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Instead of a House or $20 Banknote you can insert many other things like gold, investment wines, investment art and other things which value is dominated by expectations that somebody else will value it equally high even if it is useless (gold, wines or art stored somewhere in an underground safe in Switzerland never to see the sunshine again). Actually I once thought that this could be a good definition of a bubble - if something is valued not for the utility it provides but by how much other people are willing to buy it for in an iterative manner.

So in short, this supposed irrationality is not exclusive to money. Or in other words I do not know how your story of people willing to hold declining value of money differs from this story of somebody willing to hold gold that declines in value:

"But if my story were about a *gold*, I would buy it for (say) 20 of my dollars, and sell it for (say) 19 of her dollars next year which will then buy me 19 of his bananas etc."

So maybe gold is less liquid (but still liquid enough for some purposes) but it declines in value much slower than money to offset its lower liquidity in on-year timespan. But maybe in different timeframes you are willing to hold money in your wallet even if they lose value at higher rate than gold because money provides you with liquidity services that have much higher value than that those gold ring you wear. $100 in your wallet may be used to buy you water and food if you unexpectedly prolong your stay in a city or it can hire you a cab if you were late for the last bus in a much better rate than gold would. But that is all there is to it (I think).

PS: this whole post reminded me an excelent post by David Glasner. He named your argument about supposed worthlesness of money as a "backward induction" and there are several things that he offers as an explanation of why even fiat money can have value which has mostly to do with the fact that they actually provide some crucial service. I think that once some money emerges due to network effects it will became very powerful and it can provide very useful liquidity services in the same way as when some previously unknown artists emerges as one generally recognized for valuable art his work can provide convenient store of value for those seeking it - making those people who were endowed with pieces of art from him able to profit from rent this position creates.

It is surely a "bubble" by my definition - but it is a pretty stable one since those services this bubble good provides have non-zero value which enables it to survive temporary changes in its value.

[edited to fix typos NR]


JV: (I changed your "vines" to "wines", right? It had me really confused!)

"Instead of a House or $20 Banknote you can insert many other things like gold, investment wines, investment art and other things which value is dominated by expectations that somebody else will value it equally high even if it is useless (gold, wines or art stored somewhere in an underground safe in Switzerland never to see the sunshine again)."

I'm not sure you can insert those other things in place of the $20 banknote. Money is different. Because for money there's the failure of transitivity. Each person sells it for more than he paid for it (in his own evaluation), but its value is falling over time. It's like an Escher staircase, where each person seems to be going up, from his own perspective, even though the stairs lead down.

That's what I was trying to say in the post. I need to think of a clearer way to say what I was trying to say.

These posts could only have been written by academics with too much time on their hands. People exchange existing assets (houses, stocks of money) all the time. At the end of the day those houses and those stocks of money are the same, it is just that different people now hold them. It is a zero sum game. What those actors may have expected (or hoped for) going in to such transactions is not relevant to anyone else.

BTW: I suggest the role of money here is not as a medium of exchange, it is as a store of value.

Ed: "These posts could only have been written by academics with too much time on their hands."

You are totally right about that! As of July 1st I'm no longer associate dean, and i suddenly have some free time, and it's an exhilarating experience! And I luxuriated in the leisure of writing this post.

"At the end of the day those houses and those stocks of money are the same, it is just that different people now hold them. It is a zero sum game."

1. Owning a house also gives you somewhere to live (or income from the tenants who live there). That's a gain.

2. Suppose I want to move to where you live, and you want to move to where I live. So we swap houses. We both gain.

It's not a zero sum game.

Ha ha ha! Very clever.

But I think that J.V. Dubois is more right than you acknowledge. "I expect that what I get paid when I sell it will be worth more to me than what I paid to buy it." Your trick is that you mean more in "utility" rather than more in money. But that is true when I buy any asset that lasts longer than I do, even if purchased for "consumption". So if I buy a house to live in, rather than to sell to a greater fool, I still think the house is worth more than the money I paid for it and so does the person who buys it from me - even if I sell it for less than I paid for it.

JV, money isn't a bubble because there is a trader of last resort - the central bank.

If the CB went out of business and people kept using the money, then it would be a bubble (or possibly a speculation on the CB reemerging).

