieces of paper that underlie housing deeds are VOLUNTARY claims to goods.

There is nothing voluntary about the dollar system. You shall pay taxes in dollars whether you earn dollars, gold, or anything else. That coerces you into having to acquire dollars in the market.

The notion of "value" only makes sense in a context of private property rights. For if I point a toaster at you, and say give me your money or you will get a headache, then it would be wrong to say that you value giving me money for nothing. You were coerced.

3. Ben Johannson5:28 PM

Ultimately fiat currency is simply a form of credit. As the paper itself has no intrinsic value beyond the materials used in its construction, the currency itself is literally a claim against the economic productivity of the nation operating in it. It's value comes from its use in facilitating exchange of goods and services, and as a metric for valuation of those goods and services.

Williamson is correct in the sense that financial wealth is not the same as real wealth, although I don't think that's the point he meant to make.

4. The pieces of paper which underlie housing deeds are in no sense voluntary. The government will come and kick you off the land, with armed men, if you don't respect those pieces of paper. In fact, control of land is at the root of the entire concept of government.

The fact is, money, like "land ownership", is a *shared delusion* or a *societal construct* -- it is based on *trust* or *mutual agreement*. It's all in our heads, but that doesn't make it any less real.

2. Yes, Williamson's view of money seems nonsense to me. People who talk like this, I always tell them, "OK, send me all those fundamentally valueless pieces of paper you have."

They never do.

1. Wonks Anonymous3:42 PM

If I own a bubble asset, I want to sell it at the inflated bubble price! Don't forget the opportunity cost of some other greater fool.

2. good one
it is like the joke philosphers like to tell, no matter what your view on free will vs predistination, no one voluntarily walks out of a 3rd floor window...
This whole money debate seems really silly, like angels on the head of pin...is there some reason, aside from swatting silly people, that anyone cares about this ?

3. Gene Callahan,

THAT argument you just made has always struck me as weak.

Suppose some mafia boss threatened everyone with being thrown in a cage if they didn't send 35% of their annual income to the mafia in the form of mafia family inc. stock. Suppose that everyone then did the mafia's bidding, and sought ought the mafia family stock in exchanges in order to pay the protection racket.

If one dared asserted that the "value" of stocks are backed by nothing but brute force, nothing productive, then it would be absurd to claim that a legitimate intellectually rigorous response would be to say "If you don't think these stocks are worth anything, then send them to me! Oh that's right, you need to keep them so as to avoid getting thrown into a cage. You hypocrite. You really do value those stocks."

4. PPP,

"If one dared asserted that the "value" of stocks are backed by nothing but brute force"

This focus on force is your obsession: the original post mentioned nothing about force. It asked if money is a bubble.

5. Methinks PPP is probably a libertarian and mafia family inc enforcers are his metaphor for the IRS.
But the assertion that money is backed by nothing but brute force is weak nevertheless. Furthermore, there's intrinsic value in retaining one's freedom and not getting thrown in jail.

Regardless, your rebuttal still rings true. In spite of the libertarian obsession that taxation is theft, the original post mentioned nothing of force and only asked if money is a bubble.

3. "expected discounted consumption value". "Valued" how? In money? In which case the argument is circular. In something else? If so, what?

If valued in money is all money equal? That is, does it translate equally into expected consumption value? And what status does the "expected" have? Expectations fluctuate all the time - and whose expectations anyway?

Fortunately we do not have to float around in an-anchored abstractions like these, fun though it sometimes is. We have - ta-da - a well-documented history of the development of money, of its evolution and of changing thinking about money. You can start with any good history of ancient Mesopotamia. As with any social institution, what it is is what it does, and what it does embodies its development.

4. Fiat money has fundamental value because you need it to pay your taxes.

In that sense it is different from any other piece of paper.

1. ThrustVectoring9:44 AM

Not quite. Fiat money has fundamental value because the people that make the stuff you want need it to pay taxes. So if you have money and want steel, the money has value because the steel mill needs fiat money to pay their taxes.

It's not your taxes that are important, it's the taxes of the people and companies that make stuff in a particular country with fiat money.

2. That doesn't contradict what Dan Lynch said. For HE could be a producer that you are referring to. HE needs dollars to pay taxes from HIS productivity of goods that others want from him.

3. Ben Johannson7:38 AM

@Thrustvectoring,

Currency has value for everyone required to pay taxes in that currency. That's the ultimate reason for taxation, to create a base level of demand and get your people to accept a form of money not backed by a store of wealth (like gold).

4. Ben, while your point is largely accurate, the *ultimate* reason for taxation is redistribution of wealth away from hoarders (which is necessary for economic functioning).

5. Anonymous8:49 PM

money has no value in an Arrow Debreu world, bastard child of classical neutrality. we should quietly drown this child in a well, but Steve Williamson would probably come out of my tv with his draggly wet hair

6. Money is a technology. To get some inkling of its technological value, imagine a world without money.

1. Imagine a world of free market money.

2. Hey Pete, just one question...is your last name pronounced "puh-TEH-puh-tee"??

3. Pete, you don't have to imagine: google "Free Banking Period" in the 19th century US

7. You have just invited Williamson to regale you with how he needs to write that sort of thing for simple-minded Keynesian plebs and how his own work with Wright/Wallace identifying trade frictions, matching theory and government regulations as the source of money's value is the answer to your question.

Which may even be half-right.

Except that for a theorist who claims to model the imperfect substitutability of financial assets, he still doesn't have a good understanding of what a financial disequilibrium means. Witness his confusion of 'increase in demand' with 'excess demand' while explaining how it's the market rate, not the natural rate that is lower in a recession.

8. Neil Wallace's dictum for monetary theory went roughly like this:

"This essay argues that monetary theories should not contain an undefined object labeled money."

Stephen breaks the dictum by using an undefined object labeled money in his phrase:

"Money, for example, is a pure bubble, as its fundamental is zero."

In any case, money is a terrible word. Do gold, fiat paper, notgeld, bitcoin, yap stones, or liquid collateral fall under the word's purview? If you don't define the term from the outset you risk going off on long tangents, much like the recent debt debate.

9. Hmm. Not purely consumption value. I can still make toast if I haven't got a toaster, but it is less convenient and possibly more dangerous. I still get toast, but I may also have burned fingers.

Fiat money surely only has value if it can be used to buy goods and services. For example, I am the proud owner of some Italian Lire notes. They are - or were - money, but they are completely worthless because they have been superseded by the Euro. They are pieces of paper, no more. Therefore I agree with you that the value of money is not zero and it relates in some manner to the "value" (however defined) of the goods and services that it can purchase. I think it is rather more complex than pure consumption value, though. Are we possibly in the muddy waters of "utility"?

1. Shining Raven11:50 AM

You can most probably still redeem Italian Lire notes for Euros at the Italian central bank. The Bundesbank still redeems Deutsche Mark for Euros. Just sayin'

2. Yeah, but I can't buy a cappuccino with lire!

3. Anonymous9:38 AM

You cannot exchange Italian Lira for Euros anymore. It was only possible until last year. Euros for DM, on the other hand, is still possible. And in some shops you can still pay the bill in DM and not in Euros. But then again, the germans always had a special relationship to the DM.

10. "Or is there another way to define "fundamental value""

I like Warren Buffet's more folksy way of putting it. If you know that you can never sell some item after having acquired it, then the value you place on that item is its fundamental value. In other words, abstract from an asset's ability to be traded way, its exchangeability, and you get fundamental value.

1. Andrew11:16 PM

Doesn't that definition coincide exactly with Williamson's?

2. I think that's a good insight. But it doesn't work perfectly. Houses would be worth a lot less if people wanted to move to a different part of the country every 10 years, and couldn't sell their houses when they moved.

3. It's close to Williamson's.

I'm not sure why the fact that houses would be worth less indicates the definition doesn't work. Houses are, in a certain sense, money. Actually, better to say that they have a degree of moneyness. The bigger the degree of moneyness the bigger the premium built into their price. The premium disappears when all opportunities to sell a house disappears. This much lower price is the house's fundamental value.

4. Phil Koop10:32 AM

That's a fine definition of fundamental value - and yes, it's eerily similar to Willaimson's - but it doesn't address the main problem, which is that "non-fundamental value" is a deeply unsatisfying definition of bubble value.

Gold, for example, has tenaciously retained a non-fundamental value for a very, very long time. So if we adopt Williamson's definition then we are obliged to say either that gold is in the throes of a millenniums-long bubble or else that there cannot be a bubble in gold by definition.

Neither position is what the rest of the world means by "bubble". Some portion of gold's non-fundamental value must not be bubble value, but Williamson cannot tell us how to tease out what is bubble and what is not.

5. Noah, all your questions are answered here ;)

http://jpkoning.blogspot.ca/2012/10/would-warren-buffet-buy-green-pieces-of.html

6. "it doesn't address the main problem, which is that "non-fundamental value" is a deeply unsatisfying definition of bubble value."

Exactly. There's a large amount of "non-fundamental" value which is in no sense bubble value -- durable non-fundamental value, you might call it. The value of institutions, the value of reputation -- these things are not "fundamental" but neither are they bubbles.

