# On Fiat Money

Why do people accept fiat money? It is, after all, intrinsically useless. David Glasner has written a thoughtful post on fiat money. Glasner writes:

Why should a fiat money not be able to retain value? Well, consider the following thought experiment. For a pure medium of exchange, a fiat money, to have value, there must be an expectation that it will be accepted in exchange by someone else. Without that expectation, a fiat money could not, by definition, have value. But at some point, before the world comes to its end, it will be clear that there will be no one who will accept the money because there will be no one left with whom to exchange it. But if it is clear that at some time in the future, no one will accept fiat money and will then lose its value, a logical process of backward induction implies that it must lose its value now.

So why are people willing to accept it? Glasner suggests that the reason is because the government accepts money as payment for taxes. This is the chartalist view and has been around for some time. Glasner traces this back to Wicksteed. Ross Starr provides an analysis within the context of general equilibrium theory. However, I would like to suggest another proposition. To do so, we need to talk about two different questions: (a) why does fiat money exist?, and (b) why do people accept it?

There are a number of ways that have been suggested to explain the use of money. However, I would like to focus on one in particular. As emphasized by Brunner and Meltzer (1971) and Ostroy (1973), money is a substitute for information. To illustrate this point, consider an example. Suppose that there are three people, three goods, and three time periods. Person 1 produces Good 1 in Period 1, but wants to consume Good 2. Person 2 produces Good 2 in Period 2, but wants to consume Good 3. Person 3 produces Good 3 in Period 3, but wants to consume Good 1. Notice that there is a basic double coincidence of wants problem. This problem, however, does not necessarily require money. For example, the three individuals could get together and make a multilateral arrangement in which each individual promises to deliver the desired good to the appropriate trader in each period. No money is necessary.

The example above, however, requires that the individuals can perfectly commit to those actions. In reality, the individuals have an incentive to renege on their promises. For example, Person 3 could promise to give Good 3 to Person 2 in Period 3 so long as Person 1 supplies Good 1. However, if there is disutility associated with production, Person 3 has no incentive to produce anything given that they have already received their consumption good. But even this isn’t sufficient to require money. If trading histories are perfectly monitored and costly available to all parties, this would provide an incentive for individuals to behave honestly.

This latter assertion, however, bears little resemblance to the world in which we live. We do not have costless access to the trading histories of every possible counterparty. As such, when individuals cannot perfectly commit and there is imperfect monitoring, money is essential in the language of Hahn in that it expands the possible allocations available to economic agents. The role of money in this context is as a substitute for information. Money is memory.

The informational role of money makes money essential and is therefore preferable to other arrangements. However, this does not resolve the solution by backward induction that Glasner suggested above. Thus, we need to answer question (b) above.

In search models of money it is standard to denote the price of money as $\phi_t$. The price of money refers to the goods price of money rather than the money price of goods as we are usually accustomed to thinking. It is important to think about the price of money because it is possible that this price could be zero (i.e. we have a non-monetary economy). A condition for a monetary equilibrium in these models is that

$\phi_t \geq \beta \phi_{t + 1}$

This implies that it must be true that the price of money today is greater than or equal to the present discounted value of the price of money tomorrow. In more familiar language to monetary theorists, it must be true that the inflation rate is greater than or equal to minus the rate of time preference.

According to Glasner, we know that at some date, T, the world ends and therefore nobody would accept money. Through backward induction, nobody would accept money today. However, the solution by backward induction is contingent upon knowing the date at which the world ends. For example, suppose that the probability of the world ending tomorrow is $p(\phi_{t+1} = 0 | \Omega_t)$ where $\Omega_t$ is the information available at time t. Thus, the expected future value of the price of money at time t is:

$E_t \phi_{t + 1} = [1 - p(\phi_{t+1} = 0 | \Omega_t)] \phi_{t + 1} + p(\phi_{t+1} = 0 | \Omega_t) * 0$

Thus, we can re-write the necessary condition for equilibrium as:

$\phi_t \geq \beta [1 - p(\phi_{t+1} = 0 | \Omega_t)] \phi_{t + 1}$

So long as the probability of the world ending is not equal to one, a monetary equilibrium obtains and is therefore not subject to the backward induction critique. Fiat money can therefore be thought of as a rational bubble. We do not need to appeal to irrationality as Glasner suggests. Rather as a trader I know that money increases the set of feasible allocations in trade and therefore I have an incentive to use it and accept it so long as I anticipate that others will accept it in the future. In addition, I know that it is intrinsically worthless, but so long as the future is not certain (or time is considered infinite) it can have positive value because of its role as medium of exchange. As a result, fiat money trades above its fundamental value.

