Sunday, July 26, 2015

Resolving the paradox of fiat money

As the dimension of this simplex defined by the budget constraint Σ Ci = M increases, most points are near the budget constraint hyperplane ... and therefore the most likely point will be near the hyperplane.

In his recent post on neo-Fisherism, David Glasner links to an earlier post about the paradox of fiat money -- that money only has value because it is expected to have value:
But the problem for monetary theory is that without a real-value equivalent to assign to money, the value of money in our macroeconomic models became theoretically indeterminate. If the value of money is theoretically indeterminate, so, too, is the rate of inflation. The value of money and the rate of inflation are simply, as Fischer Black understood, whatever people in the aggregate expect them to be.
The problem then becomes the problem of the "greater sucker"; rational people would only accept money because they expect they will be able to find a greater sucker to accept it before its value vanishes. But since at some point e.g. the world will end and there won't be a greater sucker, the expected value should be zero today. Note that the idea of the future rushing into the present is a general problem of expectations, as I wrote about here.

After getting a question from Tom Brown about this, I started answering in comments. Now I think the information transfer framework gives us a way to invert that value argument -- that if you don't accept money, you are the greater sucker. The argument creates a stable system of fiat currencies.

The argument starts here; I'll quickly summarize the link. If we imagine a budget constraint that represents the total amount of money in the economy at a given time being used in transactions for various goods, services, investments, etc C₁, C₂, C₃, ... Cn, then using a maximum entropy argument with n >> 1 we find the most likely state of the economy saturates the budget constraint and minimizes non-ideal information transfer (see the picture at the top of this post for n = 3). And since:

k N/M ≥ dN/dM ≡ P

we can say minimized non-ideal information transfer maximizes prices for a given level of goods and services {Cn} because P is as close to k N/M as it can be. We would think of arrangements of trust (credit) or barter exchange as less ideal (very non-ideal) information transfer than using money or some money-like commodity.

This maximized monetary value critically depends on n >> 1 -- that as many goods and services are exchangeable for whatever is being used as money as possible. This means that whoever trades their goods and services for the most widely used money gets a higher price (more ideal information transfer) for those goods and services. If I don't accept money, then I'm getting a worse deal and I'm the greater sucker. That would stabilize an existing fiat currency system because if I refuse to take money, I'd contribute to the downfall of my own personal wealth. I'd also get a worse deal in that particular transaction.

I've explained this argument in terms of rational agents. However in the information transfer framework we'd think of this argument as money allowing agents to access larger portions of state space and hence achieve higher entropy. We would think of money as a dissipative structure, like convection cells in heated water or even life itself, arising in order to maximize entropy production to move the system towards equilibrium. Convection cells only cease to exist when the water reaches a uniform temperature. Analogously, money only loses its value when every scarce resource is equally allocated among everyone (the Star Trek economy) -- the economic equivalent of heat death.

Update +3 hours:

Although the money value argument admits a rational agent explanation, the truth is that there may not be any such explanation that is valid in terms of microeconomics -- that money is an emergent structure and its effects are entropic forces. The rational explanation may be like incentives or Calvo pricing: an attempt to 'microfound' a force (effect, or structure) that only exists at the macro level. Osmosis and diffusion have no microscopic mechanism (although you could invent one, an effective force [1]) and maybe the value of money has no micro explanation that is actually true.


[1] An example of a (possible) entropic force that we tend to explain with an invented micro force is gravity. We think of it as mediated by gravitons that behave similarly to photons, but it might be closer to the stickiness of glue. It is important to note that because it is an entropic macro force doesn't mean it is impossible to model as a micro force.


  1. I really think the Backing Theory of Money is the overall best theory of money. In a nutshell, the expected future value of the money is each bills share of the current value of the reserves the bank has. This really seems to work. At least I can not find a case really contradicting this theory.

    Now if the reserves are just bonds denominated in the same currency, you could have about the same paradox. In practice this does not seem to happen (outside of hyperinflating ones) though a few reserve currencies are mostly such bonds but with some other reserves, like gold.

    1. Vincent, what conceivable future state of a world economy would falsify the backing theory?

    2. Vincent,

      As David Glasner says at the link above:

      "The difficult question, for which [Hal] Varian struggled to find an answer, is why a fiat money, regardless of why it might once have had value, can retain any value."

      That is to say regardless of whether it is 'backed' now, how could it be possible to guarantee (i.e. rationally expect) its backing in the future.

      And what value do bank reserves have in the future unless they are tangible assets that provide services? Bottled water and ammunition come to mind, but the backing theory simply moves the paradox of fiat currency value to a paradox of its backing's value.

    3. There is a clear market value for the assets that the bank holds, whatever they are. There is no paradox about their value. That their value determines the value of the fiat money is an important insight.

      I can find no cases where central banks don't have reserves, or where the currency value is far from what you would calculate by dividing the amount of currency by the value of the assets.

      To ignore these bank assets when they really help explain the value of money seems very wrong.

    4. Tom, if there was a central bank with a stable currency and no assets, that would falsify it. Even a currency that was stable at multiples of asset share would falsify it. Or a currency valued at a fraction of the asset share.

  2. Oh, your argument works for the "medium of exchange" use of money. But for the "store of value" use of money, it does not really hold.