11. Well, in defense of Williamson, he could just dodge your whole argument by reiterating that, although money has no fundamental value, it happens to have the inflated market value it has. He could bite the bullet and say that, yes in some sense equity is fundamentally valueless insofar as it's ultimately a money claim (it's also an ownership claim, though on real assets whose value itself derives from its money-producing properties, etc.), but it's not *actually* valueless, insofar as the market (wrongly?) inflates its price. The problem is that this view is just absurd. We needn't believe things or adopt definitions that essentially take us nowhere; what use is a definition of "fundamental value" that implies the claim that nothing has fundamental value? Fine, nothing has "fundamental value".

12. Money is a "get out of jail" card. And such cards have a lot of value. Why does it get you out of jail? Because, put simply, the U.S. federal income tax laws require you to pay income tax on any income you make, even if you make it through barter (i.e. without using money). And money is the only thing you can use to pay your U.S. income tax. So, get some money, if you owe taxes from bartering or otherwise...else, you will go to jail. The value of money is as real as the federal court system. And the federal court system is pretty real! If a judge issues a judgment that sentences me to death, it's "just a piece of paper," with no "fundamental" value, Williamson could claim. But I'm 99%+ likely to wind up dead as a result. So court judgments are as real as society itself. Whatever reality you ascribe to society (very real, to anyone not engaging in a certain kind of high-end epistemology), you can ascribe to fiat currency.

1. "And money is the only thing you can use to pay your U.S. income tax. "

This is not actually true, even though it would be more convenient for the IRS if it were true. Consider tax liens -- they are a method of paying your taxes without money.

13. Anonymous11:53 PM

Noah, you have sinned.

Williams wears Delong's dunce cap as the second dumbest of the human race.

His note is so full of non-sense that he even wrote, "
One element of unusual behavior is the failure of residential construction to lead the recovery [from the Lesser Depression]."

To have replied in any way to him was not your best idea.

14. Anon722:33 AM

I like the comment above that money is a "technology." I like that way of thinking about it.

I'd like to say that money has no fundamental value in that it doesn't enter the utility function. But that's wrong because neither do any other assets, but we want to say that they have value.

Hm. Let's go all the way back to basic consumption CAPM. The fundamental value of an asset is its discounted stream of dividends in consumption units. Standard Lucas tree stuff.

By that definition, the fundamental value of a dollar is zero, because holding on to a dollar generates no dividends.

On the other hand, money is useful in ways that other assets are not: it's a technology that turns green pieces of paper into consumption goods that you couldn't get if you tried to trade your consumption goods directly for someone else's consumption goods. Other assets don't trade directly for consumption goods.

A toaster is a technology for turning bread into toast. Money is a technology for turning pieces of paper into goods.

I'm not quite to a conclusion yet, but there's a stab. Someone call Nick Rowe!

15. Anonymous3:34 AM

Imagine that suddenly all exchange is prohibited and everyone is stuck with all money & goods they have. Also, no taxes are to be paid (& there will be no income in exchange for labor etc.). Then, everyone is allowed to make only one final exchange of money for sth like a loaf of bread. How much would a 1000\$ be worth assuming all the value derived from possibility of future exchange is taken away? Probably less than a toaster.

16. Brett3:43 AM

I always thought that money was a contingent claim against a proprtion of future output of a given nation... (contingent on, amonst other things, the amount of money in circulation at the point in time you need to exchange it for consumption goods)... but that might just be me... well I got most of the intuititon from Terry Pratchet... Who, by the way, provides the best explination of fractional reserve banking I've ever seen....

17. 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.

Here you go too far. Shares in an oil company entitle their owner to dividends which will be paid in money. But even if the value of money collapses in a hyperinflation, the shares need not become worthless. (They might, of course, if the hyperinflation starts a chain of events leading to a revolution; but that doesn't have to happen.) The dividends will go from say \$1.20 to \$1.2 gazillion and the share price will presumably rise in a similar proportion.

As a disciple of Keynes, I'd say that if you do your sums in wage-units you'll be able to tell the assets which have fundamental value from those that don't. If the Euro succumbs to hyperinflation my government bonds will be worthless but my Unilever shares won't.

1. 1.2 gazillion times zero is still zero...

2. Anonymous10:09 AM

@Noah. Companies have been known to pay their stockholders physical goods.

3. Companies have been known to pay their stockholders physical goods.

Yep, and this is why I said "almost". But they're not legally obligated to do this, so if money has no fundamental value, then stock only has fundamental value inasmuch as it acts as an option on goodwill capital...

4. What Kevin said. During the crack up stage of the Zimbabwe hyperinflation, stocks had roughly same real value that they did a few years before. That's because stocks are claims on assets, not claims on nominal amounts of money.

5. "1.2 gazillion times zero is still zero..."

JP Koning gets it. If the P/E ratio is 20 and the share price and earnings are both multiplied by a gazillion, the P/E ratio is still 20.

6. Anonymous3:35 AM

"But they're not legally obligated to do this, so if money has no fundamental value, then stock only has fundamental value inasmuch as it acts as an option on goodwill capital..."

Companies are also not legally obligated to pay a dividend at all, by your sense of "legally obligated". OTOH The shareholders are able to table a motion and vote to be compensated in goods, and in this sense a company is legally obligated to pay them in goods.

A share is not a claim on money; it's a claim on real assets and real flows. The fact that these real assets and real flows are materialized in the form of money, is because the shareholders accept the exchange value and convenience of money.

18. Williamson is putting forward a decent theory of asset bubbles that defines bubbles as when the market price of the bubble is higher than the expected value of present value of those assets. But this doesn't make much sense for money.

By definition the (nominal) expected present value of money is just its face value, and if you want to find out the real value of money just go to Amazon.com or one of the million other places that display present value exchange rates for money and real goods.

The only I see that the expected present value of money would be different from the "market" price for money is if the store of value function of money was being over estimated by market participants. That is the market predicted a more deflationary environment than fundamentals did. This is pretty much the Keynesian theory of business cycles, so I'm not sure if this is where Williamson wants to go.

1. Sorry for all the typos, on my phone. Hopefully it is clear

19. heywoodjablome7:06 AM

This article and all the comments that follow illustate the age old adage that if we were to lay all the economists in the world end to end we would still not reach a conclusion.
Money is worth what someone else will trade for it.

20. But toasters deliver value whilst you hold on to them, whereas money only gets its value (in terms of getting you to consumption) by exchanging it for consumables. But toasters have that value too (without even involving money, in a barter economy), which is derived yet separate from their real value in their ability to make toast.

You have to explain how money has value as a stock, not a flow. Why do we hold stocks of money? And as Scott points out, the answer is the same reason as why we hold wallets.

1. Put it another way - you can't say that the fundamental value of a bond is positive, because other people will pay us to give it to them. Why are people willing to pass bonds around (with money flowing the other way)? Because a bond will entitle you to a stream of income just by holding it to maturity, as will a stock. That income may be received in the form of money, but people will quickly convert the money (a financial asset) into real consumables. Now how does that happen? Why do people trade real things for a piece of paper, which has no intrinsic value from being held to maturity? Bonds would have value in a barter economy.

So the only intrinsic value of money - must be the privilege of not having to live in a barter economy. But that doesn't (seem to) give the money asset any value apart from its ability to be liquidated for real things. They accept it because they will be able to liquidate it for other real things. But the same could be said of a stock bubble - people pay other valuables for the right to hold stock, because they know they will be able to pass it off to others profitably. But if that were the only value of a stock, it would be the definition of a bubble, right?

At this point you could point to the fact that money transactions solve the coincidence of wants problem, and have a special role not equivalent to passing stocks around. But that still doesn't explain why people hold money...

21. I'm very sorry to hear you can't be my exocortex, though, you'd make a fine one...

22. I think the more accurate thing to say here is that money has no non-exchange value, not that it has no fundamental value.

A pork belly has non-exchange value, because you can eat it. A smokehouse has non-exchange value because you can use it to smoke a pork belly. A painting has some combination of exchange value and non-exchange value, because it can usually be re-sold, and at the same time the connoisseur can enjoy looking at it. But the value of money is almost pure exchange value (especially money that exists as an electronic balance that can't even be used as tinder for a fire or an emergency piece of toilet paper.)

Sometimes economists say that the value of the pork belly is "intrinsic", but I don't think that's what they mean. Only certain states of human beings that are produced by the eating of the pork belly are valued intrinsically. The pork belly itself has instrumental value - "use value" - because it can be employed to produce those states. Exchange value is instrumental value of a particular kind.

The fundamental value of a good is - as I understand this concept - the value that some good would have if there were universal perfect information about that good. Since there is not universal, perfect information about things in general, the values people assign to things can be distorted and driven up by speculation, irrational exuberance, animal spirits, etc. But a monetary system is useful and rational overall. So even if there were perfect information about things, money would be valued. It does have fundamental value.

23. Anonymous8:38 AM

For all those goldbugs out there: Yes, money has no intrinsic value whatsoever. However, if you decide to not honor the social value of money, the US Army will be happy to explain to you why you should accept it.

Also, in a serious financial crisis, gold is useless, because the really valuable stuff like food is scarce enough that nobody is willing to trade your gold for their food. What you actually need when things really hit the fan are arable land, weapons, and enough friends to use your weapons to defend your land.

24. Anonymous8:57 AM

Noah misses the bigger question, which is what is the social usefulness of monetary theory ? Has there been any real insight from anybody since say Henry Thornton's Paper Credit ?
Wouldn't society be better off if say Steve Williamson and Nick Rowe and Noah were actually doing something useful ?