### 12 responses to “On Fiat Money”

1. Very informative.

Since inflation is targetied at 2%, does that imply that time preference is -2%?

Does this assume a constant quantity of money? Suppose that the day before the world ends and no one wants any more money, then the issuer will pay it all off?

Well, on end of the world day, it might be tough for someone using monetary liabilities to fund loans, but we can imagine an institutional scenario where the quantity of money will be reduced when the demand for it falls. For example, if is tied to some nonmonetary commodity, bundle of commodities, or some other nominal value determined outside the banking system.

• “Since inflation is targetied at 2%, does that imply that time preference is -2%?”

No. If the rate of time preference is -2%, this equilibrium condition just implies that the inflation rate has to be greater than or equal to -2%. If the inflation rate were less than -2%, everybody would just hoard money.

“Does this assume a constant quantity of money?”

No. Here we defined the price of money as equal to $\phi_t$. The price of money is just the inverse of the price level. Also, in these models, in equilibrium, it is true that

$\phi_t = z_t / M_t$

where z is the demand for money and M is the supply of money. As a result, the price level is determined by the ratio of the supply and demand for money. Thus, if we assume that the demand for money is constant, we could re-write the equilibrium condition as

$M_{t +1}/M_t = P_{t+1}/P_t > \beta$

where $\beta$ is the discount factor. So long as money growth is greater than minus the rate of time preference, monetary equilibrium obtains.

“Suppose that the day before the world ends and no one wants any more money, then the issuer will pay it all off?”

My assumption is that the issuer of fiat money runs for the hills and gives nothing to the people holding it. Of course, we could relax that assumption, but I think that doing so would provide a different reason for the non-zero value of fiat money.

2. Thanks.

If the rate of time preference is 2%, does that mean the inflation rate has to be greater than or equal to 2%?

• Oops. There is a typo in my comment above. It should have said that if the rate of time preference is 2%, then the inflation rate has to be greater than or equal to -2%. From the equilibrium condition above we have:

$\phi_t/\phi_{t+1} \geq \beta$

Define the $\phi_t / \phi_{t+1} = 1 + \pi$ and $\beta = 1/(1+r)$. This implies:

$\pi \geq 1/(1+r) - 1 = -r/(1+r) \approx -r$

3. Yep. Good post.

I have never accepted the “chartalist”/Wicksteed view, because the amount of base money normally increases over time. Suppose the government announces that it will sell 100 bits of paper this year, and collect back 95 bits of paper next year in taxes. The equilibrium price of those bits of paper will be zero, because 5 bits of paper will be left on the sidewalk, surplus to requirements for paying taxes.

People want to hold stocks of money because it is useful as a medium of exchange. And the stock demand is positive, not just because people want to use money rather than barter (as you explain above) but because it is very costly to have an infinite velocity of circulation.

4. paul davidson

As Keynes pointed out in the Treatise on Money– The fact is that in a money using contrctusll economy, the State is the enforcer of all contracts — so whatever the State says discharges a contractual liability is the money of the system as long as the citizens are law abiding.

See my A KEYNES SOLUTION: THE PSTH TO GLOBAL ECONOMIC PROSPERITY for a full discussion and the implications when trade occurs between residents of different nations — which money is used to settle the contractual agreement.

There sre vases knowen where the State reqwuires payment of taxes in one type of money– but citizens have little fate inenforcing privste contrcts — in which case they use State money to pay taxes and a different money to settle private contracts.

Paul Davidson

Paul Davidspn

5. Great post. You present with much greater mathematical literacy than I can produce a very similar argument to the one I made in response to David Glasner’s post.

Your argument also explains why asset bubbles happen — turning points are not known.

6. Fiat money is an imaginary concept that is no more real than the phlogiston, ether, and caloric of early physical sciences. People observe that the Fed won’t give you gold for your dollar and they jump to the conclusion that the dollar is unbacked, even when the assets backing those dollars are right there on the Fed’s balance sheet, plainly labeled as “Collateral Held Against Federal Reserve Notes”. People even observe that the government accepts dollars for taxes and, rather than reaching the obvious conclusion that those dollars are backed by the government’s assets (taxes receivable), they instead adopt the Chartalist view that taxes increase the demand for dollars.

Why do you need to believe in fiat money anyway? Why can’t you accept the much more logical and coherent idea that modern paper currencies are backed but inconvertible? The fiat money view suffers from, among other things, the Last Period Problem, indeterminate price levels, and the circular logic of “People hold dollars because they are valuable, and they are valuable because people hold them.”

7. dhlii

“All money is a matter of belief”