Thanks Phil!

"Your trick is that you mean more in "utility" rather than more in money."

Good point. I'm still trying to think of the best way to talk about this idea.

Max: But it's still paradoxical, because the CB is the one promising to make sure the value of money declines by 2% per year, and yet people hold positive quantities.

Nick: Yes it was meant to be wines, sorry for that. I will have to add that to think to check together with then/than or lose/loose. Not being native speaker can be weird (along with not using preview)

"Because for money there's the failure of transitivity. Each person sells it for more than he paid for it (in his own evaluation), but its value is falling over time."

Now it may be me who is confused. What I wanted to say is that there is no problem with transitivity. I understood your barter example as one where each transaction took some time to conduct. Otherwise if it was all real-time it would only show that barter market is imperfect as there exist an arbitrage that should be closed under more optimal conditions.

People are willing to lose by holding onto the money when conducting trades because they value the liquidity services (and store of value services) the money provides as equal or exceeding that loss (ok, maybe money also has unique risk portfolio that other liquid assets don't have because it has quite predictable purchasing power short-medium term). So there is no arbitrage, any loss just reflects the value of services (liquidity, store of value) money provides. That is the only [two] thing[s] why money is special (in this case). That is the reason why most of us have only small portion of wealth in checking account/cash in wallet and the rest is in bonds, shares, real estate etc.

JV: (Weird thing is, I had totally forgotten you were not a native speaker of English, which is why your "vines" so totally threw me "What the hell is he talking about? Do people really invest in vines stored in bank vaults??" Your English is that good.)

The idea that holding money provides "liquidity services" is like a story we tell ourselves to "explain" why people hold money despite it paying a lower yield than other assets. "Liquidity services" is like an imaginary theoretical entity we invoke, in analogy to houses providing a service of "somewhere to live", to resolve an anomaly. But I think it's better to say that the utility of the selling price exceeds the utility of the buying price for each person who buys and sells a $20 note, and then talk about the failure of transitivity because different people have different preferences.

Damn! I need to find a clearer way to say this!

Nick do you mean something like this?:

When I get paid I like to go to a restaurant that serves different dishes every time, they always have two of those. Let's say that for some unspecified reasons I prefer steak to fish and fish to salad but I prefer salad to steak. So we have a utility conundrum because my preferences are not transitive (there may be some hidden variable that makes them transitive, but you do not know). So we have money come into rescue because all of these dishes cost $10 so we can say that I always prefer to sell my labor for $10 as opposed to getting paid in one of those dishes with pretty uncertain results in terms of utility I derive by consuming/trading them - since I may trade them less "favorably".

But I would still say that money is providing me with liquidity services. I don't always use my cash to buy stuff that I see at the moment, but when I do I make sure that utility I derive from it exceeds the loss from holding money in the first place.

Nick:

I don't think there's any paradox:

the main value/utility of money, despite it losing 2% of value per year, is two main roles:

1) it's the metric everyone around you uses to price their products, services and assets, relative to each other. It's barter prices expressed in a standardized (arbitrary but constant) unit.

2) there are paper notes (and securely transacted bits in computers) issued by a central authority, which represents a standardized, physical, transferable representation of this pricing unit. It's a special "common good" everyone will barter for.

These two properties are more than worth the modest 2% cost per year.

Just like a NASDAQ data feed and a trading account is worth money, pricing and having the authorization to transact is worth money. This is why people are more than willing to hold money, up to a certain level of inflation.

(A third aspect that spurs the circulation of money is taxation: there's a constant requirement to pay income, consumption and other taxes in the local national currency - which makes it beneficial to contract and transact in this currency.)

I think dismissing so easily "liquidity services" is strange. Considering the heroic assumptions one needs to make to have individuals just writing each other I.O.U.s to exchange goods and services. It seems like money solves a bunch of those problems and it delivers without a doubt "liquidity services".

Put differently: money is a standardized "reference good" which everyone barters with. You can rent this good from a central authority. You pay a 2% annual rent for holding it.

People elect to hold it because money's utility is larger than the 2% rent/cost/fee.