25. This comment has been removed by the author.

26. Even if you set aside the very valid criticism that Noah is making, Steve Williamson's definition of a bubble is, well, unconvincing in the least, and misleading in a more important sense.

I really don't think anyone knows a bubble (whatever-t-f that is supposed to mean)until you have a collapse in that market. If Williamson actually spent any time on a trading desk, he would know "fundamental" value is nothing more than the result of the sum of all assumptions made by each trader, in order to finding the "theo" (derivatives slang for theoretical value).

So you can say that there is a distribution of the "theo" in each market and everyone is trading according to their own estimates of the parameters of this distribution. There is rarely convergence.

So are we always in little bubbles? Maybe. Maybe not. We are either quibbling or looking for the illusory particle.

27. Some here seem to be arguing that fundamental value is 'value in use,' separated from 'value in exchange.' That's possible, though as Noah notes it would apply to all financial assets.

One could argue, I suppose, that anything whose value is entirely dependent upon a Keynesian beauty contest for its value, and therefore, has multi-equilibria of values including zero is a bubble-esque asset. But one has to have some range of probability of a collapse and some idea of the institutional supports for the bubble tag to be meaningful.

28. Anonymous9:58 AM

The pieces of paper in my pocket, and presumably yours as well, bears the following words: "This note is legal tender for all debts, public and private." What this means is that men with guns will enforce transactions that include promises to pay with these pieces of paper.

Anyone who argues that money has no value has never seen a family's possessions put out by the street for failure to pay rent.

1. EXACTLY.

2. So what about money that is NOT legal tender? In Scotland, bank notes are not legal tender - only coins are. Does that make bank notes any less "money", or any less "valuable"?

3. Men with guns aren't enforcing transactions in bitcoin.

29. Gold has fundamental value because magic.

30. Williamson seems to have followed his irrational dislike of Dr. K so far into the weeds that he has become seriously lost. Not being an economist (I'd rather stay on the 'science' side of the 'science/philosophy' divide [Warning! Warning! Danger, Will Robinson! Troll Alert!]), I may not have this entirely clear, but it does seem to me that Williamson is bushwhacking into the trackless thicket of the philosophical concept of 'value'. Sure, "money" is just an arbitrary place-holder for 'value', but it can have both an intrinsic defined value and a mutually-agreed, arbitrary value at the same time, right? Each dollar bill is therefore in a sort of undefined quantum state of 'value' until it is spent, if I'm following my ludicrous thought-experiment into the woods properly. The point is, that using the amorphous idea of 'value' may make it tough to make a shiny, elegant Model, but hey, you can fudge up something that works. Isn't that kind of useful?

31. Noah,

It's true that liabilities issued by private corporations constitute claims against (fiat) money. But they are also backed by the underlying real assets of the company. In the event of bankruptcy, for example, debtors receive property rights in real property. So the logic you use to demonstrate that private liabilities are a bubble is incorrect.

1. Anonymous10:46 AM

What makes those received property rights any less ephemeral than money? After all, those property rights are nothing more than words on paper themselves.

2. In the event of bankruptcy, for example, debtors receive property rights in real property.

What??? So if I own Apple shares and Apple goes bankrupt, I am entitled to claim real physical goods from Apple??? I can have an Apple server carted over to my house and installed in my office? I can have crates of unsold iPads dumped off in my garage??

First of all, how would the real goods be divided up? What if two different shareholders both want Steve Jobs' favorite desk chair? How much of Apple Headquarters' floor space does a 2% stake in Apple legally entitle me to renovate?

Second of all, if the company goes bankrupt, I am pretty sure that management is not legally obligated to furnish shareholders with real goods. I am pretty sure that it is 100% legal for management to simply auction off all the company's real goods and deliver the money proceeds to the shareholders. And I am pretty sure that other than replacing management, shareholders have no legal recourse to prevent management paying them in fiat money. I am no lawyer, of course, so I might be wrong about this.

3. In the event of bankruptcy, for example, debtors receive property rights in real property.

Whoops, I just noticed you wrote this, though I think you meant to say "creditors".

So there are still the two problems of 1. division of real property and 2. legal obligation, discussed in my comment above. If a firm holds a fire sale of real property in order to pay creditors with fiat money, I'm pretty sure creditors have no recourse to stop them. Also, the problem of how real property gets divided among creditors seems insurmountable. So it seems to me that with our current legal system, the real-property rights of creditors cannot be well-defined.

Also, even if the real-property rights of creditors were well-defined, the fact that debtors are always allowed to pay debts in fiat money would mean that the only "non-bubble" component of the exchange value of debt would be as an option on the company actually going bankrupt.

4. Anonymous11:02 AM

The only parties who hve direct claims on physical goods in bankruptcy are secured creditors. Shareholders only get residual value, which is usually pretty small if not zero, or the company wouldn't have entered bankruptcy.

5. Secured creditors have legal claims to collateral only, right?

6. Noah,

The "technical" difficulties you describe concerning the division of property are real, but do not take away from the fact that at some level, some creditor will take possession of real property.

One other thing, I think you should slow down here. People seem to mean different things when they use the word "bubble." Steve should have used the adjective "liquidity premium."

7. The "technical" difficulties you describe concerning the division of property are real, but do not take away from the fact that at some level, some creditor will take possession of real property.

Is this true? I don't think it is. Secured creditors will keep their collateral (which may be a real good or may not), but other than that, the company will just sell off its real assets and pay creditors with money, right? And there's nothing the creditors can do about that...they legally just have to take the money.

One other thing, I think you should slow down here. People seem to mean different things when they use the word "bubble." Steve should have used the adjective "liquidity premium."

Oh, I have no problem with Steve's definition of "bubble"...the word can mean several things (in fact I spend a couple paragraphs explaining that in the intro of my job market paper!).

Actually, I don't have a problem with any of what Steve is saying...it's just weird. "Weird definition" != "wrong". And though I can't tell exactly what definition of "fundamental" Steve is using, I know it must be weird.

But I think Steve's post raises an extremely interesting, seldom-asked question: the question of "what is fundamental value?" Thinking about that question is very useful, IMHO.

8. If you don't disagree with anything that Steve says, then maybe you should tell Brad DeLong that. He says that you are right and that Steve is wrong. Most of your readers will take what you say in the same way. But whatever.

9. Well, I "disagree" in the sense that my own preferred definition of "fundamental value" doesn't even apply to money. But that's just semantics. This post is mainly just to ask "What is fundamental value?" Which is interesting as a question in its own right, but I also want to know how Steve defines it.

I already did tell Brad that, on Twitter.

10. Legally, creditors are always obligated to accept money to settle the debts, unless they have explicitly spelled out otherwise in a contract with the debtor. This is why all of our currency says "This note is legal tender for all debts, public and private."

11. Noah,

Consider a Robinson Crusoe economy. There is a coconut tree that delivers a coconut dividend. Ask how many coconuts would Crusoe be willing to sacrifice today to purchase the rights to that tree? This would be one measure of what I would label "fundamental value."

Next consider an economy with many individuals, and frictions that prevent efficient intertemporal trade (limited commitment is one such friction). In such economies, exchange media may be useful. Claims against the tree may serve as collateral for debt arrangements, for example. In an economy where debt constraints bind, such assets may trade above fundamental value--they possess "liquidity value."

The difference between market price and fundamental value, so defined, might be interpreted as a price "bubble" by an econometrician.

But as Steve emphasizes, the definition of "bubble" is model specific. Not sure what is so controversial here.

12. In an economy where debt constraints bind, such assets may trade above fundamental value--they possess "liquidity value."

That makes perfect sense to me.

The difference between market price and fundamental value, so defined, might be interpreted as a price "bubble" by an econometrician.

OK, that I see. But I don't see how this maps to what Steve is talking about...in your case, does the liquidity value of the exchange assets constitute the entire value of those assets?

But as Steve emphasizes, the definition of "bubble" is model specific. Not sure what is so controversial here.

Oh, like I said, I have no problem with the definition of "bubble"...the controversial part (well, not really; just the part I don't understand) is the idea that money has a fundamental value of zero...

13. Noah,

Steve was referring to pure fiat money; literally, a claim against nothing of value. If such an object does exist (and it may not, except in theory), then its entire value must be a liquidity premium.

As others have pointed out, fiat money may be backed in part by its ability to discharge a real tax obligation. However, even in this case, money may have value beyond this backing. This is what concerns monetary theorists: liquidity value.

I think I'll write a post on this. Not enough room here.

14. I think I'll write a post on this.

Looking forward to reading it! :)

32. Anonymous10:43 AM

There is no such thing as "fundamental value", anymore than there is a "fundamental location" or "fundamental time". The 'value' of anything is a subjective judgement based on present, local conditions and expected future conditions assuming the item is not highly perishable.

And money is 'just' paper or random bits of info: that is what makes it so damned useful as physical avatar of the ideal of 'value'. If it where something with an actual consumption use then the system would break down when people chose to transform this ideal 'value' into, well, actual consumption.

