François Velde

English

Research Papers in Economics

Chicago Fed Letter
Solving the problem of small change
by François Velde, senior economist
In the last hundred years, monetary systems have evolved from commodity-based,
meaning their value is tied to a commodity like gold, to fiat-based, meaning their value
is not tied to anything. Why did this happen? What was wrong with the old commodity-
based systems? A recent book explores these historical developments and shows how
the problem of small change played a crucial role in the introduction of fiat money.
ESSAYS ON ISSUES THE FEDERAL RESERVE BANK OCTOBER 2002
OF CHICAGO NUMBER 182
1. Price levels in various countries, 1660–2000
index 1913=100
SOURCE: Sargent and Velde (2002).
1600 1650 1700 1750 1800 1850 1900 1950 2000
106
105
104
103
102
101
Our experience of money in the twen-
tieth century has been very different
from the past. Figure 1 illustrates the
point by showing the price level over a
long period in four countries: England,
France, Spain, and the United States.
The base year for the index is 1913, so
all series coincide in that
year. The most obvious fea-
ture of this graph is the big
change around 1914, which
marks the end of the gold
standard, a commodity-
based monetary system.
Since then, we have used
fiat money, which is not tied
to the value of a commodity.
As figure 1 shows, the price
level was roughly constant
for three hundred years
before 1914—with some
fluctuations, to be sure, but
nothing like what we saw
after 1914.
In a radical departure from
previous practice, the price level was
in some sense set loose and allowed to
rise. Did the idea of fiat money occur
suddenly, or was the groundwork laid
for it earlier?
A recent book by Sargent and Velde
(Thomas Sargent and François Velde,
The Big Problem of Small Change, Princeton
University Press, 2002) explains a prob-
lem that bedeviled monetary systems for
hundreds of years, the problem of small
change. They show that: 1) we had been
learning about fiat money for a long
time before 1914; and 2) we learned
as we tried to cope with the problem
of small change. This Chicago Fed Letter
provides an overview of some of the
issues involved.
For hundreds of years, supplying small
denominations of currency was difficult.
This may seem like a trivial question to
us today, because the problem has been
solved; but in the past, this created many
recurring problems, such as shortages
of small denominations, variable ex-
change rates between coins of differ-
ent sizes, bouts of inflation, invasions
of foreign coins, and depreciation of
the currency.
As societies struggled to solve the prob-
lem, they moved from a commodity
money system, in which the value of
money was tied to that of a commodity
like gold or silver, to a fiat money system,
in which money is essentially valueless
(paper) but is valued in the marketplace.
The solution, which was considered
standard at the end of the nineteenth
century, was to make the small denom-
inations fiat but “convertible” into the
(gold-based) large denomination.
England
France
Spain
U.S.2. Stock of Venetian torneselli, 1353–1475
millions of soldini
SOURCE: Sargent and Velde (2002).
0
5
10
15
20
25
30
35
40
45
1350 1375 1400 1425 1450 1475
Making smaller denominations “fiat”
meant that their intrinsic content was
substantially lower than their face value,
which is obviously the case today with
paper money. But it also involved peg-
ging the exchange rate between small
and large coins. In the process, societies
learned a lot about managing fiat money,
its advantages, and its risks.
What’s the problem?
Why was commodity money so bad at
producing small denominations? Con-
sider the case of a single coin, for which
the properties of a commodity money
system are fairly transparent.
The main property of a commodity
money system is to tie the price level to
an external anchor, the value of the com-
modity on which it is based. It does so
by putting limits on the value of the coin,
which is inversely related to the price
level. Specifically, the system gives a
lower limit and an upper limit to the
value of coins.
The lower limit comes from the coin’s
content. If the market value of coins
containing 1 oz of silver were to fall be-
low the value of 1 oz of silver, it would
be profitable to melt them down for
their content; this would reduce their
quantity and drive up their value.
by the seigniorage rate, the
premium charged by the
mint to turn metal into
coins. If the mint has to
break even (and it usually
did), the seigniorage rate
has to cover production
costs, the costs of actually
making the coins.
Between these limits, the
value of coins (the price
level) can be thought to
fluctuate according to the
typical “quantity-theory”
relation. The reason that
coins exist as coins rather
than as metal is because
they facilitate transactions. A given (real)
volume of transactions necessitates a
certain real value of coins. If the volume
changes, and until the nominal, or
physical stock of coins changes through