    1. Hi Vincent,

      Actually it does include the "store of value" aspect. In the high dimensional simplex where n is finite, but large only ~ (n-1)/n of the money is allocated to goods and services. The remainder is held as a "store of value". The store of value aspect of money goes away in the limit n >> 1 in ideal markets as no one holds cash.

      It is like this picture where at the maximum entropy point one holds one knife, fork and spoon each with 1 € left over:

      That remaining Euro is money held as a store of value; however as the dimension of the economy increases (varieties of investments, goods and services) the store of value disappears -- no one holds cash for any economically relevant length of time.

      The fact that people hold cash is a measure of how non-ideal the economy is.

    2. Tom, it is interesting, but mindless atoms would "hold cash" in the information model above without recourse to a complicated human behavior relationship involving bounded rationality. However, Koning and I do seem to agree that holding cash is a result of imperfect markets/imperfect rationality.

    3. "mindless atoms" is why I keep coming back. (c:

  3. Quick questions.

    What about the Continental Dollar? What about Bitcoin? What about savings stamps?

    1. Hi Bill,

      I debated whether or not to include a bit on how currencies arise (or disappear, which might seem contradictory at first). There is nothing stopping them from arising. Some currencies will be a bit more common than others and will take over. Once a currency takes over however, a significant shock needs to happen to dislodge it.

      A good analogy would be species in ecological niches. Bitcoin is like a new species arising in an ecosystem where the niche has been filled by established species like the US dollar, Euro, etc. A panic of some kind can cause the collapse of a currency and another can take over (like mammals moving into the dinosaur niches after the K-T boundary).

      These panics may seem contradictory to the above post about currencies being stable, but they're not.The panics are irrational unforeseen but sporadic events (e.g. wars or collapse of governments) -- they can destroy the value of currencies if they are big enough. But the key point of the paradox of value of fiat money is that long run (trend) expectations lead to zero value, not short run (shocks).

      Using the species analogy, the difference is between a theory that says any species will eventually collapse without shocks and the theory here that says species are basically stable unless subjected to shocks.

      The continental dollar experienced a large shock (wartime hyperinflation) so that a new species of money could come in with the US Constitution.

    2. Bill, maybe stablecoin is one to add to your list? (It's a new one to me... I first read about it on that link)

    3. Backward induction without a date certain is questionable, to say the least. Axelrod demonstrated that in "The Evolution of Cooperation". I don't say that he proved it, as it is in the borderlands of epistemology and logic. The idea that fiat currency is worth nothing in the long run is dubious.

      As for the Continental Dollar, it was a wartime currency, and the colonists had experience paying for wars with fiat currency. The collapse of the Continental went far beyond their experience. The British did counterfeit quite a number of Continentals, however. Benjamin Franklin, who championed fiat currency, warned the Continental Congress to make it acceptable for taxes, but they did not. If the states had accepted Continentals in payment for taxes, would they have become almost worthless?

      Bitcoin seems to be backed by avoiding taxes. ;) I expect that as governments crack down on its illegal usage, it wil crash.

  4. Jason, have you read K. Michaelian's paper that you linked to? I didn't read it, but it strikes me that it probably overlaps with the work of bio-physicist Jeremy England of MIT (from what I can tell of England's interviews... I haven't attempted to dig into his published papers either).

    1. Yes; in fact when I first heard about England, I thought it was Michaelian's work getting recognition. Michaelian had the idea of life as an entropy dissipating system first by several years and actually had a fascinating specific mechanism for the genesis of DNA and source of the entropy process: the water cycle.

    2. Well, I hope that England gave credit where it was due (I did notice that Michaelian's paper was from 2010, which did strike me as probably being a bit earlier than England's more recent spate of publicity).

    3. Also, yesterday I listened to a wide ranging (but relatively brief) interview with Sean Carroll. In part of it he was explaining in layman's terms some of his ideas on the arrow of time. In particular he drew an analogy between the universe starting with the big bang (very low absolute entropy) and moving through time to heat death (high absolute entropy), and the idea of mixing cream into coffee. Neither the beginning nor the end of either process is interesting in terms of complexity (the beginning and "end" are simple states), but in between, when the tendrils and swirls of creams are mixing into the coffee is when you get the wonderful complex structures. I thought that was a nice image.

      I'm pretty much uneducated about thermodynamics (in fact even though I have a MS in electrical engineering (really control system) from UCSB, it was never a required part of my curriculum, so I never had a formal class in the subject beyond freshman physics & some limited attempts at self education), so I've added the qualifier "absolute" above although Carroll didn't. I did this because I recall seeing Victor Stenger argue that the big bang was both a point of minimum and maximum entropy... he had a notional chart showing entropy increasing with time, but a second curve showing the maximum possible entropy increasing at a faster rate, and the two curves intersecting at the big bang... so trying to reconcile these two physicists' statements in my own mind, I assume that when Carroll speaks of the big bang being a low entropy state he must mean that in an absolute sense rather than relative to what is possible given something else.

  5. Isn't the money market the one with the maximum demand? Therefore making money suppliers maximally connected to consumers, gives actor more degrees of freedom, access to more markets, better partitioning and so forth. I think entropy maximization demands agents to hold money

  6. I would add that the market with the maximal demand can serve as money


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