1. Anonymous11:02 AM

Exactly. Fundamental value implies something real in nature and unvarying (gravity, for example, from a terrestrial perspective). Money, and any other thing, are only ever objects w the value placed on them as agreed by society, or by buyers and sellers. But, as you say, the agreements of s civilised society are what makes it so useful

It would be interesting to understand why the wingnuts are so determined to relentlyessly tackle the fundamental underpinnings of a civilised and ordered world. Is it persistent randianism run riot?

2. Anonymous11:13 AM

I don't think the wingnuts are tackling the fundamental underpinnings of society - I think they are trying to construct a useful mythos that there are such things as "fundemantal underpinnings" which are metaphysially absolute and eternal, akin to the "laws" of physics - immutable and constant.

I believe it to be a demand for security. The notion that our institutions and systems are all contingent upon a general agreement scares the hell out of many people because it means that nothing is certain, which also means it is not secure or safe.

3. Exactly - imagine a world where "money" was chocolate - egads!
For some reason the image of people burning their own expensive furniture to keep warm in the extreme deprivations of a war winter were brought to mind as an example of a good that can be consumed in another manner.

33. If money is a bubble, why do central banks hold assets? Why are those assets identified with titles like "collateral held against federal reserve notes"? Why is every new dollar issued in exchange for bonds, rather than just being dropped from a helicopter? And since the issuer of bubble money would get a free lunch, what stops others from issuing rival moneys, until the value of the bubble money is driven to zero?

34. Our names -- each of us having what we think is our own name -- exists only due to social convention, oral tradition, and legal papers.

Your name (and thus anything in your life based upon your identity) itself has no fundamental.

35. I'm not entirely sure that everyone here is speaking the same language, even if they're using the same words. Still, there are two schools of thought about everything (as a colleague used to say, just before he started frantically bull-shitting on something he wasn't quite sure of). Partly, this type of discussion reminds me of a time years ago when I got a mushroom pro out from the local college to do a fall mushroom walk with the promise of collecting and eating edibles. He was great - we had a terrific walk, learned more than you could imagine about edibles, various dangerous ones, how to tell, how to prepare them, and how to get yourself to the ER when necessary. About half-way through the walk, I noticed an elderly Italian gentleman at the end of the line with a basket, just filling it up with Honey Mushrooms. I chatted with him a while, and asked what he thought of the guest speaker. He said "He's good, but really all you need is to know a couple different kinds of mushrooms. You just have to know those kinds very well." This may have some use in thinking about models. Another approach is to consider that a beautiful, detailed, elegant model that perfectly explains and understands a situation in Cloud-Cuckoo-Land may not be as useful as a grubby, duct-tape-and-coathanger model that gives us a handle on things here on Earth. It depends what goal you're trying to reach, I suppose.

36. Noni Mausa11:49 AM

Money is the non-specific divisible acquiescence of the energy of other people.

1. Noni Mausa12:19 PM

... dispersible across time. Forgot the essential time element.

37. Interesting topic. "Fundamental value" doesn't seem to have a whole lot of meaning. It seems like Williamson is trying to say that the "fundamental value" of an asset is the price that asset would have in equilibrium, which inherently assumes that bubbles are characterized by price realizations that are off the equilibrium path. This is pretty strange because there is no guarantee that we won't see bubble-like events (rapid rise in prices followed by a "bust"), won't happen in equilibrium. Indeed, we typically use equilibrium concepts to model bubbles.

To be perfectly honest I think that the one concept that really captures the way people think about bubbles and fundamental value is that a "bubble" is any price which would be welfare-improving to change if the government could set prices directly and "fundamental value" is any price from which there are no possible welfare-improving deviations. This definition is flexible enough to allow that bubbles may or may not be an equilibrium phenomenon, while capturing the way people typically think about bubbles being inefficient.

38. Anonymous1:57 PM

Ahem:

"In addition, rational bubbles can persist if the pure existence of the bubble enables trading opportunities that lead to a different equilibrium allocation. Fiat money in an overlapping generations (OLG) model is probably the most famous example of such a bubble."

Bubbles: Entry in New Palgrave Dictionary of Economics, Brunnermeier, Markus K., (2009), page 5

http://scholar.princeton.edu/markus/publications/new-palgrave-dictionary-economics

1. Argumentum ad verecundiam, eh?

But Brunnermeier means that fiat money can have a bubble component, not that it is a pure bubble. Which means he has to measure the FV in terms of something other than money. Which you can do. In fact, New Keynesian models rely on a fiat-money bubble, with FV defined in terms of real goods, in order for monetary easing to boost demand (I'll write a post on this later).

In any case, we don't live in an OLG model in real life, since durable goods exist.

2. Anonymous2:43 PM

Since we're arguing about semantics, I think an appeal to authority and common usage is warranted.

Brunnermeier isn't talking about a bubble component. His very next sentence says, "The intrinsic value of fiat money is zero, yet it has a positive price."

Another example of this usage (from "Bubbly Liquidity" by Farhi and Tirole):

"It has been well known since Allais (1947)’s and Samuelson (1958)’s seminal contributions that there exists economies in which money has a positive value in spite of the fact that it is intrisically useless....In those models, money can be readily reinterpreted as a rational bubble, a fact long recognized in the rational bubbles literature."

Really, I didn't think this was at all controversial.

3. Since we're arguing about semantics, I think an appeal to authority and common usage is warranted.

Those are two different things, friend...

Brunnermeier isn't talking about a bubble component. His very next sentence says, "The intrinsic value of fiat money is zero, yet it has a positive price."

Oh, OK. In that case, Brunnermeier is using a definition of "intrinsic" that does not equate to his use of "fundamental value" in Abreu & Brunnermeier (2003), in which he defines "fundamental value" as being given in money terms, and as having a nonzero value. So either Brunnermeier is defining "intrinsic" value as being different than "fundamental" value, or he is using the word differently in different contexts.

"It has been well known since Allais (1947)’s and Samuelson (1958)’s seminal contributions that there exists economies in which money has a positive value in spite of the fact that it is intrisically useless....In those models, money can be readily reinterpreted as a rational bubble, a fact long recognized in the rational bubbles literature."

Well, this makes no sense to me. In the Samuelson (1958) model, money is very useful, since there are no durable goods, and money is the only way of storing value from one period to the next. Also, a Tirole-style "rational bubble" must be always exponentially growing, which - if money's fundamental value is zero - implies perpetual deflation.

So I think this Farhi & Tirole passage is just wrong.

4. Anonymous5:49 PM

In the Samuelson (1958) model, money is very useful, since there are no durable goods, and money is the only way of storing value from one period to the next.

There are two ways to think about Samuelson. One is about stores of value, in which case the "money" could be a bond, or a claim on capital (if we had capital). However, we can also think of the OLG structure as a parable for anonymous meetings. The key friction is that each generation cannot make arbitrary contracts with other generations, since they can only deal with the previous generation (when young) and the next generation (when old). In this it is similar to a turnpike model of money. There is a deeper point here about the connection between the medium of exchange and store of value roles of money.

Also, a Tirole-style "rational bubble" must be always exponentially growing, which - if money's fundamental value is zero - implies perpetual deflation.

Right. In micro-founded models of money, you need the value of money to be growing at the rate of time-preference. The most painless way to get there is deflation -- i.e. the stock of money shrinks at the rate of time preference, which is the Friedman rule. If this does not hold, you need rents from trade. The distortions arising from these rents is why the Friedman rule is optimal in these sort of models.

5. So yeah, I think Farhi and Tirole were just wrong when they wrote that. It seems like an error.

39. Intrinsically worthless paper used as money only has value while a countries constituents have faith in the government/central bank to conduct sensible monetary policy. Paper notes will continue to retain some value while there is faith in the system. This faith is slowly being eroded (on a global basis). This loss of faith is reflected in Gold & Silver spot prices as individuals turn away from fiat money and return to hard money (unlimited vs limited). When faith is completely lost in a countries paper currency it is turned over at such a rate for real goods or hard money that it results in hyperinflation at which point the countries currency returns to it's intrinsic value, zero.

1. It's not inflation which causes people to lose trust in the money. It's general mismanagement -- corrupt legal system, high unemployment, dropping industrial production, nuclear accidents, losing foreign wars...

40. I find some of Krugman's and Noah's arguments bizarre.

Krugman claims that property rights are a bubble also. I am not sure what he means. Property rights are backed by something fundamental, a group of armed men willing to act with force on my behalf and prevent others from damaging a real object or removing it from my possession. This agreement is made between me and the government, but in the absence of a government they can be enforced by a group of hired guns or by myself.

Noah claims that because all other assets are denominated in money, they are bubbles also. I fail to see why this is the case. Since use of money is wide-spread, for convenience people use it as a unit of account. In its absence, I am sure contracts would express claims in the form of some real object.

Finally, Noah and Krugman both make it seem as if Williamson used the term "bubble" in a negative way, which he didn't. Money can be a bubble and yet be useful. Money is a bubble to the extent that if everyone in possession of it tried simultaneously to exchange it for goods and services it would become worthless. This is not true for any real asset, including gold (whose price also reflects a bubble premium).

1. Noah claims that because all other assets are denominated in money, they are bubbles also. I fail to see why this is the case.

It is only the case if you accept that the FV of money is 0 (as Williamson asserts). But the whole point of this post is that there are alternative definitions of FV. I'm wondering which Williamson is using, and I'm also wondering which is the most useful.