minting or melting, the real value of
each coin has to change. Thus, variations
in the volume of transactions lead to
proportionate variations in the value
of coins. But large variations automat-
ically induce the appropriate response
by driving the value of coins to the low-
er limit (where melting occurs) or the
upper limit (where minting occurs).
The quantity of money automatically
money, where money now takes the form
of pennies (small denominations) and
dollars (large denominations). They arise
in just the same manner as in the single-
coin case, as upper and lower limits on the
value of each coin. But the limits may not
be consistent with each other, because
pennies are more expensive to make.
Thus, if the mints are required to break
even (indeed, they were expected to yield
a monopoly profit to the government),
then they face the following dilemma:
either charge more to make pennies
than to make dollars, or charge the same
but make pennies with less metal rela-
tive to dollars. In the first case, the risk
is that, when money becomes dear, peo-
ple will come to the mint to make dol-
lars, but not pennies. If the government
wants pennies, it has to make them on
its account, and at a loss. The risk in
the second case is that pennies are then
“light,” that is, they contain proportion-
ately less metal than they ought to com-
pared with dollars. If the value of coins
rises enough, then dollars will be melt-
ed first because they are relatively more
valuable and only pennies will remain.
But the demand side has implications
as well. To see this, suppose that small
and large coins can be used for large pur-
chases, but only small coins can be used
for small purchases. This is a simple way
of creating a demand for different de-
nominations, and opens the possibility
that the existing stock of pennies might
suddenly become insufficient for the
transactions that require them.
nominal
real
The main property of a commodity money system is to
tie the price level to an external anchor, the value of the
commodity on which it is based. It does so by putting
limits on the value of the coin.
The upper limit arises because of the
way in which coins are produced. In the
classic medieval system, which remained
in place until the advent of fiat money,
the mint (where coins were produced)
stood ready to convert metal into coins
at a set price. If the value of a coin were
to rise above the price paid by the mint,
it would be profitable to bring metal
to the mint and turn it into coins.
These limits put constraints on the price
level that are essentially tied to the value
of the metal used in the coin. How far
apart these bounds stand is determined
adjusts to maintain the price level with-
in its bounds, and there can never be
a serious “shortage of money.”
At the starting point in European mon-
etary history, in 800 AD, there was in-
deed only one coin in Europe, the
penny. Later, larger coins were intro-
duced. Two things happen, on the sup-
ply side and on the demand side. I use
the words “pennies” and “dollars” to
refer to small and large coins.
On the supply side, there are now two
sets of constraints on the value ofMichael H. Moskow, President; William C. Hunter,
Senior Vice President and Director of Research;  Douglas
Evanoff, Vice President, financial studies; Charles
Evans, Vice President, macroeconomic policy research;
Daniel Sullivan, Vice President, microeconomic policy
research;  William Testa, Vice President, regional
programs and Economics Editor; Helen O’D. Koshy,
Editor; Kathryn Moran, Associate Editor.
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Why wouldn’t such a shortage cure it-
self, as in the one-coin system? Pennies
will be produced only if their value rises
enough. The value of money depends
on the whole stock of coins, both pen-
nies and silver, and there may be enough
dollars around that the value of money
(dollars or pennies) doesn’t rise enough.
And there is the additional problem
that the mint might be forced to charge
more for pennies than for dollars, dis-
couraging anyone from buying pennies.
This suggests that the relative price of
pennies to dollars should adjust, so that
pennies become more expensive rela-
tive to dollars, and their value rise to
the minting point, even if the value of
money (the inverse of the price level)
they must depreciate. The worse the
shortage, the greater the depreciation.
Thus, prices don’t adjust as they should;
in fact, they move in the wrong direc-
tion, and perverse effects ensue. Since
large coins appreciate, this induces in-
flation when prices are expressed in
pennies (which was the case at the time).
Moreover, as pennies depreciate, their
value may fall to the point where they
are worth melting; this only exacerbates
the shortage.
The solution
A short-term cure consists in debasing
pennies, i.e., putting less silver than
before in a penny. This has the effect
of catching up with the market-driven
needs to either devote resources to en-
forcing the law or possess a technology
that makes its coins harder to imitate.