I think some of the confusion is that Nick's original "transitivity does not hold" is somewhat ambiguous. It is not clear (to me, at least) what/whose preference relation it is that is violating transitivity. I don't think it is the preferences of any individual that violate transitivity. Is it the preference relation that is implied by the social welfare function?

Dr. Rowe,

The very first lines of your original post say: "I buy a house. Not because I want to live in it, or rent it out; the house will sit empty while I own it . . . . .The person I sell it to doesn't plan to live in it or rent it out either. She buys it for exactly the same reason I bought it. And she plans to sell to another person who buys it for exactly the same reason. And so on." I pointed out that a string of such transactions is a zero-sum game, because there is no net increase in utility of the houses or of the money involved.


Then you do a 180 with your opening hypothesis and say: "Suppose I want to move to where you live, and you want to move to where I live. So we swap houses. We both gain." -- and conclude it now is not a zero-sum game.

Your conclusion is different because you changed your principal hypothesis.

You lost me on this one Nick. I buy a car or a tractor, knowing it will lose 10%/year, because it will yield more than 10% in services. I buy $100 in bank notes, knowing it will lose 2%/year, because it will yield more than 2% in services. So how are bank notes different from regular goods?

Ed: Aha! Sorry. I totally misunderstood your comment. I thought you were saying that buying and selling *real world* houses (not my post's imaginary houses) was a zero sum game. If my imaginary houses were bought and sold for money, yes it would be a zero sum game. (But if they were used as a medium of exchange, to enable trade in other goods, it would not be zero sum.)

JV: No, that's not what I'm trying to say. In my monetary exchange example, each individual (presumably) has transitive preferences. But when we follow the $20 bill around in a circle, from one person to the next, it looks like preferences are intransitive. The first person who holds the $20 prefers B to A; the second person prefers C to B, and the third person prefers A to C. Each person uses the $20 note to take an upward step in value/utility (the $20 is worth more when he sells it than when he buys it), but each time it completes the circuit the value of the $20 note is no higher (and is lower with 2% inflation). Like an Escher staircase.

Anon and Iperrault: OK. Maybe I'm not so much *dismissing* liquidity services, as trying (and failing to do clearly) to *elucidate* those liquidity services.

Evan: "I think some of the confusion is that Nick's original "transitivity does not hold" is somewhat ambiguous."

Yes, I did not say it clearly enough. See my attempt to say it more clearly in my reply to JV immediately above this comment.

Mike: Sorry you got stuck in spam.

The car or tractor gives you services *while you hold it*.

The $20 note gives you zero services *while you hold it*. It only gives you a service when you sell it. And that service is like a capital gain. Because you sell it for something that is worth more (***to you***) than what you paid to buy it.

Nick, interesting post.

"The $20 note gives you zero services *while you hold it*. It only gives you a service when you sell it. And that service is like a capital gain."

Is it just me or does this contradict a paragraph from your previous post? The quote below seems to imply that a $20 bill provide a stream of services while being held, namely the service of 'keeping our options open'.

"Money is the most liquid of all goods. We don't want to place an order this year for a new car next year. We want to keep our options open, which means we want liquidity. We don't want to decide now what make of car to buy, especially since we don't even know what will be on the market next year. Or maybe to buy it the year after next. Or maybe to buy a bike instead."

An interesting post, and good as food for thought.

The main issue you seem to be trying to address is money as a store of value as it interacts with money as the medium of exchange and medium of account. The fact that money loses value over time is possibly a direct consequence of money being used as the medium of exchange. Since a central bank would have a difficult time keeping the inflation rate at 0%, the promise of 2% keeps the bank from worrying about a possible slip into deflation through fluctuations. Deflation would make using money as a medium of exchange less useful since people would hoard it instead. Also the promise of a fixed level of inflation makes using money as a medium of account more useful as quoted values are more stable and more meaningful in real terms. So the use of money as a store of value is compromised to benefit the other two uses for money.

Also the fact that you don't gain any service from money while you hold it doesn't mean that you shouldn't hold it. People pay for potential services fairly regularly. For example people pay taxes to keep fire fighting services despite not using them at all times, and some people may never require their service.

Jason,

"Deflation would make using money as a medium of exchange less useful since people would hoard it instead."