Finally, Noah and Krugman both make it seem as if Williamson used the term "bubble" in a negative way, which he didn't.

I did not think this, nor say it, nor imply it.

2. Anonymous4:31 PM

CA, those armed men are equally available to protect your pieces of paper and your right to them. If you own an apartment building, and your tenant gives you pieces of paper, then the armed men will protect their right to stay in the apartment that you own. If your tenant doesn't give you pieces of paper, then the armed men will come and dump their clothes into the street.

And of course, the only value the apartment building has for you is that it leads tenants to give you pieces of paper. You don't live there. You don't give a fig about the "fundamental" thing except as a means of getting more paper.

So I really don't see the difference between the reality of right to the apartment building and your right to the pieces of paper.

3. You are confusing money with property rights to money. Money has no legal claim on goods and services. If one day people refuse to accept dollar bills as payment, the government cannot force them to sell their products to you. On the other hand, property rights are a binding legal contract enforced by the government. It is not the same!

41. "I can use money to buy a toaster, then use a toaster to make toast, then eat the toast."

If buyers have bid up the price of tulips merely because they expect the price to go up further, then I can trade a tulip for a toaster (since presumably if a lot of people are trying to buy tulips, they will be highly liquid on the sell side, and toaster-sellers will be willing to accept tulips in exchange and earn a bid-ask spread on the tulip to make up for the inconvenience), use the toaster to make toast, and then eat the toast. (Actually, I could just sell the tulip for money, buy a toaster with the money, make toast with the toaster, and then eat the toast, so I don't need that parenthetical part about how toaster-sellers would have a motivation to become tulip brokers.) So an overpriced tulip has fundamental value in the same sense as money (I mean in addition to the fundamental value that it has because of its actual consumption value as a flower, but the during the Dutch tulip mania, the latter eventually became an insignificant portion of the total price).

So in this conception of things, how is it that anything is ever a bubble? It seems that the fundamental value of anything would be its market value, as long as a market exists, since you can always sell it in the market and use the proceeds to buy something else that has consumption value.

1. Good point Andy, I had thoughts along similar lines.

2. So an overpriced tulip has fundamental value in the same sense as money

For that definition of FV, yes! If you define FV that way, there are no bubbles (using the Williamson definition of bubble, i.e. P>FV).

And if you define FV as consumption value, then almost everything is almost always pure bubble.

Therefore, I was asking Steve to come up with a definition of FV where you can get bubbles sometimes and no bubbles other times.

3. So Brad DeLong defined FV as "the expected money-metric utility of holding an asset til maturity". I thought that was good.

Though I'd choose a slightly different definition.

4. ramsey9:45 AM

It seems that the question here is whether you consider the act of exchanging money for a good to be a transaction service of money, or a sale of money.

If the former, then money has a fundamental value under the definition "FV = present value when held to maturity." It's FV is the discounted value of the transaction service flows.

If the latter, we must ask why anyone accepts money. We conclude that they accept it only because they expect others to accept it in turn. Money never matures, and if there were an end of time it would be worthless. So under the definition above, it has a FV of 0, and so it is a bubble.

How does this compare to a toaster? A toaster is a durable consumption good that pays a stream of toasting services, which enter our utility function. Of course, such other goods as electricity, bread, and butter are complements for toasting services, so if their price goes to infinity our toaster becomes a paperweight. But that doesn't make it a bubble. It's value when held to maturity just depends on the price of other goods (relative to our income), but it has a fundamental value as defined above.

What about something like a stock? Yes, stock dividends are paid in money, because money has market value. But ultimately a stock is a claim on a real thing (the residual profits of a firm), and just happens to be paid in money because that's the accepted medium of exchange in our society. If money did not have value, dividends would be paid in some other good or asset that did. So a stock is not a bubble just because money is.

42. Anonymous10:28 PM

The Fundamental Value of good bamboo slide rules was quite high in 1950; I bet at Caltech or MIT you could trade one for a keg of beer.
In the 90s, all the ruling engines were sold for scrap metal

43. Anonymous10:43 PM

To Noah above. No Farhi and Tirole are not wrong. This refers to a long and well established literature with other "wrong" papers such as Tirole (1985) in Econometrica or Tirole (1982) in the same journal for instance...

1. Wait...so what?

You demonstrated understanding of how the Tirole "rational bubble" works. You know that permanently exponentially increasing price is an essential feature of that bubble. So how can you claim that money is a Tirole bubble? You're just not making sense...

2. ramsey9:51 AM

A relevant quote from Tirole (1985):

"In Section 6 the valuation of money is examined in the light of the distinction between market fundamental and bubble. The market fundamental of money is equal to the present discounted value of transaction savings. It is shown that money differs from other assets in that (i) its market fundamental, and not only its price, depends on future prices, (ii) if money is expected to retain its transaction value in the future, there cannot exist a bubble on money. A corollary to the latter fact is that there is fundamental dichotomy in the formalization of money: Either it is essentially depicted as a store of value (bubble) as in Samuelson, or it is assumed to serve transaction purposes. The two representations are in the long run inconsistent."

I think that the quote from Farhi and Tirole was in reference to the first interpretation. I don't think FT were wrong, they were just talking about a specific model in which money is indeed a bubble.

3. OK, so maybe it's just not clear from all these excerpts what Farhi & Tirole are talking about. Thanks for digging that up.

I conclude that Farhi & Tirole may or may not have been consistent in their definitions of "bubble" and "fundamental" from one paragraph to the next, and to really know, a more complete reading is necessary.

Kids, this is why argumentum ad verecundiam is a bad strategy! It almost always degenerates into massive text-parsing.

44. I think the problem is the insistence on the idea of value. Look at all the trouble it causes in this otherwise simple discussion. There really isn't such a thing as value; there are only prices at which transactions occur. Arguing about value is like arguing about hidden variables in quantum mechanics. There aren't any. Get over it.

Once you start thinking about price instead of value, you can focus on the mechanics of decision making and actual transactions. These can be measured and studied. Unlike value, a price can be measured whether in barter, social effect or money. When you ask someone how much they "value" something, you are going to get a meaningless answer. When you ask how much they would bid for it or ask for it, you are learning something real about their financial reasoning.

Physicists had to throw out absolute time, absolute location, a good chunk of determinism and the idea of internal state to describe the real world properly. Maybe it's time economists started moving into the 20th century and threw out value and we wouldn't have all this blind grasping at phantoms.

1. Excellent point! The absolute-ism of so many theories of economics is what makes them absolutely unworkable and inapplicable to the real world, IMO.

45. The "fundamental" vs [insert other definition of value] distinction seems a bit anathema to the standard economics because it presumes that a security can trade at a price that is different than its worth.

Of course, if the fundamental value is \$8 but I buy at \$18 and sell at \$22, I've just gained in one of the world's most fiat currencies and depending how many lots of \$4, can buy a nice real good for myself.

However I think fundamentals are meaningful as are other theories of value. To give a less famous example than train-track charting or analysis of fundamentals, http://books.google.com/books?id=nQdWRFK_2A0C&pg=PA76&lpg=PA76&dq=fill+out+a+distribution+trading&source=bl&ots=bqkdHUruSq&sig=RgT9CdUaZ7iOWoKsTMSUIjRtXgQ&hl=en&sa=X&ei=FHCGUL79LeKQyQGk6IHoDQ&ved=0CEcQuwUwAw Mark Tinghino is not the first to suppose that trading prices "fill out a distribution" and "test a range".

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?

Sure, just one example is the liquidation value of all assets the company owns. Not only is this one of the fabled Buffett tricks but book to value ratio is theorised in A Random Walk Down Wall Street to be an even better predictor of overbought-ness than P/E ratio.

1. Ack, this comes across as unclear:

fundamentals are meaningful as are other theories of value. To give a less famous example

All I mean is, no-one seems to have figured a formula for where eg stock prices are destined to go in the future or what the determinants are. Thus we're left with multiple viewpoints on what's "really" determining the value, with a survivorship bias suggesting that any of the ones you can hear of probably work at least enough of the time to convince a non-alchemist.

46. Why does Williamson get treated with respect?

He just seems like a bad tempered fool to me.

47. FSGorin9:38 AM

Dears,

As a French troll, I would like to (re)introduce you to a work by Michel Aglietta (http://en.wikipedia.org/wiki/Michel_Aglietta) and AndrÃ© OrlÃ©an, two french economists who tried to deal with money with a broader approach.
In their book "Money: between violence and confidence", they explain how money is a social institution which hold society together, beyond simple economic value. Money has a value for itself, because everyone wants it, because everyone need something to trust. I know these short sentences may seems very obvious, but the interest of their book is the way they explore, explain and transcend the obvious. Anyhow, saying that money is worthless is just showing that you economics model prevent you from seeing this obvious truth.

48. I'll do you one better...LIFE is a bubble. Broken down in its component pieces, life is just a bunch of worthless common elements...carbon, nitrogren, etc. After a short period of time -- days to centuries, depending on the form of life we're talking about -- the bubble always bursts and the organism returns to its fundamental value. And yet, for some reason we foolishly continue to value life. When will we learn?

1. You're obviously making a sarcastic analogy, but life has reproduction, which is a really big deal and which isn't obviously analogous with any property of money.

49. Noah, I have two responses to your update responding to my post.

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 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.

50. 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.