As it turns out, every breakthrough in
technology led to more experiments.
Each time the technology improves, we
see governments using the occasion to
make token coins; conversely, we see
early experiments in token coinage be-
set with problems of counterfeiting, to
the point that, even in the nineteenth
century, many people were leery of to-
ken coinage.
A second prerequisite is a theoretical
one. The standard formula also requires
the very concept of fiat money, and when
one goes back to medieval times, that
idea was alien and took time to emerge.
The third prerequisite is in the area of
policy. The standard formula for solving
the problem of small change requires
governments to run a currency board
for pennies, but currency boards cre-
ate temptations for governments, and
fiat money in general does too. Histo-
ry is replete with episodes of trial-and-
error—for example, figure 2 shows what
happened in the fifteenth century, when
Venice decided to introduce small
copper coins called “torneselli” that
were roughly twice overvalued in its
Greek territories. Initially, everything
went smoothly, as the new pennies re-
placed what old pennies were in circu-
lation. But there came a point where
the torneselli saturated the demand
The historical record shows repeated debasements of small
denominations prompted by currency shortages.
doesn’t adjust. But in fact, as Sargent–
Velde find, pennies depreciate during a
shortage. This is a counter-intuitive re-
sult, but there is sound intuition for it.
The basic idea is to remember that mon-
ey is an asset, and different monies will
be compared by their rates of return.
Most of the time, pennies and dollars
are substitutes, and people don’t care
which they hold. But in times of short-
ages, prices have to signal to people that
they must economize on their holdings
of pennies. For regular goods, this is
done by driving up the price of the good
in short supply. But for assets, this is
done by making pennies less attractive
then dollars as a store of value: that is,
by making them depreciate.
Another way to see the same idea is to
think of money as providing store-of-
value services and liquidity services. All
forms of money should provide the same
total services, or else they wouldn’t all
stay in circulation. During shortages,
pennies provide more liquidity services
relative to dollars, because they alone
can be used to buy small goods, and
there aren’t enough pennies to buy all
the desired small goods. So pennies must
provide less store-of-value services: i.e.,
depreciation and postponing the point
where pennies are melted down. If
pennies are debased enough, it can also
make it profitable to mint pennies. The
historical record shows repeated debase-
ments of small denominations prompt-
ed by currency shortages over centuries.
The long-term cure, which was a stan-
dard formula in monetary textbooks
around 1900, was to take all the small
denominations out of the market-driven
supply mechanism: make them token,
so they are cheap to produce, and make
them convertible on demand, so they
don’t lose their value and so that the
government always supplies the right
quantity. This amounts to pegging an
exchange rate. The gold standard of
1900 is just that, with silver dollars and
subsidiary coins being overvalued with
respect to their content, and the Trea-
sury legally obliged to maintain their
parity with the gold coinage.
Simple as it may seem, this solution had
three main prerequisites, which may
explain why it took so long for the so-
lution to be implemented. The first pre-
requisite is a technological one. Making
coins token creates a big incentive for
counterfeiters, so the governmentfor money balances, and real balances
of these coins hit a ceiling. The nomi-
nal balances kept going up, as Venice
continued to print them, and inflation
ensued. Authorities in Venice stopped
issuing torneselli, and then after a while
devalued them to their intrinsic content,
which is the downward shift in nomi-
nal balances we see at the end. Similar
experiments with overvalued copper
coinage were carried out, on a vastly
larger scale, in seventeenth-century
Spain and Germany, resulting in spec-
tacular bouts of inflation.
Conclusion
Sargent–Velde show many examples of
how governments have been experi-
menting with fiat-like money for centu-
ries. Not all experiments resulted in
inflation, and there are early examples
of attempts at implementing the solution
to the problem of small change, although
counterfeiting repeatedly stymied them.
And, as figure 1 suggests, learning about
how to manage fiat money continued
in the twentieth century. But enough
elements of modern fiat money had
been put in place by 1914 for the likes
of Irving Fisher to contemplate the gold
standard and propose that the U.S.
currency’s last link to a commodity be
removed.

Solving the problem of small change

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Solving the problem of small change

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