Maybe. It would also depend on risk tolerance and the potential real returns from other investments.

JP: Thanks! I was hoping you would show up here.

"Is it just me or does this contradict a paragraph from your previous post?"

It's not just you. It contradicts what I said in that previous post (and probably lots of other previous posts too)!

There are two ways of looking at the demand for money:

1. We "forget" that money circulates, and we explain why people "hold" (an average stock in inventory) money, despite it being rate of return dominated, by talking about "liquidity services". (Like in my previous post, and many others).

2. We talk about the (subjective) capital gain that people get from buying a $20 note and selling it again later for something they value more (in terms of utility). (Like in this post).

I think the second way is more fundamental. The first way is a fudge.

Jason: thanks!

1. Store of value. Hmmm. You have a point. I might want to rethink what I said about the store of value function of money in an earlier post.

2. The *option* of using it, like firefighters. Hmmm. OK. But in this post I'm imagining a world of certainty, to keep it simple.

Frank: A good point and probably does make the specifics of the change in value unimportant in moderate cases. This could also mean the question of "why do people hold money?" could still be asked even in cases of moderate deflation (eg 2% deflation instead of inflation).

Nick: In a world of high certainty, then yes holding money in high quantities wouldn't make much sense. But even when you have high certainty you would want to hold some cash if you value having choices, since even holding highly liquid investments such as stocks wouldn't let you go out and buy dinner on a whim (though I suppose a credit card would allow for payments to be made on a regular basis as to on the spot).

Nick:

"The $20 note gives you zero services *while you hold it*. It only gives you a service when you sell it. "

That works for a lot of cases, but then there are cases where people use tobacco, salt, and cows for money. There are also cases where bonds and bills of exchange start being used as money. Those don't fit very well.

Nick: All right I still do not get it, but maybe there will be something to it down the road. It would not the first time that I find something useful from the way you describe your deliberations in your blog posts. And in the meantime I did refresh my micro to see if there was something new with non-transitivity besides usual stuff of situational dependedency or other-regarding processes and other behavioral micro mumbo-jumbo I am not aware yet (not that I find something new to it, but that is my selfish me speaking - in the end it is not me who is putting my skin out there on the blog for everybody to see, right?)

So in the end I would say there is already something useful I already derived from it that I did not see immediately (that I think is something Jason described as "food for thought" and I am really grateful for it).

All that I want to say is that I really like any of your blogs even the ones where you do not have some serious wisdom to share in the end*.

*Note: not that I am *not* excited if you do some stuff like "we owe it to ourselves is bogus in OLG model" here and there :D

"2. The *option* of using it, like firefighters. Hmmm. OK. But in this post I'm imagining a world of certainty, to keep it simple. "

Fine, but if a large part of the liquidity premium comes from protection against uncertainty and information cost, you've thrown out the baby with the bath water.

Diligence friction from the need to acquire information on exchange media and lack of a single price for goods are particularly relevant results of illiquid media.

Think back to the time when there was a single nominal unit of account, but bank notes traded at discounts from nominal depending on the available information on the their issuing banks. Would that be practical in today's economy? I doubt it.


The value of saving money is protection against uncertainty. You don't know what you might need it for, so you keep the wealth in the form of money.

So I think saving of money should be viewed through the risk-assessment framework.

"2. The *option* of using it, like firefighters. Hmmm. OK. But in this post I'm imagining a world of certainty, to keep it simple. "

Failed simplification. The option value is the *entire* value of money. Try again.

I guess I'm saying that a world of certainty is a world of barter, a world without money.

*And there is historical evidence for this!*

Extremely stable "primitive" tribal societies, where the social rules are rigid and the societies are unchanging for many generations, don't usually have money.

Money is present in societies which are constantly banging up against other societies or otherwise encountering change.

For a huge example, *Ancient Egypt did fine without money for thousands of years*. With a strong, universally accepted central government and an extremely stable society, barter was carried out at universally agreed exchange rates. B

By contrast, the feuding, warring states of ancient Sumeria, which were also faced with the repeated need to relocate due to salinization of their fields.... invented money.

So there is actual empirical historical evidence that money is necessary only in an environment of change and unpredictability.

The value of money *is* the option value.

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