I think people need to start rigorously and carefully specifying their definitions of "fundamental value". What's yours?

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.

I don't even know what those sentences mean. What is "ipso facto"? NO, don't tell me.

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.

This is false. In the real world, all assets generate finite nominal revenues, not infinite. So if money has FV=0, then FV/P is zero divided by a finite number, which is zero, not "infinity divided by infinity" as you claim.

Now think carefully...

51. It seems to me that we have some fundamental issues here (having also read Krugman's take on this). There seems to be no concensus at all on:
1. What a bubble is (I like Krugman's take)
2. What value is (I like Kaleberg's take)
3. What money is (I've never come to terms with this - there are many different measures of money, which behave differently over time - and time is of the essense with money - so which captures the "concept" best?)

So what the hell are we talking about?

52. P.S.
It seems to me there might be some ambiguity between "money" as a concept and "money" as a particular instance of that concept. The value of money is its usefullness as a store of value and a means of exchange. This IS a fundamental value, in the same sense that for instance the internet has value.

But isn't something being forgotten here with money. It's supply is variable (it can shrink or expand according to need). The central bank is attempting to MAINTAIN its value in terms of other things. This is not really true of most other assets - certainly not of real assets. Equity is also a bit like this (though not exactly ). Part of the value of equity (perhaps most) is intangible - the value of a going concern is not equal to the sum of its parts. Is money like equity in the central bank?

53. Noah, You are so demanding! In truth, I have no definition of “fundamental value,” because I don’t think there is any such thing. I believe, like all Austrian economists, that all value is subjective, depending on subjective expectations of the future that are inherently ungrounded in fundamentals and are always subject to revision based on the acquisition of new (i.e., unpredictable) information (including information about the expectations of other people!) which may, or may not, be based in fact. So I think that fundamental value is a nonsense term. Sorry, but that's the best I can do.

Now here are my questions for you:

Why do you have a problem understanding that something with zero value cannot be exchanged for anything with positive value? And why do you have a problem understanding that something with zero value is inherently incapable of serving as a medium of exchange? And why do you have a problem understanding that to talk about a money whose value is identically equal to zero is to speak gibberish?

You said: “In the real world, all assets generate finite nominal revenues, not infinite. So if money have FV=0, then FV/P is zero divided by a finite number, which is zero, not “infinity divided by infinity.”

Ahem, in the real world, a medium of exchange does not have FV=O, at worst it has FV => 0. So, by insisting that FV=0, you have taken us out of the real world.

Actually, I think we are in (almost) total agreement on substance. We are just arguing about the right way to explain what we both agree to be the case.

54. Noah, You are so demanding! In truth, I have no definition of “fundamental value,” because I don’t think there is any such thing.

OK, that's fair. So you think there's just no need to define a quantity called "fundamental value". I see.

Why do you have a problem understanding that something with zero value cannot be exchanged for anything with positive value?

It is interesting that you phrase this question this way. If I answer the question, I implicitly acknowledge that I do have such a problem. It's like asking "Have you stopped beating your wife yet?"

So I'll pretend that instead, you asked me "Do you believe that something with zero value cannot be exchanged for something with positive value, and why or why not?"

My answer is: It depends on what one means by "value". If "value" means "ex post value", then it's possible for such an exchange to take place; for example, I might buy a toaster that turns out to be faulty.

If "value" means "expected value to the seller", then it also seems possible, as I would definitely be willing to exchange something I didn't value for something I did value.

If "value" means "expected value to the buyer", then definitionally, it would seem that such an exchange is not possible.

And why do you have a problem understanding that something with zero value is inherently incapable of serving as a medium of exchange?

I don't understand what this question means. Please reformulate it.

And why do you have a problem understanding that to talk about a money whose value is identically equal to zero is to speak gibberish?

I think you should address this question to Steve Williamson.

Ahem, in the real world, a medium of exchange does not have FV=O, at worst it has FV => 0. So, by insisting that FV=0, you have taken us out of the real world.

It's weird that you make this claim about real-world fundamental values after saying that you don't even like to define "fundamental value". How can you make statements about the real-world behavior of a quantity that you explicitly refuse to even define? That makes no sense to me.

It's like if I were to say "David, you fool. How can you claim that Frahrmnabble is equal to 12? In the real world, Frahrmnabble can only be approximately 12, not exactly 12. Incidentally, I refuse to tell you what Frahrmnabble means."

That would be silly gibberish.

But it appears to be exactly what you have said to me in this comment.

Why do you have a problem understanding that you are not making sense? ;-)

55. I mean, OK, here are quotes from your comment:

"In truth, I have no definition of “fundamental value,” because I don’t think there is any such thing...Ahem, in the real world, a medium of exchange does not have FV=O, at worst it has FV => 0. So, by insisting that FV=0, you have taken us out of the real world."

How on God's green Earth can you reconcile these two statements???

56. Noah, You are right. It was inappropriate for me to use that accusatory tone in posing my questions to you. Thanks for rephrasing the question and answering it anyway.

You answered the rephrased question (“Do you believe that something with zero value cannot be exchanged for something with positive value, and why or why not?”) as follows:

“It depends on what one means by "value". If "value" means "ex post value", then it's possible for such an exchange to take place; for example, I might buy a toaster that turns out to be faulty.

“If "value" means "expected value to the seller", then it also seems possible, as I would definitely be willing to exchange something I didn't value for something I did value.

“If "value" means "expected value to the buyer", then definitionally, it would seem that such an exchange is not possible.”

This is a bit confusing. If you are selling something with positive value (a toaster) why would you accept something in exchange that you expect to have zero value? If you are buying a toaster, and you expect money to have zero value, then for sure you will be prepared to give up the money for the toaster. So don’t you have it backwards?

You asked me rephrase my question. Okay, here it goes: If something is worthless, how can it function as a medium of exchange? The answer, based on your answer to the previous (rephrased) question would seem to be, it can only serve as a medium of exchange when at least one party to the transaction is mistaken about its value. Wouldn't that mean that, according to you, stocks have a positive fundamental value? It's just that some people hold stocks because they mistakenly think that money has positive value.

You said:

“It's weird that you make this claim about real-world fundamental values after saying that you don't even like to define "fundamental value". How can you make statements about the real-world behavior of a quantity that you explicitly refuse to even define? That makes no sense to me.“

When I say that I don’t think that “fundamental value” is a meaningful concept, I mean that I don’t think it’s possible to identify a particular value for an asset as being somehow more true or valid than other values in the sense that deviations from that value cannot persist over time. Here I am saying that, as a matter of logic, even if I accepted, for argument’s sake, that there is such a thing as the fundamental value of a medium of exchange, that fundamental value could not be zero. It could not be zero, because for a medium of exchange to be worthless would deprive it of the capacity to function as a medium of exchange. Of course you would say that a fundamentally worthless asset could still function as a medium of exchange because a lot people mistakenly believe that it is not worthless. But then how can you conclude that stocks are fundamentally worthless? Maybe they are fundamentally valuable; it's just that people mistakenly think the money is valuable and hold stocks even though stocks are just claims on money.

1. This is a bit confusing. If you are selling something with positive value (a toaster) why would you accept something in exchange that you expect to have zero value?

You would not, and that was my point.

Am I just poor at communicating?

You asked me rephrase my question. Okay, here it goes: If something is worthless, how can it function as a medium of exchange?

And my answer is: It depends on what "worthless" means. If something has no worth to anyone, it obviously cannot function as a medium of exchange.

The answer, based on your answer to the previous (rephrased) question would seem to be

Oh no, now you're gonna go get yourself in trouble!!

it can only serve as a medium of exchange when at least one party to the transaction is mistaken about its value.

Wow, I am just an amazingly poor communicator!

No, I don't think that at all. That is absurd.

When I say that I don’t think that “fundamental value” is a meaningful concept, I mean that I don’t think it’s possible to identify a particular value for an asset as being somehow more true or valid than other values in the sense that deviations from that value cannot persist over time. Here I am saying that, as a matter of logic, even if I accepted, for argument’s sake, that there is such a thing as the fundamental value of a medium of exchange, that fundamental value could not be zero. It could not be zero, because for a medium of exchange to be worthless would deprive it of the capacity to function as a medium of exchange. Of course you would say that a fundamentally worthless asset could still function as a medium of exchange because a lot people mistakenly believe that it is not worthless. But then how can you conclude that stocks are fundamentally worthless? Maybe they are fundamentally valuable; it's just that people mistakenly think the money is valuable and hold stocks even though stocks are just claims on money.

OK, there's a lot of verbiage here, and a hailstorm of terms that are not carefully defined. Let me see if I can parse some of this.

1. The point of my post was to ask people (Steve Williamson in particular) to define the term "fundamental value".

2. You refused to define such a term.

3. You then claimed that, no matter how the term was defined, something with FV=0 could not function as a medium of exchange. This claim is clearly false. Suppose I define the term "fundamental value" to mean "net electrical charge". Why not? Words mean what we define them to mean. In that case, money would have zero fundamental value as long as it was electrically neutral.

So this statement of yours - "even if I accepted, for argument’s sake, that there is such a thing as the fundamental value of a medium of exchange, that fundamental value could not be zero" - is wrong and false. Without defining a term, you cannot make statements about that term.

So, again, unless you agree to a definition of "fundamental value", we can't discuss what does and does not have fundamental value.

Does that clear things up a bit?

57. Anonymous10:58 PM

Noah:

I support the clamor in opposition to your point that if fiat money has zero value most financial assets must also have zero value:

Firms are more than money machines; they are entities which control hard assets. By retaining a right to those hard assets, a shareholder or creditor has a property which would not be reduced to zero, even in the event that fiat currency implodes absolutely. As long as the law of property and contract stands, a stock or a bond has a fundamental value which can be measured in things. Numerous cases in history exist when a fiat currency imploded but many local firms survived, rapidly switching dividends and operations to value-laden alternative currencies.

US Dollars were once a kind of promissory note, a contract which held a definite value measured in gold. Holders of Dollars, like owners of equity, had a claim on a tangible asset as long as the law of contracts was upheld. Since the severing of the US gold standard, Dollars can no longer be considered contracts/securities/promissory-notes. While we can imagine government doing much to support the fiat dollar's ongoing value in day-to-day exchange, no one has a contractual duty to give us anything for our dollars.

============

Regarding your larger question about a concrete basis for measuring "fundamental value," I reckon that we ought to do like the philosophers and begin from a viewpoint of calamity.

Imagine (or historically review) cases of partial or absolute collapse in currency systems, in law and order, or in civilization. What types of assets hold value in the various scenarios?

The necessaries of life invariably hold fundamental value: food, tools, arms, animals, etc.. Notably, objects which are scarce, light, beautiful, useful, non-spoilable, divisible and re-fusible, such as metals, tend to hold their value well. These objects are peculiarly suited to emerge as mediums of exchange.

In some cases, land titles are a fantastic measure of fundamental value -- land having an inherent capacity to produce the necessaries of life. In other cases, land titles become worthless, as an entire legal regime is deposed.

I like to look to Homer when attempting to grasp the measure of things: golden cups, elegant arms, heads of cattle, casks of wine and oil, an estate that you can defend, the loyalty of strong and honest men, and the favor of the gods -- these are the things that hold value in every age.

Unfortunately, my Homeric stores of value have no measurable absolute value, but rather fluctuate in relative worth depending on circumstance and preference. A measure of true fundamental value is and will always be as elusive as human taste. This is not to say it does not exist in absolute terms, only that math-loving economists will never find a way to capture it for use as a cornerstone to our reductionist theories. If we must find a measurable thing to serve as a cornerstone of fundamental value upon which to build a necessarily imprecise economics, gold has always been the best measure by far. All fiat currency is destined to burst in the long run. It always has.

Forgive my lengthy and somewhat rantish reply.

===============

Fun Post!

--Ryan

1. "By retaining a right to those hard assets, a shareholder or creditor has a property which would not be reduced to zero, even in the event that fiat currency implodes absolutely."

Shareholders, yes. Creditors, no, unless the loan recipient fails to act in their own interest. If hyperinflation comes, there is no way I will be defaulting on my mortgage; I will simply sell any minor possession for a large quantity of worthless dollars and pay off my mortgage in full. My bank is not protected from the collapse of the value of a dollar, because they are only guaranteed to be able to get the minimum of the value of my house or the money I have promised to pay; if I pay, they have no claim on my house.

2. Anonymous12:20 AM

Eric,

Too true. I thought twice about including creditors beside the shareholders in that sentence for the reasons you point out. But I figured there is always a chance that a debtor will default on some aspect of a loan, even when it becomes trivially easy to pay off the cash owed with valueless currency. This ought to give a loan a non-zero value, even as currency value approaches zero. Not an important distinction, I know...

I hope it didn't distract you from all the exciting ideas in the remainder of my post!

Cheers!

R

58. Noah, No you are not poor in communicating, but sometimes miscommunication does happen.

By the way, just as an aside, I think you overrate the importance of definitions. People generally are able to communicate quite well based on an intuitive understanding of the terms that they are using. Definitions are only necessary when there are ambiguities that have to be excluded by a precise definition that clears up the potential ambiguity. That’s usually important in doing mathematical or logical proofs, but not that important otherwise. But that’s just an aside.

You said:

“1. The point of my post was to ask people (Steve Williamson in particular) to define the term "fundamental value".

“2. You refused to define such a term.

“3. You then claimed that, no matter how the term was defined, something with FV=0 could not function as a medium of exchange. This claim is clearly false. Suppose I define the term "fundamental value" to mean "net electrical charge". Why not? Words mean what we define them to mean. In that case, money would have zero fundamental value as long as it was electrically neutral.”

I didn’t want to define “fundamental value” because I was focused on making the point that “fundamental value” doesn’t exist. (I misspoke when I called "fundamental value" a nonsense term.) That assertion, as you observe, itself requires that some implicit meaning be attached to the term, which I actually hinted at but did not state explicitly. So what I mean by “fundamental value” is a particular value such that if the market value deviates from that value, market forces will operate strongly to bring the market value back toward “fundamentaI value.” The reason that I deny that fundamental value in fact exists is that asset values depend on expectations and that expectations can be self-fulfilling, so there is no way to know whether deviations from a putative fundamental value will be self-reversing or self-fulfilling. I deny that fundamental values actually exist, but I can actually define (sort of) what I mean when I use the term. Concerning whether “words mean what we define them to mean,” there is a story about Abe Lincoln asking someone if we call a dog’s tail a leg, how many legs does a dog have. I always thought that Abe gave a good answer to that question. But again, that is just an aside.

1. I'm sorry, but this is just word salad to me...

2. Tokio7:02 AM

Noah Hello! Hajime mashite. David, nice to see you again! I'm the one who left some comments on "Krugman on Mistaken Identities" at Uneasy Money.

(Sorry, because this comment is so lengthy that the blog system can’t accept. I have to divide it to two parts. This is the part 1.)

It seems that Steve Williamson's “proof” is just a misuse of valuation technique. Let me explain.
But first "fundamental value". I think Steve's "fundamental" is not a theoretical term. The word "fundamental" is a kind of jargon in equity investment. "Fundamental analysis (research)" is what equity analysts do. They look at financial statements, economic environment, etc. to estimate the future of a company. "Fundamental investors" are the investors who rely on this method. Also there are non-fundamental analysis (investors). For example, technical analysis (investors). Technical investors only care about historical pattern of the movement of the price. They think like, "6 weeks moving average cross the 1 week moving average, let's buy" or "3 times of quick up-and-down followed by slow up going is a good sign to buy". So they don't care what the company really is. To sum up, "fundamental (value)" here can be interpreted as "a reasonable estimate of the price based on a reasonable scenario based on an appropriate fundamental research". (From Steve's context this seems to make sense.)

Next, let me review the valuation technique (i.e. calculate or estimate present value of future cash-flow or pay-off) very quickly. Roughly, there are two types.
A: Stochastic type
There are many future scenarios of cash-flow or pay-off. Calculate discounted pay-off for each scenario, and the final present value is the probability weighted sum of these discounted values. Theoretically, you should use short-risk-free rate for discounting and so called "risk-neutral probability" for weighting (academics and derivative rocket scientists), but in practice one might use "risk-free rate + risk-premium" and "real probability (i.e. the probability that you think to be real)".

B. Non-stochastic type
You choose only one scenario. Because you know that the scenario is not certain, you don't use risk-free rate for discounting, instead you use higher rate: risk-free rate + risk-premium.

It seems that Steve Williamson's style is type B. Probably he create many scenario in his mind and choose the most plausible one as the expected scenario, that is a common style for equity analysts.

In equity analysis, sometimes you want to calculate only the extra value that the company creates over the primal investment, instead of total value of the company. That is so called “residual income valuation“. Investors require for the company to earn at least risk free rate + risk premium. Residual income is defined as net income minus “risk free rate + risk premium”. The extra value is calculated as sum of those discounted residual incomes. Then the total value of the company is the sum of primal investment + the extra value. (“Value Added” or “EBO-model” approaches in equity valuation are of this kind)
For example:
You create a company with \$100 from your pocket, based on your original business-model. In your vision, this company makes \$40 in 1 year. Now, risk free rate is 2%, and risk premium for this company is supposed to be around 8%. 2% + 8% is a required return for this business. So only excess return over 10% (i.e. the return - 10%) will create additional value to your primal investment: \$100. Discount rate is 10%. The additional value that your company create is (\$40-\$10)/1.1 = \$27.3
Total present value of your company is \$100+\$27.3 = \$127.3.
If the market agrees with this analysis and you go public and sell 100% of your company, you can make \$27.3 of profit. (This example is one-period type for simplicity. We'll see infinite-period type; DDM-model later. )
So, far OK?

(The end of part one)
Tokio

59. Anonymous5:43 PM

This is one of those cases in which I think it could benefit one field (in this case, economics) to actively solicit information from another field (in this case, anthropology). One of the key insights of anthropology is that there is almost nothing 'fundamental' in all of human behavior. Gold, silver and other precious metals have no 'fundamental value' - sometimes humans choose to imbue them with culturally-induced value, and sometimes we don't. ALL exchange, no matter the medium - fiat money, 'free' money, gold, goats, etc. - is a social convention. That's Paul K's point, and it's backed up by anthropology. Humans create media of agreed-upon exchange, because we need them, and they're all essentially made up (not innate or 'fundamental').

1. Anonymous12:01 AM

Anon,

I think you are completely right about the non-existence of an asset of absolute "fundamental" worth, and in your interpretation of Paul K's point.

Given that there is no absolute standard for fundamental value, the challenge is to determine whether there are certain assets that consistently tend to have more relative worth than others in various scenarios in the long run...

Anthropological scrutiny of the differences between asset-types and mediums of exchange is definitely the route to take. I reckon such a study would identify some persistent trends. Gold and Silver have been richly valued (albeit by social convention) in every era and among nearly every culture (Thomas More's Utopians excepted!). Debased coins and fiat currencies tend to flop after a while (though they are indeed upheld by social convention during their glory days). The point here is that all socially-conventional ascriptions of value are not made equal.

Paul K says that, unlike most asset bubbles, there is no logical inevitability which dictates that a "bubble" in fiat currency must eventually burst. We could go on believing in the value of this medium of exchange, founded only on expectation of others' belief in the value of this medium of exchange, indefinitely. Paul K might be right about this. If so, it marks an unprecedented turn in the pattern of history.

You are totally right about economics needing to look beyond the traditional boundaries of the discipline to address some of these issues.

Cheers!

R

60. Anonymous4:57 PM

From an investing point of view, the fundamental value of an asset is the net present value of its future cash flows. Which is by definition subjective as nobody knows the future.

But if you then say that money has no value it means that nothing has a fundamental value. For example if you buy a house to let it but the money the tenants pay has no value then than house has no value to you.

Saying that money has no fundamental value is meaningless. It sounds smart but it's bullshit.

1. Tokio7:04 AM

(Part2)
Now, let's evaluate the "\$100 of cash" in this manner. The risk free rate is 2%, so you can make new \$2 for sure. Because there is no risk, risk premium is 0%. Then required return is 2%, and discount rate is 2%. The additional value that the cash makes is
(\$2-\$2)/1.02 = \$0
And the total value of the cash is \$100 = \$100 + \$0.
Of course you can calculate the present value directly: if you have \$100 of cash today (t=0), your total pay-off at the end of the year (t=1) is \$100*1.02=\$102. So, the present value of the cash is \$102/1.02 = \$100.

I think there are two possible mistakes in Steve's "proof". The one is what we've just seen: confusion of total value and "residual (extra, additional) value" (or confusion of total pay-off and residual pay-off). The other possibility is that he assumes that "I don't invest the cash on risk-free rate, I’ll keep the cash in the drawer". Let’s see what happens.
Now recall the DDM model (Dividend discount model, which is an infinite period type). The price of the stock whose dividend is constant d for eternity is
d/(1+r) + d/(1+r)^2 + d/(1+r)^3 + ... = d/r
(Here, “^” means power. For example, 2^3=8)
where r is an appropriate discount rate assuming the risk. Note, in this formula the principal investment value disappears far into the infinite future, and the total value is only expressed with annual returns.

Applying this to the cash with risk free-rate, we have
(because there is no risk r = risk free rate, d=\$100*r)
\$100*r/r = \$100
Applying this to the "cash in the drawer", we have
\$0/r = \$0
May be the latter is what Steve meant. But this is also wrong. Because this is not the value of the cash, instead this is the value of a particular strategy: "cash in the drawer and never use it". The risk free rate is something you can get without risk or compensation, you should count it in valuation of the cash.
For example, you know the famous Black-Sholes formula for call option. From B-S formula, you know that the call option's price is always positive. In short if you have a (equity) call option you have the right, but not the obligation to buy an equity at a certain time (the expiration date) for a certain price (the strike price). So if the equity price is higher than the strike price at that time, you can exercise your right and your profit is "the price of the stock minus the strike price". But because it is "the right, but not the obligation", you can say "I will never exercise my right". But even if that is the case, you can't say "my call option’s price is zero". It's just your decision makes your call option valueless for yourself. If you give away the call option to someone else, it has positive value for him.

There is another criticism for this "cash in the drawer" valuation. In reality if you keep cash in the drawer, that doesn't mean "I will never use it for eternity". Your intention is probably like "I will use it in an emergent situation" or “I will use it when I change my mind”. So, this strategy's future pay-off is not zero, the right scenario is a stochastic one, \$100 in one year for some probability and \$100 in two year for some probability, and so on. So, even your personal strategy's value is not zero.

Lastly, I think one can invent some measure to express how precious the things are, and apply it to the money, and say that the money is nothing. But if you choose \$ to measure \$, you have always \$100 = \$100.
TOKIO

61. Noah,

Welcome to the economists' spirit world. Just three points.

1. The tax explanation is plain balderdash nonsense attempts to deify Caesar. Forget it is cuckoo.

2. Paul Krugman solaces the labor theory of value. Not a bad idea except then there is the 'transformation' problem to deal with. That one is a multidimensional black hole with uncertain quantum tunneling.

3. Since money has been in use for millennia, better to get with the times. For the last 640 years or so the dominant assessment has been the "qualities" of money. See Nicola Oresme, "de Monetas," c 1367, in english on webpdf. Consider the following 'qualities' as APT factors (aka fundamentals).

1. Symbolic or Totem value = normally not much but can range upwards like George Best Ir 5 lb., Solidus of Julius Ceasar, Alexander Stater, and NZ Dumbledore dollar, each in its time, or downwards, like the US Susan B Anthony dollar, often mistakenly circulated as a quarter.

2. Value in Exchange, Universal Equivalent, Numeraire. As anticipated. The bubble that expands or contracts, but never pops. Poor money for the poor, through either abrasion or interest. Read Walras about how value is then throw at Williamson. Krugman was referring to this as the "consensual" value.

3. Unit of Account. The Ducat, Guilder, Pound, Dollar, Euro. Whatever your banker (not taxman) wants to see.

4. Store of Value. Easy enough to say, but just as subject to Keynes' chapter 17 as any other impersonator.

No money can possibly ever be perfect in any of its qualities.

Money rules the roost; but if you need to ask why he will peck your eyes out for even trying to find out.

Obviously, dozens of books and hundreds of articles have been written about each word in the above outline.

Money is the primary commodity.

If you are ever asked what are its fundamentals just say, "everything else." Your inquisitor will either run away or just shut up and get down to work.
Best thing all around. Or, to quote the present Dalai Lama, "Money is that thing to best obtain wishes."
Now that I think of it, wishes wouldn't include knowledge. Clever fellow, that one.

62. I think many people question the actual value of currency now that there is no gold or silver standard. It is more fluctuating and unpredictable and can be impossible to really understand the value of a dollar.

63. joeaverage10:21 AM

moeny has value

just alone the fact that people want it, people accept it as token for goods in trading and so on, makes it extremely valuable

value stems from people's assesment of somethinsg value

a painting van gogh was worth a bottle of wine in the his pub down the stret when he lived

now it is worth several mansions

even if what teh gyu claoimed was true

moeny still had teh productiuon cost so it is at least worth the paint an dteh paper

look at it this way gold or diamonds are utterly useless for the common people
yet they value them highly just beacue society does vlaue those highly

you cannot eat gold
and the technical applications for it dont justify it's price

but because eveyone thinks it is a sign of wealth and status it becomes extremely valuable

to me there is no value in owning any gold or jewlery

but that is juts me
yet if i had a piece of gold it woudl stillbe valuable because i could trade it to thers who value it

so the value isnt dependent solely on what I value

but also what society values

and those are too different values

ok lets make another image: what if there was only enough food on the planet for every 10th person?

woudl anyone sell a piece of bread for money?
no they woudlnt
becasue at some point if there is nothing left to buy that means if teh last fish is caught the last tree cut and teh last cow slaughtered

what is that last steak worth?

money is a tool for trading

we are able to trade goods by token with money

and aslong as tehir are goods tobe tradet there is a vlaue inteh commonly acepte currency

if tehre is no goods money ceases to exist too
it becoem paper

but even then there is curreecny (cigarettes/liquor and so on)

if you wanted to be objective about it value is something we humans assign to something

it isnt an independent thing

if we change and what we value changes the value of thinsg changes

if tomorrow we could turn shit into gold
nobody woudl even use gold as jewlery anymore but some teenagers
we wouldnt value gold

so scarcity and demand for a thing along with a lot of other social factors play into the value

how much is teh value of a barrel oil if there is no cars or other machinery that you can fuel with it?

what is a cow worth if everyoen is a vegan?

money isnt a bubble

it is just that value of things isnt cut in stone

they change depending on teh situation

if food became producable out of thin air by the press of a button (liek in starwars)

food would have no value

also if you had lunch how much will you be willing to pay for a steak i just grilled?

it isnt as clear cut

scarcity demand and also personal use/apreciation for a thing all factor

one man's trash is another ones treassure!

64. Anonymous7:53 PM

There is no such thing as fundamental value in an economic system. all valuations are subjective, and all valuations are made without erfect information. your attempt at determining a fundamental value reminds me of early marxist economists who thought similarily. fundamental values do not allow people to have preferencs. Difference in preferences are a fundamental componet of a sucessful trade. this is literally econ 101 in any school in america.

65. Anonymous10:41 AM

Monetary economy is an illusion. Created long ago so the weak could survive. PERIOD. In the event of economic collapse, ALL pieces of paper become worhthless. I mean really, when that happens, (and history has shown us that eventually, it will.) what would you rather have? A pound of gold, or a gallon of fresh water?